LMFDB - Embedded newform 368.2.j.e.93.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.15
Character	$\chi$	$=$	368.93
Dual form			368.2.j.e.277.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.574346 + 1.29233i) q^{2} +(-0.912995 - 0.912995i) q^{3} +(-1.34025 + 1.48449i) q^{4} +(-1.27048 + 1.27048i) q^{5} +(0.655519 - 1.70427i) q^{6} +1.31051i q^{7} +(-2.68823 - 0.879444i) q^{8} -1.33288i q^{9} +(-2.37159 - 0.912192i) q^{10} +(-1.89644 + 1.89644i) q^{11} +(2.57898 - 0.131689i) q^{12} +(-1.81279 - 1.81279i) q^{13} +(-1.69362 + 0.752688i) q^{14} +2.31989 q^{15} +(-0.407438 - 3.97920i) q^{16} -7.87779 q^{17} +(1.72253 - 0.765535i) q^{18} +(1.11814 + 1.11814i) q^{19} +(-0.183253 - 3.58879i) q^{20} +(1.19649 - 1.19649i) q^{21} +(-3.54005 - 1.36162i) q^{22} +1.00000i q^{23} +(1.65141 + 3.25727i) q^{24} +1.77174i q^{25} +(1.30156 - 3.38390i) q^{26} +(-3.95590 + 3.95590i) q^{27} +(-1.94545 - 1.75642i) q^{28} +(-5.36615 - 5.36615i) q^{29} +(1.33242 + 2.99807i) q^{30} +8.31769 q^{31} +(4.90844 - 2.81198i) q^{32} +3.46289 q^{33} +(-4.52458 - 10.1807i) q^{34} +(-1.66499 - 1.66499i) q^{35} +(1.97865 + 1.78640i) q^{36} +(-4.35968 + 4.35968i) q^{37} +(-0.802812 + 2.08721i) q^{38} +3.31014i q^{39} +(4.53267 - 2.29803i) q^{40} +4.73713i q^{41} +(2.23347 + 0.859068i) q^{42} +(-7.31171 + 7.31171i) q^{43} +(-0.273540 - 5.35697i) q^{44} +(1.69340 + 1.69340i) q^{45} +(-1.29233 + 0.574346i) q^{46} +10.6994 q^{47} +(-3.26100 + 4.00497i) q^{48} +5.28255 q^{49} +(-2.28968 + 1.01759i) q^{50} +(7.19238 + 7.19238i) q^{51} +(5.12068 - 0.261474i) q^{52} +(3.88546 - 3.88546i) q^{53} +(-7.38439 - 2.84029i) q^{54} -4.81880i q^{55} +(1.15252 - 3.52296i) q^{56} -2.04171i q^{57} +(3.85283 - 10.0169i) q^{58} +(-2.98699 + 2.98699i) q^{59} +(-3.10924 + 3.44386i) q^{60} +(1.61927 + 1.61927i) q^{61} +(4.77723 + 10.7492i) q^{62} +1.74676 q^{63} +(6.45316 + 4.72829i) q^{64} +4.60624 q^{65} +(1.98889 + 4.47520i) q^{66} +(4.91494 + 4.91494i) q^{67} +(10.5582 - 11.6945i) q^{68} +(0.912995 - 0.912995i) q^{69} +(1.19544 - 3.10800i) q^{70} +6.99806i q^{71} +(-1.17219 + 3.58309i) q^{72} -5.30322i q^{73} +(-8.13812 - 3.13020i) q^{74} +(1.61759 - 1.61759i) q^{75} +(-3.15846 + 0.161279i) q^{76} +(-2.48532 - 2.48532i) q^{77} +(-4.27780 + 1.90116i) q^{78} -12.0440 q^{79} +(5.57314 + 4.53786i) q^{80} +3.22478 q^{81} +(-6.12196 + 2.72075i) q^{82} +(-0.637386 - 0.637386i) q^{83} +(0.172580 + 3.37979i) q^{84} +(10.0086 - 10.0086i) q^{85} +(-13.6486 - 5.24972i) q^{86} +9.79853i q^{87} +(6.76589 - 3.43026i) q^{88} -10.2289i q^{89} +(-1.21584 + 3.16104i) q^{90} +(2.37569 - 2.37569i) q^{91} +(-1.48449 - 1.34025i) q^{92} +(-7.59400 - 7.59400i) q^{93} +(6.14513 + 13.8271i) q^{94} -2.84116 q^{95} +(-7.04870 - 1.91406i) q^{96} +3.09106 q^{97} +(3.03401 + 6.82682i) q^{98} +(2.52774 + 2.52774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 2 q^{2} + 6 q^{3} + 4 q^{5} + 2 q^{8} - 10 q^{10} + 4 q^{11} - 16 q^{12} + 2 q^{13} + 28 q^{14} - 12 q^{15} - 8 q^{16} - 16 q^{17} - 34 q^{18} + 4 q^{19} + 18 q^{20} - 28 q^{22} - 30 q^{24} + 2 q^{26}+ \cdots - 28 q^{99}+O(q^{100}) $ 46 * q + 2 * q^2 + 6 * q^3 + 4 * q^5 + 2 * q^8 - 10 * q^10 + 4 * q^11 - 16 * q^12 + 2 * q^13 + 28 * q^14 - 12 * q^15 - 8 * q^16 - 16 * q^17 - 34 * q^18 + 4 * q^19 + 18 * q^20 - 28 * q^22 - 30 * q^24 + 2 * q^26 - 26 * q^28 + 2 * q^29 + 56 * q^30 + 40 * q^31 - 8 * q^32 + 60 * q^33 + 10 * q^34 + 8 * q^35 + 50 * q^36 + 24 * q^37 - 56 * q^38 + 10 * q^42 - 8 * q^43 - 50 * q^44 + 12 * q^45 - 2 * q^46 + 20 * q^47 - 110 * q^49 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 64 * q^54 - 8 * q^56 - 2 * q^58 - 54 * q^59 - 90 * q^60 - 8 * q^61 + 18 * q^62 + 24 * q^63 - 6 * q^64 + 28 * q^65 + 6 * q^66 + 42 * q^68 - 6 * q^69 - 58 * q^70 + 90 * q^72 + 6 * q^74 - 30 * q^75 - 44 * q^76 - 28 * q^77 + 44 * q^78 + 16 * q^79 - 52 * q^80 - 26 * q^81 - 62 * q^82 + 28 * q^83 + 170 * q^84 - 12 * q^85 - 92 * q^86 + 64 * q^88 + 140 * q^90 + 48 * q^91 - 4 * q^92 - 48 * q^93 + 52 * q^94 - 56 * q^96 + 72 * q^97 - 44 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.574346	+	1.29233i	0.406124	+	0.913818i
$2$	0.574346	+	1.29233i	0.406124	+	0.913818i
$3$	−0.912995	−	0.912995i	−0.527118	−	0.527118i	0.392594	−	0.919712i	$-0.371578\pi$
$3$	−0.912995	−	0.912995i	−0.527118	−	0.527118i	−0.919712	+	0.392594i	$0.871578\pi$
$4$	−1.34025	+	1.48449i	−0.670127	+	0.742246i
$5$	−1.27048	+	1.27048i	−0.568177	+	0.568177i	−0.931618	−	0.363440i	$-0.881602\pi$
$5$	−1.27048	+	1.27048i	−0.568177	+	0.568177i	0.363440	+	0.931618i	$0.381602\pi$
$6$	0.655519	−	1.70427i	0.267615	−	0.695765i
$7$			1.31051i			0.495328i	0.968846	+	0.247664i	$0.0796629\pi$
$7$			1.31051i			0.495328i	−0.968846	+	0.247664i	$0.920337\pi$
$8$	−2.68823	−	0.879444i	−0.950433	−	0.310930i
$9$		−	1.33288i		−	0.444294i
$10$	−2.37159	−	0.912192i	−0.749961	−	0.288461i
$11$	−1.89644	+	1.89644i	−0.571799	+	0.571799i	−0.932631	−	0.360832i	$-0.882493\pi$
$11$	−1.89644	+	1.89644i	−0.571799	+	0.571799i	0.360832	+	0.932631i	$0.382493\pi$
$12$	2.57898	−	0.131689i	0.744487	−	0.0380154i
$13$	−1.81279	−	1.81279i	−0.502778	−	0.502778i	0.409522	−	0.912300i	$-0.365695\pi$
$13$	−1.81279	−	1.81279i	−0.502778	−	0.502778i	−0.912300	+	0.409522i	$0.865695\pi$
$14$	−1.69362	+	0.752688i	−0.452640	+	0.201164i
$15$	2.31989			0.598993
$16$	−0.407438	−	3.97920i	−0.101859	−	0.994799i
$17$	−7.87779			−1.91065			−0.955323	−	0.295565i	$-0.904492\pi$
$17$	−7.87779			−1.91065			−0.955323	+	0.295565i	$0.904492\pi$
$18$	1.72253	−	0.765535i	0.406004	−	0.180438i
$19$	1.11814	+	1.11814i	0.256519	+	0.256519i	0.823637	−	0.567118i	$-0.191942\pi$
$19$	1.11814	+	1.11814i	0.256519	+	0.256519i	−0.567118	+	0.823637i	$0.691942\pi$
$20$	−0.183253	−	3.58879i	−0.0409766	−	0.802479i
$21$	1.19649	−	1.19649i	0.261096	−	0.261096i
$22$	−3.54005	−	1.36162i	−0.754742	−	0.290299i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	1.65141	+	3.25727i	0.337093	+	0.664887i
$25$			1.77174i			0.354349i
$26$	1.30156	−	3.38390i	0.255257	−	0.663637i
$27$	−3.95590	+	3.95590i	−0.761313	+	0.761313i
$28$	−1.94545	−	1.75642i	−0.367655	−	0.331933i
$29$	−5.36615	−	5.36615i	−0.996468	−	0.996468i	0.00352536	−	0.999994i	$-0.498878\pi$
$29$	−5.36615	−	5.36615i	−0.996468	−	0.996468i	−0.999994	+	0.00352536i	$0.998878\pi$
$30$	1.33242	+	2.99807i	0.243265	+	0.547370i
$31$	8.31769			1.49390			0.746950	−	0.664880i	$-0.231517\pi$
$31$	8.31769			1.49390			0.746950	+	0.664880i	$0.231517\pi$
$32$	4.90844	−	2.81198i	0.867698	−	0.497092i
$33$	3.46289			0.602811
$34$	−4.52458	−	10.1807i	−0.775958	−	1.74598i
$35$	−1.66499	−	1.66499i	−0.281434	−	0.281434i
$36$	1.97865	+	1.78640i	0.329776	+	0.297733i
$37$	−4.35968	+	4.35968i	−0.716727	+	0.716727i	−0.967933	−	0.251207i	$-0.919173\pi$
$37$	−4.35968	+	4.35968i	−0.716727	+	0.716727i	0.251207	+	0.967933i	$0.419173\pi$
$38$	−0.802812	+	2.08721i	−0.130233	+	0.338590i
$39$			3.31014i			0.530046i
$40$	4.53267	−	2.29803i	0.716678	−	0.363351i
$41$			4.73713i			0.739816i	0.929068	+	0.369908i	$0.120611\pi$
$41$			4.73713i			0.739816i	−0.929068	+	0.369908i	$0.879389\pi$
$42$	2.23347	+	0.859068i	0.344632	+	0.132557i
$43$	−7.31171	+	7.31171i	−1.11503	+	1.11503i	−0.122565	+	0.992460i	$0.539112\pi$
$43$	−7.31171	+	7.31171i	−1.11503	+	1.11503i	−0.992460	+	0.122565i	$0.960888\pi$
$44$	−0.273540	−	5.35697i	−0.0412378	−	0.807594i
$45$	1.69340	+	1.69340i	0.252438	+	0.252438i
$46$	−1.29233	+	0.574346i	−0.190544	+	0.0846826i
$47$	10.6994			1.56066			0.780330	−	0.625368i	$-0.215051\pi$
$47$	10.6994			1.56066			0.780330	+	0.625368i	$0.215051\pi$
$48$	−3.26100	+	4.00497i	−0.470684	+	0.578068i
$49$	5.28255			0.754650
$50$	−2.28968	+	1.01759i	−0.323810	+	0.143909i
$51$	7.19238	+	7.19238i	1.00713	+	1.00713i
$52$	5.12068	−	0.261474i	0.710110	−	0.0362600i
$53$	3.88546	−	3.88546i	0.533709	−	0.533709i	−0.387965	−	0.921674i	$-0.626822\pi$
$53$	3.88546	−	3.88546i	0.533709	−	0.533709i	0.921674	+	0.387965i	$0.126822\pi$
$54$	−7.38439	−	2.84029i	−1.00489	−	0.386514i
$55$		−	4.81880i		−	0.649767i
$56$	1.15252	−	3.52296i	0.154012	−	0.470776i
$57$		−	2.04171i		−	0.270431i
$58$	3.85283	−	10.0169i	0.505901	−	1.31528i
$59$	−2.98699	+	2.98699i	−0.388873	+	0.388873i	−0.874285	−	0.485413i	$-0.838669\pi$
$59$	−2.98699	+	2.98699i	−0.388873	+	0.388873i	0.485413	+	0.874285i	$0.338669\pi$
$60$	−3.10924	+	3.44386i	−0.401401	+	0.444600i
$61$	1.61927	+	1.61927i	0.207326	+	0.207326i	0.803130	−	0.595804i	$-0.203166\pi$
$61$	1.61927	+	1.61927i	0.207326	+	0.207326i	−0.595804	+	0.803130i	$0.703166\pi$
$62$	4.77723	+	10.7492i	0.606708	+	1.36515i
$63$	1.74676			0.220071
$64$	6.45316	+	4.72829i	0.806645	+	0.591037i
$65$	4.60624			0.571334
$66$	1.98889	+	4.47520i	0.244816	+	0.550860i
$67$	4.91494	+	4.91494i	0.600456	+	0.600456i	0.940433	−	0.339978i	$-0.110420\pi$
$67$	4.91494	+	4.91494i	0.600456	+	0.600456i	−0.339978	+	0.940433i	$0.610420\pi$
$68$	10.5582	−	11.6945i	1.28038	−	1.41817i
$69$	0.912995	−	0.912995i	0.109912	−	0.109912i
$70$	1.19544	−	3.10800i	0.142883	−	0.371477i
$71$			6.99806i			0.830517i	0.909704	+	0.415258i	$0.136309\pi$
$71$			6.99806i			0.830517i	−0.909704	+	0.415258i	$0.863691\pi$
$72$	−1.17219	+	3.58309i	−0.138144	+	0.422271i
$73$		−	5.30322i		−	0.620695i	−0.950623	−	0.310348i	$-0.899555\pi$
$73$		−	5.30322i		−	0.620695i	0.950623	−	0.310348i	$-0.100445\pi$
$74$	−8.13812	−	3.13020i	−0.946038	−	0.363878i
$75$	1.61759	−	1.61759i	0.186784	−	0.186784i
$76$	−3.15846	+	0.161279i	−0.362301	+	0.0185000i
$77$	−2.48532	−	2.48532i	−0.283228	−	0.283228i
$78$	−4.27780	+	1.90116i	−0.484366	+	0.215264i
$79$	−12.0440			−1.35505			−0.677526	−	0.735498i	$-0.736948\pi$
$79$	−12.0440			−1.35505			−0.677526	+	0.735498i	$0.736948\pi$
$80$	5.57314	+	4.53786i	0.623096	+	0.507348i
$81$	3.22478			0.358309
$82$	−6.12196	+	2.72075i	−0.676057	+	0.300457i
$83$	−0.637386	−	0.637386i	−0.0699622	−	0.0699622i	0.671260	−	0.741222i	$-0.265753\pi$
$83$	−0.637386	−	0.637386i	−0.0699622	−	0.0699622i	−0.741222	+	0.671260i	$0.765753\pi$
$84$	0.172580	+	3.37979i	0.0188301	+	0.368765i
$85$	10.0086	−	10.0086i	1.08559	−	1.08559i
$86$	−13.6486	−	5.24972i	−1.47177	−	0.566092i
$87$			9.79853i			1.05051i
$88$	6.76589	−	3.43026i	0.721247	−	0.365667i
$89$		−	10.2289i		−	1.08426i	−0.840293	−	0.542132i	$-0.817617\pi$
$89$		−	10.2289i		−	1.08426i	0.840293	−	0.542132i	$-0.182383\pi$
$90$	−1.21584	+	3.16104i	−0.128161	+	0.333203i
$91$	2.37569	−	2.37569i	0.249040	−	0.249040i
$92$	−1.48449	−	1.34025i	−0.154769	−	0.139731i
$93$	−7.59400	−	7.59400i	−0.787461	−	0.787461i
$94$	6.14513	+	13.8271i	0.633821	+	1.42616i
$95$	−2.84116			−0.291497
$96$	−7.04870	−	1.91406i	−0.719405	−	0.195353i
$97$	3.09106			0.313850			0.156925	−	0.987611i	$-0.449842\pi$
$97$	3.09106			0.313850			0.156925	+	0.987611i	$0.449842\pi$
$98$	3.03401	+	6.82682i	0.306481	+	0.689613i
$99$	2.52774	+	2.52774i	0.254047	+	0.254047i
$100$	−2.63014	−	2.37459i	−0.263014	−	0.237459i
$101$	−8.59413	+	8.59413i	−0.855148	+	0.855148i	−0.990762	−	0.135614i	$-0.956699\pi$
$101$	−8.59413	+	8.59413i	−0.855148	+	0.855148i	0.135614	+	0.990762i	$0.456699\pi$
$102$	−5.16405	+	13.4259i	−0.511317	+	1.32936i
$103$		−	6.22941i		−	0.613802i	−0.951742	−	0.306901i	$-0.900708\pi$
$103$		−	6.22941i		−	0.613802i	0.951742	−	0.306901i	$-0.0992920\pi$
$104$	3.27895	+	6.46745i	0.321527	+	0.634185i
$105$			3.04025i			0.296698i
$106$	7.25291	+	2.78971i	0.704464	+	0.270961i
$107$	−11.3082	+	11.3082i	−1.09321	+	1.09321i	−0.0980216	+	0.995184i	$0.531251\pi$
$107$	−11.3082	+	11.3082i	−1.09321	+	1.09321i	−0.995184	+	0.0980216i	$0.968749\pi$
$108$	−0.570593	−	11.1744i	−0.0549054	−	1.07526i
$109$	4.85691	+	4.85691i	0.465207	+	0.465207i	0.900358	−	0.435150i	$-0.143305\pi$
$109$	4.85691	+	4.85691i	0.465207	+	0.465207i	−0.435150	+	0.900358i	$0.643305\pi$
$110$	6.22750	−	2.76766i	0.593769	−	0.263886i
$111$	7.96073			0.755599
$112$	5.21479	−	0.533953i	0.492752	−	0.0504538i
$113$	−8.50144			−0.799748			−0.399874	−	0.916570i	$-0.630946\pi$
$113$	−8.50144			−0.799748			−0.399874	+	0.916570i	$0.630946\pi$
$114$	2.63857	−	1.17265i	0.247125	−	0.109829i
$115$	−1.27048	−	1.27048i	−0.118473	−	0.118473i
$116$	15.1580	−	0.774006i	1.40739	−	0.0718646i
$117$	−2.41624	+	2.41624i	−0.223381	+	0.223381i
$118$	−5.57575	−	2.14462i	−0.513289	−	0.197429i
$119$		−	10.3240i		−	0.946396i
$120$	−6.23639	−	2.04021i	−0.569302	−	0.186245i
$121$			3.80700i			0.346091i
$122$	−1.16262	+	3.02265i	−0.105258	+	0.273658i
$123$	4.32498	−	4.32498i	0.389970	−	0.389970i
$124$	−11.1478	+	12.3475i	−1.00110	+	1.10884i
$125$	−8.60339	−	8.60339i	−0.769510	−	0.769510i
$126$	1.00324	+	2.25740i	0.0893761	+	0.201105i
$127$	−2.53369			−0.224829			−0.112415	−	0.993661i	$-0.535858\pi$
$127$	−2.53369			−0.224829			−0.112415	+	0.993661i	$0.535858\pi$
$128$	−2.40419	+	11.0553i	−0.212503	+	0.977160i
$129$	13.3511			1.17550
$130$	2.64557	+	5.95280i	0.232032	+	0.522095i
$131$	−13.7117	−	13.7117i	−1.19799	−	1.19799i	−0.974767	−	0.223227i	$-0.928341\pi$
$131$	−13.7117	−	13.7117i	−1.19799	−	1.19799i	−0.223227	−	0.974767i	$-0.571659\pi$
$132$	−4.64115	+	5.14063i	−0.403960	+	0.447434i
$133$	−1.46534	+	1.46534i	−0.127061	+	0.127061i
$134$	−3.52887	+	9.17462i	−0.304848	+	0.792566i
$135$		−	10.0518i		−	0.865122i
$136$	21.1773	+	6.92808i	1.81594	+	0.594078i
$137$			12.7247i			1.08715i	0.839361	+	0.543574i	$0.182929\pi$
$137$			12.7247i			1.08715i	−0.839361	+	0.543574i	$0.817071\pi$
$138$	1.70427	+	0.655519i	0.145077	+	0.0558015i
$139$	5.58787	−	5.58787i	0.473957	−	0.473957i	−0.429236	−	0.903193i	$-0.641217\pi$
$139$	5.58787	−	5.58787i	0.473957	−	0.473957i	0.903193	+	0.429236i	$0.141217\pi$
$140$	4.70317	−	0.240155i	0.397490	−	0.0202968i
$141$	−9.76845	−	9.76845i	−0.822652	−	0.822652i
$142$	−9.04383	+	4.01930i	−0.758941	+	0.337292i
$143$	6.87571			0.574976
$144$	−5.30380	+	0.543066i	−0.441983	+	0.0452555i
$145$	13.6352			1.13234
$146$	6.85354	−	3.04588i	0.567203	−	0.252079i
$147$	−4.82294	−	4.82294i	−0.397790	−	0.397790i
$148$	−0.628834	−	12.3150i	−0.0516898	−	1.01229i
$149$	−3.11509	+	3.11509i	−0.255198	+	0.255198i	−0.823098	−	0.567900i	$-0.807756\pi$
$149$	−3.11509	+	3.11509i	−0.255198	+	0.255198i	0.567900	+	0.823098i	$0.307756\pi$
$150$	3.01953	+	1.16141i	0.246543	+	0.0948289i
$151$		−	10.4854i		−	0.853293i	−0.904418	−	0.426646i	$-0.859695\pi$
$151$		−	10.4854i		−	0.853293i	0.904418	−	0.426646i	$-0.140305\pi$
$152$	−2.02248	−	3.98916i	−0.164044	−	0.323564i
$153$			10.5002i			0.848888i
$154$	1.78443	−	4.63929i	0.143793	−	0.373845i
$155$	−10.5675	+	10.5675i	−0.848801	+	0.848801i
$156$	−4.91387	−	4.43642i	−0.393425	−	0.355198i
$157$	3.44617	+	3.44617i	0.275034	+	0.275034i	0.831123	−	0.556089i	$-0.187699\pi$
$157$	3.44617	+	3.44617i	0.275034	+	0.275034i	−0.556089	+	0.831123i	$0.687699\pi$
$158$	−6.91740	−	15.5648i	−0.550319	−	1.23827i
$159$	−7.09480			−0.562655
$160$	−2.66352	+	9.80866i	−0.210570	+	0.775443i
$161$	−1.31051			−0.103283
$162$	1.85214	+	4.16749i	0.145518	+	0.327429i
$163$	3.86509	+	3.86509i	0.302738	+	0.302738i	0.842084	−	0.539346i	$-0.181329\pi$
$163$	3.86509	+	3.86509i	0.302738	+	0.302738i	−0.539346	+	0.842084i	$0.681329\pi$
$164$	−7.03224	−	6.34896i	−0.549126	−	0.495771i
$165$	−4.39954	+	4.39954i	−0.342504	+	0.342504i
$166$	0.457636	−	1.18980i	0.0355194	−	0.0923461i
$167$		−	10.2656i		−	0.794375i	−0.917737	−	0.397188i	$-0.869986\pi$
$167$		−	10.2656i		−	0.794375i	0.917737	−	0.397188i	$-0.130014\pi$
$168$	−4.26869	+	2.16420i	−0.329337	+	0.166972i
$169$		−	6.42758i		−	0.494429i
$170$	18.6829	+	7.18606i	1.43291	+	0.551146i
$171$	1.49035	−	1.49035i	0.113970	−	0.113970i
$172$	−1.05463	−	20.6537i	−0.0804149	−	1.57483i
$173$	−16.2140	−	16.2140i	−1.23273	−	1.23273i	−0.962912	−	0.269817i	$-0.913037\pi$
$173$	−16.2140	−	16.2140i	−1.23273	−	1.23273i	−0.269817	−	0.962912i	$-0.586963\pi$
$174$	−12.6630	+	5.62774i	−0.959977	+	0.426638i
$175$	−2.32190			−0.175519
$176$	8.31900	+	6.77364i	0.627068	+	0.510582i
$177$	5.45421			0.409963
$178$	13.2192	−	5.87494i	0.990820	−	0.440345i
$179$	9.97108	+	9.97108i	0.745273	+	0.745273i	0.973587	−	0.228314i	$-0.0733214\pi$
$179$	9.97108	+	9.97108i	0.745273	+	0.745273i	−0.228314	+	0.973587i	$0.573321\pi$
$180$	−4.78344	+	0.244254i	−0.356536	+	0.0182056i
$181$	18.4206	−	18.4206i	1.36920	−	1.36920i	0.507607	−	0.861589i	$-0.330530\pi$
$181$	18.4206	−	18.4206i	1.36920	−	1.36920i	0.861589	−	0.507607i	$-0.169470\pi$
$182$	4.43465	+	1.70572i	0.328718	+	0.126436i
$183$		−	2.95677i		−	0.218570i
$184$	0.879444	−	2.68823i	0.0648335	−	0.198179i
$185$		−	11.0778i		−	0.814456i
$186$	5.45240	−	14.1756i	0.399790	−	1.03940i
$187$	14.9398	−	14.9398i	1.09251	−	1.09251i
$188$	−14.3398	+	15.8831i	−1.04584	+	1.15839i
$189$	−5.18426	−	5.18426i	−0.377099	−	0.377099i
$190$	−1.63181	−	3.67172i	−0.118384	−	0.266375i
$191$	14.2967			1.03447			0.517235	−	0.855843i	$-0.326961\pi$
$191$	14.2967			1.03447			0.517235	+	0.855843i	$0.326961\pi$
$192$	−1.57479	−	10.2086i	−0.113651	−	0.736743i
$193$	−16.3589			−1.17754			−0.588768	−	0.808302i	$-0.700387\pi$
$193$	−16.3589			−1.17754			−0.588768	+	0.808302i	$0.700387\pi$
$194$	1.77534	+	3.99469i	0.127462	+	0.286802i
$195$	−4.20547	−	4.20547i	−0.301160	−	0.301160i
$196$	−7.07996	+	7.84191i	−0.505712	+	0.560136i
$197$	4.26974	−	4.26974i	0.304207	−	0.304207i	−0.538450	−	0.842657i	$-0.680990\pi$
$197$	4.26974	−	4.26974i	0.304207	−	0.304207i	0.842657	+	0.538450i	$0.180990\pi$
$198$	−1.81488	+	4.71847i	−0.128978	+	0.335327i
$199$			4.01184i			0.284392i	0.989839	+	0.142196i	$0.0454163\pi$
$199$			4.01184i			0.284392i	−0.989839	+	0.142196i	$0.954584\pi$
$200$	1.55815	−	4.76285i	0.110178	−	0.336785i
$201$		−	8.97463i		−	0.633022i
$202$	−16.0425	−	6.17048i	−1.12875	−	0.434154i
$203$	7.03241	−	7.03241i	0.493579	−	0.493579i
$204$	−20.3167	+	1.03742i	−1.42245	+	0.0726339i
$205$	−6.01845	−	6.01845i	−0.420347	−	0.420347i
$206$	8.05047	−	3.57783i	0.560903	−	0.249279i
$207$	1.33288			0.0926417
$208$	−6.47485	+	7.95205i	−0.448950	+	0.551375i
$209$	−4.24098			−0.293355
$210$	−3.92902	+	1.74615i	−0.271128	+	0.120496i
$211$	−3.32889	−	3.32889i	−0.229170	−	0.229170i	0.583176	−	0.812346i	$-0.301810\pi$
$211$	−3.32889	−	3.32889i	−0.229170	−	0.229170i	−0.812346	+	0.583176i	$0.801810\pi$
$212$	0.560433	+	10.9754i	0.0384907	+	0.753796i
$213$	6.38919	−	6.38919i	0.437780	−	0.437780i
$214$	−21.1088	−	8.11916i	−1.44297	−	0.555015i
$215$		−	18.5788i		−	1.26706i
$216$	14.1134	−	7.15537i	0.960292	−	0.486861i
$217$			10.9004i			0.739970i
$218$	−3.48720	+	9.06629i	−0.236183	+	0.614047i
$219$	−4.84181	+	4.84181i	−0.327179	+	0.327179i
$220$	7.15347	+	6.45842i	0.482287	+	0.435426i
$221$	14.2808	+	14.2808i	0.960630	+	0.960630i
$222$	4.57221	+	10.2879i	0.306867	+	0.690480i
$223$	−1.69791			−0.113701			−0.0568503	−	0.998383i	$-0.518106\pi$
$223$	−1.69791			−0.113701			−0.0568503	+	0.998383i	$0.518106\pi$
$224$	3.68514	+	6.43258i	0.246224	+	0.429795i
$225$	2.36153			0.157435
$226$	−4.88276	−	10.9867i	−0.324797	−	0.730824i
$227$	−1.05258	−	1.05258i	−0.0698622	−	0.0698622i	0.671312	−	0.741175i	$-0.265731\pi$
$227$	−1.05258	−	1.05258i	−0.0698622	−	0.0698622i	−0.741175	+	0.671312i	$0.765731\pi$
$228$	3.03091	+	2.73641i	0.200727	+	0.181223i
$229$	7.56257	−	7.56257i	0.499748	−	0.499748i	−0.411611	−	0.911360i	$-0.635034\pi$
$229$	7.56257	−	7.56257i	0.499748	−	0.499748i	0.911360	+	0.411611i	$0.135034\pi$
$230$	0.912192	−	2.37159i	0.0601482	−	0.156378i
$231$			4.53816i			0.298589i
$232$	9.70621	+	19.1447i	0.637244	+	1.25691i
$233$			21.5951i			1.41474i	0.706841	+	0.707372i	$0.250120\pi$
$233$			21.5951i			1.41474i	−0.706841	+	0.707372i	$0.749880\pi$
$234$	−4.51034	−	1.73483i	−0.294850	−	0.113409i
$235$	−13.5933	+	13.5933i	−0.886732	+	0.886732i
$236$	−0.430839	−	8.43749i	−0.0280452	−	0.549233i
$237$	10.9961	+	10.9961i	0.714272	+	0.714272i
$238$	13.3420	−	5.92952i	0.864834	−	0.384354i
$239$	−1.46441			−0.0947248			−0.0473624	−	0.998878i	$-0.515082\pi$
$239$	−1.46441			−0.0947248			−0.0473624	+	0.998878i	$0.515082\pi$
$240$	−0.945210	−	9.23129i	−0.0610130	−	0.595877i
$241$	−7.98924			−0.514632			−0.257316	−	0.966327i	$-0.582838\pi$
$241$	−7.98924			−0.514632			−0.257316	+	0.966327i	$0.582838\pi$
$242$	−4.91992	+	2.18654i	−0.316264	+	0.140556i
$243$	8.92348	+	8.92348i	0.572442	+	0.572442i
$244$	−4.57402	+	0.233561i	−0.292822	+	0.0149522i
$245$	−6.71139	+	6.71139i	−0.428775	+	0.428775i
$246$	8.07334	+	3.10528i	0.514738	+	0.197986i
$247$		−	4.05391i		−	0.257944i
$248$	−22.3598	−	7.31494i	−1.41985	−	0.464499i
$249$			1.16386i			0.0737567i
$250$	6.17713	−	16.0598i	0.390676	−	1.01571i
$251$	0.222330	−	0.222330i	0.0140333	−	0.0140333i	−0.700055	−	0.714089i	$-0.746841\pi$
$251$	0.222330	−	0.222330i	0.0140333	−	0.0140333i	0.714089	+	0.700055i	$0.246841\pi$
$252$	−2.34110	+	2.59305i	−0.147476	+	0.163347i
$253$	−1.89644	−	1.89644i	−0.119228	−	0.119228i
$254$	−1.45522	−	3.27438i	−0.0913084	−	0.205453i
$255$	−18.2756			−1.14446
$256$	−15.6680	+	3.24255i	−0.979249	+	0.202659i
$257$	−26.8996			−1.67795			−0.838977	−	0.544168i	$-0.816846\pi$
$257$	−26.8996			−1.67795			−0.838977	+	0.544168i	$0.816846\pi$
$258$	7.66815	+	17.2541i	0.477398	+	1.07419i
$259$	−5.71342	−	5.71342i	−0.355015	−	0.355015i
$260$	−6.17353	+	6.83793i	−0.382866	+	0.424071i
$261$	−7.15244	+	7.15244i	−0.442725	+	0.442725i
$262$	9.84481	−	25.5953i	0.608215	−	1.58128i
$263$			26.0336i			1.60530i	0.596450	+	0.802650i	$0.296577\pi$
$263$			26.0336i			1.60530i	−0.596450	+	0.802650i	$0.703423\pi$
$264$	−9.30903	−	3.04541i	−0.572931	−	0.187432i
$265$			9.87282i			0.606483i
$266$	−2.73532	−	1.05210i	−0.167713	−	0.0645082i
$267$	−9.33895	+	9.33895i	−0.571535	+	0.571535i
$268$	−13.8835	+	0.708924i	−0.848068	+	0.0433044i
$269$	8.01586	+	8.01586i	0.488736	+	0.488736i	0.907907	−	0.419171i	$-0.137679\pi$
$269$	8.01586	+	8.01586i	0.488736	+	0.488736i	−0.419171	+	0.907907i	$0.637679\pi$
$270$	12.9903	−	5.77321i	0.790564	−	0.351346i
$271$	0.209393			0.0127197			0.00635985	−	0.999980i	$-0.497976\pi$
$271$	0.209393			0.0127197			0.00635985	+	0.999980i	$0.497976\pi$
$272$	3.20971	+	31.3473i	0.194617	+	1.90071i
$273$	−4.33798			−0.262547
$274$	−16.4446	+	7.30840i	−0.993455	+	0.441516i
$275$	−3.36001	−	3.36001i	−0.202616	−	0.202616i
$276$	0.131689	+	2.57898i	0.00792675	+	0.155236i
$277$	−9.88966	+	9.88966i	−0.594212	+	0.594212i	−0.938766	−	0.344554i	$-0.888030\pi$
$277$	−9.88966	+	9.88966i	−0.594212	+	0.594212i	0.344554	+	0.938766i	$0.388030\pi$
$278$	10.4308	+	4.01203i	0.625596	+	0.240625i
$279$		−	11.0865i		−	0.663731i
$280$	3.01160	+	5.94013i	0.179978	+	0.354991i
$281$			21.2982i			1.27055i	0.772288	+	0.635273i	$0.219112\pi$
$281$			21.2982i			1.27055i	−0.772288	+	0.635273i	$0.780888\pi$
$282$	7.01363	−	18.2346i	0.417656	−	1.08585i
$283$	8.30793	−	8.30793i	0.493855	−	0.493855i	−0.415663	−	0.909519i	$-0.636450\pi$
$283$	8.30793	−	8.30793i	0.493855	−	0.493855i	0.909519	+	0.415663i	$0.136450\pi$
$284$	−10.3886	−	9.37918i	−0.616448	−	0.556552i
$285$	2.59396	+	2.59396i	0.153653	+	0.153653i
$286$	3.94903	+	8.88572i	0.233511	+	0.525423i
$287$	−6.20808			−0.366451
$288$	−3.74804	−	6.54237i	−0.220855	−	0.385513i
$289$	45.0596			2.65057
$290$	7.83132	+	17.6212i	0.459871	+	1.03475i
$291$	−2.82213	−	2.82213i	−0.165436	−	0.165436i
$292$	7.87260	+	7.10767i	0.460709	+	0.415945i
$293$	2.00670	−	2.00670i	0.117233	−	0.117233i	−0.646057	−	0.763289i	$-0.723583\pi$
$293$	2.00670	−	2.00670i	0.117233	−	0.117233i	0.763289	+	0.646057i	$0.223583\pi$
$294$	3.46282	−	9.00289i	0.201956	−	0.525059i
$295$		−	7.58984i		−	0.441897i
$296$	15.5539	−	7.88572i	0.904053	−	0.458348i
$297$		−	15.0043i		−	0.870636i
$298$	−5.81487	−	2.23660i	−0.336846	−	0.129563i
$299$	1.81279	−	1.81279i	0.104836	−	0.104836i
$300$	0.233319	+	4.56929i	0.0134707	+	0.263808i
$301$	−9.58210	−	9.58210i	−0.552303	−	0.552303i
$302$	13.5507	−	6.02227i	0.779754	−	0.346542i
$303$	15.6928			0.901527
$304$	3.99373	−	4.90487i	0.229056	−	0.281314i
$305$	−4.11451			−0.235596
$306$	−13.5697	+	6.03072i	−0.775729	+	0.344754i
$307$	6.89337	+	6.89337i	0.393426	+	0.393426i	0.875906	−	0.482481i	$-0.160264\pi$
$307$	6.89337	+	6.89337i	0.393426	+	0.393426i	−0.482481	+	0.875906i	$0.660264\pi$
$308$	7.02039	−	0.358479i	0.400024	−	0.0204262i
$309$	−5.68741	+	5.68741i	−0.323546	+	0.323546i
$310$	−19.7261	−	7.58733i	−1.12037	−	0.430931i
$311$			3.44536i			0.195369i	0.995217	+	0.0976843i	$0.0311436\pi$
$311$			3.44536i			0.195369i	−0.995217	+	0.0976843i	$0.968856\pi$
$312$	2.91108	−	8.89841i	0.164807	−	0.503773i
$313$			4.87016i			0.275278i	0.990482	+	0.137639i	$0.0439513\pi$
$313$			4.87016i			0.275278i	−0.990482	+	0.137639i	$0.956049\pi$
$314$	−2.47431	+	6.43289i	−0.139633	+	0.363029i
$315$	−2.21923	+	2.21923i	−0.125039	+	0.125039i
$316$	16.1420	−	17.8792i	0.908058	−	1.00578i
$317$	−12.4215	−	12.4215i	−0.697663	−	0.697663i	0.266243	−	0.963906i	$-0.414218\pi$
$317$	−12.4215	−	12.4215i	−0.697663	−	0.697663i	−0.963906	+	0.266243i	$0.914218\pi$
$318$	−4.07487	−	9.16886i	−0.228507	−	0.514164i
$319$	20.3532			1.13956
$320$	−14.2058	+	2.19141i	−0.794131	+	0.122503i
$321$	20.6487			1.15250
$322$	−0.752688	−	1.69362i	−0.0419457	−	0.0943819i
$323$	−8.80848	−	8.80848i	−0.490117	−	0.490117i
$324$	−4.32203	+	4.78716i	−0.240113	+	0.265954i
$325$	3.21180	−	3.21180i	0.178159	−	0.178159i
$326$	−2.77509	+	7.21489i	−0.153698	+	0.399596i
$327$		−	8.86866i		−	0.490438i
$328$	4.16604	−	12.7345i	0.230031	−	0.703145i
$329$			14.0217i			0.773039i
$330$	−8.21253	−	3.15882i	−0.452085	−	0.173887i
$331$	−7.77614	+	7.77614i	−0.427415	+	0.427415i	−0.887747	−	0.460332i	$-0.847731\pi$
$331$	−7.77614	+	7.77614i	−0.427415	+	0.427415i	0.460332	+	0.887747i	$0.347731\pi$
$332$	1.80045	−	0.0919357i	0.0988128	−	0.00504563i
$333$	5.81094	+	5.81094i	0.318437	+	0.318437i
$334$	13.2666	−	5.89600i	0.725914	−	0.322615i
$335$	−12.4887			−0.682331
$336$	−5.24857	−	4.27358i	−0.286333	−	0.233143i
$337$	−11.0621			−0.602593			−0.301296	−	0.953531i	$-0.597419\pi$
$337$	−11.0621			−0.602593			−0.301296	+	0.953531i	$0.597419\pi$
$338$	8.30658	−	3.69165i	0.451818	−	0.200799i
$339$	7.76177	+	7.76177i	0.421561	+	0.421561i
$340$	1.44363	+	28.2718i	0.0782917	+	1.53325i
$341$	−15.7740	+	15.7740i	−0.854211	+	0.854211i
$342$	2.78200	+	1.07005i	0.150434	+	0.0578618i
$343$			16.0965i			0.869127i
$344$	26.0858	−	13.2253i	1.40645	−	0.713061i
$345$			2.31989i			0.124899i
$346$	11.6415	−	30.2664i	0.625850	−	1.62713i
$347$	10.2926	−	10.2926i	0.552535	−	0.552535i	−0.374637	−	0.927172i	$-0.622233\pi$
$347$	10.2926	−	10.2926i	0.552535	−	0.552535i	0.927172	+	0.374637i	$0.122233\pi$
$348$	−14.5458	−	13.1325i	−0.779739	−	0.703977i
$349$	13.8783	+	13.8783i	0.742888	+	0.742888i	0.973133	−	0.230244i	$-0.0739526\pi$
$349$	13.8783	+	13.8783i	0.742888	+	0.742888i	−0.230244	+	0.973133i	$0.573953\pi$
$350$	−1.33357	−	3.00066i	−0.0712824	−	0.160392i
$351$	14.3424			0.765542
$352$	−3.97582	+	14.6413i	−0.211912	+	0.780386i
$353$	23.8135			1.26746			0.633732	−	0.773552i	$-0.281522\pi$
$353$	23.8135			1.26746			0.633732	+	0.773552i	$0.281522\pi$
$354$	3.13260	+	7.04866i	0.166496	+	0.374632i
$355$	−8.89092	−	8.89092i	−0.471881	−	0.471881i
$356$	15.1848	+	13.7094i	0.804791	+	0.726595i
$357$	−9.42572	+	9.42572i	−0.498862	+	0.498862i
$358$	−7.15912	+	18.6128i	−0.378371	+	0.983717i
$359$		−	1.38630i		−	0.0731659i	−0.999331	−	0.0365829i	$-0.988353\pi$
$359$		−	1.38630i		−	0.0731659i	0.999331	−	0.0365829i	$-0.0116473\pi$
$360$	−3.06300	−	6.04151i	−0.161435	−	0.318416i
$361$		−	16.4995i		−	0.868396i
$362$	34.3854	+	13.2258i	1.80726	+	0.695133i
$363$	3.47577	−	3.47577i	0.182431	−	0.182431i
$364$	0.342666	+	6.71072i	0.0179606	+	0.351737i
$365$	6.73766	+	6.73766i	0.352665	+	0.352665i
$366$	3.82113	−	1.69821i	0.199734	−	0.0887666i
$367$	−30.8493			−1.61032			−0.805160	−	0.593058i	$-0.797920\pi$
$367$	−30.8493			−1.61032			−0.805160	+	0.593058i	$0.797920\pi$
$368$	3.97920	−	0.407438i	0.207430	−	0.0212392i
$369$	6.31404			0.328696
$370$	14.3162	−	6.36249i	0.744265	−	0.330770i
$371$	5.09195	+	5.09195i	0.264361	+	0.264361i
$372$	21.4511	−	1.09535i	1.11219	−	0.0567912i
$373$	25.3705	−	25.3705i	1.31363	−	1.31363i	0.394919	−	0.918716i	$-0.370773\pi$
$373$	25.3705	−	25.3705i	1.31363	−	1.31363i	0.918716	−	0.394919i	$-0.129227\pi$
$374$	27.8878	+	10.7266i	1.44204	+	0.554659i
$375$			15.7097i			0.811245i
$376$	−28.7623	−	9.40948i	−1.48330	−	0.485257i
$377$			19.4554i			1.00200i
$378$	3.72224	−	9.67735i	0.191451	−	0.497749i
$379$	−24.0366	+	24.0366i	−1.23468	+	1.23468i	−0.272529	+	0.962148i	$0.587860\pi$
$379$	−24.0366	+	24.0366i	−1.23468	+	1.23468i	−0.962148	+	0.272529i	$0.912140\pi$
$380$	3.80787	−	4.21768i	0.195340	−	0.216362i
$381$	2.31325	+	2.31325i	0.118511	+	0.118511i
$382$	8.21123	+	18.4761i	0.420123	+	0.945318i
$383$	10.0706			0.514586			0.257293	−	0.966333i	$-0.417170\pi$
$383$	10.0706			0.514586			0.257293	+	0.966333i	$0.417170\pi$
$384$	12.2885	−	7.89842i	0.627092	−	0.403065i
$385$	6.31511			0.321848
$386$	−9.39563	−	21.1411i	−0.478225	−	1.07605i
$387$	9.74565	+	9.74565i	0.495399	+	0.495399i
$388$	−4.14281	+	4.58866i	−0.210319	+	0.232954i
$389$	−0.625098	+	0.625098i	−0.0316937	+	0.0316937i	−0.722776	−	0.691082i	$-0.757134\pi$
$389$	−0.625098	+	0.625098i	−0.0316937	+	0.0316937i	0.691082	+	0.722776i	$0.257134\pi$
$390$	3.01948	−	7.85027i	0.152897	−	0.397514i
$391$		−	7.87779i		−	0.398397i
$392$	−14.2007	−	4.64571i	−0.717244	−	0.234644i
$393$			25.0373i			1.26297i
$394$	7.97025	+	3.06563i	0.401535	+	0.154444i
$395$	15.3017	−	15.3017i	0.769910	−	0.769910i
$396$	−7.14021	+	0.364597i	−0.358809	+	0.0183217i
$397$	16.9332	+	16.9332i	0.849855	+	0.849855i	0.990115	−	0.140260i	$-0.0447938\pi$
$397$	16.9332	+	16.9332i	0.849855	+	0.849855i	−0.140260	+	0.990115i	$0.544794\pi$
$398$	−5.18463	+	2.30418i	−0.259882	+	0.115498i
$399$	2.67569			0.133952
$400$	7.05012	−	0.721875i	0.352506	−	0.0360938i
$401$	−10.1255			−0.505641			−0.252821	−	0.967513i	$-0.581358\pi$
$401$	−10.1255			−0.505641			−0.252821	+	0.967513i	$0.581358\pi$
$402$	11.5982	−	5.15454i	0.578467	−	0.257085i
$403$	−15.0782	−	15.0782i	−0.751100	−	0.751100i
$404$	−1.23961	−	24.2762i	−0.0616727	−	1.20779i
$405$	−4.09703	+	4.09703i	−0.203583	+	0.203583i
$406$	13.1273	+	5.04919i	0.651495	+	0.250587i
$407$		−	16.5358i		−	0.819648i
$408$	−13.0095	−	25.6601i	−0.644065	−	1.27036i
$409$			16.2698i			0.804489i	0.915532	+	0.402244i	$0.131770\pi$
$409$			16.2698i			0.804489i	−0.915532	+	0.402244i	$0.868230\pi$
$410$	4.32118	−	11.2345i	0.213408	−	0.554833i
$411$	11.6176	−	11.6176i	0.573055	−	0.573055i
$412$	9.24751	+	8.34899i	0.455592	+	0.411325i
$413$	−3.91449	−	3.91449i	−0.192619	−	0.192619i
$414$	0.765535	+	1.72253i	0.0376240	+	0.0846576i
$415$	1.61958			0.0795019
$416$	−13.9955	−	3.80044i	−0.686186	−	0.186332i
$417$	−10.2034			−0.499662
$418$	−2.43579	−	5.48076i	−0.119138	−	0.268073i
$419$	3.23883	+	3.23883i	0.158227	+	0.158227i	0.781781	−	0.623553i	$-0.214312\pi$
$419$	3.23883	+	3.23883i	0.158227	+	0.158227i	−0.623553	+	0.781781i	$0.714312\pi$
$420$	−4.51323	−	4.07470i	−0.220223	−	0.198825i
$421$	0.931096	−	0.931096i	0.0453789	−	0.0453789i	−0.684053	−	0.729432i	$-0.739784\pi$
$421$	0.931096	−	0.931096i	0.0453789	−	0.0453789i	0.729432	+	0.684053i	$0.239784\pi$
$422$	2.39010	−	6.21397i	0.116348	−	0.302491i
$423$		−	14.2610i		−	0.693392i
$424$	−13.8620	+	7.02796i	−0.673200	+	0.341308i
$425$		−	13.9574i		−	0.677035i
$426$	11.9266	+	4.58736i	0.577844	+	0.222258i
$427$	−2.12207	+	2.12207i	−0.102694	+	0.102694i
$428$	−1.63108	−	31.9428i	−0.0788413	−	1.54402i
$429$	−6.27749	−	6.27749i	−0.303080	−	0.303080i
$430$	24.0100	−	10.6707i	1.15787	−	0.514585i
$431$	−11.2972			−0.544167			−0.272083	−	0.962274i	$-0.587713\pi$
$431$	−11.2972			−0.544167			−0.272083	+	0.962274i	$0.587713\pi$
$432$	17.3531	+	14.1295i	0.834900	+	0.679806i
$433$	−32.8305			−1.57773			−0.788866	−	0.614565i	$-0.789331\pi$
$433$	−32.8305			−1.57773			−0.788866	+	0.614565i	$0.789331\pi$
$434$	−14.0870	+	6.26062i	−0.676198	+	0.300520i
$435$	−12.4489	−	12.4489i	−0.596877	−	0.596877i
$436$	−13.7195	+	0.700554i	−0.657047	+	0.0335504i
$437$	−1.11814	+	1.11814i	−0.0534879	+	0.0534879i
$438$	−9.03812	−	3.47637i	−0.431858	−	0.166107i
$439$			6.20225i			0.296017i	0.988986	+	0.148009i	$0.0472864\pi$
$439$			6.20225i			0.296017i	−0.988986	+	0.148009i	$0.952714\pi$
$440$	−4.23787	+	12.9540i	−0.202032	+	0.617560i
$441$		−	7.04102i		−	0.335287i
$442$	−10.2534	+	26.6577i	−0.487706	+	1.26798i
$443$	−5.51001	+	5.51001i	−0.261788	+	0.261788i	−0.825780	−	0.563992i	$-0.809265\pi$
$443$	−5.51001	+	5.51001i	−0.261788	+	0.261788i	0.563992	+	0.825780i	$0.309265\pi$
$444$	−10.6694	+	11.8176i	−0.506347	+	0.560840i
$445$	12.9957	+	12.9957i	0.616054	+	0.616054i
$446$	−0.975188	−	2.19427i	−0.0461765	−	0.103902i
$447$	5.68812			0.269039
$448$	−6.19650	+	8.45695i	−0.292757	+	0.399554i
$449$	−8.89659			−0.419856			−0.209928	−	0.977717i	$-0.567323\pi$
$449$	−8.89659			−0.419856			−0.209928	+	0.977717i	$0.567323\pi$
$450$	1.35633	+	3.05188i	0.0639381	+	0.143867i
$451$	−8.98370	−	8.98370i	−0.423026	−	0.423026i
$452$	11.3941	−	12.6203i	0.535933	−	0.593610i
$453$	−9.57315	+	9.57315i	−0.449786	+	0.449786i
$454$	0.755741	−	1.96483i	0.0354687	−	0.0922141i
$455$			6.03654i			0.282998i
$456$	−1.79557	+	5.48859i	−0.0840853	+	0.257027i
$457$		−	4.37946i		−	0.204863i	−0.994740	−	0.102431i	$-0.967338\pi$
$457$		−	4.37946i		−	0.204863i	0.994740	−	0.102431i	$-0.0326622\pi$
$458$	14.1169	+	5.42983i	0.659639	+	0.253719i
$459$	31.1637	−	31.1637i	1.45460	−	1.45460i
$460$	3.58879	−	0.183253i	0.167328	−	0.00854420i
$461$	8.42602	+	8.42602i	0.392439	+	0.392439i	0.875556	−	0.483117i	$-0.160495\pi$
$461$	8.42602	+	8.42602i	0.392439	+	0.392439i	−0.483117	+	0.875556i	$0.660495\pi$
$462$	−5.86482	+	2.60647i	−0.272856	+	0.121264i
$463$	−27.2053			−1.26434			−0.632169	−	0.774830i	$-0.717835\pi$
$463$	−27.2053			−1.26434			−0.632169	+	0.774830i	$0.717835\pi$
$464$	−19.1666	+	23.5393i	−0.889786	+	1.09279i
$465$	19.2961			0.894836
$466$	−27.9081	+	12.4031i	−1.29282	+	0.574561i
$467$	−2.85300	−	2.85300i	−0.132021	−	0.132021i	0.638008	−	0.770029i	$-0.279759\pi$
$467$	−2.85300	−	2.85300i	−0.132021	−	0.132021i	−0.770029	+	0.638008i	$0.779759\pi$
$468$	−0.348514	−	6.82525i	−0.0161101	−	0.315497i
$469$	−6.44110	+	6.44110i	−0.297422	+	0.297422i
$470$	−25.3744	−	9.75986i	−1.17043	−	0.450189i
$471$		−	6.29266i		−	0.289951i
$472$	10.6566	−	5.40282i	0.490510	−	0.248685i
$473$		−	27.7325i		−	1.27514i
$474$	−7.89506	+	20.5262i	−0.362632	+	0.942798i
$475$	−1.98106	+	1.98106i	−0.0908972	+	0.0908972i
$476$	15.3258	+	13.8367i	0.702459	+	0.634205i
$477$	−5.17886	−	5.17886i	−0.237124	−	0.237124i
$478$	−0.841078	−	1.89251i	−0.0384700	−	0.0865613i
$479$	33.4680			1.52919			0.764596	−	0.644510i	$-0.222939\pi$
$479$	33.4680			1.52919			0.764596	+	0.644510i	$0.222939\pi$
$480$	11.3870	−	6.52348i	0.519745	−	0.297755i
$481$	15.8064			0.720708
$482$	−4.58859	−	10.3248i	−0.209004	−	0.470280i
$483$	1.19649	+	1.19649i	0.0544423	+	0.0544423i
$484$	−5.65147	−	5.10235i	−0.256885	−	0.231925i
$485$	−3.92715	+	3.92715i	−0.178323	+	0.178323i
$486$	−6.40696	+	16.6573i	−0.290626	+	0.755590i
$487$			35.6975i			1.61761i	0.588078	+	0.808804i	$0.299885\pi$
$487$			35.6975i			1.61761i	−0.588078	+	0.808804i	$0.700115\pi$
$488$	−2.92891	−	5.77702i	−0.132585	−	0.261513i
$489$		−	7.05762i		−	0.319157i
$490$	−12.5280	−	4.81870i	−0.565958	−	0.217687i
$491$	25.1839	−	25.1839i	1.13653	−	1.13653i	0.147466	−	0.989067i	$-0.452888\pi$
$491$	25.1839	−	25.1839i	1.13653	−	1.13653i	0.989067	−	0.147466i	$-0.0471116\pi$
$492$	0.623829	+	12.2170i	0.0281244	+	0.550783i
$493$	42.2734	+	42.2734i	1.90390	+	1.90390i
$494$	5.23900	−	2.32834i	0.235714	−	0.104757i
$495$	−6.42289			−0.288687
$496$	−3.38894	−	33.0977i	−0.152168	−	1.48613i
$497$	−9.17105			−0.411378
$498$	−1.50410	+	0.668458i	−0.0674002	+	0.0299543i
$499$	−8.96894	−	8.96894i	−0.401505	−	0.401505i	0.477258	−	0.878763i	$-0.341631\pi$
$499$	−8.96894	−	8.96894i	−0.401505	−	0.401505i	−0.878763	+	0.477258i	$0.841631\pi$
$500$	24.3024	−	1.24094i	1.08684	−	0.0554966i
$501$	−9.37243	+	9.37243i	−0.418729	+	0.418729i
$502$	0.415019	+	0.159630i	0.0185232	+	0.00712464i
$503$			32.9585i			1.46955i	0.678313	+	0.734773i	$0.262711\pi$
$503$			32.9585i			1.46955i	−0.678313	+	0.734773i	$0.737289\pi$
$504$	−4.69569	−	1.53618i	−0.209163	−	0.0684268i
$505$		−	21.8374i		−	0.971751i
$506$	1.36162	−	3.54005i	0.0605316	−	0.157375i
$507$	−5.86835	+	5.86835i	−0.260622	+	0.260622i
$508$	3.39579	−	3.76125i	0.150664	−	0.166879i
$509$	16.2258	+	16.2258i	0.719198	+	0.719198i	0.968441	−	0.249243i	$-0.0801817\pi$
$509$	16.2258	+	16.2258i	0.719198	+	0.719198i	−0.249243	+	0.968441i	$0.580182\pi$
$510$	−10.4965	−	23.6182i	−0.464793	−	1.04583i
$511$	6.94995			0.307448
$512$	−13.1893	−	18.3859i	−0.582890	−	0.812551i
$513$	−8.84650			−0.390582
$514$	−15.4497	−	34.7633i	−0.681457	−	1.53334i
$515$	7.91436	+	7.91436i	0.348748	+	0.348748i
$516$	−17.8939	+	19.8196i	−0.787734	+	0.872510i
$517$	−20.2907	+	20.2907i	−0.892385	+	0.892385i
$518$	4.10217	−	10.6651i	0.180239	−	0.468599i
$519$			29.6066i			1.29959i
$520$	−12.3826	−	4.05093i	−0.543014	−	0.177645i
$521$			36.5355i			1.60065i	0.599566	+	0.800325i	$0.295340\pi$
$521$			36.5355i			1.60065i	−0.599566	+	0.800325i	$0.704660\pi$
$522$	−13.3513	−	5.13537i	−0.584371	−	0.224769i
$523$	−2.16837	+	2.16837i	−0.0948160	+	0.0948160i	−0.752924	−	0.658108i	$-0.771357\pi$
$523$	−2.16837	+	2.16837i	−0.0948160	+	0.0948160i	0.658108	+	0.752924i	$0.271357\pi$
$524$	38.7320	−	1.97775i	1.69201	−	0.0863985i
$525$	2.11988	+	2.11988i	0.0925191	+	0.0925191i
$526$	−33.6441	+	14.9523i	−1.46695	+	0.651951i
$527$	−65.5250			−2.85431
$528$	−1.41091	−	13.7795i	−0.0614020	−	0.599676i
$529$	−1.00000			−0.0434783
$530$	−12.7590	+	5.67041i	−0.554215	+	0.246307i
$531$	3.98130	+	3.98130i	0.172774	+	0.172774i
$532$	−0.211358	−	4.13921i	−0.00916355	−	0.179458i
$533$	8.58743	−	8.58743i	0.371963	−	0.371963i
$534$	−17.4328	−	6.70526i	−0.754393	−	0.290165i
$535$		−	28.7338i		−	1.24227i
$536$	−8.89007	−	17.5349i	−0.383993	−	0.757393i
$537$		−	18.2071i		−	0.785693i
$538$	−5.75530	+	14.9631i	−0.248128	+	0.645103i
$539$	−10.0181	+	10.0181i	−0.431509	+	0.431509i
$540$	14.9218	+	13.4720i	0.642133	+	0.579741i
$541$	−20.6596	−	20.6596i	−0.888224	−	0.888224i	0.106128	−	0.994352i	$-0.466155\pi$
$541$	−20.6596	−	20.6596i	−0.888224	−	0.888224i	−0.994352	+	0.106128i	$0.966155\pi$
$542$	0.120264	+	0.270605i	0.00516577	+	0.0116235i
$543$	−33.6359			−1.44345
$544$	−38.6677	+	22.1522i	−1.65786	+	0.949767i
$545$	−12.3412			−0.528641
$546$	−2.49150	−	5.60612i	−0.106626	−	0.239920i
$547$	−7.37984	−	7.37984i	−0.315539	−	0.315539i	0.531512	−	0.847051i	$-0.321624\pi$
$547$	−7.37984	−	7.37984i	−0.315539	−	0.315539i	−0.847051	+	0.531512i	$0.821624\pi$
$548$	−18.8898	−	17.0544i	−0.806931	−	0.728527i
$549$	2.15829	−	2.15829i	0.0921137	−	0.0921137i
$550$	2.41245	−	6.27207i	0.102867	−	0.267442i
$551$		−	12.0002i		−	0.511226i
$552$	−3.25727	+	1.65141i	−0.138638	+	0.0702887i
$553$		−	15.7838i		−	0.671195i
$554$	−18.4608	−	7.10066i	−0.784325	−	0.301678i
$555$	−10.1140	+	10.1140i	−0.429314	+	0.429314i
$556$	0.805987	+	15.7843i	0.0341814	+	0.669404i
$557$	26.3413	+	26.3413i	1.11612	+	1.11612i	0.992306	+	0.123810i	$0.0395112\pi$
$557$	26.3413	+	26.3413i	1.11612	+	1.11612i	0.123810	+	0.992306i	$0.460489\pi$
$558$	14.3274	−	6.36748i	0.606529	−	0.269557i
$559$	26.5092			1.12122
$560$	−5.94693	+	7.30368i	−0.251304	+	0.308637i
$561$	−27.2799			−1.15176
$562$	−27.5244	+	12.2325i	−1.16105	+	0.515999i
$563$	−5.43254	−	5.43254i	−0.228954	−	0.228954i	0.583301	−	0.812256i	$-0.301761\pi$
$563$	−5.43254	−	5.43254i	−0.228954	−	0.228954i	−0.812256	+	0.583301i	$0.801761\pi$
$564$	27.5934	−	1.40899i	1.16189	−	0.0593291i
$565$	10.8009	−	10.8009i	0.454399	−	0.454399i
$566$	15.5082	+	5.96500i	0.651860	+	0.250728i
$567$			4.22612i			0.177480i
$568$	6.15440	−	18.8124i	0.258233	−	0.789350i
$569$		−	45.4685i		−	1.90614i	−0.302753	−	0.953069i	$-0.597906\pi$
$569$		−	45.4685i		−	1.90614i	0.302753	−	0.953069i	$-0.402094\pi$
$570$	−1.86243	+	4.84209i	−0.0780088	+	0.202813i
$571$	16.8767	−	16.8767i	0.706267	−	0.706267i	−0.259481	−	0.965748i	$-0.583551\pi$
$571$	16.8767	−	16.8767i	0.706267	−	0.706267i	0.965748	+	0.259481i	$0.0835515\pi$
$572$	−9.21520	+	10.2069i	−0.385307	+	0.426774i
$573$	−13.0528	−	13.0528i	−0.545288	−	0.545288i
$574$	−3.56558	−	8.02291i	−0.148825	−	0.334870i
$575$	−1.77174			−0.0738868
$576$	6.30226	−	8.60129i	0.262594	−	0.358387i
$577$	−16.4011			−0.682788			−0.341394	−	0.939920i	$-0.610899\pi$
$577$	−16.4011			−0.682788			−0.341394	+	0.939920i	$0.610899\pi$
$578$	25.8798	+	58.2321i	1.07646	+	2.42213i
$579$	14.9355	+	14.9355i	0.620700	+	0.620700i
$580$	−18.2746	+	20.2414i	−0.758813	+	0.840477i
$581$	0.835304	−	0.835304i	0.0346542	−	0.0346542i
$582$	2.02625	−	5.26800i	0.0839909	−	0.218366i
$583$			14.7371i			0.610349i
$584$	−4.66389	+	14.2563i	−0.192993	+	0.589929i
$585$		−	6.13957i		−	0.253840i
$586$	3.74587	+	1.44079i	0.154741	+	0.0595185i
$587$	−16.3999	+	16.3999i	−0.676896	+	0.676896i	−0.959297	−	0.282400i	$-0.908869\pi$
$587$	−16.3999	+	16.3999i	−0.676896	+	0.676896i	0.282400	+	0.959297i	$0.408869\pi$
$588$	13.6236	−	0.695654i	0.561827	−	0.0286883i
$589$	9.30034	+	9.30034i	0.383214	+	0.383214i
$590$	9.80860	−	4.35919i	0.403814	−	0.179465i
$591$	−7.79651			−0.320705
$592$	19.1243	+	15.5717i	0.786004	+	0.639994i
$593$	−42.3337			−1.73844			−0.869219	−	0.494427i	$-0.835378\pi$
$593$	−42.3337			−1.73844			−0.869219	+	0.494427i	$0.835378\pi$
$594$	19.3905	−	8.61764i	0.795603	−	0.353586i
$595$	13.1164	+	13.1164i	0.537721	+	0.537721i
$596$	−0.449316	−	8.79933i	−0.0184047	−	0.360435i
$597$	3.66278	−	3.66278i	0.149908	−	0.149908i
$598$	3.38390	+	1.30156i	0.138378	+	0.0532249i
$599$		−	2.98211i		−	0.121846i	−0.998142	−	0.0609229i	$-0.980596\pi$
$599$		−	2.98211i		−	0.121846i	0.998142	−	0.0609229i	$-0.0194044\pi$
$600$	−5.77104	+	2.92588i	−0.235602	+	0.119448i
$601$		−	46.6280i		−	1.90200i	−0.309195	−	0.950999i	$-0.600060\pi$
$601$		−	46.6280i		−	1.90200i	0.309195	−	0.950999i	$-0.399940\pi$
$602$	6.87984	−	17.8867i	0.280401	−	0.729008i
$603$	6.55103	−	6.55103i	0.266779	−	0.266779i
$604$	15.5656	+	14.0532i	0.633354	+	0.571815i
$605$	−4.83673	−	4.83673i	−0.196641	−	0.196641i
$606$	9.01308	+	20.2803i	0.366132	+	0.823832i
$607$	−8.37839			−0.340068			−0.170034	−	0.985438i	$-0.554388\pi$
$607$	−8.37839			−0.340068			−0.170034	+	0.985438i	$0.554388\pi$
$608$	8.63251	+	2.34414i	0.350095	+	0.0950673i
$609$	−12.8411			−0.520348
$610$	−2.36315	−	5.31732i	−0.0956811	−	0.215292i
$611$	−19.3957	−	19.3957i	−0.784665	−	0.784665i
$612$	−15.5874	−	14.0729i	−0.630084	−	0.568863i
$613$	0.0106683	−	0.0106683i	0.000430887	−	0.000430887i	−0.706891	−	0.707322i	$-0.749903\pi$
$613$	0.0106683	−	0.0106683i	0.000430887	−	0.000430887i	0.707322	+	0.706891i	$0.249903\pi$
$614$	−4.94936	+	12.8677i	−0.199740	+	0.519299i
$615$			10.9896i			0.443144i
$616$	4.49540	+	8.86680i	0.181125	+	0.357253i
$617$		−	21.6810i		−	0.872845i	−0.899742	−	0.436422i	$-0.856245\pi$
$617$		−	21.6810i		−	0.872845i	0.899742	−	0.436422i	$-0.143755\pi$
$618$	−10.6166	−	4.08350i	−0.427061	−	0.164262i
$619$	−9.67538	+	9.67538i	−0.388886	+	0.388886i	−0.874290	−	0.485404i	$-0.838673\pi$
$619$	−9.67538	+	9.67538i	−0.388886	+	0.388886i	0.485404	+	0.874290i	$0.338673\pi$
$620$	−1.52424	−	29.8505i	−0.0612149	−	1.19882i
$621$	−3.95590	−	3.95590i	−0.158745	−	0.158745i
$622$	−4.45256	+	1.97883i	−0.178531	+	0.0793439i
$623$	13.4052			0.537066
$624$	13.1717	−	1.34867i	0.527289	−	0.0539902i
$625$	13.0022			0.520088
$626$	−6.29387	+	2.79715i	−0.251554	+	0.111797i
$627$	3.87199	+	3.87199i	0.154632	+	0.154632i
$628$	−9.73455	+	0.497070i	−0.388451	+	0.0198353i
$629$	34.3446	−	34.3446i	1.36941	−	1.36941i
$630$	−4.14259	−	1.59338i	−0.165045	−	0.0634818i
$631$		−	9.73410i		−	0.387508i	−0.981050	−	0.193754i	$-0.937934\pi$
$631$		−	9.73410i		−	0.387508i	0.981050	−	0.193754i	$-0.0620664\pi$
$632$	32.3770	+	10.5920i	1.28789	+	0.421327i
$633$			6.07851i			0.241599i
$634$	8.91852	−	23.1870i	0.354200	−	0.920875i
$635$	3.21902	−	3.21902i	0.127743	−	0.127743i
$636$	9.50884	−	10.5322i	0.377050	−	0.417628i
$637$	−9.57616	−	9.57616i	−0.379421	−	0.379421i
$638$	11.6898	+	26.3031i	0.462802	+	1.04135i
$639$	9.32758			0.368993
$640$	−10.9911	−	17.1001i	−0.434461	−	0.675940i
$641$	40.4118			1.59617			0.798085	−	0.602544i	$-0.205846\pi$
$641$	40.4118			1.59617			0.798085	+	0.602544i	$0.205846\pi$
$642$	11.8595	+	26.6850i	0.468056	+	1.05317i
$643$	32.8891	+	32.8891i	1.29702	+	1.29702i	0.930352	+	0.366667i	$0.119501\pi$
$643$	32.8891	+	32.8891i	1.29702	+	1.29702i	0.366667	+	0.930352i	$0.380499\pi$
$644$	1.75642	−	1.94545i	0.0692127	−	0.0766614i
$645$	−16.9624	+	16.9624i	−0.667892	+	0.667892i
$646$	6.32438	−	16.4426i	0.248830	−	0.646926i
$647$		−	14.8409i		−	0.583456i	−0.956501	−	0.291728i	$-0.905770\pi$
$647$		−	14.8409i		−	0.583456i	0.956501	−	0.291728i	$-0.0942302\pi$
$648$	−8.66895	−	2.83601i	−0.340549	−	0.111409i
$649$		−	11.3293i		−	0.444714i
$650$	5.99540	+	2.30604i	0.235159	+	0.0904502i
$651$	9.95205	−	9.95205i	0.390052	−	0.390052i
$652$	−10.9179	+	0.557496i	−0.427578	+	0.0218332i
$653$	−2.35000	−	2.35000i	−0.0919627	−	0.0919627i	0.659629	−	0.751592i	$-0.270713\pi$
$653$	−2.35000	−	2.35000i	−0.0919627	−	0.0919627i	−0.751592	+	0.659629i	$0.770713\pi$
$654$	11.4613	−	5.09368i	0.448171	−	0.199179i
$655$	34.8409			1.36135
$656$	18.8500	−	1.93009i	0.735968	−	0.0753572i
$657$	−7.06857			−0.275771
$658$	−18.1207	+	8.05327i	−0.706417	+	0.313949i
$659$	−28.2876	−	28.2876i	−1.10193	−	1.10193i	−0.994178	−	0.107750i	$-0.965635\pi$
$659$	−28.2876	−	28.2876i	−1.10193	−	1.10193i	−0.107750	−	0.994178i	$-0.534365\pi$
$660$	−0.634583	−	12.4276i	−0.0247011	−	0.483743i
$661$	−11.9368	+	11.9368i	−0.464288	+	0.464288i	−0.900058	−	0.435770i	$-0.856476\pi$
$661$	−11.9368	+	11.9368i	−0.464288	+	0.464288i	0.435770	+	0.900058i	$0.356476\pi$
$662$	−14.5156	−	5.58318i	−0.564164	−	0.216996i
$663$		−	26.0766i		−	1.01273i
$664$	1.15290	+	2.27399i	0.0447410	+	0.0882478i
$665$		−	3.72338i		−	0.144386i
$666$	−4.17218	+	10.8472i	−0.161669	+	0.420319i
$667$	5.36615	−	5.36615i	0.207778	−	0.207778i
$668$	15.2392	+	13.7585i	0.589622	+	0.532332i
$669$	1.55018	+	1.55018i	0.0599335	+	0.0599335i
$670$	−7.17283	−	16.1396i	−0.277111	−	0.623526i
$671$	−6.14170			−0.237098
$672$	2.50840	−	9.23742i	0.0967636	−	0.356341i
$673$	2.40151			0.0925713			0.0462856	−	0.998928i	$-0.485262\pi$
$673$	2.40151			0.0925713			0.0462856	+	0.998928i	$0.485262\pi$
$674$	−6.35349	−	14.2960i	−0.244727	−	0.550660i
$675$	−7.00884	−	7.00884i	−0.269770	−	0.269770i
$676$	9.54169	+	8.61459i	0.366988	+	0.331330i
$677$	19.9627	−	19.9627i	0.767228	−	0.767228i	−0.210390	−	0.977618i	$-0.567473\pi$
$677$	19.9627	−	19.9627i	0.767228	−	0.767228i	0.977618	+	0.210390i	$0.0674733\pi$
$678$	−5.57286	+	14.4887i	−0.214024	+	0.556436i
$679$			4.05088i			0.155459i
$680$	−35.7074	+	18.1034i	−1.36932	+	0.694234i
$681$			1.92200i			0.0736512i
$682$	−29.4450	−	11.3256i	−1.12751	−	0.433678i
$683$	−31.5625	+	31.5625i	−1.20770	+	1.20770i	−0.235935	+	0.971769i	$0.575815\pi$
$683$	−31.5625	+	31.5625i	−1.20770	+	1.20770i	−0.971769	+	0.235935i	$0.924185\pi$
$684$	0.214966	+	4.20986i	0.00821942	+	0.160968i
$685$	−16.1666	−	16.1666i	−0.617693	−	0.617693i
$686$	−20.8020	+	9.24493i	−0.794224	+	0.352973i
$687$	−13.8092			−0.526852
$688$	32.0738	+	26.1157i	1.22280	+	0.995650i
$689$	−14.0870			−0.536674
$690$	−2.99807	+	1.33242i	−0.114135	+	0.0507243i
$691$	22.6858	+	22.6858i	0.863008	+	0.863008i	0.991686	−	0.128678i	$-0.0410735\pi$
$691$	22.6858	+	22.6858i	0.863008	+	0.863008i	−0.128678	+	0.991686i	$0.541073\pi$
$692$	45.8005	−	2.33869i	1.74107	−	0.0889036i
$693$	−3.31263	+	3.31263i	−0.125837	+	0.125837i
$694$	19.2129	+	7.38995i	0.729314	+	0.280519i
$695$			14.1986i			0.538583i
$696$	8.61725	−	26.3407i	0.326636	−	0.998441i
$697$		−	37.3181i		−	1.41353i
$698$	−9.96446	+	25.9063i	−0.377160	+	0.980569i
$699$	19.7163	−	19.7163i	0.745737	−	0.745737i
$700$	3.11193	−	3.44684i	0.117620	−	0.130278i
$701$	6.16899	+	6.16899i	0.233000	+	0.233000i	0.813944	−	0.580944i	$-0.197316\pi$
$701$	6.16899	+	6.16899i	0.233000	+	0.233000i	−0.580944	+	0.813944i	$0.697316\pi$
$702$	8.23751	+	18.5352i	0.310905	+	0.699566i
$703$	−9.74947			−0.367708
$704$	−21.2050	+	3.27110i	−0.799193	+	0.123284i
$705$	24.8213			0.934824
$706$	13.6772	+	30.7750i	0.514747	+	1.15823i
$707$	−11.2627	−	11.2627i	−0.423579	−	0.423579i
$708$	−7.31002	+	8.09673i	−0.274728	+	0.304294i
$709$	−11.2880	+	11.2880i	−0.423930	+	0.423930i	−0.886554	−	0.462625i	$-0.846908\pi$
$709$	−11.2880	+	11.2880i	−0.423930	+	0.423930i	0.462625	+	0.886554i	$0.346908\pi$
$710$	6.38357	−	16.5965i	0.239571	−	0.622855i
$711$			16.0532i			0.602042i
$712$	−8.99577	+	27.4977i	−0.337131	+	1.03052i
$713$			8.31769i			0.311500i
$714$	−17.5948	−	6.76756i	−0.658469	−	0.253269i
$715$	−8.73548	+	8.73548i	−0.326688	+	0.326688i
$716$	−28.1658	+	1.43821i	−1.05260	+	0.0537486i
$717$	1.33700	+	1.33700i	0.0499311	+	0.0499311i
$718$	1.79156	−	0.796213i	0.0668603	−	0.0297144i
$719$	33.4628			1.24795			0.623977	−	0.781443i	$-0.285516\pi$
$719$	33.4628			1.24795			0.623977	+	0.781443i	$0.285516\pi$
$720$	6.04843	−	7.42834i	0.225412	−	0.276838i
$721$	8.16372			0.304033
$722$	21.3229	−	9.47643i	0.793556	−	0.352676i
$723$	7.29413	+	7.29413i	0.271272	+	0.271272i
$724$	2.65697	+	52.0337i	0.0987454	+	1.93382i
$725$	9.50744	−	9.50744i	0.353097	−	0.353097i
$726$	6.48815	+	2.49556i	0.240798	+	0.0926191i
$727$			27.5750i			1.02270i	0.859373	+	0.511350i	$0.170854\pi$
$727$			27.5750i			1.02270i	−0.859373	+	0.511350i	$0.829146\pi$
$728$	−8.47568	+	4.29711i	−0.314130	+	0.159262i
$729$		−	25.9685i		−	0.961797i
$730$	−4.83756	+	12.5770i	−0.179046	+	0.465497i
$731$	57.6001	−	57.6001i	2.13042	−	2.13042i
$732$	4.38930	+	3.96282i	0.162233	+	0.146470i
$733$	−5.69851	−	5.69851i	−0.210479	−	0.210479i	0.593992	−	0.804471i	$-0.297551\pi$
$733$	−5.69851	−	5.69851i	−0.210479	−	0.210479i	−0.804471	+	0.593992i	$0.797551\pi$
$734$	−17.7181	−	39.8676i	−0.653989	−	1.47154i
$735$	12.2549			0.452030
$736$	2.81198	+	4.90844i	0.103651	+	0.180927i
$737$	−18.6418			−0.686680
$738$	3.62644	+	8.15984i	0.133491	+	0.300368i
$739$	29.9448	+	29.9448i	1.10154	+	1.10154i	0.994225	+	0.107312i	$0.0342244\pi$
$739$	29.9448	+	29.9448i	1.10154	+	1.10154i	0.107312	+	0.994225i	$0.465776\pi$
$740$	16.4449	+	14.8471i	0.604527	+	0.545789i
$741$	−3.70120	+	3.70120i	−0.135967	+	0.135967i
$742$	−3.65596	+	9.50504i	−0.134214	+	0.348941i
$743$			2.29666i			0.0842562i	0.999112	+	0.0421281i	$0.0134138\pi$
$743$			2.29666i			0.0842562i	−0.999112	+	0.0421281i	$0.986586\pi$
$744$	13.7359	+	27.0929i	0.503583	+	0.993275i
$745$		−	7.91533i		−	0.289995i
$746$	47.3586	+	18.2157i	1.73392	+	0.666925i
$747$	−0.849561	+	0.849561i	−0.0310838	+	0.0310838i
$748$	2.15489	+	42.2011i	0.0787907	+	1.54303i
$749$	−14.8196	−	14.8196i	−0.541495	−	0.541495i
$750$	−20.3022	+	9.02279i	−0.741330	+	0.329466i
$751$	−34.1407			−1.24581			−0.622906	−	0.782297i	$-0.714048\pi$
$751$	−34.1407			−1.24581			−0.622906	+	0.782297i	$0.714048\pi$
$752$	−4.35932	−	42.5748i	−0.158968	−	1.55254i
$753$	−0.405972			−0.0147944
$754$	−25.1429	+	11.1741i	−0.915650	+	0.406938i
$755$	13.3216	+	13.3216i	0.484822	+	0.484822i
$756$	14.6442	−	0.747771i	0.532605	−	0.0271962i
$757$	5.46142	−	5.46142i	0.198499	−	0.198499i	−0.600857	−	0.799356i	$-0.705174\pi$
$757$	5.46142	−	5.46142i	0.198499	−	0.198499i	0.799356	+	0.600857i	$0.205174\pi$
$758$	−44.8686	−	17.2580i	−1.62970	−	0.626838i
$759$			3.46289i			0.125695i
$760$	7.63768	+	2.49864i	0.277048	+	0.0906352i
$761$		−	51.3757i		−	1.86237i	−0.364548	−	0.931185i	$-0.618776\pi$
$761$		−	51.3757i		−	1.86237i	0.364548	−	0.931185i	$-0.381224\pi$
$762$	−1.66089	+	4.31810i	−0.0601676	+	0.156428i
$763$	−6.36505	+	6.36505i	−0.230430	+	0.230430i
$764$	−19.1612	+	21.2233i	−0.693227	+	0.767832i
$765$	−13.3403	−	13.3403i	−0.482319	−	0.482319i
$766$	5.78403	+	13.0146i	0.208985	+	0.470238i
$767$	10.8296			0.391033
$768$	17.2652	+	11.3444i	0.623005	+	0.409354i
$769$	18.7730			0.676971			0.338485	−	0.940972i	$-0.390085\pi$
$769$	18.7730			0.676971			0.338485	+	0.940972i	$0.390085\pi$
$770$	3.62705	+	8.16123i	0.130710	+	0.294110i
$771$	24.5592	+	24.5592i	0.884479	+	0.884479i
$772$	21.9250	−	24.2846i	0.789099	−	0.874022i
$773$	20.8997	−	20.8997i	0.751710	−	0.751710i	−0.223088	−	0.974798i	$-0.571614\pi$
$773$	20.8997	−	20.8997i	0.751710	−	0.751710i	0.974798	+	0.223088i	$0.0716138\pi$
$774$	−6.99726	+	18.1920i	−0.251511	+	0.653898i
$775$			14.7368i			0.529362i
$776$	−8.30949	−	2.71842i	−0.298293	−	0.0975855i
$777$			10.4326i			0.374269i
$778$	−1.16686	−	0.448813i	−0.0418339	−	0.0160907i
$779$	−5.29678	+	5.29678i	−0.189777	+	0.189777i
$780$	11.8794	−	0.606592i	0.425351	−	0.0217195i
$781$	−13.2714	−	13.2714i	−0.474889	−	0.474889i
$782$	10.1807	−	4.52458i	0.364062	−	0.161798i
$783$	42.4559			1.51725
$784$	−2.15231	−	21.0203i	−0.0768682	−	0.750725i
$785$	−8.75660			−0.312536
$786$	−32.3566	+	14.3801i	−1.15412	+	0.512921i
$787$	−11.0212	−	11.0212i	−0.392865	−	0.392865i	0.482843	−	0.875707i	$-0.339604\pi$
$787$	−11.0212	−	11.0212i	−0.392865	−	0.392865i	−0.875707	+	0.482843i	$0.839604\pi$
$788$	0.615862	+	12.0609i	0.0219392	+	0.429654i
$789$	23.7685	−	23.7685i	0.846182	−	0.846182i
$790$	28.5633	+	10.9864i	1.01624	+	0.390879i
$791$		−	11.1413i		−	0.396138i
$792$	−4.57213	−	9.01813i	−0.162464	−	0.320445i
$793$		−	5.87079i		−	0.208478i
$794$	−12.1579	+	31.6089i	−0.431467	+	1.12176i
$795$	9.01383	−	9.01383i	0.319688	−	0.319688i
$796$	−5.95554	−	5.37688i	−0.211089	−	0.190578i
$797$	−32.4991	−	32.4991i	−1.15118	−	1.15118i	−0.986317	−	0.164860i	$-0.947283\pi$
$797$	−32.4991	−	32.4991i	−1.15118	−	1.15118i	−0.164860	−	0.986317i	$-0.552717\pi$
$798$	1.53677	+	3.45789i	0.0544012	+	0.122408i
$799$	−84.2873			−2.98187
$800$	4.98211	+	8.69650i	0.176144	+	0.307468i
$801$	−13.6339			−0.481732
$802$	−5.81552	−	13.0855i	−0.205353	−	0.462064i
$803$	10.0573	+	10.0573i	0.354913	+	0.354913i
$804$	13.3228	+	12.0283i	0.469858	+	0.424205i
$805$	1.66499	−	1.66499i	0.0586831	−	0.0586831i
$806$	10.8260	−	28.1462i	0.381329	−	0.991408i
$807$		−	14.6369i		−	0.515243i
$808$	30.6610	−	15.5449i	1.07865	−	0.546869i
$809$			50.0993i			1.76140i	0.473677	+	0.880698i	$0.342926\pi$
$809$			50.0993i			1.76140i	−0.473677	+	0.880698i	$0.657074\pi$
$810$	−7.64784	−	2.94162i	−0.268718	−	0.103358i
$811$	13.7860	−	13.7860i	0.484091	−	0.484091i	−0.422344	−	0.906435i	$-0.638793\pi$
$811$	13.7860	−	13.7860i	0.484091	−	0.484091i	0.906435	+	0.422344i	$0.138793\pi$
$812$	1.01435	+	19.8648i	0.0355965	+	0.697117i
$813$	−0.191174	−	0.191174i	−0.00670478	−	0.00670478i
$814$	21.3697	−	9.49725i	0.749009	−	0.332878i
$815$	−9.82107			−0.344017
$816$	25.6894	−	31.5503i	0.899310	−	1.10448i
$817$	−16.3510			−0.572050
$818$	−21.0260	+	9.34448i	−0.735157	+	0.326722i
$819$	−3.16651	−	3.16651i	−0.110647	−	0.110647i
$820$	17.0006	−	0.868093i	0.593686	−	0.0303151i
$821$	14.2801	−	14.2801i	0.498378	−	0.498378i	−0.412555	−	0.910933i	$-0.635364\pi$
$821$	14.2801	−	14.2801i	0.498378	−	0.498378i	0.910933	+	0.412555i	$0.135364\pi$
$822$	21.6864	+	8.34131i	0.756399	+	0.290937i
$823$			13.0604i			0.455256i	0.973748	+	0.227628i	$0.0730970\pi$
$823$			13.0604i			0.455256i	−0.973748	+	0.227628i	$0.926903\pi$
$824$	−5.47841	+	16.7461i	−0.190850	+	0.583377i
$825$			6.13535i			0.213605i
$826$	2.81056	−	7.30710i	0.0977918	−	0.254247i
$827$	17.5656	−	17.5656i	0.610817	−	0.610817i	−0.332342	−	0.943159i	$-0.607839\pi$
$827$	17.5656	−	17.5656i	0.610817	−	0.610817i	0.943159	+	0.332342i	$0.107839\pi$
$828$	−1.78640	+	1.97865i	−0.0620817	+	0.0687630i
$829$	20.2058	+	20.2058i	0.701777	+	0.701777i	0.964792	−	0.263015i	$-0.0847169\pi$
$829$	20.2058	+	20.2058i	0.701777	+	0.701777i	−0.263015	+	0.964792i	$0.584717\pi$
$830$	0.930197	+	2.09303i	0.0322876	+	0.0726503i
$831$	18.0584			0.626439
$832$	−3.12681	−	20.2696i	−0.108403	−	0.702723i
$833$	−41.6149			−1.44187
$834$	−5.86027	−	13.1862i	−0.202925	−	0.456600i
$835$	13.0423	+	13.0423i	0.451346	+	0.451346i
$836$	5.68399	−	6.29570i	0.196585	−	0.217741i
$837$	−32.9039	+	32.9039i	−1.13733	+	1.13733i
$838$	−2.32544	+	6.04586i	−0.0803311	+	0.208851i
$839$			23.2644i			0.803178i	0.915820	+	0.401589i	$0.131542\pi$
$839$			23.2644i			0.803178i	−0.915820	+	0.401589i	$0.868458\pi$
$840$	2.67373	−	8.17288i	0.0922524	−	0.281991i
$841$			28.5911i			0.985899i
$842$	1.73806	+	0.668516i	0.0598974	+	0.0230386i
$843$	19.4452	−	19.4452i	0.669727	−	0.669727i
$844$	9.40327	−	0.480154i	0.323674	−	0.0165276i
$845$	8.16613	+	8.16613i	0.280923	+	0.280923i
$846$	18.4299	−	8.19072i	0.633634	−	0.281603i
$847$	−4.98913			−0.171429
$848$	−17.0441	−	13.8779i	−0.585296	−	0.476570i
$849$	−15.1702			−0.520640
$850$	18.0377	−	8.01639i	0.618687	−	0.274960i
$851$	−4.35968	−	4.35968i	−0.149448	−	0.149448i
$852$	0.921568	+	18.0478i	0.0315724	+	0.618309i
$853$	−1.55289	+	1.55289i	−0.0531698	+	0.0531698i	−0.733192	−	0.680022i	$-0.761970\pi$
$853$	−1.55289	+	1.55289i	−0.0531698	+	0.0531698i	0.680022	+	0.733192i	$0.261970\pi$
$854$	−3.96123	−	1.52362i	−0.135551	−	0.0521373i
$855$			3.78693i			0.129510i
$856$	40.3440	−	20.4541i	1.37893	−	0.699108i
$857$			33.3506i			1.13923i	0.821910	+	0.569617i	$0.192908\pi$
$857$			33.3506i			1.13923i	−0.821910	+	0.569617i	$0.807092\pi$
$858$	4.50716	−	11.7181i	0.153872	−	0.400048i
$859$	1.19699	−	1.19699i	0.0408407	−	0.0408407i	−0.686391	−	0.727232i	$-0.740806\pi$
$859$	1.19699	−	1.19699i	0.0408407	−	0.0408407i	0.727232	+	0.686391i	$0.240806\pi$
$860$	27.5801	+	24.9003i	0.940474	+	0.849094i
$861$	5.66794	+	5.66794i	0.193163	+	0.193163i
$862$	−6.48849	−	14.5997i	−0.220999	−	0.497269i
$863$	53.3335			1.81549			0.907747	−	0.419519i	$-0.137801\pi$
$863$	53.3335			1.81549			0.907747	+	0.419519i	$0.137801\pi$
$864$	−8.29338	+	30.5412i	−0.282147	+	1.03903i
$865$	41.1993			1.40082
$866$	−18.8560	−	42.4279i	−0.640754	−	1.44176i
$867$	−41.1392	−	41.1392i	−1.39716	−	1.39716i
$868$	−16.1816	−	14.6094i	−0.549240	−	0.495874i
$869$	22.8407	−	22.8407i	0.774818	−	0.774818i
$870$	8.93814	−	23.2380i	0.303031	−	0.787843i
$871$		−	17.8195i		−	0.603791i
$872$	−8.78511	−	17.3279i	−0.297501	−	0.586796i
$873$		−	4.12002i		−	0.139442i
$874$	−2.08721	−	0.802812i	−0.0706009	−	0.0271555i
$875$	11.2749	−	11.2749i	0.381160	−	0.381160i
$876$	−0.698377	−	13.6769i	−0.0235960	−	0.462100i
$877$	27.9909	+	27.9909i	0.945185	+	0.945185i	0.998574	−	0.0533887i	$-0.0170022\pi$
$877$	27.9909	+	27.9909i	0.945185	+	0.945185i	−0.0533887	+	0.998574i	$0.517002\pi$
$878$	−8.01538	+	3.56224i	−0.270506	+	0.120220i
$879$	−3.66422			−0.123591
$880$	−19.1749	+	1.96336i	−0.646387	+	0.0661849i
$881$	−10.3012			−0.347057			−0.173528	−	0.984829i	$-0.555517\pi$
$881$	−10.3012			−0.347057			−0.173528	+	0.984829i	$0.555517\pi$
$882$	9.09935	−	4.04398i	0.306391	−	0.136168i
$883$	4.04987	+	4.04987i	0.136289	+	0.136289i	0.771960	−	0.635671i	$-0.219276\pi$
$883$	4.04987	+	4.04987i	0.136289	+	0.136289i	−0.635671	+	0.771960i	$0.719276\pi$
$884$	−40.3396	+	2.05984i	−1.35677	+	0.0692800i
$885$	−6.92948	+	6.92948i	−0.232932	+	0.232932i
$886$	−10.2854	−	3.95612i	−0.345545	−	0.132909i
$887$			21.2518i			0.713564i	0.934188	+	0.356782i	$0.116126\pi$
$887$			21.2518i			0.713564i	−0.934188	+	0.356782i	$0.883874\pi$
$888$	−21.4003	−	7.00101i	−0.718146	−	0.234939i
$889$		−	3.32044i		−	0.111364i
$890$	−9.33075	+	24.2588i	−0.312767	+	0.813156i
$891$	−6.11562	+	6.11562i	−0.204881	+	0.204881i
$892$	2.27563	−	2.52054i	0.0761938	−	0.0843938i
$893$	11.9634	+	11.9634i	0.400339	+	0.400339i
$894$	3.26694	+	7.35095i	0.109263	+	0.245852i
$895$	−25.3362			−0.846895
$896$	−14.4881	−	3.15073i	−0.484015	−	0.105259i
$897$	−3.31014			−0.110522
$898$	−5.10971	−	11.4974i	−0.170513	−	0.383672i
$899$	−44.6339	−	44.6339i	−1.48862	−	1.48862i
$900$	−3.16504	+	3.50567i	−0.105501	+	0.116856i
$901$	−30.6088	+	30.6088i	−1.01973	+	1.01973i
$902$	6.45019	−	16.7697i	0.214768	−	0.558370i
$903$			17.4968i			0.582258i
$904$	22.8538	+	7.47654i	0.760107	+	0.248666i
$905$			46.8062i			1.55589i
$906$	−17.8700	−	6.87341i	−0.593691	−	0.228354i
$907$	−22.8487	+	22.8487i	−0.758680	+	0.758680i	−0.976082	−	0.217402i	$-0.930242\pi$
$907$	−22.8487	+	22.8487i	−0.758680	+	0.758680i	0.217402	+	0.976082i	$0.430242\pi$
$908$	2.97327	−	0.151823i	0.0986716	−	0.00503842i
$909$	11.4550	+	11.4550i	0.379937	+	0.379937i
$910$	−7.80123	+	3.46706i	−0.258608	+	0.114932i
$911$	18.7986			0.622827			0.311413	−	0.950275i	$-0.399198\pi$
$911$	18.7986			0.622827			0.311413	+	0.950275i	$0.399198\pi$
$912$	−8.12437	+	0.831870i	−0.269025	+	0.0275460i
$913$	2.41753			0.0800087
$914$	5.65973	−	2.51532i	0.187207	−	0.0831995i
$915$	3.75652	+	3.75652i	0.124187	+	0.124187i
$916$	1.09081	+	21.3623i	0.0360415	+	0.705831i
$917$	17.9693	−	17.9693i	0.593400	−	0.593400i
$918$	58.1727	+	22.3752i	1.91999	+	0.738492i
$919$			51.7176i			1.70601i	0.521906	+	0.853003i	$0.325221\pi$
$919$			51.7176i			1.70601i	−0.521906	+	0.853003i	$0.674779\pi$
$920$	2.29803	+	4.53267i	0.0757639	+	0.149438i
$921$		−	12.5872i		−	0.414763i
$922$	−6.04978	+	15.7287i	−0.199239	+	0.517996i
$923$	12.6860	−	12.6860i	0.417565	−	0.417565i
$924$	−6.73687	−	6.08229i	−0.221627	−	0.200093i
$925$	−7.72423	−	7.72423i	−0.253971	−	0.253971i
$926$	−15.6253	−	35.1584i	−0.513478	−	1.15538i
$927$	−8.30306			−0.272708
$928$	−41.4289	−	11.2499i	−1.35997	−	0.369296i
$929$	−45.5072			−1.49304			−0.746521	−	0.665362i	$-0.768277\pi$
$929$	−45.5072			−1.49304			−0.746521	+	0.665362i	$0.768277\pi$
$930$	11.0826	+	24.9370i	0.363414	+	0.817717i
$931$	5.90663	+	5.90663i	0.193582	+	0.193582i
$932$	−32.0578	−	28.9430i	−1.05009	−	0.948059i
$933$	3.14560	−	3.14560i	0.102982	−	0.102982i
$934$	2.04842	−	5.32563i	0.0670263	−	0.174260i
$935$			37.9615i			1.24147i
$936$	8.62034	−	4.37045i	0.281765	−	0.142853i
$937$		−	4.06208i		−	0.132703i	−0.997796	−	0.0663513i	$-0.978864\pi$
$937$		−	4.06208i		−	0.132703i	0.997796	−	0.0663513i	$-0.0211358\pi$
$938$	−12.0235	−	4.62463i	−0.392580	−	0.151000i
$939$	4.44643	−	4.44643i	0.145104	−	0.145104i
$940$	−1.96069	−	38.3978i	−0.0639505	−	1.25240i
$941$	−7.80075	−	7.80075i	−0.254297	−	0.254297i	0.568433	−	0.822730i	$-0.307550\pi$
$941$	−7.80075	−	7.80075i	−0.254297	−	0.254297i	−0.822730	+	0.568433i	$0.807550\pi$
$942$	8.13222	−	3.61416i	0.264962	−	0.117756i
$943$	−4.73713			−0.154262
$944$	13.1028	+	10.6688i	0.426460	+	0.347240i
$945$	13.1730			0.428519
$946$	35.8396	−	15.9280i	1.16525	−	0.517865i
$947$	26.7568	+	26.7568i	0.869479	+	0.869479i	0.992415	−	0.122935i	$-0.0392308\pi$
$947$	26.7568	+	26.7568i	0.869479	+	0.869479i	−0.122935	+	0.992415i	$0.539231\pi$
$948$	−31.0611	+	1.58606i	−1.00882	+	0.0515128i
$949$	−9.61363	+	9.61363i	−0.312072	+	0.312072i
$950$	−3.69800	−	1.42238i	−0.119979	−	0.0461480i
$951$			22.6816i			0.735501i
$952$	−9.07934	+	27.7532i	−0.294263	+	0.899486i
$953$		−	33.0794i		−	1.07155i	−0.844362	−	0.535774i	$-0.820020\pi$
$953$		−	33.0794i		−	1.07155i	0.844362	−	0.535774i	$-0.179980\pi$
$954$	3.71836	−	9.66727i	0.120386	−	0.312989i
$955$	−18.1637	+	18.1637i	−0.587763	+	0.587763i
$956$	1.96268	−	2.17391i	0.0634777	−	0.0703092i
$957$	−18.5824	−	18.5824i	−0.600682	−	0.600682i
$958$	19.2222	+	43.2518i	0.621041	+	1.39740i
$959$	−16.6760			−0.538495
$960$	14.9706	+	10.9691i	0.483174	+	0.354027i
$961$	38.1839			1.23174
$962$	9.07832	+	20.4271i	0.292697	+	0.658596i
$963$	15.0725	+	15.0725i	0.485705	+	0.485705i
$964$	10.7076	−	11.8600i	0.344869	−	0.381984i
$965$	20.7836	−	20.7836i	0.669049	−	0.669049i
$966$	−0.859068	+	2.23347i	−0.0276400	+	0.0718607i
$967$		−	37.8272i		−	1.21644i	−0.793769	−	0.608220i	$-0.791884\pi$
$967$		−	37.8272i		−	1.21644i	0.793769	−	0.608220i	$-0.208116\pi$
$968$	3.34805	−	10.2341i	0.107610	−	0.328936i
$969$			16.0842i			0.516698i
$970$	−7.33072	−	2.81965i	−0.235375	−	0.0905333i
$971$	−31.6987	+	31.6987i	−1.01726	+	1.01726i	−0.0174123	+	0.999848i	$0.505543\pi$
$971$	−31.6987	+	31.6987i	−1.01726	+	1.01726i	−0.999848	+	0.0174123i	$0.994457\pi$
$972$	−25.2066	+	1.28711i	−0.808502	+	0.0412841i
$973$	7.32298	+	7.32298i	0.234764	+	0.234764i
$974$	−46.1331	+	20.5027i	−1.47820	+	0.656949i
$975$	−5.86471			−0.187821
$976$	5.78363	−	7.10313i	0.185130	−	0.227366i
$977$	−38.8471			−1.24283			−0.621415	−	0.783482i	$-0.713442\pi$
$977$	−38.8471			−1.24283			−0.621415	+	0.783482i	$0.713442\pi$
$978$	9.12080	−	4.05351i	0.291651	−	0.129617i
$979$	19.3986	+	19.3986i	0.619981	+	0.619981i
$980$	−0.968042	−	18.9580i	−0.0309230	−	0.605591i
$981$	6.47368	−	6.47368i	0.206689	−	0.206689i
$982$	47.0102	+	18.0817i	1.50016	+	0.577011i
$983$		−	1.75016i		−	0.0558214i	−0.999610	−	0.0279107i	$-0.991115\pi$
$983$		−	1.75016i		−	0.0558214i	0.999610	−	0.0279107i	$-0.00888541\pi$
$984$	−15.4301	+	7.82295i	−0.491894	+	0.249387i
$985$			10.8493i			0.345687i
$986$	−30.3518	+	78.9109i	−0.966598	+	2.51303i
$987$	12.8017	−	12.8017i	0.407482	−	0.407482i
$988$	6.01800	+	5.43327i	0.191458	+	0.172855i
$989$	−7.31171	−	7.31171i	−0.232499	−	0.232499i
$990$	−3.68896	−	8.30052i	−0.117243	−	0.263808i
$991$	−48.6674			−1.54597			−0.772985	−	0.634424i	$-0.781237\pi$
$991$	−48.6674			−1.54597			−0.772985	+	0.634424i	$0.781237\pi$
$992$	40.8269	−	23.3892i	1.29625	−	0.742606i
$993$	14.1992			0.450597
$994$	−5.26736	−	11.8521i	−0.167070	−	0.375925i
$995$	−5.09697	−	5.09697i	−0.161585	−	0.161585i
$996$	−1.72774	−	1.55987i	−0.0547456	−	0.0494263i
$997$	−19.4917	+	19.4917i	−0.617310	+	0.617310i	−0.944840	−	0.327531i	$-0.893783\pi$
$997$	−19.4917	+	19.4917i	−0.617310	+	0.617310i	0.327531	+	0.944840i	$0.393783\pi$
$998$	6.43960	−	16.7421i	0.203842	−	0.529963i
$999$		−	34.4929i		−	1.09131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.j.e.93.15	✓	46
4.3	odd	2		1472.2.j.e.1105.17		46
16.5	even	4	inner	368.2.j.e.277.15	yes	46
16.11	odd	4		1472.2.j.e.369.17		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.j.e.93.15	✓	46	1.1	even	1	trivial
368.2.j.e.277.15	yes	46	16.5	even	4	inner
1472.2.j.e.369.17		46	16.11	odd	4
1472.2.j.e.1105.17		46	4.3	odd	2

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.574346 + 1.29233i) q^{2} +(-0.912995 - 0.912995i) q^{3} +(-1.34025 + 1.48449i) q^{4} +(-1.27048 + 1.27048i) q^{5} +(0.655519 - 1.70427i) q^{6} +1.31051i q^{7} +(-2.68823 - 0.879444i) q^{8} -1.33288i q^{9} +(-2.37159 - 0.912192i) q^{10} +(-1.89644 + 1.89644i) q^{11} +(2.57898 - 0.131689i) q^{12} +(-1.81279 - 1.81279i) q^{13} +(-1.69362 + 0.752688i) q^{14} +2.31989 q^{15} +(-0.407438 - 3.97920i) q^{16} -7.87779 q^{17} +(1.72253 - 0.765535i) q^{18} +(1.11814 + 1.11814i) q^{19} +(-0.183253 - 3.58879i) q^{20} +(1.19649 - 1.19649i) q^{21} +(-3.54005 - 1.36162i) q^{22} +1.00000i q^{23} +(1.65141 + 3.25727i) q^{24} +1.77174i q^{25} +(1.30156 - 3.38390i) q^{26} +(-3.95590 + 3.95590i) q^{27} +(-1.94545 - 1.75642i) q^{28} +(-5.36615 - 5.36615i) q^{29} +(1.33242 + 2.99807i) q^{30} +8.31769 q^{31} +(4.90844 - 2.81198i) q^{32} +3.46289 q^{33} +(-4.52458 - 10.1807i) q^{34} +(-1.66499 - 1.66499i) q^{35} +(1.97865 + 1.78640i) q^{36} +(-4.35968 + 4.35968i) q^{37} +(-0.802812 + 2.08721i) q^{38} +3.31014i q^{39} +(4.53267 - 2.29803i) q^{40} +4.73713i q^{41} +(2.23347 + 0.859068i) q^{42} +(-7.31171 + 7.31171i) q^{43} +(-0.273540 - 5.35697i) q^{44} +(1.69340 + 1.69340i) q^{45} +(-1.29233 + 0.574346i) q^{46} +10.6994 q^{47} +(-3.26100 + 4.00497i) q^{48} +5.28255 q^{49} +(-2.28968 + 1.01759i) q^{50} +(7.19238 + 7.19238i) q^{51} +(5.12068 - 0.261474i) q^{52} +(3.88546 - 3.88546i) q^{53} +(-7.38439 - 2.84029i) q^{54} -4.81880i q^{55} +(1.15252 - 3.52296i) q^{56} -2.04171i q^{57} +(3.85283 - 10.0169i) q^{58} +(-2.98699 + 2.98699i) q^{59} +(-3.10924 + 3.44386i) q^{60} +(1.61927 + 1.61927i) q^{61} +(4.77723 + 10.7492i) q^{62} +1.74676 q^{63} +(6.45316 + 4.72829i) q^{64} +4.60624 q^{65} +(1.98889 + 4.47520i) q^{66} +(4.91494 + 4.91494i) q^{67} +(10.5582 - 11.6945i) q^{68} +(0.912995 - 0.912995i) q^{69} +(1.19544 - 3.10800i) q^{70} +6.99806i q^{71} +(-1.17219 + 3.58309i) q^{72} -5.30322i q^{73} +(-8.13812 - 3.13020i) q^{74} +(1.61759 - 1.61759i) q^{75} +(-3.15846 + 0.161279i) q^{76} +(-2.48532 - 2.48532i) q^{77} +(-4.27780 + 1.90116i) q^{78} -12.0440 q^{79} +(5.57314 + 4.53786i) q^{80} +3.22478 q^{81} +(-6.12196 + 2.72075i) q^{82} +(-0.637386 - 0.637386i) q^{83} +(0.172580 + 3.37979i) q^{84} +(10.0086 - 10.0086i) q^{85} +(-13.6486 - 5.24972i) q^{86} +9.79853i q^{87} +(6.76589 - 3.43026i) q^{88} -10.2289i q^{89} +(-1.21584 + 3.16104i) q^{90} +(2.37569 - 2.37569i) q^{91} +(-1.48449 - 1.34025i) q^{92} +(-7.59400 - 7.59400i) q^{93} +(6.14513 + 13.8271i) q^{94} -2.84116 q^{95} +(-7.04870 - 1.91406i) q^{96} +3.09106 q^{97} +(3.03401 + 6.82682i) q^{98} +(2.52774 + 2.52774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 2 q^{2} + 6 q^{3} + 4 q^{5} + 2 q^{8} - 10 q^{10} + 4 q^{11} - 16 q^{12} + 2 q^{13} + 28 q^{14} - 12 q^{15} - 8 q^{16} - 16 q^{17} - 34 q^{18} + 4 q^{19} + 18 q^{20} - 28 q^{22} - 30 q^{24} + 2 q^{26}+ \cdots - 28 q^{99}+O(q^{100}) \) 46 * q + 2 * q^2 + 6 * q^3 + 4 * q^5 + 2 * q^8 - 10 * q^10 + 4 * q^11 - 16 * q^12 + 2 * q^13 + 28 * q^14 - 12 * q^15 - 8 * q^16 - 16 * q^17 - 34 * q^18 + 4 * q^19 + 18 * q^20 - 28 * q^22 - 30 * q^24 + 2 * q^26 - 26 * q^28 + 2 * q^29 + 56 * q^30 + 40 * q^31 - 8 * q^32 + 60 * q^33 + 10 * q^34 + 8 * q^35 + 50 * q^36 + 24 * q^37 - 56 * q^38 + 10 * q^42 - 8 * q^43 - 50 * q^44 + 12 * q^45 - 2 * q^46 + 20 * q^47 - 110 * q^49 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 64 * q^54 - 8 * q^56 - 2 * q^58 - 54 * q^59 - 90 * q^60 - 8 * q^61 + 18 * q^62 + 24 * q^63 - 6 * q^64 + 28 * q^65 + 6 * q^66 + 42 * q^68 - 6 * q^69 - 58 * q^70 + 90 * q^72 + 6 * q^74 - 30 * q^75 - 44 * q^76 - 28 * q^77 + 44 * q^78 + 16 * q^79 - 52 * q^80 - 26 * q^81 - 62 * q^82 + 28 * q^83 + 170 * q^84 - 12 * q^85 - 92 * q^86 + 64 * q^88 + 140 * q^90 + 48 * q^91 - 4 * q^92 - 48 * q^93 + 52 * q^94 - 56 * q^96 + 72 * q^97 - 44 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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