LMFDB - Embedded newform 414.3.k.a.35.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.7
Character	$\chi$	$=$	414.35
Dual form			414.3.k.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(1.27049 + 4.32689i) q^{5} +(6.32390 + 7.29817i) q^{7} +(-2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(1.27049 + 4.32689i) q^{5} +(6.32390 + 7.29817i) q^{7} +(-2.79964 + 0.402527i) q^{8} +(-4.17636 + 4.81978i) q^{10} +(3.11829 - 4.85216i) q^{11} +(-1.01372 + 1.16990i) q^{13} +(-3.84759 + 13.1037i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(5.42903 - 2.47936i) q^{17} +(-12.9546 + 28.3667i) q^{19} +(-8.92731 - 1.28355i) q^{20} +8.15686 q^{22} +(1.15901 - 22.9708i) q^{23} +(3.92352 - 2.52149i) q^{25} +(-2.16692 - 0.311556i) q^{26} +(-18.5314 + 5.44131i) q^{28} +(-48.9626 + 22.3605i) q^{29} +(-0.890566 - 6.19402i) q^{31} +(1.59372 - 5.42771i) q^{32} +(7.10066 + 4.56331i) q^{34} +(-23.5439 + 36.6351i) q^{35} +(46.7073 + 13.7145i) q^{37} +(-43.6531 + 6.27636i) q^{38} +(-5.29860 - 11.6023i) q^{40} +(-3.26551 - 11.1213i) q^{41} +(-10.5745 + 73.5473i) q^{43} +(6.23659 + 9.70432i) q^{44} +(28.2148 - 16.1842i) q^{46} -22.6340i q^{47} +(-6.29815 + 43.8046i) q^{49} +(5.99969 + 2.73997i) q^{50} +(-1.28612 - 2.81622i) q^{52} +(-21.0375 + 18.2291i) q^{53} +(24.9565 + 7.32789i) q^{55} +(-20.6423 - 17.8867i) q^{56} +(-64.0384 - 41.1550i) q^{58} +(-18.7926 - 16.2839i) q^{59} +(5.46123 + 37.9837i) q^{61} +(6.68820 - 5.79535i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-6.34995 - 2.89993i) q^{65} +(40.1125 - 25.7788i) q^{67} +11.9368i q^{68} -61.5864 q^{70} +(10.1679 + 15.8216i) q^{71} +(49.0877 - 107.487i) q^{73} +(19.3952 + 66.0541i) q^{74} +(-40.8434 - 47.1358i) q^{76} +(55.1317 - 7.92674i) q^{77} +(39.8487 - 45.9878i) q^{79} +(9.75220 - 15.1747i) q^{80} +(10.7344 - 12.3882i) q^{82} +(41.5227 - 141.413i) q^{83} +(17.6254 + 20.3408i) q^{85} +(-95.5852 + 43.6523i) q^{86} +(-6.77697 + 14.8395i) q^{88} +(51.4321 + 7.39482i) q^{89} -14.9488 q^{91} +(40.8270 + 21.1933i) q^{92} +(26.9279 - 17.3055i) q^{94} +(-139.198 - 20.0137i) q^{95} +(-27.0286 + 7.93630i) q^{97} +(-56.9303 + 25.9992i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 - 16 * q^7	$ 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.764582	+	1.18971i	0.382291	+	0.594856i
$2$	0.764582	+	1.18971i	0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	+	1.81926i	−0.207708	+	0.454816i
$5$	1.27049	+	4.32689i	0.254098	+	0.865378i	0.983441	+	0.181230i	$0.0580077\pi$
$5$	1.27049	+	4.32689i	0.254098	+	0.865378i	−0.729343	+	0.684148i	$0.760174\pi$
$6$		0			0
$7$	6.32390	+	7.29817i	0.903415	+	1.04260i	0.998887	+	0.0471640i	$0.0150183\pi$
$7$	6.32390	+	7.29817i	0.903415	+	1.04260i	−0.0954726	+	0.995432i	$0.530436\pi$
$8$	−2.79964	+	0.402527i	−0.349955	+	0.0503159i
$9$		0			0
$10$	−4.17636	+	4.81978i	−0.417636	+	0.481978i
$11$	3.11829	−	4.85216i	0.283481	−	0.441105i	−0.670087	−	0.742283i	$-0.733743\pi$
$11$	3.11829	−	4.85216i	0.283481	−	0.441105i	0.953568	+	0.301177i	$0.0973796\pi$
$12$		0			0
$13$	−1.01372	+	1.16990i	−0.0779788	+	0.0899923i	−0.793398	−	0.608703i	$-0.791690\pi$
$13$	−1.01372	+	1.16990i	−0.0779788	+	0.0899923i	0.715419	+	0.698695i	$0.246236\pi$
$14$	−3.84759	+	13.1037i	−0.274828	+	0.935977i
$15$		0			0
$16$	−2.61944	−	3.02300i	−0.163715	−	0.188937i
$17$	5.42903	−	2.47936i	0.319355	−	0.145844i	−0.249287	−	0.968430i	$-0.580196\pi$
$17$	5.42903	−	2.47936i	0.319355	−	0.145844i	0.568642	+	0.822585i	$0.307469\pi$
$18$		0			0
$19$	−12.9546	+	28.3667i	−0.681823	+	1.49298i	0.178878	+	0.983871i	$0.442753\pi$
$19$	−12.9546	+	28.3667i	−0.681823	+	1.49298i	−0.860700	+	0.509112i	$0.829974\pi$
$20$	−8.92731	−	1.28355i	−0.446366	−	0.0641777i
$21$		0			0
$22$	8.15686			0.370767
$23$	1.15901	−	22.9708i	0.0503915	−	0.998730i
$23$	1.15901	−	22.9708i	0.0503915	−	0.998730i
$24$		0			0
$25$	3.92352	−	2.52149i	0.156941	−	0.100860i
$26$	−2.16692	−	0.311556i	−0.0833431	−	0.0119829i
$27$		0			0
$28$	−18.5314	+	5.44131i	−0.661835	+	0.194332i
$29$	−48.9626	+	22.3605i	−1.68836	+	0.771050i	−0.689457	+	0.724327i	$0.742151\pi$
$29$	−48.9626	+	22.3605i	−1.68836	+	0.771050i	−0.998908	+	0.0467238i	$0.985122\pi$
$30$		0			0
$31$	−0.890566	−	6.19402i	−0.0287279	−	0.199807i	0.970403	−	0.241492i	$-0.0776367\pi$
$31$	−0.890566	−	6.19402i	−0.0287279	−	0.199807i	−0.999131	+	0.0416845i	$0.986728\pi$
$32$	1.59372	−	5.42771i	0.0498038	−	0.169616i
$33$		0			0
$34$	7.10066	+	4.56331i	0.208843	+	0.134215i
$35$	−23.5439	+	36.6351i	−0.672684	+	1.04672i
$36$		0			0
$37$	46.7073	+	13.7145i	1.26236	+	0.370662i	0.843372	−	0.537330i	$-0.180567\pi$
$37$	46.7073	+	13.7145i	1.26236	+	0.370662i	0.418987	+	0.907992i	$0.362385\pi$
$38$	−43.6531	+	6.27636i	−1.14876	+	0.165167i
$39$		0			0
$40$	−5.29860	−	11.6023i	−0.132465	−	0.290058i
$41$	−3.26551	−	11.1213i	−0.0796466	−	0.271251i	0.910036	−	0.414529i	$-0.136054\pi$
$41$	−3.26551	−	11.1213i	−0.0796466	−	0.271251i	−0.989682	+	0.143278i	$0.954236\pi$
$42$		0			0
$43$	−10.5745	+	73.5473i	−0.245919	+	1.71040i	0.375414	+	0.926857i	$0.377500\pi$
$43$	−10.5745	+	73.5473i	−0.245919	+	1.71040i	−0.621333	+	0.783546i	$0.713409\pi$
$44$	6.23659	+	9.70432i	0.141741	+	0.220553i
$45$		0			0
$46$	28.2148	−	16.1842i	0.613365	−	0.351829i
$47$		−	22.6340i		−	0.481575i	−0.970578	−	0.240787i	$-0.922594\pi$
$47$		−	22.6340i		−	0.481575i	0.970578	−	0.240787i	$-0.0774056\pi$
$48$		0			0
$49$	−6.29815	+	43.8046i	−0.128534	+	0.893972i
$50$	5.99969	+	2.73997i	0.119994	+	0.0547994i
$51$		0			0
$52$	−1.28612	−	2.81622i	−0.0247332	−	0.0541581i
$53$	−21.0375	+	18.2291i	−0.396935	+	0.343946i	−0.830344	−	0.557251i	$-0.811856\pi$
$53$	−21.0375	+	18.2291i	−0.396935	+	0.343946i	0.433409	+	0.901197i	$0.357311\pi$
$54$		0			0
$55$	24.9565	+	7.32789i	0.453755	+	0.133234i
$56$	−20.6423	−	17.8867i	−0.368613	−	0.319405i
$57$		0			0
$58$	−64.0384	−	41.1550i	−1.10411	−	0.709569i
$59$	−18.7926	−	16.2839i	−0.318518	−	0.275998i	0.480896	−	0.876778i	$-0.340311\pi$
$59$	−18.7926	−	16.2839i	−0.318518	−	0.275998i	−0.799415	+	0.600780i	$0.794857\pi$
$60$		0			0
$61$	5.46123	+	37.9837i	0.0895283	+	0.622683i	0.984345	+	0.176250i	$0.0563968\pi$
$61$	5.46123	+	37.9837i	0.0895283	+	0.622683i	−0.894817	+	0.446433i	$0.852694\pi$
$62$	6.68820	−	5.79535i	0.107874	−	0.0934735i
$63$		0			0
$64$	7.67594	−	2.25386i	0.119937	−	0.0352166i
$65$	−6.34995	−	2.89993i	−0.0976916	−	0.0446143i
$66$		0			0
$67$	40.1125	−	25.7788i	0.598695	−	0.384758i	−0.205908	−	0.978571i	$-0.566015\pi$
$67$	40.1125	−	25.7788i	0.598695	−	0.384758i	0.804603	+	0.593814i	$0.202378\pi$
$68$			11.9368i			0.175541i
$69$		0			0
$70$	−61.5864			−0.879806
$71$	10.1679	+	15.8216i	0.143210	+	0.222839i	0.905447	−	0.424459i	$-0.139536\pi$
$71$	10.1679	+	15.8216i	0.143210	+	0.222839i	−0.762237	+	0.647297i	$0.775899\pi$
$72$		0			0
$73$	49.0877	−	107.487i	0.672434	−	1.47243i	−0.198031	−	0.980196i	$-0.563455\pi$
$73$	49.0877	−	107.487i	0.672434	−	1.47243i	0.870465	−	0.492230i	$-0.163818\pi$
$74$	19.3952	+	66.0541i	0.262098	+	0.892623i
$75$		0			0
$76$	−40.8434	−	47.1358i	−0.537413	−	0.620208i
$77$	55.1317	−	7.92674i	0.715996	−	0.102945i
$78$		0			0
$79$	39.8487	−	45.9878i	0.504414	−	0.582124i	−0.445246	−	0.895408i	$-0.646884\pi$
$79$	39.8487	−	45.9878i	0.504414	−	0.582124i	0.949659	+	0.313284i	$0.101429\pi$
$80$	9.75220	−	15.1747i	0.121903	−	0.189684i
$81$		0			0
$82$	10.7344	−	12.3882i	0.130907	−	0.151075i
$83$	41.5227	−	141.413i	0.500273	−	1.70377i	−0.191356	−	0.981521i	$-0.561288\pi$
$83$	41.5227	−	141.413i	0.500273	−	1.70377i	0.691629	−	0.722253i	$-0.256893\pi$
$84$		0			0
$85$	17.6254	+	20.3408i	0.207358	+	0.239304i
$86$	−95.5852	+	43.6523i	−1.11146	+	0.507585i
$87$		0			0
$88$	−6.77697	+	14.8395i	−0.0770110	+	0.168631i
$89$	51.4321	+	7.39482i	0.577888	+	0.0830878i	0.425060	−	0.905165i	$-0.360253\pi$
$89$	51.4321	+	7.39482i	0.577888	+	0.0830878i	0.152828	+	0.988253i	$0.451162\pi$
$90$		0			0
$91$	−14.9488			−0.164273
$92$	40.8270	+	21.1933i	0.443771	+	0.230362i
$93$		0			0
$94$	26.9279	−	17.3055i	0.286468	−	0.184102i
$95$	−139.198	−	20.0137i	−1.46524	−	0.210670i
$96$		0			0
$97$	−27.0286	+	7.93630i	−0.278645	+	0.0818175i	−0.418069	−	0.908415i	$-0.637293\pi$
$97$	−27.0286	+	7.93630i	−0.278645	+	0.0818175i	0.139424	+	0.990233i	$0.455475\pi$
$98$	−56.9303	+	25.9992i	−0.580922	+	0.265298i
$99$		0			0
$100$	1.32748	+	9.23284i	0.0132748	+	0.0923284i
$101$	8.72926	−	29.7291i	0.0864283	−	0.294348i	−0.904924	−	0.425573i	$-0.860073\pi$
$101$	8.72926	−	29.7291i	0.0864283	−	0.294348i	0.991353	+	0.131225i	$0.0418909\pi$
$102$		0			0
$103$	34.1635	+	21.9556i	0.331685	+	0.213161i	0.695874	−	0.718164i	$-0.255017\pi$
$103$	34.1635	+	21.9556i	0.331685	+	0.213161i	−0.364189	+	0.931325i	$0.618654\pi$
$104$	2.36714	−	3.68335i	0.0227610	−	0.0354168i
$105$		0			0
$106$	−37.7723	−	11.0910i	−0.356343	−	0.104632i
$107$	142.108	−	20.4320i	1.32811	−	0.190954i	0.558520	−	0.829491i	$-0.311369\pi$
$107$	142.108	−	20.4320i	1.32811	−	0.190954i	0.769591	+	0.638538i	$0.220460\pi$
$108$		0			0
$109$	−12.7080	−	27.8267i	−0.116588	−	0.255291i	0.842338	−	0.538950i	$-0.181179\pi$
$109$	−12.7080	−	27.8267i	−0.116588	−	0.255291i	−0.958925	+	0.283659i	$0.908452\pi$
$110$	10.3632	+	35.2938i	0.0942110	+	0.320853i
$111$		0			0
$112$	5.49726	−	38.2343i	0.0490827	−	0.341378i
$113$	34.2790	+	53.3392i	0.303354	+	0.472028i	0.959145	−	0.282914i	$-0.0913011\pi$
$113$	34.2790	+	53.3392i	0.303354	+	0.472028i	−0.655791	+	0.754942i	$0.727665\pi$
$114$		0			0
$115$	100.865	−	24.1692i	0.877083	−	0.210167i
$116$		−	107.654i		−	0.928048i
$117$		0			0
$118$	5.00465	−	34.8081i	0.0424123	−	0.294984i
$119$	52.4274	+	23.9428i	0.440567	+	0.201200i
$120$		0			0
$121$	36.4455	+	79.8045i	0.301203	+	0.659542i
$122$	−41.0141	+	35.5389i	−0.336181	+	0.291303i
$123$		0			0
$124$	12.0085	+	3.52601i	0.0968425	+	0.0284355i
$125$	101.097	+	87.6014i	0.808779	+	0.700811i
$126$		0			0
$127$	−141.841	−	91.1558i	−1.11686	−	0.717762i	−0.154082	−	0.988058i	$-0.549242\pi$
$127$	−141.841	−	91.1558i	−1.11686	−	0.717762i	−0.962777	+	0.270296i	$0.912878\pi$
$128$	8.55033	+	7.40890i	0.0667995	+	0.0578821i
$129$		0			0
$130$	−1.40498	−	9.77185i	−0.0108075	−	0.0751681i
$131$	178.043	−	154.275i	1.35911	−	1.17767i	0.392996	−	0.919540i	$-0.371439\pi$
$131$	178.043	−	154.275i	1.35911	−	1.17767i	0.966110	−	0.258132i	$-0.0831069\pi$
$132$		0			0
$133$	−288.949	+	84.8430i	−2.17255	+	0.637917i
$134$	61.3386	+	28.0124i	0.457751	+	0.209048i
$135$		0			0
$136$	−14.2013	+	9.12663i	−0.104421	+	0.0671076i
$137$			112.507i			0.821222i	0.911811	+	0.410611i	$0.134685\pi$
$137$			112.507i			0.821222i	−0.911811	+	0.410611i	$0.865315\pi$
$138$		0			0
$139$	70.0114			0.503679			0.251840	−	0.967769i	$-0.418964\pi$
$139$	70.0114			0.503679			0.251840	+	0.967769i	$0.418964\pi$
$140$	−47.0879	−	73.2701i	−0.336342	−	0.523358i
$141$		0			0
$142$	−11.0489	+	24.1938i	−0.0778093	+	0.170379i
$143$	2.51545	+	8.56685i	0.0175906	+	0.0599080i
$144$		0			0
$145$	−158.958	−	183.447i	−1.09626	−	1.26515i
$146$	165.410	−	23.7824i	1.13295	−	0.162893i
$147$		0			0
$148$	−63.7561	+	73.5785i	−0.430785	+	0.497152i
$149$	68.1741	−	106.081i	0.457544	−	0.711952i	−0.533454	−	0.845829i	$-0.679106\pi$
$149$	68.1741	−	106.081i	0.457544	−	0.711952i	0.990998	+	0.133877i	$0.0427426\pi$
$150$		0			0
$151$	39.7451	−	45.8683i	0.263213	−	0.303764i	−0.608724	−	0.793382i	$-0.708318\pi$
$151$	39.7451	−	45.8683i	0.263213	−	0.303764i	0.871937	+	0.489618i	$0.162864\pi$
$152$	24.8499	−	84.6310i	0.163486	−	0.556783i
$153$		0			0
$154$	51.5832	+	59.5302i	0.334956	+	0.386560i
$155$	25.6694	−	11.7228i	0.165609	−	0.0756311i
$156$		0			0
$157$	−125.328	+	274.430i	−0.798267	+	1.74796i	−0.146966	+	0.989141i	$0.546951\pi$
$157$	−125.328	+	274.430i	−0.798267	+	1.74796i	−0.651301	+	0.758820i	$0.725776\pi$
$158$	85.1798	+	12.2470i	0.539113	+	0.0775127i
$159$		0			0
$160$	25.5099			0.159437
$161$	174.974	−	136.806i	1.08680	−	0.849729i
$162$		0			0
$163$	251.945	−	161.915i	1.54568	−	0.993346i	0.559277	−	0.828981i	$-0.311079\pi$
$163$	251.945	−	161.915i	1.54568	−	0.993346i	0.986400	−	0.164365i	$-0.0525575\pi$
$164$	22.9457	+	3.29909i	0.139913	+	0.0201164i
$165$		0			0
$166$	199.988	−	58.7219i	1.20475	−	0.353747i
$167$	49.1133	−	22.4293i	0.294092	−	0.134307i	−0.262905	−	0.964822i	$-0.584681\pi$
$167$	49.1133	−	22.4293i	0.294092	−	0.134307i	0.556997	+	0.830514i	$0.311953\pi$
$168$		0			0
$169$	23.7102	+	164.908i	0.140297	+	0.975786i
$170$	−10.7236	+	36.5214i	−0.0630803	+	0.214832i
$171$		0			0
$172$	−125.016	−	80.3432i	−0.726840	−	0.467111i
$173$	26.7887	−	41.6841i	0.154848	−	0.240948i	−0.755158	−	0.655542i	$-0.772440\pi$
$173$	26.7887	−	41.6841i	0.154848	−	0.240948i	0.910006	+	0.414594i	$0.136076\pi$
$174$		0			0
$175$	43.2142	+	12.6888i	0.246938	+	0.0725076i
$176$	−22.8363	+	3.28336i	−0.129752	+	0.0186554i
$177$		0			0
$178$	30.5263	+	66.8433i	0.171496	+	0.375524i
$179$	59.3751	+	202.213i	0.331704	+	1.12968i	0.941469	+	0.337099i	$0.109446\pi$
$179$	59.3751	+	202.213i	0.331704	+	1.12968i	−0.609765	+	0.792582i	$0.708736\pi$
$180$		0			0
$181$	8.29341	−	57.6819i	0.0458199	−	0.318685i	−0.954002	−	0.299801i	$-0.903080\pi$
$181$	8.29341	−	57.6819i	0.0458199	−	0.318685i	0.999822	−	0.0188836i	$-0.00601119\pi$
$182$	−11.4296	−	17.7848i	−0.0628000	−	0.0977187i
$183$		0			0
$184$	6.00157	+	64.7764i	0.0326172	+	0.352046i
$185$			219.521i			1.18660i
$186$		0			0
$187$	4.89909	−	34.0739i	0.0261983	−	0.182213i
$188$	41.1772	+	18.8050i	0.219028	+	0.100027i
$189$		0			0
$190$	−82.6178	−	180.908i	−0.434831	−	0.952147i
$191$	−207.860	+	180.112i	−1.08827	+	0.942995i	−0.998596	−	0.0529761i	$-0.983129\pi$
$191$	−207.860	+	180.112i	−1.08827	+	0.942995i	−0.0896781	+	0.995971i	$0.528584\pi$
$192$		0			0
$193$	−35.8504	−	10.5266i	−0.185753	−	0.0545421i	0.187533	−	0.982258i	$-0.439951\pi$
$193$	−35.8504	−	10.5266i	−0.185753	−	0.0545421i	−0.373286	+	0.927716i	$0.621769\pi$
$194$	−30.1074	−	26.0883i	−0.155193	−	0.134476i
$195$		0			0
$196$	−74.4594	−	47.8522i	−0.379895	−	0.244144i
$197$	−87.3909	−	75.7246i	−0.443609	−	0.384389i	0.404218	−	0.914663i	$-0.367544\pi$
$197$	−87.3909	−	75.7246i	−0.443609	−	0.384389i	−0.847827	+	0.530274i	$0.822089\pi$
$198$		0			0
$199$	−35.5648	−	247.359i	−0.178718	−	1.24301i	−0.859734	−	0.510742i	$-0.829371\pi$
$199$	−35.5648	−	247.359i	−0.178718	−	1.24301i	0.681016	−	0.732268i	$-0.261538\pi$
$200$	−9.96945	+	8.63858i	−0.0498473	+	0.0431929i
$201$		0			0
$202$	42.0433	−	12.3450i	0.208135	−	0.0611141i
$203$	−472.825	−	215.932i	−2.32919	−	1.06370i
$204$		0			0
$205$	43.9719	−	28.2590i	0.214497	−	0.137849i
$206$			57.4316i			0.278794i
$207$		0			0
$208$	6.19200			0.0297692
$209$	97.2433	+	151.314i	0.465279	+	0.723988i
$210$		0			0
$211$	12.8943	−	28.2346i	0.0611105	−	0.133813i	−0.876613	−	0.481196i	$-0.840202\pi$
$211$	12.8943	−	28.2346i	0.0611105	−	0.133813i	0.937723	+	0.347383i	$0.112930\pi$
$212$	−15.6850	−	53.4182i	−0.0739858	−	0.251972i
$213$		0			0
$214$	132.961	+	153.445i	0.621314	+	0.717035i
$215$	−331.666	+	47.6864i	−1.54263	+	0.221797i
$216$		0			0
$217$	39.5732	−	45.6699i	0.182365	−	0.210460i
$218$	23.3895	−	36.3947i	0.107291	−	0.166948i
$219$		0			0
$220$	−34.0660	+	39.3143i	−0.154845	+	0.178701i
$221$	−2.60294	+	8.86481i	−0.0117780	+	0.0401123i
$222$		0			0
$223$	17.1679	+	19.8128i	0.0769859	+	0.0888465i	0.792936	−	0.609305i	$-0.208552\pi$
$223$	17.1679	+	19.8128i	0.0769859	+	0.0888465i	−0.715950	+	0.698152i	$0.754006\pi$
$224$	49.6909	−	22.6931i	0.221834	−	0.101308i
$225$		0			0
$226$	−37.2492	+	81.5644i	−0.164819	+	0.360904i
$227$	32.0720	+	4.61126i	0.141286	+	0.0203139i	0.212595	−	0.977140i	$-0.431808\pi$
$227$	32.0720	+	4.61126i	0.141286	+	0.0203139i	−0.0713087	+	0.997454i	$0.522718\pi$
$228$		0			0
$229$	185.018			0.807939			0.403969	−	0.914772i	$-0.367630\pi$
$229$	185.018			0.807939			0.403969	+	0.914772i	$0.367630\pi$
$230$	105.874	+	101.520i	0.460320	+	0.441393i
$231$		0			0
$232$	128.077	−	82.3100i	0.552055	−	0.354784i
$233$	43.4083	+	6.24117i	0.186302	+	0.0267862i	0.234834	−	0.972035i	$-0.424545\pi$
$233$	43.4083	+	6.24117i	0.186302	+	0.0267862i	−0.0485323	+	0.998822i	$0.515454\pi$
$234$		0			0
$235$	97.9348	−	28.7563i	0.416744	−	0.122367i
$236$	45.2381	−	20.6595i	0.191687	−	0.0875404i
$237$		0			0
$238$	11.6000	+	80.6798i	0.0487395	+	0.338991i
$239$	27.9584	−	95.2176i	0.116981	−	0.398400i	−0.880097	−	0.474794i	$-0.842523\pi$
$239$	27.9584	−	95.2176i	0.116981	−	0.398400i	0.997078	+	0.0763942i	$0.0243407\pi$
$240$		0			0
$241$	−355.106	−	228.213i	−1.47347	−	0.946941i	−0.997729	−	0.0673554i	$-0.978544\pi$
$241$	−355.106	−	228.213i	−1.47347	−	0.946941i	−0.475740	−	0.879586i	$-0.657820\pi$
$242$	−67.0789	+	104.377i	−0.277185	+	0.431309i
$243$		0			0
$244$	−73.6397	−	21.6226i	−0.301802	−	0.0886171i
$245$	−197.539	+	28.4019i	−0.806283	+	0.115926i
$246$		0			0
$247$	−20.0538	−	43.9116i	−0.0811893	−	0.177780i
$248$	4.98653	+	16.9825i	0.0201070	+	0.0684780i
$249$		0			0
$250$	−26.9232	+	187.255i	−0.107693	+	0.749021i
$251$	−102.370	−	159.290i	−0.407848	−	0.634623i	0.575192	−	0.818019i	$-0.304928\pi$
$251$	−102.370	−	159.290i	−0.407848	−	0.634623i	−0.983039	+	0.183395i	$0.941291\pi$
$252$		0			0
$253$	−107.844	−	77.2533i	−0.426260	−	0.305349i
$254$		−	238.446i		−	0.938764i
$255$		0			0
$256$	−2.27704	+	15.8371i	−0.00889468	+	0.0618638i
$257$	−238.931	−	109.116i	−0.929694	−	0.424577i	−0.107771	−	0.994176i	$-0.534371\pi$
$257$	−238.931	−	109.116i	−0.929694	−	0.424577i	−0.821923	+	0.569599i	$0.807099\pi$
$258$		0			0
$259$	195.282	+	427.607i	0.753983	+	1.65099i
$260$	10.5515	−	9.14290i	0.0405826	−	0.0351650i
$261$		0			0
$262$	319.671	+	93.8639i	1.22012	+	0.358259i
$263$	86.3420	+	74.8158i	0.328297	+	0.284471i	0.803376	−	0.595472i	$-0.203035\pi$
$263$	86.3420	+	74.8158i	0.328297	+	0.284471i	−0.475079	+	0.879943i	$0.657581\pi$
$264$		0			0
$265$	−105.603	−	67.8672i	−0.398504	−	0.256103i
$266$	−321.864	−	278.896i	−1.21001	−	1.04848i
$267$		0			0
$268$	13.5717	+	94.3931i	0.0506406	+	0.352213i
$269$	−125.833	+	109.035i	−0.467779	+	0.405333i	−0.856601	−	0.515980i	$-0.827428\pi$
$269$	−125.833	+	109.035i	−0.467779	+	0.405333i	0.388821	+	0.921313i	$0.372882\pi$
$270$		0			0
$271$	−25.4716	+	7.47913i	−0.0939911	+	0.0275983i	−0.328390	−	0.944542i	$-0.606506\pi$
$271$	−25.4716	+	7.47913i	−0.0939911	+	0.0275983i	0.234399	+	0.972141i	$0.424688\pi$
$272$	−21.7161	−	9.91742i	−0.0798387	−	0.0364611i
$273$		0			0
$274$	−133.852	+	86.0211i	−0.488509	+	0.313946i
$275$		−	26.9003i		−	0.0978192i
$276$		0			0
$277$	−245.267			−0.885442			−0.442721	−	0.896659i	$-0.645987\pi$
$277$	−245.267			−0.885442			−0.442721	+	0.896659i	$0.645987\pi$
$278$	53.5294	+	83.2934i	0.192552	+	0.299617i
$279$		0			0
$280$	51.1679	−	112.042i	0.182742	−	0.400150i
$281$	30.2245	+	102.935i	0.107561	+	0.366318i	0.995629	−	0.0933930i	$-0.0297713\pi$
$281$	30.2245	+	102.935i	0.107561	+	0.366318i	−0.888069	+	0.459711i	$0.847953\pi$
$282$		0			0
$283$	22.0181	+	25.4102i	0.0778025	+	0.0897889i	0.793316	−	0.608810i	$-0.208353\pi$
$283$	22.0181	+	25.4102i	0.0778025	+	0.0897889i	−0.715514	+	0.698599i	$0.753807\pi$
$284$	−37.2314	+	5.35307i	−0.131096	+	0.0188488i
$285$		0			0
$286$	−8.26881	+	9.54272i	−0.0289119	+	0.0333661i
$287$	60.5144	−	94.1623i	0.210852	−	0.328092i
$288$		0			0
$289$	−165.928	+	191.491i	−0.574144	+	0.662597i
$290$	96.7129	−	329.374i	0.333493	−	1.13577i
$291$		0			0
$292$	154.764	+	178.607i	0.530013	+	0.611668i
$293$	−498.072	+	227.462i	−1.69991	+	0.776321i	−0.701963	+	0.712213i	$0.747693\pi$
$293$	−498.072	+	227.462i	−1.69991	+	0.776321i	−0.997943	+	0.0641075i	$0.979580\pi$
$294$		0			0
$295$	46.5827	−	102.002i	0.157907	−	0.345769i
$296$	−136.284	−	19.5947i	−0.460419	−	0.0661982i
$297$		0			0
$298$	178.330			0.598424
$299$	25.6986	+	24.6420i	0.0859485	+	0.0824146i
$300$		0			0
$301$	−603.633	+	387.932i	−2.00543	+	1.28881i
$302$	84.9585	+	12.2152i	0.281320	+	0.0404476i
$303$		0			0
$304$	119.686	−	35.1431i	0.393705	−	0.115602i
$305$	−157.413	+	71.8880i	−0.516107	+	0.235698i
$306$		0			0
$307$	−49.0675	−	341.272i	−0.159829	−	1.11163i	−0.898947	−	0.438058i	$-0.855666\pi$
$307$	−49.0675	−	341.272i	−0.159829	−	1.11163i	0.739118	−	0.673576i	$-0.235243\pi$
$308$	−31.3842	+	106.885i	−0.101897	+	0.347029i
$309$		0			0
$310$	33.5731	+	21.5761i	0.108300	+	0.0696005i
$311$	−36.4048	+	56.6470i	−0.117057	+	0.182145i	−0.894838	−	0.446391i	$-0.852709\pi$
$311$	−36.4048	+	56.6470i	−0.117057	+	0.182145i	0.777781	+	0.628536i	$0.216345\pi$
$312$		0			0
$313$	494.960	+	145.333i	1.58134	+	0.464324i	0.950277	−	0.311407i	$-0.100800\pi$
$313$	494.960	+	145.333i	1.58134	+	0.464324i	0.631064	+	0.775731i	$0.282618\pi$
$314$	−422.316	+	60.7199i	−1.34496	+	0.193375i
$315$		0			0
$316$	50.5565	+	110.703i	0.159989	+	0.350327i
$317$	100.324	+	341.672i	0.316479	+	1.07783i	0.952090	+	0.305819i	$0.0989301\pi$
$317$	100.324	+	341.672i	0.316479	+	1.07783i	−0.635611	+	0.772010i	$0.719252\pi$
$318$		0			0
$319$	−44.1832	+	307.301i	−0.138505	+	0.963325i
$320$	19.5044	+	30.3494i	0.0609513	+	0.0948420i
$321$		0			0
$322$	296.542	+	103.569i	0.920938	+	0.321644i
$323$			186.123i			0.576231i
$324$		0			0
$325$	−1.02747	+	7.14622i	−0.00316145	+	0.0219884i
$326$	385.265	+	175.945i	1.18180	+	0.539708i
$327$		0			0
$328$	13.6189	+	29.8212i	0.0415209	+	0.0909182i
$329$	165.187	−	143.135i	0.502088	−	0.435061i
$330$		0			0
$331$	481.605	+	141.412i	1.45500	+	0.427227i	0.911192	−	0.411982i	$-0.135163\pi$
$331$	481.605	+	141.412i	1.45500	+	0.427227i	0.543809	+	0.839209i	$0.316982\pi$
$332$	222.770	+	193.031i	0.670993	+	0.581419i
$333$		0			0
$334$	64.2355	+	41.2817i	0.192322	+	0.123598i
$335$	162.504	+	140.811i	0.485088	+	0.420331i
$336$		0			0
$337$	−91.4659	−	636.159i	−0.271412	−	1.88771i	−0.433837	−	0.900992i	$-0.642840\pi$
$337$	−91.4659	−	636.159i	−0.271412	−	1.88771i	0.162424	−	0.986721i	$-0.448069\pi$
$338$	−178.065	+	154.294i	−0.526818	+	0.456491i
$339$		0			0
$340$	−51.6490	+	15.1655i	−0.151909	+	0.0446045i
$341$	−32.8314	−	14.9936i	−0.0962799	−	0.0439696i
$342$		0			0
$343$	38.5473	−	24.7728i	0.112383	−	0.0722240i
$344$		−	210.162i		−	0.610937i
$345$		0			0
$346$	70.0742			0.202527
$347$	30.2517	+	47.0725i	0.0871807	+	0.135656i	0.882105	−	0.471053i	$-0.156126\pi$
$347$	30.2517	+	47.0725i	0.0871807	+	0.135656i	−0.794924	+	0.606709i	$0.792490\pi$
$348$		0			0
$349$	−181.640	+	397.736i	−0.520458	+	1.13964i	0.448808	+	0.893628i	$0.351849\pi$
$349$	−181.640	+	397.736i	−0.520458	+	1.13964i	−0.969266	+	0.246015i	$0.920879\pi$
$350$	17.9447	+	61.1141i	0.0512706	+	0.174612i
$351$		0			0
$352$	−21.3664	−	24.6582i	−0.0607001	−	0.0700517i
$353$	−601.922	+	86.5434i	−1.70516	+	0.245165i	−0.924879	−	0.380261i	$-0.875834\pi$
$353$	−601.922	+	86.5434i	−1.70516	+	0.245165i	−0.780283	+	0.625426i	$0.784925\pi$
$354$		0			0
$355$	−55.5399	+	64.0965i	−0.156451	+	0.180554i
$356$	−56.1844	+	87.4247i	−0.157821	+	0.245575i
$357$		0			0
$358$	−195.178	+	225.248i	−0.545190	+	0.629183i
$359$	81.0782	−	276.127i	0.225845	−	0.769156i	−0.766126	−	0.642690i	$-0.777818\pi$
$359$	81.0782	−	276.127i	0.225845	−	0.769156i	0.991971	−	0.126466i	$-0.0403635\pi$
$360$		0			0
$361$	−400.441	−	462.134i	−1.10926	−	1.28015i
$362$	74.9659	−	34.2358i	0.207088	−	0.0945739i
$363$		0			0
$364$	12.4199	−	27.1959i	0.0341207	−	0.0747139i
$365$	527.450	+	75.8359i	1.44507	+	0.207770i
$366$		0			0
$367$	−135.215			−0.368433			−0.184216	−	0.982886i	$-0.558975\pi$
$367$	−135.215			−0.368433			−0.184216	+	0.982886i	$0.558975\pi$
$368$	−72.4766	+	56.6670i	−0.196947	+	0.153986i
$369$		0			0
$370$	−261.167	+	167.842i	−0.705858	+	0.453627i
$371$	−266.079	−	38.2564i	−0.717193	−	0.103117i
$372$		0			0
$373$	443.281	−	130.159i	1.18842	−	0.348952i	0.373006	−	0.927829i	$-0.378327\pi$
$373$	443.281	−	130.159i	1.18842	−	0.348952i	0.815415	+	0.578877i	$0.196509\pi$
$374$	44.2839	−	20.2238i	0.118406	−	0.0540742i
$375$		0			0
$376$	9.11080	+	63.3670i	0.0242309	+	0.168529i
$377$	23.4751	−	79.9487i	0.0622680	−	0.212065i
$378$		0			0
$379$	−110.123	−	70.7718i	−0.290562	−	0.186733i	0.387237	−	0.921980i	$-0.373430\pi$
$379$	−110.123	−	70.7718i	−0.290562	−	0.186733i	−0.677799	+	0.735247i	$0.737066\pi$
$380$	152.060	−	236.610i	0.400158	−	0.622659i
$381$		0			0
$382$	−373.208	−	109.584i	−0.976983	−	0.286868i
$383$	−210.212	+	30.2239i	−0.548856	+	0.0789135i	−0.411164	−	0.911562i	$-0.634878\pi$
$383$	−210.212	+	30.2239i	−0.548856	+	0.0789135i	−0.137692	+	0.990475i	$0.543968\pi$
$384$		0			0
$385$	104.342	+	228.478i	0.271019	+	0.593449i
$386$	−14.8869	−	50.7001i	−0.0385671	−	0.131347i
$387$		0			0
$388$	8.01791	−	55.7658i	0.0206647	−	0.143726i
$389$	−135.649	−	211.073i	−0.348711	−	0.542605i	0.621950	−	0.783057i	$-0.286341\pi$
$389$	−135.649	−	211.073i	−0.348711	−	0.542605i	−0.970661	+	0.240452i	$0.922704\pi$
$390$		0			0
$391$	−50.6605	−	127.583i	−0.129566	−	0.326298i
$392$		−	125.172i		−	0.319317i
$393$		0			0
$394$	23.2731	−	161.868i	0.0590687	−	0.410832i
$395$	249.611	+	113.994i	0.631928	+	0.288592i
$396$		0			0
$397$	161.184	+	352.944i	0.406005	+	0.889027i	0.996626	+	0.0820778i	$0.0261556\pi$
$397$	161.184	+	352.944i	0.406005	+	0.889027i	−0.590621	+	0.806949i	$0.701117\pi$
$398$	267.094	−	231.438i	0.671090	−	0.581503i
$399$		0			0
$400$	−17.8999	−	5.25588i	−0.0447497	−	0.0131397i
$401$	442.801	+	383.689i	1.10424	+	0.956831i	0.999291	−	0.0376470i	$-0.0119862\pi$
$401$	442.801	+	383.689i	1.10424	+	0.956831i	0.104950	+	0.994477i	$0.466532\pi$
$402$		0			0
$403$	8.14918	+	5.23716i	0.0202213	+	0.0129954i
$404$	46.8326	+	40.5807i	0.115922	+	0.100447i
$405$		0			0
$406$	−104.616	−	727.623i	−0.257676	−	1.79218i
$407$	212.192	−	183.865i	0.521356	−	0.451758i
$408$		0			0
$409$	−191.360	+	56.1884i	−0.467873	+	0.137380i	−0.507167	−	0.861848i	$-0.669307\pi$
$409$	−191.360	+	56.1884i	−0.467873	+	0.137380i	0.0392940	+	0.999228i	$0.487489\pi$
$410$	67.2401	+	30.7075i	0.164000	+	0.0748964i
$411$		0			0
$412$	−68.3271	+	43.9111i	−0.165842	+	0.106580i
$413$		−	240.129i		−	0.581426i
$414$		0			0
$415$	664.633			1.60153
$416$	4.73429	+	7.36670i	0.0113805	+	0.0177084i
$417$		0			0
$418$	−105.669	+	231.383i	−0.252797	+	0.553548i
$419$	−181.900	−	619.494i	−0.434129	−	1.47851i	−0.828727	−	0.559653i	$-0.810934\pi$
$419$	−181.900	−	619.494i	−0.434129	−	1.47851i	0.394598	−	0.918854i	$-0.370884\pi$
$420$		0			0
$421$	−48.0644	−	55.4692i	−0.114167	−	0.131756i	0.695789	−	0.718246i	$-0.255055\pi$
$421$	−48.0644	−	55.4692i	−0.114167	−	0.131756i	−0.809956	+	0.586490i	$0.800509\pi$
$422$	43.4498	−	6.24714i	0.102962	−	0.0148037i
$423$		0			0
$424$	51.5598	−	59.5032i	0.121603	−	0.140338i
$425$	15.0492	−	23.4170i	0.0354099	−	0.0550989i
$426$		0			0
$427$	−242.675	+	280.062i	−0.568326	+	0.655883i
$428$	−80.8962	+	275.507i	−0.189010	+	0.643709i
$429$		0			0
$430$	−310.319	−	358.127i	−0.721672	−	0.832853i
$431$	629.688	−	287.569i	1.46099	−	0.667213i	0.482956	−	0.875644i	$-0.339563\pi$
$431$	629.688	−	287.569i	1.46099	−	0.667213i	0.978037	+	0.208431i	$0.0668357\pi$
$432$		0			0
$433$	133.206	−	291.681i	0.307636	−	0.673628i	−0.691159	−	0.722702i	$-0.742900\pi$
$433$	133.206	−	291.681i	0.307636	−	0.673628i	0.998795	+	0.0490741i	$0.0156270\pi$
$434$	84.5910	+	12.1623i	0.194910	+	0.0280238i
$435$		0			0
$436$	61.1824			0.140327
$437$	636.590	+	330.455i	1.45673	+	0.756190i
$438$		0			0
$439$	−413.501	+	265.741i	−0.941915	+	0.605332i	−0.918937	−	0.394404i	$-0.870951\pi$
$439$	−413.501	+	265.741i	−0.941915	+	0.605332i	−0.0229777	+	0.999736i	$0.507315\pi$
$440$	−72.8189	−	10.4698i	−0.165497	−	0.0237949i
$441$		0			0
$442$	−12.5367	+	3.68112i	−0.0283636	+	0.00832832i
$443$	−692.264	+	316.146i	−1.56267	+	0.713649i	−0.994048	−	0.108947i	$-0.965252\pi$
$443$	−692.264	+	316.146i	−1.56267	+	0.713649i	−0.568626	+	0.822596i	$0.692525\pi$
$444$		0			0
$445$	33.3473	+	231.936i	0.0749379	+	0.521204i
$446$	−10.4453	+	35.5733i	−0.0234199	+	0.0797607i
$447$		0			0
$448$	64.9910	+	41.7672i	0.145069	+	0.0932303i
$449$	133.170	−	207.216i	0.296592	−	0.461506i	−0.660692	−	0.750657i	$-0.729737\pi$
$449$	133.170	−	207.216i	0.296592	−	0.461506i	0.957283	+	0.289152i	$0.0933733\pi$
$450$		0			0
$451$	−64.1452	−	18.8347i	−0.142229	−	0.0417621i
$452$	−125.518	+	18.0468i	−0.277695	+	0.0399265i
$453$		0			0
$454$	19.0356	+	41.6821i	0.0419286	+	0.0918109i
$455$	−18.9923	−	64.6819i	−0.0417414	−	0.142158i
$456$		0			0
$457$	−5.73492	+	39.8872i	−0.0125490	+	0.0872806i	−0.995133	−	0.0985362i	$-0.968584\pi$
$457$	−5.73492	+	39.8872i	−0.0125490	+	0.0872806i	0.982584	+	0.185817i	$0.0594931\pi$
$458$	141.461	+	220.118i	0.308868	+	0.480607i
$459$		0			0
$460$	−39.8310	+	203.580i	−0.0865892	+	0.442565i
$461$			193.021i			0.418701i	0.977841	+	0.209350i	$0.0671349\pi$
$461$			193.021i			0.418701i	−0.977841	+	0.209350i	$0.932865\pi$
$462$		0			0
$463$	62.6819	−	435.962i	0.135382	−	0.941604i	−0.802994	−	0.595987i	$-0.796761\pi$
$463$	62.6819	−	435.962i	0.135382	−	0.941604i	0.938376	−	0.345616i	$-0.112330\pi$
$464$	195.850	+	89.4418i	0.422091	+	0.192763i
$465$		0			0
$466$	25.7640	+	56.4153i	0.0552876	+	0.121063i
$467$	403.352	−	349.507i	0.863710	−	0.748409i	−0.105559	−	0.994413i	$-0.533663\pi$
$467$	403.352	−	349.507i	0.863710	−	0.748409i	0.969269	+	0.246004i	$0.0791177\pi$
$468$		0			0
$469$	441.806	+	129.726i	0.942016	+	0.276601i
$470$	109.091	+	94.5277i	0.232108	+	0.201123i
$471$		0			0
$472$	59.1671	+	38.0244i	0.125354	+	0.0805602i
$473$	323.889	+	280.651i	0.684755	+	0.593343i
$474$		0			0
$475$	20.6986	+	143.962i	0.0435760	+	0.303078i
$476$	−87.1166	+	75.4869i	−0.183018	+	0.158586i
$477$		0			0
$478$	134.658	−	39.5391i	0.281711	−	0.0827179i
$479$	−600.613	−	274.291i	−1.25389	−	0.572633i	−0.325959	−	0.945384i	$-0.605687\pi$
$479$	−600.613	−	274.291i	−1.25389	−	0.572633i	−0.927931	+	0.372751i	$0.878414\pi$
$480$		0			0
$481$	−63.3929	+	40.7402i	−0.131794	+	0.0846989i
$482$		−	596.961i		−	1.23851i
$483$		0			0
$484$	−175.466			−0.362532
$485$	−68.6790	−	106.867i	−0.141606	−	0.220343i
$486$		0			0
$487$	299.820	−	656.514i	0.615646	−	1.34808i	−0.302998	−	0.952991i	$-0.597987\pi$
$487$	299.820	−	656.514i	0.615646	−	1.34808i	0.918644	−	0.395086i	$-0.129285\pi$
$488$	−30.5789	−	104.142i	−0.0626617	−	0.213406i
$489$		0			0
$490$	−184.825	−	213.299i	−0.377194	−	0.435305i
$491$	548.605	−	78.8775i	1.11732	−	0.160647i	0.441180	−	0.897418i	$-0.354560\pi$
$491$	548.605	−	78.8775i	1.11732	−	0.160647i	0.676142	+	0.736772i	$0.263651\pi$
$492$		0			0
$493$	−210.380	+	242.791i	−0.426734	+	0.492477i
$494$	36.9094	−	57.4322i	0.0747155	−	0.116260i
$495$		0			0
$496$	−16.3917	+	18.9171i	−0.0330479	+	0.0381393i
$497$	−51.1677	+	174.261i	−0.102953	+	0.350626i
$498$		0			0
$499$	−437.810	−	505.260i	−0.877375	−	1.01254i	−0.999799	−	0.0200663i	$-0.993612\pi$
$499$	−437.810	−	505.260i	−0.877375	−	1.01254i	0.122424	−	0.992478i	$-0.460933\pi$
$500$	−243.365	+	111.141i	−0.486730	+	0.222282i
$501$		0			0
$502$	111.240	−	243.581i	0.221593	−	0.485221i
$503$	248.416	+	35.7168i	0.493868	+	0.0710075i	0.384749	−	0.923021i	$-0.374288\pi$
$503$	248.416	+	35.7168i	0.493868	+	0.0710075i	0.109119	+	0.994029i	$0.465197\pi$
$504$		0			0
$505$	139.725			0.276683
$506$	9.45385	−	187.370i	0.0186835	−	0.370295i
$507$		0			0
$508$	283.682	−	182.312i	0.558430	−	0.358881i
$509$	954.057	+	137.173i	1.87437	+	0.269494i	0.982977	−	0.183728i	$-0.0588166\pi$
$509$	954.057	+	137.173i	1.87437	+	0.269494i	0.891397	+	0.453222i	$0.149726\pi$
$510$		0			0
$511$	1094.89	−	321.487i	2.14263	−	0.629134i
$512$	−20.5826	+	9.39977i	−0.0402004	+	0.0183589i
$513$		0			0
$514$	−52.8655	−	367.688i	−0.102851	−	0.715346i
$515$	−51.5949	+	175.716i	−0.100184	+	0.341196i
$516$		0			0
$517$	−109.824	−	70.5795i	−0.212425	−	0.136517i
$518$	−359.421	+	559.269i	−0.693862	+	1.07967i
$519$		0			0
$520$	18.9449	+	5.56272i	0.0364324	+	0.0106975i
$521$	−816.142	+	117.343i	−1.56649	+	0.225227i	−0.870261	−	0.492591i	$-0.836050\pi$
$521$	−816.142	+	117.343i	−1.56649	+	0.225227i	−0.696230	+	0.717819i	$0.745141\pi$
$522$		0			0
$523$	−374.500	−	820.041i	−0.716062	−	1.56796i	−0.819342	−	0.573305i	$-0.805661\pi$
$523$	−374.500	−	820.041i	−0.716062	−	1.56796i	0.103280	−	0.994652i	$-0.467066\pi$
$524$	132.744	+	452.083i	0.253328	+	0.862754i
$525$		0			0
$526$	−22.9937	+	159.925i	−0.0437143	+	0.304040i
$527$	−20.1921	−	31.4195i	−0.0383152	−	0.0596196i
$528$		0			0
$529$	−526.313	−	53.2465i	−0.994921	−	0.100655i
$530$		−	177.528i		−	0.334958i
$531$		0			0
$532$	85.7155	−	596.164i	0.161119	−	1.12061i
$533$	16.3211	+	7.45362i	0.0306213	+	0.0139843i
$534$		0			0
$535$	268.954	+	588.926i	0.502717	+	1.10080i
$536$	−101.924	+	88.3176i	−0.190157	+	0.164772i
$537$		0			0
$538$	−225.929	−	66.3388i	−0.419943	−	0.123306i
$539$	192.907	+	167.155i	0.357899	+	0.310121i
$540$		0			0
$541$	−321.367	−	206.530i	−0.594025	−	0.381756i	0.208812	−	0.977956i	$-0.433040\pi$
$541$	−321.367	−	206.530i	−0.594025	−	0.381756i	−0.802836	+	0.596199i	$0.796677\pi$
$542$	−28.3731	−	24.5855i	−0.0523489	−	0.0453606i
$543$		0			0
$544$	−4.80487	−	33.4186i	−0.00883248	−	0.0614313i
$545$	104.258	−	90.3399i	0.191299	−	0.165761i
$546$		0			0
$547$	−764.887	+	224.591i	−1.39833	+	0.410587i	−0.892110	−	0.451818i	$-0.850776\pi$
$547$	−764.887	+	224.591i	−1.39833	+	0.410587i	−0.506220	+	0.862405i	$0.668958\pi$
$548$	−204.681	−	93.4746i	−0.373505	−	0.170574i
$549$		0			0
$550$	32.0036	−	20.5675i	0.0581883	−	0.0373954i
$551$		−	1678.58i		−	3.04642i
$552$		0			0
$553$	587.626			1.06262
$554$	−187.527	−	291.798i	−0.338496	−	0.526711i
$555$		0			0
$556$	−58.1676	+	127.369i	−0.104618	+	0.229081i
$557$	−135.110	−	460.141i	−0.242567	−	0.826106i	−0.987317	−	0.158763i	$-0.949249\pi$
$557$	−135.110	−	460.141i	−0.242567	−	0.826106i	0.744750	−	0.667344i	$-0.232569\pi$
$558$		0			0
$559$	−75.3234	−	86.9279i	−0.134747	−	0.155506i
$560$	172.420	−	24.7902i	0.307892	−	0.0442682i
$561$		0			0
$562$	−99.3542	+	114.661i	−0.176787	+	0.204023i
$563$	−68.3883	+	106.414i	−0.121471	+	0.189013i	−0.896664	−	0.442712i	$-0.854016\pi$
$563$	−68.3883	+	106.414i	−0.121471	+	0.189013i	0.775193	+	0.631725i	$0.217653\pi$
$564$		0			0
$565$	−187.242	+	216.088i	−0.331401	+	0.382457i
$566$	−13.3962	+	45.6234i	−0.0236683	+	0.0806067i
$567$		0			0
$568$	−34.8351	−	40.2018i	−0.0613293	−	0.0707778i
$569$	519.575	−	237.282i	0.913137	−	0.417016i	0.0972720	−	0.995258i	$-0.468988\pi$
$569$	519.575	−	237.282i	0.913137	−	0.417016i	0.815865	+	0.578242i	$0.196261\pi$
$570$		0			0
$571$	278.101	−	608.957i	0.487042	−	1.06647i	−0.493424	−	0.869789i	$-0.664255\pi$
$571$	278.101	−	608.957i	0.487042	−	1.06647i	0.980467	−	0.196685i	$-0.0630177\pi$
$572$	−17.6753	−	2.54132i	−0.0309008	−	0.00444287i
$573$		0			0
$574$	158.294			0.275774
$575$	−53.3732	−	93.0486i	−0.0928230	−	0.161824i
$576$		0			0
$577$	416.625	−	267.749i	0.722053	−	0.464036i	−0.127297	−	0.991865i	$-0.540630\pi$
$577$	416.625	−	267.749i	0.722053	−	0.464036i	0.849351	+	0.527829i	$0.176994\pi$
$578$	−354.684	−	50.9958i	−0.613640	−	0.0882281i
$579$		0			0
$580$	465.805	−	136.773i	0.803112	−	0.235815i
$581$	1294.64	−	591.244i	2.22830	−	1.01763i
$582$		0			0
$583$	22.8494	+	158.921i	0.0391929	+	0.272592i
$584$	−94.1613	+	320.684i	−0.161235	+	0.549117i
$585$		0			0
$586$	−651.431	−	418.650i	−1.11166	−	0.714419i
$587$	−397.056	+	617.831i	−0.676415	+	1.05252i	0.318113	+	0.948053i	$0.396951\pi$
$587$	−397.056	+	617.831i	−0.676415	+	1.05252i	−0.994528	+	0.104470i	$0.966685\pi$
$588$		0			0
$589$	187.241	+	54.9789i	0.317896	+	0.0933427i
$590$	156.969	−	22.5688i	0.266049	−	0.0382521i
$591$		0			0
$592$	−80.8882	−	177.120i	−0.136635	−	0.299190i
$593$	271.686	+	925.277i	0.458155	+	1.56033i	0.787618	+	0.616164i	$0.211314\pi$
$593$	271.686	+	925.277i	0.458155	+	1.56033i	−0.329463	+	0.944168i	$0.606868\pi$
$594$		0			0
$595$	−36.9894	+	257.267i	−0.0621670	+	0.432381i
$596$	136.348	+	212.162i	0.228772	+	0.355976i
$597$		0			0
$598$	−9.66816	+	49.4147i	−0.0161675	+	0.0826333i
$599$			64.3884i			0.107493i	0.998555	+	0.0537466i	$0.0171163\pi$
$599$			64.3884i			0.107493i	−0.998555	+	0.0537466i	$0.982884\pi$
$600$		0			0
$601$	113.820	−	791.635i	0.189384	−	1.31720i	−0.644222	−	0.764838i	$-0.722819\pi$
$601$	113.820	−	791.635i	0.189384	−	1.31720i	0.833607	−	0.552359i	$-0.186272\pi$
$602$	−923.054	−	421.545i	−1.53331	−	0.700240i
$603$		0			0
$604$	50.4251	+	110.416i	0.0834853	+	0.182807i
$605$	−299.002	+	259.087i	−0.494218	+	0.428242i
$606$		0			0
$607$	816.223	+	239.665i	1.34468	+	0.394835i	0.873339	−	0.487114i	$-0.161950\pi$
$607$	816.223	+	239.665i	1.34468	+	0.394835i	0.471346	+	0.881949i	$0.343768\pi$
$608$	133.320	+	115.523i	0.219276	+	0.190004i
$609$		0			0
$610$	−205.881	−	132.312i	−0.337510	−	0.216904i
$611$	26.4795	+	22.9446i	0.0433380	+	0.0375526i
$612$		0			0
$613$	6.83901	+	47.5664i	0.0111566	+	0.0775960i	0.994639	−	0.103407i	$-0.0329746\pi$
$613$	6.83901	+	47.5664i	0.0111566	+	0.0775960i	−0.983482	+	0.181003i	$0.942065\pi$
$614$	368.499	−	319.306i	0.600162	−	0.520043i
$615$		0			0
$616$	−151.158	+	44.3840i	−0.245386	+	0.0720519i
$617$	−591.746	−	270.241i	−0.959069	−	0.437992i	−0.126533	−	0.991962i	$-0.540385\pi$
$617$	−591.746	−	270.241i	−0.959069	−	0.437992i	−0.832537	+	0.553970i	$0.813112\pi$
$618$		0			0
$619$	282.315	−	181.433i	0.456082	−	0.293106i	−0.292358	−	0.956309i	$-0.594440\pi$
$619$	282.315	−	181.433i	0.456082	−	0.293106i	0.748440	+	0.663203i	$0.230803\pi$
$620$			56.4391i			0.0910308i
$621$		0			0
$622$	−95.2280			−0.153100
$623$	271.283	+	422.124i	0.435446	+	0.677567i
$624$		0			0
$625$	−202.162	+	442.673i	−0.323459	+	0.708277i
$626$	205.532	+	699.979i	0.328326	+	1.11818i
$627$		0			0
$628$	−395.134	−	456.009i	−0.629195	−	0.726129i
$629$	287.579	−	41.3476i	0.457200	−	0.0657354i
$630$		0			0
$631$	−611.444	+	705.643i	−0.969007	+	1.11829i	0.0239373	+	0.999713i	$0.492380\pi$
$631$	−611.444	+	705.643i	−0.969007	+	1.11829i	−0.992944	+	0.118580i	$0.962166\pi$
$632$	−93.0505	+	144.789i	−0.147232	+	0.229097i
$633$		0			0
$634$	−329.785	+	380.592i	−0.520166	+	0.600303i
$635$	214.213	−	729.543i	0.337344	−	1.14889i
$636$		0			0
$637$	−44.8624	−	51.7740i	−0.0704277	−	0.0812779i
$638$	−399.381	+	182.391i	−0.625989	+	0.285880i
$639$		0			0
$640$	−21.1944	+	46.4093i	−0.0331162	+	0.0725145i
$641$	−292.409	−	42.0420i	−0.456176	−	0.0655882i	−0.0896032	−	0.995978i	$-0.528560\pi$
$641$	−292.409	−	42.0420i	−0.456176	−	0.0655882i	−0.366573	+	0.930389i	$0.619469\pi$
$642$		0			0
$643$	612.302			0.952258			0.476129	−	0.879375i	$-0.342039\pi$
$643$	612.302			0.952258			0.476129	+	0.879375i	$0.342039\pi$
$644$	103.513	+	431.987i	0.160735	+	0.670787i
$645$		0			0
$646$	−221.432	+	142.306i	−0.342775	+	0.220288i
$647$	367.996	+	52.9099i	0.568774	+	0.0817773i	0.420701	−	0.907199i	$-0.361784\pi$
$647$	367.996	+	52.9099i	0.568774	+	0.0817773i	0.148072	+	0.988977i	$0.452693\pi$
$648$		0			0
$649$	−137.613	+	40.4067i	−0.212038	+	0.0622600i
$650$	−9.28753	+	4.24147i	−0.0142885	+	0.00652534i
$651$		0			0
$652$	85.2431	+	592.879i	0.130741	+	0.909324i
$653$	−281.851	+	959.897i	−0.431625	+	1.46998i	0.400966	+	0.916093i	$0.368675\pi$
$653$	−281.851	+	959.897i	−0.431625	+	1.46998i	−0.832591	+	0.553888i	$0.813144\pi$
$654$		0			0
$655$	893.732	+	574.367i	1.36448	+	0.876896i
$656$	−25.0659	+	39.0033i	−0.0382102	+	0.0594562i
$657$		0			0
$658$	296.589	+	87.0863i	0.450742	+	0.132350i
$659$	−385.796	+	55.4691i	−0.585427	+	0.0841716i	−0.428663	−	0.903464i	$-0.641015\pi$
$659$	−385.796	+	55.4691i	−0.585427	+	0.0841716i	−0.156764	+	0.987636i	$0.550106\pi$
$660$		0			0
$661$	358.040	+	783.999i	0.541665	+	1.18608i	0.960567	+	0.278049i	$0.0896878\pi$
$661$	358.040	+	783.999i	0.541665	+	1.18608i	−0.418902	+	0.908031i	$0.637585\pi$
$662$	199.987	+	681.093i	0.302095	+	1.02884i
$663$		0			0
$664$	−59.3258	+	412.620i	−0.0893460	+	0.621415i
$665$	−734.212	−	1142.46i	−1.10408	−	1.71798i
$666$		0			0
$667$	456.889	+	1150.62i	0.684992	+	1.72507i
$668$			107.985i			0.161654i
$669$		0			0
$670$	−43.2765	+	300.995i	−0.0645918	+	0.449246i
$671$	201.333	+	91.9455i	0.300049	+	0.137028i
$672$		0			0
$673$	351.976	+	770.720i	0.522995	+	1.14520i	0.968293	+	0.249818i	$0.0803707\pi$
$673$	351.976	+	770.720i	0.522995	+	1.14520i	−0.445297	+	0.895383i	$0.646902\pi$
$674$	686.913	−	595.214i	1.01916	−	0.883106i
$675$		0			0
$676$	−319.710	−	93.8754i	−0.472944	−	0.138869i
$677$	−590.509	−	511.679i	−0.872244	−	0.755803i	0.0986987	−	0.995117i	$-0.468532\pi$
$677$	−590.509	−	511.679i	−0.872244	−	0.755803i	−0.970942	+	0.239314i	$0.923077\pi$
$678$		0			0
$679$	−228.846	−	147.071i	−0.337034	−	0.216599i
$680$	−57.5325	−	49.8522i	−0.0846067	−	0.0733121i
$681$		0			0
$682$	−7.26423	−	50.5238i	−0.0106514	−	0.0740818i
$683$	−916.880	+	794.481i	−1.34243	+	1.16322i	−0.370265	+	0.928926i	$0.620733\pi$
$683$	−916.880	+	794.481i	−1.34243	+	1.16322i	−0.972165	+	0.234296i	$0.924721\pi$
$684$		0			0
$685$	−486.807	+	142.940i	−0.710668	+	0.208671i
$686$	58.9451	+	26.9193i	0.0859258	+	0.0392410i
$687$		0			0
$688$	250.033	−	160.686i	0.363420	−	0.233556i
$689$		−	43.0912i		−	0.0625416i
$690$		0			0
$691$	−321.261			−0.464921			−0.232461	−	0.972606i	$-0.574678\pi$
$691$	−321.261			−0.464921			−0.232461	+	0.972606i	$0.574678\pi$
$692$	53.5774	+	83.3681i	0.0774240	+	0.120474i
$693$		0			0
$694$	−32.8729	+	71.9816i	−0.0473673	+	0.103720i
$695$	88.9488	+	302.932i	0.127984	+	0.435873i
$696$		0			0
$697$	−45.3022	−	52.2815i	−0.0649960	−	0.0750094i
$698$	−612.069	+	88.0023i	−0.876890	+	0.126078i
$699$		0			0
$700$	−58.9880	+	68.0758i	−0.0842686	+	0.0972511i
$701$	177.279	−	275.852i	0.252894	−	0.393512i	−0.691474	−	0.722402i	$-0.743038\pi$
$701$	177.279	−	275.852i	0.252894	−	0.393512i	0.944368	+	0.328890i	$0.106675\pi$
$702$		0			0
$703$	−994.111	+	1147.26i	−1.41410	+	1.63196i
$704$	12.9998	−	44.2731i	0.0184656	−	0.0628879i
$705$		0			0
$706$	−563.180	−	649.945i	−0.797706	−	0.920602i
$707$	272.171	−	124.296i	0.384967	−	0.175808i
$708$		0			0
$709$	−174.212	+	381.470i	−0.245715	+	0.538040i	−0.991798	−	0.127812i	$-0.959205\pi$
$709$	−174.212	+	381.470i	−0.245715	+	0.538040i	0.746084	+	0.665852i	$0.231932\pi$
$710$	−118.721	−	17.0695i	−0.167213	−	0.0240416i
$711$		0			0
$712$	−146.968			−0.206415
$713$	−143.314	+	13.2781i	−0.201001	+	0.0186229i
$714$		0			0
$715$	−33.8719	+	21.7682i	−0.0473733	+	0.0304450i
$716$	−417.209	−	59.9857i	−0.582695	−	0.0837789i
$717$		0			0
$718$	390.503	−	114.662i	0.543875	−	0.159696i
$719$	−464.749	+	212.244i	−0.646383	+	0.295193i	−0.711502	−	0.702684i	$-0.751985\pi$
$719$	−464.749	+	212.244i	−0.646383	+	0.295193i	0.0651188	+	0.997878i	$0.479257\pi$
$720$		0			0
$721$	55.8113	+	388.176i	0.0774082	+	0.538386i
$722$	243.636	−	829.749i	0.337446	−	1.14924i
$723$		0			0
$724$	98.0482	+	63.0118i	0.135426	+	0.0870328i
$725$	−135.724	+	211.190i	−0.187205	+	0.291297i
$726$		0			0
$727$	−320.873	−	94.2167i	−0.441366	−	0.129597i	0.0534968	−	0.998568i	$-0.482963\pi$
$727$	−320.873	−	94.2167i	−0.441366	−	0.129597i	−0.494862	+	0.868971i	$0.664782\pi$
$728$	41.8513	−	6.01731i	0.0574881	−	0.00826553i
$729$		0			0
$730$	313.056	+	685.497i	0.428844	+	0.939036i
$731$	124.941	+	425.509i	0.170917	+	0.582091i
$732$		0			0
$733$	−71.7927	+	499.329i	−0.0979436	+	0.681213i	0.880401	+	0.474230i	$0.157274\pi$
$733$	−71.7927	+	499.329i	−0.0979436	+	0.681213i	−0.978345	+	0.206983i	$0.933636\pi$
$734$	−103.383	−	160.867i	−0.140848	−	0.219165i
$735$		0			0
$736$	−122.832	−	42.8997i	−0.166891	−	0.0582877i
$737$		−	275.018i		−	0.373159i
$738$		0			0
$739$	124.191	−	863.770i	0.168053	−	1.16884i	−0.714849	−	0.699279i	$-0.753504\pi$
$739$	124.191	−	863.770i	0.168053	−	1.16884i	0.882902	−	0.469557i	$-0.155587\pi$
$740$	−399.367	−	182.385i	−0.539686	−	0.246466i
$741$		0			0
$742$	−157.925	−	345.807i	−0.212837	−	0.466048i
$743$	−670.019	+	580.574i	−0.901775	+	0.781392i	−0.976434	−	0.215817i	$-0.930759\pi$
$743$	−670.019	+	580.574i	−0.901775	+	0.781392i	0.0746591	+	0.997209i	$0.476213\pi$
$744$		0			0
$745$	545.615	+	160.207i	0.732369	+	0.215043i
$746$	493.777	+	427.860i	0.661899	+	0.573539i
$747$		0			0
$748$	57.9191	+	37.2223i	0.0774319	+	0.0497625i
$749$	1047.79	+	907.917i	1.39892	+	1.21217i
$750$		0			0
$751$	−35.2068	−	244.869i	−0.0468799	−	0.326057i	−0.999743	−	0.0226573i	$-0.992787\pi$
$751$	−35.2068	−	244.869i	−0.0468799	−	0.326057i	0.952863	−	0.303400i	$-0.0981217\pi$
$752$	−68.4226	+	59.2885i	−0.0909874	+	0.0788411i
$753$		0			0
$754$	113.065	−	33.1987i	0.149953	−	0.0440302i
$755$	248.963	+	113.698i	0.329752	+	0.150593i
$756$		0			0
$757$	422.997	−	271.844i	0.558781	−	0.359107i	−0.230564	−	0.973057i	$-0.574057\pi$
$757$	422.997	−	271.844i	0.558781	−	0.359107i	0.789344	+	0.613951i	$0.210421\pi$
$758$		−	185.126i		−	0.244229i
$759$		0			0
$760$	397.761			0.523369
$761$	−700.275	−	1089.65i	−0.920204	−	1.43187i	−0.901858	−	0.432033i	$-0.857796\pi$
$761$	−700.275	−	1089.65i	−0.920204	−	1.43187i	−0.0183462	−	0.999832i	$-0.505840\pi$
$762$		0			0
$763$	122.720	−	268.719i	0.160839	−	0.352187i
$764$	−154.975	−	527.795i	−0.202846	−	0.690831i
$765$		0			0
$766$	−196.682	−	226.983i	−0.256765	−	0.296322i
$767$	38.1010	−	5.47810i	0.0496754	−	0.00714224i
$768$		0			0
$769$	−135.714	+	156.622i	−0.176481	+	0.203670i	−0.837098	−	0.547054i	$-0.815749\pi$
$769$	−135.714	+	156.622i	−0.176481	+	0.203670i	0.660617	+	0.750723i	$0.270295\pi$
$770$	−192.045	+	298.827i	−0.249409	+	0.388087i
$771$		0			0
$772$	48.9363	−	56.4755i	0.0633890	−	0.0731548i
$773$	191.434	−	651.966i	0.247651	−	0.843423i	−0.738025	−	0.674773i	$-0.764241\pi$
$773$	191.434	−	651.966i	0.247651	−	0.843423i	0.985676	−	0.168649i	$-0.0539405\pi$
$774$		0			0
$775$	−19.1123	−	22.0568i	−0.0246611	−	0.0284604i
$776$	72.4756	−	33.0985i	0.0933964	−	0.0426527i
$777$		0			0
$778$	147.402	−	322.766i	0.189463	−	0.414866i
$779$	357.778	+	51.4407i	0.459278	+	0.0660343i
$780$		0			0
$781$	108.475			0.138893
$782$	113.053	−	157.819i	0.144569	−	0.201814i
$783$		0			0
$784$	148.919	−	95.7044i	0.189948	−	0.122072i
$785$	−1346.66	−	193.620i	−1.71548	−	0.246649i
$786$		0			0
$787$	−981.395	+	288.164i	−1.24701	+	0.366154i	−0.837644	−	0.546217i	$-0.816067\pi$
$787$	−981.395	+	288.164i	−1.24701	+	0.366154i	−0.409364	+	0.912371i	$0.634249\pi$
$788$	210.370	−	96.0728i	0.266967	−	0.121920i
$789$		0			0
$790$	55.2286	+	384.123i	0.0699096	+	0.486232i
$791$	−172.502	+	587.486i	−0.218080	+	0.742713i
$792$		0			0
$793$	−49.9733	−	32.1159i	−0.0630180	−	0.0404992i
$794$	−296.663	+	461.617i	−0.373631	+	0.581381i
$795$		0			0
$796$	479.560	+	140.811i	0.602462	+	0.176899i
$797$	−1158.85	+	166.617i	−1.45401	+	0.209055i	−0.823584	−	0.567195i	$-0.808029\pi$
$797$	−1158.85	+	166.617i	−1.45401	+	0.209055i	−0.630426	+	0.776250i	$0.717120\pi$
$798$		0			0
$799$	−56.1177	−	122.881i	−0.0702350	−	0.153793i
$800$	−7.43294	−	25.3143i	−0.00929117	−	0.0316428i
$801$		0			0
$802$	−117.922	+	820.167i	−0.147035	+	1.02265i
$803$	−368.475	−	573.358i	−0.458873	−	0.714020i
$804$		0			0
$805$	814.249	+	583.283i	1.01149	+	0.724575i
$806$			13.6994i			0.0169968i
$807$		0			0
$808$	−12.4720	+	86.7446i	−0.0154356	+	0.107357i
$809$	−481.676	−	219.974i	−0.595396	−	0.271908i	0.0948398	−	0.995493i	$-0.469766\pi$
$809$	−481.676	−	219.974i	−0.595396	−	0.271908i	−0.690236	+	0.723584i	$0.742493\pi$
$810$		0			0
$811$	−397.309	−	869.985i	−0.489900	−	1.07273i	−0.979622	−	0.200852i	$-0.935629\pi$
$811$	−397.309	−	869.985i	−0.489900	−	1.07273i	0.489722	−	0.871879i	$-0.337098\pi$
$812$	785.675	−	680.791i	0.967579	−	0.838412i
$813$		0			0
$814$	380.985	+	111.867i	0.468041	+	0.137429i
$815$	1020.68	+	884.427i	1.25237	+	1.08519i
$816$		0			0
$817$	−1949.31	−	1252.74i	−2.38593	−	1.53334i
$818$	−213.158	−	184.703i	−0.260585	−	0.225798i
$819$		0			0
$820$	14.8774	+	103.475i	0.0181432	+	0.126189i
$821$	433.506	−	375.635i	0.528022	−	0.457533i	−0.349592	−	0.936902i	$-0.613680\pi$
$821$	433.506	−	375.635i	0.528022	−	0.457533i	0.877614	+	0.479369i	$0.159134\pi$
$822$		0			0
$823$	−822.140	+	241.402i	−0.998955	+	0.293320i	−0.740027	−	0.672577i	$-0.765187\pi$
$823$	−822.140	+	241.402i	−0.998955	+	0.293320i	−0.258928	+	0.965897i	$0.583369\pi$
$824$	−104.483	−	47.7159i	−0.126800	−	0.0579076i
$825$		0			0
$826$	285.684	−	183.598i	0.345865	−	0.222274i
$827$			578.015i			0.698930i	0.936949	+	0.349465i	$0.113637\pi$
$827$			578.015i			0.698930i	−0.936949	+	0.349465i	$0.886363\pi$
$828$		0			0
$829$	1258.20			1.51773			0.758867	−	0.651246i	$-0.225753\pi$
$829$	1258.20			1.51773			0.758867	+	0.651246i	$0.225753\pi$
$830$	508.166	+	790.722i	0.612249	+	0.952678i
$831$		0			0
$832$	−5.14450	+	11.2649i	−0.00618329	+	0.0135395i
$833$	74.4143	+	253.432i	0.0893329	+	0.304240i
$834$		0			0
$835$	159.447	+	184.012i	0.190955	+	0.220373i
$836$	−356.072	+	51.1954i	−0.425923	+	0.0612385i
$837$		0			0
$838$	597.943	−	690.063i	0.713535	−	0.823464i
$839$	−207.702	+	323.191i	−0.247559	+	0.385210i	−0.942688	−	0.333676i	$-0.891711\pi$
$839$	−207.702	+	323.191i	−0.247559	+	0.385210i	0.695129	+	0.718885i	$0.255347\pi$
$840$		0			0
$841$	1346.61	−	1554.07i	1.60120	−	1.84788i
$842$	29.2433	−	99.5935i	0.0347307	−	0.118282i
$843$		0			0
$844$	40.6532	+	46.9163i	0.0481673	+	0.0555881i
$845$	−683.415	+	312.105i	−0.808775	+	0.369355i
$846$		0			0
$847$	−351.949	+	770.662i	−0.415525	+	0.909872i
$848$	110.213	+	15.8463i	0.129969	+	0.0186867i
$849$		0			0
$850$	39.3659			0.0463128
$851$	369.167	−	1057.01i	0.433804	−	1.24208i
$852$		0			0
$853$	−497.314	+	319.604i	−0.583018	+	0.374683i	−0.798653	−	0.601791i	$-0.794454\pi$
$853$	−497.314	+	319.604i	−0.583018	+	0.374683i	0.215636	+	0.976474i	$0.430818\pi$
$854$	−518.738	−	74.5833i	−0.607422	−	0.0873341i
$855$		0			0
$856$	−389.626	+	114.405i	−0.455171	+	0.133650i
$857$	−958.814	+	437.876i	−1.11880	+	0.510940i	−0.886975	−	0.461817i	$-0.847198\pi$
$857$	−958.814	+	437.876i	−1.11880	+	0.510940i	−0.231828	+	0.972757i	$0.574471\pi$
$858$		0			0
$859$	95.9253	+	667.175i	0.111671	+	0.776689i	0.966294	+	0.257440i	$0.0828790\pi$
$859$	95.9253	+	667.175i	0.111671	+	0.776689i	−0.854623	+	0.519248i	$0.826212\pi$
$860$	188.804	−	643.007i	0.219539	−	0.747683i
$861$		0			0
$862$	823.572	+	529.278i	0.955420	+	0.614011i
$863$	−738.797	+	1149.59i	−0.856079	+	1.33209i	0.0858616	+	0.996307i	$0.472636\pi$
$863$	−738.797	+	1149.59i	−0.856079	+	1.33209i	−0.941941	+	0.335778i	$0.891001\pi$
$864$		0			0
$865$	214.397	+	62.9526i	0.247858	+	0.0727776i
$866$	448.864	−	64.5368i	0.518318	−	0.0745229i
$867$		0			0
$868$	50.2070	+	109.938i	0.0578422	+	0.126657i
$869$	−98.8804	−	336.756i	−0.113786	−	0.387521i
$870$		0			0
$871$	−10.5045	+	73.0602i	−0.0120602	+	0.0838808i
$872$	46.7789	+	72.7894i	0.0536456	+	0.0834741i
$873$		0			0
$874$	93.5788	+	1010.02i	0.107070	+	1.15563i
$875$			1291.81i			1.47635i
$876$		0			0
$877$	208.566	−	1450.61i	0.237817	−	1.65405i	−0.424941	−	0.905221i	$-0.639705\pi$
$877$	208.566	−	1450.61i	0.237817	−	1.65405i	0.662758	−	0.748833i	$-0.269386\pi$
$878$	−632.310	−	288.766i	−0.720171	−	0.328891i
$879$		0			0
$880$	−43.2200	−	94.6385i	−0.0491136	−	0.107544i
$881$	−303.021	+	262.569i	−0.343951	+	0.298035i	−0.809656	−	0.586905i	$-0.800346\pi$
$881$	−303.021	+	262.569i	−0.343951	+	0.298035i	0.465705	+	0.884940i	$0.345801\pi$
$882$		0			0
$883$	1644.55	+	482.884i	1.86246	+	0.546868i	0.999106	+	0.0422689i	$0.0134586\pi$
$883$	1644.55	+	482.884i	1.86246	+	0.546868i	0.863354	+	0.504599i	$0.168360\pi$
$884$	−13.9648	−	12.1006i	−0.0157973	−	0.0136884i
$885$		0			0
$886$	−905.416	−	581.875i	−1.02191	−	0.656744i
$887$	57.7479	+	50.0388i	0.0651047	+	0.0564135i	0.686805	−	0.726841i	$-0.259012\pi$
$887$	57.7479	+	50.0388i	0.0651047	+	0.0564135i	−0.621701	+	0.783255i	$0.713558\pi$
$888$		0			0
$889$	−231.719	−	1611.64i	−0.260651	−	1.81287i
$890$	−250.440	+	217.008i	−0.281393	+	0.243829i
$891$		0			0
$892$	−50.3082	+	14.7718i	−0.0563994	+	0.0165603i
$893$	642.051	+	293.215i	0.718983	+	0.328348i
$894$		0			0
$895$	−799.518	+	513.819i	−0.893316	+	0.574099i
$896$			109.255i			0.121936i
$897$		0			0
$898$	348.346			0.387914
$899$	182.106	+	283.362i	0.202565	+	0.315197i
$900$		0			0
$901$	−69.0170	+	151.126i	−0.0766004	+	0.167732i
$902$	−26.6363	−	90.7150i	−0.0295303	−	0.100571i
$903$		0			0
$904$	−117.439	−	135.532i	−0.129911	−	0.149925i
$905$	260.120	−	37.3996i	0.287425	−	0.0413255i
$906$		0			0
$907$	−508.076	+	586.351i	−0.560172	+	0.646473i	−0.963223	−	0.268705i	$-0.913404\pi$
$907$	−508.076	+	586.351i	−0.560172	+	0.646473i	0.403051	+	0.915178i	$0.367950\pi$
$908$	−35.0355	+	54.5163i	−0.0385853	+	0.0600400i
$909$		0			0
$910$	62.4317	−	72.0500i	0.0686062	−	0.0791758i
$911$	374.596	−	1275.76i	0.411192	−	1.40039i	−0.450416	−	0.892819i	$-0.648724\pi$
$911$	374.596	−	1275.76i	0.411192	−	1.40039i	0.861608	−	0.507574i	$-0.169458\pi$
$912$		0			0
$913$	−556.680	−	642.443i	−0.609726	−	0.703661i
$914$	−51.8391	+	23.6741i	−0.0567168	+	0.0259017i
$915$		0			0
$916$	−153.719	+	336.597i	−0.167815	+	0.367464i
$917$	2251.85	+	323.767i	2.45567	+	0.353072i
$918$		0			0
$919$	1433.38			1.55972			0.779860	−	0.625954i	$-0.215290\pi$
$919$	1433.38			1.55972			0.779860	+	0.625954i	$0.215290\pi$
$920$	−272.655	+	108.266i	−0.296364	+	0.117680i
$921$		0			0
$922$	−229.639	+	147.580i	−0.249067	+	0.160065i
$923$	−28.8171	−	4.14327i	−0.0312211	−	0.00448892i
$924$		0			0
$925$	217.838	−	63.9629i	0.235500	−	0.0691491i
$926$	566.595	−	258.755i	0.611874	−	0.279433i
$927$		0			0
$928$	43.3335	+	301.391i	0.0466956	+	0.324775i
$929$	259.189	−	882.716i	0.278998	−	0.950179i	−0.694118	−	0.719861i	$-0.744205\pi$
$929$	259.189	−	882.716i	0.278998	−	0.950179i	0.973116	−	0.230318i	$-0.0739765\pi$
$930$		0			0
$931$	−1161.00	−	746.130i	−1.24705	−	0.801429i
$932$	−47.4193	+	73.7858i	−0.0508791	+	0.0791694i
$933$		0			0
$934$	724.208	+	212.647i	0.775384	+	0.227673i
$935$	153.658	−	22.0927i	0.164340	−	0.0236286i
$936$		0			0
$937$	−446.580	−	977.873i	−0.476606	−	1.04362i	−0.983383	−	0.181544i	$-0.941891\pi$
$937$	−446.580	−	977.873i	−0.476606	−	1.04362i	0.506777	−	0.862077i	$-0.330837\pi$
$938$	183.460	+	624.807i	0.195586	+	0.666106i
$939$		0			0
$940$	−29.0520	+	202.061i	−0.0309063	+	0.214958i
$941$	−743.701	−	1157.22i	−0.790331	−	1.22978i	−0.969290	−	0.245922i	$-0.920909\pi$
$941$	−743.701	−	1157.22i	−0.790331	−	1.22978i	0.178959	−	0.983857i	$-0.442727\pi$
$942$		0			0
$943$	−259.250	+	62.1216i	−0.274920	+	0.0658766i
$944$			99.4646i			0.105365i
$945$		0			0
$946$	−86.2549	+	599.916i	−0.0911785	+	0.634160i
$947$	263.543	+	120.356i	0.278293	+	0.127092i	0.549672	−	0.835380i	$-0.314753\pi$
$947$	263.543	+	120.356i	0.278293	+	0.127092i	−0.271380	+	0.962472i	$0.587480\pi$
$948$		0			0
$949$	75.9878	+	166.390i	0.0800714	+	0.175332i
$950$	−155.448	+	134.696i	−0.163629	+	0.141785i
$951$		0			0
$952$	−156.415	−	45.9277i	−0.164302	−	0.0482434i
$953$	−1056.69	−	915.624i	−1.10880	−	0.960781i	−0.109353	−	0.994003i	$-0.534878\pi$
$953$	−1056.69	−	915.624i	−1.10880	−	0.960781i	−0.999448	+	0.0332219i	$0.989423\pi$
$954$		0			0
$955$	−1043.41	−	670.558i	−1.09257	−	0.702155i
$956$	149.997	+	129.973i	0.156901	+	0.135955i
$957$		0			0
$958$	−132.891	−	924.275i	−0.138717	−	0.964796i
$959$	−821.099	+	711.486i	−0.856203	+	0.741904i
$960$		0			0
$961$	884.500	−	259.713i	0.920395	−	0.270252i
$962$	−96.9381	−	44.2702i	−0.100767	−	0.0460189i
$963$		0			0
$964$	710.212	−	456.426i	0.736735	−	0.473471i
$965$		−	168.495i		−	0.174606i
$966$		0			0
$967$	−1514.41			−1.56609			−0.783046	−	0.621964i	$-0.786335\pi$
$967$	−1514.41			−1.56609			−0.783046	+	0.621964i	$0.786335\pi$
$968$	−134.158	−	208.754i	−0.138593	−	0.215654i
$969$		0			0
$970$	74.6298	−	163.416i	0.0769379	−	0.168471i
$971$	−256.610	−	873.932i	−0.264274	−	0.900033i	−0.979552	−	0.201193i	$-0.935518\pi$
$971$	−256.610	−	873.932i	−0.264274	−	0.900033i	0.715278	−	0.698840i	$-0.246300\pi$
$972$		0			0
$973$	442.745	+	510.955i	0.455031	+	0.525134i
$974$	1010.30	−	145.259i	1.03727	−	0.149137i
$975$		0			0
$976$	100.519	−	116.005i	0.102991	−	0.118858i
$977$	164.424	−	255.848i	0.168295	−	0.261872i	−0.746854	−	0.664988i	$-0.768437\pi$
$977$	164.424	−	255.848i	0.168295	−	0.261872i	0.915149	+	0.403116i	$0.132073\pi$
$978$		0			0
$979$	196.261	−	226.497i	0.200471	−	0.231356i
$980$	112.451	−	382.973i	0.114746	−	0.390789i
$981$		0			0
$982$	513.295	+	592.374i	0.522704	+	0.603232i
$983$	914.985	−	417.860i	0.930809	−	0.425086i	0.108480	−	0.994099i	$-0.465402\pi$
$983$	914.985	−	417.860i	0.930809	−	0.425086i	0.822329	+	0.569012i	$0.192674\pi$
$984$		0			0
$985$	216.623	−	474.338i	0.219922	−	0.481561i
$986$	−449.704	−	64.6577i	−0.456090	−	0.0655758i
$987$		0			0
$988$	96.5481			0.0977207
$989$	1677.18	+	328.147i	1.69584	+	0.331796i
$990$		0			0
$991$	−331.020	+	212.733i	−0.334026	+	0.214665i	−0.696892	−	0.717176i	$-0.745434\pi$
$991$	−331.020	+	212.733i	−0.334026	+	0.214665i	0.362867	+	0.931841i	$0.381798\pi$
$992$	−35.0387	−	5.03780i	−0.0353213	−	0.00507843i
$993$		0			0
$994$	−246.442	+	72.3620i	−0.247930	+	0.0727988i
$995$	1025.11	−	468.152i	1.03026	−	0.470504i
$996$		0			0
$997$	−107.640	−	748.650i	−0.107963	−	0.750903i	−0.969833	−	0.243772i	$-0.921615\pi$
$997$	−107.640	−	748.650i	−0.107963	−	0.750903i	0.861869	−	0.507131i	$-0.169294\pi$
$998$	266.372	−	907.180i	0.266906	−	0.908998i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.a.35.7	yes	80
3.2	odd	2	inner	414.3.k.a.35.2	✓	80
23.2	even	11	inner	414.3.k.a.71.2	yes	80
69.2	odd	22	inner	414.3.k.a.71.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.35.2	✓	80	3.2	odd	2	inner
414.3.k.a.35.7	yes	80	1.1	even	1	trivial
414.3.k.a.71.2	yes	80	23.2	even	11	inner
414.3.k.a.71.7	yes	80	69.2	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(1.27049 + 4.32689i) q^{5} +(6.32390 + 7.29817i) q^{7} +(-2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(1.27049 + 4.32689i) q^{5} +(6.32390 + 7.29817i) q^{7} +(-2.79964 + 0.402527i) q^{8} +(-4.17636 + 4.81978i) q^{10} +(3.11829 - 4.85216i) q^{11} +(-1.01372 + 1.16990i) q^{13} +(-3.84759 + 13.1037i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(5.42903 - 2.47936i) q^{17} +(-12.9546 + 28.3667i) q^{19} +(-8.92731 - 1.28355i) q^{20} +8.15686 q^{22} +(1.15901 - 22.9708i) q^{23} +(3.92352 - 2.52149i) q^{25} +(-2.16692 - 0.311556i) q^{26} +(-18.5314 + 5.44131i) q^{28} +(-48.9626 + 22.3605i) q^{29} +(-0.890566 - 6.19402i) q^{31} +(1.59372 - 5.42771i) q^{32} +(7.10066 + 4.56331i) q^{34} +(-23.5439 + 36.6351i) q^{35} +(46.7073 + 13.7145i) q^{37} +(-43.6531 + 6.27636i) q^{38} +(-5.29860 - 11.6023i) q^{40} +(-3.26551 - 11.1213i) q^{41} +(-10.5745 + 73.5473i) q^{43} +(6.23659 + 9.70432i) q^{44} +(28.2148 - 16.1842i) q^{46} -22.6340i q^{47} +(-6.29815 + 43.8046i) q^{49} +(5.99969 + 2.73997i) q^{50} +(-1.28612 - 2.81622i) q^{52} +(-21.0375 + 18.2291i) q^{53} +(24.9565 + 7.32789i) q^{55} +(-20.6423 - 17.8867i) q^{56} +(-64.0384 - 41.1550i) q^{58} +(-18.7926 - 16.2839i) q^{59} +(5.46123 + 37.9837i) q^{61} +(6.68820 - 5.79535i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-6.34995 - 2.89993i) q^{65} +(40.1125 - 25.7788i) q^{67} +11.9368i q^{68} -61.5864 q^{70} +(10.1679 + 15.8216i) q^{71} +(49.0877 - 107.487i) q^{73} +(19.3952 + 66.0541i) q^{74} +(-40.8434 - 47.1358i) q^{76} +(55.1317 - 7.92674i) q^{77} +(39.8487 - 45.9878i) q^{79} +(9.75220 - 15.1747i) q^{80} +(10.7344 - 12.3882i) q^{82} +(41.5227 - 141.413i) q^{83} +(17.6254 + 20.3408i) q^{85} +(-95.5852 + 43.6523i) q^{86} +(-6.77697 + 14.8395i) q^{88} +(51.4321 + 7.39482i) q^{89} -14.9488 q^{91} +(40.8270 + 21.1933i) q^{92} +(26.9279 - 17.3055i) q^{94} +(-139.198 - 20.0137i) q^{95} +(-27.0286 + 7.93630i) q^{97} +(-56.9303 + 25.9992i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 - 16 * q^7	\( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more