LMFDB - Embedded newform 370.2.r.e.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, degree $4$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.2
Root			$-0.709944 + 0.925217i$ of defining polynomial
Character	$\chi$	$=$	370.23
Dual form			370.2.r.e.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-2.83195 - 0.758819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17041 - 0.537883i) q^{5} +(-2.07313 - 2.07313i) q^{6} +(-1.69842 - 0.455091i) q^{7} +1.00000i q^{8} +(4.84607 + 2.79788i) q^{9} +(2.14857 + 0.619385i) q^{10} -5.29342i q^{11} +(-0.758819 - 2.83195i) q^{12} +(0.342893 - 0.197969i) q^{13} +(-1.24333 - 1.24333i) q^{14} +(-6.55465 - 0.123691i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.85382 - 3.21090i) q^{17} +(2.79788 + 4.84607i) q^{18} +(5.24257 + 1.40474i) q^{19} +(1.55103 + 1.61069i) q^{20} +(4.46452 + 2.57759i) q^{21} +(2.64671 - 4.58424i) q^{22} -7.28057i q^{23} +(0.758819 - 2.83195i) q^{24} +(4.42136 - 2.33485i) q^{25} +0.395938 q^{26} +(-5.38134 - 5.38134i) q^{27} +(-0.455091 - 1.69842i) q^{28} +(1.33851 + 1.33851i) q^{29} +(-5.61465 - 3.38445i) q^{30} +(3.75473 - 3.75473i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.01675 + 14.9907i) q^{33} +(3.21090 - 1.85382i) q^{34} +(-3.93106 - 0.0741820i) q^{35} +5.59575i q^{36} +(-5.53674 - 2.51884i) q^{37} +(3.83783 + 3.83783i) q^{38} +(-1.12128 + 0.300446i) q^{39} +(0.537883 + 2.17041i) q^{40} +(-5.24826 + 3.03009i) q^{41} +(2.57759 + 4.46452i) q^{42} +8.65292i q^{43} +(4.58424 - 2.64671i) q^{44} +(12.0229 + 3.46593i) q^{45} +(3.64029 - 6.30516i) q^{46} +(-7.10699 + 7.10699i) q^{47} +(2.07313 - 2.07313i) q^{48} +(-3.38465 - 1.95413i) q^{49} +(4.99644 + 0.188640i) q^{50} +(-7.68641 + 7.68641i) q^{51} +(0.342893 + 0.197969i) q^{52} +(8.69839 - 2.33073i) q^{53} +(-1.96971 - 7.35105i) q^{54} +(-2.84724 - 11.4889i) q^{55} +(0.455091 - 1.69842i) q^{56} +(-13.7808 - 7.95632i) q^{57} +(0.489930 + 1.82844i) q^{58} +(1.49924 + 5.59523i) q^{59} +(-3.17021 - 5.73834i) q^{60} +(-0.793650 - 0.212658i) q^{61} +(5.12906 - 1.37433i) q^{62} +(-6.95738 - 6.95738i) q^{63} -1.00000 q^{64} +(0.637734 - 0.614111i) q^{65} +(-10.9740 + 10.9740i) q^{66} +(-0.917081 + 3.42259i) q^{67} +3.70763 q^{68} +(-5.52464 + 20.6182i) q^{69} +(-3.36731 - 2.02977i) q^{70} +(-1.22491 - 2.12161i) q^{71} +(-2.79788 + 4.84607i) q^{72} +(-7.76616 + 7.76616i) q^{73} +(-3.53553 - 4.94975i) q^{74} +(-14.2928 + 3.25717i) q^{75} +(1.40474 + 5.24257i) q^{76} +(-2.40899 + 8.99046i) q^{77} +(-1.12128 - 0.300446i) q^{78} +(12.4441 + 3.33439i) q^{79} +(-0.619385 + 2.14857i) q^{80} +(2.76260 + 4.78497i) q^{81} -6.06017 q^{82} +(1.93988 - 0.519789i) q^{83} +5.15518i q^{84} +(2.29645 - 7.96612i) q^{85} +(-4.32646 + 7.49365i) q^{86} +(-2.77491 - 4.80629i) q^{87} +5.29342 q^{88} +(-0.441597 + 0.118325i) q^{89} +(8.67916 + 9.01302i) q^{90} +(-0.672471 + 0.180188i) q^{91} +(6.30516 - 3.64029i) q^{92} +(-13.4824 + 7.78405i) q^{93} +(-9.70832 + 2.60134i) q^{94} +(12.1341 + 0.228980i) q^{95} +(2.83195 - 0.758819i) q^{96} +10.7641 q^{97} +(-1.95413 - 3.38465i) q^{98} +(14.8103 - 25.6523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−2.83195	−	0.758819i	−1.63503	−	0.438104i	−0.679661	−	0.733526i	$-0.737873\pi$
$3$	−2.83195	−	0.758819i	−1.63503	−	0.438104i	−0.955367	+	0.295422i	$0.904540\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.17041	−	0.537883i	0.970637	−	0.240548i
$5$	2.17041	−	0.537883i	0.970637	−	0.240548i
$6$	−2.07313	−	2.07313i	−0.846353	−	0.846353i
$7$	−1.69842	−	0.455091i	−0.641943	−	0.172008i	−0.0768598	−	0.997042i	$-0.524489\pi$
$7$	−1.69842	−	0.455091i	−0.641943	−	0.172008i	−0.565083	+	0.825034i	$0.691156\pi$
$8$			1.00000i			0.353553i
$9$	4.84607	+	2.79788i	1.61536	+	0.932626i
$10$	2.14857	+	0.619385i	0.679438	+	0.195867i
$11$		−	5.29342i		−	1.59603i	−0.602640	−	0.798013i	$-0.705885\pi$
$11$		−	5.29342i		−	1.59603i	0.602640	−	0.798013i	$-0.294115\pi$
$12$	−0.758819	−	2.83195i	−0.219052	−	0.817514i
$13$	0.342893	−	0.197969i	0.0951013	−	0.0549068i	−0.451695	−	0.892172i	$-0.649181\pi$
$13$	0.342893	−	0.197969i	0.0951013	−	0.0549068i	0.546796	+	0.837266i	$0.315847\pi$
$14$	−1.24333	−	1.24333i	−0.332294	−	0.332294i
$15$	−6.55465	−	0.123691i	−1.69240	−	0.0319369i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.85382	−	3.21090i	0.449617	−	0.778759i	−0.548744	−	0.835990i	$-0.684894\pi$
$17$	1.85382	−	3.21090i	0.449617	−	0.778759i	0.998361	+	0.0572314i	$0.0182273\pi$
$18$	2.79788	+	4.84607i	0.659466	+	1.14223i
$19$	5.24257	+	1.40474i	1.20273	+	0.322270i	0.803905	−	0.594758i	$-0.202752\pi$
$19$	5.24257	+	1.40474i	1.20273	+	0.322270i	0.398823	+	0.917028i	$0.369419\pi$
$20$	1.55103	+	1.61069i	0.346820	+	0.360161i
$21$	4.46452	+	2.57759i	0.974238	+	0.562476i
$22$	2.64671	−	4.58424i	0.564280	−	0.977362i
$23$		−	7.28057i		−	1.51810i	−0.651030	−	0.759052i	$-0.725663\pi$
$23$		−	7.28057i		−	1.51810i	0.651030	−	0.759052i	$-0.274337\pi$
$24$	0.758819	−	2.83195i	0.154893	−	0.578070i
$25$	4.42136	−	2.33485i	0.884273	−	0.466971i
$26$	0.395938			0.0776499
$27$	−5.38134	−	5.38134i	−1.03564	−	1.03564i
$28$	−0.455091	−	1.69842i	−0.0860041	−	0.320972i
$29$	1.33851	+	1.33851i	0.248556	+	0.248556i	0.820378	−	0.571822i	$-0.193763\pi$
$29$	1.33851	+	1.33851i	0.248556	+	0.248556i	−0.571822	+	0.820378i	$0.693763\pi$
$30$	−5.61465	−	3.38445i	−1.02509	−	0.617912i
$31$	3.75473	−	3.75473i	0.674369	−	0.674369i	−0.284351	−	0.958720i	$-0.591778\pi$
$31$	3.75473	−	3.75473i	0.674369	−	0.674369i	0.958720	+	0.284351i	$0.0917780\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.01675	+	14.9907i	−0.699226	+	2.60955i
$34$	3.21090	−	1.85382i	0.550666	−	0.317927i
$35$	−3.93106	−	0.0741820i	−0.664470	−	0.0125390i
$36$			5.59575i			0.932626i
$37$	−5.53674	−	2.51884i	−0.910234	−	0.414095i
$37$	−5.53674	−	2.51884i	−0.910234	−	0.414095i
$38$	3.83783	+	3.83783i	0.622578	+	0.622578i
$39$	−1.12128	+	0.300446i	−0.179548	+	0.0481098i
$40$	0.537883	+	2.17041i	0.0850467	+	0.343172i
$41$	−5.24826	+	3.03009i	−0.819641	+	0.473220i	−0.850293	−	0.526310i	$-0.823575\pi$
$41$	−5.24826	+	3.03009i	−0.819641	+	0.473220i	0.0306518	+	0.999530i	$0.490242\pi$
$42$	2.57759	+	4.46452i	0.397731	+	0.688890i
$43$			8.65292i			1.31956i	0.751459	+	0.659779i	$0.229350\pi$
$43$			8.65292i			1.31956i	−0.751459	+	0.659779i	$0.770650\pi$
$44$	4.58424	−	2.64671i	0.691100	−	0.399007i
$45$	12.0229	+	3.46593i	1.79227	+	0.516670i
$46$	3.64029	−	6.30516i	0.536731	−	0.929645i
$47$	−7.10699	+	7.10699i	−1.03666	+	1.03666i	−0.0373585	+	0.999302i	$0.511894\pi$
$47$	−7.10699	+	7.10699i	−1.03666	+	1.03666i	−0.999302	+	0.0373585i	$0.988106\pi$
$48$	2.07313	−	2.07313i	0.299231	−	0.299231i
$49$	−3.38465	−	1.95413i	−0.483521	−	0.279161i
$50$	4.99644	+	0.188640i	0.706603	+	0.0266777i
$51$	−7.68641	+	7.68641i	−1.07631	+	1.07631i
$52$	0.342893	+	0.197969i	0.0475507	+	0.0274534i
$53$	8.69839	−	2.33073i	1.19482	−	0.320150i	0.394028	−	0.919098i	$-0.371081\pi$
$53$	8.69839	−	2.33073i	1.19482	−	0.320150i	0.800788	+	0.598948i	$0.204414\pi$
$54$	−1.96971	−	7.35105i	−0.268043	−	1.00035i
$55$	−2.84724	−	11.4889i	−0.383922	−	1.54916i
$56$	0.455091	−	1.69842i	0.0608141	−	0.226961i
$57$	−13.7808	−	7.95632i	−1.82531	−	1.05384i
$58$	0.489930	+	1.82844i	0.0643309	+	0.240086i
$59$	1.49924	+	5.59523i	0.195184	+	0.728437i	0.992219	+	0.124504i	$0.0397339\pi$
$59$	1.49924	+	5.59523i	0.195184	+	0.728437i	−0.797035	+	0.603933i	$0.793599\pi$
$60$	−3.17021	−	5.73834i	−0.409272	−	0.740817i
$61$	−0.793650	−	0.212658i	−0.101617	−	0.0272281i	0.207652	−	0.978203i	$-0.433418\pi$
$61$	−0.793650	−	0.212658i	−0.101617	−	0.0272281i	−0.309269	+	0.950975i	$0.600084\pi$
$62$	5.12906	−	1.37433i	0.651391	−	0.174540i
$63$	−6.95738	−	6.95738i	−0.876547	−	0.876547i
$64$	−1.00000			−0.125000
$65$	0.637734	−	0.614111i	0.0791011	−	0.0761710i
$66$	−10.9740	+	10.9740i	−1.35080	+	1.35080i
$67$	−0.917081	+	3.42259i	−0.112039	+	0.418136i	−0.999048	−	0.0436155i	$-0.986112\pi$
$67$	−0.917081	+	3.42259i	−0.112039	+	0.418136i	0.887009	+	0.461752i	$0.152779\pi$
$68$	3.70763			0.449617
$69$	−5.52464	+	20.6182i	−0.665088	+	2.48214i
$70$	−3.36731	−	2.02977i	−0.402470	−	0.242604i
$71$	−1.22491	−	2.12161i	−0.145370	−	0.251788i	0.784141	−	0.620583i	$-0.213104\pi$
$71$	−1.22491	−	2.12161i	−0.145370	−	0.251788i	−0.929511	+	0.368795i	$0.879771\pi$
$72$	−2.79788	+	4.84607i	−0.329733	+	0.571114i
$73$	−7.76616	+	7.76616i	−0.908961	+	0.908961i	−0.996188	−	0.0872276i	$-0.972199\pi$
$73$	−7.76616	+	7.76616i	−0.908961	+	0.908961i	0.0872276	+	0.996188i	$0.472199\pi$
$74$	−3.53553	−	4.94975i	−0.410997	−	0.575396i
$75$	−14.2928	+	3.25717i	−1.65039	+	0.376106i
$76$	1.40474	+	5.24257i	0.161135	+	0.601364i
$77$	−2.40899	+	8.99046i	−0.274530	+	1.02456i
$78$	−1.12128	−	0.300446i	−0.126960	−	0.0340188i
$79$	12.4441	+	3.33439i	1.40007	+	0.375148i	0.878370	−	0.477981i	$-0.158631\pi$
$79$	12.4441	+	3.33439i	1.40007	+	0.375148i	0.521700	+	0.853129i	$0.325298\pi$
$80$	−0.619385	+	2.14857i	−0.0692494	+	0.240218i
$81$	2.76260	+	4.78497i	0.306956	+	0.531663i
$82$	−6.06017			−0.669234
$83$	1.93988	−	0.519789i	0.212929	−	0.0570542i	−0.150778	−	0.988568i	$-0.548178\pi$
$83$	1.93988	−	0.519789i	0.212929	−	0.0570542i	0.363707	+	0.931514i	$0.381511\pi$
$84$			5.15518i			0.562476i
$85$	2.29645	−	7.96612i	0.249085	−	0.864047i
$86$	−4.32646	+	7.49365i	−0.466534	+	0.808061i
$87$	−2.77491	−	4.80629i	−0.297502	−	0.515289i
$88$	5.29342			0.564280
$89$	−0.441597	+	0.118325i	−0.0468091	+	0.0125425i	−0.282148	−	0.959371i	$-0.591047\pi$
$89$	−0.441597	+	0.118325i	−0.0468091	+	0.0125425i	0.235338	+	0.971913i	$0.424380\pi$
$90$	8.67916	+	9.01302i	0.914863	+	0.950056i
$91$	−0.672471	+	0.180188i	−0.0704941	+	0.0188888i
$92$	6.30516	−	3.64029i	0.657359	−	0.379526i
$93$	−13.4824	+	7.78405i	−1.39806	+	0.807169i
$94$	−9.70832	+	2.60134i	−1.00134	+	0.268307i
$95$	12.1341	+	0.228980i	1.24493	+	0.0234928i
$96$	2.83195	−	0.758819i	0.289035	−	0.0774466i
$97$	10.7641			1.09293			0.546466	−	0.837481i	$-0.315973\pi$
$97$	10.7641			1.09293			0.546466	+	0.837481i	$0.315973\pi$
$98$	−1.95413	−	3.38465i	−0.197397	−	0.341901i
$99$	14.8103	−	25.6523i	1.48850	−	2.57815i
$100$	4.23272	+	2.66159i	0.423272	+	0.266159i
$101$		−	1.23852i		−	0.123237i	−0.998100	−	0.0616184i	$-0.980374\pi$
$101$		−	1.23852i		−	0.123237i	0.998100	−	0.0616184i	$-0.0196262\pi$
$102$	−10.4998	+	2.81342i	−1.03964	+	0.278570i
$103$	−15.6859			−1.54558			−0.772790	−	0.634662i	$-0.781139\pi$
$103$	−15.6859			−1.54558			−0.772790	+	0.634662i	$0.781139\pi$
$104$	0.197969	+	0.342893i	0.0194125	+	0.0336234i
$105$	11.0763	+	3.19304i	1.08093	+	0.311609i
$106$	8.69839	+	2.33073i	0.844863	+	0.226380i
$107$	2.99053	+	0.801309i	0.289105	+	0.0774655i	0.400457	−	0.916316i	$-0.368851\pi$
$107$	2.99053	+	0.801309i	0.289105	+	0.0774655i	−0.111352	+	0.993781i	$0.535518\pi$
$108$	1.96971	−	7.35105i	0.189535	−	0.707355i
$109$	−0.513107	−	1.91494i	−0.0491468	−	0.183418i	0.936989	−	0.349359i	$-0.113601\pi$
$109$	−0.513107	−	1.91494i	−0.0491468	−	0.183418i	−0.986136	+	0.165941i	$0.946934\pi$
$110$	3.27867	−	11.3733i	0.312609	−	1.08440i
$111$	13.7684	+	11.3346i	1.30684	+	1.07583i
$112$	1.24333	−	1.24333i	0.117484	−	0.117484i
$113$	8.39900	−	14.5475i	0.790112	−	1.36851i	−0.135786	−	0.990738i	$-0.543356\pi$
$113$	8.39900	−	14.5475i	0.790112	−	1.36851i	0.925897	−	0.377775i	$-0.123311\pi$
$114$	−7.95632	−	13.7808i	−0.745178	−	1.29069i
$115$	−3.91610	−	15.8018i	−0.365178	−	1.47353i
$116$	−0.489930	+	1.82844i	−0.0454888	+	0.169767i
$117$	2.21557			0.204830
$118$	−1.49924	+	5.59523i	−0.138016	+	0.515082i
$119$	−4.60982	+	4.60982i	−0.422581	+	0.422581i
$120$	0.123691	−	6.55465i	0.0112914	−	0.598355i
$121$	−17.0203			−1.54730
$122$	−0.580992	−	0.580992i	−0.0526006	−	0.0526006i
$123$	17.1621	−	4.59857i	1.54746	−	0.414639i
$124$	5.12906	+	1.37433i	0.460603	+	0.123418i
$125$	8.34030	−	7.44577i	0.745979	−	0.665969i
$126$	−2.54658	−	9.50395i	−0.226867	−	0.846679i
$127$	0.832573	+	3.10721i	0.0738789	+	0.275720i	0.992977	−	0.118309i	$-0.0377475\pi$
$127$	0.832573	+	3.10721i	0.0738789	+	0.275720i	−0.919098	+	0.394029i	$0.871081\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	6.56600	−	24.5047i	0.578104	−	2.15751i
$130$	0.859349	−	0.212968i	0.0753699	−	0.0186786i
$131$	1.42519	+	5.31888i	0.124519	+	0.464713i	0.999822	−	0.0188626i	$-0.00600451\pi$
$131$	1.42519	+	5.31888i	0.124519	+	0.464713i	−0.875303	+	0.483576i	$0.839338\pi$
$132$	−14.9907	+	4.01675i	−1.30477	+	0.349613i
$133$	−8.26481	−	4.77169i	−0.716650	−	0.413758i
$134$	−2.50551	+	2.50551i	−0.216443	+	0.216443i
$135$	−14.5743	−	8.78519i	−1.25435	−	0.756109i
$136$	3.21090	+	1.85382i	0.275333	+	0.158963i
$137$	14.6294	−	14.6294i	1.24988	−	1.24988i	0.294103	−	0.955774i	$-0.404979\pi$
$137$	14.6294	−	14.6294i	1.24988	−	1.24988i	0.955774	−	0.294103i	$-0.0950210\pi$
$138$	−15.0936	+	15.0936i	−1.28485	+	1.28485i
$139$	−11.1080	+	19.2396i	−0.942165	+	1.63188i	−0.180835	+	0.983513i	$0.557880\pi$
$139$	−11.1080	+	19.2396i	−0.942165	+	1.63188i	−0.761330	+	0.648365i	$0.775453\pi$
$140$	−1.90129	−	3.44149i	−0.160688	−	0.290859i
$141$	25.5196	−	14.7337i	2.14913	−	1.24080i
$142$		−	2.44982i		−	0.205584i
$143$	−1.04793	−	1.81508i	−0.0876327	−	0.151784i
$144$	−4.84607	+	2.79788i	−0.403839	+	0.233156i
$145$	3.62509	+	2.18516i	0.301047	+	0.181468i
$146$	−10.6088	+	2.84261i	−0.877989	+	0.235256i
$147$	8.10233	+	8.10233i	0.668269	+	0.668269i
$148$	−0.586988	−	6.05437i	−0.0482502	−	0.497666i
$149$			7.99685i			0.655127i	0.944829	+	0.327564i	$0.106228\pi$
$149$			7.99685i			0.655127i	−0.944829	+	0.327564i	$0.893772\pi$
$150$	−14.0065	−	4.32561i	−1.14363	−	0.353185i
$151$	12.3792	−	7.14715i	1.00741	−	0.581627i	0.0969755	−	0.995287i	$-0.469083\pi$
$151$	12.3792	−	7.14715i	1.00741	−	0.581627i	0.910431	+	0.413660i	$0.135750\pi$
$152$	−1.40474	+	5.24257i	−0.113940	+	0.425228i
$153$	17.9674	−	10.3735i	1.45258	−	0.838648i
$154$	−6.58148	+	6.58148i	−0.530350	+	0.530350i
$155$	6.12970	−	10.1689i	0.492349	−	0.816787i
$156$	−0.820833	−	0.820833i	−0.0657192	−	0.0657192i
$157$	2.08643	+	7.78666i	0.166515	+	0.621443i	0.997842	+	0.0656592i	$0.0209150\pi$
$157$	2.08643	+	7.78666i	0.166515	+	0.621443i	−0.831327	+	0.555784i	$0.812418\pi$
$158$	9.10971	+	9.10971i	0.724730	+	0.724730i
$159$	−26.4020			−2.09382
$160$	−1.61069	+	1.55103i	−0.127336	+	0.122619i
$161$	−3.31332	+	12.3655i	−0.261126	+	0.974537i
$162$			5.52520i			0.434101i
$163$	0.300468	−	0.520426i	0.0235345	−	0.0407629i	−0.854018	−	0.520243i	$-0.825841\pi$
$163$	0.300468	−	0.520426i	0.0235345	−	0.0407629i	0.877553	+	0.479480i	$0.159175\pi$
$164$	−5.24826	−	3.03009i	−0.409820	−	0.236610i
$165$	−0.654749	+	34.6965i	−0.0509721	+	2.70112i
$166$	1.93988	+	0.519789i	0.150564	+	0.0403434i
$167$	8.10399	+	14.0365i	0.627106	+	1.08618i	0.988130	+	0.153623i	$0.0490940\pi$
$167$	8.10399	+	14.0365i	0.627106	+	1.08618i	−0.361024	+	0.932557i	$0.617573\pi$
$168$	−2.57759	+	4.46452i	−0.198865	+	0.344445i
$169$	−6.42162	+	11.1226i	−0.493970	+	0.855582i
$170$	5.97185	−	5.75063i	0.458020	−	0.441053i
$171$	21.4755	+	21.4755i	1.64227	+	1.64227i
$172$	−7.49365	+	4.32646i	−0.571386	+	0.329890i
$173$	3.45090	+	12.8789i	0.262367	+	0.979167i	0.963842	+	0.266473i	$0.0858584\pi$
$173$	3.45090	+	12.8789i	0.262367	+	0.979167i	−0.701475	+	0.712694i	$0.747475\pi$
$174$		−	5.54983i		−	0.420731i
$175$	−8.57191	+	1.95344i	−0.647976	+	0.147666i
$176$	4.58424	+	2.64671i	0.345550	+	0.199503i
$177$		−	16.9831i		−	1.27653i
$178$	−0.441597	−	0.118325i	−0.0330991	−	0.00886887i
$179$	5.55861	+	5.55861i	0.415470	+	0.415470i	0.883639	−	0.468169i	$-0.155086\pi$
$179$	5.55861	+	5.55861i	0.415470	+	0.415470i	−0.468169	+	0.883639i	$0.655086\pi$
$180$	3.00986	+	12.1451i	0.224342	+	0.905241i
$181$	1.28072	+	2.21827i	0.0951949	+	0.164882i	0.909690	−	0.415288i	$-0.136319\pi$
$181$	1.28072	+	2.21827i	0.0951949	+	0.164882i	−0.814495	+	0.580171i	$0.802986\pi$
$182$	−0.672471	−	0.180188i	−0.0498468	−	0.0133564i
$183$	2.08621	+	1.20447i	0.154217	+	0.0890373i
$184$	7.28057			0.536731
$185$	−13.3718	−	2.48880i	−0.983117	−	0.182980i
$186$	−15.5681			−1.14151
$187$	−16.9967	−	9.81303i	−1.24292	−	0.717600i
$188$	−9.70832	−	2.60134i	−0.708052	−	0.189722i
$189$	6.69079	+	11.5888i	0.486683	+	0.842960i
$190$	10.3940	+	6.26536i	0.754057	+	0.454537i
$191$	−3.22968	−	3.22968i	−0.233691	−	0.233691i	0.580540	−	0.814232i	$-0.302841\pi$
$191$	−3.22968	−	3.22968i	−0.233691	−	0.233691i	−0.814232	+	0.580540i	$0.802841\pi$
$192$	2.83195	+	0.758819i	0.204378	+	0.0547630i
$193$		−	17.5567i		−	1.26376i	−0.775066	−	0.631880i	$-0.782284\pi$
$193$		−	17.5567i		−	1.26376i	0.775066	−	0.631880i	$-0.217716\pi$
$194$	9.32202	+	5.38207i	0.669282	+	0.386410i
$195$	−2.27203	+	1.25521i	−0.162703	+	0.0898872i
$196$		−	3.90825i		−	0.279161i
$197$	0.114684	+	0.428008i	0.00817093	+	0.0304943i	0.969891	−	0.243540i	$-0.0783086\pi$
$197$	0.114684	+	0.428008i	0.00817093	+	0.0304943i	−0.961720	+	0.274034i	$0.911642\pi$
$198$	25.6523	−	14.8103i	1.82303	−	1.05252i
$199$	−19.1007	−	19.1007i	−1.35401	−	1.35401i	−0.881118	−	0.472897i	$-0.843208\pi$
$199$	−19.1007	−	19.1007i	−1.35401	−	1.35401i	−0.472897	−	0.881118i	$-0.656792\pi$
$200$	2.33485	+	4.42136i	0.165099	+	0.312638i
$201$	5.19426	−	8.99672i	0.366375	−	0.634580i
$202$	0.619258	−	1.07259i	0.0435708	−	0.0754669i
$203$	−1.66422	−	2.88251i	−0.116805	−	0.202312i
$204$	−10.4998	−	2.81342i	−0.735136	−	0.196979i
$205$	−9.76105	+	9.39948i	−0.681741	+	0.656488i
$206$	−13.5844	−	7.84296i	−0.946470	−	0.546445i
$207$	20.3702	−	35.2821i	1.41582	−	2.45228i
$208$			0.395938i			0.0274534i
$209$	7.43589	−	27.7511i	0.514351	−	1.91958i
$210$	7.99582	+	8.30339i	0.551764	+	0.572989i
$211$	−27.6353			−1.90250			−0.951248	−	0.308428i	$-0.900197\pi$
$211$	−27.6353			−1.90250			−0.951248	+	0.308428i	$0.900197\pi$
$212$	6.36767	+	6.36767i	0.437333	+	0.437333i
$213$	1.85897	+	6.93777i	0.127374	+	0.475368i
$214$	2.18922	+	2.18922i	0.149652	+	0.149652i
$215$	4.65426	+	18.7804i	0.317418	+	1.28081i
$216$	5.38134	−	5.38134i	0.366154	−	0.366154i
$217$	−8.08586	+	4.66837i	−0.548904	+	0.316910i
$218$	0.513107	−	1.91494i	0.0347520	−	0.129696i
$219$	27.8865	−	16.1003i	1.88440	−	1.08796i
$220$	8.52606	−	8.21023i	0.574827	−	0.553534i
$221$		−	1.46799i		−	0.0987480i
$222$	6.25650	+	16.7003i	0.419909	+	1.12085i
$223$	19.6785	+	19.6785i	1.31777	+	1.31777i	0.915539	+	0.402229i	$0.131764\pi$
$223$	19.6785	+	19.6785i	1.31777	+	1.31777i	0.402229	+	0.915539i	$0.368236\pi$
$224$	1.69842	−	0.455091i	0.113481	−	0.0304070i
$225$	27.9589	+	1.05558i	1.86392	+	0.0703723i
$226$	14.5475	−	8.39900i	0.967685	−	0.558693i
$227$	8.61717	+	14.9254i	0.571941	+	0.990632i	0.996367	+	0.0851686i	$0.0271429\pi$
$227$	8.61717	+	14.9254i	0.571941	+	0.990632i	−0.424425	+	0.905463i	$0.639524\pi$
$228$		−	15.9126i		−	1.05384i
$229$	−6.96524	+	4.02138i	−0.460276	+	0.265740i	−0.712160	−	0.702017i	$-0.752283\pi$
$229$	−6.96524	+	4.02138i	−0.460276	+	0.265740i	0.251884	+	0.967757i	$0.418950\pi$
$230$	4.50948	−	15.6428i	0.297346	−	1.03146i
$231$	13.6443	−	23.6326i	0.897727	−	1.55491i
$232$	−1.33851	+	1.33851i	−0.0878777	+	0.0878777i
$233$	−15.0559	+	15.0559i	−0.986346	+	0.986346i	−0.999908	−	0.0135616i	$-0.995683\pi$
$233$	−15.0559	+	15.0559i	−0.986346	+	0.986346i	0.0135616	+	0.999908i	$0.495683\pi$
$234$	1.91874	+	1.10779i	0.125432	+	0.0724183i
$235$	−11.6024	+	19.2478i	−0.756854	+	1.25559i
$236$	−4.09599	+	4.09599i	−0.266626	+	0.266626i
$237$	−32.7109	−	18.8856i	−2.12480	−	1.22675i
$238$	−6.29713	+	1.68731i	−0.408182	+	0.109372i
$239$	−2.47074	−	9.22091i	−0.159819	−	0.596451i	−0.998644	−	0.0520513i	$-0.983424\pi$
$239$	−2.47074	−	9.22091i	−0.159819	−	0.596451i	0.838826	−	0.544400i	$-0.183243\pi$
$240$	3.38445	−	5.61465i	0.218465	−	0.362424i
$241$	1.03693	−	3.86989i	0.0667947	−	0.249281i	−0.924453	−	0.381296i	$-0.875478\pi$
$241$	1.03693	−	3.86989i	0.0667947	−	0.249281i	0.991248	+	0.132015i	$0.0421446\pi$
$242$	−14.7400	−	8.51015i	−0.947524	−	0.547053i
$243$	1.71649	+	6.40605i	0.110113	+	0.410948i
$244$	−0.212658	−	0.793650i	−0.0136140	−	0.0508083i
$245$	−8.39717	−	2.42071i	−0.536475	−	0.154654i
$246$	17.1621	+	4.59857i	1.09422	+	0.293194i
$247$	2.07573	−	0.556191i	0.132076	−	0.0353896i
$248$	3.75473	+	3.75473i	0.238426	+	0.238426i
$249$	−5.88806			−0.373141
$250$	10.9458	−	2.27807i	0.692273	−	0.144078i
$251$	6.79402	−	6.79402i	0.428834	−	0.428834i	−0.459397	−	0.888231i	$-0.651934\pi$
$251$	6.79402	−	6.79402i	0.428834	−	0.428834i	0.888231	+	0.459397i	$0.151934\pi$
$252$	2.54658	−	9.50395i	0.160419	−	0.598693i
$253$	−38.5391			−2.42293
$254$	−0.832573	+	3.10721i	−0.0522403	+	0.194963i
$255$	−12.5483	+	20.8171i	−0.785804	+	1.30362i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.82581	−	4.89445i	0.176269	−	0.305307i	−0.764331	−	0.644825i	$-0.776930\pi$
$257$	2.82581	−	4.89445i	0.176269	−	0.305307i	0.940600	+	0.339517i	$0.110264\pi$
$258$	17.9387	−	17.9387i	1.11681	−	1.11681i
$259$	8.25741	+	6.79777i	0.513091	+	0.422393i
$260$	0.850702	+	0.245238i	0.0527583	+	0.0152090i
$261$	2.74153	+	10.2315i	0.169696	+	0.633315i
$262$	−1.42519	+	5.31888i	−0.0880486	+	0.328602i
$263$	6.80564	+	1.82357i	0.419654	+	0.112446i	0.462466	−	0.886637i	$-0.346965\pi$
$263$	6.80564	+	1.82357i	0.419654	+	0.112446i	−0.0428117	+	0.999083i	$0.513632\pi$
$264$	−14.9907	−	4.01675i	−0.922614	−	0.247214i
$265$	17.6254	−	9.73735i	1.08272	−	0.598161i
$266$	−4.77169	−	8.26481i	−0.292571	−	0.506748i
$267$	1.34037			0.0820291
$268$	−3.42259	+	0.917081i	−0.209068	+	0.0560197i
$269$			20.1816i			1.23049i	0.788336	+	0.615246i	$0.210943\pi$
$269$			20.1816i			1.23049i	−0.788336	+	0.615246i	$0.789057\pi$
$270$	−8.22908	−	14.8953i	−0.500806	−	0.906500i
$271$	5.27948	−	9.14432i	0.320705	−	0.555478i	−0.659928	−	0.751328i	$-0.729413\pi$
$271$	5.27948	−	9.14432i	0.320705	−	0.555478i	0.980634	+	0.195851i	$0.0627468\pi$
$272$	1.85382	+	3.21090i	0.112404	+	0.194690i
$273$	2.04113			0.123535
$274$	19.9842	−	5.35474i	1.20729	−	0.323492i
$275$	−12.3594	−	23.4041i	−0.745297	−	1.41132i
$276$	−20.6182	+	5.52464i	−1.24107	+	0.332544i
$277$	19.3754	−	11.1864i	1.16416	−	0.672126i	0.211860	−	0.977300i	$-0.432048\pi$
$277$	19.3754	−	11.1864i	1.16416	−	0.672126i	0.952297	+	0.305174i	$0.0987147\pi$
$278$	−19.2396	+	11.1080i	−1.15391	+	0.666211i
$279$	28.7009	−	7.69039i	1.71828	−	0.460412i
$280$	0.0741820	−	3.93106i	0.00443322	−	0.234926i
$281$	12.0535	−	3.22972i	0.719050	−	0.192669i	0.119302	−	0.992858i	$-0.461934\pi$
$281$	12.0535	−	3.22972i	0.719050	−	0.192669i	0.599748	+	0.800189i	$0.295268\pi$
$282$	29.4674			1.75476
$283$	−13.5429	−	23.4570i	−0.805041	−	1.39437i	−0.916263	−	0.400576i	$-0.868810\pi$
$283$	−13.5429	−	23.4570i	−0.805041	−	1.39437i	0.111223	−	0.993796i	$-0.464523\pi$
$284$	1.22491	−	2.12161i	0.0726850	−	0.125894i
$285$	−34.1895	−	9.85605i	−2.02521	−	0.583822i
$286$		−	2.09587i		−	0.123931i
$287$	10.2927	−	2.75793i	0.607561	−	0.162795i
$288$	−5.59575			−0.329733
$289$	1.62673	+	2.81757i	0.0956898	+	0.165740i
$290$	2.04684	+	3.70495i	0.120194	+	0.217562i
$291$	−30.4835	−	8.16803i	−1.78698	−	0.478819i
$292$	−10.6088	−	2.84261i	−0.620832	−	0.166351i
$293$	−5.61358	+	20.9501i	−0.327949	+	1.22392i	0.583366	+	0.812210i	$0.301735\pi$
$293$	−5.61358	+	20.9501i	−0.327949	+	1.22392i	−0.911314	+	0.411711i	$0.864931\pi$
$294$	2.96566	+	11.0680i	0.172961	+	0.645498i
$295$	6.26354	+	11.3375i	0.364677	+	0.660096i
$296$	2.51884	−	5.53674i	0.146405	−	0.321816i
$297$	−28.4857	+	28.4857i	−1.65291	+	1.65291i
$298$	−3.99842	+	6.92547i	−0.231622	+	0.401182i
$299$	−1.44133	−	2.49646i	−0.0833542	−	0.144374i
$300$	−9.96721	−	10.7494i	−0.575457	−	0.620614i
$301$	3.93787	−	14.6963i	0.226975	−	0.847082i
$302$	14.2943			0.822544
$303$	−0.939809	+	3.50742i	−0.0539906	+	0.201496i
$304$	−3.83783	+	3.83783i	−0.220114	+	0.220114i
$305$	−1.83693	−	0.0346643i	−0.105182	−	0.00198487i
$306$	20.7470			1.18603
$307$	−9.50973	−	9.50973i	−0.542749	−	0.542749i	0.381585	−	0.924334i	$-0.375378\pi$
$307$	−9.50973	−	9.50973i	−0.542749	−	0.542749i	−0.924334	+	0.381585i	$0.875378\pi$
$308$	−8.99046	+	2.40899i	−0.512279	+	0.137265i
$309$	44.4218	+	11.9028i	2.52707	+	0.677125i
$310$	10.3929	−	5.74168i	0.590279	−	0.326106i
$311$	2.08579	+	7.78427i	0.118274	+	0.441405i	0.999511	−	0.0312698i	$-0.00995511\pi$
$311$	2.08579	+	7.78427i	0.118274	+	0.441405i	−0.881237	+	0.472675i	$0.843288\pi$
$312$	−0.300446	−	1.12128i	−0.0170094	−	0.0634799i
$313$	−1.26987	−	0.733158i	−0.0717771	−	0.0414406i	0.463682	−	0.886002i	$-0.346528\pi$
$313$	−1.26987	−	0.733158i	−0.0717771	−	0.0414406i	−0.535459	+	0.844561i	$0.679861\pi$
$314$	−2.08643	+	7.78666i	−0.117744	+	0.439426i
$315$	−18.8426	−	11.3581i	−1.06166	−	0.639957i
$316$	3.33439	+	12.4441i	0.187574	+	0.700035i
$317$	12.0009	−	3.21563i	0.674037	−	0.180608i	0.0944641	−	0.995528i	$-0.469886\pi$
$317$	12.0009	−	3.21563i	0.674037	−	0.180608i	0.579572	+	0.814921i	$0.303220\pi$
$318$	−22.8648	−	13.2010i	−1.28220	−	0.740276i
$319$	7.08531	−	7.08531i	0.396701	−	0.396701i
$320$	−2.17041	+	0.537883i	−0.121330	+	0.0300686i
$321$	−7.86098	−	4.53854i	−0.438757	−	0.253317i
$322$	−9.05217	+	9.05217i	−0.504457	+	0.504457i
$323$	14.2293	−	14.2293i	0.791737	−	0.791737i
$324$	−2.76260	+	4.78497i	−0.153478	+	0.265831i
$325$	1.05382	−	1.67590i	0.0584557	−	0.0929621i
$326$	0.520426	−	0.300468i	0.0288237	−	0.0166414i
$327$			5.81238i			0.321425i
$328$	−3.03009	−	5.24826i	−0.167308	−	0.289787i
$329$	15.3050	−	8.83634i	0.843791	−	0.487163i
$330$	−17.9153	+	29.7207i	−0.986204	+	1.63607i
$331$	−2.13031	+	0.570816i	−0.117093	+	0.0313749i	−0.316889	−	0.948462i	$-0.602638\pi$
$331$	−2.13031	+	0.570816i	−0.117093	+	0.0313749i	0.199797	+	0.979837i	$0.435972\pi$
$332$	1.42009	+	1.42009i	0.0779375	+	0.0779375i
$333$	−19.7840	−	27.6976i	−1.08416	−	1.51782i
$334$			16.2080i			0.886862i
$335$	−0.149489	+	7.92172i	−0.00816744	+	0.432810i
$336$	−4.46452	+	2.57759i	−0.243559	+	0.140619i
$337$	−5.55278	+	20.7233i	−0.302479	+	1.12887i	0.632614	+	0.774467i	$0.281982\pi$
$337$	−5.55278	+	20.7233i	−0.302479	+	1.12887i	−0.935093	+	0.354401i	$0.884685\pi$
$338$	−11.1226	+	6.42162i	−0.604988	+	0.349290i
$339$	−34.8245	+	34.8245i	−1.89141	+	1.89141i
$340$	8.04709	−	1.99427i	0.436415	−	0.108155i
$341$	−19.8754	−	19.8754i	−1.07631	−	1.07631i
$342$	7.86059	+	29.3361i	0.425052	+	1.58632i
$343$	13.5626	+	13.5626i	0.732310	+	0.732310i
$344$	−8.65292			−0.466534
$345$	−0.900542	+	47.7216i	−0.0484836	+	2.56925i
$346$	−3.45090	+	12.8789i	−0.185521	+	0.692376i
$347$			15.3997i			0.826699i	0.910572	+	0.413349i	$0.135641\pi$
$347$			15.3997i			0.826699i	−0.910572	+	0.413349i	$0.864359\pi$
$348$	2.77491	−	4.80629i	0.148751	−	0.257644i
$349$	10.8175	+	6.24552i	0.579050	+	0.334315i	0.760756	−	0.649038i	$-0.224828\pi$
$349$	10.8175	+	6.24552i	0.579050	+	0.334315i	−0.181706	+	0.983353i	$0.558162\pi$
$350$	−8.40022	−	2.59423i	−0.449010	−	0.138667i
$351$	−2.91056	−	0.779883i	−0.155354	−	0.0416271i
$352$	2.64671	+	4.58424i	0.141070	+	0.244341i
$353$	−6.92318	+	11.9913i	−0.368484	+	0.638232i	−0.989329	−	0.145701i	$-0.953456\pi$
$353$	−6.92318	+	11.9913i	−0.368484	+	0.638232i	0.620845	+	0.783933i	$0.286790\pi$
$354$	8.49153	−	14.7078i	0.451320	−	0.781709i
$355$	−3.79973	−	3.94590i	−0.201669	−	0.209426i
$356$	−0.323271	−	0.323271i	−0.0171333	−	0.0171333i
$357$	16.5528	−	9.55676i	0.876067	−	0.505797i
$358$	2.03459	+	7.59321i	0.107532	+	0.401313i
$359$		−	25.9408i		−	1.36910i	−0.728964	−	0.684552i	$-0.759998\pi$
$359$		−	25.9408i		−	1.36910i	0.728964	−	0.684552i	$-0.240002\pi$
$360$	−3.46593	+	12.0229i	−0.182670	+	0.633661i
$361$	9.05673	+	5.22891i	0.476670	+	0.275206i
$362$			2.56143i			0.134626i
$363$	48.2006	+	12.9153i	2.52988	+	0.677879i
$364$	−0.492283	−	0.492283i	−0.0258026	−	0.0258026i
$365$	−12.6785	+	21.0331i	−0.663622	+	1.10092i
$366$	1.20447	+	2.08621i	0.0629589	+	0.109048i
$367$	−4.48271	−	1.20114i	−0.233996	−	0.0626990i	0.139916	−	0.990163i	$-0.455317\pi$
$367$	−4.48271	−	1.20114i	−0.233996	−	0.0626990i	−0.373911	+	0.927464i	$0.621984\pi$
$368$	6.30516	+	3.64029i	0.328679	+	0.189763i
$369$	−33.9112			−1.76535
$370$	−10.3359	−	8.84128i	−0.537340	−	0.459636i
$371$	−15.8342			−0.822073
$372$	−13.4824	−	7.78405i	−0.699029	−	0.403584i
$373$	14.0007	+	3.75148i	0.724929	+	0.194244i	0.602370	−	0.798217i	$-0.294223\pi$
$373$	14.0007	+	3.75148i	0.724929	+	0.194244i	0.122559	+	0.992461i	$0.460890\pi$
$374$	−9.81303	−	16.9967i	−0.507420	−	0.878877i
$375$	−29.2693	+	14.7573i	−1.51146	+	0.762062i
$376$	−7.10699	−	7.10699i	−0.366515	−	0.366515i
$377$	0.723951	+	0.193982i	0.0372854	+	0.00999058i
$378$			13.3816i			0.688274i
$379$	3.28199	+	1.89486i	0.168585	+	0.0973324i	0.581918	−	0.813247i	$-0.302302\pi$
$379$	3.28199	+	1.89486i	0.168585	+	0.0973324i	−0.413334	+	0.910580i	$0.635636\pi$
$380$	5.86875	+	10.6229i	0.301061	+	0.544945i
$381$		−	9.43123i		−	0.483176i
$382$	−1.18214	−	4.41182i	−0.0604838	−	0.225728i
$383$	27.1715	−	15.6875i	1.38840	−	0.801592i	0.395263	−	0.918568i	$-0.370653\pi$
$383$	27.1715	−	15.6875i	1.38840	−	0.801592i	0.993135	+	0.116976i	$0.0373201\pi$
$384$	2.07313	+	2.07313i	0.105794	+	0.105794i
$385$	−0.392676	+	20.8087i	−0.0200126	+	1.06051i
$386$	8.77836	−	15.2046i	0.446807	−	0.773892i
$387$	−24.2098	+	41.9326i	−1.23065	+	2.13156i
$388$	5.38207	+	9.32202i	0.273233	+	0.473254i
$389$	−10.3766	−	2.78041i	−0.526116	−	0.140972i	−0.0140217	−	0.999902i	$-0.504463\pi$
$389$	−10.3766	−	2.78041i	−0.526116	−	0.140972i	−0.512094	+	0.858929i	$0.671130\pi$
$390$	−2.59524	−	0.0489741i	−0.131415	−	0.00247990i
$391$	−23.3772	−	13.4968i	−1.18224	−	0.682565i
$392$	1.95413	−	3.38465i	0.0986983	−	0.170951i
$393$		−	16.1443i		−	0.814371i
$394$	−0.114684	+	0.428008i	−0.00577772	+	0.0215627i
$395$	28.8023	+	0.543521i	1.44920	+	0.0273475i
$396$	29.6207			1.48850
$397$	−1.98688	−	1.98688i	−0.0997189	−	0.0997189i	0.655487	−	0.755206i	$-0.272463\pi$
$397$	−1.98688	−	1.98688i	−0.0997189	−	0.0997189i	−0.755206	+	0.655487i	$0.772463\pi$
$398$	−6.99135	−	26.0921i	−0.350445	−	1.30788i
$399$	19.7847	+	19.7847i	0.990473	+	0.990473i
$400$	−0.188640	+	4.99644i	−0.00943201	+	0.249822i
$401$	−1.17240	+	1.17240i	−0.0585467	+	0.0585467i	−0.735774	−	0.677227i	$-0.763181\pi$
$401$	−1.17240	+	1.17240i	−0.0585467	+	0.0585467i	0.677227	+	0.735774i	$0.263181\pi$
$402$	8.99672	−	5.19426i	0.448716	−	0.259066i
$403$	0.544149	−	2.03079i	0.0271060	−	0.101161i
$404$	1.07259	−	0.619258i	0.0533631	−	0.0308092i
$405$	8.56973	+	8.89938i	0.425833	+	0.442214i
$406$		−	3.32843i		−	0.165187i
$407$	−13.3333	+	29.3083i	−0.660906	+	1.45276i
$408$	−7.68641	−	7.68641i	−0.380534	−	0.380534i
$409$	−30.9004	+	8.27974i	−1.52793	+	0.409407i	−0.922342	−	0.386373i	$-0.873728\pi$
$409$	−30.9004	+	8.27974i	−1.52793	+	0.409407i	−0.605585	+	0.795780i	$0.707061\pi$
$410$	−13.1531	+	3.25966i	−0.649583	+	0.160983i
$411$	−52.5309	+	30.3288i	−2.59116	+	1.49601i
$412$	−7.84296	−	13.5844i	−0.386395	−	0.669256i
$413$		−	10.1853i		−	0.501188i
$414$	35.2821	−	20.3702i	1.73402	−	1.00114i
$415$	3.93074	−	2.17158i	0.192953	−	0.106599i
$416$	−0.197969	+	0.342893i	−0.00970624	+	0.0168117i
$417$	46.0566	−	46.0566i	2.25540	−	2.25540i
$418$	20.3152	−	20.3152i	0.993650	−	0.993650i
$419$	3.92076	+	2.26365i	0.191542	+	0.110587i	0.592704	−	0.805420i	$-0.298060\pi$
$419$	3.92076	+	2.26365i	0.191542	+	0.110587i	−0.401162	+	0.916007i	$0.631394\pi$
$420$	2.77288	+	11.1889i	0.135303	+	0.545960i
$421$	−16.3796	+	16.3796i	−0.798291	+	0.798291i	−0.982826	−	0.184535i	$-0.940922\pi$
$421$	−16.3796	+	16.3796i	−0.798291	+	0.798291i	0.184535	+	0.982826i	$0.440922\pi$
$422$	−23.9329	−	13.8177i	−1.16504	−	0.672634i
$423$	−54.3254	+	14.5564i	−2.64139	+	0.707759i
$424$	2.33073	+	8.69839i	0.113190	+	0.422431i
$425$	0.699409	−	18.5250i	0.0339263	−	0.898593i
$426$	−1.85897	+	6.93777i	−0.0900673	+	0.336136i
$427$	1.25117	+	0.722366i	0.0605486	+	0.0349577i
$428$	0.801309	+	2.99053i	0.0387328	+	0.144553i
$429$	1.59038	+	5.93540i	0.0767845	+	0.286564i
$430$	−5.35949	+	18.5914i	−0.258458	+	0.896558i
$431$	7.19885	+	1.92893i	0.346757	+	0.0929131i	0.427994	−	0.903782i	$-0.359220\pi$
$431$	7.19885	+	1.92893i	0.346757	+	0.0929131i	−0.0812373	+	0.996695i	$0.525887\pi$
$432$	7.35105	−	1.96971i	0.353678	−	0.0947676i
$433$	4.98607	+	4.98607i	0.239615	+	0.239615i	0.816691	−	0.577075i	$-0.195806\pi$
$433$	4.98607	+	4.98607i	0.239615	+	0.239615i	−0.577075	+	0.816691i	$0.695806\pi$
$434$	−9.33675			−0.448178
$435$	−8.60792	−	8.93905i	−0.412718	−	0.428595i
$436$	1.40184	−	1.40184i	0.0671357	−	0.0671357i
$437$	10.2273	−	38.1689i	0.489239	−	1.82587i
$438$	32.2006			1.53860
$439$	0.561343	−	2.09496i	0.0267914	−	0.0999871i	−0.951235	−	0.308466i	$-0.900185\pi$
$439$	0.561343	−	2.09496i	0.0267914	−	0.0999871i	0.978027	+	0.208479i	$0.0668512\pi$
$440$	11.4889	−	2.84724i	0.547712	−	0.135737i
$441$	−10.9348	−	18.9397i	−0.520705	−	0.901888i
$442$	0.733997	−	1.27132i	0.0349127	−	0.0604705i
$443$	−15.0759	+	15.0759i	−0.716279	+	0.716279i	−0.967841	−	0.251562i	$-0.919056\pi$
$443$	−15.0759	+	15.0759i	−0.716279	+	0.716279i	0.251562	+	0.967841i	$0.419056\pi$
$444$	−2.93185	+	17.5911i	−0.139140	+	0.834837i
$445$	−0.894801	+	0.494342i	−0.0424176	+	0.0234341i
$446$	7.20282	+	26.8813i	0.341064	+	1.27287i
$447$	6.06816	−	22.6467i	0.287014	−	1.07115i
$448$	1.69842	+	0.455091i	0.0802429	+	0.0215010i
$449$	−29.8192	−	7.99003i	−1.40725	−	0.377073i	−0.526310	−	0.850293i	$-0.676425\pi$
$449$	−29.8192	−	7.99003i	−1.40725	−	0.377073i	−0.880944	+	0.473220i	$0.843092\pi$
$450$	23.6853	+	14.8936i	1.11653	+	0.702090i
$451$	16.0395	+	27.7813i	0.755271	+	1.30817i
$452$	16.7980			0.790112
$453$	−40.4808	+	10.8468i	−1.90195	+	0.509626i
$454$			17.2343i			0.808847i
$455$	−1.36262	+	0.752792i	−0.0638805	+	0.0352914i
$456$	7.95632	−	13.7808i	0.372589	−	0.645343i
$457$	3.44196	+	5.96166i	0.161008	+	0.278875i	0.935231	−	0.354039i	$-0.115192\pi$
$457$	3.44196	+	5.96166i	0.161008	+	0.278875i	−0.774222	+	0.632914i	$0.781859\pi$
$458$	−8.04277			−0.375814
$459$	−27.2550	+	7.30295i	−1.27215	+	0.340873i
$460$	11.7267	−	11.2924i	0.546762	−	0.526509i
$461$	18.2684	−	4.89500i	0.850843	−	0.227983i	0.193057	−	0.981188i	$-0.438160\pi$
$461$	18.2684	−	4.89500i	0.850843	−	0.227983i	0.657786	+	0.753205i	$0.271493\pi$
$462$	23.6326	−	13.6443i	1.09949	−	0.634789i
$463$	14.2246	−	8.21257i	0.661073	−	0.381670i	−0.131613	−	0.991301i	$-0.542016\pi$
$463$	14.2246	−	8.21257i	0.661073	−	0.381670i	0.792686	+	0.609631i	$0.208682\pi$
$464$	−1.82844	+	0.489930i	−0.0848833	+	0.0227444i
$465$	−25.0754	+	24.1465i	−1.16284	+	1.11977i
$466$	−20.5668	+	5.51085i	−0.952738	+	0.255285i
$467$	15.6616			0.724732			0.362366	−	0.932036i	$-0.381969\pi$
$467$	15.6616			0.724732			0.362366	+	0.932036i	$0.381969\pi$
$468$	1.10779	+	1.91874i	0.0512075	+	0.0886939i
$469$	3.11518	−	5.39566i	0.143846	−	0.249148i
$470$	−19.6718	+	10.8679i	−0.907394	+	0.501299i
$471$		−	23.6346i		−	1.08903i
$472$	−5.59523	+	1.49924i	−0.257541	+	0.0690080i
$473$	45.8036			2.10605
$474$	−18.8856	−	32.7109i	−0.867446	−	1.50246i
$475$	26.4592	−	6.02975i	1.21403	−	0.276664i
$476$	−6.29713	−	1.68731i	−0.288628	−	0.0773377i
$477$	48.6741	+	13.0422i	2.22863	+	0.597160i
$478$	2.47074	−	9.22091i	0.113009	−	0.421755i
$479$	−1.58757	−	5.92489i	−0.0725379	−	0.270715i	0.920126	−	0.391623i	$-0.128086\pi$
$479$	−1.58757	−	5.92489i	−0.0725379	−	0.270715i	−0.992664	+	0.120908i	$0.961419\pi$
$480$	5.73834	−	3.17021i	0.261918	−	0.144699i
$481$	−2.39716	+	0.232411i	−0.109301	+	0.0105970i
$482$	2.83295	−	2.83295i	0.129038	−	0.129038i
$483$	18.7663	−	32.5042i	0.853898	−	1.47899i
$484$	−8.51015	−	14.7400i	−0.386825	−	0.670000i
$485$	23.3626	−	5.78985i	1.06084	−	0.262903i
$486$	−1.71649	+	6.40605i	−0.0778618	+	0.290584i
$487$	−41.9951			−1.90298			−0.951490	−	0.307679i	$-0.900448\pi$
$487$	−41.9951			−1.90298			−0.951490	+	0.307679i	$0.900448\pi$
$488$	0.212658	−	0.793650i	0.00962657	−	0.0359269i
$489$	−1.24582	+	1.24582i	−0.0563379	+	0.0563379i
$490$	−6.06180	−	6.29498i	−0.273844	−	0.284378i
$491$	−1.23433			−0.0557047			−0.0278524	−	0.999612i	$-0.508867\pi$
$491$	−1.23433			−0.0557047			−0.0278524	+	0.999612i	$0.508867\pi$
$492$	12.5635	+	12.5635i	0.566408	+	0.566408i
$493$	6.77920	−	1.81648i	0.305320	−	0.0818101i
$494$	2.07573	+	0.556191i	0.0933917	+	0.0250242i
$495$	18.3466	−	63.6422i	0.824619	−	2.86050i
$496$	1.37433	+	5.12906i	0.0617091	+	0.230301i
$497$	1.11489	+	4.16083i	0.0500097	+	0.186639i
$498$	−5.09921	−	2.94403i	−0.228501	−	0.131925i
$499$	−9.97949	+	37.2439i	−0.446743	+	1.66727i	0.264550	+	0.964372i	$0.414777\pi$
$499$	−9.97949	+	37.2439i	−0.446743	+	1.66727i	−0.711293	+	0.702896i	$0.751890\pi$
$500$	10.6184	+	3.50003i	0.474868	+	0.156526i
$501$	−12.2989	−	45.9002i	−0.549476	−	2.05067i
$502$	9.28080	−	2.48678i	0.414222	−	0.110991i
$503$	21.4757	+	12.3990i	0.957553	+	0.552844i	0.895419	−	0.445224i	$-0.146876\pi$
$503$	21.4757	+	12.3990i	0.957553	+	0.552844i	0.0621341	+	0.998068i	$0.480209\pi$
$504$	6.95738	−	6.95738i	0.309906	−	0.309906i
$505$	−0.666176	−	2.68809i	−0.0296444	−	0.119618i
$506$	−33.3759	−	19.2696i	−1.48374	−	0.856637i
$507$	26.6257	−	26.6257i	1.18249	−	1.18249i
$508$	−2.27463	+	2.27463i	−0.100920	+	0.100920i
$509$	−6.82884	+	11.8279i	−0.302683	+	0.524263i	−0.976743	−	0.214414i	$-0.931216\pi$
$509$	−6.82884	+	11.8279i	−0.302683	+	0.524263i	0.674060	+	0.738677i	$0.264549\pi$
$510$	−21.2757	+	11.7540i	−0.942102	+	0.520474i
$511$	16.7245	−	9.65592i	0.739850	−	0.427153i
$512$		−	1.00000i		−	0.0441942i
$513$	−20.6527	−	35.7714i	−0.911837	−	1.57935i
$514$	4.89445	−	2.82581i	0.215885	−	0.124641i
$515$	−34.0449	+	8.43719i	−1.50020	+	0.371787i
$516$	24.5047	−	6.56600i	1.07876	−	0.289052i
$517$	37.6203	+	37.6203i	1.65454	+	1.65454i
$518$	3.75224	+	10.0158i	0.164864	+	0.440067i
$519$		−	39.0911i		−	1.71591i
$520$	0.614111	+	0.637734i	0.0269305	+	0.0279665i
$521$	5.66705	−	3.27187i	0.248278	−	0.143343i	−0.370697	−	0.928754i	$-0.620881\pi$
$521$	5.66705	−	3.27187i	0.248278	−	0.143343i	0.618976	+	0.785410i	$0.287548\pi$
$522$	−2.74153	+	10.2315i	−0.119993	+	0.447821i
$523$	31.3893	−	18.1226i	1.37256	−	0.792446i	0.381308	−	0.924448i	$-0.375474\pi$
$523$	31.3893	−	18.1226i	1.37256	−	0.792446i	0.991249	+	0.132002i	$0.0421406\pi$
$524$	−3.89369	+	3.89369i	−0.170097	+	0.170097i
$525$	25.7576	+	0.972474i	1.12415	+	0.0424423i
$526$	4.98208	+	4.98208i	0.217229	+	0.217229i
$527$	−5.09550	−	19.0167i	−0.221963	−	0.828379i
$528$	−10.9740	−	10.9740i	−0.477580	−	0.477580i
$529$	−30.0068			−1.30464
$530$	20.1327	+	0.379920i	0.874510	+	0.0165027i
$531$	−8.38936	+	31.3095i	−0.364067	+	1.35872i
$532$		−	9.54338i		−	0.413758i
$533$	−1.19973	+	2.07799i	−0.0519659	+	0.0900077i
$534$	1.16079	+	0.670184i	0.0502324	+	0.0290017i
$535$	6.92168	+	0.130617i	0.299250	+	0.00564708i
$536$	−3.42259	−	0.917081i	−0.147834	−	0.0396119i
$537$	−11.5237	−	19.9597i	−0.497286	−	0.861325i
$538$	−10.0908	+	17.4777i	−0.435044	+	0.753519i
$539$	−10.3440	+	17.9164i	−0.445548	+	0.771712i
$540$	0.321072	−	17.0143i	0.0138167	−	0.732177i
$541$	−16.4032	−	16.4032i	−0.705230	−	0.705230i	0.260298	−	0.965528i	$-0.416179\pi$
$541$	−16.4032	−	16.4032i	−0.705230	−	0.705230i	−0.965528	+	0.260298i	$0.916179\pi$
$542$	9.14432	−	5.27948i	0.392782	−	0.226773i
$543$	−1.94366	−	7.25385i	−0.0834106	−	0.311293i
$544$			3.70763i			0.158963i
$545$	−2.14367	−	3.88022i	−0.0918247	−	0.166210i
$546$	1.76767	+	1.02057i	0.0756495	+	0.0436762i
$547$			4.82213i			0.206179i	0.994672	+	0.103090i	$0.0328729\pi$
$547$			4.82213i			0.206179i	−0.994672	+	0.103090i	$0.967127\pi$
$548$	19.9842	+	5.35474i	0.853682	+	0.228743i
$549$	−3.25109	−	3.25109i	−0.138753	−	0.138753i
$550$	0.998552	−	26.4483i	0.0425784	−	1.12776i
$551$	5.13698	+	8.89751i	0.218843	+	0.379047i
$552$	−20.6182	−	5.52464i	−0.877570	−	0.235144i
$553$	−19.6179	−	11.3264i	−0.834237	−	0.481647i
$554$	22.3728			0.950529
$555$	35.9798	+	17.1950i	1.52726	+	0.729886i
$556$	−22.2159			−0.942165
$557$	−0.373616	−	0.215707i	−0.0158306	−	0.00913981i	0.492064	−	0.870559i	$-0.336243\pi$
$557$	−0.373616	−	0.215707i	−0.0158306	−	0.00913981i	−0.507894	+	0.861419i	$0.669576\pi$
$558$	28.7009	+	7.69039i	1.21501	+	0.325560i
$559$	1.71301	+	2.96702i	0.0724527	+	0.125492i
$560$	2.02977	−	3.36731i	0.0857736	−	0.142295i
$561$	40.6874	+	40.6874i	1.71782	+	1.71782i
$562$	12.0535	+	3.22972i	0.508445	+	0.136237i
$563$		−	6.79207i		−	0.286252i	−0.989704	−	0.143126i	$-0.954285\pi$
$563$		−	6.79207i		−	0.286252i	0.989704	−	0.143126i	$-0.0457154\pi$
$564$	25.5196	+	14.7337i	1.07457	+	0.620402i
$565$	10.4044	−	36.0917i	0.437718	−	1.51839i
$566$		−	27.0858i		−	1.13850i
$567$	−2.51447	−	9.38413i	−0.105598	−	0.394096i
$568$	2.12161	−	1.22491i	0.0890206	−	0.0513961i
$569$	1.81640	+	1.81640i	0.0761474	+	0.0761474i	0.744155	−	0.668007i	$-0.232853\pi$
$569$	1.81640	+	1.81640i	0.0761474	+	0.0761474i	−0.668007	+	0.744155i	$0.732853\pi$
$570$	−24.6809	−	25.6303i	−1.03377	−	1.07354i
$571$	11.8321	−	20.4938i	0.495159	−	0.857641i	−0.504825	−	0.863222i	$-0.668443\pi$
$571$	11.8321	−	20.4938i	0.495159	−	0.857641i	0.999984	+	0.00558071i	$0.00177641\pi$
$572$	1.04793	−	1.81508i	0.0438163	−	0.0758921i
$573$	6.69555	+	11.5970i	0.279711	+	0.484473i
$574$	10.2927	+	2.75793i	0.429610	+	0.115114i
$575$	−16.9991	−	32.1901i	−0.708910	−	1.34242i
$576$	−4.84607	−	2.79788i	−0.201919	−	0.116578i
$577$	−9.82363	+	17.0150i	−0.408963	+	0.708344i	−0.994774	−	0.102103i	$-0.967443\pi$
$577$	−9.82363	+	17.0150i	−0.408963	+	0.708344i	0.585811	+	0.810448i	$0.300776\pi$
$578$			3.25345i			0.135326i
$579$	−13.3224	+	49.7198i	−0.553659	+	2.06628i
$580$	−0.0798609	+	4.23200i	−0.00331604	+	0.175724i
$581$	−3.53128			−0.146502
$582$	−22.3155	−	22.3155i	−0.925007	−	0.925007i
$583$	−12.3375	−	46.0442i	−0.510968	−	1.90696i
$584$	−7.76616	−	7.76616i	−0.321366	−	0.321366i
$585$	4.80870	−	1.19172i	0.198815	−	0.0492715i
$586$	−15.3366	+	15.3366i	−0.633548	+	0.633548i
$587$	19.7273	−	11.3896i	0.814234	−	0.470098i	−0.0341902	−	0.999415i	$-0.510885\pi$
$587$	19.7273	−	11.3896i	0.814234	−	0.470098i	0.848424	+	0.529317i	$0.177552\pi$
$588$	−2.96566	+	11.0680i	−0.122302	+	0.456436i
$589$	24.9589	−	14.4100i	1.02841	−	0.593754i
$590$	−0.244383	+	12.9504i	−0.0100611	+	0.533158i
$591$		−	1.29912i		−	0.0534388i
$592$	4.94975	−	3.53553i	0.203433	−	0.145310i
$593$	7.46742	+	7.46742i	0.306650	+	0.306650i	0.843609	−	0.536958i	$-0.180427\pi$
$593$	7.46742	+	7.46742i	0.306650	+	0.306650i	−0.536958	+	0.843609i	$0.680427\pi$
$594$	−38.9122	+	10.4265i	−1.59659	+	0.427804i
$595$	−7.52566	+	12.4847i	−0.308522	+	0.511824i
$596$	−6.92547	+	3.99842i	−0.283678	+	0.163782i
$597$	39.5983	+	68.5863i	1.62065	+	2.80705i
$598$		−	2.88266i		−	0.117881i
$599$	0.384513	−	0.221999i	0.0157108	−	0.00907062i	−0.492124	−	0.870525i	$-0.663779\pi$
$599$	0.384513	−	0.221999i	0.0157108	−	0.00907062i	0.507835	+	0.861454i	$0.330446\pi$
$600$	−3.25717	−	14.2928i	−0.132974	−	0.583502i
$601$	12.2726	−	21.2568i	0.500609	−	0.867081i	−0.499390	−	0.866377i	$-0.666443\pi$
$601$	12.2726	−	21.2568i	0.500609	−	0.867081i	1.00000		0.000703826i	$-0.000224035\pi$
$602$	10.7585	−	10.7585i	0.438482	−	0.438482i
$603$	−14.0202	+	14.0202i	−0.570948	+	0.570948i
$604$	12.3792	+	7.14715i	0.503703	+	0.290813i
$605$	−36.9410	+	9.15492i	−1.50187	+	0.372201i
$606$	−2.56761	+	2.56761i	−0.104302	+	0.104302i
$607$	3.27917	+	1.89323i	0.133098	+	0.0768439i	0.565070	−	0.825043i	$-0.308849\pi$
$607$	3.27917	+	1.89323i	0.133098	+	0.0768439i	−0.431973	+	0.901887i	$0.642182\pi$
$608$	−5.24257	+	1.40474i	−0.212614	+	0.0569698i
$609$	2.52568	+	9.42595i	0.102346	+	0.381959i
$610$	−1.57350	−	0.948486i	−0.0637091	−	0.0384031i
$611$	−1.02997	+	3.84390i	−0.0416681	+	0.155507i
$612$	17.9674	+	10.3735i	0.726290	+	0.419324i
$613$	1.34180	+	5.00768i	0.0541949	+	0.202258i	0.987715	−	0.156267i	$-0.0499462\pi$
$613$	1.34180	+	5.00768i	0.0541949	+	0.202258i	−0.933520	+	0.358526i	$0.883280\pi$
$614$	−3.48080	−	12.9905i	−0.140474	−	0.524255i
$615$	34.7753	−	19.2120i	1.40228	−	0.774702i
$616$	−8.99046	−	2.40899i	−0.362236	−	0.0970609i
$617$	−30.8709	+	8.27183i	−1.24281	+	0.333011i	−0.819557	−	0.572998i	$-0.805780\pi$
$617$	−30.8709	+	8.27183i	−1.24281	+	0.333011i	−0.423258	+	0.906009i	$0.639114\pi$
$618$	32.5190	+	32.5190i	1.30811	+	1.30811i
$619$	16.9452			0.681086			0.340543	−	0.940229i	$-0.389389\pi$
$619$	16.9452			0.681086			0.340543	+	0.940229i	$0.389389\pi$
$620$	11.8714	+	0.224022i	0.476766	+	0.00899693i
$621$	−39.1793	+	39.1793i	−1.57221	+	1.57221i
$622$	−2.08579	+	7.78427i	−0.0836325	+	0.312121i
$623$	0.803866			0.0322062
$624$	0.300446	−	1.12128i	0.0120274	−	0.0448871i
$625$	14.0969	−	20.6465i	0.563877	−	0.825859i
$626$	−0.733158	−	1.26987i	−0.0293029	−	0.0507541i
$627$	−42.1161	+	72.9473i	−1.68196	+	2.91323i
$628$	−5.70023	+	5.70023i	−0.227464	+	0.227464i
$629$	−18.3519	+	13.1085i	−0.731736	+	0.522669i
$630$	−10.6391	−	19.2577i	−0.423873	−	0.767246i
$631$	4.85936	+	18.1354i	0.193448	+	0.721958i	0.992663	+	0.120913i	$0.0385822\pi$
$631$	4.85936	+	18.1354i	0.193448	+	0.721958i	−0.799215	+	0.601045i	$0.794751\pi$
$632$	−3.33439	+	12.4441i	−0.132635	+	0.495000i
$633$	78.2619	+	20.9702i	3.11063	+	0.833492i
$634$	12.0009	+	3.21563i	0.476616	+	0.127709i
$635$	3.47834	+	6.29608i	0.138034	+	0.249852i
$636$	−13.2010	−	22.8648i	−0.523454	−	0.906649i
$637$	−1.54743			−0.0613113
$638$	9.67871	−	2.59340i	0.383184	−	0.102674i
$639$		−	13.7086i		−	0.542303i
$640$	−2.14857	−	0.619385i	−0.0849298	−	0.0244833i
$641$	−21.3524	+	36.9834i	−0.843367	+	1.46076i	0.0436641	+	0.999046i	$0.486097\pi$
$641$	−21.3524	+	36.9834i	−0.843367	+	1.46076i	−0.887031	+	0.461709i	$0.847236\pi$
$642$	−4.53854	−	7.86098i	−0.179122	−	0.310248i
$643$	−40.4138			−1.59376			−0.796882	−	0.604135i	$-0.793519\pi$
$643$	−40.4138			−1.59376			−0.796882	+	0.604135i	$0.793519\pi$
$644$	−12.3655	+	3.31332i	−0.487269	+	0.130563i
$645$	1.07029	−	56.7169i	0.0421426	−	2.23323i
$646$	19.4375	−	5.20827i	0.764759	−	0.204917i
$647$	−23.4770	+	13.5544i	−0.922975	+	0.532880i	−0.884583	−	0.466383i	$-0.845557\pi$
$647$	−23.4770	+	13.5544i	−0.922975	+	0.532880i	−0.0383921	+	0.999263i	$0.512224\pi$
$648$	−4.78497	+	2.76260i	−0.187971	+	0.108525i
$649$	29.6179	−	7.93609i	1.16260	−	0.311519i
$650$	1.75059	−	0.924458i	0.0686637	−	0.0362602i
$651$	26.4412	−	7.08490i	1.03631	−	0.277679i
$652$	0.600936			0.0235345
$653$	2.13386	+	3.69595i	0.0835044	+	0.144634i	0.904753	−	0.425937i	$-0.140055\pi$
$653$	2.13386	+	3.69595i	0.0835044	+	0.144634i	−0.821249	+	0.570571i	$0.806722\pi$
$654$	−2.90619	+	5.03367i	−0.113641	+	0.196832i
$655$	5.95418	+	10.7776i	0.232649	+	0.421115i
$656$		−	6.06017i		−	0.236610i
$657$	−59.3641	+	15.9066i	−2.31601	+	0.620574i
$658$	17.6727			0.688953
$659$	−2.86699	−	4.96578i	−0.111682	−	0.193439i	0.804766	−	0.593592i	$-0.202291\pi$
$659$	−2.86699	−	4.96578i	−0.111682	−	0.193439i	−0.916449	+	0.400152i	$0.868957\pi$
$660$	−30.3755	+	16.7812i	−1.18236	+	0.653209i
$661$	26.4406	+	7.08473i	1.02842	+	0.275564i	0.733306	−	0.679899i	$-0.237976\pi$
$661$	26.4406	+	7.08473i	1.02842	+	0.275564i	0.295112	+	0.955463i	$0.404643\pi$
$662$	−2.13031	−	0.570816i	−0.0827970	−	0.0221854i
$663$	−1.11394	+	4.15729i	−0.0432619	+	0.161456i
$664$	0.519789	+	1.93988i	0.0201717	+	0.0752818i
$665$	−20.5046	−	5.91103i	−0.795136	−	0.229220i
$666$	−3.28464	−	33.8788i	−0.127277	−	1.31278i
$667$	9.74514	−	9.74514i	0.377333	−	0.377333i
$668$	−8.10399	+	14.0365i	−0.313553	+	0.543090i
$669$	−40.7961	−	70.6609i	−1.57727	−	2.73191i
$670$	−4.09032	+	6.78566i	−0.158023	+	0.262153i
$671$	−1.12569	+	4.20112i	−0.0434567	+	0.162183i
$672$	−5.15518			−0.198865
$673$	−2.51482	+	9.38545i	−0.0969393	+	0.361783i	−0.997306	−	0.0733487i	$-0.976631\pi$
$673$	−2.51482	+	9.38545i	−0.0969393	+	0.361783i	0.900367	+	0.435131i	$0.143298\pi$
$674$	−15.1705	+	15.1705i	−0.584345	+	0.584345i
$675$	−36.3575	−	11.2282i	−1.39940	−	0.432175i
$676$	−12.8432			−0.493970
$677$	−15.7154	−	15.7154i	−0.603991	−	0.603991i	0.337378	−	0.941369i	$-0.390460\pi$
$677$	−15.7154	−	15.7154i	−0.603991	−	0.603991i	−0.941369	+	0.337378i	$0.890460\pi$
$678$	−47.5711	+	12.7466i	−1.82696	+	0.489532i
$679$	−18.2821	−	4.89866i	−0.701601	−	0.187993i
$680$	7.96612	+	2.29645i	0.305487	+	0.0880650i
$681$	−13.0777	−	48.8068i	−0.501140	−	1.87028i
$682$	−7.27489	−	27.1503i	−0.278570	−	1.03964i
$683$	36.0059	+	20.7880i	1.37773	+	0.795430i	0.991885	−	0.127135i	$-0.0405782\pi$
$683$	36.0059	+	20.7880i	1.37773	+	0.795430i	0.385840	+	0.922566i	$0.373912\pi$
$684$	−7.86059	+	29.3361i	−0.300557	+	1.12169i
$685$	23.8830	−	39.6208i	0.912521	−	1.51383i
$686$	4.96425	+	18.5268i	0.189536	+	0.707357i
$687$	22.7767	−	6.10300i	0.868986	−	0.232844i
$688$	−7.49365	−	4.32646i	−0.285693	−	0.164945i
$689$	2.52120	−	2.52120i	0.0960502	−	0.0960502i
$690$	−24.6407	+	40.8779i	−0.938056	+	1.55619i
$691$	37.3098	+	21.5408i	1.41933	+	0.819451i	0.996240	−	0.0866365i	$-0.0276119\pi$
$691$	37.3098	+	21.5408i	1.41933	+	0.819451i	0.423091	+	0.906087i	$0.360945\pi$
$692$	−9.42803	+	9.42803i	−0.358400	+	0.358400i
$693$	−36.8283	+	36.8283i	−1.39899	+	1.39899i
$694$	−7.69985	+	13.3365i	−0.292282	+	0.506248i
$695$	−13.7602	+	47.7325i	−0.521955	+	1.81060i
$696$	4.80629	−	2.77491i	0.182182	−	0.105183i
$697$			22.4689i			0.851070i
$698$	6.24552	+	10.8175i	0.236396	+	0.409450i
$699$	54.0624	−	31.2129i	2.04483	−	1.18058i
$700$	−5.97769	−	6.44677i	−0.225935	−	0.243665i
$701$	23.0701	−	6.18163i	0.871347	−	0.233477i	0.204677	−	0.978830i	$-0.434386\pi$
$701$	23.0701	−	6.18163i	0.871347	−	0.233477i	0.666670	+	0.745353i	$0.267719\pi$
$702$	−2.13068	−	2.13068i	−0.0804173	−	0.0804173i
$703$	−25.4884	−	20.9829i	−0.961313	−	0.791384i
$704$			5.29342i			0.199503i
$705$	47.4629	−	45.7048i	1.78756	−	1.72134i
$706$	−11.9913	+	6.92318i	−0.451298	+	0.260557i
$707$	−0.563637	+	2.10352i	−0.0211978	+	0.0791111i
$708$	14.7078	−	8.49153i	0.552752	−	0.319131i
$709$	21.5173	−	21.5173i	0.808098	−	0.808098i	−0.176248	−	0.984346i	$-0.556396\pi$
$709$	21.5173	−	21.5173i	0.808098	−	0.808098i	0.984346	+	0.176248i	$0.0563959\pi$
$710$	−1.31772	−	5.31711i	−0.0494530	−	0.199548i
$711$	50.9757	+	50.9757i	1.91174	+	1.91174i
$712$	−0.118325	−	0.441597i	−0.00443443	−	0.0165495i
$713$	−27.3366	−	27.3366i	−1.02376	−	1.02376i
$714$	19.1135			0.715306
$715$	−3.25074	−	3.37579i	−0.121571	−	0.126247i
$716$	−2.03459	+	7.59321i	−0.0760363	+	0.283771i
$717$			27.9880i			1.04523i
$718$	12.9704	−	22.4654i	0.484052	−	0.838402i
$719$	−18.6677	−	10.7778i	−0.696188	−	0.401944i	0.109738	−	0.993961i	$-0.464999\pi$
$719$	−18.6677	−	10.7778i	−0.696188	−	0.401944i	−0.805926	+	0.592016i	$0.798332\pi$
$720$	−9.01302	+	8.67916i	−0.335895	+	0.323453i
$721$	26.6413	+	7.13852i	0.992174	+	0.265852i
$722$	5.22891	+	9.05673i	0.194600	+	0.337057i
$723$	−5.87309	+	10.1725i	−0.218423	+	0.378319i
$724$	−1.28072	+	2.21827i	−0.0475974	+	0.0824412i
$725$	9.04328	+	2.79282i	0.335859	+	0.103723i
$726$	35.2853	+	35.2853i	1.30956	+	1.30956i
$727$	23.9521	−	13.8287i	0.888333	−	0.512879i	0.0149359	−	0.999888i	$-0.495246\pi$
$727$	23.9521	−	13.8287i	0.888333	−	0.512879i	0.873397	+	0.487009i	$0.161912\pi$
$728$	−0.180188	−	0.672471i	−0.00667821	−	0.0249234i
$729$		−	36.0197i		−	1.33406i
$730$	−21.4964	+	11.8759i	−0.795618	+	0.439547i
$731$	27.7837	+	16.0409i	1.02762	+	0.593295i
$732$			2.40895i			0.0890373i
$733$	−42.4690	−	11.3795i	−1.56863	−	0.420312i	−0.633245	−	0.773951i	$-0.718277\pi$
$733$	−42.4690	−	11.3795i	−1.56863	−	0.420312i	−0.935382	+	0.353639i	$0.884944\pi$
$734$	−3.28157	−	3.28157i	−0.121125	−	0.121125i
$735$	21.9435	+	13.2273i	0.809397	+	0.487895i
$736$	3.64029	+	6.30516i	0.134183	+	0.232411i
$737$	18.1172	+	4.85450i	0.667357	+	0.178818i
$738$	−29.3680	−	16.9556i	−1.08105	−	0.624145i
$739$	−33.8211			−1.24413			−0.622064	−	0.782967i	$-0.713706\pi$
$739$	−33.8211			−1.24413			−0.622064	+	0.782967i	$0.713706\pi$
$740$	−4.53055	−	12.8247i	−0.166546	−	0.471447i
$741$	−6.30043			−0.231452
$742$	−13.7129	−	7.91712i	−0.503415	−	0.290647i
$743$	−0.287837	−	0.0771256i	−0.0105597	−	0.00282946i	0.253535	−	0.967326i	$-0.418407\pi$
$743$	−0.287837	−	0.0771256i	−0.0105597	−	0.00282946i	−0.264095	+	0.964497i	$0.585073\pi$
$744$	−7.78405	−	13.4824i	−0.285377	−	0.494288i
$745$	4.30137	+	17.3564i	0.157590	+	0.635891i
$746$	10.2492	+	10.2492i	0.375251	+	0.375251i
$747$	10.8551	+	2.90861i	0.397166	+	0.106420i
$748$		−	19.6261i		−	0.717600i
$749$	−4.71451	−	2.72192i	−0.172264	−	0.0994569i
$750$	−32.7266	−	1.85449i	−1.19501	−	0.0677163i
$751$		−	42.9846i		−	1.56853i	−0.620426	−	0.784265i	$-0.713040\pi$
$751$		−	42.9846i		−	1.56853i	0.620426	−	0.784265i	$-0.286960\pi$
$752$	−2.60134	−	9.70832i	−0.0948610	−	0.354026i
$753$	−24.3958	+	14.0849i	−0.889031	+	0.513282i
$754$	0.529969	+	0.529969i	0.0193003	+	0.0193003i
$755$	23.0237	−	22.1708i	0.837917	−	0.806879i
$756$	−6.69079	+	11.5888i	−0.243342	+	0.421480i
$757$	5.73795	−	9.93843i	0.208549	−	0.361218i	−0.742708	−	0.669615i	$-0.766459\pi$
$757$	5.73795	−	9.93843i	0.208549	−	0.361218i	0.951258	+	0.308397i	$0.0997925\pi$
$758$	1.89486	+	3.28199i	0.0688244	+	0.119207i
$759$	109.141	+	29.2442i	3.96157	+	1.06150i
$760$	−0.228980	+	12.1341i	−0.00830596	+	0.440150i
$761$	−43.7719	−	25.2717i	−1.58673	−	0.916100i	−0.993841	−	0.110817i	$-0.964653\pi$
$761$	−43.7719	−	25.2717i	−1.58673	−	0.916100i	−0.592890	−	0.805283i	$-0.702013\pi$
$762$	4.71561	−	8.16768i	0.170829	−	0.295884i
$763$			3.48589i			0.126198i
$764$	1.18214	−	4.41182i	0.0427685	−	0.159614i
$765$	33.4170	−	32.1791i	1.20819	−	1.16344i
$766$	31.3749			1.13362
$767$	1.62176	+	1.62176i	0.0585584	+	0.0585584i
$768$	0.758819	+	2.83195i	0.0273815	+	0.102189i
$769$	−20.6641	−	20.6641i	−0.745167	−	0.745167i	0.228400	−	0.973567i	$-0.426651\pi$
$769$	−20.6641	−	20.6641i	−0.745167	−	0.745167i	−0.973567	+	0.228400i	$0.926651\pi$
$770$	−10.7444	+	17.8246i	−0.387203	+	0.642353i
$771$	−11.7166	+	11.7166i	−0.421961	+	0.421961i
$772$	15.2046	−	8.77836i	0.547224	−	0.315940i
$773$	11.0713	−	41.3185i	0.398205	−	1.48612i	−0.418046	−	0.908426i	$-0.637285\pi$
$773$	11.0713	−	41.3185i	0.398205	−	1.48612i	0.816252	−	0.577697i	$-0.196048\pi$
$774$	−41.9326	+	24.2098i	−1.50724	+	0.870204i
$775$	7.83429	−	25.3678i	0.281416	−	0.911237i
$776$			10.7641i			0.386410i
$777$	−18.2263	−	25.5168i	−0.653865	−	0.915412i
$778$	−7.59621	−	7.59621i	−0.272337	−	0.272337i
$779$	−31.7709	+	8.51297i	−1.13831	+	0.305009i
$780$	−2.22306	−	1.34003i	−0.0795982	−	0.0479808i
$781$	−11.2305	+	6.48396i	−0.401861	+	0.232014i
$782$	−13.4968	−	23.3772i	−0.482646	−	0.835968i
$783$		−	14.4060i		−	0.514828i
$784$	3.38465	−	1.95413i	0.120880	−	0.0697903i
$785$	8.71671	+	15.7780i	0.311113	+	0.563140i
$786$	8.07214	−	13.9814i	0.287924	−	0.498698i
$787$	24.7659	−	24.7659i	0.882811	−	0.882811i	−0.111009	−	0.993819i	$-0.535408\pi$
$787$	24.7659	−	24.7659i	0.882811	−	0.882811i	0.993819	+	0.111009i	$0.0354082\pi$
$788$	−0.313324	+	0.313324i	−0.0111617	+	0.0111617i
$789$	−17.8895	−	10.3285i	−0.636883	−	0.367704i
$790$	24.6718	+	14.8719i	0.877782	+	0.529117i
$791$	−20.8855	+	20.8855i	−0.742602	+	0.742602i
$792$	25.6523	+	14.8103i	0.911513	+	0.526262i
$793$	−0.314237	+	0.0841995i	−0.0111589	+	0.00299001i
$794$	−0.727250	−	2.71413i	−0.0258091	−	0.0963210i
$795$	−57.3032	+	14.2012i	−2.03234	+	0.503664i
$796$	6.99135	−	26.0921i	0.247802	−	0.924809i
$797$	0.0906740	+	0.0523506i	0.00321184	+	0.00185435i	0.501605	−	0.865097i	$-0.332743\pi$
$797$	0.0906740	+	0.0523506i	0.00321184	+	0.00185435i	−0.498393	+	0.866951i	$0.666076\pi$
$798$	7.24170	+	27.0264i	0.256353	+	0.956724i
$799$	9.64481	+	35.9949i	0.341209	+	1.27341i
$800$	−2.66159	+	4.23272i	−0.0941013	+	0.149649i
$801$	−2.47107	−	0.662120i	−0.0873108	−	0.0233949i
$802$	−1.60152	+	0.429127i	−0.0565518	+	0.0151530i
$803$	41.1096	+	41.1096i	1.45073	+	1.45073i
$804$	10.3885			0.366375
$805$	−0.540087	+	28.6204i	−0.0190356	+	1.00874i
$806$	1.48664	−	1.48664i	0.0523647	−	0.0523647i
$807$	15.3141	−	57.1532i	0.539084	−	2.01189i
$808$	1.23852			0.0435708
$809$	0.335132	−	1.25073i	0.0117826	−	0.0439732i	−0.959784	−	0.280739i	$-0.909421\pi$
$809$	0.335132	−	1.25073i	0.0117826	−	0.0439732i	0.971567	+	0.236765i	$0.0760873\pi$
$810$	2.97191	+	11.9920i	0.104422	+	0.421354i
$811$	12.1384	+	21.0244i	0.426238	+	0.738267i	0.996535	−	0.0831721i	$-0.0265051\pi$
$811$	12.1384	+	21.0244i	0.426238	+	0.738267i	−0.570297	+	0.821439i	$0.693172\pi$
$812$	1.66422	−	2.88251i	0.0584025	−	0.101156i
$813$	−21.8901	+	21.8901i	−0.767719	+	0.767719i
$814$	−26.2011	+	18.7151i	−0.918348	+	0.655963i
$815$	0.372211	−	1.29115i	0.0130380	−	0.0452271i
$816$	−2.81342	−	10.4998i	−0.0984895	−	0.367568i
$817$	−12.1551	+	45.3635i	−0.425254	+	1.58707i
$818$	−30.9004	−	8.27974i	−1.08041	−	0.289494i
$819$	−3.76298	−	1.00829i	−0.131489	−	0.0352324i
$820$	−13.0207	−	3.75358i	−0.454703	−	0.131081i
$821$	−3.54806	−	6.14541i	−0.123828	−	0.214476i	0.797446	−	0.603390i	$-0.206184\pi$
$821$	−3.54806	−	6.14541i	−0.123828	−	0.214476i	−0.921274	+	0.388914i	$0.872850\pi$
$822$	−60.6575			−2.11567
$823$	−12.1969	+	3.26815i	−0.425158	+	0.113921i	−0.465052	−	0.885283i	$-0.653964\pi$
$823$	−12.1969	+	3.26815i	−0.425158	+	0.113921i	0.0398946	+	0.999204i	$0.487298\pi$
$824$		−	15.6859i		−	0.546445i
$825$	17.2416	+	75.6579i	0.600275	+	2.63407i
$826$	5.09267	−	8.82077i	0.177197	−	0.306914i
$827$	−14.3712	−	24.8917i	−0.499737	−	0.865570i	0.500263	−	0.865873i	$-0.333237\pi$
$827$	−14.3712	−	24.8917i	−0.499737	−	0.865570i	−1.00000		0.000303909i	$0.999903\pi$
$828$	40.7403			1.41582
$829$	9.88765	−	2.64939i	0.343412	−	0.0920171i	−0.0829907	−	0.996550i	$-0.526447\pi$
$829$	9.88765	−	2.64939i	0.343412	−	0.0920171i	0.426403	+	0.904533i	$0.359781\pi$
$830$	4.48992	+	0.0847280i	0.155847	+	0.00294095i
$831$	−63.3587	+	16.9769i	−2.19789	+	0.588923i
$832$	−0.342893	+	0.197969i	−0.0118877	+	0.00686335i
$833$	−12.5490	+	7.24519i	−0.434798	+	0.251031i
$834$	62.9144	−	16.8579i	2.17855	−	0.583740i
$835$	25.1390	+	26.1060i	0.869971	+	0.903437i
$836$	27.7511	−	7.43589i	0.959792	−	0.257176i
$837$	−40.4110			−1.39681
$838$	2.26365	+	3.92076i	0.0781965	+	0.135440i
$839$	−7.06834	+	12.2427i	−0.244026	+	0.422666i	−0.961857	−	0.273551i	$-0.911802\pi$
$839$	−7.06834	+	12.2427i	−0.244026	+	0.422666i	0.717831	+	0.696217i	$0.245135\pi$
$840$	−3.19304	+	11.0763i	−0.110170	+	0.382168i
$841$		−	25.4168i		−	0.876440i
$842$	−22.3749	+	5.99534i	−0.771090	+	0.206613i
$843$	−36.5856			−1.26008
$844$	−13.8177	−	23.9329i	−0.475624	−	0.823805i
$845$	−7.95491	+	27.5946i	−0.273657	+	0.949283i
$846$	−54.3254	−	14.5564i	−1.86775	−	0.500461i
$847$	28.9076	+	7.74578i	0.993279	+	0.266148i
$848$	−2.33073	+	8.69839i	−0.0800375	+	0.298704i
$849$	20.5532	+	76.7056i	0.705384	+	2.63253i
$850$	9.86819	−	15.6934i	0.338476	−	0.538279i
$851$	−18.3386	+	40.3106i	−0.628639	+	1.38183i
$852$	−5.07880	+	5.07880i	−0.173997	+	0.173997i
$853$	17.1775	−	29.7522i	0.588145	−	1.01870i	−0.406330	−	0.913726i	$-0.633192\pi$
$853$	17.1775	−	29.7522i	0.588145	−	1.01870i	0.994475	−	0.104971i	$-0.0334750\pi$
$854$	0.722366	+	1.25117i	0.0247189	+	0.0428143i
$855$	58.1620	+	35.0594i	1.98910	+	1.19901i
$856$	−0.801309	+	2.99053i	−0.0273882	+	0.102214i
$857$	−42.9846			−1.46833			−0.734164	−	0.678973i	$-0.762426\pi$
$857$	−42.9846			−1.46833			−0.734164	+	0.678973i	$0.762426\pi$
$858$	−1.59038	+	5.93540i	−0.0542948	+	0.202631i
$859$	−2.89013	+	2.89013i	−0.0986099	+	0.0986099i	−0.754691	−	0.656081i	$-0.772213\pi$
$859$	−2.89013	+	2.89013i	−0.0986099	+	0.0986099i	0.656081	+	0.754691i	$0.272213\pi$
$860$	−13.9372	+	13.4209i	−0.475254	+	0.457649i
$861$	−31.2413			−1.06470
$862$	5.26993	+	5.26993i	0.179494	+	0.179494i
$863$	14.5880	−	3.90885i	0.496582	−	0.133059i	−0.00183104	−	0.999998i	$-0.500583\pi$
$863$	14.5880	−	3.90885i	0.496582	−	0.133059i	0.498413	+	0.866939i	$0.333916\pi$
$864$	7.35105	+	1.96971i	0.250088	+	0.0670108i
$865$	14.4172	+	26.0964i	0.490200	+	0.887304i
$866$	1.82503	+	6.81110i	0.0620170	+	0.231451i
$867$	−2.46878	−	9.21362i	−0.0838442	−	0.312911i
$868$	−8.08586	−	4.66837i	−0.274452	−	0.158455i
$869$	17.6503	−	65.8718i	0.598746	−	2.23455i
$870$	−2.98516	−	12.0454i	−0.101206	−	0.408378i
$871$	0.363108	+	1.35514i	0.0123034	+	0.0459171i
$872$	1.91494	−	0.513107i	0.0648481	−	0.0173760i
$873$	52.1637	+	30.1167i	1.76547	+	1.01930i
$874$	27.9416	−	27.9416i	0.945138	−	0.945138i
$875$	−17.5538	+	8.85046i	−0.593428	+	0.299200i
$876$	27.8865	+	16.1003i	0.942198	+	0.543978i
$877$	−22.1626	+	22.1626i	−0.748378	+	0.748378i	−0.974175	−	0.225796i	$-0.927502\pi$
$877$	−22.1626	+	22.1626i	−0.748378	+	0.748378i	0.225796	+	0.974175i	$0.427502\pi$
$878$	1.53362	−	1.53362i	0.0517571	−	0.0517571i
$879$	31.7947	−	55.0701i	1.07241	−	1.85747i
$880$	11.3733	+	3.27867i	0.383394	+	0.110524i
$881$	−24.2620	+	14.0077i	−0.817407	+	0.471930i	−0.849521	−	0.527554i	$-0.823109\pi$
$881$	−24.2620	+	14.0077i	−0.817407	+	0.471930i	0.0321147	+	0.999484i	$0.489776\pi$
$882$		−	21.8696i		−	0.736389i
$883$	−11.3190	−	19.6051i	−0.380915	−	0.659764i	0.610278	−	0.792187i	$-0.291058\pi$
$883$	−11.3190	−	19.6051i	−0.380915	−	0.659764i	−0.991193	+	0.132423i	$0.957724\pi$
$884$	1.27132	−	0.733997i	0.0427591	−	0.0246870i
$885$	−9.13490	−	36.8602i	−0.307066	−	1.23904i
$886$	−20.5941	+	5.51818i	−0.691873	+	0.185387i
$887$	−31.2178	−	31.2178i	−1.04819	−	1.04819i	−0.998778	−	0.0494116i	$-0.984265\pi$
$887$	−31.2178	−	31.2178i	−1.04819	−	1.04819i	−0.0494116	−	0.998778i	$-0.515735\pi$
$888$	−11.3346	+	13.7684i	−0.380365	+	0.462038i
$889$		−	5.65624i		−	0.189704i
$890$	−1.02209	−	0.0192876i	−0.0342606	−	0.000646522i
$891$	25.3288	−	14.6236i	0.848548	−	0.489909i
$892$	−7.20282	+	26.8813i	−0.241168	+	0.900052i
$893$	−47.2423	+	27.2754i	−1.58090	+	0.912736i
$894$	16.5785	−	16.5785i	0.554469	−	0.554469i
$895$	15.0544	+	9.07459i	0.503212	+	0.303330i
$896$	1.24333	+	1.24333i	0.0415368	+	0.0415368i
$897$	2.18742	+	8.16355i	0.0730357	+	0.272573i
$898$	−21.8292	−	21.8292i	−0.728449	−	0.728449i
$899$	10.0515			0.335237
$900$	13.0653	+	24.7409i	0.435509	+	0.824696i
$901$	8.64148	−	32.2505i	0.287890	−	1.07442i
$902$			32.0790i			1.06811i
$903$	−22.3037	+	38.6311i	−0.742220	+	1.28556i
$904$	14.5475	+	8.39900i	0.483843	+	0.279347i
$905$	3.97285	+	4.12567i	0.132062	+	0.137142i
$906$	−40.4808	−	10.8468i	−1.34488	−	0.360360i
$907$	12.1415	+	21.0297i	0.403152	+	0.698280i	0.994104	−	0.108427i	$-0.0345813\pi$
$907$	12.1415	+	21.0297i	0.403152	+	0.698280i	−0.590952	+	0.806706i	$0.701248\pi$
$908$	−8.61717	+	14.9254i	−0.285971	+	0.495316i
$909$	3.46521	−	6.00193i	0.114934	−	0.199071i
$910$	−1.55646	−	0.0293715i	−0.0515961	−	0.000973656i
$911$	7.00677	+	7.00677i	0.232145	+	0.232145i	0.813587	−	0.581443i	$-0.197512\pi$
$911$	7.00677	+	7.00677i	0.232145	+	0.232145i	−0.581443	+	0.813587i	$0.697512\pi$
$912$	13.7808	−	7.95632i	0.456326	−	0.263460i
$913$	−2.75146	−	10.2686i	−0.0910600	−	0.339841i
$914$			6.88393i			0.227700i
$915$	5.17580	+	1.49207i	0.171107	+	0.0493262i
$916$	−6.96524	−	4.02138i	−0.230138	−	0.132870i
$917$		−	9.68230i		−	0.319738i
$918$	−27.2550	−	7.30295i	−0.899549	−	0.241033i
$919$	7.04314	+	7.04314i	0.232332	+	0.232332i	0.813665	−	0.581334i	$-0.197469\pi$
$919$	7.04314	+	7.04314i	0.232332	+	0.232332i	−0.581334	+	0.813665i	$0.697469\pi$
$920$	15.8018	−	3.91610i	0.520971	−	0.129110i
$921$	19.7149	+	34.1473i	0.649629	+	1.12519i
$922$	18.2684	+	4.89500i	0.601637	+	0.161208i
$923$	−0.840025	−	0.484989i	−0.0276498	−	0.0159636i
$924$	27.2885			0.897727
$925$	−30.3610	+	1.79075i	−0.998265	+	0.0588796i
$926$	16.4251			0.539764
$927$	−76.0150	−	43.8873i	−2.49666	−	1.44145i
$928$	−1.82844	−	0.489930i	−0.0600216	−	0.0160827i
$929$	−1.73828	−	3.01078i	−0.0570310	−	0.0987806i	0.836100	−	0.548577i	$-0.184830\pi$
$929$	−1.73828	−	3.01078i	−0.0570310	−	0.0987806i	−0.893131	+	0.449796i	$0.851497\pi$
$930$	−33.7892	+	8.37382i	−1.10799	+	0.274588i
$931$	−14.9992	−	14.9992i	−0.491579	−	0.491579i
$932$	−20.5668	−	5.51085i	−0.673687	−	0.180514i
$933$		−	23.6274i		−	0.773526i
$934$	13.5633	+	7.83079i	0.443806	+	0.256231i
$935$	−42.1680	−	12.1561i	−1.37904	−	0.397547i
$936$			2.21557i			0.0724183i
$937$	4.83161	+	18.0318i	0.157842	+	0.589074i	0.998845	+	0.0480439i	$0.0152987\pi$
$937$	4.83161	+	18.0318i	0.157842	+	0.589074i	−0.841003	+	0.541030i	$0.818035\pi$
$938$	5.39566	−	3.11518i	0.176174	−	0.101714i
$939$	3.03987	+	3.03987i	0.0992023	+	0.0992023i
$940$	−22.4703	−	0.424030i	−0.732899	−	0.0138303i
$941$	26.8917	−	46.5777i	0.876643	−	1.51839i	0.0216408	−	0.999766i	$-0.493111\pi$
$941$	26.8917	−	46.5777i	0.876643	−	1.51839i	0.855002	−	0.518624i	$-0.173556\pi$
$942$	11.8173	−	20.4682i	0.385029	−	0.666890i
$943$	22.0608	+	38.2104i	0.718397	+	1.24430i
$944$	−5.59523	−	1.49924i	−0.182109	−	0.0487960i
$945$	20.7552	+	21.5536i	0.675166	+	0.701138i
$946$	39.6670	+	22.9018i	1.28969	+	0.744601i
$947$	−11.0948	+	19.2168i	−0.360533	+	0.624461i	−0.988049	−	0.154143i	$-0.950738\pi$
$947$	−11.0948	+	19.2168i	−0.360533	+	0.624461i	0.627516	+	0.778604i	$0.284072\pi$
$948$		−	37.7713i		−	1.22675i
$949$	−1.12550	+	4.20042i	−0.0365353	+	0.136351i
$950$	25.9292	+	8.00767i	0.841254	+	0.259803i
$951$	−36.4260			−1.18119
$952$	−4.60982	−	4.60982i	−0.149405	−	0.149405i
$953$	−7.66607	−	28.6102i	−0.248328	−	0.926774i	−0.971681	−	0.236296i	$-0.924067\pi$
$953$	−7.66607	−	28.6102i	−0.248328	−	0.926774i	0.723353	−	0.690479i	$-0.242600\pi$
$954$	35.6319	+	35.6319i	1.15363	+	1.15363i
$955$	−8.74691	−	5.27254i	−0.283043	−	0.170615i
$956$	6.75018	−	6.75018i	0.218316	−	0.218316i
$957$	−25.4417	+	14.6888i	−0.822414	+	0.474821i
$958$	1.58757	−	5.92489i	0.0512920	−	0.191424i
$959$	−31.5047	+	18.1892i	−1.01734	+	0.587361i
$960$	6.55465	+	0.123691i	0.211551	+	0.00399211i
$961$			2.80400i			0.0904516i
$962$	−2.19221	−	0.997305i	−0.0706796	−	0.0321544i
$963$	12.2503	+	12.2503i	0.394761	+	0.394761i
$964$	3.86989	−	1.03693i	0.124641	−	0.0333974i
$965$	−9.44345	−	38.1053i	−0.303995	−	1.22665i
$966$	32.5042	−	18.7663i	1.04581	−	0.603797i
$967$	−26.6289	−	46.1225i	−0.856327	−	1.48320i	−0.875409	−	0.483383i	$-0.839408\pi$
$967$	−26.6289	−	46.1225i	−0.856327	−	1.48320i	0.0190824	−	0.999818i	$-0.493926\pi$
$968$		−	17.0203i		−	0.547053i
$969$	−51.0940	+	29.4991i	−1.64137	+	0.947648i
$970$	23.1275	+	6.66715i	0.742580	+	0.214069i
$971$	−19.1752	+	33.2124i	−0.615361	+	1.06584i	0.374960	+	0.927041i	$0.377657\pi$
$971$	−19.1752	+	33.2124i	−0.615361	+	1.06584i	−0.990321	+	0.138796i	$0.955677\pi$
$972$	−4.68955	+	4.68955i	−0.150417	+	0.150417i
$973$	27.6218	−	27.6218i	0.885513	−	0.885513i
$974$	−36.3688	−	20.9976i	−1.16533	−	0.672805i
$975$	−4.25608	+	3.94640i	−0.136304	+	0.126386i
$976$	0.580992	−	0.580992i	0.0185971	−	0.0185971i
$977$	19.6214	+	11.3284i	0.627744	+	0.362428i	0.779878	−	0.625932i	$-0.215281\pi$
$977$	19.6214	+	11.3284i	0.627744	+	0.362428i	−0.152134	+	0.988360i	$0.548614\pi$
$978$	−1.70182	+	0.456001i	−0.0544182	+	0.0145813i
$979$	0.626346	+	2.33756i	0.0200181	+	0.0747086i
$980$	−2.10218	−	8.48252i	−0.0671518	−	0.270964i
$981$	2.87122	−	10.7155i	0.0916711	−	0.342121i
$982$	−1.06896	−	0.617167i	−0.0341120	−	0.0196946i
$983$	−8.67568	−	32.3781i	−0.276711	−	1.03270i	−0.954686	−	0.297615i	$-0.903809\pi$
$983$	−8.67568	−	32.3781i	−0.276711	−	1.03270i	0.677975	−	0.735085i	$-0.262858\pi$
$984$	4.59857	+	17.1621i	0.146597	+	0.547108i
$985$	0.479131	+	0.867267i	0.0152664	+	0.0276334i
$986$	6.77920	+	1.81648i	0.215894	+	0.0578485i
$987$	−50.0482	+	13.4104i	−1.59305	+	0.426857i
$988$	1.51954	+	1.51954i	0.0483431	+	0.0483431i
$989$	62.9983			2.00323
$990$	47.7097	−	45.9424i	1.51631	−	1.46015i
$991$	22.5979	−	22.5979i	0.717847	−	0.717847i	−0.250317	−	0.968164i	$-0.580535\pi$
$991$	22.5979	−	22.5979i	0.717847	−	0.717847i	0.968164	+	0.250317i	$0.0805347\pi$
$992$	−1.37433	+	5.12906i	−0.0436349	+	0.162848i
$993$	6.46609			0.205195
$994$	−1.11489	+	4.16083i	−0.0353622	+	0.131973i
$995$	−51.7304	−	31.1825i	−1.63996	−	0.988551i
$996$	−2.94403	−	5.09921i	−0.0932852	−	0.161575i
$997$	−15.0881	+	26.1333i	−0.477845	+	0.827651i	−0.999677	−	0.0253965i	$-0.991915\pi$
$997$	−15.0881	+	26.1333i	−0.477845	+	0.827651i	0.521833	+	0.853048i	$0.325249\pi$
$998$	−27.2645	+	27.2645i	−0.863041	+	0.863041i
$999$	16.2403	+	43.3498i	0.513821	+	1.37153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.e.23.2	yes	16
5.2	odd	4		370.2.q.e.97.1	✓	16
37.29	odd	12		370.2.q.e.103.1	yes	16
185.177	even	12	inner	370.2.r.e.177.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.97.1	✓	16	5.2	odd	4
370.2.q.e.103.1	yes	16	37.29	odd	12
370.2.r.e.23.2	yes	16	1.1	even	1	trivial
370.2.r.e.177.2	yes	16	185.177	even	12	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-2.83195 - 0.758819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17041 - 0.537883i) q^{5} +(-2.07313 - 2.07313i) q^{6} +(-1.69842 - 0.455091i) q^{7} +1.00000i q^{8} +(4.84607 + 2.79788i) q^{9} +(2.14857 + 0.619385i) q^{10} -5.29342i q^{11} +(-0.758819 - 2.83195i) q^{12} +(0.342893 - 0.197969i) q^{13} +(-1.24333 - 1.24333i) q^{14} +(-6.55465 - 0.123691i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.85382 - 3.21090i) q^{17} +(2.79788 + 4.84607i) q^{18} +(5.24257 + 1.40474i) q^{19} +(1.55103 + 1.61069i) q^{20} +(4.46452 + 2.57759i) q^{21} +(2.64671 - 4.58424i) q^{22} -7.28057i q^{23} +(0.758819 - 2.83195i) q^{24} +(4.42136 - 2.33485i) q^{25} +0.395938 q^{26} +(-5.38134 - 5.38134i) q^{27} +(-0.455091 - 1.69842i) q^{28} +(1.33851 + 1.33851i) q^{29} +(-5.61465 - 3.38445i) q^{30} +(3.75473 - 3.75473i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.01675 + 14.9907i) q^{33} +(3.21090 - 1.85382i) q^{34} +(-3.93106 - 0.0741820i) q^{35} +5.59575i q^{36} +(-5.53674 - 2.51884i) q^{37} +(3.83783 + 3.83783i) q^{38} +(-1.12128 + 0.300446i) q^{39} +(0.537883 + 2.17041i) q^{40} +(-5.24826 + 3.03009i) q^{41} +(2.57759 + 4.46452i) q^{42} +8.65292i q^{43} +(4.58424 - 2.64671i) q^{44} +(12.0229 + 3.46593i) q^{45} +(3.64029 - 6.30516i) q^{46} +(-7.10699 + 7.10699i) q^{47} +(2.07313 - 2.07313i) q^{48} +(-3.38465 - 1.95413i) q^{49} +(4.99644 + 0.188640i) q^{50} +(-7.68641 + 7.68641i) q^{51} +(0.342893 + 0.197969i) q^{52} +(8.69839 - 2.33073i) q^{53} +(-1.96971 - 7.35105i) q^{54} +(-2.84724 - 11.4889i) q^{55} +(0.455091 - 1.69842i) q^{56} +(-13.7808 - 7.95632i) q^{57} +(0.489930 + 1.82844i) q^{58} +(1.49924 + 5.59523i) q^{59} +(-3.17021 - 5.73834i) q^{60} +(-0.793650 - 0.212658i) q^{61} +(5.12906 - 1.37433i) q^{62} +(-6.95738 - 6.95738i) q^{63} -1.00000 q^{64} +(0.637734 - 0.614111i) q^{65} +(-10.9740 + 10.9740i) q^{66} +(-0.917081 + 3.42259i) q^{67} +3.70763 q^{68} +(-5.52464 + 20.6182i) q^{69} +(-3.36731 - 2.02977i) q^{70} +(-1.22491 - 2.12161i) q^{71} +(-2.79788 + 4.84607i) q^{72} +(-7.76616 + 7.76616i) q^{73} +(-3.53553 - 4.94975i) q^{74} +(-14.2928 + 3.25717i) q^{75} +(1.40474 + 5.24257i) q^{76} +(-2.40899 + 8.99046i) q^{77} +(-1.12128 - 0.300446i) q^{78} +(12.4441 + 3.33439i) q^{79} +(-0.619385 + 2.14857i) q^{80} +(2.76260 + 4.78497i) q^{81} -6.06017 q^{82} +(1.93988 - 0.519789i) q^{83} +5.15518i q^{84} +(2.29645 - 7.96612i) q^{85} +(-4.32646 + 7.49365i) q^{86} +(-2.77491 - 4.80629i) q^{87} +5.29342 q^{88} +(-0.441597 + 0.118325i) q^{89} +(8.67916 + 9.01302i) q^{90} +(-0.672471 + 0.180188i) q^{91} +(6.30516 - 3.64029i) q^{92} +(-13.4824 + 7.78405i) q^{93} +(-9.70832 + 2.60134i) q^{94} +(12.1341 + 0.228980i) q^{95} +(2.83195 - 0.758819i) q^{96} +10.7641 q^{97} +(-1.95413 - 3.38465i) q^{98} +(14.8103 - 25.6523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

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