LMFDB - Embedded newform 7.17.d.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,17,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, 17, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 17 $
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:	$11.3627180700$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 470221 x^{18} - 17792382 x^{17} + 149610140535 x^{16} - 5885709493452 x^{15} + \cdots + 26\!\cdots\!25 $ x^20 - 2x^19 + 470221x^18 - 17792382x^17 + 149610140535x^16 - 5885709493452x^15 + 25413927970368382x^14 - 921982218074544860x^13 + 3092605513604061172669x^12 - 78217760507911051825254x^11 + 217775891572550635786539387x^10 - 772894989756975230685011586x^9 + 10848813785145958185022965942709x^8 + 50328102663961537370536178622316x^7 + 292280160701254761307491650568975646x^6 + 6884264619587692201297746565224842172x^5 + 5465648386210730671112398026225318665199x^4 + 69498817213798305204024309903431721187110x^3 + 44558299163904360256389313185385225104835245x^2 - 34923314543744821707168835219945993579648950*x + 261490399505792227817024003348104130194641159225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{38}\cdot 3^{16}\cdot 7^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$-187.565 - 324.873i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.17.d.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-183.065 + 317.078i) q^{2} +(-5337.54 + 3081.63i) q^{3} +(-34257.8 - 59336.2i) q^{4} +(-149102. - 86084.1i) q^{5} -2.25656e6i q^{6} +(303703. - 5.75680e6i) q^{7} +1.09092e6 q^{8} +(-2.53044e6 + 4.38285e6i) q^{9} +O(q^{10})$	\(q+(-183.065 + 317.078i) q^{2} +(-5337.54 + 3081.63i) q^{3} +(-34257.8 - 59336.2i) q^{4} +(-149102. - 86084.1i) q^{5} -2.25656e6i q^{6} +(303703. - 5.75680e6i) q^{7} +1.09092e6 q^{8} +(-2.53044e6 + 4.38285e6i) q^{9} +(5.45908e7 - 3.15180e7i) q^{10} +(2.15282e7 + 3.72879e7i) q^{11} +(3.65705e8 + 2.11140e8i) q^{12} +9.75919e8i q^{13} +(1.76976e9 + 1.15017e9i) q^{14} +1.06112e9 q^{15} +(2.04541e9 - 3.54275e9i) q^{16} +(4.97420e9 - 2.87185e9i) q^{17} +(-9.26471e8 - 1.60470e9i) q^{18} +(-7.94173e9 - 4.58516e9i) q^{19} +1.17962e10i q^{20} +(1.61193e10 + 3.16631e10i) q^{21} -1.57643e10 q^{22} +(-2.03156e10 + 3.51877e10i) q^{23} +(-5.82282e9 + 3.36180e9i) q^{24} +(-6.14730e10 - 1.06474e11i) q^{25} +(-3.09443e11 - 1.78657e11i) q^{26} -2.96500e11i q^{27} +(-3.51991e11 + 1.79194e11i) q^{28} +6.70144e11 q^{29} +(-1.94254e11 + 3.36458e11i) q^{30} +(9.28533e11 - 5.36089e11i) q^{31} +(7.84634e11 + 1.35903e12i) q^{32} +(-2.29815e11 - 1.32684e11i) q^{33} +2.10295e12i q^{34} +(-5.40852e11 + 8.32206e11i) q^{35} +3.46749e11 q^{36} +(2.44056e12 - 4.22717e12i) q^{37} +(2.90771e12 - 1.67877e12i) q^{38} +(-3.00742e12 - 5.20901e12i) q^{39} +(-1.62658e11 - 9.39106e10i) q^{40} +9.25310e12i q^{41} +(-1.29906e13 - 6.85325e11i) q^{42} -6.77014e12 q^{43} +(1.47502e12 - 2.55480e12i) q^{44} +(7.54588e11 - 4.35661e11i) q^{45} +(-7.43818e12 - 1.28833e13i) q^{46} +(1.13952e13 + 6.57901e12i) q^{47} +2.52128e13i q^{48} +(-3.30485e13 - 3.49672e12i) q^{49} +4.50143e13 q^{50} +(-1.77000e13 + 3.06573e13i) q^{51} +(5.79073e13 - 3.34328e13i) q^{52} +(-5.78861e13 - 1.00262e14i) q^{53} +(9.40137e13 + 5.42788e13i) q^{54} -7.41295e12i q^{55} +(3.31315e11 - 6.28018e12i) q^{56} +5.65191e13 q^{57} +(-1.22680e14 + 2.12488e14i) q^{58} +(1.76124e14 - 1.01685e14i) q^{59} +(-3.63516e13 - 6.29628e13i) q^{60} +(-7.45549e13 - 4.30443e13i) q^{61} +3.92557e14i q^{62} +(2.44627e13 + 1.58983e13i) q^{63} -3.06461e14 q^{64} +(8.40111e13 - 1.45512e14i) q^{65} +(8.41425e13 - 4.85797e13i) q^{66} +(-3.69776e14 - 6.40471e14i) q^{67} +(-3.40810e14 - 1.96767e14i) q^{68} -2.50421e14i q^{69} +(-1.64863e14 - 3.23840e14i) q^{70} +6.18883e14 q^{71} +(-2.76050e12 + 4.78132e12i) q^{72} +(-1.06453e15 + 6.14609e14i) q^{73} +(8.93563e14 + 1.54770e15i) q^{74} +(6.56230e14 + 3.78874e14i) q^{75} +6.28310e14i q^{76} +(2.21197e14 - 1.12609e14i) q^{77} +2.20222e15 q^{78} +(6.89263e14 - 1.19384e15i) q^{79} +(-6.09950e14 + 3.52155e14i) q^{80} +(8.04777e14 + 1.39391e15i) q^{81} +(-2.93396e15 - 1.69392e15i) q^{82} -1.94472e13i q^{83} +(1.32655e15 - 2.04116e15i) q^{84} -9.88884e14 q^{85} +(1.23938e15 - 2.14667e15i) q^{86} +(-3.57692e15 + 2.06514e15i) q^{87} +(2.34855e13 + 4.06780e13i) q^{88} +(-4.18619e15 - 2.41690e15i) q^{89} +3.19018e14i q^{90} +(5.61816e15 + 2.96390e14i) q^{91} +2.78388e15 q^{92} +(-3.30406e15 + 5.72279e15i) q^{93} +(-4.17212e15 + 2.40878e15i) q^{94} +(7.89419e14 + 1.36731e15i) q^{95} +(-8.37604e15 - 4.83591e15i) q^{96} +6.78438e15i q^{97} +(7.15876e15 - 9.83882e15i) q^{98} -2.17903e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9}+O(q^{10}) $ 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} - 567579804 q^{10} + 487037030 q^{11} - 2240722092 q^{12} + 598121216 q^{14} - 2098975212 q^{15} - 13522996616 q^{16} + 16479299850 q^{17} - 21631627512 q^{18} - 29753076894 q^{19} + 30310552398 q^{21} + 143879888720 q^{22} - 199076938822 q^{23} + 613456300512 q^{24} + 212723266388 q^{25} - 1359419612544 q^{26} + 2531834927748 q^{28} + 438309600272 q^{29} - 2296351012392 q^{30} + 1037434908306 q^{31} - 3523947158064 q^{32} + 411779151054 q^{33} - 7248579242478 q^{35} - 2493315404256 q^{36} + 5318067734218 q^{37} - 9079217417208 q^{38} + 13250117821332 q^{39} + 15010293809208 q^{40} + 16256122433712 q^{42} - 621187489400 q^{43} + 25172272315980 q^{44} - 85040191344096 q^{45} - 15614039192704 q^{46} + 106960600327866 q^{47} - 52978127838580 q^{49} + 35872835226128 q^{50} + 4235281588962 q^{51} + 126484190926632 q^{52} + 29048763888218 q^{53} - 635343594055560 q^{54} + 230352840277168 q^{56} + 366396034764636 q^{57} - 279762037805080 q^{58} - 99092116656282 q^{59} - 173605217618196 q^{60} - 904353032308434 q^{61} + 11\!\cdots\!92 q^{63}+ \cdots + 14\!\cdots\!92 q^{99}+O(q^{100}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9 - 567579804 * q^10 + 487037030 * q^11 - 2240722092 * q^12 + 598121216 * q^14 - 2098975212 * q^15 - 13522996616 * q^16 + 16479299850 * q^17 - 21631627512 * q^18 - 29753076894 * q^19 + 30310552398 * q^21 + 143879888720 * q^22 - 199076938822 * q^23 + 613456300512 * q^24 + 212723266388 * q^25 - 1359419612544 * q^26 + 2531834927748 * q^28 + 438309600272 * q^29 - 2296351012392 * q^30 + 1037434908306 * q^31 - 3523947158064 * q^32 + 411779151054 * q^33 - 7248579242478 * q^35 - 2493315404256 * q^36 + 5318067734218 * q^37 - 9079217417208 * q^38 + 13250117821332 * q^39 + 15010293809208 * q^40 + 16256122433712 * q^42 - 621187489400 * q^43 + 25172272315980 * q^44 - 85040191344096 * q^45 - 15614039192704 * q^46 + 106960600327866 * q^47 - 52978127838580 * q^49 + 35872835226128 * q^50 + 4235281588962 * q^51 + 126484190926632 * q^52 + 29048763888218 * q^53 - 635343594055560 * q^54 + 230352840277168 * q^56 + 366396034764636 * q^57 - 279762037805080 * q^58 - 99092116656282 * q^59 - 173605217618196 * q^60 - 904353032308434 * q^61 + 1188663557133192 * q^63 + 2502182430870944 * q^64 - 500211967540404 * q^65 - 951679982792988 * q^66 - 33326890567694 * q^67 - 964537664673492 * q^68 - 569178593140080 * q^70 + 3111156268483352 * q^71 + 936737429904432 * q^72 - 1146801010325370 * q^73 - 2161044304782140 * q^74 - 4935640048894356 * q^75 + 1321278185203718 * q^77 + 13747974994685232 * q^78 + 126874036566250 * q^79 - 18764997660746184 * q^80 - 2081051947014102 * q^81 - 11916006908925168 * q^82 + 17065299612720828 * q^84 + 27928718307758508 * q^85 - 7493915124549152 * q^86 - 4167264363403248 * q^87 - 10398917942882000 * q^88 - 34000447101257730 * q^89 + 6895892767523928 * q^91 + 113018032389709752 * q^92 - 15597881218045122 * q^93 - 7183919979926376 * q^94 - 19569222088313322 * q^95 - 137281944028491360 * q^96 + 65453414234371436 * q^98 + 142672614742345392 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−183.065	+	317.078i	−0.715099	+	1.23859i	0.247823	+	0.968805i	$0.420285\pi$
$2$	−183.065	+	317.078i	−0.715099	+	1.23859i	−0.962921	+	0.269782i	$0.913048\pi$
$3$	−5337.54	+	3081.63i	−0.813526	+	0.469689i	−0.848179	−	0.529710i	$-0.822301\pi$
$3$	−5337.54	+	3081.63i	−0.813526	+	0.469689i	0.0346528	+	0.999399i	$0.488967\pi$
$4$	−34257.8	−	59336.2i	−0.522732	−	0.905399i
$5$	−149102.	−	86084.1i	−0.381701	−	0.220375i	0.296857	−	0.954922i	$-0.404062\pi$
$5$	−149102.	−	86084.1i	−0.381701	−	0.220375i	−0.678558	+	0.734547i	$0.737395\pi$
$6$		−	2.25656e6i		−	1.34350i
$7$	303703.	−	5.75680e6i	0.0526824	−	0.998611i
$7$	303703.	−	5.75680e6i	0.0526824	−	0.998611i
$8$	1.09092e6			0.0650237
$9$	−2.53044e6	+	4.38285e6i	−0.0587836	+	0.101816i
$10$	5.45908e7	−	3.15180e7i	0.545908	−	0.315180i
$11$	2.15282e7	+	3.72879e7i	0.100431	+	0.173951i	0.911862	−	0.410497i	$-0.134645\pi$
$11$	2.15282e7	+	3.72879e7i	0.100431	+	0.173951i	−0.811432	+	0.584448i	$0.801311\pi$
$12$	3.65705e8	+	2.11140e8i	0.850513	+	0.491044i
$13$			9.75919e8i			1.19637i	0.801357	+	0.598187i	$0.204112\pi$
$13$			9.75919e8i			1.19637i	−0.801357	+	0.598187i	$0.795888\pi$
$14$	1.76976e9	+	1.15017e9i	1.19919	+	0.779357i
$15$	1.06112e9			0.414032
$16$	2.04541e9	−	3.54275e9i	0.476234	−	0.824862i
$17$	4.97420e9	−	2.87185e9i	0.713069	−	0.411690i	−0.0991274	−	0.995075i	$-0.531605\pi$
$17$	4.97420e9	−	2.87185e9i	0.713069	−	0.411690i	0.812196	+	0.583384i	$0.198272\pi$
$18$	−9.26471e8	−	1.60470e9i	−0.0840721	−	0.145617i
$19$	−7.94173e9	−	4.58516e9i	−0.467613	−	0.269976i	0.247627	−	0.968855i	$-0.420349\pi$
$19$	−7.94173e9	−	4.58516e9i	−0.467613	−	0.269976i	−0.715240	+	0.698879i	$0.753683\pi$
$20$			1.17962e10i			0.460789i
$21$	1.61193e10	+	3.16631e10i	0.426179	+	0.837141i
$22$	−1.57643e10			−0.287271
$23$	−2.03156e10	+	3.51877e10i	−0.259423	+	0.449333i	−0.966087	−	0.258215i	$-0.916866\pi$
$23$	−2.03156e10	+	3.51877e10i	−0.259423	+	0.449333i	0.706665	+	0.707549i	$0.250199\pi$
$24$	−5.82282e9	+	3.36180e9i	−0.0528985	+	0.0305409i
$25$	−6.14730e10	−	1.06474e11i	−0.402869	−	0.697790i
$26$	−3.09443e11	−	1.78657e11i	−1.48181	−	0.855525i
$27$		−	2.96500e11i		−	1.04982i
$28$	−3.51991e11	+	1.79194e11i	−0.931681	+	0.474308i
$29$	6.70144e11			1.33963			0.669814	−	0.742529i	$-0.266374\pi$
$29$	6.70144e11			1.33963			0.669814	+	0.742529i	$0.266374\pi$
$30$	−1.94254e11	+	3.36458e11i	−0.296074	+	0.512815i
$31$	9.28533e11	−	5.36089e11i	1.08869	−	0.628555i	0.155461	−	0.987842i	$-0.450314\pi$
$31$	9.28533e11	−	5.36089e11i	1.08869	−	0.628555i	0.933227	+	0.359287i	$0.116980\pi$
$32$	7.84634e11	+	1.35903e12i	0.713621	+	1.23603i
$33$	−2.29815e11	−	1.32684e11i	−0.163406	−	0.0943424i
$34$			2.10295e12i			1.17760i
$35$	−5.40852e11	+	8.32206e11i	−0.240178	+	0.369561i
$36$	3.46749e11			0.122912
$37$	2.44056e12	−	4.22717e12i	0.694825	−	1.20347i	−0.275414	−	0.961326i	$-0.588815\pi$
$37$	2.44056e12	−	4.22717e12i	0.694825	−	1.20347i	0.970240	−	0.242147i	$-0.0778516\pi$
$38$	2.90771e12	−	1.67877e12i	0.668778	−	0.386119i
$39$	−3.00742e12	−	5.20901e12i	−0.561924	−	0.973281i
$40$	−1.62658e11	−	9.39106e10i	−0.0248196	−	0.0143296i
$41$			9.25310e12i			1.15882i	0.815036	+	0.579411i	$0.196717\pi$
$41$			9.25310e12i			1.15882i	−0.815036	+	0.579411i	$0.803283\pi$
$42$	−1.29906e13	−	6.85325e11i	−1.34163	−	0.0707786i
$43$	−6.77014e12			−0.579229			−0.289614	−	0.957143i	$-0.593527\pi$
$43$	−6.77014e12			−0.579229			−0.289614	+	0.957143i	$0.593527\pi$
$44$	1.47502e12	−	2.55480e12i	0.104997	−	0.181860i
$45$	7.54588e11	−	4.35661e11i	0.0448755	−	0.0259089i
$46$	−7.43818e12	−	1.28833e13i	−0.371026	−	0.642635i
$47$	1.13952e13	+	6.57901e12i	0.478562	+	0.276298i	0.719817	−	0.694164i	$-0.244226\pi$
$47$	1.13952e13	+	6.57901e12i	0.478562	+	0.276298i	−0.241255	+	0.970462i	$0.577559\pi$
$48$			2.52128e13i			0.894729i
$49$	−3.30485e13	−	3.49672e12i	−0.994449	−	0.105218i
$50$	4.50143e13			1.15237
$51$	−1.77000e13	+	3.06573e13i	−0.386733	+	0.669842i
$52$	5.79073e13	−	3.34328e13i	1.08320	−	0.625383i
$53$	−5.78861e13	−	1.00262e14i	−0.929752	−	1.61038i	−0.783735	−	0.621095i	$-0.786688\pi$
$53$	−5.78861e13	−	1.00262e14i	−0.929752	−	1.61038i	−0.146017	−	0.989282i	$-0.546645\pi$
$54$	9.40137e13	+	5.42788e13i	1.30029	+	0.750724i
$55$		−	7.41295e12i		−	0.0885298i
$56$	3.31315e11	−	6.28018e12i	0.00342560	−	0.0649334i
$57$	5.65191e13			0.507220
$58$	−1.22680e14	+	2.12488e14i	−0.957966	+	1.65925i
$59$	1.76124e14	−	1.01685e14i	1.19951	−	0.692535i	0.239061	−	0.971004i	$-0.423160\pi$
$59$	1.76124e14	−	1.01685e14i	1.19951	−	0.692535i	0.960445	+	0.278469i	$0.0898269\pi$
$60$	−3.63516e13	−	6.29628e13i	−0.216428	−	0.374864i
$61$	−7.45549e13	−	4.30443e13i	−0.388900	−	0.224531i	0.292784	−	0.956179i	$-0.405418\pi$
$61$	−7.45549e13	−	4.30443e13i	−0.388900	−	0.224531i	−0.681683	+	0.731647i	$0.738752\pi$
$62$			3.92557e14i			1.79791i
$63$	2.44627e13	+	1.58983e13i	0.0985779	+	0.0640658i
$64$	−3.06461e14			−1.08877
$65$	8.40111e13	−	1.45512e14i	0.263651	−	0.456657i
$66$	8.41425e13	−	4.85797e13i	0.233703	−	0.134928i
$67$	−3.69776e14	−	6.40471e14i	−0.910627	−	1.57725i	−0.813181	−	0.582011i	$-0.802266\pi$
$67$	−3.69776e14	−	6.40471e14i	−0.910627	−	1.57725i	−0.0974454	−	0.995241i	$-0.531067\pi$
$68$	−3.40810e14	−	1.96767e14i	−0.745488	−	0.430408i
$69$		−	2.50421e14i		−	0.487392i
$70$	−1.64863e14	−	3.23840e14i	−0.285983	−	0.561755i
$71$	6.18883e14			0.958389			0.479194	−	0.877709i	$-0.340929\pi$
$71$	6.18883e14			0.958389			0.479194	+	0.877709i	$0.340929\pi$
$72$	−2.76050e12	+	4.78132e12i	−0.00382232	+	0.00662046i
$73$	−1.06453e15	+	6.14609e14i	−1.32001	+	0.762107i	−0.983730	−	0.179655i	$-0.942502\pi$
$73$	−1.06453e15	+	6.14609e14i	−1.32001	+	0.762107i	−0.336279	+	0.941763i	$0.609168\pi$
$74$	8.93563e14	+	1.54770e15i	0.993737	+	1.72120i
$75$	6.56230e14	+	3.78874e14i	0.655489	+	0.378447i
$76$			6.28310e14i			0.564501i
$77$	2.21197e14	−	1.12609e14i	0.179000	−	0.0911270i
$78$	2.20222e15			1.60732
$79$	6.89263e14	−	1.19384e15i	0.454327	−	0.786917i	−0.544322	−	0.838876i	$-0.683213\pi$
$79$	6.89263e14	−	1.19384e15i	0.454327	−	0.786917i	0.998649	+	0.0519590i	$0.0165465\pi$
$80$	−6.09950e14	+	3.52155e14i	−0.363558	+	0.209901i
$81$	8.04777e14	+	1.39391e15i	0.434305	+	0.752239i
$82$	−2.93396e15	−	1.69392e15i	−1.43530	−	0.828672i
$83$		−	1.94472e13i		−	0.00863441i	−0.999991	−	0.00431720i	$-0.998626\pi$
$83$		−	1.94472e13i		−	0.00863441i	0.999991	−	0.00431720i	$-0.00137421\pi$
$84$	1.32655e15	−	2.04116e15i	0.535169	−	0.823462i
$85$	−9.88884e14			−0.362906
$86$	1.23938e15	−	2.14667e15i	0.414206	−	0.717425i
$87$	−3.57692e15	+	2.06514e15i	−1.08982	+	0.629209i
$88$	2.34855e13	+	4.06780e13i	0.00653037	+	0.0113109i
$89$	−4.18619e15	−	2.41690e15i	−1.06341	−	0.613958i	−0.137034	−	0.990566i	$-0.543757\pi$
$89$	−4.18619e15	−	2.41690e15i	−1.06341	−	0.613958i	−0.926372	+	0.376609i	$0.877090\pi$
$90$			3.19018e14i			0.0741097i
$91$	5.61816e15	+	2.96390e14i	1.19471	+	0.0630278i
$92$	2.78388e15			0.542435
$93$	−3.30406e15	+	5.72279e15i	−0.590451	+	1.02269i
$94$	−4.17212e15	+	2.40878e15i	−0.684438	+	0.395161i
$95$	7.89419e14	+	1.36731e15i	0.118992	+	0.206101i
$96$	−8.37604e15	−	4.83591e15i	−1.16110	−	0.670360i
$97$			6.78438e15i			0.865638i	0.901481	+	0.432819i	$0.142481\pi$
$97$			6.78438e15i			0.865638i	−0.901481	+	0.432819i	$0.857519\pi$
$98$	7.15876e15	−	9.83882e15i	0.841452	−	1.15647i
$99$	−2.17903e14			−0.0236147
$100$	−4.21186e15	+	7.29515e15i	−0.421186	+	0.729515i
$101$	7.18599e15	−	4.14883e15i	0.663614	−	0.383138i	−0.130038	−	0.991509i	$-0.541510\pi$
$101$	7.18599e15	−	4.14883e15i	0.663614	−	0.383138i	0.793653	+	0.608371i	$0.208177\pi$
$102$	−6.48051e15	−	1.12246e16i	−0.553105	−	0.958006i
$103$	8.00090e15	+	4.61932e15i	0.631598	+	0.364653i	0.781371	−	0.624067i	$-0.214521\pi$
$103$	8.00090e15	+	4.61932e15i	0.631598	+	0.364653i	−0.149773	+	0.988720i	$0.547854\pi$
$104$			1.06465e15i			0.0777926i
$105$	3.22265e14	−	6.10864e15i	0.0218122	−	0.413457i
$106$	4.23877e16			2.65946
$107$	9.78136e14	−	1.69418e15i	0.0569284	−	0.0986029i	−0.836157	−	0.548491i	$-0.815203\pi$
$107$	9.78136e14	−	1.69418e15i	0.0569284	−	0.0986029i	0.893085	+	0.449888i	$0.148536\pi$
$108$	−1.75932e16	+	1.01574e16i	−0.950505	+	0.548774i
$109$	−4.83379e14	−	8.37236e14i	−0.0242591	−	0.0420181i	0.853641	−	0.520862i	$-0.174389\pi$
$109$	−4.83379e14	−	8.37236e14i	−0.0242591	−	0.0420181i	−0.877900	+	0.478844i	$0.841056\pi$
$110$	2.35049e15	+	1.35705e15i	0.109652	+	0.0633075i
$111$			3.00836e16i			1.30541i
$112$	−1.97737e16	−	1.28510e16i	−0.798627	−	0.519028i
$113$	6.68974e15			0.251641			0.125821	−	0.992053i	$-0.459844\pi$
$113$	6.68974e15			0.251641			0.125821	+	0.992053i	$0.459844\pi$
$114$	−1.03467e16	+	1.79210e16i	−0.362712	+	0.628236i
$115$	6.05821e15	−	3.49771e15i	0.198044	−	0.114341i
$116$	−2.29576e16	−	3.97638e16i	−0.700267	−	1.21290i
$117$	−4.27731e15	−	2.46950e15i	−0.121810	−	0.0703271i
$118$			7.44602e16i			1.98092i
$119$	−1.50220e16	−	2.95076e16i	−0.373553	−	0.733767i
$120$	1.15759e15			0.0269219
$121$	2.20479e16	−	3.81881e16i	0.479827	−	0.831085i
$122$	2.72968e16	−	1.57598e16i	0.556203	−	0.321124i
$123$	−2.85147e16	−	4.93888e16i	−0.544286	−	0.942731i
$124$	−6.36190e16	−	3.67304e16i	−1.13819	−	0.657132i
$125$			4.74382e16i			0.795881i
$126$	−9.51928e15	+	4.84615e15i	−0.149844	+	0.0762839i
$127$	−3.14501e16			−0.464721			−0.232361	−	0.972630i	$-0.574645\pi$
$127$	−3.14501e16			−0.464721			−0.232361	+	0.972630i	$0.574645\pi$
$128$	4.68061e15	−	8.10705e15i	0.0649565	−	0.112508i
$129$	3.61359e16	−	2.08631e16i	0.471218	−	0.272058i
$130$	3.07590e16	+	5.32762e16i	0.377073	+	0.653110i
$131$	−3.80903e16	−	2.19915e16i	−0.439182	−	0.253562i	0.264069	−	0.964504i	$-0.414935\pi$
$131$	−3.80903e16	−	2.19915e16i	−0.439182	−	0.253562i	−0.703251	+	0.710942i	$0.748269\pi$
$132$			1.81818e16i			0.197263i
$133$	−2.88078e16	+	4.43264e16i	−0.294236	+	0.452740i
$134$	2.70773e17			2.60475
$135$	−2.55239e16	+	4.42088e16i	−0.231354	+	0.400717i
$136$	5.42643e15	−	3.13295e15i	0.0463664	−	0.0267696i
$137$	3.94862e16	+	6.83920e16i	0.318185	+	0.551113i	0.980109	−	0.198458i	$-0.0635932\pi$
$137$	3.94862e16	+	6.83920e16i	0.318185	+	0.551113i	−0.661924	+	0.749571i	$0.730260\pi$
$138$	7.94032e16	+	4.58435e16i	0.603678	+	0.348534i
$139$		−	2.85397e16i		−	0.204801i	−0.994743	−	0.102400i	$-0.967348\pi$
$139$		−	2.85397e16i		−	0.204801i	0.994743	−	0.102400i	$-0.0326523\pi$
$140$	6.79084e16	+	3.58255e15i	0.460150	+	0.0242755i
$141$	−8.10964e16			−0.519097
$142$	−1.13296e17	+	1.96234e17i	−0.685342	+	1.18705i
$143$	−3.63900e16	+	2.10098e16i	−0.208110	+	0.120153i
$144$	1.03516e16	+	1.79294e16i	0.0559895	+	0.0969766i
$145$	−9.99198e16	−	5.76887e16i	−0.511338	−	0.295221i
$146$		−	4.50054e17i		−	2.17993i
$147$	1.87173e17	−	8.31793e16i	0.858430	−	0.381484i
$148$	−3.34433e17			−1.45283
$149$	2.37381e17	−	4.11155e17i	0.977136	−	1.69245i	0.304439	−	0.952532i	$-0.401531\pi$
$149$	2.37381e17	−	4.11155e17i	0.977136	−	1.69245i	0.672697	−	0.739918i	$-0.265136\pi$
$150$	−2.40266e17	+	1.38717e17i	−0.937479	+	0.541254i
$151$	−5.19660e16	−	9.00077e16i	−0.192266	−	0.333015i	0.753735	−	0.657179i	$-0.228250\pi$
$151$	−5.19660e16	−	9.00077e16i	−0.192266	−	0.333015i	−0.946001	+	0.324164i	$0.894917\pi$
$152$	−8.66376e15	−	5.00203e15i	−0.0304059	−	0.0175549i
$153$			2.90682e16i			0.0968025i
$154$	−4.78766e15	+	9.07517e16i	−0.0151341	+	0.286872i
$155$	−1.84595e17			−0.554072
$156$	−2.06055e17	+	3.56898e17i	−0.587472	+	1.01753i
$157$	−4.63040e17	+	2.67336e17i	−1.25436	+	0.724203i	−0.971972	−	0.235098i	$-0.924459\pi$
$157$	−4.63040e17	+	2.67336e17i	−1.25436	+	0.724203i	−0.282385	+	0.959301i	$0.591126\pi$
$158$	2.52360e17	+	4.37101e17i	0.649777	+	1.12545i
$159$	6.17939e17	+	3.56767e17i	1.51275	+	0.873389i
$160$		−	2.70178e17i		−	0.629058i
$161$	1.96399e17	+	1.27640e17i	0.435042	+	0.282734i
$162$	−5.89307e17			−1.24229
$163$	3.62115e17	−	6.27201e17i	0.726683	−	1.25865i	−0.231594	−	0.972813i	$-0.574394\pi$
$163$	3.62115e17	−	6.27201e17i	0.726683	−	1.25865i	0.958277	−	0.285840i	$-0.0922726\pi$
$164$	5.49044e17	−	3.16991e17i	1.04920	−	0.605753i
$165$	2.28440e16	+	3.95669e16i	0.0415815	+	0.0720213i
$166$	6.16629e15	+	3.56011e15i	0.0106945	+	0.00617445i
$167$		−	3.83013e16i		−	0.0633113i	−0.999499	−	0.0316556i	$-0.989922\pi$
$167$		−	3.83013e16i		−	0.0633113i	0.999499	−	0.0316556i	$-0.0100780\pi$
$168$	1.75848e16	+	3.45417e16i	0.0277117	+	0.0544340i
$169$	−2.87001e17			−0.431310
$170$	1.81030e17	−	3.13554e17i	0.259514	−	0.449491i
$171$	4.01921e16	−	2.32049e16i	0.0549759	−	0.0317403i
$172$	2.31930e17	+	4.01715e17i	0.302782	+	0.524433i
$173$	3.84549e17	+	2.22020e17i	0.479273	+	0.276709i	0.720114	−	0.693856i	$-0.244090\pi$
$173$	3.84549e17	+	2.22020e17i	0.479273	+	0.276709i	−0.240840	+	0.970565i	$0.577423\pi$
$174$		−	1.51222e18i		−	1.79979i
$175$	−6.31621e17	+	3.21551e17i	−0.718045	+	0.365549i
$176$	1.76136e17			0.191314
$177$	−6.26713e17	+	1.08550e18i	−0.650553	+	1.12679i
$178$	1.53269e18	−	8.84901e17i	1.52088	−	0.878081i
$179$	3.53523e17	+	6.12320e17i	0.335423	+	0.580971i	0.983566	−	0.180548i	$-0.0577873\pi$
$179$	3.53523e17	+	6.12320e17i	0.335423	+	0.580971i	−0.648143	+	0.761519i	$0.724454\pi$
$180$	−5.17010e16	−	2.98496e16i	−0.0469158	−	0.0270868i
$181$			1.01550e18i			0.881562i	0.897615	+	0.440781i	$0.145298\pi$
$181$			1.01550e18i			0.881562i	−0.897615	+	0.440781i	$0.854702\pi$
$182$	−1.12247e18	+	1.72714e18i	−0.932403	+	1.43468i
$183$	5.30587e17			0.421840
$184$	−2.21627e16	+	3.83869e16i	−0.0168686	+	0.0292173i
$185$	−7.27785e17	+	4.20187e17i	−0.530431	+	0.306245i
$186$	−1.20972e18	−	2.09529e18i	−0.844461	−	1.46265i
$187$	2.14171e17	+	1.23652e17i	0.143228	+	0.0826927i
$188$		−	9.01529e17i		−	0.577720i
$189$	−1.70689e18	−	9.00480e16i	−1.04836	−	0.0553070i
$190$	−5.78061e17			−0.340365
$191$	5.01455e17	−	8.68546e17i	0.283117	−	0.490372i	−0.689034	−	0.724729i	$-0.741965\pi$
$191$	5.01455e17	−	8.68546e17i	0.283117	−	0.490372i	0.972151	+	0.234357i	$0.0752983\pi$
$192$	1.63575e18	−	9.44401e17i	0.885742	−	0.511383i
$193$	−6.15496e17	−	1.06607e18i	−0.319718	−	0.553768i	0.660711	−	0.750640i	$-0.270255\pi$
$193$	−6.15496e17	−	1.06607e18i	−0.319718	−	0.553768i	−0.980429	+	0.196873i	$0.936921\pi$
$194$	−2.15118e18	−	1.24198e18i	−1.07217	−	0.619016i
$195$			1.03557e18i			0.495337i
$196$	9.24685e17	+	2.08076e18i	0.424566	+	0.955374i
$197$	−3.52539e18			−1.55409			−0.777047	−	0.629443i	$-0.783283\pi$
$197$	−3.52539e18			−1.55409			−0.777047	+	0.629443i	$0.783283\pi$
$198$	3.98905e16	−	6.90924e16i	0.0168868	−	0.0292489i
$199$	3.22861e18	−	1.86404e18i	1.31278	−	0.757931i	0.330220	−	0.943904i	$-0.392877\pi$
$199$	3.22861e18	−	1.86404e18i	1.31278	−	0.757931i	0.982555	+	0.185973i	$0.0595437\pi$
$200$	−6.70619e16	−	1.16155e17i	−0.0261961	−	0.0453729i
$201$	3.94739e18	+	2.27903e18i	1.48164	+	0.855423i
$202$			3.03803e18i			1.09593i
$203$	2.03525e17	−	3.85788e18i	0.0705747	−	1.33777i
$204$	2.42545e18			0.808632
$205$	7.96545e17	−	1.37966e18i	0.255376	−	0.442324i
$206$	−2.92937e18	+	1.69127e18i	−0.903310	+	0.521526i
$207$	−1.02815e17	−	1.78081e17i	−0.0304996	−	0.0528268i
$208$	3.45744e18	+	1.99615e18i	0.986843	+	0.569754i
$209$		−	3.94841e17i		−	0.108456i
$210$	1.87792e18	+	1.22046e18i	0.496505	+	0.322679i
$211$	2.68626e18			0.683736			0.341868	−	0.939748i	$-0.388940\pi$
$211$	2.68626e18			0.683736			0.341868	+	0.939748i	$0.388940\pi$
$212$	−3.96610e18	+	6.86948e18i	−0.972023	+	1.68359i
$213$	−3.30331e18	+	1.90717e18i	−0.779674	+	0.450145i
$214$	3.58126e17	+	6.20292e17i	0.0814189	+	0.141022i
$215$	1.00944e18	+	5.82802e17i	0.221092	+	0.127648i
$216$		−	3.23457e17i		−	0.0682631i
$217$	−2.80415e18	−	5.50818e18i	−0.570327	−	1.12029i
$218$	3.53959e17			0.0693907
$219$	3.78800e18	−	6.56101e18i	0.715907	−	1.23999i
$220$	−4.39856e17	+	2.53951e17i	−0.0801548	+	0.0462774i
$221$	2.80270e18	+	4.85441e18i	0.492536	+	0.853097i
$222$	−9.53887e18	−	5.50727e18i	−1.61686	−	0.933496i
$223$		−	6.51769e18i		−	1.06575i	−0.846194	−	0.532875i	$-0.821112\pi$
$223$		−	6.51769e18i		−	1.06575i	0.846194	−	0.532875i	$-0.178888\pi$
$224$	8.06193e18	−	4.10424e18i	1.27191	−	0.647513i
$225$	6.22215e17			0.0947284
$226$	−1.22466e18	+	2.12117e18i	−0.179948	+	0.311680i
$227$	−1.00198e19	+	5.78494e18i	−1.42119	+	0.820525i	−0.996401	−	0.0847665i	$-0.972986\pi$
$227$	−1.00198e19	+	5.78494e18i	−1.42119	+	0.820525i	−0.424790	+	0.905292i	$0.639652\pi$
$228$	−1.93622e18	−	3.35363e18i	−0.265140	−	0.459237i
$229$	−4.79294e18	−	2.76720e18i	−0.633750	−	0.365896i	0.148453	−	0.988919i	$-0.452571\pi$
$229$	−4.79294e18	−	2.76720e18i	−0.633750	−	0.365896i	−0.782203	+	0.623024i	$0.785904\pi$
$230$			2.56124e18i			0.327060i
$231$	−8.33631e17	+	1.28270e18i	−0.102820	+	0.158209i
$232$	7.31071e17			0.0871075
$233$	−3.15840e18	+	5.47050e18i	−0.363596	+	0.629767i	−0.988550	−	0.150895i	$-0.951785\pi$
$233$	−3.15840e18	+	5.47050e18i	−0.363596	+	0.629767i	0.624954	+	0.780662i	$0.285118\pi$
$234$	1.56605e18	−	9.04161e17i	0.174213	−	0.100582i
$235$	−1.13270e18	−	1.96189e18i	−0.121779	−	0.210927i
$236$	−1.20672e19	−	6.96703e18i	−1.25404	−	0.724021i
$237$			8.49622e18i			0.853570i
$238$	1.21062e19	+	6.38672e17i	1.17596	+	0.0620386i
$239$	7.72016e18			0.725176			0.362588	−	0.931950i	$-0.381893\pi$
$239$	7.72016e18			0.725176			0.362588	+	0.931950i	$0.381893\pi$
$240$	2.17042e18	−	3.75928e18i	0.197176	−	0.341519i
$241$	−5.81471e18	+	3.35713e18i	−0.510966	+	0.295006i	−0.733231	−	0.679980i	$-0.761988\pi$
$241$	−5.81471e18	+	3.35713e18i	−0.510966	+	0.295006i	0.222265	+	0.974986i	$0.428655\pi$
$242$	8.07242e18	+	1.39818e19i	0.686248	+	1.18862i
$243$	2.46232e18	+	1.42162e18i	0.202532	+	0.116932i
$244$			5.89841e18i			0.469479i
$245$	4.62658e18	+	3.36632e18i	0.356395	+	0.259314i
$246$	2.08802e19			1.55687
$247$	4.47474e18	−	7.75048e18i	0.322992	−	0.559439i
$248$	1.01295e18	−	5.84828e17i	0.0707905	−	0.0408709i
$249$	5.99292e16	+	1.03800e17i	0.00405549	+	0.00702432i
$250$	−1.50416e19	−	8.68429e18i	−0.985768	−	0.569133i
$251$			1.28466e18i			0.0815451i	0.999168	+	0.0407726i	$0.0129819\pi$
$251$			1.28466e18i			0.0815451i	−0.999168	+	0.0407726i	$0.987018\pi$
$252$	1.05309e17	−	1.99616e18i	0.00647531	−	0.122742i
$253$	−1.74944e18			−0.104216
$254$	5.75743e18	−	9.97216e18i	0.332322	−	0.575598i
$255$	5.27821e18	−	3.04738e18i	0.295233	−	0.170453i
$256$	−8.32840e18	−	1.44252e19i	−0.451484	−	0.781993i
$257$	6.23849e18	+	3.60180e18i	0.327804	+	0.189258i	0.654866	−	0.755745i	$-0.272725\pi$
$257$	6.23849e18	+	3.60180e18i	0.327804	+	0.189258i	−0.327062	+	0.945003i	$0.606058\pi$
$258$			1.52772e19i			0.778192i
$259$	−2.35938e19	−	1.53336e19i	−1.16520	−	0.757262i
$260$	−1.15121e19			−0.551276
$261$	−1.69576e18	+	2.93714e18i	−0.0787481	+	0.136396i
$262$	1.39460e19	−	8.05175e18i	0.628117	−	0.362644i
$263$	3.13166e18	+	5.42419e18i	0.136813	+	0.236968i	0.926289	−	0.376815i	$-0.122981\pi$
$263$	3.13166e18	+	5.42419e18i	0.136813	+	0.236968i	−0.789475	+	0.613782i	$0.789647\pi$
$264$	−2.50709e17	−	1.44747e17i	−0.0106253	−	0.00613449i
$265$			1.99323e19i			0.819578i
$266$	−8.78124e18	−	1.72489e19i	−0.350350	−	0.688191i
$267$	2.97920e19			1.15348
$268$	−2.53354e19	+	4.38822e19i	−0.952028	+	1.64896i
$269$	−1.09741e19	+	6.33588e18i	−0.400266	+	0.231094i	−0.686599	−	0.727036i	$-0.740897\pi$
$269$	−1.09741e19	+	6.33588e18i	−0.400266	+	0.231094i	0.286333	+	0.958130i	$0.407564\pi$
$270$	−9.34509e18	−	1.61862e19i	−0.330882	−	0.573105i
$271$	4.10827e19	+	2.37191e19i	1.41223	+	0.815350i	0.995598	−	0.0937269i	$-0.0298780\pi$
$271$	4.10827e19	+	2.37191e19i	1.41223	+	0.815350i	0.416629	+	0.909077i	$0.363211\pi$
$272$		−	2.34965e19i		−	0.784244i
$273$	−3.09006e19	+	1.57311e19i	−1.00153	+	0.509869i
$274$	−2.89142e19			−0.910136
$275$	2.64681e18	−	4.58440e18i	0.0809209	−	0.140159i
$276$	−1.48591e19	+	8.57889e18i	−0.441285	+	0.254776i
$277$	−1.67888e19	−	2.90791e19i	−0.484376	−	0.838963i	0.515463	−	0.856912i	$-0.327620\pi$
$277$	−1.67888e19	−	2.90791e19i	−0.484376	−	0.838963i	−0.999839	+	0.0179485i	$0.994287\pi$
$278$	9.04934e18	+	5.22464e18i	0.253664	+	0.146453i
$279$			5.42616e18i			0.147795i
$280$	−5.90024e17	+	9.07868e17i	−0.0156173	+	0.0240302i
$281$	−2.67935e19			−0.689255			−0.344627	−	0.938740i	$-0.611995\pi$
$281$	−2.67935e19			−0.689255			−0.344627	+	0.938740i	$0.611995\pi$
$282$	1.48459e19	−	2.57139e19i	0.371206	−	0.642947i
$283$	5.45677e19	−	3.15047e19i	1.32631	−	0.765743i	0.341580	−	0.939853i	$-0.389038\pi$
$283$	5.45677e19	−	3.15047e19i	1.32631	−	0.765743i	0.984726	+	0.174109i	$0.0557047\pi$
$284$	−2.12016e19	−	3.67222e19i	−0.500981	−	0.867724i
$285$	−8.42712e18	−	4.86540e18i	−0.193607	−	0.111779i
$286$		−	1.53846e19i		−	0.343684i
$287$	5.32682e19	+	2.81020e18i	1.15721	+	0.0610495i
$288$	−7.94188e18			−0.167797
$289$	−7.83552e18	+	1.35715e19i	−0.161022	+	0.278898i
$290$	3.65837e19	−	2.11216e19i	0.731314	−	0.422224i
$291$	−2.09070e19	−	3.62119e19i	−0.406581	−	0.704219i
$292$	7.29372e19	+	4.21103e19i	1.38002	+	0.796756i
$293$			4.43533e19i			0.816555i	0.912858	+	0.408277i	$0.133870\pi$
$293$			4.43533e19i			0.816555i	−0.912858	+	0.408277i	$0.866130\pi$
$294$	−7.89055e18	+	7.45758e19i	−0.141361	+	1.33604i
$295$	−3.50140e19			−0.610471
$296$	2.66245e18	−	4.61149e18i	0.0451801	−	0.0782542i
$297$	1.10559e19	−	6.38311e18i	0.182617	−	0.105434i
$298$	8.69123e19	+	1.50537e20i	1.39750	+	2.42054i
$299$	−3.43404e19	−	1.98264e19i	−0.537570	−	0.310366i
$300$		−	5.19176e19i		−	0.791306i
$301$	−2.05612e18	+	3.89743e19i	−0.0305152	+	0.578424i
$302$	3.80527e19			0.549958
$303$	−2.55704e19	+	4.42892e19i	−0.359912	+	0.623385i
$304$	−3.24882e19	+	1.87571e19i	−0.445386	+	0.257144i
$305$	7.41086e18	+	1.28360e19i	0.0989624	+	0.171408i
$306$	−9.21690e18	−	5.32138e18i	−0.119898	−	0.0692234i
$307$		−	1.16989e20i		−	1.48265i	−0.671144	−	0.741327i	$-0.734197\pi$
$307$		−	1.16989e20i		−	1.48265i	0.671144	−	0.741327i	$-0.265803\pi$
$308$	−1.42595e19	−	9.26728e18i	−0.176076	−	0.114432i
$309$	−5.69402e19			−0.685095
$310$	3.37929e19	−	5.85310e19i	0.396216	−	0.686266i
$311$	3.71699e19	−	2.14600e19i	0.424725	−	0.245215i	−0.272372	−	0.962192i	$-0.587808\pi$
$311$	3.71699e19	−	2.14600e19i	0.424725	−	0.245215i	0.697097	+	0.716977i	$0.254475\pi$
$312$	−3.28085e18	−	5.68259e18i	−0.0365384	−	0.0632863i
$313$	−7.14696e19	−	4.12630e19i	−0.775830	−	0.447926i	0.0591202	−	0.998251i	$-0.481170\pi$
$313$	−7.14696e19	−	4.12630e19i	−0.775830	−	0.447926i	−0.834950	+	0.550325i	$0.814504\pi$
$314$		−	1.95760e20i		−	2.07151i
$315$	−2.27884e18	−	4.47632e18i	−0.0235088	−	0.0461782i
$316$	−9.44505e19			−0.949965
$317$	2.36350e19	−	4.09371e19i	0.231783	−	0.401461i	−0.726550	−	0.687114i	$-0.758877\pi$
$317$	2.36350e19	−	4.09371e19i	0.231783	−	0.401461i	0.958333	+	0.285653i	$0.0922106\pi$
$318$	−2.26246e20	+	1.30623e20i	−2.16354	+	1.24912i
$319$	1.44270e19	+	2.49883e19i	0.134540	+	0.233029i
$320$	4.56940e19	+	2.63814e19i	0.415585	+	0.239938i
$321$			1.20570e19i			0.106955i
$322$	−7.64255e19	+	3.89074e19i	−0.661289	+	0.336655i
$323$	−5.26716e19			−0.444587
$324$	5.51397e19	−	9.55048e19i	0.454051	−	0.786439i
$325$	1.03910e20	−	5.99926e19i	0.834818	−	0.481982i
$326$	1.32581e20	+	2.29637e20i	1.03930	+	1.80012i
$327$	5.16011e18	+	2.97919e18i	0.0394709	+	0.0227885i
$328$			1.00944e19i			0.0753508i
$329$	4.13348e19	−	6.36016e19i	0.301126	−	0.463341i
$330$	−1.67278e19			−0.118940
$331$	−1.10405e18	+	1.91228e18i	−0.00766243	+	0.0132717i	−0.869831	−	0.493349i	$-0.835772\pi$
$331$	−1.10405e18	+	1.91228e18i	−0.00766243	+	0.0132717i	0.862169	+	0.506621i	$0.169106\pi$
$332$	−1.15392e18	+	6.66218e17i	−0.00781758	+	0.00451348i
$333$	1.23514e19	+	2.13932e19i	0.0816886	+	0.141489i
$334$	1.21445e19	+	7.01163e18i	0.0784166	+	0.0452738i
$335$			1.27327e20i			0.802719i
$336$	1.45145e20	+	7.65722e18i	0.893486	+	0.0471364i
$337$	4.48963e18			0.0269881			0.0134940	−	0.999909i	$-0.495705\pi$
$337$	4.48963e18			0.0269881			0.0134940	+	0.999909i	$0.495705\pi$
$338$	5.25399e19	−	9.10017e19i	0.308429	−	0.534215i
$339$	−3.57068e19	+	2.06153e19i	−0.204717	+	0.118193i
$340$	3.38770e19	+	5.86767e19i	0.189703	+	0.328575i
$341$	3.99793e19	+	2.30820e19i	0.218675	+	0.126252i
$342$			1.69921e19i			0.0907899i
$343$	−3.01668e19	+	1.89191e20i	−0.157462	+	0.987525i
$344$	−7.38566e18			−0.0376636
$345$	−2.15573e19	+	3.73384e19i	−0.107409	+	0.186038i
$346$	−1.40795e20	+	8.12882e19i	−0.685456	+	0.395748i
$347$	−1.52261e20	−	2.63725e20i	−0.724360	−	1.25463i	−0.959237	−	0.282603i	$-0.908802\pi$
$347$	−1.52261e20	−	2.63725e20i	−0.724360	−	1.25463i	0.234877	−	0.972025i	$-0.424531\pi$
$348$	2.45075e20	+	1.41494e20i	1.13937	+	0.657816i
$349$		−	1.66082e20i		−	0.754604i	−0.926090	−	0.377302i	$-0.876852\pi$
$349$		−	1.66082e20i		−	0.754604i	0.926090	−	0.377302i	$-0.123148\pi$
$350$	1.36710e19	−	2.59138e20i	0.0607094	−	1.15077i
$351$	2.89360e20			1.25598
$352$	−3.37835e19	+	5.85148e19i	−0.143339	+	0.248270i
$353$	3.53893e20	−	2.04320e20i	1.46782	−	0.847448i	0.468473	−	0.883478i	$-0.344804\pi$
$353$	3.53893e20	−	2.04320e20i	1.46782	−	0.847448i	0.999351	+	0.0360296i	$0.0114711\pi$
$354$	−2.29459e20	−	3.97435e20i	−0.930420	−	1.61153i
$355$	−9.22767e19	−	5.32760e19i	−0.365818	−	0.211205i
$356$			3.31191e20i			1.28374i
$357$	1.71112e20	+	1.11206e20i	0.648538	+	0.421485i
$358$	−2.58871e20			−0.959444
$359$	−2.28764e20	+	3.96231e20i	−0.829148	+	1.43613i	0.0695599	+	0.997578i	$0.477841\pi$
$359$	−2.28764e20	+	3.96231e20i	−0.829148	+	1.43613i	−0.898708	+	0.438548i	$0.855493\pi$
$360$	8.23192e17	−	4.75270e17i	0.00291797	−	0.00168469i
$361$	−1.02173e20	−	1.76969e20i	−0.354226	−	0.613537i
$362$	−3.21994e20	−	1.85903e20i	−1.09189	−	0.630404i
$363$			2.71775e20i			0.901479i
$364$	−1.74879e20	−	3.43514e20i	−0.567449	−	1.11464i
$365$	2.11632e20			0.671799
$366$	−9.71321e19	+	1.68238e20i	−0.301657	+	0.522486i
$367$	1.34859e19	−	7.78606e18i	0.0409779	−	0.0236586i	−0.479371	−	0.877612i	$-0.659135\pi$
$367$	1.34859e19	−	7.78606e18i	0.0409779	−	0.0236586i	0.520349	+	0.853954i	$0.325802\pi$
$368$	8.31076e19	+	1.43947e20i	0.247092	+	0.427976i
$369$	−4.05550e19	−	2.34144e19i	−0.117987	−	0.0681196i
$370$		−	3.07687e20i		−	0.875981i
$371$	−5.94766e20	+	3.02788e20i	−1.65712	+	0.843622i
$372$	4.52759e20			1.23459
$373$	−1.36620e20	+	2.36632e20i	−0.364622	+	0.631544i	−0.988715	−	0.149806i	$-0.952135\pi$
$373$	−1.36620e20	+	2.36632e20i	−0.364622	+	0.631544i	0.624093	+	0.781350i	$0.285469\pi$
$374$	−7.84145e19	+	4.52727e19i	−0.204844	+	0.118267i
$375$	−1.46187e20	−	2.53203e20i	−0.373817	−	0.647470i
$376$	1.24312e19	+	7.17715e18i	0.0311179	+	0.0179659i
$377$			6.54006e20i			1.60269i
$378$	3.41024e20	−	5.24733e20i	0.818184	−	1.25894i
$379$	7.33317e19			0.172257			0.0861287	−	0.996284i	$-0.472550\pi$
$379$	7.33317e19			0.172257			0.0861287	+	0.996284i	$0.472550\pi$
$380$	5.40875e19	−	9.36823e19i	0.124402	−	0.215471i
$381$	1.67866e20	−	9.69177e19i	0.378063	−	0.218275i
$382$	1.83598e20	+	3.18001e20i	0.404913	+	0.701329i
$383$	−1.15093e20	−	6.64491e19i	−0.248576	−	0.143515i	0.370536	−	0.928818i	$-0.379174\pi$
$383$	−1.15093e20	−	6.64491e19i	−0.248576	−	0.143515i	−0.619112	+	0.785303i	$0.712507\pi$
$384$			5.76957e19i			0.122038i
$385$	−4.26748e19	−	2.25134e18i	−0.0884068	−	0.00466396i
$386$	4.50704e20			0.914519
$387$	1.71314e19	−	2.96725e19i	0.0340491	−	0.0589748i
$388$	4.02559e20	−	2.32418e20i	0.783748	−	0.452497i
$389$	−3.21835e20	−	5.57434e20i	−0.613813	−	1.06315i	−0.990592	−	0.136852i	$-0.956302\pi$
$389$	−3.21835e20	−	5.57434e20i	−0.613813	−	1.06315i	0.376779	−	0.926303i	$-0.377032\pi$
$390$	−3.28355e20	−	1.89576e20i	−0.613518	−	0.354215i
$391$			2.33374e20i			0.427207i
$392$	−3.60531e19	−	3.81463e18i	−0.0646628	−	0.00684169i
$393$	2.71079e20			0.476381
$394$	6.45376e20	−	1.11782e21i	1.11133	−	1.92488i
$395$	−2.05541e20	+	1.18669e20i	−0.346834	+	0.200245i
$396$	7.46488e18	+	1.29296e19i	0.0123442	+	0.0213807i
$397$	4.87814e20	+	2.81639e20i	0.790551	+	0.456425i	0.840156	−	0.542344i	$-0.182463\pi$
$397$	4.87814e20	+	2.81639e20i	0.790551	+	0.456425i	−0.0496056	+	0.998769i	$0.515796\pi$
$398$			1.36496e21i			2.16798i
$399$	1.71650e19	−	3.25369e20i	0.0267216	−	0.506516i
$400$	−5.02950e20			−0.767440
$401$	6.58539e19	−	1.14062e20i	0.0984978	−	0.170603i	−0.812565	−	0.582870i	$-0.801930\pi$
$401$	6.58539e19	−	1.14062e20i	0.0984978	−	0.170603i	0.911063	+	0.412267i	$0.135263\pi$
$402$	−1.44526e21	+	8.34422e20i	−2.11903	+	1.22342i
$403$	5.23179e20	+	9.06172e20i	0.751986	+	1.30248i
$404$	−4.92352e20	−	2.84260e20i	−0.693786	−	0.400557i
$405$		−	2.77114e20i		−	0.382841i
$406$	1.18599e21	+	7.70777e20i	1.60647	+	1.04405i
$407$	2.10163e20			0.279127
$408$	−1.93092e19	+	3.34445e19i	−0.0251468	+	0.0435556i
$409$	8.77090e20	−	5.06388e20i	1.12010	−	0.646691i	0.178675	−	0.983908i	$-0.442819\pi$
$409$	8.77090e20	−	5.06388e20i	1.12010	−	0.646691i	0.941427	+	0.337217i	$0.109486\pi$
$410$	2.91640e20	+	5.05135e20i	0.365238	+	0.632610i
$411$	−4.21518e20	−	2.43364e20i	−0.517704	−	0.298897i
$412$		−	6.32991e20i		−	0.762464i
$413$	−5.31892e20	−	1.04479e21i	−0.628381	−	1.23433i
$414$	7.52875e19			0.0872408
$415$	−1.67410e18	+	2.89962e18i	−0.00190281	+	0.00329577i
$416$	−1.32630e21	+	7.65739e20i	−1.47875	+	0.853757i
$417$	8.79490e19	+	1.52332e20i	0.0961928	+	0.166611i
$418$	1.25195e20	+	7.22817e19i	0.134332	+	0.0775564i
$419$		−	1.33070e21i		−	1.40077i	−0.713763	−	0.700387i	$-0.753011\pi$
$419$		−	1.33070e21i		−	1.40077i	0.713763	−	0.700387i	$-0.246989\pi$
$420$	−3.73504e20	+	1.90147e20i	−0.385746	+	0.196379i
$421$	−4.91810e20			−0.498357			−0.249179	−	0.968458i	$-0.580161\pi$
$421$	−4.91810e20			−0.498357			−0.249179	+	0.968458i	$0.580161\pi$
$422$	−4.91761e20	+	8.51756e20i	−0.488939	+	0.846867i
$423$	−5.76696e19	+	3.32956e19i	−0.0562632	+	0.0324836i
$424$	−6.31489e19	−	1.09377e20i	−0.0604559	−	0.104713i
$425$	−6.11557e20	−	3.53083e20i	−0.574547	−	0.331715i
$426$		−	1.39655e21i		−	1.28759i
$427$	−2.70440e20	+	4.16125e20i	−0.244708	+	0.376531i
$428$	−1.34035e20			−0.119033
$429$	1.29489e20	−	2.24281e20i	0.112869	−	0.195495i
$430$	−3.69588e20	+	2.13382e20i	−0.316206	+	0.182562i
$431$	−9.08213e20	−	1.57307e21i	−0.762728	−	1.32108i	−0.941439	−	0.337182i	$-0.890526\pi$
$431$	−9.08213e20	−	1.57307e21i	−0.762728	−	1.32108i	0.178711	−	0.983902i	$-0.442807\pi$
$432$	−1.05043e21	−	6.06464e20i	−0.865955	−	0.499960i
$433$		−	1.07304e21i		−	0.868384i	−0.900820	−	0.434192i	$-0.857034\pi$
$433$		−	1.07304e21i		−	0.868384i	0.900820	−	0.434192i	$-0.142966\pi$
$434$	2.25987e21	+	1.19221e20i	1.79542	+	0.0947184i
$435$	7.11102e20			0.554649
$436$	−3.31190e19	+	5.73637e19i	−0.0253621	+	0.0439284i
$437$	3.22683e20	−	1.86301e20i	0.242619	−	0.140076i
$438$	1.38690e21	+	2.40218e21i	1.02389	+	1.77343i
$439$	2.13480e21	+	1.23253e21i	1.54754	+	0.893472i	0.998329	+	0.0577870i	$0.0184044\pi$
$439$	2.13480e21	+	1.23253e21i	1.54754	+	0.893472i	0.549209	+	0.835685i	$0.314929\pi$
$440$		−	8.08691e18i		−	0.00575653i
$441$	9.89527e19	−	1.35998e20i	0.0691702	−	0.0950658i
$442$	−2.05230e21			−1.40885
$443$	−8.86891e20	+	1.53614e21i	−0.597916	+	1.03562i	0.395212	+	0.918590i	$0.370671\pi$
$443$	−8.86891e20	+	1.53614e21i	−0.597916	+	1.03562i	−0.993128	+	0.117032i	$0.962662\pi$
$444$	1.78505e21	−	1.03060e21i	1.18192	−	0.682379i
$445$	4.16113e20	+	7.20730e20i	0.270602	+	0.468697i
$446$	2.06662e21	+	1.19316e21i	1.32002	+	0.762116i
$447$			2.92608e21i			1.83580i
$448$	−9.30733e19	+	1.76423e21i	−0.0573589	+	1.08726i
$449$	−4.92707e20			−0.298276			−0.149138	−	0.988816i	$-0.547650\pi$
$449$	−4.92707e20			−0.298276			−0.149138	+	0.988816i	$0.547650\pi$
$450$	−1.13906e20	+	1.97291e20i	−0.0677402	+	0.117329i
$451$	−3.45029e20	+	1.99203e20i	−0.201578	+	0.116381i
$452$	−2.29176e20	−	3.96944e20i	−0.131541	−	0.227836i
$453$	5.54741e20	+	3.20280e20i	0.312827	+	0.180611i
$454$		−	4.23609e21i		−	2.34703i
$455$	−8.12166e20	−	5.27827e20i	−0.442134	−	0.287343i
$456$	6.16576e19			0.0329813
$457$	2.63108e20	−	4.55717e20i	0.138295	−	0.239533i	−0.788557	−	0.614962i	$-0.789171\pi$
$457$	2.63108e20	−	4.55717e20i	0.138295	−	0.239533i	0.926851	+	0.375429i	$0.122505\pi$
$458$	1.75484e21	−	1.01316e21i	0.906387	−	0.523303i
$459$	−8.51504e20	−	1.47485e21i	−0.432201	−	0.748593i
$460$	−4.15082e20	−	2.39648e20i	−0.207048	−	0.119539i
$461$			1.93370e21i			0.947942i	0.880540	+	0.473971i	$0.157180\pi$
$461$			1.93370e21i			0.947942i	−0.880540	+	0.473971i	$0.842820\pi$
$462$	−2.54109e20	−	4.99145e20i	−0.122429	−	0.240487i
$463$	−3.43425e21			−1.62624			−0.813118	−	0.582099i	$-0.802232\pi$
$463$	−3.43425e21			−1.62624			−0.813118	+	0.582099i	$0.802232\pi$
$464$	1.37072e21	−	2.37415e21i	0.637976	−	1.10501i
$465$	9.85283e20	−	5.68854e20i	0.450752	−	0.260242i
$466$	−1.15639e21	−	2.00292e21i	−0.520014	−	0.900691i
$467$	1.58993e21	+	9.17946e20i	0.702818	+	0.405772i	0.808396	−	0.588639i	$-0.200336\pi$
$467$	1.58993e21	+	9.17946e20i	0.702818	+	0.405772i	−0.105578	+	0.994411i	$0.533669\pi$
$468$			3.38399e20i			0.147049i
$469$	−3.79936e21	+	1.93421e21i	−1.62304	+	0.826269i
$470$	8.29430e20			0.348335
$471$	1.64766e21	−	2.85384e21i	0.680302	−	1.17832i
$472$	1.92137e20	−	1.10930e20i	0.0779963	−	0.0450312i
$473$	−1.45749e20	−	2.52445e20i	−0.0581723	−	0.100757i
$474$	−2.69397e21	−	1.55536e21i	−1.05722	−	0.610387i
$475$			1.12745e21i			0.435061i
$476$	−1.23625e21	+	1.90221e21i	−0.469084	+	0.721778i
$477$	5.85909e20			0.218617
$478$	−1.41329e21	+	2.44790e21i	−0.518572	+	0.898193i
$479$	−1.31363e21	+	7.58425e20i	−0.474012	+	0.273671i	−0.717917	−	0.696128i	$-0.754905\pi$
$479$	−1.31363e21	+	7.58425e20i	−0.474012	+	0.273671i	0.243906	+	0.969799i	$0.421571\pi$
$480$	8.32590e20	+	1.44209e21i	0.295462	+	0.511755i
$481$	4.12538e21	+	2.38179e21i	1.43980	+	0.831270i
$482$		−	2.45829e21i		−	0.843835i
$483$	−1.44163e21	−	7.60539e19i	−0.486716	−	0.0256770i
$484$	−3.02125e21			−1.00329
$485$	5.84027e20	−	1.01156e21i	0.190765	−	0.330415i
$486$	−9.01531e20	+	5.20499e20i	−0.289661	+	0.167236i
$487$	−1.43212e21	−	2.48051e21i	−0.452636	−	0.783988i	0.545913	−	0.837842i	$-0.316183\pi$
$487$	−1.43212e21	−	2.48051e21i	−0.452636	−	0.783988i	−0.998549	+	0.0538536i	$0.982850\pi$
$488$	−8.13332e19	−	4.69577e19i	−0.0252877	−	0.0145999i
$489$			4.46362e21i			1.36526i
$490$	−1.91435e21	+	8.50734e20i	−0.576041	+	0.255991i
$491$	5.07694e21			1.50297			0.751485	−	0.659751i	$-0.229338\pi$
$491$	5.07694e21			1.50297			0.751485	+	0.659751i	$0.229338\pi$
$492$	−1.95370e21	+	3.38391e21i	−0.569032	+	0.985592i
$493$	3.33343e21	−	1.92455e21i	0.955246	−	0.551512i
$494$	1.63834e21	+	2.83769e21i	0.461943	+	0.800109i
$495$	3.24898e19	+	1.87580e19i	0.00901376	+	0.00520410i
$496$		−	4.38608e21i		−	1.19736i
$497$	1.87957e20	−	3.56278e21i	0.0504902	−	0.957058i
$498$	−4.38838e19			−0.0116003
$499$	7.64190e20	−	1.32362e21i	0.198791	−	0.344316i	−0.749346	−	0.662179i	$-0.769632\pi$
$499$	7.64190e20	−	1.32362e21i	0.198791	−	0.344316i	0.948137	+	0.317863i	$0.102965\pi$
$500$	2.81480e21	−	1.62513e21i	0.720590	−	0.416033i
$501$	1.18030e20	+	2.04435e20i	0.0297367	+	0.0515054i
$502$	−4.07338e20	−	2.35176e20i	−0.101001	−	0.0583128i
$503$		−	1.58284e21i		−	0.386272i	−0.981172	−	0.193136i	$-0.938134\pi$
$503$		−	1.58284e21i		−	0.386272i	0.981172	−	0.193136i	$-0.0618658\pi$
$504$	2.66867e19	+	1.73437e19i	0.00640990	+	0.00416580i
$505$	−1.42860e21			−0.337737
$506$	3.20261e20	−	5.54709e20i	0.0745247	−	0.129081i
$507$	1.53188e21	−	8.84431e20i	0.350882	−	0.202582i
$508$	1.07741e21	+	1.86613e21i	0.242925	+	0.420758i
$509$	−3.48952e21	−	2.01467e21i	−0.774503	−	0.447160i	0.0599754	−	0.998200i	$-0.480898\pi$
$509$	−3.48952e21	−	2.01467e21i	−0.774503	−	0.447160i	−0.834479	+	0.551040i	$0.814231\pi$
$510$			2.23148e21i			0.487563i
$511$	3.21488e21	+	6.31496e21i	0.691508	+	1.35832i
$512$	6.71206e21			1.42133
$513$	−1.35950e21	+	2.35472e21i	−0.283426	+	0.490909i
$514$	−2.28410e21	+	1.31873e21i	−0.468825	+	0.270676i
$515$	−7.95300e20	−	1.37750e21i	−0.160721	−	0.278377i
$516$	−2.47587e21	−	1.42945e21i	−0.492642	−	0.284427i
$517$			5.66537e20i			0.110995i
$518$	9.18115e21	−	4.67402e21i	1.77117	−	0.901680i
$519$	−2.73673e21			−0.519869
$520$	9.16491e19	−	1.58741e20i	0.0171436	−	0.0296936i
$521$	−6.66267e21	+	3.84670e21i	−1.22729	+	0.708575i	−0.966462	−	0.256810i	$-0.917328\pi$
$521$	−6.66267e21	+	3.84670e21i	−1.22729	+	0.708575i	−0.260827	+	0.965386i	$0.583995\pi$
$522$	−6.20869e20	−	1.07538e21i	−0.112625	−	0.195073i
$523$	2.33431e21	+	1.34771e21i	0.417008	+	0.240760i	0.693796	−	0.720171i	$-0.255937\pi$
$523$	2.33431e21	+	1.34771e21i	0.417008	+	0.240760i	−0.276788	+	0.960931i	$0.589270\pi$
$524$			3.01352e21i			0.530180i
$525$	2.38040e21	−	3.66271e21i	0.412454	−	0.634642i
$526$	−2.29319e21			−0.391340
$527$	3.07913e21	−	5.33322e21i	0.517540	−	0.896405i
$528$	−9.40134e20	+	5.42786e20i	−0.155639	+	0.0898582i
$529$	2.24085e21	+	3.88127e21i	0.365400	+	0.632891i
$530$	−6.32010e21	−	3.64891e21i	−1.01512	−	0.586079i
$531$			1.02923e21i			0.162839i
$532$	3.61705e21	+	1.90820e20i	0.563717	+	0.0297393i
$533$	−9.03028e21			−1.38638
$534$	−5.45388e21	+	9.44639e21i	−0.824851	+	1.42868i
$535$	−2.91684e20	+	1.68404e20i	−0.0434593	+	0.0250912i
$536$	−4.03395e20	−	6.98700e20i	−0.0592123	−	0.102559i
$537$	−3.77389e21	−	2.17886e21i	−0.545751	−	0.315090i
$538$		−	4.63952e21i		−	0.661020i
$539$	−5.81089e20	−	1.30759e21i	−0.0815703	−	0.183553i
$540$	3.49758e21			0.483746
$541$	−1.46498e21	+	2.53742e21i	−0.199643	+	0.345792i	−0.948413	−	0.317038i	$-0.897312\pi$
$541$	−1.46498e21	+	2.53742e21i	−0.199643	+	0.345792i	0.748770	+	0.662830i	$0.230645\pi$
$542$	−1.50416e22	+	8.68429e21i	−2.01976	+	1.16611i
$543$	−3.12941e21	−	5.42029e21i	−0.414060	−	0.717173i
$544$	7.80585e21	+	4.50671e21i	1.01772	+	0.587582i
$545$			1.66445e20i			0.0213845i
$546$	6.68821e20	−	1.26777e22i	0.0846777	−	1.60509i
$547$	1.24749e22			1.55646			0.778231	−	0.627978i	$-0.216117\pi$
$547$	1.24749e22			1.55646			0.778231	+	0.627978i	$0.216117\pi$
$548$	2.70542e21	−	4.68592e21i	0.332652	−	0.576170i
$549$	3.77313e20	−	2.17842e20i	0.0457218	−	0.0263975i
$550$	9.69076e20	+	1.67849e21i	0.115733	+	0.200455i
$551$	−5.32210e21	−	3.07272e21i	−0.626426	−	0.361668i
$552$		−	2.73189e20i		−	0.0316921i
$553$	−6.66335e21	−	4.33052e21i	−0.761889	−	0.495153i
$554$	1.22938e22			1.38551
$555$	2.58972e21	−	4.48553e21i	0.287680	−	0.498276i
$556$	−1.69344e21	+	9.77709e20i	−0.185426	+	0.107056i
$557$	2.16376e21	+	3.74774e21i	0.233543	+	0.404509i	0.958848	−	0.283919i	$-0.0916346\pi$
$557$	2.16376e21	+	3.74774e21i	0.233543	+	0.404509i	−0.725305	+	0.688428i	$0.758301\pi$
$558$	−1.72052e21	−	9.93341e20i	−0.183057	−	0.105688i
$559$		−	6.60711e21i		−	0.692974i
$560$	1.84204e21	+	3.61831e21i	0.190456	+	0.374112i
$561$	−1.52420e21			−0.155360
$562$	4.90497e21	−	8.49565e21i	0.492885	−	0.853702i
$563$	−4.07153e21	+	2.35070e21i	−0.403358	+	0.232879i	−0.687932	−	0.725775i	$-0.741481\pi$
$563$	−4.07153e21	+	2.35070e21i	−0.403358	+	0.232879i	0.284574	+	0.958654i	$0.408148\pi$
$564$	2.77818e21	+	4.81195e21i	0.271349	+	0.469990i
$565$	−9.97454e20	−	5.75880e20i	−0.0960518	−	0.0554555i
$566$			2.30696e22i			2.19033i
$567$	8.26889e21	−	4.20960e21i	0.774075	−	0.394073i
$568$	6.75149e20			0.0623180
$569$	−6.99227e21	+	1.21110e22i	−0.636385	+	1.10225i	0.349835	+	0.936811i	$0.386238\pi$
$569$	−6.99227e21	+	1.21110e22i	−0.636385	+	1.10225i	−0.986220	+	0.165439i	$0.947096\pi$
$570$	3.08542e21	−	1.78137e21i	0.276896	−	0.159866i
$571$	4.40599e20	+	7.63139e20i	0.0389901	+	0.0675328i	0.884862	−	0.465853i	$-0.154253\pi$
$571$	4.40599e20	+	7.63139e20i	0.0389901	+	0.0675328i	−0.845872	+	0.533386i	$0.820919\pi$
$572$	2.49328e21	+	1.43950e21i	0.217572	+	0.125615i
$573$			6.18120e21i			0.531908i
$574$	−1.06426e22	+	1.63757e22i	−0.903136	+	1.38965i
$575$	4.99545e21			0.418054
$576$	7.75481e20	−	1.34317e21i	0.0640017	−	0.110854i
$577$	1.70462e22	−	9.84163e21i	1.38746	−	0.801051i	0.394433	−	0.918925i	$-0.370941\pi$
$577$	1.70462e22	−	9.84163e21i	1.38746	−	0.801051i	0.993029	+	0.117873i	$0.0376077\pi$
$578$	−2.86882e21	−	4.96895e21i	−0.230293	−	0.398879i
$579$	6.57048e21	+	3.79347e21i	0.520198	+	0.300336i
$580$			7.90516e21i			0.617286i
$581$	−1.11954e20	−	5.90618e18i	−0.00862242	−	0.000454881i
$582$	1.53094e22			1.16298
$583$	2.49237e21	−	4.31690e21i	0.186751	−	0.323463i
$584$	−1.16132e21	+	6.70487e20i	−0.0858318	+	0.0495550i
$585$	4.25170e20	+	7.36416e20i	0.0309967	+	0.0536879i
$586$	−1.40635e22	−	8.11956e21i	−1.01137	−	0.583917i
$587$			3.52027e21i			0.249730i	0.992174	+	0.124865i	$0.0398498\pi$
$587$			3.52027e21i			0.249730i	−0.992174	+	0.124865i	$0.960150\pi$
$588$	−1.13477e22	−	8.25661e21i	−0.794125	−	0.577808i
$589$	−9.83220e21			−0.678779
$590$	6.40984e21	−	1.11022e22i	0.436547	−	0.756122i
$591$	1.88169e22	−	1.08639e22i	1.26430	−	0.729941i
$592$	−9.98389e21	−	1.72926e22i	−0.661799	−	1.14627i
$593$	−1.15289e22	−	6.65619e21i	−0.753961	−	0.435299i	0.0731626	−	0.997320i	$-0.476691\pi$
$593$	−1.15289e22	−	6.65619e21i	−0.753961	−	0.435299i	−0.827123	+	0.562021i	$0.810024\pi$
$594$			4.67410e21i			0.301583i
$595$	−3.00327e20	+	5.69280e21i	−0.0191187	+	0.362402i
$596$	−3.25285e22			−2.04312
$597$	−1.14885e22	+	1.98988e22i	−0.711984	+	1.23319i
$598$	1.25731e22	−	7.25906e21i	0.768832	−	0.443885i
$599$	−2.94803e21	−	5.10613e21i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$599$	−2.94803e21	−	5.10613e21i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$600$	7.15892e20	+	4.13320e20i	0.0426223	+	0.0246080i
$601$		−	1.41944e22i		−	0.833913i	−0.908926	−	0.416956i	$-0.863097\pi$
$601$		−	1.41944e22i		−	0.833913i	0.908926	−	0.416956i	$-0.136903\pi$
$602$	−1.19815e22	−	7.78679e21i	−0.694608	−	0.451426i
$603$	3.74278e21			0.214119
$604$	−3.56048e21	+	6.16693e21i	−0.201008	+	0.348156i
$605$	−6.57479e21	+	3.79596e21i	−0.366302	+	0.211484i
$606$	−9.36209e21	−	1.62156e22i	−0.514745	−	0.891564i
$607$	−8.59174e21	−	4.96044e21i	−0.466199	−	0.269160i	0.248448	−	0.968645i	$-0.420079\pi$
$607$	−8.59174e21	−	4.96044e21i	−0.466199	−	0.269160i	−0.714647	+	0.699485i	$0.753413\pi$
$608$		−	1.43907e22i		−	0.770642i
$609$	1.08022e22	+	2.12188e22i	0.570921	+	1.12146i
$610$	−5.42669e21			−0.283072
$611$	−6.42058e21	+	1.11208e22i	−0.330556	+	0.572539i
$612$	1.72480e21	−	9.95812e20i	0.0876449	−	0.0506018i
$613$	1.52319e21	+	2.63824e21i	0.0763957	+	0.132321i	0.901692	−	0.432378i	$-0.142325\pi$
$613$	1.52319e21	+	2.63824e21i	0.0763957	+	0.132321i	−0.825297	+	0.564699i	$0.808992\pi$
$614$	3.70948e22	+	2.14167e22i	1.83640	+	1.06024i
$615$			9.81864e21i			0.479789i
$616$	2.41308e20	−	1.22847e20i	0.0116393	−	0.00592542i
$617$	2.74214e22			1.30560			0.652798	−	0.757532i	$-0.273595\pi$
$617$	2.74214e22			1.30560			0.652798	+	0.757532i	$0.273595\pi$
$618$	1.04238e22	−	1.80545e22i	0.489911	−	0.848550i
$619$	−1.70049e22	+	9.81777e21i	−0.788948	+	0.455499i	−0.839592	−	0.543218i	$-0.817206\pi$
$619$	−1.70049e22	+	9.81777e21i	−0.788948	+	0.455499i	0.0506443	+	0.998717i	$0.483873\pi$
$620$	6.32381e21	+	1.09532e22i	0.289631	+	0.501656i
$621$	1.04332e22	+	6.02359e21i	0.471719	+	0.272347i
$622$			1.57143e22i			0.701412i
$623$	−1.51850e22	+	2.33650e22i	−0.669128	+	1.02958i
$624$	−2.46056e22			−1.07043
$625$	−5.29636e21	+	9.17356e21i	−0.227477	+	0.394001i
$626$	2.61672e22	−	1.51076e22i	1.10959	−	0.640622i
$627$	1.21675e21	+	2.10748e21i	0.0509404	+	0.0882314i
$628$	3.17255e22	+	1.83167e22i	1.31139	+	0.757129i
$629$		−	2.80357e22i		−	1.14421i
$630$	1.83652e21	+	9.68868e19i	0.0740068	+	0.00390428i
$631$	4.71844e21			0.187743			0.0938715	−	0.995584i	$-0.470076\pi$
$631$	4.71844e21			0.187743			0.0938715	+	0.995584i	$0.470076\pi$
$632$	7.51929e20	−	1.30238e21i	0.0295420	−	0.0511683i
$633$	−1.43380e22	+	8.27807e21i	−0.556237	+	0.321144i
$634$	8.65351e21	+	1.49883e22i	0.331496	+	0.574168i
$635$	4.68928e21	+	2.70736e21i	0.177385	+	0.102413i
$636$		−	4.88882e22i		−	1.82620i
$637$	3.41251e21	−	3.22526e22i	0.125881	−	1.18973i
$638$	−1.05643e22			−0.384836
$639$	−1.56605e21	+	2.71247e21i	−0.0563375	+	0.0975794i
$640$	−1.39578e21	+	8.05852e20i	−0.0495880	+	0.0286296i
$641$	1.20711e22	+	2.09077e22i	0.423527	+	0.733571i	0.996282	−	0.0861561i	$-0.0274584\pi$
$641$	1.20711e22	+	2.09077e22i	0.423527	+	0.733571i	−0.572754	+	0.819727i	$0.694125\pi$
$642$	−3.82302e21	−	2.20722e21i	−0.132473	−	0.0764832i
$643$		−	5.46955e22i		−	1.87182i	−0.352239	−	0.935910i	$-0.614580\pi$
$643$		−	5.46955e22i		−	1.87182i	0.352239	−	0.935910i	$-0.385420\pi$
$644$	8.45473e20	−	1.60262e22i	0.0285767	−	0.541681i
$645$	−7.18393e21			−0.239819
$646$	9.64234e21	−	1.67010e22i	0.317923	−	0.550659i
$647$	−3.60635e22	+	2.08213e22i	−1.17445	+	0.678068i	−0.954724	−	0.297494i	$-0.903849\pi$
$647$	−3.60635e22	+	2.08213e22i	−1.17445	+	0.678068i	−0.219725	+	0.975562i	$0.570516\pi$
$648$	8.77944e20	+	1.52064e21i	0.0282401	+	0.0489134i
$649$	7.58327e21	+	4.37820e21i	0.240934	+	0.139104i
$650$			4.39303e22i			1.37866i
$651$	3.19415e22	+	2.07588e22i	0.990164	+	0.643509i
$652$	−4.96210e22			−1.51944
$653$	1.93052e22	−	3.34375e22i	0.583940	−	1.01141i	−0.411067	−	0.911605i	$-0.634844\pi$
$653$	1.93052e22	−	3.34375e22i	0.583940	−	1.01141i	0.995007	−	0.0998079i	$-0.0318228\pi$
$654$	−1.88927e21	+	1.09077e21i	−0.0564512	+	0.0325921i
$655$	3.78623e21	+	6.55795e21i	0.111758	+	0.193570i
$656$	3.27815e22	+	1.89264e22i	0.955867	+	0.551870i
$657$		−	6.22092e21i		−	0.179197i
$658$	1.25997e22	+	2.47496e22i	0.358554	+	0.704306i
$659$	−4.01978e22			−1.13011			−0.565053	−	0.825054i	$-0.691144\pi$
$659$	−4.01978e22			−1.13011			−0.565053	+	0.825054i	$0.691144\pi$
$660$	1.56517e21	−	2.71095e21i	0.0434720	−	0.0752957i
$661$	1.38024e22	−	7.96883e21i	0.378742	−	0.218667i	−0.298529	−	0.954401i	$-0.596496\pi$
$661$	1.38024e22	−	7.96883e21i	0.378742	−	0.218667i	0.677271	+	0.735734i	$0.263163\pi$
$662$	−4.04228e20	−	7.00144e20i	−0.0109588	−	0.0189812i
$663$	−2.99190e22	−	1.72738e22i	−0.801381	−	0.462678i
$664$		−	2.12153e19i		−	0.000561441i
$665$	8.11109e21	−	4.12927e21i	0.212083	−	0.107969i
$666$	−9.04443e21			−0.233662
$667$	−1.36144e22	+	2.35808e22i	−0.347530	+	0.601939i
$668$	−2.27265e21	+	1.31212e21i	−0.0573220	+	0.0330949i
$669$	2.00851e22	+	3.47885e22i	0.500571	+	0.867015i
$670$	−4.03728e22	−	2.33092e22i	−0.994237	−	0.574023i
$671$		−	3.70667e21i		−	0.0901993i
$672$	−3.03832e22	+	4.67505e22i	−0.730599	+	1.12417i
$673$	1.60283e21			0.0380861			0.0190431	−	0.999819i	$-0.493938\pi$
$673$	1.60283e21			0.0380861			0.0190431	+	0.999819i	$0.493938\pi$
$674$	−8.21896e20	+	1.42357e21i	−0.0192991	+	0.0334271i
$675$	−3.15696e22	+	1.82267e22i	−0.732553	+	0.422940i
$676$	9.83201e21	+	1.70295e22i	0.225460	+	0.390507i
$677$	−5.75294e22	−	3.32146e22i	−1.30371	−	0.752696i	−0.322670	−	0.946512i	$-0.604580\pi$
$677$	−5.75294e22	−	3.32146e22i	−1.30371	−	0.752696i	−0.981038	+	0.193816i	$0.937914\pi$
$678$		−	1.50958e22i		−	0.338079i
$679$	3.90563e22	+	2.06044e21i	0.864436	+	0.0456038i
$680$	−1.07879e21			−0.0235975
$681$	3.56541e22	−	6.17547e22i	0.770784	−	1.33504i
$682$	−1.46376e22	+	8.45104e21i	−0.312749	+	0.180566i
$683$	−7.86402e21	−	1.36209e22i	−0.166065	−	0.287634i	0.770968	−	0.636874i	$-0.219773\pi$
$683$	−7.86402e21	−	1.36209e22i	−0.166065	−	0.287634i	−0.937033	+	0.349241i	$0.886440\pi$
$684$	−2.75379e21	−	1.58990e21i	−0.0574753	−	0.0331834i
$685$		−	1.35965e22i		−	0.280481i
$686$	−5.44660e22	−	4.41996e22i	−1.11053	−	0.901209i
$687$	3.41100e22			0.687429
$688$	−1.38477e22	+	2.39849e22i	−0.275848	+	0.477784i
$689$	9.78472e22	−	5.64921e22i	1.92661	−	1.11233i
$690$	−7.89279e21	−	1.36707e22i	−0.153617	−	0.266072i
$691$	−2.92712e22	−	1.68998e22i	−0.563140	−	0.325129i	0.191265	−	0.981538i	$-0.438741\pi$
$691$	−2.92712e22	−	1.68998e22i	−0.563140	−	0.325129i	−0.754405	+	0.656409i	$0.772074\pi$
$692$		−	3.04236e22i		−	0.578578i
$693$	−6.61780e19	+	1.25442e21i	−0.00124408	+	0.0235819i
$694$	1.11495e23			2.07195
$695$	−2.45682e21	+	4.25534e21i	−0.0451331	+	0.0781728i
$696$	−3.90212e21	+	2.25289e21i	−0.0708642	+	0.0409135i
$697$	2.65735e22	+	4.60267e22i	0.477076	+	0.826319i
$698$	5.26610e22	+	3.04038e22i	0.934643	+	0.539616i
$699$		−	3.89321e22i		−	0.683109i
$700$	4.07175e22	+	2.64624e22i	0.706313	+	0.459033i
$701$	−3.85864e22			−0.661744			−0.330872	−	0.943676i	$-0.607343\pi$
$701$	−3.85864e22			−0.661744			−0.330872	+	0.943676i	$0.607343\pi$
$702$	−5.29717e22	+	9.17497e22i	−0.898147	+	1.55564i
$703$	−3.87645e22	+	2.23807e22i	−0.649818	+	0.375173i
$704$	−6.59756e21	−	1.14273e22i	−0.109346	−	0.189392i
$705$	1.20916e22	+	6.98111e21i	0.198140	+	0.114396i
$706$			1.49616e23i			2.42404i
$707$	−2.17016e22	−	4.26283e22i	−0.347645	−	0.682877i
$708$	8.58793e22			1.36026
$709$	−4.46709e21	+	7.73724e21i	−0.0699609	+	0.121176i	−0.898884	−	0.438187i	$-0.855621\pi$
$709$	−4.46709e21	+	7.73724e21i	−0.0699609	+	0.121176i	0.828923	+	0.559363i	$0.188954\pi$
$710$	3.37853e22	−	1.95060e22i	0.523192	−	0.302065i
$711$	3.48828e21	+	6.04187e21i	0.0534139	+	0.0925156i
$712$	−4.56679e21	−	2.63664e21i	−0.0691466	−	0.0399218i
$713$			4.35639e22i			0.652245i
$714$	−6.65857e22	+	3.38980e22i	−0.985815	+	0.501867i
$715$	7.23443e21			0.105915
$716$	2.42218e22	−	4.19535e22i	0.350673	−	0.607384i
$717$	−4.12067e22	+	2.37907e22i	−0.589949	+	0.340607i
$718$	−8.37575e22	−	1.45072e23i	−1.18585	−	2.05394i
$719$	1.04644e23	+	6.04164e22i	1.46516	+	0.845909i	0.999242	−	0.0389195i	$-0.0123916\pi$
$719$	1.04644e23	+	6.04164e22i	1.46516	+	0.845909i	0.465916	+	0.884829i	$0.345725\pi$
$720$		−	3.56442e21i		−	0.0493548i
$721$	2.90224e22	−	4.46566e22i	0.397421	−	0.611510i
$722$	7.48176e22			1.01323
$723$	2.06909e22	−	3.58376e22i	0.277123	−	0.479991i
$724$	6.02561e22	−	3.47889e22i	0.798165	−	0.460821i
$725$	−4.11957e22	−	7.13531e22i	−0.539695	−	0.934779i
$726$	−8.61738e22	−	4.97525e22i	−1.11656	−	0.644647i
$727$			1.52182e23i			1.95024i	0.221668	+	0.975122i	$0.428850\pi$
$727$			1.52182e23i			1.95024i	−0.221668	+	0.975122i	$0.571150\pi$
$728$	6.12895e21	+	3.23337e20i	0.0776846	+	0.00409830i
$729$	−8.68097e22			−1.08830
$730$	−3.87425e22	+	6.71040e22i	−0.480402	+	0.832081i
$731$	−3.36760e22	+	1.94429e22i	−0.413030	+	0.238463i
$732$	−1.81767e22	−	3.14830e22i	−0.220510	−	0.381934i
$733$	−2.79416e22	−	1.61321e22i	−0.335289	−	0.193579i	0.322898	−	0.946434i	$-0.395343\pi$
$733$	−2.79416e22	−	1.61321e22i	−0.335289	−	0.193579i	−0.658187	+	0.752855i	$0.728676\pi$
$734$			5.70143e21i			0.0676730i
$735$	−3.50683e22	−	3.71043e21i	−0.411734	−	0.0435638i
$736$	−6.37614e22			−0.740517
$737$	1.59212e22	−	2.75764e22i	0.182910	−	0.316809i
$738$	1.48484e22	−	8.57273e21i	0.168744	−	0.0974245i
$739$	9.56448e21	+	1.65662e22i	0.107524	+	0.186237i	0.914767	−	0.403983i	$-0.132374\pi$
$739$	9.56448e21	+	1.65662e22i	0.107524	+	0.186237i	−0.807243	+	0.590220i	$0.799041\pi$
$740$	4.98646e22	+	2.87893e22i	0.554547	+	0.320168i
$741$			5.51580e22i			0.606825i
$742$	1.28733e22	−	2.44017e23i	0.140107	−	2.65576i
$743$	−4.33327e22			−0.466557			−0.233279	−	0.972410i	$-0.574945\pi$
$743$	−4.33327e22			−0.466557			−0.233279	+	0.972410i	$0.574945\pi$
$744$	−3.60445e21	+	6.24309e21i	−0.0383933	+	0.0664991i
$745$	−7.07879e22	+	4.08694e22i	−0.745949	+	0.430674i
$746$	−5.00207e22	−	8.66384e22i	−0.521482	−	0.903233i
$747$	8.52342e19	+	4.92100e19i	0.000879122	+	0.000507561i
$748$		−	1.69441e22i		−	0.172905i
$749$	−9.45599e21	−	6.14546e21i	−0.0954669	−	0.0620440i
$750$	1.07047e23			1.06926
$751$	−1.77899e22	+	3.08130e22i	−0.175814	+	0.304520i	−0.940443	−	0.339952i	$-0.889589\pi$
$751$	−1.77899e22	+	3.08130e22i	−0.175814	+	0.304520i	0.764628	+	0.644471i	$0.222923\pi$
$752$	4.66156e22	−	2.69135e22i	0.455815	−	0.263165i
$753$	−3.95885e21	−	6.85692e21i	−0.0383009	−	0.0663391i
$754$	−2.07371e23	−	1.19726e23i	−1.98508	−	1.14608i
$755$			1.78938e22i			0.169483i
$756$	5.31311e22	+	1.04365e23i	0.497938	+	0.978096i
$757$	1.06877e23			0.991099			0.495550	−	0.868580i	$-0.334967\pi$
$757$	1.06877e23			0.991099			0.495550	+	0.868580i	$0.334967\pi$
$758$	−1.34245e22	+	2.32519e22i	−0.123181	+	0.213356i
$759$	9.33770e21	−	5.39112e21i	0.0847824	−	0.0489491i
$760$	8.61190e20	+	1.49162e21i	0.00773731	+	0.0134014i
$761$	1.73737e23	+	1.00307e23i	1.54459	+	0.891772i	0.998540	+	0.0540231i	$0.0172045\pi$
$761$	1.73737e23	+	1.00307e23i	1.54459	+	0.891772i	0.546055	+	0.837749i	$0.316129\pi$
$762$			7.09691e22i			0.624352i
$763$	−4.96660e21	+	2.52844e21i	−0.0432377	+	0.0220118i
$764$	−6.87150e22			−0.591977
$765$	2.50231e21	−	4.33413e21i	0.0213329	−	0.0369497i
$766$	4.21391e22	−	2.43290e22i	0.355513	−	0.205255i
$767$	9.92366e22	+	1.71883e23i	0.828531	+	1.43506i
$768$	8.89065e22	+	5.13302e22i	0.734588	+	0.424114i
$769$		−	1.85562e22i		−	0.151732i	−0.997118	−	0.0758662i	$-0.975828\pi$
$769$		−	1.85562e22i		−	0.151732i	0.997118	−	0.0758662i	$-0.0241722\pi$
$770$	8.52613e21	−	1.31191e22i	0.0689963	−	0.106164i
$771$	−4.43976e22			−0.355570
$772$	−4.21711e22	+	7.30425e22i	−0.334254	+	0.578945i
$773$	−1.41774e23	+	8.18533e22i	−1.11214	+	0.642096i	−0.939384	−	0.342867i	$-0.888602\pi$
$773$	−1.41774e23	+	8.18533e22i	−1.11214	+	0.642096i	−0.172760	+	0.984964i	$0.555268\pi$
$774$	6.27234e21	+	1.08640e22i	0.0486970	+	0.0843456i
$775$	−1.14159e23	−	6.59099e22i	−0.877198	−	0.506451i
$776$			7.40119e21i			0.0562870i
$777$	1.73185e23	+	9.13650e21i	1.30360	+	0.0687720i
$778$	2.35667e23			1.75575
$779$	4.24269e22	−	7.34856e22i	0.312854	−	0.541879i
$780$	6.14466e22	−	3.54762e22i	0.448478	−	0.258929i
$781$	1.33234e22	+	2.30769e22i	0.0962516	+	0.166713i
$782$	−7.39979e22	−	4.27227e22i	−0.529134	−	0.305495i
$783$		−	1.98698e23i		−	1.40637i
$784$	−7.99856e22	+	1.09930e23i	−0.560381	+	0.770174i
$785$	9.20536e22			0.638387
$786$	−4.96251e22	+	8.59531e22i	−0.340660	+	0.590040i
$787$	9.89153e21	−	5.71088e21i	0.0672149	−	0.0388065i	−0.466016	−	0.884776i	$-0.654311\pi$
$787$	9.89153e21	−	5.71088e21i	0.0672149	−	0.0388065i	0.533231	+	0.845970i	$0.320978\pi$
$788$	1.20772e23	+	2.09183e23i	0.812375	+	1.40707i
$789$	−3.34307e22	−	1.93012e22i	−0.222602	−	0.128520i
$790$		−	8.68969e22i		−	0.572779i
$791$	2.03170e21	−	3.85115e22i	0.0132571	−	0.251292i
$792$	−2.37714e20			−0.00153551
$793$	4.20077e22	−	7.27595e22i	0.268623	−	0.465269i
$794$	−1.78603e23	+	1.03117e23i	−1.13064	+	0.652778i
$795$	−6.14240e22	−	1.06389e23i	−0.384947	−	0.666748i
$796$	−2.21210e23	−	1.27716e23i	−1.37246	−	0.792390i
$797$		−	1.79511e23i		−	1.10262i	−0.834302	−	0.551308i	$-0.814129\pi$
$797$		−	1.79511e23i		−	1.10262i	0.834302	−	0.551308i	$-0.185871\pi$
$798$	1.00025e23	+	6.50064e22i	0.608255	+	0.395306i
$799$	7.55758e22			0.454997
$800$	9.64676e22	−	1.67087e23i	0.574992	−	0.995915i
$801$	2.11858e22	−	1.22316e22i	0.125022	−	0.0721813i
$802$	2.41111e22	+	4.17617e22i	0.140871	+	0.243996i
$803$	−4.58350e22	−	2.64629e22i	−0.265139	−	0.153078i
$804$		−	3.12298e23i		−	1.78863i
$805$	−1.82957e22	−	3.59382e22i	−0.103749	−	0.203793i
$806$	−3.83104e23			−2.15098
$807$	3.90497e22	−	6.76360e22i	0.217085	−	0.376002i
$808$	7.83932e21	−	4.52603e21i	0.0431507	−	0.0249130i
$809$	5.02117e22	+	8.69691e22i	0.273663	+	0.473999i	0.969797	−	0.243914i	$-0.0784313\pi$
$809$	5.02117e22	+	8.69691e22i	0.273663	+	0.473999i	−0.696134	+	0.717912i	$0.745098\pi$
$810$	8.78669e22	+	5.07300e22i	0.474182	+	0.273769i
$811$			2.42289e23i			1.29469i	0.762196	+	0.647346i	$0.224121\pi$
$811$			2.42289e23i			1.29469i	−0.762196	+	0.647346i	$0.775879\pi$
$812$	−2.35884e23	+	1.20086e23i	−1.24810	+	0.635396i
$813$	−2.92374e23			−1.53184
$814$	−3.84736e22	+	6.66383e22i	−0.199603	+	0.345723i
$815$	−1.07984e23	+	6.23447e22i	−0.554752	+	0.320286i
$816$	7.24075e22	+	1.25413e23i	0.368351	+	0.638003i
$817$	5.37666e22	+	3.10422e22i	0.270855	+	0.156378i
$818$			3.70808e23i			1.84979i
$819$	−1.55155e22	+	2.38736e22i	−0.0766467	+	0.117936i
$820$	−1.09152e23			−0.533973
$821$	1.01922e23	−	1.76534e23i	0.493768	−	0.855232i	−0.506206	−	0.862413i	$-0.668952\pi$
$821$	1.01922e23	−	1.76534e23i	0.493768	−	0.855232i	0.999974	+	0.00718089i	$0.00228577\pi$
$822$	1.54331e23	−	8.91029e22i	0.740419	−	0.427481i
$823$	1.83583e22	+	3.17976e22i	0.0872238	+	0.151076i	0.906337	−	0.422556i	$-0.138867\pi$
$823$	1.83583e22	+	3.17976e22i	0.0872238	+	0.151076i	−0.819113	+	0.573632i	$0.805534\pi$
$824$	8.72831e21	+	5.03929e21i	0.0410688	+	0.0237111i
$825$			3.26259e22i			0.152031i
$826$	4.28652e23	+	2.26138e22i	1.97817	+	0.104360i
$827$	−4.55274e22			−0.208079			−0.104040	−	0.994573i	$-0.533177\pi$
$827$	−4.55274e22			−0.208079			−0.104040	+	0.994573i	$0.533177\pi$
$828$	−7.04443e21	+	1.22013e22i	−0.0318862	+	0.0552286i
$829$	−1.20625e23	+	6.96429e22i	−0.540756	+	0.312205i	−0.745385	−	0.666634i	$-0.767734\pi$
$829$	−1.20625e23	+	6.96429e22i	−0.540756	+	0.312205i	0.204630	+	0.978839i	$0.434401\pi$
$830$	−6.12938e20	−	1.06164e21i	−0.00272140	−	0.00471360i
$831$	1.79222e23	+	1.03474e23i	0.788104	+	0.455012i
$832$		−	2.99081e23i		−	1.30257i
$833$	−1.74432e23	+	7.75170e22i	−0.752428	+	0.334377i
$834$	−6.44016e22			−0.275149
$835$	−3.29713e21	+	5.71080e21i	−0.0139523	+	0.0241660i
$836$	−2.34284e22	+	1.35264e22i	−0.0981956	+	0.0566932i
$837$	−1.58950e23	−	2.75310e23i	−0.659869	−	1.14293i
$838$	4.21937e23	+	2.43605e23i	1.73498	+	1.00169i
$839$		−	3.91887e23i		−	1.59612i	−0.602579	−	0.798059i	$-0.705860\pi$
$839$		−	3.91887e23i		−	1.59612i	0.602579	−	0.798059i	$-0.294140\pi$
$840$	3.51565e20	−	6.66402e21i	0.00141831	−	0.0268845i
$841$	1.98846e23			0.794601
$842$	9.00334e22	−	1.55942e23i	0.356375	−	0.617259i
$843$	1.43012e23	−	8.25679e22i	0.560727	−	0.323736i
$844$	−9.20254e22	−	1.59393e23i	−0.357411	−	0.619054i
$845$	4.27924e22	+	2.47062e22i	0.164632	+	0.0950501i
$846$		−	2.43811e22i		−	0.0929158i
$847$	−2.13145e23	−	1.38523e23i	−0.804653	−	0.522945i
$848$	−4.73603e23			−1.77112
$849$	−1.94172e23	+	3.36315e23i	−0.719323	+	1.24590i
$850$	2.23910e23	−	1.29274e23i	0.821716	−	0.474418i
$851$	9.91631e22	+	1.71755e23i	0.360507	+	0.624416i
$852$	2.26329e23	+	1.30671e23i	0.815122	+	0.470611i
$853$			1.94066e23i			0.692402i	0.938160	+	0.346201i	$0.112528\pi$
$853$			1.94066e23i			0.692402i	−0.938160	+	0.346201i	$0.887472\pi$
$854$	−8.24360e22	−	1.61929e23i	−0.291376	−	0.572349i
$855$	−7.99031e21			−0.0279792
$856$	1.06706e21	−	1.84821e21i	0.00370170	−	0.00641153i
$857$	−1.04126e22	+	6.01169e21i	−0.0357858	+	0.0206609i	−0.517786	−	0.855510i	$-0.673244\pi$
$857$	−1.04126e22	+	6.01169e21i	−0.0357858	+	0.0206609i	0.482000	+	0.876171i	$0.339910\pi$
$858$	4.74098e22	+	8.21162e22i	0.161425	+	0.279596i
$859$	−9.26687e22	−	5.35023e22i	−0.312599	−	0.180479i	0.335490	−	0.942044i	$-0.391098\pi$
$859$	−9.26687e22	−	5.35023e22i	−0.312599	−	0.180479i	−0.648089	+	0.761565i	$0.724431\pi$
$860$		−	7.98620e22i		−	0.266903i
$861$	−2.92981e23	+	1.49154e23i	−0.970097	+	0.493865i
$862$	6.65049e23			2.18170
$863$	−9.29800e22	+	1.61046e23i	−0.302206	+	0.523436i	−0.976635	−	0.214903i	$-0.931056\pi$
$863$	−9.29800e22	+	1.61046e23i	−0.302206	+	0.523436i	0.674429	+	0.738339i	$0.264390\pi$
$864$	4.02951e23	−	2.32644e23i	1.29760	−	0.749173i
$865$	−3.82248e22	−	6.62072e22i	−0.121960	−	0.211240i
$866$	3.40237e23	+	1.96436e23i	1.07557	+	0.620980i
$867$		−	9.65847e22i		−	0.302521i
$868$	−2.30771e23	+	3.55086e23i	−0.716181	+	1.10199i
$869$	5.93544e22			0.182513
$870$	−1.30178e23	+	2.25475e23i	−0.396628	+	0.686981i
$871$	6.25047e23	−	3.60871e23i	1.88698	−	1.08945i
$872$	−5.27326e20	−	9.13355e20i	−0.00157742	−	0.00273217i
$873$	−2.97349e22	−	1.71675e22i	−0.0881359	−	0.0508853i
$874$			1.36421e23i			0.400672i
$875$	2.73092e23	+	1.44071e22i	0.794776	+	0.0419289i
$876$	−5.19074e23			−1.49691
$877$	−1.62759e23	+	2.81906e23i	−0.465101	+	0.805579i	−0.999206	−	0.0398394i	$-0.987315\pi$
$877$	−1.62759e23	+	2.81906e23i	−0.465101	+	0.805579i	0.534105	+	0.845418i	$0.320649\pi$
$878$	−7.81616e23	+	4.51266e23i	−2.21329	+	1.27784i
$879$	−1.36681e23	−	2.36738e23i	−0.383527	−	0.664289i
$880$	−2.62622e22	−	1.51625e22i	−0.0730248	−	0.0421609i
$881$			2.40638e23i			0.663065i	0.943444	+	0.331533i	$0.107566\pi$
$881$			2.40638e23i			0.663065i	−0.943444	+	0.331533i	$0.892434\pi$
$882$	2.50073e22	+	5.62723e22i	0.0682838	+	0.153655i
$883$	2.22650e22			0.0602472			0.0301236	−	0.999546i	$-0.490410\pi$
$883$	2.22650e22			0.0602472			0.0301236	+	0.999546i	$0.490410\pi$
$884$	1.92028e23	−	3.32603e23i	0.514929	−	0.891883i
$885$	1.86889e23	−	1.07900e23i	0.496634	−	0.286732i
$886$	−3.24718e23	−	5.62428e23i	−0.855139	−	1.48114i
$887$	1.72883e23	+	9.98143e22i	0.451195	+	0.260498i	0.708335	−	0.705877i	$-0.249447\pi$
$887$	1.72883e23	+	9.98143e22i	0.451195	+	0.260498i	−0.257140	+	0.966374i	$0.582780\pi$
$888$			3.28187e22i			0.0848825i
$889$	−9.55151e21	+	1.81052e23i	−0.0244826	+	0.464076i
$890$	−3.04704e23			−0.774030
$891$	−3.46508e22	+	6.00169e22i	−0.0872352	+	0.151096i
$892$	−3.86735e23	+	2.23282e23i	−0.964928	+	0.557102i
$893$	−6.03316e22	−	1.04497e23i	−0.149188	−	0.258401i
$894$	−9.27797e23	−	5.35664e23i	−2.27380	−	1.31278i
$895$		−	1.21731e23i		−	0.295676i
$896$	−4.52491e22	−	2.94074e22i	−0.108930	−	0.0707935i
$897$	2.44391e23			0.583103
$898$	9.01975e22	−	1.56227e23i	0.213297	−	0.369440i
$899$	6.22250e23	−	3.59256e23i	1.45844	−	0.842029i
$900$	−2.13157e22	−	3.69199e22i	−0.0495176	−	0.0857670i
$901$	−5.75873e23	−	3.32481e23i	−1.32595	−	0.765540i
$902$		−	1.45868e23i		−	0.332896i
$903$	−1.09130e23	−	2.14363e23i	−0.246855	−	0.484896i
$904$	7.29795e21			0.0163626
$905$	8.74187e22	−	1.51414e23i	0.194275	−	0.336493i
$906$	−2.03108e23	+	1.17264e23i	−0.447405	+	0.258309i
$907$	−2.58992e21	−	4.48587e21i	−0.00565493	−	0.00979463i	0.863184	−	0.504889i	$-0.168467\pi$
$907$	−2.58992e21	−	4.48587e21i	−0.00565493	−	0.00979463i	−0.868839	+	0.495095i	$0.835133\pi$
$908$	6.86513e23	+	3.96358e23i	1.48581	+	0.857830i
$909$			4.19935e22i			0.0900889i
$910$	3.16042e23	−	1.60893e23i	0.672069	−	0.342142i
$911$	2.40243e23			0.506411			0.253205	−	0.967413i	$-0.418515\pi$
$911$	2.40243e23			0.506411			0.253205	+	0.967413i	$0.418515\pi$
$912$	1.15605e23	−	2.00233e23i	0.241555	−	0.418386i
$913$	7.25146e20	−	4.18663e20i	0.00150196	−	0.000867159i
$914$	9.63320e22	+	1.66852e23i	0.197789	+	0.342580i
$915$	−7.91116e22	−	4.56751e22i	−0.161017	−	0.0929632i
$916$			3.79193e23i			0.765062i
$917$	−1.38169e23	+	2.12599e23i	−0.276347	+	0.425214i
$918$	6.23523e23			1.23626
$919$	−2.74378e23	+	4.75236e23i	−0.539293	+	0.934083i	0.459649	+	0.888101i	$0.347975\pi$
$919$	−2.74378e23	+	4.75236e23i	−0.539293	+	0.934083i	−0.998942	+	0.0459828i	$0.985358\pi$
$920$	6.60900e21	−	3.81571e21i	0.0128776	−	0.00743486i
$921$	3.60519e23	+	6.24437e23i	0.696387	+	1.20618i
$922$	−6.13134e23	−	3.53993e23i	−1.17411	−	0.677872i
$923$			6.03979e23i			1.14659i
$924$	1.04669e23	+	5.52189e21i	0.196989	+	0.0103923i
$925$	−6.00114e23			−1.11970
$926$	6.28691e23	−	1.08893e24i	1.16292	−	2.01424i
$927$	−4.04916e22	+	2.33778e22i	−0.0742552	+	0.0428712i
$928$	5.25818e23	+	9.10743e23i	0.955986	+	1.65582i
$929$	4.72457e23	+	2.72773e23i	0.851602	+	0.491672i	0.861191	−	0.508282i	$-0.169719\pi$
$929$	4.72457e23	+	2.72773e23i	0.851602	+	0.491672i	−0.00958933	+	0.999954i	$0.503052\pi$
$930$			4.16549e23i			0.744394i
$931$	2.46429e23	+	1.79302e23i	0.436610	+	0.317679i
$932$	4.32799e23			0.760254
$933$	−1.32264e23	+	2.29088e23i	−0.230350	+	0.398978i
$934$	−5.82122e23	+	3.36088e23i	−1.00517	+	0.580334i
$935$	−2.12889e22	−	3.68734e22i	−0.0364469	−	0.0631278i
$936$	−4.66618e21	−	2.69402e21i	−0.00792054	−	0.00457293i
$937$		−	1.82039e23i		−	0.306371i	−0.988197	−	0.153186i	$-0.951047\pi$
$937$		−	1.82039e23i		−	0.306371i	0.988197	−	0.153186i	$-0.0489532\pi$
$938$	8.22346e22	−	1.55878e24i	0.137225	−	2.60113i
$939$	5.08630e23			0.841544
$940$	−7.76074e22	+	1.34420e23i	−0.127315	+	0.220516i
$941$	−1.03404e24	+	5.97006e23i	−1.68198	+	0.971094i	−0.721645	+	0.692264i	$0.756614\pi$
$941$	−1.03404e24	+	5.97006e23i	−1.68198	+	0.971094i	−0.960340	+	0.278831i	$0.910053\pi$
$942$	6.03260e23	+	1.04488e24i	0.972966	+	1.68523i
$943$	−3.25596e23	−	1.87983e23i	−0.520697	−	0.300625i
$944$		−	8.31952e23i		−	1.31924i
$945$	2.46749e23	+	1.60362e23i	0.387973	+	0.252144i
$946$	1.06726e23			0.166396
$947$	4.40693e21	−	7.63303e21i	0.00681297	−	0.0118004i	−0.862599	−	0.505889i	$-0.831165\pi$
$947$	4.40693e21	−	7.63303e21i	0.00681297	−	0.0118004i	0.869412	+	0.494088i	$0.164498\pi$
$948$	5.04134e23	−	2.91062e23i	0.772822	−	0.446189i
$949$	−5.99808e23	−	1.03890e24i	−0.911765	−	1.57922i
$950$	−3.57491e23	−	2.06398e23i	−0.538861	−	0.311111i
$951$			2.91338e23i			0.435465i
$952$	−1.63877e22	−	3.21903e22i	−0.0242898	−	0.0477123i
$953$	7.93626e23			1.16647			0.583234	−	0.812304i	$-0.301787\pi$
$953$	7.93626e23			1.16647			0.583234	+	0.812304i	$0.301787\pi$
$954$	−1.07260e23	+	1.85779e23i	−0.156332	+	0.270776i
$955$	−1.49536e23	+	8.63347e22i	−0.216132	+	0.124784i
$956$	−2.64476e23	−	4.58085e23i	−0.379073	−	0.656573i
$957$	−1.54009e23	−	8.89174e22i	−0.218903	−	0.126384i
$958$		−	5.55365e23i		−	0.782806i
$959$	4.05711e23	−	2.06543e23i	0.567111	−	0.288710i
$960$	−3.25192e23			−0.450785
$961$	2.11070e23	−	3.65584e23i	0.290162	−	0.502575i
$962$	−1.51043e24	+	8.72045e23i	−2.05920	+	1.18888i
$963$	4.95023e21	+	8.57405e21i	0.00669291	+	0.0115925i
$964$	3.98398e23	+	2.30015e23i	0.534197	+	0.308419i
$965$			2.11938e23i			0.281832i
$966$	2.88027e23	−	4.43185e23i	0.379853	−	0.584478i
$967$	−9.52331e23			−1.24559			−0.622796	−	0.782384i	$-0.714003\pi$
$967$	−9.52331e23			−1.24559			−0.622796	+	0.782384i	$0.714003\pi$
$968$	2.40525e22	−	4.16601e22i	0.0312001	−	0.0540402i
$969$	2.81137e23	−	1.62315e23i	0.361683	−	0.208818i
$970$	2.13830e23	+	3.70365e23i	0.272832	+	0.472559i
$971$	−2.65188e23	−	1.53106e23i	−0.335583	−	0.193749i	0.322734	−	0.946490i	$-0.395398\pi$
$971$	−2.65188e23	−	1.53106e23i	−0.335583	−	0.193749i	−0.658317	+	0.752741i	$0.728731\pi$
$972$		−	1.94807e23i		−	0.244497i
$973$	−1.64297e23	−	8.66762e21i	−0.204516	−	0.0107894i
$974$	1.04869e24			1.29472
$975$	−3.69751e23	+	6.40427e23i	−0.452764	+	0.784210i
$976$	−3.04991e23	+	1.76086e23i	−0.370415	+	0.213859i
$977$	−4.87141e23	−	8.43752e23i	−0.586811	−	1.01639i	−0.994647	−	0.103331i	$-0.967050\pi$
$977$	−4.87141e23	−	8.43752e23i	−0.586811	−	1.01639i	0.407837	−	0.913055i	$-0.366283\pi$
$978$	−1.41532e24	−	8.17133e23i	−1.69100	−	0.976297i
$979$		−	2.08126e23i		−	0.246641i
$980$	4.12480e22	−	3.89847e23i	0.0484835	−	0.458232i
$981$	4.89264e21			0.00570415
$982$	−9.29411e23	+	1.60979e24i	−1.07477	+	1.86156i
$983$	8.07662e23	−	4.66304e23i	0.926406	−	0.534861i	0.0407328	−	0.999170i	$-0.487031\pi$
$983$	8.07662e23	−	4.66304e23i	0.926406	−	0.534861i	0.885673	+	0.464309i	$0.153697\pi$
$984$	−3.11071e22	−	5.38791e22i	−0.0353915	−	0.0612999i
$985$	5.25643e23	+	3.03480e23i	0.593200	+	0.342484i
$986$			1.40928e24i			1.57754i
$987$	−2.46292e22	+	4.66855e23i	−0.0273473	+	0.518376i
$988$	−6.13179e23			−0.675354
$989$	1.37540e23	−	2.38226e23i	0.150265	−	0.260267i
$990$	−1.18955e22	+	6.86788e21i	−0.0128915	+	0.00744288i
$991$	−4.69032e23	−	8.12387e23i	−0.504212	−	0.873320i	−0.999988	−	0.00487000i	$-0.998450\pi$
$991$	−4.69032e23	−	8.12387e23i	−0.504212	−	0.873320i	0.495777	−	0.868450i	$-0.334884\pi$
$992$	1.45712e24	+	8.41267e23i	1.55382	+	0.897099i
$993$		−	1.36092e22i		−	0.0143959i
$994$	1.09527e24	+	7.11819e23i	1.14929	+	0.746927i
$995$	−6.41856e23			−0.668117
$996$	4.10608e21	−	7.11194e21i	0.00423987	−	0.00734367i
$997$	1.05680e24	−	6.10142e23i	1.08251	−	0.624986i	0.150935	−	0.988544i	$-0.451772\pi$
$997$	1.05680e24	−	6.10142e23i	1.08251	−	0.624986i	0.931572	+	0.363558i	$0.118438\pi$
$998$	2.79793e23	+	4.84616e23i	0.284311	+	0.492440i
$999$	−1.25336e24	−	7.23626e23i	−1.26343	−	0.729441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.d.a.5.2	yes	20
7.2	even	3		49.17.b.a.48.17		20
7.3	odd	6	inner	7.17.d.a.3.2	✓	20
7.5	odd	6		49.17.b.a.48.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.d.a.3.2	✓	20	7.3	odd	6	inner
7.17.d.a.5.2	yes	20	1.1	even	1	trivial
49.17.b.a.48.17		20	7.2	even	3
49.17.b.a.48.18		20	7.5	odd	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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-183.065 + 317.078i) q^{2} +(-5337.54 + 3081.63i) q^{3} +(-34257.8 - 59336.2i) q^{4} +(-149102. - 86084.1i) q^{5} -2.25656e6i q^{6} +(303703. - 5.75680e6i) q^{7} +1.09092e6 q^{8} +(-2.53044e6 + 4.38285e6i) q^{9} +O(q^{10})\)	\(q+(-183.065 + 317.078i) q^{2} +(-5337.54 + 3081.63i) q^{3} +(-34257.8 - 59336.2i) q^{4} +(-149102. - 86084.1i) q^{5} -2.25656e6i q^{6} +(303703. - 5.75680e6i) q^{7} +1.09092e6 q^{8} +(-2.53044e6 + 4.38285e6i) q^{9} +(5.45908e7 - 3.15180e7i) q^{10} +(2.15282e7 + 3.72879e7i) q^{11} +(3.65705e8 + 2.11140e8i) q^{12} +9.75919e8i q^{13} +(1.76976e9 + 1.15017e9i) q^{14} +1.06112e9 q^{15} +(2.04541e9 - 3.54275e9i) q^{16} +(4.97420e9 - 2.87185e9i) q^{17} +(-9.26471e8 - 1.60470e9i) q^{18} +(-7.94173e9 - 4.58516e9i) q^{19} +1.17962e10i q^{20} +(1.61193e10 + 3.16631e10i) q^{21} -1.57643e10 q^{22} +(-2.03156e10 + 3.51877e10i) q^{23} +(-5.82282e9 + 3.36180e9i) q^{24} +(-6.14730e10 - 1.06474e11i) q^{25} +(-3.09443e11 - 1.78657e11i) q^{26} -2.96500e11i q^{27} +(-3.51991e11 + 1.79194e11i) q^{28} +6.70144e11 q^{29} +(-1.94254e11 + 3.36458e11i) q^{30} +(9.28533e11 - 5.36089e11i) q^{31} +(7.84634e11 + 1.35903e12i) q^{32} +(-2.29815e11 - 1.32684e11i) q^{33} +2.10295e12i q^{34} +(-5.40852e11 + 8.32206e11i) q^{35} +3.46749e11 q^{36} +(2.44056e12 - 4.22717e12i) q^{37} +(2.90771e12 - 1.67877e12i) q^{38} +(-3.00742e12 - 5.20901e12i) q^{39} +(-1.62658e11 - 9.39106e10i) q^{40} +9.25310e12i q^{41} +(-1.29906e13 - 6.85325e11i) q^{42} -6.77014e12 q^{43} +(1.47502e12 - 2.55480e12i) q^{44} +(7.54588e11 - 4.35661e11i) q^{45} +(-7.43818e12 - 1.28833e13i) q^{46} +(1.13952e13 + 6.57901e12i) q^{47} +2.52128e13i q^{48} +(-3.30485e13 - 3.49672e12i) q^{49} +4.50143e13 q^{50} +(-1.77000e13 + 3.06573e13i) q^{51} +(5.79073e13 - 3.34328e13i) q^{52} +(-5.78861e13 - 1.00262e14i) q^{53} +(9.40137e13 + 5.42788e13i) q^{54} -7.41295e12i q^{55} +(3.31315e11 - 6.28018e12i) q^{56} +5.65191e13 q^{57} +(-1.22680e14 + 2.12488e14i) q^{58} +(1.76124e14 - 1.01685e14i) q^{59} +(-3.63516e13 - 6.29628e13i) q^{60} +(-7.45549e13 - 4.30443e13i) q^{61} +3.92557e14i q^{62} +(2.44627e13 + 1.58983e13i) q^{63} -3.06461e14 q^{64} +(8.40111e13 - 1.45512e14i) q^{65} +(8.41425e13 - 4.85797e13i) q^{66} +(-3.69776e14 - 6.40471e14i) q^{67} +(-3.40810e14 - 1.96767e14i) q^{68} -2.50421e14i q^{69} +(-1.64863e14 - 3.23840e14i) q^{70} +6.18883e14 q^{71} +(-2.76050e12 + 4.78132e12i) q^{72} +(-1.06453e15 + 6.14609e14i) q^{73} +(8.93563e14 + 1.54770e15i) q^{74} +(6.56230e14 + 3.78874e14i) q^{75} +6.28310e14i q^{76} +(2.21197e14 - 1.12609e14i) q^{77} +2.20222e15 q^{78} +(6.89263e14 - 1.19384e15i) q^{79} +(-6.09950e14 + 3.52155e14i) q^{80} +(8.04777e14 + 1.39391e15i) q^{81} +(-2.93396e15 - 1.69392e15i) q^{82} -1.94472e13i q^{83} +(1.32655e15 - 2.04116e15i) q^{84} -9.88884e14 q^{85} +(1.23938e15 - 2.14667e15i) q^{86} +(-3.57692e15 + 2.06514e15i) q^{87} +(2.34855e13 + 4.06780e13i) q^{88} +(-4.18619e15 - 2.41690e15i) q^{89} +3.19018e14i q^{90} +(5.61816e15 + 2.96390e14i) q^{91} +2.78388e15 q^{92} +(-3.30406e15 + 5.72279e15i) q^{93} +(-4.17212e15 + 2.40878e15i) q^{94} +(7.89419e14 + 1.36731e15i) q^{95} +(-8.37604e15 - 4.83591e15i) q^{96} +6.78438e15i q^{97} +(7.15876e15 - 9.83882e15i) q^{98} -2.17903e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9}+O(q^{10}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} - 567579804 q^{10} + 487037030 q^{11} - 2240722092 q^{12} + 598121216 q^{14} - 2098975212 q^{15} - 13522996616 q^{16} + 16479299850 q^{17} - 21631627512 q^{18} - 29753076894 q^{19} + 30310552398 q^{21} + 143879888720 q^{22} - 199076938822 q^{23} + 613456300512 q^{24} + 212723266388 q^{25} - 1359419612544 q^{26} + 2531834927748 q^{28} + 438309600272 q^{29} - 2296351012392 q^{30} + 1037434908306 q^{31} - 3523947158064 q^{32} + 411779151054 q^{33} - 7248579242478 q^{35} - 2493315404256 q^{36} + 5318067734218 q^{37} - 9079217417208 q^{38} + 13250117821332 q^{39} + 15010293809208 q^{40} + 16256122433712 q^{42} - 621187489400 q^{43} + 25172272315980 q^{44} - 85040191344096 q^{45} - 15614039192704 q^{46} + 106960600327866 q^{47} - 52978127838580 q^{49} + 35872835226128 q^{50} + 4235281588962 q^{51} + 126484190926632 q^{52} + 29048763888218 q^{53} - 635343594055560 q^{54} + 230352840277168 q^{56} + 366396034764636 q^{57} - 279762037805080 q^{58} - 99092116656282 q^{59} - 173605217618196 q^{60} - 904353032308434 q^{61} + 11\!\cdots\!92 q^{63}+ \cdots + 14\!\cdots\!92 q^{99}+O(q^{100}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9 - 567579804 * q^10 + 487037030 * q^11 - 2240722092 * q^12 + 598121216 * q^14 - 2098975212 * q^15 - 13522996616 * q^16 + 16479299850 * q^17 - 21631627512 * q^18 - 29753076894 * q^19 + 30310552398 * q^21 + 143879888720 * q^22 - 199076938822 * q^23 + 613456300512 * q^24 + 212723266388 * q^25 - 1359419612544 * q^26 + 2531834927748 * q^28 + 438309600272 * q^29 - 2296351012392 * q^30 + 1037434908306 * q^31 - 3523947158064 * q^32 + 411779151054 * q^33 - 7248579242478 * q^35 - 2493315404256 * q^36 + 5318067734218 * q^37 - 9079217417208 * q^38 + 13250117821332 * q^39 + 15010293809208 * q^40 + 16256122433712 * q^42 - 621187489400 * q^43 + 25172272315980 * q^44 - 85040191344096 * q^45 - 15614039192704 * q^46 + 106960600327866 * q^47 - 52978127838580 * q^49 + 35872835226128 * q^50 + 4235281588962 * q^51 + 126484190926632 * q^52 + 29048763888218 * q^53 - 635343594055560 * q^54 + 230352840277168 * q^56 + 366396034764636 * q^57 - 279762037805080 * q^58 - 99092116656282 * q^59 - 173605217618196 * q^60 - 904353032308434 * q^61 + 1188663557133192 * q^63 + 2502182430870944 * q^64 - 500211967540404 * q^65 - 951679982792988 * q^66 - 33326890567694 * q^67 - 964537664673492 * q^68 - 569178593140080 * q^70 + 3111156268483352 * q^71 + 936737429904432 * q^72 - 1146801010325370 * q^73 - 2161044304782140 * q^74 - 4935640048894356 * q^75 + 1321278185203718 * q^77 + 13747974994685232 * q^78 + 126874036566250 * q^79 - 18764997660746184 * q^80 - 2081051947014102 * q^81 - 11916006908925168 * q^82 + 17065299612720828 * q^84 + 27928718307758508 * q^85 - 7493915124549152 * q^86 - 4167264363403248 * q^87 - 10398917942882000 * q^88 - 34000447101257730 * q^89 + 6895892767523928 * q^91 + 113018032389709752 * q^92 - 15597881218045122 * q^93 - 7183919979926376 * q^94 - 19569222088313322 * q^95 - 137281944028491360 * q^96 + 65453414234371436 * q^98 + 142672614742345392 * q^99

Introduction

L-functions

Modular forms

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