LMFDB - Embedded newform 403.2.l.c.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +O(q^{10})$	\(q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +(1.32652 - 2.29760i) q^{10} +(2.29914 + 1.32741i) q^{11} +(0.793644 + 1.37463i) q^{12} +(1.98762 + 3.00822i) q^{13} +(-3.56964 - 6.18280i) q^{14} -0.894018i q^{15} -3.36799 q^{16} +(-0.311325 - 0.539231i) q^{17} +(-4.50337 - 2.60002i) q^{18} +(-3.82177 + 2.20650i) q^{19} +(-2.53011 - 1.46076i) q^{20} +(-2.08347 - 1.20289i) q^{21} +(2.74536 - 4.75510i) q^{22} -2.13692 q^{23} +(0.346410 - 0.200000i) q^{24} +(-1.67725 - 2.90508i) q^{25} +(6.22163 - 4.11082i) q^{26} -3.84313 q^{27} +(-6.80846 + 3.93087i) q^{28} -4.05259 q^{29} -1.84902 q^{30} +(5.48436 - 0.960081i) q^{31} +8.11358i q^{32} -1.85025i q^{33} +(-1.11524 + 0.643887i) q^{34} +4.42801 q^{35} +(-2.86313 + 4.95909i) q^{36} +(-5.19824 + 3.00121i) q^{37} +(4.56351 + 7.90423i) q^{38} +(1.12304 - 2.24794i) q^{39} +(-0.368114 + 0.637592i) q^{40} +(-0.662206 - 0.382325i) q^{41} +(-2.48784 + 4.30906i) q^{42} +(5.41024 + 9.37081i) q^{43} +(-5.23629 - 3.02317i) q^{44} +(2.79314 - 1.61262i) q^{45} +4.41960i q^{46} -8.87335i q^{47} +(1.17365 + 2.03281i) q^{48} +(2.45784 - 4.25711i) q^{49} +(-6.00832 + 3.46891i) q^{50} +(-0.216976 + 0.375813i) q^{51} +(-4.52681 - 6.85122i) q^{52} +(-5.00538 + 8.66957i) q^{53} +7.94841i q^{54} +(1.70276 + 2.94927i) q^{55} +(0.990586 + 1.71575i) q^{56} +(2.66355 + 1.53780i) q^{57} +8.38163i q^{58} +(5.08142 - 2.93376i) q^{59} +2.03613i q^{60} +4.84999 q^{61} +(-1.98565 - 11.3428i) q^{62} -8.67904i q^{63} +10.0446 q^{64} +(0.278647 + 4.61670i) q^{65} -3.82671 q^{66} +(7.78781 + 4.49629i) q^{67} +(0.709044 + 1.22810i) q^{68} +(0.744655 + 1.28978i) q^{69} -9.15807i q^{70} +(6.12061 + 3.53374i) q^{71} +(1.24970 + 0.721514i) q^{72} +(0.366719 + 0.211725i) q^{73} +(6.20714 + 10.7511i) q^{74} +(-1.16895 + 2.02467i) q^{75} +(8.70409 - 5.02531i) q^{76} +9.16418 q^{77} +(-4.64923 - 2.32268i) q^{78} +(-3.01527 - 5.22259i) q^{79} +(-3.74154 - 2.16018i) q^{80} +(-2.43219 - 4.21267i) q^{81} +(-0.790729 + 1.36958i) q^{82} +(-9.86842 - 5.69753i) q^{83} +(4.74511 + 2.73959i) q^{84} -0.798718i q^{85} +(19.3808 - 11.1895i) q^{86} +(1.41221 + 2.44602i) q^{87} +(-0.761845 + 1.31955i) q^{88} -11.5953i q^{89} +(-3.33524 - 5.77680i) q^{90} +(11.1339 + 5.56234i) q^{91} +4.86684 q^{92} +(-2.49062 - 2.97564i) q^{93} -18.3520 q^{94} -5.66087 q^{95} +(4.89711 - 2.82735i) q^{96} +18.6165i q^{97} +(-8.80461 - 5.08335i) q^{98} +(5.78065 - 3.33746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.06821i		−	1.46245i	−0.682138	−	0.731224i	$-0.738950\pi$
$2$		−	2.06821i		−	1.46245i	0.682138	−	0.731224i	$-0.261050\pi$
$3$	−0.348471	−	0.603570i	−0.201190	−	0.348471i	0.747722	−	0.664012i	$-0.231148\pi$
$3$	−0.348471	−	0.603570i	−0.201190	−	0.348471i	−0.948912	+	0.315541i	$0.897814\pi$
$4$	−2.27750			−1.13875
$5$	1.11091	+	0.641386i	0.496815	+	0.286836i	0.727397	−	0.686216i	$-0.240730\pi$
$5$	1.11091	+	0.641386i	0.496815	+	0.286836i	−0.230582	+	0.973053i	$0.574063\pi$
$6$	−1.24831	+	0.720713i	−0.509621	+	0.294230i
$7$	2.98944	−	1.72596i	1.12990	−	0.652350i	0.185993	−	0.982551i	$-0.440450\pi$
$7$	2.98944	−	1.72596i	1.12990	−	0.652350i	0.943911	+	0.330201i	$0.107117\pi$
$8$			0.573935i			0.202917i
$9$	1.25714	−	2.17742i	0.419045	−	0.725808i
$10$	1.32652	−	2.29760i	0.419483	−	0.726566i
$11$	2.29914	+	1.32741i	0.693216	+	0.400228i	0.804816	−	0.593525i	$-0.202264\pi$
$11$	2.29914	+	1.32741i	0.693216	+	0.400228i	−0.111600	+	0.993753i	$0.535598\pi$
$12$	0.793644	+	1.37463i	0.229105	+	0.396822i
$13$	1.98762	+	3.00822i	0.551267	+	0.834329i
$13$	1.98762	+	3.00822i	0.551267	+	0.834329i
$14$	−3.56964	−	6.18280i	−0.954027	−	1.65242i
$15$		−	0.894018i		−	0.230834i
$16$	−3.36799			−0.841997
$17$	−0.311325	−	0.539231i	−0.0755075	−	0.130783i	0.825799	−	0.563964i	$-0.190724\pi$
$17$	−0.311325	−	0.539231i	−0.0755075	−	0.130783i	−0.901307	+	0.433181i	$0.857391\pi$
$18$	−4.50337	−	2.60002i	−1.06146	−	0.612831i
$19$	−3.82177	+	2.20650i	−0.876773	+	0.506205i	−0.869593	−	0.493769i	$-0.835619\pi$
$19$	−3.82177	+	2.20650i	−0.876773	+	0.506205i	−0.00718028	+	0.999974i	$0.502286\pi$
$20$	−2.53011	−	1.46076i	−0.565749	−	0.326635i
$21$	−2.08347	−	1.20289i	−0.454650	−	0.262492i
$22$	2.74536	−	4.75510i	0.585313	−	1.01379i
$23$	−2.13692			−0.445578			−0.222789	−	0.974867i	$-0.571516\pi$
$23$	−2.13692			−0.445578			−0.222789	+	0.974867i	$0.571516\pi$
$24$	0.346410	−	0.200000i	0.0707106	−	0.0408248i
$25$	−1.67725	−	2.90508i	−0.335450	−	0.581016i
$26$	6.22163	−	4.11082i	1.22016	−	0.806199i
$27$	−3.84313			−0.739611
$28$	−6.80846	+	3.93087i	−1.28668	+	0.742864i
$29$	−4.05259			−0.752548			−0.376274	−	0.926508i	$-0.622795\pi$
$29$	−4.05259			−0.752548			−0.376274	+	0.926508i	$0.622795\pi$
$30$	−1.84902			−0.337583
$31$	5.48436	−	0.960081i	0.985021	−	0.172436i
$31$	5.48436	−	0.960081i	0.985021	−	0.172436i
$32$			8.11358i			1.43429i
$33$		−	1.85025i		−	0.322088i
$34$	−1.11524	+	0.643887i	−0.191263	+	0.110426i
$35$	4.42801			0.748471
$36$	−2.86313	+	4.95909i	−0.477188	+	0.826514i
$37$	−5.19824	+	3.00121i	−0.854586	+	0.493396i	−0.862196	−	0.506575i	$-0.830911\pi$
$37$	−5.19824	+	3.00121i	−0.854586	+	0.493396i	0.00760943	+	0.999971i	$0.497578\pi$
$38$	4.56351	+	7.90423i	0.740299	+	1.28223i
$39$	1.12304	−	2.24794i	0.179830	−	0.359959i
$40$	−0.368114	+	0.637592i	−0.0582039	+	0.100812i
$41$	−0.662206	−	0.382325i	−0.103419	−	0.0597091i	0.447398	−	0.894335i	$-0.352351\pi$
$41$	−0.662206	−	0.382325i	−0.103419	−	0.0597091i	−0.550818	+	0.834626i	$0.685684\pi$
$42$	−2.48784	+	4.30906i	−0.383881	+	0.664902i
$43$	5.41024	+	9.37081i	0.825054	+	1.42904i	0.901878	+	0.431990i	$0.142189\pi$
$43$	5.41024	+	9.37081i	0.825054	+	1.42904i	−0.0768244	+	0.997045i	$0.524478\pi$
$44$	−5.23629	−	3.02317i	−0.789400	−	0.455760i
$45$	2.79314	−	1.61262i	0.416376	−	0.240395i
$46$			4.41960i			0.651635i
$47$		−	8.87335i		−	1.29431i	−0.762358	−	0.647156i	$-0.775958\pi$
$47$		−	8.87335i		−	1.29431i	0.762358	−	0.647156i	$-0.224042\pi$
$48$	1.17365	+	2.03281i	0.169401	+	0.293412i
$49$	2.45784	−	4.25711i	0.351121	−	0.608159i
$50$	−6.00832	+	3.46891i	−0.849705	+	0.490577i
$51$	−0.216976	+	0.375813i	−0.0303827	+	0.0526244i
$52$	−4.52681	−	6.85122i	−0.627756	−	0.950093i
$53$	−5.00538	+	8.66957i	−0.687541	+	1.19086i	0.285089	+	0.958501i	$0.407977\pi$
$53$	−5.00538	+	8.66957i	−0.687541	+	1.19086i	−0.972631	+	0.232356i	$0.925357\pi$
$54$			7.94841i			1.08164i
$55$	1.70276	+	2.94927i	0.229600	+	0.397679i
$56$	0.990586	+	1.71575i	0.132373	+	0.229276i
$57$	2.66355	+	1.53780i	0.352796	+	0.203687i
$58$			8.38163i			1.10056i
$59$	5.08142	−	2.93376i	0.661544	−	0.381943i	−0.131321	−	0.991340i	$-0.541922\pi$
$59$	5.08142	−	2.93376i	0.661544	−	0.381943i	0.792865	+	0.609397i	$0.208588\pi$
$60$			2.03613i			0.262863i
$61$	4.84999			0.620978			0.310489	−	0.950577i	$-0.399507\pi$
$61$	4.84999			0.620978			0.310489	+	0.950577i	$0.399507\pi$
$62$	−1.98565	−	11.3428i	−0.252178	−	1.44054i
$63$		−	8.67904i		−	1.09346i
$64$	10.0446			1.25558
$65$	0.278647	+	4.61670i	0.0345619	+	0.572631i
$66$	−3.82671			−0.471036
$67$	7.78781	+	4.49629i	0.951432	+	0.549310i	0.893526	−	0.449012i	$-0.148224\pi$
$67$	7.78781	+	4.49629i	0.951432	+	0.549310i	0.0579067	+	0.998322i	$0.481557\pi$
$68$	0.709044	+	1.22810i	0.0859842	+	0.148929i
$69$	0.744655	+	1.28978i	0.0896459	+	0.155271i
$70$		−	9.15807i		−	1.09460i
$71$	6.12061	+	3.53374i	0.726383	+	0.419378i	0.817098	−	0.576499i	$-0.195582\pi$
$71$	6.12061	+	3.53374i	0.726383	+	0.419378i	−0.0907143	+	0.995877i	$0.528915\pi$
$72$	1.24970	+	0.721514i	0.147278	+	0.0850312i
$73$	0.366719	+	0.211725i	0.0429212	+	0.0247806i	0.521307	−	0.853369i	$-0.325445\pi$
$73$	0.366719	+	0.211725i	0.0429212	+	0.0247806i	−0.478386	+	0.878150i	$0.658778\pi$
$74$	6.20714	+	10.7511i	0.721565	+	1.24979i
$75$	−1.16895	+	2.02467i	−0.134978	+	0.233789i
$76$	8.70409	−	5.02531i	0.998427	−	0.576442i
$77$	9.16418			1.04436
$78$	−4.64923	−	2.32268i	−0.526421	−	0.262992i
$79$	−3.01527	−	5.22259i	−0.339244	−	0.587588i	0.645047	−	0.764143i	$-0.276838\pi$
$79$	−3.01527	−	5.22259i	−0.339244	−	0.587588i	−0.984291	+	0.176555i	$0.943505\pi$
$80$	−3.74154	−	2.16018i	−0.418317	−	0.241515i
$81$	−2.43219	−	4.21267i	−0.270243	−	0.468075i
$82$	−0.790729	+	1.36958i	−0.0873214	+	0.151245i
$83$	−9.86842	−	5.69753i	−1.08320	−	0.625386i	−0.151442	−	0.988466i	$-0.548392\pi$
$83$	−9.86842	−	5.69753i	−1.08320	−	0.625386i	−0.931758	+	0.363081i	$0.881725\pi$
$84$	4.74511	+	2.73959i	0.517734	+	0.298914i
$85$		−	0.798718i		−	0.0866332i
$86$	19.3808	−	11.1895i	2.08989	−	1.20660i
$87$	1.41221	+	2.44602i	0.151405	+	0.262241i
$88$	−0.761845	+	1.31955i	−0.0812130	+	0.140665i
$89$		−	11.5953i		−	1.22910i	−0.788879	−	0.614549i	$-0.789338\pi$
$89$		−	11.5953i		−	1.22910i	0.788879	−	0.614549i	$-0.210662\pi$
$90$	−3.33524	−	5.77680i	−0.351565	−	0.608928i
$91$	11.1339	+	5.56234i	1.16715	+	0.583092i
$92$	4.86684			0.507403
$93$	−2.49062	−	2.97564i	−0.258265	−	0.308559i
$94$	−18.3520			−1.89286
$95$	−5.66087			−0.580793
$96$	4.89711	−	2.82735i	0.499810	−	0.288565i
$97$			18.6165i			1.89022i	0.326751	+	0.945110i	$0.394046\pi$
$97$			18.6165i			1.89022i	−0.326751	+	0.945110i	$0.605954\pi$
$98$	−8.80461	−	5.08335i	−0.889400	−	0.513495i
$99$	5.78065	−	3.33746i	0.580977	−	0.335427i
$100$	3.81994	+	6.61633i	0.381994	+	0.661633i
$101$	−12.9078			−1.28438			−0.642190	−	0.766546i	$-0.721974\pi$
$101$	−12.9078			−1.28438			−0.642190	+	0.766546i	$0.721974\pi$
$102$	0.777261	+	0.448752i	0.0769603	+	0.0444331i
$103$	−4.32061	+	7.48352i	−0.425723	+	0.737373i	−0.996488	−	0.0837403i	$-0.973313\pi$
$103$	−4.32061	+	7.48352i	−0.425723	+	0.737373i	0.570765	+	0.821113i	$0.306647\pi$
$104$	−1.72652	+	1.14077i	−0.169299	+	0.111861i
$105$	−1.54304	−	2.67262i	−0.150585	−	0.260821i
$106$	17.9305	+	10.3522i	1.74156	+	1.00549i
$107$	−2.90223	−	5.02681i	−0.280569	−	0.485960i	0.690956	−	0.722897i	$-0.257190\pi$
$107$	−2.90223	−	5.02681i	−0.280569	−	0.485960i	−0.971525	+	0.236937i	$0.923857\pi$
$108$	8.75274			0.842233
$109$			9.17119i			0.878441i	0.898379	+	0.439220i	$0.144745\pi$
$109$			9.17119i			0.878441i	−0.898379	+	0.439220i	$0.855255\pi$
$110$	6.09971	−	3.52167i	0.581585	−	0.335778i
$111$	3.62288	+	2.09167i	0.343868	+	0.198532i
$112$	−10.0684	+	5.81299i	−0.951375	+	0.549276i
$113$	3.60544	−	6.24481i	0.339171	−	0.587462i	−0.645106	−	0.764093i	$-0.723187\pi$
$113$	3.60544	−	6.24481i	0.339171	−	0.587462i	0.984277	+	0.176631i	$0.0565200\pi$
$114$	3.18050	−	5.50879i	0.297881	−	0.515946i
$115$	−2.37393	−	1.37059i	−0.221370	−	0.127808i
$116$	9.22980			0.856965
$117$	9.04887	−	0.546157i	0.836568	−	0.0504922i
$118$	−6.06763	−	10.5095i	−0.558571	−	0.967473i
$119$	−1.86138	−	1.07467i	−0.170632	−	0.0985146i
$120$	0.513108			0.0468402
$121$	−1.97598	−	3.42250i	−0.179635	−	0.311137i
$122$		−	10.0308i		−	0.908147i
$123$			0.532917i			0.0480515i
$124$	−12.4907	+	2.18659i	−1.12169	+	0.196361i
$125$		−	10.7169i		−	0.958550i
$126$	−17.9501			−1.59912
$127$	6.26347	+	10.8487i	0.555793	+	0.962662i	0.997841	+	0.0656710i	$0.0209188\pi$
$127$	6.26347	+	10.8487i	0.555793	+	0.962662i	−0.442048	+	0.896991i	$0.645748\pi$
$128$		−	4.54728i		−	0.401927i
$129$	3.77063	−	6.53091i	0.331985	−	0.575015i
$130$	9.54831	−	0.576301i	0.837442	−	0.0505450i
$131$	7.15699	+	12.3963i	0.625309	+	1.08307i	0.988481	+	0.151344i	$0.0483603\pi$
$131$	7.15699	+	12.3963i	0.625309	+	1.08307i	−0.363172	+	0.931722i	$0.618306\pi$
$132$			4.21395i			0.366778i
$133$	−7.61664	+	13.1924i	−0.660446	+	1.14393i
$134$	9.29929	−	16.1068i	0.803336	−	1.39142i
$135$	−4.26938	−	2.46493i	−0.367450	−	0.212147i
$136$	0.309484	−	0.178680i	0.0265380	−	0.0153217i
$137$	8.49148	+	4.90256i	0.725476	+	0.418854i	0.816765	−	0.576971i	$-0.195765\pi$
$137$	8.49148	+	4.90256i	0.725476	+	0.418854i	−0.0912890	+	0.995824i	$0.529099\pi$
$138$	2.66754	−	1.54010i	0.227076	−	0.131102i
$139$	17.1513			1.45475			0.727377	−	0.686238i	$-0.240739\pi$
$139$	17.1513			1.45475			0.727377	+	0.686238i	$0.240739\pi$
$140$	−10.0848			−0.852322
$141$	−5.35569	+	3.09211i	−0.451030	+	0.260402i
$142$	7.30852	−	12.6587i	0.613317	−	1.06230i
$143$	0.576686	+	9.55468i	0.0482249	+	0.799002i
$144$	−4.23402	+	7.33353i	−0.352835	+	0.611128i
$145$	−4.50208	−	2.59928i	−0.373877	−	0.215858i
$146$	0.437893	−	0.758453i	0.0362403	−	0.0627700i
$147$	−3.42595			−0.282568
$148$	11.8390	−	6.83526i	0.973161	−	0.561855i
$149$	−1.18527	+	0.684314i	−0.0971008	+	0.0560611i	−0.547764	−	0.836633i	$-0.684521\pi$
$149$	−1.18527	+	0.684314i	−0.0971008	+	0.0560611i	0.450663	+	0.892694i	$0.351188\pi$
$150$	4.18745	+	2.41763i	0.341904	+	0.197398i
$151$			17.3987i			1.41588i	0.706270	+	0.707942i	$0.250376\pi$
$151$			17.3987i			1.41588i	−0.706270	+	0.707942i	$0.749624\pi$
$152$	−1.26639	−	2.19345i	−0.102718	−	0.177912i
$153$	−1.56551			−0.126564
$154$		−	18.9535i		−	1.52731i
$155$	6.70843	+	2.45103i	0.538834	+	0.196871i
$156$	−2.55773	+	5.11970i	−0.204782	+	0.409904i
$157$	−15.3718			−1.22681			−0.613403	−	0.789770i	$-0.710200\pi$
$157$	−15.3718			−1.22681			−0.613403	+	0.789770i	$0.710200\pi$
$158$	−10.8014	+	6.23621i	−0.859316	+	0.496126i
$159$	6.97692			0.553306
$160$	−5.20394	+	9.01348i	−0.411407	+	0.712578i
$161$	−6.38819	+	3.68823i	−0.503460	+	0.290673i
$162$	−8.71270	+	5.03028i	−0.684534	+	0.395216i
$163$			3.80971i			0.298400i	0.988807	+	0.149200i	$0.0476698\pi$
$163$			3.80971i			0.298400i	−0.988807	+	0.149200i	$0.952330\pi$
$164$	1.50818	+	0.870746i	0.117769	+	0.0679938i
$165$	1.18673	−	2.05547i	0.0923865	−	0.160018i
$166$	−11.7837	+	20.4100i	−0.914593	+	1.58412i
$167$	12.1600	−	7.02055i	0.940966	−	0.543267i	0.0507028	−	0.998714i	$-0.483854\pi$
$167$	12.1600	−	7.02055i	0.940966	−	0.543267i	0.890263	+	0.455447i	$0.150521\pi$
$168$	0.690382	−	1.19578i	0.0532641	−	0.0922561i
$169$	−5.09872	+	11.9584i	−0.392209	+	0.919876i
$170$	−1.65192			−0.126696
$171$			11.0955i			0.848492i
$172$	−12.3218	−	21.3420i	−0.939531	−	1.62732i
$173$	5.66149	−	9.80598i	0.430435	−	0.745535i	−0.566476	−	0.824078i	$-0.691694\pi$
$173$	5.66149	−	9.80598i	0.430435	−	0.745535i	0.996911	+	0.0785434i	$0.0250269\pi$
$174$	5.05890	−	2.92076i	0.383514	−	0.221422i
$175$	−10.0281	−	5.78971i	−0.758051	−	0.437661i
$176$	−7.74346	−	4.47069i	−0.583685	−	0.336991i
$177$	−3.54146	−	2.04466i	−0.266192	−	0.153686i
$178$	−23.9815			−1.79749
$179$	5.99710	+	10.3873i	0.448245	+	0.776382i	0.998272	−	0.0587644i	$-0.0187161\pi$
$179$	5.99710	+	10.3873i	0.448245	+	0.776382i	−0.550027	+	0.835147i	$0.685383\pi$
$180$	−6.36138	+	3.67274i	−0.474149	+	0.273750i
$181$	4.35364	−	7.54072i	0.323603	−	0.560497i	−0.657625	−	0.753345i	$-0.728439\pi$
$181$	4.35364	−	7.54072i	0.323603	−	0.560497i	0.981229	+	0.192848i	$0.0617724\pi$
$182$	11.5041	−	23.0273i	0.852741	−	1.70690i
$183$	−1.69008	−	2.92731i	−0.124935	−	0.216393i
$184$		−	1.22645i		−	0.0904153i
$185$	−7.69973			−0.566095
$186$	−6.15425	+	5.15113i	−0.451251	+	0.377699i
$187$		−	1.65302i		−	0.120881i
$188$			20.2091i			1.47390i
$189$	−11.4888	+	6.63307i	−0.835688	+	0.482485i
$190$			11.7079i			0.849379i
$191$	−0.249217	+	0.431657i	−0.0180327	+	0.0312336i	−0.874901	−	0.484302i	$-0.839074\pi$
$191$	−0.249217	+	0.431657i	−0.0180327	+	0.0312336i	0.856868	+	0.515535i	$0.172407\pi$
$192$	−3.50027	−	6.06264i	−0.252610	−	0.437533i
$193$	3.56944	−	2.06082i	0.256934	−	0.148341i	−0.366001	−	0.930614i	$-0.619273\pi$
$193$	3.56944	−	2.06082i	0.256934	−	0.148341i	0.622935	+	0.782274i	$0.285940\pi$
$194$	38.5029			2.76435
$195$	2.68940	−	1.77697i	0.192592	−	0.127251i
$196$	−5.59775	+	9.69558i	−0.399839	+	0.692542i
$197$	−19.3805	−	11.1893i	−1.38080	−	0.797206i	−0.388546	−	0.921429i	$-0.627023\pi$
$197$	−19.3805	−	11.1893i	−1.38080	−	0.797206i	−0.992254	+	0.124224i	$0.960356\pi$
$198$	−6.90258	−	11.9556i	−0.490545	−	0.849649i
$199$	9.89986	−	17.1471i	0.701782	−	1.21552i	−0.266058	−	0.963957i	$-0.585721\pi$
$199$	9.89986	−	17.1471i	0.701782	−	1.21552i	0.967840	−	0.251565i	$-0.0809454\pi$
$200$	1.66733	−	0.962631i	0.117898	−	0.0680683i
$201$		−	6.26731i		−	0.442062i
$202$			26.6962i			1.87834i
$203$	−12.1150	+	6.99460i	−0.850306	+	0.490925i
$204$	0.494163	−	0.855915i	0.0345983	−	0.0599261i
$205$	−0.490435	−	0.849459i	−0.0342535	−	0.0593288i
$206$	15.4775	+	8.93594i	1.07837	+	0.622597i
$207$	−2.68640	+	4.65297i	−0.186717	+	0.323404i
$208$	−6.69428	−	10.1316i	−0.464165	−	0.702502i
$209$	−11.7157			−0.810391
$210$	−5.52754	+	3.19132i	−0.381436	+	0.220222i
$211$	−6.72757	−	11.6525i	−0.463145	−	0.802191i	0.535971	−	0.844237i	$-0.319946\pi$
$211$	−6.72757	−	11.6525i	−0.463145	−	0.802191i	−0.999116	+	0.0420460i	$0.986612\pi$
$212$	11.3998	−	19.7450i	0.782939	−	1.35609i
$213$		−	4.92562i		−	0.337498i
$214$	−10.3965	+	6.00243i	−0.710691	+	0.410318i
$215$			13.8802i			0.946622i
$216$		−	2.20571i		−	0.150079i
$217$	14.7381	−	12.3359i	1.00049	−	0.837414i
$218$	18.9680			1.28467
$219$		−	0.295121i		−	0.0199424i
$220$	−3.87804	−	6.71696i	−0.261457	−	0.452858i
$221$	1.00333	−	2.00832i	0.0674911	−	0.135094i
$222$	4.32602	−	7.49288i	0.290343	−	0.502889i
$223$	−12.9438	+	7.47308i	−0.866778	+	0.500435i	−0.866276	−	0.499565i	$-0.833493\pi$
$223$	−12.9438	+	7.47308i	−0.866778	+	0.500435i	−0.000501934		1.00000i	$0.500160\pi$
$224$	14.0037	+	24.2551i	0.935660	+	1.62061i
$225$	−8.43412			−0.562274
$226$	−12.9156	−	7.45682i	−0.859132	−	0.496020i
$227$	−9.55725	−	5.51788i	−0.634337	−	0.366234i	0.148093	−	0.988973i	$-0.452687\pi$
$227$	−9.55725	−	5.51788i	−0.634337	−	0.366234i	−0.782430	+	0.622739i	$0.786020\pi$
$228$	−6.06625	−	3.50235i	−0.401747	−	0.231949i
$229$	1.53880	−	0.888428i	0.101687	−	0.0587090i	−0.448294	−	0.893886i	$-0.647968\pi$
$229$	1.53880	−	0.888428i	0.101687	−	0.0587090i	0.549981	+	0.835177i	$0.314635\pi$
$230$	−2.83467	+	4.90979i	−0.186913	+	0.323742i
$231$	−3.19345	−	5.53122i	−0.210114	−	0.363928i
$232$		−	2.32593i		−	0.152704i
$233$	−29.5964			−1.93893			−0.969463	−	0.245236i	$-0.921135\pi$
$233$	−29.5964			−1.93893			−0.969463	+	0.245236i	$0.921135\pi$
$234$	−1.12957	−	18.7150i	−0.0738422	−	1.22344i
$235$	5.69124	−	9.85752i	0.371256	−	0.643034i
$236$	−11.5729	+	6.68164i	−0.753334	+	0.434938i
$237$	−2.10147	+	3.63985i	−0.136505	+	0.236434i
$238$	−2.22264	+	3.84972i	−0.144072	+	0.249541i
$239$	21.6614	+	12.5062i	1.40116	+	0.808961i	0.994512	−	0.104624i	$-0.0333639\pi$
$239$	21.6614	+	12.5062i	1.40116	+	0.808961i	0.406649	+	0.913584i	$0.366697\pi$
$240$			3.01104i			0.194362i
$241$	3.34243	−	1.92975i	0.215305	−	0.124306i	−0.388469	−	0.921462i	$-0.626996\pi$
$241$	3.34243	−	1.92975i	0.215305	−	0.124306i	0.603774	+	0.797155i	$0.293663\pi$
$242$	−7.07846	+	4.08675i	−0.455021	+	0.262706i
$243$	−7.45979	+	12.9207i	−0.478546	+	0.828865i
$244$	−11.0459			−0.707140
$245$	5.46090	−	3.15285i	0.348884	−	0.201428i
$246$	1.10218			0.0702727
$247$	−14.2338	−	7.11102i	−0.905678	−	0.452463i
$248$	0.551024	+	3.14767i	0.0349901	+	0.199877i
$249$			7.94171i			0.503285i
$250$	−22.1649			−1.40183
$251$	5.31184	+	9.20038i	0.335281	+	0.580723i	0.983539	−	0.180698i	$-0.0578355\pi$
$251$	5.31184	+	9.20038i	0.335281	+	0.580723i	−0.648258	+	0.761421i	$0.724502\pi$
$252$			19.7665i			1.24517i
$253$	−4.91307	−	2.83656i	−0.308882	−	0.178333i
$254$	22.4373	−	12.9542i	1.40784	−	0.812818i
$255$	−0.482082	+	0.278330i	−0.0301892	+	0.0174297i
$256$	10.6845			0.667783
$257$	15.0513	−	26.0696i	0.938873	−	1.62618i	0.171296	−	0.985220i	$-0.445204\pi$
$257$	15.0513	−	26.0696i	0.938873	−	1.62618i	0.767577	−	0.640957i	$-0.221462\pi$
$258$	−13.5073	−	7.79845i	−0.840929	−	0.485511i
$259$	−10.3599	+	17.9439i	−0.643733	+	1.11498i
$260$	−0.634620	−	10.5145i	−0.0393574	−	0.652084i
$261$	−5.09466	+	8.82421i	−0.315352	+	0.546205i
$262$	25.6381	−	14.8022i	1.58393	−	0.914481i
$263$	1.94425			0.119887			0.0599437	−	0.998202i	$-0.480908\pi$
$263$	1.94425			0.119887			0.0599437	+	0.998202i	$0.480908\pi$
$264$	1.06192			0.0653569
$265$	−11.1211	+	6.42076i	−0.683162	+	0.394424i
$266$	27.2847	+	15.7528i	1.67293	+	0.965867i
$267$	−6.99856	+	4.04062i	−0.428305	+	0.247282i
$268$	−17.7368	−	10.2403i	−1.08344	−	0.625527i
$269$	−0.863890	+	1.49630i	−0.0526723	+	0.0912311i	−0.891159	−	0.453690i	$-0.850107\pi$
$269$	−0.863890	+	1.49630i	−0.0526723	+	0.0912311i	0.838487	+	0.544921i	$0.183441\pi$
$270$	−5.09800	+	8.82999i	−0.310254	+	0.537376i
$271$		−	17.1850i		−	1.04392i	−0.852971	−	0.521959i	$-0.825202\pi$
$271$		−	17.1850i		−	1.04392i	0.852971	−	0.521959i	$-0.174798\pi$
$272$	1.04854	+	1.81612i	0.0635770	+	0.110119i
$273$	−0.522591	−	8.65842i	−0.0316286	−	0.524031i
$274$	10.1395	−	17.5622i	0.612551	−	1.06097i
$275$		−	8.90556i		−	0.537026i
$276$	−1.69595	−	2.93748i	−0.102084	−	0.176815i
$277$	−19.9631			−1.19947			−0.599735	−	0.800199i	$-0.704727\pi$
$277$	−19.9631			−1.19947			−0.599735	+	0.800199i	$0.704727\pi$
$278$		−	35.4725i		−	2.12750i
$279$	4.80409	−	13.1487i	0.287613	−	0.787194i
$280$			2.54139i			0.151877i
$281$			13.1808i			0.786301i	0.919474	+	0.393151i	$0.128615\pi$
$281$			13.1808i			0.786301i	−0.919474	+	0.393151i	$0.871385\pi$
$282$	6.39513	+	11.0767i	0.380825	+	0.659608i
$283$	−7.22978			−0.429766			−0.214883	−	0.976640i	$-0.568937\pi$
$283$	−7.22978			−0.429766			−0.214883	+	0.976640i	$0.568937\pi$
$284$	−13.9397	−	8.04810i	−0.827170	−	0.477567i
$285$	1.97265	+	3.41673i	0.116850	+	0.202390i
$286$	19.7611	−	1.19271i	1.16850	−	0.0705263i
$287$	−2.63950			−0.155805
$288$	17.6667	+	10.1999i	1.04102	+	0.601033i
$289$	8.30615	−	14.3867i	0.488597	−	0.846275i
$290$	−5.37586	+	9.31126i	−0.315681	+	0.546776i
$291$	11.2364	−	6.48732i	0.658688	−	0.380293i
$292$	−0.835203	−	0.482205i	−0.0488766	−	0.0282189i
$293$	12.8562	−	7.42253i	0.751067	−	0.433629i	−0.0750123	−	0.997183i	$-0.523900\pi$
$293$	12.8562	−	7.42253i	0.751067	−	0.433629i	0.826079	+	0.563554i	$0.190566\pi$
$294$			7.08560i			0.413240i
$295$	7.52668			0.438220
$296$	−1.72250	−	2.98345i	−0.100118	−	0.173410i
$297$	−8.83588	−	5.10140i	−0.512710	−	0.296013i
$298$	1.41531	+	2.45138i	0.0819865	+	0.142005i
$299$	−4.24738	−	6.42831i	−0.245633	−	0.371759i
$300$	2.66228	−	4.61120i	0.153707	−	0.266228i
$301$	32.3472	+	18.6757i	1.86446	+	1.07645i
$302$	35.9842			2.07066
$303$	4.49801	+	7.79079i	0.258404	+	0.447569i
$304$	12.8717	−	7.43146i	0.738240	−	0.426223i
$305$	5.38792	+	3.11072i	0.308511	+	0.178119i
$306$			3.23781i			0.185093i
$307$	19.0027	−	10.9712i	1.08454	−	0.626161i	0.152425	−	0.988315i	$-0.451292\pi$
$307$	19.0027	−	10.9712i	1.08454	−	0.626161i	0.932118	+	0.362154i	$0.117958\pi$
$308$	−20.8714			−1.18926
$309$	6.02244			0.342604
$310$	5.06924	−	13.8745i	0.287914	−	0.788017i
$311$	−13.2676			−0.752337			−0.376169	−	0.926551i	$-0.622759\pi$
$311$	−13.2676			−0.752337			−0.376169	+	0.926551i	$0.622759\pi$
$312$	1.29017	+	0.644552i	0.0730417	+	0.0364905i
$313$	1.21832	+	2.11020i	0.0688637	+	0.119275i	0.898401	−	0.439175i	$-0.144729\pi$
$313$	1.21832	+	2.11020i	0.0688637	+	0.119275i	−0.829538	+	0.558451i	$0.811396\pi$
$314$			31.7922i			1.79414i
$315$	5.56661	−	9.64166i	0.313643	−	0.543246i
$316$	6.86728	+	11.8945i	0.386315	+	0.669116i
$317$	−13.1774	+	7.60797i	−0.740116	+	0.427306i	−0.822112	−	0.569326i	$-0.807204\pi$
$317$	−13.1774	+	7.60797i	−0.740116	+	0.427306i	0.0819953	+	0.996633i	$0.473871\pi$
$318$		−	14.4298i		−	0.809180i
$319$	−9.31747	−	5.37944i	−0.521678	−	0.301191i
$320$	11.1587	+	6.44249i	0.623791	+	0.360146i
$321$	−2.02269	+	3.50340i	−0.112895	+	0.195541i
$322$	7.62804	+	13.2121i	0.425094	+	0.736284i
$323$	2.37963	+	1.37388i	0.132406	+	0.0764446i
$324$	5.53931	+	9.59437i	0.307740	+	0.533021i
$325$	5.40537	−	10.8197i	0.299836	−	0.600170i
$326$	7.87930			0.436394
$327$	5.53545	−	3.19590i	0.306111	−	0.176733i
$328$	0.219430	−	0.380063i	0.0121160	−	0.0209855i
$329$	−15.3150	−	26.5264i	−0.844344	−	1.46245i
$330$	−4.25115	−	2.45440i	−0.234018	−	0.135110i
$331$	−7.48571	−	4.32187i	−0.411452	−	0.237552i	0.279962	−	0.960011i	$-0.409678\pi$
$331$	−7.48571	−	4.32187i	−0.411452	−	0.237552i	−0.691413	+	0.722459i	$0.743012\pi$
$332$	22.4753	+	12.9761i	1.23349	+	0.712159i
$333$			15.0917i			0.827020i
$334$	−14.5200	−	25.1494i	−0.794499	−	1.37611i
$335$	5.76772	+	9.98998i	0.315124	+	0.545811i
$336$	7.01710	+	4.05132i	0.382814	+	0.221018i
$337$	−0.0583086			−0.00317627			−0.00158814	−	0.999999i	$-0.500506\pi$
$337$	−0.0583086			−0.00317627			−0.00158814	+	0.999999i	$0.500506\pi$
$338$	24.7325	+	10.5452i	1.34527	+	0.573586i
$339$	−5.02557			−0.272952
$340$			1.81908i			0.0986536i
$341$	13.8837	+	5.07263i	0.751845	+	0.274698i
$342$	22.9478			1.24087
$343$			7.19485i			0.388486i
$344$	−5.37824	+	3.10513i	−0.289975	+	0.167417i
$345$			1.91044i			0.102855i
$346$	−20.2809	−	11.7092i	−1.09031	−	0.629488i
$347$	−10.5059	−	18.1968i	−0.563986	−	0.976853i	−0.997143	−	0.0755344i	$-0.975934\pi$
$347$	−10.5059	−	18.1968i	−0.563986	−	0.976853i	0.433157	−	0.901319i	$-0.357400\pi$
$348$	−3.21632	−	5.57083i	−0.172413	−	0.298628i
$349$			0.151167i			0.00809178i	0.999992	+	0.00404589i	$0.00128785\pi$
$349$			0.151167i			0.00809178i	−0.999992	+	0.00404589i	$0.998712\pi$
$350$	−11.9744	+	20.7402i	−0.640056	+	1.10861i
$351$	−7.63869	−	11.5610i	−0.407723	−	0.617079i
$352$	−10.7700	+	18.6542i	−0.574044	+	0.994274i
$353$	−2.43304	+	1.40472i	−0.129498	+	0.0747655i	−0.563349	−	0.826219i	$-0.690487\pi$
$353$	−2.43304	+	1.40472i	−0.129498	+	0.0747655i	0.433852	+	0.900984i	$0.357154\pi$
$354$	−4.22879	+	7.32448i	−0.224758	+	0.389292i
$355$	4.53298	+	7.85135i	0.240586	+	0.416706i
$356$			26.4083i			1.39964i
$357$			1.49796i			0.0792806i
$358$	21.4831	−	12.4033i	1.13542	−	0.655534i
$359$	3.52243	+	2.03367i	0.185906	+	0.107333i	0.590065	−	0.807356i	$-0.299102\pi$
$359$	3.52243	+	2.03367i	0.185906	+	0.107333i	−0.404158	+	0.914689i	$0.632436\pi$
$360$	0.925538	+	1.60308i	0.0487801	+	0.0844897i
$361$	0.237269	−	0.410962i	0.0124878	−	0.0216296i
$362$	−15.5958	−	9.00424i	−0.819697	−	0.473253i
$363$	−1.37715	+	2.38529i	−0.0722814	+	0.125195i
$364$	−25.3575	−	12.6683i	−1.32910	−	0.663997i
$365$	0.271595	+	0.470417i	0.0142159	+	0.0246227i
$366$	−6.05430	+	3.49545i	−0.316463	+	0.182710i
$367$	−15.1851	+	26.3013i	−0.792655	+	1.37292i	0.131663	+	0.991295i	$0.457968\pi$
$367$	−15.1851	+	26.3013i	−0.792655	+	1.37292i	−0.924318	+	0.381624i	$0.875365\pi$
$368$	7.19711			0.375175
$369$	−1.66497	+	0.961268i	−0.0866746	+	0.0500416i
$370$			15.9247i			0.827884i
$371$			34.5562i			1.79407i
$372$	5.67239	+	6.77702i	0.294100	+	0.351372i
$373$	24.7458			1.28129			0.640645	−	0.767838i	$-0.278667\pi$
$373$	24.7458			1.28129			0.640645	+	0.767838i	$0.278667\pi$
$374$	−3.41880			−0.176782
$375$	−6.46840	+	3.73454i	−0.334027	+	0.192851i
$376$	5.09273			0.262637
$377$	−8.05502	−	12.1911i	−0.414855	−	0.627872i
$378$	13.7186	+	23.7613i	0.705609	+	1.22215i
$379$	15.6277	−	9.02266i	0.802741	−	0.463463i	−0.0416878	−	0.999131i	$-0.513273\pi$
$379$	15.6277	−	9.02266i	0.802741	−	0.463463i	0.844429	+	0.535668i	$0.179940\pi$
$380$	12.8926			0.661379
$381$	4.36528	−	7.56089i	0.223640	−	0.387356i
$382$	0.892758	+	0.515434i	0.0456775	+	0.0263719i
$383$	13.1254	+	7.57795i	0.670676	+	0.387215i	0.796333	−	0.604859i	$-0.206770\pi$
$383$	13.1254	+	7.57795i	0.670676	+	0.387215i	−0.125657	+	0.992074i	$0.540104\pi$
$384$	−2.74460	+	1.58460i	−0.140060	+	0.0808636i
$385$	10.1806	+	5.87778i	0.518852	+	0.299559i
$386$	−4.26220	−	7.38236i	−0.216941	−	0.375752i
$387$	27.2056			1.38294
$388$		−	42.3992i		−	2.15249i
$389$	−16.5610	−	28.6845i	−0.839675	−	1.45436i	−0.890166	−	0.455635i	$-0.849412\pi$
$389$	−16.5610	−	28.6845i	−0.839675	−	1.45436i	0.0504913	−	0.998725i	$-0.483921\pi$
$390$	−3.67515	−	5.56225i	−0.186098	−	0.281655i
$391$	0.665277	+	1.15229i	0.0336445	+	0.0582740i
$392$	2.44331	+	1.41064i	0.123406	+	0.0712482i
$393$	4.98801	−	8.63948i	0.251612	−	0.435804i
$394$	−23.1419	+	40.0829i	−1.16587	+	2.01935i
$395$		−	7.73580i		−	0.389230i
$396$	−13.1655	+	7.60108i	−0.661589	+	0.381968i
$397$	−10.8382	+	6.25743i	−0.543953	+	0.314052i	−0.746680	−	0.665184i	$-0.768353\pi$
$397$	−10.8382	+	6.25743i	−0.543953	+	0.314052i	0.202726	+	0.979235i	$0.435020\pi$
$398$	−35.4638	−	20.4750i	−1.77764	−	1.02632i
$399$	10.6167			0.531500
$400$	5.64895	+	9.78427i	0.282447	+	0.489213i
$401$		−	15.2680i		−	0.762449i	−0.924482	−	0.381225i	$-0.875502\pi$
$401$		−	15.2680i		−	0.762449i	0.924482	−	0.381225i	$-0.124498\pi$
$402$	−12.9621			−0.646493
$403$	13.7890	+	14.5899i	0.686877	+	0.726773i
$404$	29.3977			1.46259
$405$		−	6.23988i		−	0.310062i
$406$	14.4663	+	25.0564i	0.717951	+	1.24353i
$407$	−15.9353			−0.789883
$408$	−0.215692	−	0.124530i	−0.0106784	−	0.00616515i
$409$	−0.298830	+	0.172530i	−0.0147762	+	0.00853104i	−0.507370	−	0.861728i	$-0.669382\pi$
$409$	−0.298830	+	0.172530i	−0.0147762	+	0.00853104i	0.492594	+	0.870259i	$0.336049\pi$
$410$	−1.75686	+	1.01432i	−0.0867652	+	0.0500939i
$411$		−	6.83360i		−	0.337077i
$412$	9.84021	−	17.0437i	0.484792	−	0.839685i
$413$	10.1271	−	17.5406i	0.498321	−	0.863117i
$414$	9.62334	+	5.55604i	0.472961	+	0.273064i
$415$	−7.30863	−	12.6589i	−0.358767	−	0.621402i
$416$	−24.4074	+	16.1267i	−1.19667	+	0.790678i
$417$	−5.97673	−	10.3520i	−0.292682	−	0.506940i
$418$			24.2305i			1.18515i
$419$	−27.6444			−1.35052			−0.675258	−	0.737582i	$-0.735968\pi$
$419$	−27.6444			−1.35052			−0.675258	+	0.737582i	$0.735968\pi$
$420$	3.51427	+	6.08689i	0.171479	+	0.297010i
$421$	−15.4574	−	8.92435i	−0.753349	−	0.434946i	0.0735539	−	0.997291i	$-0.476566\pi$
$421$	−15.4574	−	8.92435i	−0.753349	−	0.434946i	−0.826903	+	0.562345i	$0.809899\pi$
$422$	−24.0998	+	13.9140i	−1.17316	+	0.677325i
$423$	−19.3210	−	11.1550i	−0.939421	−	0.542375i
$424$	−4.97577	−	2.87276i	−0.241645	−	0.139514i
$425$	−1.04434	+	1.80885i	−0.0506579	+	0.0877421i
$426$	−10.1872			−0.493573
$427$	14.4988	−	8.37087i	0.701645	−	0.405095i
$428$	6.60984	+	11.4486i	0.319499	+	0.553388i
$429$	5.56596	−	3.67760i	0.268727	−	0.177556i
$430$	28.7072			1.38438
$431$	8.13460	−	4.69651i	0.391830	−	0.226223i	−0.291123	−	0.956686i	$-0.594029\pi$
$431$	8.13460	−	4.69651i	0.391830	−	0.226223i	0.682953	+	0.730463i	$0.260695\pi$
$432$	12.9436			0.622750
$433$	−28.9476			−1.39113			−0.695567	−	0.718461i	$-0.744847\pi$
$433$	−28.9476			−1.39113			−0.695567	+	0.718461i	$0.744847\pi$
$434$	−25.5132	−	30.4816i	−1.22467	−	1.46316i
$435$			3.62309i			0.173714i
$436$		−	20.8874i		−	1.00033i
$437$	8.16680	−	4.71511i	0.390671	−	0.225554i
$438$	−0.610372			−0.0291647
$439$	−7.38765	+	12.7958i	−0.352593	+	0.610710i	−0.986703	−	0.162533i	$-0.948033\pi$
$439$	−7.38765	+	12.7958i	−0.352593	+	0.610710i	0.634110	+	0.773243i	$0.281367\pi$
$440$	−1.69269	+	0.977273i	−0.0806957	+	0.0465897i
$441$	−6.17969	−	10.7035i	−0.294271	−	0.509692i
$442$	−4.15363	−	2.07509i	−0.197568	−	0.0987021i
$443$	−3.34122	+	5.78716i	−0.158746	+	0.274956i	−0.934417	−	0.356182i	$-0.884078\pi$
$443$	−3.34122	+	5.78716i	−0.158746	+	0.274956i	0.775671	+	0.631138i	$0.217412\pi$
$444$	−8.25111	−	4.76378i	−0.391581	−	0.226079i
$445$	7.43705	−	12.8814i	0.352550	−	0.610635i
$446$	15.4559	+	26.7704i	0.731859	+	1.26762i
$447$	0.826062	+	0.476927i	0.0390714	+	0.0225579i
$448$	30.0279	−	17.3366i	1.41868	−	0.819077i
$449$			18.2760i			0.862498i	0.902233	+	0.431249i	$0.141927\pi$
$449$			18.2760i			0.862498i	−0.902233	+	0.431249i	$0.858073\pi$
$450$			17.4435i			0.822296i
$451$	−1.01500	−	1.75803i	−0.0477945	−	0.0827826i
$452$	−8.21140	+	14.2226i	−0.386232	+	0.668973i
$453$	10.5013	−	6.06294i	0.493395	−	0.284862i
$454$	−11.4121	+	19.7664i	−0.535598	+	0.927684i
$455$	8.80121	+	13.3204i	0.412607	+	0.624471i
$456$	−0.882598	+	1.52871i	−0.0413315	+	0.0715882i
$457$			6.65501i			0.311308i	0.987812	+	0.155654i	$0.0497485\pi$
$457$			6.65501i			0.311308i	−0.987812	+	0.155654i	$0.950251\pi$
$458$	−1.83746	−	3.18257i	−0.0858588	−	0.148712i
$459$	1.19646	+	2.07234i	0.0558461	+	0.0967283i
$460$	5.40663	+	3.12152i	0.252086	+	0.145542i
$461$			14.2356i			0.663019i	0.943452	+	0.331510i	$0.107558\pi$
$461$			14.2356i			0.663019i	−0.943452	+	0.331510i	$0.892442\pi$
$462$	−11.4397	+	6.60474i	−0.532225	+	0.307280i
$463$		−	14.8710i		−	0.691112i	−0.938398	−	0.345556i	$-0.887690\pi$
$463$		−	14.8710i		−	0.691112i	0.938398	−	0.345556i	$-0.112310\pi$
$464$	13.6491			0.633643
$465$	−0.858330	−	4.90312i	−0.0398041	−	0.227377i
$466$			61.2117i			2.83558i
$467$	−31.3260			−1.44959			−0.724797	−	0.688963i	$-0.758066\pi$
$467$	−31.3260			−1.44959			−0.724797	+	0.688963i	$0.758066\pi$
$468$	−20.6088	+	1.24387i	−0.952643	+	0.0574981i
$469$	31.0416			1.43337
$470$	−20.3874	−	11.7707i	−0.940403	−	0.542942i
$471$	5.35664	+	9.27797i	0.246821	+	0.427506i
$472$	1.68379	+	2.91640i	0.0775025	+	0.134238i
$473$			28.7264i			1.32084i
$474$	7.52798	+	4.34628i	0.345772	+	0.199631i
$475$	12.8201	+	7.40169i	0.588227	+	0.339613i
$476$	4.23929	+	2.44756i	0.194308	+	0.112184i
$477$	12.5849	+	21.7976i	0.576222	+	0.998046i
$478$	25.8655	−	44.8004i	1.18306	−	2.04912i
$479$	−1.28492	+	0.741848i	−0.0587094	+	0.0338959i	−0.529067	−	0.848580i	$-0.677458\pi$
$479$	−1.28492	+	0.741848i	−0.0587094	+	0.0338959i	0.470358	+	0.882476i	$0.344125\pi$
$480$	7.25369			0.331084
$481$	−19.3604	−	9.67218i	−0.882759	−	0.441013i
$482$	−3.99114	−	6.91286i	−0.181791	−	0.314872i
$483$	4.45220	+	2.57048i	0.202582	+	0.116961i
$484$	4.50031	+	7.79476i	0.204559	+	0.354307i
$485$	−11.9404	+	20.6813i	−0.542184	+	0.939091i
$486$	26.7228	+	15.4284i	1.21217	+	0.699848i
$487$	−23.0573	−	13.3121i	−1.04482	−	0.603229i	−0.123628	−	0.992329i	$-0.539453\pi$
$487$	−23.0573	−	13.3121i	−1.04482	−	0.603229i	−0.921196	+	0.389099i	$0.872786\pi$
$488$			2.78358i			0.126007i
$489$	2.29943	−	1.32758i	0.103984	−	0.0600351i
$490$	−6.52077	−	11.2943i	−0.294578	−	0.510225i
$491$	1.47636	−	2.55713i	0.0666271	−	0.115401i	−0.830788	−	0.556590i	$-0.812110\pi$
$491$	1.47636	−	2.55713i	0.0666271	−	0.115401i	0.897415	+	0.441188i	$0.145443\pi$
$492$		−	1.21372i		−	0.0547187i
$493$	1.26167	+	2.18529i	0.0568230	+	0.0984203i
$494$	−14.7071	+	29.4386i	−0.661703	+	1.32451i
$495$	8.56240			0.384851
$496$	−18.4713	+	3.23354i	−0.829384	+	0.145190i
$497$	24.3963			1.09432
$498$	16.4251			0.736028
$499$	10.3354	−	5.96714i	0.462676	−	0.267126i	−0.250493	−	0.968118i	$-0.580593\pi$
$499$	10.3354	−	5.96714i	0.462676	−	0.267126i	0.713169	+	0.700992i	$0.247259\pi$
$500$			24.4078i			1.09155i
$501$	−8.47479	−	4.89292i	−0.378626	−	0.218600i
$502$	19.0283	−	10.9860i	0.849277	−	0.490330i
$503$	−0.399467	−	0.691896i	−0.0178113	−	0.0308501i	0.856982	−	0.515346i	$-0.172336\pi$
$503$	−0.399467	−	0.691896i	−0.0178113	−	0.0308501i	−0.874794	+	0.484496i	$0.839003\pi$
$504$	4.98120			0.221880
$505$	−14.3395	−	8.27891i	−0.638099	−	0.368407i
$506$	−5.86661	+	10.1613i	−0.260803	+	0.451723i
$507$	8.99448	−	1.08972i	0.399459	−	0.0483961i
$508$	−14.2651	−	24.7078i	−0.632911	−	1.09623i
$509$	−3.60542	−	2.08159i	−0.159807	−	0.0922648i	0.417964	−	0.908464i	$-0.362744\pi$
$509$	−3.60542	−	2.08159i	−0.159807	−	0.0922648i	−0.577771	+	0.816199i	$0.696077\pi$
$510$	0.575646	+	0.997049i	0.0254900	+	0.0441501i
$511$	1.46171			0.0646624
$512$		−	31.1924i		−	1.37852i
$513$	14.6875	−	8.47986i	0.648471	−	0.374395i
$514$	−53.9175	−	31.1293i	−2.37820	−	1.37305i
$515$	−9.59965	+	5.54236i	−0.423011	+	0.244226i
$516$	−8.58761	+	14.8742i	−0.378048	+	0.654799i
$517$	11.7785	−	20.4010i	0.518020	−	0.897237i
$518$	37.1118	+	21.4265i	1.63060	+	0.941426i
$519$	−7.89146			−0.346397
$520$	−2.64968	+	0.159925i	−0.116196	+	0.00701319i
$521$	16.9377	+	29.3369i	0.742053	+	1.28527i	0.951559	+	0.307467i	$0.0994813\pi$
$521$	16.9377	+	29.3369i	0.742053	+	1.28527i	−0.209505	+	0.977808i	$0.567185\pi$
$522$	18.2503	+	10.5368i	0.798796	+	0.461185i
$523$	24.4347			1.06845			0.534227	−	0.845341i	$-0.320603\pi$
$523$	24.4347			1.06845			0.534227	+	0.845341i	$0.320603\pi$
$524$	−16.3001	−	28.2325i	−0.712071	−	1.23334i
$525$			8.07019i			0.352212i
$526$		−	4.02112i		−	0.175329i
$527$	−2.22513	−	2.65844i	−0.0969280	−	0.115804i
$528$			6.23162i			0.271197i
$529$	−18.4336			−0.801460
$530$	13.2795	+	23.0007i	0.576824	+	0.999089i
$531$		−	14.7525i		−	0.640205i
$532$	17.3469	−	30.0457i	0.752084	−	1.30265i
$533$	−0.166099	−	2.75198i	−0.00719456	−	0.119201i
$534$	8.35687	+	14.4745i	0.361637	+	0.626374i
$535$		−	7.44580i		−	0.321910i
$536$	−2.58058	+	4.46970i	−0.111464	+	0.193061i
$537$	4.17964	−	7.23934i	0.180365	−	0.312401i
$538$	3.09467	+	1.78671i	0.133421	+	0.0770304i
$539$	11.3018	−	6.52512i	0.486805	−	0.281057i
$540$	9.72353	+	5.61388i	0.418434	+	0.241583i
$541$	24.2487	−	14.0000i	1.04253	−	0.601906i	0.121983	−	0.992532i	$-0.461075\pi$
$541$	24.2487	−	14.0000i	1.04253	−	0.601906i	0.920550	+	0.390626i	$0.127741\pi$
$542$	−35.5423			−1.52667
$543$	−6.06847			−0.260423
$544$	4.37510	−	2.52596i	0.187581	−	0.108300i
$545$	−5.88227	+	10.1884i	−0.251969	+	0.436423i
$546$	−17.9074	+	1.08083i	−0.766368	+	0.0462552i
$547$	21.1582	−	36.6471i	0.904661	−	1.56692i	0.0832896	−	0.996525i	$-0.473457\pi$
$547$	21.1582	−	36.6471i	0.904661	−	1.56692i	0.821372	−	0.570394i	$-0.193209\pi$
$548$	−19.3394	−	11.1656i	−0.826137	−	0.476970i
$549$	6.09710	−	10.5605i	0.260218	−	0.450711i
$550$	−18.4186			−0.785372
$551$	15.4881	−	8.94204i	0.659814	−	0.380944i
$552$	−0.740250	+	0.427383i	−0.0315071	+	0.0181906i
$553$	−18.0279	−	10.4084i	−0.766626	−	0.442612i
$554$			41.2880i			1.75416i
$555$	2.68313	+	4.64732i	0.113893	+	0.197268i
$556$	−39.0621			−1.65660
$557$			11.8516i			0.502168i	0.967965	+	0.251084i	$0.0807871\pi$
$557$			11.8516i			0.502168i	−0.967965	+	0.251084i	$0.919213\pi$
$558$	−27.1944	−	9.93587i	−1.15123	−	0.420619i
$559$	−17.4359	+	34.9008i	−0.737460	+	1.47615i
$560$	−14.9135			−0.630210
$561$	−0.997714	+	0.576030i	−0.0421235	+	0.0243200i
$562$	27.2607			1.14992
$563$	−10.8835	+	18.8508i	−0.458685	+	0.794466i	−0.998892	−	0.0470662i	$-0.985013\pi$
$563$	−10.8835	+	18.8508i	−0.458685	+	0.794466i	0.540206	+	0.841533i	$0.318346\pi$
$564$	12.1976	−	7.04228i	0.513611	−	0.296534i
$565$	8.01066	−	4.62496i	0.337011	−	0.194573i
$566$			14.9527i			0.628510i
$567$	−14.5418	−	8.39569i	−0.610697	−	0.352586i
$568$	−2.02814	+	3.51283i	−0.0850987	+	0.147395i
$569$	−4.98669	+	8.63719i	−0.209053	+	0.362090i	−0.951416	−	0.307907i	$-0.900371\pi$
$569$	−4.98669	+	8.63719i	−0.209053	+	0.362090i	0.742364	+	0.669997i	$0.233705\pi$
$570$	7.06652	−	4.07986i	0.295984	−	0.170886i
$571$	−4.00159	+	6.93096i	−0.167461	+	0.290052i	−0.937527	−	0.347914i	$-0.886890\pi$
$571$	−4.00159	+	6.93096i	−0.167461	+	0.290052i	0.770065	+	0.637965i	$0.220224\pi$
$572$	−1.31340	−	21.7608i	−0.0549162	−	0.909865i
$573$	0.347380			0.0145120
$574$			5.45905i			0.227856i
$575$	3.58414	+	6.20792i	0.149469	+	0.258888i
$576$	12.6275	−	21.8714i	0.526145	−	0.911309i
$577$	9.40891	−	5.43224i	0.391698	−	0.226147i	−0.291198	−	0.956663i	$-0.594054\pi$
$577$	9.40891	−	5.43224i	0.391698	−	0.226147i	0.682896	+	0.730516i	$0.260720\pi$
$578$	−29.7547	−	17.1789i	−1.23763	−	0.714548i
$579$	−2.48769	−	1.43627i	−0.103385	−	0.0596893i
$580$	10.2535	+	5.91986i	0.425753	+	0.245809i
$581$	−39.3348			−1.63188
$582$	−13.4172	−	23.2392i	−0.556159	−	0.963296i
$583$	−23.0161	+	13.2883i	−0.953229	+	0.550347i
$584$	−0.121517	+	0.210473i	−0.00502839	+	0.00870943i
$585$	10.4028	+	5.19708i	0.430103	+	0.214873i
$586$	−15.3514	−	26.5893i	−0.634159	−	1.09840i
$587$		−	38.3811i		−	1.58416i	−0.610419	−	0.792079i	$-0.708999\pi$
$587$		−	38.3811i		−	1.58416i	0.610419	−	0.792079i	$-0.291001\pi$
$588$	7.80262			0.321774
$589$	−18.8415	+	15.7704i	−0.776352	+	0.649810i
$590$		−	15.5668i		−	0.640874i
$591$			15.5966i			0.641559i
$592$	17.5076	−	10.1080i	0.719559	−	0.415437i
$593$		−	44.9193i		−	1.84461i	−0.386457	−	0.922307i	$-0.626301\pi$
$593$		−	44.9193i		−	1.84461i	0.386457	−	0.922307i	$-0.373699\pi$
$594$	−10.5508	+	18.2745i	−0.432903	+	0.749811i
$595$	−1.37855	−	2.38772i	−0.0565151	−	0.0978871i
$596$	2.69945	−	1.55853i	0.110574	−	0.0638397i
$597$	−13.7993			−0.564766
$598$	−13.2951	+	8.78449i	−0.543678	+	0.359225i
$599$	18.5605	−	32.1476i	0.758359	−	1.31352i	−0.185327	−	0.982677i	$-0.559335\pi$
$599$	18.5605	−	32.1476i	0.758359	−	1.31352i	0.943687	−	0.330840i	$-0.107332\pi$
$600$	−1.16203	−	0.670899i	−0.0474397	−	0.0273893i
$601$	−17.3184	−	29.9963i	−0.706432	−	1.22358i	−0.966172	−	0.257897i	$-0.916970\pi$
$601$	−17.3184	−	29.9963i	−0.706432	−	1.22358i	0.259741	−	0.965678i	$-0.416363\pi$
$602$	38.6252	−	66.9009i	1.57425	−	2.72668i
$603$	19.5807	−	11.3049i	0.797386	−	0.460371i
$604$		−	39.6255i		−	1.61234i
$605$		−	5.06947i		−	0.206103i
$606$	16.1130	−	9.30285i	0.654546	−	0.377902i
$607$	3.14460	−	5.44661i	0.127635	−	0.221071i	−0.795125	−	0.606446i	$-0.792595\pi$
$607$	3.14460	−	5.44661i	0.127635	−	0.221071i	0.922760	+	0.385375i	$0.125928\pi$
$608$	−17.9026	−	31.0082i	−0.726046	−	1.25755i
$609$	8.44346	+	4.87483i	0.342146	+	0.197538i
$610$	6.43362	−	11.1434i	0.260490	−	0.451182i
$611$	26.6930	−	17.6369i	1.07988	−	0.713511i
$612$	3.56546			0.144125
$613$	−19.8622	+	11.4674i	−0.802226	+	0.463165i	−0.844249	−	0.535951i	$-0.819953\pi$
$613$	−19.8622	+	11.4674i	−0.802226	+	0.463165i	0.0420229	+	0.999117i	$0.486620\pi$
$614$	−22.6908	−	39.3017i	−0.915728	−	1.58609i
$615$	−0.341805	+	0.592024i	−0.0137829	+	0.0238727i
$616$			5.25964i			0.211917i
$617$	−32.4430	+	18.7310i	−1.30611	+	0.754080i	−0.981444	−	0.191750i	$-0.938584\pi$
$617$	−32.4430	+	18.7310i	−1.30611	+	0.754080i	−0.324662	+	0.945830i	$0.605250\pi$
$618$		−	12.4557i		−	0.501041i
$619$		−	32.2512i		−	1.29629i	−0.761518	−	0.648143i	$-0.775546\pi$
$619$		−	32.2512i		−	1.29629i	0.761518	−	0.648143i	$-0.224454\pi$
$620$	−15.2785	−	5.58222i	−0.613598	−	0.224187i
$621$	8.21245			0.329554
$622$			27.4402i			1.10025i
$623$	−20.0129	−	34.6634i	−0.801802	−	1.38876i
$624$	−3.78238	+	7.57105i	−0.151416	+	0.303084i
$625$	−1.51257	+	2.61984i	−0.0605027	+	0.104794i
$626$	4.36434	−	2.51975i	0.174434	−	0.100710i
$627$	4.08258	+	7.07123i	0.163042	+	0.282398i
$628$	35.0094			1.39703
$629$	3.23669	+	1.86870i	0.129055	+	0.0745101i
$630$	−19.9410	−	11.5129i	−0.794468	−	0.458687i
$631$	12.5595	+	7.25123i	0.499986	+	0.288667i	0.728708	−	0.684825i	$-0.240121\pi$
$631$	12.5595	+	7.25123i	0.499986	+	0.288667i	−0.228722	+	0.973492i	$0.573455\pi$
$632$	2.99743	−	1.73057i	0.119231	−	0.0688382i
$633$	−4.68873	+	8.12111i	−0.186360	+	0.322785i
$634$	15.7349	+	27.2537i	0.624913	+	1.08238i
$635$			16.0692i			0.637687i
$636$	−15.8900			−0.630078
$637$	17.6916	−	1.06780i	0.700966	−	0.0423077i
$638$	−11.1258	+	19.2705i	−0.440476	+	0.762926i
$639$	15.3889	−	8.88478i	0.608775	−	0.351476i
$640$	2.91656	−	5.05163i	0.115287	−	0.199683i
$641$	−11.1942	+	19.3889i	−0.442143	+	0.765814i	−0.997848	−	0.0655651i	$-0.979115\pi$
$641$	−11.1942	+	19.3889i	−0.442143	+	0.765814i	0.555705	+	0.831379i	$0.312448\pi$
$642$	7.24577	+	4.18335i	0.285968	+	0.165104i
$643$			15.6445i			0.616961i	0.951231	+	0.308480i	$0.0998204\pi$
$643$			15.6445i			0.616961i	−0.951231	+	0.308480i	$0.900180\pi$
$644$	14.5491	−	8.39995i	0.573316	−	0.331004i
$645$	8.37767	−	4.83685i	0.329871	−	0.190451i
$646$	2.84147	−	4.92157i	0.111796	−	0.193637i
$647$	−15.6047			−0.613484			−0.306742	−	0.951793i	$-0.599239\pi$
$647$	−15.6047			−0.613484			−0.306742	+	0.951793i	$0.599239\pi$
$648$	2.41780	−	1.39592i	0.0949801	−	0.0548368i
$649$	15.5772			0.611457
$650$	−22.3775	−	11.1795i	−0.877717	−	0.438494i
$651$	−12.5814	−	4.59680i	−0.493103	−	0.180163i
$652$		−	8.67664i		−	0.339803i
$653$	45.3275			1.77380			0.886901	−	0.461960i	$-0.152854\pi$
$653$	45.3275			1.77380			0.886901	+	0.461960i	$0.152854\pi$
$654$	−6.60979	−	11.4485i	−0.258463	−	0.447672i
$655$			18.3616i			0.717445i
$656$	2.23030	+	1.28766i	0.0870786	+	0.0502749i
$657$	0.922031	−	0.532335i	0.0359719	−	0.0207684i
$658$	−54.8622	+	31.6747i	−2.13875	+	1.23481i
$659$	3.01576			0.117477			0.0587387	−	0.998273i	$-0.481292\pi$
$659$	3.01576			0.117477			0.0587387	+	0.998273i	$0.481292\pi$
$660$	−2.70277	+	4.68134i	−0.105205	+	0.182221i
$661$	−15.0536	−	8.69118i	−0.585516	−	0.338048i	0.177807	−	0.984065i	$-0.443100\pi$
$661$	−15.0536	−	8.69118i	−0.585516	−	0.338048i	−0.763322	+	0.646018i	$0.776433\pi$
$662$	−8.93856	+	15.4820i	−0.347407	+	0.601726i
$663$	−1.56179	+	0.0942641i	−0.0606550	+	0.00366091i
$664$	3.27001	−	5.66383i	0.126901	−	0.219799i
$665$	−16.9228	+	9.77040i	−0.656239	+	0.378880i
$666$	31.2128			1.20947
$667$	8.66006			0.335319
$668$	−27.6943	+	15.9893i	−1.07153	+	0.618646i
$669$	9.02105	+	5.20831i	0.348774	+	0.201365i
$670$	20.6614	−	11.9289i	0.798220	−	0.460852i
$671$	11.1508	+	6.43791i	0.430472	+	0.248533i
$672$	9.75976	−	16.9044i	0.376491	−	0.652101i
$673$	3.69020	−	6.39162i	0.142247	−	0.246379i	−0.786096	−	0.618105i	$-0.787901\pi$
$673$	3.69020	−	6.39162i	0.142247	−	0.246379i	0.928342	+	0.371726i	$0.121234\pi$
$674$			0.120595i			0.00464513i
$675$	6.44588	+	11.1646i	0.248102	+	0.429726i
$676$	11.6124	−	27.2353i	0.446629	−	1.04751i
$677$	−19.0668	+	33.0247i	−0.732797	+	1.26924i	0.222887	+	0.974844i	$0.428452\pi$
$677$	−19.0668	+	33.0247i	−0.732797	+	1.26924i	−0.955683	+	0.294397i	$0.904881\pi$
$678$			10.3939i			0.399177i
$679$	32.1313	+	55.6530i	1.23309	+	2.13577i
$680$	0.458412			0.0175793
$681$			7.69129i			0.294731i
$682$	10.4913	−	28.7145i	0.401731	−	1.09953i
$683$			2.32957i			0.0891384i	0.999006	+	0.0445692i	$0.0141915\pi$
$683$			2.32957i			0.0891384i	−0.999006	+	0.0445692i	$0.985808\pi$
$684$		−	25.2700i		−	0.966221i
$685$	6.28886	+	10.8926i	0.240285	+	0.416186i
$686$	14.8805			0.568140
$687$	−1.07246	−	0.619183i	−0.0409168	−	0.0236233i
$688$	−18.2216	−	31.5608i	−0.694692	−	1.20324i
$689$	−36.0287	+	2.17456i	−1.37259	+	0.0828442i
$690$	3.95120			0.150420
$691$	−22.2531	−	12.8478i	−0.846548	−	0.488755i	0.0129363	−	0.999916i	$-0.495882\pi$
$691$	−22.2531	−	12.8478i	−0.846548	−	0.488755i	−0.859485	+	0.511161i	$0.829215\pi$
$692$	−12.8941	+	22.3332i	−0.490158	+	0.848979i
$693$	11.5206	−	19.9543i	0.437632	−	0.758001i
$694$	−37.6348	+	21.7284i	−1.42860	+	0.824800i
$695$	19.0536	+	11.0006i	0.722744	+	0.417276i
$696$	−1.40386	+	0.810518i	−0.0532131	+	0.0307226i
$697$			0.476109i			0.0180339i
$698$	0.312645			0.0118338
$699$	10.3135	+	17.8635i	0.390093	+	0.675660i
$700$	22.8390	+	13.1861i	0.863232	+	0.498387i
$701$	10.9402	+	18.9490i	0.413205	+	0.715693i	0.995238	−	0.0974726i	$-0.0310758\pi$
$701$	10.9402	+	18.9490i	0.413205	+	0.715693i	−0.582033	+	0.813165i	$0.697743\pi$
$702$	−23.9105	+	15.7984i	−0.902445	+	0.596273i
$703$	13.2443	−	22.9398i	0.499519	−	0.865192i
$704$	23.0940	+	13.3333i	0.870387	+	0.502518i
$705$	−7.93293			−0.298772
$706$	2.90525	+	5.03204i	0.109341	+	0.189383i
$707$	−38.5873	+	22.2784i	−1.45122	+	0.837864i
$708$	8.06568	+	4.65672i	0.303127	+	0.175010i
$709$			8.58474i			0.322407i	0.986921	+	0.161203i	$0.0515375\pi$
$709$			8.58474i			0.322407i	−0.986921	+	0.161203i	$0.948463\pi$
$710$	16.2383	−	9.37516i	0.609411	−	0.351844i
$711$	−15.1624			−0.568634
$712$	6.65494			0.249404
$713$	−11.7196	+	2.05161i	−0.438904	+	0.0768336i
$714$	3.09810			0.115944
$715$	−5.48759	+	10.9843i	−0.205224	+	0.410789i
$716$	−13.6584	−	23.6571i	−0.510439	−	0.884106i
$717$		−	17.4322i		−	0.651019i
$718$	4.20607	−	7.28512i	0.156969	−	0.271878i
$719$	−12.7692	−	22.1169i	−0.476210	−	0.824820i	0.523418	−	0.852076i	$-0.324657\pi$
$719$	−12.7692	−	22.1169i	−0.476210	−	0.824820i	−0.999628	+	0.0272556i	$0.991323\pi$
$720$	−9.40724	+	5.43128i	−0.350587	+	0.202412i
$721$			29.8287i			1.11088i
$722$	−0.849957	−	0.490723i	−0.0316321	−	0.0182628i
$723$	−2.32948	−	1.34493i	−0.0866344	−	0.0500184i
$724$	−9.91542	+	17.1740i	−0.368504	+	0.638267i
$725$	6.79721	+	11.7731i	0.252442	+	0.437242i
$726$	4.93328	+	2.84823i	0.183091	+	0.105708i
$727$	−6.30710	−	10.9242i	−0.233917	−	0.405157i	0.725040	−	0.688707i	$-0.241821\pi$
$727$	−6.30710	−	10.9242i	−0.233917	−	0.405157i	−0.958958	+	0.283550i	$0.908488\pi$
$728$	−3.19242	+	6.39015i	−0.118319	+	0.236835i
$729$	−4.19504			−0.155372
$730$	0.972922	−	0.561717i	0.0360094	−	0.0207901i
$731$	3.36869	−	5.83474i	0.124595	−	0.215806i
$732$	3.84917	+	6.66696i	0.142269	+	0.246418i
$733$	37.3182	+	21.5457i	1.37838	+	0.795808i	0.991964	−	0.126517i	$-0.0403797\pi$
$733$	37.3182	+	21.5457i	1.37838	+	0.795808i	0.386416	+	0.922325i	$0.373713\pi$
$734$	54.3968	+	31.4060i	2.00782	+	1.15922i
$735$	−3.80593	−	2.19736i	−0.140384	−	0.0810507i
$736$		−	17.3381i		−	0.639089i
$737$	11.9368	+	20.6752i	0.439698	+	0.761580i
$738$	1.98811	+	3.44350i	0.0731832	+	0.126757i
$739$	10.7108	+	6.18386i	0.394002	+	0.227477i	0.683893	−	0.729583i	$-0.260286\pi$
$739$	10.7108	+	6.18386i	0.394002	+	0.227477i	−0.289891	+	0.957060i	$0.593619\pi$
$740$	17.5362			0.644642
$741$	0.668091	+	11.0691i	0.0245429	+	0.406634i
$742$	71.4696			2.62373
$743$			45.8218i			1.68104i	0.541783	+	0.840519i	$0.317750\pi$
$743$			45.8218i			1.68104i	−0.541783	+	0.840519i	$0.682250\pi$
$744$	1.70782	−	1.42945i	0.0626118	−	0.0524063i
$745$	−1.75564			−0.0643215
$746$		−	51.1796i		−	1.87382i
$747$	−24.8119	+	14.3251i	−0.907819	+	0.524130i
$748$			3.76476i			0.137653i
$749$	−17.3521	−	10.0182i	−0.634032	−	0.366059i
$750$	7.72381	+	13.3780i	0.282034	+	0.488497i
$751$	12.3709	+	21.4271i	0.451422	+	0.781885i	0.998475	−	0.0552127i	$-0.0175837\pi$
$751$	12.3709	+	21.4271i	0.451422	+	0.781885i	−0.547053	+	0.837098i	$0.684250\pi$
$752$			29.8853i			1.08981i
$753$	3.70205	−	6.41214i	0.134910	−	0.233671i
$754$	−25.2137	+	16.6595i	−0.918230	+	0.606703i
$755$	−11.1593	+	19.3284i	−0.406127	+	0.703433i
$756$	26.1658	−	15.1068i	0.951641	−	0.549430i
$757$	−26.5987	+	46.0703i	−0.966746	+	1.67445i	−0.261896	+	0.965096i	$0.584348\pi$
$757$	−26.5987	+	46.0703i	−0.966746	+	1.67445i	−0.704850	+	0.709357i	$0.748986\pi$
$758$	−18.6608	−	32.3214i	−0.677790	−	1.17397i
$759$			3.95384i			0.143515i
$760$		−	3.24897i		−	0.117853i
$761$	17.9406	−	10.3580i	0.650345	−	0.375477i	−0.138243	−	0.990398i	$-0.544146\pi$
$761$	17.9406	−	10.3580i	0.650345	−	0.375477i	0.788588	+	0.614921i	$0.210812\pi$
$762$	−15.6375	−	9.02833i	−0.566488	−	0.327062i
$763$	15.8291	+	27.4167i	0.573051	+	0.992553i
$764$	0.567593	−	0.983099i	0.0205348	−	0.0355673i
$765$	−1.73915	−	1.00410i	−0.0628790	−	0.0363032i
$766$	15.6728	−	27.1461i	0.566282	−	0.980829i
$767$	18.9253	+	9.45480i	0.683353	+	0.341393i
$768$	−3.72325	−	6.44886i	−0.134351	−	0.232703i
$769$	−11.9972	+	6.92656i	−0.432628	+	0.249778i	−0.700466	−	0.713686i	$-0.747024\pi$
$769$	−11.9972	+	6.92656i	−0.432628	+	0.249778i	0.267837	+	0.963464i	$0.413691\pi$
$770$	12.1565	−	21.0557i	0.438089	−	0.758793i
$771$	−20.9798			−0.755568
$772$	−8.12940	+	4.69351i	−0.292584	+	0.168923i
$773$		−	25.8256i		−	0.928881i	−0.885604	−	0.464440i	$-0.846256\pi$
$773$		−	25.8256i		−	0.928881i	0.885604	−	0.464440i	$-0.153744\pi$
$774$		−	56.2670i		−	2.02248i
$775$	−11.9878	−	14.3222i	−0.430613	−	0.514469i
$776$	−10.6847			−0.383557
$777$	14.4405			0.518050
$778$	−59.3256	+	34.2516i	−2.12692	+	1.22798i
$779$	3.37440			0.120900
$780$	−6.12511	+	4.04705i	−0.219314	+	0.144908i
$781$	9.38142	+	16.2491i	0.335693	+	0.581438i
$782$	2.38319	−	1.37593i	0.0852226	−	0.0492033i
$783$	15.5746			0.556592
$784$	−8.27799	+	14.3379i	−0.295642	+	0.512068i
$785$	−17.0768	−	9.85927i	−0.609496	−	0.351893i
$786$	−17.8683	−	10.3163i	−0.637340	−	0.367969i
$787$	13.3028	−	7.68040i	0.474195	−	0.273777i	−0.243799	−	0.969826i	$-0.578394\pi$
$787$	13.3028	−	7.68040i	0.474195	−	0.273777i	0.717994	+	0.696049i	$0.245060\pi$
$788$	44.1391	+	25.4837i	1.57239	+	0.907819i
$789$	−0.677514	−	1.17349i	−0.0241201	−	0.0417773i
$790$	−15.9993			−0.569229
$791$		−	24.8913i		−	0.885034i
$792$	1.91549	+	3.31772i	0.0680638	+	0.117890i
$793$	9.63995	+	14.5898i	0.342325	+	0.518100i
$794$	12.9417	+	22.4157i	0.459284	+	0.795503i
$795$	7.75075	+	4.47490i	0.274891	+	0.158708i
$796$	−22.5470	+	39.0525i	−0.799156	+	1.38418i
$797$	0.917246	−	1.58872i	0.0324905	−	0.0562752i	−0.849323	−	0.527874i	$-0.822989\pi$
$797$	0.917246	−	1.58872i	0.0324905	−	0.0562752i	0.881813	+	0.471598i	$0.156323\pi$
$798$		−	21.9576i		−	0.777291i
$799$	−4.78479	+	2.76250i	−0.169274	+	0.0977302i
$800$	23.5706	−	13.6085i	0.833347	−	0.481133i
$801$	−25.2478	−	14.5768i	−0.892089	−	0.515048i
$802$	−31.5775			−1.11504
$803$	0.562091	+	0.973570i	0.0198358	+	0.0343566i
$804$			14.2738i			0.503399i
$805$	−9.46230			−0.333502
$806$	30.1750	−	28.5185i	1.06287	−	1.00452i
$807$	1.20416			0.0423885
$808$		−	7.40827i		−	0.260622i
$809$	−0.215790	−	0.373759i	−0.00758676	−	0.0131407i	0.862207	−	0.506556i	$-0.169082\pi$
$809$	−0.215790	−	0.373759i	−0.00758676	−	0.0131407i	−0.869794	+	0.493415i	$0.835748\pi$
$810$	−12.9054			−0.453450
$811$	−19.2010	−	11.0857i	−0.674237	−	0.389271i	0.123443	−	0.992352i	$-0.460606\pi$
$811$	−19.2010	−	11.0857i	−0.674237	−	0.389271i	−0.797680	+	0.603081i	$0.793940\pi$
$812$	27.5919	−	15.9302i	0.968287	−	0.559041i
$813$	−10.3724	+	5.98849i	−0.363775	+	0.210026i
$814$			32.9576i			1.15516i
$815$	−2.44350	+	4.23226i	−0.0855920	+	0.148250i
$816$	0.730771	−	1.26573i	0.0255821	−	0.0443095i
$817$	−41.3534	−	23.8754i	−1.44677	−	0.835293i
$818$	0.356828	+	0.618044i	0.0124762	+	0.0216094i
$819$	26.1084	−	17.2506i	0.912302	−	0.602786i
$820$	1.11697	+	1.93465i	0.0390062	+	0.0675607i
$821$		−	50.5491i		−	1.76417i	−0.471086	−	0.882087i	$-0.656138\pi$
$821$		−	50.5491i		−	1.76417i	0.471086	−	0.882087i	$-0.343862\pi$
$822$	−14.1333			−0.492957
$823$	23.8624	+	41.3310i	0.831792	+	1.44071i	0.896616	+	0.442810i	$0.146018\pi$
$823$	23.8624	+	41.3310i	0.831792	+	1.44071i	−0.0648232	+	0.997897i	$0.520648\pi$
$824$	−4.29505	−	2.47975i	−0.149625	−	0.0863862i
$825$	−5.37513	+	3.10333i	−0.187138	+	0.108044i
$826$	−36.2777	−	20.9449i	−1.26226	−	0.728768i
$827$	−22.0531	−	12.7324i	−0.766863	−	0.442749i	0.0648914	−	0.997892i	$-0.479330\pi$
$827$	−22.0531	−	12.7324i	−0.766863	−	0.442749i	−0.831754	+	0.555144i	$0.812663\pi$
$828$	6.11828	−	10.5972i	0.212625	−	0.368277i
$829$	35.4185			1.23014			0.615068	−	0.788474i	$-0.289129\pi$
$829$	35.4185			1.23014			0.615068	+	0.788474i	$0.289129\pi$
$830$	−26.1813	+	15.1158i	−0.908768	+	0.524677i
$831$	6.95658	+	12.0492i	0.241321	+	0.417981i
$832$	19.9649	+	30.2164i	0.692160	+	1.04757i
$833$	−3.06076			−0.106049
$834$	−21.4101	+	12.3611i	−0.741372	+	0.428032i
$835$	18.0115			0.623315
$836$	26.6825			0.922834
$837$	−21.0771	+	3.68972i	−0.728532	+	0.127535i
$838$			57.1744i			1.97506i
$839$			20.7238i			0.715466i	0.933824	+	0.357733i	$0.116450\pi$
$839$			20.7238i			0.715466i	−0.933824	+	0.357733i	$0.883550\pi$
$840$	1.53391	−	0.885602i	0.0529248	−	0.0305562i
$841$	−12.5765			−0.433672
$842$	−18.4574	+	31.9692i	−0.636086	+	1.10173i
$843$	7.95554	−	4.59313i	0.274003	−	0.158196i
$844$	15.3221	+	26.5386i	0.527407	+	0.913496i
$845$	−13.3342	+	10.0145i	−0.458710	+	0.344508i
$846$	−23.0709	+	39.9600i	−0.793195	+	1.37385i
$847$	−11.8142	−	6.82092i	−0.405940	−	0.234369i
$848$	16.8580	−	29.1990i	0.578908	−	1.00270i
$849$	2.51937	+	4.36368i	0.0864646	+	0.149761i
$850$	3.74108	+	2.15992i	0.128318	+	0.0740845i
$851$	11.1082	−	6.41334i	0.380785	−	0.219846i
$852$			11.2181i			0.384327i
$853$			12.2928i			0.420897i	0.977605	+	0.210449i	$0.0674925\pi$
$853$			12.2928i			0.420897i	−0.977605	+	0.210449i	$0.932508\pi$
$854$	−17.3127	−	29.9865i	−0.592430	−	1.02612i
$855$	−7.11648	+	12.3261i	−0.243378	+	0.421544i
$856$	2.88506	−	1.66569i	0.0986094	−	0.0569322i
$857$	−7.55748	+	13.0899i	−0.258158	+	0.447144i	−0.965749	−	0.259480i	$-0.916449\pi$
$857$	−7.55748	+	13.0899i	−0.258158	+	0.447144i	0.707590	+	0.706623i	$0.249782\pi$
$858$	−7.60606	−	11.5116i	−0.259667	−	0.392999i
$859$	10.3279	−	17.8884i	0.352382	−	0.610344i	−0.634284	−	0.773100i	$-0.718705\pi$
$859$	10.3279	−	17.8884i	0.352382	−	0.610344i	0.986666	+	0.162756i	$0.0520384\pi$
$860$		−	31.6122i		−	1.07797i
$861$	0.919791	+	1.59312i	0.0313464	+	0.0542935i
$862$	−9.71339	−	16.8241i	−0.330839	−	0.573031i
$863$	20.0223	+	11.5599i	0.681566	+	0.393502i	0.800445	−	0.599406i	$-0.204597\pi$
$863$	20.0223	+	11.5599i	0.681566	+	0.393502i	−0.118879	+	0.992909i	$0.537930\pi$
$864$		−	31.1815i		−	1.06082i
$865$	12.5788	−	7.26239i	0.427693	−	0.246929i
$866$			59.8699i			2.03446i
$867$	−11.5778			−0.393203
$868$	−33.5661	+	28.0950i	−1.13931	+	0.953606i
$869$		−	16.0099i		−	0.543100i
$870$	7.49332			0.254048
$871$	1.95339	+	32.3643i	0.0661882	+	1.09662i
$872$	−5.26367			−0.178250
$873$	40.5360	+	23.4035i	1.37194	+	0.792088i
$874$	−9.75184	−	16.8907i	−0.329861	−	0.571336i
$875$	−18.4969	−	32.0376i	−0.625310	−	1.08307i
$876$			0.672138i			0.0227094i
$877$	8.27462	+	4.77735i	0.279414	+	0.161320i	0.633158	−	0.774023i	$-0.281758\pi$
$877$	8.27462	+	4.77735i	0.279414	+	0.161320i	−0.353744	+	0.935342i	$0.615092\pi$
$878$	26.4644	+	15.2792i	0.893131	+	0.515649i
$879$	−8.96003	−	5.17307i	−0.302214	−	0.174483i
$880$	−5.73487	−	9.93309i	−0.193322	−	0.334844i
$881$	−2.18777	+	3.78932i	−0.0737077	+	0.127665i	−0.900524	−	0.434807i	$-0.856817\pi$
$881$	−2.18777	+	3.78932i	−0.0737077	+	0.127665i	0.826816	+	0.562473i	$0.190150\pi$
$882$	−22.1372	+	12.7809i	−0.745398	+	0.430356i
$883$	−33.4967			−1.12725			−0.563627	−	0.826029i	$-0.690594\pi$
$883$	−33.4967			−1.12725			−0.563627	+	0.826029i	$0.690594\pi$
$884$	−2.28508	+	4.57396i	−0.0768556	+	0.153839i
$885$	−2.62283	−	4.54288i	−0.0881655	−	0.152707i
$886$	11.9691	+	6.91035i	0.402109	+	0.232158i
$887$	−19.4356	−	33.6634i	−0.652583	−	1.13031i	−0.982494	−	0.186294i	$-0.940352\pi$
$887$	−19.4356	−	33.6634i	−0.652583	−	1.13031i	0.329911	−	0.944012i	$-0.392981\pi$
$888$	−1.20048	+	2.07930i	−0.0402855	+	0.0697766i
$889$	37.4486	+	21.6210i	1.25599	+	0.725144i
$890$	−26.6414	−	15.3814i	−0.893021	−	0.515586i
$891$		−	12.9140i		−	0.432635i
$892$	29.4794	−	17.0200i	0.987045	−	0.569871i
$893$	19.5790	+	33.9119i	0.655187	+	1.13482i
$894$	0.986387	−	1.70847i	0.0329897	−	0.0571398i
$895$			15.3858i			0.514291i
$896$	−7.84841	−	13.5938i	−0.262197	−	0.454138i
$897$	−2.39984	+	4.80367i	−0.0801285	+	0.160390i
$898$	37.7987			1.26136
$899$	−22.2259	+	3.89082i	−0.741275	+	0.129766i
$900$	19.2087			0.640291
$901$	6.23320			0.207658
$902$	−3.63599	+	2.09924i	−0.121065	+	0.0698970i
$903$		−	26.0317i		−	0.866282i
$904$	3.58411	+	2.06929i	0.119206	+	0.0688235i
$905$	9.67302	−	5.58472i	0.321542	−	0.185642i
$906$	−12.5394	−	21.7190i	−0.416595	−	0.721564i
$907$	−16.3040			−0.541367			−0.270683	−	0.962668i	$-0.587250\pi$
$907$	−16.3040			−0.541367			−0.270683	+	0.962668i	$0.587250\pi$
$908$	21.7667	+	12.5670i	0.722352	+	0.417050i
$909$	−16.2269	+	28.1058i	−0.538213	+	0.932212i
$910$	27.5495	−	18.2028i	0.913256	−	0.603416i
$911$	10.1810	+	17.6340i	0.337311	+	0.584239i	0.983926	−	0.178577i	$-0.0571494\pi$
$911$	10.1810	+	17.6340i	0.337311	+	0.584239i	−0.646615	+	0.762816i	$0.723816\pi$
$912$	−8.97081	−	5.17930i	−0.297053	−	0.171504i
$913$	−15.1259	−	26.1988i	−0.500594	−	0.867054i
$914$	13.7640			0.455272
$915$		−	4.33598i		−	0.143343i
$916$	−3.50463	+	2.02340i	−0.115796	+	0.0668549i
$917$	42.7908	+	24.7053i	1.41308	+	0.815840i
$918$	4.28603	−	2.47454i	0.141460	−	0.0816720i
$919$	25.6591	−	44.4428i	0.846415	−	1.46603i	−0.0379716	−	0.999279i	$-0.512090\pi$
$919$	25.6591	−	44.4428i	0.846415	−	1.46603i	0.884387	−	0.466755i	$-0.154577\pi$
$920$	0.786629	−	1.36248i	0.0259344	−	0.0449197i
$921$	−13.2438	−	7.64632i	−0.436398	−	0.251955i
$922$	29.4423			0.969631
$923$	1.53522	+	25.4359i	0.0505323	+	0.837232i
$924$	7.27310	+	12.5974i	0.239267	+	0.414423i
$925$	17.4375	+	10.0675i	0.573341	+	0.331019i
$926$	−30.7563			−1.01071
$927$	10.8632	+	18.8156i	0.356794	+	0.617985i
$928$		−	32.8811i		−	1.07937i
$929$		−	19.5220i		−	0.640497i	−0.947334	−	0.320248i	$-0.896234\pi$
$929$		−	19.5220i		−	0.640497i	0.947334	−	0.320248i	$-0.103766\pi$
$930$	−10.1407	+	1.77521i	−0.332526	+	0.0582114i
$931$			21.6929i			0.710957i
$932$	67.4060			2.20796
$933$	4.62338	+	8.00793i	0.151363	+	0.262168i
$934$			64.7888i			2.11995i
$935$	1.06022	−	1.83636i	0.0346730	−	0.0600555i
$936$	0.313458	+	5.19346i	0.0102457	+	0.169754i
$937$	−12.7106	−	22.0153i	−0.415236	−	0.719210i	0.580217	−	0.814462i	$-0.302968\pi$
$937$	−12.7106	−	22.0153i	−0.415236	−	0.719210i	−0.995453	+	0.0952518i	$0.969634\pi$
$938$		−	64.2006i		−	2.09623i
$939$	0.849101	−	1.47069i	0.0277094	−	0.0479940i
$940$	−12.9618	+	22.4505i	−0.422768	+	0.732255i
$941$	5.36968	+	3.10019i	0.175047	+	0.101063i	0.584963	−	0.811060i	$-0.301109\pi$
$941$	5.36968	+	3.10019i	0.175047	+	0.101063i	−0.409917	+	0.912123i	$0.634442\pi$
$942$	19.1888	−	11.0787i	0.625205	−	0.360963i
$943$	1.41508	+	0.816997i	0.0460813	+	0.0266051i
$944$	−17.1141	+	9.88086i	−0.557018	+	0.321595i
$945$	−17.0174			−0.553577
$946$	59.4122			1.93166
$947$	0.410197	−	0.236827i	0.0133296	−	0.00769585i	−0.493320	−	0.869848i	$-0.664217\pi$
$947$	0.410197	−	0.236827i	0.0133296	−	0.00769585i	0.506650	+	0.862152i	$0.330884\pi$
$948$	4.78610	−	8.28976i	0.155445	−	0.269239i
$949$	0.0919831	+	1.52400i	0.00298590	+	0.0494711i
$950$	15.3083	−	26.5147i	0.496666	−	0.860251i
$951$	9.18389	+	5.30232i	0.297808	+	0.171939i
$952$	0.616789	−	1.06831i	0.0199902	−	0.0346241i
$953$	14.4609			0.468434			0.234217	−	0.972184i	$-0.424747\pi$
$953$	14.4609			0.468434			0.234217	+	0.972184i	$0.424747\pi$
$954$	45.0822	−	26.0282i	1.45959	−	0.842694i
$955$	−0.553717	+	0.319689i	−0.0179179	+	0.0103449i
$956$	−49.3339	−	28.4830i	−1.59557	−	0.921205i
$957$			7.49832i			0.242386i
$958$	1.53430	+	2.65748i	0.0495709	+	0.0858594i
$959$	33.8464			1.09296
$960$		−	8.98009i		−	0.289831i
$961$	29.1565	−	10.5309i	0.940532	−	0.339705i
$962$	−20.0041	+	40.0415i	−0.644959	+	1.29099i
$963$	−14.5940			−0.470285
$964$	−7.61240	+	4.39502i	−0.245179	+	0.141554i
$965$	5.28711			0.170198
$966$	5.31630	−	9.20810i	0.171049	−	0.296266i
$967$	−24.8458	+	14.3448i	−0.798989	+	0.461296i	−0.843117	−	0.537730i	$-0.819282\pi$
$967$	−24.8458	+	14.3448i	−0.798989	+	0.461296i	0.0441288	+	0.999026i	$0.485949\pi$
$968$	1.96429	−	1.13409i	0.0631348	−	0.0364509i
$969$		−	1.91503i		−	0.0615195i
$970$	42.7734	+	24.6952i	1.37337	+	0.792916i
$971$	−25.5397	+	44.2360i	−0.819607	+	1.41960i	0.0863648	+	0.996264i	$0.472475\pi$
$971$	−25.5397	+	44.2360i	−0.819607	+	1.41960i	−0.905972	+	0.423338i	$0.860858\pi$
$972$	16.9897	−	29.4270i	0.544945	−	0.943872i
$973$	51.2728	−	29.6024i	1.64373	−	0.949008i
$974$	−27.5323	+	47.6873i	−0.882191	+	1.52800i
$975$	−8.41407	+	0.507843i	−0.269466	+	0.0162640i
$976$	−16.3347			−0.522861
$977$		−	61.8002i		−	1.97717i	−0.150680	−	0.988583i	$-0.548146\pi$
$977$		−	61.8002i		−	1.97717i	0.150680	−	0.988583i	$-0.451854\pi$
$978$	−2.74571	−	4.75571i	−0.0877981	−	0.152071i
$979$	15.3917	−	26.6591i	0.491920	−	0.852030i
$980$	−12.4372	+	7.18063i	−0.397292	+	0.229377i
$981$	19.9696	+	11.5294i	0.637579	+	0.368106i
$982$	−5.28868	−	3.05342i	−0.168769	−	0.0974386i
$983$	25.3891	+	14.6584i	0.809786	+	0.467530i	0.846882	−	0.531782i	$-0.178477\pi$
$983$	25.3891	+	14.6584i	0.809786	+	0.467530i	−0.0370956	+	0.999312i	$0.511811\pi$
$984$	−0.305860			−0.00975045
$985$	−14.3533	−	24.8607i	−0.457335	−	0.792128i
$986$	4.51963	−	2.60941i	0.143934	−	0.0831006i
$987$	−10.6737	+	18.4874i	−0.339747	+	0.588459i
$988$	32.4176	+	16.1954i	1.03134	+	0.515243i
$989$	−11.5612	−	20.0247i	−0.367626	−	0.636747i
$990$		−	17.7089i		−	0.562825i
$991$	−33.2222			−1.05534			−0.527670	−	0.849450i	$-0.676934\pi$
$991$	−33.2222			−1.05534			−0.527670	+	0.849450i	$0.676934\pi$
$992$	7.78969	+	44.4978i	0.247323	+	1.41281i
$993$			6.02420i			0.191172i
$994$		−	50.4567i		−	1.60039i
$995$	21.9958	−	12.6993i	0.697312	−	0.402593i
$996$		−	18.0873i		−	0.573117i
$997$	8.71084	−	15.0876i	0.275875	−	0.477829i	−0.694481	−	0.719511i	$-0.744366\pi$
$997$	8.71084	−	15.0876i	0.275875	−	0.477829i	0.970355	+	0.241682i	$0.0776991\pi$
$998$	−12.3413	−	21.3758i	−0.390658	−	0.676639i
$999$	19.9775	−	11.5340i	0.632061	−	0.364921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.6	✓	68
13.12	even	2	inner	403.2.l.c.25.29	yes	68
31.5	even	3	inner	403.2.l.c.129.6	yes	68
403.129	even	6	inner	403.2.l.c.129.29	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.6	✓	68	1.1	even	1	trivial
403.2.l.c.25.29	yes	68	13.12	even	2	inner
403.2.l.c.129.6	yes	68	31.5	even	3	inner
403.2.l.c.129.29	yes	68	403.129	even	6	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +O(q^{10})\)	\(q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +(1.32652 - 2.29760i) q^{10} +(2.29914 + 1.32741i) q^{11} +(0.793644 + 1.37463i) q^{12} +(1.98762 + 3.00822i) q^{13} +(-3.56964 - 6.18280i) q^{14} -0.894018i q^{15} -3.36799 q^{16} +(-0.311325 - 0.539231i) q^{17} +(-4.50337 - 2.60002i) q^{18} +(-3.82177 + 2.20650i) q^{19} +(-2.53011 - 1.46076i) q^{20} +(-2.08347 - 1.20289i) q^{21} +(2.74536 - 4.75510i) q^{22} -2.13692 q^{23} +(0.346410 - 0.200000i) q^{24} +(-1.67725 - 2.90508i) q^{25} +(6.22163 - 4.11082i) q^{26} -3.84313 q^{27} +(-6.80846 + 3.93087i) q^{28} -4.05259 q^{29} -1.84902 q^{30} +(5.48436 - 0.960081i) q^{31} +8.11358i q^{32} -1.85025i q^{33} +(-1.11524 + 0.643887i) q^{34} +4.42801 q^{35} +(-2.86313 + 4.95909i) q^{36} +(-5.19824 + 3.00121i) q^{37} +(4.56351 + 7.90423i) q^{38} +(1.12304 - 2.24794i) q^{39} +(-0.368114 + 0.637592i) q^{40} +(-0.662206 - 0.382325i) q^{41} +(-2.48784 + 4.30906i) q^{42} +(5.41024 + 9.37081i) q^{43} +(-5.23629 - 3.02317i) q^{44} +(2.79314 - 1.61262i) q^{45} +4.41960i q^{46} -8.87335i q^{47} +(1.17365 + 2.03281i) q^{48} +(2.45784 - 4.25711i) q^{49} +(-6.00832 + 3.46891i) q^{50} +(-0.216976 + 0.375813i) q^{51} +(-4.52681 - 6.85122i) q^{52} +(-5.00538 + 8.66957i) q^{53} +7.94841i q^{54} +(1.70276 + 2.94927i) q^{55} +(0.990586 + 1.71575i) q^{56} +(2.66355 + 1.53780i) q^{57} +8.38163i q^{58} +(5.08142 - 2.93376i) q^{59} +2.03613i q^{60} +4.84999 q^{61} +(-1.98565 - 11.3428i) q^{62} -8.67904i q^{63} +10.0446 q^{64} +(0.278647 + 4.61670i) q^{65} -3.82671 q^{66} +(7.78781 + 4.49629i) q^{67} +(0.709044 + 1.22810i) q^{68} +(0.744655 + 1.28978i) q^{69} -9.15807i q^{70} +(6.12061 + 3.53374i) q^{71} +(1.24970 + 0.721514i) q^{72} +(0.366719 + 0.211725i) q^{73} +(6.20714 + 10.7511i) q^{74} +(-1.16895 + 2.02467i) q^{75} +(8.70409 - 5.02531i) q^{76} +9.16418 q^{77} +(-4.64923 - 2.32268i) q^{78} +(-3.01527 - 5.22259i) q^{79} +(-3.74154 - 2.16018i) q^{80} +(-2.43219 - 4.21267i) q^{81} +(-0.790729 + 1.36958i) q^{82} +(-9.86842 - 5.69753i) q^{83} +(4.74511 + 2.73959i) q^{84} -0.798718i q^{85} +(19.3808 - 11.1895i) q^{86} +(1.41221 + 2.44602i) q^{87} +(-0.761845 + 1.31955i) q^{88} -11.5953i q^{89} +(-3.33524 - 5.77680i) q^{90} +(11.1339 + 5.56234i) q^{91} +4.86684 q^{92} +(-2.49062 - 2.97564i) q^{93} -18.3520 q^{94} -5.66087 q^{95} +(4.89711 - 2.82735i) q^{96} +18.6165i q^{97} +(-8.80461 - 5.08335i) q^{98} +(5.78065 - 3.33746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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