LMFDB - Embedded newform 490.2.w.a.103.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,2,Mod(3,490)] 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("490.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.w (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	490.103
Dual form			490.2.w.a.157.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.593820 - 0.804598i) q^{2} +(-1.64884 + 0.311978i) q^{3} +(-0.294755 - 0.955573i) q^{4} +(1.39094 - 1.75080i) q^{5} +(-0.728099 + 1.51191i) q^{6} +(2.64015 - 0.172004i) q^{7} +(-0.943883 - 0.330279i) q^{8} +(-0.171274 + 0.0672200i) q^{9} +(-0.582721 - 2.15880i) q^{10} +(0.483621 - 1.23225i) q^{11} +(0.784122 + 1.48363i) q^{12} +(4.81429 + 0.542440i) q^{13} +(1.42938 - 2.22640i) q^{14} +(-1.74723 + 3.32073i) q^{15} +(-0.826239 + 0.563320i) q^{16} +(-6.93104 - 0.259341i) q^{17} +(-0.0476208 + 0.177723i) q^{18} +(1.16007 - 2.00930i) q^{19} +(-2.08300 - 0.813085i) q^{20} +(-4.29953 + 1.10728i) q^{21} +(-0.704278 - 1.12085i) q^{22} +(-0.293061 - 7.83223i) q^{23} +(1.65935 + 0.250107i) q^{24} +(-1.13059 - 4.87050i) q^{25} +(3.29527 - 3.55145i) q^{26} +(4.52409 - 2.84267i) q^{27} +(-0.942561 - 2.47216i) q^{28} +(-4.04070 + 0.922264i) q^{29} +(1.63431 + 3.37773i) q^{30} +(7.60947 - 4.39333i) q^{31} +(-0.0373912 + 0.999301i) q^{32} +(-0.412981 + 2.18266i) q^{33} +(-4.32445 + 5.42269i) q^{34} +(3.37115 - 4.86162i) q^{35} +(0.114718 + 0.143851i) q^{36} +(-4.18511 + 2.21190i) q^{37} +(-0.927804 - 2.12655i) q^{38} +(-8.10723 + 0.607553i) q^{39} +(-1.89113 + 1.19315i) q^{40} +(4.78974 + 9.94600i) q^{41} +(-1.66224 + 4.11692i) q^{42} +(-1.93032 - 5.51652i) q^{43} +(-1.32005 - 0.0989241i) q^{44} +(-0.120543 + 0.393365i) q^{45} +(-6.47582 - 4.41514i) q^{46} +(-4.14606 - 3.05993i) q^{47} +(1.18659 - 1.18659i) q^{48} +(6.94083 - 0.908233i) q^{49} +(-4.59016 - 1.98253i) q^{50} +(11.5091 - 1.73472i) q^{51} +(-0.900696 - 4.76029i) q^{52} +(0.584880 + 0.309118i) q^{53} +(0.399286 - 5.32811i) q^{54} +(-1.48473 - 2.56070i) q^{55} +(-2.54881 - 0.709636i) q^{56} +(-1.28591 + 3.67493i) q^{57} +(-1.65740 + 3.79880i) q^{58} +(0.771226 + 10.2913i) q^{59} +(3.68820 + 0.690799i) q^{60} +(-2.14990 + 6.96980i) q^{61} +(0.983794 - 8.73141i) q^{62} +(-0.440627 + 0.206931i) q^{63} +(0.781831 + 0.623490i) q^{64} +(7.64608 - 7.67435i) q^{65} +(1.51092 + 1.62839i) q^{66} +(0.988548 + 0.264881i) q^{67} +(1.79514 + 6.69955i) q^{68} +(2.92669 + 12.8227i) q^{69} +(-1.90980 - 5.59935i) q^{70} +(-2.83098 + 12.4033i) q^{71} +(0.183864 - 0.00687970i) q^{72} +(8.99805 - 6.64086i) q^{73} +(-0.705517 + 4.68080i) q^{74} +(3.38364 + 7.67796i) q^{75} +(-2.26196 - 0.516279i) q^{76} +(1.06488 - 3.33650i) q^{77} +(-4.32540 + 6.88383i) q^{78} +(-3.19066 - 1.84213i) q^{79} +(-0.162987 + 2.23012i) q^{80} +(-6.16802 + 5.72309i) q^{81} +(10.8468 + 2.05232i) q^{82} +(0.628653 + 5.57945i) q^{83} +(2.32539 + 3.78214i) q^{84} +(-10.0947 + 11.7741i) q^{85} +(-5.58484 - 1.72270i) q^{86} +(6.37475 - 2.78128i) q^{87} +(-0.863466 + 1.00337i) q^{88} +(3.46806 + 8.83647i) q^{89} +(0.244920 + 0.330576i) q^{90} +(12.8038 + 0.604050i) q^{91} +(-7.39788 + 2.58863i) q^{92} +(-11.1762 + 9.61789i) q^{93} +(-4.92402 + 1.51886i) q^{94} +(-1.90429 - 4.82585i) q^{95} +(-0.250107 - 1.65935i) q^{96} +(3.17289 + 3.17289i) q^{97} +(3.39084 - 6.12390i) q^{98} +0.243560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + 12 q^{10} + 4 q^{11} - 44 q^{15} - 56 q^{16} + 8 q^{17} + 28 q^{21} + 20 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 4 q^{28} - 12 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{35}+ \cdots - 40 q^{98}+O(q^{100}) $ 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7 + 12 * q^10 + 4 * q^11 - 44 * q^15 - 56 * q^16 + 8 * q^17 + 28 * q^21 + 20 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 4 * q^28 - 12 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^35 + 92 * q^36 - 12 * q^37 - 24 * q^38 - 112 * q^41 + 76 * q^42 + 24 * q^43 - 100 * q^45 - 160 * q^46 + 72 * q^47 + 32 * q^50 - 208 * q^51 + 160 * q^53 - 84 * q^55 - 52 * q^56 - 92 * q^57 + 128 * q^58 - 212 * q^61 + 36 * q^63 - 16 * q^67 + 36 * q^68 - 16 * q^70 - 16 * q^71 + 12 * q^73 + 132 * q^75 - 16 * q^77 + 80 * q^78 + 12 * q^80 - 36 * q^81 + 48 * q^82 - 308 * q^83 - 40 * q^85 - 4 * q^86 + 52 * q^87 - 4 * q^88 + 84 * q^90 - 124 * q^91 - 8 * q^92 - 536 * q^93 - 28 * q^95 - 12 * q^96 - 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.593820	−	0.804598i	0.419894	−	0.568937i
$2$	0.593820	−	0.804598i	0.419894	−	0.568937i
$3$	−1.64884	+	0.311978i	−0.951959	+	0.180120i	−0.638621	−	0.769521i	$-0.720495\pi$
$3$	−1.64884	+	0.311978i	−0.951959	+	0.180120i	−0.313338	+	0.949642i	$0.601447\pi$
$4$	−0.294755	−	0.955573i	−0.147378	−	0.477786i
$5$	1.39094	−	1.75080i	0.622046	−	0.782981i
$5$	1.39094	−	1.75080i	0.622046	−	0.782981i
$6$	−0.728099	+	1.51191i	−0.297245	+	0.617236i
$7$	2.64015	−	0.172004i	0.997885	−	0.0650113i
$7$	2.64015	−	0.172004i	0.997885	−	0.0650113i
$8$	−0.943883	−	0.330279i	−0.333713	−	0.116771i
$9$	−0.171274	+	0.0672200i	−0.0570913	+	0.0224067i
$10$	−0.582721	−	2.15880i	−0.184273	−	0.682674i
$11$	0.483621	−	1.23225i	0.145817	−	0.371536i	−0.839241	−	0.543760i	$-0.817000\pi$
$11$	0.483621	−	1.23225i	0.145817	−	0.371536i	0.985058	+	0.172224i	$0.0550954\pi$
$12$	0.784122	+	1.48363i	0.226356	+	0.428287i
$13$	4.81429	+	0.542440i	1.33524	+	0.150446i	0.750553	−	0.660810i	$-0.229787\pi$
$13$	4.81429	+	0.542440i	1.33524	+	0.150446i	0.584691	+	0.811256i	$0.301216\pi$
$14$	1.42938	−	2.22640i	0.382019	−	0.595031i
$15$	−1.74723	+	3.32073i	−0.451132	+	0.857409i
$16$	−0.826239	+	0.563320i	−0.206560	+	0.140830i
$17$	−6.93104	−	0.259341i	−1.68102	−	0.0628994i	−0.820287	−	0.571952i	$-0.806186\pi$
$17$	−6.93104	−	0.259341i	−1.68102	−	0.0628994i	−0.860736	+	0.509052i	$0.829996\pi$
$18$	−0.0476208	+	0.177723i	−0.0112243	+	0.0418898i
$19$	1.16007	−	2.00930i	0.266138	−	0.460964i	−0.701723	−	0.712450i	$-0.747586\pi$
$19$	1.16007	−	2.00930i	0.266138	−	0.460964i	0.967861	+	0.251485i	$0.0809191\pi$
$20$	−2.08300	−	0.813085i	−0.465773	−	0.181811i
$21$	−4.29953	+	1.10728i	−0.938235	+	0.241627i
$22$	−0.704278	−	1.12085i	−0.150153	−	0.238967i
$23$	−0.293061	−	7.83223i	−0.0611075	−	1.63313i	−0.606594	−	0.795012i	$-0.707464\pi$
$23$	−0.293061	−	7.83223i	−0.0611075	−	1.63313i	0.545486	−	0.838120i	$-0.316345\pi$
$24$	1.65935	+	0.250107i	0.338714	+	0.0510529i
$25$	−1.13059	−	4.87050i	−0.226117	−	0.974100i
$26$	3.29527	−	3.55145i	0.646255	−	0.696498i
$27$	4.52409	−	2.84267i	0.870661	−	0.547072i
$28$	−0.942561	−	2.47216i	−0.178127	−	0.467194i
$29$	−4.04070	+	0.922264i	−0.750340	+	0.171260i	−0.580555	−	0.814221i	$-0.697164\pi$
$29$	−4.04070	+	0.922264i	−0.750340	+	0.171260i	−0.169785	+	0.985481i	$0.554307\pi$
$30$	1.63431	+	3.37773i	0.298383	+	0.616686i
$31$	7.60947	−	4.39333i	1.36670	−	0.789066i	0.376196	−	0.926540i	$-0.377232\pi$
$31$	7.60947	−	4.39333i	1.36670	−	0.789066i	0.990505	+	0.137474i	$0.0438985\pi$
$32$	−0.0373912	+	0.999301i	−0.00660989	+	0.176653i
$33$	−0.412981	+	2.18266i	−0.0718907	+	0.379952i
$34$	−4.32445	+	5.42269i	−0.741638	+	0.929984i
$35$	3.37115	−	4.86162i	0.569828	−	0.821764i
$36$	0.114718	+	0.143851i	0.0191196	+	0.0239752i
$37$	−4.18511	+	2.21190i	−0.688028	+	0.363634i	−0.774459	−	0.632624i	$-0.781978\pi$
$37$	−4.18511	+	2.21190i	−0.688028	+	0.363634i	0.0864304	+	0.996258i	$0.472454\pi$
$38$	−0.927804	−	2.12655i	−0.150510	−	0.344972i
$39$	−8.10723	+	0.607553i	−1.29820	+	0.0972863i
$40$	−1.89113	+	1.19315i	−0.299015	+	0.188654i
$41$	4.78974	+	9.94600i	0.748032	+	1.55330i	0.830696	+	0.556727i	$0.187943\pi$
$41$	4.78974	+	9.94600i	0.748032	+	1.55330i	−0.0826640	+	0.996577i	$0.526343\pi$
$42$	−1.66224	+	4.11692i	−0.256489	+	0.635254i
$43$	−1.93032	−	5.51652i	−0.294370	−	0.841262i	−0.992162	−	0.124961i	$-0.960119\pi$
$43$	−1.93032	−	5.51652i	−0.294370	−	0.841262i	0.697791	−	0.716301i	$-0.254166\pi$
$44$	−1.32005	−	0.0989241i	−0.199005	−	0.0149134i
$45$	−0.120543	+	0.393365i	−0.0179694	+	0.0586394i
$46$	−6.47582	−	4.41514i	−0.954807	−	0.650976i
$47$	−4.14606	−	3.05993i	−0.604764	−	0.446336i	0.247907	−	0.968784i	$-0.420257\pi$
$47$	−4.14606	−	3.05993i	−0.604764	−	0.446336i	−0.852672	+	0.522447i	$0.825019\pi$
$48$	1.18659	−	1.18659i	0.171270	−	0.171270i
$49$	6.94083	−	0.908233i	0.991547	−	0.129748i
$50$	−4.59016	−	1.98253i	−0.649146	−	0.280373i
$51$	11.5091	−	1.73472i	1.61159	−	0.242909i
$52$	−0.900696	−	4.76029i	−0.124904	−	0.660134i
$53$	0.584880	+	0.309118i	0.0803394	+	0.0424606i	0.506956	−	0.861972i	$-0.330771\pi$
$53$	0.584880	+	0.309118i	0.0803394	+	0.0424606i	−0.426616	+	0.904433i	$0.640295\pi$
$54$	0.399286	−	5.32811i	0.0543360	−	0.725063i
$55$	−1.48473	−	2.56070i	−0.200200	−	0.345285i
$56$	−2.54881	−	0.709636i	−0.340599	−	0.0948291i
$57$	−1.28591	+	3.67493i	−0.170323	+	0.486756i
$58$	−1.65740	+	3.79880i	−0.217627	+	0.498807i
$59$	0.771226	+	10.2913i	0.100405	+	1.33981i	0.788877	+	0.614551i	$0.210663\pi$
$59$	0.771226	+	10.2913i	0.100405	+	1.33981i	−0.688472	+	0.725263i	$0.741718\pi$
$60$	3.68820	+	0.690799i	0.476145	+	0.0891818i
$61$	−2.14990	+	6.96980i	−0.275266	+	0.892392i	0.707369	+	0.706845i	$0.249882\pi$
$61$	−2.14990	+	6.96980i	−0.275266	+	0.892392i	−0.982635	+	0.185547i	$0.940594\pi$
$62$	0.983794	−	8.73141i	0.124942	−	1.10889i
$63$	−0.440627	+	0.206931i	−0.0555138	+	0.0260709i
$64$	0.781831	+	0.623490i	0.0977289	+	0.0779362i
$65$	7.64608	−	7.67435i	0.948379	−	0.951886i
$66$	1.51092	+	1.62839i	0.185982	+	0.200441i
$67$	0.988548	+	0.264881i	0.120770	+	0.0323603i	0.318698	−	0.947856i	$-0.396754\pi$
$67$	0.988548	+	0.264881i	0.120770	+	0.0323603i	−0.197928	+	0.980217i	$0.563421\pi$
$68$	1.79514	+	6.69955i	0.217693	+	0.812440i
$69$	2.92669	+	12.8227i	0.352332	+	1.54367i
$70$	−1.90980	−	5.59935i	−0.228264	−	0.669250i
$71$	−2.83098	+	12.4033i	−0.335975	+	1.47200i	0.471376	+	0.881932i	$0.343757\pi$
$71$	−2.83098	+	12.4033i	−0.335975	+	1.47200i	−0.807351	+	0.590071i	$0.799100\pi$
$72$	0.183864	−	0.00687970i	0.0216686	−	0.000810781i
$73$	8.99805	−	6.64086i	1.05314	−	0.777254i	0.0775819	−	0.996986i	$-0.475280\pi$
$73$	8.99805	−	6.64086i	1.05314	−	0.777254i	0.975560	+	0.219732i	$0.0705182\pi$
$74$	−0.705517	+	4.68080i	−0.0820147	+	0.544132i
$75$	3.38364	+	7.67796i	0.390710	+	0.886575i
$76$	−2.26196	−	0.516279i	−0.259465	−	0.0592212i
$77$	1.06488	−	3.33650i	0.121355	−	0.380230i
$78$	−4.32540	+	6.88383i	−0.489755	+	0.779441i
$79$	−3.19066	−	1.84213i	−0.358977	−	0.207256i	0.309655	−	0.950849i	$-0.399787\pi$
$79$	−3.19066	−	1.84213i	−0.358977	−	0.207256i	−0.668632	+	0.743593i	$0.733120\pi$
$80$	−0.162987	+	2.23012i	−0.0182225	+	0.249335i
$81$	−6.16802	+	5.72309i	−0.685336	+	0.635899i
$82$	10.8468	+	2.05232i	1.19783	+	0.226641i
$83$	0.628653	+	5.57945i	0.0690037	+	0.612424i	0.979858	+	0.199696i	$0.0639955\pi$
$83$	0.628653	+	5.57945i	0.0690037	+	0.612424i	−0.910854	+	0.412728i	$0.864576\pi$
$84$	2.32539	+	3.78214i	0.253721	+	0.412666i
$85$	−10.0947	+	11.7741i	−1.09492	+	1.27708i
$86$	−5.58484	−	1.72270i	−0.602229	−	0.185763i
$87$	6.37475	−	2.78128i	0.683445	−	0.298184i
$88$	−0.863466	+	1.00337i	−0.0920458	+	0.106959i
$89$	3.46806	+	8.83647i	0.367614	+	0.936664i	0.988289	+	0.152596i	$0.0487635\pi$
$89$	3.46806	+	8.83647i	0.367614	+	0.936664i	−0.620675	+	0.784068i	$0.713141\pi$
$90$	0.244920	+	0.330576i	0.0258168	+	0.0348458i
$91$	12.8038	+	0.604050i	1.34220	+	0.0633216i
$92$	−7.39788	+	2.58863i	−0.771282	+	0.269883i
$93$	−11.1762	+	9.61789i	−1.15892	+	0.997329i
$94$	−4.92402	+	1.51886i	−0.507874	+	0.156658i
$95$	−1.90429	−	4.82585i	−0.195376	−	0.495122i
$96$	−0.250107	−	1.65935i	−0.0255265	−	0.169357i
$97$	3.17289	+	3.17289i	0.322158	+	0.322158i	0.849595	−	0.527436i	$-0.176847\pi$
$97$	3.17289	+	3.17289i	0.322158	+	0.322158i	−0.527436	+	0.849595i	$0.676847\pi$
$98$	3.39084	−	6.12390i	0.342527	−	0.618608i
$99$			0.243560i			0.0244787i
$100$	−4.32087	+	2.51596i	−0.432087	+	0.251596i
$101$	8.29023	−	12.1595i	0.824908	−	1.20992i	−0.150303	−	0.988640i	$-0.548025\pi$
$101$	8.29023	−	12.1595i	0.824908	−	1.20992i	0.975211	−	0.221278i	$-0.0710229\pi$
$102$	5.43858	−	10.2903i	0.538500	−	1.01889i
$103$	5.04710	+	5.86483i	0.497305	+	0.577879i	0.949392	−	0.314095i	$-0.101701\pi$
$103$	5.04710	+	5.86483i	0.497305	+	0.577879i	−0.452086	+	0.891974i	$0.649320\pi$
$104$	−4.36497	−	2.10206i	−0.428021	−	0.206124i
$105$	−4.04177	+	9.06777i	−0.394436	+	0.884923i
$106$	0.596029	−	0.287033i	0.0578915	−	0.0278791i
$107$	0.930544	+	0.405992i	0.0899591	+	0.0392488i	0.444390	−	0.895834i	$-0.353421\pi$
$107$	0.930544	+	0.405992i	0.0899591	+	0.0392488i	−0.354431	+	0.935082i	$0.615325\pi$
$108$	−4.04988	−	3.48520i	−0.389700	−	0.335364i
$109$	−3.13782	−	1.23150i	−0.300549	−	0.117957i	0.210275	−	0.977642i	$-0.432564\pi$
$109$	−3.13782	−	1.23150i	−0.300549	−	0.117957i	−0.510823	+	0.859686i	$0.670659\pi$
$110$	−2.94199	−	0.325987i	−0.280508	−	0.0310816i
$111$	6.21053	−	4.95273i	0.589477	−	0.470092i
$112$	−2.08450	+	1.62937i	−0.196967	+	0.153961i
$113$	0.409854	−	0.0461795i	0.0385558	−	0.00434420i	−0.0926655	−	0.995697i	$-0.529539\pi$
$113$	0.409854	−	0.0461795i	0.0385558	−	0.00434420i	0.131221	+	0.991353i	$0.458110\pi$
$114$	2.19324	+	3.21689i	0.205415	+	0.301289i
$115$	−14.1203	−	10.3810i	−1.31672	−	0.968037i
$116$	2.07231	+	3.58934i	0.192409	+	0.333262i
$117$	−0.861025	+	0.230711i	−0.0796018	+	0.0213292i
$118$	8.73833	+	5.49066i	0.804428	+	0.505456i
$119$	−18.3436	+	0.507464i	−1.68156	+	0.0465191i
$120$	2.74594	−	2.55731i	0.250669	−	0.233449i
$121$	6.77903	+	6.29002i	0.616276	+	0.571820i
$122$	4.33123	+	5.86861i	0.392132	+	0.531319i
$123$	−11.0005	−	14.9051i	−0.991877	−	1.34395i
$124$	−6.44108	−	5.97645i	−0.578426	−	0.536701i
$125$	−10.0998	−	4.79513i	−0.903357	−	0.428890i
$126$	−0.0951572	+	0.477408i	−0.00847728	+	0.0425309i
$127$	9.29754	+	5.84203i	0.825024	+	0.518397i	0.877135	−	0.480245i	$-0.159452\pi$
$127$	9.29754	+	5.84203i	0.825024	+	0.518397i	−0.0521110	+	0.998641i	$0.516595\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	4.90382	+	8.49366i	0.431757	+	0.747825i
$130$	−1.63437	−	10.7092i	−0.143343	−	0.939259i
$131$	5.23346	+	7.67608i	0.457249	+	0.670662i	0.983756	−	0.179509i	$-0.0574509\pi$
$131$	5.23346	+	7.67608i	0.457249	+	0.670662i	−0.526507	+	0.850171i	$0.676499\pi$
$132$	2.20741	−	0.248716i	0.192131	−	0.0216479i
$133$	2.71715	−	5.50439i	0.235607	−	0.477291i
$134$	0.800142	−	0.638092i	0.0691217	−	0.0551227i
$135$	1.31578	−	11.8747i	0.113244	−	1.02201i
$136$	6.45643	+	2.53396i	0.553635	+	0.217286i
$137$	−1.43502	−	1.23493i	−0.122602	−	0.105507i	0.588850	−	0.808242i	$-0.299581\pi$
$137$	−1.43502	−	1.23493i	−0.122602	−	0.105507i	−0.711452	+	0.702735i	$0.751962\pi$
$138$	12.0550	+	5.25955i	1.02619	+	0.447723i
$139$	12.8866	−	6.20584i	1.09302	−	0.526372i	0.201565	−	0.979475i	$-0.435397\pi$
$139$	12.8866	−	6.20584i	1.09302	−	0.526372i	0.891458	+	0.453103i	$0.149683\pi$
$140$	−5.63930	−	1.78839i	−0.476608	−	0.151146i
$141$	7.79082	+	3.75186i	0.656105	+	0.315964i
$142$	8.29859	+	9.64314i	0.696402	+	0.809234i
$143$	2.99671	−	5.67005i	0.250597	−	0.474153i
$144$	0.103647	−	0.152022i	0.00863723	−	0.0126685i
$145$	−4.00567	+	8.35727i	−0.332653	+	0.694033i
$146$		−	11.1833i		−	0.925536i
$147$	−11.1610	+	3.66292i	−0.920542	+	0.302112i
$148$	3.34721	+	3.34721i	0.275139	+	0.275139i
$149$	2.65999	+	17.6479i	0.217914	+	1.44577i	0.783661	+	0.621189i	$0.213350\pi$
$149$	2.65999	+	17.6479i	0.217914	+	1.44577i	−0.565746	+	0.824579i	$0.691412\pi$
$150$	8.18695	+	1.83686i	0.668462	+	0.149979i
$151$	0.295307	−	0.0910903i	0.0240318	−	0.00741282i	−0.282716	−	0.959204i	$-0.591235\pi$
$151$	0.295307	−	0.0910903i	0.0240318	−	0.00741282i	0.306748	+	0.951791i	$0.400759\pi$
$152$	−1.75860	+	1.51340i	−0.142641	+	0.122753i
$153$	1.20454	−	0.421486i	0.0973811	−	0.0340751i
$154$	−2.05219	−	2.83808i	−0.165371	−	0.228699i
$155$	2.89247	−	19.4335i	0.232328	−	1.56094i
$156$	2.97021	+	7.56797i	0.237807	+	0.605922i
$157$	−5.22979	+	6.07712i	−0.417382	+	0.485007i	−0.926823	−	0.375499i	$-0.877471\pi$
$157$	−5.22979	+	6.07712i	−0.417382	+	0.485007i	0.509441	+	0.860506i	$0.329852\pi$
$158$	−3.37685	+	1.47331i	−0.268648	+	0.117210i
$159$	−1.06081	−	0.327217i	−0.0841279	−	0.0259500i
$160$	1.69756	+	1.45543i	0.134204	+	0.115062i
$161$	−2.12090	−	20.6279i	−0.167150	−	1.62570i
$162$	0.942088	+	8.36126i	0.0740174	+	0.656923i
$163$	−15.6420	−	2.95962i	−1.22517	−	0.231815i	−0.467230	−	0.884136i	$-0.654748\pi$
$163$	−15.6420	−	2.95962i	−1.22517	−	0.231815i	−0.757944	+	0.652320i	$0.773796\pi$
$164$	8.09233	−	7.50858i	0.631904	−	0.586322i
$165$	3.24696	+	3.75898i	0.252775	+	0.292636i
$166$	4.86252	+	2.80738i	0.377405	+	0.217895i
$167$	8.86409	−	14.1071i	0.685924	−	1.09164i	−0.304357	−	0.952558i	$-0.598442\pi$
$167$	8.86409	−	14.1071i	0.685924	−	1.09164i	0.990281	−	0.139083i	$-0.0444156\pi$
$168$	4.42397	+	0.374907i	0.341317	+	0.0289247i
$169$	10.2091	+	2.33016i	0.785314	+	0.179243i
$170$	3.47900	+	15.1139i	0.266827	+	1.15918i
$171$	−0.0636243	+	0.422120i	−0.00486547	+	0.0322803i
$172$	−4.70247	+	3.47058i	−0.358560	+	0.264629i
$173$	−23.8485	+	0.892348i	−1.81317	+	0.0678439i	−0.922313	−	0.386445i	$-0.873703\pi$
$173$	−23.8485	+	0.892348i	−1.81317	+	0.0678439i	−0.890855	+	0.454289i	$0.849893\pi$
$174$	1.54765	−	6.78069i	0.117327	−	0.514043i
$175$	−3.82267	−	12.6644i	−0.288966	−	0.957339i
$176$	0.294562	+	1.29056i	0.0222035	+	0.0972798i
$177$	−4.48229	−	16.7281i	−0.336909	−	1.25736i
$178$	9.16921	+	2.45688i	0.687262	+	0.184151i
$179$	4.46246	+	4.80938i	0.333540	+	0.359470i	0.877446	−	0.479676i	$-0.159246\pi$
$179$	4.46246	+	4.80938i	0.333540	+	0.359470i	−0.543906	+	0.839146i	$0.683055\pi$
$180$	0.411419		0.000759134i	0.0306654		5.65825e-5i
$181$	−12.3726	−	9.86683i	−0.919649	−	0.733395i	0.0444299	−	0.999013i	$-0.485853\pi$
$181$	−12.3726	−	9.86683i	−0.919649	−	0.733395i	−0.964079	+	0.265617i	$0.914424\pi$
$182$	8.08915	−	9.94319i	0.599608	−	0.737038i
$183$	1.37042	−	12.1628i	0.101304	−	0.899101i
$184$	−2.31020	+	7.48950i	−0.170311	+	0.552133i
$185$	−1.94865	+	10.4039i	−0.143267	+	0.764910i
$186$	1.10189	+	14.7036i	0.0807941	+	1.07812i
$187$	−3.67156	+	8.41531i	−0.268491	+	0.615389i
$188$	−1.70191	+	4.86379i	−0.124125	+	0.354728i
$189$	11.4553	−	8.28325i	0.833253	−	0.602518i
$190$	−5.01367	−	1.33350i	−0.363730	−	0.0967422i
$191$	1.73067	−	23.0942i	0.125227	−	1.67103i	−0.481746	−	0.876311i	$-0.659997\pi$
$191$	1.73067	−	23.0942i	0.125227	−	1.67103i	0.606972	−	0.794723i	$-0.292384\pi$
$192$	−1.48363	−	0.784122i	−0.107072	−	0.0565891i
$193$	−2.13659	−	11.2921i	−0.153795	−	0.812826i	−0.971473	−	0.237150i	$-0.923787\pi$
$193$	−2.13659	−	11.2921i	−0.153795	−	0.812826i	0.817678	−	0.575676i	$-0.195261\pi$
$194$	4.43703	−	0.668775i	0.318560	−	0.0480152i
$195$	−10.2129	+	15.0392i	−0.731364	+	1.07698i
$196$	−2.91373	−	6.36476i	−0.208123	−	0.454626i
$197$	−4.12723	+	4.12723i	−0.294053	+	0.294053i	−0.838679	−	0.544626i	$-0.816672\pi$
$197$	−4.12723	+	4.12723i	−0.294053	+	0.294053i	0.544626	+	0.838679i	$0.316672\pi$
$198$	0.195968	+	0.144631i	0.0139269	+	0.0102785i
$199$	1.12916	+	0.769850i	0.0800442	+	0.0545732i	0.602681	−	0.797982i	$-0.294099\pi$
$199$	1.12916	+	0.769850i	0.0800442	+	0.0545732i	−0.522637	+	0.852555i	$0.675052\pi$
$200$	−0.541483	+	4.97059i	−0.0382886	+	0.351474i
$201$	−1.71259	−	0.128341i	−0.120797	−	0.00905249i
$202$	−4.86063	−	13.8909i	−0.341992	−	0.977358i
$203$	−10.5094	+	3.12994i	−0.737619	+	0.219678i
$204$	−5.05001	−	10.4865i	−0.353571	−	0.734199i
$205$	24.0757	+	5.44839i	1.68152	+	0.380532i
$206$	7.71590	−	0.578227i	0.537592	−	0.0402870i
$207$	0.576676	+	1.32176i	0.0400818	+	0.0918684i
$208$	−4.28332	+	2.26380i	−0.296995	+	0.156966i
$209$	−1.91491	−	2.40123i	−0.132457	−	0.166096i
$210$	4.89582	+	8.63662i	0.337844	+	0.595983i
$211$	−7.23655	+	9.07435i	−0.498185	+	0.624704i	−0.965819	−	0.259218i	$-0.916535\pi$
$211$	−7.23655	+	9.07435i	−0.498185	+	0.624704i	0.467634	+	0.883922i	$0.345107\pi$
$212$	0.122988	−	0.650010i	0.00844688	−	0.0446428i
$213$	0.798273	−	21.3343i	0.0546968	−	1.46180i
$214$	0.879236	−	0.507627i	0.0601034	−	0.0347007i
$215$	−12.3433	−	4.29355i	−0.841804	−	0.292818i
$216$	−5.20909	+	1.18894i	−0.354433	+	0.0808971i
$217$	19.3345	−	12.9079i	1.31251	−	0.876247i
$218$	−2.85417	+	1.79339i	−0.193309	+	0.121464i
$219$	−12.7646	+	13.7569i	−0.862549	+	0.929607i
$220$	−2.00930	+	2.17354i	−0.135467	+	0.146540i
$221$	−33.2273	−	5.00821i	−2.23511	−	0.336889i
$222$	−0.297019	−	7.93801i	−0.0199346	−	0.532764i
$223$	10.1451	+	16.1459i	0.679367	+	1.08121i	0.991366	+	0.131124i	$0.0418586\pi$
$223$	10.1451	+	16.1459i	0.679367	+	1.08121i	−0.311999	+	0.950082i	$0.600999\pi$
$224$	0.0731649	+	2.64474i	0.00488854	+	0.176709i
$225$	0.521035	+	0.758192i	0.0347357	+	0.0505461i
$226$	0.206224	−	0.357190i	0.0137178	−	0.0237599i
$227$	−5.51242	+	20.5726i	−0.365872	+	1.36545i	0.500362	+	0.865816i	$0.333200\pi$
$227$	−5.51242	+	20.5726i	−0.365872	+	1.36545i	−0.866235	+	0.499638i	$0.833467\pi$
$228$	3.89069	+	0.145579i	0.257667	+	0.00964122i
$229$	−10.5260	+	7.17649i	−0.695577	+	0.474236i	−0.858772	−	0.512358i	$-0.828772\pi$
$229$	−10.5260	+	7.17649i	−0.695577	+	0.474236i	0.163196	+	0.986594i	$0.447820\pi$
$230$	−16.7375	+	5.19667i	−1.10364	+	0.342658i
$231$	−0.714908	+	5.83358i	−0.0470375	+	0.383822i
$232$	4.11856	+	0.464050i	0.270397	+	0.0304664i
$233$	10.3328	+	19.5507i	0.676926	+	1.28081i	0.948007	+	0.318250i	$0.103095\pi$
$233$	10.3328	+	19.5507i	0.676926	+	1.28081i	−0.271081	+	0.962557i	$0.587381\pi$
$234$	−0.325664	+	0.829780i	−0.0212894	+	0.0542444i
$235$	−11.1242	+	3.00274i	−0.725664	+	0.195877i
$236$	9.60676	−	3.77038i	0.625347	−	0.245431i
$237$	5.83560	+	2.04196i	0.379063	+	0.132640i
$238$	−10.4845	+	15.0606i	−0.679609	+	0.976232i
$239$	1.71774	−	3.56693i	0.111112	−	0.230726i	−0.837997	−	0.545675i	$-0.816273\pi$
$239$	1.71774	−	3.56693i	0.111112	−	0.230726i	0.949108	+	0.314950i	$0.101988\pi$
$240$	−0.427008	−	3.72796i	−0.0275632	−	0.240639i
$241$	8.94453	+	28.9975i	0.576168	+	1.86789i	0.490237	+	0.871589i	$0.336910\pi$
$241$	8.94453	+	28.9975i	0.576168	+	1.86789i	0.0859314	+	0.996301i	$0.472613\pi$
$242$	9.08646	−	1.71925i	0.584100	−	0.110518i
$243$	−1.13381	+	1.53626i	−0.0727341	+	0.0985512i
$244$	7.29385			0.466941
$245$	8.06413	−	13.4153i	0.515198	−	0.857071i
$246$	−18.5249			−1.18110
$247$	6.67482	−	9.04407i	0.424709	−	0.575460i
$248$	−8.63348	+	1.63354i	−0.548226	+	0.103730i
$249$	−2.77721	−	9.00350i	−0.175999	−	0.570574i
$250$	−9.85564	+	5.27886i	−0.623325	+	0.333864i
$251$	4.19253	−	8.70587i	0.264630	−	0.549510i	−0.725738	−	0.687971i	$-0.758501\pi$
$251$	4.19253	−	8.70587i	0.264630	−	0.549510i	0.990368	+	0.138462i	$0.0442158\pi$
$252$	0.327615	+	0.360058i	0.0206378	+	0.0226815i
$253$	−9.79295	−	3.42670i	−0.615678	−	0.215435i
$254$	10.2216	−	4.01167i	0.641358	−	0.251714i
$255$	12.9713	−	22.5630i	0.812293	−	1.41295i
$256$	0.365341	−	0.930874i	0.0228338	−	0.0581796i
$257$	−1.36735	−	2.58715i	−0.0852930	−	0.161382i	0.837779	−	0.546010i	$-0.183854\pi$
$257$	−1.36735	−	2.58715i	−0.0852930	−	0.161382i	−0.923072	+	0.384627i	$0.874330\pi$
$258$	9.74596	+	1.09811i	0.606757	+	0.0683651i
$259$	−10.6689	+	6.55961i	−0.662933	+	0.407594i
$260$	−9.58712	−	5.04433i	−0.594568	−	0.312836i
$261$	0.630072	−	0.429576i	0.0390005	−	0.0265901i
$262$	9.28389	+	0.347379i	0.573560	+	0.0214611i
$263$	1.45752	−	5.43955i	0.0898747	−	0.335417i	−0.906318	−	0.422597i	$-0.861119\pi$
$263$	1.45752	−	5.43955i	0.0898747	−	0.335417i	0.996193	+	0.0871797i	$0.0277854\pi$
$264$	1.11069	−	1.92377i	0.0683583	−	0.118400i
$265$	1.35473	−	0.594043i	0.0832207	−	0.0364917i
$266$	−2.81532	−	5.45483i	−0.172618	−	0.334457i
$267$	−8.47506	−	13.4880i	−0.518665	−	0.825451i
$268$	−0.0382669	−	1.02270i	−0.00233752	−	0.0624716i
$269$	−11.6944	−	1.76265i	−0.713020	−	0.107470i	−0.217492	−	0.976062i	$-0.569787\pi$
$269$	−11.6944	−	1.76265i	−0.713020	−	0.107470i	−0.495528	+	0.868592i	$0.665026\pi$
$270$	−8.77305	−	8.11013i	−0.533911	−	0.493567i
$271$	−11.3423	+	12.2241i	−0.688996	+	0.742561i	−0.976571	−	0.215197i	$-0.930961\pi$
$271$	−11.3423	+	12.2241i	−0.688996	+	0.742561i	0.287575	+	0.957758i	$0.407151\pi$
$272$	5.87278	−	3.69011i	0.356090	−	0.223746i
$273$	−21.2998	+	2.99851i	−1.28912	+	0.181478i
$274$	−1.84576	+	0.421284i	−0.111507	+	0.0254507i
$275$	−6.54843	−	0.962315i	−0.394885	−	0.0580298i
$276$	11.3903	−	6.57621i	0.685618	−	0.395842i
$277$	−0.713482	+	19.0682i	−0.0428690	+	1.14570i	0.797373	+	0.603486i	$0.206222\pi$
$277$	−0.713482	+	19.0682i	−0.0428690	+	1.14570i	−0.840242	+	0.542211i	$0.817587\pi$
$278$	2.65909	−	14.0536i	0.159482	−	0.842882i
$279$	−1.00798	+	1.26397i	−0.0603464	+	0.0756720i
$280$	−4.78766	+	3.47539i	−0.286117	+	0.207694i
$281$	−12.4981	−	15.6721i	−0.745571	−	0.934917i	0.253907	−	0.967229i	$-0.418284\pi$
$281$	−12.4981	−	15.6721i	−0.745571	−	0.934917i	−0.999478	+	0.0323119i	$0.989713\pi$
$282$	7.64508	−	4.04054i	0.455258	−	0.240611i
$283$	−9.14616	−	20.9632i	−0.543683	−	1.24613i	−0.944057	−	0.329782i	$-0.893025\pi$
$283$	−9.14616	−	20.9632i	−0.543683	−	1.24613i	0.400374	−	0.916352i	$-0.368880\pi$
$284$	12.6867	−	0.950738i	0.752818	−	0.0564159i
$285$	4.64543	+	7.36296i	0.275171	+	0.436144i
$286$	−2.78260	−	5.77814i	−0.164539	−	0.341668i
$287$	14.3564	+	25.4351i	0.847432	+	1.50139i
$288$	−0.0607689	−	0.173668i	−0.00358084	−	0.0102335i
$289$	31.0195	+	2.32459i	1.82468	+	0.136741i
$290$	4.34559	+	8.18567i	0.255182	+	0.480679i
$291$	−6.22147	−	4.24172i	−0.364709	−	0.248654i
$292$	−8.99805	−	6.64086i	−0.526571	−	0.388627i
$293$	16.4658	−	16.4658i	0.961942	−	0.961942i	−0.0373601	−	0.999302i	$-0.511895\pi$
$293$	16.4658	−	16.4658i	0.961942	−	0.961942i	0.999302	+	0.0373601i	$0.0118948\pi$
$294$	−3.68044	+	11.1552i	−0.214648	+	0.650585i
$295$	19.0907	+	12.9643i	1.11150	+	0.754810i
$296$	4.68080	−	0.705517i	0.272066	−	0.0410074i
$297$	−1.31493	−	6.94956i	−0.0762998	−	0.403254i
$298$	15.7790	+	8.33943i	0.914051	+	0.483090i
$299$	2.83763	−	37.8656i	0.164105	−	2.18982i
$300$	6.33951	−	5.49644i	0.366012	−	0.317337i
$301$	−6.04519	−	14.2325i	−0.348439	−	0.820345i
$302$	0.102068	−	0.291695i	0.00587338	−	0.0167852i
$303$	−9.87576	+	22.6355i	−0.567348	+	1.30038i
$304$	0.173384	+	2.31365i	0.00994425	+	0.132697i
$305$	9.21234	+	13.4586i	0.527497	+	0.770637i
$306$	0.376152	−	1.21946i	0.0215032	−	0.0697116i
$307$	−1.46102	+	12.9669i	−0.0833850	+	0.740063i	0.880555	+	0.473944i	$0.157170\pi$
$307$	−1.46102	+	12.9669i	−0.0833850	+	0.740063i	−0.963940	+	0.266119i	$0.914259\pi$
$308$	−3.50215	−	0.0341213i	−0.199554	−	0.00194424i
$309$	−10.1516	−	8.09560i	−0.577502	−	0.460542i
$310$	−13.9185	−	13.8673i	−0.790520	−	0.787608i
$311$	−1.67241	−	1.80243i	−0.0948335	−	0.102206i	0.683852	−	0.729621i	$-0.260304\pi$
$311$	−1.67241	−	1.80243i	−0.0948335	−	0.102206i	−0.778685	+	0.627415i	$0.784113\pi$
$312$	7.85294	+	2.10419i	0.444585	+	0.119126i
$313$	−2.47698	−	9.24421i	−0.140007	−	0.522513i	−0.999927	−	0.0120844i	$-0.996153\pi$
$313$	−2.47698	−	9.24421i	−0.140007	−	0.522513i	0.859920	−	0.510429i	$-0.170513\pi$
$314$	1.78409	+	7.81659i	0.100682	+	0.441116i
$315$	−0.250591	+	1.05928i	−0.0141192	+	0.0596835i
$316$	−0.819824	+	3.59189i	−0.0461187	+	0.202059i
$317$	−5.12471	+	0.191753i	−0.287832	+	0.0107699i	−0.180917	−	0.983498i	$-0.557907\pi$
$317$	−5.12471	+	0.191753i	−0.287832	+	0.0107699i	−0.106915	+	0.994268i	$0.534097\pi$
$318$	−0.893210	+	0.659219i	−0.0500887	+	0.0369672i
$319$	−0.817712	+	5.42517i	−0.0457831	+	0.303751i
$320$	2.17908	−	0.501594i	0.121814	−	0.0280399i
$321$	−1.66098	−	0.379108i	−0.0927069	−	0.0211597i
$322$	−17.8566	−	10.5428i	−0.995108	−	0.587526i
$323$	−8.56156	+	13.6256i	−0.476378	+	0.758151i
$324$	7.28688	+	4.20708i	0.404827	+	0.233727i
$325$	−2.80101	−	24.0613i	−0.155372	−	1.33468i
$326$	−11.6698	+	10.8280i	−0.646332	+	0.599708i
$327$	5.55797	+	1.05162i	0.307356	+	0.0581550i
$328$	−1.23600	−	10.9698i	−0.0682467	−	0.605707i
$329$	−11.4725	−	7.36555i	−0.632502	−	0.406076i
$330$	4.95258	−	0.380335i	0.272631	−	0.0209368i
$331$	−4.14582	−	1.27882i	−0.227875	−	0.0702901i	0.178715	−	0.983901i	$-0.442806\pi$
$331$	−4.14582	−	1.27882i	−0.227875	−	0.0702901i	−0.406590	+	0.913611i	$0.633282\pi$
$332$	5.14627	−	2.24530i	0.282438	−	0.123227i
$333$	0.568117	−	0.660164i	0.0311326	−	0.0361768i
$334$	−6.08688	−	15.5091i	−0.333059	−	0.848621i
$335$	1.83876	−	1.36231i	0.100462	−	0.0744312i
$336$	2.92869	−	3.33689i	0.159773	−	0.182042i
$337$	23.4642	−	8.21048i	1.27818	−	0.447254i	0.396035	−	0.918236i	$-0.370386\pi$
$337$	23.4642	−	8.21048i	1.27818	−	0.447254i	0.882143	+	0.470982i	$0.156100\pi$
$338$	7.93719	−	6.83051i	0.431726	−	0.371531i
$339$	−0.661377	+	0.204008i	−0.0359211	+	0.0110802i
$340$	14.2265	+	6.17573i	0.771539	+	0.334926i
$341$	−1.73356	−	11.5014i	−0.0938777	−	0.622838i
$342$	0.301855	+	0.301855i	0.0163225	+	0.0163225i
$343$	18.1686	−	3.59172i	0.981014	−	0.193935i
$344$			5.84450i			0.315114i
$345$	26.5207	+	12.7115i	1.42783	+	0.684363i
$346$	−13.4437	+	19.7183i	−0.722740	+	1.06006i
$347$	4.38992	−	8.30613i	0.235663	−	0.445896i	−0.737712	−	0.675116i	$-0.764094\pi$
$347$	4.38992	−	8.30613i	0.235663	−	0.445896i	0.973375	+	0.229220i	$0.0736174\pi$
$348$	−4.53670	−	5.27175i	−0.243193	−	0.282595i
$349$	1.47470	+	0.710179i	0.0789390	+	0.0380150i	0.472937	−	0.881096i	$-0.343194\pi$
$349$	1.47470	+	0.710179i	0.0789390	+	0.0380150i	−0.393998	+	0.919111i	$0.628908\pi$
$350$	−12.4597	−	4.44467i	−0.666001	−	0.237578i
$351$	23.3222	−	11.2314i	1.24485	−	0.599488i
$352$	1.21330	+	0.529358i	0.0646691	+	0.0282149i
$353$	−10.7934	−	9.28851i	−0.574477	−	0.494378i	0.316398	−	0.948627i	$-0.397527\pi$
$353$	−10.7934	−	9.28851i	−0.574477	−	0.494378i	−0.890875	+	0.454249i	$0.849908\pi$
$354$	−16.1211	−	6.32706i	−0.856826	−	0.336279i
$355$	17.7780	+	22.2087i	0.943558	+	1.17872i
$356$	7.42167	−	5.91858i	0.393348	−	0.313684i
$357$	30.0874	−	6.55952i	1.59239	−	0.347167i
$358$	6.51952	−	0.734573i	0.344567	−	0.0388234i
$359$	−2.75746	−	4.04446i	−0.145533	−	0.213458i	0.746550	−	0.665330i	$-0.231709\pi$
$359$	−2.75746	−	4.04446i	−0.145533	−	0.213458i	−0.892083	+	0.451871i	$0.850757\pi$
$360$	0.243698	−	0.331478i	0.0128440	−	0.0174704i
$361$	6.80849	+	11.7926i	0.358341	+	0.620665i
$362$	−15.2859	+	4.09585i	−0.803411	+	0.215273i
$363$	−13.1399	−	8.25634i	−0.689665	−	0.433345i
$364$	−3.19676	−	12.4130i	−0.167556	−	0.650617i
$365$	0.888916	−	24.9908i	0.0465280	−	1.30808i
$366$	−8.97239	−	8.32517i	−0.468995	−	0.435163i
$367$	−16.6304	−	22.5334i	−0.868099	−	1.17623i	−0.983137	−	0.182871i	$-0.941461\pi$
$367$	−16.6304	−	22.5334i	−0.868099	−	1.17623i	0.115038	−	0.993361i	$-0.463301\pi$
$368$	4.65419	+	6.30620i	0.242616	+	0.328733i
$369$	−1.48893	−	1.38152i	−0.0775105	−	0.0719192i
$370$	7.21381	+	7.74592i	0.375028	+	0.402691i
$371$	1.59734	+	0.715518i	0.0829299	+	0.0371478i
$372$	12.4848	+	7.84474i	0.647309	+	0.406731i
$373$	7.62334	−	2.04267i	0.394721	−	0.105765i	−0.0559981	−	0.998431i	$-0.517834\pi$
$373$	7.62334	−	2.04267i	0.394721	−	0.105765i	0.450720	+	0.892666i	$0.351167\pi$
$374$	4.59069	+	7.95132i	0.237379	+	0.411153i
$375$	18.1490	+	4.75549i	0.937210	+	0.245573i
$376$	2.90276	+	4.25757i	0.149699	+	0.219567i
$377$	−19.9534	+	2.24821i	−1.02765	+	0.115789i
$378$	0.137723	−	14.1357i	0.00708373	−	0.727062i
$379$	11.1262	−	8.87282i	0.571513	−	0.455766i	−0.294596	−	0.955622i	$-0.595185\pi$
$379$	11.1262	−	8.87282i	0.571513	−	0.455766i	0.866109	+	0.499856i	$0.166614\pi$
$380$	−4.05015	+	3.24213i	−0.207768	+	0.166318i
$381$	−17.1528	−	6.73196i	−0.878762	−	0.344889i
$382$	−17.5538	−	15.1063i	−0.898130	−	0.772904i
$383$	26.9909	+	11.7760i	1.37917	+	0.601725i	0.953014	−	0.302926i	$-0.0979634\pi$
$383$	26.9909	+	11.7760i	1.37917	+	0.601725i	0.426154	+	0.904651i	$0.359868\pi$
$384$	−1.51191	+	0.728099i	−0.0771545	+	0.0371556i
$385$	−4.36036	−	6.50526i	−0.222224	−	0.331539i
$386$	−10.3544	−	4.98641i	−0.527024	−	0.253801i
$387$	0.701434	+	0.815081i	0.0356559	+	0.0414329i
$388$	2.09670	−	3.96716i	0.106444	−	0.201402i
$389$	−10.6182	+	15.5740i	−0.538364	+	0.789634i	−0.994985	−	0.100027i	$-0.968107\pi$
$389$	−10.6182	+	15.5740i	−0.538364	+	0.789634i	0.456621	+	0.889661i	$0.349060\pi$
$390$	6.03584	+	17.1479i	0.305637	+	0.868317i
$391$			54.3614i			2.74918i
$392$	−6.85130	−	1.43514i	−0.346043	−	0.0724858i
$393$	−11.0239	−	11.0239i	−0.556083	−	0.556083i
$394$	0.869927	+	5.77159i	0.0438263	+	0.290768i
$395$	−7.66320	+	3.02392i	−0.385578	+	0.152150i
$396$	0.232740	−	0.0717907i	0.0116956	−	0.00360762i
$397$	−15.6122	+	13.4354i	−0.783553	+	0.674302i	−0.950174	−	0.311719i	$-0.899095\pi$
$397$	−15.6122	+	13.4354i	−0.783553	+	0.674302i	0.166622	+	0.986021i	$0.446714\pi$
$398$	1.28994	−	0.451369i	0.0646588	−	0.0226251i
$399$	−2.76291	+	9.92355i	−0.138318	+	0.496799i
$400$	3.67778	+	3.38731i	0.183889	+	0.169366i
$401$	−2.88111	−	7.34094i	−0.143876	−	0.366589i	0.840712	−	0.541483i	$-0.182137\pi$
$401$	−2.88111	−	7.34094i	−0.143876	−	0.366589i	−0.984587	+	0.174894i	$0.944042\pi$
$402$	−1.12024	+	1.30174i	−0.0558723	+	0.0649248i
$403$	39.0173	−	17.0231i	1.94359	−	0.847980i
$404$	−14.0629	−	4.33783i	−0.699655	−	0.215815i
$405$	1.44064	+	18.7594i	0.0715858	+	0.932163i
$406$	−3.72238	+	10.3145i	−0.184739	+	0.511900i
$407$	0.701593	+	6.22681i	0.0347767	+	0.308651i
$408$	−11.4362	−	2.16384i	−0.566175	−	0.107126i
$409$	−5.37276	+	4.98519i	−0.265666	+	0.246502i	−0.801746	−	0.597665i	$-0.796095\pi$
$409$	−5.37276	+	4.98519i	−0.265666	+	0.246502i	0.536080	+	0.844167i	$0.319905\pi$
$410$	18.6804	−	16.1359i	0.922558	−	0.796893i
$411$	2.75139	+	1.58851i	0.135716	+	0.0783556i
$412$	4.11662	−	6.55156i	0.202811	−	0.322772i
$413$	3.80630	+	27.0380i	0.187296	+	1.33045i
$414$	1.40592	+	0.320893i	0.0690974	+	0.0157710i
$415$	10.6429	+	6.66002i	0.522440	+	0.326928i
$416$	−0.722073	+	4.79064i	−0.0354025	+	0.234880i
$417$	−19.3118	+	14.2528i	−0.945703	+	0.697960i
$418$	−3.06913	+	0.114839i	−0.150116	+	0.00561696i
$419$	−0.521878	+	2.28649i	−0.0254954	+	0.111703i	−0.986074	−	0.166304i	$-0.946817\pi$
$419$	−0.521878	+	2.28649i	−0.0254954	+	0.111703i	0.960579	+	0.278007i	$0.0896738\pi$
$420$	9.85624	+	1.18943i	0.480935	+	0.0580383i
$421$	3.71912	+	16.2945i	0.181259	+	0.794147i	0.981032	+	0.193845i	$0.0620959\pi$
$421$	3.71912	+	16.2945i	0.181259	+	0.794147i	−0.799773	+	0.600302i	$0.795047\pi$
$422$	3.00399	+	11.2110i	0.146232	+	0.545745i
$423$	0.915800	+	0.245388i	0.0445277	+	0.0119312i
$424$	−0.449963	−	0.484945i	−0.0218521	−	0.0235510i
$425$	6.57301	+	34.0508i	0.318838	+	1.65171i
$426$	−16.6915	−	13.3110i	−0.808706	−	0.644922i
$427$	−4.47723	+	18.7711i	−0.216669	+	0.908399i
$428$	0.113672	−	1.00887i	0.00549457	−	0.0487656i
$429$	−3.17217	+	10.2839i	−0.153154	+	0.496512i
$430$	−10.7843	+	7.38177i	−0.520063	+	0.355981i
$431$	−1.86716	−	24.9155i	−0.0899378	−	1.20014i	−0.841419	−	0.540383i	$-0.818279\pi$
$431$	−1.86716	−	24.9155i	−0.0899378	−	1.20014i	0.751481	−	0.659754i	$-0.229340\pi$
$432$	−2.13664	+	4.89723i	−0.102799	+	0.235618i
$433$	−4.06772	+	11.6249i	−0.195482	+	0.558656i	−0.999346	−	0.0361571i	$-0.988488\pi$
$433$	−4.06772	+	11.6249i	−0.195482	+	0.558656i	0.803864	+	0.594813i	$0.202774\pi$
$434$	1.09553	−	23.2215i	0.0525872	−	1.11467i
$435$	3.99743	−	15.0295i	0.191662	−	0.720609i
$436$	−0.251903	+	3.36141i	−0.0120640	+	0.160982i
$437$	−16.0772	−	8.49706i	−0.769078	−	0.406470i
$438$	3.48894	+	18.4395i	0.166708	+	0.881072i
$439$	−23.9460	+	3.60928i	−1.14288	+	0.172262i	−0.693075	−	0.720865i	$-0.743745\pi$
$439$	−23.9460	+	3.60928i	−1.14288	+	0.172262i	−0.449805	+	0.893127i	$0.648507\pi$
$440$	0.555664	+	2.90737i	0.0264902	+	0.138604i
$441$	−1.12773	+	0.622119i	−0.0537015	+	0.0296247i
$442$	−23.7607	+	23.7607i	−1.13018	+	1.13018i
$443$	−10.7303	−	7.91933i	−0.509813	−	0.376259i	0.308325	−	0.951281i	$-0.400232\pi$
$443$	−10.7303	−	7.91933i	−0.509813	−	0.376259i	−0.818138	+	0.575022i	$0.804993\pi$
$444$	−6.56328	−	4.47477i	−0.311479	−	0.212363i
$445$	20.2947	+	6.21911i	0.962063	+	0.294814i
$446$	19.0153	+	1.42500i	0.900400	+	0.0674757i
$447$	−9.89163	−	28.2686i	−0.467858	−	1.33706i
$448$	2.17140	+	1.51163i	0.102589	+	0.0714179i
$449$	6.95590	+	14.4441i	0.328269	+	0.681658i	0.998149	−	0.0608111i	$-0.0193687\pi$
$449$	6.95590	+	14.4441i	0.328269	+	0.681658i	−0.669880	+	0.742469i	$0.733654\pi$
$450$	0.919440	+	0.0310057i	0.0433428	+	0.00146162i
$451$	14.5723	−	1.09205i	0.686184	−	0.0514224i
$452$	−0.164934	−	0.378034i	−0.00775786	−	0.0177812i
$453$	−0.458497	+	0.242323i	−0.0215421	+	0.0113853i
$454$	13.2793	+	16.6517i	0.623229	+	0.781504i
$455$	18.8668	−	21.5766i	0.884490	−	1.01153i
$456$	2.42750	−	3.04399i	0.113678	−	0.142548i
$457$	1.36248	−	7.20089i	0.0637342	−	0.336843i	−0.936157	−	0.351582i	$-0.885644\pi$
$457$	1.36248	−	7.20089i	0.0637342	−	0.336843i	0.999891	+	0.0147384i	$0.00469155\pi$
$458$	−0.476350	+	12.7307i	−0.0222584	+	0.594868i
$459$	−32.0938	+	18.5294i	−1.49801	+	0.864877i
$460$	−5.75782	+	16.5528i	−0.268460	+	0.771779i
$461$	9.02396	−	2.05966i	0.420288	−	0.0959279i	−0.00714641	−	0.999974i	$-0.502275\pi$
$461$	9.02396	−	2.05966i	0.420288	−	0.0959279i	0.427434	+	0.904047i	$0.359418\pi$
$462$	4.26916	+	4.03931i	0.198619	+	0.187926i
$463$	−0.564532	+	0.354719i	−0.0262360	+	0.0164852i	−0.545086	−	0.838380i	$-0.683503\pi$
$463$	−0.564532	+	0.354719i	−0.0262360	+	0.0164852i	0.518850	+	0.854865i	$0.326360\pi$
$464$	2.81906	−	3.03822i	0.130871	−	0.141046i
$465$	1.29360	+	32.9451i	0.0599892	+	1.52779i
$466$	21.8663	+	3.29581i	1.01294	+	0.152675i
$467$	−0.913329	−	24.4092i	−0.0422638	−	1.12952i	−0.845538	−	0.533915i	$-0.820720\pi$
$467$	−0.913329	−	24.4092i	−0.0422638	−	1.12952i	0.803274	−	0.595609i	$-0.203089\pi$
$468$	0.474253	+	0.754769i	0.0219223	+	0.0348892i
$469$	2.65548	+	0.529292i	0.122619	+	0.0244404i
$470$	−4.18979	+	10.7336i	−0.193261	+	0.495105i
$471$	6.72716	−	11.6518i	0.309971	−	0.536886i
$472$	2.67105	−	9.96851i	0.122945	−	0.458838i
$473$	−7.73125	−	0.289283i	−0.355483	−	0.0133013i
$474$	5.10825	−	3.48275i	0.234630	−	0.159968i
$475$	−11.0978	−	3.37843i	−0.509204	−	0.155013i
$476$	5.89179	+	17.3791i	0.270050	+	0.796569i
$477$	−0.120954	−	0.0136282i	−0.00553808	−	0.000623992i
$478$	−1.84991	−	3.50021i	−0.0846131	−	0.160096i
$479$	−4.35922	+	11.1071i	−0.199178	+	0.507497i	−0.995210	−	0.0977568i	$-0.968833\pi$
$479$	−4.35922	+	11.1071i	−0.199178	+	0.507497i	0.796032	+	0.605254i	$0.206928\pi$
$480$	−3.25308	−	1.87017i	−0.148482	−	0.0853612i
$481$	−21.3482	+	8.37854i	−0.973393	+	0.382029i
$482$	28.6427	+	10.0225i	1.30464	+	0.456514i
$483$	9.93246	+	33.3504i	0.451943	+	1.51750i
$484$	4.01242	−	8.33187i	0.182383	−	0.378722i
$485$	9.96839	−	1.14180i	0.452641	−	0.0518464i
$486$	0.562792	+	1.82453i	0.0255287	+	0.0827622i
$487$	−4.08005	+	0.771987i	−0.184885	+	0.0349821i	−0.277529	−	0.960717i	$-0.589516\pi$
$487$	−4.08005	+	0.771987i	−0.184885	+	0.0349821i	0.0926446	+	0.995699i	$0.470468\pi$
$488$	4.33123	−	5.86861i	0.196066	−	0.265660i
$489$	26.7145			1.20807
$490$	−6.00527	−	14.4546i	−0.271290	−	0.652994i
$491$	−2.31769			−0.104596			−0.0522979	−	0.998632i	$-0.516655\pi$
$491$	−2.31769			−0.104596			−0.0522979	+	0.998632i	$0.516655\pi$
$492$	−11.0005	+	14.9051i	−0.495939	+	0.671973i
$493$	28.2454	−	5.34433i	1.27211	−	0.240696i
$494$	−3.31319	−	10.7411i	−0.149067	−	0.483265i
$495$	0.426425	+	0.338777i	0.0191664	+	0.0152269i
$496$	−3.81239	+	7.91651i	−0.171181	+	0.355462i
$497$	−5.34080	+	33.2336i	−0.239568	+	1.49073i
$498$	−8.89337	−	3.11192i	−0.398521	−	0.139449i
$499$	11.9680	−	4.69708i	0.535760	−	0.210270i	−0.0820067	−	0.996632i	$-0.526133\pi$
$499$	11.9680	−	4.69708i	0.535760	−	0.210270i	0.617767	+	0.786362i	$0.288038\pi$
$500$	−1.60512	+	11.0645i	−0.0717832	+	0.494820i
$501$	−10.2144	+	26.0258i	−0.456344	+	1.16275i
$502$	−4.51512	−	8.54302i	−0.201520	−	0.381294i
$503$	12.5020	+	1.40864i	0.557438	+	0.0628082i	0.386189	−	0.922420i	$-0.373791\pi$
$503$	12.5020	+	1.40864i	0.557438	+	0.0628082i	0.171249	+	0.985228i	$0.445220\pi$
$504$	0.484246	−	0.0497888i	0.0215700	−	0.00221777i
$505$	−9.75769	−	31.4276i	−0.434211	−	1.39851i
$506$	−8.57237	+	5.84454i	−0.381088	+	0.259822i
$507$	−17.5601	−	0.657053i	−0.779872	−	0.0291807i
$508$	2.84199	−	10.6065i	0.126093	−	0.470585i
$509$	16.9163	−	29.2999i	0.749802	−	1.29870i	−0.198115	−	0.980179i	$-0.563482\pi$
$509$	16.9163	−	29.2999i	0.749802	−	1.29870i	0.947917	−	0.318517i	$-0.103185\pi$
$510$	−10.4515	−	23.8350i	−0.462800	−	1.05543i
$511$	22.6140	−	19.0806i	1.00038	−	0.844076i
$512$	−0.532032	−	0.846724i	−0.0235127	−	0.0374203i
$513$	−0.463523	−	12.3879i	−0.0204651	−	0.546940i
$514$	−2.89358	−	0.436137i	−0.127630	−	0.0192372i
$515$	17.2883	−	0.678830i	0.761815	−	0.0299128i
$516$	6.67088	−	7.18950i	0.293669	−	0.316500i
$517$	−5.77570	+	3.62911i	−0.254015	+	0.159608i
$518$	−1.05756	+	12.4794i	−0.0464665	+	0.548313i
$519$	39.0440	−	8.91153i	1.71384	−	0.391173i
$520$	−9.75168	+	4.71835i	−0.427640	+	0.206913i
$521$	21.5326	−	12.4319i	0.943362	−	0.544650i	0.0523495	−	0.998629i	$-0.483329\pi$
$521$	21.5326	−	12.4319i	0.943362	−	0.544650i	0.891013	+	0.453978i	$0.149996\pi$
$522$	0.0285137	−	0.762046i	0.00124801	−	0.0333538i
$523$	1.85058	−	9.78053i	0.0809200	−	0.427673i	−0.918556	−	0.395292i	$-0.870643\pi$
$523$	1.85058	−	9.78053i	0.0809200	−	0.427673i	0.999476	−	0.0323807i	$-0.0103089\pi$
$524$	5.79246	−	7.26351i	0.253045	−	0.317308i
$525$	10.2540	+	19.6890i	0.447520	+	0.859299i
$526$	−3.51114	−	4.40283i	−0.153093	−	0.191973i
$527$	−53.8809	+	28.4769i	−2.34709	+	1.24047i
$528$	−0.888313	−	2.03604i	−0.0386589	−	0.0886071i
$529$	−38.3222	+	2.87185i	−1.66618	+	0.124863i
$530$	0.326503	−	1.44277i	0.0141824	−	0.0626700i
$531$	−0.823873	−	1.71079i	−0.0357530	−	0.0742419i
$532$	−6.06074	−	0.973989i	−0.262766	−	0.0422278i
$533$	17.6641	+	50.4811i	0.765117	+	2.18658i
$534$	−15.8851	−	1.19042i	−0.687414	−	0.0515146i
$535$	2.00514	−	1.06448i	0.0866897	−	0.0460217i
$536$	−0.845589	−	0.576513i	−0.0365239	−	0.0249016i
$537$	−8.85830	−	6.53772i	−0.382264	−	0.282124i
$538$	−8.36259	+	8.36259i	−0.360537	+	0.360537i
$539$	2.23756	−	8.99205i	0.0963787	−	0.387315i
$540$	−11.7350	+	2.24282i	−0.504994	+	0.0965156i
$541$	−10.7426	+	1.61918i	−0.461860	+	0.0696141i	−0.375851	−	0.926680i	$-0.622649\pi$
$541$	−10.7426	+	1.61918i	−0.461860	+	0.0696141i	−0.0860090	+	0.996294i	$0.527411\pi$
$542$	3.10019	+	16.3849i	0.133165	+	0.703792i
$543$	23.4787	+	12.4089i	1.00757	+	0.532515i
$544$	0.518319	−	6.91649i	0.0222228	−	0.296542i
$545$	−6.52063	+	3.78074i	−0.279313	+	0.161949i
$546$	−10.2357	+	18.9184i	−0.438047	+	0.809632i
$547$	−9.18115	+	26.2382i	−0.392558	+	1.12186i	0.562846	+	0.826562i	$0.309706\pi$
$547$	−9.18115	+	26.2382i	−0.392558	+	1.12186i	−0.955404	+	0.295303i	$0.904579\pi$
$548$	−0.757088	+	1.73527i	−0.0323412	+	0.0741269i
$549$	−0.100289	−	1.33826i	−0.00428022	−	0.0571156i
$550$	−4.66287	+	4.69741i	−0.198825	+	0.200298i
$551$	−2.83439	+	9.18886i	−0.120749	+	0.391459i
$552$	1.47260	−	13.0697i	0.0626782	−	0.556285i
$553$	−8.74069	−	4.31470i	−0.371692	−	0.183480i
$554$	14.9186	+	11.8972i	0.633829	+	0.505462i
$555$	−0.0327743	−	17.7623i	−0.00139119	−	0.753968i
$556$	−9.72851	−	10.4848i	−0.412581	−	0.444656i
$557$	14.5021	+	3.88582i	0.614472	+	0.164647i	0.552614	−	0.833438i	$-0.313631\pi$
$557$	14.5021	+	3.88582i	0.614472	+	0.164647i	0.0618586	+	0.998085i	$0.480297\pi$
$558$	0.418428	+	1.56159i	0.0177135	+	0.0661075i
$559$	−6.30071	−	27.6052i	−0.266492	−	1.16758i
$560$	−0.0467216	+	5.91590i	−0.00197435	+	0.249992i
$561$	3.42844	−	15.0210i	0.144749	−	0.634186i
$562$	−20.0313	+	0.749518i	−0.844970	+	0.0316165i
$563$	−25.1278	+	18.5451i	−1.05901	+	0.781584i	−0.976611	−	0.215016i	$-0.931020\pi$
$563$	−25.1278	+	18.5451i	−1.05901	+	0.781584i	−0.0823978	+	0.996600i	$0.526258\pi$
$564$	1.28879	−	8.55057i	0.0542679	−	0.360044i
$565$	0.489231	−	0.781804i	0.0205821	−	0.0328908i
$566$	−22.2981	−	5.08940i	−0.937260	−	0.213924i
$567$	−15.3001	+	16.1708i	−0.642545	+	0.679108i
$568$	6.76867	−	10.7723i	0.284007	−	0.451995i
$569$	−28.9833	−	16.7335i	−1.21504	−	0.701505i	−0.251189	−	0.967938i	$-0.580822\pi$
$569$	−28.9833	−	16.7335i	−1.21504	−	0.701505i	−0.963853	+	0.266433i	$0.914155\pi$
$570$	8.68277	+	0.634575i	0.363681	+	0.0265794i
$571$	7.83946	−	7.27396i	0.328071	−	0.304406i	−0.498889	−	0.866666i	$-0.666259\pi$
$571$	7.83946	−	7.27396i	0.328071	−	0.304406i	0.826960	+	0.562260i	$0.190068\pi$
$572$	−6.30144	−	1.19230i	−0.263477	−	0.0498525i
$573$	4.35126	+	38.6185i	0.181777	+	1.61331i
$574$	28.9902	+	3.55276i	1.21003	+	0.148289i
$575$	−37.8155	+	10.2824i	−1.57702	+	0.428804i
$576$	−0.175818	−	0.0542328i	−0.00732576	−	0.00225970i
$577$	6.64012	−	2.89705i	0.276432	−	0.120606i	−0.257103	−	0.966384i	$-0.582768\pi$
$577$	6.64012	−	2.89705i	0.276432	−	0.120606i	0.533535	+	0.845778i	$0.320863\pi$
$578$	20.2904	−	23.5779i	0.843969	−	0.980709i
$579$	7.04579	+	17.9524i	0.292813	+	0.746075i
$580$	9.16667	+	1.36436i	0.380625	+	0.0566520i
$581$	2.61943	+	14.6225i	0.108672	+	0.606643i
$582$	−7.10731	+	2.48696i	−0.294608	+	0.103088i
$583$	0.663769	−	0.571220i	0.0274905	−	0.0236575i
$584$	−10.6864	+	3.29633i	−0.442208	+	0.136403i
$585$	−0.793704	+	1.82838i	−0.0328156	+	0.0755944i
$586$	−3.47062	−	23.0261i	−0.143370	−	0.951198i
$587$	17.1930	+	17.1930i	0.709633	+	0.709633i	0.966458	−	0.256825i	$-0.0826765\pi$
$587$	17.1930	+	17.1930i	0.709633	+	0.709633i	−0.256825	+	0.966458i	$0.582676\pi$
$588$	6.78994	+	9.58546i	0.280012	+	0.395298i
$589$		−	20.3862i		−	0.840001i
$590$	21.7675	−	7.66189i	0.896154	−	0.315435i
$591$	5.51754	−	8.09275i	0.226961	−	0.332891i
$592$	2.21190	−	4.18511i	0.0909084	−	0.172007i
$593$	11.8673	+	13.7900i	0.487331	+	0.566288i	0.946766	−	0.321923i	$-0.104329\pi$
$593$	11.8673	+	13.7900i	0.487331	+	0.566288i	−0.459435	+	0.888211i	$0.651948\pi$
$594$	−6.37243	−	3.06880i	−0.261464	−	0.125914i
$595$	−24.6263	+	32.8218i	−1.00958	+	1.34556i
$596$	16.0798	−	7.74360i	0.658653	−	0.317190i
$597$	−2.10199	−	0.917087i	−0.0860285	−	0.0375339i
$598$	−28.7815	−	24.7685i	−1.17696	−	1.01286i
$599$	25.3574	+	9.95207i	1.03608	+	0.406630i	0.821579	−	0.570094i	$-0.193093\pi$
$599$	25.3574	+	9.95207i	1.03608	+	0.406630i	0.214498	+	0.976724i	$0.431189\pi$
$600$	−0.657894	−	8.36465i	−0.0268584	−	0.341485i
$601$	11.6105	−	9.25909i	0.473604	−	0.377686i	−0.357402	−	0.933951i	$-0.616337\pi$
$601$	11.6105	−	9.25909i	0.473604	−	0.377686i	0.831005	+	0.556265i	$0.187766\pi$
$602$	−15.0412	−	3.58757i	−0.613032	−	0.146218i
$603$	−0.187118	+	0.0210831i	−0.00762002	+	0.000858570i
$604$	−0.174087	−	0.255338i	−0.00708349	−	0.0103896i
$605$	20.4418	−	3.11969i	0.831076	−	0.126833i
$606$	12.3480	+	21.3874i	0.501605	+	0.868805i
$607$	−3.80580	+	1.01976i	−0.154473	+	0.0413908i	−0.335227	−	0.942138i	$-0.608813\pi$
$607$	−3.80580	+	1.01976i	−0.154473	+	0.0413908i	0.180754	+	0.983528i	$0.442146\pi$
$608$	1.96451	+	1.23439i	0.0796716	+	0.0500610i
$609$	16.3519	−	8.43948i	0.662614	−	0.341985i
$610$	16.2992	+	0.579760i	0.659937	+	0.0234738i
$611$	−18.3005	−	16.9804i	−0.740358	−	0.686952i
$612$	−0.757805	−	1.02679i	−0.0306324	−	0.0415055i
$613$	−10.3847	−	14.0708i	−0.419436	−	0.568315i	0.543032	−	0.839712i	$-0.317276\pi$
$613$	−10.3847	−	14.0708i	−0.419436	−	0.568315i	−0.962468	+	0.271397i	$0.912514\pi$
$614$	9.56559	+	8.87557i	0.386036	+	0.358189i
$615$	−41.3967	−	1.47247i	−1.66928	−	0.0593758i
$616$	−2.10710	+	2.79756i	−0.0848976	+	0.112717i
$617$	−8.43929	−	5.30276i	−0.339753	−	0.213481i	0.351338	−	0.936249i	$-0.385727\pi$
$617$	−8.43929	−	5.30276i	−0.339753	−	0.213481i	−0.691091	+	0.722768i	$0.742870\pi$
$618$	−12.5419	+	3.36059i	−0.504509	+	0.135183i
$619$	−11.2632	−	19.5084i	−0.452706	−	0.784110i	0.545847	−	0.837885i	$-0.316208\pi$
$619$	−11.2632	−	19.5084i	−0.452706	−	0.784110i	−0.998553	+	0.0537748i	$0.982875\pi$
$620$	−19.4227	+	2.96416i	−0.780034	+	0.119044i
$621$	−23.5903	−	34.6006i	−0.946645	−	1.38847i
$622$	−2.44334	+	0.275298i	−0.0979689	+	0.0110384i
$623$	10.6761	+	22.7331i	0.427730	+	0.910784i
$624$	6.35626	−	5.06895i	0.254454	−	0.202920i
$625$	−22.4436	+	11.0130i	−0.897742	+	0.440522i
$626$	−8.90875	−	3.49643i	−0.356065	−	0.139745i
$627$	3.90652	+	3.36183i	0.156011	+	0.134259i
$628$	7.34864	+	3.20618i	0.293243	+	0.127940i
$629$	29.5808	−	14.2454i	1.17946	−	0.568000i
$630$	0.703487	+	0.830645i	0.0280276	+	0.0330937i
$631$	−5.35441	−	2.57855i	−0.213156	−	0.102650i	0.324260	−	0.945968i	$-0.394885\pi$
$631$	−5.35441	−	2.57855i	−0.213156	−	0.102650i	−0.537415	+	0.843318i	$0.680599\pi$
$632$	2.40319	+	2.79256i	0.0955939	+	0.111082i
$633$	9.10093	−	17.2198i	0.361729	−	0.684426i
$634$	−2.88887	+	4.23719i	−0.114732	+	0.168280i
$635$	23.1605	−	8.15222i	0.919097	−	0.323511i
$636$			1.11013i			0.0440196i
$637$	33.9078	−	0.607511i	1.34348	−	0.0240705i
$638$	3.87950	+	3.87950i	0.153591	+	0.153591i
$639$	−0.348879	−	2.31466i	−0.0138015	−	0.0915667i
$640$	0.890403	−	2.05114i	0.0351963	−	0.0810785i
$641$	37.0224	−	11.4199i	1.46230	−	0.451059i	0.541367	−	0.840786i	$-0.317907\pi$
$641$	37.0224	−	11.4199i	1.46230	−	0.451059i	0.920930	+	0.389727i	$0.127431\pi$
$642$	−1.29135	+	1.11130i	−0.0509656	+	0.0438595i
$643$	−12.0151	+	4.20426i	−0.473828	+	0.165800i	−0.556620	−	0.830767i	$-0.687902\pi$
$643$	−12.0151	+	4.20426i	−0.473828	+	0.165800i	0.0827919	+	0.996567i	$0.473616\pi$
$644$	−19.0863	+	8.10685i	−0.752105	+	0.319455i
$645$	21.6916	+	3.22856i	0.854105	+	0.127124i
$646$	5.87914	+	14.9798i	0.231312	+	0.589372i
$647$	−9.17923	+	10.6665i	−0.360873	+	0.419342i	−0.908831	−	0.417164i	$-0.863024\pi$
$647$	−9.17923	+	10.6665i	−0.360873	+	0.419342i	0.547959	+	0.836505i	$0.315405\pi$
$648$	7.71211	−	3.36476i	0.302960	−	0.132180i
$649$	13.0544	+	4.02675i	0.512430	+	0.158064i
$650$	−21.0229	−	12.0344i	−0.824588	−	0.472027i
$651$	−27.8526	+	27.3151i	−1.09163	+	1.07056i
$652$	1.78242	+	15.8194i	0.0698049	+	0.619536i
$653$	−25.5257	−	4.82973i	−0.998898	−	0.189002i	−0.339347	−	0.940661i	$-0.610206\pi$
$653$	−25.5257	−	4.82973i	−0.998898	−	0.189002i	−0.659551	+	0.751659i	$0.729254\pi$
$654$	4.14657	−	3.84745i	0.162144	−	0.150447i
$655$	20.7187	+	1.51421i	0.809545	+	0.0591651i
$656$	−9.56025	−	5.51961i	−0.373265	−	0.215505i
$657$	−1.09473	+	1.74226i	−0.0427096	+	0.0679719i
$658$	−12.7389	+	4.85698i	−0.496615	+	0.189345i
$659$	17.0935	+	3.90148i	0.665868	+	0.151980i	0.542078	−	0.840328i	$-0.317638\pi$
$659$	17.0935	+	3.90148i	0.665868	+	0.151980i	0.123790	+	0.992308i	$0.460495\pi$
$660$	2.63492	−	4.21069i	0.102564	−	0.163901i
$661$	−3.53077	+	23.4251i	−0.137331	+	0.911132i	0.808971	+	0.587848i	$0.200025\pi$
$661$	−3.53077	+	23.4251i	−0.137331	+	0.911132i	−0.946302	+	0.323283i	$0.895213\pi$
$662$	−3.49080	+	2.57633i	−0.135674	+	0.100132i
$663$	56.3490	−	2.10843i	2.18842	−	0.0818847i
$664$	1.24940	−	5.47398i	0.0484862	−	0.212432i
$665$	−5.85768	−	12.4134i	−0.227151	−	0.481373i
$666$	−0.193807	−	0.849124i	−0.00750987	−	0.0329029i
$667$	8.40756	+	31.3774i	0.325542	+	1.21494i
$668$	−16.0931	−	4.31214i	−0.622661	−	0.166842i
$669$	−21.7648	−	23.4569i	−0.841477	−	0.906896i
$670$	−0.00422252	−	2.28843i	−0.000163130	−	0.0884098i
$671$	7.54877	+	6.01995i	0.291417	+	0.232397i
$672$	−0.945737	−	4.33793i	−0.0364826	−	0.167339i
$673$	0.200860	−	1.78268i	0.00774259	−	0.0687174i	−0.989247	−	0.146256i	$-0.953278\pi$
$673$	0.200860	−	1.78268i	0.00774259	−	0.0687174i	0.996989	+	0.0775388i	$0.0247062\pi$
$674$	7.32739	−	23.7548i	0.282240	−	0.915001i
$675$	−18.9601	−	18.8207i	−0.729775	−	0.724408i
$676$	−0.782545	−	10.4423i	−0.0300979	−	0.401629i
$677$	14.8863	−	34.1197i	0.572126	−	1.31133i	−0.354399	−	0.935094i	$-0.615315\pi$
$677$	14.8863	−	34.1197i	0.572126	−	1.31133i	0.926525	−	0.376233i	$-0.122781\pi$
$678$	−0.228595	+	0.653287i	−0.00877914	+	0.0250893i
$679$	8.92267	+	7.83118i	0.342421	+	0.300533i
$680$	13.4170	−	7.77933i	0.514517	−	0.298323i
$681$	2.67091	−	35.6408i	0.102349	−	1.36576i
$682$	−10.2835	−	5.43497i	−0.393774	−	0.208116i
$683$	0.966890	+	5.11014i	0.0369970	+	0.195534i	0.996189	−	0.0872220i	$-0.0277989\pi$
$683$	0.966890	+	5.11014i	0.0369970	+	0.195534i	−0.959192	+	0.282756i	$0.908751\pi$
$684$	0.422120	−	0.0636243i	0.0161402	−	0.00243274i
$685$	−4.15813	+	0.794711i	−0.158874	+	0.0303644i
$686$	7.89901	−	16.7513i	0.301586	−	0.639567i
$687$	15.1168	−	15.1168i	0.576741	−	0.576741i
$688$	4.70247	+	3.47058i	0.179280	+	0.132315i
$689$	2.64810	+	1.80545i	0.100885	+	0.0687820i
$690$	25.9762	−	13.7902i	0.988896	−	0.524984i
$691$	3.57033	+	0.267559i	0.135822	+	0.0101784i	0.142467	−	0.989799i	$-0.454496\pi$
$691$	3.57033	+	0.267559i	0.135822	+	0.0101784i	−0.00664572	+	0.999978i	$0.502115\pi$
$692$	7.88217	+	22.5259i	0.299635	+	0.856308i
$693$	0.0418933	+	0.643037i	0.00159140	+	0.0244270i
$694$	−4.07627	−	8.46446i	−0.154733	−	0.321307i
$695$	7.05922	−	31.1937i	0.267772	−	1.18324i
$696$	−6.93562	+	0.519753i	−0.262894	+	0.0197012i
$697$	−30.6185	−	70.1782i	−1.15976	−	2.65819i
$698$	1.44712	−	0.764823i	0.0547742	−	0.0289490i
$699$	−23.1366	−	29.0123i	−0.875105	−	1.09735i
$700$	−10.9750	+	7.38574i	−0.414817	+	0.279155i
$701$	−15.3184	+	19.2087i	−0.578568	+	0.725501i	−0.981868	−	0.189567i	$-0.939292\pi$
$701$	−15.3184	+	19.2087i	−0.578568	+	0.725501i	0.403300	+	0.915068i	$0.367863\pi$
$702$	4.81246	−	25.4345i	0.181635	−	0.959962i
$703$	−0.410659	+	10.9751i	−0.0154883	+	0.413933i
$704$	1.14640	−	0.661876i	0.0432067	−	0.0249454i
$705$	17.4053	−	8.42154i	0.655521	−	0.317174i
$706$	−13.8829	+	3.16868i	−0.522489	+	0.119255i
$707$	19.7960	−	33.5290i	0.744505	−	1.26099i
$708$	−14.6638	+	9.21385i	−0.551098	+	0.346278i
$709$	9.88651	−	10.6551i	0.371296	−	0.400162i	−0.519570	−	0.854428i	$-0.673908\pi$
$709$	9.88651	−	10.6551i	0.371296	−	0.400162i	0.890866	+	0.454266i	$0.150098\pi$
$710$	28.4260	−	1.11615i	1.06681	−	0.0418885i
$711$	0.670305	+	0.101032i	0.0251384	+	0.00378900i
$712$	−0.354942	−	9.48603i	−0.0133020	−	0.355504i
$713$	−36.6396	−	58.3116i	−1.37216	−	2.18379i
$714$	12.5887	−	28.1034i	0.471121	−	1.05174i
$715$	−5.75888	−	13.1333i	−0.215370	−	0.491158i
$716$	3.28038	−	5.68179i	0.122594	−	0.212339i
$717$	−1.71948	+	6.41720i	−0.0642153	+	0.239655i
$718$	−4.89160	−	0.183031i	−0.182553	−	0.00683065i
$719$	33.6106	−	22.9153i	1.25347	−	0.854598i	0.259656	−	0.965701i	$-0.416391\pi$
$719$	33.6106	−	22.9153i	1.25347	−	0.854598i	0.993809	+	0.111103i	$0.0354383\pi$
$720$	−0.121993	−	0.392917i	−0.00454642	−	0.0146432i
$721$	14.3339	+	14.6159i	0.533822	+	0.544326i
$722$	13.5314	+	1.52462i	0.503585	+	0.0567404i
$723$	−23.7947	−	45.0217i	−0.884933	−	1.67438i
$724$	−5.78158	+	14.7312i	−0.214871	+	0.547482i
$725$	9.06025	+	18.6376i	0.336489	+	0.692181i
$726$	−14.4458	+	5.66955i	−0.536133	+	0.210417i
$727$	13.5721	+	4.74909i	0.503362	+	0.176134i	0.570002	−	0.821643i	$-0.306942\pi$
$727$	13.5721	+	4.74909i	0.503362	+	0.176134i	−0.0666404	+	0.997777i	$0.521228\pi$
$728$	−11.8858	−	4.79897i	−0.440516	−	0.177862i
$729$	12.3425	−	25.6295i	0.457130	−	0.949240i
$730$	−19.5797	−	15.5553i	−0.724677	−	0.575726i
$731$	11.9484	+	38.7358i	0.441928	+	1.43270i
$732$	−12.0264	+	2.27552i	−0.444508	+	0.0841055i
$733$	−8.62231	+	11.6828i	−0.318472	+	0.431515i	−0.934366	−	0.356315i	$-0.884033\pi$
$733$	−8.62231	+	11.6828i	−0.318472	+	0.431515i	0.615894	+	0.787829i	$0.288795\pi$
$734$	−28.0058			−1.03371
$735$	−9.11120	+	24.6355i	−0.336072	+	0.908694i
$736$	7.83771			0.288902
$737$	0.804480	−	1.09003i	0.0296334	−	0.0401518i
$738$	−1.99573	+	0.377612i	−0.0734637	+	0.0139001i
$739$	−10.2663	−	33.2826i	−0.377653	−	1.22432i	−0.922570	−	0.385831i	$-0.873915\pi$
$739$	−10.2663	−	33.2826i	−0.377653	−	1.22432i	0.544916	−	0.838490i	$-0.316561\pi$
$740$	10.5161	−	1.20453i	0.386578	−	0.0442794i
$741$	−8.18418	+	16.9946i	−0.300653	+	0.624313i
$742$	1.52424	−	0.860329i	0.0559566	−	0.0315837i
$743$	−13.1244	−	4.59241i	−0.481486	−	0.168479i	0.0786124	−	0.996905i	$-0.474951\pi$
$743$	−13.1244	−	4.59241i	−0.481486	−	0.168479i	−0.560099	+	0.828426i	$0.689237\pi$
$744$	13.7256	−	5.38690i	0.503205	−	0.197493i
$745$	34.5977	+	19.8900i	1.26756	+	0.728712i
$746$	2.88337	−	7.34670i	0.105568	−	0.268982i
$747$	−0.482723	−	0.913356i	−0.0176619	−	0.0334180i
$748$	9.12366	+	1.02799i	0.333594	+	0.0375870i
$749$	2.52661	+	0.911825i	0.0923204	+	0.0333174i
$750$	14.6035	−	11.7787i	0.533244	−	0.430099i
$751$	−10.1260	+	6.90377i	−0.369502	+	0.251922i	−0.733808	−	0.679357i	$-0.762259\pi$
$751$	−10.1260	+	6.90377i	−0.369502	+	0.251922i	0.364306	+	0.931279i	$0.381306\pi$
$752$	5.14935	+	0.192675i	0.187778	+	0.00702614i
$753$	−4.19677	+	15.6626i	−0.152939	+	0.570776i
$754$	−10.0398	+	17.3895i	−0.365629	+	0.633288i
$755$	0.251273	−	0.643724i	0.00914478	−	0.0234275i
$756$	−11.2918	−	8.50488i	−0.410678	−	0.309319i
$757$	−19.6849	−	31.3284i	−0.715461	−	1.13865i	−0.984477	−	0.175515i	$-0.943841\pi$
$757$	−19.6849	−	31.3284i	−0.715461	−	1.13865i	0.269015	−	0.963136i	$-0.413302\pi$
$758$	−0.532110	−	14.2209i	−0.0193271	−	0.516528i
$759$	17.2161	+	2.59491i	0.624904	+	0.0941892i
$760$	0.203550	+	5.18399i	0.00738355	+	0.188043i
$761$	−17.6131	+	18.9824i	−0.638475	+	0.688112i	−0.966532	−	0.256546i	$-0.917416\pi$
$761$	−17.6131	+	18.9824i	−0.638475	+	0.688112i	0.328057	+	0.944658i	$0.393606\pi$
$762$	−15.6022	+	9.80350i	−0.565207	+	0.355143i
$763$	−8.49615	−	2.71164i	−0.307581	−	0.0981681i
$764$	−22.5783	+	5.15334i	−0.816853	+	0.186441i
$765$	0.937500	−	2.69516i	0.0338954	−	0.0974439i
$766$	25.5026	−	14.7240i	0.921448	−	0.531998i
$767$	−1.86951	+	49.9636i	−0.0675040	+	1.80408i
$768$	−0.311978	+	1.64884i	−0.0112575	+	0.0594974i
$769$	1.01983	−	1.27882i	0.0367758	−	0.0461154i	−0.763103	−	0.646276i	$-0.776325\pi$
$769$	1.01983	−	1.27882i	0.0367758	−	0.0461154i	0.799879	+	0.600161i	$0.204897\pi$
$770$	−7.82339	−	0.354622i	−0.281935	−	0.0127797i
$771$	3.06168	+	3.83922i	0.110264	+	0.138266i
$772$	−10.1607	+	5.37008i	−0.365691	+	0.193273i
$773$	−6.71226	−	15.3847i	−0.241423	−	0.553348i	0.753095	−	0.657912i	$-0.228560\pi$
$773$	−6.71226	−	15.3847i	−0.241423	−	0.553348i	−0.994518	+	0.104564i	$0.966655\pi$
$774$	1.07234	−	0.0803606i	0.0385444	−	0.00288850i
$775$	−30.0009	−	32.0949i	−1.07766	−	1.15288i
$776$	−1.94690	−	4.04278i	−0.0698896	−	0.145127i
$777$	15.5449	−	14.1442i	0.557669	−	0.507420i
$778$	6.22553	+	17.7915i	0.223196	+	0.637858i
$779$	25.5409	+	1.91402i	0.915097	+	0.0685770i
$780$	17.3814	+	5.32634i	0.622352	+	0.190713i
$781$	13.9148	+	9.48696i	0.497911	+	0.339470i
$782$	43.7391	+	32.2809i	1.56411	+	1.15436i
$783$	−15.6588	+	15.6588i	−0.559600	+	0.559600i
$784$	−5.22316	+	4.66033i	−0.186541	+	0.166440i
$785$	3.36551	+	17.6092i	0.120120	+	0.628499i
$786$	−15.4160	+	2.32359i	−0.549872	+	0.0828798i
$787$	4.70902	+	24.8878i	0.167858	+	0.887153i	0.960671	+	0.277688i	$0.0895680\pi$
$787$	4.70902	+	24.8878i	0.167858	+	0.887153i	−0.792813	+	0.609465i	$0.791384\pi$
$788$	5.16039	+	2.72734i	0.183831	+	0.0971576i
$789$	−0.706206	+	9.42366i	−0.0251416	+	0.335491i
$790$	−2.11753	+	7.96146i	−0.0753383	+	0.283256i
$791$	1.07414	−	0.192417i	0.0381918	−	0.00684157i
$792$	0.0804429	−	0.229893i	0.00285841	−	0.00816888i
$793$	−14.1309	+	32.3885i	−0.501804	+	1.15015i
$794$	1.53924	+	20.5397i	0.0546255	+	0.728927i
$795$	−2.04841	+	1.40213i	−0.0726498	+	0.0497284i
$796$	0.402821	−	1.30591i	0.0142776	−	0.0462869i
$797$	4.48545	−	39.8095i	0.158883	−	1.41012i	−0.620809	−	0.783962i	$-0.713196\pi$
$797$	4.48545	−	39.8095i	0.158883	−	1.41012i	0.779692	−	0.626163i	$-0.215376\pi$
$798$	6.34380	+	8.11583i	0.224568	+	0.287297i
$799$	27.9429	+	22.2837i	0.988549	+	0.788341i
$800$	4.90937	−	0.947682i	0.173572	−	0.0335056i
$801$	−1.18798	−	1.28033i	−0.0419751	−	0.0452384i
$802$	−7.61737	−	2.04107i	−0.268979	−	0.0720726i
$803$	−3.83153	−	14.2995i	−0.135212	−	0.504617i
$804$	0.382157	+	1.67434i	0.0134776	+	0.0590494i
$805$	−39.0653	−	24.9788i	−1.37687	−	0.880388i
$806$	9.47254	−	41.5019i	0.333656	−	1.46184i
$807$	19.8321	−	0.742065i	0.698123	−	0.0261219i
$808$	−11.8410	+	8.73909i	−0.416566	+	0.307440i
$809$	5.29997	−	35.1630i	0.186337	−	1.23627i	−0.678647	−	0.734465i	$-0.737433\pi$
$809$	5.29997	−	35.1630i	0.186337	−	1.23627i	0.864984	−	0.501800i	$-0.167329\pi$
$810$	15.9493	+	9.98059i	0.560400	+	0.350682i
$811$	−40.4945	−	9.24260i	−1.42195	−	0.324552i	−0.558720	−	0.829356i	$-0.688707\pi$
$811$	−40.4945	−	9.24260i	−1.42195	−	0.324552i	−0.863234	+	0.504805i	$0.831565\pi$
$812$	6.08860	+	9.11998i	0.213668	+	0.320049i
$813$	14.8880	−	23.6941i	0.522145	−	0.830990i
$814$	5.42669	+	3.13310i	0.190206	+	0.109815i
$815$	−26.9387	+	23.2693i	−0.943622	+	0.815087i
$816$	−8.53205	+	7.91659i	−0.298682	+	0.277136i
$817$	−13.3236	−	2.52097i	−0.466135	−	0.0881975i
$818$	0.820622	+	7.28322i	0.0286924	+	0.254652i
$819$	−2.23356	+	0.757212i	−0.0780467	+	0.0264591i
$820$	−1.89009	−	24.6120i	−0.0660047	−	0.859488i
$821$	5.59030	+	1.72438i	0.195103	+	0.0601812i	0.390767	−	0.920490i	$-0.372210\pi$
$821$	5.59030	+	1.72438i	0.195103	+	0.0601812i	−0.195664	+	0.980671i	$0.562686\pi$
$822$	2.91194	−	1.27047i	0.101566	−	0.0443126i
$823$	15.2743	−	17.7491i	0.532429	−	0.618693i	−0.425758	−	0.904837i	$-0.639993\pi$
$823$	15.2743	−	17.7491i	0.532429	−	0.618693i	0.958187	+	0.286144i	$0.0923735\pi$
$824$	−2.82684	−	7.20267i	−0.0984776	−	0.250917i
$825$	11.0975	−	0.456257i	0.386367	−	0.0158848i
$826$	24.0149	+	12.9932i	0.835587	+	0.452090i
$827$	2.33960	−	0.818662i	0.0813559	−	0.0284677i	−0.289294	−	0.957240i	$-0.593421\pi$
$827$	2.33960	−	0.818662i	0.0813559	−	0.0284677i	0.370650	+	0.928773i	$0.379135\pi$
$828$	1.09306	−	0.940651i	0.0379863	−	0.0326899i
$829$	−28.5200	+	8.79725i	−0.990540	+	0.305541i	−0.747345	−	0.664436i	$-0.768672\pi$
$829$	−28.5200	+	8.79725i	−0.990540	+	0.305541i	−0.243195	+	0.969977i	$0.578196\pi$
$830$	11.6786	−	4.60840i	0.405371	−	0.159960i
$831$	−4.77243	−	31.6630i	−0.165554	−	1.09838i
$832$	3.42576	+	3.42576i	0.118767	+	0.118767i
$833$	−48.3427	+	4.49495i	−1.67497	+	0.155741i
$834$			24.0018i			0.831114i
$835$	−12.3693	−	35.1413i	−0.428058	−	1.21612i
$836$	−1.73012	+	2.53761i	−0.0598373	+	0.0877652i
$837$	21.9371	−	41.5070i	0.758258	−	1.43469i
$838$	1.52981	+	1.77767i	0.0528463	+	0.0614085i
$839$	−19.0351	−	9.16684i	−0.657166	−	0.316474i	0.0754172	−	0.997152i	$-0.475971\pi$
$839$	−19.0351	−	9.16684i	−0.657166	−	0.316474i	−0.732583	+	0.680678i	$0.761685\pi$
$840$	6.80985	−	7.22400i	0.234962	−	0.249252i
$841$	−10.6514	+	5.12943i	−0.367289	+	0.176877i
$842$	15.3190	+	6.68363i	0.527929	+	0.230333i
$843$	25.4966	+	21.9416i	0.878151	+	0.755710i
$844$	10.8042	+	4.24034i	0.371896	+	0.145959i
$845$	18.2798	−	14.6329i	0.628845	−	0.503388i
$846$	0.741259	−	0.591134i	0.0254850	−	0.0203236i
$847$	18.9796	+	15.4406i	0.652147	+	0.530546i
$848$	−0.657383	+	0.0740693i	−0.0225746	+	0.00254355i
$849$	21.6206	+	31.7116i	0.742018	+	1.08834i
$850$	31.3004	+	14.9314i	1.07359	+	0.512144i
$851$	18.5506	+	32.1305i	0.635905	+	1.10142i
$852$	−20.6218	+	5.52559i	−0.706490	+	0.189304i
$853$	36.5906	+	22.9914i	1.25284	+	0.787211i	0.984376	−	0.176080i	$-0.0563416\pi$
$853$	36.5906	+	22.9914i	1.25284	+	0.787211i	0.268462	+	0.963290i	$0.413484\pi$
$854$	12.4446	+	14.7491i	0.425844	+	0.504702i
$855$	0.650549	+	0.698536i	0.0222483	+	0.0238894i
$856$	−0.744234	−	0.690549i	−0.0254374	−	0.0236025i
$857$	6.14341	+	8.32403i	0.209855	+	0.284343i	0.896865	−	0.442305i	$-0.145839\pi$
$857$	6.14341	+	8.32403i	0.209855	+	0.284343i	−0.687010	+	0.726648i	$0.741077\pi$
$858$	6.39072	+	8.65912i	0.218176	+	0.295617i
$859$	−15.6825	−	14.5512i	−0.535079	−	0.496481i	0.365715	−	0.930727i	$-0.380824\pi$
$859$	−15.6825	−	14.5512i	−0.535079	−	0.496481i	−0.900794	+	0.434246i	$0.857015\pi$
$860$	−0.464556	+	13.0604i	−0.0158412	+	0.445357i
$861$	−31.6066	−	37.4596i	−1.07715	−	1.27662i
$862$	−21.1557	−	13.2930i	−0.720566	−	0.452762i
$863$	−25.2651	+	6.76977i	−0.860036	+	0.230446i	−0.661774	−	0.749703i	$-0.730196\pi$
$863$	−25.2651	+	6.76977i	−0.860036	+	0.230446i	−0.198261	+	0.980149i	$0.563530\pi$
$864$	2.67152	+	4.62721i	0.0908871	+	0.157421i
$865$	−31.6094	+	42.9951i	−1.07475	+	1.46188i
$866$	6.93786	+	10.1760i	0.235758	+	0.345794i
$867$	−51.8715	+	5.84451i	−1.76165	+	0.198490i
$868$	−18.0334	−	14.6709i	−0.612094	−	0.497961i
$869$	−3.81302	+	3.04079i	−0.129348	+	0.103152i
$870$	−9.71894	−	12.1411i	−0.329503	−	0.411623i
$871$	4.61547	+	1.81144i	0.156389	+	0.0613783i
$872$	2.55500	+	2.19875i	0.0865231	+	0.0744591i
$873$	−0.756716	−	0.330152i	−0.0256109	−	0.0111739i
$874$	−16.3837	+	7.88998i	−0.554187	+	0.266882i
$875$	−27.4899	−	10.9227i	−0.929328	−	0.369254i
$876$	16.9082	+	8.14254i	0.571274	+	0.275111i
$877$	7.39101	+	8.58851i	0.249577	+	0.290013i	0.868760	−	0.495233i	$-0.164917\pi$
$877$	7.39101	+	8.58851i	0.249577	+	0.290013i	−0.619184	+	0.785246i	$0.712536\pi$
$878$	−11.3156	+	21.4102i	−0.381883	+	0.722558i
$879$	−22.0125	+	32.2864i	−0.742464	+	1.08899i
$880$	2.66923	+	1.27937i	0.0899798	+	0.0431276i
$881$			19.0612i			0.642188i	0.947047	+	0.321094i	$0.104051\pi$
$881$			19.0612i			0.642188i	−0.947047	+	0.321094i	$0.895949\pi$
$882$	−0.169114	+	1.27680i	−0.00569436	+	0.0429920i
$883$	−1.34342	−	1.34342i	−0.0452098	−	0.0452098i	0.684140	−	0.729350i	$-0.260178\pi$
$883$	−1.34342	−	1.34342i	−0.0452098	−	0.0452098i	−0.729350	+	0.684140i	$0.760178\pi$
$884$	5.00821	+	33.2273i	0.168444	+	1.11756i
$885$	−35.5221	−	15.4202i	−1.19406	−	0.518344i
$886$	−12.7438	+	3.93093i	−0.428135	+	0.132062i
$887$	10.5494	−	9.07850i	0.354214	−	0.304826i	−0.457124	−	0.889403i	$-0.651120\pi$
$887$	10.5494	−	9.07850i	0.354214	−	0.304826i	0.811338	+	0.584577i	$0.198739\pi$
$888$	−7.49779	+	2.62359i	−0.251610	+	0.0880420i
$889$	25.5518	+	13.8247i	0.856980	+	0.463664i
$890$	17.0553	−	12.6361i	0.571695	−	0.423562i
$891$	4.06927	+	10.3683i	0.136326	+	0.347352i
$892$	12.4382	−	14.4535i	0.416462	−	0.483938i
$893$	−10.9580	+	4.78093i	−0.366696	+	0.159988i
$894$	−28.6187	−	8.82771i	−0.957154	−	0.295243i
$895$	14.6273	−	1.12331i	0.488935	−	0.0375480i
$896$	2.50568	−	0.849465i	0.0837087	−	0.0283786i
$897$	7.13440	+	63.3196i	0.238211	+	2.11418i
$898$	15.7522	+	2.98048i	0.525659	+	0.0994600i
$899$	−26.6958	+	24.7701i	−0.890355	+	0.826129i
$900$	0.570929	−	0.721368i	0.0190310	−	0.0240456i
$901$	−3.97366	−	2.29419i	−0.132382	−	0.0764306i
$902$	7.77469	−	12.3733i	0.258869	−	0.411987i
$903$	14.4078	+	21.5811i	0.479461	+	0.718174i
$904$	−0.402107	−	0.0917782i	−0.0133739	−	0.00305250i
$905$	−34.4843	+	7.93780i	−1.14630	+	0.263861i
$906$	−0.0772924	+	0.512802i	−0.00256787	+	0.0170367i
$907$	−40.0842	+	29.5835i	−1.33097	+	0.982303i	−0.331731	+	0.943374i	$0.607633\pi$
$907$	−40.0842	+	29.5835i	−1.33097	+	0.982303i	−0.999242	+	0.0389288i	$0.987605\pi$
$908$	21.2835	−	0.796371i	0.706317	−	0.0264285i
$909$	−0.602535	+	2.63988i	−0.0199848	+	0.0875593i
$910$	−6.15700	−	27.9928i	−0.204103	−	0.927953i
$911$	−5.33187	−	23.3604i	−0.176653	−	0.773966i	−0.983161	−	0.182743i	$-0.941502\pi$
$911$	−5.33187	−	23.3604i	−0.176653	−	0.773966i	0.806508	−	0.591223i	$-0.201355\pi$
$912$	−1.00769	−	3.76075i	−0.0333679	−	0.124531i
$913$	7.17928	+	1.92368i	0.237600	+	0.0636646i
$914$	−4.98475	−	5.37228i	−0.164881	−	0.177699i
$915$	−19.3885	−	19.3171i	−0.640963	−	0.638602i
$916$	9.96025	+	7.94304i	0.329096	+	0.262445i
$917$	15.1375	+	19.3658i	0.499883	+	0.639517i
$918$	−4.14926	+	36.8257i	−0.136946	+	1.21543i
$919$	15.1708	−	49.1826i	0.500439	−	1.62238i	−0.254842	−	0.966983i	$-0.582023\pi$
$919$	15.1708	−	49.1826i	0.500439	−	1.62238i	0.755281	−	0.655401i	$-0.227500\pi$
$920$	9.89925	+	14.4621i	0.326369	+	0.476802i
$921$	−1.63640	−	21.8362i	−0.0539212	−	0.719529i
$922$	3.70141	−	8.48372i	0.121899	−	0.279397i
$923$	−20.3572	+	58.1775i	−0.670065	+	1.91494i
$924$	5.78514	−	1.03633i	0.190317	−	0.0340928i
$925$	15.5047	+	17.8829i	0.509791	+	0.587985i
$926$	−0.0498244	+	0.664861i	−0.00163733	+	0.0218487i
$927$	−1.25867	−	0.665227i	−0.0413401	−	0.0218489i
$928$	−0.770533	−	4.07236i	−0.0252940	−	0.133682i
$929$	−25.7792	+	3.88559i	−0.845787	+	0.127482i	−0.557618	−	0.830098i	$-0.688285\pi$
$929$	−25.7792	+	3.88559i	−0.845787	+	0.127482i	−0.288169	+	0.957580i	$0.593047\pi$
$930$	27.2757	+	18.5227i	0.894407	+	0.607382i
$931$	6.22692	−	14.9998i	0.204079	−	0.491598i
$932$	15.6364	−	15.6364i	0.512188	−	0.512188i
$933$	3.31985	+	2.45016i	0.108687	+	0.0802147i
$934$	−20.1820	−	13.7598i	−0.660374	−	0.450235i
$935$	9.62660	+	18.1333i	0.314823	+	0.593024i
$936$	0.888906	+	0.0666143i	0.0290548	+	0.00217736i
$937$	−4.46367	−	12.7564i	−0.145822	−	0.416735i	0.847686	−	0.530498i	$-0.177995\pi$
$937$	−4.46367	−	12.7564i	−0.145822	−	0.416735i	−0.993508	+	0.113764i	$0.963709\pi$
$938$	2.00274	−	1.82229i	0.0653919	−	0.0594998i
$939$	6.96813	+	14.4695i	0.227396	+	0.472193i
$940$	6.14826	+	9.74493i	0.200534	+	0.317845i
$941$	−15.7648	+	1.18141i	−0.513918	+	0.0385128i	−0.329166	−	0.944272i	$-0.606767\pi$
$941$	−15.7648	+	1.18141i	−0.513918	+	0.0385128i	−0.184753	+	0.982785i	$0.559148\pi$
$942$	−5.38028	−	12.3317i	−0.175299	−	0.401789i
$943$	76.4956	−	40.4291i	2.49104	−	1.31655i
$944$	−6.43451	−	8.06862i	−0.209426	−	0.262611i
$945$	1.43136	−	31.5775i	0.0465620	−	1.02722i
$946$	−4.82373	+	6.04877i	−0.156833	+	0.196662i
$947$	−3.13458	+	16.5667i	−0.101860	+	0.538344i	0.894048	+	0.447972i	$0.147853\pi$
$947$	−3.13458	+	16.5667i	−0.101860	+	0.538344i	−0.995908	+	0.0903726i	$0.971194\pi$
$948$	0.231173	−	6.17822i	0.00750813	−	0.200659i
$949$	46.9215	−	27.0901i	1.52314	−	0.879383i
$950$	−9.30839	+	6.92311i	−0.302004	+	0.224615i
$951$	8.39000	−	1.91496i	0.272065	−	0.0620969i
$952$	17.4818	+	5.57952i	0.566589	+	0.180833i
$953$	−9.60624	+	6.03600i	−0.311177	+	0.195525i	−0.678561	−	0.734544i	$-0.737396\pi$
$953$	−9.60624	+	6.03600i	−0.311177	+	0.195525i	0.367384	+	0.930069i	$0.380253\pi$
$954$	−0.0827899	+	0.0892263i	−0.00268042	+	0.00288881i
$955$	−38.0259	−	35.1526i	−1.23049	−	1.13751i
$956$	−3.91477	−	0.590057i	−0.126613	−	0.0190838i
$957$	−0.344253	−	9.20034i	−0.0111281	−	0.297405i
$958$	6.34817	+	10.1031i	0.205100	+	0.326415i
$959$	−4.00108	−	3.01358i	−0.129202	−	0.0973136i
$960$	−3.43648	+	1.50687i	−0.110912	+	0.0486341i
$961$	23.1027	−	40.0151i	0.745249	−	1.29081i
$962$	−5.93562	+	22.1520i	−0.191372	+	0.714210i
$963$	−0.186669	−	0.00698465i	−0.00601532	−	0.000225077i
$964$	25.0727	−	17.0943i	0.807538	−	0.550570i
$965$	−22.7421	−	11.9659i	−0.732094	−	0.385197i
$966$	32.7318	+	11.8125i	1.05313	+	0.380061i
$967$	−48.3003	−	5.44214i	−1.55323	−	0.175007i	−0.706766	−	0.707448i	$-0.749847\pi$
$967$	−48.3003	−	5.44214i	−1.55323	−	0.175007i	−0.846468	+	0.532440i	$0.821275\pi$
$968$	−4.32115	−	8.17602i	−0.138887	−	0.262787i
$969$	9.86576	−	25.1375i	0.316934	−	0.807534i
$970$	5.00074	−	8.69857i	0.160564	−	0.279294i
$971$	−52.6662	+	20.6700i	−1.69014	+	0.663330i	−0.998276	−	0.0586992i	$-0.981305\pi$
$971$	−52.6662	+	20.6700i	−1.69014	+	0.663330i	−0.691862	+	0.722029i	$0.743209\pi$
$972$	1.80221	+	0.630619i	0.0578058	+	0.0202271i
$973$	32.9551	−	18.6009i	1.05649	−	0.596318i
$974$	−1.80168	+	3.74122i	−0.0577295	+	0.119877i
$975$	12.1250	+	38.7994i	0.388311	+	1.24257i
$976$	−2.14990	−	6.96980i	−0.0688166	−	0.223098i
$977$	33.0081	−	6.24546i	1.05602	−	0.199810i	0.371224	−	0.928543i	$-0.378938\pi$
$977$	33.0081	−	6.24546i	1.05602	−	0.199810i	0.684798	+	0.728733i	$0.259891\pi$
$978$	15.8636	−	21.4944i	0.507262	−	0.687315i
$979$	12.5659			0.401609
$980$	−15.1962	−	3.75164i	−0.485426	−	0.119842i
$981$	0.620208			0.0198017
$982$	−1.37629	+	1.86481i	−0.0439192	+	0.0595084i
$983$	28.3992	−	5.37341i	0.905792	−	0.171385i	0.287912	−	0.957657i	$-0.407039\pi$
$983$	28.3992	−	5.37341i	0.905792	−	0.171385i	0.617881	+	0.786272i	$0.287991\pi$
$984$	5.46031	+	17.7019i	0.174068	+	0.564315i
$985$	1.48523	+	12.9667i	0.0473232	+	0.413152i
$986$	12.4727	−	25.8998i	0.397211	−	0.824817i
$987$	21.2143	+	8.56544i	0.675258	+	0.272641i
$988$	−10.6097	−	3.71250i	−0.337540	−	0.118110i
$989$	−42.6410	+	16.7353i	−1.35590	+	0.532153i
$990$	0.525799	−	0.141928i	0.0167110	−	0.00451076i
$991$	−4.06560	+	10.3590i	−0.129148	+	0.329064i	−0.980792	−	0.195057i	$-0.937511\pi$
$991$	−4.06560	+	10.3590i	−0.129148	+	0.329064i	0.851644	+	0.524121i	$0.175606\pi$
$992$	4.10573	+	7.76842i	0.130357	+	0.246648i
$993$	7.23476	+	0.815162i	0.229588	+	0.0258684i
$994$	23.5682	+	24.0320i	0.747539	+	0.762248i
$995$	2.91845	−	0.906122i	0.0925210	−	0.0287260i
$996$	−7.78491	+	5.30766i	−0.246674	+	0.168180i
$997$	46.7061	+	1.74762i	1.47920	+	0.0553476i	0.764743	−	0.644335i	$-0.222866\pi$
$997$	46.7061	+	1.74762i	1.47920	+	0.0553476i	0.714454	+	0.699683i	$0.246675\pi$
$998$	3.32756	−	12.4186i	0.105332	−	0.393105i
$999$	−12.6461	+	21.9037i	−0.400105	+	0.693003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.w.a.103.18	✓	672
5.2	odd	4	inner	490.2.w.a.397.25	yes	672
49.10	odd	42	inner	490.2.w.a.353.25	yes	672
245.157	even	84	inner	490.2.w.a.157.18	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.w.a.103.18	✓	672	1.1	even	1	trivial
490.2.w.a.157.18	yes	672	245.157	even	84	inner
490.2.w.a.353.25	yes	672	49.10	odd	42	inner
490.2.w.a.397.25	yes	672	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.w (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.593820 - 0.804598i) q^{2} +(-1.64884 + 0.311978i) q^{3} +(-0.294755 - 0.955573i) q^{4} +(1.39094 - 1.75080i) q^{5} +(-0.728099 + 1.51191i) q^{6} +(2.64015 - 0.172004i) q^{7} +(-0.943883 - 0.330279i) q^{8} +(-0.171274 + 0.0672200i) q^{9} +(-0.582721 - 2.15880i) q^{10} +(0.483621 - 1.23225i) q^{11} +(0.784122 + 1.48363i) q^{12} +(4.81429 + 0.542440i) q^{13} +(1.42938 - 2.22640i) q^{14} +(-1.74723 + 3.32073i) q^{15} +(-0.826239 + 0.563320i) q^{16} +(-6.93104 - 0.259341i) q^{17} +(-0.0476208 + 0.177723i) q^{18} +(1.16007 - 2.00930i) q^{19} +(-2.08300 - 0.813085i) q^{20} +(-4.29953 + 1.10728i) q^{21} +(-0.704278 - 1.12085i) q^{22} +(-0.293061 - 7.83223i) q^{23} +(1.65935 + 0.250107i) q^{24} +(-1.13059 - 4.87050i) q^{25} +(3.29527 - 3.55145i) q^{26} +(4.52409 - 2.84267i) q^{27} +(-0.942561 - 2.47216i) q^{28} +(-4.04070 + 0.922264i) q^{29} +(1.63431 + 3.37773i) q^{30} +(7.60947 - 4.39333i) q^{31} +(-0.0373912 + 0.999301i) q^{32} +(-0.412981 + 2.18266i) q^{33} +(-4.32445 + 5.42269i) q^{34} +(3.37115 - 4.86162i) q^{35} +(0.114718 + 0.143851i) q^{36} +(-4.18511 + 2.21190i) q^{37} +(-0.927804 - 2.12655i) q^{38} +(-8.10723 + 0.607553i) q^{39} +(-1.89113 + 1.19315i) q^{40} +(4.78974 + 9.94600i) q^{41} +(-1.66224 + 4.11692i) q^{42} +(-1.93032 - 5.51652i) q^{43} +(-1.32005 - 0.0989241i) q^{44} +(-0.120543 + 0.393365i) q^{45} +(-6.47582 - 4.41514i) q^{46} +(-4.14606 - 3.05993i) q^{47} +(1.18659 - 1.18659i) q^{48} +(6.94083 - 0.908233i) q^{49} +(-4.59016 - 1.98253i) q^{50} +(11.5091 - 1.73472i) q^{51} +(-0.900696 - 4.76029i) q^{52} +(0.584880 + 0.309118i) q^{53} +(0.399286 - 5.32811i) q^{54} +(-1.48473 - 2.56070i) q^{55} +(-2.54881 - 0.709636i) q^{56} +(-1.28591 + 3.67493i) q^{57} +(-1.65740 + 3.79880i) q^{58} +(0.771226 + 10.2913i) q^{59} +(3.68820 + 0.690799i) q^{60} +(-2.14990 + 6.96980i) q^{61} +(0.983794 - 8.73141i) q^{62} +(-0.440627 + 0.206931i) q^{63} +(0.781831 + 0.623490i) q^{64} +(7.64608 - 7.67435i) q^{65} +(1.51092 + 1.62839i) q^{66} +(0.988548 + 0.264881i) q^{67} +(1.79514 + 6.69955i) q^{68} +(2.92669 + 12.8227i) q^{69} +(-1.90980 - 5.59935i) q^{70} +(-2.83098 + 12.4033i) q^{71} +(0.183864 - 0.00687970i) q^{72} +(8.99805 - 6.64086i) q^{73} +(-0.705517 + 4.68080i) q^{74} +(3.38364 + 7.67796i) q^{75} +(-2.26196 - 0.516279i) q^{76} +(1.06488 - 3.33650i) q^{77} +(-4.32540 + 6.88383i) q^{78} +(-3.19066 - 1.84213i) q^{79} +(-0.162987 + 2.23012i) q^{80} +(-6.16802 + 5.72309i) q^{81} +(10.8468 + 2.05232i) q^{82} +(0.628653 + 5.57945i) q^{83} +(2.32539 + 3.78214i) q^{84} +(-10.0947 + 11.7741i) q^{85} +(-5.58484 - 1.72270i) q^{86} +(6.37475 - 2.78128i) q^{87} +(-0.863466 + 1.00337i) q^{88} +(3.46806 + 8.83647i) q^{89} +(0.244920 + 0.330576i) q^{90} +(12.8038 + 0.604050i) q^{91} +(-7.39788 + 2.58863i) q^{92} +(-11.1762 + 9.61789i) q^{93} +(-4.92402 + 1.51886i) q^{94} +(-1.90429 - 4.82585i) q^{95} +(-0.250107 - 1.65935i) q^{96} +(3.17289 + 3.17289i) q^{97} +(3.39084 - 6.12390i) q^{98} +0.243560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + 12 q^{10} + 4 q^{11} - 44 q^{15} - 56 q^{16} + 8 q^{17} + 28 q^{21} + 20 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 4 q^{28} - 12 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{35}+ \cdots - 40 q^{98}+O(q^{100}) \) 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7 + 12 * q^10 + 4 * q^11 - 44 * q^15 - 56 * q^16 + 8 * q^17 + 28 * q^21 + 20 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 4 * q^28 - 12 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^35 + 92 * q^36 - 12 * q^37 - 24 * q^38 - 112 * q^41 + 76 * q^42 + 24 * q^43 - 100 * q^45 - 160 * q^46 + 72 * q^47 + 32 * q^50 - 208 * q^51 + 160 * q^53 - 84 * q^55 - 52 * q^56 - 92 * q^57 + 128 * q^58 - 212 * q^61 + 36 * q^63 - 16 * q^67 + 36 * q^68 - 16 * q^70 - 16 * q^71 + 12 * q^73 + 132 * q^75 - 16 * q^77 + 80 * q^78 + 12 * q^80 - 36 * q^81 + 48 * q^82 - 308 * q^83 - 40 * q^85 - 4 * q^86 + 52 * q^87 - 4 * q^88 + 84 * q^90 - 124 * q^91 - 8 * q^92 - 536 * q^93 - 28 * q^95 - 12 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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