LMFDB - Embedded newform 7.13.d.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,13,Mod(3,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 13, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.39795672093$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 21402 x^{12} - 299884 x^{11} + 348641804 x^{10} - 4374947304 x^{9} + \cdots + 49\!\cdots\!64 $ x^14 - 2x^13 + 21402x^12 - 299884x^11 + 348641804x^10 - 4374947304x^9 + 2052539647664x^8 - 27763204911808x^7 + 8779059695080896x^6 - 118618117216505984x^5 + 18423033030099279616x^4 - 304844700548141343744x^3 + 28028086321184511372288x^2 - 355339753830883178883072*x + 4956543686460383583473664
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{5}\cdot 7^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.4
Root			$7.24567 + 12.5499i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.13.d.a.5.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.2457 + 17.7460i) q^{2} +(953.136 + 550.294i) q^{3} +(1838.05 - 3183.60i) q^{4} +(-7383.58 + 4262.91i) q^{5} +22552.5i q^{6} +(106852. + 49233.1i) q^{7} +159261. q^{8} +(339926. + 588768. i) q^{9} +O(q^{10})$	\(q+(10.2457 + 17.7460i) q^{2} +(953.136 + 550.294i) q^{3} +(1838.05 - 3183.60i) q^{4} +(-7383.58 + 4262.91i) q^{5} +22552.5i q^{6} +(106852. + 49233.1i) q^{7} +159261. q^{8} +(339926. + 588768. i) q^{9} +(-151299. - 87352.7i) q^{10} +(-808753. + 1.40080e6i) q^{11} +(3.50383e6 - 2.02294e6i) q^{12} -1.05260e6i q^{13} +(221079. + 2.40063e6i) q^{14} -9.38341e6 q^{15} +(-5.89693e6 - 1.02138e7i) q^{16} +(-3.25679e7 - 1.88031e7i) q^{17} +(-6.96553e6 + 1.20647e7i) q^{18} +(6.31626e7 - 3.64669e7i) q^{19} +3.13418e7i q^{20} +(7.47520e7 + 1.05726e8i) q^{21} -3.31448e7 q^{22} +(-7.54272e7 - 1.30644e8i) q^{23} +(1.51797e8 + 8.76402e7i) q^{24} +(-8.57255e7 + 1.48481e8i) q^{25} +(1.86795e7 - 1.07846e7i) q^{26} +1.63338e8i q^{27} +(3.53139e8 - 2.49681e8i) q^{28} -8.76074e7 q^{29} +(-9.61393e7 - 1.66518e8i) q^{30} +(-9.82708e8 - 5.67367e8i) q^{31} +(4.47002e8 - 7.74230e8i) q^{32} +(-1.54170e9 + 8.90103e8i) q^{33} -7.70601e8i q^{34} +(-9.98828e8 + 9.19844e7i) q^{35} +2.49920e9 q^{36} +(1.53339e9 + 2.65591e9i) q^{37} +(1.29429e9 + 7.47256e8i) q^{38} +(5.79239e8 - 1.00327e9i) q^{39} +(-1.17591e9 + 6.78914e8i) q^{40} -1.94473e9i q^{41} +(-1.11033e9 + 2.40978e9i) q^{42} +2.80588e9 q^{43} +(2.97306e9 + 5.14949e9i) q^{44} +(-5.01973e9 - 2.89814e9i) q^{45} +(1.54560e9 - 2.67706e9i) q^{46} +(-4.52049e9 + 2.60991e9i) q^{47} -1.29802e10i q^{48} +(8.99348e9 + 1.05213e10i) q^{49} -3.51326e9 q^{50} +(-2.06944e10 - 3.58438e10i) q^{51} +(-3.35106e9 - 1.93474e9i) q^{52} +(-2.08933e10 + 3.61883e10i) q^{53} +(-2.89860e9 + 1.67351e9i) q^{54} -1.37906e10i q^{55} +(1.70174e10 + 7.84091e9i) q^{56} +8.02701e10 q^{57} +(-8.97596e8 - 1.55468e9i) q^{58} +(2.90619e9 + 1.67789e9i) q^{59} +(-1.72472e10 + 2.98730e10i) q^{60} +(-1.62011e9 + 9.35372e8i) q^{61} -2.32522e10i q^{62} +(7.33486e9 + 7.96468e10i) q^{63} -2.99883e10 q^{64} +(4.48714e9 + 7.77196e9i) q^{65} +(-3.15916e10 - 1.82394e10i) q^{66} +(4.93631e10 - 8.54995e10i) q^{67} +(-1.19723e11 + 6.91221e10i) q^{68} -1.66028e11i q^{69} +(-1.18660e10 - 1.67828e10i) q^{70} +1.90075e11 q^{71} +(5.41368e10 + 9.37677e10i) q^{72} +(-1.09740e11 - 6.33586e10i) q^{73} +(-3.14212e10 + 5.44231e10i) q^{74} +(-1.63416e11 + 9.43484e10i) q^{75} -2.68113e11i q^{76} +(-1.55383e11 + 1.09861e11i) q^{77} +2.37388e10 q^{78} +(9.80023e8 + 1.69745e9i) q^{79} +(8.70809e10 + 5.02762e10i) q^{80} +(9.07664e10 - 1.57212e11i) q^{81} +(3.45112e10 - 1.99250e10i) q^{82} +6.01627e11i q^{83} +(4.73987e11 - 4.36506e10i) q^{84} +3.20623e11 q^{85} +(2.87482e10 + 4.97933e10i) q^{86} +(-8.35018e10 - 4.82098e10i) q^{87} +(-1.28803e11 + 2.23093e11i) q^{88} +(-4.54265e10 + 2.62270e10i) q^{89} -1.18774e11i q^{90} +(5.18228e10 - 1.12473e11i) q^{91} -5.54556e11 q^{92} +(-6.24437e11 - 1.08156e12i) q^{93} +(-9.26310e10 - 5.34805e10i) q^{94} +(-3.10911e11 + 5.38513e11i) q^{95} +(8.52108e11 - 4.91965e11i) q^{96} +8.01082e10i q^{97} +(-9.45676e10 + 2.67397e11i) q^{98} -1.09966e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 44 q^{2} - 3 q^{3} - 14404 q^{4} - 9075 q^{5} + 334278 q^{7} - 52112 q^{8} + 265974 q^{9}+O(q^{10}) $ 14 * q + 44 * q^2 - 3 * q^3 - 14404 * q^4 - 9075 * q^5 + 334278 * q^7 - 52112 * q^8 + 265974 * q^9	\( 14 q + 44 q^{2} - 3 q^{3} - 14404 q^{4} - 9075 q^{5} + 334278 q^{7} - 52112 q^{8} + 265974 q^{9} + 3406596 q^{10} - 2085193 q^{11} - 12871740 q^{12} + 21936320 q^{14} + 21308298 q^{15} - 64542600 q^{16} + 46675437 q^{17} + 12781272 q^{18} - 153598539 q^{19} + 46954005 q^{21} + 138292528 q^{22} + 230058719 q^{23} - 265960656 q^{24} + 19748318 q^{25} + 590880528 q^{26} + 229618900 q^{28} - 714663796 q^{29} + 999571848 q^{30} - 5040285435 q^{31} + 1011711600 q^{32} - 2159472843 q^{33} + 2425404597 q^{35} + 17119036896 q^{36} - 5044805001 q^{37} + 3238109592 q^{38} - 5776828680 q^{39} - 35225923512 q^{40} + 27354512640 q^{42} + 40132389276 q^{43} - 11796090372 q^{44} - 18717971166 q^{45} - 12430801472 q^{46} - 53247355563 q^{47} + 16893431198 q^{49} + 178352838608 q^{50} + 1366166853 q^{51} - 136241043960 q^{52} - 35499894841 q^{53} - 154061995896 q^{54} + 42830066608 q^{56} + 371092140234 q^{57} - 21841743752 q^{58} - 138067877811 q^{59} - 146425754916 q^{60} - 287167557435 q^{61} + 240766542198 q^{63} + 1077334893984 q^{64} - 121576543704 q^{65} - 358267134060 q^{66} - 104132716721 q^{67} - 1346622176340 q^{68} + 620078986800 q^{70} + 809521279196 q^{71} - 435854437392 q^{72} + 4606244997 q^{73} - 229538257100 q^{74} - 692089720566 q^{75} + 408395115359 q^{77} + 1860221591760 q^{78} + 53291758879 q^{79} - 1497721732104 q^{80} - 82850395887 q^{81} - 27489500640 q^{82} - 28369303620 q^{84} + 402017692458 q^{85} + 1190361662368 q^{86} - 603786809646 q^{87} + 342437177984 q^{88} + 77396974197 q^{89} - 1437510415152 q^{91} - 3683682769320 q^{92} - 509894759883 q^{93} + 2011339035528 q^{94} + 690022114413 q^{95} + 5403247899840 q^{96} + 153246523724 q^{98} - 5499432555540 q^{99}+O(q^{100}) \) 14 * q + 44 * q^2 - 3 * q^3 - 14404 * q^4 - 9075 * q^5 + 334278 * q^7 - 52112 * q^8 + 265974 * q^9 + 3406596 * q^10 - 2085193 * q^11 - 12871740 * q^12 + 21936320 * q^14 + 21308298 * q^15 - 64542600 * q^16 + 46675437 * q^17 + 12781272 * q^18 - 153598539 * q^19 + 46954005 * q^21 + 138292528 * q^22 + 230058719 * q^23 - 265960656 * q^24 + 19748318 * q^25 + 590880528 * q^26 + 229618900 * q^28 - 714663796 * q^29 + 999571848 * q^30 - 5040285435 * q^31 + 1011711600 * q^32 - 2159472843 * q^33 + 2425404597 * q^35 + 17119036896 * q^36 - 5044805001 * q^37 + 3238109592 * q^38 - 5776828680 * q^39 - 35225923512 * q^40 + 27354512640 * q^42 + 40132389276 * q^43 - 11796090372 * q^44 - 18717971166 * q^45 - 12430801472 * q^46 - 53247355563 * q^47 + 16893431198 * q^49 + 178352838608 * q^50 + 1366166853 * q^51 - 136241043960 * q^52 - 35499894841 * q^53 - 154061995896 * q^54 + 42830066608 * q^56 + 371092140234 * q^57 - 21841743752 * q^58 - 138067877811 * q^59 - 146425754916 * q^60 - 287167557435 * q^61 + 240766542198 * q^63 + 1077334893984 * q^64 - 121576543704 * q^65 - 358267134060 * q^66 - 104132716721 * q^67 - 1346622176340 * q^68 + 620078986800 * q^70 + 809521279196 * q^71 - 435854437392 * q^72 + 4606244997 * q^73 - 229538257100 * q^74 - 692089720566 * q^75 + 408395115359 * q^77 + 1860221591760 * q^78 + 53291758879 * q^79 - 1497721732104 * q^80 - 82850395887 * q^81 - 27489500640 * q^82 - 28369303620 * q^84 + 402017692458 * q^85 + 1190361662368 * q^86 - 603786809646 * q^87 + 342437177984 * q^88 + 77396974197 * q^89 - 1437510415152 * q^91 - 3683682769320 * q^92 - 509894759883 * q^93 + 2011339035528 * q^94 + 690022114413 * q^95 + 5403247899840 * q^96 + 153246523724 * q^98 - 5499432555540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	10.2457	+	17.7460i	0.160089	+	0.277282i	0.934900	−	0.354911i	$-0.115489\pi$
$2$	10.2457	+	17.7460i	0.160089	+	0.277282i	−0.774812	+	0.632192i	$0.782155\pi$
$3$	953.136	+	550.294i	1.30746	+	0.754861i	0.981671	−	0.190583i	$-0.0610377\pi$
$3$	953.136	+	550.294i	1.30746	+	0.754861i	0.325786	+	0.945443i	$0.394371\pi$
$4$	1838.05	−	3183.60i	0.448743	−	0.777246i
$5$	−7383.58	+	4262.91i	−0.472549	+	0.272826i	−0.717306	−	0.696758i	$-0.754625\pi$
$5$	−7383.58	+	4262.91i	−0.472549	+	0.272826i	0.244757	+	0.969584i	$0.421292\pi$
$6$			22552.5i			0.483378i
$7$	106852.	+	49233.1i	0.908228	+	0.418475i
$7$	106852.	+	49233.1i	0.908228	+	0.418475i
$8$	159261.			0.607532
$9$	339926.	+	588768.i	0.639630	+	1.10787i
$10$	−151299.	−	87352.7i	−0.151299	−	0.0873527i
$11$	−808753.	+	1.40080e6i	−0.456520	+	0.790715i	−0.998774	−	0.0494989i	$-0.984238\pi$
$11$	−808753.	+	1.40080e6i	−0.456520	+	0.790715i	0.542254	+	0.840214i	$0.317571\pi$
$12$	3.50383e6	−	2.02294e6i	1.17343	−	0.677478i
$13$		−	1.05260e6i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$13$		−	1.05260e6i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$14$	221079.	+	2.40063e6i	0.0293616	+	0.318828i
$15$	−9.38341e6			−0.823783
$16$	−5.89693e6	−	1.02138e7i	−0.351484	−	0.608789i
$17$	−3.25679e7	−	1.88031e7i	−1.34926	−	0.778997i	−0.361117	−	0.932521i	$-0.617604\pi$
$17$	−3.25679e7	−	1.88031e7i	−1.34926	−	0.778997i	−0.988145	+	0.153524i	$0.950938\pi$
$18$	−6.96553e6	+	1.20647e7i	−0.204795	+	0.354715i
$19$	6.31626e7	−	3.64669e7i	1.34257	−	0.775136i	0.355390	−	0.934718i	$-0.384348\pi$
$19$	6.31626e7	−	3.64669e7i	1.34257	−	0.775136i	0.987185	+	0.159583i	$0.0510148\pi$
$20$			3.13418e7i			0.489716i
$21$	7.47520e7	+	1.05726e8i	0.871580	+	1.23272i
$22$	−3.31448e7			−0.292334
$23$	−7.54272e7	−	1.30644e8i	−0.509520	−	0.882514i	−0.999939	−	0.0110273i	$-0.996490\pi$
$23$	−7.54272e7	−	1.30644e8i	−0.509520	−	0.882514i	0.490420	−	0.871486i	$-0.336843\pi$
$24$	1.51797e8	+	8.76402e7i	0.794322	+	0.458602i
$25$	−8.57255e7	+	1.48481e8i	−0.351132	+	0.608178i
$26$	1.86795e7	−	1.07846e7i	0.0604678	−	0.0349111i
$27$			1.63338e8i			0.421605i
$28$	3.53139e8	−	2.49681e8i	0.732819	−	0.518129i
$29$	−8.76074e7			−0.147283			−0.0736415	−	0.997285i	$-0.523462\pi$
$29$	−8.76074e7			−0.147283			−0.0736415	+	0.997285i	$0.523462\pi$
$30$	−9.61393e7	−	1.66518e8i	−0.131878	−	0.228420i
$31$	−9.82708e8	−	5.67367e8i	−1.10727	−	0.639284i	−0.169151	−	0.985590i	$-0.554102\pi$
$31$	−9.82708e8	−	5.67367e8i	−1.10727	−	0.639284i	−0.938122	+	0.346306i	$0.887436\pi$
$32$	4.47002e8	−	7.74230e8i	0.416303	−	0.721058i
$33$	−1.54170e9	+	8.90103e8i	−1.19376	+	0.689218i
$34$		−	7.70601e8i		−	0.498834i
$35$	−9.98828e8	+	9.19844e7i	−0.543353	+	0.0500387i
$36$	2.49920e9			1.14812
$37$	1.53339e9	+	2.65591e9i	0.597643	+	1.03515i	0.993168	+	0.116693i	$0.0372294\pi$
$37$	1.53339e9	+	2.65591e9i	0.597643	+	1.03515i	−0.395525	+	0.918455i	$0.629437\pi$
$38$	1.29429e9	+	7.47256e8i	0.429862	+	0.248181i
$39$	5.79239e8	−	1.00327e9i	0.164615	−	0.285122i
$40$	−1.17591e9	+	6.78914e8i	−0.287088	+	0.165751i
$41$		−	1.94473e9i		−	0.409407i	−0.978824	−	0.204704i	$-0.934377\pi$
$41$		−	1.94473e9i		−	0.409407i	0.978824	−	0.204704i	$-0.0656231\pi$
$42$	−1.11033e9	+	2.40978e9i	−0.202282	+	0.439018i
$43$	2.80588e9			0.443873			0.221937	−	0.975061i	$-0.428762\pi$
$43$	2.80588e9			0.443873			0.221937	+	0.975061i	$0.428762\pi$
$44$	2.97306e9	+	5.14949e9i	0.409720	+	0.709657i
$45$	−5.01973e9	−	2.89814e9i	−0.604513	−	0.349016i
$46$	1.54560e9	−	2.67706e9i	0.163136	−	0.282561i
$47$	−4.52049e9	+	2.60991e9i	−0.419371	+	0.242124i	−0.694808	−	0.719195i	$-0.744511\pi$
$47$	−4.52049e9	+	2.60991e9i	−0.419371	+	0.242124i	0.275437	+	0.961319i	$0.411177\pi$
$48$		−	1.29802e10i		−	1.06129i
$49$	8.99348e9	+	1.05213e10i	0.649758	+	0.760141i
$50$	−3.51326e9			−0.224849
$51$	−2.06944e10	−	3.58438e10i	−1.17607	−	2.03701i
$52$	−3.35106e9	−	1.93474e9i	−0.169497	−	0.0978591i
$53$	−2.08933e10	+	3.61883e10i	−0.942653	+	1.63272i	−0.182269	+	0.983249i	$0.558344\pi$
$53$	−2.08933e10	+	3.61883e10i	−0.942653	+	1.63272i	−0.760384	+	0.649474i	$0.774989\pi$
$54$	−2.89860e9	+	1.67351e9i	−0.116903	+	0.0674941i
$55$		−	1.37906e10i		−	0.498202i
$56$	1.70174e10	+	7.84091e9i	0.551778	+	0.254237i
$57$	8.02701e10			2.34048
$58$	−8.97596e8	−	1.55468e9i	−0.0235783	−	0.0408389i
$59$	2.90619e9	+	1.67789e9i	0.0688988	+	0.0397787i	0.534054	−	0.845451i	$-0.320668\pi$
$59$	2.90619e9	+	1.67789e9i	0.0688988	+	0.0397787i	−0.465155	+	0.885229i	$0.654001\pi$
$60$	−1.72472e10	+	2.98730e10i	−0.369667	+	0.640282i
$61$	−1.62011e9	+	9.35372e8i	−0.0314460	+	0.0181554i	−0.515641	−	0.856805i	$-0.672446\pi$
$61$	−1.62011e9	+	9.35372e8i	−0.0314460	+	0.0181554i	0.484195	+	0.874960i	$0.339113\pi$
$62$		−	2.32522e10i		−	0.409368i
$63$	7.33486e9	+	7.96468e10i	0.117314	+	1.27387i
$64$	−2.99883e10			−0.436387
$65$	4.48714e9	+	7.77196e9i	0.0594962	+	0.103051i
$66$	−3.15916e10	−	1.82394e10i	−0.382215	−	0.220672i
$67$	4.93631e10	−	8.54995e10i	0.545700	−	0.945180i	−0.452862	−	0.891580i	$-0.649597\pi$
$67$	4.93631e10	−	8.54995e10i	0.545700	−	0.945180i	0.998562	−	0.0535998i	$-0.0170695\pi$
$68$	−1.19723e11	+	6.91221e10i	−1.21094	+	0.699139i
$69$		−	1.66028e11i		−	1.53847i
$70$	−1.18660e10	−	1.67828e10i	−0.100859	−	0.142651i
$71$	1.90075e11			1.48380			0.741898	−	0.670513i	$-0.233926\pi$
$71$	1.90075e11			1.48380			0.741898	+	0.670513i	$0.233926\pi$
$72$	5.41368e10	+	9.37677e10i	0.388596	+	0.673067i
$73$	−1.09740e11	−	6.33586e10i	−0.725153	−	0.418667i	0.0914936	−	0.995806i	$-0.470836\pi$
$73$	−1.09740e11	−	6.33586e10i	−0.725153	−	0.418667i	−0.816646	+	0.577139i	$0.804169\pi$
$74$	−3.14212e10	+	5.44231e10i	−0.191352	+	0.331431i
$75$	−1.63416e11	+	9.43484e10i	−0.918180	+	0.530111i
$76$		−	2.68113e11i		−	1.39135i
$77$	−1.55383e11	+	1.09861e11i	−0.745519	+	0.527108i
$78$	2.37388e10			0.105412
$79$	9.80023e8	+	1.69745e9i	0.00403157	+	0.00698288i	0.868034	−	0.496504i	$-0.165383\pi$
$79$	9.80023e8	+	1.69745e9i	0.00403157	+	0.00698288i	−0.864003	+	0.503487i	$0.832050\pi$
$80$	8.70809e10	+	5.02762e10i	0.332187	+	0.191788i
$81$	9.07664e10	−	1.57212e11i	0.321377	−	0.556641i
$82$	3.45112e10	−	1.99250e10i	0.113521	−	0.0655415i
$83$			6.01627e11i			1.84017i	0.391716	+	0.920086i	$0.371882\pi$
$83$			6.01627e11i			1.84017i	−0.391716	+	0.920086i	$0.628118\pi$
$84$	4.73987e11	−	4.36506e10i	1.34925	−	0.124255i
$85$	3.20623e11			0.850123
$86$	2.87482e10	+	4.97933e10i	0.0710590	+	0.123078i
$87$	−8.35018e10	−	4.82098e10i	−0.192566	−	0.111178i
$88$	−1.28803e11	+	2.23093e11i	−0.277350	+	0.480385i
$89$	−4.54265e10	+	2.62270e10i	−0.0914048	+	0.0527726i	−0.545006	−	0.838432i	$-0.683473\pi$
$89$	−4.54265e10	+	2.62270e10i	−0.0914048	+	0.0527726i	0.453601	+	0.891205i	$0.350139\pi$
$90$		−	1.18774e11i		−	0.223494i
$91$	5.18228e10	−	1.12473e11i	0.0912584	−	0.198061i
$92$	−5.54556e11			−0.914574
$93$	−6.24437e11	−	1.08156e12i	−0.965141	−	1.67167i
$94$	−9.26310e10	−	5.34805e10i	−0.134273	−	0.0775226i
$95$	−3.10911e11	+	5.38513e11i	−0.422955	+	0.732579i
$96$	8.52108e11	−	4.91965e11i	1.08860	−	0.628502i
$97$			8.01082e10i			0.0961715i	0.998843	+	0.0480858i	$0.0153121\pi$
$97$			8.01082e10i			0.0961715i	−0.998843	+	0.0480858i	$0.984688\pi$
$98$	−9.45676e10	+	2.67397e11i	−0.106754	+	0.301856i
$99$	−1.09966e12			−1.16801
$100$	3.15136e11	+	5.45832e11i	0.315136	+	0.545832i
$101$	3.89277e11	+	2.24749e11i	0.366716	+	0.211724i	0.672023	−	0.740530i	$-0.265426\pi$
$101$	3.89277e11	+	2.24749e11i	0.366716	+	0.211724i	−0.305307	+	0.952254i	$0.598759\pi$
$102$	4.24057e11	−	7.34488e11i	0.376550	−	0.652204i
$103$	6.63114e11	−	3.82849e11i	0.555348	−	0.320630i	−0.195928	−	0.980618i	$-0.562772\pi$
$103$	6.63114e11	−	3.82849e11i	0.555348	−	0.320630i	0.751276	+	0.659988i	$0.229439\pi$
$104$		−	1.67638e11i		−	0.132487i
$105$	−1.00264e12	−	4.61975e11i	−0.748183	−	0.344733i
$106$	−8.56263e11			−0.603632
$107$	6.68982e11	+	1.15871e12i	0.445771	+	0.772098i	0.998106	−	0.0615244i	$-0.0195962\pi$
$107$	6.68982e11	+	1.15871e12i	0.445771	+	0.772098i	−0.552334	+	0.833623i	$0.686263\pi$
$108$	5.20004e11	+	3.00224e11i	0.327691	+	0.189192i
$109$	4.38892e11	−	7.60183e11i	0.261697	−	0.453272i	−0.704996	−	0.709211i	$-0.749051\pi$
$109$	4.38892e11	−	7.60183e11i	0.261697	−	0.453272i	0.966693	+	0.255939i	$0.0823846\pi$
$110$	2.44727e11	−	1.41293e11i	0.138142	−	0.0797565i
$111$			3.37526e12i			1.80455i
$112$	−1.27243e11	−	1.38169e12i	−0.0644653	−	0.700007i
$113$	1.23979e12			0.595493			0.297746	−	0.954645i	$-0.403765\pi$
$113$	1.23979e12			0.595493			0.297746	+	0.954645i	$0.403765\pi$
$114$	8.22421e11	+	1.42447e12i	0.374684	+	0.648971i
$115$	1.11384e12	+	6.43078e11i	0.481546	+	0.278021i
$116$	−1.61027e11	+	2.78907e11i	−0.0660923	+	0.114475i
$117$	6.19738e11	−	3.57806e11i	0.241598	−	0.139487i
$118$			6.87643e10i			0.0254725i
$119$	−2.55422e12	−	3.61257e12i	−0.899447	−	1.27214i
$120$	−1.49441e12			−0.500475
$121$	2.61053e11	+	4.52156e11i	0.0831794	+	0.144071i
$122$	−3.31982e10	−	1.91670e10i	−0.0100683	−	0.00581294i
$123$	1.07017e12	−	1.85359e12i	0.309046	−	0.535283i
$124$	−3.61254e12	+	2.08570e12i	−0.993762	+	0.573749i
$125$		−	3.54326e12i		−	0.928844i
$126$	−1.33826e12	+	9.46199e11i	−0.334440	+	0.236461i
$127$	−4.10326e12			−0.977928			−0.488964	−	0.872304i	$-0.662625\pi$
$127$	−4.10326e12			−0.977928			−0.488964	+	0.872304i	$0.662625\pi$
$128$	−2.13817e12	−	3.70342e12i	−0.486164	−	0.842060i
$129$	2.67439e12	+	1.54406e12i	0.580345	+	0.335063i
$130$	−9.19475e10	+	1.59258e11i	−0.0190493	+	0.0329944i
$131$	4.13305e12	−	2.38622e12i	0.817792	−	0.472152i	−0.0318627	−	0.999492i	$-0.510144\pi$
$131$	4.13305e12	−	2.38622e12i	0.817792	−	0.472152i	0.849654	+	0.527340i	$0.176811\pi$
$132$			6.54422e12i			1.23713i
$133$	8.54444e12	−	7.86878e11i	1.54374	−	0.142167i
$134$	2.02303e12			0.349441
$135$	−6.96296e11	−	1.20602e12i	−0.115025	−	0.199229i
$136$	−5.18679e12	−	2.99459e12i	−0.819719	−	0.473265i
$137$	−2.51789e12	+	4.36112e12i	−0.380815	+	0.659591i	−0.991179	−	0.132530i	$-0.957690\pi$
$137$	−2.51789e12	+	4.36112e12i	−0.380815	+	0.659591i	0.610364	+	0.792121i	$0.291023\pi$
$138$	2.94634e12	−	1.70107e12i	0.426588	−	0.246291i
$139$			4.13736e12i			0.573634i	0.957985	+	0.286817i	$0.0925971\pi$
$139$			4.13736e12i			0.573634i	−0.957985	+	0.286817i	$0.907403\pi$
$140$	−1.54306e12	+	3.34894e12i	−0.204934	+	0.444774i
$141$	−5.74486e12			−0.731080
$142$	1.94744e12	+	3.37307e12i	0.237539	+	0.411429i
$143$	1.47448e12	+	8.51293e11i	0.172434	+	0.0995550i
$144$	4.00903e12	−	6.94385e12i	0.449640	−	0.778799i
$145$	6.46856e11	−	3.73462e11i	0.0695984	−	0.0401827i
$146$		−	2.59661e12i		−	0.268095i
$147$	2.78219e12	+	1.49773e13i	0.275729	+	1.48433i
$148$	1.12738e13			1.07275
$149$	−2.10272e12	−	3.64201e12i	−0.192160	−	0.332831i	0.753806	−	0.657097i	$-0.228216\pi$
$149$	−2.10272e12	−	3.64201e12i	−0.192160	−	0.332831i	−0.945966	+	0.324266i	$0.894883\pi$
$150$	−3.34862e12	−	1.93332e12i	−0.293980	−	0.169729i
$151$	−7.64394e12	+	1.32397e13i	−0.644846	+	1.11691i	0.339492	+	0.940609i	$0.389745\pi$
$151$	−7.64394e12	+	1.32397e13i	−0.644846	+	1.11691i	−0.984337	+	0.176296i	$0.943588\pi$
$152$	1.00593e13	−	5.80775e12i	0.815657	−	0.470920i
$153$		−	2.55666e13i		−	1.99308i
$154$	−3.54160e12	−	1.63182e12i	−0.265506	−	0.122335i
$155$	9.67454e12			0.697654
$156$	−2.12934e12	−	3.68813e12i	−0.147740	−	0.255893i
$157$	−1.40599e13	−	8.11751e12i	−0.938827	−	0.542032i	−0.0492344	−	0.998787i	$-0.515678\pi$
$157$	−1.40599e13	−	8.11751e12i	−0.938827	−	0.542032i	−0.889592	+	0.456755i	$0.849011\pi$
$158$	−2.00820e10	+	3.47830e10i	−0.00129082	+	0.00223576i
$159$	−3.98283e13	+	2.29949e13i	−2.46496	+	1.42314i
$160$			7.62212e12i			0.454314i
$161$	−1.62756e12	−	1.76731e13i	−0.0934503	−	1.01475i
$162$	3.71985e12			0.205795
$163$	4.45891e12	+	7.72306e12i	0.237740	+	0.411778i	0.960066	−	0.279775i	$-0.0902599\pi$
$163$	4.45891e12	+	7.72306e12i	0.237740	+	0.411778i	−0.722325	+	0.691554i	$0.756927\pi$
$164$	−6.19124e12	−	3.57451e12i	−0.318210	−	0.183719i
$165$	7.58886e12	−	1.31443e13i	0.376073	−	0.651378i
$166$	−1.06765e13	+	6.16407e12i	−0.510246	+	0.294591i
$167$		−	2.29880e13i		−	1.05975i	−0.848077	−	0.529874i	$-0.822239\pi$
$167$		−	2.29880e13i		−	1.05975i	0.848077	−	0.529874i	$-0.177761\pi$
$168$	1.19051e13	+	1.68380e13i	0.529512	+	0.748919i
$169$	2.21901e13			0.952444
$170$	3.28500e12	+	5.68979e12i	0.136095	+	0.235723i
$171$	4.29412e13	+	2.47921e13i	1.71750	+	0.991600i
$172$	5.15736e12	−	8.93281e12i	0.199185	−	0.344999i
$173$	−3.77691e12	+	2.18060e12i	−0.140883	+	0.0813391i	−0.568785	−	0.822486i	$-0.692586\pi$
$173$	−3.77691e12	+	2.18060e12i	−0.140883	+	0.0813391i	0.427902	+	0.903825i	$0.359253\pi$
$174$		−	1.97577e12i		−	0.0711934i
$175$	−1.64701e13	+	1.16450e13i	−0.573415	+	0.405425i
$176$	1.90766e13			0.641838
$177$	1.84666e12	+	3.19851e12i	0.0600548	+	0.104018i
$178$	−9.30849e11	−	5.37426e11i	−0.0292657	−	0.0168966i
$179$	−2.32042e13	+	4.01909e13i	−0.705422	+	1.22183i	0.261117	+	0.965307i	$0.415909\pi$
$179$	−2.32042e13	+	4.01909e13i	−0.705422	+	1.22183i	−0.966539	+	0.256520i	$0.917424\pi$
$180$	−1.84531e13	+	1.06539e13i	−0.542542	+	0.313237i
$181$		−	2.14075e13i		−	0.608829i	−0.952540	−	0.304414i	$-0.901539\pi$
$181$		−	2.14075e13i		−	0.608829i	0.952540	−	0.304414i	$-0.0984608\pi$
$182$	2.52690e12	−	2.32708e11i	0.0695280	−	0.00640300i
$183$	−2.05892e12			−0.0548191
$184$	−1.20126e13	−	2.08064e13i	−0.309549	−	0.536155i
$185$	−2.26438e13	−	1.30734e13i	−0.564831	−	0.326106i
$186$	1.27955e13	−	2.21625e13i	0.309016	−	0.535232i
$187$	5.26787e13	−	3.04141e13i	1.23193	−	0.711255i
$188$			1.91886e13i			0.434606i
$189$	−8.04166e12	+	1.74531e13i	−0.176431	+	0.382913i
$190$	−1.27419e13			−0.270841
$191$	−9.46099e12	−	1.63869e13i	−0.194866	−	0.337518i	0.751991	−	0.659174i	$-0.229094\pi$
$191$	−9.46099e12	−	1.63869e13i	−0.194866	−	0.337518i	−0.946857	+	0.321656i	$0.895761\pi$
$192$	−2.85830e13	−	1.65024e13i	−0.570558	−	0.329412i
$193$	−1.66104e13	+	2.87700e13i	−0.321393	+	0.556668i	−0.980776	−	0.195139i	$-0.937484\pi$
$193$	−1.66104e13	+	2.87700e13i	−0.321393	+	0.556668i	0.659383	+	0.751807i	$0.270818\pi$
$194$	−1.42160e12	+	8.20762e11i	−0.0266666	+	0.0153960i
$195$			9.87698e12i			0.179646i
$196$	5.00262e13	−	9.29288e12i	0.882391	−	0.163913i
$197$	−2.70074e13			−0.462046			−0.231023	−	0.972948i	$-0.574207\pi$
$197$	−2.70074e13			−0.462046			−0.231023	+	0.972948i	$0.574207\pi$
$198$	−1.12668e13	−	1.95146e13i	−0.186986	−	0.323869i
$199$	−4.08153e13	−	2.35647e13i	−0.657211	−	0.379441i	0.134002	−	0.990981i	$-0.457217\pi$
$199$	−4.08153e13	−	2.35647e13i	−0.657211	−	0.379441i	−0.791213	+	0.611540i	$0.790550\pi$
$200$	−1.36527e13	+	2.36472e13i	−0.213324	+	0.369487i
$201$	9.40996e13	−	5.43284e13i	1.42696	−	0.823855i
$202$			9.21082e12i			0.135578i
$203$	−9.36104e12	−	4.31319e12i	−0.133767	−	0.0616342i
$204$	−1.52150e14			−2.11101
$205$	8.29020e12	+	1.43590e13i	0.111697	+	0.193465i
$206$	1.35881e13	+	7.84509e12i	0.177810	+	0.102658i
$207$	5.12793e13	−	8.88183e13i	0.651808	−	1.12896i
$208$	−1.07510e13	+	6.20711e12i	−0.132761	+	0.0766495i
$209$			1.17971e14i			1.41546i
$210$	−2.07448e12	−	2.25261e13i	−0.0241876	−	0.262645i
$211$	9.81709e13			1.11247			0.556235	−	0.831025i	$-0.312246\pi$
$211$	9.81709e13			1.11247			0.556235	+	0.831025i	$0.312246\pi$
$212$	7.68060e13	+	1.33032e14i	0.846018	+	1.46535i
$213$	1.81167e14	+	1.04597e14i	1.94000	+	1.12006i
$214$	−1.37083e13	+	2.37435e13i	−0.142726	+	0.247208i
$215$	−2.07175e13	+	1.19612e13i	−0.209752	+	0.121100i
$216$			2.60134e13i			0.256138i
$217$	−7.70712e13	−	1.09006e14i	−0.738132	−	1.04398i
$218$	1.79870e13			0.167579
$219$	−6.97317e13	−	1.20779e14i	−0.632071	−	1.09478i
$220$	−4.39036e13	−	2.53478e13i	−0.387226	−	0.223565i
$221$	−1.97921e13	+	3.42810e13i	−0.169879	+	0.294239i
$222$	−5.98974e13	+	3.45818e13i	−0.500368	+	0.288888i
$223$			3.21619e13i			0.261525i	0.991414	+	0.130762i	$0.0417425\pi$
$223$			3.21619e13i			0.261525i	−0.991414	+	0.130762i	$0.958258\pi$
$224$	8.58809e13	−	6.07209e13i	0.679843	−	0.480673i
$225$	−1.16561e14			−0.898377
$226$	1.27024e13	+	2.20013e13i	0.0953316	+	0.165119i
$227$	−3.46273e12	−	1.99921e12i	−0.0253083	−	0.0146118i	0.487292	−	0.873239i	$-0.337985\pi$
$227$	−3.46273e12	−	1.99921e12i	−0.0253083	−	0.0146118i	−0.512601	+	0.858627i	$0.671318\pi$
$228$	1.47541e14	−	2.55548e14i	1.05027	−	1.81913i
$229$	−5.53584e13	+	3.19612e13i	−0.383858	+	0.221620i	−0.679495	−	0.733680i	$-0.737801\pi$
$229$	−5.53584e13	+	3.19612e13i	−0.383858	+	0.221620i	0.295638	+	0.955300i	$0.404468\pi$
$230$			2.63551e13i			0.178032i
$231$	−2.08557e14	+	1.92065e13i	−1.37263	+	0.126409i
$232$	−1.39524e13			−0.0894791
$233$	4.97656e13	+	8.61966e13i	0.311024	+	0.538709i	0.978584	−	0.205846i	$-0.0659947\pi$
$233$	4.97656e13	+	8.61966e13i	0.311024	+	0.538709i	−0.667560	+	0.744556i	$0.732661\pi$
$234$	1.26993e13	+	7.33192e12i	0.0773541	+	0.0446604i
$235$	2.22516e13	−	3.85409e13i	0.132116	−	0.228831i
$236$	1.06834e13	−	6.16809e12i	0.0618357	−	0.0357009i
$237$			2.15720e12i			0.0121731i
$238$	3.79391e13	−	8.23403e13i	0.208749	−	0.453055i
$239$	−1.60896e14			−0.863291			−0.431646	−	0.902043i	$-0.642067\pi$
$239$	−1.60896e14			−0.863291			−0.431646	+	0.902043i	$0.642067\pi$
$240$	5.53333e13	+	9.58401e13i	0.289547	+	0.501510i
$241$	−3.34982e13	−	1.93402e13i	−0.170970	−	0.0987093i	0.412073	−	0.911151i	$-0.364805\pi$
$241$	−3.34982e13	−	1.93402e13i	−0.170970	−	0.0987093i	−0.583043	+	0.812441i	$0.698138\pi$
$242$	−5.34932e12	+	9.26529e12i	−0.0266321	+	0.0461282i
$243$	2.48201e14	−	1.43299e14i	1.20549	−	0.695992i
$244$			6.87705e12i			0.0325884i
$245$	−1.11256e14	−	3.93467e13i	−0.514429	−	0.181933i
$246$	4.38585e13			0.197899
$247$	−3.83851e13	−	6.64850e13i	−0.169037	−	0.292780i
$248$	−1.56507e14	−	9.03593e13i	−0.672703	−	0.388385i
$249$	−3.31071e14	+	5.73432e14i	−1.38907	+	2.40595i
$250$	6.28787e13	−	3.63031e13i	0.257551	−	0.148697i
$251$		−	1.36774e14i		−	0.546966i	−0.961877	−	0.273483i	$-0.911824\pi$
$251$		−	1.36774e14i		−	0.546966i	0.961877	−	0.273483i	$-0.0881757\pi$
$252$	2.67045e14	+	1.23044e14i	1.04275	+	0.480459i
$253$	2.44008e14			0.930423
$254$	−4.20406e13	−	7.28165e13i	−0.156555	−	0.271161i
$255$	3.05598e14	+	1.76437e14i	1.11150	+	0.641724i
$256$	−1.76021e13	+	3.04877e13i	−0.0625351	+	0.108314i
$257$	1.93072e14	−	1.11470e14i	0.670070	−	0.386865i	−0.126033	−	0.992026i	$-0.540225\pi$
$257$	1.93072e14	−	1.11470e14i	0.670070	−	0.386865i	0.796103	+	0.605161i	$0.206891\pi$
$258$			6.32797e13i			0.214559i
$259$	3.30872e13	+	3.59283e14i	0.109613	+	1.19025i
$260$	3.29904e13			0.106794
$261$	−2.97800e13	−	5.15805e13i	−0.0942066	−	0.163171i
$262$	8.46917e13	+	4.88968e13i	0.261838	+	0.151172i
$263$	1.87363e14	−	3.24522e14i	0.566173	−	0.980641i	−0.430766	−	0.902464i	$-0.641757\pi$
$263$	1.87363e14	−	3.24522e14i	0.566173	−	0.980641i	0.996939	−	0.0781773i	$-0.0249100\pi$
$264$	−2.45533e14	+	1.41758e14i	−0.725247	+	0.418722i
$265$		−	3.56265e14i		−	1.02872i
$266$	1.01507e14	+	1.43568e14i	0.286555	+	0.405291i
$267$	−5.77302e13			−0.159344
$268$	−1.81464e14	−	3.14305e14i	−0.489759	−	0.848287i
$269$	−4.23831e14	−	2.44699e14i	−1.11861	−	0.645831i	−0.177566	−	0.984109i	$-0.556822\pi$
$269$	−4.23831e14	−	2.44699e14i	−1.11861	−	0.645831i	−0.941046	+	0.338278i	$0.890156\pi$
$270$	1.42680e13	−	2.47130e13i	0.0368283	−	0.0637885i
$271$	−2.87745e14	+	1.66130e14i	−0.726427	+	0.419403i	−0.817114	−	0.576477i	$-0.804427\pi$
$271$	−2.87745e14	+	1.66130e14i	−0.726427	+	0.419403i	0.0906866	+	0.995879i	$0.471094\pi$
$272$			4.43522e14i			1.09522i
$273$	1.11287e14	−	7.86840e13i	0.268825	−	0.190069i
$274$	−1.03190e14			−0.243857
$275$	−1.38661e14	−	2.40169e14i	−0.320597	−	0.555291i
$276$	−5.28568e14	−	3.05169e14i	−1.19577	−	0.690376i
$277$	−3.02951e14	+	5.24726e14i	−0.670646	+	1.16159i	0.307076	+	0.951685i	$0.400650\pi$
$277$	−3.02951e14	+	5.24726e14i	−0.670646	+	1.16159i	−0.977721	+	0.209907i	$0.932684\pi$
$278$	−7.34217e13	+	4.23900e13i	−0.159058	+	0.0918322i
$279$		−	7.71450e14i		−	1.63562i
$280$	−1.59074e14	+	1.46495e13i	−0.330104	+	0.0304001i
$281$	7.11709e14			1.44565			0.722827	−	0.691029i	$-0.242842\pi$
$281$	7.11709e14			1.44565			0.722827	+	0.691029i	$0.242842\pi$
$282$	−5.88600e13	−	1.01948e14i	−0.117038	−	0.202715i
$283$	7.62544e14	+	4.40255e14i	1.48438	+	0.857009i	0.999842	−	0.0177593i	$-0.00565325\pi$
$283$	7.62544e14	+	4.40255e14i	1.48438	+	0.857009i	0.484541	+	0.874768i	$0.338987\pi$
$284$	3.49367e14	−	6.05122e14i	0.665844	−	1.15327i
$285$	−5.92680e14	+	3.42184e14i	−1.10599	+	0.638544i
$286$			3.48883e13i			0.0637505i
$287$	9.57451e13	−	2.07798e14i	0.171327	−	0.371835i
$288$	6.07790e14			1.06512
$289$	4.15801e14	+	7.20188e14i	0.713672	+	1.23612i
$290$	1.32549e13	+	7.65274e12i	0.0222838	+	0.0128656i
$291$	−4.40830e13	+	7.63540e13i	−0.0725961	+	0.125740i
$292$	−4.03417e14	+	2.32913e14i	−0.650815	+	0.375748i
$293$		−	7.23797e14i		−	1.14396i	−0.820267	−	0.571980i	$-0.806175\pi$
$293$		−	7.23797e14i		−	1.14396i	0.820267	−	0.571980i	$-0.193825\pi$
$294$	−2.37282e14	+	2.02826e14i	−0.367436	+	0.314079i
$295$	−2.86107e13			−0.0434107
$296$	2.44209e14	+	4.22982e14i	0.363087	+	0.628886i
$297$	−2.28804e14	−	1.32100e14i	−0.333369	−	0.192471i
$298$	4.30875e13	−	7.46298e13i	0.0615253	−	0.106565i
$299$	−1.37516e14	+	7.93947e13i	−0.192453	+	0.111113i
$300$			6.93669e14i			0.951535i
$301$	2.99815e14	+	1.38143e14i	0.403138	+	0.185750i
$302$	−3.13269e14			−0.412930
$303$	2.47356e14	+	4.28433e14i	0.319644	+	0.553640i
$304$	−7.44931e14	−	4.30086e14i	−0.943788	−	0.544896i
$305$	7.97481e12	−	1.38128e13i	0.00990652	−	0.0171586i
$306$	4.53705e14	−	2.61947e14i	0.552644	−	0.319069i
$307$		−	5.07486e14i		−	0.606169i	−0.952964	−	0.303084i	$-0.901984\pi$
$307$		−	5.07486e14i		−	0.606169i	0.952964	−	0.303084i	$-0.0980164\pi$
$308$	6.41522e13	+	6.96607e14i	0.0751463	+	0.815988i
$309$	8.42718e14			0.968124
$310$	9.91221e13	+	1.71684e14i	0.111686	+	0.193446i
$311$	4.18139e14	+	2.41413e14i	0.462124	+	0.266808i	0.712937	−	0.701228i	$-0.247365\pi$
$311$	4.18139e14	+	2.41413e14i	0.462124	+	0.266808i	−0.250813	+	0.968036i	$0.580698\pi$
$312$	9.22501e13	−	1.59782e14i	0.100009	−	0.173221i
$313$	2.34756e14	−	1.35537e14i	0.249661	−	0.144142i	−0.369948	−	0.929053i	$-0.620624\pi$
$313$	2.34756e14	−	1.35537e14i	0.249661	−	0.144142i	0.619609	+	0.784910i	$0.287291\pi$
$314$		−	3.32677e14i		−	0.347092i
$315$	−3.93685e14	−	5.56810e14i	−0.402981	−	0.569959i
$316$	7.20534e12			0.00723655
$317$	−4.63434e14	−	8.02692e14i	−0.456702	−	0.791031i	0.542082	−	0.840325i	$-0.317636\pi$
$317$	−4.63434e14	−	8.02692e14i	−0.456702	−	0.791031i	−0.998784	+	0.0492946i	$0.984303\pi$
$318$	−8.16136e14	−	4.71196e14i	−0.789223	−	0.455658i
$319$	7.08527e13	−	1.22720e14i	0.0672376	−	0.116459i
$320$	2.21421e14	−	1.27837e14i	0.206214	−	0.119058i
$321$			1.47255e15i			1.34598i
$322$	2.96951e14	−	2.09955e14i	0.266410	−	0.188361i
$323$	−2.74276e15			−2.41531
$324$	−3.33667e14	−	5.77928e14i	−0.288432	−	0.499578i
$325$	1.56291e14	+	9.02347e13i	0.132628	+	0.0765726i
$326$	−9.13690e13	+	1.58256e14i	−0.0761190	+	0.131842i
$327$	8.36647e14	−	4.83039e14i	0.684315	−	0.395089i
$328$		−	3.09719e14i		−	0.248728i
$329$	−6.11519e14	+	5.63162e13i	−0.482208	+	0.0444077i
$330$	3.11012e14			0.240820
$331$	−1.21615e15	−	2.10643e15i	−0.924736	−	1.60169i	−0.791986	−	0.610539i	$-0.790953\pi$
$331$	−1.21615e15	−	2.10643e15i	−0.924736	−	1.60169i	−0.132750	−	0.991150i	$-0.542381\pi$
$332$	1.91534e15	+	1.10582e15i	1.43027	+	0.825765i
$333$	−1.04248e15	+	1.80562e15i	−0.764541	+	1.32422i
$334$	4.07945e14	−	2.35527e14i	0.293848	−	0.169653i
$335$			8.41722e14i			0.595525i
$336$	6.39055e14	−	1.38696e15i	0.444122	−	0.963891i
$337$	−1.08862e15			−0.743183			−0.371591	−	0.928396i	$-0.621188\pi$
$337$	−1.08862e15			−0.743183			−0.371591	+	0.928396i	$0.621188\pi$
$338$	2.27353e14	+	3.93786e14i	0.152475	+	0.264095i
$339$	1.18169e15	+	6.82247e14i	0.778582	+	0.449514i
$340$	5.89323e14	−	1.02074e15i	0.381487	−	0.660755i
$341$	1.58954e15	−	9.17719e14i	1.01098	−	0.583692i
$342$			1.01605e15i			0.634975i
$343$	4.42974e14	+	1.56700e15i	0.272028	+	0.962289i
$344$	4.46867e14			0.269667
$345$	7.07764e14	+	1.22588e15i	0.419734	+	0.727000i
$346$	−7.73939e13	−	4.46834e13i	−0.0451077	−	0.0260429i
$347$	−1.90725e14	+	3.30346e14i	−0.109252	+	0.189231i	−0.915468	−	0.402392i	$-0.868179\pi$
$347$	−1.90725e14	+	3.30346e14i	−0.109252	+	0.189231i	0.806215	+	0.591622i	$0.201512\pi$
$348$	−3.06961e14	+	1.77224e14i	−0.172826	+	0.0997809i
$349$			7.31499e14i			0.404819i	0.979301	+	0.202410i	$0.0648772\pi$
$349$			7.31499e14i			0.404819i	−0.979301	+	0.202410i	$0.935123\pi$
$350$	−3.75399e14	−	1.72969e14i	−0.204214	−	0.0940935i
$351$	1.71930e14			0.0919409
$352$	7.23028e14	+	1.25232e15i	0.380101	+	0.658355i
$353$	−1.23331e15	−	7.12050e14i	−0.637416	−	0.368012i	0.146202	−	0.989255i	$-0.453295\pi$
$353$	−1.23331e15	−	7.12050e14i	−0.637416	−	0.368012i	−0.783618	+	0.621242i	$0.786628\pi$
$354$	−3.78406e13	+	6.55418e13i	−0.0192282	+	0.0333042i
$355$	−1.40343e15	+	8.10271e14i	−0.701166	+	0.404818i
$356$			1.92826e14i			0.0947253i
$357$	−4.46541e14	−	4.84884e15i	−0.215701	−	2.34223i
$358$	−9.50971e14			−0.451720
$359$	9.64380e14	+	1.67036e15i	0.450486	+	0.780265i	0.998416	−	0.0562589i	$-0.0179172\pi$
$359$	9.64380e14	+	1.67036e15i	0.450486	+	0.780265i	−0.547930	+	0.836524i	$0.684584\pi$
$360$	−7.99447e14	−	4.61561e14i	−0.367261	−	0.212038i
$361$	1.55302e15	−	2.68991e15i	0.701671	−	1.21533i
$362$	3.79899e14	−	2.19335e14i	0.168817	−	0.0974665i
$363$			5.74622e14i			0.251156i
$364$	−2.62815e14	−	3.71714e14i	−0.112990	−	0.159809i
$365$	1.08037e15			0.456893
$366$	−2.10950e13	−	3.65376e13i	−0.00877592	−	0.0152003i
$367$	2.04995e15	+	1.18354e15i	0.838969	+	0.484379i	0.856914	−	0.515460i	$-0.172379\pi$
$367$	2.04995e15	+	1.18354e15i	0.838969	+	0.484379i	−0.0179447	+	0.999839i	$0.505712\pi$
$368$	−8.89578e14	+	1.54079e15i	−0.358176	+	0.620380i
$369$	1.14499e15	−	6.61063e14i	0.453571	−	0.261869i
$370$		−	5.35783e14i		−	0.208823i
$371$	−4.01416e15	+	2.83815e15i	−1.53940	+	1.08841i
$372$	−4.59099e15			−1.73240
$373$	−1.08078e15	−	1.87196e15i	−0.401312	−	0.695094i	0.592572	−	0.805517i	$-0.298113\pi$
$373$	−1.08078e15	−	1.87196e15i	−0.401312	−	0.695094i	−0.993885	+	0.110424i	$0.964779\pi$
$374$	1.07946e15	+	6.23225e14i	0.394436	+	0.227727i
$375$	1.94983e15	−	3.37721e15i	0.701148	−	1.21442i
$376$	−7.19938e14	+	4.15656e14i	−0.254781	+	0.147098i
$377$			9.22156e13i			0.0321186i
$378$	−3.92114e14	+	3.61107e13i	−0.134419	+	0.0123790i
$379$	2.06467e15			0.696651			0.348325	−	0.937374i	$-0.386750\pi$
$379$	2.06467e15			0.696651			0.348325	+	0.937374i	$0.386750\pi$
$380$	1.14294e15	+	1.97963e15i	0.379596	+	0.657480i
$381$	−3.91097e15	−	2.25800e15i	−1.27860	−	0.738199i
$382$	1.93868e14	−	3.35790e14i	0.0623917	−	0.108066i
$383$	−1.34776e15	+	7.78127e14i	−0.426991	+	0.246523i	−0.698064	−	0.716035i	$-0.745955\pi$
$383$	−1.34776e15	+	7.78127e14i	−0.426991	+	0.246523i	0.271073	+	0.962559i	$0.412622\pi$
$384$		−	4.70649e15i		−	1.46794i
$385$	6.78953e14	−	1.47355e15i	0.208485	−	0.452481i
$386$	−6.80738e14			−0.205805
$387$	9.53792e14	+	1.65202e15i	0.283915	+	0.491755i
$388$	2.55033e14	+	1.47243e14i	0.0747490	+	0.0431563i
$389$	1.36773e14	−	2.36897e14i	0.0394731	−	0.0683694i	−0.845614	−	0.533795i	$-0.820765\pi$
$389$	1.36773e14	−	2.36897e14i	0.0394731	−	0.0683694i	0.885087	+	0.465426i	$0.154099\pi$
$390$	−1.75277e14	+	1.01196e14i	−0.0498124	+	0.0287592i
$391$			5.67305e15i			1.58766i
$392$	1.43231e15	+	1.67564e15i	0.394748	+	0.461810i
$393$	5.25248e15			1.42564
$394$	−2.76709e14	−	4.79273e14i	−0.0739683	−	0.128117i
$395$	−1.44722e13	−	8.35550e12i	−0.00381022	−	0.00219983i
$396$	−2.02124e15	+	3.50089e15i	−0.524139	+	0.907835i
$397$	4.85054e14	−	2.80046e14i	0.123893	−	0.0715297i	−0.436773	−	0.899572i	$-0.643879\pi$
$397$	4.85054e14	−	2.80046e14i	0.123893	−	0.0715297i	0.560666	+	0.828042i	$0.310545\pi$
$398$		−	9.65746e14i		−	0.242977i
$399$	8.57703e15	+	3.95195e15i	2.12569	+	0.979431i
$400$	2.02207e15			0.493669
$401$	−9.14133e14	−	1.58332e15i	−0.219858	−	0.380806i	0.734906	−	0.678169i	$-0.237226\pi$
$401$	−9.14133e14	−	1.58332e15i	−0.219858	−	0.380806i	−0.954765	+	0.297363i	$0.903893\pi$
$402$	1.92823e15	+	1.11326e15i	0.456880	+	0.263780i
$403$	−5.97211e14	+	1.03440e15i	−0.139411	+	0.241467i
$404$	1.43102e15	−	8.26201e14i	0.329123	−	0.190019i
$405$			1.54772e15i			0.350720i
$406$	−1.93682e13	−	2.10313e14i	−0.00432447	−	0.0469580i
$407$	−4.96053e15			−1.09134
$408$	−3.29581e15	−	5.70851e15i	−0.714499	−	1.23755i
$409$	−7.51399e14	−	4.33821e14i	−0.160521	−	0.0926767i	0.417588	−	0.908637i	$-0.362876\pi$
$409$	−7.51399e14	−	4.33821e14i	−0.160521	−	0.0926767i	−0.578108	+	0.815960i	$0.696209\pi$
$410$	−1.69877e14	+	2.94236e14i	−0.0357629	+	0.0619431i
$411$	−4.79979e15	+	2.77116e15i	−0.995799	+	0.574925i
$412$		−	2.81479e15i		−	0.575522i
$413$	2.27925e14	+	3.22367e14i	0.0459294	+	0.0649606i
$414$	2.10156e15			0.417388
$415$	−2.56468e15	−	4.44216e15i	−0.502047	−	0.869571i
$416$	−8.14955e14	−	4.70515e14i	−0.157244	−	0.0907848i
$417$	−2.27676e15	+	3.94347e15i	−0.433014	+	0.750002i
$418$	−2.09351e15	+	1.20869e15i	−0.392481	+	0.226599i
$419$		−	1.05141e16i		−	1.94307i	−0.236897	−	0.971535i	$-0.576130\pi$
$419$		−	1.05141e16i		−	1.94307i	0.236897	−	0.971535i	$-0.423870\pi$
$420$	−3.31364e15	+	2.34286e15i	−0.603684	+	0.426826i
$421$	3.81787e15			0.685691			0.342845	−	0.939392i	$-0.388609\pi$
$421$	3.81787e15			0.685691			0.342845	+	0.939392i	$0.388609\pi$
$422$	1.00583e15	+	1.74214e15i	0.178094	+	0.308467i
$423$	−3.07326e15	−	1.77435e15i	−0.536485	−	0.309740i
$424$	−3.32748e15	+	5.76337e15i	−0.572692	+	0.991931i
$425$	5.58380e15	−	3.22381e15i	0.947537	−	0.547061i
$426$			4.28666e15i			0.717235i
$427$	−2.19164e14	+	2.01833e13i	−0.0361577	+	0.00332985i
$428$	4.91850e15			0.800147
$429$	9.36923e14	+	1.62280e15i	0.150300	+	0.260328i
$430$	−4.24528e14	−	2.45102e14i	−0.0671577	−	0.0387735i
$431$	2.87834e15	−	4.98543e15i	0.449033	−	0.777748i	−0.549290	−	0.835632i	$-0.685102\pi$
$431$	2.87834e15	−	4.98543e15i	0.449033	−	0.777748i	0.998323	+	0.0578834i	$0.0184352\pi$
$432$	1.66830e15	−	9.63195e14i	0.256668	−	0.148187i
$433$		−	3.23731e15i		−	0.491198i	−0.969371	−	0.245599i	$-0.921015\pi$
$433$		−	3.23731e15i		−	0.491198i	0.969371	−	0.245599i	$-0.0789847\pi$
$434$	1.14478e15	−	2.48455e15i	0.171310	−	0.371800i
$435$	8.22056e14			0.121329
$436$	−1.61341e15	−	2.79451e15i	−0.234869	−	0.406806i
$437$	−9.52835e15	−	5.50120e15i	−1.36814	−	0.789894i
$438$	1.42890e15	−	2.47492e15i	0.202375	−	0.350523i
$439$	−7.10660e15	+	4.10300e15i	−0.992829	+	0.573210i	−0.906119	−	0.423023i	$-0.860969\pi$
$439$	−7.10660e15	+	4.10300e15i	−0.992829	+	0.573210i	−0.0867105	+	0.996234i	$0.527636\pi$
$440$		−	2.19630e15i		−	0.302674i
$441$	−3.13752e15	+	8.87155e15i	−0.426535	+	1.20606i
$442$	−8.11135e14			−0.108783
$443$	5.71355e15	+	9.89615e15i	0.755933	+	1.30931i	0.944909	+	0.327333i	$0.106150\pi$
$443$	5.71355e15	+	9.89615e15i	0.755933	+	1.30931i	−0.188976	+	0.981982i	$0.560517\pi$
$444$	1.07455e16	+	6.20390e15i	1.40258	+	0.809780i
$445$	2.23606e14	−	3.87298e14i	0.0287955	−	0.0498752i
$446$	−5.70745e14	+	3.29520e14i	−0.0725159	+	0.0418671i
$447$		−	4.62845e15i		−	0.580217i
$448$	−3.20432e15	−	1.47642e15i	−0.396339	−	0.182617i
$449$	2.30831e14			0.0281719			0.0140859	−	0.999901i	$-0.495516\pi$
$449$	2.30831e14			0.0281719			0.0140859	+	0.999901i	$0.495516\pi$
$450$	−1.19425e15	−	2.06850e15i	−0.143820	−	0.249103i
$451$	2.72418e15	+	1.57280e15i	0.323725	+	0.186903i
$452$	2.27879e15	−	3.94699e15i	0.267223	−	0.462845i
$453$	−1.45714e16	+	8.41282e15i	−1.68622	+	0.973537i
$454$		−	8.19329e13i		−	0.00935671i
$455$	9.68228e13	+	1.05137e15i	0.0109121	+	0.118491i
$456$	1.27839e16			1.42192
$457$	8.79271e15	+	1.52294e16i	0.965218	+	1.67181i	0.709028	+	0.705180i	$0.249134\pi$
$457$	8.79271e15	+	1.52294e16i	0.965218	+	1.67181i	0.256190	+	0.966626i	$0.417533\pi$
$458$	−1.13437e15	−	6.54927e14i	−0.122903	−	0.0709578i
$459$	3.07126e15	−	5.31959e15i	0.328429	−	0.568855i
$460$	4.09461e15	−	2.36402e15i	0.432181	−	0.249520i
$461$			2.18802e15i			0.227953i	0.993483	+	0.113976i	$0.0363588\pi$
$461$			2.18802e15i			0.227953i	−0.993483	+	0.113976i	$0.963641\pi$
$462$	−2.47764e15	−	3.50427e15i	−0.254793	−	0.360368i
$463$	−7.23344e15			−0.734276			−0.367138	−	0.930167i	$-0.619662\pi$
$463$	−7.23344e15			−0.734276			−0.367138	+	0.930167i	$0.619662\pi$
$464$	5.16615e14	+	8.94803e14i	0.0517677	+	0.0896643i
$465$	9.22115e15	+	5.32383e15i	0.912153	+	0.526632i
$466$	−1.01976e15	+	1.76628e15i	−0.0995827	+	0.172482i
$467$	1.23136e16	−	7.10928e15i	1.18709	−	0.685369i	0.229449	−	0.973321i	$-0.426308\pi$
$467$	1.23136e16	−	7.10928e15i	1.18709	−	0.685369i	0.957645	+	0.287952i	$0.0929743\pi$
$468$		−	2.63066e15i		−	0.250375i
$469$	9.48397e15	−	6.70550e15i	0.891154	−	0.630078i
$470$	9.11930e14			0.0846008
$471$	−8.93403e15	−	1.54742e16i	−0.818317	−	1.41737i
$472$	4.62842e14	+	2.67222e14i	0.0418582	+	0.0241668i
$473$	−2.26927e15	+	3.93048e15i	−0.202637	+	0.350977i
$474$	−3.82817e13	+	2.21020e13i	−0.00337537	+	0.00194877i
$475$			1.25046e16i			1.08870i
$476$	−1.61958e16	+	1.49151e15i	−1.39239	+	0.128228i
$477$	−2.84087e16			−2.41180
$478$	−1.64848e15	−	2.85526e15i	−0.138203	−	0.239375i
$479$	−1.64372e16	−	9.49004e15i	−1.36087	−	0.785697i	−0.371128	−	0.928582i	$-0.621029\pi$
$479$	−1.64372e16	−	9.49004e15i	−1.36087	−	0.785697i	−0.989739	+	0.142885i	$0.954362\pi$
$480$	−4.19440e15	+	7.26492e15i	−0.342944	+	0.593996i
$481$	2.79561e15	−	1.61405e15i	0.225739	−	0.130330i
$482$		−	7.92612e14i		−	0.0632089i
$483$	8.17410e15	−	1.77405e16i	0.643809	−	1.39728i
$484$	1.91931e15			0.149305
$485$	−3.41494e14	−	5.91485e14i	−0.0262381	−	0.0454458i
$486$	5.08596e15	+	2.93638e15i	0.385972	+	0.222841i
$487$	−1.63442e14	+	2.83089e14i	−0.0122515	+	0.0212202i	−0.872086	−	0.489352i	$-0.837233\pi$
$487$	−1.63442e14	+	2.83089e14i	−0.0122515	+	0.0212202i	0.859835	+	0.510573i	$0.170567\pi$
$488$	−2.58020e14	+	1.48968e14i	−0.0191045	+	0.0110300i
$489$			9.81484e15i			0.717844i
$490$	−4.41641e14	−	2.37748e15i	−0.0319075	−	0.171767i
$491$	1.11406e16			0.795094			0.397547	−	0.917582i	$-0.369862\pi$
$491$	1.11406e16			0.795094			0.397547	+	0.917582i	$0.369862\pi$
$492$	−3.93406e15	−	6.81400e15i	−0.277364	−	0.480409i
$493$	2.85319e15	+	1.64729e15i	0.198723	+	0.114733i
$494$	7.86562e14	−	1.36237e15i	0.0541217	−	0.0937415i
$495$	8.11944e15	−	4.68776e15i	0.551944	−	0.318665i
$496$			1.33829e16i			0.898793i
$497$	2.03099e16	+	9.35798e15i	1.34763	+	0.620931i
$498$	−1.35682e16			−0.889499
$499$	−5.10846e15	−	8.84811e15i	−0.330892	−	0.573122i	0.651795	−	0.758395i	$-0.274016\pi$
$499$	−5.10846e15	−	8.84811e15i	−0.330892	−	0.573122i	−0.982687	+	0.185273i	$0.940683\pi$
$500$	−1.12803e16	−	6.51270e15i	−0.721941	−	0.416813i
$501$	1.26501e16	−	2.19107e16i	0.799962	−	1.38557i
$502$	2.42719e15	−	1.40134e15i	0.151663	−	0.0875629i
$503$			1.97479e16i			1.21931i	0.792669	+	0.609653i	$0.208691\pi$
$503$			1.97479e16i			1.21931i	−0.792669	+	0.609653i	$0.791309\pi$
$504$	1.16816e15	+	1.26846e16i	0.0712718	+	0.773916i
$505$	−3.83234e15			−0.231055
$506$	2.50002e15	+	4.33016e15i	0.148950	+	0.257989i
$507$	2.11502e16	+	1.22111e16i	1.24528	+	0.718963i
$508$	−7.54201e15	+	1.30631e16i	−0.438838	+	0.760091i
$509$	1.47198e16	−	8.49848e15i	0.846438	−	0.488691i	−0.0130093	−	0.999915i	$-0.504141\pi$
$509$	1.47198e16	−	8.49848e15i	0.846438	−	0.488691i	0.859447	+	0.511224i	$0.170808\pi$
$510$			7.23086e15i			0.410931i
$511$	−8.60665e15	−	1.21729e16i	−0.483403	−	0.683703i
$512$	−1.82373e16			−1.01237
$513$	5.95645e15	+	1.03169e16i	0.326801	+	0.566036i
$514$	3.95630e15	+	2.28417e15i	0.214541	+	0.123865i
$515$	−3.26410e15	+	5.65359e15i	−0.174953	+	0.303027i
$516$	9.83134e15	−	5.67613e15i	0.520852	−	0.300714i
$517$		−	8.44308e15i		−	0.442138i
$518$	−6.03684e15	+	4.26826e15i	−0.312487	+	0.220939i
$519$	−4.79988e15			−0.245599
$520$	7.14626e14	+	1.23777e15i	0.0361459	+	0.0626065i
$521$	−1.24294e16	−	7.17612e15i	−0.621476	−	0.358809i	0.155968	−	0.987762i	$-0.450150\pi$
$521$	−1.24294e16	−	7.17612e15i	−0.621476	−	0.358809i	−0.777443	+	0.628953i	$0.783484\pi$
$522$	6.10232e14	−	1.05695e15i	0.0301628	−	0.0522435i
$523$	1.43014e16	−	8.25693e15i	0.698826	−	0.403468i	−0.108084	−	0.994142i	$-0.534471\pi$
$523$	1.43014e16	−	8.25693e15i	0.698826	−	0.403468i	0.806910	+	0.590674i	$0.201138\pi$
$524$		−	1.75440e16i		−	0.847501i
$525$	−2.21064e16	+	2.03584e15i	−1.05575	+	0.0972270i
$526$	7.67864e15			0.362551
$527$	2.13365e16	+	3.69559e16i	0.996000	+	1.72512i
$528$	1.81826e16	+	1.04977e16i	0.839176	+	0.484499i
$529$	−4.21205e14	+	7.29548e14i	−0.0192203	+	0.0332905i
$530$	6.32229e15	−	3.65017e15i	0.285246	−	0.164687i
$531$			2.28143e15i			0.101775i
$532$	1.32000e16	−	2.86484e16i	0.582244	−	1.26366i
$533$	−2.04702e15			−0.0892810
$534$	−5.91484e14	−	1.02448e15i	−0.0255091	−	0.0441831i
$535$	−9.87896e15	−	5.70362e15i	−0.421297	−	0.243236i
$536$	7.86161e15	−	1.36167e16i	0.331530	−	0.574227i
$537$	−4.42336e16	+	2.55383e16i	−1.84462	+	1.06499i
$538$		−	1.00284e16i		−	0.413560i
$539$	−2.20118e16	+	4.08892e15i	−0.897683	+	0.166754i
$540$	−5.11932e15			−0.206466
$541$	−1.84261e16	−	3.19149e16i	−0.734936	−	1.27295i	−0.954751	−	0.297405i	$-0.903879\pi$
$541$	−1.84261e16	−	3.19149e16i	−0.734936	−	1.27295i	0.219815	−	0.975542i	$-0.429455\pi$
$542$	−5.89628e15	−	3.40422e15i	−0.232585	−	0.134283i
$543$	1.17804e16	−	2.04043e16i	0.459581	−	0.796018i
$544$	−2.91158e16	+	1.68100e16i	−1.12340	+	0.648598i
$545$			7.48382e15i			0.285591i
$546$	2.53654e15	+	1.16873e15i	0.0957383	+	0.0441123i
$547$	1.16960e16			0.436629			0.218315	−	0.975878i	$-0.429944\pi$
$547$	1.16960e16			0.436629			0.218315	+	0.975878i	$0.429944\pi$
$548$	9.25604e15	+	1.60319e16i	0.341776	+	0.591974i
$549$	−1.10143e15	−	6.35914e14i	−0.0402276	−	0.0232254i
$550$	2.84136e15	−	4.92138e15i	0.102648	−	0.177791i
$551$	−5.53351e15	+	3.19477e15i	−0.197738	+	0.114164i
$552$		−	2.64418e16i		−	0.934667i
$553$	2.11468e13	+	2.29626e14i	0.000739424	+	0.00802916i
$554$	−1.24157e16			−0.429451
$555$	−1.43884e16	−	2.49215e16i	−0.492329	−	0.852738i
$556$	1.31717e16	+	7.60469e15i	0.445855	+	0.257414i
$557$	−6.90689e15	+	1.19631e16i	−0.231287	+	0.400601i	−0.958187	−	0.286142i	$-0.907627\pi$
$557$	−6.90689e15	+	1.19631e16i	−0.231287	+	0.400601i	0.726900	+	0.686743i	$0.240960\pi$
$558$	1.36902e16	−	7.90402e15i	0.453527	−	0.261844i
$559$		−	2.95347e15i		−	0.0967971i
$560$	6.82952e15	+	9.65938e15i	0.221443	+	0.313200i
$561$	6.69467e16			2.14759
$562$	7.29193e15	+	1.26300e16i	0.231433	+	0.400853i
$563$	−1.61056e16	−	9.29857e15i	−0.505739	−	0.291988i	0.225341	−	0.974280i	$-0.427650\pi$
$563$	−1.61056e16	−	9.29857e15i	−0.505739	−	0.291988i	−0.731080	+	0.682291i	$0.760984\pi$
$564$	−1.05594e16	+	1.82894e16i	−0.328067	+	0.568229i
$565$	−9.15406e15	+	5.28510e15i	−0.281399	+	0.162466i
$566$			1.80428e16i			0.548789i
$567$	1.74386e16	−	1.23297e16i	0.524824	−	0.371069i
$568$	3.02715e16			0.901453
$569$	1.95102e16	+	3.37927e16i	0.574895	+	0.995747i	0.996053	+	0.0887596i	$0.0282903\pi$
$569$	1.95102e16	+	3.37927e16i	0.574895	+	0.995747i	−0.421159	+	0.906987i	$0.638376\pi$
$570$	−1.21448e16	−	7.01181e15i	−0.354113	−	0.204447i
$571$	−1.94349e16	+	3.36622e16i	−0.560745	+	0.971238i	0.436687	+	0.899613i	$0.356152\pi$
$571$	−1.94349e16	+	3.36622e16i	−0.560745	+	0.971238i	−0.997432	+	0.0716246i	$0.977182\pi$
$572$	5.42036e15	−	3.12944e15i	0.154757	−	0.0893493i
$573$		−	2.08253e16i		−	0.588387i
$574$	4.66857e15	−	4.29939e14i	0.130531	−	0.0120209i
$575$	2.58641e16			0.715634
$576$	−1.01938e16	−	1.76562e16i	−0.279126	−	0.483461i
$577$	4.93322e16	+	2.84820e16i	1.33683	+	0.771818i	0.986336	−	0.164747i	$-0.0526808\pi$
$577$	4.93322e16	+	2.84820e16i	1.33683	+	0.771818i	0.350493	+	0.936566i	$0.386014\pi$
$578$	−8.52032e15	+	1.47576e16i	−0.228501	+	0.395776i
$579$	−3.16639e16	+	1.82812e16i	−0.840414	+	0.485213i
$580$		−	2.74577e15i		−	0.0721268i
$581$	−2.96200e16	+	6.42851e16i	−0.770066	+	1.67130i
$582$	−1.80664e15			−0.0464872
$583$	−3.37950e16	−	5.85347e16i	−0.860679	−	1.49074i
$584$	−1.74773e16	−	1.00906e16i	−0.440553	−	0.254354i
$585$	−3.05059e15	+	5.28377e15i	−0.0761112	+	0.131828i
$586$	1.28445e16	−	7.41578e15i	0.317199	−	0.183135i
$587$		−	3.98544e16i		−	0.974199i	−0.873346	−	0.487100i	$-0.838055\pi$
$587$		−	3.98544e16i		−	0.974199i	0.873346	−	0.487100i	$-0.161945\pi$
$588$	5.27956e16	+	1.86717e16i	1.27742	+	0.451773i
$589$	−8.27605e16			−1.98213
$590$	−2.93136e14	−	5.07726e14i	−0.00694956	−	0.0120370i
$591$	−2.57417e16	−	1.48620e16i	−0.604105	−	0.348780i
$592$	1.80846e16	−	3.13234e16i	0.420125	−	0.727677i
$593$	6.74532e16	−	3.89441e16i	1.55122	−	0.895599i	0.553180	−	0.833062i	$-0.313414\pi$
$593$	6.74532e16	−	3.89441e16i	1.55122	−	0.895599i	0.998043	−	0.0625372i	$-0.0199192\pi$
$594$		−	5.41382e15i		−	0.123250i
$595$	3.42593e16	+	1.57853e16i	0.772106	+	0.355755i
$596$	−1.54596e16			−0.344922
$597$	−2.59351e16	−	4.49208e16i	−0.572850	−	0.992206i
$598$	−2.81788e15	−	1.62690e15i	−0.0616191	−	0.0355758i
$599$	−1.22700e16	+	2.12522e16i	−0.265633	+	0.460090i	−0.967729	−	0.251992i	$-0.918914\pi$
$599$	−1.22700e16	+	2.12522e16i	−0.265633	+	0.460090i	0.702096	+	0.712082i	$0.252248\pi$
$600$	−2.60258e16	+	1.50260e16i	−0.557823	+	0.322059i
$601$			3.41013e16i			0.723644i	0.932247	+	0.361822i	$0.117845\pi$
$601$			3.41013e16i			0.723644i	−0.932247	+	0.361822i	$0.882155\pi$
$602$	6.20323e14	+	6.73588e15i	0.0130328	+	0.141519i
$603$	6.71192e16			1.39618
$604$	2.80999e16	+	4.86705e16i	0.578740	+	1.00241i
$605$	−3.85500e15	−	2.22569e15i	−0.0786127	−	0.0453870i
$606$	−5.06865e15	+	8.77916e15i	−0.102343	+	0.177263i
$607$	−4.65238e16	+	2.68605e16i	−0.930129	+	0.537010i	−0.886852	−	0.462053i	$-0.847113\pi$
$607$	−4.65238e16	+	2.68605e16i	−0.930129	+	0.537010i	−0.0432769	+	0.999063i	$0.513780\pi$
$608$		−	6.52032e16i		−	1.29077i
$609$	−6.54883e15	−	9.26238e15i	−0.128369	−	0.181559i
$610$	3.26829e14			0.00634369
$611$	2.74719e15	+	4.75827e15i	0.0528009	+	0.0914539i
$612$	−8.13938e16	−	4.69928e16i	−1.54911	−	0.894381i
$613$	2.87754e16	−	4.98404e16i	0.542323	−	0.939331i	−0.456447	−	0.889750i	$-0.650878\pi$
$613$	2.87754e16	−	4.98404e16i	0.542323	−	0.939331i	0.998770	−	0.0495802i	$-0.0157883\pi$
$614$	9.00585e15	−	5.19953e15i	0.168079	−	0.0970407i
$615$			1.82482e16i			0.337263i
$616$	−2.47464e16	+	1.74966e16i	−0.452926	+	0.320235i
$617$	−2.50243e16			−0.453577			−0.226789	−	0.973944i	$-0.572823\pi$
$617$	−2.50243e16			−0.453577			−0.226789	+	0.973944i	$0.572823\pi$
$618$	8.63420e15	+	1.49549e16i	0.154986	+	0.268443i
$619$	−3.97031e16	−	2.29226e16i	−0.705798	−	0.407493i	0.103705	−	0.994608i	$-0.466930\pi$
$619$	−3.97031e16	−	2.29226e16i	−0.705798	−	0.407493i	−0.809503	+	0.587115i	$0.800264\pi$
$620$	1.77823e16	−	3.07999e16i	0.313067	−	0.542249i
$621$	2.13391e16	−	1.23201e16i	0.372072	−	0.214816i
$622$			9.89374e15i			0.170851i
$623$	−6.14515e15	+	5.65922e14i	−0.105100	+	0.00967895i
$624$	−1.36629e16			−0.231439
$625$	−5.82449e15	−	1.00883e16i	−0.0977187	−	0.169254i
$626$	4.81047e15	+	2.77733e15i	0.0799359	+	0.0461510i
$627$	−6.49186e16	+	1.12442e17i	−1.06847	+	1.85065i
$628$	−5.16858e16	+	2.98408e16i	−0.842584	+	0.486466i
$629$		−	1.15330e17i		−	1.86225i
$630$	5.84760e15	−	1.26912e16i	0.0935265	−	0.202983i
$631$	1.11806e17			1.77129			0.885646	−	0.464361i	$-0.153716\pi$
$631$	1.11806e17			1.77129			0.885646	+	0.464361i	$0.153716\pi$
$632$	1.56079e14	+	2.70337e14i	0.00244930	+	0.00424232i
$633$	9.35703e16	+	5.40228e16i	1.45451	+	0.839759i
$634$	9.49639e15	−	1.64482e16i	0.146225	−	0.253270i
$635$	3.02967e16	−	1.74918e16i	0.462119	−	0.266804i
$636$			1.69063e17i			2.55450i
$637$	1.10748e16	−	9.46654e15i	0.165767	−	0.141695i
$638$	2.90373e15			0.0430559
$639$	6.46113e16	+	1.11910e17i	0.949080	+	1.64386i
$640$	3.15747e16	+	1.82297e16i	0.459472	+	0.265276i
$641$	5.69949e16	−	9.87181e16i	0.821652	−	1.42314i	−0.0827995	−	0.996566i	$-0.526386\pi$
$641$	5.69949e16	−	9.87181e16i	0.821652	−	1.42314i	0.904451	−	0.426577i	$-0.140281\pi$
$642$	−2.61318e16	+	1.50872e16i	−0.373216	+	0.215476i
$643$			4.96642e16i			0.702712i	0.936242	+	0.351356i	$0.114279\pi$
$643$			4.96642e16i			0.702712i	−0.936242	+	0.351356i	$0.885721\pi$
$644$	−5.92556e16	−	2.73026e16i	−0.830642	−	0.382726i
$645$	−2.63288e16			−0.365655
$646$	−2.81014e16	−	4.86731e16i	−0.386664	−	0.669721i
$647$	8.55718e16	+	4.94049e16i	1.16655	+	0.673511i	0.952866	−	0.303391i	$-0.0981189\pi$
$647$	8.55718e16	+	4.94049e16i	1.16655	+	0.673511i	0.213689	+	0.976902i	$0.431452\pi$
$648$	1.44555e16	−	2.50377e16i	0.195247	−	0.338177i
$649$	−4.70077e15	+	2.71399e15i	−0.0629073	+	0.0363195i
$650$			3.69806e15i			0.0490336i
$651$	−1.34740e16	−	1.46310e17i	−0.177015	−	1.92215i
$652$	3.27828e16			0.426738
$653$	1.82533e16	+	3.16157e16i	0.235431	+	0.407778i	0.959398	−	0.282056i	$-0.0910165\pi$
$653$	1.82533e16	+	3.16157e16i	0.235431	+	0.407778i	−0.723967	+	0.689835i	$0.757683\pi$
$654$	1.71440e16	+	9.89810e15i	0.219102	+	0.126499i
$655$	−2.03444e16	+	3.52376e16i	−0.257631	+	0.446230i
$656$	−1.98630e16	+	1.14679e16i	−0.249243	+	0.143900i
$657$		−	8.61489e16i		−	1.07117i
$658$	−7.26480e15	−	1.02750e16i	−0.0895094	−	0.126598i
$659$	−1.26261e17			−1.54155			−0.770775	−	0.637108i	$-0.780131\pi$
$659$	−1.26261e17			−1.54155			−0.770775	+	0.637108i	$0.780131\pi$
$660$	−2.78974e16	−	4.83198e16i	−0.337521	−	0.584603i
$661$	−2.50525e16	−	1.44640e16i	−0.300360	−	0.173413i	0.342245	−	0.939611i	$-0.388813\pi$
$661$	−2.50525e16	−	1.44640e16i	−0.300360	−	0.173413i	−0.642604	+	0.766198i	$0.722146\pi$
$662$	2.49204e16	−	4.31635e16i	0.296079	−	0.512824i
$663$	−3.77292e16	+	2.17830e16i	−0.444218	+	0.256470i
$664$			9.58155e16i			1.11796i
$665$	−5.97341e16	+	4.22342e16i	−0.690705	+	0.488353i
$666$	−4.27235e16			−0.489577
$667$	6.60798e15	+	1.14454e16i	0.0750436	+	0.129979i
$668$	−7.31846e16	−	4.22531e16i	−0.823684	−	0.475554i
$669$	−1.76985e16	+	3.06547e16i	−0.197415	+	0.341932i
$670$	−1.49372e16	+	8.62401e15i	−0.165128	+	0.0953368i
$671$		−	3.02594e15i		−	0.0331532i
$672$	1.15271e17	−	1.06155e16i	1.25171	−	0.115273i
$673$	−1.35739e17			−1.46087			−0.730437	−	0.682980i	$-0.760684\pi$
$673$	−1.35739e17			−1.46087			−0.730437	+	0.682980i	$0.760684\pi$
$674$	−1.11536e16	−	1.93186e16i	−0.118975	−	0.206071i
$675$	−2.42526e16	−	1.40023e16i	−0.256411	−	0.148039i
$676$	4.07866e16	−	7.06445e16i	0.427403	−	0.740283i
$677$	1.47265e17	−	8.50236e16i	1.52957	−	0.883095i	0.530186	−	0.847882i	$-0.322122\pi$
$677$	1.47265e17	−	8.50236e16i	1.52957	−	0.883095i	0.999380	−	0.0352134i	$-0.0112111\pi$
$678$			2.79603e16i			0.287848i
$679$	−3.94398e15	+	8.55973e15i	−0.0402454	+	0.0873457i
$680$	5.10627e16			0.516477
$681$	−2.20030e15	−	3.81104e15i	−0.0220597	−	0.0382085i
$682$	3.25717e16	+	1.88053e16i	0.323694	+	0.186885i
$683$	−5.68196e16	+	9.84144e16i	−0.559724	+	0.969470i	0.437795	+	0.899075i	$0.355759\pi$
$683$	−5.68196e16	+	9.84144e16i	−0.559724	+	0.969470i	−0.997519	+	0.0703956i	$0.977574\pi$
$684$	1.57856e17	−	9.11383e16i	1.54143	−	0.889948i
$685$		−	4.29342e16i		−	0.415585i
$686$	−2.32695e16	+	2.39160e16i	−0.223276	+	0.229480i
$687$	−7.03521e16			−0.669170
$688$	−1.65461e16	−	2.86587e16i	−0.156015	−	0.270225i
$689$	3.80918e16	+	2.19923e16i	0.356054	+	0.205568i
$690$	−1.45030e16	+	2.51200e16i	−0.134389	+	0.232769i
$691$	6.23575e16	−	3.60021e16i	0.572823	−	0.330720i	−0.185453	−	0.982653i	$-0.559375\pi$
$691$	6.23575e16	−	3.60021e16i	0.572823	−	0.330720i	0.758276	+	0.651933i	$0.226042\pi$
$692$			1.60322e16i			0.146002i
$693$	−1.17501e17	−	5.41399e16i	−1.06082	−	0.488785i
$694$	−7.81642e15			−0.0699602
$695$	−1.76372e16	−	3.05485e16i	−0.156502	−	0.271070i
$696$	−1.32986e16	−	7.67793e15i	−0.116990	−	0.0675443i
$697$	−3.65669e16	+	6.33357e16i	−0.318927	+	0.552398i
$698$	−1.29812e16	+	7.49469e15i	−0.112249	+	0.0648069i
$699$			1.09543e17i			0.939119i
$700$	6.79996e15	+	7.38384e16i	0.0577987	+	0.627616i
$701$	−4.72947e16			−0.398570			−0.199285	−	0.979942i	$-0.563862\pi$
$701$	−4.72947e16			−0.398570			−0.199285	+	0.979942i	$0.563862\pi$
$702$	1.76154e15	+	3.05107e15i	0.0147187	+	0.0254935i
$703$	1.93706e17	+	1.11836e17i	1.60476	+	0.926509i
$704$	2.42531e16	−	4.20076e16i	0.199219	−	0.345058i
$705$	4.24176e16	−	2.44898e16i	0.345471	−	0.199458i
$706$		−	2.91817e16i		−	0.235658i
$707$	3.05300e16	+	4.31802e16i	0.244461	+	0.345755i
$708$	1.35770e16			0.107797
$709$	−2.82062e16	−	4.88545e16i	−0.222058	−	0.384616i	0.733375	−	0.679825i	$-0.237944\pi$
$709$	−2.82062e16	−	4.88545e16i	−0.222058	−	0.384616i	−0.955433	+	0.295209i	$0.904611\pi$
$710$	−2.87582e16	−	1.66035e16i	−0.224497	−	0.129614i
$711$	−6.66270e14	+	1.15401e15i	−0.00515742	+	0.00893292i
$712$	−7.23466e15	+	4.17693e15i	−0.0555313	+	0.0320610i
$713$			1.71180e17i			1.30291i
$714$	8.14725e16	−	5.76039e16i	0.614924	−	0.434773i
$715$	−1.45159e16			−0.108645
$716$	8.53012e16	+	1.47746e17i	0.633107	+	1.09657i
$717$	−1.53356e17	−	8.85399e16i	−1.12872	−	0.651665i
$718$	−1.97614e16	+	3.42278e16i	−0.144235	+	0.249823i
$719$	9.11380e16	−	5.26186e16i	0.659669	−	0.380860i	−0.132482	−	0.991185i	$-0.542295\pi$
$719$	9.11380e16	−	5.26186e16i	0.659669	−	0.380860i	0.792151	+	0.610325i	$0.208961\pi$
$720$			6.83606e16i			0.490694i
$721$	8.97040e16	−	8.26106e15i	0.638558	−	0.0588063i
$722$	6.36468e16			0.449318
$723$	−2.12855e16	−	3.68677e16i	−0.149024	−	0.258116i
$724$	−6.81530e16	−	3.93482e16i	−0.473210	−	0.273208i
$725$	7.51019e15	−	1.30080e16i	0.0517157	−	0.0895743i
$726$	−1.01973e16	+	5.88739e15i	−0.0696408	+	0.0402071i
$727$		−	1.80571e17i		−	1.22305i	−0.791227	−	0.611523i	$-0.790557\pi$
$727$		−	1.80571e17i		−	1.22305i	0.791227	−	0.611523i	$-0.209443\pi$
$728$	8.25335e15	−	1.79125e16i	0.0554424	−	0.120328i
$729$	2.18951e17			1.45876
$730$	1.10691e16	+	1.91722e16i	0.0731434	+	0.126688i
$731$	−9.13817e16	−	5.27593e16i	−0.598901	−	0.345776i
$732$	−3.78440e15	+	6.55477e15i	−0.0245997	+	0.0426080i
$733$	−1.95378e17	+	1.12802e17i	−1.25966	+	0.727264i	−0.973008	−	0.230771i	$-0.925875\pi$
$733$	−1.95378e17	+	1.12802e17i	−1.25966	+	0.727264i	−0.286650	+	0.958035i	$0.592542\pi$
$734$			4.85045e16i			0.310174i
$735$	−8.43895e16	−	9.87260e16i	−0.535260	−	0.626192i
$736$	−1.34864e17			−0.848458
$737$	7.98451e16	+	1.38296e17i	0.498246	+	0.862987i
$738$	2.34625e16	+	1.35461e16i	0.145223	+	0.0838445i
$739$	8.17073e16	−	1.41521e17i	0.501643	−	0.868870i	−0.498356	−	0.866973i	$-0.666063\pi$
$739$	8.17073e16	−	1.41521e17i	0.501643	−	0.868870i	0.999998	−	0.00189768i	$-0.000604050\pi$
$740$	−8.32410e16	+	4.80592e16i	−0.506929	+	0.292675i
$741$		−	8.44923e16i		−	0.510397i
$742$	−9.14936e16	−	4.21565e16i	−0.548236	−	0.252605i
$743$	−1.40573e17			−0.835546			−0.417773	−	0.908551i	$-0.637189\pi$
$743$	−1.40573e17			−0.835546			−0.417773	+	0.908551i	$0.637189\pi$
$744$	−9.94483e16	−	1.72250e17i	−0.586354	−	1.01559i
$745$	3.10512e16	+	1.79274e16i	0.181610	+	0.104853i
$746$	2.21465e16	−	3.83589e16i	0.128491	−	0.222553i
$747$	−3.54219e17	+	2.04508e17i	−2.03867	+	1.17703i
$748$		−	2.23611e17i		−	1.27668i
$749$	1.44352e16	+	1.56747e17i	0.0817583	+	0.887785i
$750$	7.99094e16			0.448983
$751$	−8.68520e16	−	1.50432e17i	−0.484106	−	0.838496i	0.515728	−	0.856753i	$-0.327522\pi$
$751$	−8.68520e16	−	1.50432e17i	−0.484106	−	0.838496i	−0.999833	+	0.0182569i	$0.994188\pi$
$752$	5.33141e16	+	3.07809e16i	0.294805	+	0.170206i
$753$	7.52656e16	−	1.30364e17i	0.412883	−	0.715134i
$754$	−1.63646e15	+	9.44810e14i	−0.00890589	+	0.00514182i
$755$		−	1.30342e17i		−	0.703723i
$756$	4.07825e16	+	5.76811e16i	0.218446	+	0.308960i
$757$	3.42061e17			1.81773			0.908864	−	0.417093i	$-0.136951\pi$
$757$	3.42061e17			1.81773			0.908864	+	0.417093i	$0.136951\pi$
$758$	2.11539e16	+	3.66396e16i	0.111526	+	0.193168i
$759$	2.32573e17	+	1.34276e17i	1.21649	+	0.702340i
$760$	−4.95159e16	+	8.57640e16i	−0.256958	+	0.445065i
$761$	−1.24209e17	+	7.17119e16i	−0.639505	+	0.369218i	−0.784424	−	0.620225i	$-0.787041\pi$
$761$	−1.24209e17	+	7.17119e16i	−0.639505	+	0.369218i	0.144919	+	0.989444i	$0.453708\pi$
$762$		−	9.25388e16i		−	0.472709i
$763$	8.43227e16	−	5.96191e16i	0.427363	−	0.302161i
$764$	−6.95592e16			−0.349779
$765$	1.08988e17	+	1.88773e17i	0.543764	+	0.941827i
$766$	−2.76173e16	−	1.59449e16i	−0.136713	−	0.0789311i
$767$	1.76615e15	−	3.05905e15i	0.00867469	−	0.0150250i
$768$	−3.35544e16	+	1.93726e16i	−0.163524	+	0.0944107i
$769$			8.08856e16i			0.391123i	0.980691	+	0.195561i	$0.0626529\pi$
$769$			8.08856e16i			0.391123i	−0.980691	+	0.195561i	$0.937347\pi$
$770$	3.31060e16	−	3.04881e15i	0.158841	−	0.0146280i
$771$	2.45365e17			1.16812
$772$	6.10615e16	+	1.05762e17i	0.288445	+	0.499602i
$773$	−2.90934e17	−	1.67971e17i	−1.36370	−	0.787330i	−0.373582	−	0.927597i	$-0.621871\pi$
$773$	−2.90934e17	−	1.67971e17i	−1.36370	−	0.787330i	−0.990114	+	0.140267i	$0.955204\pi$
$774$	−1.95445e16	+	3.38520e16i	−0.0909030	+	0.157449i
$775$	1.68486e17	−	9.72756e16i	0.777597	−	0.448946i
$776$			1.27581e16i			0.0584273i
$777$	−1.66175e17	+	3.60654e17i	−0.755159	+	1.63894i
$778$	5.60530e15			0.0252768
$779$	−7.09183e16	−	1.22834e17i	−0.317346	−	0.549660i
$780$	3.14444e16	+	1.81544e16i	0.139629	+	0.0806147i
$781$	−1.53723e17	+	2.66257e17i	−0.677382	+	1.17326i
$782$	−1.00674e17	+	5.81242e16i	−0.440228	+	0.254166i
$783$		−	1.43096e16i		−	0.0620952i
$784$	5.44287e16	−	1.53901e17i	0.234386	−	0.662743i
$785$	1.38417e17			0.591522
$786$	5.38151e16	+	9.32106e16i	0.228228	+	0.395303i
$787$	−1.77946e17	−	1.02737e17i	−0.748928	−	0.432394i	0.0763787	−	0.997079i	$-0.475664\pi$
$787$	−1.77946e17	−	1.02737e17i	−0.748928	−	0.432394i	−0.825306	+	0.564685i	$0.808998\pi$
$788$	−4.96410e16	+	8.59807e16i	−0.207340	+	0.359123i
$789$	3.57165e17	−	2.06209e17i	1.48049	−	0.854764i
$790$		−	3.42431e14i		−	0.00140867i
$791$	1.32474e17	+	6.10386e16i	0.540843	+	0.249199i
$792$	−1.75133e17			−0.709606
$793$	9.84573e14	+	1.70533e15i	0.00395921	+	0.00685756i
$794$	9.93940e15	+	5.73852e15i	0.0396677	+	0.0229022i
$795$	1.96050e17	−	3.39569e17i	0.776542	−	1.34501i
$796$	−1.50041e17	+	8.66265e16i	−0.589838	+	0.340543i
$797$			1.47396e17i			0.575089i	0.957767	+	0.287544i	$0.0928389\pi$
$797$			1.47396e17i			0.575089i	−0.957767	+	0.287544i	$0.907161\pi$
$798$	1.77461e16	+	1.92699e17i	0.0687203	+	0.746210i
$799$	1.96297e17			0.754456
$800$	7.66390e16	+	1.32743e17i	0.292354	+	0.506373i
$801$	−3.08832e16	−	1.78304e16i	−0.116930	−	0.0675098i
$802$	1.87318e16	−	3.24444e16i	0.0703936	−	0.121925i
$803$	1.77506e17	−	1.02483e17i	0.662093	−	0.382260i
$804$		−	3.99434e17i		−	1.47880i
$805$	8.73559e16	+	1.23552e17i	0.321009	+	0.454021i
$806$	−2.44753e16			−0.0892725
$807$	−2.69313e17	−	4.66463e17i	−0.975025	−	1.68879i
$808$	6.19965e16	+	3.57937e16i	0.222792	+	0.128629i
$809$	−1.31755e17	+	2.28206e17i	−0.469975	+	0.814020i	−0.999411	−	0.0343299i	$-0.989070\pi$
$809$	−1.31755e17	+	2.28206e17i	−0.469975	+	0.814020i	0.529436	+	0.848350i	$0.322404\pi$
$810$	−2.74658e16	+	1.58574e16i	−0.0972483	+	0.0561463i
$811$			5.36385e16i			0.188517i	0.995548	+	0.0942586i	$0.0300481\pi$
$811$			5.36385e16i			0.188517i	−0.995548	+	0.0942586i	$0.969952\pi$
$812$	−3.09375e16	+	2.18739e16i	−0.107932	+	0.0763117i
$813$	−3.65680e17			−1.26636
$814$	−5.08239e16	−	8.80297e16i	−0.174712	−	0.302610i
$815$	−6.58454e16	−	3.80159e16i	−0.224688	−	0.129724i
$816$	−2.44067e17	+	4.22737e17i	−0.826739	+	1.43195i
$817$	1.77227e17	−	1.02322e17i	0.595933	−	0.344062i
$818$		−	1.77791e16i		−	0.0593459i
$819$	8.38362e16	−	7.72068e15i	0.277798	−	0.0255830i
$820$	6.09513e16			0.200493
$821$	−9.81111e16	−	1.69933e17i	−0.320375	−	0.554906i	0.660190	−	0.751099i	$-0.270476\pi$
$821$	−9.81111e16	−	1.69933e17i	−0.320375	−	0.554906i	−0.980565	+	0.196192i	$0.937142\pi$
$822$	−9.83542e16	−	5.67848e16i	−0.318832	−	0.184078i
$823$	−1.55396e17	+	2.69155e17i	−0.500083	+	0.866169i	0.499917	+	0.866073i	$0.333364\pi$
$823$	−1.55396e17	+	2.69155e17i	−0.500083	+	0.866169i	−1.00000		9.58798e-5i	$0.999969\pi$
$824$	1.05608e17	−	6.09729e16i	0.337391	−	0.194793i
$825$		−	3.05218e17i		−	0.968025i
$826$	−3.38548e15	+	7.34762e15i	−0.0106596	+	0.0231348i
$827$	1.22172e17			0.381890			0.190945	−	0.981601i	$-0.438845\pi$
$827$	1.22172e17			0.381890			0.190945	+	0.981601i	$0.438845\pi$
$828$	−1.88508e17	−	3.26505e17i	−0.584989	−	1.01323i
$829$	−2.29159e17	−	1.32305e17i	−0.706008	−	0.407614i	0.103573	−	0.994622i	$-0.466972\pi$
$829$	−2.29159e17	−	1.32305e17i	−0.706008	−	0.407614i	−0.809581	+	0.587008i	$0.800306\pi$
$830$	5.25537e16	−	9.10257e16i	0.160744	−	0.278417i
$831$	−5.77506e17	+	3.33423e17i	−1.75368	+	1.01249i
$832$			3.15657e16i			0.0951646i
$833$	−9.50652e16	−	5.11763e17i	−0.284545	−	1.53179i
$834$	−9.33079e16			−0.277282
$835$	9.79957e16	+	1.69734e17i	0.289127	+	0.500782i
$836$	3.75572e17	+	2.16837e17i	1.10016	+	0.635178i
$837$	9.26727e16	−	1.60514e17i	0.269525	−	0.466831i
$838$	1.86584e17	−	1.07724e17i	0.538777	−	0.311063i
$839$			4.15912e17i			1.19242i	0.802828	+	0.596210i	$0.203328\pi$
$839$			4.15912e17i			1.19242i	−0.802828	+	0.596210i	$0.796672\pi$
$840$	−1.59681e17	−	7.35745e16i	−0.454545	−	0.209436i
$841$	−3.46140e17			−0.978308
$842$	3.91166e16	+	6.77519e16i	0.109771	+	0.190129i
$843$	6.78356e17	+	3.91649e17i	1.89013	+	1.09127i
$844$	1.80443e17	−	3.12537e17i	0.499213	−	0.864662i
$845$	−1.63842e17	+	9.45945e16i	−0.450076	+	0.259852i
$846$		−	7.27176e16i		−	0.198343i
$847$	5.63295e15	+	6.11663e16i	0.0152558	+	0.165658i
$848$	4.92825e17			1.32531
$849$	4.84539e17	+	8.39246e17i	1.29385	+	2.24101i
$850$	1.14420e17	+	6.60601e16i	0.303380	+	0.175156i
$851$	2.31318e17	−	4.00655e17i	0.609022	−	1.05486i
$852$	6.65989e17	−	3.84509e17i	1.74112	−	1.00524i
$853$			4.39634e17i			1.14129i	0.821196	+	0.570646i	$0.193307\pi$
$853$			4.39634e17i			1.14129i	−0.821196	+	0.570646i	$0.806693\pi$
$854$	−2.60365e15	−	3.68249e15i	−0.00671175	−	0.00949280i
$855$	−4.22746e17			−1.08214
$856$	1.06543e17	+	1.84537e17i	0.270820	+	0.469074i
$857$	−3.01014e17	−	1.73791e17i	−0.759806	−	0.438674i	0.0694204	−	0.997587i	$-0.477885\pi$
$857$	−3.01014e17	−	1.73791e17i	−0.759806	−	0.438674i	−0.829226	+	0.558914i	$0.811218\pi$
$858$	−1.91988e16	+	3.32533e16i	−0.0481227	+	0.0833510i
$859$	−4.85979e17	+	2.80580e17i	−1.20965	+	0.698390i	−0.962682	−	0.270635i	$-0.912766\pi$
$859$	−4.85979e17	+	2.80580e17i	−1.20965	+	0.698390i	−0.246965	+	0.969025i	$0.579433\pi$
$860$			8.79415e16i			0.217372i
$861$	2.05608e17	−	1.45372e17i	0.504686	−	0.356831i
$862$	1.17962e17			0.287540
$863$	−2.90366e17	−	5.02929e17i	−0.702880	−	1.21742i	−0.967451	−	0.253058i	$-0.918564\pi$
$863$	−2.90366e17	−	5.02929e17i	−0.702880	−	1.21742i	0.264571	−	0.964366i	$-0.414770\pi$
$864$	1.26461e17	+	7.30126e16i	0.304002	+	0.175515i
$865$	1.85914e16	−	3.22013e16i	0.0443829	−	0.0768734i
$866$	5.74494e16	−	3.31684e16i	0.136200	−	0.0786352i
$867$			9.15250e17i			2.15489i
$868$	−4.88693e17	+	4.50049e16i	−1.14266	+	0.105231i
$869$	−3.17039e15			−0.00736196
$870$	8.42251e15	+	1.45882e16i	0.0194234	+	0.0336424i
$871$	−8.99968e16	−	5.19597e16i	−0.206119	−	0.119003i
$872$	6.98982e16	−	1.21067e17i	0.158989	−	0.275377i
$873$	−4.71652e16	+	2.72308e16i	−0.106546	+	0.0615142i
$874$		−	2.25454e17i		−	0.505812i
$875$	1.74446e17	−	3.78605e17i	0.388698	−	0.843603i
$876$	−5.12682e17			−1.13455
$877$	1.76218e17	+	3.05219e17i	0.387305	+	0.670832i	0.992086	−	0.125560i	$-0.0400726\pi$
$877$	1.76218e17	+	3.05219e17i	0.387305	+	0.670832i	−0.604781	+	0.796392i	$0.706739\pi$
$878$	−1.45624e17	−	8.40759e16i	−0.317881	−	0.183529i
$879$	3.98301e17	−	6.89877e17i	0.863531	−	1.49568i
$880$	−1.40854e17	+	8.13219e16i	−0.303300	+	0.175110i
$881$		−	7.39205e17i		−	1.58092i	−0.612514	−	0.790459i	$-0.709842\pi$
$881$		−	7.39205e17i		−	1.58092i	0.612514	−	0.790459i	$-0.290158\pi$
$882$	−1.89581e17	+	3.52165e16i	−0.402701	+	0.0748058i
$883$	2.54616e16			0.0537182			0.0268591	−	0.999639i	$-0.491449\pi$
$883$	2.54616e16			0.0537182			0.0268591	+	0.999639i	$0.491449\pi$
$884$	7.27580e16	+	1.26021e17i	0.152464	+	0.264075i
$885$	−2.72699e16	−	1.57443e16i	−0.0567576	−	0.0327690i
$886$	−1.17078e17	+	2.02785e17i	−0.242032	+	0.419213i
$887$	−1.73169e17	+	9.99793e16i	−0.355573	+	0.205290i	−0.667137	−	0.744935i	$-0.732481\pi$
$887$	−1.73169e17	+	9.99793e16i	−0.355573	+	0.205290i	0.311564	+	0.950225i	$0.399147\pi$
$888$			5.37546e17i			1.09632i
$889$	−4.38442e17	−	2.02016e17i	−0.888182	−	0.409238i
$890$	9.16399e15			0.0184393
$891$	1.46815e17	+	2.54291e17i	0.293430	+	0.508236i
$892$	1.02391e17	+	5.91152e16i	0.203269	+	0.117357i
$893$	−1.90351e17	+	3.29697e17i	−0.375358	+	0.650139i
$894$	8.21365e16	−	4.74216e16i	0.160883	−	0.0928861i
$895$		−	3.95670e17i		−	0.769830i
$896$	−4.61371e16	−	5.00987e17i	−0.0891667	−	0.968230i
$897$	−1.74762e17			−0.335499
$898$	2.36501e15	+	4.09633e15i	0.00450999	+	0.00781154i
$899$	8.60925e16	+	4.97055e16i	0.163082	+	0.0941557i
$900$	−2.14246e17	+	3.71084e17i	−0.403141	+	0.698260i
$901$	1.36090e18	−	7.85717e17i	2.54377	−	1.46865i
$902$			6.44577e16i			0.119684i
$903$	2.09745e17	+	2.96655e17i	0.386871	+	0.547173i
$904$	1.97450e17			0.361781
$905$	9.12584e16	+	1.58064e17i	0.166104	+	0.287701i
$906$	−2.98588e17	−	1.72390e17i	−0.539888	−	0.311704i
$907$	9.41572e16	−	1.63085e17i	0.169126	−	0.292934i	−0.768987	−	0.639264i	$-0.779239\pi$
$907$	9.41572e16	−	1.63085e17i	0.169126	−	0.292934i	0.938113	+	0.346330i	$0.112572\pi$
$908$	−1.27294e16	+	7.34930e15i	−0.0227139	+	0.0131139i
$909$			3.05592e17i			0.541699i
$910$	−1.76655e16	+	1.24902e16i	−0.0311085	+	0.0219948i
$911$	−9.49806e17			−1.66159			−0.830796	−	0.556577i	$-0.812115\pi$
$911$	−9.49806e17			−1.66159			−0.830796	+	0.556577i	$0.812115\pi$
$912$	−4.73347e17	−	8.19861e17i	−0.822642	−	1.42486i
$913$	−8.42759e17	−	4.86567e17i	−1.45505	−	0.840075i
$914$	−1.80174e17	+	3.12071e17i	−0.309041	+	0.535274i
$915$	1.52022e16	−	8.77697e15i	0.0259047	−	0.0149561i
$916$			2.34985e17i			0.397803i
$917$	5.59106e17	−	5.14894e16i	0.940325	−	0.0865968i
$918$	1.25869e17			0.210311
$919$	9.56123e15	+	1.65605e16i	0.0158716	+	0.0274904i	0.873852	−	0.486192i	$-0.161614\pi$
$919$	9.56123e15	+	1.65605e16i	0.0158716	+	0.0274904i	−0.857981	+	0.513682i	$0.828281\pi$
$920$	1.77392e17	+	1.02417e17i	0.292554	+	0.168906i
$921$	2.79266e17	−	4.83703e17i	0.457573	−	0.792540i
$922$	−3.88286e16	+	2.24177e16i	−0.0632071	+	0.0364926i
$923$		−	2.00073e17i		−	0.323577i
$924$	−3.22193e17	+	6.99264e17i	−0.517707	+	1.12359i
$925$	−5.25802e17			−0.839406
$926$	−7.41114e16	−	1.28365e17i	−0.117549	−	0.203601i
$927$	4.50819e17	+	2.60280e17i	0.710434	+	0.410169i
$928$	−3.91607e16	+	6.78283e16i	−0.0613144	+	0.106200i
$929$	−3.22338e16	+	1.86102e16i	−0.0501438	+	0.0289506i	−0.524862	−	0.851187i	$-0.675883\pi$
$929$	−3.22338e16	+	1.86102e16i	−0.0501438	+	0.0289506i	0.474719	+	0.880138i	$0.342550\pi$
$930$			2.18185e17i			0.337231i
$931$	9.51733e17	+	3.36590e17i	1.46156	+	0.516896i
$932$	3.65887e17			0.558280
$933$	2.65696e17	+	4.60199e17i	0.402805	+	0.697679i
$934$	2.52323e17	+	1.45679e17i	0.380080	+	0.219439i
$935$	−2.59305e17	+	4.49129e17i	−0.388098	+	0.672205i
$936$	9.87000e16	−	5.69844e16i	0.146778	−	0.0847425i
$937$			1.06613e18i			1.57533i	0.616104	+	0.787665i	$0.288710\pi$
$937$			1.06613e18i			1.57533i	−0.616104	+	0.787665i	$0.711290\pi$
$938$	2.16166e17	+	9.96003e16i	0.317373	+	0.146232i
$939$	2.98340e17			0.435229
$940$	−8.17993e16	−	1.41680e17i	−0.118572	−	0.205373i
$941$	1.04532e18	+	6.03518e17i	1.50561	+	0.869265i	0.999979	+	0.00651680i	$0.00207438\pi$
$941$	1.04532e18	+	6.03518e17i	1.50561	+	0.869265i	0.505633	+	0.862749i	$0.331259\pi$
$942$	1.83070e17	−	3.17087e17i	0.262006	−	0.453809i
$943$	−2.54066e17	+	1.46685e17i	−0.361308	+	0.208601i
$944$		−	3.95775e16i		−	0.0559264i
$945$	−1.50246e16	−	1.63147e17i	−0.0210966	−	0.229080i
$946$	−9.30006e16			−0.129759
$947$	−6.35906e17	−	1.10142e18i	−0.881643	−	1.52705i	−0.849513	−	0.527567i	$-0.823104\pi$
$947$	−6.35906e17	−	1.10142e18i	−0.881643	−	1.52705i	−0.0321298	−	0.999484i	$-0.510229\pi$
$948$	6.86767e15	+	3.96505e15i	0.00946149	+	0.00546259i
$949$	−6.66913e16	+	1.15513e17i	−0.0913003	+	0.158137i
$950$	−2.21907e17	+	1.28118e17i	−0.301876	+	0.174288i
$951$		−	1.02010e18i		−	1.37899i
$952$	−4.06786e17	−	5.75341e17i	−0.546443	−	0.772865i
$953$	1.06163e18			1.41715			0.708573	−	0.705637i	$-0.249339\pi$
$953$	1.06163e18			1.41715			0.708573	+	0.705637i	$0.249339\pi$
$954$	−2.91066e17	−	5.04141e17i	−0.386101	−	0.668747i
$955$	1.39712e17	+	8.06627e16i	0.184167	+	0.106329i
$956$	−2.95735e17	+	5.12228e17i	−0.387396	+	0.670990i
$957$	1.35065e17	−	7.79796e16i	0.175821	−	0.101510i
$958$		−	3.88927e17i		−	0.503124i
$959$	−4.83754e17	+	3.42031e17i	−0.621889	+	0.439698i
$960$	2.81393e17			0.359489
$961$	2.49979e17	+	4.32976e17i	0.317368	+	0.549698i
$962$	5.72858e16	+	3.30740e16i	0.0722764	+	0.0417288i
$963$	−4.54808e17	+	7.87751e17i	−0.570257	+	0.987714i
$964$	−1.23143e17	+	7.10965e16i	−0.153443	+	0.0885903i
$965$		−	2.83234e17i		−	0.350737i
$966$	3.98572e17	−	3.67055e16i	0.490506	−	0.0451719i
$967$	4.22414e17			0.516630			0.258315	−	0.966061i	$-0.416833\pi$
$967$	4.22414e17			0.516630			0.258315	+	0.966061i	$0.416833\pi$
$968$	4.15755e16	+	7.20108e16i	0.0505341	+	0.0875277i
$969$	−2.61423e18	−	1.50933e18i	−3.15792	−	1.82322i
$970$	6.99767e15	−	1.21203e16i	0.00840084	−	0.0145507i
$971$	−1.16850e18	+	6.74631e17i	−1.39416	+	0.804917i	−0.993772	−	0.111430i	$-0.964457\pi$
$971$	−1.16850e18	+	6.74631e17i	−1.39416	+	0.804917i	−0.400385	+	0.916347i	$0.631124\pi$
$972$		−	1.05356e18i		−	1.24929i
$973$	−2.03695e17	+	4.42086e17i	−0.240051	+	0.520991i
$974$	−6.69828e15			−0.00784530
$975$	9.93112e16	+	1.72012e17i	0.115603	+	0.200231i
$976$	1.91074e16	+	1.10316e16i	0.0221056	+	0.0127627i
$977$	2.85715e17	−	4.94873e17i	0.328523	−	0.569019i	−0.653696	−	0.756757i	$-0.726782\pi$
$977$	2.85715e17	−	4.94873e17i	0.328523	−	0.569019i	0.982219	+	0.187739i	$0.0601158\pi$
$978$	−1.74174e17	+	1.00560e17i	−0.199045	+	0.114919i
$979$		−	8.48446e16i		−	0.0963669i
$980$	−3.29758e17	+	2.81872e17i	−0.372253	+	0.318197i
$981$	5.96762e17			0.669556
$982$	1.14143e17	+	1.97701e17i	0.127285	+	0.220465i
$983$	1.49111e18	+	8.60891e17i	1.65268	+	0.954173i	0.975966	+	0.217923i	$0.0699283\pi$
$983$	1.49111e18	+	8.60891e17i	1.65268	+	0.954173i	0.676710	+	0.736250i	$0.263405\pi$
$984$	1.70436e17	−	2.95204e17i	0.187755	−	0.325201i
$985$	1.99411e17	−	1.15130e17i	0.218339	−	0.126058i
$986$			6.75103e16i			0.0734698i
$987$	−6.13851e17	−	2.82838e17i	−0.663988	−	0.305939i
$988$	−2.82215e17			−0.303416
$989$	−2.11640e17	−	3.66571e17i	−0.226162	−	0.391724i
$990$	1.66378e17	+	9.60585e16i	0.176720	+	0.102029i
$991$	5.50013e17	−	9.52651e17i	0.580673	−	1.00575i	−0.414727	−	0.909946i	$-0.636123\pi$
$991$	5.50013e17	−	9.52651e17i	0.580673	−	1.00575i	0.995400	−	0.0958085i	$-0.0305437\pi$
$992$	−8.78545e17	+	5.07228e17i	−0.921922	+	0.532272i
$993$		−	2.67695e18i		−	2.79219i
$994$	4.20216e16	+	4.56298e17i	0.0435667	+	0.473076i
$995$	4.01817e17			0.414086
$996$	1.21705e18	+	2.10800e18i	1.24668	+	2.15931i
$997$	−4.74286e17	−	2.73829e17i	−0.482914	−	0.278810i	0.238716	−	0.971089i	$-0.423273\pi$
$997$	−4.74286e17	−	2.73829e17i	−0.482914	−	0.278810i	−0.721630	+	0.692279i	$0.756607\pi$
$998$	1.04679e17	−	1.81310e17i	0.105944	−	0.183501i
$999$	−4.33812e17	+	2.50461e17i	−0.436424	+	0.251969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.13.d.a.3.4	✓	14
3.2	odd	2		63.13.m.a.10.4		14
4.3	odd	2		112.13.s.a.17.1		14
7.2	even	3		49.13.d.c.19.4		14
7.3	odd	6		49.13.b.a.48.8		14
7.4	even	3		49.13.b.a.48.7		14
7.5	odd	6	inner	7.13.d.a.5.4	yes	14
7.6	odd	2		49.13.d.c.31.4		14
21.5	even	6		63.13.m.a.19.4		14
28.19	even	6		112.13.s.a.33.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.13.d.a.3.4	✓	14	1.1	even	1	trivial
7.13.d.a.5.4	yes	14	7.5	odd	6	inner
49.13.b.a.48.7		14	7.4	even	3
49.13.b.a.48.8		14	7.3	odd	6
49.13.d.c.19.4		14	7.2	even	3
49.13.d.c.31.4		14	7.6	odd	2
63.13.m.a.10.4		14	3.2	odd	2
63.13.m.a.19.4		14	21.5	even	6
112.13.s.a.17.1		14	4.3	odd	2
112.13.s.a.33.1		14	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(10.2457 + 17.7460i) q^{2} +(953.136 + 550.294i) q^{3} +(1838.05 - 3183.60i) q^{4} +(-7383.58 + 4262.91i) q^{5} +22552.5i q^{6} +(106852. + 49233.1i) q^{7} +159261. q^{8} +(339926. + 588768. i) q^{9} +O(q^{10})\)	\(q+(10.2457 + 17.7460i) q^{2} +(953.136 + 550.294i) q^{3} +(1838.05 - 3183.60i) q^{4} +(-7383.58 + 4262.91i) q^{5} +22552.5i q^{6} +(106852. + 49233.1i) q^{7} +159261. q^{8} +(339926. + 588768. i) q^{9} +(-151299. - 87352.7i) q^{10} +(-808753. + 1.40080e6i) q^{11} +(3.50383e6 - 2.02294e6i) q^{12} -1.05260e6i q^{13} +(221079. + 2.40063e6i) q^{14} -9.38341e6 q^{15} +(-5.89693e6 - 1.02138e7i) q^{16} +(-3.25679e7 - 1.88031e7i) q^{17} +(-6.96553e6 + 1.20647e7i) q^{18} +(6.31626e7 - 3.64669e7i) q^{19} +3.13418e7i q^{20} +(7.47520e7 + 1.05726e8i) q^{21} -3.31448e7 q^{22} +(-7.54272e7 - 1.30644e8i) q^{23} +(1.51797e8 + 8.76402e7i) q^{24} +(-8.57255e7 + 1.48481e8i) q^{25} +(1.86795e7 - 1.07846e7i) q^{26} +1.63338e8i q^{27} +(3.53139e8 - 2.49681e8i) q^{28} -8.76074e7 q^{29} +(-9.61393e7 - 1.66518e8i) q^{30} +(-9.82708e8 - 5.67367e8i) q^{31} +(4.47002e8 - 7.74230e8i) q^{32} +(-1.54170e9 + 8.90103e8i) q^{33} -7.70601e8i q^{34} +(-9.98828e8 + 9.19844e7i) q^{35} +2.49920e9 q^{36} +(1.53339e9 + 2.65591e9i) q^{37} +(1.29429e9 + 7.47256e8i) q^{38} +(5.79239e8 - 1.00327e9i) q^{39} +(-1.17591e9 + 6.78914e8i) q^{40} -1.94473e9i q^{41} +(-1.11033e9 + 2.40978e9i) q^{42} +2.80588e9 q^{43} +(2.97306e9 + 5.14949e9i) q^{44} +(-5.01973e9 - 2.89814e9i) q^{45} +(1.54560e9 - 2.67706e9i) q^{46} +(-4.52049e9 + 2.60991e9i) q^{47} -1.29802e10i q^{48} +(8.99348e9 + 1.05213e10i) q^{49} -3.51326e9 q^{50} +(-2.06944e10 - 3.58438e10i) q^{51} +(-3.35106e9 - 1.93474e9i) q^{52} +(-2.08933e10 + 3.61883e10i) q^{53} +(-2.89860e9 + 1.67351e9i) q^{54} -1.37906e10i q^{55} +(1.70174e10 + 7.84091e9i) q^{56} +8.02701e10 q^{57} +(-8.97596e8 - 1.55468e9i) q^{58} +(2.90619e9 + 1.67789e9i) q^{59} +(-1.72472e10 + 2.98730e10i) q^{60} +(-1.62011e9 + 9.35372e8i) q^{61} -2.32522e10i q^{62} +(7.33486e9 + 7.96468e10i) q^{63} -2.99883e10 q^{64} +(4.48714e9 + 7.77196e9i) q^{65} +(-3.15916e10 - 1.82394e10i) q^{66} +(4.93631e10 - 8.54995e10i) q^{67} +(-1.19723e11 + 6.91221e10i) q^{68} -1.66028e11i q^{69} +(-1.18660e10 - 1.67828e10i) q^{70} +1.90075e11 q^{71} +(5.41368e10 + 9.37677e10i) q^{72} +(-1.09740e11 - 6.33586e10i) q^{73} +(-3.14212e10 + 5.44231e10i) q^{74} +(-1.63416e11 + 9.43484e10i) q^{75} -2.68113e11i q^{76} +(-1.55383e11 + 1.09861e11i) q^{77} +2.37388e10 q^{78} +(9.80023e8 + 1.69745e9i) q^{79} +(8.70809e10 + 5.02762e10i) q^{80} +(9.07664e10 - 1.57212e11i) q^{81} +(3.45112e10 - 1.99250e10i) q^{82} +6.01627e11i q^{83} +(4.73987e11 - 4.36506e10i) q^{84} +3.20623e11 q^{85} +(2.87482e10 + 4.97933e10i) q^{86} +(-8.35018e10 - 4.82098e10i) q^{87} +(-1.28803e11 + 2.23093e11i) q^{88} +(-4.54265e10 + 2.62270e10i) q^{89} -1.18774e11i q^{90} +(5.18228e10 - 1.12473e11i) q^{91} -5.54556e11 q^{92} +(-6.24437e11 - 1.08156e12i) q^{93} +(-9.26310e10 - 5.34805e10i) q^{94} +(-3.10911e11 + 5.38513e11i) q^{95} +(8.52108e11 - 4.91965e11i) q^{96} +8.01082e10i q^{97} +(-9.45676e10 + 2.67397e11i) q^{98} -1.09966e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 44 q^{2} - 3 q^{3} - 14404 q^{4} - 9075 q^{5} + 334278 q^{7} - 52112 q^{8} + 265974 q^{9}+O(q^{10}) \) 14 * q + 44 * q^2 - 3 * q^3 - 14404 * q^4 - 9075 * q^5 + 334278 * q^7 - 52112 * q^8 + 265974 * q^9	\( 14 q + 44 q^{2} - 3 q^{3} - 14404 q^{4} - 9075 q^{5} + 334278 q^{7} - 52112 q^{8} + 265974 q^{9} + 3406596 q^{10} - 2085193 q^{11} - 12871740 q^{12} + 21936320 q^{14} + 21308298 q^{15} - 64542600 q^{16} + 46675437 q^{17} + 12781272 q^{18} - 153598539 q^{19} + 46954005 q^{21} + 138292528 q^{22} + 230058719 q^{23} - 265960656 q^{24} + 19748318 q^{25} + 590880528 q^{26} + 229618900 q^{28} - 714663796 q^{29} + 999571848 q^{30} - 5040285435 q^{31} + 1011711600 q^{32} - 2159472843 q^{33} + 2425404597 q^{35} + 17119036896 q^{36} - 5044805001 q^{37} + 3238109592 q^{38} - 5776828680 q^{39} - 35225923512 q^{40} + 27354512640 q^{42} + 40132389276 q^{43} - 11796090372 q^{44} - 18717971166 q^{45} - 12430801472 q^{46} - 53247355563 q^{47} + 16893431198 q^{49} + 178352838608 q^{50} + 1366166853 q^{51} - 136241043960 q^{52} - 35499894841 q^{53} - 154061995896 q^{54} + 42830066608 q^{56} + 371092140234 q^{57} - 21841743752 q^{58} - 138067877811 q^{59} - 146425754916 q^{60} - 287167557435 q^{61} + 240766542198 q^{63} + 1077334893984 q^{64} - 121576543704 q^{65} - 358267134060 q^{66} - 104132716721 q^{67} - 1346622176340 q^{68} + 620078986800 q^{70} + 809521279196 q^{71} - 435854437392 q^{72} + 4606244997 q^{73} - 229538257100 q^{74} - 692089720566 q^{75} + 408395115359 q^{77} + 1860221591760 q^{78} + 53291758879 q^{79} - 1497721732104 q^{80} - 82850395887 q^{81} - 27489500640 q^{82} - 28369303620 q^{84} + 402017692458 q^{85} + 1190361662368 q^{86} - 603786809646 q^{87} + 342437177984 q^{88} + 77396974197 q^{89} - 1437510415152 q^{91} - 3683682769320 q^{92} - 509894759883 q^{93} + 2011339035528 q^{94} + 690022114413 q^{95} + 5403247899840 q^{96} + 153246523724 q^{98} - 5499432555540 q^{99}+O(q^{100}) \) 14 * q + 44 * q^2 - 3 * q^3 - 14404 * q^4 - 9075 * q^5 + 334278 * q^7 - 52112 * q^8 + 265974 * q^9 + 3406596 * q^10 - 2085193 * q^11 - 12871740 * q^12 + 21936320 * q^14 + 21308298 * q^15 - 64542600 * q^16 + 46675437 * q^17 + 12781272 * q^18 - 153598539 * q^19 + 46954005 * q^21 + 138292528 * q^22 + 230058719 * q^23 - 265960656 * q^24 + 19748318 * q^25 + 590880528 * q^26 + 229618900 * q^28 - 714663796 * q^29 + 999571848 * q^30 - 5040285435 * q^31 + 1011711600 * q^32 - 2159472843 * q^33 + 2425404597 * q^35 + 17119036896 * q^36 - 5044805001 * q^37 + 3238109592 * q^38 - 5776828680 * q^39 - 35225923512 * q^40 + 27354512640 * q^42 + 40132389276 * q^43 - 11796090372 * q^44 - 18717971166 * q^45 - 12430801472 * q^46 - 53247355563 * q^47 + 16893431198 * q^49 + 178352838608 * q^50 + 1366166853 * q^51 - 136241043960 * q^52 - 35499894841 * q^53 - 154061995896 * q^54 + 42830066608 * q^56 + 371092140234 * q^57 - 21841743752 * q^58 - 138067877811 * q^59 - 146425754916 * q^60 - 287167557435 * q^61 + 240766542198 * q^63 + 1077334893984 * q^64 - 121576543704 * q^65 - 358267134060 * q^66 - 104132716721 * q^67 - 1346622176340 * q^68 + 620078986800 * q^70 + 809521279196 * q^71 - 435854437392 * q^72 + 4606244997 * q^73 - 229538257100 * q^74 - 692089720566 * q^75 + 408395115359 * q^77 + 1860221591760 * q^78 + 53291758879 * q^79 - 1497721732104 * q^80 - 82850395887 * q^81 - 27489500640 * q^82 - 28369303620 * q^84 + 402017692458 * q^85 + 1190361662368 * q^86 - 603786809646 * q^87 + 342437177984 * q^88 + 77396974197 * q^89 - 1437510415152 * q^91 - 3683682769320 * q^92 - 509894759883 * q^93 + 2011339035528 * q^94 + 690022114413 * q^95 + 5403247899840 * q^96 + 153246523724 * q^98 - 5499432555540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more