LMFDB - Embedded newform 296.2.q.a.85.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [296,2,Mod(85,296)] 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("296.85"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(296, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 296 = 2^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	296.q (of order $6$, degree $2$, 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:	$2.36357189983$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.23
Character	$\chi$	$=$	296.85
Dual form			296.2.q.a.101.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.423750 - 1.34924i) q^{2} +(-0.600244 - 0.346551i) q^{3} +(-1.64087 - 1.14348i) q^{4} +(-1.31034 + 2.26957i) q^{5} +(-0.721932 + 0.663020i) q^{6} +(-1.74382 + 3.02039i) q^{7} +(-2.23814 + 1.72938i) q^{8} +(-1.25980 - 2.18205i) q^{9} +(2.50693 + 2.72968i) q^{10} -1.40440i q^{11} +(0.588651 + 1.25501i) q^{12} +(-2.32009 + 4.01851i) q^{13} +(3.33627 + 3.63272i) q^{14} +(1.57304 - 0.908198i) q^{15} +(1.38493 + 3.75260i) q^{16} +(-5.28425 + 3.05086i) q^{17} +(-3.47793 + 0.775132i) q^{18} +(1.73592 - 3.00670i) q^{19} +(4.74529 - 2.22574i) q^{20} +(2.09344 - 1.20865i) q^{21} +(-1.89486 - 0.595113i) q^{22} -6.02292i q^{23} +(1.94275 - 0.262419i) q^{24} +(-0.933966 - 1.61768i) q^{25} +(4.43878 + 4.83318i) q^{26} +3.82565i q^{27} +(6.31514 - 2.96206i) q^{28} +6.17494 q^{29} +(-0.558795 - 2.50726i) q^{30} -1.36885i q^{31} +(5.65000 - 0.278429i) q^{32} +(-0.486696 + 0.842982i) q^{33} +(1.87713 + 8.42250i) q^{34} +(-4.56999 - 7.91546i) q^{35} +(-0.427938 + 5.02101i) q^{36} +(-5.70217 - 2.11785i) q^{37} +(-3.32115 - 3.61625i) q^{38} +(2.78524 - 1.60806i) q^{39} +(-0.992226 - 7.34568i) q^{40} +(-3.13563 + 5.43107i) q^{41} +(-0.743656 - 3.33671i) q^{42} -2.90404 q^{43} +(-1.60590 + 2.30444i) q^{44} +6.60307 q^{45} +(-8.12634 - 2.55221i) q^{46} -8.48133 q^{47} +(0.469173 - 2.73242i) q^{48} +(-2.58184 - 4.47188i) q^{49} +(-2.57839 + 0.574650i) q^{50} +4.22912 q^{51} +(8.40203 - 3.94090i) q^{52} +(-2.05008 + 1.18361i) q^{53} +(5.16171 + 1.62112i) q^{54} +(3.18738 + 1.84023i) q^{55} +(-1.32047 - 9.77577i) q^{56} +(-2.08395 + 1.20317i) q^{57} +(2.61663 - 8.33144i) q^{58} +(1.01427 + 1.75677i) q^{59} +(-3.61967 - 0.308502i) q^{60} +(-6.65507 + 11.5269i) q^{61} +(-1.84690 - 0.580049i) q^{62} +8.78751 q^{63} +(2.01852 - 7.74116i) q^{64} +(-6.08019 - 10.5312i) q^{65} +(0.931144 + 1.01388i) q^{66} +(4.98642 + 2.87891i) q^{67} +(12.1594 + 1.03633i) q^{68} +(-2.08725 + 3.61522i) q^{69} +(-12.6163 + 2.81182i) q^{70} +(3.65561 - 6.33170i) q^{71} +(6.59319 + 2.70504i) q^{72} -10.9720 q^{73} +(-5.27377 + 6.79613i) q^{74} +1.29467i q^{75} +(-6.28650 + 2.94863i) q^{76} +(4.24183 + 2.44902i) q^{77} +(-0.989405 - 4.43935i) q^{78} +(7.01349 + 4.04924i) q^{79} +(-10.3315 - 1.77398i) q^{80} +(-2.45363 + 4.24981i) q^{81} +(5.99907 + 6.53212i) q^{82} +(8.75178 - 5.05285i) q^{83} +(-4.81713 - 0.410561i) q^{84} -15.9906i q^{85} +(-1.23058 + 3.91823i) q^{86} +(-3.70647 - 2.13993i) q^{87} +(2.42873 + 3.14324i) q^{88} +(15.2905 - 8.82800i) q^{89} +(2.79805 - 8.90910i) q^{90} +(-8.09164 - 14.0151i) q^{91} +(-6.88706 + 9.88284i) q^{92} +(-0.474376 + 0.821644i) q^{93} +(-3.59396 + 11.4433i) q^{94} +(4.54927 + 7.87957i) q^{95} +(-3.48787 - 1.79089i) q^{96} +5.77275i q^{97} +(-7.12767 + 1.58855i) q^{98} +(-3.06446 + 1.76927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 6 q^{2} - 2 q^{4} + 2 q^{7} + 30 q^{9} - 12 q^{12} - 6 q^{15} - 6 q^{16} - 12 q^{17} - 48 q^{18} + 18 q^{20} - 12 q^{22} - 6 q^{24} - 32 q^{25} - 16 q^{26} + 10 q^{28} - 14 q^{30} - 6 q^{32} + 4 q^{33}+ \cdots + 48 q^{98}+O(q^{100}) $ 72 * q - 6 * q^2 - 2 * q^4 + 2 * q^7 + 30 * q^9 - 12 * q^12 - 6 * q^15 - 6 * q^16 - 12 * q^17 - 48 * q^18 + 18 * q^20 - 12 * q^22 - 6 * q^24 - 32 * q^25 - 16 * q^26 + 10 * q^28 - 14 * q^30 - 6 * q^32 + 4 * q^33 + 8 * q^34 + 4 * q^36 - 24 * q^38 - 6 * q^39 - 18 * q^40 + 6 * q^42 - 10 * q^44 - 8 * q^46 + 32 * q^47 + 20 * q^48 - 18 * q^49 + 12 * q^50 + 42 * q^52 + 30 * q^54 + 24 * q^55 - 24 * q^56 - 6 * q^57 - 8 * q^58 + 32 * q^62 + 8 * q^63 - 68 * q^64 + 6 * q^65 + 20 * q^70 + 18 * q^71 + 18 * q^72 - 64 * q^73 - 12 * q^74 - 72 * q^76 + 54 * q^78 + 54 * q^79 - 16 * q^81 - 12 * q^84 + 48 * q^86 - 108 * q^87 - 36 * q^89 + 24 * q^90 - 120 * q^92 - 72 * q^94 + 50 * q^95 + 36 * q^96 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/296\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.423750	−	1.34924i	0.299636	−	0.954054i
$2$	0.423750	−	1.34924i	0.299636	−	0.954054i
$3$	−0.600244	−	0.346551i	−0.346551	−	0.200081i	0.316614	−	0.948554i	$-0.397454\pi$
$3$	−0.600244	−	0.346551i	−0.346551	−	0.200081i	−0.663165	+	0.748473i	$0.730787\pi$
$4$	−1.64087	−	1.14348i	−0.820436	−	0.571738i
$5$	−1.31034	+	2.26957i	−0.586001	+	1.01498i	0.408749	+	0.912647i	$0.365965\pi$
$5$	−1.31034	+	2.26957i	−0.586001	+	1.01498i	−0.994750	+	0.102336i	$0.967368\pi$
$6$	−0.721932	+	0.663020i	−0.294728	+	0.270677i
$7$	−1.74382	+	3.02039i	−0.659103	+	1.14160i	0.321745	+	0.946826i	$0.395731\pi$
$7$	−1.74382	+	3.02039i	−0.659103	+	1.14160i	−0.980848	+	0.194774i	$0.937603\pi$
$8$	−2.23814	+	1.72938i	−0.791301	+	0.611427i
$9$	−1.25980	−	2.18205i	−0.419935	−	0.727348i
$10$	2.50693	+	2.72968i	0.792761	+	0.863201i
$11$		−	1.40440i		−	0.423442i	−0.977330	−	0.211721i	$-0.932093\pi$
$11$		−	1.40440i		−	0.423442i	0.977330	−	0.211721i	$-0.0679068\pi$
$12$	0.588651	+	1.25501i	0.169929	+	0.362291i
$13$	−2.32009	+	4.01851i	−0.643476	+	1.11453i	0.341175	+	0.940000i	$0.389175\pi$
$13$	−2.32009	+	4.01851i	−0.643476	+	1.11453i	−0.984651	+	0.174534i	$0.944158\pi$
$14$	3.33627	+	3.63272i	0.891657	+	0.970885i
$15$	1.57304	−	0.908198i	0.406158	−	0.234496i
$16$	1.38493	+	3.75260i	0.346231	+	0.938149i
$17$	−5.28425	+	3.05086i	−1.28162	+	0.739943i	−0.977144	−	0.212578i	$-0.931814\pi$
$17$	−5.28425	+	3.05086i	−1.28162	+	0.739943i	−0.304474	+	0.952521i	$0.598481\pi$
$18$	−3.47793	+	0.775132i	−0.819757	+	0.182700i
$19$	1.73592	−	3.00670i	0.398247	−	0.689784i	−0.595263	−	0.803531i	$-0.702952\pi$
$19$	1.73592	−	3.00670i	0.398247	−	0.689784i	0.993510	+	0.113747i	$0.0362855\pi$
$20$	4.74529	−	2.22574i	1.06108	−	0.497690i
$21$	2.09344	−	1.20865i	0.456826	−	0.263749i
$22$	−1.89486	−	0.595113i	−0.403986	−	0.126879i
$23$		−	6.02292i		−	1.25587i	−0.778268	−	0.627933i	$-0.783901\pi$
$23$		−	6.02292i		−	1.25587i	0.778268	−	0.627933i	$-0.216099\pi$
$24$	1.94275	−	0.262419i	0.396561	−	0.0535660i
$25$	−0.933966	−	1.61768i	−0.186793	−	0.323535i
$26$	4.43878	+	4.83318i	0.870516	+	0.947865i
$27$			3.82565i			0.736247i
$28$	6.31514	−	2.96206i	1.19345	−	0.559776i
$29$	6.17494			1.14666			0.573328	−	0.819326i	$-0.305652\pi$
$29$	6.17494			1.14666			0.573328	+	0.819326i	$0.305652\pi$
$30$	−0.558795	−	2.50726i	−0.102022	−	0.457760i
$31$		−	1.36885i		−	0.245852i	−0.992416	−	0.122926i	$-0.960772\pi$
$31$		−	1.36885i		−	0.245852i	0.992416	−	0.122926i	$-0.0392279\pi$
$32$	5.65000	−	0.278429i	0.998788	−	0.0492197i
$33$	−0.486696	+	0.842982i	−0.0847228	+	0.146744i
$34$	1.87713	+	8.42250i	0.321926	+	1.44445i
$35$	−4.56999	−	7.91546i	−0.772470	−	1.33796i
$36$	−0.427938	+	5.02101i	−0.0713230	+	0.836836i
$37$	−5.70217	−	2.11785i	−0.937430	−	0.348173i
$37$	−5.70217	−	2.11785i	−0.937430	−	0.348173i
$38$	−3.32115	−	3.61625i	−0.538761	−	0.586633i
$39$	2.78524	−	1.60806i	0.445995	−	0.257495i
$40$	−0.992226	−	7.34568i	−0.156885	−	1.16145i
$41$	−3.13563	+	5.43107i	−0.489703	+	0.848191i	−0.999930	−	0.0118490i	$-0.996228\pi$
$41$	−3.13563	+	5.43107i	−0.489703	+	0.848191i	0.510226	+	0.860040i	$0.329562\pi$
$42$	−0.743656	−	3.33671i	−0.114749	−	0.514865i
$43$	−2.90404			−0.442862			−0.221431	−	0.975176i	$-0.571073\pi$
$43$	−2.90404			−0.442862			−0.221431	+	0.975176i	$0.571073\pi$
$44$	−1.60590	+	2.30444i	−0.242098	+	0.347407i
$45$	6.60307			0.984328
$46$	−8.12634	−	2.55221i	−1.19816	−	0.376303i
$47$	−8.48133			−1.23713			−0.618565	−	0.785734i	$-0.712286\pi$
$47$	−8.48133			−1.23713			−0.618565	+	0.785734i	$0.712286\pi$
$48$	0.469173	−	2.73242i	0.0677193	−	0.394391i
$49$	−2.58184	−	4.47188i	−0.368834	−	0.638839i
$50$	−2.57839	+	0.574650i	−0.364640	+	0.0812678i
$51$	4.22912			0.592195
$52$	8.40203	−	3.94090i	1.16515	−	0.546504i
$53$	−2.05008	+	1.18361i	−0.281600	+	0.162582i	−0.634148	−	0.773212i	$-0.718649\pi$
$53$	−2.05008	+	1.18361i	−0.281600	+	0.162582i	0.352548	+	0.935794i	$0.385315\pi$
$54$	5.16171	+	1.62112i	0.702420	+	0.220606i
$55$	3.18738	+	1.84023i	0.429786	+	0.248137i
$56$	−1.32047	−	9.77577i	−0.176456	−	1.30634i
$57$	−2.08395	+	1.20317i	−0.276026	+	0.159364i
$58$	2.61663	−	8.33144i	0.343580	−	1.09397i
$59$	1.01427	+	1.75677i	0.132047	+	0.228712i	0.924465	−	0.381266i	$-0.124512\pi$
$59$	1.01427	+	1.75677i	0.132047	+	0.228712i	−0.792419	+	0.609978i	$0.791178\pi$
$60$	−3.61967	−	0.308502i	−0.467297	−	0.0398274i
$61$	−6.65507	+	11.5269i	−0.852094	+	1.47587i	0.0272208	+	0.999629i	$0.491334\pi$
$61$	−6.65507	+	11.5269i	−0.852094	+	1.47587i	−0.879315	+	0.476241i	$0.841999\pi$
$62$	−1.84690	−	0.580049i	−0.234556	−	0.0736663i
$63$	8.78751			1.10712
$64$	2.01852	−	7.74116i	0.252315	−	0.967645i
$65$	−6.08019	−	10.5312i	−0.754155	−	1.30623i
$66$	0.931144	+	1.01388i	0.114616	+	0.124800i
$67$	4.98642	+	2.87891i	0.609188	+	0.351715i	0.772648	−	0.634835i	$-0.218932\pi$
$67$	4.98642	+	2.87891i	0.609188	+	0.351715i	−0.163460	+	0.986550i	$0.552265\pi$
$68$	12.1594	+	1.03633i	1.47454	+	0.125674i
$69$	−2.08725	+	3.61522i	−0.251275	+	0.435222i
$70$	−12.6163	+	2.81182i	−1.50794	+	0.336077i
$71$	3.65561	−	6.33170i	0.433841	−	0.751434i	−0.563360	−	0.826212i	$-0.690491\pi$
$71$	3.65561	−	6.33170i	0.433841	−	0.751434i	0.997200	+	0.0747777i	$0.0238247\pi$
$72$	6.59319	+	2.70504i	0.777015	+	0.318792i
$73$	−10.9720			−1.28418			−0.642088	−	0.766631i	$-0.721932\pi$
$73$	−10.9720			−1.28418			−0.642088	+	0.766631i	$0.721932\pi$
$74$	−5.27377	+	6.79613i	−0.613063	+	0.790034i
$75$			1.29467i			0.149495i
$76$	−6.28650	+	2.94863i	−0.721112	+	0.338231i
$77$	4.24183	+	2.44902i	0.483401	+	0.279092i
$78$	−0.989405	−	4.43935i	−0.112028	−	0.502658i
$79$	7.01349	+	4.04924i	0.789080	+	0.455575i	0.839638	−	0.543146i	$-0.182767\pi$
$79$	7.01349	+	4.04924i	0.789080	+	0.455575i	−0.0505587	+	0.998721i	$0.516100\pi$
$80$	−10.3315	−	1.77398i	−1.15510	−	0.198337i
$81$	−2.45363	+	4.24981i	−0.272625	+	0.472201i
$82$	5.99907	+	6.53212i	0.662487	+	0.721352i
$83$	8.75178	−	5.05285i	0.960633	−	0.554622i	0.0642653	−	0.997933i	$-0.479530\pi$
$83$	8.75178	−	5.05285i	0.960633	−	0.554622i	0.896368	+	0.443311i	$0.146196\pi$
$84$	−4.81713	−	0.410561i	−0.525592	−	0.0447959i
$85$		−	15.9906i		−	1.73443i
$86$	−1.23058	+	3.91823i	−0.132697	+	0.422514i
$87$	−3.70647	−	2.13993i	−0.397375	−	0.229425i
$88$	2.42873	+	3.14324i	0.258904	+	0.335070i
$89$	15.2905	−	8.82800i	1.62079	−	0.935766i	0.634087	−	0.773262i	$-0.281376\pi$
$89$	15.2905	−	8.82800i	1.62079	−	0.935766i	0.986708	−	0.162505i	$-0.0519572\pi$
$90$	2.79805	−	8.90910i	0.294940	−	0.939102i
$91$	−8.09164	−	14.0151i	−0.848234	−	1.46919i
$92$	−6.88706	+	9.88284i	−0.718026	+	1.03036i
$93$	−0.474376	+	0.821644i	−0.0491905	+	0.0852005i
$94$	−3.59396	+	11.4433i	−0.370689	+	1.18029i
$95$	4.54927	+	7.87957i	0.466746	+	0.808427i
$96$	−3.48787	−	1.79089i	−0.355979	−	0.182782i
$97$			5.77275i			0.586134i	0.956092	+	0.293067i	$0.0946758\pi$
$97$			5.77275i			0.586134i	−0.956092	+	0.293067i	$0.905324\pi$
$98$	−7.12767	+	1.58855i	−0.720003	+	0.160468i
$99$	−3.06446	+	1.76927i	−0.307990	+	0.177818i
$100$	−0.317255	+	3.72237i	−0.0317255	+	0.372237i
$101$			1.89789i			0.188847i	0.995532	+	0.0944237i	$0.0301008\pi$
$101$			1.89789i			0.188847i	−0.995532	+	0.0944237i	$0.969899\pi$
$102$	1.79209	−	5.70608i	0.177443	−	0.564986i
$103$			13.1957i			1.30022i	0.759842	+	0.650108i	$0.225276\pi$
$103$			13.1957i			1.30022i	−0.759842	+	0.650108i	$0.774724\pi$
$104$	−1.75684	−	13.0063i	−0.172272	−	1.27537i
$105$			6.33494i			0.618227i
$106$	0.728253	+	3.26759i	0.0707342	+	0.317377i
$107$	−12.2473	−	7.07096i	−1.18399	−	0.683576i	−0.227054	−	0.973882i	$-0.572909\pi$
$107$	−12.2473	−	7.07096i	−1.18399	−	0.683576i	−0.956934	+	0.290306i	$0.906243\pi$
$108$	4.37454	−	6.27741i	0.420941	−	0.604044i
$109$	0.366699	+	0.635142i	0.0351234	+	0.0608355i	0.883053	−	0.469274i	$-0.155484\pi$
$109$	0.366699	+	0.635142i	0.0351234	+	0.0608355i	−0.847929	+	0.530109i	$0.822151\pi$
$110$	3.83356	−	3.52073i	0.365516	−	0.335688i
$111$	2.68875	+	3.24732i	0.255205	+	0.308222i
$112$	−13.7494	−	2.36085i	−1.29919	−	0.223079i
$113$	7.97540	−	4.60460i	0.750262	−	0.433164i	−0.0755264	−	0.997144i	$-0.524064\pi$
$113$	7.97540	−	4.60460i	0.750262	−	0.433164i	0.825789	+	0.563980i	$0.190730\pi$
$114$	0.740285	+	3.32158i	0.0693340	+	0.311094i
$115$	13.6694	+	7.89205i	1.27468	+	0.735938i
$116$	−10.1323	−	7.06089i	−0.940759	−	0.655587i
$117$	11.6914			1.08087
$118$	2.80009	−	0.624060i	0.257769	−	0.0574494i
$119$		−	21.2807i		−	1.95079i
$120$	−1.95007	+	4.75306i	−0.178017	+	0.433893i
$121$	9.02767			0.820697
$122$	12.7324	+	13.8638i	1.15274	+	1.25517i
$123$	3.76429	−	2.17331i	0.339415	−	0.195961i
$124$	−1.56525	+	2.24611i	−0.140563	+	0.201706i
$125$	−8.20813			−0.734157
$126$	3.72370	−	11.8564i	0.331734	−	1.05625i
$127$	8.46777	+	14.6666i	0.751393	+	1.30145i	0.947148	+	0.320798i	$0.103951\pi$
$127$	8.46777	+	14.6666i	0.751393	+	1.30145i	−0.195754	+	0.980653i	$0.562716\pi$
$128$	−9.58930	−	6.00377i	−0.847583	−	0.530663i
$129$	1.74313	+	1.00640i	0.153474	+	0.0886084i
$130$	−16.7855	+	3.74102i	−1.47219	+	0.328109i
$131$	−2.43628	−	4.21977i	−0.212859	−	0.368683i	0.739749	−	0.672883i	$-0.234944\pi$
$131$	−2.43628	−	4.21977i	−0.212859	−	0.368683i	−0.952608	+	0.304200i	$0.901611\pi$
$132$	1.76253	−	0.826701i	0.153409	−	0.0719551i
$133$	6.05427	+	10.4863i	0.524971	+	0.909277i
$134$	5.99732	−	5.50791i	0.518089	−	0.475811i
$135$	−8.68259	−	5.01290i	−0.747278	−	0.431441i
$136$	6.55079	−	15.9667i	0.561725	−	1.36913i
$137$	2.90456			0.248153			0.124077	−	0.992273i	$-0.460403\pi$
$137$	2.90456			0.248153			0.124077	+	0.992273i	$0.460403\pi$
$138$	3.99332	+	4.34814i	0.339934	+	0.370138i
$139$	−16.2192	+	9.36418i	−1.37570	+	0.794259i	−0.991638	−	0.129050i	$-0.958807\pi$
$139$	−16.2192	+	9.36418i	−1.37570	+	0.794259i	−0.384059	+	0.923309i	$0.625474\pi$
$140$	−1.55236	+	18.2139i	−0.131199	+	1.53936i
$141$	5.09087	+	2.93922i	0.428729	+	0.247527i
$142$	−6.99389	−	7.61533i	−0.586914	−	0.639064i
$143$	5.64358	+	3.25832i	0.471940	+	0.272475i
$144$	6.44360	−	7.74951i	0.536967	−	0.645792i
$145$	−8.09125	+	14.0144i	−0.671941	+	1.16384i
$146$	−4.64938	+	14.8038i	−0.384786	+	1.22517i
$147$			3.57896i			0.295187i
$148$	6.93482	+	9.99541i	0.570038	+	0.821618i
$149$		−	2.04062i		−	0.167174i	−0.996500	−	0.0835871i	$-0.973362\pi$
$149$		−	2.04062i		−	0.167174i	0.996500	−	0.0835871i	$-0.0266377\pi$
$150$	1.74681	+	0.548615i	0.142627	+	0.0447942i
$151$	−10.8539	+	18.7994i	−0.883274	+	1.52988i	−0.0355947	+	0.999366i	$0.511333\pi$
$151$	−10.8539	+	18.7994i	−0.883274	+	1.52988i	−0.847679	+	0.530509i	$0.822001\pi$
$152$	1.31449	+	9.73145i	0.106619	+	0.789325i
$153$	13.3142	+	7.68698i	1.07639	+	0.621455i
$154$	5.10178	−	4.68545i	0.411113	−	0.377565i
$155$	3.10670	+	1.79365i	0.249536	+	0.144070i
$156$	−6.40899	−	0.546235i	−0.513130	−	0.0437338i
$157$	3.39674	−	1.96111i	0.271089	−	0.156513i	−0.358293	−	0.933609i	$-0.616641\pi$
$157$	3.39674	−	1.96111i	0.271089	−	0.156513i	0.629383	+	0.777096i	$0.283308\pi$
$158$	8.43535	−	7.74699i	0.671080	−	0.616317i
$159$	1.64073			0.130118
$160$	−6.77149	+	13.1879i	−0.535333	+	1.04260i
$161$	18.1916	+	10.5029i	1.43370	+	0.827745i
$162$	4.69427	+	5.11138i	0.368817	+	0.401588i
$163$	−3.24296	−	5.61697i	−0.254008	−	0.439955i	0.710617	−	0.703579i	$-0.248416\pi$
$163$	−3.24296	−	5.61697i	−0.254008	−	0.439955i	−0.964626	+	0.263623i	$0.915082\pi$
$164$	11.3555	−	5.32618i	0.886714	−	0.415905i
$165$	−1.27547	−	2.20918i	−0.0992953	−	0.171984i
$166$	−3.10891	−	13.9494i	−0.241298	−	1.08268i
$167$	−6.01201	−	3.47104i	−0.465223	−	0.268597i	0.249015	−	0.968500i	$-0.419893\pi$
$167$	−6.01201	−	3.47104i	−0.465223	−	0.268597i	−0.714238	+	0.699903i	$0.753227\pi$
$168$	−2.59520	+	6.32546i	−0.200224	+	0.488020i
$169$	−4.26560	−	7.38824i	−0.328123	−	0.568326i
$170$	−21.5751	−	6.77602i	−1.65474	−	0.519697i
$171$	−8.74767			−0.668951
$172$	4.76515	+	3.32070i	0.363340	+	0.253201i
$173$	4.77237	−	2.75533i	0.362837	−	0.209484i	−0.307488	−	0.951552i	$-0.599488\pi$
$173$	4.77237	−	2.75533i	0.362837	−	0.209484i	0.670324	+	0.742068i	$0.266155\pi$
$174$	−4.45789	+	4.09411i	−0.337951	+	0.310373i
$175$	6.51469			0.492464
$176$	5.27014	−	1.94499i	0.397252	−	0.146609i
$177$		−	1.40599i		−	0.105680i
$178$	−5.43169	−	24.3714i	−0.407122	−	1.82671i
$179$	19.3287			1.44469			0.722347	−	0.691531i	$-0.243063\pi$
$179$	19.3287			1.44469			0.722347	+	0.691531i	$0.243063\pi$
$180$	−10.8348	−	7.55046i	−0.807579	−	0.562778i
$181$	−5.14145	−	2.96842i	−0.382161	−	0.220641i	0.296597	−	0.955003i	$-0.404148\pi$
$181$	−5.14145	−	2.96842i	−0.382161	−	0.220641i	−0.678758	+	0.734362i	$0.737481\pi$
$182$	−22.3385	+	4.97862i	−1.65584	+	0.369040i
$183$	7.98933	−	4.61264i	0.590588	−	0.340976i
$184$	10.4159	+	13.4801i	0.767870	+	0.993768i
$185$	12.2784	−	10.1664i	0.902724	−	0.747446i
$186$	0.907574	+	0.988216i	0.0665465	+	0.0724595i
$187$	4.28462	+	7.42119i	0.313323	+	0.542691i
$188$	13.9168	+	9.69820i	1.01499	+	0.707314i
$189$	−11.5550	−	6.67126i	−0.840500	−	0.485263i
$190$	12.5592	−	2.79907i	0.911137	−	0.203066i
$191$		−	17.4298i		−	1.26117i	−0.776118	−	0.630587i	$-0.782814\pi$
$191$		−	17.4298i		−	1.26117i	0.776118	−	0.630587i	$-0.217186\pi$
$192$	−3.89431	+	3.94707i	−0.281048	+	0.284855i
$193$			7.94976i			0.572236i	0.958194	+	0.286118i	$0.0923649\pi$
$193$			7.94976i			0.572236i	−0.958194	+	0.286118i	$0.907635\pi$
$194$	7.78879	+	2.44620i	0.559203	+	0.175627i
$195$			8.42839i			0.603569i
$196$	−0.877014	+	10.2900i	−0.0626439	+	0.735003i
$197$	−18.5852	+	10.7302i	−1.32414	+	0.764495i	−0.984387	−	0.176018i	$-0.943678\pi$
$197$	−18.5852	+	10.7302i	−1.32414	+	0.764495i	−0.339757	+	0.940513i	$0.610345\pi$
$198$	1.08859	+	4.88440i	0.0773630	+	0.347119i
$199$		−	6.39905i		−	0.453616i	−0.973939	−	0.226808i	$-0.927171\pi$
$199$		−	6.39905i		−	0.453616i	0.973939	−	0.226808i	$-0.0728291\pi$
$200$	4.88791	+	2.00540i	0.345628	+	0.141803i
$201$	−1.99538	−	3.45610i	−0.140743	−	0.243774i
$202$	2.56070	+	0.804231i	0.180171	+	0.0565855i
$203$	−10.7680	+	18.6507i	−0.755765	+	1.30902i
$204$	−6.93944	−	4.83590i	−0.485858	−	0.338580i
$205$	−8.21747	−	14.2331i	−0.573933	−	0.994081i
$206$	17.8042	+	5.59169i	1.24048	+	0.389592i
$207$	−13.1423	+	7.58770i	−0.913452	+	0.527382i
$208$	−18.2930	−	3.14102i	−1.26839	−	0.217790i
$209$	−4.22260	−	2.43792i	−0.292083	−	0.168634i
$210$	8.54733	+	2.68443i	0.589822	+	0.185243i
$211$			16.2987i			1.12205i	0.827800	+	0.561023i	$0.189592\pi$
$211$			16.2987i			1.12205i	−0.827800	+	0.561023i	$0.810408\pi$
$212$	4.71735	+	0.402057i	0.323989	+	0.0276134i
$213$	−4.38851	+	2.53371i	−0.300696	+	0.173607i
$214$	−14.7302	+	13.5281i	−1.00693	+	0.924764i
$215$	3.80527	−	6.59092i	0.259517	−	0.449497i
$216$	−6.61599	−	8.56234i	−0.450161	−	0.582593i
$217$	4.13446	+	2.38703i	0.280665	+	0.162042i
$218$	1.01234	−	0.225622i	0.0685646	−	0.0152811i
$219$	6.58588	+	3.80236i	0.445033	+	0.256940i
$220$	−3.12582	−	6.66428i	−0.210743	−	0.449306i
$221$		−	28.3131i		−	1.90454i
$222$	5.52076	−	2.25170i	0.370529	−	0.151125i
$223$	−12.4528			−0.833901			−0.416950	−	0.908929i	$-0.636901\pi$
$223$	−12.4528			−0.833901			−0.416950	+	0.908929i	$0.636901\pi$
$224$	−9.01163	+	17.5507i	−0.602115	+	1.17266i
$225$	−2.35323	+	4.07591i	−0.156882	+	0.271727i
$226$	−2.83312	−	12.7119i	−0.188456	−	0.845582i
$227$	−9.94347	+	17.2226i	−0.659971	+	1.14310i	0.320652	+	0.947197i	$0.396098\pi$
$227$	−9.94347	+	17.2226i	−0.659971	+	1.14310i	−0.980623	+	0.195906i	$0.937235\pi$
$228$	4.79529	+	0.408699i	0.317576	+	0.0270668i
$229$	4.65780	+	2.68918i	0.307796	+	0.177706i	0.645940	−	0.763388i	$-0.276466\pi$
$229$	4.65780	+	2.68918i	0.307796	+	0.177706i	−0.338144	+	0.941094i	$0.609799\pi$
$230$	16.4407	−	15.0990i	1.08406	−	0.995601i
$231$	−1.69742	−	2.94002i	−0.111682	−	0.193439i
$232$	−13.8204	+	10.6788i	−0.907351	+	0.701097i
$233$	−12.8147			−0.839517			−0.419759	−	0.907636i	$-0.637885\pi$
$233$	−12.8147			−0.839517			−0.419759	+	0.907636i	$0.637885\pi$
$234$	4.95424	−	15.7745i	0.323869	−	1.03121i
$235$	11.1134	−	19.2490i	0.724959	−	1.25567i
$236$	0.344534	−	4.04243i	0.0224272	−	0.263140i
$237$	−2.80654	−	4.86107i	−0.182304	−	0.315760i
$238$	−28.7126	−	9.01767i	−1.86116	−	0.584529i
$239$	−10.6859	+	6.16951i	−0.691214	+	0.399072i	−0.804067	−	0.594539i	$-0.797334\pi$
$239$	−10.6859	+	6.16951i	−0.691214	+	0.399072i	0.112853	+	0.993612i	$0.464001\pi$
$240$	5.58665	+	4.64522i	0.360617	+	0.299847i
$241$	−11.0429	−	6.37565i	−0.711338	−	0.410691i	0.100218	−	0.994966i	$-0.468046\pi$
$241$	−11.0429	−	6.37565i	−0.711338	−	0.410691i	−0.811556	+	0.584274i	$0.801379\pi$
$242$	3.82547	−	12.1804i	0.245911	−	0.782989i
$243$	12.8849	−	7.43910i	0.826566	−	0.477218i
$244$	24.1009	−	11.3043i	1.54290	−	0.723683i
$245$	13.5323			0.864548
$246$	−1.33720	−	5.99985i	−0.0852565	−	0.382537i
$247$	8.05496	+	13.9516i	0.512525	+	0.887719i
$248$	2.36725	+	3.06367i	0.150321	+	0.194543i
$249$	−7.00428			−0.443878
$250$	−3.47819	+	11.0747i	−0.219980	+	0.700425i
$251$	−14.2951			−0.902300			−0.451150	−	0.892448i	$-0.648986\pi$
$251$	−14.2951			−0.902300			−0.451150	+	0.892448i	$0.648986\pi$
$252$	−14.4192	−	10.0483i	−0.908323	−	0.632984i
$253$	−8.45858			−0.531786
$254$	23.3769	−	5.21005i	1.46680	−	0.326907i
$255$	−5.54157	+	9.59828i	−0.347027	+	0.601068i
$256$	−12.1640	+	10.3941i	−0.760248	+	0.649633i
$257$	13.3711	−	7.71979i	0.834064	−	0.481547i	−0.0211781	−	0.999776i	$-0.506742\pi$
$257$	13.3711	−	7.71979i	0.834064	−	0.481547i	0.855242	+	0.518229i	$0.173408\pi$
$258$	2.09652	−	1.92543i	0.130524	−	0.119872i
$259$	16.3403	−	13.5296i	1.01534	−	0.840689i
$260$	−2.06536	+	24.2329i	−0.128088	+	1.50286i
$261$	−7.77921	−	13.4740i	−0.481521	−	0.834019i
$262$	−6.72583	+	1.49900i	−0.415523	+	0.0926083i
$263$	−1.80085	+	3.11917i	−0.111045	+	0.192336i	−0.916192	−	0.400740i	$-0.868753\pi$
$263$	−1.80085	+	3.11917i	−0.111045	+	0.192336i	0.805147	+	0.593076i	$0.202087\pi$
$264$	−0.368540	−	2.72839i	−0.0226821	−	0.167921i
$265$		−	6.20373i		−	0.381092i
$266$	16.7140	−	3.72507i	1.02480	−	0.228398i
$267$	−12.2374			−0.748918
$268$	−4.89011	−	10.4258i	−0.298711	−	0.636855i
$269$			16.4424i			1.00251i	0.865299	+	0.501256i	$0.167128\pi$
$269$			16.4424i			1.00251i	−0.865299	+	0.501256i	$0.832872\pi$
$270$	−10.4428	+	9.59065i	−0.635530	+	0.583668i
$271$	−15.1587	−	26.2556i	−0.920824	−	1.59491i	−0.798143	−	0.602468i	$-0.794184\pi$
$271$	−15.1587	−	26.2556i	−0.920824	−	1.59491i	−0.122681	−	0.992446i	$-0.539149\pi$
$272$	−18.7669	−	15.6044i	−1.13791	−	0.946158i
$273$			11.2167i			0.678864i
$274$	1.23081	−	3.91893i	0.0743557	−	0.236751i
$275$	−2.27186	+	1.31166i	−0.136998	+	0.0790961i
$276$	7.55883	−	3.54540i	0.454988	−	0.213408i
$277$	3.67666	−	6.36815i	0.220909	−	0.382625i	−0.734175	−	0.678960i	$-0.762431\pi$
$277$	3.67666	−	6.36815i	0.220909	−	0.382625i	0.955084	+	0.296335i	$0.0957643\pi$
$278$	5.76159	+	25.8516i	0.345557	+	1.55048i
$279$	−2.98689	+	1.72448i	−0.178820	+	0.103242i
$280$	23.9171	+	9.81265i	1.42932	+	0.586418i
$281$	−22.2865	+	12.8671i	−1.32950	+	0.767588i	−0.985223	−	0.171279i	$-0.945210\pi$
$281$	−22.2865	+	12.8671i	−1.32950	+	0.767588i	−0.344279	+	0.938867i	$0.611877\pi$
$282$	6.12295	−	5.62329i	0.364616	−	0.334862i
$283$	13.1118	−	22.7102i	0.779413	−	1.34998i	−0.152867	−	0.988247i	$-0.548851\pi$
$283$	13.1118	−	22.7102i	0.779413	−	1.34998i	0.932280	−	0.361737i	$-0.117816\pi$
$284$	−13.2385	+	6.20941i	−0.785562	+	0.368461i
$285$		−	6.30622i		−	0.373548i
$286$	6.78771	−	6.23381i	0.401366	−	0.368613i
$287$	−10.9360	−	18.9417i	−0.645530	−	1.11809i
$288$	−7.72544	−	11.9778i	−0.455226	−	0.705798i
$289$	10.1155	−	17.5206i	0.595030	−	1.03062i
$290$	15.4801	+	16.8556i	0.909025	+	0.989796i
$291$	2.00055	−	3.46506i	0.117274	−	0.203125i
$292$	18.0037	+	12.5462i	1.05358	+	0.734212i
$293$	24.5313	+	14.1632i	1.43314	+	0.827421i	0.997359	−	0.0726333i	$-0.0231403\pi$
$293$	24.5313	+	14.1632i	1.43314	+	0.827421i	0.435777	+	0.900055i	$0.356474\pi$
$294$	4.82886	+	1.51658i	0.281625	+	0.0884488i
$295$	−5.31615			−0.309518
$296$	16.4248	−	5.12115i	0.954672	−	0.297661i
$297$	5.37274			0.311758
$298$	−2.75328	−	0.864712i	−0.159493	−	0.0500914i
$299$	24.2031	+	13.9737i	1.39970	+	0.808120i
$300$	1.48042	−	2.12439i	0.0854722	−	0.122651i
$301$	5.06413	−	8.77133i	0.291891	−	0.505571i
$302$	20.7655	+	22.6106i	1.19492	+	1.30110i
$303$	0.657717	−	1.13920i	0.0377849	−	0.0654453i
$304$	13.6870	+	2.35015i	0.785005	+	0.134790i
$305$	−17.4408	−	30.2083i	−0.998655	−	1.72972i
$306$	16.0134	−	14.7067i	0.915428	−	0.840725i
$307$		−	14.9305i		−	0.852129i	−0.904693	−	0.426065i	$-0.859900\pi$
$307$		−	14.9305i		−	0.852129i	0.904693	−	0.426065i	$-0.140100\pi$
$308$	−4.15990	−	8.86896i	−0.237033	−	0.505356i
$309$	4.57300	−	7.92067i	0.260149	−	0.450591i
$310$	3.73652	−	3.43161i	0.212220	−	0.194902i
$311$	−9.15710	+	5.28686i	−0.519252	+	0.299790i	−0.736628	−	0.676298i	$-0.763583\pi$
$311$	−9.15710	+	5.28686i	−0.519252	+	0.299790i	0.217377	+	0.976088i	$0.430250\pi$
$312$	−3.45281	+	8.41578i	−0.195477	+	0.476449i
$313$	9.02371	−	5.20984i	0.510050	−	0.294478i	−0.222804	−	0.974863i	$-0.571521\pi$
$313$	9.02371	−	5.20984i	0.510050	−	0.294478i	0.732854	+	0.680386i	$0.238188\pi$
$314$	−1.20663	−	5.41402i	−0.0680941	−	0.305531i
$315$	−11.5146	+	19.9439i	−0.648774	+	1.12371i
$316$	−6.87804	−	14.6641i	−0.386920	−	0.824917i
$317$	17.4111	−	10.0523i	0.977903	−	0.564593i	0.0762666	−	0.997087i	$-0.475700\pi$
$317$	17.4111	−	10.0523i	0.977903	−	0.564593i	0.901636	+	0.432495i	$0.142367\pi$
$318$	0.695259	−	2.21373i	0.0389882	−	0.124140i
$319$		−	8.67207i		−	0.485542i
$320$	14.9242	+	14.7247i	0.834286	+	0.823136i
$321$	4.90090	+	8.48861i	0.273542	+	0.473788i
$322$	21.8796	−	20.0941i	1.21930	−	1.11980i
$323$			21.1842i			1.17872i
$324$	8.88565	−	4.16773i	0.493647	−	0.231541i
$325$	8.66753			0.480788
$326$	−8.95282	+	1.99533i	−0.495851	+	0.110511i
$327$		−	0.508320i		−	0.0281102i
$328$	−2.37439	−	17.5782i	−0.131104	−	0.970592i
$329$	14.7899	−	25.6169i	0.815396	−	1.41231i
$330$	−3.52118	+	0.784771i	−0.193835	+	0.0432002i
$331$	3.80995	+	6.59903i	0.209414	+	0.362715i	0.951530	−	0.307556i	$-0.0995111\pi$
$331$	3.80995	+	6.59903i	0.209414	+	0.362715i	−0.742116	+	0.670271i	$0.766178\pi$
$332$	−20.1384	−	1.71638i	−1.10524	−	0.0941986i
$333$	2.56237	+	15.1105i	0.140417	+	0.828048i
$334$	−7.23083	+	6.64077i	−0.395654	+	0.363367i
$335$	−13.0678	+	7.54468i	−0.713969	+	0.412210i
$336$	7.43483	+	6.18195i	0.405603	+	0.337253i
$337$	−3.26278	+	5.65130i	−0.177735	+	0.307846i	−0.941104	−	0.338116i	$-0.890210\pi$
$337$	−3.26278	+	5.65130i	−0.177735	+	0.307846i	0.763369	+	0.645962i	$0.223544\pi$
$338$	−11.7760	+	2.62454i	−0.640531	+	0.142756i
$339$	−6.38292			−0.346672
$340$	−18.2849	+	26.2386i	−0.991638	+	1.42299i
$341$	−1.92241			−0.104104
$342$	−3.70682	+	11.8027i	−0.200442	+	0.638215i
$343$	−6.40444			−0.345808
$344$	6.49963	−	5.02217i	0.350437	−	0.270777i
$345$	−5.47000	−	9.47432i	−0.294495	−	0.510080i
$346$	−1.69530	−	7.60662i	−0.0911398	−	0.408934i
$347$	−21.2631			−1.14146			−0.570731	−	0.821137i	$-0.693340\pi$
$347$	−21.2631			−1.14146			−0.570731	+	0.821137i	$0.693340\pi$
$348$	3.63488	+	7.74961i	0.194850	+	0.415423i
$349$	−25.0721	+	14.4754i	−1.34208	+	0.774848i	−0.987112	−	0.160031i	$-0.948841\pi$
$349$	−25.0721	+	14.4754i	−1.34208	+	0.774848i	−0.354965	+	0.934880i	$0.615507\pi$
$350$	2.76060	−	8.78984i	0.147560	−	0.469837i
$351$	−15.3734	−	8.87585i	−0.820572	−	0.473758i
$352$	−0.391025	−	7.93484i	−0.0208417	−	0.422929i
$353$	5.86370	−	3.38541i	0.312093	−	0.180187i	−0.335770	−	0.941944i	$-0.608996\pi$
$353$	5.86370	−	3.38541i	0.312093	−	0.180187i	0.647863	+	0.761757i	$0.275663\pi$
$354$	−1.89701	−	0.595787i	−0.100825	−	0.0316657i
$355$	9.58015	+	16.5933i	0.508462	+	0.880682i
$356$	−35.1844	−	2.99875i	−1.86477	−	0.158933i
$357$	−7.37484	+	12.7736i	−0.390318	+	0.676050i
$358$	8.19052	−	26.0790i	0.432883	−	1.37832i
$359$	−10.3495			−0.546228			−0.273114	−	0.961982i	$-0.588054\pi$
$359$	−10.3495			−0.546228			−0.273114	+	0.961982i	$0.588054\pi$
$360$	−14.7786	+	11.4192i	−0.778900	+	0.601845i
$361$	3.47318	+	6.01573i	0.182799	+	0.316617i
$362$	−6.18378	+	5.67916i	−0.325012	+	0.298490i
$363$	−5.41881	−	3.12855i	−0.284414	−	0.164206i
$364$	−2.74862	+	32.2496i	−0.144067	+	1.69034i
$365$	14.3770	−	24.9017i	0.752528	−	1.30342i
$366$	−2.83807	−	12.7341i	−0.148348	−	0.665622i
$367$	11.2161	−	19.4269i	0.585477	−	1.01408i	−0.409338	−	0.912383i	$-0.634240\pi$
$367$	11.2161	−	19.4269i	0.585477	−	1.01408i	0.994816	−	0.101694i	$-0.0324262\pi$
$368$	22.6016	−	8.34129i	1.17819	−	0.434820i
$369$	15.8011			0.822574
$370$	−8.51387	−	20.8744i	−0.442615	−	1.08521i
$371$		−	8.25605i		−	0.428633i
$372$	1.71792	−	0.805775i	0.0890700	−	0.0417775i
$373$	10.6644	+	6.15707i	0.552180	+	0.318801i	0.750001	−	0.661437i	$-0.230053\pi$
$373$	10.6644	+	6.15707i	0.552180	+	0.318801i	−0.197821	+	0.980238i	$0.563386\pi$
$374$	11.8285	−	2.63624i	0.611639	−	0.136317i
$375$	4.92688	+	2.84454i	0.254423	+	0.146891i
$376$	18.9824	−	14.6674i	0.978942	−	0.756414i
$377$	−14.3264	+	24.8140i	−0.737846	+	1.27799i
$378$	−13.8975	+	12.7634i	−0.714811	+	0.656480i
$379$	−23.9363	+	13.8196i	−1.22953	+	0.709867i	−0.966931	−	0.255040i	$-0.917911\pi$
$379$	−23.9363	+	13.8196i	−1.22953	+	0.709867i	−0.262595	+	0.964906i	$0.584578\pi$
$380$	1.54532	−	18.1314i	0.0792735	−	0.930119i
$381$		−	11.7381i		−	0.601359i
$382$	−23.5169	−	7.38586i	−1.20323	−	0.377893i
$383$	−14.1371	−	8.16208i	−0.722374	−	0.417063i	0.0932518	−	0.995643i	$-0.470274\pi$
$383$	−14.1371	−	8.16208i	−0.722374	−	0.417063i	−0.815626	+	0.578580i	$0.803607\pi$
$384$	3.67531	+	6.92691i	0.187555	+	0.353488i
$385$	−11.1165	+	6.41809i	−0.566547	+	0.327096i
$386$	10.7261	+	3.36871i	0.545944	+	0.171463i
$387$	3.65852	+	6.33674i	0.185973	+	0.322115i
$388$	6.60100	−	9.47234i	0.335115	−	0.480885i
$389$	−2.21787	+	3.84146i	−0.112450	+	0.194770i	−0.916758	−	0.399444i	$-0.869203\pi$
$389$	−2.21787	+	3.84146i	−0.112450	+	0.194770i	0.804307	+	0.594214i	$0.202537\pi$
$390$	11.3719	+	3.57153i	0.575838	+	0.180851i
$391$	18.3751	+	31.8266i	0.929268	+	1.60954i
$392$	13.5121	+	5.54370i	0.682462	+	0.279999i
$393$			3.37719i			0.170357i
$394$	6.60207	+	29.6228i	0.332608	+	1.49237i
$395$	−18.3801	+	10.6117i	−0.924802	+	0.533935i
$396$	7.05150	+	0.600995i	0.354351	+	0.0302011i
$397$		−	1.37426i		−	0.0689722i	−0.999405	−	0.0344861i	$-0.989021\pi$
$397$		−	1.37426i		−	0.0689722i	0.999405	−	0.0344861i	$-0.0109794\pi$
$398$	−8.63382	−	2.71159i	−0.432774	−	0.135920i
$399$		−	8.39245i		−	0.420148i
$400$	4.77701	−	5.74516i	0.238851	−	0.287258i
$401$			13.9783i			0.698041i	0.937115	+	0.349021i	$0.113486\pi$
$401$			13.9783i			0.698041i	−0.937115	+	0.349021i	$0.886514\pi$
$402$	−5.50863	+	1.22772i	−0.274745	+	0.0612329i
$403$	5.50073	+	3.17585i	0.274011	+	0.158200i
$404$	2.17020	−	3.11420i	0.107971	−	0.154937i
$405$	−6.43016	−	11.1374i	−0.319517	−	0.553420i
$406$	20.6013	+	22.4318i	1.02242	+	1.11327i
$407$	−2.97431	+	8.00811i	−0.147431	+	0.396947i
$408$	−9.46535	+	7.31374i	−0.468605	+	0.362084i
$409$	13.5079	−	7.79876i	0.667920	−	0.385624i	−0.127368	−	0.991856i	$-0.540653\pi$
$409$	13.5079	−	7.79876i	0.667920	−	0.385624i	0.795288	+	0.606232i	$0.207320\pi$
$410$	−22.6859	+	5.05604i	−1.12038	+	0.249700i
$411$	−1.74344	−	1.00658i	−0.0859978	−	0.0496508i
$412$	15.0890	−	21.6525i	0.743383	−	1.06674i
$413$	−7.07484			−0.348130
$414$	4.66856	+	20.9473i	0.229447	+	1.02950i
$415$			26.4837i			1.30003i
$416$	−11.9896	+	23.3505i	−0.587839	+	1.14485i
$417$	12.9807			0.635666
$418$	−5.07865	+	4.66421i	−0.248405	+	0.228134i
$419$	16.8597	−	9.73392i	0.823648	−	0.475533i	−0.0280249	−	0.999607i	$-0.508922\pi$
$419$	16.8597	−	9.73392i	0.823648	−	0.475533i	0.851673	+	0.524074i	$0.175588\pi$
$420$	7.24386	−	10.3948i	0.353464	−	0.507216i
$421$	−8.61019			−0.419635			−0.209817	−	0.977741i	$-0.567287\pi$
$421$	−8.61019			−0.419635			−0.209817	+	0.977741i	$0.567287\pi$
$422$	21.9907	+	6.90655i	1.07049	+	0.336206i
$423$	10.6848	+	18.5067i	0.519514	+	0.899825i
$424$	2.54145	−	6.19445i	0.123423	−	0.300829i
$425$	9.87061	+	5.69880i	0.478795	+	0.276432i
$426$	1.55894	+	6.99480i	0.0755309	+	0.338899i
$427$	−23.2105	−	40.2018i	−1.12324	−	1.94550i
$428$	12.0107	+	25.6070i	0.580560	+	1.23776i
$429$	−2.25835	−	3.91158i	−0.109034	−	0.188853i
$430$	−7.28022	−	7.92710i	−0.351083	−	0.382279i
$431$	11.3703	+	6.56466i	0.547689	+	0.316208i	0.748189	−	0.663485i	$-0.230923\pi$
$431$	11.3703	+	6.56466i	0.547689	+	0.316208i	−0.200500	+	0.979694i	$0.564257\pi$
$432$	−14.3561	+	5.29825i	−0.690710	+	0.254912i
$433$	−25.2262			−1.21229			−0.606147	−	0.795353i	$-0.707286\pi$
$433$	−25.2262			−1.21229			−0.606147	+	0.795353i	$0.707286\pi$
$434$	4.97264	−	4.56685i	0.238694	−	0.219216i
$435$	9.71345	−	5.60806i	0.465724	−	0.268886i
$436$	0.124563	−	1.46150i	0.00596546	−	0.0699931i
$437$	−18.1091	−	10.4553i	−0.866275	−	0.500144i
$438$	7.92105	−	7.27466i	0.378482	−	0.347597i
$439$	−12.0495	−	6.95676i	−0.575089	−	0.332028i	0.184090	−	0.982909i	$-0.441066\pi$
$439$	−12.0495	−	6.95676i	−0.575089	−	0.332028i	−0.759179	+	0.650881i	$0.774400\pi$
$440$	−10.3162	+	1.39348i	−0.491808	+	0.0664315i
$441$	−6.50522	+	11.2674i	−0.309773	+	0.536542i
$442$	−38.2010	−	11.9976i	−1.81703	−	0.570670i
$443$			5.57558i			0.264904i	0.991189	+	0.132452i	$0.0422850\pi$
$443$			5.57558i			0.264904i	−0.991189	+	0.132452i	$0.957715\pi$
$444$	−0.698661	−	8.40296i	−0.0331570	−	0.398787i
$445$			46.2706i			2.19344i
$446$	−5.27687	+	16.8018i	−0.249867	+	0.795586i
$447$	−0.707180	+	1.22487i	−0.0334485	+	0.0579344i
$448$	19.8614	+	19.5959i	0.938363	+	0.925821i
$449$	−24.0246	−	13.8706i	−1.13379	−	0.654594i	−0.188904	−	0.981996i	$-0.560494\pi$
$449$	−24.0246	−	13.8706i	−1.13379	−	0.654594i	−0.944885	+	0.327402i	$0.893827\pi$
$450$	4.50219	+	4.90223i	0.212235	+	0.231093i
$451$	7.62739	+	4.40367i	0.359160	+	0.207361i
$452$	−18.3519	−	1.56412i	−0.863199	−	0.0735699i
$453$	13.0299	−	7.52283i	0.612199	−	0.353453i
$454$	19.0238	+	20.7141i	0.892830	+	0.972163i
$455$	42.4111			1.98826
$456$	2.58343	−	6.29679i	0.120980	−	0.294874i
$457$	9.12318	+	5.26727i	0.426764	+	0.246392i	0.697967	−	0.716130i	$-0.254088\pi$
$457$	9.12318	+	5.26727i	0.426764	+	0.246392i	−0.271203	+	0.962522i	$0.587421\pi$
$458$	5.60208	−	5.14492i	0.261768	−	0.240407i
$459$	−11.6715	−	20.2157i	−0.544781	−	0.943588i
$460$	−13.4054	−	28.5805i	−0.625032	−	1.33257i
$461$	4.18615	+	7.25063i	0.194969	+	0.337696i	0.946890	−	0.321557i	$-0.104206\pi$
$461$	4.18615	+	7.25063i	0.194969	+	0.337696i	−0.751922	+	0.659253i	$0.770873\pi$
$462$	−4.68606	+	1.04439i	−0.218015	+	0.0485894i
$463$	13.6238	+	7.86569i	0.633150	+	0.365549i	0.781971	−	0.623315i	$-0.214214\pi$
$463$	13.6238	+	7.86569i	0.633150	+	0.365549i	−0.148821	+	0.988864i	$0.547548\pi$
$464$	8.55182	+	23.1720i	0.397008	+	1.07574i
$465$	−1.24319	−	2.15326i	−0.0576513	−	0.0998550i
$466$	−5.43021	+	17.2900i	−0.251550	+	0.800945i
$467$	16.9874			0.786082			0.393041	−	0.919521i	$-0.371423\pi$
$467$	16.9874			0.786082			0.393041	+	0.919521i	$0.371423\pi$
$468$	−19.1841	−	13.3689i	−0.886787	−	0.617976i
$469$	−17.3909	+	10.0406i	−0.803035	+	0.463633i
$470$	−21.2621	−	23.1514i	−0.980748	−	1.06789i
$471$	−2.71850			−0.125262
$472$	−5.30819	−	2.17783i	−0.244329	−	0.100243i
$473$			4.07842i			0.187526i
$474$	−7.74800	+	1.72681i	−0.355877	+	0.0793149i
$475$	−6.48515			−0.297559
$476$	−24.3339	+	34.9188i	−1.11534	+	1.60050i
$477$	5.16540	+	2.98224i	0.236507	+	0.136548i
$478$	3.79597	+	17.0321i	0.173624	+	0.779031i
$479$	9.99128	−	5.76847i	0.456513	−	0.263568i	−0.254064	−	0.967187i	$-0.581767\pi$
$479$	9.99128	−	5.76847i	0.456513	−	0.263568i	0.710577	+	0.703619i	$0.248434\pi$
$480$	8.63483	−	5.56930i	0.394124	−	0.254202i
$481$	21.7401	−	18.0006i	0.991264	−	0.820757i
$482$	−13.2817	+	12.1979i	−0.604964	+	0.555597i
$483$	−7.27959	−	12.6086i	−0.331233	−	0.573712i
$484$	−14.8133	−	10.3229i	−0.673330	−	0.469224i
$485$	−13.1017	−	7.56424i	−0.594915	−	0.343475i
$486$	−4.57712	−	20.5371i	−0.207623	−	0.931580i
$487$			36.6685i			1.66161i	0.556565	+	0.830804i	$0.312119\pi$
$487$			36.6685i			1.66161i	−0.556565	+	0.830804i	$0.687881\pi$
$488$	−5.03941	−	37.3079i	−0.228124	−	1.68885i
$489$			4.49541i			0.203289i
$490$	5.73431	−	18.2583i	0.259050	−	0.824825i
$491$			37.2517i			1.68114i	0.541700	+	0.840572i	$0.317781\pi$
$491$			37.2517i			1.68114i	−0.541700	+	0.840572i	$0.682219\pi$
$492$	−8.66185	−	0.738244i	−0.390506	−	0.0332826i
$493$	−32.6299	+	18.8389i	−1.46958	+	0.848460i
$494$	22.2373	−	4.95605i	1.00050	−	0.222983i
$495$		−	9.27334i		−	0.416806i
$496$	5.13674	−	1.89575i	0.230646	−	0.0851218i
$497$	12.7495	+	22.0827i	0.571892	+	0.990545i
$498$	−2.96806	+	9.45042i	−0.133002	+	0.423483i
$499$	11.9236	−	20.6523i	0.533774	−	0.924523i	−0.465448	−	0.885075i	$-0.654107\pi$
$499$	11.9236	−	20.6523i	0.533774	−	0.924523i	0.999222	−	0.0394480i	$-0.0125599\pi$
$500$	13.4685	+	9.38580i	0.602329	+	0.419746i
$501$	2.40578	+	4.16694i	0.107482	+	0.186165i
$502$	−6.05755	+	19.2875i	−0.270362	+	0.860843i
$503$	13.9748	−	8.06836i	0.623106	−	0.359750i	−0.154971	−	0.987919i	$-0.549529\pi$
$503$	13.9748	−	8.06836i	0.623106	−	0.359750i	0.778077	+	0.628169i	$0.216195\pi$
$504$	−19.6676	+	15.1969i	−0.876067	+	0.676924i
$505$	−4.30740	−	2.48688i	−0.191677	−	0.110665i
$506$	−3.58432	+	11.4126i	−0.159342	+	0.507352i
$507$			5.91300i			0.262605i
$508$	2.87638	−	33.7487i	0.127619	−	1.49736i
$509$	15.6827	−	9.05444i	0.695125	−	0.401331i	−0.110404	−	0.993887i	$-0.535214\pi$
$509$	15.6827	−	9.05444i	0.695125	−	0.401331i	0.805529	+	0.592556i	$0.201881\pi$
$510$	10.6021	+	11.5442i	0.469469	+	0.511184i
$511$	19.1332	−	33.1397i	0.846405	−	1.46602i
$512$	8.86966	+	20.8166i	0.391987	+	0.919971i
$513$	11.5026	+	6.64102i	0.507851	+	0.293208i
$514$	−4.74983	−	21.3120i	−0.209506	−	0.940031i
$515$	−29.9487	−	17.2909i	−1.31970	−	0.761927i
$516$	−1.70947	−	3.64460i	−0.0752550	−	0.160445i
$517$			11.9112i			0.523853i
$518$	−11.3304	−	27.7801i	−0.497831	−	1.22059i
$519$	−3.81945			−0.167655
$520$	31.8207	+	13.0553i	1.39543	+	0.572514i
$521$	−1.07067	+	1.85446i	−0.0469071	+	0.0812454i	−0.888526	−	0.458827i	$-0.848270\pi$
$521$	−1.07067	+	1.85446i	−0.0469071	+	0.0812454i	0.841619	+	0.540072i	$0.181603\pi$
$522$	−21.4760	+	4.78639i	−0.939980	+	0.209495i
$523$	3.65794	−	6.33574i	0.159951	−	0.277043i	−0.774900	−	0.632084i	$-0.782200\pi$
$523$	3.65794	−	6.33574i	0.159951	−	0.277043i	0.934851	+	0.355041i	$0.115533\pi$
$524$	−0.827571	+	9.70993i	−0.0361526	+	0.424180i
$525$	−3.91040	−	2.25767i	−0.170664	−	0.0985329i
$526$	3.44538	+	3.75152i	0.150226	+	0.163574i
$527$	4.17617	+	7.23334i	0.181917	+	0.315089i
$528$	−3.83741	−	0.658906i	−0.167002	−	0.0286752i
$529$	−13.2756			−0.577198
$530$	−8.37029	−	2.62883i	−0.363582	−	0.114189i
$531$	2.55557	−	4.42637i	0.110902	−	0.192088i
$532$	2.05655	−	24.1296i	0.0891627	−	1.04615i
$533$	−14.5499	−	25.2011i	−0.630225	−	1.09158i
$534$	−5.18560	+	16.5112i	−0.224403	+	0.714508i
$535$	32.0961	−	18.5307i	1.38764	−	0.801152i
$536$	−16.1390	+	2.17999i	−0.697099	+	0.0941614i
$537$	−11.6019	−	6.69838i	−0.500660	−	0.289056i
$538$	22.1847	+	6.96746i	0.956449	+	0.300389i
$539$	−6.28029	+	3.62593i	−0.270511	+	0.156180i
$540$	8.51490	+	18.1539i	0.366423	+	0.781218i
$541$	35.7156			1.53553			0.767767	−	0.640729i	$-0.221368\pi$
$541$	35.7156			1.53553			0.767767	+	0.640729i	$0.221368\pi$
$542$	−41.8485	+	9.32683i	−1.79755	+	0.400621i
$543$	2.05742	+	3.56355i	0.0882922	+	0.152927i
$544$	−29.0065	+	18.7086i	−1.24365	+	0.802127i
$545$	−1.92200			−0.0823293
$546$	15.1339	+	4.75306i	0.647672	+	0.203412i
$547$	25.8078			1.10346			0.551731	−	0.834022i	$-0.313967\pi$
$547$	25.8078			1.10346			0.551731	+	0.834022i	$0.313967\pi$
$548$	−4.76601	−	3.32129i	−0.203594	−	0.141879i
$549$	33.5363			1.43130
$550$	0.807037	+	3.62109i	0.0344122	+	0.154404i
$551$	10.7192	−	18.5662i	0.456652	−	0.790945i
$552$	−1.58053	−	11.7010i	−0.0672717	−	0.498028i
$553$	−24.4606	+	14.1223i	−1.04017	+	0.600542i
$554$	−7.03416	−	7.65918i	−0.298853	−	0.325407i
$555$	−10.8932	+	1.84722i	−0.462390	+	0.0784101i
$556$	37.3214	+	3.18088i	1.58278	+	0.134899i
$557$	−18.5715	−	32.1667i	−0.786898	−	1.36295i	−0.927859	−	0.372932i	$-0.878353\pi$
$557$	−18.5715	−	32.1667i	−0.786898	−	1.36295i	0.140961	−	0.990015i	$-0.454981\pi$
$558$	1.06104	+	4.76077i	0.0449173	+	0.201539i
$559$	6.73762	−	11.6699i	0.284971	−	0.493584i
$560$	23.3744	−	28.1117i	0.987750	−	1.18793i
$561$		−	5.93937i		−	0.250760i
$562$	7.91688	+	35.5222i	0.333953	+	1.49841i
$563$	31.8755			1.34339			0.671697	−	0.740826i	$-0.265566\pi$
$563$	31.8755			1.34339			0.671697	+	0.740826i	$0.265566\pi$
$564$	−4.99255	−	10.6442i	−0.210224	−	0.448200i
$565$			24.1343i			1.01534i
$566$	−25.0854	−	27.3143i	−1.05442	−	1.14811i
$567$	−8.55739	−	14.8218i	−0.359377	−	0.622458i
$568$	2.76813	+	20.4931i	0.116148	+	0.859872i
$569$		−	10.6251i		−	0.445427i	−0.974884	−	0.222714i	$-0.928509\pi$
$569$		−	10.6251i		−	0.445427i	0.974884	−	0.222714i	$-0.0714915\pi$
$570$	−8.50858	−	2.67226i	−0.356385	−	0.111929i
$571$	0.0493315	−	0.0284815i	0.00206446	−	0.00119192i	−0.498967	−	0.866621i	$-0.666287\pi$
$571$	0.0493315	−	0.0284815i	0.00206446	−	0.00119192i	0.501032	+	0.865429i	$0.332954\pi$
$572$	−5.53459	−	11.7998i	−0.231413	−	0.493374i
$573$	−6.04031	+	10.4621i	−0.252338	+	0.437061i
$574$	−30.1909	+	6.72868i	−1.26014	+	0.280850i
$575$	−9.74314	+	5.62520i	−0.406317	+	0.234587i
$576$	−19.4345	+	5.34785i	−0.809771	+	0.222827i
$577$	−5.24502	+	3.02821i	−0.218353	+	0.126066i	−0.605187	−	0.796083i	$-0.706902\pi$
$577$	−5.24502	+	3.02821i	−0.218353	+	0.126066i	0.386834	+	0.922149i	$0.373568\pi$
$578$	−19.3529	−	21.0726i	−0.804976	−	0.876503i
$579$	2.75500	−	4.77180i	0.114494	−	0.198309i
$580$	29.3019	−	13.7438i	1.21669	−	0.570679i
$581$			35.2451i			1.46221i
$582$	−3.82745	−	4.16753i	−0.158653	−	0.172750i
$583$	1.66226	+	2.87913i	0.0688439	+	0.119241i
$584$	24.5569	−	18.9747i	1.01617	−	0.785179i
$585$	−15.3197	+	26.5345i	−0.633392	+	1.09707i
$586$	29.5046	−	27.0969i	1.21882	−	1.11936i
$587$	11.9031	−	20.6168i	0.491294	−	0.850946i	−0.508656	−	0.860970i	$-0.669857\pi$
$587$	11.9031	−	20.6168i	0.491294	−	0.850946i	0.999950	+	0.0100239i	$0.00319077\pi$
$588$	4.09245	−	5.87261i	0.168770	−	0.242182i
$589$	−4.11571	−	2.37621i	−0.169585	−	0.0979099i
$590$	−2.25272	+	7.17273i	−0.0927428	+	0.295297i
$591$	14.8742			0.611845
$592$	0.0503661	−	24.3310i	0.00207003	−	0.999998i
$593$	−20.1628			−0.827987			−0.413994	−	0.910280i	$-0.635866\pi$
$593$	−20.1628			−0.827987			−0.413994	+	0.910280i	$0.635866\pi$
$594$	2.27670	−	7.24909i	0.0934140	−	0.297434i
$595$	48.2979	+	27.8848i	1.98002	+	1.14317i
$596$	−2.33340	+	3.34840i	−0.0955798	+	0.137156i
$597$	−2.21760	+	3.84099i	−0.0907602	+	0.157201i
$598$	29.1099	−	26.7344i	1.19039	−	1.09325i
$599$	2.61567	−	4.53047i	0.106873	−	0.185110i	−0.807629	−	0.589691i	$-0.799249\pi$
$599$	2.61567	−	4.53047i	0.106873	−	0.185110i	0.914502	+	0.404581i	$0.132583\pi$
$600$	−2.23897	−	2.89764i	−0.0914055	−	0.118296i
$601$	13.5778	+	23.5174i	0.553849	+	0.959295i	0.997992	+	0.0633393i	$0.0201750\pi$
$601$	13.5778	+	23.5174i	0.553849	+	0.959295i	−0.444143	+	0.895956i	$0.646492\pi$
$602$	−9.68866	−	10.5495i	−0.394880	−	0.429967i
$603$		−	14.5075i		−	0.590789i
$604$	39.3065	−	18.4363i	1.59936	−	0.750164i
$605$	−11.8293	+	20.4889i	−0.480929	+	0.832993i
$606$	−1.25834	−	1.37015i	−0.0511166	−	0.0556586i
$607$	20.5366	−	11.8568i	0.833555	−	0.481253i	−0.0215130	−	0.999769i	$-0.506848\pi$
$607$	20.5366	−	11.8568i	0.833555	−	0.481253i	0.855068	+	0.518515i	$0.173515\pi$
$608$	8.97078	−	17.4712i	0.363813	−	0.708549i
$609$	12.9269	−	7.46332i	0.523823	−	0.302429i
$610$	−48.1486	+	10.7309i	−1.94948	+	0.434483i
$611$	19.6774	−	34.0823i	0.796064	−	1.37882i
$612$	−13.0571	−	27.8379i	−0.527802	−	1.12528i
$613$	0.108917	−	0.0628834i	0.00439912	−	0.00253983i	−0.497799	−	0.867293i	$-0.665858\pi$
$613$	0.108917	−	0.0628834i	0.00439912	−	0.00253983i	0.502198	+	0.864753i	$0.332525\pi$
$614$	−20.1448	−	6.32680i	−0.812977	−	0.255329i
$615$			11.3911i			0.459333i
$616$	−13.7291	+	1.85447i	−0.553160	+	0.0747188i
$617$	−2.03784	−	3.52965i	−0.0820405	−	0.142098i	0.822086	−	0.569364i	$-0.192810\pi$
$617$	−2.03784	−	3.52965i	−0.0820405	−	0.142098i	−0.904126	+	0.427265i	$0.859477\pi$
$618$	−8.74904	−	9.52644i	−0.351938	−	0.383209i
$619$			28.8858i			1.16102i	0.814254	+	0.580509i	$0.197146\pi$
$619$			28.8858i			1.16102i	−0.814254	+	0.580509i	$0.802854\pi$
$620$	−3.04670	−	6.49559i	−0.122358	−	0.260869i
$621$	23.0416			0.924628
$622$	3.25289	+	14.5954i	0.130429	+	0.585222i
$623$			61.5779i			2.46707i
$624$	9.89174	+	8.22483i	0.395986	+	0.329257i
$625$	15.4252	−	26.7173i	0.617010	−	1.06869i
$626$	−3.20551	−	14.3828i	−0.128118	−	0.574851i
$627$	1.68973	+	2.92669i	0.0674812	+	0.116881i
$628$	−7.81610	−	0.666161i	−0.311896	−	0.0265827i
$629$	36.5929	−	6.20527i	1.45906	−	0.247420i
$630$	22.0297	+	23.9871i	0.877683	+	0.955669i
$631$	−9.83642	+	5.67906i	−0.391582	+	0.226080i	−0.682845	−	0.730563i	$-0.739258\pi$
$631$	−9.83642	+	5.67906i	−0.391582	+	0.226080i	0.291264	+	0.956643i	$0.405924\pi$
$632$	−22.6998	+	3.06621i	−0.902951	+	0.121967i
$633$	5.64832	−	9.78318i	0.224501	−	0.388846i
$634$	−6.18497	−	27.7513i	−0.245636	−	1.10214i
$635$	−44.3825			−1.76127
$636$	−2.69223	−	1.87614i	−0.106754	−	0.0743936i
$637$	23.9604			0.949344
$638$	−11.7007	−	3.67478i	−0.463234	−	0.145486i
$639$	−18.4214			−0.728739
$640$	26.1912	−	13.8966i	1.03530	−	0.549313i
$641$	20.9224	+	36.2387i	0.826386	+	1.43134i	0.900855	+	0.434120i	$0.142941\pi$
$641$	20.9224	+	36.2387i	0.826386	+	1.43134i	−0.0744689	+	0.997223i	$0.523726\pi$
$642$	13.5299	−	3.01542i	0.533982	−	0.119009i
$643$	26.9915			1.06444			0.532221	−	0.846605i	$-0.321357\pi$
$643$	26.9915			1.06444			0.532221	+	0.846605i	$0.321357\pi$
$644$	−17.8402	−	38.0356i	−0.703003	−	1.49881i
$645$	−4.56818	+	2.63744i	−0.179872	+	0.103849i
$646$	28.5824	+	8.97679i	1.12456	+	0.353187i
$647$	0.566118	+	0.326848i	0.0222564	+	0.0128497i	0.511087	−	0.859529i	$-0.329243\pi$
$647$	0.566118	+	0.326848i	0.0222564	+	0.0128497i	−0.488831	+	0.872379i	$0.662576\pi$
$648$	−1.85796	−	13.7549i	−0.0729876	−	0.540344i
$649$	2.46720	−	1.42444i	0.0968462	−	0.0559142i
$650$	3.67286	−	11.6945i	0.144061	−	0.458697i
$651$	−1.65446	−	2.86560i	−0.0648433	−	0.112312i
$652$	−1.10159	+	12.9250i	−0.0431415	+	0.506182i
$653$	−14.9459	+	25.8871i	−0.584878	+	1.01304i	0.410012	+	0.912080i	$0.365524\pi$
$653$	−14.9459	+	25.8871i	−0.584878	+	1.01304i	−0.994891	+	0.100959i	$0.967809\pi$
$654$	−0.685843	−	0.215400i	−0.0268186	−	0.00842282i
$655$	12.7694			0.498942
$656$	−24.7232	−	4.24513i	−0.965280	−	0.165744i
$657$	13.8226	+	23.9414i	0.539270	+	0.934043i
$658$	−28.2961	−	30.8103i	−1.10309	−	1.20111i
$659$	−34.1975	−	19.7439i	−1.33215	−	0.769115i	−0.346518	−	0.938043i	$-0.612636\pi$
$659$	−34.1975	−	19.7439i	−1.33215	−	0.769115i	−0.985628	+	0.168929i	$0.945969\pi$
$660$	−0.433260	+	5.08345i	−0.0168646	+	0.197873i
$661$	16.0529	−	27.8045i	0.624387	−	1.08147i	−0.364273	−	0.931292i	$-0.618682\pi$
$661$	16.0529	−	27.8045i	0.624387	−	1.08147i	0.988659	−	0.150177i	$-0.0479843\pi$
$662$	10.5181	−	2.34419i	0.408798	−	0.0911094i
$663$	−9.81192	+	16.9947i	−0.381063	+	0.660021i
$664$	−10.8494	+	26.4441i	−0.421039	+	1.02623i
$665$	−31.7325			−1.23053
$666$	21.4734	+	2.94582i	0.832077	+	0.114148i
$667$		−	37.1911i		−	1.44005i
$668$	5.89590	+	12.5701i	0.228119	+	0.486353i
$669$	7.47472	+	4.31553i	0.288989	+	0.166848i
$670$	4.64209	+	20.8286i	0.179340	+	0.804677i
$671$	16.1884	+	9.34636i	0.624945	+	0.360812i
$672$	11.4914	−	7.41173i	0.443291	−	0.285914i
$673$	18.3322	−	31.7524i	0.706656	−	1.22396i	−0.259434	−	0.965761i	$-0.583536\pi$
$673$	18.3322	−	31.7524i	0.706656	−	1.22396i	0.966090	−	0.258204i	$-0.0831306\pi$
$674$	6.24233	+	6.79699i	0.240446	+	0.261810i
$675$	6.18867	−	3.57303i	0.238202	−	0.137526i
$676$	−1.44897	+	17.0008i	−0.0557294	+	0.653876i
$677$			19.5264i			0.750461i	0.926931	+	0.375231i	$0.122437\pi$
$677$			19.5264i			0.750461i	−0.926931	+	0.375231i	$0.877563\pi$
$678$	−2.70476	+	8.61206i	−0.103876	+	0.330744i
$679$	−17.4359	−	10.0666i	−0.669130	−	0.386323i
$680$	27.6538	+	35.7892i	1.06047	+	1.37245i
$681$	11.9370	−	6.89184i	0.457427	−	0.264096i
$682$	−0.814620	+	2.59378i	−0.0311934	+	0.0993210i
$683$	−15.1594	−	26.2569i	−0.580060	−	1.00469i	−0.995472	−	0.0950594i	$-0.969696\pi$
$683$	−15.1594	−	26.2569i	−0.580060	−	1.00469i	0.415412	−	0.909633i	$-0.363637\pi$
$684$	14.3538	+	10.0027i	0.548831	+	0.382465i
$685$	−3.80595	+	6.59210i	−0.145418	+	0.251871i
$686$	−2.71388	+	8.64110i	−0.103616	+	0.329919i
$687$	−1.86388	−	3.22833i	−0.0711113	−	0.123168i
$688$	−4.02187	−	10.8977i	−0.153333	−	0.415470i
$689$		−	10.9843i		−	0.418470i
$690$	−15.1010	+	3.36558i	−0.574885	+	0.128125i
$691$	−36.4542	+	21.0469i	−1.38678	+	0.800660i	−0.992951	−	0.118522i	$-0.962184\pi$
$691$	−36.4542	+	21.0469i	−1.38678	+	0.800660i	−0.393833	+	0.919182i	$0.628851\pi$
$692$	−10.9815	−	0.935947i	−0.417454	−	0.0355794i
$693$		−	12.3412i		−	0.468802i
$694$	−9.01022	+	28.6889i	−0.342023	+	1.08902i
$695$		−	49.0809i		−	1.86174i
$696$	11.9963	−	1.62042i	0.454720	−	0.0614218i
$697$		−	38.2655i		−	1.44941i
$698$	8.90640	+	39.9620i	0.337112	+	1.51259i
$699$	7.69194	+	4.44094i	0.290936	+	0.167972i
$700$	−10.6898	−	7.44939i	−0.404035	−	0.281560i
$701$	5.19744	+	9.00222i	0.196304	+	0.340009i	0.947327	−	0.320267i	$-0.103773\pi$
$701$	5.19744	+	9.00222i	0.196304	+	0.340009i	−0.751023	+	0.660276i	$0.770439\pi$
$702$	−18.4901	+	16.9812i	−0.697863	+	0.640915i
$703$	−16.2662	+	13.4683i	−0.613492	+	0.507966i
$704$	−10.8717	−	2.83480i	−0.409741	−	0.106841i
$705$	−13.3415	+	7.70273i	−0.502471	+	0.290102i
$706$	−2.08297	−	9.34607i	−0.0783937	−	0.351744i
$707$	−5.73238	−	3.30959i	−0.215588	−	0.124470i
$708$	−1.60771	+	2.30705i	−0.0604215	+	0.0867041i
$709$	−47.5114			−1.78433			−0.892163	−	0.451713i	$-0.850813\pi$
$709$	−47.5114			−1.78433			−0.892163	+	0.451713i	$0.850813\pi$
$710$	26.4479	−	5.89447i	0.992571	−	0.221216i
$711$		−	20.4050i		−	0.765248i
$712$	−18.9554	+	46.2014i	−0.710384	+	1.73147i
$713$	−8.24447			−0.308758
$714$	14.1095	+	15.3632i	0.528035	+	0.574953i
$715$	−14.7900	+	8.53901i	−0.553114	+	0.319341i
$716$	−31.7159	−	22.1019i	−1.18528	−	0.825986i
$717$	8.55220			0.319388
$718$	−4.38561	+	13.9640i	−0.163670	+	0.521131i
$719$	−13.7518	−	23.8189i	−0.512857	−	0.888294i	−0.999889	−	0.0149099i	$-0.995254\pi$
$719$	−13.7518	−	23.8189i	−0.512857	−	0.888294i	0.487032	−	0.873384i	$-0.338079\pi$
$720$	9.14476	+	24.7787i	0.340805	+	0.923447i
$721$	−39.8563	−	23.0110i	−1.48433	−	0.856976i
$722$	9.58839	−	2.13698i	0.356843	−	0.0795301i
$723$	4.41898	+	7.65389i	0.164343	+	0.284651i
$724$	5.04215	+	10.7499i	0.187390	+	0.399517i
$725$	−5.76718	−	9.98905i	−0.214188	−	0.370984i
$726$	−6.51737	+	5.98552i	−0.241882	+	0.222144i
$727$	−7.83020	−	4.52077i	−0.290406	−	0.167666i	0.347719	−	0.937599i	$-0.386956\pi$
$727$	−7.83020	−	4.52077i	−0.290406	−	0.167666i	−0.638125	+	0.769933i	$0.720290\pi$
$728$	42.3476	+	17.3743i	1.56951	+	0.643935i
$729$	4.40966			0.163321
$730$	−27.5060	−	29.9501i	−1.01804	−	1.10850i
$731$	15.3457	−	8.85982i	0.567579	−	0.327692i
$732$	−18.3839	−	1.56685i	−0.679489	−	0.0579125i
$733$	−1.85986	−	1.07379i	−0.0686954	−	0.0396613i	0.465259	−	0.885175i	$-0.345961\pi$
$733$	−1.85986	−	1.07379i	−0.0686954	−	0.0396613i	−0.533954	+	0.845513i	$0.679295\pi$
$734$	−21.4586	−	23.3653i	−0.792053	−	0.862431i
$735$	−8.12269	−	4.68964i	−0.299610	−	0.172980i
$736$	−1.67695	−	34.0295i	−0.0618134	−	1.25434i
$737$	4.04313	−	7.00291i	0.148931	−	0.257956i
$738$	6.69572	−	21.3194i	0.246473	−	0.784780i
$739$		−	3.19816i		−	0.117646i	−0.998268	−	0.0588231i	$-0.981265\pi$
$739$		−	3.19816i		−	0.117646i	0.998268	−	0.0588231i	$-0.0187348\pi$
$740$	−31.7722	+	2.64169i	−1.16797	+	0.0971105i
$741$		−	11.1658i		−	0.410187i
$742$	−11.1394	−	3.49850i	−0.408939	−	0.128434i
$743$	5.72632	−	9.91827i	0.210078	−	0.363866i	−0.741661	−	0.670775i	$-0.765961\pi$
$743$	5.72632	−	9.91827i	0.210078	−	0.363866i	0.951739	+	0.306909i	$0.0992948\pi$
$744$	−0.359212	−	2.65933i	−0.0131693	−	0.0974956i
$745$	4.63133	+	2.67390i	0.169679	+	0.0979642i
$746$	12.8264	−	11.7797i	0.469606	−	0.431285i
$747$	−22.0511	−	12.7312i	−0.806807	−	0.465810i
$748$	1.45543	−	17.0766i	0.0532157	−	0.624382i
$749$	42.7141	−	24.6610i	1.56074	−	0.901094i
$750$	5.92571	−	5.44215i	0.216377	−	0.198719i
$751$	−12.7402			−0.464898			−0.232449	−	0.972609i	$-0.574674\pi$
$751$	−12.7402			−0.464898			−0.232449	+	0.972609i	$0.574674\pi$
$752$	−11.7460	−	31.8270i	−0.428333	−	1.16061i
$753$	8.58057	+	4.95399i	0.312693	+	0.180534i
$754$	27.4092	+	29.8446i	0.998183	+	1.08688i
$755$	−28.4444	−	49.2672i	−1.03520	−	1.79302i
$756$	11.3318	+	24.1595i	0.412134	+	0.878673i
$757$	7.72440	+	13.3791i	0.280748	+	0.486270i	0.971569	−	0.236756i	$-0.0760841\pi$
$757$	7.72440	+	13.3791i	0.280748	+	0.486270i	−0.690821	+	0.723026i	$0.742751\pi$
$758$	8.50294	+	38.1518i	0.308841	+	1.38573i
$759$	5.07721	+	2.93133i	0.184291	+	0.106401i
$760$	−23.8086	−	9.76816i	−0.863630	−	0.354328i
$761$	23.7367	+	41.1132i	0.860454	+	1.49035i	0.871491	+	0.490412i	$0.163154\pi$
$761$	23.7367	+	41.1132i	0.860454	+	1.49035i	−0.0110363	+	0.999939i	$0.503513\pi$
$762$	−15.8374	−	4.97400i	−0.573729	−	0.180189i
$763$	−2.55783			−0.0925998
$764$	−19.9305	+	28.6000i	−0.721061	+	1.03471i
$765$	−34.8923	+	20.1451i	−1.26153	+	0.728346i
$766$	−17.0032	+	15.6157i	−0.614350	+	0.564216i
$767$	−9.41278			−0.339876
$768$	10.9034	−	2.02358i	0.393444	−	0.0730197i
$769$			26.9989i			0.973603i	0.873512	+	0.486802i	$0.161837\pi$
$769$			26.9989i			0.973603i	−0.873512	+	0.486802i	$0.838163\pi$
$770$	3.94892	+	17.7184i	0.142309	+	0.638526i
$771$	−10.7012			−0.385394
$772$	9.09036	−	13.0445i	0.327169	−	0.469483i
$773$	−25.6379	−	14.8020i	−0.922130	−	0.532392i	−0.0378164	−	0.999285i	$-0.512040\pi$
$773$	−25.6379	−	14.8020i	−0.922130	−	0.532392i	−0.884314	+	0.466892i	$0.845374\pi$
$774$	10.1001	−	2.25101i	0.363039	−	0.0809110i
$775$	−2.21435	+	1.27846i	−0.0795420	+	0.0459236i
$776$	−9.98325	−	12.9202i	−0.358378	−	0.463808i
$777$	−14.4969	+	2.45832i	−0.520073	+	0.0881917i
$778$	4.24321	+	4.62024i	0.152127	+	0.165644i
$779$	10.8864	+	18.8558i	0.390046	+	0.675579i
$780$	9.63766	−	13.8299i	0.345084	−	0.495190i
$781$	−8.89222	−	5.13393i	−0.318189	−	0.183706i
$782$	50.7280	−	11.3058i	1.81403	−	0.404295i
$783$			23.6232i			0.844223i
$784$	13.2055	−	15.8818i	0.471625	−	0.567208i
$785$			10.2789i			0.366868i
$786$	4.55662	+	1.43108i	0.162529	+	0.0510450i
$787$		−	15.9305i		−	0.567861i	−0.958845	−	0.283931i	$-0.908361\pi$
$787$		−	15.9305i		−	0.567861i	0.958845	−	0.283931i	$-0.0916386\pi$
$788$	42.7657	+	3.64490i	1.52347	+	0.129844i
$789$	2.16190	−	1.24817i	0.0769658	−	0.0444362i
$790$	6.52919	+	29.2958i	0.232298	+	1.04230i
$791$			32.1184i			1.14200i
$792$	3.79896	−	9.25946i	0.134990	−	0.329021i
$793$	−30.8807	−	53.4869i	−1.09660	−	1.89937i
$794$	−1.85420	−	0.582343i	−0.0658031	−	0.0206666i
$795$	−2.14991	+	3.72375i	−0.0762494	+	0.132068i
$796$	−7.31716	+	10.5000i	−0.259350	+	0.372163i
$797$	−10.3462	−	17.9201i	−0.366480	−	0.634761i	0.622533	−	0.782594i	$-0.286104\pi$
$797$	−10.3462	−	17.9201i	−0.366480	−	0.634761i	−0.989012	+	0.147832i	$0.952770\pi$
$798$	−11.3234	−	3.55630i	−0.400844	−	0.125892i
$799$	44.8175	−	25.8754i	1.58553	−	0.915405i
$800$	−5.72731	−	8.87983i	−0.202491	−	0.313949i
$801$	−38.5262	−	22.2431i	−1.36126	−	0.785922i
$802$	18.8600	+	5.92328i	0.665969	+	0.209158i
$803$			15.4091i			0.543774i
$804$	−0.677802	+	7.95268i	−0.0239042	+	0.280469i
$805$	−47.6742	+	27.5247i	−1.68029	+	0.970118i
$806$	6.61590	−	6.07601i	0.233035	−	0.214018i
$807$	5.69814	−	9.86946i	0.200584	−	0.347421i
$808$	−3.28217	−	4.24775i	−0.115466	−	0.149435i
$809$	−19.5032	−	11.2602i	−0.685695	−	0.395886i	0.116302	−	0.993214i	$-0.462896\pi$
$809$	−19.5032	−	11.2602i	−0.685695	−	0.395886i	−0.801997	+	0.597328i	$0.796229\pi$
$810$	−17.7517	+	3.95635i	−0.623731	+	0.139012i
$811$	47.9210	+	27.6672i	1.68274	+	0.971528i	0.959831	+	0.280579i	$0.0905266\pi$
$811$	47.9210	+	27.6672i	1.68274	+	0.971528i	0.722904	+	0.690948i	$0.242807\pi$
$812$	38.9956	−	18.2905i	1.36848	−	0.641871i
$813$			21.0130i			0.736959i
$814$	9.54447	+	7.40647i	0.334533	+	0.259597i
$815$	16.9975			0.595396
$816$	5.85701	+	15.8702i	0.205036	+	0.555567i
$817$	−5.04117	+	8.73156i	−0.176368	+	0.305479i
$818$	−4.79842	−	21.5300i	−0.167773	−	0.752779i
$819$	−20.3878	+	35.3127i	−0.712406	+	1.23392i
$820$	−2.79136	+	32.7511i	−0.0974785	+	1.14372i
$821$	25.1480	+	14.5192i	0.877671	+	0.506724i	0.869890	−	0.493246i	$-0.164190\pi$
$821$	25.1480	+	14.5192i	0.877671	+	0.506724i	0.00778147	+	0.999970i	$0.497523\pi$
$822$	−2.09689	+	1.92578i	−0.0731376	+	0.0671693i
$823$	20.3878	+	35.3127i	0.710674	+	1.23092i	0.964604	+	0.263701i	$0.0849434\pi$
$823$	20.3878	+	35.3127i	0.710674	+	1.23092i	−0.253930	+	0.967223i	$0.581723\pi$
$824$	−22.8204	−	29.5339i	−0.794986	−	1.02886i
$825$	1.81823			0.0633026
$826$	−2.99796	+	9.54562i	−0.104312	+	0.332135i
$827$	−4.58292	+	7.93785i	−0.159364	+	0.276026i	−0.934639	−	0.355597i	$-0.884278\pi$
$827$	−4.58292	+	7.93785i	−0.159364	+	0.276026i	0.775276	+	0.631623i	$0.217611\pi$
$828$	30.2412	+	2.57744i	1.05095	+	0.0895721i
$829$	17.0732	+	29.5717i	0.592977	+	1.02707i	0.993829	+	0.110924i	$0.0353809\pi$
$829$	17.0732	+	29.5717i	0.592977	+	1.02707i	−0.400852	+	0.916143i	$0.631286\pi$
$830$	35.7328	+	11.2225i	1.24030	+	0.389537i
$831$	−4.41378	+	2.54830i	−0.153112	+	0.0883995i
$832$	26.4248	+	26.0716i	0.916114	+	0.903870i
$833$	27.2861	+	15.7537i	0.945409	+	0.545832i
$834$	5.50055	−	17.5140i	0.190469	−	0.606459i
$835$	15.7555	−	9.09646i	0.545242	−	0.314796i
$836$	4.14104	+	8.82875i	0.143221	+	0.305349i
$837$	5.23674			0.181008
$838$	−5.98908	−	26.8724i	−0.206889	−	0.928291i
$839$	−5.81696	−	10.0753i	−0.200824	−	0.347837i	0.747970	−	0.663732i	$-0.231029\pi$
$839$	−5.81696	−	10.0753i	−0.200824	−	0.347837i	−0.948794	+	0.315895i	$0.897695\pi$
$840$	−10.9555	−	14.1785i	−0.378001	−	0.489204i
$841$	9.12983			0.314822
$842$	−3.64856	+	11.6172i	−0.125738	+	0.400354i
$843$	17.8365			0.614321
$844$	18.6371	−	26.7440i	0.641516	−	0.920567i
$845$	22.3575			0.769122
$846$	29.4975	−	6.57415i	1.01415	−	0.226024i
$847$	−15.7427	+	27.2671i	−0.540924	+	0.936908i
$848$	−7.28083	−	6.05390i	−0.250025	−	0.207892i
$849$	−15.7405	+	9.08779i	−0.540213	+	0.311892i
$850$	11.8717	−	10.9029i	0.407196	−	0.373967i
$851$	−12.7556	+	34.3437i	−0.437258	+	1.17729i
$852$	10.0982	+	0.860666i	0.345960	+	0.0294859i
$853$	−28.1032	−	48.6762i	−0.962235	−	1.66664i	−0.716867	−	0.697210i	$-0.754424\pi$
$853$	−28.1032	−	48.6762i	−0.962235	−	1.66664i	−0.245368	−	0.969430i	$-0.578909\pi$
$854$	−64.0771	+	14.2810i	−2.19267	+	0.488684i
$855$	11.4624	−	19.8534i	0.392005	−	0.678973i
$856$	39.6394	−	5.35434i	1.35485	−	0.183008i
$857$		−	1.03365i		−	0.0353088i	−0.999844	−	0.0176544i	$-0.994380\pi$
$857$		−	1.03365i		−	0.0353088i	0.999844	−	0.0176544i	$-0.00561987\pi$
$858$	−6.23462	+	1.38952i	−0.212846	+	0.0474374i
$859$	−13.4962			−0.460486			−0.230243	−	0.973133i	$-0.573952\pi$
$859$	−13.4962			−0.460486			−0.230243	+	0.973133i	$0.573952\pi$
$860$	−13.7805	+	6.46362i	−0.469912	+	0.220408i
$861$			15.1595i			0.516634i
$862$	13.6754	−	12.5595i	0.465787	−	0.427777i
$863$	17.0449	+	29.5227i	0.580216	+	1.00496i	0.995453	+	0.0952500i	$0.0303650\pi$
$863$	17.0449	+	29.5227i	0.580216	+	1.00496i	−0.415238	+	0.909713i	$0.636302\pi$
$864$	1.06517	+	21.6149i	0.0362379	+	0.735355i
$865$			14.4416i			0.491030i
$866$	−10.6896	+	34.0361i	−0.363247	+	1.15659i
$867$	−12.1436	+	7.01109i	−0.412417	+	0.238109i
$868$	−4.05461	−	8.64446i	−0.137622	−	0.293412i
$869$	5.68675	−	9.84974i	0.192910	−	0.334129i
$870$	−3.45053	−	15.4821i	−0.116984	−	0.524894i
$871$	−23.1378	+	13.3586i	−0.783996	+	0.452640i
$872$	−1.91912	−	0.787373i	−0.0649897	−	0.0266638i
$873$	12.5964	−	7.27253i	0.426323	−	0.246138i
$874$	−21.7804	+	20.0030i	−0.736732	+	0.676612i
$875$	14.3135	−	24.7918i	0.483886	−	0.838114i
$876$	−6.45869	−	13.7700i	−0.218219	−	0.465245i
$877$			9.79987i			0.330918i	0.986217	+	0.165459i	$0.0529106\pi$
$877$			9.79987i			0.330918i	−0.986217	+	0.165459i	$0.947089\pi$
$878$	−14.4923	+	13.3096i	−0.489090	+	0.449178i
$879$	−9.81653	−	17.0027i	−0.331103	−	0.573488i
$880$	−2.49137	+	14.5095i	−0.0839842	+	0.489116i
$881$	4.17589	−	7.23285i	0.140689	−	0.243681i	−0.787067	−	0.616867i	$-0.788402\pi$
$881$	4.17589	−	7.23285i	0.140689	−	0.243681i	0.927756	+	0.373187i	$0.121735\pi$
$882$	12.4458	+	13.5516i	0.419071	+	0.456307i
$883$	25.2912	−	43.8056i	0.851117	−	1.47418i	−0.0290850	−	0.999577i	$-0.509259\pi$
$883$	25.2912	−	43.8056i	0.851117	−	1.47418i	0.880202	−	0.474600i	$-0.157407\pi$
$884$	−32.3753	+	46.4581i	−1.08890	+	1.56256i
$885$	3.19099	+	1.84232i	0.107264	+	0.0619288i
$886$	7.52278	+	2.36265i	0.252733	+	0.0793748i
$887$	−35.2796			−1.18457			−0.592286	−	0.805728i	$-0.701774\pi$
$887$	−35.2796			−1.18457			−0.592286	+	0.805728i	$0.701774\pi$
$888$	−11.6336	−	2.61809i	−0.390399	−	0.0878574i
$889$	−59.0652			−1.98098
$890$	62.4300	+	19.6072i	2.09266	+	0.657234i
$891$	5.96842	+	3.44587i	0.199950	+	0.115441i
$892$	20.4335	+	14.2395i	0.684163	+	0.476773i
$893$	−14.7229	+	25.5008i	−0.492683	+	0.853352i
$894$	1.35297	+	1.47319i	0.0452502	+	0.0492709i
$895$	−25.3271	+	43.8678i	−0.846591	+	1.46634i
$896$	34.8558	−	18.4939i	1.16445	−	0.617839i
$897$	−9.68520	−	16.7753i	−0.323379	−	0.560110i
$898$	−28.8951	+	26.5371i	−0.964242	+	0.885556i
$899$		−	8.45255i		−	0.281908i
$900$	8.52206	−	3.99719i	0.284069	−	0.133240i
$901$	7.22208	−	12.5090i	0.240602	−	0.416736i
$902$	9.17370	−	8.42509i	0.305451	−	0.280525i
$903$	−6.07943	+	3.50996i	−0.202311	+	0.116804i
$904$	−9.88696	+	24.0982i	−0.328835	+	0.801494i
$905$	13.4741	−	7.77925i	0.447893	−	0.258591i
$906$	−4.62864	−	20.7682i	−0.153776	−	0.689978i
$907$	−9.36007	+	16.2121i	−0.310796	+	0.538315i	−0.978535	−	0.206081i	$-0.933929\pi$
$907$	−9.36007	+	16.2121i	−0.310796	+	0.538315i	0.667739	+	0.744396i	$0.267262\pi$
$908$	36.0096	−	16.8900i	1.19502	−	0.560513i
$909$	4.14129	−	2.39097i	0.137358	−	0.0793036i
$910$	17.9717	−	57.2226i	0.595756	−	1.89691i
$911$		−	32.3563i		−	1.07201i	−0.844214	−	0.536007i	$-0.819932\pi$
$911$		−	32.3563i		−	1.07201i	0.844214	−	0.536007i	$-0.180068\pi$
$912$	−7.40112	−	6.15392i	−0.245076	−	0.203777i
$913$	−7.09620	−	12.2910i	−0.234850	−	0.406772i
$914$	10.9727	−	10.0773i	0.362946	−	0.333328i
$915$			24.1765i			0.799249i
$916$	−4.56784	−	9.73868i	−0.150926	−	0.321775i
$917$	16.9938			0.561184
$918$	−32.2216	+	7.18126i	−1.06347	+	0.237017i
$919$		−	39.7288i		−	1.31053i	−0.755399	−	0.655266i	$-0.772557\pi$
$919$		−	39.7288i		−	1.31053i	0.755399	−	0.655266i	$-0.227443\pi$
$920$	−44.2424	+	5.97610i	−1.45863	+	0.197026i
$921$	−5.17419	+	8.96195i	−0.170495	+	0.295306i
$922$	11.5567	−	2.57566i	0.380599	−	0.0848247i
$923$	16.9626	+	29.3802i	0.558332	+	0.967060i
$924$	−0.576591	+	6.76516i	−0.0189684	+	0.222558i
$925$	1.89963	+	11.2023i	0.0624595	+	0.368328i
$926$	16.3857	−	15.0486i	0.538468	−	0.494527i
$927$	28.7937	−	16.6241i	0.945710	−	0.546006i
$928$	34.8884	−	1.71928i	1.14527	−	0.0564381i
$929$	−16.7015	+	28.9279i	−0.547960	+	0.949095i	0.450454	+	0.892800i	$0.351262\pi$
$929$	−16.7015	+	28.9279i	−0.547960	+	0.949095i	−0.998414	+	0.0562951i	$0.982071\pi$
$930$	−3.43205	+	0.764906i	−0.112541	+	0.0250823i
$931$	−17.9274			−0.587548
$932$	21.0273	+	14.6533i	0.688771	+	0.479984i
$933$	7.32867			0.239930
$934$	7.19839	−	22.9200i	0.235539	−	0.749964i
$935$	−22.4572			−0.734429
$936$	−26.1670	+	20.2189i	−0.855295	+	0.660874i
$937$	12.2026	+	21.1356i	0.398643	+	0.690470i	0.993559	−	0.113318i	$-0.0361480\pi$
$937$	12.2026	+	21.1356i	0.398643	+	0.690470i	−0.594916	+	0.803788i	$0.702815\pi$
$938$	6.17779	+	27.7191i	0.201712	+	0.905060i
$939$	−7.22190			−0.235678
$940$	−40.2464	+	18.8772i	−1.31269	+	0.615707i
$941$	−7.02050	+	4.05329i	−0.228862	+	0.132133i	−0.610047	−	0.792365i	$-0.708849\pi$
$941$	−7.02050	+	4.05329i	−0.228862	+	0.132133i	0.381185	+	0.924499i	$0.375516\pi$
$942$	−1.15196	+	3.66789i	−0.0375330	+	0.119506i
$943$	32.7109	+	18.8857i	1.06521	+	0.615002i
$944$	−5.18776	+	6.23914i	−0.168847	+	0.203067i
$945$	30.2818	−	17.4832i	0.985067	−	0.568729i
$946$	5.50275	+	1.72823i	0.178910	+	0.0561896i
$947$	29.3977	+	50.9184i	0.955298	+	1.65462i	0.733685	+	0.679490i	$0.237799\pi$
$947$	29.3977	+	50.9184i	0.955298	+	1.65462i	0.221613	+	0.975135i	$0.428868\pi$
$948$	−0.953342	+	11.1856i	−0.0309631	+	0.363292i
$949$	25.4560	−	44.0911i	0.826337	−	1.43126i
$950$	−2.74808	+	8.74999i	−0.0891595	+	0.283887i
$951$	−13.9345			−0.451858
$952$	36.8022	+	47.6290i	1.19277	+	1.54367i
$953$	26.1096	+	45.2231i	0.845772	+	1.46492i	0.884949	+	0.465688i	$0.154193\pi$
$953$	26.1096	+	45.2231i	0.845772	+	1.46492i	−0.0391763	+	0.999232i	$0.512473\pi$
$954$	6.21258	−	5.70561i	0.201140	−	0.184726i
$955$	39.5581	+	22.8389i	1.28007	+	0.739049i
$956$	24.5889	+	2.09570i	0.795261	+	0.0677796i
$957$	−3.00531	+	5.20536i	−0.0971480	+	0.168265i
$958$	−3.54922	−	15.9250i	−0.114670	−	0.514513i
$959$	−5.06504	+	8.77290i	−0.163559	+	0.283292i
$960$	−3.85529	−	14.0104i	−0.124429	−	0.452184i
$961$	29.1263			0.939557
$962$	−15.0747	−	36.9603i	−0.486027	−	1.19165i
$963$			35.6321i			1.14823i
$964$	10.8297	+	23.0890i	0.348800	+	0.743645i
$965$	−18.0425	−	10.4169i	−0.580810	−	0.335331i
$966$	−20.0967	+	4.47898i	−0.646601	+	0.144109i
$967$	−33.2292	−	19.1849i	−1.06858	−	0.616945i	−0.140787	−	0.990040i	$-0.544963\pi$
$967$	−33.2292	−	19.1849i	−1.06858	−	0.616945i	−0.927793	+	0.373095i	$0.878297\pi$
$968$	−20.2052	+	15.6122i	−0.649418	+	0.501796i
$969$	7.34140	−	12.7157i	0.235840	−	0.408486i
$970$	−15.7578	+	14.4719i	−0.505951	+	0.464664i
$971$	−13.5779	+	7.83921i	−0.435736	+	0.251572i	−0.701787	−	0.712387i	$-0.747614\pi$
$971$	−13.5779	+	7.83921i	−0.435736	+	0.251572i	0.266051	+	0.963959i	$0.414281\pi$
$972$	−29.6489	−	2.52696i	−0.950989	−	0.0810522i
$973$		−	65.3179i		−	2.09399i
$974$	49.4744	+	15.5383i	1.58526	+	0.497878i
$975$	−5.20263	−	3.00374i	−0.166618	−	0.0961967i
$976$	−52.4726	−	9.00987i	−1.67961	−	0.288399i
$977$	−8.60492	+	4.96805i	−0.275296	+	0.158942i	−0.631292	−	0.775545i	$-0.717475\pi$
$977$	−8.60492	+	4.96805i	−0.275296	+	0.158942i	0.355996	+	0.934487i	$0.384142\pi$
$978$	6.06536	+	1.90493i	0.193949	+	0.0609129i
$979$	−12.3980	−	21.4740i	−0.396243	−	0.686312i
$980$	−22.2048	−	15.4739i	−0.709306	−	0.494295i
$981$	0.923939	−	1.60031i	0.0294991	−	0.0510939i
$982$	50.2613	+	15.7854i	1.60390	+	0.503732i
$983$	5.40211	+	9.35672i	0.172300	+	0.298433i	0.939224	−	0.343306i	$-0.111547\pi$
$983$	5.40211	+	9.35672i	0.172300	+	0.298433i	−0.766923	+	0.641739i	$0.778213\pi$
$984$	−4.66652	+	11.3740i	−0.148763	+	0.362591i
$985$		−	56.2407i		−	1.79198i
$986$	11.5912	+	52.0084i	0.369138	+	1.65628i
$987$	−17.7552	+	10.2509i	−0.565153	+	0.326291i
$988$	2.73616	−	32.1034i	0.0870487	−	1.02135i
$989$			17.4908i			0.556175i
$990$	−12.5119	−	3.92958i	−0.397655	−	0.124890i
$991$			25.7334i			0.817450i	0.912658	+	0.408725i	$0.134026\pi$
$991$			25.7334i			0.817450i	−0.912658	+	0.408725i	$0.865974\pi$
$992$	−0.381127	−	7.73399i	−0.0121008	−	0.245555i
$993$		−	5.28137i		−	0.167599i
$994$	35.1974	−	7.84448i	1.11639	−	0.248812i
$995$	14.5231	+	8.38491i	0.460413	+	0.265819i
$996$	11.4931	+	8.00922i	0.364174	+	0.253782i
$997$	0.571620	+	0.990075i	0.0181034	+	0.0313560i	0.874935	−	0.484240i	$-0.160904\pi$
$997$	0.571620	+	0.990075i	0.0181034	+	0.0313560i	−0.856832	+	0.515596i	$0.827571\pi$
$998$	−22.8122	−	24.8391i	−0.722107	−	0.786269i
$999$	8.10217	−	21.8145i	0.256341	−	0.690181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	296.2.q.a.85.23	✓	72
4.3	odd	2		1184.2.y.a.529.23		72
8.3	odd	2		1184.2.y.a.529.14		72
8.5	even	2	inner	296.2.q.a.85.35	yes	72
37.27	even	6	inner	296.2.q.a.101.35	yes	72
148.27	odd	6		1184.2.y.a.1137.14		72
296.27	odd	6		1184.2.y.a.1137.23		72
296.101	even	6	inner	296.2.q.a.101.23	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.23	✓	72	1.1	even	1	trivial
296.2.q.a.85.35	yes	72	8.5	even	2	inner
296.2.q.a.101.23	yes	72	296.101	even	6	inner
296.2.q.a.101.35	yes	72	37.27	even	6	inner
1184.2.y.a.529.14		72	8.3	odd	2
1184.2.y.a.529.23		72	4.3	odd	2
1184.2.y.a.1137.14		72	148.27	odd	6
1184.2.y.a.1137.23		72	296.27	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.423750 - 1.34924i) q^{2} +(-0.600244 - 0.346551i) q^{3} +(-1.64087 - 1.14348i) q^{4} +(-1.31034 + 2.26957i) q^{5} +(-0.721932 + 0.663020i) q^{6} +(-1.74382 + 3.02039i) q^{7} +(-2.23814 + 1.72938i) q^{8} +(-1.25980 - 2.18205i) q^{9} +(2.50693 + 2.72968i) q^{10} -1.40440i q^{11} +(0.588651 + 1.25501i) q^{12} +(-2.32009 + 4.01851i) q^{13} +(3.33627 + 3.63272i) q^{14} +(1.57304 - 0.908198i) q^{15} +(1.38493 + 3.75260i) q^{16} +(-5.28425 + 3.05086i) q^{17} +(-3.47793 + 0.775132i) q^{18} +(1.73592 - 3.00670i) q^{19} +(4.74529 - 2.22574i) q^{20} +(2.09344 - 1.20865i) q^{21} +(-1.89486 - 0.595113i) q^{22} -6.02292i q^{23} +(1.94275 - 0.262419i) q^{24} +(-0.933966 - 1.61768i) q^{25} +(4.43878 + 4.83318i) q^{26} +3.82565i q^{27} +(6.31514 - 2.96206i) q^{28} +6.17494 q^{29} +(-0.558795 - 2.50726i) q^{30} -1.36885i q^{31} +(5.65000 - 0.278429i) q^{32} +(-0.486696 + 0.842982i) q^{33} +(1.87713 + 8.42250i) q^{34} +(-4.56999 - 7.91546i) q^{35} +(-0.427938 + 5.02101i) q^{36} +(-5.70217 - 2.11785i) q^{37} +(-3.32115 - 3.61625i) q^{38} +(2.78524 - 1.60806i) q^{39} +(-0.992226 - 7.34568i) q^{40} +(-3.13563 + 5.43107i) q^{41} +(-0.743656 - 3.33671i) q^{42} -2.90404 q^{43} +(-1.60590 + 2.30444i) q^{44} +6.60307 q^{45} +(-8.12634 - 2.55221i) q^{46} -8.48133 q^{47} +(0.469173 - 2.73242i) q^{48} +(-2.58184 - 4.47188i) q^{49} +(-2.57839 + 0.574650i) q^{50} +4.22912 q^{51} +(8.40203 - 3.94090i) q^{52} +(-2.05008 + 1.18361i) q^{53} +(5.16171 + 1.62112i) q^{54} +(3.18738 + 1.84023i) q^{55} +(-1.32047 - 9.77577i) q^{56} +(-2.08395 + 1.20317i) q^{57} +(2.61663 - 8.33144i) q^{58} +(1.01427 + 1.75677i) q^{59} +(-3.61967 - 0.308502i) q^{60} +(-6.65507 + 11.5269i) q^{61} +(-1.84690 - 0.580049i) q^{62} +8.78751 q^{63} +(2.01852 - 7.74116i) q^{64} +(-6.08019 - 10.5312i) q^{65} +(0.931144 + 1.01388i) q^{66} +(4.98642 + 2.87891i) q^{67} +(12.1594 + 1.03633i) q^{68} +(-2.08725 + 3.61522i) q^{69} +(-12.6163 + 2.81182i) q^{70} +(3.65561 - 6.33170i) q^{71} +(6.59319 + 2.70504i) q^{72} -10.9720 q^{73} +(-5.27377 + 6.79613i) q^{74} +1.29467i q^{75} +(-6.28650 + 2.94863i) q^{76} +(4.24183 + 2.44902i) q^{77} +(-0.989405 - 4.43935i) q^{78} +(7.01349 + 4.04924i) q^{79} +(-10.3315 - 1.77398i) q^{80} +(-2.45363 + 4.24981i) q^{81} +(5.99907 + 6.53212i) q^{82} +(8.75178 - 5.05285i) q^{83} +(-4.81713 - 0.410561i) q^{84} -15.9906i q^{85} +(-1.23058 + 3.91823i) q^{86} +(-3.70647 - 2.13993i) q^{87} +(2.42873 + 3.14324i) q^{88} +(15.2905 - 8.82800i) q^{89} +(2.79805 - 8.90910i) q^{90} +(-8.09164 - 14.0151i) q^{91} +(-6.88706 + 9.88284i) q^{92} +(-0.474376 + 0.821644i) q^{93} +(-3.59396 + 11.4433i) q^{94} +(4.54927 + 7.87957i) q^{95} +(-3.48787 - 1.79089i) q^{96} +5.77275i q^{97} +(-7.12767 + 1.58855i) q^{98} +(-3.06446 + 1.76927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 6 q^{2} - 2 q^{4} + 2 q^{7} + 30 q^{9} - 12 q^{12} - 6 q^{15} - 6 q^{16} - 12 q^{17} - 48 q^{18} + 18 q^{20} - 12 q^{22} - 6 q^{24} - 32 q^{25} - 16 q^{26} + 10 q^{28} - 14 q^{30} - 6 q^{32} + 4 q^{33}+ \cdots + 48 q^{98}+O(q^{100}) \) 72 * q - 6 * q^2 - 2 * q^4 + 2 * q^7 + 30 * q^9 - 12 * q^12 - 6 * q^15 - 6 * q^16 - 12 * q^17 - 48 * q^18 + 18 * q^20 - 12 * q^22 - 6 * q^24 - 32 * q^25 - 16 * q^26 + 10 * q^28 - 14 * q^30 - 6 * q^32 + 4 * q^33 + 8 * q^34 + 4 * q^36 - 24 * q^38 - 6 * q^39 - 18 * q^40 + 6 * q^42 - 10 * q^44 - 8 * q^46 + 32 * q^47 + 20 * q^48 - 18 * q^49 + 12 * q^50 + 42 * q^52 + 30 * q^54 + 24 * q^55 - 24 * q^56 - 6 * q^57 - 8 * q^58 + 32 * q^62 + 8 * q^63 - 68 * q^64 + 6 * q^65 + 20 * q^70 + 18 * q^71 + 18 * q^72 - 64 * q^73 - 12 * q^74 - 72 * q^76 + 54 * q^78 + 54 * q^79 - 16 * q^81 - 12 * q^84 + 48 * q^86 - 108 * q^87 - 36 * q^89 + 24 * q^90 - 120 * q^92 - 72 * q^94 + 50 * q^95 + 36 * q^96 + 48 * q^98

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