LMFDB - Embedded newform 5.21.c.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,21,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$12.6756882551$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 $ x^18 + 7326009x^16 + 21914129354136x^14 + 34716886079362208784x^12 + 31708037646565185778430976x^10 + 17074068956994774485619232997376x^8 + 5289719974975064649188570034899779584x^6 + 860456443567863287787024826102919920091136x^4 + 56032264901085762369236000491606259366923075584x^2 + 797517854172776133766249661927470942176176766976
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{16}\cdot 5^{32} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.8
Root			$836.109i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.21.c.a.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(836.109 - 836.109i) q^{2} +(68486.6 + 68486.6i) q^{3} -349580. i q^{4} +(7.10218e6 - 6.70272e6i) q^{5} +1.14524e8 q^{6} +(-2.53016e8 + 2.53016e8i) q^{7} +(5.84437e8 + 5.84437e8i) q^{8} +5.89403e9i q^{9} +O(q^{10})$	\(q+(836.109 - 836.109i) q^{2} +(68486.6 + 68486.6i) q^{3} -349580. i q^{4} +(7.10218e6 - 6.70272e6i) q^{5} +1.14524e8 q^{6} +(-2.53016e8 + 2.53016e8i) q^{7} +(5.84437e8 + 5.84437e8i) q^{8} +5.89403e9i q^{9} +(3.33994e8 - 1.15424e10i) q^{10} +3.06850e10 q^{11} +(2.39415e10 - 2.39415e10i) q^{12} +(-1.19203e11 - 1.19203e11i) q^{13} +4.23098e11i q^{14} +(9.45450e11 + 2.73578e10i) q^{15} +1.34387e12 q^{16} +(4.41705e11 - 4.41705e11i) q^{17} +(4.92805e12 + 4.92805e12i) q^{18} -3.31039e12i q^{19} +(-2.34313e12 - 2.48278e12i) q^{20} -3.46564e13 q^{21} +(2.56560e13 - 2.56560e13i) q^{22} +(7.65974e11 + 7.65974e11i) q^{23} +8.00522e13i q^{24} +(5.51453e12 - 9.52079e13i) q^{25} -1.99333e14 q^{26} +(-1.64864e14 + 1.64864e14i) q^{27} +(8.84493e13 + 8.84493e13i) q^{28} -1.13448e14i q^{29} +(8.13373e14 - 7.67625e14i) q^{30} -8.39103e14 q^{31} +(5.10792e14 - 5.10792e14i) q^{32} +(2.10151e15 + 2.10151e15i) q^{33} -7.38627e14i q^{34} +(-1.01070e14 + 3.49286e15i) q^{35} +2.06043e15 q^{36} +(-2.17750e15 + 2.17750e15i) q^{37} +(-2.76784e15 - 2.76784e15i) q^{38} -1.63276e16i q^{39} +(8.06809e15 + 2.33460e14i) q^{40} -7.50950e15 q^{41} +(-2.89765e16 + 2.89765e16i) q^{42} +(-2.71958e16 - 2.71958e16i) q^{43} -1.07269e16i q^{44} +(3.95061e16 + 4.18605e16i) q^{45} +1.28088e15 q^{46} +(3.40208e16 - 3.40208e16i) q^{47} +(9.20368e16 + 9.20368e16i) q^{48} -4.82421e16i q^{49} +(-7.49934e16 - 8.42149e16i) q^{50} +6.05018e16 q^{51} +(-4.16709e16 + 4.16709e16i) q^{52} +(-4.53794e16 - 4.53794e16i) q^{53} +2.75689e17i q^{54} +(2.17931e17 - 2.05673e17i) q^{55} -2.95744e17 q^{56} +(2.26717e17 - 2.26717e17i) q^{57} +(-9.48549e16 - 9.48549e16i) q^{58} +7.34186e17i q^{59} +(9.56372e15 - 3.30510e17i) q^{60} -2.68866e16 q^{61} +(-7.01582e17 + 7.01582e17i) q^{62} +(-1.49129e18 - 1.49129e18i) q^{63} +5.54991e17i q^{64} +(-1.64558e18 - 4.76170e16i) q^{65} +3.51418e18 q^{66} +(1.71038e18 - 1.71038e18i) q^{67} +(-1.54411e17 - 1.54411e17i) q^{68} +1.04918e17i q^{69} +(2.83591e18 + 3.00492e18i) q^{70} +2.52274e18 q^{71} +(-3.44469e18 + 3.44469e18i) q^{72} +(-8.36398e17 - 8.36398e17i) q^{73} +3.64126e18i q^{74} +(6.89813e18 - 6.14279e18i) q^{75} -1.15724e18 q^{76} +(-7.76381e18 + 7.76381e18i) q^{77} +(-1.36516e19 - 1.36516e19i) q^{78} -3.07434e18i q^{79} +(9.54438e18 - 9.00756e18i) q^{80} -2.03074e18 q^{81} +(-6.27876e18 + 6.27876e18i) q^{82} +(6.40039e18 + 6.40039e18i) q^{83} +1.21152e19i q^{84} +(1.76444e17 - 6.09770e18i) q^{85} -4.54773e19 q^{86} +(7.76967e18 - 7.76967e18i) q^{87} +(1.79335e19 + 1.79335e19i) q^{88} +2.47634e19i q^{89} +(6.80313e19 + 1.96857e18i) q^{90} +6.03206e19 q^{91} +(2.67769e17 - 2.67769e17i) q^{92} +(-5.74673e19 - 5.74673e19i) q^{93} -5.68902e19i q^{94} +(-2.21886e19 - 2.35110e19i) q^{95} +6.99648e19 q^{96} +(-9.21143e19 + 9.21143e19i) q^{97} +(-4.03357e19 - 4.03357e19i) q^{98} +1.80858e20i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	836.109	−	836.109i	0.816512	−	0.816512i	−0.169088	−	0.985601i	$-0.554082\pi$
$2$	836.109	−	836.109i	0.816512	−	0.816512i	0.985601	+	0.169088i	$0.0540824\pi$
$3$	68486.6	+	68486.6i	1.15983	+	1.15983i	0.984513	+	0.175313i	$0.0560938\pi$
$3$	68486.6	+	68486.6i	1.15983	+	1.15983i	0.175313	+	0.984513i	$0.443906\pi$
$4$		−	349580.i		−	0.333385i
$5$	7.10218e6	−	6.70272e6i	0.727263	−	0.686358i
$5$	7.10218e6	−	6.70272e6i	0.727263	−	0.686358i
$6$	1.14524e8			1.89402
$7$	−2.53016e8	+	2.53016e8i	−0.895711	+	0.895711i	−0.995053	−	0.0993422i	$-0.968326\pi$
$7$	−2.53016e8	+	2.53016e8i	−0.895711	+	0.895711i	0.0993422	+	0.995053i	$0.468326\pi$
$8$	5.84437e8	+	5.84437e8i	0.544299	+	0.544299i
$9$			5.89403e9i			1.69039i
$10$	3.33994e8	−	1.15424e10i	0.0333994	−	1.15424i
$11$	3.06850e10			1.18304			0.591520	−	0.806290i	$-0.298528\pi$
$11$	3.06850e10			1.18304			0.591520	+	0.806290i	$0.298528\pi$
$12$	2.39415e10	−	2.39415e10i	0.386669	−	0.386669i
$13$	−1.19203e11	−	1.19203e11i	−0.864676	−	0.864676i	0.127201	−	0.991877i	$-0.459401\pi$
$13$	−1.19203e11	−	1.19203e11i	−0.864676	−	0.864676i	−0.991877	+	0.127201i	$0.959401\pi$
$14$			4.23098e11i			1.46272i
$15$	9.45450e11	+	2.73578e10i	1.63956	+	0.0474426i
$16$	1.34387e12			1.22224
$17$	4.41705e11	−	4.41705e11i	0.219101	−	0.219101i	−0.589019	−	0.808119i	$-0.700486\pi$
$17$	4.41705e11	−	4.41705e11i	0.219101	−	0.219101i	0.808119	+	0.589019i	$0.200486\pi$
$18$	4.92805e12	+	4.92805e12i	1.38023	+	1.38023i
$19$		−	3.31039e12i		−	0.539937i	−0.962869	−	0.269968i	$-0.912987\pi$
$19$		−	3.31039e12i		−	0.539937i	0.962869	−	0.269968i	$-0.0870132\pi$
$20$	−2.34313e12	−	2.48278e12i	−0.228822	−	0.242459i
$21$	−3.46564e13			−2.07774
$22$	2.56560e13	−	2.56560e13i	0.965967	−	0.965967i
$23$	7.65974e11	+	7.65974e11i	0.0184899	+	0.0184899i	0.716291	−	0.697801i	$-0.245838\pi$
$23$	7.65974e11	+	7.65974e11i	0.0184899	+	0.0184899i	−0.697801	+	0.716291i	$0.745838\pi$
$24$			8.00522e13i			1.26258i
$25$	5.51453e12	−	9.52079e13i	0.0578241	−	0.998327i
$26$	−1.99333e14			−1.41204
$27$	−1.64864e14	+	1.64864e14i	−0.800735	+	0.800735i
$28$	8.84493e13	+	8.84493e13i	0.298617	+	0.298617i
$29$		−	1.13448e14i		−	0.269660i	−0.990869	−	0.134830i	$-0.956951\pi$
$29$		−	1.13448e14i		−	0.269660i	0.990869	−	0.134830i	$-0.0430489\pi$
$30$	8.13373e14	−	7.67625e14i	1.37745	−	1.29998i
$31$	−8.39103e14			−1.02376			−0.511880	−	0.859057i	$-0.671051\pi$
$31$	−8.39103e14			−1.02376			−0.511880	+	0.859057i	$0.671051\pi$
$32$	5.10792e14	−	5.10792e14i	0.453674	−	0.453674i
$33$	2.10151e15	+	2.10151e15i	1.37212	+	1.37212i
$34$		−	7.38627e14i		−	0.357797i
$35$	−1.01070e14	+	3.49286e15i	−0.0366390	+	1.26620i
$36$	2.06043e15			0.563552
$37$	−2.17750e15	+	2.17750e15i	−0.452837	+	0.452837i	−0.896295	−	0.443458i	$-0.853751\pi$
$37$	−2.17750e15	+	2.17750e15i	−0.452837	+	0.452837i	0.443458	+	0.896295i	$0.353751\pi$
$38$	−2.76784e15	−	2.76784e15i	−0.440865	−	0.440865i
$39$		−	1.63276e16i		−	2.00575i
$40$	8.06809e15	+	2.33460e14i	0.769433	+	0.0222645i
$41$	−7.50950e15			−0.559465			−0.279732	−	0.960078i	$-0.590246\pi$
$41$	−7.50950e15			−0.559465			−0.279732	+	0.960078i	$0.590246\pi$
$42$	−2.89765e16	+	2.89765e16i	−1.69650	+	1.69650i
$43$	−2.71958e16	−	2.71958e16i	−1.25840	−	1.25840i	−0.951858	−	0.306538i	$-0.900829\pi$
$43$	−2.71958e16	−	2.71958e16i	−1.25840	−	1.25840i	−0.306538	−	0.951858i	$-0.599171\pi$
$44$		−	1.07269e16i		−	0.394408i
$45$	3.95061e16	+	4.18605e16i	1.16022	+	1.22936i
$46$	1.28088e15			0.0301945
$47$	3.40208e16	−	3.40208e16i	0.646794	−	0.646794i	−0.305423	−	0.952217i	$-0.598798\pi$
$47$	3.40208e16	−	3.40208e16i	0.646794	−	0.646794i	0.952217	+	0.305423i	$0.0987977\pi$
$48$	9.20368e16	+	9.20368e16i	1.41759	+	1.41759i
$49$		−	4.82421e16i		−	0.604597i
$50$	−7.49934e16	−	8.42149e16i	−0.767932	−	0.862360i
$51$	6.05018e16			0.508237
$52$	−4.16709e16	+	4.16709e16i	−0.288270	+	0.288270i
$53$	−4.53794e16	−	4.53794e16i	−0.259478	−	0.259478i	0.565364	−	0.824842i	$-0.308736\pi$
$53$	−4.53794e16	−	4.53794e16i	−0.259478	−	0.259478i	−0.824842	+	0.565364i	$0.808736\pi$
$54$			2.75689e17i			1.30762i
$55$	2.17931e17	−	2.05673e17i	0.860382	−	0.811990i
$56$	−2.95744e17			−0.975070
$57$	2.26717e17	−	2.26717e17i	0.626233	−	0.626233i
$58$	−9.48549e16	−	9.48549e16i	−0.220181	−	0.220181i
$59$			7.34186e17i			1.43644i	0.695818	+	0.718218i	$0.255042\pi$
$59$			7.34186e17i			1.43644i	−0.695818	+	0.718218i	$0.744958\pi$
$60$	9.56372e15	−	3.30510e17i	0.0158166	−	0.546603i
$61$	−2.68866e16			−0.0376910			−0.0188455	−	0.999822i	$-0.505999\pi$
$61$	−2.68866e16			−0.0376910			−0.0188455	+	0.999822i	$0.505999\pi$
$62$	−7.01582e17	+	7.01582e17i	−0.835914	+	0.835914i
$63$	−1.49129e18	−	1.49129e18i	−1.51410	−	1.51410i
$64$			5.54991e17i			0.481378i
$65$	−1.64558e18	−	4.76170e16i	−1.22232	−	0.0353695i
$66$	3.51418e18			2.24071
$67$	1.71038e18	−	1.71038e18i	0.938304	−	0.938304i	−0.0599002	−	0.998204i	$-0.519078\pi$
$67$	1.71038e18	−	1.71038e18i	0.938304	−	0.938304i	0.998204	+	0.0599002i	$0.0190783\pi$
$68$	−1.54411e17	−	1.54411e17i	−0.0730449	−	0.0730449i
$69$			1.04918e17i			0.0428902i
$70$	2.83591e18	+	3.00492e18i	1.00395	+	1.06378i
$71$	2.52274e18			0.774978			0.387489	−	0.921874i	$-0.373342\pi$
$71$	2.52274e18			0.774978			0.387489	+	0.921874i	$0.373342\pi$
$72$	−3.44469e18	+	3.44469e18i	−0.920079	+	0.920079i
$73$	−8.36398e17	−	8.36398e17i	−0.194619	−	0.194619i	0.603070	−	0.797688i	$-0.293944\pi$
$73$	−8.36398e17	−	8.36398e17i	−0.194619	−	0.194619i	−0.797688	+	0.603070i	$0.793944\pi$
$74$			3.64126e18i			0.739494i
$75$	6.89813e18	−	6.14279e18i	1.22495	−	1.09082i
$76$	−1.15724e18			−0.180007
$77$	−7.76381e18	+	7.76381e18i	−1.05966	+	1.05966i
$78$	−1.36516e19	−	1.36516e19i	−1.63772	−	1.63772i
$79$		−	3.07434e18i		−	0.324699i	−0.986733	−	0.162350i	$-0.948093\pi$
$79$		−	3.07434e18i		−	0.324699i	0.986733	−	0.162350i	$-0.0519072\pi$
$80$	9.54438e18	−	9.00756e18i	0.888890	−	0.838894i
$81$	−2.03074e18			−0.167034
$82$	−6.27876e18	+	6.27876e18i	−0.456810	+	0.456810i
$83$	6.40039e18	+	6.40039e18i	0.412501	+	0.412501i	0.882609	−	0.470108i	$-0.155785\pi$
$83$	6.40039e18	+	6.40039e18i	0.412501	+	0.412501i	−0.470108	+	0.882609i	$0.655785\pi$
$84$			1.21152e19i			0.692687i
$85$	1.76444e17	−	6.09770e18i	0.00896229	−	0.309725i
$86$	−4.54773e19			−2.05499
$87$	7.76967e18	−	7.76967e18i	0.312759	−	0.312759i
$88$	1.79335e19	+	1.79335e19i	0.643928	+	0.643928i
$89$			2.47634e19i			0.794165i	0.917783	+	0.397082i	$0.129977\pi$
$89$			2.47634e19i			0.794165i	−0.917783	+	0.397082i	$0.870023\pi$
$90$	6.80313e19	+	1.96857e18i	1.95112	+	0.0564580i
$91$	6.03206e19			1.54900
$92$	2.67769e17	−	2.67769e17i	0.00616427	−	0.00616427i
$93$	−5.74673e19	−	5.74673e19i	−1.18738	−	1.18738i
$94$		−	5.68902e19i		−	1.05623i
$95$	−2.21886e19	−	2.35110e19i	−0.370590	−	0.392676i
$96$	6.99648e19			1.05237
$97$	−9.21143e19	+	9.21143e19i	−1.24914	+	1.24914i	−0.293033	+	0.956102i	$0.594665\pi$
$97$	−9.21143e19	+	9.21143e19i	−1.24914	+	1.24914i	−0.956102	+	0.293033i	$0.905335\pi$
$98$	−4.03357e19	−	4.03357e19i	−0.493661	−	0.493661i
$99$			1.80858e20i			1.99980i
$100$	−3.32827e19	−	1.92777e18i	−0.332827	−	0.0192777i
$101$	1.17977e20			1.06803			0.534015	−	0.845475i	$-0.320683\pi$
$101$	1.17977e20			1.06803			0.534015	+	0.845475i	$0.320683\pi$
$102$	5.05861e19	−	5.05861e19i	0.414982	−	0.414982i
$103$	−9.55040e19	−	9.55040e19i	−0.710640	−	0.710640i	0.256029	−	0.966669i	$-0.417586\pi$
$103$	−9.55040e19	−	9.55040e19i	−0.710640	−	0.710640i	−0.966669	+	0.256029i	$0.917586\pi$
$104$		−	1.39333e20i		−	0.941285i
$105$	−2.46136e20	+	2.32292e20i	−1.51106	+	1.42607i
$106$	−7.58842e19			−0.423734
$107$	2.58308e20	−	2.58308e20i	1.31311	−	1.31311i	0.393998	−	0.919111i	$-0.371092\pi$
$107$	2.58308e20	−	2.58308e20i	1.31311	−	1.31311i	0.919111	−	0.393998i	$-0.128908\pi$
$108$	5.76332e19	+	5.76332e19i	0.266953	+	0.266953i
$109$			1.70093e20i			0.718492i	0.933243	+	0.359246i	$0.116966\pi$
$109$			1.70093e20i			0.718492i	−0.933243	+	0.359246i	$0.883034\pi$
$110$	1.02486e19	−	3.54179e20i	0.0395128	−	1.36551i
$111$	−2.98260e20			−1.05042
$112$	−3.40020e20	+	3.40020e20i	−1.09477	+	1.09477i
$113$	3.51258e20	+	3.51258e20i	1.03476	+	1.03476i	0.999374	+	0.0353907i	$0.0112676\pi$
$113$	3.51258e20	+	3.51258e20i	1.03476	+	1.03476i	0.0353907	+	0.999374i	$0.488732\pi$
$114$		−	3.79120e20i		−	1.02265i
$115$	1.05742e19	+	3.05977e17i	0.0261378	+	0.000756329i
$116$	−3.96591e19			−0.0899008
$117$	7.02586e20	−	7.02586e20i	1.46164	−	1.46164i
$118$	6.13860e20	+	6.13860e20i	1.17287	+	1.17287i
$119$			2.23517e20i			0.392502i
$120$	5.36567e20	+	5.68545e20i	0.866586	+	0.918232i
$121$	2.68820e20			0.399584
$122$	−2.24802e19	+	2.24802e19i	−0.0307752	+	0.0307752i
$123$	−5.14300e20	−	5.14300e20i	−0.648881	−	0.648881i
$124$			2.93333e20i			0.341307i
$125$	−5.98986e20	−	7.13146e20i	−0.643157	−	0.765735i
$126$	−2.49375e21			−2.47257
$127$	−7.98508e20	+	7.98508e20i	−0.731547	+	0.731547i	−0.970926	−	0.239379i	$-0.923056\pi$
$127$	−7.98508e20	+	7.98508e20i	−0.731547	+	0.731547i	0.239379	+	0.970926i	$0.423056\pi$
$128$	9.99637e20	+	9.99637e20i	0.846725	+	0.846725i
$129$		−	3.72509e21i		−	2.91904i
$130$	−1.41570e21	+	1.33607e21i	−1.02692	+	0.969164i
$131$	8.42443e20			0.566015			0.283007	−	0.959118i	$-0.408668\pi$
$131$	8.42443e20			0.566015			0.283007	+	0.959118i	$0.408668\pi$
$132$	7.34645e20	−	7.34645e20i	0.457445	−	0.457445i
$133$	8.37582e20	+	8.37582e20i	0.483627	+	0.483627i
$134$		−	2.86012e21i		−	1.53227i
$135$	−6.58570e19	+	2.27593e21i	−0.0327540	+	1.13194i
$136$	5.16298e20			0.238513
$137$	−1.68872e21	+	1.68872e21i	−0.725023	+	0.725023i	−0.969624	−	0.244601i	$-0.921343\pi$
$137$	−1.68872e21	+	1.68872e21i	−0.725023	+	0.725023i	0.244601	+	0.969624i	$0.421343\pi$
$138$	8.77227e19	+	8.77227e19i	0.0350204	+	0.0350204i
$139$			2.64286e21i			0.981580i	0.871278	+	0.490790i	$0.163292\pi$
$139$			2.64286e21i			0.981580i	−0.871278	+	0.490790i	$0.836708\pi$
$140$	1.22103e21	+	3.53321e19i	0.422131	+	0.0122149i
$141$	4.65994e21			1.50034
$142$	2.10929e21	−	2.10929e21i	0.632779	−	0.632779i
$143$	−3.65774e21	−	3.65774e21i	−1.02295	−	1.02295i
$144$			7.92079e21i			2.06606i
$145$	−7.60411e20	−	8.05729e20i	−0.185084	−	0.196114i
$146$	−1.39864e21			−0.317817
$147$	3.30394e21	−	3.30394e21i	0.701227	−	0.701227i
$148$	7.61211e20	+	7.61211e20i	0.150969	+	0.150969i
$149$		−	2.97818e21i		−	0.552191i	−0.961130	−	0.276095i	$-0.910959\pi$
$149$		−	2.97818e21i		−	0.552191i	0.961130	−	0.276095i	$-0.0890405\pi$
$150$	6.31549e20	−	1.09036e22i	0.109520	−	1.89086i
$151$	−1.75104e21			−0.284137			−0.142068	−	0.989857i	$-0.545375\pi$
$151$	−1.75104e21			−0.284137			−0.142068	+	0.989857i	$0.545375\pi$
$152$	1.93471e21	−	1.93471e21i	0.293887	−	0.293887i
$153$	2.60343e21	+	2.60343e21i	0.370366	+	0.370366i
$154$			1.29828e22i			1.73045i
$155$	−5.95946e21	+	5.62427e21i	−0.744544	+	0.702667i
$156$	−5.70780e21			−0.668686
$157$	−8.66574e21	+	8.66574e21i	−0.952377	+	0.952377i	−0.998916	−	0.0465393i	$-0.985181\pi$
$157$	−8.66574e21	+	8.66574e21i	−0.952377	+	0.952377i	0.0465393	+	0.998916i	$0.485181\pi$
$158$	−2.57048e21	−	2.57048e21i	−0.265121	−	0.265121i
$159$		−	6.21576e21i		−	0.601898i
$160$	2.04042e20	−	7.05143e21i	0.0185575	−	0.641324i
$161$	−3.87608e20			−0.0331233
$162$	−1.69792e21	+	1.69792e21i	−0.136385	+	0.136385i
$163$	−6.86958e21	−	6.86958e21i	−0.518864	−	0.518864i	0.398363	−	0.917228i	$-0.369578\pi$
$163$	−6.86958e21	−	6.86958e21i	−0.518864	−	0.518864i	−0.917228	+	0.398363i	$0.869578\pi$
$164$			2.62517e21i			0.186517i
$165$	2.90112e22	+	8.39473e20i	1.93966	+	0.0561264i
$166$	1.07028e22			0.673625
$167$	9.52727e19	−	9.52727e19i	0.00564682	−	0.00564682i	−0.704278	−	0.709925i	$-0.748729\pi$
$167$	9.52727e19	−	9.52727e19i	0.00564682	−	0.00564682i	0.709925	+	0.704278i	$0.248729\pi$
$168$	−2.02545e22	−	2.02545e22i	−1.13091	−	1.13091i
$169$			9.41371e21i			0.495329i
$170$	−4.95081e21	−	5.24587e21i	−0.245577	−	0.260212i
$171$	1.95115e22			0.912705
$172$	−9.50710e21	+	9.50710e21i	−0.419531	+	0.419531i
$173$	−2.70861e21	−	2.70861e21i	−0.112794	−	0.112794i	0.648457	−	0.761251i	$-0.275415\pi$
$173$	−2.70861e21	−	2.70861e21i	−0.112794	−	0.112794i	−0.761251	+	0.648457i	$0.775415\pi$
$174$		−	1.29926e22i		−	0.510743i
$175$	2.26939e22	+	2.54844e22i	0.842419	+	0.946006i
$176$	4.12366e22			1.44596
$177$	−5.02819e22	+	5.02819e22i	−1.66602	+	1.66602i
$178$	2.07049e22	+	2.07049e22i	0.648445	+	0.648445i
$179$		−	1.98148e22i		−	0.586758i	−0.955996	−	0.293379i	$-0.905220\pi$
$179$		−	1.98148e22i		−	0.586758i	0.955996	−	0.293379i	$-0.0947799\pi$
$180$	1.46336e22	−	1.38105e22i	0.409850	−	0.386798i
$181$	−3.49387e22			−0.925808			−0.462904	−	0.886408i	$-0.653193\pi$
$181$	−3.49387e22			−0.925808			−0.462904	+	0.886408i	$0.653193\pi$
$182$	5.04345e22	−	5.04345e22i	1.26478	−	1.26478i
$183$	−1.84137e21	−	1.84137e21i	−0.0437150	−	0.0437150i
$184$			8.95327e20i			0.0201281i
$185$	−8.69830e20	+	3.00602e22i	−0.0185232	+	0.640140i
$186$	−9.60978e22			−1.93903
$187$	1.35537e22	−	1.35537e22i	0.259205	−	0.259205i
$188$	−1.18930e22	−	1.18930e22i	−0.215632	−	0.215632i
$189$		−	8.34266e22i		−	1.43445i
$190$	−3.82098e22	−	1.10565e21i	−0.623216	−	0.0180335i
$191$	−1.78027e22			−0.275519			−0.137759	−	0.990466i	$-0.543990\pi$
$191$	−1.78027e22			−0.275519			−0.137759	+	0.990466i	$0.543990\pi$
$192$	−3.80094e22	+	3.80094e22i	−0.558315	+	0.558315i
$193$	−2.05748e22	−	2.05748e22i	−0.286921	−	0.286921i	0.548940	−	0.835862i	$-0.315031\pi$
$193$	−2.05748e22	−	2.05748e22i	−0.286921	−	0.286921i	−0.835862	+	0.548940i	$0.815031\pi$
$194$			1.54035e23i			2.03987i
$195$	−1.09439e23	−	1.15962e23i	−1.37666	−	1.45871i
$196$	−1.68645e22			−0.201564
$197$	6.77107e22	−	6.77107e22i	0.769122	−	0.769122i	−0.208830	−	0.977952i	$-0.566966\pi$
$197$	6.77107e22	−	6.77107e22i	0.769122	−	0.769122i	0.977952	+	0.208830i	$0.0669655\pi$
$198$	1.51217e23	+	1.51217e23i	1.63286	+	1.63286i
$199$			9.45105e22i			0.970396i	0.874404	+	0.485198i	$0.161253\pi$
$199$			9.45105e22i			0.970396i	−0.874404	+	0.485198i	$0.838747\pi$
$200$	5.88659e22	−	5.24201e22i	0.574862	−	0.511915i
$201$	2.34276e23			2.17654
$202$	9.86415e22	−	9.86415e22i	0.872059	−	0.872059i
$203$	2.87042e22	+	2.87042e22i	0.241538	+	0.241538i
$204$		−	2.11502e22i		−	0.169439i
$205$	−5.33338e22	+	5.03341e22i	−0.406878	+	0.383993i
$206$	−1.59704e23			−1.16049
$207$	−4.51468e21	+	4.51468e21i	−0.0312553	+	0.0312553i
$208$	−1.60193e23	−	1.60193e23i	−1.05684	−	1.05684i
$209$		−	1.01579e23i		−	0.638767i
$210$	−1.15750e22	+	4.00018e23i	−0.0693951	+	2.39821i
$211$	1.21588e23			0.695130			0.347565	−	0.937656i	$-0.387009\pi$
$211$	1.21588e23			0.695130			0.347565	+	0.937656i	$0.387009\pi$
$212$	−1.58637e22	+	1.58637e22i	−0.0865060	+	0.0865060i
$213$	1.72774e23	+	1.72774e23i	0.898840	+	0.898840i
$214$		−	4.31948e23i		−	2.14434i
$215$	−3.75435e23	−	1.08637e22i	−1.77890	−	0.0514746i
$216$	−1.92705e23			−0.871679
$217$	2.12307e23	−	2.12307e23i	0.916994	−	0.916994i
$218$	1.42216e23	+	1.42216e23i	0.586657	+	0.586657i
$219$		−	1.14564e23i		−	0.451448i
$220$	−7.18991e22	−	7.61841e22i	−0.270705	−	0.286838i
$221$	−1.05305e23			−0.378902
$222$	−2.49377e23	+	2.49377e23i	−0.857684	+	0.857684i
$223$	−2.58107e23	−	2.58107e23i	−0.848693	−	0.848693i	0.141277	−	0.989970i	$-0.454879\pi$
$223$	−2.58107e23	−	2.58107e23i	−0.848693	−	0.848693i	−0.989970	+	0.141277i	$0.954879\pi$
$224$			2.58477e23i			0.812722i
$225$	5.61158e23	+	3.25028e22i	1.68756	+	0.0977453i
$226$	5.87379e23			1.68980
$227$	−3.52399e23	+	3.52399e23i	−0.970009	+	0.970009i	−0.999563	−	0.0295538i	$-0.990591\pi$
$227$	−3.52399e23	+	3.52399e23i	−0.970009	+	0.970009i	0.0295538	+	0.999563i	$0.490591\pi$
$228$	−7.92557e22	−	7.92557e22i	−0.208777	−	0.208777i
$229$			4.37192e23i			1.10235i	0.834391	+	0.551173i	$0.185820\pi$
$229$			4.37192e23i			1.10235i	−0.834391	+	0.551173i	$0.814180\pi$
$230$	9.09701e21	−	8.58535e21i	0.0219594	−	0.0207243i
$231$	−1.06343e24			−2.45805
$232$	6.63033e22	−	6.63033e22i	0.146776	−	0.146776i
$233$	1.72120e23	+	1.72120e23i	0.364983	+	0.364983i	0.865644	−	0.500661i	$-0.166910\pi$
$233$	1.72120e23	+	1.72120e23i	0.364983	+	0.364983i	−0.500661	+	0.865644i	$0.666910\pi$
$234$		−	1.17488e24i		−	2.38690i
$235$	1.35900e22	−	4.69654e23i	0.0264571	−	0.914323i
$236$	2.56657e23			0.478886
$237$	2.10551e23	−	2.10551e23i	0.376595	−	0.376595i
$238$	1.86885e23	+	1.86885e23i	0.320482	+	0.320482i
$239$			8.47258e23i			1.39328i	0.717423	+	0.696638i	$0.245321\pi$
$239$			8.47258e23i			1.39328i	−0.717423	+	0.696638i	$0.754679\pi$
$240$	1.27056e24	+	3.67652e22i	2.00393	+	0.0579862i
$241$	3.89268e23			0.588949			0.294475	−	0.955659i	$-0.404855\pi$
$241$	3.89268e23			0.588949			0.294475	+	0.955659i	$0.404855\pi$
$242$	2.24763e23	−	2.24763e23i	0.326265	−	0.326265i
$243$	4.35767e23	+	4.35767e23i	0.607005	+	0.607005i
$244$			9.39902e21i			0.0125656i
$245$	−3.23354e23	−	3.42624e23i	−0.414970	−	0.439701i
$246$	−8.60021e23			−1.05964
$247$	−3.94608e23	+	3.94608e23i	−0.466870	+	0.466870i
$248$	−4.90403e23	−	4.90403e23i	−0.557232	−	0.557232i
$249$			8.76681e23i			0.956860i
$250$	−1.09709e24	−	9.54497e22i	−1.15038	−	0.100086i
$251$	7.73889e23			0.779725			0.389863	−	0.920873i	$-0.372522\pi$
$251$	7.73889e23			0.779725			0.389863	+	0.920873i	$0.372522\pi$
$252$	−5.21323e23	+	5.21323e23i	−0.504779	+	0.504779i
$253$	2.35039e22	+	2.35039e22i	0.0218743	+	0.0218743i
$254$			1.33528e24i			1.19463i
$255$	4.29695e23	−	4.05526e23i	0.369622	−	0.348833i
$256$	1.08966e24			0.901346
$257$	2.59553e23	−	2.59553e23i	0.206488	−	0.206488i	−0.596285	−	0.802773i	$-0.703357\pi$
$257$	2.59553e23	−	2.59553e23i	0.206488	−	0.206488i	0.802773	+	0.596285i	$0.203357\pi$
$258$	−3.11458e24	−	3.11458e24i	−2.38343	−	2.38343i
$259$		−	1.10189e24i		−	0.811222i
$260$	−1.66459e22	+	5.75263e23i	−0.0117917	+	0.407505i
$261$	6.68667e23			0.455832
$262$	7.04374e23	−	7.04374e23i	0.462158	−	0.462158i
$263$	−1.42844e24	−	1.42844e24i	−0.902202	−	0.902202i	0.0934247	−	0.995626i	$-0.470219\pi$
$263$	−1.42844e24	−	1.42844e24i	−0.902202	−	0.902202i	−0.995626	+	0.0934247i	$0.970219\pi$
$264$			2.45640e24i			1.49369i
$265$	−6.26458e23	−	1.81273e22i	−0.366803	−	0.0106139i
$266$	1.40062e24			0.789775
$267$	−1.69596e24	+	1.69596e24i	−0.921093	+	0.921093i
$268$	−5.97913e23	−	5.97913e23i	−0.312817	−	0.312817i
$269$		−	2.31886e24i		−	1.16883i	−0.811455	−	0.584415i	$-0.801324\pi$
$269$		−	2.31886e24i		−	1.16883i	0.811455	−	0.584415i	$-0.198676\pi$
$270$	1.84786e24	+	1.95799e24i	0.897496	+	0.950984i
$271$	1.93847e23			0.0907332			0.0453666	−	0.998970i	$-0.485554\pi$
$271$	1.93847e23			0.0907332			0.0453666	+	0.998970i	$0.485554\pi$
$272$	5.93593e23	−	5.93593e23i	0.267793	−	0.267793i
$273$	4.13115e24	+	4.13115e24i	1.79657	+	1.79657i
$274$			2.82390e24i			1.18398i
$275$	1.69213e23	−	2.92145e24i	0.0684082	−	1.18106i
$276$	3.66771e22			0.0142990
$277$	−1.74148e24	+	1.74148e24i	−0.654818	+	0.654818i	−0.954149	−	0.299332i	$-0.903236\pi$
$277$	−1.74148e24	+	1.74148e24i	−0.654818	+	0.654818i	0.299332	+	0.954149i	$0.403236\pi$
$278$	2.20972e24	+	2.20972e24i	0.801472	+	0.801472i
$279$		−	4.94570e24i		−	1.73056i
$280$	−2.10043e24	+	1.98229e24i	−0.709133	+	0.669248i
$281$	1.79983e24			0.586365			0.293182	−	0.956057i	$-0.405286\pi$
$281$	1.79983e24			0.586365			0.293182	+	0.956057i	$0.405286\pi$
$282$	3.89622e24	−	3.89622e24i	1.22504	−	1.22504i
$283$	2.05155e23	+	2.05155e23i	0.0622614	+	0.0622614i	0.737552	−	0.675290i	$-0.235982\pi$
$283$	2.05155e23	+	2.05155e23i	0.0622614	+	0.0622614i	−0.675290	+	0.737552i	$0.735982\pi$
$284$		−	8.81900e23i		−	0.258366i
$285$	9.05648e22	−	3.12981e24i	0.0256160	−	0.885256i
$286$	−6.11654e24			−1.67050
$287$	1.90003e24	−	1.90003e24i	0.501119	−	0.501119i
$288$	3.01063e24	+	3.01063e24i	0.766888	+	0.766888i
$289$			3.67402e24i			0.903990i
$290$	−1.30946e24	−	3.78909e22i	−0.311253	−	0.00900648i
$291$	−1.26172e25			−2.89756
$292$	−2.92388e23	+	2.92388e23i	−0.0648830	+	0.0648830i
$293$	−3.04781e24	−	3.04781e24i	−0.653599	−	0.653599i	0.300259	−	0.953858i	$-0.402927\pi$
$293$	−3.04781e24	−	3.04781e24i	−0.653599	−	0.653599i	−0.953858	+	0.300259i	$0.902927\pi$
$294$		−	5.52490e24i		−	1.14512i
$295$	4.92104e24	+	5.21432e24i	0.985910	+	1.04467i
$296$	−2.54523e24			−0.492958
$297$	−5.05886e24	+	5.05886e24i	−0.947301	+	0.947301i
$298$	−2.49009e24	−	2.49009e24i	−0.450870	−	0.450870i
$299$		−	1.82613e23i		−	0.0319756i
$300$	−2.14739e24	−	2.41145e24i	−0.363663	−	0.408380i
$301$	1.37620e25			2.25432
$302$	−1.46406e24	+	1.46406e24i	−0.232001	+	0.232001i
$303$	8.07983e24	+	8.07983e24i	1.23873	+	1.23873i
$304$		−	4.44872e24i		−	0.659932i
$305$	−1.90954e23	+	1.80214e23i	−0.0274113	+	0.0258696i
$306$	4.35350e24			0.604817
$307$	−8.44353e22	+	8.44353e22i	−0.0113538	+	0.0113538i	−0.712761	−	0.701407i	$-0.752556\pi$
$307$	−8.44353e22	+	8.44353e22i	−0.0113538	+	0.0113538i	0.701407	+	0.712761i	$0.252556\pi$
$308$	2.71407e24	+	2.71407e24i	0.353276	+	0.353276i
$309$		−	1.30815e25i		−	1.64844i
$310$	−2.80255e23	+	9.68527e24i	−0.0341930	+	1.18167i
$311$	−1.12550e25			−1.32966			−0.664829	−	0.746996i	$-0.731496\pi$
$311$	−1.12550e25			−1.32966			−0.664829	+	0.746996i	$0.731496\pi$
$312$	9.54245e24	−	9.54245e24i	1.09173	−	1.09173i
$313$	1.44051e24	+	1.44051e24i	0.159615	+	0.159615i	0.782396	−	0.622781i	$-0.213997\pi$
$313$	1.44051e24	+	1.44051e24i	0.159615	+	0.159615i	−0.622781	+	0.782396i	$0.713997\pi$
$314$			1.44910e25i			1.55526i
$315$	−2.05871e25	−	5.95712e23i	−2.14037	−	0.0619342i
$316$	−1.07473e24			−0.108250
$317$	9.10172e24	−	9.10172e24i	0.888241	−	0.888241i	−0.106113	−	0.994354i	$-0.533840\pi$
$317$	9.10172e24	−	9.10172e24i	0.888241	−	0.888241i	0.994354	+	0.106113i	$0.0338405\pi$
$318$	−5.19705e24	−	5.19705e24i	−0.491457	−	0.491457i
$319$		−	3.48116e24i		−	0.319019i
$320$	3.71995e24	+	3.94165e24i	0.330398	+	0.350088i
$321$	3.53813e25			3.04596
$322$	−3.24082e23	+	3.24082e23i	−0.0270456	+	0.0270456i
$323$	−1.46222e24	−	1.46222e24i	−0.118300	−	0.118300i
$324$			7.09906e23i			0.0556866i
$325$	−1.20064e25	+	1.06917e25i	−0.913228	+	0.813230i
$326$	−1.14874e25			−0.847319
$327$	−1.16491e25	+	1.16491e25i	−0.833325	+	0.833325i
$328$	−4.38883e24	−	4.38883e24i	−0.304516	−	0.304516i
$329$			1.72156e25i			1.15868i
$330$	2.49584e25	−	2.35546e25i	1.62958	−	1.53793i
$331$	2.34181e25			1.48345			0.741724	−	0.670705i	$-0.234008\pi$
$331$	2.34181e25			1.48345			0.741724	+	0.670705i	$0.234008\pi$
$332$	2.23745e24	−	2.23745e24i	0.137522	−	0.137522i
$333$	−1.28343e25	−	1.28343e25i	−0.765472	−	0.765472i
$334$		−	1.59317e23i		−	0.00922139i
$335$	6.83230e23	−	2.36116e25i	0.0383812	−	1.32641i
$336$	−4.65736e25			−2.53949
$337$	−2.06463e25	+	2.06463e25i	−1.09281	+	1.09281i	−0.0975788	+	0.995228i	$0.531110\pi$
$337$	−2.06463e25	+	2.06463e25i	−1.09281	+	1.09281i	−0.995228	+	0.0975788i	$0.968890\pi$
$338$	7.87089e24	+	7.87089e24i	0.404442	+	0.404442i
$339$			4.81129e25i			2.40029i
$340$	−2.13163e24	−	6.16814e22i	−0.103258	−	0.00298789i
$341$	−2.57479e25			−1.21115
$342$	1.63138e25	−	1.63138e25i	0.745235	−	0.745235i
$343$	−7.98269e24	−	7.98269e24i	−0.354167	−	0.354167i
$344$		−	3.17885e25i		−	1.36989i
$345$	7.03235e23	+	7.45146e23i	0.0294381	+	0.0311925i
$346$	−4.52939e24			−0.184195
$347$	−3.07804e24	+	3.07804e24i	−0.121613	+	0.121613i	−0.765294	−	0.643681i	$-0.777406\pi$
$347$	−3.07804e24	+	3.07804e24i	−0.121613	+	0.121613i	0.643681	+	0.765294i	$0.277406\pi$
$348$	−2.71612e24	−	2.71612e24i	−0.104269	−	0.104269i
$349$		−	4.88992e25i		−	1.82410i	−0.410084	−	0.912048i	$-0.634501\pi$
$349$		−	4.88992e25i		−	1.82410i	0.410084	−	0.912048i	$-0.365499\pi$
$350$	4.02823e25	+	2.33319e24i	1.46027	+	0.0845803i
$351$	3.93046e25			1.38475
$352$	1.56737e25	−	1.56737e25i	0.536715	−	0.536715i
$353$	1.42667e25	+	1.42667e25i	0.474872	+	0.474872i	0.903487	−	0.428615i	$-0.140998\pi$
$353$	1.42667e25	+	1.42667e25i	0.474872	+	0.474872i	−0.428615	+	0.903487i	$0.640998\pi$
$354$			8.40823e25i			2.72064i
$355$	1.79170e25	−	1.69092e25i	0.563613	−	0.531913i
$356$	8.65679e24			0.264763
$357$	−1.53079e25	+	1.53079e25i	−0.455234	+	0.455234i
$358$	−1.65673e25	−	1.65673e25i	−0.479096	−	0.479096i
$359$		−	2.66205e25i		−	0.748638i	−0.927300	−	0.374319i	$-0.877877\pi$
$359$		−	2.66205e25i		−	0.748638i	0.927300	−	0.374319i	$-0.122123\pi$
$360$	−1.37602e24	+	4.75536e25i	−0.0376358	+	1.30064i
$361$	2.66313e25			0.708468
$362$	−2.92126e25	+	2.92126e25i	−0.755934	+	0.755934i
$363$	1.84106e25	+	1.84106e25i	0.463448	+	0.463448i
$364$		−	2.10868e25i		−	0.516414i
$365$	−1.15464e25	−	3.34109e23i	−0.275117	−	0.00796086i
$366$	−3.07918e24			−0.0713878
$367$	−2.50036e25	+	2.50036e25i	−0.564082	+	0.564082i	−0.930464	−	0.366382i	$-0.880596\pi$
$367$	−2.50036e25	+	2.50036e25i	−0.564082	+	0.564082i	0.366382	+	0.930464i	$0.380596\pi$
$368$	1.02937e24	+	1.02937e24i	0.0225991	+	0.0225991i
$369$		−	4.42613e25i		−	0.945715i
$370$	2.44064e25	+	2.58609e25i	0.507558	+	0.537807i
$371$	2.29635e25			0.464834
$372$	−2.00894e25	+	2.00894e25i	−0.395856	+	0.395856i
$373$	−6.72241e25	−	6.72241e25i	−1.28955	−	1.28955i	−0.935062	−	0.354485i	$-0.884656\pi$
$373$	−6.72241e25	−	6.72241e25i	−1.28955	−	1.28955i	−0.354485	−	0.935062i	$-0.615344\pi$
$374$		−	2.26648e25i		−	0.423288i
$375$	7.81839e24	−	8.98634e25i	0.142169	−	1.63407i
$376$	3.97661e25			0.704100
$377$	−1.35233e25	+	1.35233e25i	−0.233169	+	0.233169i
$378$	−6.97537e25	−	6.97537e25i	−1.17125	−	1.17125i
$379$		−	3.61618e25i		−	0.591368i	−0.955286	−	0.295684i	$-0.904452\pi$
$379$		−	3.61618e25i		−	0.591368i	0.955286	−	0.295684i	$-0.0955476\pi$
$380$	−8.21896e24	+	7.75668e24i	−0.130912	+	0.123549i
$381$	−1.09374e26			−1.69693
$382$	−1.48850e25	+	1.48850e25i	−0.224965	+	0.224965i
$383$	7.17429e25	+	7.17429e25i	1.05631	+	1.05631i	0.998317	+	0.0579931i	$0.0184702\pi$
$383$	7.17429e25	+	7.17429e25i	1.05631	+	1.05631i	0.0579931	+	0.998317i	$0.481530\pi$
$384$			1.36923e26i			1.96411i
$385$	−3.10134e24	+	1.07179e26i	−0.0433454	+	1.49796i
$386$	−3.44056e25			−0.468550
$387$	1.60293e26	−	1.60293e26i	2.12718	−	2.12718i
$388$	3.22013e25	+	3.22013e25i	0.416443	+	0.416443i
$389$			7.10072e25i			0.894966i	0.894292	+	0.447483i	$0.147680\pi$
$389$			7.10072e25i			0.894966i	−0.894292	+	0.447483i	$0.852320\pi$
$390$	−1.88460e26	−	5.45331e24i	−2.31511	−	0.0669907i
$391$	6.76670e23			0.00810231
$392$	2.81945e25	−	2.81945e25i	0.329082	−	0.329082i
$393$	5.76961e25	+	5.76961e25i	0.656479	+	0.656479i
$394$		−	1.13227e26i		−	1.25600i
$395$	−2.06064e25	−	2.18345e25i	−0.222860	−	0.236142i
$396$	6.32245e25			0.666704
$397$	−3.29480e25	+	3.29480e25i	−0.338785	+	0.338785i	−0.855910	−	0.517125i	$-0.827002\pi$
$397$	−3.29480e25	+	3.29480e25i	−0.338785	+	0.338785i	0.517125	+	0.855910i	$0.327002\pi$
$398$	7.90210e25	+	7.90210e25i	0.792341	+	0.792341i
$399$			1.14726e26i			1.12185i
$400$	7.41079e24	−	1.27947e26i	0.0706748	−	1.22019i
$401$	5.14527e24			0.0478591			0.0239296	−	0.999714i	$-0.492382\pi$
$401$	5.14527e24			0.0478591			0.0239296	+	0.999714i	$0.492382\pi$
$402$	1.95880e26	−	1.95880e26i	1.77717	−	1.77717i
$403$	1.00024e26	+	1.00024e26i	0.885222	+	0.885222i
$404$		−	4.12423e25i		−	0.356065i
$405$	−1.44227e25	+	1.36115e25i	−0.121478	+	0.114645i
$406$	4.79997e25			0.394437
$407$	−6.68168e25	+	6.68168e25i	−0.535724	+	0.535724i
$408$	3.53595e25	+	3.53595e25i	0.276633	+	0.276633i
$409$		−	1.79187e26i		−	1.36796i	−0.729500	−	0.683981i	$-0.760247\pi$
$409$		−	1.79187e26i		−	1.36796i	0.729500	−	0.683981i	$-0.239753\pi$
$410$	−2.50813e24	+	8.66777e25i	−0.0186858	+	0.645756i
$411$	−2.31309e26			−1.68180
$412$	−3.33863e25	+	3.33863e25i	−0.236917	+	0.236917i
$413$	−1.85761e26	−	1.85761e26i	−1.28663	−	1.28663i
$414$			7.54952e24i			0.0510406i
$415$	8.83567e25	+	2.55671e24i	0.583121	+	0.0168733i
$416$	−1.21776e26			−0.784563
$417$	−1.81000e26	+	1.81000e26i	−1.13846	+	1.13846i
$418$	−8.49313e25	−	8.49313e25i	−0.521561	−	0.521561i
$419$			1.99075e26i			1.19365i	0.802372	+	0.596824i	$0.203571\pi$
$419$			1.99075e26i			1.19365i	−0.802372	+	0.596824i	$0.796429\pi$
$420$	8.12047e25	+	8.60442e25i	0.475432	+	0.503766i
$421$	1.35804e26			0.776410			0.388205	−	0.921573i	$-0.373095\pi$
$421$	1.35804e26			0.776410			0.388205	+	0.921573i	$0.373095\pi$
$422$	1.01661e26	−	1.01661e26i	0.567582	−	0.567582i
$423$	2.00520e26	+	2.00520e26i	1.09334	+	1.09334i
$424$		−	5.30428e25i		−	0.282467i
$425$	−3.96180e25	−	4.44896e25i	−0.206065	−	0.231403i
$426$	2.88916e26			1.46783
$427$	6.80276e24	−	6.80276e24i	0.0337603	−	0.0337603i
$428$	−9.02994e25	−	9.02994e25i	−0.437771	−	0.437771i
$429$		−	5.01013e26i		−	2.37288i
$430$	−3.22988e26	+	3.04822e26i	−1.49452	+	1.41046i
$431$	−2.23506e26			−1.01046			−0.505228	−	0.862986i	$-0.668591\pi$
$431$	−2.23506e26			−1.01046			−0.505228	+	0.862986i	$0.668591\pi$
$432$	−2.21555e26	+	2.21555e26i	−0.978690	+	0.978690i
$433$	2.66718e25	+	2.66718e25i	0.115126	+	0.115126i	0.762323	−	0.647197i	$-0.224059\pi$
$433$	2.66718e25	+	2.66718e25i	0.115126	+	0.115126i	−0.647197	+	0.762323i	$0.724059\pi$
$434$		−	3.55023e26i		−	1.49747i
$435$	3.10369e24	−	1.07260e26i	0.0127934	−	0.442123i
$436$	5.94611e25			0.239534
$437$	2.53567e24	−	2.53567e24i	0.00998340	−	0.00998340i
$438$	−9.57880e25	−	9.57880e25i	−0.368613	−	0.368613i
$439$			1.81936e26i			0.684344i	0.939637	+	0.342172i	$0.111163\pi$
$439$			1.81936e26i			0.684344i	−0.939637	+	0.342172i	$0.888837\pi$
$440$	2.47570e26	+	7.16373e24i	0.910271	+	0.0263398i
$441$	2.84341e26			1.02201
$442$	−8.80466e25	+	8.80466e25i	−0.309378	+	0.309378i
$443$	1.29026e26	+	1.29026e26i	0.443243	+	0.443243i	0.893100	−	0.449858i	$-0.148525\pi$
$443$	1.29026e26	+	1.29026e26i	0.443243	+	0.443243i	−0.449858	+	0.893100i	$0.648525\pi$
$444$			1.04265e26i			0.350196i
$445$	1.65982e26	+	1.75874e26i	0.545082	+	0.577567i
$446$	−4.31610e26			−1.38594
$447$	2.03966e26	−	2.03966e26i	0.640445	−	0.640445i
$448$	−1.40422e26	−	1.40422e26i	−0.431176	−	0.431176i
$449$			4.59748e26i			1.38056i	0.723540	+	0.690282i	$0.242514\pi$
$449$			4.59748e26i			1.38056i	−0.723540	+	0.690282i	$0.757486\pi$
$450$	4.96365e26	−	4.42013e26i	1.45773	−	1.29811i
$451$	−2.30429e26			−0.661869
$452$	1.22793e26	−	1.22793e26i	0.344975	−	0.344975i
$453$	−1.19923e26	−	1.19923e26i	−0.329549	−	0.329549i
$454$			5.89288e26i			1.58405i
$455$	4.28407e26	−	4.04312e26i	1.12653	−	1.06317i
$456$	2.65004e26			0.681716
$457$	1.58610e26	−	1.58610e26i	0.399179	−	0.399179i	−0.478764	−	0.877944i	$-0.658915\pi$
$457$	1.58610e26	−	1.58610e26i	0.399179	−	0.399179i	0.877944	+	0.478764i	$0.158915\pi$
$458$	3.65540e26	+	3.65540e26i	0.900079	+	0.900079i
$459$			1.45643e26i			0.350883i
$460$	1.06963e23	−	3.69652e24i	0.000252149	−	0.00871395i
$461$	6.04026e26			1.39331			0.696653	−	0.717409i	$-0.254672\pi$
$461$	6.04026e26			1.39331			0.696653	+	0.717409i	$0.254672\pi$
$462$	−8.89145e26	+	8.89145e26i	−2.00703	+	2.00703i
$463$	−4.64953e26	−	4.64953e26i	−1.02707	−	1.02707i	−0.999623	−	0.0274453i	$-0.991263\pi$
$463$	−4.64953e26	−	4.64953e26i	−1.02707	−	1.02707i	−0.0274453	−	0.999623i	$-0.508737\pi$
$464$		−	1.52459e26i		−	0.329590i
$465$	−7.93330e26	−	2.29560e25i	−1.67851	−	0.0485698i
$466$	2.87822e26			0.596026
$467$	6.61149e26	−	6.61149e26i	1.34008	−	1.34008i	0.444106	−	0.895974i	$-0.353521\pi$
$467$	6.61149e26	−	6.61149e26i	1.34008	−	1.34008i	0.895974	−	0.444106i	$-0.146479\pi$
$468$	−2.45610e26	−	2.45610e26i	−0.487290	−	0.487290i
$469$			8.65506e26i			1.68090i
$470$	−3.81319e26	−	4.04045e26i	−0.724953	−	0.768158i
$471$	−1.18697e27			−2.20918
$472$	−4.29086e26	+	4.29086e26i	−0.781851	+	0.781851i
$473$	−8.34504e26	−	8.34504e26i	−1.48873	−	1.48873i
$474$		−	3.52087e26i		−	0.614988i
$475$	−3.15175e26	−	1.82552e25i	−0.539033	−	0.0312213i
$476$	7.81371e25			0.130854
$477$	2.67468e26	−	2.67468e26i	0.438619	−	0.438619i
$478$	7.08400e26	+	7.08400e26i	1.13763	+	1.13763i
$479$			1.10702e26i			0.174100i	0.996204	+	0.0870502i	$0.0277441\pi$
$479$			1.10702e26i			0.174100i	−0.996204	+	0.0870502i	$0.972256\pi$
$480$	4.96903e26	−	4.68954e26i	0.765348	−	0.722301i
$481$	5.19130e26			0.783115
$482$	3.25470e26	−	3.25470e26i	0.480884	−	0.480884i
$483$	−2.65459e25	−	2.65459e25i	−0.0384173	−	0.0384173i
$484$		−	9.39740e25i		−	0.133215i
$485$	−3.67961e25	+	1.27163e27i	−0.0510958	+	1.76581i
$486$	7.28698e26			0.991254
$487$	−2.24501e25	+	2.24501e25i	−0.0299178	+	0.0299178i	−0.721907	−	0.691990i	$-0.756734\pi$
$487$	−2.24501e25	+	2.24501e25i	−0.0299178	+	0.0299178i	0.691990	+	0.721907i	$0.256734\pi$
$488$	−1.57135e25	−	1.57135e25i	−0.0205152	−	0.0205152i
$489$		−	9.40947e26i		−	1.20358i
$490$	−5.56830e26	−	1.61126e25i	−0.697850	−	0.0201931i
$491$	1.00417e27			1.23309			0.616544	−	0.787320i	$-0.288532\pi$
$491$	1.00417e27			1.23309			0.616544	+	0.787320i	$0.288532\pi$
$492$	−1.79789e26	+	1.79789e26i	−0.216327	+	0.216327i
$493$	−5.01106e25	−	5.01106e25i	−0.0590827	−	0.0590827i
$494$			6.59870e26i			0.762411i
$495$	1.21224e27	+	1.28449e27i	1.37258	+	1.45438i
$496$	−1.12764e27			−1.25128
$497$	−6.38295e26	+	6.38295e26i	−0.694157	+	0.694157i
$498$	7.33001e26	+	7.33001e26i	0.781288	+	0.781288i
$499$		−	5.02301e26i		−	0.524757i	−0.964965	−	0.262379i	$-0.915493\pi$
$499$		−	5.02301e26i		−	0.524757i	0.964965	−	0.262379i	$-0.0845070\pi$
$500$	−2.49301e26	+	2.09393e26i	−0.255285	+	0.214419i
$501$	1.30498e25			0.0130986
$502$	6.47056e26	−	6.47056e26i	0.636656	−	0.636656i
$503$	−4.88945e26	−	4.88945e26i	−0.471607	−	0.471607i	0.430828	−	0.902434i	$-0.358222\pi$
$503$	−4.88945e26	−	4.88945e26i	−0.471607	−	0.471607i	−0.902434	+	0.430828i	$0.858222\pi$
$504$		−	1.74313e27i		−	1.64825i
$505$	8.37893e26	−	7.90766e26i	0.776739	−	0.733051i
$506$	3.93037e25			0.0357214
$507$	−6.44713e26	+	6.44713e26i	−0.574496	+	0.574496i
$508$	2.79142e26	+	2.79142e26i	0.243887	+	0.243887i
$509$			6.17698e26i			0.529174i	0.964362	+	0.264587i	$0.0852357\pi$
$509$			6.17698e26i			0.529174i	−0.964362	+	0.264587i	$0.914764\pi$
$510$	2.02072e25	−	6.98335e26i	0.0169748	−	0.586627i
$511$	4.23245e26			0.348644
$512$	−1.37121e26	+	1.37121e26i	−0.110765	+	0.110765i
$513$	5.45764e26	+	5.45764e26i	0.432346	+	0.432346i
$514$		−	4.34029e26i		−	0.337200i
$515$	−1.31842e27	−	3.81502e25i	−1.00458	−	0.0290686i
$516$	−1.30222e27			−0.973165
$517$	1.04393e27	−	1.04393e27i	0.765184	−	0.765184i
$518$	−9.21298e26	−	9.21298e26i	−0.662373	−	0.662373i
$519$		−	3.71007e26i		−	0.261643i
$520$	−9.33911e26	−	9.89570e26i	−0.646059	−	0.684562i
$521$	−1.62073e27			−1.09985			−0.549925	−	0.835214i	$-0.685344\pi$
$521$	−1.62073e27			−1.09985			−0.549925	+	0.835214i	$0.685344\pi$
$522$	5.59078e26	−	5.59078e26i	0.372192	−	0.372192i
$523$	2.10258e27	+	2.10258e27i	1.37321	+	1.37321i	0.855646	+	0.517562i	$0.173160\pi$
$523$	2.10258e27	+	2.10258e27i	1.37321	+	1.37321i	0.517562	+	0.855646i	$0.326840\pi$
$524$		−	2.94501e26i		−	0.188701i
$525$	−1.91114e26	+	3.29956e27i	−0.120143	+	2.07426i
$526$	−2.38866e27			−1.47332
$527$	−3.70636e26	+	3.70636e26i	−0.224307	+	0.224307i
$528$	2.82415e27	+	2.82415e27i	1.67706	+	1.67706i
$529$		−	1.71498e27i		−	0.999316i
$530$	−5.38944e26	+	5.08631e26i	−0.308166	+	0.290833i
$531$	−4.32732e27			−2.42814
$532$	2.92802e26	−	2.92802e26i	0.161234	−	0.161234i
$533$	8.95155e26	+	8.95155e26i	0.483756	+	0.483756i
$534$			2.83602e27i			1.50417i
$535$	1.03184e26	−	3.56592e27i	0.0537126	−	1.85624i
$536$	1.99921e27			1.02144
$537$	1.35705e27	−	1.35705e27i	0.680538	−	0.680538i
$538$	−1.93882e27	−	1.93882e27i	−0.954364	−	0.954364i
$539$		−	1.48031e27i		−	0.715262i
$540$	7.95620e26	+	2.30223e25i	0.377371	+	0.0109197i
$541$	2.95389e27			1.37538			0.687689	−	0.726006i	$-0.258625\pi$
$541$	2.95389e27			1.37538			0.687689	+	0.726006i	$0.258625\pi$
$542$	1.62077e26	−	1.62077e26i	0.0740848	−	0.0740848i
$543$	−2.39283e27	−	2.39283e27i	−1.07378	−	1.07378i
$544$		−	4.51239e26i		−	0.198801i
$545$	1.14009e27	+	1.20803e27i	0.493143	+	0.522533i
$546$	6.90818e27			2.93384
$547$	−2.09128e27	+	2.09128e27i	−0.872046	+	0.872046i	−0.992695	−	0.120650i	$-0.961502\pi$
$547$	−2.09128e27	+	2.09128e27i	−0.872046	+	0.872046i	0.120650	+	0.992695i	$0.461502\pi$
$548$	5.90342e26	+	5.90342e26i	0.241712	+	0.241712i
$549$		−	1.58471e26i		−	0.0637126i
$550$	−2.30117e27	−	2.58413e27i	−0.908495	−	1.02021i
$551$	−3.75557e26			−0.145600
$552$	−6.13179e25	+	6.13179e25i	−0.0233451	+	0.0233451i
$553$	7.77858e26	+	7.77858e26i	0.290837	+	0.290837i
$554$			2.91213e27i			1.06933i
$555$	−2.11829e27	+	1.99915e27i	−0.763935	+	0.720967i
$556$	9.23889e26			0.327244
$557$	7.63088e26	−	7.63088e26i	0.265474	−	0.265474i	−0.561799	−	0.827274i	$-0.689891\pi$
$557$	7.63088e26	−	7.63088e26i	0.265474	−	0.265474i	0.827274	+	0.561799i	$0.189891\pi$
$558$	−4.13515e27	−	4.13515e27i	−1.41302	−	1.41302i
$559$			6.48364e27i			2.17621i
$560$	−1.35825e26	+	4.69394e27i	−0.0447816	+	1.54760i
$561$	1.85650e27			0.601265
$562$	1.50485e27	−	1.50485e27i	0.478774	−	0.478774i
$563$	−2.52227e27	−	2.52227e27i	−0.788329	−	0.788329i	0.192891	−	0.981220i	$-0.438214\pi$
$563$	−2.52227e27	−	2.52227e27i	−0.788329	−	0.788329i	−0.981220	+	0.192891i	$0.938214\pi$
$564$		−	1.62902e27i		−	0.500190i
$565$	4.84908e27	+	1.40314e26i	1.46277	+	0.0423269i
$566$	3.43065e26			0.101674
$567$	5.13811e26	−	5.13811e26i	0.149614	−	0.149614i
$568$	1.47438e27	+	1.47438e27i	0.421820	+	0.421820i
$569$		−	8.75678e26i		−	0.246162i	−0.992397	−	0.123081i	$-0.960722\pi$
$569$		−	8.75678e26i		−	0.246162i	0.992397	−	0.123081i	$-0.0392775\pi$
$570$	−2.54114e27	−	2.69258e27i	−0.701907	−	0.743738i
$571$	−1.49545e27			−0.405894			−0.202947	−	0.979190i	$-0.565052\pi$
$571$	−1.49545e27			−0.405894			−0.202947	+	0.979190i	$0.565052\pi$
$572$	−1.27867e27	+	1.27867e27i	−0.341035	+	0.341035i
$573$	−1.21924e27	−	1.21924e27i	−0.319554	−	0.319554i
$574$		−	3.17726e27i		−	0.818339i
$575$	7.71507e25	−	6.87028e25i	0.0195282	−	0.0173898i
$576$	−3.27113e27			−0.813717
$577$	1.52053e27	−	1.52053e27i	0.371738	−	0.371738i	−0.496372	−	0.868110i	$-0.665335\pi$
$577$	1.52053e27	−	1.52053e27i	0.371738	−	0.371738i	0.868110	+	0.496372i	$0.165335\pi$
$578$	3.07188e27	+	3.07188e27i	0.738119	+	0.738119i
$579$		−	2.81820e27i		−	0.665557i
$580$	−2.81666e26	+	2.65824e26i	−0.0653815	+	0.0617042i
$581$	−3.23880e27			−0.738964
$582$	−1.05493e28	+	1.05493e28i	−2.36589	+	2.36589i
$583$	−1.39247e27	−	1.39247e27i	−0.306973	−	0.306973i
$584$		−	9.77644e26i		−	0.211862i
$585$	2.80656e26	−	9.69913e27i	0.0597883	−	2.06621i
$586$	−5.09660e27			−1.06734
$587$	3.90882e27	−	3.90882e27i	0.804758	−	0.804758i	−0.179077	−	0.983835i	$-0.557311\pi$
$587$	3.90882e27	−	3.90882e27i	0.804758	−	0.804758i	0.983835	+	0.179077i	$0.0573113\pi$
$588$	−1.15499e27	−	1.15499e27i	−0.233779	−	0.233779i
$589$			2.77776e27i			0.552766i
$590$	8.47427e27	+	2.45213e26i	1.65799	+	0.0479760i
$591$	9.27455e27			1.78410
$592$	−2.92628e27	+	2.92628e27i	−0.553475	+	0.553475i
$593$	−3.90188e27	−	3.90188e27i	−0.725649	−	0.725649i	0.244101	−	0.969750i	$-0.421507\pi$
$593$	−3.90188e27	−	3.90188e27i	−0.725649	−	0.725649i	−0.969750	+	0.244101i	$0.921507\pi$
$594$			8.45952e27i			1.54697i
$595$	1.49817e27	+	1.58746e27i	0.269397	+	0.285452i
$596$	−1.04111e27			−0.184092
$597$	−6.47270e27	+	6.47270e27i	−1.12549	+	1.12549i
$598$	−1.52684e26	−	1.52684e26i	−0.0261085	−	0.0261085i
$599$		−	2.20561e27i		−	0.370903i	−0.982653	−	0.185451i	$-0.940625\pi$
$599$		−	2.20561e27i		−	0.370903i	0.982653	−	0.185451i	$-0.0593747\pi$
$600$	7.62159e27	+	4.41450e26i	1.26047	+	0.0730078i
$601$	−5.80199e27			−0.943696			−0.471848	−	0.881680i	$-0.656413\pi$
$601$	−5.80199e27			−0.943696			−0.471848	+	0.881680i	$0.656413\pi$
$602$	1.15065e28	−	1.15065e28i	1.84068	−	1.84068i
$603$	1.00810e28	+	1.00810e28i	1.58610	+	1.58610i
$604$			6.12129e26i			0.0947269i
$605$	1.90921e27	−	1.80183e27i	0.290603	−	0.274258i
$606$	1.35112e28			2.02287
$607$	2.59334e27	−	2.59334e27i	0.381920	−	0.381920i	−0.489874	−	0.871794i	$-0.662957\pi$
$607$	2.59334e27	−	2.59334e27i	0.381920	−	0.381920i	0.871794	+	0.489874i	$0.162957\pi$
$608$	−1.69092e27	−	1.69092e27i	−0.244955	−	0.244955i
$609$			3.93170e27i			0.560284i
$610$	−8.97996e24	+	3.10336e26i	−0.00125886	+	0.0435045i
$611$	−8.11076e27			−1.11854
$612$	9.10105e26	−	9.10105e26i	0.123474	−	0.123474i
$613$	7.01792e27	+	7.01792e27i	0.936706	+	0.936706i	0.998113	−	0.0614064i	$-0.0195586\pi$
$613$	7.01792e27	+	7.01792e27i	0.936706	+	0.936706i	−0.0614064	+	0.998113i	$0.519559\pi$
$614$			1.41194e26i			0.0185410i
$615$	−7.09986e27	−	2.05443e26i	−0.917273	−	0.0265424i
$616$	−9.07491e27			−1.15355
$617$	−4.22276e27	+	4.22276e27i	−0.528135	+	0.528135i	−0.920016	−	0.391881i	$-0.871825\pi$
$617$	−4.22276e27	+	4.22276e27i	−0.528135	+	0.528135i	0.391881	+	0.920016i	$0.371825\pi$
$618$	−1.09375e28	−	1.09375e28i	−1.34597	−	1.34597i
$619$		−	1.97383e27i		−	0.239003i	−0.992834	−	0.119501i	$-0.961870\pi$
$619$		−	1.97383e27i		−	0.239003i	0.992834	−	0.119501i	$-0.0381296\pi$
$620$	1.96613e27	+	2.08331e27i	0.234259	+	0.248220i
$621$	−2.52563e26			−0.0296111
$622$	−9.41037e27	+	9.41037e27i	−1.08568	+	1.08568i
$623$	−6.26555e27	−	6.26555e27i	−0.711342	−	0.711342i
$624$		−	2.19421e28i		−	2.45150i
$625$	−9.03413e27	−	1.05005e27i	−0.993313	−	0.115455i
$626$	2.40885e27			0.260656
$627$	6.95682e27	−	6.95682e27i	0.740858	−	0.740858i
$628$	3.02937e27	+	3.02937e27i	0.317508	+	0.317508i
$629$			1.92363e27i			0.198434i
$630$	−1.77111e28	+	1.67149e28i	−1.79821	+	1.69707i
$631$	1.79815e28			1.79694			0.898468	−	0.439038i	$-0.144681\pi$
$631$	1.79815e28			1.79694			0.898468	+	0.439038i	$0.144681\pi$
$632$	1.79676e27	−	1.79676e27i	0.176734	−	0.176734i
$633$	8.32714e27	+	8.32714e27i	0.806230	+	0.806230i
$634$		−	1.52201e28i		−	1.45052i
$635$	−3.18974e26	+	1.10233e28i	−0.0299239	+	1.03413i
$636$	−2.17290e27			−0.200664
$637$	−5.75061e27	+	5.75061e27i	−0.522780	+	0.522780i
$638$	−2.91062e27	−	2.91062e27i	−0.260483	−	0.260483i
$639$			1.48691e28i			1.31002i
$640$	1.37999e28	+	3.99317e26i	1.19695	+	0.0346352i
$641$	−1.27054e28			−1.08495			−0.542475	−	0.840072i	$-0.682513\pi$
$641$	−1.27054e28			−1.08495			−0.542475	+	0.840072i	$0.682513\pi$
$642$	2.95826e28	−	2.95826e28i	2.48706	−	2.48706i
$643$	−6.99826e26	−	6.99826e26i	−0.0579269	−	0.0579269i	0.677550	−	0.735477i	$-0.263042\pi$
$643$	−6.99826e26	−	6.99826e26i	−0.0579269	−	0.0579269i	−0.735477	+	0.677550i	$0.763042\pi$
$644$			1.35500e26i			0.0110428i
$645$	−2.49683e28	−	2.64563e28i	−2.00351	−	2.12291i
$646$	−2.44514e27			−0.193188
$647$	−1.59048e28	+	1.59048e28i	−1.23733	+	1.23733i	−0.276244	+	0.961088i	$0.589090\pi$
$647$	−1.59048e28	+	1.59048e28i	−1.23733	+	1.23733i	−0.961088	+	0.276244i	$0.910910\pi$
$648$	−1.18684e27	−	1.18684e27i	−0.0909164	−	0.0909164i
$649$			2.25285e28i			1.69936i
$650$	−1.09923e27	+	1.89781e28i	−0.0816497	+	1.40967i
$651$	2.90803e28			2.12711
$652$	−2.40146e27	+	2.40146e27i	−0.172982	+	0.172982i
$653$	1.21366e27	+	1.21366e27i	0.0860922	+	0.0860922i	0.748841	−	0.662749i	$-0.230610\pi$
$653$	1.21366e27	+	1.21366e27i	0.0860922	+	0.0860922i	−0.662749	+	0.748841i	$0.730610\pi$
$654$			1.94798e28i			1.36084i
$655$	5.98319e27	−	5.64666e27i	0.411642	−	0.388489i
$656$	−1.00918e28			−0.683800
$657$	4.92976e27	−	4.92976e27i	0.328982	−	0.328982i
$658$	1.43941e28	+	1.43941e28i	0.946078	+	0.946078i
$659$		−	2.58303e28i		−	1.67215i	−0.548614	−	0.836076i	$-0.684844\pi$
$659$		−	2.58303e28i		−	1.67215i	0.548614	−	0.836076i	$-0.315156\pi$
$660$	2.93463e26	−	1.01417e28i	0.0187117	−	0.646654i
$661$	−6.51946e26			−0.0409446			−0.0204723	−	0.999790i	$-0.506517\pi$
$661$	−6.51946e26			−0.0409446			−0.0204723	+	0.999790i	$0.506517\pi$
$662$	1.95801e28	−	1.95801e28i	1.21125	−	1.21125i
$663$	−7.21199e27	−	7.21199e27i	−0.439460	−	0.439460i
$664$			7.48125e27i			0.449048i
$665$	1.15627e28	+	3.34582e26i	0.683666	+	0.0197827i
$666$	−2.14617e28			−1.25003
$667$	8.68983e25	−	8.68983e25i	0.00498601	−	0.00498601i
$668$	−3.33054e25	−	3.33054e25i	−0.00188256	−	0.00188256i
$669$		−	3.53537e28i		−	1.96867i
$670$	−1.91706e28	−	2.03131e28i	−1.05169	−	1.11437i
$671$	−8.25017e26			−0.0445900
$672$	−1.77022e28	+	1.77022e28i	−0.942617	+	0.942617i
$673$	2.32982e28	+	2.32982e28i	1.22228	+	1.22228i	0.966819	+	0.255464i	$0.0822281\pi$
$673$	2.32982e28	+	2.32982e28i	1.22228	+	1.22228i	0.255464	+	0.966819i	$0.417772\pi$
$674$			3.45251e28i			1.78458i
$675$	1.47872e28	+	1.66055e28i	0.753093	+	0.845697i
$676$	3.29084e27			0.165135
$677$	2.81466e28	−	2.81466e28i	1.39168	−	1.39168i	0.570118	−	0.821563i	$-0.306897\pi$
$677$	2.81466e28	−	2.81466e28i	1.39168	−	1.39168i	0.821563	−	0.570118i	$-0.193103\pi$
$678$	4.02276e28	+	4.02276e28i	1.95987	+	1.95987i
$679$		−	4.66128e28i		−	2.23773i
$680$	3.66684e27	−	3.46060e27i	0.173461	−	0.163705i
$681$	−4.82692e28			−2.25008
$682$	−2.15280e28	+	2.15280e28i	−0.988919	+	0.988919i
$683$	4.29253e27	+	4.29253e27i	0.194315	+	0.194315i	0.797558	−	0.603243i	$-0.206125\pi$
$683$	4.29253e27	+	4.29253e27i	0.194315	+	0.194315i	−0.603243	+	0.797558i	$0.706125\pi$
$684$		−	6.82084e27i		−	0.304282i
$685$	−6.74579e26	+	2.33126e28i	−0.0296570	+	1.02491i
$686$	−1.33488e28			−0.578364
$687$	−2.99418e28	+	2.99418e28i	−1.27853	+	1.27853i
$688$	−3.65475e28	−	3.65475e28i	−1.53806	−	1.53806i
$689$			1.08187e28i			0.448728i
$690$	1.21100e27	+	3.50419e25i	0.0495056	+	0.00143251i
$691$	1.45645e28			0.586834			0.293417	−	0.955984i	$-0.405207\pi$
$691$	1.45645e28			0.586834			0.293417	+	0.955984i	$0.405207\pi$
$692$	−9.46875e26	+	9.46875e26i	−0.0376038	+	0.0376038i
$693$	−4.57601e28	−	4.57601e28i	−1.79124	−	1.79124i
$694$			5.14715e27i			0.198597i
$695$	1.77143e28	+	1.87701e28i	0.673716	+	0.713867i
$696$	9.08176e27			0.340469
$697$	−3.31699e27	+	3.31699e27i	−0.122579	+	0.122579i
$698$	−4.08850e28	−	4.08850e28i	−1.48940	−	1.48940i
$699$			2.35758e28i			0.846634i
$700$	8.90883e27	−	7.93331e27i	0.315384	−	0.280850i
$701$	3.91239e28			1.36540			0.682702	−	0.730697i	$-0.260805\pi$
$701$	3.91239e28			1.36540			0.682702	+	0.730697i	$0.260805\pi$
$702$	3.28629e28	−	3.28629e28i	1.13067	−	1.13067i
$703$	7.20838e27	+	7.20838e27i	0.244503	+	0.244503i
$704$			1.70299e28i			0.569489i
$705$	3.30957e28	−	3.12343e28i	1.09114	−	1.02977i
$706$	2.38570e28			0.775478
$707$	−2.98501e28	+	2.98501e28i	−0.956646	+	0.956646i
$708$	1.75775e28	+	1.75775e28i	0.555425	+	0.555425i
$709$		−	4.88462e28i		−	1.52184i	−0.648847	−	0.760919i	$-0.724748\pi$
$709$		−	4.88462e28i		−	1.52184i	0.648847	−	0.760919i	$-0.275252\pi$
$710$	8.42580e26	−	2.91185e28i	0.0258838	−	0.894511i
$711$	1.81203e28			0.548869
$712$	−1.44727e28	+	1.44727e28i	−0.432263	+	0.432263i
$713$	−6.42731e26	−	6.42731e26i	−0.0189293	−	0.0189293i
$714$			2.55982e28i			0.743408i
$715$	−5.04948e28	−	1.46113e27i	−1.44606	−	0.0418435i
$716$	−6.92685e27			−0.195617
$717$	−5.80258e28	+	5.80258e28i	−1.61596	+	1.61596i
$718$	−2.22576e28	−	2.22576e28i	−0.611272	−	0.611272i
$719$		−	1.52760e28i		−	0.413733i	−0.978369	−	0.206867i	$-0.933673\pi$
$719$		−	1.52760e28i		−	0.413733i	0.978369	−	0.206867i	$-0.0663266\pi$
$720$	5.30909e28	+	5.62549e28i	1.41806	+	1.50257i
$721$	4.83281e28			1.27306
$722$	2.22667e28	−	2.22667e28i	0.578473	−	0.578473i
$723$	2.66596e28	+	2.66596e28i	0.683079	+	0.683079i
$724$			1.22139e28i			0.308651i
$725$	−1.08011e28	−	6.25613e26i	−0.269209	−	0.0155929i
$726$	3.07865e28			0.756822
$727$	4.00092e28	−	4.00092e28i	0.970099	−	0.970099i	−0.0294670	−	0.999566i	$-0.509381\pi$
$727$	4.00092e28	−	4.00092e28i	0.970099	−	0.970099i	0.999566	+	0.0294670i	$0.00938099\pi$
$728$	3.52536e28	+	3.52536e28i	0.843120	+	0.843120i
$729$			6.67692e28i			1.57507i
$730$	−9.93339e27	+	9.37469e27i	−0.231137	+	0.218136i
$731$	−2.40251e28			−0.551431
$732$	−6.43707e26	+	6.43707e26i	−0.0145739	+	0.0145739i
$733$	−3.60812e28	−	3.60812e28i	−0.805827	−	0.805827i	0.178173	−	0.983999i	$-0.442981\pi$
$733$	−3.60812e28	−	3.60812e28i	−0.805827	−	0.805827i	−0.983999	+	0.178173i	$0.942981\pi$
$734$			4.18115e28i			0.921160i
$735$	1.31980e27	−	4.56105e28i	0.0286836	−	0.991270i
$736$	7.82507e26			0.0167768
$737$	5.24829e28	−	5.24829e28i	1.11005	−	1.11005i
$738$	−3.70072e28	−	3.70072e28i	−0.772188	−	0.772188i
$739$		−	2.42792e28i		−	0.499793i	−0.968273	−	0.249897i	$-0.919603\pi$
$739$		−	2.42792e28i		−	0.499793i	0.968273	−	0.249897i	$-0.0803966\pi$
$740$	1.05084e28	+	3.04075e26i	0.213413	+	0.00617538i
$741$	−5.40507e28			−1.08298
$742$	1.91999e28	−	1.91999e28i	0.379543	−	0.379543i
$743$	−9.51531e27	−	9.51531e27i	−0.185582	−	0.185582i	0.608201	−	0.793783i	$-0.291891\pi$
$743$	−9.51531e27	−	9.51531e27i	−0.185582	−	0.185582i	−0.793783	+	0.608201i	$0.791891\pi$
$744$		−	6.71720e28i		−	1.29259i
$745$	−1.99619e28	−	2.11516e28i	−0.379001	−	0.401588i
$746$	−1.12413e29			−2.10586
$747$	−3.77241e28	+	3.77241e28i	−0.697289	+	0.697289i
$748$	−4.73811e27	−	4.73811e27i	−0.0864150	−	0.0864150i
$749$			1.30712e29i			2.35233i
$750$	−6.85986e28	−	8.16726e28i	−1.21815	−	1.45032i
$751$	6.20523e28			1.08732			0.543662	−	0.839305i	$-0.317038\pi$
$751$	6.20523e28			1.08732			0.543662	+	0.839305i	$0.317038\pi$
$752$	4.57194e28	−	4.57194e28i	0.790538	−	0.790538i
$753$	5.30010e28	+	5.30010e28i	0.904346	+	0.904346i
$754$			2.26140e28i			0.380771i
$755$	−1.24362e28	+	1.17367e28i	−0.206642	+	0.195020i
$756$	−2.91643e28			−0.478226
$757$	−4.85930e28	+	4.85930e28i	−0.786348	+	0.786348i	−0.980894	−	0.194545i	$-0.937677\pi$
$757$	−4.85930e28	+	4.85930e28i	−0.786348	+	0.786348i	0.194545	+	0.980894i	$0.437677\pi$
$758$	−3.02352e28	−	3.02352e28i	−0.482859	−	0.482859i
$759$			3.21941e27i			0.0507409i
$760$	7.72844e26	−	2.67085e28i	0.0120214	−	0.415445i
$761$	−4.77109e28			−0.732438			−0.366219	−	0.930529i	$-0.619348\pi$
$761$	−4.77109e28			−0.732438			−0.366219	+	0.930529i	$0.619348\pi$
$762$	−9.14487e28	+	9.14487e28i	−1.38557	+	1.38557i
$763$	−4.30363e28	−	4.30363e28i	−0.643561	−	0.643561i
$764$			6.22345e27i			0.0918539i
$765$	3.59400e28	+	1.03997e27i	0.523557	+	0.0151498i
$766$	1.19970e29			1.72498
$767$	8.75172e28	−	8.75172e28i	1.24205	−	1.24205i
$768$	7.46271e28	+	7.46271e28i	1.04540	+	1.04540i
$769$			1.53685e28i			0.212504i	0.994339	+	0.106252i	$0.0338850\pi$
$769$			1.53685e28i			0.212504i	−0.994339	+	0.106252i	$0.966115\pi$
$770$	8.70199e28	+	9.22060e28i	1.18771	+	1.25850i
$771$	3.55518e28			0.478980
$772$	−7.19253e27	+	7.19253e27i	−0.0956553	+	0.0956553i
$773$	2.99561e28	+	2.99561e28i	0.393270	+	0.393270i	0.875851	−	0.482581i	$-0.160301\pi$
$773$	2.99561e28	+	2.99561e28i	0.393270	+	0.393270i	−0.482581	+	0.875851i	$0.660301\pi$
$774$		−	2.68045e29i		−	3.47374i
$775$	−4.62726e27	+	7.98892e28i	−0.0591980	+	1.02205i
$776$	−1.07670e29			−1.35981
$777$	7.54645e28	−	7.54645e28i	0.940877	−	0.940877i
$778$	5.93698e28	+	5.93698e28i	0.730751	+	0.730751i
$779$			2.48594e28i			0.302075i
$780$	−4.05378e28	+	3.82578e28i	−0.486311	+	0.458959i
$781$	7.74104e28			0.916830
$782$	5.65769e26	−	5.65769e26i	0.00661564	−	0.00661564i
$783$	1.87035e28	+	1.87035e28i	0.215926	+	0.215926i
$784$		−	6.48310e28i		−	0.738962i
$785$	−3.46163e27	+	1.19630e29i	−0.0389569	+	1.34630i
$786$	9.64803e28			1.07205
$787$	−4.07377e28	+	4.07377e28i	−0.446940	+	0.446940i	−0.894336	−	0.447396i	$-0.852351\pi$
$787$	−4.07377e28	+	4.07377e28i	−0.446940	+	0.446940i	0.447396	+	0.894336i	$0.352351\pi$
$788$	−2.36703e28	−	2.36703e28i	−0.256414	−	0.256414i
$789$		−	1.95657e29i		−	2.09279i
$790$	−3.54853e28	−	1.02681e27i	−0.374781	−	0.0108447i
$791$	−1.77748e29			−1.85370
$792$	−1.05700e29	+	1.05700e29i	−1.08849	+	1.08849i
$793$	3.20497e27	+	3.20497e27i	0.0325905	+	0.0325905i
$794$			5.50962e28i			0.553244i
$795$	−4.16625e28	−	4.41455e28i	−0.413118	−	0.437738i
$796$	3.30389e28			0.323516
$797$	2.43929e28	−	2.43929e28i	0.235874	−	0.235874i	−0.579265	−	0.815139i	$-0.696660\pi$
$797$	2.43929e28	−	2.43929e28i	0.235874	−	0.235874i	0.815139	+	0.579265i	$0.196660\pi$
$798$	9.59236e28	+	9.59236e28i	0.916002	+	0.916002i
$799$		−	3.00544e28i		−	0.283426i
$800$	−4.58146e28	−	5.14482e28i	−0.426682	−	0.479149i
$801$	−1.45956e29			−1.34245
$802$	4.30201e27	−	4.30201e27i	0.0390776	−	0.0390776i
$803$	−2.56649e28	−	2.56649e28i	−0.230242	−	0.230242i
$804$		−	8.18980e28i		−	0.725626i
$805$	−2.75286e27	+	2.59803e27i	−0.0240894	+	0.0227345i
$806$	1.67261e29			1.44559
$807$	1.58811e29	−	1.58811e29i	1.35564	−	1.35564i
$808$	6.89500e28	+	6.89500e28i	0.581328	+	0.581328i
$809$			2.30547e28i			0.191988i	0.995382	+	0.0959941i	$0.0306030\pi$
$809$			2.30547e28i			0.191988i	−0.995382	+	0.0959941i	$0.969397\pi$
$810$	−6.78255e26	+	2.34396e28i	−0.00557882	+	0.192797i
$811$	−1.58059e29			−1.28413			−0.642067	−	0.766649i	$-0.721923\pi$
$811$	−1.58059e29			−1.28413			−0.642067	+	0.766649i	$0.721923\pi$
$812$	1.00344e28	−	1.00344e28i	0.0805251	−	0.0805251i
$813$	1.32759e28	+	1.32759e28i	0.105235	+	0.105235i
$814$			1.11732e29i			0.874851i
$815$	−9.48338e28	−	2.74413e27i	−0.733478	−	0.0212241i
$816$	8.13063e28			0.621187
$817$	−9.00287e28	+	9.00287e28i	−0.679454	+	0.679454i
$818$	−1.49820e29	−	1.49820e29i	−1.11696	−	1.11696i
$819$			3.55531e29i			2.61842i
$820$	1.75958e28	+	1.86444e28i	0.128018	+	0.135647i
$821$	2.18525e29			1.57062			0.785309	−	0.619105i	$-0.212504\pi$
$821$	2.18525e29			1.57062			0.785309	+	0.619105i	$0.212504\pi$
$822$	−1.93400e29	+	1.93400e29i	−1.37321	+	1.37321i
$823$	−1.36414e29	−	1.36414e29i	−0.956889	−	0.956889i	0.0422189	−	0.999108i	$-0.486557\pi$
$823$	−1.36414e29	−	1.36414e29i	−0.956889	−	0.956889i	−0.999108	+	0.0422189i	$0.986557\pi$
$824$		−	1.11632e29i		−	0.773602i
$825$	2.11669e29	−	1.88492e29i	1.44917	−	1.29048i
$826$	−3.10633e29			−2.10110
$827$	1.34967e29	−	1.34967e29i	0.901926	−	0.901926i	−0.0936762	−	0.995603i	$-0.529862\pi$
$827$	1.34967e29	−	1.34967e29i	0.901926	−	0.901926i	0.995603	+	0.0936762i	$0.0298619\pi$
$828$	1.57824e27	+	1.57824e27i	0.0104200	+	0.0104200i
$829$		−	3.08421e28i		−	0.201186i	−0.994928	−	0.100593i	$-0.967926\pi$
$829$		−	3.08421e28i		−	0.201186i	0.994928	−	0.100593i	$-0.0320741\pi$
$830$	7.60135e28	−	7.17381e28i	0.489903	−	0.462348i
$831$	−2.38536e29			−1.51895
$832$	6.61565e28	−	6.61565e28i	0.416236	−	0.416236i
$833$	−2.13088e28	−	2.13088e28i	−0.132467	−	0.132467i
$834$			3.02672e29i			1.85914i
$835$	3.80578e25	−	1.31523e27i	0.000230982	−	0.00798246i
$836$	−3.55101e28			−0.212955
$837$	1.38338e29	−	1.38338e29i	0.819761	−	0.819761i
$838$	1.66448e29	+	1.66448e29i	0.974629	+	0.974629i
$839$		−	1.57595e29i		−	0.911851i	−0.890018	−	0.455926i	$-0.849308\pi$
$839$		−	1.57595e29i		−	0.911851i	0.890018	−	0.455926i	$-0.150692\pi$
$840$	−2.79611e29	−	8.09090e27i	−1.59868	−	0.0462598i
$841$	1.64124e29			0.927283
$842$	1.13547e29	−	1.13547e29i	0.633948	−	0.633948i
$843$	1.23264e29	+	1.23264e29i	0.680081	+	0.680081i
$844$		−	4.25047e28i		−	0.231746i
$845$	6.30975e28	+	6.68579e28i	0.339973	+	0.360235i
$846$	3.35313e29			1.78545
$847$	−6.80158e28	+	6.80158e28i	−0.357912	+	0.357912i
$848$	−6.09839e28	−	6.09839e28i	−0.317144	−	0.317144i
$849$			2.81008e28i			0.144425i
$850$	−7.03231e28	−	4.07318e27i	−0.357198	−	0.0206893i
$851$	−3.33582e27			−0.0167459
$852$	6.03983e28	−	6.03983e28i	0.299660	−	0.299660i
$853$	1.73047e29	+	1.73047e29i	0.848544	+	0.848544i	0.989951	−	0.141408i	$-0.0451628\pi$
$853$	1.73047e29	+	1.73047e29i	0.848544	+	0.848544i	−0.141408	+	0.989951i	$0.545163\pi$
$854$		−	1.13757e28i		−	0.0551314i
$855$	1.38574e29	−	1.30780e29i	0.663777	−	0.626443i
$856$	3.01930e29			1.42945
$857$	−5.98040e28	+	5.98040e28i	−0.279848	+	0.279848i	−0.833048	−	0.553200i	$-0.813406\pi$
$857$	−5.98040e28	+	5.98040e28i	−0.279848	+	0.279848i	0.553200	+	0.833048i	$0.313406\pi$
$858$	−4.18901e29	−	4.18901e29i	−1.93749	−	1.93749i
$859$			3.40454e29i			1.55642i	0.628003	+	0.778211i	$0.283872\pi$
$859$			3.40454e29i			1.55642i	−0.628003	+	0.778211i	$0.716128\pi$
$860$	−3.79772e27	+	1.31245e29i	−0.0171609	+	0.593058i
$861$	2.60252e29			1.16242
$862$	−1.86876e29	+	1.86876e29i	−0.825049	+	0.825049i
$863$	4.54405e28	+	4.54405e28i	0.198306	+	0.198306i	0.799273	−	0.600968i	$-0.205218\pi$
$863$	4.54405e28	+	4.54405e28i	0.198306	+	0.198306i	−0.600968	+	0.799273i	$0.705218\pi$
$864$			1.68423e29i			0.726546i
$865$	−3.73921e28	−	1.08199e27i	−0.159448	−	0.00461382i
$866$	4.46011e28			0.188004
$867$	−2.51621e29	+	2.51621e29i	−1.04847	+	1.04847i
$868$	−7.42181e28	−	7.42181e28i	−0.305712	−	0.305712i
$869$		−	9.43362e28i		−	0.384132i
$870$	−8.70856e28	−	9.22756e28i	−0.350553	−	0.371445i
$871$	−4.07764e29			−1.62266
$872$	−9.94087e28	+	9.94087e28i	−0.391075	+	0.391075i
$873$	−5.42925e29	−	5.42925e29i	−2.11153	−	2.11153i
$874$		−	4.24019e27i		−	0.0163031i
$875$	3.31991e29	+	2.88842e28i	1.26196	+	0.109794i
$876$	−4.00493e28			−0.150506
$877$	−1.86354e29	+	1.86354e29i	−0.692377	+	0.692377i	−0.962754	−	0.270377i	$-0.912852\pi$
$877$	−1.86354e29	+	1.86354e29i	−0.692377	+	0.692377i	0.270377	+	0.962754i	$0.412852\pi$
$878$	1.52119e29	+	1.52119e29i	0.558775	+	0.558775i
$879$		−	4.17468e29i		−	1.51612i
$880$	2.92870e29	−	2.76397e29i	1.05159	−	0.992446i
$881$	5.57257e26			0.00197832			0.000989160	−	1.00000i	$-0.499685\pi$
$881$	5.57257e26			0.00197832			0.000989160		1.00000i	$0.499685\pi$
$882$	2.37740e29	−	2.37740e29i	0.834480	−	0.834480i
$883$	−1.70361e29	−	1.70361e29i	−0.591238	−	0.591238i	0.346728	−	0.937966i	$-0.387293\pi$
$883$	−1.70361e29	−	1.70361e29i	−0.591238	−	0.591238i	−0.937966	+	0.346728i	$0.887293\pi$
$884$			3.68125e28i			0.126320i
$885$	−2.00857e28	+	6.94137e29i	−0.0681482	+	2.35512i
$886$	2.15760e29			0.723826
$887$	−1.02027e29	+	1.02027e29i	−0.338438	+	0.338438i	−0.855779	−	0.517341i	$-0.826922\pi$
$887$	−1.02027e29	+	1.02027e29i	−0.338438	+	0.338438i	0.517341	+	0.855779i	$0.326922\pi$
$888$	−1.74314e29	−	1.74314e29i	−0.571745	−	0.571745i
$889$		−	4.04071e29i		−	1.31051i
$890$	2.85829e29	+	8.27082e27i	0.916657	+	0.0265246i
$891$	−6.23133e28			−0.197608
$892$	−9.02288e28	+	9.02288e28i	−0.282941	+	0.282941i
$893$	−1.12622e29	−	1.12622e29i	−0.349228	−	0.349228i
$894$		−	3.41075e29i		−	1.04586i
$895$	−1.32813e29	−	1.40728e29i	−0.402727	−	0.426728i
$896$	−5.05849e29			−1.51684
$897$	1.25065e28	−	1.25065e28i	0.0370862	−	0.0370862i
$898$	3.84400e29	+	3.84400e29i	1.12725	+	1.12725i
$899$			9.51947e28i			0.276068i
$900$	1.13623e28	−	1.96170e29i	0.0325868	−	0.562609i
$901$	−4.00887e28			−0.113703
$902$	−1.92664e29	+	1.92664e29i	−0.540424	+	0.540424i
$903$	9.42509e29	+	9.42509e29i	2.61462	+	2.61462i
$904$			4.10576e29i			1.12644i
$905$	−2.48141e29	+	2.34184e29i	−0.673307	+	0.635436i
$906$	−2.00537e29			−0.538162
$907$	3.10684e29	−	3.10684e29i	0.824606	−	0.824606i	−0.162158	−	0.986765i	$-0.551846\pi$
$907$	3.10684e29	−	3.10684e29i	0.824606	−	0.824606i	0.986765	+	0.162158i	$0.0518456\pi$
$908$	1.23191e29	+	1.23191e29i	0.323387	+	0.323387i
$909$			6.95360e29i			1.80539i
$910$	2.01467e28	−	6.96244e29i	0.0517356	−	1.78792i
$911$	2.15732e29			0.547937			0.273969	−	0.961739i	$-0.411664\pi$
$911$	2.15732e29			0.547937			0.273969	+	0.961739i	$0.411664\pi$
$912$	3.04677e29	−	3.04677e29i	0.765406	−	0.765406i
$913$	1.96396e29	+	1.96396e29i	0.488006	+	0.488006i
$914$		−	2.65230e29i		−	0.651870i
$915$	−2.54200e28	−	7.35558e26i	−0.0617965	−	0.00178816i
$916$	1.52834e29			0.367506
$917$	−2.13152e29	+	2.13152e29i	−0.506986	+	0.506986i
$918$	1.21773e29	+	1.21773e29i	0.286500	+	0.286500i
$919$		−	4.31804e29i		−	1.00492i	−0.864601	−	0.502460i	$-0.832429\pi$
$919$		−	4.31804e29i		−	1.00492i	0.864601	−	0.502460i	$-0.167571\pi$
$920$	6.00113e27	+	6.35877e27i	0.0138151	+	0.0146385i
$921$	−1.15654e28			−0.0263368
$922$	5.05031e29	−	5.05031e29i	1.13765	−	1.13765i
$923$	−3.00718e29	−	3.00718e29i	−0.670105	−	0.670105i
$924$			3.71754e29i			0.819476i
$925$	1.95308e29	+	2.19323e29i	0.425894	+	0.478264i
$926$	−7.77503e29			−1.67723
$927$	5.62904e29	−	5.62904e29i	1.20126	−	1.20126i
$928$	−5.79484e28	−	5.79484e28i	−0.122338	−	0.122338i
$929$			8.51661e28i			0.177873i	0.996037	+	0.0889365i	$0.0283468\pi$
$929$			8.51661e28i			0.177873i	−0.996037	+	0.0889365i	$0.971653\pi$
$930$	−6.82504e29	+	6.44117e29i	−1.41018	+	1.33087i
$931$	−1.59700e29			−0.326444
$932$	6.01697e28	−	6.01697e28i	0.121680	−	0.121680i
$933$	−7.70813e29	−	7.70813e29i	−1.54217	−	1.54217i
$934$		−	1.10559e30i		−	2.18838i
$935$	5.41420e27	−	1.87108e29i	0.0106027	−	0.366417i
$936$	8.21235e29			1.59114
$937$	−5.36903e27	+	5.36903e27i	−0.0102920	+	0.0102920i	−0.712234	−	0.701942i	$-0.752317\pi$
$937$	−5.36903e27	+	5.36903e27i	−0.0102920	+	0.0102920i	0.701942	+	0.712234i	$0.252317\pi$
$938$	7.23657e29	+	7.23657e29i	1.37247	+	1.37247i
$939$			1.97312e29i			0.370252i
$940$	−1.64182e29	−	4.75080e27i	−0.304822	−	0.00882039i
$941$	3.07219e29			0.564354			0.282177	−	0.959362i	$-0.408943\pi$
$941$	3.07219e29			0.564354			0.282177	+	0.959362i	$0.408943\pi$
$942$	−9.92439e29	+	9.92439e29i	−1.80383	+	1.80383i
$943$	−5.75208e27	−	5.75208e27i	−0.0103445	−	0.0103445i
$944$			9.86648e29i			1.75567i
$945$	−5.59185e29	−	5.92511e29i	−0.984550	−	1.04323i
$946$	−1.39547e30			−2.43114
$947$	−1.88234e29	+	1.88234e29i	−0.324488	+	0.324488i	−0.850486	−	0.525998i	$-0.823692\pi$
$947$	−1.88234e29	+	1.88234e29i	−0.324488	+	0.324488i	0.525998	+	0.850486i	$0.323692\pi$
$948$	−7.36044e28	−	7.36044e28i	−0.125551	−	0.125551i
$949$			1.99402e29i			0.336564i
$950$	−2.78784e29	+	2.48257e29i	−0.465620	+	0.414635i
$951$	1.24669e30			2.06041
$952$	−1.30632e29	+	1.30632e29i	−0.213638	+	0.213638i
$953$	−8.29443e29	−	8.29443e29i	−1.34233	−	1.34233i	−0.893740	−	0.448585i	$-0.851928\pi$
$953$	−8.29443e29	−	8.29443e29i	−1.34233	−	1.34233i	−0.448585	−	0.893740i	$-0.648072\pi$
$954$		−	4.47264e29i		−	0.716276i
$955$	−1.26438e29	+	1.19326e29i	−0.200375	+	0.189105i
$956$	2.96184e29			0.464497
$957$	2.38412e29	−	2.38412e29i	0.370007	−	0.370007i
$958$	9.25588e28	+	9.25588e28i	0.142155	+	0.142155i
$959$		−	8.54546e29i		−	1.29882i
$960$	−1.51833e28	+	5.24716e29i	−0.0228378	+	0.789246i
$961$	3.23040e28			0.0480864
$962$	4.34049e29	−	4.34049e29i	0.639423	−	0.639423i
$963$	1.52248e30	+	1.52248e30i	2.21967	+	2.21967i
$964$		−	1.36080e29i		−	0.196347i
$965$	−2.84033e29	−	8.21885e27i	−0.405598	−	0.0117365i
$966$	−4.43905e28			−0.0627363
$967$	6.11556e29	−	6.11556e29i	0.855404	−	0.855404i	−0.135388	−	0.990793i	$-0.543228\pi$
$967$	6.11556e29	−	6.11556e29i	0.855404	−	0.855404i	0.990793	+	0.135388i	$0.0432281\pi$
$968$	1.57108e29	+	1.57108e29i	0.217493	+	0.217493i
$969$		−	2.00284e29i		−	0.274416i
$970$	1.03245e30	+	1.09399e30i	1.40008	+	1.48352i
$971$	7.12112e29			0.955776			0.477888	−	0.878421i	$-0.341402\pi$
$971$	7.12112e29			0.955776			0.477888	+	0.878421i	$0.341402\pi$
$972$	1.52335e29	−	1.52335e29i	0.202366	−	0.202366i
$973$	−6.68686e29	−	6.68686e29i	−0.879212	−	0.879212i
$974$			3.75415e28i			0.0488565i
$975$	−1.55452e30	−	9.00391e28i	−2.00239	−	0.115980i
$976$	−3.61321e28			−0.0460675
$977$	1.52475e29	−	1.52475e29i	0.192421	−	0.192421i	−0.604320	−	0.796741i	$-0.706555\pi$
$977$	1.52475e29	−	1.52475e29i	0.192421	−	0.192421i	0.796741	+	0.604320i	$0.206555\pi$
$978$	−7.86734e29	−	7.86734e29i	−0.982742	−	0.982742i
$979$			7.59866e29i			0.939529i
$980$	−1.19775e29	+	1.13038e29i	−0.146590	+	0.138345i
$981$	−1.00253e30			−1.21453
$982$	8.39599e29	−	8.39599e29i	1.00683	−	1.00683i
$983$	−7.93810e28	−	7.93810e28i	−0.0942283	−	0.0942283i	0.658421	−	0.752650i	$-0.271225\pi$
$983$	−7.93810e28	−	7.93810e28i	−0.0942283	−	0.0942283i	−0.752650	+	0.658421i	$0.771225\pi$
$984$		−	6.01152e29i		−	0.706371i
$985$	2.70479e28	−	9.34740e29i	0.0314609	−	1.08725i
$986$	−8.37959e28			−0.0964836
$987$	−1.17904e30	+	1.17904e30i	−1.34387	+	1.34387i
$988$	1.37947e29	+	1.37947e29i	0.155648	+	0.155648i
$989$		−	4.16626e28i		−	0.0465354i
$990$	2.08754e30	+	6.04056e28i	2.30825	+	0.0667921i
$991$	−4.97430e29			−0.544497			−0.272249	−	0.962227i	$-0.587767\pi$
$991$	−4.97430e29			−0.544497			−0.272249	+	0.962227i	$0.587767\pi$
$992$	−4.28607e29	+	4.28607e29i	−0.464454	+	0.464454i
$993$	1.60383e30	+	1.60383e30i	1.72054	+	1.72054i
$994$			1.06737e30i			1.13357i
$995$	6.33477e29	+	6.71230e29i	0.666040	+	0.705734i
$996$	3.06470e29			0.319003
$997$	−7.34129e29	+	7.34129e29i	−0.756521	+	0.756521i	−0.975687	−	0.219167i	$-0.929666\pi$
$997$	−7.34129e29	+	7.34129e29i	−0.756521	+	0.756521i	0.219167	+	0.975687i	$0.429666\pi$
$998$	−4.19978e29	−	4.19978e29i	−0.428471	−	0.428471i
$999$		−	7.17985e29i		−	0.725205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.21.c.a.3.8	yes	18
3.2	odd	2		45.21.g.a.28.2		18
5.2	odd	4	inner	5.21.c.a.2.8	✓	18
5.3	odd	4		25.21.c.b.7.2		18
5.4	even	2		25.21.c.b.18.2		18
15.2	even	4		45.21.g.a.37.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.8	✓	18	5.2	odd	4	inner
5.21.c.a.3.8	yes	18	1.1	even	1	trivial
25.21.c.b.7.2		18	5.3	odd	4
25.21.c.b.18.2		18	5.4	even	2
45.21.g.a.28.2		18	3.2	odd	2
45.21.g.a.37.2		18	15.2	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(836.109 - 836.109i) q^{2} +(68486.6 + 68486.6i) q^{3} -349580. i q^{4} +(7.10218e6 - 6.70272e6i) q^{5} +1.14524e8 q^{6} +(-2.53016e8 + 2.53016e8i) q^{7} +(5.84437e8 + 5.84437e8i) q^{8} +5.89403e9i q^{9} +O(q^{10})\)	\(q+(836.109 - 836.109i) q^{2} +(68486.6 + 68486.6i) q^{3} -349580. i q^{4} +(7.10218e6 - 6.70272e6i) q^{5} +1.14524e8 q^{6} +(-2.53016e8 + 2.53016e8i) q^{7} +(5.84437e8 + 5.84437e8i) q^{8} +5.89403e9i q^{9} +(3.33994e8 - 1.15424e10i) q^{10} +3.06850e10 q^{11} +(2.39415e10 - 2.39415e10i) q^{12} +(-1.19203e11 - 1.19203e11i) q^{13} +4.23098e11i q^{14} +(9.45450e11 + 2.73578e10i) q^{15} +1.34387e12 q^{16} +(4.41705e11 - 4.41705e11i) q^{17} +(4.92805e12 + 4.92805e12i) q^{18} -3.31039e12i q^{19} +(-2.34313e12 - 2.48278e12i) q^{20} -3.46564e13 q^{21} +(2.56560e13 - 2.56560e13i) q^{22} +(7.65974e11 + 7.65974e11i) q^{23} +8.00522e13i q^{24} +(5.51453e12 - 9.52079e13i) q^{25} -1.99333e14 q^{26} +(-1.64864e14 + 1.64864e14i) q^{27} +(8.84493e13 + 8.84493e13i) q^{28} -1.13448e14i q^{29} +(8.13373e14 - 7.67625e14i) q^{30} -8.39103e14 q^{31} +(5.10792e14 - 5.10792e14i) q^{32} +(2.10151e15 + 2.10151e15i) q^{33} -7.38627e14i q^{34} +(-1.01070e14 + 3.49286e15i) q^{35} +2.06043e15 q^{36} +(-2.17750e15 + 2.17750e15i) q^{37} +(-2.76784e15 - 2.76784e15i) q^{38} -1.63276e16i q^{39} +(8.06809e15 + 2.33460e14i) q^{40} -7.50950e15 q^{41} +(-2.89765e16 + 2.89765e16i) q^{42} +(-2.71958e16 - 2.71958e16i) q^{43} -1.07269e16i q^{44} +(3.95061e16 + 4.18605e16i) q^{45} +1.28088e15 q^{46} +(3.40208e16 - 3.40208e16i) q^{47} +(9.20368e16 + 9.20368e16i) q^{48} -4.82421e16i q^{49} +(-7.49934e16 - 8.42149e16i) q^{50} +6.05018e16 q^{51} +(-4.16709e16 + 4.16709e16i) q^{52} +(-4.53794e16 - 4.53794e16i) q^{53} +2.75689e17i q^{54} +(2.17931e17 - 2.05673e17i) q^{55} -2.95744e17 q^{56} +(2.26717e17 - 2.26717e17i) q^{57} +(-9.48549e16 - 9.48549e16i) q^{58} +7.34186e17i q^{59} +(9.56372e15 - 3.30510e17i) q^{60} -2.68866e16 q^{61} +(-7.01582e17 + 7.01582e17i) q^{62} +(-1.49129e18 - 1.49129e18i) q^{63} +5.54991e17i q^{64} +(-1.64558e18 - 4.76170e16i) q^{65} +3.51418e18 q^{66} +(1.71038e18 - 1.71038e18i) q^{67} +(-1.54411e17 - 1.54411e17i) q^{68} +1.04918e17i q^{69} +(2.83591e18 + 3.00492e18i) q^{70} +2.52274e18 q^{71} +(-3.44469e18 + 3.44469e18i) q^{72} +(-8.36398e17 - 8.36398e17i) q^{73} +3.64126e18i q^{74} +(6.89813e18 - 6.14279e18i) q^{75} -1.15724e18 q^{76} +(-7.76381e18 + 7.76381e18i) q^{77} +(-1.36516e19 - 1.36516e19i) q^{78} -3.07434e18i q^{79} +(9.54438e18 - 9.00756e18i) q^{80} -2.03074e18 q^{81} +(-6.27876e18 + 6.27876e18i) q^{82} +(6.40039e18 + 6.40039e18i) q^{83} +1.21152e19i q^{84} +(1.76444e17 - 6.09770e18i) q^{85} -4.54773e19 q^{86} +(7.76967e18 - 7.76967e18i) q^{87} +(1.79335e19 + 1.79335e19i) q^{88} +2.47634e19i q^{89} +(6.80313e19 + 1.96857e18i) q^{90} +6.03206e19 q^{91} +(2.67769e17 - 2.67769e17i) q^{92} +(-5.74673e19 - 5.74673e19i) q^{93} -5.68902e19i q^{94} +(-2.21886e19 - 2.35110e19i) q^{95} +6.99648e19 q^{96} +(-9.21143e19 + 9.21143e19i) q^{97} +(-4.03357e19 - 4.03357e19i) q^{98} +1.80858e20i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Introduction

L-functions

Modular forms

Varieties

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