LMFDB - Embedded newform 820.2.bk.c.267.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(43,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			267.36
Character	$\chi$	$=$	820.267
Dual form			820.2.bk.c.43.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.910966 - 1.08173i) q^{2} -0.848586i q^{3} +(-0.340282 + 1.97084i) q^{4} +(0.879185 + 2.05598i) q^{5} +(-0.917941 + 0.773033i) q^{6} +(0.799062 + 2.45926i) q^{7} +(2.44190 - 1.42727i) q^{8} +2.27990 q^{9} +(1.42310 - 2.82396i) q^{10} +(-0.280850 + 1.77322i) q^{11} +(1.67243 + 0.288758i) q^{12} +(-0.676408 + 2.08177i) q^{13} +(1.93234 - 3.10467i) q^{14} +(1.74467 - 0.746064i) q^{15} +(-3.76842 - 1.34128i) q^{16} +(-4.40160 + 3.19795i) q^{17} +(-2.07691 - 2.46624i) q^{18} +(-6.06554 - 3.09055i) q^{19} +(-4.35117 + 1.03312i) q^{20} +(2.08689 - 0.678072i) q^{21} +(2.17399 - 1.31154i) q^{22} +(-3.78420 + 1.92814i) q^{23} +(-1.21116 - 2.07216i) q^{24} +(-3.45407 + 3.61517i) q^{25} +(2.86810 - 1.16473i) q^{26} -4.48045i q^{27} +(-5.11871 + 0.737981i) q^{28} +(-2.94682 + 0.466730i) q^{29} +(-2.39638 - 1.20762i) q^{30} +(3.17243 + 4.36648i) q^{31} +(1.98199 + 5.29827i) q^{32} +(1.50473 + 0.238326i) q^{33} +(7.46903 + 1.84812i) q^{34} +(-4.35365 + 3.80500i) q^{35} +(-0.775810 + 4.49332i) q^{36} +(1.04582 + 6.60307i) q^{37} +(2.18236 + 9.37666i) q^{38} +(1.76656 + 0.573990i) q^{39} +(5.08132 + 3.76565i) q^{40} +(6.12880 + 1.85414i) q^{41} +(-2.63458 - 1.63975i) q^{42} +(-5.36862 - 10.5365i) q^{43} +(-3.39916 - 1.15691i) q^{44} +(2.00446 + 4.68742i) q^{45} +(5.53301 + 2.33701i) q^{46} +(-11.9292 - 3.87605i) q^{47} +(-1.13819 + 3.19782i) q^{48} +(0.253659 - 0.184294i) q^{49} +(7.05717 + 0.443078i) q^{50} +(2.71373 + 3.73514i) q^{51} +(-3.87266 - 2.04148i) q^{52} +(-0.279001 - 0.202706i) q^{53} +(-4.84664 + 4.08154i) q^{54} +(-3.89261 + 0.981566i) q^{55} +(5.46127 + 4.86479i) q^{56} +(-2.62259 + 5.14713i) q^{57} +(3.18933 + 2.76249i) q^{58} +(0.807500 - 2.48523i) q^{59} +(0.876692 + 3.69234i) q^{60} +(11.1131 - 3.61088i) q^{61} +(1.83338 - 7.40944i) q^{62} +(1.82178 + 5.60687i) q^{63} +(3.92578 - 6.97053i) q^{64} +(-4.87476 + 0.439583i) q^{65} +(-1.11295 - 1.84482i) q^{66} +(1.82702 - 2.51467i) q^{67} +(-4.80486 - 9.76305i) q^{68} +(1.63620 + 3.21121i) q^{69} +(8.08201 + 1.24326i) q^{70} +(0.786938 - 4.96853i) q^{71} +(5.56730 - 3.25405i) q^{72} +(5.24712 + 5.24712i) q^{73} +(6.19004 - 7.14648i) q^{74} +(3.06778 + 2.93107i) q^{75} +(8.15497 - 10.9026i) q^{76} +(-4.58522 + 0.726228i) q^{77} +(-0.988373 - 2.43383i) q^{78} +(10.3820 + 10.3820i) q^{79} +(-0.555492 - 8.92701i) q^{80} +3.03766 q^{81} +(-3.57744 - 8.31877i) q^{82} +(8.56967 + 8.56967i) q^{83} +(0.626240 + 4.34367i) q^{84} +(-10.4447 - 6.23799i) q^{85} +(-6.50703 + 15.4058i) q^{86} +(0.396060 + 2.50063i) q^{87} +(1.84506 + 4.73088i) q^{88} +(-12.3575 - 6.29646i) q^{89} +(3.24454 - 6.43836i) q^{90} -5.66011 q^{91} +(-2.51237 - 8.11416i) q^{92} +(3.70533 - 2.69208i) q^{93} +(6.67430 + 16.4352i) q^{94} +(1.02136 - 15.1878i) q^{95} +(4.49604 - 1.68189i) q^{96} +(-8.28892 - 6.02225i) q^{97} +(-0.430431 - 0.106505i) q^{98} +(-0.640311 + 4.04277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.910966	−	1.08173i	−0.644150	−	0.764899i
$2$	−0.910966	−	1.08173i	−0.644150	−	0.764899i
$3$		−	0.848586i		−	0.489931i	−0.969532	−	0.244966i	$-0.921223\pi$
$3$		−	0.848586i		−	0.489931i	0.969532	−	0.244966i	$-0.0787767\pi$
$4$	−0.340282	+	1.97084i	−0.170141	+	0.985420i
$5$	0.879185	+	2.05598i	0.393184	+	0.919460i
$5$	0.879185	+	2.05598i	0.393184	+	0.919460i
$6$	−0.917941	+	0.773033i	−0.374748	+	0.315589i
$7$	0.799062	+	2.45926i	0.302017	+	0.929513i	0.980774	+	0.195149i	$0.0625192\pi$
$7$	0.799062	+	2.45926i	0.302017	+	0.929513i	−0.678756	+	0.734363i	$0.737481\pi$
$8$	2.44190	−	1.42727i	0.863343	−	0.504618i
$9$	2.27990			0.759968
$10$	1.42310	−	2.82396i	0.450025	−	0.893016i
$11$	−0.280850	+	1.77322i	−0.0846796	+	0.534646i	0.908484	+	0.417919i	$0.137240\pi$
$11$	−0.280850	+	1.77322i	−0.0846796	+	0.534646i	−0.993164	+	0.116727i	$0.962760\pi$
$12$	1.67243	+	0.288758i	0.482788	+	0.0833574i
$13$	−0.676408	+	2.08177i	−0.187602	+	0.577379i	−0.999983	−	0.00574701i	$-0.998171\pi$
$13$	−0.676408	+	2.08177i	−0.187602	+	0.577379i	0.812382	+	0.583126i	$0.198171\pi$
$14$	1.93234	−	3.10467i	0.516439	−	0.829759i
$15$	1.74467	−	0.746064i	0.450472	−	0.192633i
$16$	−3.76842	−	1.34128i	−0.942104	−	0.335321i
$17$	−4.40160	+	3.19795i	−1.06755	+	0.775617i	−0.975469	−	0.220135i	$-0.929350\pi$
$17$	−4.40160	+	3.19795i	−1.06755	+	0.775617i	−0.0920757	+	0.995752i	$0.529350\pi$
$18$	−2.07691	−	2.46624i	−0.489533	−	0.581298i
$19$	−6.06554	−	3.09055i	−1.39153	−	0.709020i	−0.412164	−	0.911110i	$-0.635227\pi$
$19$	−6.06554	−	3.09055i	−1.39153	−	0.709020i	−0.979367	+	0.202090i	$0.935227\pi$
$20$	−4.35117	+	1.03312i	−0.972951	+	0.231013i
$21$	2.08689	−	0.678072i	0.455397	−	0.147968i
$22$	2.17399	−	1.31154i	0.463496	−	0.279621i
$23$	−3.78420	+	1.92814i	−0.789060	+	0.402046i	−0.801589	−	0.597876i	$-0.796012\pi$
$23$	−3.78420	+	1.92814i	−0.789060	+	0.402046i	0.0125293	+	0.999922i	$0.496012\pi$
$24$	−1.21116	−	2.07216i	−0.247228	−	0.422979i
$25$	−3.45407	+	3.61517i	−0.690813	+	0.723033i
$26$	2.86810	−	1.16473i	0.562480	−	0.228422i
$27$		−	4.48045i		−	0.862263i
$28$	−5.11871	+	0.737981i	−0.967346	+	0.139465i
$29$	−2.94682	+	0.466730i	−0.547210	+	0.0866696i	−0.423918	−	0.905701i	$-0.639345\pi$
$29$	−2.94682	+	0.466730i	−0.547210	+	0.0866696i	−0.123293	+	0.992370i	$0.539345\pi$
$30$	−2.39638	−	1.20762i	−0.437516	−	0.220481i
$31$	3.17243	+	4.36648i	0.569786	+	0.784243i	0.992529	−	0.122006i	$-0.0389328\pi$
$31$	3.17243	+	4.36648i	0.569786	+	0.784243i	−0.422743	+	0.906249i	$0.638933\pi$
$32$	1.98199	+	5.29827i	0.350370	+	0.936611i
$33$	1.50473	+	0.238326i	0.261940	+	0.0414871i
$34$	7.46903	+	1.84812i	1.28093	+	0.316950i
$35$	−4.35365	+	3.80500i	−0.735902	+	0.643162i
$36$	−0.775810	+	4.49332i	−0.129302	+	0.748887i
$37$	1.04582	+	6.60307i	0.171932	+	1.08554i	0.911151	+	0.412073i	$0.135195\pi$
$37$	1.04582	+	6.60307i	0.171932	+	1.08554i	−0.739218	+	0.673466i	$0.764805\pi$
$38$	2.18236	+	9.37666i	0.354026	+	1.52110i
$39$	1.76656	+	0.573990i	0.282876	+	0.0919120i
$40$	5.08132	+	3.76565i	0.803428	+	0.595402i
$41$	6.12880	+	1.85414i	0.957157	+	0.289569i
$41$	6.12880	+	1.85414i	0.957157	+	0.289569i
$42$	−2.63458	−	1.63975i	−0.406524	−	0.253020i
$43$	−5.36862	−	10.5365i	−0.818706	−	1.60680i	−0.794632	−	0.607091i	$-0.792336\pi$
$43$	−5.36862	−	10.5365i	−0.818706	−	1.60680i	−0.0240742	−	0.999710i	$-0.507664\pi$
$44$	−3.39916	−	1.15691i	−0.512443	−	0.174410i
$45$	2.00446	+	4.68742i	0.298807	+	0.698760i
$46$	5.53301	+	2.33701i	0.815797	+	0.344573i
$47$	−11.9292	−	3.87605i	−1.74006	−	0.565380i	−0.745218	−	0.666821i	$-0.767654\pi$
$47$	−11.9292	−	3.87605i	−1.74006	−	0.565380i	−0.994841	+	0.101442i	$0.967654\pi$
$48$	−1.13819	+	3.19782i	−0.164284	+	0.461566i
$49$	0.253659	−	0.184294i	0.0362370	−	0.0263277i
$50$	7.05717	+	0.443078i	0.998035	+	0.0626606i
$51$	2.71373	+	3.73514i	0.379999	+	0.523024i
$52$	−3.87266	−	2.04148i	−0.537042	−	0.283102i
$53$	−0.279001	−	0.202706i	−0.0383237	−	0.0278438i	0.568458	−	0.822712i	$-0.307540\pi$
$53$	−0.279001	−	0.202706i	−0.0383237	−	0.0278438i	−0.606782	+	0.794868i	$0.707540\pi$
$54$	−4.84664	+	4.08154i	−0.659544	+	0.555427i
$55$	−3.89261	+	0.981566i	−0.524880	+	0.132354i
$56$	5.46127	+	4.86479i	0.729793	+	0.650085i
$57$	−2.62259	+	5.14713i	−0.347371	+	0.681754i
$58$	3.18933	+	2.76249i	0.418779	+	0.362732i
$59$	0.807500	−	2.48523i	0.105128	−	0.323549i	−0.884633	−	0.466288i	$-0.845591\pi$
$59$	0.807500	−	2.48523i	0.105128	−	0.323549i	0.989760	+	0.142739i	$0.0455909\pi$
$60$	0.876692	+	3.69234i	0.113180	+	0.476679i
$61$	11.1131	−	3.61088i	1.42289	−	0.462325i	0.506371	−	0.862315i	$-0.330986\pi$
$61$	11.1131	−	3.61088i	1.42289	−	0.462325i	0.916519	+	0.399990i	$0.130986\pi$
$62$	1.83338	−	7.40944i	0.232839	−	0.940999i
$63$	1.82178	+	5.60687i	0.229523	+	0.706400i
$64$	3.92578	−	6.97053i	0.490722	−	0.871316i
$65$	−4.87476	+	0.439583i	−0.604639	+	0.0545235i
$66$	−1.11295	−	1.84482i	−0.136995	−	0.227081i
$67$	1.82702	−	2.51467i	0.223206	−	0.307216i	−0.682698	−	0.730701i	$-0.739193\pi$
$67$	1.82702	−	2.51467i	0.223206	−	0.307216i	0.905903	+	0.423485i	$0.139193\pi$
$68$	−4.80486	−	9.76305i	−0.582675	−	1.18394i
$69$	1.63620	+	3.21121i	0.196975	+	0.386585i
$70$	8.08201	+	1.24326i	0.965985	+	0.148598i
$71$	0.786938	−	4.96853i	0.0933924	−	0.589656i	−0.895962	−	0.444131i	$-0.853513\pi$
$71$	0.786938	−	4.96853i	0.0933924	−	0.589656i	0.989354	−	0.145526i	$-0.0464874\pi$
$72$	5.56730	−	3.25405i	0.656113	−	0.383493i
$73$	5.24712	+	5.24712i	0.614129	+	0.614129i	0.944019	−	0.329891i	$-0.107012\pi$
$73$	5.24712	+	5.24712i	0.614129	+	0.614129i	−0.329891	+	0.944019i	$0.607012\pi$
$74$	6.19004	−	7.14648i	0.719577	−	0.830761i
$75$	3.06778	+	2.93107i	0.354236	+	0.338451i
$76$	8.15497	−	10.9026i	0.935439	−	1.25061i
$77$	−4.58522	+	0.726228i	−0.522535	+	0.0827614i
$78$	−0.988373	−	2.43383i	−0.111911	−	0.275577i
$79$	10.3820	+	10.3820i	1.16807	+	1.16807i	0.982662	+	0.185407i	$0.0593603\pi$
$79$	10.3820	+	10.3820i	1.16807	+	1.16807i	0.185407	+	0.982662i	$0.440640\pi$
$80$	−0.555492	−	8.92701i	−0.0621059	−	0.998070i
$81$	3.03766			0.337518
$82$	−3.57744	−	8.31877i	−0.395062	−	0.918654i
$83$	8.56967	+	8.56967i	0.940643	+	0.940643i	0.998334	−	0.0576914i	$-0.0183739\pi$
$83$	8.56967	+	8.56967i	0.940643	+	0.940643i	−0.0576914	+	0.998334i	$0.518374\pi$
$84$	0.626240	+	4.34367i	0.0683284	+	0.473933i
$85$	−10.4447	−	6.23799i	−1.13289	−	0.676605i
$86$	−6.50703	+	15.4058i	−0.701671	+	1.66125i
$87$	0.396060	+	2.50063i	0.0424621	+	0.268095i
$88$	1.84506	+	4.73088i	0.196684	+	0.504313i
$89$	−12.3575	−	6.29646i	−1.30989	−	0.667424i	−0.347142	−	0.937813i	$-0.612848\pi$
$89$	−12.3575	−	6.29646i	−1.30989	−	0.667424i	−0.962751	+	0.270389i	$0.912848\pi$
$90$	3.24454	−	6.43836i	0.342004	−	0.678663i
$91$	−5.66011			−0.593340
$92$	−2.51237	−	8.11416i	−0.261933	−	0.845959i
$93$	3.70533	−	2.69208i	0.384225	−	0.279156i
$94$	6.67430	+	16.4352i	0.688401	+	1.69516i
$95$	1.02136	−	15.1878i	0.104789	−	1.55823i
$96$	4.49604	−	1.68189i	0.458875	−	0.171657i
$97$	−8.28892	−	6.02225i	−0.841612	−	0.611467i	0.0812083	−	0.996697i	$-0.474122\pi$
$97$	−8.28892	−	6.02225i	−0.841612	−	0.611467i	−0.922821	+	0.385230i	$0.874122\pi$
$98$	−0.430431	−	0.106505i	−0.0434801	−	0.0107586i
$99$	−0.640311	+	4.04277i	−0.0643537	+	0.406313i
$100$	−5.94955	−	8.03759i	−0.594955	−	0.803759i
$101$	12.0124	+	6.12064i	1.19528	+	0.609027i	0.934359	−	0.356333i	$-0.115973\pi$
$101$	12.0124	+	6.12064i	1.19528	+	0.609027i	0.260923	+	0.965360i	$0.415973\pi$
$102$	1.56829	−	6.33811i	0.155284	−	0.627566i
$103$	12.6193	+	6.42985i	1.24341	+	0.633551i	0.946916	−	0.321482i	$-0.104181\pi$
$103$	12.6193	+	6.42985i	1.24341	+	0.633551i	0.296499	+	0.955033i	$0.404181\pi$
$104$	1.31953	+	6.04890i	0.129391	+	0.593143i
$105$	3.22886	+	3.69445i	0.315105	+	0.360541i
$106$	0.0348870	+	0.486462i	0.00338853	+	0.0472494i
$107$	7.04723	+	3.59074i	0.681281	+	0.347130i	0.760143	−	0.649756i	$-0.225129\pi$
$107$	7.04723	+	3.59074i	0.681281	+	0.347130i	−0.0788623	+	0.996886i	$0.525129\pi$
$108$	8.83025	+	1.52462i	0.849691	+	0.146706i
$109$	6.25654	+	6.25654i	0.599268	+	0.599268i	0.940118	−	0.340850i	$-0.110715\pi$
$109$	6.25654	+	6.25654i	0.599268	+	0.599268i	−0.340850	+	0.940118i	$0.610715\pi$
$110$	4.60783	+	3.31659i	0.439339	+	0.316224i
$111$	5.60327	−	0.887471i	0.531839	−	0.0842350i
$112$	0.287364	−	10.3393i	0.0271533	−	0.976970i
$113$	−2.24255	+	14.1589i	−0.210962	+	1.33196i	0.623902	+	0.781502i	$0.285546\pi$
$113$	−2.24255	+	14.1589i	−0.210962	+	1.33196i	−0.834864	+	0.550456i	$0.814454\pi$
$114$	7.95690	−	1.85192i	0.745232	−	0.173448i
$115$	−7.29123	−	6.08502i	−0.679910	−	0.567431i
$116$	0.0828989	−	5.96652i	0.00769697	−	0.553978i
$117$	−1.54214	+	4.74623i	−0.142571	+	0.438789i
$118$	−3.42395	+	1.39046i	−0.315201	+	0.128002i
$119$	−11.3817	−	8.26932i	−1.04336	−	0.758047i
$120$	3.19548	−	4.31194i	0.291706	−	0.393624i
$121$	7.39619	+	2.40317i	0.672381	+	0.218470i
$122$	−14.0297	−	8.73203i	−1.27019	−	0.790561i
$123$	1.57340	−	5.20081i	0.141869	−	0.468941i
$124$	−9.68516	+	4.76652i	−0.869753	+	0.428046i
$125$	−10.4695	−	3.92308i	−0.936416	−	0.350891i
$126$	4.40554	−	7.07835i	0.392477	−	0.630590i
$127$	−8.10650	+	1.28394i	−0.719335	+	0.113931i	−0.505361	−	0.862908i	$-0.668641\pi$
$127$	−8.10650	+	1.28394i	−0.719335	+	0.113931i	−0.213974	+	0.976839i	$0.568641\pi$
$128$	−11.1165	+	2.10328i	−0.982568	+	0.185906i
$129$	−8.94112	+	4.55573i	−0.787222	+	0.401110i
$130$	4.91625	+	4.87273i	0.431183	+	0.427366i
$131$	−2.31107	+	1.67909i	−0.201919	+	0.146703i	−0.684150	−	0.729341i	$-0.739827\pi$
$131$	−2.31107	+	1.67909i	−0.201919	+	0.146703i	0.482231	+	0.876044i	$0.339827\pi$
$132$	−0.981733	+	2.88448i	−0.0854489	+	0.251062i
$133$	2.75372	−	17.3863i	0.238778	−	1.50758i
$134$	−4.38455	+	0.314442i	−0.378767	+	0.0271636i
$135$	9.21169	−	3.93914i	0.792816	−	0.339028i
$136$	−6.18393	+	14.0914i	−0.530268	+	1.20833i
$137$	−4.93259			−0.421419			−0.210710	−	0.977549i	$-0.567577\pi$
$137$	−4.93259			−0.421419			−0.210710	+	0.977549i	$0.567577\pi$
$138$	1.98315	−	4.69523i	0.168817	−	0.399685i
$139$	2.49100	+	7.66650i	0.211284	+	0.650264i	0.999397	+	0.0347337i	$0.0110583\pi$
$139$	2.49100	+	7.66650i	0.211284	+	0.650264i	−0.788113	+	0.615531i	$0.788942\pi$
$140$	−6.01757	−	9.87513i	−0.508577	−	0.834600i
$141$	−3.28916	+	10.1230i	−0.276997	+	0.852509i
$142$	−6.09149	+	3.67491i	−0.511186	+	0.308392i
$143$	−3.50146	−	1.78409i	−0.292807	−	0.149193i
$144$	−8.59162	−	3.05799i	−0.715969	−	0.254833i
$145$	−3.55038	−	5.64824i	−0.294843	−	0.469061i
$146$	0.896022	−	10.4559i	0.0741553	−	0.865337i
$147$	−0.156389	−	0.215251i	−0.0128988	−	0.0177536i
$148$	−13.3695	−	0.185756i	−1.09896	−	0.0152690i
$149$	−0.686330	−	4.33332i	−0.0562263	−	0.354999i	−0.999721	−	0.0236120i	$-0.992483\pi$
$149$	−0.686330	−	4.33332i	−0.0562263	−	0.354999i	0.943495	−	0.331387i	$-0.107517\pi$
$150$	0.375989	−	5.98861i	0.0306994	−	0.488968i
$151$	7.95891	+	15.6202i	0.647687	+	1.27116i	0.948289	+	0.317407i	$0.102812\pi$
$151$	7.95891	+	15.6202i	0.647687	+	1.27116i	−0.300603	+	0.953749i	$0.597188\pi$
$152$	−19.2225	+	1.11037i	−1.55915	+	0.0900633i
$153$	−10.0352	+	7.29102i	−0.811300	+	0.589444i
$154$	4.96257	+	4.29841i	0.399895	+	0.346376i
$155$	−6.18822	+	10.3614i	−0.497050	+	0.832247i
$156$	−1.73237	+	3.28629i	−0.138701	+	0.263114i
$157$	21.9236	−	7.12339i	1.74969	−	0.568509i	0.753639	−	0.657289i	$-0.228297\pi$
$157$	21.9236	−	7.12339i	1.74969	−	0.568509i	0.996051	+	0.0887803i	$0.0282969\pi$
$158$	1.77288	−	20.6882i	0.141043	−	1.64587i
$159$	−0.172013	+	0.236756i	−0.0136416	+	0.0187760i
$160$	−9.15058	+	8.73309i	−0.723417	+	0.690411i
$161$	−7.76562	−	7.76562i	−0.612016	−	0.612016i
$162$	−2.76721	−	3.28593i	−0.217412	−	0.258167i
$163$	2.66790	+	2.66790i	0.208966	+	0.208966i	0.803828	−	0.594862i	$-0.202793\pi$
$163$	2.66790	+	2.66790i	0.208966	+	0.208966i	−0.594862	+	0.803828i	$0.702793\pi$
$164$	−5.73974	+	11.4479i	−0.448198	+	0.893934i
$165$	0.832943	+	3.30322i	0.0648445	+	0.257155i
$166$	1.46340	−	17.0767i	0.113582	−	1.32541i
$167$	21.1319			1.63523			0.817617	−	0.575762i	$-0.195295\pi$
$167$	21.1319			1.63523			0.817617	+	0.575762i	$0.195295\pi$
$168$	4.12819	−	4.63435i	0.318497	−	0.357548i
$169$	6.64098	+	4.82496i	0.510845	+	0.371150i
$170$	2.76697	+	16.9810i	0.212217	+	1.30238i
$171$	−13.8288	−	7.04615i	−1.05752	−	0.538832i
$172$	22.5926	−	6.99530i	1.72267	−	0.533386i
$173$	−8.21513	−	8.21513i	−0.624585	−	0.624585i	0.322115	−	0.946700i	$-0.395606\pi$
$173$	−8.21513	−	8.21513i	−0.624585	−	0.624585i	−0.946700	+	0.322115i	$0.895606\pi$
$174$	2.34421	−	2.70642i	0.177714	−	0.205173i
$175$	−11.6506	−	5.60571i	−0.880706	−	0.423752i
$176$	3.43675	−	6.30553i	0.259055	−	0.475297i
$177$	−2.10893	−	0.685233i	−0.158517	−	0.0515053i
$178$	4.44619	+	19.1034i	0.333256	+	1.43186i
$179$	−3.24001	+	0.513168i	−0.242170	+	0.0383560i	−0.276339	−	0.961060i	$-0.589121\pi$
$179$	−3.24001	+	0.513168i	−0.242170	+	0.0383560i	0.0341695	+	0.999416i	$0.489121\pi$
$180$	−9.92024	+	2.35542i	−0.739411	+	0.175562i
$181$	0.567190	−	3.58110i	0.0421589	−	0.266181i	−0.957601	−	0.288098i	$-0.906977\pi$
$181$	0.567190	−	3.58110i	0.0421589	−	0.266181i	0.999760	+	0.0219172i	$0.00697702\pi$
$182$	5.15616	+	6.12271i	0.382200	+	0.453845i
$183$	−3.06414	−	9.43044i	−0.226508	−	0.697118i
$184$	−6.48865	+	10.1094i	−0.478350	+	0.745277i
$185$	−12.6563	+	7.95551i	−0.930508	+	0.584901i
$186$	−6.28754	−	1.55578i	−0.461025	−	0.114075i
$187$	−4.43448	−	8.70315i	−0.324281	−	0.636437i
$188$	11.6984	−	22.1917i	0.853192	−	1.61849i
$189$	11.0186	−	3.58016i	0.801484	−	0.260418i
$190$	−17.3595	+	12.7307i	−1.25939	+	0.923582i
$191$	4.00486	+	4.00486i	0.289781	+	0.289781i	0.836994	−	0.547212i	$-0.184311\pi$
$191$	4.00486	+	4.00486i	0.289781	+	0.289781i	−0.547212	+	0.836994i	$0.684311\pi$
$192$	−5.91509	−	3.33136i	−0.426885	−	0.240420i
$193$	−2.96688	−	2.15557i	−0.213561	−	0.155161i	0.475863	−	0.879520i	$-0.342136\pi$
$193$	−2.96688	−	2.15557i	−0.213561	−	0.155161i	−0.689423	+	0.724359i	$0.742136\pi$
$194$	1.03647	+	14.4524i	0.0744141	+	1.03763i
$195$	0.373024	+	4.13665i	0.0267128	+	0.296231i
$196$	0.276898	+	0.562633i	0.0197785	+	0.0401881i
$197$	0.895792	−	5.65581i	0.0638225	−	0.402960i	−0.935009	−	0.354625i	$-0.884609\pi$
$197$	0.895792	−	5.65581i	0.0638225	−	0.402960i	0.998831	−	0.0483348i	$-0.0153914\pi$
$198$	4.95649	−	2.99018i	0.352242	−	0.212503i
$199$	−3.02201	−	5.93102i	−0.214224	−	0.420439i	0.758740	−	0.651393i	$-0.225815\pi$
$199$	−3.02201	−	5.93102i	−0.214224	−	0.420439i	−0.972965	+	0.230954i	$0.925815\pi$
$200$	−3.27466	+	13.7578i	−0.231554	+	0.972822i
$201$	−2.13392	−	1.55038i	−0.150515	−	0.109355i
$202$	−4.32203	−	18.5699i	−0.304097	−	1.30657i
$203$	−3.50250	−	6.87404i	−0.245827	−	0.482463i
$204$	−8.28479	+	4.07734i	−0.580051	+	0.285471i
$205$	1.57627	+	14.2308i	0.110092	+	0.993921i
$206$	−4.54038	−	19.5080i	−0.316343	−	1.35919i
$207$	−8.62760	+	4.39598i	−0.599660	+	0.305542i
$208$	5.34123	−	6.93772i	0.370348	−	0.481044i
$209$	7.18373	−	9.88755i	0.496909	−	0.683936i
$210$	1.05501	−	6.85828i	0.0728027	−	0.473266i
$211$	10.5563	−	5.37871i	0.726727	−	0.370286i	−0.0511598	−	0.998690i	$-0.516292\pi$
$211$	10.5563	−	5.37871i	0.726727	−	0.370286i	0.777887	+	0.628405i	$0.216292\pi$
$212$	0.494440	−	0.480889i	0.0339583	−	0.0330276i
$213$	−4.21622	−	0.667784i	−0.288891	−	0.0457558i
$214$	−2.53557	−	10.8942i	−0.173328	−	0.744715i
$215$	16.9428	−	20.3013i	1.15549	−	1.38454i
$216$	−6.39483	−	10.9408i	−0.435113	−	0.744429i
$217$	−8.20334	+	11.2909i	−0.556879	+	0.766478i
$218$	1.06840	−	12.4674i	0.0723609	−	0.844398i
$219$	4.45263	−	4.45263i	0.300881	−	0.300881i
$220$	−0.609924	−	8.00573i	−0.0411210	−	0.539746i
$221$	−3.68012	−	11.3262i	−0.247552	−	0.761885i
$222$	−6.06440	−	5.25278i	−0.407016	−	0.352543i
$223$	−22.5958	+	11.5131i	−1.51312	+	0.770975i	−0.996368	−	0.0851571i	$-0.972861\pi$
$223$	−22.5958	+	11.5131i	−1.51312	+	0.770975i	−0.516757	+	0.856132i	$0.672861\pi$
$224$	−11.4461	+	9.10789i	−0.764775	+	0.608546i
$225$	−7.87494	+	8.24222i	−0.524996	+	0.549482i
$226$	17.3590	−	10.4725i	1.15470	−	0.696617i
$227$	8.27806	−	2.68971i	0.549434	−	0.178522i	−0.0211273	−	0.999777i	$-0.506726\pi$
$227$	8.27806	−	2.68971i	0.549434	−	0.178522i	0.570562	+	0.821255i	$0.306726\pi$
$228$	−9.25175	−	6.92019i	−0.612712	−	0.458301i
$229$	−3.61154	−	0.572011i	−0.238657	−	0.0377996i	0.0359600	−	0.999353i	$-0.488551\pi$
$229$	−3.61154	−	0.572011i	−0.238657	−	0.0377996i	−0.274617	+	0.961554i	$0.588551\pi$
$230$	0.0597088	+	13.4304i	0.00393708	+	0.885574i
$231$	0.616267	+	3.89095i	0.0405474	+	0.256006i
$232$	−6.52969	+	5.34562i	−0.428695	+	0.350957i
$233$	−2.66237	+	8.19393i	−0.174418	+	0.536802i	−0.999606	−	0.0280549i	$-0.991069\pi$
$233$	−2.66237	+	8.19393i	−0.174418	+	0.536802i	0.825189	+	0.564857i	$0.191069\pi$
$234$	6.53899	−	2.65547i	0.427467	−	0.173594i
$235$	−2.51896	−	27.9340i	−0.164319	−	1.82221i
$236$	4.62321	+	2.43713i	0.300945	+	0.158644i
$237$	8.81003	−	8.81003i	0.572273	−	0.572273i
$238$	1.42320	+	19.8451i	0.0922526	+	1.28636i
$239$	−3.83108	+	7.51893i	−0.247812	+	0.486359i	−0.981085	−	0.193575i	$-0.937992\pi$
$239$	−3.83108	+	7.51893i	−0.247812	+	0.486359i	0.733273	+	0.679934i	$0.237992\pi$
$240$	−7.57533	+	0.471383i	−0.488985	+	0.0304276i
$241$	9.71971	−	13.3780i	0.626102	−	0.861755i	−0.371678	−	0.928362i	$-0.621217\pi$
$241$	9.71971	−	13.3780i	0.626102	−	0.861755i	0.997779	+	0.0666069i	$0.0212173\pi$
$242$	−4.13810	−	10.1899i	−0.266007	−	0.655031i
$243$		−	16.0191i		−	1.02762i
$244$	3.33486	+	23.1309i	0.213492	+	1.48081i
$245$	0.601917	+	0.359488i	0.0384551	+	0.0229668i
$246$	−7.05919	+	3.03576i	−0.450077	+	0.193553i
$247$	10.5366	−	10.5366i	0.670427	−	0.670427i
$248$	13.9789	+	6.13459i	0.887664	+	0.389547i
$249$	7.27209	−	7.27209i	0.460850	−	0.460850i
$250$	5.29360	+	14.8989i	0.334797	+	0.942290i
$251$	−10.2472	−	7.44503i	−0.646798	−	0.469926i	0.215381	−	0.976530i	$-0.430901\pi$
$251$	−10.2472	−	7.44503i	−0.646798	−	0.469926i	−0.862179	+	0.506604i	$0.830901\pi$
$252$	−11.6702	+	1.68252i	−0.735151	+	0.105989i
$253$	−2.35623	−	7.25173i	−0.148135	−	0.455912i
$254$	8.77362	+	7.59942i	0.550506	+	0.476830i
$255$	−5.29347	+	8.86325i	−0.331490	+	0.555038i
$256$	12.4019	+	10.1090i	0.775120	+	0.631814i
$257$	−6.25642	−	8.61122i	−0.390265	−	0.537153i	0.568003	−	0.823027i	$-0.307716\pi$
$257$	−6.25642	−	8.61122i	−0.390265	−	0.537153i	−0.958267	+	0.285874i	$0.907716\pi$
$258$	13.0731	+	5.52177i	0.813898	+	0.343770i
$259$	−15.4030	+	7.84822i	−0.957096	+	0.487665i
$260$	0.792444	−	9.75694i	0.0491453	−	0.605100i
$261$	−6.71845	+	1.06410i	−0.415862	+	0.0658661i
$262$	3.92162	+	0.970359i	0.242279	+	0.0599490i
$263$	11.8063	−	8.57775i	0.728005	−	0.528927i	−0.160926	−	0.986966i	$-0.551448\pi$
$263$	11.8063	−	8.57775i	0.728005	−	0.528927i	0.888932	+	0.458040i	$0.151448\pi$
$264$	4.01456	−	1.56569i	0.247079	−	0.0963617i
$265$	0.171465	−	0.751835i	0.0105330	−	0.0461849i
$266$	−21.3158	+	12.8595i	−1.30696	+	0.788469i
$267$	−5.34309	+	10.4864i	−0.326992	+	0.641757i
$268$	4.33432	+	4.45646i	0.264761	+	0.272221i
$269$	−8.29951	−	2.69667i	−0.506030	−	0.164419i	0.0448661	−	0.998993i	$-0.485714\pi$
$269$	−8.29951	−	2.69667i	−0.506030	−	0.164419i	−0.550896	+	0.834574i	$0.685714\pi$
$270$	−12.6526	−	6.37614i	−0.770015	−	0.388040i
$271$	9.24128	−	3.00267i	0.561368	−	0.182399i	−0.0145688	−	0.999894i	$-0.504638\pi$
$271$	9.24128	−	3.00267i	0.561368	−	0.182399i	0.575936	+	0.817494i	$0.304638\pi$
$272$	20.8764	−	6.14742i	1.26582	−	0.372742i
$273$			4.80308i			0.290696i
$274$	4.49342	+	5.33573i	0.271457	+	0.322343i
$275$	−5.44040	−	7.14014i	−0.328069	−	0.430567i
$276$	−6.88556	+	2.13196i	−0.414462	+	0.128329i
$277$	2.81108	+	0.445231i	0.168901	+	0.0267513i	0.240312	−	0.970696i	$-0.422750\pi$
$277$	2.81108	+	0.445231i	0.168901	+	0.0267513i	−0.0714109	+	0.997447i	$0.522750\pi$
$278$	6.02388	−	9.67851i	0.361288	−	0.580479i
$279$	7.23284	+	9.95515i	0.433019	+	0.595999i
$280$	−5.20043	+	15.5053i	−0.310785	+	0.926618i
$281$	2.99131	+	5.87078i	0.178447	+	0.350221i	0.962853	−	0.270026i	$-0.0870322\pi$
$281$	2.99131	+	5.87078i	0.178447	+	0.350221i	−0.784406	+	0.620247i	$0.787032\pi$
$282$	13.9467	−	5.66371i	0.830511	−	0.337269i
$283$	4.56122	+	28.7984i	0.271136	+	1.71189i	0.628406	+	0.777886i	$0.283708\pi$
$283$	4.56122	+	28.7984i	0.271136	+	1.71189i	−0.357270	+	0.934001i	$0.616292\pi$
$284$	9.52440	+	3.24163i	0.565169	+	0.192355i
$285$	−12.8881	−	0.866708i	−0.763426	−	0.0513393i
$286$	1.25982	+	5.41288i	0.0744945	+	0.320070i
$287$	0.337467	+	16.5539i	0.0199200	+	0.977145i
$288$	4.51875	+	12.0795i	0.266270	+	0.711794i
$289$	3.89392	−	11.9842i	0.229054	−	0.704956i
$290$	−2.87560	+	8.98591i	−0.168861	+	0.527671i
$291$	−5.11040	+	7.03386i	−0.299577	+	0.412332i
$292$	−12.1267	+	8.55573i	−0.709663	+	0.500686i
$293$	−26.0475	−	8.46335i	−1.52171	−	0.494434i	−0.575450	−	0.817837i	$-0.695173\pi$
$293$	−26.0475	−	8.46335i	−1.52171	−	0.494434i	−0.946261	+	0.323403i	$0.895173\pi$
$294$	−0.0903787	+	0.365258i	−0.00527099	+	0.0213023i
$295$	5.81951	−	0.524777i	0.338825	−	0.0305537i
$296$	11.9782	+	14.6314i	0.696219	+	0.850432i
$297$	7.94482	+	1.25834i	0.461005	+	0.0730160i
$298$	−4.06226	+	4.68993i	−0.235320	+	0.271680i
$299$	−1.45429	−	9.18204i	−0.0841039	−	0.531011i
$300$	−6.82058	+	5.04870i	−0.393786	+	0.291487i
$301$	21.6221	−	21.6221i	1.24628	−	1.24628i
$302$	9.64659	−	22.8389i	0.555099	−	1.31423i
$303$	5.19389	−	10.1936i	0.298381	−	0.585606i
$304$	18.7122	+	19.7821i	1.07322	+	1.13458i
$305$	17.1944	+	19.6737i	0.984547	+	1.12651i
$306$	17.0287	+	4.21354i	0.973464	+	0.240872i
$307$	−11.0682	+	21.7226i	−0.631696	+	1.23977i	0.324178	+	0.945996i	$0.394912\pi$
$307$	−11.0682	+	21.7226i	−0.631696	+	1.23977i	−0.955874	+	0.293777i	$0.905088\pi$
$308$	0.128990	−	9.28386i	0.00734989	−	0.528997i
$309$	5.45627	−	10.7085i	0.310397	−	0.609188i
$310$	16.8455	−	2.74489i	0.956760	−	0.155899i
$311$	−20.4787	−	3.24350i	−1.16124	−	0.183922i	−0.454070	−	0.890966i	$-0.650028\pi$
$311$	−20.4787	−	3.24350i	−1.16124	−	0.183922i	−0.707170	+	0.707044i	$0.750028\pi$
$312$	5.13301	−	1.11974i	0.290599	−	0.0633927i
$313$	17.2602	−	23.7566i	0.975604	−	1.34280i	0.0364403	−	0.999336i	$-0.488398\pi$
$313$	17.2602	−	23.7566i	0.975604	−	1.34280i	0.939164	−	0.343468i	$-0.111602\pi$
$314$	−27.6772	−	17.2262i	−1.56191	−	0.972131i
$315$	−9.92591	+	8.67502i	−0.559262	+	0.488782i
$316$	−23.9941	+	16.9285i	−1.34977	+	0.952302i
$317$	−3.43768	−	4.73156i	−0.193080	−	0.265751i	0.701491	−	0.712679i	$-0.252518\pi$
$317$	−3.43768	−	4.73156i	−0.193080	−	0.265751i	−0.894570	+	0.446927i	$0.852518\pi$
$318$	0.412805	−	0.0296046i	0.0231489	−	0.00166015i
$319$		−	5.35643i		−	0.299903i
$320$	17.7827	+	1.94291i	0.994084	+	0.108612i
$321$	3.04705	−	5.98017i	0.170070	−	0.333781i
$322$	−1.32609	+	15.4745i	−0.0739002	+	0.862361i
$323$	36.5815	−	5.79394i	2.03545	−	0.322384i
$324$	−1.03366	+	5.98675i	−0.0574257	+	0.332597i
$325$	−5.18958	−	9.63590i	−0.287866	−	0.534504i
$326$	0.455584	−	5.31632i	0.0252324	−	0.294444i
$327$	5.30921	−	5.30921i	0.293600	−	0.293600i
$328$	17.6123	−	4.21983i	0.972476	−	0.233001i
$329$		−	32.4343i		−	1.78816i
$330$	2.81441	−	3.91014i	0.154928	−	0.215246i
$331$	−21.7478	+	21.7478i	−1.19536	+	1.19536i	−0.219826	+	0.975539i	$0.570549\pi$
$331$	−21.7478	+	21.7478i	−1.19536	+	1.19536i	−0.975539	+	0.219826i	$0.929451\pi$
$332$	−19.8055	+	13.9733i	−1.08697	+	0.766886i
$333$	2.38438	+	15.0544i	0.130663	+	0.824974i
$334$	−19.2504	−	22.8590i	−1.05334	−	1.25079i
$335$	6.77639	+	1.54544i	0.370234	+	0.0844363i
$336$	−8.77377	−	0.243853i	−0.478648	−	0.0133033i
$337$	0.751472	−	0.751472i	0.0409353	−	0.0409353i	−0.686343	−	0.727278i	$-0.740785\pi$
$337$	0.751472	−	0.751472i	0.0409353	−	0.0409353i	0.727278	+	0.686343i	$0.240785\pi$
$338$	−0.830407	−	11.5791i	−0.0451682	−	0.629821i
$339$	12.0150	+	1.90300i	0.652568	+	0.103357i
$340$	15.8482	−	18.4622i	0.859491	−	1.00125i
$341$	−8.63371	+	4.39909i	−0.467541	+	0.238224i
$342$	4.97557	+	21.3779i	0.269048	+	1.15598i
$343$	15.2997	+	11.1159i	0.826107	+	0.600202i
$344$	−28.1481	−	18.0666i	−1.51764	−	0.974087i
$345$	−5.16366	+	6.18723i	−0.278002	+	0.333109i
$346$	−1.40285	+	16.3703i	−0.0754179	+	0.880071i
$347$	20.7254	−	6.73410i	1.11260	−	0.361506i	0.305661	−	0.952140i	$-0.401123\pi$
$347$	20.7254	−	6.73410i	1.11260	−	0.361506i	0.806939	+	0.590635i	$0.201123\pi$
$348$	−5.06310	−	0.0703468i	−0.271411	−	0.00377099i
$349$	−7.58897	−	23.3564i	−0.406228	−	1.25024i	−0.919865	−	0.392234i	$-0.871702\pi$
$349$	−7.58897	−	23.3564i	−0.406228	−	1.25024i	0.513637	−	0.858007i	$-0.328298\pi$
$350$	4.54948	+	17.7095i	0.243180	+	0.946611i
$351$	9.32726	+	3.03061i	0.497853	+	0.161762i
$352$	−9.95164	+	2.02649i	−0.530424	+	0.108012i
$353$	−6.98750	−	3.56031i	−0.371907	−	0.189496i	0.258040	−	0.966134i	$-0.416923\pi$
$353$	−6.98750	−	3.56031i	−0.371907	−	0.189496i	−0.629947	+	0.776638i	$0.716923\pi$
$354$	1.17993	+	2.90552i	0.0627124	+	0.154427i
$355$	10.9070	−	2.75033i	0.578886	−	0.145973i
$356$	16.6144	−	22.2121i	0.880559	−	1.17724i
$357$	−7.01723	+	9.65838i	−0.371391	+	0.511176i
$358$	3.50665	+	3.03734i	0.185332	+	0.160529i
$359$	−4.29447	+	3.12011i	−0.226653	+	0.164673i	−0.695317	−	0.718704i	$-0.744736\pi$
$359$	−4.29447	+	3.12011i	−0.226653	+	0.164673i	0.468663	+	0.883377i	$0.344736\pi$
$360$	11.5849	+	8.58532i	0.610579	+	0.452486i
$361$	16.0714	+	22.1204i	0.845862	+	1.16423i
$362$	−4.39048	+	2.64871i	−0.230758	+	0.139213i
$363$	2.03929	−	6.27630i	0.107035	−	0.329420i
$364$	1.92603	−	11.1552i	0.100952	−	0.584689i
$365$	−6.17476	+	15.4011i	−0.323201	+	0.806132i
$366$	−7.40987	+	11.9054i	−0.387320	+	0.622304i
$367$	12.1816	−	6.20681i	0.635872	−	0.323993i	−0.106168	−	0.994348i	$-0.533858\pi$
$367$	12.1816	−	6.20681i	0.635872	−	0.323993i	0.742040	+	0.670355i	$0.233858\pi$
$368$	16.8466	−	2.19038i	0.878191	−	0.114181i
$369$	13.9731	+	4.22727i	0.727408	+	0.220063i
$370$	20.1352	+	6.44349i	1.04678	+	0.334981i
$371$	0.275568	−	0.848110i	0.0143068	−	0.0440317i
$372$	4.04480	+	8.21868i	0.209713	+	0.426119i
$373$	15.9227	−	2.52191i	0.824446	−	0.130579i	0.270065	−	0.962842i	$-0.412955\pi$
$373$	15.9227	−	2.52191i	0.824446	−	0.130579i	0.554381	+	0.832263i	$0.312955\pi$
$374$	−5.37481	+	12.7252i	−0.277925	+	0.658003i
$375$	−3.32907	+	8.88423i	−0.171912	+	0.458780i
$376$	−34.6622	+	7.56138i	−1.78757	+	0.389948i
$377$	1.02163	−	6.45029i	0.0526164	−	0.332207i
$378$	−13.9103	−	8.65774i	−0.715470	−	0.445306i
$379$	21.4949	−	15.6170i	1.10412	−	0.802190i	0.122392	−	0.992482i	$-0.460944\pi$
$379$	21.4949	−	15.6170i	1.10412	−	0.802190i	0.981727	+	0.190292i	$0.0609436\pi$
$380$	29.5851	+	7.18105i	1.51768	+	0.368380i
$381$	1.08954	+	6.87905i	0.0558186	+	0.352425i
$382$	0.683888	−	7.98046i	0.0349907	−	0.408316i
$383$	−12.9647			−0.662467			−0.331233	−	0.943549i	$-0.607465\pi$
$383$	−12.9647			−0.662467			−0.331233	+	0.943549i	$0.607465\pi$
$384$	1.78482	+	9.43329i	0.0910810	+	0.481390i
$385$	−5.52437	−	8.78862i	−0.281548	−	0.447909i
$386$	0.370987	+	5.17301i	0.0188827	+	0.263299i
$387$	−12.2399	−	24.0222i	−0.622190	−	1.22112i
$388$	14.6895	−	14.2869i	0.745744	−	0.725306i
$389$	−0.622907	−	1.91711i	−0.0315826	−	0.0972014i	0.934023	−	0.357214i	$-0.116273\pi$
$389$	−0.622907	−	1.91711i	−0.0315826	−	0.0972014i	−0.965605	+	0.260013i	$0.916273\pi$
$390$	4.13493	−	4.17186i	0.209380	−	0.211250i
$391$	10.4904	−	20.5886i	0.530523	−	1.04121i
$392$	0.356372	−	0.812069i	0.0179995	−	0.0410157i
$393$	1.42485	+	1.96114i	0.0718742	+	0.0989263i
$394$	−6.93410	+	4.18324i	−0.349335	+	0.210749i
$395$	−12.2175	+	30.4729i	−0.614727	+	1.53326i
$396$	−7.74976	−	2.63763i	−0.389440	−	0.132546i
$397$	11.9801	+	3.89257i	0.601264	+	0.195362i	0.593804	−	0.804610i	$-0.297625\pi$
$397$	11.9801	+	3.89257i	0.601264	+	0.195362i	0.00745975	+	0.999972i	$0.497625\pi$
$398$	−3.66282	+	8.67196i	−0.183601	+	0.434686i
$399$	−14.7537	−	2.33676i	−0.738611	−	0.116985i
$400$	17.8653	−	8.99057i	0.893266	−	0.449528i
$401$			15.1450i			0.756305i	0.925743	+	0.378153i	$0.123441\pi$
$401$			15.1450i			0.756305i	−0.925743	+	0.378153i	$0.876559\pi$
$402$	0.266831	+	3.72067i	0.0133083	+	0.185570i
$403$	−11.2359	+	3.65076i	−0.559699	+	0.181857i
$404$	−16.1504	+	21.5918i	−0.803513	+	1.07423i
$405$	2.67067	+	6.24536i	0.132707	+	0.310334i
$406$	−4.24520	+	10.0508i	−0.210686	+	0.498812i
$407$	−12.0024			−0.594938
$408$	11.9577	+	5.24759i	0.591996	+	0.259795i
$409$		−	24.9238i		−	1.23240i	−0.787588	−	0.616202i	$-0.788671\pi$
$409$		−	24.9238i		−	1.23240i	0.787588	−	0.616202i	$-0.211329\pi$
$410$	13.9579	−	14.6689i	0.689334	−	0.724444i
$411$			4.18572i			0.206466i
$412$	−16.9663	+	22.6826i	−0.835870	+	1.11749i
$413$	6.75707			0.332494
$414$	12.6147	+	5.32815i	0.619980	+	0.261864i
$415$	−10.0847	+	25.1533i	−0.495038	+	1.23473i
$416$	−12.3704	+	0.542258i	−0.606510	+	0.0265864i
$417$	6.50568	−	2.11382i	0.318585	−	0.103514i
$418$	−17.2398	+	1.23637i	−0.843226	+	0.0604727i
$419$		−	20.0228i		−	0.978176i	−0.872234	−	0.489088i	$-0.837330\pi$
$419$		−	20.0228i		−	0.978176i	0.872234	−	0.489088i	$-0.162670\pi$
$420$	−8.37989	+	5.10642i	−0.408897	+	0.249168i
$421$	−8.00995	−	1.26865i	−0.390381	−	0.0618303i	−0.0418413	−	0.999124i	$-0.513322\pi$
$421$	−8.00995	−	1.26865i	−0.390381	−	0.0618303i	−0.348540	+	0.937294i	$0.613322\pi$
$422$	−15.4348	−	6.51927i	−0.751352	−	0.317353i
$423$	−27.1975	−	8.83701i	−1.32239	−	0.429670i
$424$	−0.970610	−	0.0967775i	−0.0471370	−	0.00469993i
$425$	3.64231	−	26.9585i	0.176678	−	1.30768i
$426$	3.11847	+	5.16915i	0.151091	+	0.250446i
$427$	17.7602	+	24.4448i	0.859475	+	1.18297i
$428$	−9.47482	+	12.6671i	−0.457983	+	0.612287i
$429$	−1.51395	+	2.97129i	−0.0730941	+	0.143455i
$430$	−37.3948	+	0.166250i	−1.80334	+	0.00801728i
$431$	1.13727	+	3.50016i	0.0547805	+	0.168597i	0.974703	−	0.223502i	$-0.0717490\pi$
$431$	1.13727	+	3.50016i	0.0547805	+	0.168597i	−0.919923	+	0.392099i	$0.871749\pi$
$432$	−6.00955	+	16.8842i	−0.289134	+	0.812341i
$433$	11.6565	+	22.8772i	0.560176	+	1.09941i	0.981314	+	0.192411i	$0.0616307\pi$
$433$	11.6565	+	22.8772i	0.560176	+	1.09941i	−0.421138	+	0.906996i	$0.638369\pi$
$434$	19.6867	−	1.41185i	0.944992	−	0.0677709i
$435$	−4.79301	+	3.01280i	−0.229807	+	0.144453i
$436$	−14.4596	+	10.2017i	−0.692491	+	0.488571i
$437$	28.9122			1.38306
$438$	−8.87274	−	0.760351i	−0.423956	−	0.0363310i
$439$	4.00446	+	25.2832i	0.191122	+	1.20670i	0.877544	+	0.479496i	$0.159180\pi$
$439$	4.00446	+	25.2832i	0.191122	+	1.20670i	−0.686422	+	0.727204i	$0.740820\pi$
$440$	−8.10442	+	7.95272i	−0.386363	+	0.379131i
$441$	0.578318	−	0.420172i	0.0275389	−	0.0200082i
$442$	−8.89948	+	14.2987i	−0.423305	+	0.680121i
$443$	−4.42900	+	27.9636i	−0.210428	+	1.32859i	0.625703	+	0.780062i	$0.284812\pi$
$443$	−4.42900	+	27.9636i	−0.210428	+	1.32859i	−0.836131	+	0.548530i	$0.815188\pi$
$444$	−0.157630	+	11.3451i	−0.00748077	+	0.538417i
$445$	2.08084	−	30.9425i	0.0986412	−	1.46681i
$446$	33.0381	+	13.9545i	1.56440	+	0.660763i
$447$	−3.67719	+	0.582410i	−0.173925	+	0.0275470i
$448$	20.2793	+	4.08462i	0.958106	+	0.192980i
$449$	−9.93993	+	30.5920i	−0.469094	+	1.44372i	0.384665	+	0.923056i	$0.374317\pi$
$449$	−9.93993	+	30.5920i	−0.469094	+	1.44372i	−0.853759	+	0.520668i	$0.825683\pi$
$450$	16.0897	+	1.01017i	0.758474	+	0.0476200i
$451$	−5.00908	+	10.3470i	−0.235868	+	0.487219i
$452$	−27.1418	−	9.23773i	−1.27665	−	0.434506i
$453$	13.2551	−	6.75381i	0.622779	−	0.317322i
$454$	−10.4506	−	6.50440i	−0.490470	−	0.305267i
$455$	−4.97628	−	11.6370i	−0.233292	−	0.545553i
$456$	0.942248	+	16.3120i	0.0441248	+	0.763877i
$457$	−6.74777	+	20.7675i	−0.315647	+	0.971462i	0.659840	+	0.751406i	$0.270624\pi$
$457$	−6.74777	+	20.7675i	−0.315647	+	0.971462i	−0.975487	+	0.220056i	$0.929376\pi$
$458$	2.67123	+	4.42779i	0.124818	+	0.206897i
$459$	14.3283	+	19.7211i	0.668786	+	0.920504i
$460$	14.4737	−	12.2992i	0.674838	−	0.573454i
$461$	21.2443	−	15.4349i	0.989445	−	0.718874i	0.0296455	−	0.999560i	$-0.490562\pi$
$461$	21.2443	−	15.4349i	0.989445	−	0.718874i	0.959799	+	0.280687i	$0.0905622\pi$
$462$	3.64757	−	4.21116i	0.169700	−	0.195921i
$463$	−7.23440	+	9.95730i	−0.336211	+	0.462755i	−0.943330	−	0.331856i	$-0.892325\pi$
$463$	−7.23440	+	9.95730i	−0.336211	+	0.462755i	0.607119	+	0.794611i	$0.292325\pi$
$464$	11.7308	+	2.19368i	0.544591	+	0.101839i
$465$	8.79253	+	5.25123i	0.407744	+	0.243520i
$466$	11.2889	−	4.58442i	0.522950	−	0.212369i
$467$	−12.7591	−	6.50111i	−0.590423	−	0.300836i	0.133136	−	0.991098i	$-0.457495\pi$
$467$	−12.7591	−	6.50111i	−0.590423	−	0.300836i	−0.723559	+	0.690262i	$0.757495\pi$
$468$	−8.82930	−	4.65438i	−0.408134	−	0.215149i
$469$	7.64414	+	2.48373i	0.352973	+	0.114688i
$470$	−27.9224	+	28.1718i	−1.28796	+	1.29947i
$471$	−6.04481	−	18.6040i	−0.278530	−	0.857227i
$472$	−1.57527	−	7.22121i	−0.0725076	−	0.332383i
$473$	20.1913	−	6.56055i	0.928397	−	0.301655i
$474$	−17.5557	−	1.50444i	−0.806361	−	0.0691013i
$475$	32.1236	−	11.2530i	1.47393	−	0.516322i
$476$	20.1705	−	19.6177i	0.924514	−	0.899175i
$477$	−0.636095	−	0.462150i	−0.0291248	−	0.0211604i
$478$	11.6234	−	2.70529i	0.531644	−	0.123737i
$479$	11.7246	−	5.97398i	0.535711	−	0.272958i	−0.165135	−	0.986271i	$-0.552806\pi$
$479$	11.7246	−	5.97398i	0.535711	−	0.272958i	0.700846	+	0.713313i	$0.252806\pi$
$480$	7.41077	+	7.76505i	0.338254	+	0.354424i
$481$	−14.4535	−	2.28921i	−0.659022	−	0.104379i
$482$	−23.3258	+	1.67283i	−1.06246	+	0.0761951i
$483$	−6.58979	+	6.58979i	−0.299846	+	0.299846i
$484$	−7.25305	+	13.7590i	−0.329684	+	0.625407i
$485$	5.09411	−	22.3365i	0.231311	−	1.01425i
$486$	−17.3283	+	14.5928i	−0.786028	+	0.661944i
$487$	−0.680666	−	4.29755i	−0.0308439	−	0.194741i	0.967455	−	0.253043i	$-0.0814313\pi$
$487$	−0.680666	−	4.29755i	−0.0308439	−	0.194741i	−0.998299	+	0.0583021i	$0.981431\pi$
$488$	21.9835	−	24.6789i	0.995145	−	1.11716i
$489$	2.26395	−	2.26395i	0.102379	−	0.102379i
$490$	−0.159457	−	0.978593i	−0.00720353	−	0.0442083i
$491$		−	26.6465i		−	1.20254i	−0.799045	−	0.601271i	$-0.794661\pi$
$491$		−	26.6465i		−	1.20254i	0.799045	−	0.601271i	$-0.205339\pi$
$492$	9.71456	+	4.87066i	0.437966	+	0.219586i
$493$	11.4781	−	11.4781i	0.516949	−	0.516949i
$494$	−20.9962	−	1.79928i	−0.944665	−	0.0809533i
$495$	−8.87478	+	2.23788i	−0.398892	+	0.100585i
$496$	−6.09837	−	20.7098i	−0.273825	−	0.929900i
$497$	12.8477	−	2.03488i	0.576299	−	0.0912768i
$498$	−14.4911	−	1.24182i	−0.649361	−	0.0556471i
$499$	12.1709	−	23.8867i	0.544844	−	1.06932i	−0.440342	−	0.897830i	$-0.645143\pi$
$499$	12.1709	−	23.8867i	0.544844	−	1.06932i	0.985186	−	0.171487i	$-0.0548572\pi$
$500$	11.2943	−	19.2987i	0.505097	−	0.863062i
$501$		−	17.9322i		−	0.801152i
$502$	1.28134	+	17.8669i	0.0571890	+	0.797439i
$503$	1.85539	+	2.55372i	0.0827277	+	0.113865i	0.848375	−	0.529396i	$-0.177581\pi$
$503$	1.85539	+	2.55372i	0.0827277	+	0.113865i	−0.765647	+	0.643260i	$0.777581\pi$
$504$	12.4512	+	11.0913i	0.554619	+	0.494044i
$505$	−2.02273	+	30.0784i	−0.0900104	+	1.33847i
$506$	−5.69797	+	9.15489i	−0.253306	+	0.406984i
$507$	4.09439	−	5.63544i	0.181838	−	0.250279i
$508$	0.228049	−	16.4135i	0.0101181	−	0.728231i
$509$	14.4361	+	2.28646i	0.639870	+	0.101345i	0.467935	−	0.883763i	$-0.344998\pi$
$509$	14.4361	+	2.28646i	0.639870	+	0.101345i	0.171935	+	0.985108i	$0.444998\pi$
$510$	14.4098	−	2.34801i	0.638077	−	0.103971i
$511$	−8.71125	+	17.0968i	−0.385363	+	0.756318i
$512$	−0.362494	−	22.6245i	−0.0160201	−	0.999872i
$513$	−13.8470	+	27.1763i	−0.611362	+	1.19987i
$514$	−3.61564	+	14.6123i	−0.159479	+	0.644520i
$515$	−2.12492	+	31.5980i	−0.0936351	+	1.39237i
$516$	−5.93611	−	19.1718i	−0.261323	−	0.843989i
$517$	10.2234	−	20.0646i	0.449625	−	0.882439i
$518$	22.5213	+	9.51243i	0.989528	+	0.417952i
$519$	−6.97124	+	6.97124i	−0.306004	+	0.306004i
$520$	−11.2763	+	8.03103i	−0.494497	+	0.352184i
$521$	2.47305	+	15.6142i	0.108346	+	0.684071i	0.980747	+	0.195281i	$0.0625617\pi$
$521$	2.47305	+	15.6142i	0.108346	+	0.684071i	−0.872401	+	0.488790i	$0.837438\pi$
$522$	7.27135	+	6.29820i	0.318258	+	0.275665i
$523$	5.76406	+	0.912938i	0.252045	+	0.0399200i	0.281178	−	0.959656i	$-0.409275\pi$
$523$	5.76406	+	0.912938i	0.252045	+	0.0399200i	−0.0291334	+	0.999576i	$0.509275\pi$
$524$	−2.52280	−	5.12610i	−0.110209	−	0.223935i
$525$	−4.75692	+	9.88657i	−0.207609	+	0.431485i
$526$	−20.0339	−	4.95716i	−0.873520	−	0.216142i
$527$	−27.9276	−	9.07422i	−1.21654	−	0.395279i
$528$	−5.35078	−	2.91637i	−0.232863	−	0.126919i
$529$	−2.91666	+	4.01443i	−0.126811	+	0.174541i
$530$	−0.969482	+	0.499417i	−0.0421116	+	0.0216933i
$531$	1.84102	−	5.66608i	0.0798935	−	0.245887i
$532$	33.3285	+	11.3434i	1.44498	+	0.491798i
$533$	−8.00547	+	11.5046i	−0.346755	+	0.498319i
$534$	16.2108	−	3.77297i	0.701511	−	0.163272i
$535$	−1.18666	+	17.6458i	−0.0513037	+	0.762896i
$536$	0.872269	−	8.74824i	0.0376763	−	0.377867i
$537$	0.435467	+	2.74943i	0.0187918	+	0.118647i
$538$	4.64349	+	11.4344i	0.200195	+	0.492972i
$539$	0.255553	+	0.501552i	0.0110075	+	0.0216034i
$540$	4.62885	+	19.4952i	0.199194	+	0.838939i
$541$	−10.2100	−	14.0528i	−0.438960	−	0.604177i	0.531020	−	0.847359i	$-0.321809\pi$
$541$	−10.2100	−	14.0528i	−0.438960	−	0.604177i	−0.969981	+	0.243182i	$0.921809\pi$
$542$	−11.6666	−	7.26124i	−0.501122	−	0.311897i
$543$	−3.03887	−	0.481310i	−0.130410	−	0.0206550i
$544$	−25.6676	−	16.9826i	−1.10049	−	0.728122i
$545$	−7.36264	+	18.3640i	−0.315381	+	0.786625i
$546$	5.19564	−	4.37545i	0.222353	−	0.187252i
$547$		−	14.5194i		−	0.620804i	−0.950605	−	0.310402i	$-0.899536\pi$
$547$		−	14.5194i		−	0.620804i	0.950605	−	0.310402i	$-0.100464\pi$
$548$	1.67847	−	9.72133i	0.0717007	−	0.415275i
$549$	25.3369	−	8.23245i	1.08135	−	0.351352i
$550$	−2.76768	+	12.3895i	−0.118014	+	0.528289i
$551$	19.3165	+	6.27631i	0.822910	+	0.267380i
$552$	8.57871	+	5.50617i	0.365134	+	0.234358i
$553$	−17.2362	+	33.8280i	−0.732958	+	1.43851i
$554$	−2.07918	−	3.44642i	−0.0883357	−	0.146424i
$555$	6.75093	+	10.7399i	0.286561	+	0.455885i
$556$	−15.9571	+	2.30058i	−0.676731	+	0.0975665i
$557$	0.697422	−	0.506707i	0.0295507	−	0.0214699i	−0.572912	−	0.819617i	$-0.694186\pi$
$557$	0.697422	−	0.506707i	0.0295507	−	0.0214699i	0.602463	+	0.798147i	$0.294186\pi$
$558$	4.17992	−	16.8928i	0.176950	−	0.715129i
$559$	25.5659	−	4.04925i	1.08132	−	0.171265i
$560$	21.5100	−	8.49933i	0.908962	−	0.359162i
$561$	−7.38537	+	3.76303i	−0.311810	+	0.158875i
$562$	3.62562	−	8.58388i	0.152938	−	0.362089i
$563$	−1.52307	−	2.09632i	−0.0641896	−	0.0883494i	0.775715	−	0.631083i	$-0.217389\pi$
$563$	−1.52307	−	2.09632i	−0.0641896	−	0.0883494i	−0.839905	+	0.542734i	$0.817389\pi$
$564$	−18.8315	−	9.92707i	−0.792951	−	0.418005i
$565$	−31.0820	+	7.83768i	−1.30763	+	0.329733i
$566$	26.9970	−	31.1684i	1.13477	−	1.31010i
$567$	2.42728	+	7.47040i	0.101936	+	0.313727i
$568$	−5.16983	−	13.2558i	−0.216921	−	0.556203i
$569$	−19.5257	−	14.1862i	−0.818559	−	0.594718i	0.0977400	−	0.995212i	$-0.468839\pi$
$569$	−19.5257	−	14.1862i	−0.818559	−	0.594718i	−0.916300	+	0.400494i	$0.868839\pi$
$570$	10.8031	+	14.7310i	0.452492	+	0.617014i
$571$	9.72633	−	9.72633i	0.407034	−	0.407034i	−0.473669	−	0.880703i	$-0.657071\pi$
$571$	9.72633	−	9.72633i	0.407034	−	0.407034i	0.880703	+	0.473669i	$0.157071\pi$
$572$	4.70763	−	6.29373i	0.196836	−	0.263154i
$573$	3.39846	−	3.39846i	0.141973	−	0.141973i
$574$	17.5994	−	15.4451i	0.734586	−	0.644665i
$575$	6.10031	−	20.3404i	0.254400	−	0.848255i
$576$	8.95039	−	15.8921i	0.372933	−	0.662172i
$577$			32.3413i			1.34639i	0.739467	+	0.673193i	$0.235078\pi$
$577$			32.3413i			1.34639i	−0.739467	+	0.673193i	$0.764922\pi$
$578$	−16.5110	+	6.70507i	−0.686765	+	0.278894i
$579$	−1.82918	+	2.51765i	−0.0760182	+	0.104630i
$580$	12.3399	−	5.07524i	0.512387	−	0.210738i
$581$	−14.2273	+	27.9227i	−0.590250	+	1.15843i
$582$	12.2641	−	0.879533i	0.508365	−	0.0364578i
$583$	0.437800	−	0.437800i	0.0181318	−	0.0181318i
$584$	20.3020	+	5.32387i	0.840104	+	0.220303i
$585$	−11.1140	+	1.00221i	−0.459506	+	0.0414361i
$586$	14.5733	+	35.8862i	0.602019	+	1.48245i
$587$	−5.68571	+	17.4988i	−0.234674	+	0.722254i	0.762490	+	0.647000i	$0.223977\pi$
$587$	−5.68571	+	17.4988i	−0.234674	+	0.722254i	−0.997164	+	0.0752537i	$0.976023\pi$
$588$	0.477442	−	0.234972i	0.0196894	−	0.00969008i
$589$	−5.74771	−	36.2896i	−0.236830	−	1.49529i
$590$	−5.86905	−	5.81709i	−0.241625	−	0.239486i
$591$	−4.79944	−	0.760156i	−0.197422	−	0.0312687i
$592$	4.91549	−	26.2859i	0.202025	−	1.08034i
$593$	−10.2714	+	3.33736i	−0.421794	+	0.137049i	−0.512220	−	0.858854i	$-0.671177\pi$
$593$	−10.2714	+	3.33736i	−0.421794	+	0.137049i	0.0904266	+	0.995903i	$0.471177\pi$
$594$	−5.87628	−	9.74045i	−0.241107	−	0.399656i
$595$	6.99486	−	30.6708i	0.286761	−	1.25738i
$596$	8.77382	+	0.121903i	0.359390	+	0.00499336i
$597$	−5.03298	+	2.56443i	−0.205986	+	0.104955i
$598$	−8.60768	+	9.93768i	−0.351994	+	0.406382i
$599$	4.08458	+	12.5710i	0.166891	+	0.513639i	0.999171	−	0.0407176i	$-0.0129644\pi$
$599$	4.08458	+	12.5710i	0.166891	+	0.513639i	−0.832279	+	0.554357i	$0.812964\pi$
$600$	11.6747	+	2.77883i	0.476616	+	0.113445i
$601$	3.41425	−	3.41425i	0.139270	−	0.139270i	−0.634034	−	0.773305i	$-0.718602\pi$
$601$	3.41425	−	3.41425i	0.139270	−	0.139270i	0.773305	+	0.634034i	$0.218602\pi$
$602$	−43.0864	−	3.69230i	−1.75607	−	0.150487i
$603$	4.16542	−	5.73321i	0.169629	−	0.233474i
$604$	−33.4933	+	10.3704i	−1.36282	+	0.421967i
$605$	1.56177	+	17.3192i	0.0634949	+	0.704126i
$606$	−15.7582	+	3.66762i	−0.640132	+	0.148987i
$607$	−38.6058	−	6.11455i	−1.56696	−	0.248182i	−0.688227	−	0.725495i	$-0.741611\pi$
$607$	−38.6058	−	6.11455i	−1.56696	−	0.248182i	−0.878733	+	0.477313i	$0.841611\pi$
$608$	4.35271	−	38.2623i	0.176526	−	1.55174i
$609$	−5.83321	+	2.97217i	−0.236374	+	0.120438i
$610$	5.61815	−	36.5217i	0.227472	−	1.47872i
$611$	16.1381	−	22.2122i	0.652877	−	0.898608i
$612$	−10.9546	−	22.2588i	−0.442814	−	0.899759i
$613$	−4.58937	+	2.33840i	−0.185363	+	0.0944470i	−0.544209	−	0.838950i	$-0.683170\pi$
$613$	−4.58937	+	2.33840i	−0.185363	+	0.0944470i	0.358846	+	0.933397i	$0.383170\pi$
$614$	33.5808	−	7.81572i	1.35521	−	0.315417i
$615$	12.0760	−	1.33760i	0.486953	−	0.0539373i
$616$	−10.1601	+	8.31775i	−0.409364	+	0.335132i
$617$	5.11178	+	10.0324i	0.205792	+	0.403890i	0.970716	−	0.240231i	$-0.0772232\pi$
$617$	5.11178	+	10.0324i	0.205792	+	0.403890i	−0.764923	+	0.644121i	$0.777223\pi$
$618$	−16.5542	+	3.85290i	−0.665909	+	0.154986i
$619$	−1.89332	−	1.37558i	−0.0760991	−	0.0552892i	0.549085	−	0.835766i	$-0.314976\pi$
$619$	−1.89332	−	1.37558i	−0.0760991	−	0.0552892i	−0.625184	+	0.780477i	$0.714976\pi$
$620$	−18.3149	−	15.7218i	−0.735544	−	0.631402i
$621$	8.63895	+	16.9549i	0.346669	+	0.680377i
$622$	15.1468	+	25.1071i	0.607330	+	1.00670i
$623$	5.61023	−	35.4216i	0.224769	−	1.41914i
$624$	−5.88725	−	4.53249i	−0.235679	−	0.181445i
$625$	−1.13884	−	24.9740i	−0.0455535	−	0.998962i
$626$	−41.4217	+	2.97059i	−1.65555	+	0.118729i
$627$	−8.39043	−	6.09601i	−0.335082	−	0.243451i
$628$	6.57888	+	45.6318i	0.262526	+	1.82091i
$629$	−25.7196	−	25.7196i	−1.02551	−	1.02551i
$630$	18.4262	+	2.83451i	0.734117	+	0.112930i
$631$	−1.11304	+	0.361650i	−0.0443096	+	0.0143971i	−0.331088	−	0.943600i	$-0.607416\pi$
$631$	−1.11304	+	0.361650i	−0.0443096	+	0.0143971i	0.286778	+	0.957997i	$0.407416\pi$
$632$	40.1699	+	10.5339i	1.59787	+	0.419016i
$633$	−4.56430	−	8.95794i	−0.181415	−	0.356046i
$634$	−1.98667	+	8.02894i	−0.0789006	+	0.318870i
$635$	−9.76686	−	15.5379i	−0.387586	−	0.616604i
$636$	−0.408075	−	0.419575i	−0.0161812	−	0.0166372i
$637$	0.212081	+	0.652718i	0.00840295	+	0.0258616i
$638$	−5.79422	+	4.87953i	−0.229395	+	0.193182i
$639$	1.79414	−	11.3278i	0.0709752	−	0.448120i
$640$	−14.0977	−	21.0060i	−0.557262	−	0.830337i
$641$	−17.7440	+	2.81037i	−0.700845	+	0.111003i	−0.496680	−	0.867934i	$-0.665448\pi$
$641$	−17.7440	+	2.81037i	−0.700845	+	0.111003i	−0.204165	+	0.978937i	$0.565448\pi$
$642$	−9.24470	+	2.15165i	−0.364859	+	0.0849187i
$643$	−29.7124	−	9.65414i	−1.17174	−	0.380722i	−0.342449	−	0.939536i	$-0.611256\pi$
$643$	−29.7124	−	9.65414i	−1.17174	−	0.380722i	−0.829293	+	0.558814i	$0.811256\pi$
$644$	17.9473	−	12.6623i	0.707222	−	0.498964i
$645$	−17.2274	−	14.3774i	−0.678327	−	0.566109i
$646$	−39.5920	−	34.2933i	−1.55773	−	1.34925i
$647$	−18.4451	−	18.4451i	−0.725153	−	0.725153i	0.244497	−	0.969650i	$-0.421377\pi$
$647$	−18.4451	−	18.4451i	−0.725153	−	0.725153i	−0.969650	+	0.244497i	$0.921377\pi$
$648$	7.41768	−	4.33558i	0.291394	−	0.170318i
$649$	4.18007	+	2.12985i	0.164082	+	0.0836040i
$650$	−5.69591	+	14.3917i	−0.223412	+	0.564489i
$651$	9.58132	+	6.96124i	0.375522	+	0.272832i
$652$	−6.16585	+	4.35017i	−0.241473	+	0.170366i
$653$	−8.46592			−0.331297			−0.165648	−	0.986185i	$-0.552972\pi$
$653$	−8.46592			−0.331297			−0.165648	+	0.986185i	$0.552972\pi$
$654$	−10.5796	−	0.906625i	−0.413697	−	0.0354519i
$655$	−5.48402	−	3.27527i	−0.214278	−	0.127975i
$656$	−20.6089	−	15.2076i	−0.804643	−	0.593758i
$657$	11.9629	+	11.9629i	0.466718	+	0.466718i
$658$	−35.0852	+	29.5466i	−1.36776	+	1.15184i
$659$	13.7781	+	13.7781i	0.536719	+	0.536719i	0.922564	−	0.385845i	$-0.126090\pi$
$659$	13.7781	+	13.7781i	0.536719	+	0.536719i	−0.385845	+	0.922564i	$0.626090\pi$
$660$	−6.79354	+	0.517572i	−0.264438	+	0.0201465i
$661$	20.4822	−	28.1913i	0.796665	−	1.09652i	−0.196581	−	0.980488i	$-0.562984\pi$
$661$	20.4822	−	28.1913i	0.796665	−	1.09652i	0.993246	−	0.116028i	$-0.0370163\pi$
$662$	43.3367	+	3.71375i	1.68433	+	0.144339i
$663$	−9.61128	+	3.12290i	−0.373271	+	0.121283i
$664$	33.1576	+	8.69503i	1.28676	+	0.337432i
$665$	38.1668	−	9.62419i	1.48004	−	0.373210i
$666$	14.1127	−	16.2933i	0.546855	−	0.631351i
$667$	10.2514	−	7.44809i	0.396936	−	0.288391i
$668$	−7.19080	+	41.6475i	−0.278220	+	1.61139i
$669$	9.76986	+	19.1744i	0.377725	+	0.741327i
$670$	−4.50131	−	8.73807i	−0.173901	−	0.337581i
$671$	3.28175	+	20.7201i	0.126690	+	0.799892i
$672$	7.72882	+	9.71299i	0.298146	+	0.374687i
$673$	−12.4258	−	17.1026i	−0.478979	−	0.659258i	0.499330	−	0.866412i	$-0.333580\pi$
$673$	−12.4258	−	17.1026i	−0.478979	−	0.659258i	−0.978308	+	0.207155i	$0.933580\pi$
$674$	−1.49746	−	0.128325i	−0.0576798	−	0.00494289i
$675$	16.1976	+	15.4758i	0.623445	+	0.595663i
$676$	−11.7690	+	11.4465i	−0.452655	+	0.440249i
$677$	7.75036	+	3.94900i	0.297870	+	0.151773i	0.596538	−	0.802585i	$-0.296542\pi$
$677$	7.75036	+	3.94900i	0.297870	+	0.151773i	−0.298668	+	0.954357i	$0.596542\pi$
$678$	−8.88677	−	14.7306i	−0.341294	−	0.565726i
$679$	8.18692	−	25.1968i	0.314185	−	0.966963i
$680$	−34.4083	−	0.325077i	−1.31950	−	0.0124661i
$681$	−2.28245	−	7.02465i	−0.0874635	−	0.269185i
$682$	12.6236	+	5.33192i	0.483384	+	0.204170i
$683$	−0.959444			−0.0367121			−0.0183561	−	0.999832i	$-0.505843\pi$
$683$	−0.959444			−0.0367121			−0.0183561	+	0.999832i	$0.505843\pi$
$684$	18.5925	−	24.8568i	0.710903	−	0.950422i
$685$	−4.33666	−	10.1413i	−0.165695	−	0.387478i
$686$	−1.91312	−	26.6764i	−0.0730432	−	1.01851i
$687$	−0.485401	+	3.06470i	−0.0185192	+	0.116926i
$688$	6.09876	+	46.9068i	0.232513	+	1.78830i
$689$	0.610706	−	0.443704i	0.0232660	−	0.0169038i
$690$	11.3968	−	0.0506681i	0.433870	−	0.00192890i
$691$	19.8835	−	10.1311i	0.756403	−	0.385406i	−0.0328618	−	0.999460i	$-0.510462\pi$
$691$	19.8835	−	10.1311i	0.756403	−	0.385406i	0.789264	+	0.614054i	$0.210462\pi$
$692$	18.9862	−	13.3952i	0.721746	−	0.509211i
$693$	−10.4539	+	1.65573i	−0.397109	+	0.0628960i
$694$	−26.1647	−	16.2848i	−0.993197	−	0.618163i
$695$	−13.5721	+	11.8617i	−0.514819	+	0.449940i
$696$	4.53622	+	5.54100i	0.171945	+	0.210031i
$697$	−32.9060	+	11.4384i	−1.24640	+	0.433260i
$698$	−18.3521	+	29.4861i	−0.694637	+	1.11607i
$699$	6.95325	+	2.25925i	0.262996	+	0.0854526i
$700$	15.0125	−	21.0540i	0.567418	−	0.795768i
$701$	23.7710	+	17.2706i	0.897818	+	0.652303i	0.937905	−	0.346893i	$-0.112763\pi$
$701$	23.7710	+	17.2706i	0.897818	+	0.652303i	−0.0400869	+	0.999196i	$0.512763\pi$
$702$	−5.21851	−	12.8504i	−0.196960	−	0.485006i
$703$	14.0636	−	43.2834i	0.530420	−	1.63246i
$704$	11.2577	+	8.91894i	0.424291	+	0.336145i
$705$	−23.7044	+	2.13755i	−0.892759	+	0.0805049i
$706$	2.51408	+	10.8019i	0.0946187	+	0.406536i
$707$	−5.45357	+	34.4325i	−0.205103	+	1.29497i
$708$	2.06812	−	3.92319i	0.0777245	−	0.147443i
$709$	−37.3295	+	5.91240i	−1.40194	+	0.222045i	−0.811176	−	0.584802i	$-0.801172\pi$
$709$	−37.3295	+	5.91240i	−1.40194	+	0.222045i	−0.590761	+	0.806847i	$0.701172\pi$
$710$	−12.9111	−	9.29302i	−0.484544	−	0.348761i
$711$	23.6700	+	23.6700i	0.887694	+	0.887694i
$712$	−39.1626	+	2.26220i	−1.46768	+	0.0847795i
$713$	−20.4243	−	10.4067i	−0.764897	−	0.389734i
$714$	16.8402	−	1.20771i	0.630230	−	0.0451974i
$715$	0.589600	−	8.76747i	0.0220498	−	0.327885i
$716$	0.0911470	−	6.56017i	0.00340632	−	0.245165i
$717$	6.38045	+	3.25100i	0.238282	+	0.121411i
$718$	7.28724	+	1.80314i	0.271957	+	0.0672926i
$719$	15.7797	+	8.04013i	0.588482	+	0.299846i	0.722762	−	0.691097i	$-0.242872\pi$
$719$	15.7797	+	8.04013i	0.588482	+	0.299846i	−0.134280	+	0.990943i	$0.542872\pi$
$720$	−1.26647	−	20.3527i	−0.0471985	−	0.758500i
$721$	−5.72907	+	36.1719i	−0.213362	+	1.34711i
$722$	9.28779	−	37.5358i	0.345656	−	1.39694i
$723$	−11.3524	−	8.24801i	−0.422201	−	0.306747i
$724$	6.86477	+	2.33643i	0.255127	+	0.0868326i
$725$	8.49120	−	12.2653i	0.315355	−	0.455523i
$726$	−8.64700	+	3.51153i	−0.320920	+	0.130325i
$727$	18.3525	−	13.3339i	0.680657	−	0.494527i	−0.192918	−	0.981215i	$-0.561795\pi$
$727$	18.3525	−	13.3339i	0.680657	−	0.494527i	0.873576	+	0.486688i	$0.161795\pi$
$728$	−13.8214	+	8.07852i	−0.512256	+	0.299410i
$729$	−4.48056			−0.165947
$730$	22.2849	−	7.35048i	0.824800	−	0.272054i
$731$	57.3257	+	29.2089i	2.12027	+	1.08033i
$732$	19.6286	−	2.82991i	0.725493	−	0.104597i
$733$	−5.93927	−	37.4991i	−0.219372	−	1.38506i	−0.813909	−	0.580992i	$-0.802665\pi$
$733$	−5.93927	−	37.4991i	−0.219372	−	1.38506i	0.594537	−	0.804068i	$-0.297335\pi$
$734$	−17.8111	−	7.52296i	−0.657419	−	0.277678i
$735$	0.305056	−	0.510778i	0.0112522	−	0.0188403i
$736$	−17.7161	−	16.2281i	−0.653024	−	0.598177i
$737$	3.94595	+	3.94595i	0.145351	+	0.145351i
$738$	−8.15622	−	18.9660i	−0.300235	−	0.698147i
$739$	−47.6660			−1.75342			−0.876710	−	0.481019i	$-0.840267\pi$
$739$	−47.6660			−1.75342			−0.876710	+	0.481019i	$0.840267\pi$
$740$	−11.3723	−	27.6506i	−0.418055	−	1.01646i
$741$	−8.94120	−	8.94120i	−0.328463	−	0.328463i
$742$	−1.16846	+	0.474510i	−0.0428955	+	0.0174198i
$743$	−4.21580	+	0.667716i	−0.154663	+	0.0244961i	−0.233286	−	0.972408i	$-0.574948\pi$
$743$	−4.21580	+	0.667716i	−0.154663	+	0.0244961i	0.0786230	+	0.996904i	$0.474948\pi$
$744$	5.20572	−	11.8623i	0.190851	−	0.434894i
$745$	8.30578	−	5.22086i	0.304300	−	0.191278i
$746$	−17.2331	−	14.9267i	−0.630947	−	0.546505i
$747$	19.5380	+	19.5380i	0.714858	+	0.714858i
$748$	18.6615	−	5.77811i	0.682331	−	0.211269i
$749$	−3.19939	+	20.2002i	−0.116903	+	0.738099i
$750$	12.6430	−	4.49208i	0.461657	−	0.164027i
$751$	−11.2443	−	22.0681i	−0.410309	−	0.805277i	0.589688	−	0.807631i	$-0.299251\pi$
$751$	−11.2443	−	22.0681i	−0.410309	−	0.805277i	−0.999997	+	0.00235426i	$0.999251\pi$
$752$	39.7555	+	30.6070i	1.44973	+	1.11612i
$753$	−6.31775	+	8.69563i	−0.230232	+	0.316887i
$754$	−7.90815	+	4.77087i	−0.287998	+	0.173745i
$755$	−25.1175	+	30.0964i	−0.914118	+	1.09532i
$756$	3.30649	+	22.9341i	0.120256	+	0.834106i
$757$	−11.6732	−	35.9264i	−0.424269	−	1.30577i	−0.903692	−	0.428183i	$-0.859154\pi$
$757$	−11.6732	−	35.9264i	−0.424269	−	1.30577i	0.479423	−	0.877584i	$-0.340846\pi$
$758$	−36.4745	−	9.02517i	−1.32481	−	0.327809i
$759$	−6.15371	+	1.99946i	−0.223366	+	0.0725759i
$760$	−19.1831	−	38.5448i	−0.695843	−	1.39817i
$761$	0.422502	−	1.30033i	0.0153157	−	0.0471369i	−0.943107	−	0.332491i	$-0.892111\pi$
$761$	0.422502	−	1.30033i	0.0153157	−	0.0471369i	0.958422	+	0.285354i	$0.0921111\pi$
$762$	6.44875	−	7.44517i	0.233614	−	0.269710i
$763$	−10.3871	+	20.3858i	−0.376038	+	0.738017i
$764$	−9.25571	+	6.53015i	−0.334860	+	0.236252i
$765$	−23.8130	−	14.2220i	−0.860960	−	0.514198i
$766$	11.8104	+	14.0243i	0.426728	+	0.506720i
$767$	4.62748	+	3.36206i	0.167089	+	0.121397i
$768$	8.57837	−	10.5241i	0.309545	−	0.379755i
$769$	7.49680	+	10.3185i	0.270342	+	0.372093i	0.922505	−	0.385985i	$-0.126138\pi$
$769$	7.49680	+	10.3185i	0.270342	+	0.372093i	−0.652163	+	0.758078i	$0.726138\pi$
$770$	−4.47440	+	13.9820i	−0.161246	+	0.503877i
$771$	−7.30736	+	5.30910i	−0.263168	+	0.191203i
$772$	5.25785	−	5.11375i	0.189234	−	0.184048i
$773$	−22.9188	−	7.44676i	−0.824331	−	0.267841i	−0.133675	−	0.991025i	$-0.542678\pi$
$773$	−22.9188	−	7.44676i	−0.824331	−	0.267841i	−0.690655	+	0.723184i	$0.742678\pi$
$774$	−14.8354	+	35.1237i	−0.533247	+	1.26250i
$775$	−26.7434	−	3.61325i	−0.960650	−	0.129792i
$776$	−28.8361	−	2.87519i	−1.03516	−	0.103213i
$777$	6.65989	+	13.0708i	0.238922	+	0.468911i
$778$	−1.50635	+	2.42024i	−0.0540053	+	0.0867698i
$779$	−31.4441	−	30.1877i	−1.12660	−	1.08159i
$780$	−8.27960	−	0.672457i	−0.296457	−	0.0240778i
$781$	8.58928	+	2.79083i	0.307349	+	0.0998637i
$782$	−31.8277	+	7.40771i	−1.13816	+	0.264899i
$783$	2.09116	+	13.2031i	0.0747319	+	0.471839i
$784$	−1.20308	+	0.354268i	−0.0429672	+	0.0126524i
$785$	33.9204	+	38.8115i	1.21067	+	1.38524i
$786$	0.823433	−	3.32783i	0.0293709	−	0.118700i
$787$	1.29327	+	0.204833i	0.0461000	+	0.00730152i	0.179442	−	0.983769i	$-0.442571\pi$
$787$	1.29327	+	0.204833i	0.0461000	+	0.00730152i	−0.133342	+	0.991070i	$0.542571\pi$
$788$	10.8419	+	3.69003i	0.386226	+	0.131452i
$789$	−7.27896	−	10.0186i	−0.259138	−	0.356672i
$790$	44.0932	−	14.5438i	1.56876	−	0.517444i
$791$	−36.6124	+	5.79883i	−1.30179	+	0.206183i
$792$	4.20656	+	10.7859i	0.149474	+	0.383262i
$793$			25.5774i			0.908281i
$794$	−6.70275	−	16.5052i	−0.237872	−	0.585749i
$795$	−0.637996	−	0.145503i	−0.0226274	−	0.00516045i
$796$	12.7174	−	3.93767i	0.450757	−	0.139567i
$797$	26.2099	−	13.3546i	0.928403	−	0.473045i	0.0766911	−	0.997055i	$-0.475564\pi$
$797$	26.2099	−	13.3546i	0.928403	−	0.473045i	0.851712	+	0.524010i	$0.175564\pi$
$798$	10.9124	+	18.0883i	0.386295	+	0.640319i
$799$	64.9032	−	21.0883i	2.29611	−	0.746051i
$800$	−26.0001	−	11.1354i	−0.919241	−	0.393694i
$801$	−28.1739	−	14.3553i	−0.995476	−	0.507220i
$802$	16.3828	−	13.7966i	0.578497	−	0.487174i
$803$	−10.7779	+	7.83063i	−0.380345	+	0.276337i
$804$	3.78168	−	3.67804i	0.133370	−	0.129714i
$805$	9.13850	−	22.7933i	0.322090	−	0.803359i
$806$	14.1846	+	8.82847i	0.499632	+	0.310970i
$807$	−2.28836	+	7.04284i	−0.0805540	+	0.247920i
$808$	38.0690	−	2.19903i	1.33926	−	0.0773616i
$809$	0.701398	−	4.42845i	0.0246598	−	0.155696i	−0.972286	−	0.233796i	$-0.924885\pi$
$809$	0.701398	−	4.42845i	0.0246598	−	0.155696i	0.996946	+	0.0780998i	$0.0248853\pi$
$810$	4.32291	−	8.57825i	0.151892	−	0.301409i
$811$	−38.5988			−1.35539			−0.677693	−	0.735345i	$-0.737020\pi$
$811$	−38.5988			−1.35539			−0.677693	+	0.735345i	$0.737020\pi$
$812$	14.7395	−	4.56375i	0.517254	−	0.160156i
$813$	−2.54803	−	7.84201i	−0.0893631	−	0.275031i
$814$	10.9338	+	12.9834i	0.383229	+	0.455067i
$815$	−3.13956	+	7.83073i	−0.109974	+	0.274298i
$816$	−5.21661	−	17.7154i	−0.182618	−	0.620164i
$817$			80.5015i			2.81639i
$818$	−26.9609	+	22.7048i	−0.942664	+	0.793853i
$819$	−12.9045			−0.450919
$820$	−28.5830	−	1.73590i	−0.998161	−	0.0606203i
$821$	−36.1567			−1.26188			−0.630939	−	0.775833i	$-0.717330\pi$
$821$	−36.1567			−1.26188			−0.630939	+	0.775833i	$0.717330\pi$
$822$	4.52782	−	3.81305i	0.157926	−	0.132995i
$823$		−	29.9058i		−	1.04245i	−0.853420	−	0.521225i	$-0.825475\pi$
$823$		−	29.9058i		−	1.04245i	0.853420	−	0.521225i	$-0.174525\pi$
$824$	39.9922	−	2.31012i	1.39319	−	0.0804769i
$825$	−6.05902	+	4.61665i	−0.210948	+	0.160731i
$826$	−6.15546	−	7.30933i	−0.214176	−	0.254324i
$827$	5.91510	+	18.2048i	0.205688	+	0.633043i	0.999684	+	0.0251204i	$0.00799691\pi$
$827$	5.91510	+	18.2048i	0.205688	+	0.633043i	−0.793996	+	0.607923i	$0.792003\pi$
$828$	−5.72796	−	18.4995i	−0.199060	−	0.642902i
$829$	−25.7983			−0.896011			−0.448005	−	0.894031i	$-0.647865\pi$
$829$	−25.7983			−0.896011			−0.448005	+	0.894031i	$0.647865\pi$
$830$	36.3960	−	12.0049i	1.26332	−	0.416697i
$831$	0.377817	−	2.38544i	0.0131063	−	0.0827500i
$832$	11.8556	+	12.8875i	0.411019	+	0.446793i
$833$	−0.527142	+	1.62238i	−0.0182644	+	0.0562121i
$834$	−8.21305	−	5.11177i	−0.284395	−	0.177006i
$835$	18.5788	+	43.4466i	0.642947	+	1.50353i
$836$	17.0423	+	17.5225i	0.589420	+	0.606029i
$837$	19.5638	−	14.2139i	0.676224	−	0.491305i
$838$	−21.6592	+	18.2401i	−0.748206	+	0.630093i
$839$	9.80309	+	4.99492i	0.338440	+	0.172444i	0.614948	−	0.788568i	$-0.289177\pi$
$839$	9.80309	+	4.99492i	0.338440	+	0.172444i	−0.276508	+	0.961012i	$0.589177\pi$
$840$	13.1576	+	4.41301i	0.453979	+	0.152263i
$841$	−19.1147	+	6.21076i	−0.659129	+	0.214164i
$842$	5.92445	+	9.82031i	0.204170	+	0.338430i
$843$	4.98186	−	2.53838i	0.171584	−	0.0874266i
$844$	7.00845	+	22.6351i	0.241241	+	0.779132i
$845$	−4.08134	+	17.8957i	−0.140402	+	0.615632i
$846$	15.2167	+	37.4706i	0.523163	+	1.28827i
$847$			20.1094i			0.690969i
$848$	0.779506	+	1.13810i	0.0267683	+	0.0390825i
$849$	24.4379	−	3.87058i	0.838707	−	0.132838i
$850$	−32.4798	+	20.6182i	−1.11405	+	0.707200i
$851$	−16.6893	−	22.9708i	−0.572101	−	0.787430i
$852$	2.75080	−	8.08227i	0.0942409	−	0.276894i
$853$	23.6001	+	3.73788i	0.808051	+	0.127983i	0.546773	−	0.837281i	$-0.315856\pi$
$853$	23.6001	+	3.73788i	0.808051	+	0.127983i	0.261278	+	0.965264i	$0.415856\pi$
$854$	10.2637	−	41.4801i	0.351218	−	1.41942i
$855$	2.32859	−	34.6266i	0.0796361	−	1.18421i
$856$	22.3336	−	1.29008i	0.763347	−	0.0440942i
$857$	4.22695	+	26.6879i	0.144390	+	0.911642i	0.948412	+	0.317042i	$0.102690\pi$
$857$	4.22695	+	26.6879i	0.144390	+	0.911642i	−0.804022	+	0.594600i	$0.797310\pi$
$858$	4.59329	−	1.06906i	0.156812	−	0.0364971i
$859$	−27.5618	−	8.95536i	−0.940396	−	0.305553i	−0.201589	−	0.979470i	$-0.564610\pi$
$859$	−27.5618	−	8.95536i	−0.940396	−	0.305553i	−0.738807	+	0.673917i	$0.764610\pi$
$860$	34.2452	+	40.2997i	1.16775	+	1.37421i
$861$	14.0474	−	0.286369i	0.478734	−	0.00975944i
$862$	2.75022	−	4.41875i	0.0936728	−	0.150503i
$863$	1.70653	+	3.34925i	0.0580909	+	0.114010i	0.918227	−	0.396056i	$-0.129621\pi$
$863$	1.70653	+	3.34925i	0.0580909	+	0.114010i	−0.860136	+	0.510065i	$0.829621\pi$
$864$	23.7386	−	8.88022i	0.807605	−	0.302111i
$865$	9.66749	−	24.1127i	0.328704	−	0.819857i
$866$	14.1283	−	33.4495i	0.480098	−	1.13666i
$867$	−10.1697	−	3.30432i	−0.345380	−	0.112221i
$868$	−19.4612	−	20.0096i	−0.660555	−	0.679169i
$869$	−21.3254	+	15.4938i	−0.723414	+	0.525591i
$870$	7.62531	+	2.44019i	0.258522	+	0.0827302i
$871$	3.99916	+	5.50437i	0.135506	+	0.186509i
$872$	24.2077	+	6.34807i	0.819775	+	0.214973i
$873$	−18.8979	−	13.7301i	−0.639598	−	0.464695i
$874$	−26.3381	−	31.2752i	−0.890898	−	1.05790i
$875$	1.28212	−	28.8819i	0.0433437	−	0.976386i
$876$	7.26027	+	10.2906i	0.245302	+	0.347686i
$877$	6.50453	−	12.7659i	0.219642	−	0.431072i	−0.754723	−	0.656043i	$-0.772229\pi$
$877$	6.50453	−	12.7659i	0.219642	−	0.431072i	0.974365	+	0.224971i	$0.0722288\pi$
$878$	23.7016	−	27.3639i	0.799892	−	0.923485i
$879$	−7.18187	+	22.1035i	−0.242239	+	0.745534i
$880$	15.9855	+	1.52214i	0.538873	+	0.0513114i
$881$	−49.7461	+	16.1635i	−1.67599	+	0.544562i	−0.984127	−	0.177467i	$-0.943210\pi$
$881$	−49.7461	+	16.1635i	−1.67599	+	0.544562i	−0.691863	+	0.722029i	$0.743210\pi$
$882$	−0.981341	−	0.242821i	−0.0330435	−	0.00817621i
$883$	−1.98321	−	6.10370i	−0.0667404	−	0.205406i	0.912125	−	0.409913i	$-0.134441\pi$
$883$	−1.98321	−	6.10370i	−0.0667404	−	0.205406i	−0.978865	+	0.204507i	$0.934441\pi$
$884$	23.5745	−	3.39881i	0.792896	−	0.114314i
$885$	−0.445318	−	4.93835i	−0.0149692	−	0.166001i
$886$	34.2838	−	20.6829i	1.15179	−	0.694856i
$887$	−4.72557	+	6.50419i	−0.158669	+	0.218389i	−0.880949	−	0.473212i	$-0.843094\pi$
$887$	−4.72557	+	6.50419i	−0.158669	+	0.218389i	0.722279	+	0.691601i	$0.243094\pi$
$888$	12.4160	−	10.1645i	0.416653	−	0.341099i
$889$	−9.63514	−	18.9100i	−0.323152	−	0.634222i
$890$	−35.3670	+	25.9366i	−1.18550	+	0.869398i
$891$	−0.853129	+	5.38644i	−0.0285809	+	0.180453i
$892$	−15.0016	−	48.4503i	−0.502290	−	1.62224i
$893$	60.3782	+	60.3782i	2.02048	+	2.02048i
$894$	3.97980	+	3.44717i	0.133105	+	0.115291i
$895$	−3.90363	−	6.21022i	−0.130484	−	0.207585i
$896$	−14.0553	−	25.6577i	−0.469554	−	0.857163i
$897$	−7.79175	+	1.23409i	−0.260159	+	0.0412051i
$898$	42.1472	−	17.1159i	1.40647	−	0.571165i
$899$	−11.3865	−	11.3865i	−0.379763	−	0.379763i
$900$	−13.5644	−	18.3249i	−0.452147	−	0.610831i
$901$	1.87629			0.0625084
$902$	15.7557	−	4.00726i	0.524608	−	0.133427i
$903$	−18.3482	−	18.3482i	−0.610591	−	0.610591i
$904$	14.7326	+	37.7754i	0.489998	+	1.25639i
$905$	7.86132	−	1.98232i	0.261319	−	0.0658945i
$906$	−19.3808	−	8.18596i	−0.643883	−	0.271960i
$907$	−3.46963	−	21.9064i	−0.115207	−	0.727390i	−0.975892	−	0.218252i	$-0.929964\pi$
$907$	−3.46963	−	21.9064i	−0.115207	−	0.727390i	0.860685	−	0.509138i	$-0.170036\pi$
$908$	2.48410	+	17.2300i	0.0824379	+	0.571797i
$909$	27.3872	+	13.9545i	0.908375	+	0.462840i
$910$	−8.05492	+	15.9839i	−0.267018	+	0.529862i
$911$	−36.1229			−1.19680			−0.598402	−	0.801196i	$-0.704197\pi$
$911$	−36.1229			−1.19680			−0.598402	+	0.801196i	$0.704197\pi$
$912$	16.7868	−	15.8789i	0.555866	−	0.525803i
$913$	−17.6027	+	12.7891i	−0.582564	+	0.423258i
$914$	28.6118	−	11.6192i	0.946395	−	0.384329i
$915$	16.6948	−	14.5909i	0.551914	−	0.482360i
$916$	2.35628	−	6.92312i	0.0778538	−	0.228746i
$917$	−5.97600	−	4.34182i	−0.197345	−	0.143379i
$918$	8.28042	−	33.4646i	0.273295	−	1.10450i
$919$	−3.49503	+	22.0667i	−0.115290	+	0.727915i	0.860540	+	0.509384i	$0.170127\pi$
$919$	−3.49503	+	22.0667i	−0.115290	+	0.727915i	−0.975830	+	0.218531i	$0.929873\pi$
$920$	−26.4895	−	4.45244i	−0.873332	−	0.146793i
$921$	18.4335	+	9.39232i	0.607404	+	0.309488i
$922$	−36.0492	−	8.91995i	−1.18722	−	0.293763i
$923$	9.81105	+	4.99898i	0.322935	+	0.164543i
$924$	−7.87815	−	0.109459i	−0.259172	−	0.00360094i
$925$	−27.4836	−	19.0266i	−0.903654	−	0.625592i
$926$	17.3614	−	1.24509i	0.570531	−	0.0409161i
$927$	28.7707	+	14.6594i	0.944955	+	0.481479i
$928$	−8.31343	−	14.6880i	−0.272902	−	0.482157i
$929$	26.1062	+	26.1062i	0.856518	+	0.856518i	0.990926	−	0.134408i	$-0.0429134\pi$
$929$	26.1062	+	26.1062i	0.856518	+	0.856518i	−0.134408	+	0.990926i	$0.542913\pi$
$930$	−2.32927	−	14.2948i	−0.0763799	−	0.468746i
$931$	−2.10815	+	0.333898i	−0.0690918	+	0.0109431i
$932$	−15.2430	−	8.03535i	−0.499300	−	0.263207i
$933$	−2.75239	+	17.3779i	−0.0901092	+	0.568927i
$934$	4.59070	+	19.7243i	0.150212	+	0.645397i
$935$	13.9947	−	16.7688i	0.457677	−	0.548400i
$936$	3.00841	+	13.7909i	0.0983329	+	0.450770i
$937$	12.8488	−	39.5446i	0.419753	−	1.29187i	−0.488177	−	0.872745i	$-0.662338\pi$
$937$	12.8488	−	39.5446i	0.419753	−	1.29187i	0.907930	−	0.419122i	$-0.137662\pi$
$938$	−4.27682	−	10.5315i	−0.139643	−	0.343865i
$939$	−20.1595	−	14.6468i	−0.657882	−	0.477979i
$940$	55.9106	+	4.54097i	1.82360	+	0.148110i
$941$	50.2557	+	16.3291i	1.63829	+	0.532313i	0.976155	−	0.217073i	$-0.0696509\pi$
$941$	50.2557	+	16.3291i	1.63829	+	0.532313i	0.662134	+	0.749385i	$0.269651\pi$
$942$	−14.6179	+	23.4865i	−0.476277	+	0.765231i
$943$	−26.7676	+	4.80076i	−0.871674	+	0.156334i
$944$	−6.37639	+	8.28230i	−0.207534	+	0.269566i
$945$	17.0481	+	19.5063i	0.554574	+	0.634541i
$946$	−25.4903	−	15.8651i	−0.828762	−	0.515819i
$947$	29.9027	−	4.73613i	0.971709	−	0.153904i	0.349655	−	0.936878i	$-0.386299\pi$
$947$	29.9027	−	4.73613i	0.971709	−	0.153904i	0.622053	+	0.782975i	$0.286299\pi$
$948$	14.3653	+	20.3611i	0.466562	+	0.661296i
$949$	−14.4725	+	7.37410i	−0.469797	+	0.239373i
$950$	−41.4362	−	24.4980i	−1.34437	−	0.794821i
$951$	−4.01514	+	2.91717i	−0.130200	+	0.0945957i
$952$	−39.5957	−	3.94801i	−1.28330	−	0.127956i
$953$	5.87689	−	37.1052i	0.190371	−	1.20196i	−0.688622	−	0.725121i	$-0.741784\pi$
$953$	5.87689	−	37.1052i	0.190371	−	1.20196i	0.878993	−	0.476835i	$-0.158216\pi$
$954$	0.0795390	+	1.10909i	0.00257517	+	0.0359080i
$955$	−4.71288	+	11.7549i	−0.152505	+	0.380379i
$956$	−13.5149	−	10.1090i	−0.437105	−	0.326949i
$957$	−4.54539			−0.146932
$958$	−17.1430	−	7.24077i	−0.553864	−	0.233939i
$959$	−3.94144	−	12.1305i	−0.127276	−	0.391715i
$960$	1.64873	−	15.0902i	0.0532125	−	0.487033i
$961$	0.577708	−	1.77800i	0.0186357	−	0.0573549i
$962$	10.6903	+	17.7202i	0.344670	+	0.571321i
$963$	16.0670	+	8.18654i	0.517751	+	0.263808i
$964$	23.0585	+	23.7083i	0.742665	+	0.763593i
$965$	1.82335	−	7.99497i	0.0586957	−	0.257367i
$966$	13.1315	+	1.12530i	0.422498	+	0.0362060i
$967$	5.80059	+	7.98383i	0.186535	+	0.256743i	0.892035	−	0.451967i	$-0.149278\pi$
$967$	5.80059	+	7.98383i	0.186535	+	0.256743i	−0.705500	+	0.708710i	$0.749278\pi$
$968$	21.4908	−	4.68809i	0.690739	−	0.150681i
$969$	−4.91666	−	31.0425i	−0.157946	−	0.997230i
$970$	−28.8026	+	14.8373i	−0.924796	+	0.476398i
$971$	−17.6639	−	34.6673i	−0.566860	−	1.11253i	−0.979465	−	0.201615i	$-0.935381\pi$
$971$	−17.6639	−	34.6673i	−0.566860	−	1.11253i	0.412605	−	0.910910i	$-0.364619\pi$
$972$	31.5710	+	5.45100i	1.01264	+	0.174841i
$973$	−16.8635	+	12.2520i	−0.540618	+	0.392782i
$974$	−4.02873	+	4.65122i	−0.129089	+	0.149035i
$975$	−8.17689	+	4.40381i	−0.261870	+	0.141035i
$976$	−46.7221	−	1.29857i	−1.49554	−	0.0415661i
$977$	56.7655	−	18.4442i	1.81609	−	0.590083i	0.816165	−	0.577819i	$-0.196096\pi$
$977$	56.7655	−	18.4442i	1.81609	−	0.590083i	0.999925	−	0.0122645i	$-0.00390401\pi$
$978$	−4.51136	−	0.386602i	−0.144257	−	0.0123622i
$979$	14.6356	−	20.1442i	0.467756	−	0.643811i
$980$	−0.913315	+	1.06395i	−0.0291748	+	0.0339868i
$981$	14.2643	+	14.2643i	0.455424	+	0.455424i
$982$	−28.8244	+	24.2741i	−0.919823	+	0.774618i
$983$	32.7050	+	32.7050i	1.04313	+	1.04313i	0.999027	+	0.0441013i	$0.0140424\pi$
$983$	32.7050	+	32.7050i	1.04313	+	1.04313i	0.0441013	+	0.999027i	$0.485958\pi$
$984$	−3.58089	−	14.9455i	−0.114155	−	0.476446i
$985$	12.4158	−	3.13078i	0.395599	−	0.0997548i
$986$	−22.8724	−	1.96006i	−0.728407	−	0.0624210i
$987$	−27.5233			−0.876076
$988$	17.1805	+	24.3513i	0.546585	+	0.774719i
$989$	40.6318	+	29.5207i	1.29202	+	0.938705i
$990$	10.5054	+	7.56149i	0.333884	+	0.240320i
$991$	36.9447	+	18.8243i	1.17359	+	0.597973i	0.928429	−	0.371510i	$-0.121160\pi$
$991$	36.9447	+	18.8243i	1.17359	+	0.597973i	0.245159	+	0.969483i	$0.421160\pi$
$992$	−16.8471	+	25.4628i	−0.534895	+	0.808443i
$993$	18.4548	+	18.4548i	0.585646	+	0.585646i
$994$	−13.9050	−	12.0441i	−0.441041	−	0.382015i
$995$	9.53713	−	11.4276i	0.302347	−	0.362281i
$996$	11.8576	+	16.8067i	0.375721	+	0.532541i
$997$	−30.2714	−	9.83576i	−0.958703	−	0.311502i	−0.212456	−	0.977171i	$-0.568146\pi$
$997$	−30.2714	−	9.83576i	−0.958703	−	0.311502i	−0.746247	+	0.665669i	$0.768146\pi$
$998$	−36.9263	+	8.59437i	−1.16888	+	0.272050i
$999$	29.5847	−	4.68576i	0.936020	−	0.148251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bk.c.267.36	yes	960
4.3	odd	2	inner	820.2.bk.c.267.51	yes	960
5.3	odd	4		820.2.bv.c.103.27	yes	960
20.3	even	4		820.2.bv.c.103.11	yes	960
41.2	even	20		820.2.bv.c.207.11	yes	960
164.43	odd	20		820.2.bv.c.207.27	yes	960
205.43	odd	20	inner	820.2.bk.c.43.51	yes	960
820.43	even	20	inner	820.2.bk.c.43.36	✓	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.36	✓	960	820.43	even	20	inner
820.2.bk.c.43.51	yes	960	205.43	odd	20	inner
820.2.bk.c.267.36	yes	960	1.1	even	1	trivial
820.2.bk.c.267.51	yes	960	4.3	odd	2	inner
820.2.bv.c.103.11	yes	960	20.3	even	4
820.2.bv.c.103.27	yes	960	5.3	odd	4
820.2.bv.c.207.11	yes	960	41.2	even	20
820.2.bv.c.207.27	yes	960	164.43	odd	20

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.910966 - 1.08173i) q^{2} -0.848586i q^{3} +(-0.340282 + 1.97084i) q^{4} +(0.879185 + 2.05598i) q^{5} +(-0.917941 + 0.773033i) q^{6} +(0.799062 + 2.45926i) q^{7} +(2.44190 - 1.42727i) q^{8} +2.27990 q^{9} +(1.42310 - 2.82396i) q^{10} +(-0.280850 + 1.77322i) q^{11} +(1.67243 + 0.288758i) q^{12} +(-0.676408 + 2.08177i) q^{13} +(1.93234 - 3.10467i) q^{14} +(1.74467 - 0.746064i) q^{15} +(-3.76842 - 1.34128i) q^{16} +(-4.40160 + 3.19795i) q^{17} +(-2.07691 - 2.46624i) q^{18} +(-6.06554 - 3.09055i) q^{19} +(-4.35117 + 1.03312i) q^{20} +(2.08689 - 0.678072i) q^{21} +(2.17399 - 1.31154i) q^{22} +(-3.78420 + 1.92814i) q^{23} +(-1.21116 - 2.07216i) q^{24} +(-3.45407 + 3.61517i) q^{25} +(2.86810 - 1.16473i) q^{26} -4.48045i q^{27} +(-5.11871 + 0.737981i) q^{28} +(-2.94682 + 0.466730i) q^{29} +(-2.39638 - 1.20762i) q^{30} +(3.17243 + 4.36648i) q^{31} +(1.98199 + 5.29827i) q^{32} +(1.50473 + 0.238326i) q^{33} +(7.46903 + 1.84812i) q^{34} +(-4.35365 + 3.80500i) q^{35} +(-0.775810 + 4.49332i) q^{36} +(1.04582 + 6.60307i) q^{37} +(2.18236 + 9.37666i) q^{38} +(1.76656 + 0.573990i) q^{39} +(5.08132 + 3.76565i) q^{40} +(6.12880 + 1.85414i) q^{41} +(-2.63458 - 1.63975i) q^{42} +(-5.36862 - 10.5365i) q^{43} +(-3.39916 - 1.15691i) q^{44} +(2.00446 + 4.68742i) q^{45} +(5.53301 + 2.33701i) q^{46} +(-11.9292 - 3.87605i) q^{47} +(-1.13819 + 3.19782i) q^{48} +(0.253659 - 0.184294i) q^{49} +(7.05717 + 0.443078i) q^{50} +(2.71373 + 3.73514i) q^{51} +(-3.87266 - 2.04148i) q^{52} +(-0.279001 - 0.202706i) q^{53} +(-4.84664 + 4.08154i) q^{54} +(-3.89261 + 0.981566i) q^{55} +(5.46127 + 4.86479i) q^{56} +(-2.62259 + 5.14713i) q^{57} +(3.18933 + 2.76249i) q^{58} +(0.807500 - 2.48523i) q^{59} +(0.876692 + 3.69234i) q^{60} +(11.1131 - 3.61088i) q^{61} +(1.83338 - 7.40944i) q^{62} +(1.82178 + 5.60687i) q^{63} +(3.92578 - 6.97053i) q^{64} +(-4.87476 + 0.439583i) q^{65} +(-1.11295 - 1.84482i) q^{66} +(1.82702 - 2.51467i) q^{67} +(-4.80486 - 9.76305i) q^{68} +(1.63620 + 3.21121i) q^{69} +(8.08201 + 1.24326i) q^{70} +(0.786938 - 4.96853i) q^{71} +(5.56730 - 3.25405i) q^{72} +(5.24712 + 5.24712i) q^{73} +(6.19004 - 7.14648i) q^{74} +(3.06778 + 2.93107i) q^{75} +(8.15497 - 10.9026i) q^{76} +(-4.58522 + 0.726228i) q^{77} +(-0.988373 - 2.43383i) q^{78} +(10.3820 + 10.3820i) q^{79} +(-0.555492 - 8.92701i) q^{80} +3.03766 q^{81} +(-3.57744 - 8.31877i) q^{82} +(8.56967 + 8.56967i) q^{83} +(0.626240 + 4.34367i) q^{84} +(-10.4447 - 6.23799i) q^{85} +(-6.50703 + 15.4058i) q^{86} +(0.396060 + 2.50063i) q^{87} +(1.84506 + 4.73088i) q^{88} +(-12.3575 - 6.29646i) q^{89} +(3.24454 - 6.43836i) q^{90} -5.66011 q^{91} +(-2.51237 - 8.11416i) q^{92} +(3.70533 - 2.69208i) q^{93} +(6.67430 + 16.4352i) q^{94} +(1.02136 - 15.1878i) q^{95} +(4.49604 - 1.68189i) q^{96} +(-8.28892 - 6.02225i) q^{97} +(-0.430431 - 0.106505i) q^{98} +(-0.640311 + 4.04277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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