LMFDB - Embedded newform 675.2.ba.b.443.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.1
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.b.32.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.237511 - 2.71476i) q^{2} +(-0.914466 - 1.47097i) q^{3} +(-5.34392 + 0.942278i) q^{4} +(-3.77614 + 2.83193i) q^{6} +(-0.907744 - 1.29639i) q^{7} +(2.41667 + 9.01913i) q^{8} +(-1.32750 + 2.69030i) q^{9} +(0.162954 + 0.447712i) q^{11} +(6.27290 + 6.99907i) q^{12} +(-2.76700 - 0.242081i) q^{13} +(-3.30380 + 2.77222i) q^{14} +(13.7126 - 4.99098i) q^{16} +(-0.898665 + 3.35386i) q^{17} +(7.61884 + 2.96488i) q^{18} +(1.97319 + 1.13922i) q^{19} +(-1.07685 + 2.52077i) q^{21} +(1.17673 - 0.548719i) q^{22} +(0.329603 + 0.230790i) q^{23} +(11.0569 - 11.8025i) q^{24} +7.56924i q^{26} +(5.17131 - 0.507474i) q^{27} +(6.07248 + 6.07248i) q^{28} +(-4.29568 - 3.60450i) q^{29} +(0.908475 + 5.15222i) q^{31} +(-8.91403 - 19.1162i) q^{32} +(0.509556 - 0.649118i) q^{33} +(9.31839 + 1.64308i) q^{34} +(4.55906 - 15.6276i) q^{36} +(-1.44483 - 0.387140i) q^{37} +(2.62407 - 5.62733i) q^{38} +(2.17423 + 4.29154i) q^{39} +(-4.99389 - 5.95149i) q^{41} +(7.09907 + 2.32469i) q^{42} +(1.07467 + 0.501128i) q^{43} +(-1.29268 - 2.23899i) q^{44} +(0.548257 - 0.949609i) q^{46} +(-9.92230 + 6.94767i) q^{47} +(-19.8813 - 15.6068i) q^{48} +(1.53751 - 4.22426i) q^{49} +(5.75523 - 1.74508i) q^{51} +(15.0147 - 1.31362i) q^{52} +(-0.274270 + 0.274270i) q^{53} +(-2.60592 - 13.9184i) q^{54} +(9.49862 - 11.3200i) q^{56} +(-0.128655 - 3.94428i) q^{57} +(-8.76510 + 12.5179i) q^{58} +(3.33385 + 1.21342i) q^{59} +(-1.59716 + 9.05792i) q^{61} +(13.7713 - 3.69001i) q^{62} +(4.69272 - 0.721141i) q^{63} +(-24.5036 + 14.1471i) q^{64} +(-1.88323 - 1.22915i) q^{66} +(-1.15101 + 13.1561i) q^{67} +(1.64212 - 18.7696i) q^{68} +(0.0380751 - 0.695886i) q^{69} +(-13.8198 + 7.97886i) q^{71} +(-27.4723 - 5.47136i) q^{72} +(7.73957 - 2.07381i) q^{73} +(-0.707832 + 4.01431i) q^{74} +(-11.6180 - 4.22862i) q^{76} +(0.432491 - 0.617661i) q^{77} +(11.1341 - 6.92182i) q^{78} +(2.85683 - 3.40464i) q^{79} +(-5.47547 - 7.14278i) q^{81} +(-14.9708 + 14.9708i) q^{82} +(2.90211 - 0.253902i) q^{83} +(3.37935 - 14.4855i) q^{84} +(1.10520 - 3.03651i) q^{86} +(-1.37386 + 9.61501i) q^{87} +(-3.64417 + 2.55168i) q^{88} +(-3.50126 + 6.06435i) q^{89} +(2.19789 + 3.80686i) q^{91} +(-1.97884 - 0.922748i) q^{92} +(6.74799 - 6.04787i) q^{93} +(21.2179 + 25.2866i) q^{94} +(-19.9678 + 30.5934i) q^{96} +(3.19969 - 6.86175i) q^{97} +(-11.8331 - 3.17066i) q^{98} +(-1.42080 - 0.155944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.237511	−	2.71476i	−0.167946	−	1.91963i	−0.350732	−	0.936476i	$-0.614067\pi$
$2$	−0.237511	−	2.71476i	−0.167946	−	1.91963i	0.182786	−	0.983153i	$-0.441488\pi$
$3$	−0.914466	−	1.47097i	−0.527967	−	0.849265i
$3$	−0.914466	−	1.47097i	−0.527967	−	0.849265i
$4$	−5.34392	+	0.942278i	−2.67196	+	0.471139i
$5$		0			0
$5$		0			0
$6$	−3.77614	+	2.83193i	−1.54160	+	1.15613i
$7$	−0.907744	−	1.29639i	−0.343095	−	0.489990i	0.610109	−	0.792317i	$-0.291126\pi$
$7$	−0.907744	−	1.29639i	−0.343095	−	0.489990i	−0.953204	+	0.302327i	$0.902237\pi$
$8$	2.41667	+	9.01913i	0.854422	+	3.18874i
$9$	−1.32750	+	2.69030i	−0.442501	+	0.896768i
$10$		0			0
$11$	0.162954	+	0.447712i	0.0491325	+	0.134990i	0.961832	−	0.273642i	$-0.0882282\pi$
$11$	0.162954	+	0.447712i	0.0491325	+	0.134990i	−0.912699	+	0.408632i	$0.866006\pi$
$12$	6.27290	+	6.99907i	1.81083	+	2.02046i
$13$	−2.76700	−	0.242081i	−0.767427	−	0.0671411i	−0.303282	−	0.952901i	$-0.598083\pi$
$13$	−2.76700	−	0.242081i	−0.767427	−	0.0671411i	−0.464144	+	0.885760i	$0.653638\pi$
$14$	−3.30380	+	2.77222i	−0.882978	+	0.740907i
$15$		0			0
$16$	13.7126	−	4.99098i	3.42815	−	1.24775i
$17$	−0.898665	+	3.35386i	−0.217958	+	0.813431i	0.767146	+	0.641473i	$0.221676\pi$
$17$	−0.898665	+	3.35386i	−0.217958	+	0.813431i	−0.985104	+	0.171959i	$0.944990\pi$
$18$	7.61884	+	2.96488i	1.79578	+	0.698830i
$19$	1.97319	+	1.13922i	0.452681	+	0.261356i	0.708962	−	0.705247i	$-0.249164\pi$
$19$	1.97319	+	1.13922i	0.452681	+	0.261356i	−0.256281	+	0.966602i	$0.582497\pi$
$20$		0			0
$21$	−1.07685	+	2.52077i	−0.234989	+	0.550077i
$22$	1.17673	−	0.548719i	0.250880	−	0.116987i
$23$	0.329603	+	0.230790i	0.0687269	+	0.0481231i	0.607435	−	0.794369i	$-0.292199\pi$
$23$	0.329603	+	0.230790i	0.0687269	+	0.0481231i	−0.538708	+	0.842493i	$0.681087\pi$
$24$	11.0569	−	11.8025i	2.25698	−	2.40918i
$25$		0			0
$26$			7.56924i			1.48445i
$27$	5.17131	−	0.507474i	0.995220	−	0.0976633i
$28$	6.07248	+	6.07248i	1.14759	+	1.14759i
$29$	−4.29568	−	3.60450i	−0.797687	−	0.669339i	0.149948	−	0.988694i	$-0.452089\pi$
$29$	−4.29568	−	3.60450i	−0.797687	−	0.669339i	−0.947635	+	0.319355i	$0.896534\pi$
$30$		0			0
$31$	0.908475	+	5.15222i	0.163167	+	0.925366i	0.950934	+	0.309393i	$0.100126\pi$
$31$	0.908475	+	5.15222i	0.163167	+	0.925366i	−0.787767	+	0.615973i	$0.788763\pi$
$32$	−8.91403	−	19.1162i	−1.57579	−	3.37930i
$33$	0.509556	−	0.649118i	0.0887022	−	0.112997i
$34$	9.31839	+	1.64308i	1.59809	+	0.281787i
$35$		0			0
$36$	4.55906	−	15.6276i	0.759844	−	2.60461i
$37$	−1.44483	−	0.387140i	−0.237528	−	0.0636454i	0.138091	−	0.990420i	$-0.455903\pi$
$37$	−1.44483	−	0.387140i	−0.237528	−	0.0636454i	−0.375619	+	0.926774i	$0.622570\pi$
$38$	2.62407	−	5.62733i	0.425680	−	0.912873i
$39$	2.17423	+	4.29154i	0.348156	+	0.687197i
$40$		0			0
$41$	−4.99389	−	5.95149i	−0.779915	−	0.929467i	0.219015	−	0.975722i	$-0.429716\pi$
$41$	−4.99389	−	5.95149i	−0.779915	−	0.929467i	−0.998930	+	0.0462550i	$0.985271\pi$
$42$	7.09907	+	2.32469i	1.09541	+	0.358708i
$43$	1.07467	+	0.501128i	0.163886	+	0.0764213i	0.502830	−	0.864385i	$-0.332292\pi$
$43$	1.07467	+	0.501128i	0.163886	+	0.0764213i	−0.338944	+	0.940806i	$0.610070\pi$
$44$	−1.29268	−	2.23899i	−0.194879	−	0.337541i
$45$		0			0
$46$	0.548257	−	0.949609i	0.0808361	−	0.140012i
$47$	−9.92230	+	6.94767i	−1.44732	+	1.01342i	−0.454894	+	0.890546i	$0.650323\pi$
$47$	−9.92230	+	6.94767i	−1.44732	+	1.01342i	−0.992422	+	0.122876i	$0.960788\pi$
$48$	−19.8813	−	15.6068i	−2.86962	−	2.25264i
$49$	1.53751	−	4.22426i	0.219644	−	0.603466i
$50$		0			0
$51$	5.75523	−	1.74508i	0.805893	−	0.244361i
$52$	15.0147	−	1.31362i	2.08217	−	0.182166i
$53$	−0.274270	+	0.274270i	−0.0376738	+	0.0376738i	−0.725693	−	0.688019i	$-0.758481\pi$
$53$	−0.274270	+	0.274270i	−0.0376738	+	0.0376738i	0.688019	+	0.725693i	$0.258481\pi$
$54$	−2.60592	−	13.9184i	−0.354620	−	1.89405i
$55$		0			0
$56$	9.49862	−	11.3200i	1.26931	−	1.51270i
$57$	−0.128655	−	3.94428i	−0.0170407	−	0.522433i
$58$	−8.76510	+	12.5179i	−1.15091	+	1.64368i
$59$	3.33385	+	1.21342i	0.434031	+	0.157974i	0.549790	−	0.835303i	$-0.314708\pi$
$59$	3.33385	+	1.21342i	0.434031	+	0.157974i	−0.115759	+	0.993277i	$0.536930\pi$
$60$		0			0
$61$	−1.59716	+	9.05792i	−0.204495	+	1.15975i	0.693738	+	0.720228i	$0.255963\pi$
$61$	−1.59716	+	9.05792i	−0.204495	+	1.15975i	−0.898233	+	0.439520i	$0.855149\pi$
$62$	13.7713	−	3.69001i	1.74896	−	0.468631i
$63$	4.69272	−	0.721141i	0.591228	−	0.0908552i
$64$	−24.5036	+	14.1471i	−3.06294	+	1.76839i
$65$		0			0
$66$	−1.88323	−	1.22915i	−0.231809	−	0.151298i
$67$	−1.15101	+	13.1561i	−0.140618	+	1.60727i	0.518394	+	0.855142i	$0.326530\pi$
$67$	−1.15101	+	13.1561i	−0.140618	+	1.60727i	−0.659012	+	0.752132i	$0.729025\pi$
$68$	1.64212	−	18.7696i	0.199137	−	2.27614i
$69$	0.0380751	−	0.695886i	0.00458370	−	0.0837748i
$70$		0			0
$71$	−13.8198	+	7.97886i	−1.64011	+	0.946916i	−0.659313	+	0.751869i	$0.729153\pi$
$71$	−13.8198	+	7.97886i	−1.64011	+	0.946916i	−0.980794	+	0.195047i	$0.937514\pi$
$72$	−27.4723	−	5.47136i	−3.23765	−	0.644806i
$73$	7.73957	−	2.07381i	0.905849	−	0.242721i	0.224322	−	0.974515i	$-0.427983\pi$
$73$	7.73957	−	2.07381i	0.905849	−	0.242721i	0.681526	+	0.731794i	$0.261317\pi$
$74$	−0.707832	+	4.01431i	−0.0822838	+	0.466655i
$75$		0			0
$76$	−11.6180	−	4.22862i	−1.33268	−	0.485056i
$77$	0.432491	−	0.617661i	0.0492869	−	0.0703890i
$78$	11.1341	−	6.92182i	1.26069	−	0.783741i
$79$	2.85683	−	3.40464i	0.321418	−	0.383051i	−0.581006	−	0.813899i	$-0.697341\pi$
$79$	2.85683	−	3.40464i	0.321418	−	0.383051i	0.902425	+	0.430848i	$0.141785\pi$
$80$		0			0
$81$	−5.47547	−	7.14278i	−0.608385	−	0.793642i
$82$	−14.9708	+	14.9708i	−1.65325	+	1.65325i
$83$	2.90211	−	0.253902i	0.318548	−	0.0278694i	0.0732395	−	0.997314i	$-0.476666\pi$
$83$	2.90211	−	0.253902i	0.318548	−	0.0278694i	0.245309	+	0.969445i	$0.421111\pi$
$84$	3.37935	−	14.4855i	0.368718	−	1.58050i
$85$		0			0
$86$	1.10520	−	3.03651i	0.119177	−	0.327435i
$87$	−1.37386	+	9.61501i	−0.147293	+	1.03084i
$88$	−3.64417	+	2.55168i	−0.388470	+	0.272010i
$89$	−3.50126	+	6.06435i	−0.371132	+	0.642820i	−0.989740	−	0.142880i	$-0.954364\pi$
$89$	−3.50126	+	6.06435i	−0.371132	+	0.642820i	0.618608	+	0.785700i	$0.287697\pi$
$90$		0			0
$91$	2.19789	+	3.80686i	0.230402	+	0.399068i
$92$	−1.97884	−	0.922748i	−0.206308	−	0.0962031i
$93$	6.74799	−	6.04787i	0.699734	−	0.627135i
$94$	21.2179	+	25.2866i	2.18846	+	2.60811i
$95$		0			0
$96$	−19.9678	+	30.5934i	−2.03795	+	3.12242i
$97$	3.19969	−	6.86175i	0.324879	−	0.696705i	−0.674247	−	0.738506i	$-0.735532\pi$
$97$	3.19969	−	6.86175i	0.324879	−	0.696705i	0.999126	+	0.0418007i	$0.0133095\pi$
$98$	−11.8331	−	3.17066i	−1.19532	−	0.320285i
$99$	−1.42080	−	0.155944i	−0.142796	−	0.0156730i
$100$		0			0
$101$	5.72678	+	1.00979i	0.569836	+	0.100477i	0.451140	−	0.892453i	$-0.351017\pi$
$101$	5.72678	+	1.00979i	0.569836	+	0.100477i	0.118696	+	0.992931i	$0.462129\pi$
$102$	−6.10443	−	15.2096i	−0.604428	−	1.50598i
$103$	1.89098	+	4.05522i	0.186324	+	0.399573i	0.977175	−	0.212436i	$-0.0681395\pi$
$103$	1.89098	+	4.05522i	0.186324	+	0.399573i	−0.790851	+	0.612009i	$0.790362\pi$
$104$	−4.50356	−	25.5409i	−0.441610	−	2.50450i
$105$		0			0
$106$	0.809720	+	0.679435i	0.0786469	+	0.0659926i
$107$	0.577939	+	0.577939i	0.0558714	+	0.0558714i	0.734490	−	0.678619i	$-0.237421\pi$
$107$	0.577939	+	0.577939i	0.0558714	+	0.0558714i	−0.678619	+	0.734490i	$0.737421\pi$
$108$	−27.1569	+	7.58471i	−2.61317	+	0.729839i
$109$			8.45996i			0.810317i	0.914246	+	0.405159i	$0.132784\pi$
$109$			8.45996i			0.810317i	−0.914246	+	0.405159i	$0.867216\pi$
$110$		0			0
$111$	0.751773	+	2.47932i	0.0713552	+	0.235327i
$112$	−18.9178	−	13.2464i	−1.78757	−	1.25167i
$113$	−1.97616	+	0.921497i	−0.185901	+	0.0866871i	−0.513340	−	0.858185i	$-0.671592\pi$
$113$	−1.97616	+	0.921497i	−0.185901	+	0.0866871i	0.327439	+	0.944872i	$0.393814\pi$
$114$	−10.6772	+	1.28608i	−1.00002	+	0.120452i
$115$		0			0
$116$	26.3522	+	15.2145i	2.44674	+	1.41263i
$117$	4.32447	−	7.12270i	0.399797	−	0.658494i
$118$	2.50233	−	9.33883i	0.230358	−	0.859709i
$119$	5.16368	−	1.87943i	0.473354	−	0.172287i
$120$		0			0
$121$	8.25260	−	6.92475i	0.750236	−	0.629523i
$122$	24.9695	+	2.18454i	2.26063	+	0.197779i
$123$	−4.18772	+	12.7883i	−0.377594	+	1.15308i
$124$	−9.70964	−	26.6770i	−0.871952	−	2.39567i
$125$		0			0
$126$	−3.07230	−	12.5684i	−0.273702	−	1.11968i
$127$	−0.923874	−	3.44795i	−0.0819806	−	0.305956i	0.912745	−	0.408530i	$-0.133959\pi$
$127$	−0.923874	−	3.44795i	−0.0819806	−	0.305956i	−0.994725	+	0.102575i	$0.967292\pi$
$128$	20.0298	+	28.6056i	1.77040	+	2.52840i
$129$	−0.245607	−	2.03908i	−0.0216245	−	0.179531i
$130$		0			0
$131$	−3.02885	+	0.534068i	−0.264632	+	0.0466617i	−0.304390	−	0.952548i	$-0.598452\pi$
$131$	−3.02885	+	0.534068i	−0.264632	+	0.0466617i	0.0397579	+	0.999209i	$0.487341\pi$
$132$	−2.11138	+	3.94898i	−0.183772	+	0.343715i
$133$	−0.314273	−	3.59215i	−0.0272509	−	0.311479i
$134$	35.9891			3.10899
$135$		0			0
$136$	−32.4207			−2.78005
$137$	0.181036	+	2.06926i	0.0154670	+	0.176788i	0.999999	+	0.00158226i	$0.000503650\pi$
$137$	0.181036	+	2.06926i	0.0154670	+	0.176788i	−0.984532	+	0.175206i	$0.943941\pi$
$138$	−1.89821	+	0.0619158i	−0.161586	+	0.00527062i
$139$	−15.2015	+	2.68044i	−1.28938	+	0.227352i	−0.775957	−	0.630785i	$-0.782733\pi$
$139$	−15.2015	+	2.68044i	−1.28938	+	0.227352i	−0.513420	+	0.858137i	$0.671622\pi$
$140$		0			0
$141$	19.2934	+	8.24199i	1.62480	+	0.694101i
$142$	24.9431	+	35.6224i	2.09318	+	2.98937i
$143$	−0.342511	−	1.27827i	−0.0286422	−	0.106894i
$144$	−4.77629	+	43.5167i	−0.398024	+	3.62639i
$145$		0			0
$146$	−7.46815	−	20.5186i	−0.618068	−	1.69813i
$147$	−7.61976	+	1.60132i	−0.628467	+	0.132075i
$148$	8.08583	+	0.707419i	0.664651	+	0.0581495i
$149$	−12.0609	+	10.1203i	−0.988065	+	0.829085i	−0.985286	−	0.170911i	$-0.945329\pi$
$149$	−12.0609	+	10.1203i	−0.988065	+	0.829085i	−0.00277827	+	0.999996i	$0.500884\pi$
$150$		0			0
$151$	−1.00956	+	0.367451i	−0.0821571	+	0.0299027i	−0.382772	−	0.923843i	$-0.625030\pi$
$151$	−1.00956	+	0.367451i	−0.0821571	+	0.0299027i	0.300615	+	0.953746i	$0.402808\pi$
$152$	−5.50625	+	20.5496i	−0.446616	+	1.66679i
$153$	−7.82993	−	6.86995i	−0.633012	−	0.555402i
$154$	−1.77953	−	1.02741i	−0.143398	−	0.0827910i
$155$		0			0
$156$	−15.6627	−	20.8849i	−1.25402	−	1.67213i
$157$	15.6022	−	7.27543i	1.24519	−	0.580643i	0.315481	−	0.948932i	$-0.397834\pi$
$157$	15.6022	−	7.27543i	1.24519	−	0.580643i	0.929711	+	0.368289i	$0.120056\pi$
$158$	−9.92131	−	6.94698i	−0.789297	−	0.552672i
$159$	0.654253	+	0.152632i	0.0518856	+	0.0121045i
$160$		0			0
$161$		−	0.636793i		−	0.0501863i
$162$	−18.0905	+	16.5611i	−1.42132	+	1.30116i
$163$	−2.47310	−	2.47310i	−0.193708	−	0.193708i	0.603588	−	0.797296i	$-0.293737\pi$
$163$	−2.47310	−	2.47310i	−0.193708	−	0.193708i	−0.797296	+	0.603588i	$0.793737\pi$
$164$	32.2949	+	27.0987i	2.52181	+	2.11605i
$165$		0			0
$166$	−1.37857	−	7.81825i	−0.106998	−	0.606814i
$167$	−2.78431	−	5.97097i	−0.215456	−	0.462048i	0.768640	−	0.639681i	$-0.220934\pi$
$167$	−2.78431	−	5.97097i	−0.215456	−	0.462048i	−0.984097	+	0.177634i	$0.943156\pi$
$168$	−25.3376	−	3.62041i	−1.95484	−	0.279321i
$169$	−5.20483	−	0.917752i	−0.400372	−	0.0705963i
$170$		0			0
$171$	−5.68427	+	3.79616i	−0.434687	+	0.290300i
$172$	−6.21517	−	1.66535i	−0.473902	−	0.126982i
$173$	−4.51859	+	9.69016i	−0.343542	+	0.736729i	−0.999842	−	0.0177714i	$-0.994343\pi$
$173$	−4.51859	+	9.69016i	−0.343542	+	0.736729i	0.656300	+	0.754500i	$0.272121\pi$
$174$	26.4288	+	1.44604i	2.00356	+	0.109624i
$175$		0			0
$176$	4.46905	+	5.32601i	0.336867	+	0.401463i
$177$	−1.26379	−	6.01363i	−0.0949920	−	0.452012i
$178$	17.2949	+	8.06473i	1.29631	+	0.604477i
$179$	3.31311	+	5.73847i	0.247633	+	0.428913i	0.962869	−	0.269970i	$-0.0870139\pi$
$179$	3.31311	+	5.73847i	0.247633	+	0.428913i	−0.715235	+	0.698884i	$0.753681\pi$
$180$		0			0
$181$	−4.36897	+	7.56727i	−0.324743	+	0.562471i	−0.981460	−	0.191666i	$-0.938611\pi$
$181$	−4.36897	+	7.56727i	−0.324743	+	0.562471i	0.656717	+	0.754137i	$0.271944\pi$
$182$	9.81271	−	6.87094i	0.727367	−	0.509308i
$183$	14.7845	−	5.93379i	1.09290	−	0.438639i
$184$	−1.28499	+	3.53048i	−0.0947306	+	0.260270i
$185$		0			0
$186$	−18.0213	−	16.8828i	−1.32138	−	1.23790i
$187$	−1.64801	+	0.144182i	−0.120514	+	0.0105436i
$188$	46.4773	−	46.4773i	3.38971	−	3.38971i
$189$	−5.35211	−	6.24340i	−0.389309	−	0.454140i
$190$		0			0
$191$	−12.9658	+	15.4521i	−0.938176	+	1.11807i	0.0546500	+	0.998506i	$0.482596\pi$
$191$	−12.9658	+	15.4521i	−0.938176	+	1.11807i	−0.992826	+	0.119569i	$0.961849\pi$
$192$	43.2177	+	23.1069i	3.11897	+	1.66760i
$193$	−10.7709	+	15.3824i	−0.775303	+	1.10725i	0.216096	+	0.976372i	$0.430668\pi$
$193$	−10.7709	+	15.3824i	−0.775303	+	1.10725i	−0.991399	+	0.130875i	$0.958221\pi$
$194$	−19.3880	−	7.05665i	−1.39198	−	0.506638i
$195$		0			0
$196$	−4.23588	+	24.0229i	−0.302563	+	1.71592i
$197$	4.84019	−	1.29693i	0.344849	−	0.0924021i	−0.0822373	−	0.996613i	$-0.526207\pi$
$197$	4.84019	−	1.29693i	0.344849	−	0.0924021i	0.427087	+	0.904211i	$0.359540\pi$
$198$	−0.0858949	+	3.89419i	−0.00610428	+	0.276748i
$199$	14.4356	−	8.33443i	1.02332	−	0.590812i	0.108253	−	0.994123i	$-0.465474\pi$
$199$	14.4356	−	8.33443i	1.02332	−	0.590812i	0.915063	+	0.403312i	$0.132141\pi$
$200$		0			0
$201$	20.4048	−	10.3377i	1.43924	−	0.729166i
$202$	1.38116	−	15.7867i	0.0971779	−	1.11075i
$203$	−0.773474	+	8.84085i	−0.0542872	+	0.620506i
$204$	−29.1111	+	14.7486i	−2.03819	+	1.03261i
$205$		0			0
$206$	10.5599	−	6.09673i	0.735740	−	0.424779i
$207$	−1.05845	+	0.580357i	−0.0735670	+	0.0403376i
$208$	−39.1510	+	10.4905i	−2.71463	+	0.727384i
$209$	−0.188505	+	1.06906i	−0.0130391	+	0.0739486i
$210$		0			0
$211$	9.81899	+	3.57382i	0.675967	+	0.246032i	0.657115	−	0.753790i	$-0.271777\pi$
$211$	9.81899	+	3.57382i	0.675967	+	0.246032i	0.0188522	+	0.999822i	$0.493999\pi$
$212$	1.20724	−	1.72411i	0.0829134	−	0.118413i
$213$	24.3744	+	13.0321i	1.67010	+	0.892944i
$214$	1.43170	−	1.70623i	0.0978690	−	0.116636i
$215$		0			0
$216$	17.0743	+	45.4144i	1.16176	+	3.09006i
$217$	5.85464	−	5.85464i	0.397439	−	0.397439i
$218$	22.9668	−	2.00934i	1.55551	−	0.136089i
$219$	−10.1281	−	9.48825i	−0.684393	−	0.641156i
$220$		0			0
$221$	3.29851	−	9.06258i	0.221882	−	0.609615i
$222$	6.55222	−	2.62975i	0.439756	−	0.176498i
$223$	−19.2158	+	13.4550i	−1.28678	+	0.901015i	−0.998403	−	0.0565006i	$-0.982006\pi$
$223$	−19.2158	+	13.4550i	−1.28678	+	0.901015i	−0.288381	+	0.957516i	$0.593117\pi$
$224$	−16.6904	+	28.9087i	−1.11518	+	1.93154i
$225$		0			0
$226$	2.97101	+	5.14593i	0.197628	+	0.342302i
$227$	−18.1424	−	8.45994i	−1.20415	−	0.561506i	−0.286191	−	0.958173i	$-0.592389\pi$
$227$	−18.1424	−	8.45994i	−1.20415	−	0.561506i	−0.917963	+	0.396667i	$0.870167\pi$
$228$	4.40413	+	20.9567i	0.291671	+	1.38789i
$229$	−14.1827	−	16.9023i	−0.937218	−	1.11693i	−0.992955	−	0.118488i	$-0.962195\pi$
$229$	−14.1827	−	16.9023i	−0.937218	−	1.11693i	0.0557370	−	0.998445i	$-0.482249\pi$
$230$		0			0
$231$	−1.30406	−	0.0713510i	−0.0858007	−	0.00469455i
$232$	22.1282	−	47.4542i	1.45279	−	3.11552i
$233$	−18.0369	−	4.83296i	−1.18163	−	0.316618i	−0.386059	−	0.922474i	$-0.626164\pi$
$233$	−18.0369	−	4.83296i	−1.18163	−	0.316618i	−0.795574	+	0.605856i	$0.792831\pi$
$234$	−20.3636	−	10.0482i	−1.33121	−	0.656871i
$235$		0			0
$236$	−18.9592	−	3.34302i	−1.23414	−	0.217612i
$237$	−7.62059	−	1.08888i	−0.495010	−	0.0707306i
$238$	−6.32863	−	13.5718i	−0.410224	−	0.879729i
$239$	3.38846	+	19.2169i	0.219181	+	1.24304i	0.873502	+	0.486821i	$0.161844\pi$
$239$	3.38846	+	19.2169i	0.219181	+	1.24304i	−0.654320	+	0.756218i	$0.727045\pi$
$240$		0			0
$241$	−3.76991	−	3.16333i	−0.242841	−	0.203768i	0.513241	−	0.858244i	$-0.328445\pi$
$241$	−3.76991	−	3.16333i	−0.242841	−	0.203768i	−0.756082	+	0.654476i	$0.772889\pi$
$242$	−20.7592	−	20.7592i	−1.33445	−	1.33445i
$243$	−5.49968	+	14.5861i	−0.352805	+	0.935697i
$244$		−	49.9098i		−	3.19515i
$245$		0			0
$246$	35.7119	+	8.33130i	2.27690	+	0.531184i
$247$	−5.18403	−	3.62990i	−0.329852	−	0.230965i
$248$	−44.2731	+	20.6449i	−2.81134	+	1.31095i
$249$	−3.02737	−	4.03673i	−0.191851	−	0.255818i
$250$		0			0
$251$	−18.1080	−	10.4546i	−1.14297	−	0.659892i	−0.195803	−	0.980643i	$-0.562731\pi$
$251$	−18.1080	−	10.4546i	−1.14297	−	0.659892i	−0.947163	+	0.320752i	$0.896065\pi$
$252$	−24.3980	+	8.27557i	−1.53693	+	0.521312i
$253$	−0.0496176	+	0.185175i	−0.00311943	+	0.0116419i
$254$	−9.14093	+	3.32703i	−0.573553	+	0.208756i
$255$		0			0
$256$	29.5507	−	24.7960i	1.84692	−	1.54975i
$257$	−14.5430	−	1.27235i	−0.907166	−	0.0793667i	−0.375986	−	0.926626i	$-0.622696\pi$
$257$	−14.5430	−	1.27235i	−0.907166	−	0.0793667i	−0.531180	+	0.847259i	$0.678251\pi$
$258$	−5.47728	+	1.15107i	−0.341000	+	0.0716625i
$259$	0.809647	+	2.22449i	0.0503090	+	0.138223i
$260$		0			0
$261$	15.3997	−	6.77169i	0.953219	−	0.419157i
$262$	2.16925	+	8.09576i	0.134017	+	0.500158i
$263$	−17.5612	−	25.0799i	−1.08287	−	1.54650i	−0.811801	−	0.583935i	$-0.801512\pi$
$263$	−17.5612	−	25.0799i	−1.08287	−	1.54650i	−0.271067	−	0.962561i	$-0.587376\pi$
$264$	7.08591	+	3.02704i	0.436108	+	0.186302i
$265$		0			0
$266$	−9.67721	+	1.70635i	−0.593348	+	0.104623i
$267$	12.1223	−	0.395404i	0.741870	−	0.0241983i
$268$	−6.24580	−	71.3898i	−0.381523	−	4.36083i
$269$	−23.6912			−1.44448			−0.722239	−	0.691643i	$-0.756887\pi$
$269$	−23.6912			−1.44448			−0.722239	+	0.691643i	$0.756887\pi$
$270$		0			0
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	4.41603	+	50.4755i	0.267761	+	3.06052i
$273$	3.58988	−	6.71428i	0.217269	−	0.406367i
$274$	5.57454	−	0.982943i	0.336771	−	0.0593817i
$275$		0			0
$276$	0.452247	+	3.75464i	0.0272221	+	0.226002i
$277$	−8.72217	−	12.4565i	−0.524064	−	0.748441i	0.466644	−	0.884445i	$-0.345463\pi$
$277$	−8.72217	−	12.4565i	−0.524064	−	0.748441i	−0.990708	+	0.136004i	$0.956574\pi$
$278$	10.8873	+	40.6320i	0.652977	+	2.43694i
$279$	−15.0670	−	4.39552i	−0.902040	−	0.263153i
$280$		0			0
$281$	−8.16607	−	22.4361i	−0.487147	−	1.33842i	−0.903253	−	0.429108i	$-0.858828\pi$
$281$	−8.16607	−	22.4361i	−0.487147	−	1.33842i	0.416106	−	0.909316i	$-0.363394\pi$
$282$	17.7927	−	54.3346i	1.05954	−	3.23558i
$283$	0.284217	+	0.0248657i	0.0168949	+	0.00147811i	0.0956001	−	0.995420i	$-0.469523\pi$
$283$	0.284217	+	0.0248657i	0.0168949	+	0.00147811i	−0.0787051	+	0.996898i	$0.525079\pi$
$284$	66.3335	−	55.6605i	3.93617	−	3.30284i
$285$		0			0
$286$	−3.38884	+	1.23344i	−0.200387	+	0.0729347i
$287$	−3.18229	+	11.8765i	−0.187845	+	0.701046i
$288$	63.2618	+	1.39538i	3.72774	+	0.0822234i
$289$	4.28164	+	2.47200i	0.251861	+	0.145412i
$290$		0			0
$291$	−13.0194	+	1.56820i	−0.763213	+	0.0919292i
$292$	−39.4056	+	18.3751i	−2.30604	+	1.07532i
$293$	12.7347	+	8.91694i	0.743969	+	0.520933i	0.883010	−	0.469354i	$-0.155513\pi$
$293$	12.7347	+	8.91694i	0.743969	+	0.520933i	−0.139041	+	0.990287i	$0.544402\pi$
$294$	6.15698	+	20.3055i	0.359083	+	1.18424i
$295$		0			0
$296$		−	13.9667i		−	0.811796i
$297$	1.06989	+	2.23257i	0.0620812	+	0.129547i
$298$	30.3387	+	30.3387i	1.75748	+	1.75748i
$299$	−0.856140	−	0.718387i	−0.0495119	−	0.0415454i
$300$		0			0
$301$	−0.325869	−	1.84809i	−0.0187828	−	0.106522i
$302$	1.23733	+	2.65345i	0.0712001	+	0.152689i
$303$	−3.75158	−	9.34734i	−0.215523	−	0.536990i
$304$	32.7435	+	5.77355i	1.87797	+	0.331136i
$305$		0			0
$306$	−16.7906	+	22.8881i	−0.959854	+	1.30843i
$307$	10.1671	+	2.72426i	0.580267	+	0.155482i	0.537001	−	0.843582i	$-0.319557\pi$
$307$	10.1671	+	2.72426i	0.580267	+	0.155482i	0.0432656	+	0.999064i	$0.486224\pi$
$308$	−1.72919	+	3.70826i	−0.0985297	+	0.211298i
$309$	4.23587	−	6.48994i	0.240970	−	0.369200i
$310$		0			0
$311$	2.06659	+	2.46287i	0.117186	+	0.139657i	0.821448	−	0.570283i	$-0.193167\pi$
$311$	2.06659	+	2.46287i	0.117186	+	0.139657i	−0.704262	+	0.709940i	$0.748722\pi$
$312$	−33.4516	+	29.9809i	−1.89382	+	1.69734i
$313$	−22.0403	−	10.2775i	−1.24579	−	0.580921i	−0.315911	−	0.948789i	$-0.602310\pi$
$313$	−22.0403	−	10.2775i	−1.24579	−	0.580921i	−0.929878	+	0.367868i	$0.880088\pi$
$314$	−23.4568	−	40.6283i	−1.32374	−	2.29279i
$315$		0			0
$316$	−12.0586	+	20.8860i	−0.678347	+	1.17493i
$317$	−17.0133	+	11.9128i	−0.955562	+	0.669092i	−0.943688	−	0.330838i	$-0.892669\pi$
$317$	−17.0133	+	11.9128i	−0.955562	+	0.669092i	−0.0118742	+	0.999929i	$0.503780\pi$
$318$	0.258968	−	1.81239i	0.0145222	−	0.101634i
$319$	0.913782	−	2.51060i	0.0511620	−	0.140566i
$320$		0			0
$321$	0.321625	−	1.37864i	0.0179514	−	0.0769479i
$322$	−1.72874	+	0.151246i	−0.0963391	+	0.00842858i
$323$	−5.59403	+	5.59403i	−0.311260	+	0.311260i
$324$	35.9909	+	33.0110i	1.99950	+	1.83395i
$325$		0			0
$326$	−6.12650	+	7.30128i	−0.339315	+	0.404380i
$327$	12.4443	−	7.73635i	0.688174	−	0.427821i
$328$	41.6087	−	59.4234i	2.29746	−	3.28111i
$329$	18.0138	+	6.55649i	0.993134	+	0.361471i
$330$		0			0
$331$	1.03458	−	5.86738i	0.0568655	−	0.322500i	−0.943084	−	0.332555i	$-0.892089\pi$
$331$	1.03458	−	5.86738i	0.0568655	−	0.322500i	0.999949	+	0.0100545i	$0.00320050\pi$
$332$	−15.2694	+	4.09143i	−0.838018	+	0.224546i
$333$	2.95954	−	3.37309i	0.162182	−	0.184844i
$334$	−15.5485	+	8.97692i	−0.850775	+	0.491195i
$335$		0			0
$336$	−2.18535	+	39.9409i	−0.119221	+	2.17896i
$337$	0.971978	−	11.1098i	0.0529470	−	0.605187i	−0.922653	−	0.385631i	$-0.873984\pi$
$337$	0.971978	−	11.1098i	0.0529470	−	0.605187i	0.975600	−	0.219556i	$-0.0704608\pi$
$338$	−1.25528	+	14.3479i	−0.0682780	+	0.780421i
$339$	3.16262	+	2.06419i	0.171770	+	0.112111i
$340$		0			0
$341$	−2.15867	+	1.24631i	−0.116899	+	0.0674915i
$342$	11.6558	+	14.5298i	0.630271	+	0.785683i
$343$	−17.5727	+	4.70859i	−0.948837	+	0.254240i
$344$	−1.92261	+	10.9037i	−0.103660	+	0.587887i
$345$		0			0
$346$	27.3797	+	9.96540i	1.47194	+	0.535743i
$347$	13.6142	−	19.4431i	0.730851	−	1.04376i	−0.265962	−	0.963984i	$-0.585690\pi$
$347$	13.6142	−	19.4431i	0.730851	−	1.04376i	0.996813	−	0.0797793i	$-0.0254216\pi$
$348$	−1.71820	−	52.6764i	−0.0921051	−	2.82375i
$349$	4.82633	−	5.75179i	0.258347	−	0.307886i	−0.621243	−	0.783618i	$-0.713372\pi$
$349$	4.82633	−	5.75179i	0.258347	−	0.307886i	0.879591	+	0.475731i	$0.157817\pi$
$350$		0			0
$351$	−14.4319	+	0.152302i	−0.770315	+	0.00812929i
$352$	7.10598	−	7.10598i	0.378750	−	0.378750i
$353$	5.16281	−	0.451688i	0.274789	−	0.0240409i	0.0510716	−	0.998695i	$-0.483736\pi$
$353$	5.16281	−	0.451688i	0.274789	−	0.0240409i	0.223717	+	0.974654i	$0.428181\pi$
$354$	−16.0254	+	4.85919i	−0.851742	+	0.258263i
$355$		0			0
$356$	12.9961	−	35.7066i	0.688793	−	1.89244i
$357$	−7.48659	−	5.87695i	−0.396232	−	0.311041i
$358$	14.7917	−	10.3573i	0.781765	−	0.547398i
$359$	−6.82697	+	11.8247i	−0.360314	+	0.624082i	−0.988012	−	0.154375i	$-0.950664\pi$
$359$	−6.82697	+	11.8247i	−0.360314	+	0.624082i	0.627699	+	0.778457i	$0.283997\pi$
$360$		0			0
$361$	−6.90435	−	11.9587i	−0.363387	−	0.629404i
$362$	21.5810	+	10.0634i	1.13427	+	0.528921i
$363$	−17.7328	−	5.80687i	−0.930732	−	0.304782i
$364$	−15.3325	−	18.2725i	−0.803641	−	0.957742i
$365$		0			0
$366$	−19.6203	−	38.7270i	−1.02557	−	2.02429i
$367$	−9.11448	+	19.5461i	−0.475772	+	1.02030i	0.511208	+	0.859457i	$0.329198\pi$
$367$	−9.11448	+	19.5461i	−0.475772	+	1.02030i	−0.986981	+	0.160840i	$0.948580\pi$
$368$	5.67159	+	1.51970i	0.295652	+	0.0792197i
$369$	22.6407	−	5.53446i	1.17863	−	0.288113i
$370$		0			0
$371$	0.604528	+	0.106595i	0.0313855	+	0.00553411i
$372$	−30.3620	+	38.6778i	−1.57419	+	2.00535i
$373$	5.59299	+	11.9942i	0.289594	+	0.621037i	0.996250	−	0.0865206i	$-0.0275748\pi$
$373$	5.59299	+	11.9942i	0.289594	+	0.621037i	−0.706656	+	0.707557i	$0.749797\pi$
$374$	0.782840	+	4.43971i	0.0404797	+	0.229572i
$375$		0			0
$376$	−86.6408	−	72.7003i	−4.46816	−	3.74923i
$377$	11.0135	+	11.0135i	0.567226	+	0.567226i
$378$	−15.6782	+	16.0126i	−0.806398	+	0.823600i
$379$			27.4089i			1.40790i	0.710249	+	0.703951i	$0.248583\pi$
$379$			27.4089i			1.40790i	−0.710249	+	0.703951i	$0.751417\pi$
$380$		0			0
$381$	−4.22697	+	4.51202i	−0.216554	+	0.231158i
$382$	45.0283	+	31.5292i	2.30385	+	1.61317i
$383$	32.7469	−	15.2701i	1.67329	−	0.780267i	0.674157	−	0.738588i	$-0.264507\pi$
$383$	32.7469	−	15.2701i	1.67329	−	0.780267i	0.999131	−	0.0416793i	$-0.0132708\pi$
$384$	23.7613	−	55.6221i	1.21256	−	2.83845i
$385$		0			0
$386$	44.3177	+	25.5869i	2.25571	+	1.30234i
$387$	−2.77482	+	2.22595i	−0.141052	+	0.113151i
$388$	−10.6332	+	39.6836i	−0.539819	+	2.01463i
$389$	17.3733	−	6.32335i	0.880860	−	0.320607i	0.138303	−	0.990390i	$-0.455835\pi$
$389$	17.3733	−	6.32335i	0.880860	−	0.320607i	0.742557	+	0.669783i	$0.233613\pi$
$390$		0			0
$391$	−1.07024	+	0.898039i	−0.0541244	+	0.0454158i
$392$	41.8148	+	3.65832i	2.11197	+	0.184773i
$393$	3.55538	+	3.96696i	0.179345	+	0.200106i
$394$	−4.67045	−	12.8320i	−0.235294	−	0.646464i
$395$		0			0
$396$	7.73961	−	0.505439i	0.388930	−	0.0253992i
$397$	−7.80671	−	29.1350i	−0.391807	−	1.46224i	−0.827151	−	0.561980i	$-0.810040\pi$
$397$	−7.80671	−	29.1350i	−0.391807	−	1.46224i	0.435343	−	0.900265i	$-0.356627\pi$
$398$	−26.0546	−	37.2099i	−1.30600	−	1.86516i
$399$	−4.99656	+	3.74719i	−0.250141	+	0.187594i
$400$		0			0
$401$	34.2820	−	6.04485i	1.71196	−	0.301865i	0.770115	−	0.637905i	$-0.220199\pi$
$401$	34.2820	−	6.04485i	1.71196	−	0.301865i	0.941848	+	0.336040i	$0.109088\pi$
$402$	−32.9108	−	52.9389i	−1.64144	−	2.64035i
$403$	−1.26649	−	14.4761i	−0.0630886	−	0.721106i
$404$	−31.5550			−1.56992
$405$		0			0
$406$	24.1845			1.20026
$407$	−0.0621128	−	0.709953i	−0.00307882	−	0.0351911i
$408$	29.6476	+	47.6899i	1.46778	+	2.36100i
$409$	21.8207	−	3.84758i	1.07897	−	0.190251i	0.394208	−	0.919021i	$-0.371019\pi$
$409$	21.8207	−	3.84758i	1.07897	−	0.190251i	0.684758	+	0.728771i	$0.259908\pi$
$410$		0			0
$411$	2.87826	−	2.15856i	0.141974	−	0.106474i
$412$	−13.9264	−	19.8890i	−0.686105	−	0.979859i
$413$	−1.45321	−	5.42346i	−0.0715079	−	0.266871i
$414$	1.82692	+	2.73559i	0.0897884	+	0.134447i
$415$		0			0
$416$	20.0374	+	55.0524i	0.982415	+	2.69916i
$417$	17.8441	+	19.9098i	0.873831	+	0.974989i
$418$	2.94703	+	0.257831i	0.144144	+	0.0126109i
$419$	3.82900	−	3.21291i	0.187059	−	0.156961i	−0.544449	−	0.838794i	$-0.683261\pi$
$419$	3.82900	−	3.21291i	0.187059	−	0.156961i	0.731508	+	0.681833i	$0.238817\pi$
$420$		0			0
$421$	12.3825	−	4.50685i	0.603485	−	0.219651i	−0.0221653	−	0.999754i	$-0.507056\pi$
$421$	12.3825	−	4.50685i	0.603485	−	0.219651i	0.625650	+	0.780104i	$0.284834\pi$
$422$	7.36996	−	27.5051i	0.358764	−	1.33893i
$423$	−5.51945	−	35.9170i	−0.268365	−	1.74635i
$424$	−3.13649	−	1.81086i	−0.152322	−	0.0879429i
$425$		0			0
$426$	29.5899	−	69.2660i	1.43363	−	3.35595i
$427$	13.1924	−	6.15173i	0.638426	−	0.297703i
$428$	−3.63304	−	2.54388i	−0.175609	−	0.122963i
$429$	−1.56708	+	1.67275i	−0.0756592	+	0.0807613i
$430$		0			0
$431$		−	14.5168i		−	0.699251i	−0.936890	−	0.349625i	$-0.886309\pi$
$431$		−	14.5168i		−	0.699251i	0.936890	−	0.349625i	$-0.113691\pi$
$432$	68.3794	−	32.7687i	3.28991	−	1.57659i
$433$	16.6348	+	16.6348i	0.799416	+	0.799416i	0.983003	−	0.183587i	$-0.0587710\pi$
$433$	16.6348	+	16.6348i	0.799416	+	0.799416i	−0.183587	+	0.983003i	$0.558771\pi$
$434$	−17.2845	−	14.5034i	−0.829683	−	0.696187i
$435$		0			0
$436$	−7.97163	−	45.2094i	−0.381772	−	2.16514i
$437$	0.387448	+	0.830884i	0.0185341	+	0.0397466i
$438$	−23.3528	+	29.7490i	−1.11584	+	1.42146i
$439$	21.2894	+	3.75390i	1.01609	+	0.179164i	0.656801	−	0.754064i	$-0.271909\pi$
$439$	21.2894	+	3.75390i	1.01609	+	0.179164i	0.359287	+	0.933227i	$0.383020\pi$
$440$		0			0
$441$	9.32350	+	9.74408i	0.443976	+	0.464004i
$442$	−25.3862	−	6.80221i	−1.20750	−	0.323548i
$443$	5.07285	−	10.8788i	0.241018	−	0.516866i	−0.748172	−	0.663505i	$-0.769068\pi$
$443$	5.07285	−	10.8788i	0.241018	−	0.516866i	0.989190	+	0.146640i	$0.0468458\pi$
$444$	−6.35363	−	12.5409i	−0.301530	−	0.595166i
$445$		0			0
$446$	41.0912	+	48.9706i	1.94572	+	2.31882i
$447$	25.9159	+	8.48653i	1.22578	+	0.401399i
$448$	40.5832	+	18.9243i	1.91738	+	0.894087i
$449$	−15.1373	−	26.2186i	−0.714374	−	1.23733i	−0.963200	−	0.268784i	$-0.913378\pi$
$449$	−15.1373	−	26.2186i	−0.714374	−	1.23733i	0.248826	−	0.968548i	$-0.419955\pi$
$450$		0			0
$451$	1.85078	−	3.20565i	0.0871499	−	0.150948i
$452$	9.69212	−	6.78649i	0.455879	−	0.319210i
$453$	1.46372	+	1.14902i	0.0687716	+	0.0539855i
$454$	−18.6577	+	51.2617i	−0.875651	+	2.40583i
$455$		0			0
$456$	35.2631	−	10.6924i	1.65135	−	0.500717i
$457$	−41.4537	+	3.62673i	−1.93912	+	0.169651i	−0.989579	−	0.143990i	$-0.954007\pi$
$457$	−41.4537	+	3.62673i	−1.93912	+	0.169651i	−0.949541	+	0.313642i	$0.898451\pi$
$458$	−42.5171	+	42.5171i	−1.98670	+	1.98670i
$459$	−2.94528	+	17.7999i	−0.137474	+	0.830829i
$460$		0			0
$461$	−11.0916	+	13.2184i	−0.516586	+	0.615643i	−0.959770	−	0.280788i	$-0.909404\pi$
$461$	−11.0916	+	13.2184i	−0.516586	+	0.615643i	0.443184	+	0.896431i	$0.353849\pi$
$462$	0.116027	+	3.55716i	0.00539808	+	0.165494i
$463$	−9.45428	+	13.5021i	−0.439378	+	0.627496i	−0.976374	−	0.216088i	$-0.930670\pi$
$463$	−9.45428	+	13.5021i	−0.439378	+	0.627496i	0.536996	+	0.843585i	$0.319559\pi$
$464$	−76.8950	−	27.9875i	−3.56976	−	1.29929i
$465$		0			0
$466$	−8.83640	+	50.1137i	−0.409338	+	2.32147i
$467$	−3.84448	+	1.03012i	−0.177901	+	0.0476685i	−0.346670	−	0.937987i	$-0.612688\pi$
$467$	−3.84448	+	1.03012i	−0.177901	+	0.0476685i	0.168769	+	0.985656i	$0.446021\pi$
$468$	−16.3981	+	42.1380i	−0.758001	+	1.94783i
$469$	18.1003	−	10.4502i	0.835795	−	0.482546i
$470$		0			0
$471$	−24.9696	−	16.2972i	−1.15054	−	0.750937i
$472$	−2.88720	+	33.0009i	−0.132894	+	1.51899i
$473$	−0.0492391	+	0.562805i	−0.00226402	+	0.0258778i
$474$	−1.14609	+	20.9467i	−0.0526417	+	0.962115i
$475$		0			0
$476$	−25.8234	+	14.9091i	−1.18361	+	0.683359i
$477$	−0.373775	−	1.10196i	−0.0171140	−	0.0504554i
$478$	51.3646	−	13.7631i	2.34936	−	0.629510i
$479$	0.246236	−	1.39648i	0.0112508	−	0.0638066i	−0.978665	−	0.205460i	$-0.934131\pi$
$479$	0.246236	−	1.39648i	0.0112508	−	0.0638066i	0.989916	+	0.141654i	$0.0452420\pi$
$480$		0			0
$481$	3.90411	+	1.42098i	0.178012	+	0.0647911i
$482$	−7.69230	+	10.9857i	−0.350375	+	0.500387i
$483$	−0.936704	+	0.582326i	−0.0426215	+	0.0264967i
$484$	−37.5762	+	44.7816i	−1.70801	+	2.03553i
$485$		0			0
$486$	40.9040	+	11.4660i	1.85544	+	0.520107i
$487$	5.92999	−	5.92999i	0.268714	−	0.268714i	−0.559868	−	0.828582i	$-0.689148\pi$
$487$	5.92999	−	5.92999i	0.268714	−	0.268714i	0.828582	+	0.559868i	$0.189148\pi$
$488$	−85.5544	+	7.48504i	−3.87286	+	0.338832i
$489$	−1.37629	+	5.89942i	−0.0622380	+	0.266781i
$490$		0			0
$491$	−9.16760	+	25.1878i	−0.413728	+	1.13671i	0.541464	+	0.840724i	$0.317870\pi$
$491$	−9.16760	+	25.1878i	−0.413728	+	1.13671i	−0.955193	+	0.295985i	$0.904352\pi$
$492$	10.3287	−	72.2857i	0.465654	−	3.25889i
$493$	15.9494	−	11.1679i	0.718324	−	0.502976i
$494$	−8.62305	+	14.9356i	−0.387969	+	0.671983i
$495$		0			0
$496$	38.1722	+	66.1162i	1.71398	+	2.96871i
$497$	22.8886	+	10.6731i	1.02669	+	0.478754i
$498$	−10.2398	+	9.17735i	−0.458854	+	0.411247i
$499$	−7.19594	−	8.57579i	−0.322134	−	0.383905i	0.580538	−	0.814233i	$-0.302842\pi$
$499$	−7.19594	−	8.57579i	−0.322134	−	0.383905i	−0.902672	+	0.430328i	$0.858398\pi$
$500$		0			0
$501$	−6.23696	+	9.55588i	−0.278647	+	0.426925i
$502$	−24.0811	+	51.6420i	−1.07479	+	2.30490i
$503$	−12.8521	−	3.44372i	−0.573049	−	0.153548i	−0.0393543	−	0.999225i	$-0.512530\pi$
$503$	−12.8521	−	3.44372i	−0.573049	−	0.153548i	−0.533694	+	0.845677i	$0.679197\pi$
$504$	17.8448	+	40.5815i	0.794872	+	1.80765i
$505$		0			0
$506$	0.514493	+	0.0907189i	0.0228720	+	0.00403295i
$507$	3.40966	+	8.49540i	0.151428	+	0.377294i
$508$	8.18603	+	17.5550i	0.363197	+	0.778877i
$509$	1.12261	+	6.36664i	0.0497588	+	0.282196i	0.999527	−	0.0307584i	$-0.00979226\pi$
$509$	1.12261	+	6.36664i	0.0497588	+	0.282196i	−0.949768	+	0.312955i	$0.898681\pi$
$510$		0			0
$511$	−9.71403	−	8.15104i	−0.429723	−	0.360581i
$512$	−24.9482	−	24.9482i	−1.10257	−	1.10257i
$513$	10.7821	+	4.88993i	0.476042	+	0.215896i
$514$			39.7830i			1.75475i
$515$		0			0
$516$	3.23388	+	10.6652i	0.142364	+	0.469511i
$517$	−4.72744	−	3.31019i	−0.207912	−	0.145582i
$518$	5.84666	−	2.72634i	0.256887	−	0.119789i
$519$	18.3860	−	2.21460i	0.807057	−	0.0972103i
$520$		0			0
$521$	−6.34977	−	3.66604i	−0.278188	−	0.160612i	0.354415	−	0.935088i	$-0.384680\pi$
$521$	−6.34977	−	3.66604i	−0.278188	−	0.160612i	−0.632603	+	0.774476i	$0.718013\pi$
$522$	−22.0411	−	40.1983i	−0.964715	−	1.75943i
$523$	3.37240	−	12.5860i	0.147465	−	0.550346i	−0.852168	−	0.523268i	$-0.824713\pi$
$523$	3.37240	−	12.5860i	0.147465	−	0.550346i	0.999633	−	0.0270787i	$-0.00862048\pi$
$524$	15.6827	−	5.70803i	0.685101	−	0.249356i
$525$		0			0
$526$	−63.9152	+	53.6312i	−2.78683	+	2.33843i
$527$	−18.0963	−	1.58322i	−0.788285	−	0.0689660i
$528$	3.74760	−	11.4443i	0.163093	−	0.498049i
$529$	−7.81109	−	21.4608i	−0.339613	−	0.933078i
$530$		0			0
$531$	−7.69018	+	7.35825i	−0.333725	+	0.319321i
$532$	5.06425	+	18.9001i	0.219563	+	0.819421i
$533$	12.3773	+	17.6767i	0.536122	+	0.765662i
$534$	−3.95260	−	32.8152i	−0.171046	−	1.42005i
$535$		0			0
$536$	−121.438	+	21.4128i	−5.24534	+	0.924894i
$537$	5.41139	−	10.1211i	0.233519	−	0.436758i
$538$	5.62693	+	64.3161i	0.242594	+	2.77286i
$539$	2.14180			0.0922537
$540$		0			0
$541$	−19.4815			−0.837576			−0.418788	−	0.908084i	$-0.637545\pi$
$541$	−19.4815			−0.837576			−0.418788	+	0.908084i	$0.637545\pi$
$542$	−4.77786	−	54.6112i	−0.205227	−	2.34575i
$543$	15.1265	−	0.493396i	0.649140	−	0.0211737i
$544$	72.1238	−	12.7174i	3.09228	−	0.545253i
$545$		0			0
$546$	−19.0803	−	8.15097i	−0.816563	−	0.348829i
$547$	8.23625	+	11.7626i	0.352157	+	0.502932i	0.955678	−	0.294415i	$-0.0951249\pi$
$547$	8.23625	+	11.7626i	0.352157	+	0.502932i	−0.603521	+	0.797347i	$0.706236\pi$
$548$	−2.91726	−	10.8874i	−0.124619	−	0.465085i
$549$	−22.2483	−	16.3213i	−0.949535	−	0.696574i
$550$		0			0
$551$	−4.36986	−	12.0061i	−0.186162	−	0.511477i
$552$	6.36830	−	1.33832i	0.271053	−	0.0569627i
$553$	−7.00702	−	0.613034i	−0.297969	−	0.0260689i
$554$	−31.7450	+	26.6372i	−1.34871	+	1.13171i
$555$		0			0
$556$	78.7101	−	28.6481i	3.33805	−	1.21495i
$557$	−5.99902	+	22.3886i	−0.254187	+	0.948637i	0.714355	+	0.699784i	$0.246720\pi$
$557$	−5.99902	+	22.3886i	−0.254187	+	0.948637i	−0.968541	+	0.248853i	$0.919946\pi$
$558$	−8.35420	+	41.9475i	−0.353662	+	1.77578i
$559$	−2.85230	−	1.64678i	−0.120640	−	0.0696513i
$560$		0			0
$561$	1.71913	+	2.29232i	0.0725819	+	0.0967818i
$562$	−58.9691	+	27.4978i	−2.48746	+	1.15992i
$563$	24.6767	+	17.2788i	1.04000	+	0.728214i	0.963187	−	0.268832i	$-0.0866377\pi$
$563$	24.6767	+	17.2788i	1.04000	+	0.728214i	0.0768099	+	0.997046i	$0.475527\pi$
$564$	−110.869	−	25.8648i	−4.66842	−	1.08911i
$565$		0			0
$566$		−	0.777487i		−	0.0326802i
$567$	−4.28952	+	13.5822i	−0.180143	+	0.570398i
$568$	−105.360	−	105.360i	−4.42082	−	4.42082i
$569$	−14.2448	−	11.9528i	−0.597173	−	0.501088i	0.293362	−	0.956001i	$-0.405226\pi$
$569$	−14.2448	−	11.9528i	−0.597173	−	0.501088i	−0.890536	+	0.454913i	$0.849670\pi$
$570$		0			0
$571$	6.82003	+	38.6783i	0.285409	+	1.61864i	0.703819	+	0.710379i	$0.251476\pi$
$571$	6.82003	+	38.6783i	0.285409	+	1.61864i	−0.418410	+	0.908258i	$0.637412\pi$
$572$	3.03483	+	6.50822i	0.126893	+	0.272122i
$573$	34.5864	+	4.94195i	1.44487	+	0.206453i
$574$	32.9977	+	5.81838i	1.37730	+	0.242854i
$575$		0			0
$576$	−5.53153	−	84.7024i	−0.230480	−	3.52927i
$577$	42.2673	+	11.3255i	1.75961	+	0.471486i	0.986634	−	0.162950i	$-0.0521010\pi$
$577$	42.2673	+	11.3255i	1.75961	+	0.471486i	0.772975	+	0.634436i	$0.218768\pi$
$578$	5.69397	−	12.2108i	0.236838	−	0.507901i
$579$	32.4766	+	1.77694i	1.34968	+	0.0738472i
$580$		0			0
$581$	−2.96353	−	3.53180i	−0.122948	−	0.146524i
$582$	7.34954	+	34.9722i	0.304648	+	1.44965i
$583$	−0.167487	−	0.0781006i	−0.00693661	−	0.00323460i
$584$	37.4080	+	64.7925i	1.54795	+	2.68113i
$585$		0			0
$586$	21.1828	−	36.6896i	0.875051	−	1.51563i
$587$	16.5731	−	11.6046i	0.684046	−	0.478974i	−0.179164	−	0.983819i	$-0.557339\pi$
$587$	16.5731	−	11.6046i	0.684046	−	0.478974i	0.863210	+	0.504845i	$0.168450\pi$
$588$	39.2105	−	15.7373i	1.61701	−	0.648993i
$589$	−4.07693	+	11.2013i	−0.167987	+	0.461540i
$590$		0			0
$591$	−6.33393	−	5.93378i	−0.260543	−	0.244083i
$592$	−21.7446	+	1.90240i	−0.893696	+	0.0781883i
$593$	−2.27116	+	2.27116i	−0.0932652	+	0.0932652i	−0.752200	−	0.658935i	$-0.771007\pi$
$593$	−2.27116	+	2.27116i	−0.0932652	+	0.0932652i	0.658935	+	0.752200i	$0.271007\pi$
$594$	5.80678	−	3.43475i	0.238255	−	0.140930i
$595$		0			0
$596$	54.9162	−	65.4466i	2.24946	−	2.68080i
$597$	−25.4606	−	13.6129i	−1.04203	−	0.557137i
$598$	−1.74691	+	2.49484i	−0.0714364	+	0.102022i
$599$	−11.3910	−	4.14598i	−0.465423	−	0.169400i	0.0986548	−	0.995122i	$-0.468546\pi$
$599$	−11.3910	−	4.14598i	−0.465423	−	0.169400i	−0.564078	+	0.825722i	$0.690768\pi$
$600$		0			0
$601$	2.78962	−	15.8207i	0.113791	−	0.645340i	−0.873551	−	0.486733i	$-0.838189\pi$
$601$	2.78962	−	15.8207i	0.113791	−	0.645340i	0.987342	−	0.158607i	$-0.0507003\pi$
$602$	−4.93974	+	1.32360i	−0.201329	+	0.0539459i
$603$	−33.8660	−	20.5614i	−1.37913	−	0.837323i
$604$	5.04879	−	2.91492i	0.205432	−	0.118606i
$605$		0			0
$606$	−24.4848	+	12.4048i	−0.994626	+	0.503909i
$607$	1.10665	−	12.6491i	0.0449177	−	0.513412i	−0.940093	−	0.340918i	$-0.889262\pi$
$607$	1.10665	−	12.6491i	0.0449177	−	0.513412i	0.985011	−	0.172494i	$-0.0551824\pi$
$608$	4.18852	−	47.8750i	0.169867	−	1.94159i
$609$	13.7119	−	6.94690i	0.555636	−	0.281503i
$610$		0			0
$611$	29.1369	−	16.8222i	1.17875	−	0.680552i
$612$	48.3159	+	29.3345i	1.95306	+	1.18578i
$613$	11.7830	−	3.15725i	0.475912	−	0.127520i	−0.0128866	−	0.999917i	$-0.504102\pi$
$613$	11.7830	−	3.15725i	0.475912	−	0.127520i	0.488798	+	0.872397i	$0.337435\pi$
$614$	4.98094	−	28.2483i	0.201014	−	1.14001i
$615$		0			0
$616$	6.61595	+	2.40801i	0.266564	+	0.0970215i
$617$	−5.34672	+	7.63591i	−0.215251	+	0.307410i	−0.912228	−	0.409684i	$-0.865639\pi$
$617$	−5.34672	+	7.63591i	−0.215251	+	0.307410i	0.696977	+	0.717094i	$0.254528\pi$
$618$	−18.6247	−	9.95797i	−0.749197	−	0.400568i
$619$	−10.1944	+	12.1492i	−0.409748	+	0.488319i	−0.930967	−	0.365104i	$-0.881033\pi$
$619$	−10.1944	+	12.1492i	−0.409748	+	0.488319i	0.521218	+	0.853423i	$0.325478\pi$
$620$		0			0
$621$	1.82160	+	1.02622i	0.0730982	+	0.0411810i
$622$	6.19528	−	6.19528i	0.248408	−	0.248408i
$623$	11.0400	−	0.965877i	0.442309	−	0.0386971i
$624$	51.2334	+	47.9967i	2.05098	+	1.92141i
$625$		0			0
$626$	−22.6663	+	62.2751i	−0.905927	+	2.48901i
$627$	1.74494	−	0.700337i	0.0696862	−	0.0279688i
$628$	−76.5215	+	53.5809i	−3.05354	+	2.13811i
$629$	2.59683	−	4.49784i	0.103542	−	0.179341i
$630$		0			0
$631$	−12.2239	−	21.1724i	−0.486626	−	0.842861i	0.513256	−	0.858236i	$-0.328439\pi$
$631$	−12.2239	−	21.1724i	−0.486626	−	0.842861i	−0.999882	+	0.0153745i	$0.995106\pi$
$632$	37.6109	+	17.5382i	1.49608	+	0.697634i
$633$	−3.72215	−	17.7116i	−0.147942	−	0.703972i
$634$	36.3814	+	43.3577i	1.44489	+	1.72195i
$635$		0			0
$636$	−3.64010	−	0.199166i	−0.144339	−	0.00789745i
$637$	−5.27689	+	11.3163i	−0.209078	+	0.448369i
$638$	−7.03271	−	1.88441i	−0.278428	−	0.0746045i
$639$	−3.11973	−	47.7714i	−0.123415	−	1.88981i
$640$		0			0
$641$	−5.87001	−	1.03504i	−0.231852	−	0.0408817i	0.0565151	−	0.998402i	$-0.482001\pi$
$641$	−5.87001	−	1.03504i	−0.231852	−	0.0408817i	−0.288367	+	0.957520i	$0.593112\pi$
$642$	−3.81906	−	0.545695i	−0.150726	−	0.0215369i
$643$	13.5999	+	29.1651i	0.536328	+	1.15016i	0.968648	+	0.248438i	$0.0799172\pi$
$643$	13.5999	+	29.1651i	0.536328	+	1.15016i	−0.432320	+	0.901720i	$0.642305\pi$
$644$	0.600036	+	3.40297i	0.0236447	+	0.134096i
$645$		0			0
$646$	16.5151	+	13.8578i	0.649779	+	0.545229i
$647$	−5.43613	−	5.43613i	−0.213717	−	0.213717i	0.592128	−	0.805844i	$-0.298288\pi$
$647$	−5.43613	−	5.43613i	−0.213717	−	0.213717i	−0.805844	+	0.592128i	$0.798288\pi$
$648$	51.1892	−	66.6457i	2.01090	−	2.61809i
$649$			1.69034i			0.0663516i
$650$		0			0
$651$	−13.9659	−	3.25813i	−0.547365	−	0.127696i
$652$	15.5464	+	10.8857i	0.608844	+	0.426317i
$653$	−14.5983	+	6.80729i	−0.571275	+	0.266390i	−0.686717	−	0.726924i	$-0.740949\pi$
$653$	−14.5983	+	6.80729i	−0.571275	+	0.266390i	0.115443	+	0.993314i	$0.463171\pi$
$654$	−23.9580	−	31.9460i	−0.936833	−	1.24919i
$655$		0			0
$656$	−98.1831	−	56.6861i	−3.83341	−	2.21322i
$657$	−4.69513	+	23.5748i	−0.183174	+	0.919740i
$658$	13.5209	−	50.4605i	0.527098	−	1.96716i
$659$	31.0994	−	11.3193i	1.21146	−	0.440936i	0.344250	−	0.938878i	$-0.388133\pi$
$659$	31.0994	−	11.3193i	1.21146	−	0.440936i	0.867210	+	0.497942i	$0.165911\pi$
$660$		0			0
$661$	22.7885	−	19.1218i	0.886369	−	0.743752i	−0.0811098	−	0.996705i	$-0.525846\pi$
$661$	22.7885	−	19.1218i	0.886369	−	0.743752i	0.967478	+	0.252954i	$0.0814020\pi$
$662$	−16.1743	−	1.41507i	−0.628631	−	0.0549981i
$663$	−16.3472	+	3.43541i	−0.634871	+	0.133420i
$664$	9.30342	+	25.5609i	0.361043	+	0.991957i
$665$		0			0
$666$	−9.86008	−	7.23330i	−0.382070	−	0.280285i
$667$	−0.583983	−	2.17945i	−0.0226119	−	0.0843888i
$668$	20.5054	+	29.2848i	0.793379	+	1.13306i
$669$	37.3641	+	15.9617i	1.44458	+	0.617113i
$670$		0			0
$671$	−4.31561	+	0.760958i	−0.166602	+	0.0293764i
$672$	57.7867	−	1.88488i	2.22917	−	0.0727110i
$673$	−3.02767	−	34.6064i	−0.116708	−	1.33398i	−0.798306	−	0.602252i	$-0.794270\pi$
$673$	−3.02767	−	34.6064i	−0.116708	−	1.33398i	0.681598	−	0.731727i	$-0.261285\pi$
$674$	−30.3912			−1.17063
$675$		0			0
$676$	28.6790			1.10304
$677$	−1.51507	−	17.3173i	−0.0582289	−	0.665560i	−0.968083	−	0.250631i	$-0.919362\pi$
$677$	−1.51507	−	17.3173i	−0.0582289	−	0.665560i	0.909854	−	0.414929i	$-0.136194\pi$
$678$	4.85263	−	9.07604i	0.186364	−	0.348563i
$679$	−11.8000	+	2.08066i	−0.452843	+	0.0798485i
$680$		0			0
$681$	4.14629	+	34.4233i	0.158886	+	1.31910i
$682$	3.89615	+	5.56428i	0.149191	+	0.213067i
$683$	2.94108	+	10.9763i	0.112537	+	0.419995i	0.999091	−	0.0426308i	$-0.0135739\pi$
$683$	2.94108	+	10.9763i	0.112537	+	0.419995i	−0.886554	+	0.462626i	$0.846907\pi$
$684$	26.7993	−	25.6425i	1.02470	−	0.980467i
$685$		0			0
$686$	16.9564	+	46.5874i	0.647400	+	1.77872i
$687$	−11.8931	+	36.3189i	−0.453752	+	1.38565i
$688$	17.2377	+	1.50810i	0.657181	+	0.0574959i
$689$	0.825299	−	0.692508i	0.0314414	−	0.0263824i
$690$		0			0
$691$	−22.0909	+	8.04044i	−0.840378	+	0.305873i	−0.726111	−	0.687577i	$-0.758674\pi$
$691$	−22.0909	+	8.04044i	−0.840378	+	0.305873i	−0.114267	+	0.993450i	$0.536452\pi$
$692$	15.0162	−	56.0412i	0.570830	−	2.13037i
$693$	1.08756	+	1.98348i	0.0413131	+	0.0753461i
$694$	−56.0171	−	32.3415i	−2.12638	−	1.22767i
$695$		0			0
$696$	−90.0392	+	10.8453i	−3.41293	+	0.411088i
$697$	24.4483	−	11.4004i	0.926046	−	0.431822i
$698$	−16.7611	−	11.7362i	−0.634416	−	0.444223i
$699$	9.38495	+	30.9512i	0.354971	+	1.17068i
$700$		0			0
$701$			44.6039i			1.68467i	0.538956	+	0.842334i	$0.318819\pi$
$701$			44.6039i			1.68467i	−0.538956	+	0.842334i	$0.681181\pi$
$702$	3.84119	+	39.1429i	0.144976	+	1.47735i
$703$	−2.40988	−	2.40988i	−0.0908903	−	0.0908903i
$704$	−10.3268	−	8.66522i	−0.389206	−	0.326583i
$705$		0			0
$706$	−2.45245	−	13.9085i	−0.0922992	−	0.523455i
$707$	−3.88937	−	8.34079i	−0.146275	−	0.313688i
$708$	12.4201	+	30.9455i	0.466775	+	1.16300i
$709$	−36.4781	−	6.43207i	−1.36996	−	0.241562i	−0.560219	−	0.828344i	$-0.689283\pi$
$709$	−36.4781	−	6.43207i	−1.36996	−	0.241562i	−0.809744	+	0.586783i	$0.800394\pi$
$710$		0			0
$711$	5.36705	+	12.2054i	0.201280	+	0.457738i
$712$	−63.1566	−	16.9228i	−2.36689	−	0.634207i
$713$	−0.889647	+	1.90785i	−0.0333175	+	0.0714497i
$714$	−14.1764	+	21.7202i	−0.530538	+	0.812857i
$715$		0			0
$716$	−23.1122	−	27.5441i	−0.863744	−	1.02937i
$717$	25.1689	−	22.5575i	0.939949	−	0.842427i
$718$	33.7227	+	15.7251i	1.25852	+	0.586857i
$719$	19.2483	+	33.3390i	0.717839	+	1.24333i	0.961854	+	0.273562i	$0.0882018\pi$
$719$	19.2483	+	33.3390i	0.717839	+	1.24333i	−0.244016	+	0.969771i	$0.578465\pi$
$720$		0			0
$721$	3.54064	−	6.13256i	0.131860	−	0.228389i
$722$	−30.8251	+	21.5840i	−1.14719	+	0.803273i
$723$	−1.20571	+	8.43818i	−0.0448408	+	0.313819i
$724$	16.2169	−	44.5557i	0.602698	−	1.65590i
$725$		0			0
$726$	−11.5525	+	49.5196i	−0.428755	+	1.83785i
$727$	25.9897	−	2.27381i	0.963906	−	0.0843308i	0.405676	−	0.914017i	$-0.367036\pi$
$727$	25.9897	−	2.27381i	0.963906	−	0.0843308i	0.558230	+	0.829686i	$0.311481\pi$
$728$	−29.0230	+	29.0230i	−1.07566	+	1.07566i
$729$	26.4849	−	5.24861i	0.980924	−	0.194393i
$730$		0			0
$731$	−2.64649	+	3.15396i	−0.0978838	+	0.116653i
$732$	−73.4158	+	45.6408i	−2.71352	+	1.68693i
$733$	27.9576	−	39.9276i	1.03264	−	1.47476i	0.159555	−	0.987189i	$-0.448994\pi$
$733$	27.9576	−	39.9276i	1.03264	−	1.47476i	0.873083	−	0.487571i	$-0.162117\pi$
$734$	55.2278	+	20.1013i	2.03849	+	0.741951i
$735$		0			0
$736$	1.47374	−	8.35802i	0.0543230	−	0.308081i
$737$	−6.07772	+	1.62852i	−0.223876	+	0.0599873i
$738$	−20.4022	−	60.1498i	−0.751015	−	2.21414i
$739$	−11.7531	+	6.78566i	−0.432345	+	0.249614i	−0.700345	−	0.713804i	$-0.746971\pi$
$739$	−11.7531	+	6.78566i	−0.432345	+	0.249614i	0.268000	+	0.963419i	$0.413637\pi$
$740$		0			0
$741$	−0.598849	+	10.9450i	−0.0219993	+	0.402073i
$742$	0.145797	−	1.66647i	0.00535238	−	0.0611780i
$743$	−0.108282	+	1.23767i	−0.00397247	+	0.0454055i	−0.997922	−	0.0644303i	$-0.979477\pi$
$743$	−0.108282	+	1.23767i	−0.00397247	+	0.0454055i	0.993950	+	0.109836i	$0.0350325\pi$
$744$	70.8542	+	46.2453i	2.59764	+	1.69544i
$745$		0			0
$746$	31.2331	−	18.0324i	1.14352	−	0.660214i
$747$	−3.16949	+	8.14462i	−0.115966	+	0.297996i
$748$	8.67096	−	2.32338i	0.317042	−	0.0849511i
$749$	0.224615	−	1.27386i	0.00820726	−	0.0465457i
$750$		0			0
$751$	−8.15950	−	2.96982i	−0.297745	−	0.108370i	0.188828	−	0.982010i	$-0.439531\pi$
$751$	−8.15950	−	2.96982i	−0.297745	−	0.108370i	−0.486573	+	0.873640i	$0.661753\pi$
$752$	−101.385	+	144.793i	−3.69713	+	5.28005i
$753$	1.18066	+	36.1967i	0.0430258	+	1.31908i
$754$	27.2833	−	32.5150i	0.993601	−	1.18413i
$755$		0			0
$756$	34.4843	+	28.3210i	1.25418	+	1.03003i
$757$	−29.4262	+	29.4262i	−1.06951	+	1.06951i	−0.0721170	+	0.997396i	$0.522975\pi$
$757$	−29.4262	+	29.4262i	−1.06951	+	1.06951i	−0.997396	+	0.0721170i	$0.977025\pi$
$758$	74.4088	−	6.50993i	2.70265	−	0.236451i
$759$	0.317761	−	0.0963507i	0.0115340	−	0.00349731i
$760$		0			0
$761$	14.0169	−	38.5111i	0.508112	−	1.39603i	−0.375071	−	0.926996i	$-0.622382\pi$
$761$	14.0169	−	38.5111i	0.508112	−	1.39603i	0.883183	−	0.469029i	$-0.155396\pi$
$762$	13.2530	+	10.4036i	0.480107	+	0.376882i
$763$	10.9674	−	7.67948i	0.397048	−	0.278016i
$764$	54.7283	−	94.7922i	1.98000	−	3.42946i
$765$		0			0
$766$	−49.2326	−	85.2733i	−1.77884	−	3.08105i
$767$	−8.93101	−	4.16460i	−0.322480	−	0.150375i
$768$	−63.4973	−	20.7931i	−2.29126	−	0.750307i
$769$	3.94057	+	4.69619i	0.142100	+	0.169349i	0.832401	−	0.554174i	$-0.186966\pi$
$769$	3.94057	+	4.69619i	0.142100	+	0.169349i	−0.690300	+	0.723523i	$0.742521\pi$
$770$		0			0
$771$	11.4275	+	22.5558i	0.411550	+	0.812327i
$772$	43.0641	−	92.3513i	1.54991	−	3.32380i
$773$	9.19044	+	2.46257i	0.330557	+	0.0885726i	0.420281	−	0.907394i	$-0.361932\pi$
$773$	9.19044	+	2.46257i	0.330557	+	0.0885726i	−0.0897234	+	0.995967i	$0.528598\pi$
$774$	6.70197	+	7.00429i	0.240897	+	0.251764i
$775$		0			0
$776$	69.6196	+	12.2758i	2.49920	+	0.440676i
$777$	2.53176	−	3.22518i	0.0908263	−	0.115703i
$778$	−21.2928	−	45.6625i	−0.763382	−	1.63708i
$779$	−3.07383	−	17.4326i	−0.110132	−	0.624587i
$780$		0			0
$781$	−5.82422	−	4.88710i	−0.208407	−	0.174874i
$782$	2.69216	+	2.69216i	0.0962714	+	0.0962714i
$783$	−24.0435	−	16.4601i	−0.859244	−	0.588235i
$784$		−	65.5994i		−	2.34283i
$785$		0			0
$786$	9.92491	−	10.5942i	0.354010	−	0.377883i
$787$	6.94038	+	4.85971i	0.247398	+	0.173230i	0.690698	−	0.723143i	$-0.257303\pi$
$787$	6.94038	+	4.85971i	0.247398	+	0.173230i	−0.443300	+	0.896373i	$0.646192\pi$
$788$	−24.6435	+	11.4915i	−0.877890	+	0.409367i
$789$	−20.8327	+	48.7667i	−0.741665	+	1.73614i
$790$		0			0
$791$	2.98847	+	1.72539i	0.106258	+	0.0613479i
$792$	−2.02713	−	13.1913i	−0.0720310	−	0.468732i
$793$	6.61207	−	24.6766i	0.234802	−	0.876291i
$794$	−77.2406	+	28.1133i	−2.74116	+	0.997702i
$795$		0			0
$796$	−69.2896	+	58.1409i	−2.45591	+	2.06075i
$797$	28.1786	+	2.46530i	0.998136	+	0.0873256i	0.574498	−	0.818506i	$-0.305197\pi$
$797$	28.1786	+	2.46530i	0.998136	+	0.0873256i	0.423638	+	0.905832i	$0.360753\pi$
$798$	11.3595	+	12.6745i	0.402121	+	0.448672i
$799$	−14.3847	−	39.5216i	−0.508894	−	1.39818i
$800$		0			0
$801$	−11.6670	−	17.4699i	−0.412234	−	0.617268i
$802$	−24.5527	−	91.6319i	−0.866986	−	3.23564i
$803$	2.18967	+	3.12717i	0.0772716	+	0.110355i
$804$	−99.3006	+	74.4709i	−3.50206	+	2.62639i
$805$		0			0
$806$	−38.9984	+	6.87647i	−1.37366	+	0.242213i
$807$	21.6648	+	34.8490i	0.762637	+	1.22674i
$808$	4.73234	+	54.0909i	0.166483	+	1.90291i
$809$	2.28591			0.0803683			0.0401841	−	0.999192i	$-0.487206\pi$
$809$	2.28591			0.0803683			0.0401841	+	0.999192i	$0.487206\pi$
$810$		0			0
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	−4.19715	−	47.9736i	−0.147291	−	1.68354i
$813$	−18.3957	−	29.5906i	−0.645166	−	1.03779i
$814$	−1.91260	+	0.337243i	−0.0670367	+	0.0118204i
$815$		0			0
$816$	70.2096	−	52.6539i	2.45783	−	1.84326i
$817$	1.54964	+	2.21311i	0.0542150	+	0.0774270i
$818$	−15.6279	−	58.3243i	−0.546418	−	2.03926i
$819$	−13.1593	+	0.859376i	−0.459824	+	0.0300290i
$820$		0			0
$821$	7.91413	+	21.7439i	0.276205	+	0.758867i	0.997784	+	0.0665351i	$0.0211944\pi$
$821$	7.91413	+	21.7439i	0.276205	+	0.758867i	−0.721579	+	0.692332i	$0.756583\pi$
$822$	−6.54361	−	7.30112i	−0.228235	−	0.254656i
$823$	6.50574	+	0.569178i	0.226776	+	0.0198403i	0.199977	−	0.979801i	$-0.435913\pi$
$823$	6.50574	+	0.569178i	0.226776	+	0.0198403i	0.0267986	+	0.999641i	$0.491469\pi$
$824$	−32.0047	+	26.8552i	−1.11494	+	0.935544i
$825$		0			0
$826$	−14.3783	+	5.23326i	−0.500284	+	0.182088i
$827$	−2.39679	+	8.94494i	−0.0833445	+	0.311046i	−0.994996	−	0.0999193i	$-0.968142\pi$
$827$	−2.39679	+	8.94494i	−0.0833445	+	0.311046i	0.911651	+	0.410965i	$0.134808\pi$
$828$	5.10939	−	4.09873i	0.177564	−	0.142441i
$829$	−2.45210	−	1.41572i	−0.0851648	−	0.0491699i	0.456813	−	0.889563i	$-0.348991\pi$
$829$	−2.45210	−	1.41572i	−0.0851648	−	0.0491699i	−0.541978	+	0.840393i	$0.682324\pi$
$830$		0			0
$831$	−10.3471	+	24.2211i	−0.358936	+	0.840222i
$832$	71.2260	−	33.2132i	2.46932	−	1.15146i
$833$	12.7859	+	8.95278i	0.443005	+	0.310195i
$834$	49.8123	−	53.1715i	1.72486	−	1.84118i
$835$		0			0
$836$		−	5.89061i		−	0.203731i
$837$	7.31263	+	26.1827i	0.252761	+	0.905007i
$838$	−9.63173	−	9.63173i	−0.332723	−	0.332723i
$839$	32.4518	+	27.2303i	1.12036	+	0.940095i	0.998623	−	0.0524668i	$-0.0167084\pi$
$839$	32.4518	+	27.2303i	1.12036	+	0.940095i	0.121739	+	0.992562i	$0.461153\pi$
$840$		0			0
$841$	0.424617	+	2.40812i	0.0146420	+	0.0830387i
$842$	−15.1760	−	32.5451i	−0.523000	−	1.12158i
$843$	−25.5352	+	32.5291i	−0.879479	+	1.12036i
$844$	−55.8394	−	9.84600i	−1.92207	−	0.338913i
$845$		0			0
$846$	−96.1954	+	23.5147i	−3.30727	+	0.808452i
$847$	−16.4684	−	4.41271i	−0.565862	−	0.151622i
$848$	−2.39208	+	5.12983i	−0.0821443	+	0.176159i
$849$	−0.223330	−	0.440813i	−0.00766466	−	0.0151287i
$850$		0			0
$851$	−0.386871	−	0.461054i	−0.0132618	−	0.0158047i
$852$	−142.535	−	46.6750i	−4.88316	−	1.59906i
$853$	−30.1905	−	14.0780i	−1.03370	−	0.482023i	−0.169691	−	0.985497i	$-0.554277\pi$
$853$	−30.1905	−	14.0780i	−1.03370	−	0.482023i	−0.864010	+	0.503474i	$0.832055\pi$
$854$	−19.8339	−	34.3532i	−0.678701	−	1.17554i
$855$		0			0
$856$	−3.81582	+	6.60919i	−0.130422	+	0.225897i
$857$	25.1791	−	17.6306i	0.860100	−	0.602249i	−0.0581240	−	0.998309i	$-0.518512\pi$
$857$	25.1791	−	17.6306i	0.860100	−	0.602249i	0.918224	+	0.396061i	$0.129623\pi$
$858$	4.91333	+	3.85695i	0.167738	+	0.131674i
$859$	−17.6716	+	48.5522i	−0.602946	+	1.65658i	0.142326	+	0.989820i	$0.454542\pi$
$859$	−17.6716	+	48.5522i	−0.602946	+	1.65658i	−0.745272	+	0.666760i	$0.767680\pi$
$860$		0			0
$861$	20.3800	−	6.17958i	0.694550	−	0.210600i
$862$	−39.4098	+	3.44791i	−1.34230	+	0.117436i
$863$	−31.9076	+	31.9076i	−1.08615	+	1.08615i	−0.0902264	+	0.995921i	$0.528759\pi$
$863$	−31.9076	+	31.9076i	−1.08615	+	1.08615i	−0.995921	+	0.0902264i	$0.971241\pi$
$864$	−55.7982	−	94.3322i	−1.89829	−	3.20925i
$865$		0			0
$866$	41.2086	−	49.1104i	1.40032	−	1.66884i
$867$	−0.279168	−	8.55872i	−0.00948105	−	0.290669i
$868$	−25.7700	+	36.8034i	−0.874692	+	1.24919i
$869$	1.98983	+	0.724239i	0.0675003	+	0.0245681i
$870$		0			0
$871$	6.36968	−	36.1243i	0.215829	−	1.22402i
$872$	−76.3015	+	20.4449i	−2.58390	+	0.692353i
$873$	14.2126	+	17.7171i	0.481023	+	0.599634i
$874$	2.16363	−	1.24917i	0.0731860	−	0.0422539i
$875$		0			0
$876$	63.0643	+	41.1610i	2.13074	+	1.39070i
$877$	−3.42618	+	39.1615i	−0.115694	+	1.32239i	0.687288	+	0.726385i	$0.258801\pi$
$877$	−3.42618	+	39.1615i	−0.115694	+	1.32239i	−0.802982	+	0.596003i	$0.796755\pi$
$878$	5.13448	−	58.6873i	0.173280	−	1.98060i
$879$	1.47109	−	26.8866i	0.0496186	−	0.906863i
$880$		0			0
$881$	−34.0163	+	19.6393i	−1.14604	+	0.661666i	−0.947919	−	0.318512i	$-0.896817\pi$
$881$	−34.0163	+	19.6393i	−1.14604	+	0.661666i	−0.198120	+	0.980178i	$0.563484\pi$
$882$	24.2385	−	27.6254i	0.816151	−	0.930197i
$883$	−17.3273	+	4.64284i	−0.583111	+	0.156244i	−0.538303	−	0.842752i	$-0.680934\pi$
$883$	−17.3273	+	4.64284i	−0.583111	+	0.156244i	−0.0448081	+	0.998996i	$0.514268\pi$
$884$	−9.08751	+	51.5378i	−0.305646	+	1.73340i
$885$		0			0
$886$	−30.7381	−	11.1878i	−1.03267	−	0.375860i
$887$	9.98188	−	14.2556i	0.335159	−	0.478656i	−0.615831	−	0.787878i	$-0.711180\pi$
$887$	9.98188	−	14.2556i	0.335159	−	0.478656i	0.950990	+	0.309222i	$0.100069\pi$
$888$	−20.5446	+	12.7720i	−0.689430	+	0.428602i
$889$	−3.63125	+	4.32756i	−0.121788	+	0.145142i
$890$		0			0
$891$	2.30566	−	3.61538i	0.0772425	−	0.121120i
$892$	90.0092	−	90.0092i	3.01373	−	3.01373i
$893$	−27.4935	+	2.40537i	−0.920036	+	0.0804927i
$894$	16.8836	−	72.3711i	0.564673	−	2.42045i
$895$		0			0
$896$	18.9021	−	51.9330i	0.631474	−	1.73496i
$897$	−0.273814	+	1.91630i	−0.00914239	+	0.0639833i
$898$	−67.5821	+	47.3215i	−2.25524	+	1.57914i
$899$	14.6687	−	25.4069i	0.489227	−	0.847367i
$900$		0			0
$901$	−0.673386	−	1.16634i	−0.0224337	−	0.0388564i
$902$	−9.14216	−	4.26306i	−0.304401	−	0.141944i
$903$	−2.42050	+	2.16936i	−0.0805490	+	0.0721919i
$904$	−13.0868	−	15.5963i	−0.435261	−	0.518724i
$905$		0			0
$906$	2.77166	−	4.24656i	0.0920821	−	0.141083i
$907$	8.34207	−	17.8896i	0.276994	−	0.594015i	−0.717763	−	0.696288i	$-0.754834\pi$
$907$	8.34207	−	17.8896i	0.276994	−	0.594015i	0.994756	+	0.102273i	$0.0326115\pi$
$908$	104.923	+	28.1141i	3.48200	+	0.932999i
$909$	−10.3190	+	14.0663i	−0.342258	+	0.466549i
$910$		0			0
$911$	29.7171	+	5.23993i	0.984571	+	0.173606i	0.642681	−	0.766134i	$-0.277822\pi$
$911$	29.7171	+	5.23993i	0.984571	+	0.173606i	0.341890	+	0.939740i	$0.388933\pi$
$912$	−21.4501	−	53.4443i	−0.710282	−	1.76972i
$913$	0.586586	+	1.25794i	0.0194132	+	0.0416317i
$914$	19.6914	+	111.676i	0.651334	+	3.69390i
$915$		0			0
$916$	91.7178	+	76.9604i	3.03044	+	2.54284i
$917$	3.44178	+	3.44178i	0.113658	+	0.113658i
$918$	49.0221	+	3.76806i	1.61797	+	0.124365i
$919$			5.90514i			0.194793i	0.995246	+	0.0973964i	$0.0310515\pi$
$919$			5.90514i			0.194793i	−0.995246	+	0.0973964i	$0.968949\pi$
$920$		0			0
$921$	−5.29015	−	17.4467i	−0.174316	−	0.574889i
$922$	38.5192	+	26.9715i	1.26856	+	0.888258i
$923$	40.1708	−	18.7320i	1.32224	−	0.616570i
$924$	7.03602	−	0.847491i	0.231468	−	0.0278804i
$925$		0			0
$926$	38.9006	+	22.4592i	1.27835	+	0.738057i
$927$	−13.4201	−	0.296009i	−0.440773	−	0.00972221i
$928$	−30.6126	+	114.248i	−1.00491	+	3.75036i
$929$	6.36097	−	2.31520i	0.208697	−	0.0759593i	−0.235557	−	0.971861i	$-0.575691\pi$
$929$	6.36097	−	2.31520i	0.208697	−	0.0759593i	0.444253	+	0.895901i	$0.353469\pi$
$930$		0			0
$931$	7.84617	−	6.58371i	0.257148	−	0.215773i
$932$	100.942	+	8.83124i	3.30645	+	0.289277i
$933$	1.73298	−	5.29211i	0.0567352	−	0.173256i
$934$	3.70965	+	10.1922i	0.121383	+	0.333498i
$935$		0			0
$936$	74.6914	+	21.7898i	2.44136	+	0.712220i
$937$	1.63137	+	6.08835i	0.0532945	+	0.198898i	0.987440	−	0.157995i	$-0.0505029\pi$
$937$	1.63137	+	6.08835i	0.0532945	+	0.198898i	−0.934145	+	0.356892i	$0.883836\pi$
$938$	−32.6689	−	46.6560i	−1.06668	−	1.52337i
$939$	5.03711	+	41.8190i	0.164380	+	1.36471i
$940$		0			0
$941$	26.7793	−	4.72192i	0.872981	−	0.153930i	0.280831	−	0.959757i	$-0.409390\pi$
$941$	26.7793	−	4.72192i	0.872981	−	0.153930i	0.592151	+	0.805827i	$0.298279\pi$
$942$	−38.3126	+	71.6575i	−1.24829	+	2.33473i
$943$	−0.272455	−	3.11417i	−0.00887234	−	0.101411i
$944$	51.7720			1.68504
$945$		0			0
$946$	1.53958			0.0500560
$947$	4.20583	+	48.0728i	0.136671	+	1.56216i	0.686656	+	0.726982i	$0.259078\pi$
$947$	4.20583	+	48.0728i	0.136671	+	1.56216i	−0.549985	+	0.835174i	$0.685367\pi$
$948$	41.7499	−	1.36180i	1.35597	−	0.0442291i
$949$	−21.9174	+	3.86463i	−0.711469	+	0.125451i
$950$		0			0
$951$	33.0815	+	14.1322i	1.07274	+	0.458267i
$952$	29.4297	+	42.0300i	0.953822	+	1.36220i
$953$	5.07394	+	18.9362i	0.164361	+	0.613404i	0.998121	+	0.0612767i	$0.0195172\pi$
$953$	5.07394	+	18.9362i	0.164361	+	0.613404i	−0.833760	+	0.552128i	$0.813816\pi$
$954$	−2.90279	+	1.27644i	−0.0939814	+	0.0413262i
$955$		0			0
$956$	−36.2153	−	99.5008i	−1.17129	−	3.21809i
$957$	−4.52863	+	0.951709i	−0.146390	+	0.0307644i
$958$	−3.84959	−	0.336795i	−0.124375	−	0.0108814i
$959$	2.51823	−	2.11305i	0.0813180	−	0.0682339i
$960$		0			0
$961$	3.41043	−	1.24130i	0.110014	−	0.0400418i
$962$	2.93036	−	10.9362i	0.0944785	−	0.352599i
$963$	−2.32205	+	0.787615i	−0.0748269	+	0.0253805i
$964$	23.1268	+	13.3523i	0.744865	+	0.430048i
$965$		0			0
$966$	1.80336	+	2.40462i	0.0580220	+	0.0773674i
$967$	3.93769	−	1.83617i	0.126628	−	0.0590474i	−0.358272	−	0.933617i	$-0.616634\pi$
$967$	3.93769	−	1.83617i	0.126628	−	0.0590474i	0.484900	+	0.874570i	$0.338856\pi$
$968$	82.3990	+	57.6964i	2.64841	+	1.85443i
$969$	13.3442	+	3.11310i	0.428678	+	0.100007i
$970$		0			0
$971$		−	17.3753i		−	0.557601i	−0.960349	−	0.278800i	$-0.910063\pi$
$971$		−	17.3753i		−	0.557601i	0.960349	−	0.278800i	$-0.0899367\pi$
$972$	15.6457	−	83.1291i	0.501837	−	2.66637i
$973$	17.2740	+	17.2740i	0.553779	+	0.553779i
$974$	−17.5070	−	14.6901i	−0.560960	−	0.470701i
$975$		0			0
$976$	23.3068	+	132.179i	0.746031	+	4.23095i
$977$	10.2242	+	21.9259i	0.327101	+	0.701470i	0.999241	−	0.0389538i	$-0.0124025\pi$
$977$	10.2242	+	21.9259i	0.327101	+	0.701470i	−0.672140	+	0.740424i	$0.734625\pi$
$978$	16.3424	+	2.33512i	0.522573	+	0.0746690i
$979$	−3.28563	−	0.579345i	−0.105009	−	0.0185159i
$980$		0			0
$981$	−22.7599	−	11.2306i	−0.726667	−	0.358566i
$982$	70.5563	+	18.9055i	2.25154	+	0.603299i
$983$	10.2662	−	22.0159i	0.327441	−	0.702199i	−0.671817	−	0.740717i	$-0.734486\pi$
$983$	10.2662	−	22.0159i	0.327441	−	0.702199i	0.999258	+	0.0385180i	$0.0122637\pi$
$984$	−125.460	−	6.86447i	−3.99951	−	0.218831i
$985$		0			0
$986$	−34.1063	−	40.6463i	−1.08617	−	1.29444i
$987$	−6.82862	−	32.4935i	−0.217357	−	1.03428i
$988$	31.1234	+	14.5131i	0.990168	+	0.461723i
$989$	0.238560	+	0.413197i	0.00758575	+	0.0131389i
$990$		0			0
$991$	−18.0498	+	31.2632i	−0.573372	+	0.993110i	0.422844	+	0.906202i	$0.361032\pi$
$991$	−18.0498	+	31.2632i	−0.573372	+	0.993110i	−0.996216	+	0.0869073i	$0.972302\pi$
$992$	90.3927	−	63.2936i	2.86997	−	2.00957i
$993$	−9.57682	+	3.84369i	−0.303911	+	0.121976i
$994$	23.5387	−	64.6720i	0.746602	−	2.05127i
$995$		0			0
$996$	19.9817	+	18.7194i	0.633145	+	0.593146i
$997$	−19.8840	+	1.73962i	−0.629732	+	0.0550944i	−0.397554	−	0.917579i	$-0.630141\pi$
$997$	−19.8840	+	1.73962i	−0.629732	+	0.0550944i	−0.232178	+	0.972673i	$0.574585\pi$
$998$	−21.5721	+	21.5721i	−0.682854	+	0.682854i
$999$	−7.66811	−	1.26881i	−0.242608	−	0.0401434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.443.1		192
5.2	odd	4	inner	675.2.ba.b.632.16		192
5.3	odd	4		135.2.q.a.92.1	yes	192
5.4	even	2		135.2.q.a.38.16	yes	192
15.8	even	4		405.2.r.a.197.16		192
15.14	odd	2		405.2.r.a.278.1		192
27.5	odd	18	inner	675.2.ba.b.518.16		192
135.32	even	36	inner	675.2.ba.b.32.1		192
135.49	even	18		405.2.r.a.368.16		192
135.59	odd	18		135.2.q.a.113.1	yes	192
135.103	odd	36		405.2.r.a.287.1		192
135.113	even	36		135.2.q.a.32.16	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	135.113	even	36
135.2.q.a.38.16	yes	192	5.4	even	2
135.2.q.a.92.1	yes	192	5.3	odd	4
135.2.q.a.113.1	yes	192	135.59	odd	18
405.2.r.a.197.16		192	15.8	even	4
405.2.r.a.278.1		192	15.14	odd	2
405.2.r.a.287.1		192	135.103	odd	36
405.2.r.a.368.16		192	135.49	even	18
675.2.ba.b.32.1		192	135.32	even	36	inner
675.2.ba.b.443.1		192	1.1	even	1	trivial
675.2.ba.b.518.16		192	27.5	odd	18	inner
675.2.ba.b.632.16		192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.237511 - 2.71476i) q^{2} +(-0.914466 - 1.47097i) q^{3} +(-5.34392 + 0.942278i) q^{4} +(-3.77614 + 2.83193i) q^{6} +(-0.907744 - 1.29639i) q^{7} +(2.41667 + 9.01913i) q^{8} +(-1.32750 + 2.69030i) q^{9} +(0.162954 + 0.447712i) q^{11} +(6.27290 + 6.99907i) q^{12} +(-2.76700 - 0.242081i) q^{13} +(-3.30380 + 2.77222i) q^{14} +(13.7126 - 4.99098i) q^{16} +(-0.898665 + 3.35386i) q^{17} +(7.61884 + 2.96488i) q^{18} +(1.97319 + 1.13922i) q^{19} +(-1.07685 + 2.52077i) q^{21} +(1.17673 - 0.548719i) q^{22} +(0.329603 + 0.230790i) q^{23} +(11.0569 - 11.8025i) q^{24} +7.56924i q^{26} +(5.17131 - 0.507474i) q^{27} +(6.07248 + 6.07248i) q^{28} +(-4.29568 - 3.60450i) q^{29} +(0.908475 + 5.15222i) q^{31} +(-8.91403 - 19.1162i) q^{32} +(0.509556 - 0.649118i) q^{33} +(9.31839 + 1.64308i) q^{34} +(4.55906 - 15.6276i) q^{36} +(-1.44483 - 0.387140i) q^{37} +(2.62407 - 5.62733i) q^{38} +(2.17423 + 4.29154i) q^{39} +(-4.99389 - 5.95149i) q^{41} +(7.09907 + 2.32469i) q^{42} +(1.07467 + 0.501128i) q^{43} +(-1.29268 - 2.23899i) q^{44} +(0.548257 - 0.949609i) q^{46} +(-9.92230 + 6.94767i) q^{47} +(-19.8813 - 15.6068i) q^{48} +(1.53751 - 4.22426i) q^{49} +(5.75523 - 1.74508i) q^{51} +(15.0147 - 1.31362i) q^{52} +(-0.274270 + 0.274270i) q^{53} +(-2.60592 - 13.9184i) q^{54} +(9.49862 - 11.3200i) q^{56} +(-0.128655 - 3.94428i) q^{57} +(-8.76510 + 12.5179i) q^{58} +(3.33385 + 1.21342i) q^{59} +(-1.59716 + 9.05792i) q^{61} +(13.7713 - 3.69001i) q^{62} +(4.69272 - 0.721141i) q^{63} +(-24.5036 + 14.1471i) q^{64} +(-1.88323 - 1.22915i) q^{66} +(-1.15101 + 13.1561i) q^{67} +(1.64212 - 18.7696i) q^{68} +(0.0380751 - 0.695886i) q^{69} +(-13.8198 + 7.97886i) q^{71} +(-27.4723 - 5.47136i) q^{72} +(7.73957 - 2.07381i) q^{73} +(-0.707832 + 4.01431i) q^{74} +(-11.6180 - 4.22862i) q^{76} +(0.432491 - 0.617661i) q^{77} +(11.1341 - 6.92182i) q^{78} +(2.85683 - 3.40464i) q^{79} +(-5.47547 - 7.14278i) q^{81} +(-14.9708 + 14.9708i) q^{82} +(2.90211 - 0.253902i) q^{83} +(3.37935 - 14.4855i) q^{84} +(1.10520 - 3.03651i) q^{86} +(-1.37386 + 9.61501i) q^{87} +(-3.64417 + 2.55168i) q^{88} +(-3.50126 + 6.06435i) q^{89} +(2.19789 + 3.80686i) q^{91} +(-1.97884 - 0.922748i) q^{92} +(6.74799 - 6.04787i) q^{93} +(21.2179 + 25.2866i) q^{94} +(-19.9678 + 30.5934i) q^{96} +(3.19969 - 6.86175i) q^{97} +(-11.8331 - 3.17066i) q^{98} +(-1.42080 - 0.155944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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