LMFDB - Embedded newform 961.2.g.j.338.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,-3,-14,-3,-11,-13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.j.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86683 + 1.35633i) q^{2} +(-0.265787 + 2.52879i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 - 2.16373i) q^{5} +(-2.93370 - 5.08132i) q^{6} +(-1.56687 + 0.333049i) q^{7} +(0.944583 + 2.90713i) q^{8} +(-3.38972 - 0.720507i) q^{9} +(0.602634 + 5.73368i) q^{10} +(-0.490912 - 0.545213i) q^{11} +(7.72288 + 3.43845i) q^{12} +(1.73206 - 0.771163i) q^{13} +(2.47336 - 2.74694i) q^{14} +(5.13960 + 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(2.93028 - 3.25441i) q^{17} +(7.30526 - 3.25251i) q^{18} +(-4.23705 - 1.88646i) q^{19} +(-5.55818 - 6.17299i) q^{20} +(-0.425758 - 4.05082i) q^{21} +(1.65594 + 0.351980i) q^{22} +(2.19973 + 6.77006i) q^{23} +(-7.60258 + 1.61598i) q^{24} +(-0.621150 - 1.07586i) q^{25} +(-2.18751 + 3.78887i) q^{26} +(0.365721 - 1.12557i) q^{27} +(-0.556691 + 5.29656i) q^{28} +(-0.104314 + 0.0757884i) q^{29} -14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(-1.05628 + 10.0499i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 + 9.97791i) q^{36} +(4.21474 + 7.30014i) q^{37} +(10.4685 - 2.22515i) q^{38} +(1.48975 + 4.58499i) q^{39} +(7.47024 + 1.58785i) q^{40} +(0.770791 + 7.33358i) q^{41} +(6.28907 + 6.98472i) q^{42} +(-0.210565 - 0.0937494i) q^{43} +(-2.22830 + 0.992101i) q^{44} +(-5.79352 + 6.43435i) q^{45} +(-13.2889 - 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(0.687602 - 0.763659i) q^{48} +(-4.05065 + 1.80346i) q^{49} +(2.61881 + 1.16597i) q^{50} +(7.45090 + 8.27507i) q^{51} +(-0.658896 - 6.26898i) q^{52} +(5.60893 + 1.19222i) q^{53} +(0.843912 + 2.59729i) q^{54} +(-1.79296 + 0.381105i) q^{55} +(-2.44826 - 4.24051i) q^{56} +(5.89661 - 10.2132i) q^{57} +(0.0919419 - 0.282968i) q^{58} +(-0.993409 + 9.45166i) q^{59} +(17.0875 - 12.4148i) q^{60} +7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(0.495153 - 4.71107i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 + 4.17994i) q^{67} +(-7.27978 - 12.6090i) q^{68} +(-17.7047 + 3.76326i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(3.33061 + 0.707943i) q^{71} +(-1.10726 - 10.5349i) q^{72} +(-1.80133 - 2.00058i) q^{73} +(-17.7696 - 7.91153i) q^{74} +(2.88573 - 1.28481i) q^{75} +(-10.3180 + 11.4593i) q^{76} +(0.950780 + 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(-3.02979 + 3.36492i) q^{79} +(-0.922421 + 0.410688i) q^{80} +(-6.74838 - 3.00457i) q^{81} +(-11.3857 - 12.6451i) q^{82} +(0.279128 + 2.65572i) q^{83} +(-13.2459 - 2.81551i) q^{84} +(-3.38106 - 10.4058i) q^{85} +(0.520243 - 0.110581i) q^{86} +(-0.163928 - 0.283932i) q^{87} +(1.12130 - 1.94214i) q^{88} +(0.681255 - 2.09669i) q^{89} +(2.08840 - 19.8698i) q^{90} +(-2.45708 + 1.78518i) q^{91} +23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(1.37702 - 13.1015i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 - 8.86077i) q^{98} +(1.27122 + 2.20182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.320115	+	0.947379i	$0.603722\pi$
$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.999932	+	0.0116917i	$0.996278\pi$
$3$	−0.265787	+	2.52879i	−0.153452	+	1.46000i	0.598680	+	0.800988i	$0.295692\pi$
$3$	−0.265787	+	2.52879i	−0.153452	+	1.46000i	−0.752132	+	0.659012i	$0.770975\pi$
$4$	1.02738	−	3.16196i	0.513691	−	1.58098i
$5$	1.24923	−	2.16373i	0.558673	−	0.967649i	−0.438935	−	0.898519i	$-0.644644\pi$
$5$	1.24923	−	2.16373i	0.558673	−	0.967649i	0.997608	−	0.0691304i	$-0.0220225\pi$
$6$	−2.93370	−	5.08132i	−1.19768	−	2.07444i
$7$	−1.56687	+	0.333049i	−0.592223	+	0.125881i	−0.494267	−	0.869310i	$-0.664564\pi$
$7$	−1.56687	+	0.333049i	−0.592223	+	0.125881i	−0.0979553	+	0.995191i	$0.531230\pi$
$8$	0.944583	+	2.90713i	0.333960	+	1.02782i
$9$	−3.38972	−	0.720507i	−1.12991	−	0.240169i
$10$	0.602634	+	5.73368i	0.190570	+	1.81315i
$11$	−0.490912	−	0.545213i	−0.148016	−	0.164388i	0.664578	−	0.747219i	$-0.268612\pi$
$11$	−0.490912	−	0.545213i	−0.148016	−	0.164388i	−0.812593	+	0.582831i	$0.801945\pi$
$12$	7.72288	+	3.43845i	2.22940	+	0.992594i
$13$	1.73206	−	0.771163i	0.480387	−	0.213882i	−0.152233	−	0.988345i	$-0.548646\pi$
$13$	1.73206	−	0.771163i	0.480387	−	0.213882i	0.632620	+	0.774463i	$0.281980\pi$
$14$	2.47336	−	2.74694i	0.661033	−	0.734152i
$15$	5.13960	+	3.73414i	1.32704	+	0.964150i
$16$	−0.326952	−	0.237545i	−0.0817381	−	0.0593862i
$17$	2.93028	−	3.25441i	0.710698	−	0.789310i	−0.274343	−	0.961632i	$-0.588460\pi$
$17$	2.93028	−	3.25441i	0.710698	−	0.789310i	0.985041	+	0.172322i	$0.0551269\pi$
$18$	7.30526	−	3.25251i	1.72187	−	0.766625i
$19$	−4.23705	−	1.88646i	−0.972045	−	0.432783i	−0.141625	−	0.989920i	$-0.545233\pi$
$19$	−4.23705	−	1.88646i	−0.972045	−	0.432783i	−0.830420	+	0.557138i	$0.811900\pi$
$20$	−5.55818	−	6.17299i	−1.24285	−	1.38032i
$21$	−0.425758	−	4.05082i	−0.0929081	−	0.883962i
$22$	1.65594	+	0.351980i	0.353047	+	0.0750425i
$23$	2.19973	+	6.77006i	0.458675	+	1.41166i	0.866766	+	0.498714i	$0.166194\pi$
$23$	2.19973	+	6.77006i	0.458675	+	1.41166i	−0.408092	+	0.912941i	$0.633806\pi$
$24$	−7.60258	+	1.61598i	−1.55187	+	0.329860i
$25$	−0.621150	−	1.07586i	−0.124230	−	0.215173i
$26$	−2.18751	+	3.78887i	−0.429005	+	0.743059i
$27$	0.365721	−	1.12557i	0.0703831	−	0.216617i
$28$	−0.556691	+	5.29656i	−0.105205	+	1.00096i
$29$	−0.104314	+	0.0757884i	−0.0193706	+	0.0140736i	−0.597428	−	0.801922i	$-0.703811\pi$
$29$	−0.104314	+	0.0757884i	−0.0193706	+	0.0140736i	0.578058	+	0.815996i	$0.303811\pi$
$30$	−14.6595			−2.67644
$31$		0			0
$31$		0			0
$32$	−5.18091			−0.915865
$33$	1.50921	−	1.09651i	0.262720	−	0.190877i
$34$	−1.05628	+	10.0499i	−0.181151	+	1.72354i
$35$	−1.23676	+	3.80635i	−0.209050	+	0.643390i
$36$	−5.76075	+	9.97791i	−0.960125	+	1.66298i
$37$	4.21474	+	7.30014i	0.692899	+	1.20014i	0.970884	+	0.239550i	$0.0770000\pi$
$37$	4.21474	+	7.30014i	0.692899	+	1.20014i	−0.277985	+	0.960585i	$0.589667\pi$
$38$	10.4685	−	2.22515i	1.69821	−	0.360967i
$39$	1.48975	+	4.58499i	0.238551	+	0.734186i
$40$	7.47024	+	1.58785i	1.18115	+	0.251061i
$41$	0.770791	+	7.33358i	0.120377	+	1.14531i	0.873293	+	0.487196i	$0.161980\pi$
$41$	0.770791	+	7.33358i	0.120377	+	1.14531i	−0.752915	+	0.658117i	$0.771353\pi$
$42$	6.28907	+	6.98472i	0.970424	+	1.07777i
$43$	−0.210565	−	0.0937494i	−0.0321108	−	0.0142967i	0.390618	−	0.920553i	$-0.372261\pi$
$43$	−0.210565	−	0.0937494i	−0.0321108	−	0.0142967i	−0.422729	+	0.906256i	$0.638928\pi$
$44$	−2.22830	+	0.992101i	−0.335928	+	0.149565i
$45$	−5.79352	+	6.43435i	−0.863646	+	0.959177i
$46$	−13.2889	−	9.65498i	−1.95935	−	1.42355i
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	0.950420	−	0.310968i	$-0.100653\pi$
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	−0.00205222	+	0.999998i	$0.500653\pi$
$48$	0.687602	−	0.763659i	0.0992468	−	0.110225i
$49$	−4.05065	+	1.80346i	−0.578664	+	0.257638i
$50$	2.61881	+	1.16597i	0.370355	+	0.164893i
$51$	7.45090	+	8.27507i	1.04333	+	1.15874i
$52$	−0.658896	−	6.26898i	−0.0913725	−	0.869351i
$53$	5.60893	+	1.19222i	0.770446	+	0.163763i	0.576332	−	0.817216i	$-0.304483\pi$
$53$	5.60893	+	1.19222i	0.770446	+	0.163763i	0.194114	+	0.980979i	$0.437817\pi$
$54$	0.843912	+	2.59729i	0.114842	+	0.353447i
$55$	−1.79296	+	0.381105i	−0.241762	+	0.0513881i
$56$	−2.44826	−	4.24051i	−0.327162	−	0.566662i
$57$	5.89661	−	10.2132i	0.781025	−	1.35278i
$58$	0.0919419	−	0.282968i	0.0120726	−	0.0371555i
$59$	−0.993409	+	9.45166i	−0.129331	+	1.23050i	0.716706	+	0.697376i	$0.245649\pi$
$59$	−0.993409	+	9.45166i	−0.129331	+	1.23050i	−0.846037	+	0.533125i	$0.821018\pi$
$60$	17.0875	−	12.4148i	2.20599	−	1.60274i
$61$	7.84044			1.00387			0.501933	−	0.864907i	$-0.332623\pi$
$61$	7.84044			1.00387			0.501933	+	0.864907i	$0.332623\pi$
$62$		0			0
$63$	5.55122			0.699388
$64$	10.3258	−	7.50212i	1.29072	−	0.937765i
$65$	0.495153	−	4.71107i	0.0614162	−	0.584336i
$66$	−1.33021	+	4.09397i	−0.163738	+	0.503933i
$67$	−2.41329	+	4.17994i	−0.294830	+	0.510661i	−0.974945	−	0.222444i	$-0.928596\pi$
$67$	−2.41329	+	4.17994i	−0.294830	+	0.510661i	0.680115	+	0.733105i	$0.261930\pi$
$68$	−7.27978	−	12.6090i	−0.882804	−	1.52906i
$69$	−17.7047	+	3.76326i	−2.13140	+	0.453043i
$70$	−2.85385	−	8.78324i	−0.341100	−	1.04980i
$71$	3.33061	+	0.707943i	0.395271	+	0.0840174i	0.401259	−	0.915965i	$-0.368573\pi$
$71$	3.33061	+	0.707943i	0.395271	+	0.0840174i	−0.00598824	+	0.999982i	$0.501906\pi$
$72$	−1.10726	−	10.5349i	−0.130492	−	1.24155i
$73$	−1.80133	−	2.00058i	−0.210830	−	0.234150i	0.628450	−	0.777850i	$-0.283690\pi$
$73$	−1.80133	−	2.00058i	−0.210830	−	0.234150i	−0.839280	+	0.543700i	$0.817023\pi$
$74$	−17.7696	−	7.91153i	−2.06567	−	0.919697i
$75$	2.88573	−	1.28481i	0.333215	−	0.148357i
$76$	−10.3180	+	11.4593i	−1.18355	+	1.31447i
$77$	0.950780	+	0.690782i	0.108351	+	0.0787219i
$78$	−8.99987	−	6.53879i	−1.01903	−	0.740372i
$79$	−3.02979	+	3.36492i	−0.340878	+	0.378583i	−0.889072	−	0.457768i	$-0.848649\pi$
$79$	−3.02979	+	3.36492i	−0.340878	+	0.378583i	0.548194	+	0.836351i	$0.315316\pi$
$80$	−0.922421	+	0.410688i	−0.103130	+	0.0459164i
$81$	−6.74838	−	3.00457i	−0.749820	−	0.333841i
$82$	−11.3857	−	12.6451i	−1.25734	−	1.39642i
$83$	0.279128	+	2.65572i	0.0306382	+	0.291503i	0.999103	+	0.0423518i	$0.0134850\pi$
$83$	0.279128	+	2.65572i	0.0306382	+	0.291503i	−0.968465	+	0.249151i	$0.919848\pi$
$84$	−13.2459	−	2.81551i	−1.44525	−	0.307198i
$85$	−3.38106	−	10.4058i	−0.366728	−	1.12867i
$86$	0.520243	−	0.110581i	0.0560993	−	0.0119243i
$87$	−0.163928	−	0.283932i	−0.0175749	−	0.0304407i
$88$	1.12130	−	1.94214i	0.119531	−	0.207033i
$89$	0.681255	−	2.09669i	0.0722129	−	0.222248i	−0.908436	−	0.418025i	$-0.862723\pi$
$89$	0.681255	−	2.09669i	0.0722129	−	0.222248i	0.980649	+	0.195776i	$0.0627226\pi$
$90$	2.08840	−	19.8698i	0.220136	−	2.09446i
$91$	−2.45708	+	1.78518i	−0.257572	+	0.187137i
$92$	23.6666			2.46741
$93$		0			0
$94$	−18.5445			−1.91272
$95$	−9.37482	+	6.81121i	−0.961837	+	0.698815i
$96$	1.37702	−	13.1015i	0.140541	−	1.33716i
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	−0.550434	−	0.834879i	$-0.685538\pi$
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	0.936040	−	0.351894i	$-0.114462\pi$
$98$	5.11577	−	8.86077i	0.516771	−	0.895073i
$99$	1.27122	+	2.20182i	0.127763	+	0.221292i
$100$	−4.03999	+	0.858727i	−0.403999	+	0.0858727i
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	0.998207	+	0.0598605i	$0.0190656\pi$
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	−0.772381	+	0.635159i	$0.780934\pi$
$102$	−25.1333	−	5.34224i	−2.48857	−	0.528961i
$103$	−0.584184	−	5.55814i	−0.0575613	−	0.547659i	−0.984862	−	0.173342i	$-0.944544\pi$
$103$	−0.584184	−	5.55814i	−0.0575613	−	0.547659i	0.927300	−	0.374318i	$-0.122123\pi$
$104$	3.87794	+	4.30689i	0.380263	+	0.422325i
$105$	−9.29675	−	4.13918i	−0.907270	−	0.403943i
$106$	−12.0880	+	5.38190i	−1.17409	+	0.522737i
$107$	1.22060	−	1.35562i	0.118000	−	0.131052i	−0.681250	−	0.732051i	$-0.738563\pi$
$107$	1.22060	−	1.35562i	0.118000	−	0.131052i	0.799250	+	0.600998i	$0.205230\pi$
$108$	−3.18328	−	2.31279i	−0.306312	−	0.222548i
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	0.0297521	−	0.999557i	$-0.490528\pi$
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	−0.941442	+	0.337176i	$0.890528\pi$
$110$	2.83024	−	3.14330i	0.269853	−	0.299702i
$111$	−19.5808	+	8.71793i	−1.85853	+	0.827469i
$112$	0.591407	+	0.263311i	0.0558827	+	0.0248806i
$113$	7.39693	+	8.21512i	0.695844	+	0.772813i	0.982709	−	0.185158i	$-0.0592796\pi$
$113$	7.39693	+	8.21512i	0.695844	+	0.772813i	−0.286864	+	0.957971i	$0.592613\pi$
$114$	2.84455	+	27.0641i	0.266417	+	2.53478i
$115$	17.3965	+	3.69775i	1.62224	+	0.344817i
$116$	0.132470	+	0.407700i	0.0122995	+	0.0378540i
$117$	−6.42682	+	1.36606i	−0.594160	+	0.126293i
$118$	−10.9650	−	18.9920i	−1.00941	−	1.74836i
$119$	−3.50750	+	6.07518i	−0.321532	+	0.556911i
$120$	−6.00083	+	18.4687i	−0.547799	+	1.68595i
$121$	1.09355	−	10.4044i	0.0994137	−	0.945858i
$122$	−14.6368	+	10.6342i	−1.32515	+	0.962777i
$123$	−18.7500			−1.69063
$124$		0			0
$125$	9.38846			0.839730
$126$	−10.3632	+	7.52929i	−0.923225	+	0.670762i
$127$	−0.134532	+	1.27998i	−0.0119377	+	0.113580i	−0.998868	−	0.0475679i	$-0.984853\pi$
$127$	−0.134532	+	1.27998i	−0.0119377	+	0.113580i	0.986930	+	0.161148i	$0.0515196\pi$
$128$	−5.89913	+	18.1557i	−0.521414	+	1.60475i
$129$	0.293038	−	0.507557i	0.0258006	−	0.0446879i
$130$	5.46540	+	9.46635i	0.479347	+	0.830254i
$131$	7.84509	−	1.66753i	0.685429	−	0.145692i	0.147982	−	0.988990i	$-0.452722\pi$
$131$	7.84509	−	1.66753i	0.685429	−	0.145692i	0.537447	+	0.843298i	$0.319389\pi$
$132$	−1.91657	−	5.89859i	−0.166816	−	0.513406i
$133$	7.26720	+	1.54469i	0.630146	+	0.133942i
$134$	−1.16418	−	11.0764i	−0.100570	−	0.956859i
$135$	−1.97857	−	2.19742i	−0.170288	−	0.189124i
$136$	12.2289	+	5.44465i	1.04862	+	0.466875i
$137$	15.0523	−	6.70170i	1.28600	−	0.572565i	0.354077	−	0.935216i	$-0.384795\pi$
$137$	15.0523	−	6.70170i	1.28600	−	0.572565i	0.931925	+	0.362651i	$0.118128\pi$
$138$	27.9475	−	31.0388i	2.37905	−	2.64220i
$139$	5.93804	+	4.31424i	0.503658	+	0.365929i	0.810412	−	0.585860i	$-0.199243\pi$
$139$	5.93804	+	4.31424i	0.503658	+	0.365929i	−0.306755	+	0.951789i	$0.599243\pi$
$140$	10.7649	+	7.82114i	0.909799	+	0.661007i
$141$	−13.6735	+	15.1859i	−1.15151	+	1.27888i
$142$	−7.17788	+	3.19580i	−0.602354	+	0.268185i
$143$	−1.27074	−	0.565769i	−0.106264	−	0.0473120i
$144$	0.937123	+	1.04078i	0.0780936	+	0.0867317i
$145$	0.0336737	+	0.320384i	0.00279645	+	0.0266064i
$146$	6.07622	+	1.29154i	0.502872	+	0.106889i
$147$	−3.48398	−	10.7226i	−0.287354	−	0.884385i
$148$	27.4129	−	5.82679i	2.25333	−	0.478959i
$149$	3.18096	+	5.50959i	0.260595	+	0.451363i	0.966400	−	0.257043i	$-0.0827480\pi$
$149$	3.18096	+	5.50959i	0.260595	+	0.451363i	−0.705805	+	0.708406i	$0.749415\pi$
$150$	−3.64454	+	6.31252i	−0.297575	+	0.515415i
$151$	1.70724	−	5.25433i	0.138933	−	0.427592i	−0.857248	−	0.514904i	$-0.827828\pi$
$151$	1.70724	−	5.25433i	0.138933	−	0.427592i	0.996181	+	0.0873120i	$0.0278277\pi$
$152$	1.48192	−	14.0995i	0.120200	−	1.14362i
$153$	−12.2777	+	8.92024i	−0.992590	+	0.721159i
$154$	−2.71187			−0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	−0.815161	−	0.579234i	$-0.803352\pi$
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	0.298985	+	0.954258i	$0.403352\pi$
$158$	1.09215	−	10.3911i	0.0868868	−	0.826673i
$159$	−4.50565	+	13.8670i	−0.357321	+	1.09972i
$160$	−6.47215	+	11.2101i	−0.511669	+	0.886236i
$161$	−5.70146	−	9.87521i	−0.449338	−	0.778276i
$162$	16.6733	−	3.54401i	1.30998	−	0.278444i
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	−0.913981	−	0.405756i	$-0.867008\pi$
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	0.500929	−	0.865488i	$-0.332992\pi$
$164$	23.9804	+	5.09719i	1.87255	+	0.398024i
$165$	−0.487191	−	4.63531i	−0.0379277	−	0.360858i
$166$	−4.12312	−	4.57919i	−0.320016	−	0.355414i
$167$	22.2651	+	9.91307i	1.72293	+	0.767096i	0.996835	+	0.0794987i	$0.0253320\pi$
$167$	22.2651	+	9.91307i	1.72293	+	0.767096i	0.726092	+	0.687598i	$0.241335\pi$
$168$	11.3741	−	5.06407i	0.877530	−	0.390701i
$169$	−6.29336	+	6.98948i	−0.484104	+	0.537652i
$170$	20.4256	+	14.8401i	1.56657	+	1.13818i
$171$	13.0032	+	9.44737i	0.994379	+	0.722458i
$172$	−0.512762	+	0.569480i	−0.0390978	+	0.0434225i
$173$	8.19779	−	3.64989i	0.623267	−	0.277496i	−0.0707063	−	0.997497i	$-0.522525\pi$
$173$	8.19779	−	3.64989i	0.623267	−	0.277496i	0.693973	+	0.720001i	$0.255859\pi$
$174$	0.691131	+	0.307711i	0.0523945	+	0.0233275i
$175$	1.33158	+	1.47887i	0.100658	+	0.111792i
$176$	0.0309923	+	0.294872i	0.00233614	+	0.0222268i
$177$	−23.6373	−	5.02425i	−1.77669	−	0.377646i
$178$	1.57201	+	4.83816i	0.117827	+	0.362635i
$179$	−11.0438	+	2.34743i	−0.825452	+	0.175455i	−0.601223	−	0.799081i	$-0.705320\pi$
$179$	−11.0438	+	2.34743i	−0.825452	+	0.175455i	−0.224229	+	0.974537i	$0.571986\pi$
$180$	14.3930	+	24.9294i	1.07279	+	1.85813i
$181$	−7.47052	+	12.9393i	−0.555279	+	0.961772i	0.442602	+	0.896718i	$0.354055\pi$
$181$	−7.47052	+	12.9393i	−0.555279	+	0.961772i	−0.997882	+	0.0650542i	$0.979278\pi$
$182$	2.16567	−	6.66523i	0.160530	−	0.494060i
$183$	−2.08389	+	19.8269i	−0.154045	+	1.46564i
$184$	−17.6036	+	12.7898i	−1.29775	+	0.942874i
$185$	21.0607			1.54841
$186$		0			0
$187$	−3.21286			−0.234947
$188$	21.6160	−	15.7050i	1.57651	−	1.14540i
$189$	−0.198167	+	1.88544i	−0.0144146	+	0.137145i
$190$	8.26294	−	25.4307i	0.599457	−	1.84494i
$191$	−1.13046	+	1.95802i	−0.0817975	+	0.141677i	−0.904022	−	0.427486i	$-0.859399\pi$
$191$	−1.13046	+	1.95802i	−0.0817975	+	0.141677i	0.822225	+	0.569163i	$0.192733\pi$
$192$	16.2269	+	28.1057i	1.17107	+	2.02836i
$193$	−25.1034	+	5.33590i	−1.80698	+	0.384086i	−0.983158	−	0.182756i	$-0.941498\pi$
$193$	−25.1034	+	5.33590i	−1.80698	+	0.384086i	−0.823826	+	0.566843i	$0.808165\pi$
$194$	8.76347	+	26.9712i	0.629181	+	1.93642i
$195$	11.7817	+	2.50428i	0.843706	+	0.179335i
$196$	1.54091	+	14.6608i	0.110065	+	1.04720i
$197$	4.14574	+	4.60431i	0.295372	+	0.328044i	0.872504	−	0.488607i	$-0.162495\pi$
$197$	4.14574	+	4.60431i	0.295372	+	0.328044i	−0.577132	+	0.816651i	$0.695828\pi$
$198$	−5.35956	−	2.38623i	−0.380887	−	0.169582i
$199$	4.17429	−	1.85851i	0.295908	−	0.131747i	−0.253413	−	0.967358i	$-0.581553\pi$
$199$	4.17429	−	1.85851i	0.295908	−	0.131747i	0.549321	+	0.835612i	$0.314887\pi$
$200$	2.54094	−	2.82200i	0.179672	−	0.199546i
$201$	−9.92879	−	7.21369i	−0.700323	−	0.508814i
$202$	−13.7106	−	9.96132i	−0.964673	−	0.700876i
$203$	0.138205	−	0.153493i	0.00970011	−	0.0107731i
$204$	33.8203	−	15.0578i	2.36790	−	1.05426i
$205$	16.8308	+	7.49355i	1.17551	+	0.523372i
$206$	8.62924	+	9.58374i	0.601227	+	0.667731i
$207$	−2.57858	−	24.5335i	−0.179223	−	1.70520i
$208$	−0.749487	−	0.159308i	−0.0519676	−	0.0110460i
$209$	1.05150	+	3.23618i	0.0727336	+	0.223851i
$210$	22.9695	−	4.88233i	1.58505	−	0.336912i
$211$	9.30839	+	16.1226i	0.640816	+	1.10993i	0.985251	+	0.171115i	$0.0547371\pi$
$211$	9.30839	+	16.1226i	0.640816	+	1.10993i	−0.344435	+	0.938810i	$0.611930\pi$
$212$	9.53225	−	16.5103i	0.654678	−	1.13394i
$213$	−2.67547	+	8.23426i	−0.183321	+	0.564203i
$214$	−0.439991	+	4.18624i	−0.0300772	+	0.286165i
$215$	−0.465892	+	0.338490i	−0.0317736	+	0.0230849i
$216$	3.61764			0.246149
$217$		0			0
$218$	27.1487			1.83874
$219$	5.53783	−	4.02347i	0.374212	−	0.271881i
$220$	−0.637015	+	6.06079i	−0.0429475	+	0.408618i
$221$	2.56575	−	7.89656i	0.172591	−	0.531180i
$222$	24.7296	−	42.8329i	1.65974	−	2.87475i
$223$	3.10748	+	5.38231i	0.208092	+	0.360426i	0.951113	−	0.308842i	$-0.0999413\pi$
$223$	3.10748	+	5.38231i	0.208092	+	0.360426i	−0.743021	+	0.669268i	$0.766608\pi$
$224$	8.11784	−	1.72550i	0.542396	−	0.115290i
$225$	1.33036	+	4.09441i	0.0886904	+	0.272961i
$226$	−24.9512	−	5.30354i	−1.65973	−	0.352786i
$227$	1.36387	+	12.9763i	0.0905230	+	0.861269i	0.941714	+	0.336413i	$0.109214\pi$
$227$	1.36387	+	12.9763i	0.0905230	+	0.861269i	−0.851191	+	0.524855i	$0.824119\pi$
$228$	−26.2357	−	29.1377i	−1.73750	−	1.92969i
$229$	−13.9571	−	6.21410i	−0.922310	−	0.410639i	−0.110045	−	0.993927i	$-0.535099\pi$
$229$	−13.9571	−	6.21410i	−0.922310	−	0.410639i	−0.812266	+	0.583288i	$0.801766\pi$
$230$	−37.4917	+	16.6924i	−2.47213	+	1.10066i
$231$	−1.99955	+	2.22073i	−0.131561	+	0.146113i
$232$	−0.318860	−	0.231665i	−0.0209342	−	0.0152096i
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	0.185147	−	0.982711i	$-0.440724\pi$
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	−0.877400	+	0.479760i	$0.840724\pi$
$234$	10.1449	−	11.2671i	0.663195	−	0.736553i
$235$	18.3430	−	8.16684i	1.19657	−	0.532746i
$236$	28.8651	+	12.8516i	1.87896	+	0.836567i
$237$	−7.70391	−	8.55606i	−0.500423	−	0.555776i
$238$	−1.69204	−	16.0986i	−0.109678	−	1.04352i
$239$	−22.9300	−	4.87391i	−1.48322	−	0.315267i	−0.606039	−	0.795435i	$-0.707242\pi$
$239$	−22.9300	−	4.87391i	−1.48322	−	0.315267i	−0.877177	+	0.480168i	$0.840576\pi$
$240$	−0.793379	−	2.44177i	−0.0512124	−	0.157616i
$241$	24.1721	−	5.13793i	1.55706	−	0.330963i	0.652660	−	0.757651i	$-0.273653\pi$
$241$	24.1721	−	5.13793i	1.55706	−	0.330963i	0.904399	+	0.426687i	$0.140319\pi$
$242$	12.0704	+	20.9065i	0.775914	+	1.34392i
$243$	11.1668	−	19.3415i	0.716353	−	1.24076i
$244$	8.05513	−	24.7911i	0.515677	−	1.58709i
$245$	−1.15798	+	11.0174i	−0.0739806	+	0.703879i
$246$	35.0030	−	25.4312i	2.23171	−	1.62143i
$247$	−8.79358			−0.559522
$248$		0			0
$249$	−6.78996			−0.430296
$250$	−17.5266	+	12.7339i	−1.10848	+	0.805360i
$251$	−2.42445	+	23.0671i	−0.153030	+	1.45598i	0.601057	+	0.799206i	$0.294747\pi$
$251$	−2.42445	+	23.0671i	−0.153030	+	1.45598i	−0.754087	+	0.656775i	$0.771920\pi$
$252$	5.70323	−	17.5527i	0.359270	−	1.10572i
$253$	2.61125	−	4.52282i	0.164168	−	0.284348i
$254$	−1.48493	−	2.57198i	−0.0931729	−	0.161380i
$255$	27.2129	−	5.78428i	1.70414	−	0.362226i
$256$	−5.72420	−	17.6173i	−0.357763	−	1.10108i
$257$	−15.0108	−	3.19064i	−0.936345	−	0.199026i	−0.285623	−	0.958342i	$-0.592201\pi$
$257$	−15.0108	−	3.19064i	−0.936345	−	0.199026i	−0.650722	+	0.759316i	$0.725534\pi$
$258$	0.141363	+	1.34498i	0.00880088	+	0.0837348i
$259$	−9.03527	−	10.0347i	−0.561424	−	0.623525i
$260$	−14.3875	−	6.40572i	−0.892274	−	0.397266i
$261$	0.408200	−	0.181743i	0.0252670	−	0.0112496i
$262$	−12.3837	+	13.7535i	−0.765069	+	0.849695i
$263$	−5.50607	−	4.00039i	−0.339519	−	0.246675i	0.404940	−	0.914343i	$-0.367292\pi$
$263$	−5.50607	−	4.00039i	−0.339519	−	0.246675i	−0.744459	+	0.667668i	$0.767292\pi$
$264$	4.61325	+	3.35173i	0.283926	+	0.206284i
$265$	9.58648	−	10.6469i	0.588893	−	0.654031i
$266$	−15.6617	+	6.97305i	−0.960282	+	0.427545i
$267$	5.12102	+	2.28003i	0.313401	+	0.139535i
$268$	10.7374	+	11.9251i	0.655893	+	0.728442i
$269$	1.09960	+	10.4620i	0.0670439	+	0.637881i	0.975515	+	0.219933i	$0.0705838\pi$
$269$	1.09960	+	10.4620i	0.0670439	+	0.637881i	−0.908471	+	0.417948i	$0.862750\pi$
$270$	6.67408	+	1.41862i	0.406172	+	0.0863344i
$271$	0.487363	+	1.49995i	0.0296052	+	0.0911154i	0.964767	−	0.263105i	$-0.0847464\pi$
$271$	0.487363	+	1.49995i	0.0296052	+	0.0911154i	−0.935162	+	0.354220i	$0.884746\pi$
$272$	−1.73113	+	0.367963i	−0.104965	+	0.0223111i
$273$	−3.86128	−	6.68794i	−0.233695	−	0.404772i
$274$	−19.0103	+	32.9268i	−1.14845	+	1.98918i
$275$	−0.281645	+	0.866813i	−0.0169838	+	0.0522708i
$276$	−6.29028	+	59.8480i	−0.378630	+	3.60243i
$277$	9.79020	−	7.11300i	0.588236	−	0.427379i	−0.253448	−	0.967349i	$-0.581565\pi$
$277$	9.79020	−	7.11300i	0.588236	−	0.427379i	0.841684	+	0.539970i	$0.181565\pi$
$278$	−16.9368			−1.01580
$279$		0			0
$280$	−12.2337			−0.731106
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.0667525	−	0.997770i	$-0.478736\pi$
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.969563	+	0.244842i	$0.0787362\pi$
$282$	4.92889	−	46.8952i	0.293511	−	2.79257i
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	−0.957184	−	0.289482i	$-0.906517\pi$
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	0.944531	+	0.328423i	$0.106517\pi$
$284$	5.66030	−	9.80392i	0.335877	−	0.581756i
$285$	−14.7324	−	25.5173i	−0.872675	−	1.51152i
$286$	3.13962	−	0.667346i	0.185649	−	0.0394610i
$287$	−3.65018	−	11.2341i	−0.215463	−	0.663127i
$288$	17.5618	+	3.73288i	1.03484	+	0.219962i
$289$	−0.227636	−	2.16581i	−0.0133904	−	0.127401i
$290$	−0.497410	−	0.552429i	−0.0292089	−	0.0324398i
$291$	28.5481	+	12.7104i	1.67352	+	0.745098i
$292$	−8.17641	+	3.64037i	−0.478488	+	0.213037i
$293$	6.03012	−	6.69713i	0.352284	−	0.391251i	−0.540793	−	0.841156i	$-0.681876\pi$
$293$	6.03012	−	6.69713i	0.352284	−	0.391251i	0.893076	+	0.449905i	$0.148542\pi$
$294$	21.0474	+	15.2918i	1.22751	+	0.891837i
$295$	19.2098	+	13.9568i	1.11844	+	0.812594i
$296$	−17.2413	+	19.1484i	−1.00213	+	1.11298i
$297$	−0.793215	+	0.353162i	−0.0460270	+	0.0204925i
$298$	−13.4111	−	5.97102i	−0.776886	−	0.345892i
$299$	9.03087	+	10.0298i	0.522269	+	0.580038i
$300$	−1.09777	−	10.4445i	−0.0633796	−	0.603016i
$301$	0.361151	+	0.0767651i	0.0208164	+	0.00442467i
$302$	3.93949	+	12.1245i	0.226692	+	0.697688i
$303$	−18.2665	+	3.88266i	−1.04938	+	0.223053i
$304$	0.937195	+	1.62327i	0.0537518	+	0.0931009i
$305$	9.79451	−	16.9646i	0.560832	−	0.971389i
$306$	10.8215	−	33.3051i	0.618623	−	1.90393i
$307$	3.27515	−	31.1610i	0.186923	−	1.77845i	−0.351904	−	0.936036i	$-0.614466\pi$
$307$	3.27515	−	31.1610i	0.186923	−	1.77845i	0.538827	−	0.842416i	$-0.318868\pi$
$308$	3.16104	−	2.29663i	0.180117	−	0.130863i
$309$	14.2107			0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	−11.9219	+	8.66180i	−0.674947	+	0.490378i
$313$	−2.26500	+	21.5500i	−0.128025	+	1.21808i	0.722210	+	0.691674i	$0.243127\pi$
$313$	−2.26500	+	21.5500i	−0.128025	+	1.21808i	−0.850235	+	0.526404i	$0.823540\pi$
$314$	5.70058	−	17.5446i	0.321702	−	0.990098i
$315$	6.93475	−	12.0113i	0.390729	−	0.676762i
$316$	7.52698	+	13.0371i	0.423426	+	0.733395i
$317$	−0.993843	+	0.211248i	−0.0558198	+	0.0118649i	−0.235737	−	0.971817i	$-0.575750\pi$
$317$	−0.993843	+	0.211248i	−0.0558198	+	0.0118649i	0.179917	+	0.983682i	$0.442417\pi$
$318$	−10.3969	−	31.9984i	−0.583030	−	1.79438i
$319$	0.0925298	+	0.0196678i	0.00518067	+	0.00110119i
$320$	−3.33328	−	31.7141i	−0.186336	−	1.77287i
$321$	3.10365	+	3.44696i	0.173229	+	0.192390i
$322$	24.0377	+	10.7023i	1.33957	+	0.596414i
$323$	−18.5550	+	8.26124i	−1.03243	+	0.459668i
$324$	−16.4335	+	18.2513i	−0.912973	+	1.01396i
$325$	−1.90553	−	1.38445i	−0.105700	−	0.0767955i
$326$	31.8582	+	23.1463i	1.76446	+	1.28196i
$327$	20.0176	−	22.2318i	1.10698	−	1.22942i
$328$	−20.5916	+	9.16796i	−1.13698	+	0.506216i
$329$	−11.7606	−	5.23614i	−0.648381	−	0.288678i
$330$	7.19651	+	7.99254i	0.396155	+	0.439975i
$331$	2.78981	+	26.5432i	0.153342	+	1.45895i	0.752645	+	0.658426i	$0.228778\pi$
$331$	2.78981	+	26.5432i	0.153342	+	1.45895i	−0.599304	+	0.800522i	$0.704556\pi$
$332$	8.68405	+	1.84585i	0.476599	+	0.101304i
$333$	−9.02697	−	27.7822i	−0.494675	−	1.52245i
$334$	−55.0106	+	11.6929i	−3.01004	+	0.639805i
$335$	6.02951	+	10.4434i	0.329427	+	0.570584i
$336$	−0.823049	+	1.42556i	−0.0449010	+	0.0777708i
$337$	−9.87048	+	30.3782i	−0.537679	+	1.65481i	0.200108	+	0.979774i	$0.435871\pi$
$337$	−9.87048	+	30.3782i	−0.537679	+	1.65481i	−0.737788	+	0.675033i	$0.764129\pi$
$338$	2.26857	−	21.5840i	0.123394	−	1.17402i
$339$	−22.7404	+	16.5218i	−1.23509	+	0.897343i
$340$	−36.3765			−1.97279
$341$		0			0
$342$	−37.0885			−2.00552
$343$	14.8178	−	10.7658i	0.800088	−	0.581298i
$344$	0.0736457	−	0.700692i	0.00397071	−	0.0377788i
$345$	−13.9746	+	43.0095i	−0.752368	+	2.31555i
$346$	−10.3534	+	17.9326i	−0.556603	+	0.964065i
$347$	1.56066	+	2.70314i	0.0837804	+	0.145112i	0.904871	−	0.425686i	$-0.139967\pi$
$347$	1.56066	+	2.70314i	0.0837804	+	0.145112i	−0.821090	+	0.570798i	$0.806634\pi$
$348$	−1.06620	+	0.226627i	−0.0571542	+	0.0121485i
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	−0.950389	−	0.311063i	$-0.899315\pi$
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	0.586043	−	0.810280i	$-0.300685\pi$
$350$	−4.49166	−	0.954732i	−0.240089	−	0.0510326i
$351$	−0.234550	−	2.23159i	−0.0125193	−	0.119114i
$352$	2.54337	+	2.82470i	0.135562	+	0.150557i
$353$	−4.50596	−	2.00618i	−0.239828	−	0.106778i	0.283303	−	0.959030i	$-0.408570\pi$
$353$	−4.50596	−	2.00618i	−0.239828	−	0.106778i	−0.523132	+	0.852252i	$0.675236\pi$
$354$	50.9413	−	22.6805i	2.70750	−	1.20546i
$355$	5.69249	−	6.32215i	0.302126	−	0.335545i
$356$	−5.92973	−	4.30820i	−0.314275	−	0.228334i
$357$	−14.4306	−	10.4845i	−0.763750	−	0.554897i
$358$	17.4330	−	19.3613i	0.921361	−	1.02328i
$359$	−0.329662	+	0.146775i	−0.0173989	+	0.00774648i	−0.415418	−	0.909631i	$-0.636365\pi$
$359$	−0.329662	+	0.146775i	−0.0173989	+	0.00774648i	0.398019	+	0.917377i	$0.369698\pi$
$360$	−24.1779	−	10.7647i	−1.27429	−	0.567350i
$361$	1.68038	+	1.86625i	0.0884410	+	0.0982237i
$362$	−3.60381	−	34.2880i	−0.189412	−	1.80214i
$363$	26.0200	+	5.53073i	1.36570	+	0.290288i
$364$	3.12029	+	9.60325i	0.163547	+	0.503347i
$365$	−6.57899	+	1.39841i	−0.344360	+	0.0731960i
$366$	−23.0015	−	39.8398i	−1.20231	−	2.08246i
$367$	−14.6935	+	25.4498i	−0.766992	+	1.32847i	0.172195	+	0.985063i	$0.444914\pi$
$367$	−14.6935	+	25.4498i	−0.766992	+	1.32847i	−0.939187	+	0.343406i	$0.888419\pi$
$368$	0.888987	−	2.73602i	0.0463416	−	0.142625i
$369$	2.67113	−	25.4141i	0.139054	−	1.32301i
$370$	−39.3167	+	28.5653i	−2.04398	+	1.48504i
$371$	−9.18555			−0.476890
$372$		0			0
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	5.99786	−	4.35770i	0.310142	−	0.225331i
$375$	−2.49533	+	23.7415i	−0.128858	+	1.22601i
$376$	−7.59116	+	23.3632i	−0.391484	+	1.20486i
$377$	−0.122233	+	0.211713i	−0.00629530	+	0.0109038i
$378$	−2.18733	−	3.78857i	−0.112504	−	0.194863i
$379$	2.40665	−	0.511550i	0.123622	−	0.0262766i	−0.145685	−	0.989331i	$-0.546539\pi$
$379$	2.40665	−	0.511550i	0.123622	−	0.0262766i	0.269307	+	0.963054i	$0.413205\pi$
$380$	11.9052	+	36.6405i	0.610725	+	1.87962i
$381$	−3.20106	−	0.680405i	−0.163995	−	0.0348582i
$382$	−0.545341	−	5.18857i	−0.0279021	−	0.265470i
$383$	12.7924	+	14.2074i	0.653660	+	0.725963i	0.975296	−	0.220900i	$-0.0708995\pi$
$383$	12.7924	+	14.2074i	0.653660	+	0.725963i	−0.321636	+	0.946863i	$0.604233\pi$
$384$	−44.3440	−	19.7432i	−2.26292	−	1.00752i
$385$	2.68241	−	1.19429i	0.136708	−	0.0608664i
$386$	39.6265	−	44.0097i	2.01694	−	2.24004i
$387$	0.646208	+	0.469497i	0.0328486	+	0.0238659i
$388$	−33.0563	−	24.0168i	−1.67818	−	1.21927i
$389$	−3.52703	+	3.91716i	−0.178827	+	0.198608i	−0.825894	−	0.563826i	$-0.809329\pi$
$389$	−3.52703	+	3.91716i	−0.178827	+	0.198608i	0.647066	+	0.762434i	$0.275996\pi$
$390$	−25.3911	+	11.3048i	−1.28573	+	0.572443i
$391$	28.4784	+	12.6794i	1.44021	+	0.641224i
$392$	−9.06907	−	10.0722i	−0.458057	−	0.508724i
$393$	2.13171	+	20.2818i	0.107530	+	1.02308i
$394$	−13.9843	−	2.97247i	−0.704521	−	0.149751i
$395$	3.49587	+	10.7592i	0.175897	+	0.541354i
$396$	8.26811	−	1.75744i	0.415488	−	0.0883147i
$397$	−8.46275	−	14.6579i	−0.424733	−	0.735660i	0.571662	−	0.820489i	$-0.306299\pi$
$397$	−8.46275	−	14.6579i	−0.424733	−	0.735660i	−0.996395	+	0.0848295i	$0.972965\pi$
$398$	−5.27193	+	9.13124i	−0.264258	+	0.457708i
$399$	−5.83773	+	17.9667i	−0.292252	+	0.899460i
$400$	−0.0524793	+	0.499307i	−0.00262396	+	0.0249653i
$401$	30.7747	−	22.3591i	1.53682	−	1.11656i	0.584524	−	0.811377i	$-0.301281\pi$
$401$	30.7747	−	22.3591i	1.53682	−	1.11656i	0.952293	−	0.305186i	$-0.0987186\pi$
$402$	28.3195			1.41245
$403$		0			0
$404$	24.4175			1.21482
$405$	−14.9314	+	10.8483i	−0.741945	+	0.539055i
$406$	−0.0498190	+	0.473996i	−0.00247248	+	0.0235240i
$407$	1.91107	−	5.88166i	0.0947281	−	0.291543i
$408$	−17.0187	+	29.4772i	−0.842550	+	1.45934i
$409$	0.249342	+	0.431873i	0.0123292	+	0.0213547i	0.872124	−	0.489285i	$-0.162742\pi$
$409$	0.249342	+	0.431873i	0.0123292	+	0.0213547i	−0.859795	+	0.510639i	$0.829409\pi$
$410$	−41.5839	+	8.83893i	−2.05368	+	0.436524i
$411$	12.9465	+	39.8453i	0.638605	+	1.96542i
$412$	−18.1748	−	3.86317i	−0.895407	−	0.190325i
$413$	−1.59132	−	15.1404i	−0.0783038	−	0.745010i
$414$	38.0893	+	42.3024i	1.87199	+	2.07905i
$415$	6.09496	+	2.71365i	0.299190	+	0.133208i
$416$	−8.97365	+	3.99533i	−0.439970	+	0.195887i
$417$	−12.4881	+	13.8694i	−0.611544	+	0.679188i
$418$	−6.35229	−	4.61521i	−0.310701	−	0.225737i
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	0.287879	−	0.957667i	$-0.407050\pi$
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	−0.821836	+	0.569725i	$0.807050\pi$
$420$	−22.6392	+	25.1434i	−1.10468	+	1.22687i
$421$	−28.2424	+	12.5743i	−1.37645	+	0.612834i	−0.955700	−	0.294343i	$-0.904899\pi$
$421$	−28.2424	+	12.5743i	−1.37645	+	0.612834i	−0.420749	+	0.907177i	$0.638233\pi$
$422$	−39.2447	−	17.4729i	−1.91040	−	0.850566i
$423$	−18.6354	−	20.6967i	−0.906083	−	1.00631i
$424$	1.83218	+	17.4320i	0.0889785	+	0.846574i
$425$	−5.32144	−	1.13111i	−0.258128	−	0.0548668i
$426$	−6.17373	−	19.0008i	−0.299118	−	0.920591i
$427$	−12.2850	+	2.61125i	−0.594512	+	0.126367i
$428$	−3.03237	−	5.25223i	−0.146575	−	0.253876i
$429$	1.76846	−	3.06306i	0.0853820	−	0.147886i
$430$	0.410636	−	1.26381i	0.0198026	−	0.0609462i
$431$	1.26007	−	11.9888i	0.0606954	−	0.577478i	−0.921337	−	0.388765i	$-0.872902\pi$
$431$	1.26007	−	11.9888i	0.0606954	−	0.577478i	0.982032	−	0.188713i	$-0.0604316\pi$
$432$	−0.386948	+	0.281134i	−0.0186170	+	0.0135261i
$433$	32.3919			1.55665			0.778327	−	0.627860i	$-0.216069\pi$
$433$	32.3919			1.55665			0.778327	+	0.627860i	$0.216069\pi$
$434$		0			0
$435$	−0.819136			−0.0392745
$436$	−31.6454	+	22.9917i	−1.51554	+	1.10110i
$437$	3.45107	−	32.8348i	0.165087	−	1.57070i
$438$	−4.88102	+	15.0222i	−0.233224	+	0.717790i
$439$	−6.18408	+	10.7111i	−0.295150	+	0.511215i	−0.975020	−	0.222118i	$-0.928703\pi$
$439$	−6.18408	+	10.7111i	−0.295150	+	0.511215i	0.679870	+	0.733333i	$0.262036\pi$
$440$	−2.80151	−	4.85236i	−0.133557	−	0.231327i
$441$	15.0300	−	3.19472i	0.715712	−	0.152129i
$442$	5.92053	+	18.2215i	0.281611	+	0.866709i
$443$	4.62019	+	0.982051i	0.219512	+	0.0466587i	0.316355	−	0.948641i	$-0.397541\pi$
$443$	4.62019	+	0.982051i	0.219512	+	0.0466587i	−0.0968428	+	0.995300i	$0.530874\pi$
$444$	7.44876	+	70.8703i	0.353503	+	3.36335i
$445$	−3.68562	−	4.09329i	−0.174715	−	0.194041i
$446$	−13.1013	−	5.83308i	−0.620365	−	0.276204i
$447$	−14.7781	+	6.57963i	−0.698979	+	0.311206i
$448$	−13.6806	+	15.1939i	−0.646348	+	0.717843i
$449$	−12.9315	−	9.39528i	−0.610275	−	0.443390i	0.239236	−	0.970961i	$-0.423103\pi$
$449$	−12.9315	−	9.39528i	−0.610275	−	0.443390i	−0.849511	+	0.527571i	$0.823103\pi$
$450$	−8.03692	−	5.83917i	−0.378864	−	0.275261i
$451$	3.61998	−	4.02039i	0.170458	−	0.189313i
$452$	33.5753	−	14.9487i	1.57925	−	0.703128i
$453$	12.8334	+	5.71379i	0.602964	+	0.268457i
$454$	−20.1463	−	22.3747i	−0.945512	−	1.05010i
$455$	0.793175	+	7.54656i	0.0371846	+	0.353788i
$456$	35.2610	+	7.49495i	1.65125	+	0.350983i
$457$	−1.40842	−	4.33468i	−0.0658832	−	0.202768i	0.912696	−	0.408640i	$-0.133997\pi$
$457$	−1.40842	−	4.33468i	−0.0658832	−	0.202768i	−0.978579	+	0.205872i	$0.933997\pi$
$458$	34.4839	−	7.32977i	1.61132	−	0.342498i
$459$	−2.59141	−	4.48846i	−0.120957	−	0.209503i
$460$	29.5650	−	51.2081i	1.37848	−	2.38759i
$461$	5.25050	−	16.1594i	0.244540	−	0.752618i	−0.751171	−	0.660107i	$-0.770511\pi$
$461$	5.25050	−	16.1594i	0.244540	−	0.752618i	0.995712	−	0.0925105i	$-0.0294892\pi$
$462$	0.720780	−	6.85777i	0.0335337	−	0.319052i
$463$	22.1896	−	16.1217i	1.03124	−	0.749239i	0.0626822	−	0.998034i	$-0.480035\pi$
$463$	22.1896	−	16.1217i	1.03124	−	0.749239i	0.968556	+	0.248795i	$0.0800345\pi$
$464$	0.0521088			0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	−0.0695608	−	0.997578i	$-0.522160\pi$
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	0.927257	+	0.374425i	$0.122160\pi$
$468$	−2.28337	+	21.7248i	−0.105549	+	1.00423i
$469$	2.38919	−	7.35318i	0.110323	−	0.339538i
$470$	−23.1663	+	40.1253i	−1.06858	+	1.85084i
$471$	−10.1639	−	17.6043i	−0.468327	−	0.811165i
$472$	−28.4155	+	6.03990i	−1.30793	+	0.278009i
$473$	0.0522553	+	0.160825i	0.00240270	+	0.00739476i
$474$	25.9867	+	5.52365i	1.19361	+	0.253710i
$475$	0.602274	+	5.73025i	0.0276342	+	0.262922i
$476$	15.6059	+	17.3321i	0.715295	+	0.794416i
$477$	−18.1537	−	8.08255i	−0.831201	−	0.370074i
$478$	49.4169	−	22.0018i	2.26028	−	1.00634i
$479$	6.05366	−	6.72327i	0.276599	−	0.307194i	−0.588799	−	0.808279i	$-0.700399\pi$
$479$	6.05366	−	6.72327i	0.276599	−	0.307194i	0.865398	+	0.501085i	$0.167066\pi$
$480$	−26.6278	−	19.3462i	−1.21539	−	0.883031i
$481$	12.9298	+	9.39403i	0.589547	+	0.428331i
$482$	−38.1564	+	42.3769i	−1.73797	+	1.93022i
$483$	26.4878	−	11.7931i	1.20523	−	0.536605i
$484$	−31.7749	−	14.1471i	−1.44431	−	0.643050i
$485$	−20.5461	−	22.8188i	−0.932952	−	1.03615i
$486$	5.38693	+	51.2532i	0.244356	+	2.32489i
$487$	−23.1065	−	4.91143i	−1.04705	−	0.222558i	−0.347901	−	0.937531i	$-0.613106\pi$
$487$	−23.1065	−	4.91143i	−1.04705	−	0.222558i	−0.699152	+	0.714973i	$0.746439\pi$
$488$	7.40594	+	22.7931i	0.335251	+	1.03180i
$489$	42.4444	−	9.02183i	1.91940	−	0.407981i
$490$	−12.7815	−	22.1383i	−0.577411	−	1.00011i
$491$	4.61346	−	7.99074i	0.208202	−	0.360617i	−0.742946	−	0.669351i	$-0.766572\pi$
$491$	4.61346	−	7.99074i	0.208202	−	0.360617i	0.951148	+	0.308734i	$0.0999054\pi$
$492$	−19.2634	+	59.2867i	−0.868462	+	2.67285i
$493$	−0.0590225	+	0.561562i	−0.00265824	+	0.0252915i
$494$	16.4161	−	11.9270i	0.738596	−	0.536621i
$495$	6.35220			0.285510
$496$		0			0
$497$	−5.45442			−0.244664
$498$	12.6757	−	9.20943i	0.568011	−	0.412684i
$499$	2.97007	−	28.2583i	0.132958	−	1.26501i	−0.700989	−	0.713172i	$-0.747258\pi$
$499$	2.97007	−	28.2583i	0.132958	−	1.26501i	0.833948	−	0.551843i	$-0.186075\pi$
$500$	9.64554	−	29.6859i	0.431362	−	1.32759i
$501$	−30.9859	+	53.6692i	−1.38435	+	2.39776i
$502$	−26.7606	−	46.3506i	−1.19438	−	2.06873i
$503$	−17.8786	+	3.80022i	−0.797170	+	0.169444i	−0.588452	−	0.808532i	$-0.700262\pi$
$503$	−17.8786	+	3.80022i	−0.797170	+	0.169444i	−0.208718	+	0.977976i	$0.566929\pi$
$504$	5.24359	+	16.1381i	0.233568	+	0.718848i
$505$	17.9485	+	3.81507i	0.798698	+	0.169768i
$506$	1.25968	+	11.9851i	0.0559996	+	0.532801i
$507$	−16.0023	−	17.7723i	−0.710686	−	0.789297i
$508$	3.90903	+	1.74041i	0.173435	+	0.0772184i
$509$	−9.48841	+	4.22451i	−0.420566	+	0.187248i	−0.606098	−	0.795390i	$-0.707266\pi$
$509$	−9.48841	+	4.22451i	−0.420566	+	0.187248i	0.185532	+	0.982638i	$0.440599\pi$
$510$	−42.9564	+	47.7079i	−1.90214	+	2.11254i
$511$	3.48875	+	2.53472i	0.154333	+	0.112130i
$512$	3.69272	+	2.68292i	0.163197	+	0.118569i
$513$	−3.67293	+	4.07920i	−0.162164	+	0.180101i
$514$	32.3501	−	14.4032i	1.42690	−	0.635297i
$515$	−12.7561	−	5.67937i	−0.562100	−	0.250263i
$516$	−1.30381	−	1.44803i	−0.0573972	−	0.0637460i
$517$	−0.616305	−	5.86375i	−0.0271051	−	0.257887i
$518$	30.4776	+	6.47822i	1.33911	+	0.284637i
$519$	7.05096	+	21.7006i	0.309503	+	0.952552i
$520$	14.1634	−	3.01052i	0.621105	−	0.132020i
$521$	−4.62522	−	8.01111i	−0.202635	−	0.350973i	0.746742	−	0.665114i	$-0.231617\pi$
$521$	−4.62522	−	8.01111i	−0.202635	−	0.350973i	−0.949376	+	0.314141i	$0.898284\pi$
$522$	−0.515537	+	0.892937i	−0.0225645	+	0.0390828i
$523$	2.03184	−	6.25335i	0.0888461	−	0.273440i	−0.896755	−	0.442527i	$-0.854082\pi$
$523$	2.03184	−	6.25335i	0.0888461	−	0.273440i	0.985601	+	0.169087i	$0.0540820\pi$
$524$	2.78726	−	26.5190i	0.121762	−	1.15849i
$525$	−4.09367	+	2.97422i	−0.178662	+	0.129806i
$526$	15.7047			0.684759
$527$		0			0
$528$	−0.753909			−0.0328097
$529$	−22.3875	+	16.2655i	−0.973371	+	0.707195i
$530$	−3.45565	+	32.8783i	−0.150104	+	1.42814i
$531$	10.1774	−	31.3227i	0.441660	−	1.35929i
$532$	12.3504	−	21.3916i	0.535460	−	0.927443i
$533$	6.99044	+	12.1078i	0.302790	+	0.524447i
$534$	−12.6525	+	2.68938i	−0.547529	+	0.116381i
$535$	−1.40837	−	4.33453i	−0.0608893	−	0.187398i
$536$	−14.4312	−	3.06744i	−0.623331	−	0.132493i
$537$	−3.00087	−	28.5514i	−0.129497	−	1.23208i
$538$	−16.2427	−	18.0394i	−0.700273	−	0.777732i
$539$	2.97178	+	1.32312i	0.128004	+	0.0569910i
$540$	−8.98091	+	3.99856i	−0.386477	+	0.172071i
$541$	−1.47428	+	1.63735i	−0.0633842	+	0.0703953i	−0.774003	−	0.633182i	$-0.781748\pi$
$541$	−1.47428	+	1.63735i	−0.0633842	+	0.0703953i	0.710619	+	0.703577i	$0.248415\pi$
$542$	−2.94425	−	2.13912i	−0.126466	−	0.0918831i
$543$	−30.7353	−	22.3305i	−1.31898	−	0.958294i
$544$	−15.1815	+	16.8608i	−0.650903	+	0.722902i
$545$	−26.8538	+	11.9561i	−1.15029	+	0.512141i
$546$	16.2794	+	7.24806i	0.696694	+	0.310188i
$547$	−3.25428	−	3.61424i	−0.139143	−	0.154534i	0.669546	−	0.742771i	$-0.266489\pi$
$547$	−3.25428	−	3.61424i	−0.139143	−	0.154534i	−0.808689	+	0.588237i	$0.799822\pi$
$548$	−5.72606	−	54.4798i	−0.244605	−	2.32726i
$549$	−26.5769	−	5.64909i	−1.13427	−	0.241097i
$550$	−0.649903	−	2.00019i	−0.0277119	−	0.0852886i
$551$	0.584954	−	0.124336i	0.0249199	−	0.00529689i
$552$	−27.6639	−	47.9152i	−1.17745	−	2.03941i
$553$	3.62661	−	6.28147i	0.154219	−	0.267115i
$554$	−8.62905	+	26.5575i	−0.366613	+	1.12832i
$555$	−5.59766	+	53.2582i	−0.237608	+	2.26068i
$556$	19.7421	−	14.3435i	0.837251	−	0.608298i
$557$	−11.0363			−0.467623			−0.233811	−	0.972282i	$-0.575120\pi$
$557$	−11.0363			−0.467623			−0.233811	+	0.972282i	$0.575120\pi$
$558$		0			0
$559$	−0.437007			−0.0184834
$560$	1.30854	−	0.950708i	0.0552958	−	0.0401748i
$561$	0.853936	−	8.12466i	0.0360532	−	0.343023i
$562$	−15.3115	+	47.1238i	−0.645875	+	1.98780i
$563$	5.59621	−	9.69292i	0.235852	−	0.408508i	−0.723668	−	0.690148i	$-0.757545\pi$
$563$	5.59621	−	9.69292i	0.235852	−	0.408508i	0.959520	+	0.281641i	$0.0908786\pi$
$564$	33.9694	+	58.8366i	1.43037	+	2.47747i
$565$	27.0158	−	5.74238i	1.13656	−	0.241584i
$566$	−0.491164	−	1.51165i	−0.0206452	−	0.0635393i
$567$	11.5745	+	2.46024i	0.486085	+	0.103320i
$568$	1.08796	+	10.3512i	0.0456496	+	0.434327i
$569$	31.3969	+	34.8698i	1.31623	+	1.46182i	0.792410	+	0.609989i	$0.208826\pi$
$569$	31.3969	+	34.8698i	1.31623	+	1.46182i	0.523818	+	0.851830i	$0.324507\pi$
$570$	62.1129	+	27.6544i	2.60162	+	1.15832i
$571$	18.6908	−	8.32170i	0.782187	−	0.348252i	0.0235138	−	0.999724i	$-0.492515\pi$
$571$	18.6908	−	8.32170i	0.782187	−	0.348252i	0.758673	+	0.651471i	$0.225848\pi$
$572$	−3.09447	+	3.43676i	−0.129386	+	0.143698i
$573$	−4.65097	−	3.37913i	−0.194297	−	0.141165i
$574$	22.0514	+	16.0213i	0.920407	+	0.668715i
$575$	5.91730	−	6.57182i	0.246768	−	0.274064i
$576$	−40.4068	+	17.9903i	−1.68362	+	0.749595i
$577$	3.33293	+	1.48392i	0.138752	+	0.0617762i	0.474938	−	0.880019i	$-0.342470\pi$
$577$	3.33293	+	1.48392i	0.138752	+	0.0617762i	−0.336186	+	0.941796i	$0.609137\pi$
$578$	3.36251	+	3.73445i	0.139862	+	0.155333i
$579$	−6.82123	−	64.8996i	−0.283480	−	2.69714i
$580$	1.04764	+	0.222682i	0.0435008	+	0.00924637i
$581$	−1.32184	−	4.06822i	−0.0548393	−	0.168778i
$582$	−70.5338	+	14.9924i	−2.92372	+	0.621456i
$583$	−2.10348	−	3.64334i	−0.0871173	−	0.150892i
$584$	4.11443	−	7.12641i	0.170256	−	0.294893i
$585$	−5.07279	+	15.6124i	−0.209734	+	0.645494i
$586$	−2.17369	+	20.6812i	−0.0897941	+	0.854334i
$587$	−18.5043	+	13.4442i	−0.763755	+	0.554901i	−0.900060	−	0.435766i	$-0.856477\pi$
$587$	−18.5043	+	13.4442i	−0.763755	+	0.554901i	0.136305	+	0.990667i	$0.456477\pi$
$588$	−37.4838			−1.54580
$589$		0			0
$590$	−54.7914			−2.25573
$591$	−12.7452	+	9.25996i	−0.524269	+	0.380904i
$592$	0.356092	−	3.38799i	0.0146353	−	0.139245i
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	0.748371	+	0.663281i	$0.230837\pi$
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	−0.995311	+	0.0967243i	$0.969163\pi$
$594$	1.00179	−	1.73515i	0.0411040	−	0.0711943i
$595$	8.76336	+	15.1786i	0.359263	+	0.622261i
$596$	20.6892	−	4.39762i	0.847461	−	0.180133i
$597$	3.59033	+	11.0499i	0.146942	+	0.452242i
$598$	−30.4628	−	6.47507i	−1.24572	−	0.264785i
$599$	−3.67646	−	34.9792i	−0.150216	−	1.42921i	−0.766782	−	0.641907i	$-0.778143\pi$
$599$	−3.67646	−	34.9792i	−0.150216	−	1.42921i	0.616566	−	0.787303i	$-0.288523\pi$
$600$	6.46091	+	7.17557i	0.263766	+	0.292942i
$601$	−5.37901	−	2.39489i	−0.219414	−	0.0976895i	0.294086	−	0.955779i	$-0.404985\pi$
$601$	−5.37901	−	2.39489i	−0.219414	−	0.0976895i	−0.513500	+	0.858089i	$0.671651\pi$
$602$	−0.778326	+	0.346533i	−0.0317222	+	0.0141236i
$603$	11.1920	−	12.4300i	0.455775	−	0.506190i
$604$	−14.8600	−	10.7964i	−0.604645	−	0.439300i
$605$	−21.1463	−	15.3637i	−0.859719	−	0.624622i
$606$	28.8342	−	32.0237i	1.17131	−	1.30087i
$607$	35.5231	−	15.8159i	1.44184	−	0.641947i	0.471097	−	0.882081i	$-0.343858\pi$
$607$	35.5231	−	15.8159i	1.44184	−	0.641947i	0.970740	+	0.240134i	$0.0771915\pi$
$608$	21.9518	+	9.77356i	0.890262	+	0.396370i
$609$	0.351418	+	0.390289i	0.0142402	+	0.0158153i
$610$	4.72491	+	44.9546i	0.191306	+	1.82016i
$611$	14.9041	+	3.16796i	0.602955	+	0.128162i
$612$	15.5916	+	47.9859i	0.630252	+	1.93972i
$613$	−44.6059	+	9.48127i	−1.80161	+	0.382945i	−0.981835	−	0.189736i	$-0.939237\pi$
$613$	−44.6059	+	9.48127i	−1.80161	+	0.382945i	−0.819779	+	0.572681i	$0.805904\pi$
$614$	36.1505	+	62.6144i	1.45891	+	2.52691i
$615$	−23.4231	+	40.5699i	−0.944509	+	1.63594i
$616$	−1.11010	+	3.41654i	−0.0447272	+	0.137656i
$617$	0.692656	−	6.59018i	0.0278853	−	0.265311i	−0.971692	−	0.236250i	$-0.924082\pi$
$617$	0.692656	−	6.59018i	0.0278853	−	0.265311i	0.999578	−	0.0290609i	$-0.00925166\pi$
$618$	−26.5288	+	19.2743i	−1.06715	+	0.775328i
$619$	−41.5360			−1.66947			−0.834736	−	0.550650i	$-0.814380\pi$
$619$	−41.5360			−1.66947			−0.834736	+	0.550650i	$0.814380\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	33.0689	−	24.0260i	1.32594	−	0.963353i
$623$	−0.369140	+	3.51213i	−0.0147893	+	0.140711i
$624$	0.602062	−	1.85296i	0.0241018	−	0.0741776i
$625$	14.8341	−	25.6934i	0.593364	−	1.02774i
$626$	−25.0006	−	43.3022i	−0.999223	−	1.73071i
$627$	−8.46310	+	1.79889i	−0.337984	+	0.0718407i
$628$	8.21338	+	25.2782i	0.327750	+	1.00871i
$629$	36.1080	+	7.67500i	1.43972	+	0.306022i
$630$	3.34535	+	31.8289i	0.133282	+	1.26809i
$631$	−7.45727	−	8.28213i	−0.296869	−	0.329707i	0.576195	−	0.817312i	$-0.304537\pi$
$631$	−7.45727	−	8.28213i	−0.296869	−	0.329707i	−0.873064	+	0.487606i	$0.837870\pi$
$632$	−12.6441	−	5.62953i	−0.502956	−	0.223931i
$633$	−43.2448	+	19.2538i	−1.71883	+	0.765271i
$634$	1.56881	−	1.74234i	0.0623055	−	0.0691973i
$635$	2.60147	+	1.89008i	0.103236	+	0.0750056i
$636$	39.2177	+	28.4934i	1.55508	+	1.12983i
$637$	−5.62520	+	6.24742i	−0.222879	+	0.247532i
$638$	−0.199413	+	0.0887845i	−0.00789485	+	0.00351501i
$639$	−10.7797	−	4.79945i	−0.426440	−	0.189863i
$640$	31.9146	+	35.4447i	1.26153	+	1.40107i
$641$	1.83482	+	17.4571i	0.0724710	+	0.689516i	0.969089	+	0.246711i	$0.0793498\pi$
$641$	1.83482	+	17.4571i	0.0724710	+	0.689516i	−0.896618	+	0.442805i	$0.853983\pi$
$642$	−10.4692	−	2.22530i	−0.413186	−	0.0878254i
$643$	0.678617	+	2.08857i	0.0267621	+	0.0823651i	0.963545	−	0.267545i	$-0.0862123\pi$
$643$	0.678617	+	2.08857i	0.0267621	+	0.0823651i	−0.936783	+	0.349910i	$0.886212\pi$
$644$	−37.0826	+	7.88214i	−1.46126	+	0.310600i
$645$	−0.732145	−	1.26811i	−0.0288282	−	0.0499318i
$646$	23.4341	−	40.5891i	0.922003	−	1.59696i
$647$	10.0259	−	30.8566i	0.394160	−	1.21310i	−0.535454	−	0.844564i	$-0.679860\pi$
$647$	10.0259	−	30.8566i	0.394160	−	1.21310i	0.929614	−	0.368535i	$-0.120140\pi$
$648$	2.36027	−	22.4565i	0.0927202	−	0.882173i
$649$	5.64084	−	4.09831i	0.221422	−	0.160873i
$650$	5.43508			0.213181
$651$		0			0
$652$	−56.7370			−2.22199
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	−0.817380	−	0.576099i	$-0.804574\pi$
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	0.295319	+	0.955399i	$0.404574\pi$
$654$	−7.21578	+	68.6535i	−0.282159	+	2.68457i
$655$	6.19225	−	19.0578i	0.241951	−	0.744649i
$656$	1.49004	−	2.58083i	0.0581764	−	0.100764i
$657$	4.66457	+	8.07927i	0.181982	+	0.315202i
$658$	29.0569	−	6.17623i	1.13275	−	0.240774i
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	−0.996760	−	0.0804282i	$-0.974371\pi$
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	0.759122	−	0.650949i	$-0.225629\pi$
$660$	−15.1572	−	3.22176i	−0.589993	−	0.125407i
$661$	−1.23143	−	11.7163i	−0.0478971	−	0.455710i	−0.992017	−	0.126107i	$-0.959752\pi$
$661$	−1.23143	−	11.7163i	−0.0478971	−	0.455710i	0.944120	−	0.329603i	$-0.106915\pi$
$662$	−41.2095	−	45.7678i	−1.60165	−	1.77881i
$663$	19.2868	+	8.58705i	0.749038	+	0.333493i
$664$	−7.45686	+	3.32001i	−0.289382	+	0.128841i
$665$	12.4207	−	13.7946i	0.481654	−	0.534931i
$666$	54.5336	+	39.6210i	2.11313	+	1.53528i
$667$	−0.742554	−	0.539497i	−0.0287518	−	0.0208894i
$668$	54.2195	−	60.2169i	2.09782	−	2.32986i
$669$	−14.4367	+	6.42762i	−0.558154	+	0.248506i
$670$	−25.4208	−	11.3181i	−0.982090	−	0.437255i
$671$	−3.84897	−	4.27471i	−0.148588	−	0.165023i
$672$	2.20582	+	20.9870i	0.0850913	+	0.809590i
$673$	49.2811	+	10.4750i	1.89965	+	0.403783i	0.999495	−	0.0317890i	$-0.0101204\pi$
$673$	49.2811	+	10.4750i	1.89965	+	0.403783i	0.900154	+	0.435572i	$0.143454\pi$
$674$	−22.7764	−	70.0985i	−0.877314	−	2.70009i
$675$	−1.43813	+	0.305684i	−0.0553537	+	0.0117658i
$676$	15.6348	+	27.0802i	0.601337	+	1.04155i
$677$	−1.98998	+	3.44674i	−0.0764810	+	0.132469i	−0.901729	−	0.432301i	$-0.857702\pi$
$677$	−1.98998	+	3.44674i	−0.0764810	+	0.132469i	0.825248	+	0.564770i	$0.191035\pi$
$678$	20.0433	−	61.6869i	0.769758	−	2.36907i
$679$	−2.05784	+	19.5790i	−0.0789726	+	0.751374i
$680$	27.0574	−	19.6584i	1.03760	−	0.753864i
$681$	−33.1770			−1.27134
$682$		0			0
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	43.2314	−	31.4095i	1.65300	−	1.20097i
$685$	4.30307	−	40.9410i	0.164412	−	1.56427i
$686$	−13.0604	+	40.1958i	−0.498648	+	1.53468i
$687$	19.4238	−	33.6430i	0.741064	−	1.28356i
$688$	0.0465749	+	0.0806701i	0.00177565	+	0.00307552i
$689$	10.6344	−	2.26041i	0.405138	−	0.0861148i
$690$	−32.2468	−	99.2455i	−1.22762	−	3.77821i
$691$	−8.99459	−	1.91186i	−0.342170	−	0.0727305i	0.0336216	−	0.999435i	$-0.489296\pi$
$691$	−8.99459	−	1.91186i	−0.342170	−	0.0727305i	−0.375792	+	0.926704i	$0.622629\pi$
$692$	−3.11854	−	29.6709i	−0.118549	−	1.12792i
$693$	−2.72516	−	3.02660i	−0.103520	−	0.114971i
$694$	−6.57982	−	2.92952i	−0.249767	−	0.111203i
$695$	16.7528	−	7.45883i	0.635471	−	0.282930i
$696$	0.670582	−	0.744757i	0.0254184	−	0.0282299i
$697$	26.1251	+	18.9810i	0.989560	+	0.718957i
$698$	41.1196	+	29.8751i	1.55640	+	1.13079i
$699$	22.2226	−	24.6807i	0.840536	−	0.933510i
$700$	6.04416	−	2.69103i	0.228448	−	0.101711i
$701$	−37.0482	−	16.4949i	−1.39929	−	0.623005i	−0.438110	−	0.898921i	$-0.644352\pi$
$701$	−37.0482	−	16.4949i	−1.39929	−	0.623005i	−0.961182	+	0.275917i	$0.911019\pi$
$702$	3.46464	+	3.84787i	0.130764	+	0.145229i
$703$	−4.08666	−	38.8820i	−0.154131	−	1.46646i
$704$	−9.15931	−	1.94687i	−0.345204	−	0.0733754i
$705$	15.7769	+	48.5564i	0.594193	+	1.82874i
$706$	11.1329	−	2.36637i	0.418993	−	0.0890596i
$707$	−5.88235	−	10.1885i	−0.221229	−	0.383179i
$708$	−40.1710	+	69.5782i	−1.50972	+	2.61491i
$709$	11.5220	−	35.4612i	0.432719	−	1.33177i	−0.462687	−	0.886521i	$-0.653115\pi$
$709$	11.5220	−	35.4612i	0.432719	−	1.33177i	0.895406	−	0.445250i	$-0.146885\pi$
$710$	−2.05198	+	19.5233i	−0.0770094	+	0.732695i
$711$	12.6946	−	9.22314i	0.476083	−	0.345895i
$712$	6.73883			0.252548
$713$		0			0
$714$	41.1599			1.54037
$715$	−2.81161	+	2.04276i	−0.105148	+	0.0763948i
$716$	−3.92372	+	37.3317i	−0.146636	+	1.39515i
$717$	18.4196	−	56.6897i	0.687893	−	2.11712i
$718$	0.416347	−	0.721134i	0.0155379	−	0.0269125i
$719$	−9.28994	−	16.0906i	−0.346456	−	0.600080i	0.639161	−	0.769073i	$-0.279282\pi$
$719$	−9.28994	−	16.0906i	−0.346456	−	0.600080i	−0.985617	+	0.168993i	$0.945948\pi$
$720$	3.42265	−	0.727507i	0.127555	−	0.0271126i
$721$	2.76647	+	8.51433i	0.103029	+	0.317090i
$722$	−5.66823	−	1.20482i	−0.210950	−	0.0448387i
$723$	6.56815	+	62.4918i	0.244272	+	2.32409i
$724$	33.2385	+	36.9151i	1.23530	+	1.37194i
$725$	0.146332	+	0.0651514i	0.00543465	+	0.00241966i
$726$	−56.0764	+	24.9668i	−2.08119	+	0.926606i
$727$	10.9585	−	12.1706i	0.406427	−	0.451383i	−0.504831	−	0.863218i	$-0.668445\pi$
$727$	10.9585	−	12.1706i	0.406427	−	0.451383i	0.911258	+	0.411835i	$0.135112\pi$
$728$	−7.51065	−	5.45681i	−0.278363	−	0.202243i
$729$	28.0140	+	20.3534i	1.03756	+	0.753829i
$730$	10.3851	−	11.5339i	0.384371	−	0.426888i
$731$	−0.922113	+	0.410551i	−0.0341056	+	0.0151848i
$732$	60.5507	+	26.9589i	2.23802	+	0.996431i
$733$	−0.770396	−	0.855611i	−0.0284552	−	0.0316027i	0.728749	−	0.684781i	$-0.240102\pi$
$733$	−0.770396	−	0.855611i	−0.0284552	−	0.0316027i	−0.757204	+	0.653178i	$0.773435\pi$
$734$	−7.08819	−	67.4396i	−0.261630	−	2.48924i
$735$	−27.5531	−	5.85659i	−1.01631	−	0.216024i
$736$	−11.3966	−	35.0751i	−0.420084	−	1.29289i
$737$	3.46367	−	0.736226i	0.127586	−	0.0271192i
$738$	29.4834	+	51.0668i	1.08530	+	1.87979i
$739$	−10.3579	+	17.9404i	−0.381022	+	0.659949i	−0.991209	−	0.132309i	$-0.957761\pi$
$739$	−10.3579	+	17.9404i	−0.381022	+	0.659949i	0.610187	+	0.792257i	$0.291094\pi$
$740$	21.6374	−	66.5931i	0.795407	−	2.44801i
$741$	2.33722	−	22.2372i	0.0858600	−	0.816903i
$742$	17.1479	−	12.4586i	0.629517	−	0.457371i
$743$	35.2367			1.29271			0.646354	−	0.763038i	$-0.276293\pi$
$743$	35.2367			1.29271			0.646354	+	0.763038i	$0.276293\pi$
$744$		0			0
$745$	15.8950			0.582348
$746$	−33.0959	+	24.0456i	−1.21173	+	0.880370i
$747$	0.967301	−	9.20326i	0.0353917	−	0.336730i
$748$	−3.30083	+	10.1589i	−0.120690	+	0.371447i
$749$	−1.46104	+	2.53060i	−0.0533853	+	0.0924660i
$750$	−27.5429	−	47.7058i	−1.00573	−	1.74197i
$751$	42.2030	−	8.97053i	1.54001	−	0.327339i	0.641788	−	0.766882i	$-0.278193\pi$
$751$	42.2030	−	8.97053i	1.54001	−	0.327339i	0.898222	+	0.439543i	$0.144859\pi$
$752$	−1.00364	−	3.08888i	−0.0365989	−	0.112640i
$753$	−57.6875	−	12.2619i	−2.10225	−	0.446847i
$754$	−0.0589655	−	0.561020i	−0.00214740	−	0.0204311i
$755$	−9.23623	−	10.2579i	−0.336141	−	0.373322i
$756$	5.75808	+	2.56366i	0.209419	+	0.0932395i
$757$	24.9750	−	11.1196i	0.907733	−	0.404149i	0.100878	−	0.994899i	$-0.467835\pi$
$757$	24.9750	−	11.1196i	0.907733	−	0.404149i	0.806855	+	0.590750i	$0.201168\pi$
$758$	−3.79898	+	4.21919i	−0.137985	+	0.153248i
$759$	10.7433	+	7.80543i	0.389955	+	0.283319i
$760$	−28.6563	−	20.8201i	−1.03947	−	0.755223i
$761$	−11.5037	+	12.7761i	−0.417008	+	0.463134i	−0.914649	−	0.404249i	$-0.867533\pi$
$761$	−11.5037	+	12.7761i	−0.417008	+	0.463134i	0.497641	+	0.867383i	$0.334200\pi$
$762$	6.89867	−	3.07149i	0.249913	−	0.111268i
$763$	17.2172	+	7.66559i	0.623304	+	0.277513i
$764$	5.02976	+	5.58612i	0.181970	+	0.202099i
$765$	3.96337	+	37.7089i	0.143296	+	1.36337i
$766$	−43.1511	−	9.17204i	−1.55911	−	0.331399i
$767$	5.56812	+	17.1369i	0.201053	+	0.618778i
$768$	46.0719	−	9.79289i	1.66248	−	0.353371i
$769$	−7.02837	−	12.1735i	−0.253450	−	0.438987i	0.711024	−	0.703168i	$-0.248232\pi$
$769$	−7.02837	−	12.1735i	−0.253450	−	0.438987i	−0.964473	+	0.264181i	$0.914899\pi$
$770$	−3.38775	+	5.86776i	−0.122086	+	0.211459i
$771$	12.0581	−	37.1111i	0.434263	−	1.33652i
$772$	−8.91893	+	84.8580i	−0.320999	+	3.05411i
$773$	−17.9900	+	13.0705i	−0.647054	+	0.470112i	−0.862266	−	0.506455i	$-0.830956\pi$
$773$	−17.9900	+	13.0705i	−0.647054	+	0.470112i	0.215212	+	0.976567i	$0.430956\pi$
$774$	−1.84315			−0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	27.7771	−	20.1813i	0.996498	−	0.723998i
$778$	1.27139	−	12.0965i	0.0455816	−	0.433680i
$779$	10.5686	−	32.5268i	0.378659	−	1.16539i
$780$	20.0228	−	34.6804i	0.716930	−	1.24176i
$781$	−1.24906	−	2.16343i	−0.0446948	−	0.0774136i
$782$	−70.3617	+	14.9558i	−2.51613	+	0.534819i
$783$	0.0471557	+	0.145130i	0.00168521	+	0.00518654i
$784$	1.75277	+	0.372563i	0.0625990	+	0.0133058i
$785$	2.08784	+	19.8645i	0.0745181	+	0.708993i
$786$	−31.4884	−	34.9714i	−1.12315	−	1.24739i
$787$	−29.2643	−	13.0293i	−1.04316	−	0.464445i	−0.187654	−	0.982235i	$-0.560088\pi$
$787$	−29.2643	−	13.0293i	−1.04316	−	0.464445i	−0.855508	+	0.517790i	$0.826755\pi$
$788$	18.8179	−	8.37827i	0.670360	−	0.298463i
$789$	11.5796	−	12.8605i	0.412245	−	0.457845i
$790$	−21.1192	−	15.3440i	−0.751388	−	0.545915i
$791$	−14.3261	−	10.4085i	−0.509377	−	0.370084i
$792$	−5.20020	+	5.77541i	−0.184781	+	0.205220i
$793$	13.5801	−	6.04625i	0.482244	−	0.214709i
$794$	35.6795	+	15.8855i	1.26622	+	0.563756i
$795$	24.3758	+	27.0720i	0.864519	+	0.960146i
$796$	−1.58795	−	15.1083i	−0.0562834	−	0.535501i
$797$	25.4800	+	5.41595i	0.902549	+	0.191843i	0.635737	−	0.771906i	$-0.280696\pi$
$797$	25.4800	+	5.41595i	0.902549	+	0.191843i	0.266812	+	0.963749i	$0.414030\pi$
$798$	−13.4707	−	41.4586i	−0.476859	−	1.46762i
$799$	34.4248	−	7.31722i	1.21786	−	0.258864i
$800$	3.21812	+	5.57395i	0.113778	+	0.197069i
$801$	−3.81994	+	6.61633i	−0.134971	+	0.233776i
$802$	−27.1247	+	83.4814i	−0.957808	+	2.94783i
$803$	−0.206448	+	1.96422i	−0.00728538	+	0.0693157i
$804$	−33.0100	+	23.9832i	−1.16417	+	0.845822i
$805$	−28.4897			−1.00413
$806$		0			0
$807$	−26.7486			−0.941594
$808$	−18.1621	+	13.1956i	−0.638942	+	0.464218i
$809$	−0.912472	+	8.68159i	−0.0320808	+	0.305229i	0.966702	+	0.255905i	$0.0823733\pi$
$809$	−0.912472	+	8.68159i	−0.0320808	+	0.305229i	−0.998783	+	0.0493239i	$0.984293\pi$
$810$	13.1605	−	40.5037i	0.462411	−	1.42316i
$811$	25.0392	−	43.3692i	0.879245	−	1.52290i	0.0270750	−	0.999633i	$-0.491381\pi$
$811$	25.0392	−	43.3692i	0.879245	−	1.52290i	0.852170	−	0.523264i	$-0.175286\pi$
$812$	−0.343347	−	0.594695i	−0.0120491	−	0.0208697i
$813$	−3.92260	+	0.833774i	−0.137571	+	0.0292417i
$814$	4.40984	+	13.5721i	0.154565	+	0.475701i
$815$	−41.7055	−	8.86477i	−1.46088	−	0.310520i
$816$	−0.470391	−	4.47547i	−0.0164670	−	0.156673i
$817$	0.715318	+	0.794442i	0.0250258	+	0.0277940i
$818$	−1.05124	−	0.468042i	−0.0367558	−	0.0163647i
$819$	9.61505	−	4.28090i	0.335977	−	0.149587i
$820$	40.9859	−	45.5195i	1.43129	−	1.58961i
$821$	−41.0844	−	29.8495i	−1.43385	−	1.04176i	−0.989283	−	0.146013i	$-0.953356\pi$
$821$	−41.0844	−	29.8495i	−1.43385	−	1.04176i	−0.444572	−	0.895743i	$-0.646644\pi$
$822$	−78.2123	−	56.8246i	−2.72797	−	1.98199i
$823$	4.23506	−	4.70351i	0.147625	−	0.163954i	−0.664797	−	0.747024i	$-0.731482\pi$
$823$	4.23506	−	4.70351i	0.147625	−	0.163954i	0.812422	+	0.583070i	$0.198149\pi$
$824$	15.6064	−	6.94841i	0.543674	−	0.242059i
$825$	−2.11713	−	0.942609i	−0.0737092	−	0.0328174i
$826$	23.5061	+	26.1062i	0.817882	+	0.908350i
$827$	0.386489	+	3.67720i	0.0134395	+	0.127869i	0.999184	−	0.0403779i	$-0.0128562\pi$
$827$	0.386489	+	3.67720i	0.0134395	+	0.127869i	−0.985745	+	0.168247i	$0.946190\pi$
$828$	−80.2231	−	17.0519i	−2.78795	−	0.592596i
$829$	−8.04729	−	24.7670i	−0.279494	−	0.860193i	−0.987995	−	0.154484i	$-0.950628\pi$
$829$	−8.04729	−	24.7670i	−0.279494	−	0.860193i	0.708501	−	0.705709i	$-0.249372\pi$
$830$	−15.0588	+	3.20086i	−0.522700	+	0.111103i
$831$	15.3852	+	26.6479i	0.533707	+	0.924407i
$832$	12.0995	−	20.9570i	0.419475	−	0.726553i
$833$	−6.00033	+	18.4671i	−0.207899	+	0.639848i
$834$	4.50159	−	42.8298i	0.155877	−	1.48307i
$835$	49.2635	−	35.7920i	1.70483	−	1.23863i
$836$	11.3130			0.391267
$837$		0			0
$838$	31.1747			1.07691
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	−0.687489	−	0.726195i	$-0.741287\pi$
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	0.478207	+	0.878247i	$0.341287\pi$
$840$	3.25157	−	30.9366i	0.112190	−	1.06742i
$841$	−8.95636	+	27.5648i	−0.308840	+	0.950511i
$842$	35.6687	−	61.7800i	1.22923	−	2.12908i
$843$	27.2996	+	47.2843i	0.940249	+	1.62856i
$844$	60.5423	−	12.8687i	2.08395	−	0.442957i
$845$	7.26150	+	22.3486i	0.249803	+	0.768815i
$846$	62.8606	+	13.3614i	2.16119	+	0.459375i
$847$	1.75173	+	16.6666i	0.0601903	+	0.572673i
$848$	−1.55065	−	1.72217i	−0.0532495	−	0.0591396i
$849$	−1.60002	−	0.712377i	−0.0549127	−	0.0244487i
$850$	11.4684	−	5.10605i	0.393362	−	0.175136i
$851$	−40.1511	+	44.5923i	−1.37636	+	1.52861i
$852$	23.2877	+	16.9195i	0.797822	+	0.579652i
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.994989	−	0.0999836i	$-0.0318790\pi$
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.212378	+	0.977187i	$0.431879\pi$
$854$	19.3922	−	21.5372i	0.663588	−	0.736989i
$855$	36.6855	−	16.3334i	1.25462	−	0.558592i
$856$	5.09390	+	2.26795i	0.174106	+	0.0775170i
$857$	26.2452	+	29.1482i	0.896518	+	0.995684i	0.999999	+	0.00105245i	$0.000335004\pi$
$857$	26.2452	+	29.1482i	0.896518	+	0.995684i	−0.103482	+	0.994631i	$0.532998\pi$
$858$	0.853112	+	8.11682i	0.0291248	+	0.277104i
$859$	−17.8036	−	3.78426i	−0.607449	−	0.129117i	−0.106090	−	0.994357i	$-0.533833\pi$
$859$	−17.8036	−	3.78426i	−0.607449	−	0.129117i	−0.501359	+	0.865239i	$0.667167\pi$
$860$	0.591643	+	1.82089i	0.0201749	+	0.0620918i
$861$	29.3789	−	6.24467i	1.00123	−	0.212818i
$862$	13.9084	+	24.0900i	0.473721	+	0.820509i
$863$	22.4738	−	38.9258i	0.765018	−	1.32505i	−0.175219	−	0.984530i	$-0.556063\pi$
$863$	22.4738	−	38.9258i	0.765018	−	1.32505i	0.940237	−	0.340521i	$-0.110603\pi$
$864$	−1.89477	+	5.83151i	−0.0644614	+	0.198392i
$865$	2.34355	−	22.2974i	0.0796830	−	0.758133i
$866$	−60.4700	+	43.9340i	−2.05486	+	1.49294i
$867$	5.53740			0.188060
$868$		0			0
$869$	3.32196			0.112690
$870$	1.52919	−	1.11102i	0.0518442	−	0.0376670i
$871$	−0.956548	+	9.10095i	−0.0324114	+	0.308374i
$872$	11.1133	−	34.2032i	0.376343	−	1.15827i
$873$	−21.2949	+	36.8839i	−0.720724	+	1.24833i
$874$	38.0922	+	65.9776i	1.28849	+	2.23173i
$875$	−14.7105	+	3.12682i	−0.497307	+	0.105706i
$876$	−7.03257	−	21.6440i	−0.237608	−	0.731283i
$877$	41.7190	+	8.86765i	1.40875	+	0.299439i	0.848637	−	0.528976i	$-0.177424\pi$
$877$	41.7190	+	8.86765i	1.40875	+	0.299439i	0.560114	+	0.828415i	$0.310757\pi$
$878$	−2.98323	−	28.3835i	−0.100679	−	0.957897i
$879$	15.3329	+	17.0290i	0.517167	+	0.574372i
$880$	0.676740	+	0.301304i	0.0228129	+	0.0101570i
$881$	8.14565	−	3.62668i	0.274434	−	0.122186i	−0.264905	−	0.964274i	$-0.585341\pi$
$881$	8.14565	−	3.62668i	0.274434	−	0.122186i	0.539339	+	0.842089i	$0.318674\pi$
$882$	−23.7253	+	26.3496i	−0.798871	+	0.887236i
$883$	38.0791	+	27.6661i	1.28146	+	0.931038i	0.999596	−	0.0284158i	$-0.00904624\pi$
$883$	38.0791	+	27.6661i	1.28146	+	0.931038i	0.281867	+	0.959453i	$0.409046\pi$
$884$	−22.3326	−	16.2256i	−0.751126	−	0.545725i
$885$	−40.3995	+	44.8682i	−1.35801	+	1.50823i
$886$	−9.95708	+	4.43318i	−0.334515	+	0.148936i
$887$	2.88367	+	1.28389i	0.0968241	+	0.0431089i	0.454577	−	0.890707i	$-0.349790\pi$
$887$	2.88367	+	1.28389i	0.0968241	+	0.0431089i	−0.357753	+	0.933816i	$0.616457\pi$
$888$	−43.8398	−	48.6890i	−1.47117	−	1.63390i
$889$	−0.215503	−	2.05038i	−0.00722774	−	0.0687674i
$890$	12.4323	+	2.64256i	0.416731	+	0.0885789i
$891$	1.67473	+	5.15429i	0.0561056	+	0.172675i
$892$	20.2112	−	4.29602i	0.676721	−	0.143841i
$893$	−18.6368	−	32.2799i	−0.623657	−	1.08021i
$894$	18.6640	−	32.3270i	0.624217	−	1.08118i
$895$	−8.71703	+	26.8283i	−0.291378	+	0.896770i
$896$	3.19646	−	30.4123i	0.106786	−	1.01600i
$897$	−27.7636	+	20.1714i	−0.927000	+	0.673505i
$898$	36.8840			1.23083
$899$		0			0
$900$	14.3131			0.477105
$901$	20.3157	−	14.7602i	0.676815	−	0.491735i
$902$	−1.30490	+	12.4153i	−0.0434483	+	0.413383i
$903$	−0.290113	+	0.892875i	−0.00965434	+	0.0297130i
$904$	−16.8954	+	29.2637i	−0.561932	+	0.973295i
$905$	18.6648	+	32.3284i	0.620439	+	1.07463i
$906$	−31.7075	+	6.73963i	−1.05341	+	0.223909i
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	0.988775	+	0.149413i	$0.0477384\pi$
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	−0.712113	+	0.702065i	$0.752262\pi$
$908$	42.4318	+	9.01916i	1.40815	+	0.299311i
$909$	−2.66039	−	25.3119i	−0.0882395	−	0.839543i
$910$	−11.7163	−	13.0123i	−0.388393	−	0.431354i
$911$	−4.63900	−	2.06542i	−0.153697	−	0.0684303i	0.328446	−	0.944523i	$-0.393475\pi$
$911$	−4.63900	−	2.06542i	−0.153697	−	0.0684303i	−0.482143	+	0.876092i	$0.660142\pi$
$912$	−4.35401	+	1.93853i	−0.144176	+	0.0641911i
$913$	1.31091	−	1.45591i	0.0433847	−	0.0481836i
$914$	8.50854	+	6.18181i	0.281437	+	0.204476i
$915$	40.2967	+	29.2773i	1.33217	+	0.967876i
$916$	−33.9880	+	37.7475i	−1.12299	+	1.24721i
$917$	−11.7369	+	5.22560i	−0.387586	+	0.172565i
$918$	10.9256	+	4.86437i	0.360597	+	0.160548i
$919$	−32.9727	−	36.6199i	−1.08767	−	1.20798i	−0.976802	−	0.214145i	$-0.931304\pi$
$919$	−32.9727	−	36.6199i	−1.08767	−	1.20798i	−0.110868	−	0.993835i	$-0.535363\pi$
$920$	5.68265	+	54.0668i	0.187351	+	1.78253i
$921$	77.9293	+	16.5644i	2.56786	+	0.545815i
$922$	12.1157	+	37.2882i	0.399009	+	1.22802i
$923$	6.31475	−	1.34224i	0.207853	−	0.0441804i
$924$	4.96754	+	8.60403i	0.163420	+	0.283052i
$925$	5.23597	−	9.06896i	0.172158	−	0.298186i
$926$	−19.5578	+	60.1929i	−0.642711	+	1.97806i
$927$	−2.02446	+	19.2614i	−0.0664919	+	0.632628i
$928$	0.540441	−	0.392653i	0.0177408	−	0.0128895i
$929$	39.9606			1.31107			0.655533	−	0.755167i	$-0.272444\pi$
$929$	39.9606			1.31107			0.655533	+	0.755167i	$0.272444\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	−35.1311	+	25.5243i	−1.15076	+	0.836075i
$933$	4.70814	−	44.7949i	0.154137	−	1.46652i
$934$	−16.3367	+	50.2791i	−0.534552	+	1.64518i
$935$	−4.01360	+	6.95176i	−0.131259	+	0.227347i
$936$	−10.0420	−	17.3932i	−0.328232	−	0.568515i
$937$	−44.1040	+	9.37459i	−1.44081	+	0.306255i	−0.861046	−	0.508527i	$-0.830190\pi$
$937$	−44.1040	+	9.37459i	−1.44081	+	0.306255i	−0.579768	+	0.814781i	$0.696857\pi$
$938$	5.51313	+	16.9677i	0.180010	+	0.554014i
$939$	−53.8935	−	11.4554i	−1.75875	−	0.373834i
$940$	−6.97790	−	66.3903i	−0.227594	−	2.16541i
$941$	−33.5852	−	37.3002i	−1.09485	−	1.21595i	−0.974776	−	0.223185i	$-0.928354\pi$
$941$	−33.5852	−	37.3002i	−1.09485	−	1.21595i	−0.120071	−	0.992765i	$-0.538312\pi$
$942$	42.8515	+	19.0787i	1.39618	+	0.621618i
$943$	−47.9533	+	21.3502i	−1.56157	+	0.695257i
$944$	2.56999	−	2.85426i	0.0836460	−	0.0928983i
$945$	3.83202	+	2.78412i	0.124656	+	0.0905675i
$946$	−0.315684	−	0.229358i	−0.0102638	−	0.00745707i
$947$	−20.2920	+	22.5366i	−0.659402	+	0.732340i	−0.976372	−	0.216095i	$-0.930668\pi$
$947$	−20.2920	+	22.5366i	−0.659402	+	0.732340i	0.316970	+	0.948435i	$0.397334\pi$
$948$	−34.9688	+	15.5691i	−1.13573	+	0.505661i
$949$	−4.66278	−	2.07601i	−0.151360	−	0.0673900i
$950$	−8.89646	−	9.88052i	−0.288639	−	0.320566i
$951$	−0.270052	−	2.56937i	−0.00875703	−	0.0833176i
$952$	−20.9744	−	4.45825i	−0.679785	−	0.144493i
$953$	10.9631	+	33.7411i	0.355131	+	1.09298i	0.955934	+	0.293583i	$0.0948477\pi$
$953$	10.9631	+	33.7411i	0.355131	+	1.09298i	−0.600803	+	0.799397i	$0.705152\pi$
$954$	44.8524	−	9.53368i	1.45215	−	0.308664i
$955$	2.82442	+	4.89204i	0.0913961	+	0.158303i
$956$	−38.9689	+	67.4962i	−1.26035	+	2.18298i
$957$	−0.0743291	+	0.228761i	−0.00240272	+	0.00739481i
$958$	−2.18217	+	20.7620i	−0.0705027	+	0.670788i
$959$	−21.3530	+	15.5139i	−0.689524	+	0.500969i
$960$	81.0843			2.61698
$961$		0			0
$962$	−36.8791			−1.18903
$963$	−5.11422	+	3.71570i	−0.164804	+	0.119737i
$964$	8.58803	−	81.7097i	0.276602	−	2.63169i
$965$	−19.8145	+	60.9828i	−0.637852	+	1.96311i
$966$	−33.4527	+	57.9418i	−1.07632	+	1.86425i
$967$	−17.7222	−	30.6957i	−0.569906	−	0.987107i	−0.996575	−	0.0826987i	$-0.973646\pi$
$967$	−17.7222	−	30.6957i	−0.569906	−	0.987107i	0.426668	−	0.904408i	$-0.359687\pi$
$968$	31.2800	−	6.64876i	1.00538	−	0.213699i
$969$	−15.9593	−	49.1176i	−0.512686	−	1.57789i
$970$	69.3060	+	14.7314i	2.22528	+	0.472998i
$971$	4.19130	+	39.8776i	0.134505	+	1.27973i	0.828597	+	0.559846i	$0.189140\pi$
$971$	4.19130	+	39.8776i	0.134505	+	1.27973i	−0.694092	+	0.719887i	$0.744194\pi$
$972$	−49.6845	−	55.1802i	−1.59363	−	1.76991i
$973$	−10.7410	−	4.78221i	−0.344341	−	0.153310i
$974$	49.7973	−	22.1712i	1.59561	−	0.710411i
$975$	4.00746	−	4.45073i	0.128341	−	0.142538i
$976$	−2.56345	−	1.86246i	−0.0820540	−	0.0596157i
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.962283	−	0.272052i	$-0.0877022\pi$
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.0386252	+	0.999254i	$0.487702\pi$
$978$	−66.9998	+	74.4108i	−2.14242	+	2.37939i
$979$	−1.47758	+	0.657860i	−0.0472236	+	0.0210253i
$980$	33.6470	+	14.9806i	1.07481	+	0.478538i
$981$	27.2818	+	30.2995i	0.871040	+	0.967388i
$982$	2.22555	+	21.1747i	0.0710202	+	0.675712i
$983$	−21.1080	−	4.48665i	−0.673242	−	0.143102i	−0.141409	−	0.989951i	$-0.545163\pi$
$983$	−21.1080	−	4.48665i	−0.673242	−	0.143102i	−0.531833	+	0.846849i	$0.678497\pi$
$984$	−17.7109	−	54.5086i	−0.564604	−	1.73767i
$985$	15.1415	−	3.21842i	0.482447	−	0.102547i
$986$	−0.651478	−	1.12839i	−0.0207473	−	0.0359354i
$987$	16.3669	−	28.3483i	0.520965	−	0.902338i
$988$	−9.03438	+	27.8049i	−0.287422	+	0.884593i
$989$	0.171505	−	1.63176i	0.00545353	−	0.0518869i
$990$	−11.8585	+	8.61568i	−0.376887	+	0.273824i
$991$	−46.8764			−1.48908			−0.744538	−	0.667580i	$-0.767330\pi$
$991$	−46.8764			−1.48908			−0.744538	+	0.667580i	$0.767330\pi$
$992$		0			0
$993$	−67.8639			−2.15360
$994$	10.1825	−	7.39800i	0.322968	−	0.234650i
$995$	1.19333	−	11.3537i	0.0378310	−	0.359938i
$996$	−6.97589	+	21.4696i	−0.221039	+	0.680290i
$997$	−22.2695	+	38.5718i	−0.705281	+	1.22158i	0.261309	+	0.965255i	$0.415846\pi$
$997$	−22.2695	+	38.5718i	−0.705281	+	1.22158i	−0.966590	+	0.256327i	$0.917488\pi$
$998$	32.7830	+	56.7818i	1.03773	+	1.79740i
$999$	9.75827	−	2.07419i	0.308738	−	0.0656243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.j.338.1		16
31.2	even	5		961.2.g.l.732.1		16
31.3	odd	30		961.2.d.p.531.4		16
31.4	even	5		961.2.g.n.448.2		16
31.5	even	3		961.2.g.l.235.1		16
31.6	odd	6		961.2.d.o.388.1		16
31.7	even	15		961.2.d.q.628.4		16
31.8	even	5		961.2.c.i.521.8		16
31.9	even	15		961.2.c.i.439.8		16
31.10	even	15	inner	961.2.g.j.816.1		16
31.11	odd	30		961.2.g.s.846.2		16
31.12	odd	30		961.2.d.o.374.1		16
31.13	odd	30		961.2.g.t.547.2		16
31.14	even	15		961.2.a.j.1.8		8
31.15	odd	10		961.2.g.s.844.2		16
31.16	even	5		961.2.g.m.844.2		16
31.17	odd	30		961.2.a.i.1.8		8
31.18	even	15		961.2.g.n.547.2		16
31.19	even	15		961.2.d.n.374.1		16
31.20	even	15		961.2.g.m.846.2		16
31.21	odd	30		961.2.g.k.816.1		16
31.22	odd	30		961.2.c.j.439.8		16
31.23	odd	10		961.2.c.j.521.8		16
31.24	odd	30		961.2.d.p.628.4		16
31.25	even	3		961.2.d.n.388.1		16
31.26	odd	6		31.2.g.a.18.1	✓	16
31.27	odd	10		961.2.g.t.448.2		16
31.28	even	15		961.2.d.q.531.4		16
31.29	odd	10		31.2.g.a.19.1	yes	16
31.30	odd	2		961.2.g.k.338.1		16
93.14	odd	30		8649.2.a.be.1.1		8
93.17	even	30		8649.2.a.bf.1.1		8
93.26	even	6		279.2.y.c.235.2		16
93.29	even	10		279.2.y.c.19.2		16
124.91	even	10		496.2.bg.c.81.2		16
124.119	even	6		496.2.bg.c.49.2		16
155.29	odd	10		775.2.bl.a.701.2		16
155.57	even	12		775.2.ck.a.49.1		32
155.88	even	12		775.2.ck.a.49.4		32
155.119	odd	6		775.2.bl.a.576.2		16
155.122	even	20		775.2.ck.a.174.4		32
155.153	even	20		775.2.ck.a.174.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.26	odd	6
31.2.g.a.19.1	yes	16	31.29	odd	10
279.2.y.c.19.2		16	93.29	even	10
279.2.y.c.235.2		16	93.26	even	6
496.2.bg.c.49.2		16	124.119	even	6
496.2.bg.c.81.2		16	124.91	even	10
775.2.bl.a.576.2		16	155.119	odd	6
775.2.bl.a.701.2		16	155.29	odd	10
775.2.ck.a.49.1		32	155.57	even	12
775.2.ck.a.49.4		32	155.88	even	12
775.2.ck.a.174.1		32	155.153	even	20
775.2.ck.a.174.4		32	155.122	even	20
961.2.a.i.1.8		8	31.17	odd	30
961.2.a.j.1.8		8	31.14	even	15
961.2.c.i.439.8		16	31.9	even	15
961.2.c.i.521.8		16	31.8	even	5
961.2.c.j.439.8		16	31.22	odd	30
961.2.c.j.521.8		16	31.23	odd	10
961.2.d.n.374.1		16	31.19	even	15
961.2.d.n.388.1		16	31.25	even	3
961.2.d.o.374.1		16	31.12	odd	30
961.2.d.o.388.1		16	31.6	odd	6
961.2.d.p.531.4		16	31.3	odd	30
961.2.d.p.628.4		16	31.24	odd	30
961.2.d.q.531.4		16	31.28	even	15
961.2.d.q.628.4		16	31.7	even	15
961.2.g.j.338.1		16	1.1	even	1	trivial
961.2.g.j.816.1		16	31.10	even	15	inner
961.2.g.k.338.1		16	31.30	odd	2
961.2.g.k.816.1		16	31.21	odd	30
961.2.g.l.235.1		16	31.5	even	3
961.2.g.l.732.1		16	31.2	even	5
961.2.g.m.844.2		16	31.16	even	5
961.2.g.m.846.2		16	31.20	even	15
961.2.g.n.448.2		16	31.4	even	5
961.2.g.n.547.2		16	31.18	even	15
961.2.g.s.844.2		16	31.15	odd	10
961.2.g.s.846.2		16	31.11	odd	30
961.2.g.t.448.2		16	31.27	odd	10
961.2.g.t.547.2		16	31.13	odd	30
8649.2.a.be.1.1		8	93.14	odd	30
8649.2.a.bf.1.1		8	93.17	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86683 + 1.35633i) q^{2} +(-0.265787 + 2.52879i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 - 2.16373i) q^{5} +(-2.93370 - 5.08132i) q^{6} +(-1.56687 + 0.333049i) q^{7} +(0.944583 + 2.90713i) q^{8} +(-3.38972 - 0.720507i) q^{9} +(0.602634 + 5.73368i) q^{10} +(-0.490912 - 0.545213i) q^{11} +(7.72288 + 3.43845i) q^{12} +(1.73206 - 0.771163i) q^{13} +(2.47336 - 2.74694i) q^{14} +(5.13960 + 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(2.93028 - 3.25441i) q^{17} +(7.30526 - 3.25251i) q^{18} +(-4.23705 - 1.88646i) q^{19} +(-5.55818 - 6.17299i) q^{20} +(-0.425758 - 4.05082i) q^{21} +(1.65594 + 0.351980i) q^{22} +(2.19973 + 6.77006i) q^{23} +(-7.60258 + 1.61598i) q^{24} +(-0.621150 - 1.07586i) q^{25} +(-2.18751 + 3.78887i) q^{26} +(0.365721 - 1.12557i) q^{27} +(-0.556691 + 5.29656i) q^{28} +(-0.104314 + 0.0757884i) q^{29} -14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(-1.05628 + 10.0499i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 + 9.97791i) q^{36} +(4.21474 + 7.30014i) q^{37} +(10.4685 - 2.22515i) q^{38} +(1.48975 + 4.58499i) q^{39} +(7.47024 + 1.58785i) q^{40} +(0.770791 + 7.33358i) q^{41} +(6.28907 + 6.98472i) q^{42} +(-0.210565 - 0.0937494i) q^{43} +(-2.22830 + 0.992101i) q^{44} +(-5.79352 + 6.43435i) q^{45} +(-13.2889 - 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(0.687602 - 0.763659i) q^{48} +(-4.05065 + 1.80346i) q^{49} +(2.61881 + 1.16597i) q^{50} +(7.45090 + 8.27507i) q^{51} +(-0.658896 - 6.26898i) q^{52} +(5.60893 + 1.19222i) q^{53} +(0.843912 + 2.59729i) q^{54} +(-1.79296 + 0.381105i) q^{55} +(-2.44826 - 4.24051i) q^{56} +(5.89661 - 10.2132i) q^{57} +(0.0919419 - 0.282968i) q^{58} +(-0.993409 + 9.45166i) q^{59} +(17.0875 - 12.4148i) q^{60} +7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(0.495153 - 4.71107i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 + 4.17994i) q^{67} +(-7.27978 - 12.6090i) q^{68} +(-17.7047 + 3.76326i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(3.33061 + 0.707943i) q^{71} +(-1.10726 - 10.5349i) q^{72} +(-1.80133 - 2.00058i) q^{73} +(-17.7696 - 7.91153i) q^{74} +(2.88573 - 1.28481i) q^{75} +(-10.3180 + 11.4593i) q^{76} +(0.950780 + 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(-3.02979 + 3.36492i) q^{79} +(-0.922421 + 0.410688i) q^{80} +(-6.74838 - 3.00457i) q^{81} +(-11.3857 - 12.6451i) q^{82} +(0.279128 + 2.65572i) q^{83} +(-13.2459 - 2.81551i) q^{84} +(-3.38106 - 10.4058i) q^{85} +(0.520243 - 0.110581i) q^{86} +(-0.163928 - 0.283932i) q^{87} +(1.12130 - 1.94214i) q^{88} +(0.681255 - 2.09669i) q^{89} +(2.08840 - 19.8698i) q^{90} +(-2.45708 + 1.78518i) q^{91} +23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(1.37702 - 13.1015i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 - 8.86077i) q^{98} +(1.27122 + 2.20182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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