LMFDB - Embedded newform 740.2.be.a.251.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(51,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			251.4
Character	$\chi$	$=$	740.251
Dual form			740.2.be.a.171.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41314 + 0.0551022i) q^{2} +(0.149741 - 0.259359i) q^{3} +(1.99393 - 0.155734i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-0.197314 + 0.374762i) q^{6} +(1.02790 + 0.593457i) q^{7} +(-2.80912 + 0.329944i) q^{8} +(1.45516 + 2.52040i) q^{9} +(0.418972 + 1.35073i) q^{10} -6.42954 q^{11} +(0.258182 - 0.540463i) q^{12} +(0.502065 + 1.87373i) q^{13} +(-1.48526 - 0.781998i) q^{14} +(-0.289278 - 0.0775117i) q^{15} +(3.95149 - 0.621045i) q^{16} +(-7.21119 - 1.93223i) q^{17} +(-2.19522 - 3.48150i) q^{18} +(-1.42528 + 0.381903i) q^{19} +(-0.666494 - 1.88568i) q^{20} +(0.307837 - 0.177730i) q^{21} +(9.08584 - 0.354282i) q^{22} +(-2.99709 - 2.99709i) q^{23} +(-0.335066 + 0.777976i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.812735 - 2.62018i) q^{26} +1.77003 q^{27} +(2.14198 + 1.02323i) q^{28} +(3.40677 + 3.40677i) q^{29} +(0.413061 + 0.0935950i) q^{30} +(-2.04373 + 2.04373i) q^{31} +(-5.54979 + 1.09536i) q^{32} +(-0.962767 + 1.66756i) q^{33} +(10.2969 + 2.33316i) q^{34} +(0.307196 - 1.14647i) q^{35} +(3.29399 + 4.79888i) q^{36} +(-4.59319 + 3.98781i) q^{37} +(1.99308 - 0.618218i) q^{38} +(0.561149 + 0.150360i) q^{39} +(1.04575 + 2.62800i) q^{40} +(5.05443 + 2.91817i) q^{41} +(-0.425223 + 0.268120i) q^{42} +(-3.13663 - 3.13663i) q^{43} +(-12.8200 + 1.00130i) q^{44} +(2.05790 - 2.05790i) q^{45} +(4.40045 + 4.07016i) q^{46} -4.87415i q^{47} +(0.430627 - 1.11785i) q^{48} +(-2.79562 - 4.84215i) q^{49} +(1.19626 - 0.754290i) q^{50} +(-1.58095 + 1.58095i) q^{51} +(1.29289 + 3.65790i) q^{52} +(-2.55145 - 4.41924i) q^{53} +(-2.50130 + 0.0975327i) q^{54} +(1.66409 + 6.21046i) q^{55} +(-3.08329 - 1.32794i) q^{56} +(-0.114373 + 0.426846i) q^{57} +(-5.00196 - 4.62652i) q^{58} +(-2.89540 + 10.8058i) q^{59} +(-0.588870 - 0.109502i) q^{60} +(-4.51374 + 1.20945i) q^{61} +(2.77546 - 3.00069i) q^{62} +3.45429i q^{63} +(7.78227 - 1.85370i) q^{64} +(1.67994 - 0.969915i) q^{65} +(1.26864 - 2.40955i) q^{66} +(-5.64462 + 9.77678i) q^{67} +(-14.6795 - 2.72970i) q^{68} +(-1.22611 + 0.328535i) q^{69} +(-0.370938 + 1.63705i) q^{70} +(14.0212 + 8.09513i) q^{71} +(-4.91929 - 6.59999i) q^{72} -15.2007i q^{73} +(6.27108 - 5.88843i) q^{74} +0.299482i q^{75} +(-2.78243 + 0.983451i) q^{76} +(-6.60892 - 3.81566i) q^{77} +(-0.801268 - 0.181558i) q^{78} +(-7.62925 + 2.04425i) q^{79} +(-1.62261 - 3.65611i) q^{80} +(-4.10042 + 7.10213i) q^{81} +(-7.30341 - 3.84528i) q^{82} +(-12.9236 + 7.46145i) q^{83} +(0.586126 - 0.402321i) q^{84} +7.46558i q^{85} +(4.60533 + 4.25966i) q^{86} +(1.39371 - 0.373443i) q^{87} +(18.0613 - 2.12139i) q^{88} +(1.45843 - 5.44295i) q^{89} +(-2.79471 + 3.02150i) q^{90} +(-0.595908 + 2.22396i) q^{91} +(-6.44273 - 5.50923i) q^{92} +(0.224030 + 0.836091i) q^{93} +(0.268576 + 6.88786i) q^{94} +(0.737779 + 1.27787i) q^{95} +(-0.546940 + 1.60341i) q^{96} +(-1.27664 + 1.27664i) q^{97} +(4.21741 + 6.68859i) q^{98} +(-9.35599 - 16.2050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−1.41314	+	0.0551022i	−0.999241	+	0.0389631i
$2$	−1.41314	+	0.0551022i	−0.999241	+	0.0389631i
$3$	0.149741	−	0.259359i	0.0864531	−	0.149741i	−0.819556	−	0.572999i	$-0.805780\pi$
$3$	0.149741	−	0.259359i	0.0864531	−	0.149741i	0.906009	+	0.423257i	$0.139113\pi$
$4$	1.99393	−	0.155734i	0.996964	−	0.0778671i
$5$	−0.258819	−	0.965926i	−0.115747	−	0.431975i
$5$	−0.258819	−	0.965926i	−0.115747	−	0.431975i
$6$	−0.197314	+	0.374762i	−0.0805530	+	0.152996i
$7$	1.02790	+	0.593457i	0.388509	+	0.224306i	0.681514	−	0.731805i	$-0.261322\pi$
$7$	1.02790	+	0.593457i	0.388509	+	0.224306i	−0.293005	+	0.956111i	$0.594655\pi$
$8$	−2.80912	+	0.329944i	−0.993173	+	0.116653i
$9$	1.45516	+	2.52040i	0.485052	+	0.840134i
$10$	0.418972	+	1.35073i	0.132491	+	0.427137i
$11$	−6.42954			−1.93858			−0.969290	−	0.245919i	$-0.920910\pi$
$11$	−6.42954			−1.93858			−0.969290	+	0.245919i	$0.920910\pi$
$12$	0.258182	−	0.540463i	0.0745307	−	0.156018i
$13$	0.502065	+	1.87373i	0.139248	+	0.519680i	0.999944	+	0.0105613i	$0.00336184\pi$
$13$	0.502065	+	1.87373i	0.139248	+	0.519680i	−0.860696	+	0.509119i	$0.829971\pi$
$14$	−1.48526	−	0.781998i	−0.396954	−	0.208998i
$15$	−0.289278	−	0.0775117i	−0.0746911	−	0.0200134i
$16$	3.95149	−	0.621045i	0.987873	−	0.155261i
$17$	−7.21119	−	1.93223i	−1.74897	−	0.468635i	−0.764565	−	0.644546i	$-0.777046\pi$
$17$	−7.21119	−	1.93223i	−1.74897	−	0.468635i	−0.984406	+	0.175911i	$0.943713\pi$
$18$	−2.19522	−	3.48150i	−0.517418	−	0.820597i
$19$	−1.42528	+	0.381903i	−0.326982	+	0.0876145i	−0.418576	−	0.908182i	$-0.637470\pi$
$19$	−1.42528	+	0.381903i	−0.326982	+	0.0876145i	0.0915939	+	0.995796i	$0.470804\pi$
$20$	−0.666494	−	1.88568i	−0.149033	−	0.421651i
$21$	0.307837	−	0.177730i	0.0671756	−	0.0387838i
$22$	9.08584	−	0.354282i	1.93711	−	0.0755332i
$23$	−2.99709	−	2.99709i	−0.624936	−	0.624936i	0.321853	−	0.946790i	$-0.395694\pi$
$23$	−2.99709	−	2.99709i	−0.624936	−	0.624936i	−0.946790	+	0.321853i	$0.895694\pi$
$24$	−0.335066	+	0.777976i	−0.0683951	+	0.158804i
$25$	−0.866025	+	0.500000i	−0.173205	+	0.100000i
$26$	−0.812735	−	2.62018i	−0.159390	−	0.513860i
$27$	1.77003			0.340643
$28$	2.14198	+	1.02323i	0.404795	+	0.193373i
$29$	3.40677	+	3.40677i	0.632621	+	0.632621i	0.948725	−	0.316104i	$-0.102375\pi$
$29$	3.40677	+	3.40677i	0.632621	+	0.632621i	−0.316104	+	0.948725i	$0.602375\pi$
$30$	0.413061	+	0.0935950i	0.0754142	+	0.0170880i
$31$	−2.04373	+	2.04373i	−0.367065	+	0.367065i	−0.866406	−	0.499341i	$-0.833576\pi$
$31$	−2.04373	+	2.04373i	−0.367065	+	0.367065i	0.499341	+	0.866406i	$0.333576\pi$
$32$	−5.54979	+	1.09536i	−0.981074	+	0.193634i
$33$	−0.962767	+	1.66756i	−0.167596	+	0.290285i
$34$	10.2969	+	2.33316i	1.76590	+	0.400134i
$35$	0.307196	−	1.14647i	0.0519256	−	0.193789i
$36$	3.29399	+	4.79888i	0.548998	+	0.799814i
$37$	−4.59319	+	3.98781i	−0.755115	+	0.655592i
$37$	−4.59319	+	3.98781i	−0.755115	+	0.655592i
$38$	1.99308	−	0.618218i	0.323320	−	0.100288i
$39$	0.561149	+	0.150360i	0.0898558	+	0.0240768i
$40$	1.04575	+	2.62800i	0.165348	+	0.415524i
$41$	5.05443	+	2.91817i	0.789369	+	0.455742i	0.839740	−	0.542988i	$-0.182707\pi$
$41$	5.05443	+	2.91817i	0.789369	+	0.455742i	−0.0503715	+	0.998731i	$0.516041\pi$
$42$	−0.425223	+	0.268120i	−0.0656134	+	0.0413717i
$43$	−3.13663	−	3.13663i	−0.478331	−	0.478331i	0.426267	−	0.904598i	$-0.359829\pi$
$43$	−3.13663	−	3.13663i	−0.478331	−	0.478331i	−0.904598	+	0.426267i	$0.859829\pi$
$44$	−12.8200	+	1.00130i	−1.93269	+	0.150952i
$45$	2.05790	−	2.05790i	0.306774	−	0.306774i
$46$	4.40045	+	4.07016i	0.648811	+	0.600112i
$47$		−	4.87415i		−	0.710968i	−0.934682	−	0.355484i	$-0.884316\pi$
$47$		−	4.87415i		−	0.710968i	0.934682	−	0.355484i	$-0.115684\pi$
$48$	0.430627	−	1.11785i	0.0621557	−	0.161348i
$49$	−2.79562	−	4.84215i	−0.399374	−	0.691736i
$50$	1.19626	−	0.754290i	0.169177	−	0.106673i
$51$	−1.58095	+	1.58095i	−0.221378	+	0.221378i
$52$	1.29289	+	3.65790i	0.179291	+	0.507259i
$53$	−2.55145	−	4.41924i	−0.350469	−	0.607030i	0.635863	−	0.771802i	$-0.280644\pi$
$53$	−2.55145	−	4.41924i	−0.350469	−	0.607030i	−0.986332	+	0.164772i	$0.947311\pi$
$54$	−2.50130	+	0.0975327i	−0.340384	+	0.0132725i
$55$	1.66409	+	6.21046i	0.224386	+	0.837419i
$56$	−3.08329	−	1.32794i	−0.412022	−	0.177454i
$57$	−0.114373	+	0.426846i	−0.0151491	+	0.0565371i
$58$	−5.00196	−	4.62652i	−0.656789	−	0.607491i
$59$	−2.89540	+	10.8058i	−0.376949	+	1.40679i	0.473528	+	0.880779i	$0.342980\pi$
$59$	−2.89540	+	10.8058i	−0.376949	+	1.40679i	−0.850477	+	0.526013i	$0.823686\pi$
$60$	−0.588870	−	0.109502i	−0.0760227	−	0.0141367i
$61$	−4.51374	+	1.20945i	−0.577925	+	0.154855i	−0.535929	−	0.844263i	$-0.680038\pi$
$61$	−4.51374	+	1.20945i	−0.577925	+	0.154855i	−0.0419964	+	0.999118i	$0.513372\pi$
$62$	2.77546	−	3.00069i	0.352484	−	0.381088i
$63$			3.45429i			0.435199i
$64$	7.78227	−	1.85370i	0.972784	−	0.231713i
$65$	1.67994	−	0.969915i	0.208371	−	0.120303i
$66$	1.26864	−	2.40955i	0.156159	−	0.296595i
$67$	−5.64462	+	9.77678i	−0.689601	+	1.19442i	0.282366	+	0.959307i	$0.408881\pi$
$67$	−5.64462	+	9.77678i	−0.689601	+	1.19442i	−0.971967	+	0.235117i	$0.924453\pi$
$68$	−14.6795	−	2.72970i	−1.78015	−	0.331025i
$69$	−1.22611	+	0.328535i	−0.147606	+	0.0395510i
$70$	−0.370938	+	1.63705i	−0.0443355	+	0.195665i
$71$	14.0212	+	8.09513i	1.66401	+	0.960715i	0.970772	+	0.240004i	$0.0771489\pi$
$71$	14.0212	+	8.09513i	1.66401	+	0.960715i	0.693236	+	0.720711i	$0.256184\pi$
$72$	−4.91929	−	6.59999i	−0.579744	−	0.777816i
$73$		−	15.2007i		−	1.77911i	−0.456832	−	0.889553i	$-0.651016\pi$
$73$		−	15.2007i		−	1.77911i	0.456832	−	0.889553i	$-0.348984\pi$
$74$	6.27108	−	5.88843i	0.728998	−	0.684516i
$75$			0.299482i			0.0345812i
$76$	−2.78243	+	0.983451i	−0.319167	+	0.112810i
$77$	−6.60892	−	3.81566i	−0.753156	−	0.434835i
$78$	−0.801268	−	0.181558i	−0.0907257	−	0.0205574i
$79$	−7.62925	+	2.04425i	−0.858357	+	0.229996i	−0.661047	−	0.750345i	$-0.729887\pi$
$79$	−7.62925	+	2.04425i	−0.858357	+	0.229996i	−0.197311	+	0.980341i	$0.563221\pi$
$80$	−1.62261	−	3.65611i	−0.181413	−	0.408766i
$81$	−4.10042	+	7.10213i	−0.455602	+	0.789126i
$82$	−7.30341	−	3.84528i	−0.806527	−	0.424640i
$83$	−12.9236	+	7.46145i	−1.41855	+	0.819001i	−0.996172	−	0.0874182i	$-0.972138\pi$
$83$	−12.9236	+	7.46145i	−1.41855	+	0.819001i	−0.422379	+	0.906419i	$0.638805\pi$
$84$	0.586126	−	0.402321i	0.0639516	−	0.0438968i
$85$			7.46558i			0.809756i
$86$	4.60533	+	4.25966i	0.496605	+	0.459330i
$87$	1.39371	−	0.373443i	0.149421	−	0.0400373i
$88$	18.0613	−	2.12139i	1.92535	−	0.226141i
$89$	1.45843	−	5.44295i	0.154594	−	0.576952i	−0.844546	−	0.535483i	$-0.820130\pi$
$89$	1.45843	−	5.44295i	0.154594	−	0.576952i	0.999140	−	0.0414688i	$-0.0132037\pi$
$90$	−2.79471	+	3.02150i	−0.294588	+	0.318494i
$91$	−0.595908	+	2.22396i	−0.0624681	+	0.233134i
$92$	−6.44273	−	5.50923i	−0.671701	−	0.574377i
$93$	0.224030	+	0.836091i	0.0232308	+	0.0866986i
$94$	0.268576	+	6.88786i	0.0277015	+	0.710428i
$95$	0.737779	+	1.27787i	0.0756945	+	0.131107i
$96$	−0.546940	+	1.60341i	−0.0558218	+	0.163647i
$97$	−1.27664	+	1.27664i	−0.129623	+	0.129623i	−0.768942	−	0.639319i	$-0.779216\pi$
$97$	−1.27664	+	1.27664i	−0.129623	+	0.129623i	0.639319	+	0.768942i	$0.279216\pi$
$98$	4.21741	+	6.68859i	0.426023	+	0.675650i
$99$	−9.35599	−	16.2050i	−0.940312	−	1.62867i
$100$	−1.64892	+	1.13183i	−0.164892	+	0.113183i
$101$			2.62820i			0.261516i	0.991414	+	0.130758i	$0.0417411\pi$
$101$			2.62820i			0.261516i	−0.991414	+	0.130758i	$0.958259\pi$
$102$	2.14700	−	2.32122i	0.212584	−	0.229835i
$103$	−0.880891	+	0.880891i	−0.0867968	+	0.0867968i	−0.749172	−	0.662375i	$-0.769548\pi$
$103$	−0.880891	+	0.880891i	−0.0867968	+	0.0867968i	0.662375	+	0.749172i	$0.269548\pi$
$104$	−2.02859	−	5.09788i	−0.198919	−	0.499888i
$105$	−0.251348	−	0.251348i	−0.0245290	−	0.0245290i
$106$	3.84907	+	6.10442i	0.373855	+	0.592914i
$107$	6.62506	+	3.82498i	0.640469	+	0.369775i	0.784795	−	0.619755i	$-0.212768\pi$
$107$	6.62506	+	3.82498i	0.640469	+	0.369775i	−0.144326	+	0.989530i	$0.546101\pi$
$108$	3.52932	−	0.275655i	0.339609	−	0.0265249i
$109$	−12.5358	−	3.35896i	−1.20071	−	0.321730i	−0.397601	−	0.917558i	$-0.630157\pi$
$109$	−12.5358	−	3.35896i	−1.20071	−	0.321730i	−0.803112	+	0.595828i	$0.796824\pi$
$110$	−2.69380	−	8.68456i	−0.256844	−	0.828040i
$111$	0.346487	+	1.78842i	0.0328871	+	0.169750i
$112$	4.43030	+	1.70667i	0.418624	+	0.161265i
$113$	−1.16647	+	4.35331i	−0.109732	+	0.409525i	−0.998839	−	0.0481741i	$-0.984660\pi$
$113$	−1.16647	+	4.35331i	−0.109732	+	0.409525i	0.889107	+	0.457699i	$0.151326\pi$
$114$	0.138105	−	0.609495i	0.0129347	−	0.0570844i
$115$	−2.11926	+	3.67067i	−0.197622	+	0.342292i
$116$	7.32340	+	6.26230i	0.679960	+	0.581440i
$117$	−3.99198	+	3.99198i	−0.369058	+	0.369058i
$118$	3.49618	−	15.4296i	0.321849	−	1.42041i
$119$	−6.26567	−	6.26567i	−0.574373	−	0.574373i
$120$	0.838189	+	0.122294i	0.0765158	+	0.0111639i
$121$	30.3390			2.75809
$122$	6.31190	−	1.95784i	0.571453	−	0.177255i
$123$	1.51371	−	0.873941i	0.136487	−	0.0788006i
$124$	−3.75677	+	4.39333i	−0.337368	+	0.394533i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.190339	−	4.88139i	−0.0169567	−	0.434869i
$127$	4.19635	−	2.42276i	0.372366	−	0.214985i	−0.302126	−	0.953268i	$-0.597696\pi$
$127$	4.19635	−	2.42276i	0.372366	−	0.214985i	0.674491	+	0.738283i	$0.264363\pi$
$128$	−10.8953	+	3.04836i	−0.963017	+	0.269440i
$129$	−1.28319	+	0.343831i	−0.112979	+	0.0302726i
$130$	−2.32055	+	1.46319i	−0.203526	+	0.128331i
$131$	8.53305	+	2.28642i	0.745536	+	0.199766i	0.611537	−	0.791216i	$-0.290552\pi$
$131$	8.53305	+	2.28642i	0.745536	+	0.199766i	0.133999	+	0.990982i	$0.457218\pi$
$132$	−1.65999	+	3.47493i	−0.144484	+	0.302454i
$133$	−1.69168	−	0.453286i	−0.146688	−	0.0393048i
$134$	7.43792	−	14.1270i	0.642539	−	1.22039i
$135$	−0.458118	−	1.70972i	−0.0394285	−	0.147149i
$136$	20.8946	+	3.04858i	1.79170	+	0.261414i
$137$	16.4469			1.40516			0.702578	−	0.711607i	$-0.252032\pi$
$137$	16.4469			1.40516			0.702578	+	0.711607i	$0.252032\pi$
$138$	1.71456	−	0.531828i	0.145953	−	0.0452722i
$139$	0.0345084	+	0.0597704i	0.00292697	+	0.00506966i	0.867485	−	0.497463i	$-0.165735\pi$
$139$	0.0345084	+	0.0597704i	0.00292697	+	0.00506966i	−0.864558	+	0.502533i	$0.832402\pi$
$140$	0.433982	−	2.33382i	0.0366782	−	0.197244i
$141$	−1.26416	−	0.729861i	−0.106461	−	0.0614654i
$142$	−20.2599	−	10.6670i	−1.70018	−	0.895151i
$143$	−3.22805	−	12.0472i	−0.269943	−	1.00744i
$144$	7.31532	+	9.05564i	0.609610	+	0.754637i
$145$	2.40895	−	4.17242i	0.200052	−	0.346501i
$146$	0.837591	+	21.4807i	0.0693196	+	1.77776i
$147$	−1.67448			−0.138108
$148$	−8.53744	+	8.66672i	−0.701773	+	0.712400i
$149$	−16.8682			−1.38189			−0.690947	−	0.722906i	$-0.742806\pi$
$149$	−16.8682			−1.38189			−0.690947	+	0.722906i	$0.742806\pi$
$150$	−0.0165021	−	0.423210i	−0.00134739	−	0.0345550i
$151$	−6.13307	+	10.6228i	−0.499102	+	0.864471i	−0.999999	−	0.00103622i	$-0.999670\pi$
$151$	−6.13307	+	10.6228i	−0.499102	+	0.864471i	0.500897	+	0.865507i	$0.333003\pi$
$152$	3.87777	−	1.54307i	0.314529	−	0.125160i
$153$	−5.62340	−	20.9868i	−0.454625	−	1.69668i
$154$	9.54957	+	5.02789i	0.769526	+	0.405159i
$155$	2.50305	+	1.44514i	0.201050	+	0.116076i
$156$	1.14231	+	0.212416i	0.0914578	+	0.0170069i
$157$	6.91226	+	11.9724i	0.551658	+	0.955500i	0.998155	+	0.0607147i	$0.0193380\pi$
$157$	6.91226	+	11.9724i	0.551658	+	0.955500i	−0.446497	+	0.894785i	$0.647329\pi$
$158$	10.6685	−	3.30920i	0.848744	−	0.263266i
$159$	−1.52823			−0.121196
$160$	2.49443	+	5.07719i	0.197202	+	0.401387i
$161$	−1.30206	−	4.85935i	−0.102617	−	0.382970i
$162$	5.40312	−	10.2622i	0.424509	−	0.806278i
$163$	1.59123	+	0.426369i	0.124635	+	0.0333958i	0.320597	−	0.947216i	$-0.396116\pi$
$163$	1.59123	+	0.426369i	0.124635	+	0.0333958i	−0.195962	+	0.980611i	$0.562783\pi$
$164$	10.5326	+	5.03148i	0.822459	+	0.392893i
$165$	1.85992	+	0.498365i	0.144795	+	0.0387977i
$166$	17.8517	−	11.2562i	1.38556	−	0.873650i
$167$	4.31364	−	1.15584i	0.333799	−	0.0894412i	−0.0880266	−	0.996118i	$-0.528056\pi$
$167$	4.31364	−	1.15584i	0.333799	−	0.0894412i	0.421826	+	0.906677i	$0.361389\pi$
$168$	−0.806109	+	0.600833i	−0.0621927	+	0.0463553i
$169$	7.99953	−	4.61853i	0.615348	−	0.355271i
$170$	−0.411370	−	10.5499i	−0.0315506	−	0.809141i
$171$	−3.03655	−	3.03655i	−0.232211	−	0.232211i
$172$	−6.74268	−	5.76572i	−0.514125	−	0.439632i
$173$	1.85751	−	1.07244i	0.141224	−	0.0815358i	−0.427723	−	0.903910i	$-0.640684\pi$
$173$	1.85751	−	1.07244i	0.141224	−	0.0815358i	0.568947	+	0.822374i	$0.307351\pi$
$174$	−1.94893	+	0.604524i	−0.147748	+	0.0458288i
$175$	−1.18691			−0.0897223
$176$	−25.4063	+	3.99304i	−1.91507	+	0.300987i
$177$	2.36902	+	2.36902i	0.178066	+	0.178066i
$178$	−1.76105	+	7.77201i	−0.131996	+	0.582537i
$179$	9.03287	−	9.03287i	0.675149	−	0.675149i	−0.283750	−	0.958898i	$-0.591579\pi$
$179$	9.03287	−	9.03287i	0.675149	−	0.675149i	0.958898	+	0.283750i	$0.0915785\pi$
$180$	3.78282	−	4.42379i	0.281955	−	0.329730i
$181$	5.71173	−	9.89301i	0.424550	−	0.735342i	−0.571828	−	0.820373i	$-0.693766\pi$
$181$	5.71173	−	9.89301i	0.424550	−	0.735342i	0.996378	+	0.0850314i	$0.0270990\pi$
$182$	0.719556	−	3.17560i	0.0533371	−	0.235391i
$183$	−0.362210	+	1.35178i	−0.0267753	+	0.0999268i
$184$	9.40805	+	7.43030i	0.693571	+	0.547769i
$185$	5.04073	+	3.40456i	0.370602	+	0.250308i
$186$	−0.362656	−	1.16917i	−0.0265912	−	0.0857276i
$187$	46.3647	+	12.4234i	3.39052	+	0.908488i
$188$	−0.759072	−	9.71870i	−0.0553610	−	0.708809i
$189$	1.81941	+	1.05044i	0.132343	+	0.0764081i
$190$	−1.11300	−	1.76516i	−0.0807454	−	0.128058i
$191$	−8.69125	−	8.69125i	−0.628877	−	0.628877i	0.318909	−	0.947785i	$-0.396684\pi$
$191$	−8.69125	−	8.69125i	−0.628877	−	0.628877i	−0.947785	+	0.318909i	$0.896684\pi$
$192$	0.684551	−	2.29598i	0.0494032	−	0.165698i
$193$	6.64802	−	6.64802i	0.478535	−	0.478535i	−0.426128	−	0.904663i	$-0.640123\pi$
$193$	6.64802	−	6.64802i	0.478535	−	0.478535i	0.904663	+	0.426128i	$0.140123\pi$
$194$	1.73372	−	1.87441i	0.124474	−	0.134575i
$195$		−	0.580945i		−	0.0416023i
$196$	−6.32835	−	9.21953i	−0.452025	−	0.658538i
$197$	−5.87888	−	10.1825i	−0.418853	−	0.725475i	0.576971	−	0.816764i	$-0.304234\pi$
$197$	−5.87888	−	10.1825i	−0.418853	−	0.725475i	−0.995824	+	0.0912898i	$0.970901\pi$
$198$	14.1142	+	22.3845i	1.00306	+	1.59079i
$199$	9.83905	−	9.83905i	0.697472	−	0.697472i	−0.266393	−	0.963865i	$-0.585832\pi$
$199$	9.83905	−	9.83905i	0.697472	−	0.697472i	0.963865	+	0.266393i	$0.0858319\pi$
$200$	2.26779	−	1.69030i	0.160357	−	0.119522i
$201$	1.69046	+	2.92797i	0.119236	+	0.206523i
$202$	−0.144820	−	3.71402i	−0.0101895	−	0.261317i
$203$	1.48004	+	5.52358i	0.103878	+	0.387679i
$204$	−2.90610	+	3.39852i	−0.203468	+	0.237944i
$205$	1.51056	−	5.63748i	0.105502	−	0.393739i
$206$	1.19628	−	1.29336i	0.0833490	−	0.0901127i
$207$	3.19264	−	11.9151i	0.221904	−	0.828157i
$208$	3.14758	+	7.09224i	0.218245	+	0.491758i
$209$	9.16390	−	2.45546i	0.633880	−	0.169848i
$210$	0.369040	+	0.341340i	0.0254661	+	0.0235547i
$211$		−	9.24796i		−	0.636656i	−0.947981	−	0.318328i	$-0.896879\pi$
$211$		−	9.24796i		−	0.636656i	0.947981	−	0.318328i	$-0.103121\pi$
$212$	−5.77564	−	8.41431i	−0.396672	−	0.577897i
$213$	4.19909	−	2.42435i	0.287717	−	0.166114i
$214$	−9.57291	−	5.04018i	−0.654390	−	0.344540i
$215$	−2.21793	+	3.84157i	−0.151262	+	0.261993i
$216$	−4.97223	+	0.584012i	−0.338317	+	0.0397370i
$217$	−3.31361	+	0.887880i	−0.224943	+	0.0602732i
$218$	17.8999	+	4.05593i	1.21234	+	0.274702i
$219$	−3.94244	−	2.27617i	−0.266405	−	0.153809i
$220$	4.28525	+	12.1241i	0.288912	+	0.817404i
$221$		−	14.4820i		−	0.974162i
$222$	−0.588181	−	2.50820i	−0.0394761	−	0.168339i
$223$			8.60273i			0.576081i	0.957618	+	0.288041i	$0.0930038\pi$
$223$			8.60273i			0.576081i	−0.957618	+	0.288041i	$0.906996\pi$
$224$	−6.35467	−	2.16765i	−0.424589	−	0.144832i
$225$	−2.52040	−	1.45516i	−0.168027	−	0.0970103i
$226$	1.40850	−	6.21612i	0.0936923	−	0.413490i
$227$	7.84235	−	2.10135i	0.520515	−	0.139472i	0.0110101	−	0.999939i	$-0.496495\pi$
$227$	7.84235	−	2.10135i	0.520515	−	0.139472i	0.509505	+	0.860468i	$0.329829\pi$
$228$	−0.161577	+	0.868912i	−0.0107007	+	0.0575451i
$229$	7.84252	−	13.5836i	0.518248	−	0.897632i	−0.481527	−	0.876431i	$-0.659918\pi$
$229$	7.84252	−	13.5836i	0.518248	−	0.897632i	0.999775	−	0.0212010i	$-0.00674898\pi$
$230$	2.79255	−	5.30395i	0.184135	−	0.349732i
$231$	−1.97925	+	1.14272i	−0.130225	+	0.0751856i
$232$	−10.6940	−	8.44596i	−0.702099	−	0.554505i
$233$			13.2676i			0.869187i	0.900627	+	0.434594i	$0.143108\pi$
$233$			13.2676i			0.869187i	−0.900627	+	0.434594i	$0.856892\pi$
$234$	5.42126	−	5.86119i	0.354399	−	0.383158i
$235$	−4.70807	+	1.26152i	−0.307121	+	0.0822927i
$236$	−4.09038	+	21.9968i	−0.266261	+	1.43187i
$237$	−0.612217	+	2.28482i	−0.0397677	+	0.148415i
$238$	9.19952	+	8.50902i	0.596317	+	0.551558i
$239$	1.45537	−	5.43152i	0.0941401	−	0.351336i	−0.902748	−	0.430171i	$-0.858453\pi$
$239$	1.45537	−	5.43152i	0.0941401	−	0.351336i	0.996888	+	0.0788350i	$0.0251200\pi$
$240$	−1.19122	−	0.126632i	−0.0768927	−	0.00817409i
$241$	4.62261	+	17.2518i	0.297768	+	1.11129i	0.938994	+	0.343934i	$0.111760\pi$
$241$	4.62261	+	17.2518i	0.297768	+	1.11129i	−0.641225	+	0.767353i	$0.721574\pi$
$242$	−42.8733	+	1.67175i	−2.75600	+	0.107464i
$243$	3.88305	+	6.72564i	0.249098	+	0.431450i
$244$	−8.81172	+	3.11451i	−0.564112	+	0.199386i
$245$	−3.95360	+	3.95360i	−0.252586	+	0.252586i
$246$	−2.09093	+	1.31841i	−0.133313	+	0.0840587i
$247$	−1.43117	−	2.47885i	−0.0910629	−	0.157726i
$248$	5.06676	−	6.41540i	0.321740	−	0.407378i
$249$			4.46914i			0.283221i
$250$	−1.03820	−	0.960278i	−0.0656618	−	0.0607333i
$251$	14.7374	−	14.7374i	0.930217	−	0.930217i	−0.0675022	−	0.997719i	$-0.521503\pi$
$251$	14.7374	−	14.7374i	0.930217	−	0.930217i	0.997719	+	0.0675022i	$0.0215030\pi$
$252$	0.537951	+	6.88760i	0.0338877	+	0.433878i
$253$	19.2699	+	19.2699i	1.21149	+	1.21149i
$254$	−5.79652	+	3.65493i	−0.363706	+	0.229331i
$255$	1.93627	+	1.11790i	0.121254	+	0.0700058i
$256$	15.2286	−	4.90811i	0.951788	−	0.306757i
$257$	−9.91088	−	2.65561i	−0.618224	−	0.165652i	−0.0639034	−	0.997956i	$-0.520355\pi$
$257$	−9.91088	−	2.65561i	−0.618224	−	0.165652i	−0.554320	+	0.832304i	$0.687022\pi$
$258$	1.79439	−	0.556588i	0.111714	−	0.0346517i
$259$	−7.08792	+	1.37320i	−0.440422	+	0.0853268i
$260$	3.19863	−	2.19557i	0.198371	−	0.136163i
$261$	−3.62905	+	13.5438i	−0.224633	+	0.838340i
$262$	−12.1844	−	2.76085i	−0.752753	−	0.170566i
$263$	−3.76960	+	6.52914i	−0.232443	+	0.402604i	−0.958527	−	0.285003i	$-0.908005\pi$
$263$	−3.76960	+	6.52914i	−0.232443	+	0.402604i	0.726083	+	0.687607i	$0.241339\pi$
$264$	2.15432	−	5.00203i	0.132589	−	0.307854i
$265$	−3.60830	+	3.60830i	−0.221656	+	0.221656i
$266$	2.41556	+	0.547340i	0.148108	+	0.0335596i
$267$	−1.19329	−	1.19329i	−0.0730283	−	0.0730283i
$268$	−9.73239	+	20.3732i	−0.594501	+	1.24449i
$269$	−26.2699			−1.60170			−0.800852	−	0.598862i	$-0.795620\pi$
$269$	−26.2699			−1.60170			−0.800852	+	0.598862i	$0.795620\pi$
$270$	0.741594	+	2.39083i	0.0451320	+	0.145501i
$271$	−20.5767	+	11.8800i	−1.24995	+	0.721657i	−0.971099	−	0.238679i	$-0.923286\pi$
$271$	−20.5767	+	11.8800i	−1.24995	+	0.721657i	−0.278848	+	0.960335i	$0.589952\pi$
$272$	−29.6950	−	3.15673i	−1.80052	−	0.191405i
$273$	0.487572	+	0.487572i	0.0295092	+	0.0295092i
$274$	−23.2418	+	0.906262i	−1.40409	+	0.0547493i
$275$	5.56815	−	3.21477i	0.335772	−	0.193858i
$276$	−2.39361	+	0.846023i	−0.144078	+	0.0509246i
$277$	−14.0773	+	3.77201i	−0.845825	+	0.226638i	−0.655605	−	0.755104i	$-0.727587\pi$
$277$	−14.0773	+	3.77201i	−0.845825	+	0.226638i	−0.190219	+	0.981742i	$0.560920\pi$
$278$	−0.0520587	−	0.0825624i	−0.00312227	−	0.00495176i
$279$	−8.12497	−	2.17708i	−0.486429	−	0.130338i
$280$	−0.484678	+	3.32193i	−0.0289651	+	0.198523i
$281$	−8.39284	−	2.24886i	−0.500675	−	0.134155i	−0.000361822	−	1.00000i	$-0.500115\pi$
$281$	−8.39284	−	2.24886i	−0.500675	−	0.134155i	−0.500313	+	0.865844i	$0.666782\pi$
$282$	1.82665	+	0.961737i	0.108775	+	0.0572706i
$283$	−7.89904	−	29.4796i	−0.469549	−	1.75238i	−0.641348	−	0.767250i	$-0.721624\pi$
$283$	−7.89904	−	29.4796i	−0.469549	−	1.75238i	0.171798	−	0.985132i	$-0.445042\pi$
$284$	29.2179	+	13.9575i	1.73376	+	0.828227i
$285$	0.441903			0.0261761
$286$	5.22551	+	16.8466i	0.308991	+	0.996158i
$287$	3.46362	+	5.99917i	0.204451	+	0.354120i
$288$	−10.8366	−	12.3938i	−0.638550	−	0.730311i
$289$	33.5454	+	19.3674i	1.97326	+	1.13926i
$290$	−3.17427	+	6.02895i	−0.186400	+	0.354032i
$291$	0.139943	+	0.522273i	0.00820359	+	0.0306162i
$292$	−2.36727	−	30.3091i	−0.138534	−	1.77370i
$293$	−7.40598	+	12.8275i	−0.432662	+	0.749393i	−0.997102	−	0.0760817i	$-0.975759\pi$
$293$	−7.40598	+	12.8275i	−0.432662	+	0.749393i	0.564439	+	0.825474i	$0.309092\pi$
$294$	2.36627	−	0.0922673i	0.138003	−	0.00538114i
$295$	11.1870			0.651330
$296$	11.5870	−	12.7177i	0.673483	−	0.739203i
$297$	−11.3805			−0.660364
$298$	23.8371	−	0.929473i	1.38084	−	0.0538429i
$299$	4.11101	−	7.12048i	0.237746	−	0.411788i
$300$	0.0466396	+	0.597146i	0.00269274	+	0.0344762i
$301$	−1.36268	−	5.08558i	−0.0785435	−	0.293128i
$302$	8.08155	−	15.3494i	0.465041	−	0.883261i
$303$	0.681649	+	0.393550i	0.0391597	+	0.0226089i
$304$	−5.39481	+	2.39425i	−0.309413	+	0.137320i
$305$	2.33648	+	4.04691i	0.133787	+	0.231725i
$306$	9.10307	+	29.3474i	0.520388	+	1.67768i
$307$	16.4935			0.941331			0.470666	−	0.882312i	$-0.344014\pi$
$307$	16.4935			0.941331			0.470666	+	0.882312i	$0.344014\pi$
$308$	−13.7719	−	6.57891i	−0.784728	−	0.374868i
$309$	0.0965616	+	0.360373i	0.00549320	+	0.0205009i
$310$	−3.61679	−	1.90426i	−0.205420	−	0.108154i
$311$	7.02943	+	1.88353i	0.398603	+	0.106805i	0.452551	−	0.891738i	$-0.350514\pi$
$311$	7.02943	+	1.88353i	0.398603	+	0.106805i	−0.0539485	+	0.998544i	$0.517181\pi$
$312$	−1.62594	−	0.237230i	−0.0920510	−	0.0134305i
$313$	−17.8164	−	4.77389i	−1.00704	−	0.269836i	−0.282649	−	0.959223i	$-0.591213\pi$
$313$	−17.8164	−	4.77389i	−1.00704	−	0.269836i	−0.724393	+	0.689387i	$0.757880\pi$
$314$	−10.4277	−	16.5378i	−0.588468	−	0.933280i
$315$	3.33659	−	0.894036i	0.187995	−	0.0503732i
$316$	−14.8938	+	5.26422i	−0.837842	+	0.296136i
$317$	4.05476	−	2.34102i	0.227738	−	0.131485i	−0.381790	−	0.924249i	$-0.624692\pi$
$317$	4.05476	−	2.34102i	0.227738	−	0.131485i	0.609528	+	0.792765i	$0.291359\pi$
$318$	2.15960	−	0.0842088i	0.121104	−	0.00472219i
$319$	−21.9040	−	21.9040i	−1.22639	−	1.22639i
$320$	−3.80474	−	7.03733i	−0.212691	−	0.393398i
$321$	1.98409	−	1.14551i	0.110741	−	0.0639364i
$322$	2.10775	+	6.79519i	0.117460	+	0.378681i
$323$	11.0159			0.612941
$324$	−7.06989	+	14.7997i	−0.392772	+	0.822206i
$325$	−1.37167	−	1.37167i	−0.0760864	−	0.0760864i
$326$	−2.27213	−	0.514839i	−0.125841	−	0.0285143i
$327$	−2.74830	+	2.74830i	−0.151981	+	0.151981i
$328$	−15.1613	−	6.52982i	−0.837143	−	0.360549i
$329$	2.89260	−	5.01013i	0.159474	−	0.276217i
$330$	−2.65579	−	0.601773i	−0.146197	−	0.0331265i
$331$	−2.69214	+	10.0472i	−0.147973	+	0.552244i	0.851632	+	0.524141i	$0.175613\pi$
$331$	−2.69214	+	10.0472i	−0.147973	+	0.552244i	−0.999605	+	0.0281031i	$0.991053\pi$
$332$	−24.6068	+	16.8902i	−1.35047	+	0.926973i
$333$	−16.7347	−	5.77379i	−0.917055	−	0.316402i
$334$	−6.03208	+	1.87105i	−0.330061	+	0.102379i
$335$	10.9046	+	2.92187i	0.595781	+	0.159639i
$336$	1.10604	−	0.893479i	0.0603393	−	0.0487433i
$337$	−12.3017	−	7.10240i	−0.670118	−	0.386893i	0.126004	−	0.992030i	$-0.459785\pi$
$337$	−12.3017	−	7.10240i	−0.670118	−	0.386893i	−0.796121	+	0.605137i	$0.793118\pi$
$338$	−11.0500	+	6.96742i	−0.601038	+	0.378978i
$339$	0.954404	+	0.954404i	0.0518361	+	0.0518361i
$340$	1.16265	+	14.8858i	0.0630533	+	0.807297i
$341$	13.1403	−	13.1403i	0.711585	−	0.711585i
$342$	4.45839	+	4.12375i	0.241082	+	0.222987i
$343$		−	14.9447i		−	0.806939i
$344$	9.84606	+	7.77624i	0.530864	+	0.419267i
$345$	0.634681	+	1.09930i	0.0341701	+	0.0591843i
$346$	−2.56583	+	1.61786i	−0.137940	+	0.0869764i
$347$	−20.1705	+	20.1705i	−1.08281	+	1.08281i	−0.0865616	+	0.996247i	$0.527588\pi$
$347$	−20.1705	+	20.1705i	−1.08281	+	1.08281i	−0.996247	+	0.0865616i	$0.972412\pi$
$348$	2.72080	−	0.961667i	0.145850	−	0.0515508i
$349$	11.6439	+	20.1679i	0.623286	+	1.07956i	0.988870	+	0.148785i	$0.0475361\pi$
$349$	11.6439	+	20.1679i	0.623286	+	1.07956i	−0.365583	+	0.930779i	$0.619131\pi$
$350$	1.67728	−	0.0654016i	0.0896541	−	0.00349586i
$351$	0.888672	+	3.31657i	0.0474338	+	0.177025i
$352$	35.6826	−	7.04267i	1.90189	−	0.375375i
$353$	−4.08656	+	15.2512i	−0.217506	+	0.811742i	0.767764	+	0.640733i	$0.221369\pi$
$353$	−4.08656	+	15.2512i	−0.217506	+	0.811742i	−0.985269	+	0.171009i	$0.945297\pi$
$354$	−3.47829	−	3.21721i	−0.184869	−	0.170993i
$355$	4.19035	−	15.6386i	0.222401	−	0.830010i
$356$	2.06036	−	11.0800i	0.109199	−	0.587238i
$357$	−2.56329	+	0.686831i	−0.135664	+	0.0363510i
$358$	−12.2670	+	13.2624i	−0.648330	+	0.700942i
$359$			15.1351i			0.798802i	0.916776	+	0.399401i	$0.130782\pi$
$359$			15.1351i			0.798802i	−0.916776	+	0.399401i	$0.869218\pi$
$360$	−5.10189	+	6.45987i	−0.268893	+	0.340465i
$361$	−14.5689	+	8.41136i	−0.766785	+	0.442703i
$362$	−7.52635	+	14.2949i	−0.395576	+	0.751325i
$363$	4.54300	−	7.86871i	0.238446	−	0.413000i
$364$	−0.841851	+	4.52722i	−0.0441250	+	0.237291i
$365$	−14.6827	+	3.93423i	−0.768530	+	0.205927i
$366$	0.437366	−	1.93022i	0.0228615	−	0.100894i
$367$	−22.4599	−	12.9672i	−1.17240	−	0.676884i	−0.218154	−	0.975914i	$-0.570004\pi$
$367$	−22.4599	−	12.9672i	−1.17240	−	0.676884i	−0.954244	+	0.299030i	$0.903337\pi$
$368$	−13.7043	−	9.98165i	−0.714387	−	0.520330i
$369$			16.9856i			0.884234i
$370$	−7.31086	−	4.53336i	−0.380074	−	0.235678i
$371$		−	6.05671i		−	0.314449i
$372$	0.576907	+	1.63222i	0.0299113	+	0.0846264i
$373$	21.1211	+	12.1943i	1.09361	+	0.631397i	0.934536	−	0.355870i	$-0.115815\pi$
$373$	21.1211	+	12.1943i	1.09361	+	0.631397i	0.159076	+	0.987266i	$0.449149\pi$
$374$	−66.2043	−	15.0012i	−3.42335	−	0.775692i
$375$	0.289278	−	0.0775117i	0.0149382	−	0.00400269i
$376$	1.60820	+	13.6921i	0.0829364	+	0.706114i
$377$	−4.67295	+	8.09379i	−0.240669	+	0.416851i
$378$	−2.62897	−	1.38416i	−0.135219	−	0.0711936i
$379$	−26.6061	+	15.3610i	−1.36666	+	0.789043i	−0.990500	−	0.137511i	$-0.956090\pi$
$379$	−26.6061	+	15.3610i	−1.36666	+	0.789043i	−0.376162	+	0.926554i	$0.622756\pi$
$380$	1.67009	+	2.43308i	0.0856736	+	0.124815i
$381$		−	1.45115i		−	0.0743446i
$382$	12.7609	+	11.8030i	0.652902	+	0.603896i
$383$	13.2868	−	3.56018i	0.678922	−	0.181916i	0.0971513	−	0.995270i	$-0.469027\pi$
$383$	13.2868	−	3.56018i	0.678922	−	0.181916i	0.581770	+	0.813353i	$0.302360\pi$
$384$	−0.840853	+	3.28226i	−0.0429096	+	0.167497i
$385$	−1.97513	+	7.37129i	−0.100662	+	0.375676i
$386$	−9.02827	+	9.76091i	−0.459527	+	0.496817i
$387$	3.34128	−	12.4698i	0.169847	−	0.633878i
$388$	−2.34671	+	2.74434i	−0.119136	+	0.139323i
$389$	−7.55715	−	28.2037i	−0.383163	−	1.42998i	−0.841042	−	0.540969i	$-0.818058\pi$
$389$	−7.55715	−	28.2037i	−0.383163	−	1.42998i	0.457879	−	0.889014i	$-0.348609\pi$
$390$	0.0320113	+	0.820956i	0.00162096	+	0.0415707i
$391$	15.8215	+	27.4037i	0.800129	+	1.38586i
$392$	9.45085	+	12.6798i	0.477340	+	0.640425i
$393$	1.87075	−	1.87075i	0.0943670	−	0.0943670i
$394$	8.86876	+	14.0654i	0.446802	+	0.708604i
$395$	3.94919	+	6.84020i	0.198705	+	0.344168i
$396$	−21.1788	−	30.8546i	−1.06428	−	1.55050i
$397$		−	20.7738i		−	1.04261i	−0.853371	−	0.521304i	$-0.825446\pi$
$397$		−	20.7738i		−	1.04261i	0.853371	−	0.521304i	$-0.174554\pi$
$398$	−13.3618	+	14.4461i	−0.669766	+	0.724118i
$399$	−0.370878	+	0.370878i	−0.0185671	+	0.0185671i
$400$	−3.11157	+	2.51359i	−0.155579	+	0.125679i
$401$	8.48698	+	8.48698i	0.423820	+	0.423820i	0.886517	−	0.462697i	$-0.153118\pi$
$401$	8.48698	+	8.48698i	0.423820	+	0.423820i	−0.462697	+	0.886517i	$0.653118\pi$
$402$	−2.55020	−	4.04448i	−0.127192	−	0.201720i
$403$	−4.85549	−	2.80332i	−0.241869	−	0.139643i
$404$	0.409301	+	5.24045i	0.0203635	+	0.260722i
$405$	7.92140	+	2.12253i	0.393618	+	0.105470i
$406$	−2.39586	−	7.72403i	−0.118905	−	0.383337i
$407$	29.5321	−	25.6398i	1.46385	−	1.27092i
$408$	3.91946	−	4.96271i	0.194042	−	0.245691i
$409$	7.16979	−	26.7580i	0.354523	−	1.32310i	−0.526561	−	0.850138i	$-0.676519\pi$
$409$	7.16979	−	26.7580i	0.354523	−	1.32310i	0.881084	−	0.472960i	$-0.156815\pi$
$410$	−1.82399	+	8.04978i	−0.0900806	+	0.397550i
$411$	2.46278	−	4.26566i	0.121480	−	0.210409i
$412$	−1.61925	+	1.89362i	−0.0797746	+	0.0932918i
$413$	−9.38893	+	9.38893i	−0.461999	+	0.461999i
$414$	−3.85510	+	17.0136i	−0.189468	+	0.836174i
$415$	10.5521	+	10.5521i	0.517982	+	0.517982i
$416$	−4.83877	−	9.84888i	−0.237240	−	0.482881i
$417$	0.0206693			0.00101218
$418$	−12.8146	+	3.97486i	−0.626781	+	0.194417i
$419$	14.9540	−	8.63369i	0.730550	−	0.421783i	−0.0880731	−	0.996114i	$-0.528071\pi$
$419$	14.9540	−	8.63369i	0.730550	−	0.421783i	0.818623	+	0.574331i	$0.194738\pi$
$420$	−0.540313	−	0.462026i	−0.0263646	−	0.0225446i
$421$	2.79197	+	2.79197i	0.136072	+	0.136072i	0.771862	−	0.635790i	$-0.219325\pi$
$421$	2.79197	+	2.79197i	0.136072	+	0.136072i	−0.635790	+	0.771862i	$0.719325\pi$
$422$	0.509583	+	13.0687i	0.0248061	+	0.636172i
$423$	12.2848	−	7.09265i	0.597309	−	0.344856i
$424$	8.62543	+	11.5723i	0.418888	+	0.562002i
$425$	7.21119	−	1.93223i	0.349794	−	0.0937271i
$426$	−5.80032	+	3.65732i	−0.281026	+	0.177198i
$427$	−5.35742	−	1.43552i	−0.259264	−	0.0694695i
$428$	13.8056	+	6.59499i	0.667318	+	0.318781i
$429$	−3.60794	−	0.966743i	−0.174193	−	0.0466748i
$430$	2.92257	−	5.55088i	0.140939	−	0.267687i
$431$	−5.50912	−	20.5603i	−0.265365	−	0.990356i	−0.962027	−	0.272956i	$-0.911999\pi$
$431$	−5.50912	−	20.5603i	−0.265365	−	0.990356i	0.696662	−	0.717400i	$-0.254668\pi$
$432$	6.99427	−	1.09927i	0.336512	−	0.0528887i
$433$	37.2530			1.79026			0.895132	−	0.445801i	$-0.147081\pi$
$433$	37.2530			1.79026			0.895132	+	0.445801i	$0.147081\pi$
$434$	4.63368	−	1.43729i	0.222424	−	0.0689919i
$435$	−0.721437	−	1.24957i	−0.0345903	−	0.0599121i
$436$	−25.5186	−	4.74527i	−1.22212	−	0.227257i
$437$	5.41629	+	3.12710i	0.259096	+	0.149589i
$438$	5.69664	+	2.99931i	0.272196	+	0.143312i
$439$	−10.4760	−	39.0970i	−0.499992	−	1.86600i	−0.500051	−	0.865996i	$-0.666685\pi$
$439$	−10.4760	−	39.0970i	−0.499992	−	1.86600i	5.84152e−5	−	1.00000i	$-0.499981\pi$
$440$	−6.72372	−	16.8969i	−0.320541	−	0.805526i
$441$	8.13611	−	14.0922i	0.387434	−	0.671055i
$442$	0.797988	+	20.4650i	0.0379564	+	0.973422i
$443$	13.3266			0.633168			0.316584	−	0.948565i	$-0.397464\pi$
$443$	13.3266			0.633168			0.316584	+	0.948565i	$0.397464\pi$
$444$	0.969389	+	3.51203i	0.0460052	+	0.166673i
$445$	−5.63496			−0.267123
$446$	−0.474029	−	12.1569i	−0.0224459	−	0.575644i
$447$	−2.52586	+	4.37491i	−0.119469	+	0.206926i
$448$	9.09948	+	2.71303i	0.429910	+	0.128179i
$449$	0.0421488	+	0.157302i	0.00198913	+	0.00742352i	0.966913	−	0.255105i	$-0.0821102\pi$
$449$	0.0421488	+	0.157302i	0.00198913	+	0.00742352i	−0.964924	+	0.262529i	$0.915443\pi$
$450$	3.64186	+	1.91746i	0.171679	+	0.0903898i
$451$	−32.4977	−	18.7625i	−1.53026	−	0.883493i
$452$	−1.64789	+	8.86185i	−0.0775102	+	0.416826i
$453$	1.83675	+	3.18134i	0.0862978	+	0.149472i
$454$	−10.9665	+	3.40163i	−0.514685	+	0.159647i
$455$	2.30241			0.107939
$456$	0.180452	−	1.23680i	0.00845043	−	0.0579183i
$457$	2.62260	+	9.78766i	0.122680	+	0.457848i	0.999746	−	0.0225214i	$-0.00716941\pi$
$457$	2.62260	+	9.78766i	0.122680	+	0.457848i	−0.877066	+	0.480369i	$0.840503\pi$
$458$	−10.3341	+	19.6277i	−0.482880	+	0.917143i
$459$	−12.7640	−	3.42012i	−0.595775	−	0.159637i
$460$	−3.65401	+	7.64909i	−0.170369	+	0.356641i
$461$	−26.5962	−	7.12643i	−1.23871	−	0.331911i	−0.420744	−	0.907180i	$-0.638231\pi$
$461$	−26.5962	−	7.12643i	−1.23871	−	0.331911i	−0.817964	+	0.575269i	$0.804897\pi$
$462$	2.73399	−	1.72389i	0.127197	−	0.0802025i
$463$	−19.1492	+	5.13101i	−0.889938	+	0.238458i	−0.674690	−	0.738101i	$-0.735723\pi$
$463$	−19.1492	+	5.13101i	−0.889938	+	0.238458i	−0.215248	+	0.976559i	$0.569056\pi$
$464$	15.5776	+	11.3461i	0.723171	+	0.526728i
$465$	0.749619	−	0.432793i	0.0347627	−	0.0200703i
$466$	−0.731072	−	18.7489i	−0.0338663	−	0.868527i
$467$	12.1526	+	12.1526i	0.562357	+	0.562357i	0.929976	−	0.367619i	$-0.119827\pi$
$467$	12.1526	+	12.1526i	0.562357	+	0.562357i	−0.367619	+	0.929976i	$0.619827\pi$
$468$	−7.33803	+	8.58140i	−0.339200	+	0.396675i
$469$	−11.6042	+	6.69969i	−0.535832	+	0.309363i
$470$	6.58365	−	2.04213i	0.303681	−	0.0941966i
$471$	4.14019			0.190770
$472$	4.56821	−	31.3100i	0.210269	−	1.44116i
$473$	20.1671	+	20.1671i	0.927283	+	0.927283i
$474$	0.739249	−	3.26251i	0.0339548	−	0.149852i
$475$	1.04338	−	1.04338i	0.0478734	−	0.0478734i
$476$	−13.4691	−	11.5175i	−0.617354	−	0.527905i
$477$	7.42552	−	12.8614i	0.339991	−	0.588882i
$478$	−1.75735	+	7.75569i	−0.0803795	+	0.354737i
$479$	−7.25483	+	27.0754i	−0.331481	+	1.23711i	0.576152	+	0.817342i	$0.304554\pi$
$479$	−7.25483	+	27.0754i	−0.331481	+	1.23711i	−0.907634	+	0.419763i	$0.862113\pi$
$480$	1.69033	+	0.113311i	0.0771528	+	0.00517190i
$481$	−9.77817	−	6.60426i	−0.445846	−	0.301128i
$482$	−7.48300	−	24.1245i	−0.340842	−	1.09884i
$483$	−1.45529	−	0.389943i	−0.0662179	−	0.0177430i
$484$	60.4939	−	4.72483i	2.74972	−	0.214765i
$485$	1.56356	+	0.902720i	0.0709975	+	0.0409904i
$486$	−5.85789	−	9.29031i	−0.265719	−	0.421417i
$487$	23.6092	+	23.6092i	1.06983	+	1.06983i	0.997371	+	0.0724625i	$0.0230858\pi$
$487$	23.6092	+	23.6092i	1.06983	+	1.06983i	0.0724625	+	0.997371i	$0.476914\pi$
$488$	12.2806	−	4.88678i	0.555915	−	0.221214i
$489$	0.348855	−	0.348855i	0.0157758	−	0.0157758i
$490$	5.36914	−	5.80484i	0.242553	−	0.262236i
$491$		−	11.9057i		−	0.537296i	−0.963238	−	0.268648i	$-0.913423\pi$
$491$		−	11.9057i		−	0.537296i	0.963238	−	0.268648i	$-0.0865768\pi$
$492$	2.88213	−	1.97831i	0.129936	−	0.0891892i
$493$	−17.9842	−	31.1495i	−0.809967	−	1.40290i
$494$	2.15903	+	3.42410i	0.0971393	+	0.154058i
$495$	−13.2314	+	13.2314i	−0.594705	+	0.594705i
$496$	−6.80654	+	9.34504i	−0.305623	+	0.419605i
$497$	9.60823	+	16.6419i	0.430988	+	0.746493i
$498$	−0.246260	−	6.31553i	−0.0110352	−	0.283005i
$499$	2.13442	+	7.96577i	0.0955498	+	0.356597i	0.997102	−	0.0760731i	$-0.0242382\pi$
$499$	2.13442	+	7.96577i	0.0955498	+	0.356597i	−0.901552	+	0.432670i	$0.857572\pi$
$500$	1.52004	+	1.29980i	0.0679783	+	0.0581288i
$501$	0.346152	−	1.29186i	0.0154649	−	0.0577159i
$502$	−20.0140	+	21.6381i	−0.893266	+	0.965755i
$503$	3.48745	−	13.0154i	0.155498	−	0.580326i	−0.843564	−	0.537028i	$-0.819547\pi$
$503$	3.48745	−	13.0154i	0.155498	−	0.580326i	0.999062	−	0.0432979i	$-0.0137865\pi$
$504$	−1.13972	−	9.70350i	−0.0507672	−	0.432228i
$505$	2.53865	−	0.680229i	0.112968	−	0.0302698i
$506$	−28.2929	−	26.1693i	−1.25777	−	1.16337i
$507$		−	2.76633i		−	0.122857i
$508$	7.98990	−	5.48433i	0.354495	−	0.243328i
$509$	−18.6661	+	10.7769i	−0.827359	+	0.477676i	−0.852948	−	0.521997i	$-0.825187\pi$
$509$	−18.6661	+	10.7769i	−0.827359	+	0.477676i	0.0255885	+	0.999673i	$0.491854\pi$
$510$	−2.79781	−	1.47306i	−0.123889	−	0.0652283i
$511$	9.02096	−	15.6248i	0.399064	−	0.691199i
$512$	−21.2497	+	7.77498i	−0.939113	+	0.343609i
$513$	−2.52279	+	0.675980i	−0.111384	+	0.0298452i
$514$	14.1518	+	3.20664i	0.624208	+	0.141439i
$515$	1.07887	+	0.622884i	0.0475405	+	0.0274475i
$516$	−2.50505	+	0.885411i	−0.110279	+	0.0389781i
$517$			31.3386i			1.37827i
$518$	9.94056	−	2.33109i	0.436763	−	0.102422i
$519$		−	0.642351i		−	0.0281961i
$520$	−4.39914	+	3.27889i	−0.192915	+	0.143789i
$521$	4.93841	+	2.85119i	0.216356	+	0.124913i	0.604262	−	0.796786i	$-0.293468\pi$
$521$	4.93841	+	2.85119i	0.216356	+	0.124913i	−0.387906	+	0.921699i	$0.626801\pi$
$522$	4.38206	−	19.3392i	0.191798	−	0.846456i
$523$	−6.27439	+	1.68122i	−0.274360	+	0.0735146i	−0.393376	−	0.919378i	$-0.628693\pi$
$523$	−6.27439	+	1.68122i	−0.274360	+	0.0735146i	0.119016	+	0.992892i	$0.462026\pi$
$524$	17.3704	+	3.23007i	0.758827	+	0.141106i
$525$	−0.177730	+	0.307837i	−0.00775677	+	0.0134351i
$526$	4.96720	−	9.43429i	0.216580	−	0.411355i
$527$	18.6867	−	10.7888i	0.814006	−	0.469966i
$528$	−2.76874	+	7.18728i	−0.120494	+	0.312786i
$529$		−	5.03490i		−	0.218909i
$530$	4.90020	−	5.29785i	0.212851	−	0.230124i
$531$	−31.4481	+	8.42650i	−1.36473	+	0.365679i
$532$	−3.44369	−	0.640365i	−0.149303	−	0.0277634i
$533$	−2.93023	+	10.9358i	−0.126922	+	0.473680i
$534$	1.75204	+	1.62053i	0.0758182	+	0.0701274i
$535$	1.97996	−	7.38930i	0.0856010	−	0.319467i
$536$	12.6306	−	29.3265i	0.545560	−	1.26671i
$537$	−0.990166	−	3.69535i	−0.0427288	−	0.159466i
$538$	37.1230	−	1.44753i	1.60049	−	0.0624074i
$539$	17.9745	+	31.1328i	0.774219	+	1.34099i
$540$	−1.17972	−	3.33771i	−0.0507669	−	0.143632i
$541$	7.41990	−	7.41990i	0.319007	−	0.319007i	−0.529379	−	0.848385i	$-0.677575\pi$
$541$	7.41990	−	7.41990i	0.319007	−	0.319007i	0.848385	+	0.529379i	$0.177575\pi$
$542$	28.4232	−	17.9219i	1.22088	−	0.769811i
$543$	−1.71056	−	2.96278i	−0.0734073	−	0.127145i
$544$	42.1371	+	2.82464i	1.80661	+	0.121105i
$545$			12.9780i			0.555917i
$546$	−0.715874	−	0.662142i	−0.0306366	−	0.0283370i
$547$	−25.5703	+	25.5703i	−1.09331	+	1.09331i	−0.0981360	+	0.995173i	$0.531288\pi$
$547$	−25.5703	+	25.5703i	−1.09331	+	1.09331i	−0.995173	+	0.0981360i	$0.968712\pi$
$548$	32.7940	−	2.56135i	1.40089	−	0.109415i
$549$	−9.61650	−	9.61650i	−0.410422	−	0.410422i
$550$	−7.69143	+	4.84974i	−0.327964	+	0.206794i
$551$	−6.15665	−	3.55454i	−0.262282	−	0.151429i
$552$	3.33589	−	1.32744i	0.141985	−	0.0564997i
$553$	−9.05526	−	2.42635i	−0.385069	−	0.103179i
$554$	19.6854	−	6.10607i	0.836352	−	0.259422i
$555$	1.63781	−	0.797559i	0.0695211	−	0.0338545i
$556$	0.0781156	+	0.113804i	0.00331284	+	0.00482635i
$557$	−9.96622	+	37.1944i	−0.422282	+	1.57598i	0.347505	+	0.937678i	$0.387029\pi$
$557$	−9.96622	+	37.1944i	−0.422282	+	1.57598i	−0.769787	+	0.638301i	$0.779638\pi$
$558$	11.6017	+	2.62881i	0.491138	+	0.111287i
$559$	4.30241	−	7.45199i	0.181972	−	0.315186i
$560$	0.501872	−	4.72106i	0.0212080	−	0.199501i
$561$	10.1648	−	10.1648i	0.429159	−	0.429159i
$562$	11.9842	+	2.71548i	0.505522	+	0.114546i
$563$	−19.2720	−	19.2720i	−0.812218	−	0.812218i	0.172748	−	0.984966i	$-0.444735\pi$
$563$	−19.2720	−	19.2720i	−0.812218	−	0.812218i	−0.984966	+	0.172748i	$0.944735\pi$
$564$	−2.63430	−	1.25842i	−0.110924	−	0.0529889i
$565$	4.50688			0.189606
$566$	12.7868	+	41.2236i	0.537471	+	1.73276i
$567$	−8.42962	+	4.86685i	−0.354011	+	0.204388i
$568$	−42.0581	−	18.1140i	−1.76472	−	0.760045i
$569$	16.1287	+	16.1287i	0.676148	+	0.676148i	0.959126	−	0.282978i	$-0.0913224\pi$
$569$	16.1287	+	16.1287i	0.676148	+	0.676148i	−0.282978	+	0.959126i	$0.591322\pi$
$570$	−0.624471	+	0.0243498i	−0.0261562	+	0.00101990i
$571$	4.27558	−	2.46851i	0.178927	−	0.103304i	−0.407861	−	0.913044i	$-0.633725\pi$
$571$	4.27558	−	2.46851i	0.178927	−	0.103304i	0.586789	+	0.809740i	$0.300392\pi$
$572$	−8.31267	−	23.5186i	−0.347570	−	0.983363i
$573$	−3.55559	+	0.952718i	−0.148537	+	0.0398004i
$574$	−5.22515	−	8.28681i	−0.218094	−	0.345885i
$575$	4.09410	+	1.09701i	0.170736	+	0.0457485i
$576$	15.9965	+	16.9170i	0.666521	+	0.704877i
$577$	16.3970	+	4.39357i	0.682618	+	0.182907i	0.583432	−	0.812162i	$-0.301710\pi$
$577$	16.3970	+	4.39357i	0.682618	+	0.182907i	0.0991858	+	0.995069i	$0.468376\pi$
$578$	−48.4715	−	25.5205i	−2.01615	−	1.06151i
$579$	−0.728744	−	2.71971i	−0.0302856	−	0.113027i
$580$	4.15348	−	8.69466i	0.172464	−	0.361026i
$581$	−17.7122			−0.734826
$582$	−0.226537	−	0.730334i	−0.00939026	−	0.0302733i
$583$	16.4047	+	28.4137i	0.679412	+	1.17678i
$584$	5.01538	+	42.7005i	0.207538	+	1.76696i
$585$	4.88915	+	2.82275i	0.202142	+	0.116707i
$586$	9.75886	−	18.5352i	0.403135	−	0.765682i
$587$	8.58005	+	32.0212i	0.354137	+	1.32166i	0.881567	+	0.472058i	$0.156489\pi$
$587$	8.58005	+	32.0212i	0.354137	+	1.32166i	−0.527431	+	0.849598i	$0.676845\pi$
$588$	−3.33878	+	0.260773i	−0.137689	+	0.0107541i
$589$	2.13238	−	3.69340i	0.0878633	−	0.152184i
$590$	−15.8087	+	0.616426i	−0.650835	+	0.0253779i
$591$	−3.52124			−0.144844
$592$	−15.6733	+	18.6104i	−0.644170	+	0.764882i
$593$	−10.6304			−0.436540			−0.218270	−	0.975888i	$-0.570041\pi$
$593$	−10.6304			−0.436540			−0.218270	+	0.975888i	$0.570041\pi$
$594$	16.0822	−	0.627091i	0.659862	−	0.0257298i
$595$	−4.43050	+	7.67385i	−0.181633	+	0.314597i
$596$	−33.6339	+	2.62695i	−1.37770	+	0.107604i
$597$	−1.07854	−	4.02516i	−0.0441416	−	0.164739i
$598$	−5.41708	+	10.2888i	−0.221521	+	0.420739i
$599$	−17.9770	−	10.3790i	−0.734520	−	0.424075i	0.0855534	−	0.996334i	$-0.472734\pi$
$599$	−17.9770	−	10.3790i	−0.734520	−	0.424075i	−0.820073	+	0.572258i	$0.806068\pi$
$600$	−0.0988123	−	0.841280i	−0.00403400	−	0.0343451i
$601$	4.97524	+	8.61737i	0.202944	+	0.351510i	0.949476	−	0.313840i	$-0.101616\pi$
$601$	4.97524	+	8.61737i	0.202944	+	0.351510i	−0.746531	+	0.665350i	$0.768282\pi$
$602$	2.20588	+	7.11155i	0.0899050	+	0.289845i
$603$	−32.8552			−1.33797
$604$	−10.5746	+	22.1362i	−0.430273	+	0.900710i
$605$	−7.85232	−	29.3053i	−0.319242	−	1.19143i
$606$	−0.984950	−	0.518581i	−0.0400109	−	0.0210659i
$607$	17.8829	+	4.79170i	0.725843	+	0.194489i	0.602777	−	0.797910i	$-0.294061\pi$
$607$	17.8829	+	4.79170i	0.725843	+	0.194489i	0.123066	+	0.992399i	$0.460727\pi$
$608$	7.49168	−	3.68067i	0.303828	−	0.149271i
$609$	1.65421	+	0.443245i	0.0670321	+	0.0179612i
$610$	−3.52477	−	5.59010i	−0.142714	−	0.226337i
$611$	9.13285	−	2.44714i	0.369476	−	0.0990007i
$612$	−14.4810	−	40.9704i	−0.585360	−	1.65613i
$613$	−11.3883	+	6.57504i	−0.459969	+	0.265563i	−0.712031	−	0.702148i	$-0.752225\pi$
$613$	−11.3883	+	6.57504i	−0.459969	+	0.265563i	0.252062	+	0.967711i	$0.418891\pi$
$614$	−23.3076	+	0.908826i	−0.940617	+	0.0366772i
$615$	−1.23594	−	1.23594i	−0.0498379	−	0.0498379i
$616$	19.8242	+	8.53806i	0.798738	+	0.344008i
$617$	17.4067	−	10.0498i	0.700768	−	0.404588i	−0.106866	−	0.994273i	$-0.534081\pi$
$617$	17.4067	−	10.0498i	0.700768	−	0.404588i	0.807633	+	0.589685i	$0.200748\pi$
$618$	−0.156312	−	0.503936i	−0.00628780	−	0.0202713i
$619$	1.75303			0.0704603			0.0352301	−	0.999379i	$-0.488784\pi$
$619$	1.75303			0.0704603			0.0352301	+	0.999379i	$0.488784\pi$
$620$	5.21596	+	2.49169i	0.209478	+	0.100069i
$621$	−5.30495	−	5.30495i	−0.212880	−	0.212880i
$622$	−10.0374	−	2.27436i	−0.402461	−	0.0911933i
$623$	4.72928	−	4.72928i	0.189475	−	0.189475i
$624$	2.31076	+	0.245645i	0.0925044	+	0.00983369i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	25.4401	+	5.76445i	1.01679	+	0.230394i
$627$	0.735366	−	2.74442i	0.0293677	−	0.109602i
$628$	15.6470	+	22.7956i	0.624385	+	0.909643i
$629$	40.8277	−	19.8818i	1.62791	−	0.792738i
$630$	−4.66580	+	1.44725i	−0.185890	+	0.0576598i
$631$	−36.3599	−	9.74260i	−1.44746	−	0.387847i	−0.552323	−	0.833630i	$-0.686258\pi$
$631$	−36.3599	−	9.74260i	−1.44746	−	0.387847i	−0.895141	+	0.445784i	$0.852925\pi$
$632$	20.7570	−	8.25976i	0.825667	−	0.328556i
$633$	−2.39854	−	1.38480i	−0.0953335	−	0.0550408i
$634$	−5.60094	+	3.53161i	−0.222442	+	0.140258i
$635$	−3.42630	−	3.42630i	−0.135969	−	0.135969i
$636$	−3.04718	+	0.237998i	−0.120828	+	0.00943722i
$637$	7.66931	−	7.66931i	0.303869	−	0.303869i
$638$	32.1603	+	29.7464i	1.27324	+	1.17767i
$639$			47.1187i			1.86399i
$640$	5.76440	+	9.73507i	0.227858	+	0.384813i
$641$	4.01373	+	6.95199i	0.158533	+	0.274587i	0.934340	−	0.356383i	$-0.115990\pi$
$641$	4.01373	+	6.95199i	0.158533	+	0.274587i	−0.775807	+	0.630970i	$0.782657\pi$
$642$	−2.74067	+	1.72810i	−0.108166	+	0.0682026i
$643$	17.9169	−	17.9169i	0.706575	−	0.706575i	−0.259238	−	0.965813i	$-0.583472\pi$
$643$	17.9169	−	17.9169i	0.706575	−	0.706575i	0.965813	+	0.259238i	$0.0834715\pi$
$644$	−3.35298	−	9.48641i	−0.132126	−	0.373817i
$645$	0.664230	+	1.15048i	0.0261540	+	0.0453001i
$646$	−15.5670	+	0.607000i	−0.612475	+	0.0238821i
$647$	6.18311	+	23.0757i	0.243083	+	0.907199i	0.974337	+	0.225094i	$0.0722689\pi$
$647$	6.18311	+	23.0757i	0.243083	+	0.907199i	−0.731254	+	0.682105i	$0.761064\pi$
$648$	9.17525	−	21.3036i	0.360438	−	0.836886i
$649$	18.6161	−	69.4762i	0.730745	−	2.72718i
$650$	2.01394	+	1.86278i	0.0789932	+	0.0730641i
$651$	−0.265904	+	0.992368i	−0.0104216	+	0.0388940i
$652$	3.23920	+	0.602340i	0.126857	+	0.0235895i
$653$	−1.38850	+	0.372047i	−0.0543361	+	0.0145593i	−0.285885	−	0.958264i	$-0.592287\pi$
$653$	−1.38850	+	0.372047i	−0.0543361	+	0.0145593i	0.231549	+	0.972823i	$0.425621\pi$
$654$	3.73230	−	4.03517i	0.145944	−	0.157788i
$655$		−	8.83406i		−	0.345175i
$656$	21.7849	+	8.39212i	0.850556	+	0.327657i
$657$	38.3119	−	22.1194i	1.49469	−	0.862959i
$658$	−3.81158	+	7.23940i	−0.148591	+	0.282221i
$659$	18.6392	−	32.2841i	0.726081	−	1.25761i	−0.232446	−	0.972609i	$-0.574673\pi$
$659$	18.6392	−	32.2841i	0.726081	−	1.25761i	0.958527	−	0.285000i	$-0.0919936\pi$
$660$	3.78616	+	0.704050i	0.147376	+	0.0274051i
$661$	1.26503	−	0.338963i	0.0492038	−	0.0131841i	−0.234133	−	0.972205i	$-0.575225\pi$
$661$	1.26503	−	0.338963i	0.0492038	−	0.0131841i	0.283337	+	0.959020i	$0.408559\pi$
$662$	3.25074	−	14.3464i	0.126344	−	0.557590i
$663$	−3.75603	−	2.16854i	−0.145872	−	0.0842193i
$664$	33.8421	−	25.2242i	1.31333	−	0.978887i
$665$			1.75136i			0.0679149i
$666$	23.9666	+	7.23706i	0.928687	+	0.280430i
$667$		−	20.4208i		−	0.790695i
$668$	8.42108	−	2.97643i	0.325821	−	0.115162i
$669$	2.23120	+	1.28818i	0.0862630	+	0.0498040i
$670$	−15.5707	−	3.52815i	−0.601548	−	0.136304i
$671$	29.0213	−	7.77623i	1.12035	−	0.300198i
$672$	−1.51375	+	1.32356i	−0.0583943	+	0.0510573i
$673$	−0.331665	+	0.574460i	−0.0127847	+	0.0221438i	−0.872347	−	0.488887i	$-0.837403\pi$
$673$	−0.331665	+	0.574460i	−0.0127847	+	0.0221438i	0.859562	+	0.511031i	$0.170736\pi$
$674$	17.7754	+	9.35884i	0.684683	+	0.360489i
$675$	−1.53289	+	0.885016i	−0.0590011	+	0.0340643i
$676$	15.2312	−	10.4548i	0.585816	−	0.402108i
$677$			44.2738i			1.70158i	0.525506	+	0.850790i	$0.323876\pi$
$677$			44.2738i			1.70158i	−0.525506	+	0.850790i	$0.676124\pi$
$678$	−1.40130	−	1.29612i	−0.0538164	−	0.0497770i
$679$	−2.06988	+	0.554624i	−0.0794349	+	0.0212845i
$680$	−2.46322	−	20.9717i	−0.0944603	−	0.804227i
$681$	0.629317	−	2.34864i	0.0241155	−	0.0900002i
$682$	−17.8450	+	19.2931i	−0.683319	+	0.738770i
$683$	−0.345918	+	1.29098i	−0.0132362	+	0.0493981i	−0.972228	−	0.234035i	$-0.924807\pi$
$683$	−0.345918	+	1.29098i	−0.0132362	+	0.0493981i	0.958992	+	0.283433i	$0.0914735\pi$
$684$	−6.52756	−	5.58177i	−0.249587	−	0.213424i
$685$	−4.25678	−	15.8865i	−0.162643	−	0.606992i
$686$	0.823487	+	21.1190i	0.0314409	+	0.806326i
$687$	−2.34869	−	4.06806i	−0.0896083	−	0.155206i
$688$	−14.3423	−	10.4464i	−0.546797	−	0.398264i
$689$	6.99949	−	6.99949i	0.266659	−	0.266659i
$690$	−0.957467	−	1.51849i	−0.0364502	−	0.0578080i
$691$	21.0868	+	36.5233i	0.802178	+	1.38941i	0.918180	+	0.396164i	$0.129659\pi$
$691$	21.0868	+	36.5233i	0.802178	+	1.38941i	−0.116002	+	0.993249i	$0.537008\pi$
$692$	3.53673	−	2.42764i	0.134446	−	0.0922850i
$693$		−	22.2095i		−	0.843669i
$694$	27.3923	−	29.6151i	1.03980	−	1.12418i
$695$	0.0488023	−	0.0488023i	0.00185118	−	0.00185118i
$696$	−3.79188	+	1.50889i	−0.143731	+	0.0571944i
$697$	−30.8099	−	30.8099i	−1.16701	−	1.16701i
$698$	−17.5658	−	27.8585i	−0.664876	−	1.05446i
$699$	3.44106	+	1.98670i	0.130153	+	0.0751439i
$700$	−2.36662	+	0.184843i	−0.0894499	+	0.00698641i
$701$	8.30682	+	2.22581i	0.313744	+	0.0840675i	0.412255	−	0.911068i	$-0.364741\pi$
$701$	8.30682	+	2.22581i	0.313744	+	0.0840675i	−0.0985108	+	0.995136i	$0.531408\pi$
$702$	−1.43857	−	4.63780i	−0.0542952	−	0.175043i
$703$	5.02362	−	7.43790i	0.189469	−	0.280526i
$704$	−50.0365	+	11.9185i	−1.88582	+	0.449194i
$705$	−0.377804	+	1.40998i	−0.0142289	+	0.0531030i
$706$	4.93450	−	21.7773i	0.185712	−	0.819600i
$707$	−1.55973	+	2.70153i	−0.0586595	+	0.101601i
$708$	5.09258	+	4.35471i	0.191391	+	0.163660i
$709$	−23.3817	+	23.3817i	−0.878119	+	0.878119i	−0.993340	−	0.115221i	$-0.963243\pi$
$709$	−23.3817	+	23.3817i	−0.878119	+	0.878119i	0.115221	+	0.993340i	$0.463243\pi$
$710$	−5.05983	+	22.3304i	−0.189892	+	0.838045i
$711$	−16.2541	−	16.2541i	−0.609575	−	0.609575i
$712$	−2.30104	+	15.7711i	−0.0862352	+	0.591046i
$713$	12.2505			0.458785
$714$	3.58444	−	1.11183i	0.134144	−	0.0416092i
$715$	−10.8013	+	6.23611i	−0.403944	+	0.233217i
$716$	16.6042	−	19.4176i	0.620527	−	0.725670i
$717$	−1.19078	−	1.19078i	−0.0444707	−	0.0444707i
$718$	−0.833979	−	21.3881i	−0.0311238	−	0.798195i
$719$	5.17883	−	2.99000i	0.193138	−	0.111508i	−0.400313	−	0.916379i	$-0.631099\pi$
$719$	5.17883	−	2.99000i	0.193138	−	0.111508i	0.593451	+	0.804870i	$0.297765\pi$
$720$	6.85373	−	9.40983i	0.255423	−	0.350684i
$721$	−1.42824	+	0.382695i	−0.0531903	+	0.0142523i
$722$	20.1244	−	12.6892i	0.748953	−	0.472244i
$723$	5.16661	+	1.38439i	0.192148	+	0.0514860i
$724$	9.84810	−	20.6155i	0.366002	−	0.766168i
$725$	−4.65373	−	1.24696i	−0.172835	−	0.0463110i
$726$	−5.98631	+	11.3699i	−0.222173	+	0.421977i
$727$	11.0927	+	41.3984i	0.411404	+	1.53538i	0.791931	+	0.610611i	$0.209076\pi$
$727$	11.0927	+	41.3984i	0.411404	+	1.53538i	−0.380527	+	0.924770i	$0.624257\pi$
$728$	0.940193	−	6.44398i	0.0348459	−	0.238830i
$729$	−22.2767			−0.825063
$730$	20.5320	−	6.36866i	0.759923	−	0.235715i
$731$	16.5581	+	28.6795i	0.612424	+	1.06075i
$732$	−0.511701	+	2.75177i	−0.0189130	+	0.101708i
$733$	−32.5598	−	18.7984i	−1.20262	−	0.694334i	−0.241485	−	0.970405i	$-0.577634\pi$
$733$	−32.5598	−	18.7984i	−1.20262	−	0.694334i	−0.961137	+	0.276070i	$0.910968\pi$
$734$	32.4535	+	17.0869i	1.19788	+	0.630690i
$735$	0.433386	+	1.61742i	0.0159857	+	0.0596594i
$736$	19.9161	+	13.3503i	0.734118	+	0.492100i
$737$	36.2924	−	62.8602i	1.33685	−	2.31549i
$738$	−0.935943	−	24.0030i	−0.0344525	−	0.883563i
$739$	−12.6269			−0.464487			−0.232244	−	0.972658i	$-0.574607\pi$
$739$	−12.6269			−0.464487			−0.232244	+	0.972658i	$0.574607\pi$
$740$	10.5811	+	6.00342i	0.388968	+	0.220690i
$741$	−0.857218			−0.0314907
$742$	0.333738	+	8.55898i	0.0122519	+	0.314210i
$743$	−21.6833	+	37.5566i	−0.795485	+	1.37782i	0.127046	+	0.991897i	$0.459450\pi$
$743$	−21.6833	+	37.5566i	−0.795485	+	1.37782i	−0.922531	+	0.385923i	$0.873883\pi$
$744$	−0.905189	−	2.27476i	−0.0331859	−	0.0833967i
$745$	4.36580	+	16.2934i	0.159951	+	0.596944i
$746$	−30.5191	−	16.0684i	−1.11738	−	0.588307i
$747$	−37.6117	−	21.7151i	−1.37614	−	0.794516i
$748$	94.3826	+	17.5508i	3.45097	+	0.641719i
$749$	4.53993	+	7.86338i	0.165885	+	0.287322i
$750$	−0.404519	+	0.125475i	−0.0147709	+	0.00458169i
$751$	39.7107			1.44906			0.724532	−	0.689241i	$-0.242056\pi$
$751$	39.7107			1.44906			0.724532	+	0.689241i	$0.242056\pi$
$752$	−3.02707	−	19.2602i	−0.110386	−	0.702346i
$753$	−1.61549	−	6.02908i	−0.0588716	−	0.219712i
$754$	6.15755	−	11.6951i	0.224245	−	0.425912i
$755$	11.8482	+	3.17471i	0.431200	+	0.115540i
$756$	3.79137	+	1.81115i	0.137891	+	0.0658710i
$757$	6.52060	+	1.74719i	0.236995	+	0.0635027i	0.375362	−	0.926878i	$-0.377519\pi$
$757$	6.52060	+	1.74719i	0.236995	+	0.0635027i	−0.138366	+	0.990381i	$0.544185\pi$
$758$	36.7517	−	23.1733i	1.33488	−	0.841693i
$759$	7.88333	−	2.11233i	0.286147	−	0.0766728i
$760$	−2.49413	−	3.34626i	−0.0904717	−	0.121382i
$761$	−30.3106	+	17.4998i	−1.09876	+	0.634368i	−0.935894	−	0.352281i	$-0.885406\pi$
$761$	−30.3106	+	17.4998i	−1.09876	+	0.634368i	−0.162863	+	0.986649i	$0.552073\pi$
$762$	0.0799615	+	2.05067i	0.00289670	+	0.0742881i
$763$	−10.8921	−	10.8921i	−0.394322	−	0.394322i
$764$	−18.6833	−	15.9762i	−0.675936	−	0.577999i
$765$	−18.8163	+	10.8636i	−0.680303	+	0.392773i
$766$	−18.5799	+	5.76316i	−0.671318	+	0.208231i
$767$	−21.7008			−0.783570
$768$	1.00738	−	4.68462i	0.0363508	−	0.169042i
$769$	5.39991	+	5.39991i	0.194726	+	0.194726i	0.797735	−	0.603009i	$-0.206032\pi$
$769$	5.39991	+	5.39991i	0.194726	+	0.194726i	−0.603009	+	0.797735i	$0.706032\pi$
$770$	2.38496	−	10.5255i	0.0859480	−	0.379312i
$771$	−2.17282	+	2.17282i	−0.0782523	+	0.0782523i
$772$	12.2204	−	14.2910i	0.439820	−	0.514344i
$773$	19.6300	−	34.0002i	0.706044	−	1.22290i	−0.260270	−	0.965536i	$-0.583811\pi$
$773$	19.6300	−	34.0002i	0.706044	−	1.22290i	0.966314	−	0.257368i	$-0.0828552\pi$
$774$	−4.03458	+	17.8057i	−0.145020	+	0.640014i
$775$	0.748058	−	2.79179i	0.0268710	−	0.100284i
$776$	3.16501	−	4.00745i	0.113617	−	0.143859i
$777$	−0.705200	+	2.04394i	−0.0252989	+	0.0733260i
$778$	12.2334	+	39.4393i	0.438589	+	1.41397i
$779$	−8.31843	−	2.22892i	−0.298039	−	0.0798592i
$780$	−0.0904730	−	1.15836i	−0.00323945	−	0.0414760i
$781$	−90.1498	−	52.0480i	−3.22581	−	1.86242i
$782$	−23.8680	−	37.8534i	−0.853519	−	1.35364i
$783$	6.03009	+	6.03009i	0.215498	+	0.215498i
$784$	−14.0541	−	17.3975i	−0.501931	−	0.621340i
$785$	9.77541	−	9.77541i	0.348899	−	0.348899i
$786$	−2.54055	+	2.74672i	−0.0906185	+	0.0979722i
$787$			20.6260i			0.735239i	0.929976	+	0.367619i	$0.119827\pi$
$787$			20.6260i			0.735239i	−0.929976	+	0.367619i	$0.880173\pi$
$788$	−13.3078	−	19.3877i	−0.474072	−	0.690657i
$789$	1.12893	+	1.95536i	0.0401909	+	0.0696126i
$790$	−5.95767	−	9.44854i	−0.211964	−	0.336164i
$791$	−3.78251	+	3.78251i	−0.134491	+	0.134491i
$792$	31.6288	+	42.4349i	1.12388	+	1.50786i
$793$	−4.53238	−	7.85032i	−0.160950	−	0.278773i
$794$	1.14468	+	29.3563i	0.0406233	+	1.04182i
$795$	0.395535	+	1.47616i	0.0140282	+	0.0523538i
$796$	18.0861	−	21.1506i	0.641044	−	0.749664i
$797$	−4.73828	+	17.6835i	−0.167839	+	0.626382i	0.829823	+	0.558027i	$0.188442\pi$
$797$	−4.73828	+	17.6835i	−0.167839	+	0.626382i	−0.997661	+	0.0683545i	$0.978225\pi$
$798$	0.503667	−	0.544539i	0.0178296	−	0.0192765i
$799$	−9.41800	+	35.1484i	−0.333185	+	1.24346i
$800$	4.25858	−	3.72351i	0.150564	−	0.131646i
$801$	15.8407	−	4.24450i	0.559703	−	0.149972i
$802$	−12.4609	−	11.5256i	−0.440011	−	0.406985i
$803$			97.7335i			3.44894i
$804$	3.82665	+	5.57490i	0.134955	+	0.196611i
$805$	−4.35677	+	2.51538i	−0.153556	+	0.0886556i
$806$	7.01596	+	3.69393i	0.247127	+	0.130113i
$807$	−3.93368	+	6.81334i	−0.138472	+	0.239841i
$808$	−0.867160	−	7.38293i	−0.0305066	−	0.259731i
$809$	−54.1240	+	14.5025i	−1.90290	+	0.509880i	−0.906807	+	0.421545i	$0.861488\pi$
$809$	−54.1240	+	14.5025i	−1.90290	+	0.509880i	−0.996091	+	0.0883346i	$0.971846\pi$
$810$	−11.3110	−	2.56295i	−0.397428	−	0.0900529i
$811$	−8.27970	−	4.78029i	−0.290740	−	0.167859i	0.347536	−	0.937667i	$-0.387019\pi$
$811$	−8.27970	−	4.78029i	−0.290740	−	0.167859i	−0.638275	+	0.769808i	$0.720352\pi$
$812$	3.81130	+	10.7831i	0.133750	+	0.378413i
$813$			7.11568i			0.249558i
$814$	−40.3202	+	37.8599i	−1.41322	+	1.32699i
$815$		−	1.64736i		−	0.0577046i
$816$	−5.26529	+	7.22898i	−0.184322	+	0.253065i
$817$	5.66846	+	3.27268i	0.198314	+	0.114497i
$818$	−8.65748	+	38.2079i	−0.302702	+	1.33591i
$819$	−6.47241	+	1.73428i	−0.226164	+	0.0606006i
$820$	2.13400	−	11.4760i	0.0745223	−	0.400758i
$821$	−14.5308	+	25.1682i	−0.507130	+	0.878375i	0.492836	+	0.870122i	$0.335960\pi$
$821$	−14.5308	+	25.1682i	−0.507130	+	0.878375i	−0.999966	+	0.00825272i	$0.997373\pi$
$822$	−3.24520	+	6.16368i	−0.113190	+	0.214983i
$823$	−34.5001	+	19.9186i	−1.20260	+	0.694320i	−0.961132	−	0.276089i	$-0.910962\pi$
$823$	−34.5001	+	19.9186i	−1.20260	+	0.694320i	−0.241466	+	0.970409i	$0.577628\pi$
$824$	2.18388	−	2.76517i	0.0760791	−	0.0963293i
$825$		−	1.92553i		−	0.0670385i
$826$	12.7505	−	13.7852i	0.443647	−	0.479649i
$827$	−13.1091	+	3.51256i	−0.455846	+	0.122144i	−0.479434	−	0.877578i	$-0.659158\pi$
$827$	−13.1091	+	3.51256i	−0.455846	+	0.122144i	0.0235873	+	0.999722i	$0.492491\pi$
$828$	4.51031	−	24.2551i	0.156744	−	0.842922i
$829$	−11.5461	+	43.0906i	−0.401012	+	1.49660i	0.410282	+	0.911959i	$0.365430\pi$
$829$	−11.5461	+	43.0906i	−0.401012	+	1.49660i	−0.811294	+	0.584638i	$0.801236\pi$
$830$	−15.4930	−	14.3301i	−0.537771	−	0.497406i
$831$	−1.12965	+	4.21591i	−0.0391871	+	0.146248i
$832$	7.38055	+	13.6512i	0.255875	+	0.473271i
$833$	10.8036	+	40.3195i	0.374322	+	1.39699i
$834$	−0.0292086	+	0.00113893i	−0.00101141	+	3.94378e-5i
$835$	−2.23290	−	3.86750i	−0.0772728	−	0.133840i
$836$	17.8898	−	6.32314i	0.618730	−	0.218690i
$837$	−3.61747	+	3.61747i	−0.125038	+	0.125038i
$838$	−20.6563	+	13.0246i	−0.713562	+	0.449928i
$839$	−8.19510	−	14.1943i	−0.282926	−	0.490043i	0.689178	−	0.724592i	$-0.257972\pi$
$839$	−8.19510	−	14.1943i	−0.282926	−	0.490043i	−0.972104	+	0.234549i	$0.924639\pi$
$840$	0.788996	+	0.623135i	0.0272230	+	0.0215002i
$841$		−	5.78788i		−	0.199582i
$842$	−4.09929	−	3.79160i	−0.141271	−	0.130667i
$843$	−1.84002	+	1.84002i	−0.0633735	+	0.0633735i
$844$	−1.44022	−	18.4398i	−0.0495745	−	0.634723i
$845$	−6.53159	−	6.53159i	−0.224693	−	0.224693i
$846$	−16.9694	+	10.6998i	−0.583418	+	0.367867i
$847$	31.1854	+	18.0049i	1.07154	+	0.618656i
$848$	−12.8266	−	15.8781i	−0.440467	−	0.545254i
$849$	−8.82862	−	2.36562i	−0.302998	−	0.0811880i
$850$	−10.0840	+	3.12787i	−0.345877	+	0.107285i
$851$	25.7180	+	1.81436i	0.881602	+	0.0621954i
$852$	7.99513	−	5.48791i	0.273909	−	0.188013i
$853$	4.44072	−	16.5730i	0.152047	−	0.567449i	−0.847293	−	0.531126i	$-0.821769\pi$
$853$	4.44072	−	16.5730i	0.152047	−	0.567449i	0.999340	−	0.0363225i	$-0.0115643\pi$
$854$	7.64989	+	1.73338i	0.261774	+	0.0593150i
$855$	−2.14717	+	3.71900i	−0.0734315	+	0.127187i
$856$	−19.8726	−	8.55892i	−0.679232	−	0.292538i
$857$	5.16963	−	5.16963i	0.176591	−	0.176591i	−0.613277	−	0.789868i	$-0.710149\pi$
$857$	5.16963	−	5.16963i	0.176591	−	0.176591i	0.789868	+	0.613277i	$0.210149\pi$
$858$	5.15179	+	1.16734i	0.175879	+	0.0398523i
$859$	−25.4515	−	25.4515i	−0.868395	−	0.868395i	0.123899	−	0.992295i	$-0.460460\pi$
$859$	−25.4515	−	25.4515i	−0.868395	−	0.868395i	−0.992295	+	0.123899i	$0.960460\pi$
$860$	−3.82413	+	8.00521i	−0.130402	+	0.272975i
$861$	2.07459			0.0707017
$862$	8.91807	+	28.7510i	0.303751	+	0.979264i
$863$	−17.2319	+	9.94886i	−0.586582	+	0.338663i	−0.763745	−	0.645518i	$-0.776641\pi$
$863$	−17.2319	+	9.94886i	−0.586582	+	0.338663i	0.177163	+	0.984182i	$0.443308\pi$
$864$	−9.82331	+	1.93882i	−0.334196	+	0.0659601i
$865$	−1.51665	−	1.51665i	−0.0515678	−	0.0515678i
$866$	−52.6437	+	2.05272i	−1.78891	+	0.0697543i
$867$	10.0462	−	5.80020i	0.341188	−	0.196985i
$868$	−6.46883	+	2.28641i	−0.219566	+	0.0776059i
$869$	49.0526	−	13.1436i	1.66399	−	0.445866i
$870$	1.08834	+	1.72606i	0.0368983	+	0.0585188i
$871$	−21.1530	−	5.66794i	−0.716743	−	0.192051i
$872$	36.3228	+	5.29959i	1.23005	+	0.179467i
$873$	−5.07535	−	1.35994i	−0.171775	−	0.0460269i
$874$	−7.82628	−	4.12057i	−0.264728	−	0.139380i
$875$	0.307196	+	1.14647i	0.0103851	+	0.0387578i
$876$	−8.21541	−	3.92454i	−0.277573	−	0.132598i
$877$	−51.9548			−1.75439			−0.877195	−	0.480134i	$-0.840588\pi$
$877$	−51.9548			−1.75439			−0.877195	+	0.480134i	$0.840588\pi$
$878$	16.9584	+	54.6722i	0.572318	+	1.84510i
$879$	2.21796	+	3.84162i	0.0748099	+	0.129575i
$880$	10.4326	+	23.5071i	0.351683	+	0.792425i
$881$	−3.22822	−	1.86381i	−0.108761	−	0.0627934i	0.444633	−	0.895713i	$-0.353334\pi$
$881$	−3.22822	−	1.86381i	−0.108761	−	0.0627934i	−0.553394	+	0.832920i	$0.686668\pi$
$882$	−10.7210	+	20.3625i	−0.360993	+	0.685641i
$883$	−2.29643	−	8.57040i	−0.0772811	−	0.288417i	0.916460	−	0.400127i	$-0.131034\pi$
$883$	−2.29643	−	8.57040i	−0.0772811	−	0.288417i	−0.993741	+	0.111710i	$0.964367\pi$
$884$	−2.25534	−	28.8760i	−0.0758552	−	0.971204i
$885$	1.67515	−	2.90144i	0.0563094	−	0.0975308i
$886$	−18.8324	+	0.734327i	−0.632687	+	0.0246702i
$887$	−15.4412			−0.518464			−0.259232	−	0.965815i	$-0.583469\pi$
$887$	−15.4412			−0.518464			−0.259232	+	0.965815i	$0.583469\pi$
$888$	−1.56340	−	4.90957i	−0.0524643	−	0.164754i
$889$	5.75122			0.192890
$890$	7.96298	−	0.310499i	0.266920	−	0.0104079i
$891$	26.3638	−	45.6635i	0.883221	−	1.52978i
$892$	1.33974	+	17.1532i	0.0448578	+	0.574332i
$893$	1.86145	+	6.94703i	0.0622911	+	0.232473i
$894$	3.32832	−	6.32154i	0.111316	−	0.211424i
$895$	−11.0630	−	6.38720i	−0.369794	−	0.213501i
$896$	−13.0083	−	3.33249i	−0.434578	−	0.111331i
$897$	−1.23117	−	2.13246i	−0.0411077	−	0.0712006i
$898$	−0.0682298	−	0.219967i	−0.00227686	−	0.00734038i
$899$	−13.9250			−0.464426
$900$	−5.25212	−	2.50896i	−0.175071	−	0.0836320i
$901$	9.86000	+	36.7980i	0.328484	+	1.22592i
$902$	46.9576	+	24.7234i	1.56352	+	0.823199i
$903$	−1.52304	−	0.408098i	−0.0506837	−	0.0135806i
$904$	1.84039	−	12.6138i	0.0612105	−	0.419530i
$905$	−11.0342	−	2.95661i	−0.366790	−	0.0982811i
$906$	−2.77088	−	4.39446i	−0.0920562	−	0.145996i
$907$	−22.6143	+	6.05948i	−0.750895	+	0.201202i	−0.613915	−	0.789372i	$-0.710406\pi$
$907$	−22.6143	+	6.05948i	−0.750895	+	0.201202i	−0.136980	+	0.990574i	$0.543740\pi$
$908$	15.3098	−	5.41126i	0.508074	−	0.179579i
$909$	−6.62413	+	3.82444i	−0.219709	+	0.126849i
$910$	−3.25363	+	0.126868i	−0.107857	+	0.00420563i
$911$	−13.5486	−	13.5486i	−0.448884	−	0.448884i	0.446099	−	0.894983i	$-0.352813\pi$
$911$	−13.5486	−	13.5486i	−0.448884	−	0.448884i	−0.894983	+	0.446099i	$0.852813\pi$
$912$	−0.186854	+	1.75771i	−0.00618734	+	0.0582036i
$913$	83.0930	−	47.9737i	2.74998	−	1.58770i
$914$	−4.24542	−	13.6868i	−0.140426	−	0.452720i
$915$	1.39947			0.0462651
$916$	13.5220	−	28.3061i	0.446779	−	0.935261i
$917$	7.41421	+	7.41421i	0.244839	+	0.244839i
$918$	18.2258	+	4.12978i	0.601542	+	0.136303i
$919$	35.2263	−	35.2263i	1.16201	−	1.16201i	0.177971	−	0.984036i	$-0.443047\pi$
$919$	35.2263	−	35.2263i	1.16201	−	1.16201i	0.984036	−	0.177971i	$-0.0569534\pi$
$920$	4.74214	−	11.0106i	0.156344	−	0.363008i
$921$	2.46975	−	4.27773i	0.0813810	−	0.140956i
$922$	37.9768	+	8.60513i	1.25070	+	0.283395i
$923$	−8.12856	+	30.3362i	−0.267555	+	0.998529i
$924$	−3.76852	+	2.58674i	−0.123975	+	0.0850976i
$925$	1.98391	−	5.75014i	0.0652305	−	0.189063i
$926$	26.7777	−	8.30599i	0.879971	−	0.272952i
$927$	−3.50203	−	0.938367i	−0.115022	−	0.0308200i
$928$	−22.6385	−	15.1752i	−0.743145	−	0.498151i
$929$	−15.0447	−	8.68606i	−0.493601	−	0.284980i	0.232466	−	0.972604i	$-0.425320\pi$
$929$	−15.0447	−	8.68606i	−0.493601	−	0.284980i	−0.726067	+	0.687624i	$0.758654\pi$
$930$	−1.03547	+	0.652902i	−0.0339543	+	0.0214095i
$931$	5.83377	+	5.83377i	0.191194	+	0.191194i
$932$	2.06621	+	26.4546i	0.0676811	+	0.866548i
$933$	1.54111	−	1.54111i	0.0504535	−	0.0504535i
$934$	−17.8430	−	16.5038i	−0.583842	−	0.540019i
$935$		−	48.0003i		−	1.56978i
$936$	9.89680	−	12.5311i	0.323487	−	0.409591i
$937$	16.8131	+	29.1211i	0.549260	+	0.951346i	0.998325	+	0.0578470i	$0.0184236\pi$
$937$	16.8131	+	29.1211i	0.549260	+	0.951346i	−0.449066	+	0.893499i	$0.648243\pi$
$938$	16.0292	−	10.1070i	0.523371	−	0.330005i
$939$	−3.90600	+	3.90600i	−0.127467	+	0.127467i
$940$	−9.19108	+	3.24859i	−0.299780	+	0.105957i
$941$	10.0905	+	17.4772i	0.328940	+	0.569740i	0.982302	−	0.187305i	$-0.0599754\pi$
$941$	10.0905	+	17.4772i	0.328940	+	0.569740i	−0.653362	+	0.757046i	$0.726642\pi$
$942$	−5.85067	+	0.228134i	−0.190625	+	0.00743300i
$943$	−6.40254	−	23.8946i	−0.208495	−	0.778115i
$944$	−4.73027	+	44.4971i	−0.153957	+	1.44826i
$945$	0.543747	−	2.02929i	0.0176881	−	0.0660128i
$946$	−29.6101	−	27.3876i	−0.962709	−	0.890449i
$947$	13.9282	−	51.9808i	0.452606	−	1.68915i	−0.242427	−	0.970170i	$-0.577944\pi$
$947$	13.9282	−	51.9808i	0.452606	−	1.68915i	0.695033	−	0.718978i	$-0.255390\pi$
$948$	−0.864890	+	4.65112i	−0.0280903	+	0.151061i
$949$	28.4820	−	7.63174i	0.924566	−	0.247737i
$950$	−1.41695	+	1.53193i	−0.0459718	+	0.0497024i
$951$		−	1.40218i		−	0.0454689i
$952$	19.6683	+	15.5337i	0.637454	+	0.503450i
$953$	−4.74437	+	2.73916i	−0.153685	+	0.0887302i	−0.574870	−	0.818244i	$-0.694948\pi$
$953$	−4.74437	+	2.73916i	−0.153685	+	0.0887302i	0.421185	+	0.906975i	$0.361614\pi$
$954$	−9.78460	+	18.5841i	−0.316788	+	0.601682i
$955$	−6.14564	+	10.6446i	−0.198868	+	0.344450i
$956$	2.05603	−	11.0567i	0.0664968	−	0.357599i
$957$	−8.96091	+	2.40107i	−0.289665	+	0.0776156i
$958$	8.76017	−	38.6610i	0.283028	−	1.24908i
$959$	16.9058	+	9.76054i	0.545915	+	0.315184i
$960$	−2.39492	−	0.0669827i	−0.0772957	−	0.00216186i
$961$			22.6463i			0.730527i
$962$	14.1818	+	8.79394i	0.457241	+	0.283528i
$963$			22.2638i			0.717440i
$964$	11.9038	+	33.6790i	0.383397	+	1.08473i
$965$	−8.14213	−	4.70086i	−0.262105	−	0.151326i
$966$	2.07801	+	0.470855i	0.0668589	+	0.0151495i
$967$	−25.4049	+	6.80722i	−0.816966	+	0.218905i	−0.643019	−	0.765850i	$-0.722319\pi$
$967$	−25.4049	+	6.80722i	−0.816966	+	0.218905i	−0.173946	+	0.984755i	$0.555652\pi$
$968$	−85.2259	+	10.0102i	−2.73926	+	0.321740i
$969$	1.64953	−	2.85707i	0.0529906	−	0.0917824i
$970$	−2.25927	−	1.18951i	−0.0725407	−	0.0381930i
$971$	−11.2481	+	6.49407i	−0.360968	+	0.208405i	−0.669505	−	0.742807i	$-0.733494\pi$
$971$	−11.2481	+	6.49407i	−0.360968	+	0.208405i	0.308538	+	0.951212i	$0.400160\pi$
$972$	8.78994	+	12.8057i	0.281937	+	0.410744i
$973$			0.0819171i			0.00262614i
$974$	−34.6640	−	32.0621i	−1.11071	−	1.02734i
$975$	−0.561149	+	0.150360i	−0.0179712	+	0.00481536i
$976$	−17.0849	+	7.58238i	−0.546874	+	0.242706i
$977$	1.67731	−	6.25980i	0.0536618	−	0.200269i	−0.933891	−	0.357559i	$-0.883609\pi$
$977$	1.67731	−	6.25980i	0.0536618	−	0.200269i	0.987552	+	0.157290i	$0.0502758\pi$
$978$	−0.473759	+	0.512204i	−0.0151491	+	0.0163785i
$979$	−9.37707	+	34.9957i	−0.299692	+	1.11847i
$980$	−7.26748	+	8.49890i	−0.232151	+	0.271487i
$981$	−9.77561	−	36.4831i	−0.312111	−	1.16482i
$982$	0.656029	+	16.8244i	0.0209347	+	0.536888i
$983$	7.73543	+	13.3982i	0.246722	+	0.427335i	0.962614	−	0.270876i	$-0.0873132\pi$
$983$	7.73543	+	13.3982i	0.246722	+	0.427335i	−0.715892	+	0.698211i	$0.753980\pi$
$984$	−3.96384	+	2.95444i	−0.126363	+	0.0941842i
$985$	−8.31399	+	8.31399i	−0.264906	+	0.264906i
$986$	27.1306	+	43.0277i	0.864014	+	1.37028i
$987$	−0.866282	−	1.50044i	−0.0275741	−	0.0477597i
$988$	−3.23968	−	4.71977i	−0.103068	−	0.150156i
$989$			18.8015i			0.597853i
$990$	17.9687	−	19.4268i	0.571082	−	0.617425i
$991$	−0.900973	+	0.900973i	−0.0286204	+	0.0286204i	−0.721272	−	0.692652i	$-0.756442\pi$
$991$	−0.900973	+	0.900973i	−0.0286204	+	0.0286204i	0.692652	+	0.721272i	$0.256442\pi$
$992$	9.10366	−	13.5809i	0.289042	−	0.431194i
$993$	2.20271	+	2.20271i	0.0699008	+	0.0699008i
$994$	−14.4948	−	22.9879i	−0.459746	−	0.729133i
$995$	−12.0503	−	6.95726i	−0.382021	−	0.220560i
$996$	0.695999	+	8.91115i	0.0220536	+	0.282361i
$997$	46.3785	+	12.4271i	1.46882	+	0.393570i	0.902527	−	0.430632i	$-0.141709\pi$
$997$	46.3785	+	12.4271i	1.46882	+	0.393570i	0.566296	+	0.824202i	$0.308376\pi$
$998$	−3.45517	−	11.1391i	−0.109371	−	0.352603i
$999$	−8.13009	+	7.05856i	−0.257225	+	0.223323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.251.4	yes	304
4.3	odd	2	inner	740.2.be.a.251.62	yes	304
37.23	odd	12	inner	740.2.be.a.171.62	yes	304
148.23	even	12	inner	740.2.be.a.171.4	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.171.4	✓	304	148.23	even	12	inner
740.2.be.a.171.62	yes	304	37.23	odd	12	inner
740.2.be.a.251.4	yes	304	1.1	even	1	trivial
740.2.be.a.251.62	yes	304	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41314 + 0.0551022i) q^{2} +(0.149741 - 0.259359i) q^{3} +(1.99393 - 0.155734i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-0.197314 + 0.374762i) q^{6} +(1.02790 + 0.593457i) q^{7} +(-2.80912 + 0.329944i) q^{8} +(1.45516 + 2.52040i) q^{9} +(0.418972 + 1.35073i) q^{10} -6.42954 q^{11} +(0.258182 - 0.540463i) q^{12} +(0.502065 + 1.87373i) q^{13} +(-1.48526 - 0.781998i) q^{14} +(-0.289278 - 0.0775117i) q^{15} +(3.95149 - 0.621045i) q^{16} +(-7.21119 - 1.93223i) q^{17} +(-2.19522 - 3.48150i) q^{18} +(-1.42528 + 0.381903i) q^{19} +(-0.666494 - 1.88568i) q^{20} +(0.307837 - 0.177730i) q^{21} +(9.08584 - 0.354282i) q^{22} +(-2.99709 - 2.99709i) q^{23} +(-0.335066 + 0.777976i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.812735 - 2.62018i) q^{26} +1.77003 q^{27} +(2.14198 + 1.02323i) q^{28} +(3.40677 + 3.40677i) q^{29} +(0.413061 + 0.0935950i) q^{30} +(-2.04373 + 2.04373i) q^{31} +(-5.54979 + 1.09536i) q^{32} +(-0.962767 + 1.66756i) q^{33} +(10.2969 + 2.33316i) q^{34} +(0.307196 - 1.14647i) q^{35} +(3.29399 + 4.79888i) q^{36} +(-4.59319 + 3.98781i) q^{37} +(1.99308 - 0.618218i) q^{38} +(0.561149 + 0.150360i) q^{39} +(1.04575 + 2.62800i) q^{40} +(5.05443 + 2.91817i) q^{41} +(-0.425223 + 0.268120i) q^{42} +(-3.13663 - 3.13663i) q^{43} +(-12.8200 + 1.00130i) q^{44} +(2.05790 - 2.05790i) q^{45} +(4.40045 + 4.07016i) q^{46} -4.87415i q^{47} +(0.430627 - 1.11785i) q^{48} +(-2.79562 - 4.84215i) q^{49} +(1.19626 - 0.754290i) q^{50} +(-1.58095 + 1.58095i) q^{51} +(1.29289 + 3.65790i) q^{52} +(-2.55145 - 4.41924i) q^{53} +(-2.50130 + 0.0975327i) q^{54} +(1.66409 + 6.21046i) q^{55} +(-3.08329 - 1.32794i) q^{56} +(-0.114373 + 0.426846i) q^{57} +(-5.00196 - 4.62652i) q^{58} +(-2.89540 + 10.8058i) q^{59} +(-0.588870 - 0.109502i) q^{60} +(-4.51374 + 1.20945i) q^{61} +(2.77546 - 3.00069i) q^{62} +3.45429i q^{63} +(7.78227 - 1.85370i) q^{64} +(1.67994 - 0.969915i) q^{65} +(1.26864 - 2.40955i) q^{66} +(-5.64462 + 9.77678i) q^{67} +(-14.6795 - 2.72970i) q^{68} +(-1.22611 + 0.328535i) q^{69} +(-0.370938 + 1.63705i) q^{70} +(14.0212 + 8.09513i) q^{71} +(-4.91929 - 6.59999i) q^{72} -15.2007i q^{73} +(6.27108 - 5.88843i) q^{74} +0.299482i q^{75} +(-2.78243 + 0.983451i) q^{76} +(-6.60892 - 3.81566i) q^{77} +(-0.801268 - 0.181558i) q^{78} +(-7.62925 + 2.04425i) q^{79} +(-1.62261 - 3.65611i) q^{80} +(-4.10042 + 7.10213i) q^{81} +(-7.30341 - 3.84528i) q^{82} +(-12.9236 + 7.46145i) q^{83} +(0.586126 - 0.402321i) q^{84} +7.46558i q^{85} +(4.60533 + 4.25966i) q^{86} +(1.39371 - 0.373443i) q^{87} +(18.0613 - 2.12139i) q^{88} +(1.45843 - 5.44295i) q^{89} +(-2.79471 + 3.02150i) q^{90} +(-0.595908 + 2.22396i) q^{91} +(-6.44273 - 5.50923i) q^{92} +(0.224030 + 0.836091i) q^{93} +(0.268576 + 6.88786i) q^{94} +(0.737779 + 1.27787i) q^{95} +(-0.546940 + 1.60341i) q^{96} +(-1.27664 + 1.27664i) q^{97} +(4.21741 + 6.68859i) q^{98} +(-9.35599 - 16.2050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more