LMFDB - Embedded newform 961.2.g.m.732.1

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)

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);

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")

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 = [16,4,-3,6,-3,-11,-3] 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			732.1
Root			$0.333129i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.m.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67638 - 1.21796i) q^{2} +(1.95443 + 0.870169i) q^{3} +(0.708788 + 2.18143i) q^{4} +(-1.17396 + 2.03335i) q^{5} +(-2.21654 - 3.83916i) q^{6} +(-2.45875 + 2.73072i) q^{7} +(0.188054 - 0.578772i) q^{8} +(1.05522 + 1.17194i) q^{9} +(4.44454 - 1.97884i) q^{10} +(-4.18710 - 0.889995i) q^{11} +(-0.512931 + 4.88021i) q^{12} +(-0.218172 - 2.07577i) q^{13} +(7.44771 - 1.58306i) q^{14} +(-4.06377 + 2.95251i) q^{15} +(2.69109 - 1.95519i) q^{16} +(2.08159 - 0.442455i) q^{17} +(-0.341570 - 3.24983i) q^{18} +(0.0648092 - 0.616619i) q^{19} +(-5.26769 - 1.11968i) q^{20} +(-7.18164 + 3.19747i) q^{21} +(5.93519 + 6.59170i) q^{22} +(1.03640 - 3.18973i) q^{23} +(0.871168 - 0.967530i) q^{24} +(-0.256344 - 0.444001i) q^{25} +(-2.16247 + 3.74550i) q^{26} +(-0.940760 - 2.89536i) q^{27} +(-7.69959 - 3.42808i) q^{28} +(-1.11435 - 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 - 5.38292i) q^{33} +(-4.02843 - 1.79357i) q^{34} +(-2.66604 - 8.20524i) q^{35} +(-1.80857 + 3.13253i) q^{36} +(0.137239 + 0.237704i) q^{37} +(-0.859664 + 0.954753i) q^{38} +(1.37986 - 4.24679i) q^{39} +(0.956078 + 1.06183i) q^{40} +(-3.90807 + 1.73998i) q^{41} +(15.9336 + 3.38678i) q^{42} +(0.0281905 - 0.268215i) q^{43} +(-1.02631 - 9.76467i) q^{44} +(-3.62173 + 0.769824i) q^{45} +(-5.62238 + 4.08489i) q^{46} +(-4.35183 + 3.16179i) q^{47} +(6.96090 - 1.47959i) q^{48} +(-0.679670 - 6.46663i) q^{49} +(-0.111046 + 1.05653i) q^{50} +(4.45333 + 0.946585i) q^{51} +(4.37349 - 1.94720i) q^{52} +(-6.36255 - 7.06633i) q^{53} +(-1.94937 + 5.99954i) q^{54} +(6.72514 - 7.46903i) q^{55} +(1.11808 + 1.93658i) q^{56} +(0.663228 - 1.14874i) q^{57} +(0.881988 + 2.71448i) q^{58} +(-5.32363 - 2.37023i) q^{59} +(-9.32103 - 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 + 5.96700i) q^{64} +(4.47688 + 1.99324i) q^{65} +(5.86404 + 18.0477i) q^{66} +(6.80719 - 11.7904i) q^{67} +(2.44059 + 4.22722i) q^{68} +(4.80118 - 5.33225i) q^{69} +(-5.52437 + 17.0022i) q^{70} +(-0.893908 - 0.992785i) q^{71} +(0.876721 - 0.390342i) q^{72} +(-13.8565 - 2.94528i) q^{73} +(0.0594505 - 0.565634i) q^{74} +(-0.114651 - 1.09083i) q^{75} +(1.39104 - 0.295676i) q^{76} +(12.7253 - 9.24551i) q^{77} +(-7.48561 + 5.43861i) q^{78} +(8.48701 - 1.80397i) q^{79} +(0.816370 + 7.76724i) q^{80} +(1.17533 - 11.1825i) q^{81} +(8.67065 + 1.84300i) q^{82} +(4.73717 - 2.10912i) q^{83} +(-12.0653 - 13.3999i) q^{84} +(-1.54403 + 4.75202i) q^{85} +(-0.373934 + 0.415296i) q^{86} +(-1.47342 - 2.55203i) q^{87} +(-1.30251 + 2.25601i) q^{88} +(-1.54897 - 4.76725i) q^{89} +(7.00903 + 3.12062i) q^{90} +(6.20475 + 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 + 0.855663i) q^{95} +(-15.8500 - 7.05686i) q^{96} +(2.07474 + 6.38538i) q^{97} +(-6.73673 + 11.6684i) q^{98} +(-3.37528 - 5.84615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} + 2 q^{11} + 20 q^{12} + 27 q^{13} - 6 q^{14} - 4 q^{15} - 2 q^{16} + 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 + 2 * q^11 + 20 * q^12 + 27 * q^13 - 6 * q^14 - 4 * q^15 - 2 * q^16 + 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 - 29 * q^21 - 4 * q^22 - 21 * q^23 + 25 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 40 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 + 51 * q^42 - 8 * q^43 - 4 * q^44 + 25 * q^45 + 16 * q^46 + 4 * q^47 + 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 - 24 * q^52 - 66 * q^53 - 39 * q^54 + 52 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 - 51 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 18 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 - 27 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 + 42 * q^77 + 15 * q^78 - 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 - 4 * q^83 + 27 * q^84 + 63 * q^85 - 34 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 + 57 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 + 62 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−1.67638	−	1.21796i	−1.18538	−	0.861230i	−0.192612	−	0.981275i	$-0.561696\pi$
$2$	−1.67638	−	1.21796i	−1.18538	−	0.861230i	−0.992768	+	0.120045i	$0.961696\pi$
$3$	1.95443	+	0.870169i	1.12839	+	0.502392i	0.884094	−	0.467308i	$-0.154776\pi$
$3$	1.95443	+	0.870169i	1.12839	+	0.502392i	0.244297	+	0.969700i	$0.421443\pi$
$4$	0.708788	+	2.18143i	0.354394	+	1.09071i
$5$	−1.17396	+	2.03335i	−0.525009	+	0.909342i	0.474567	+	0.880219i	$0.342605\pi$
$5$	−1.17396	+	2.03335i	−0.525009	+	0.909342i	−0.999576	+	0.0291228i	$0.990729\pi$
$6$	−2.21654	−	3.83916i	−0.904898	−	1.56733i
$7$	−2.45875	+	2.73072i	−0.929319	+	1.03211i	0.0700828	+	0.997541i	$0.477674\pi$
$7$	−2.45875	+	2.73072i	−0.929319	+	1.03211i	−0.999402	+	0.0345725i	$0.988993\pi$
$8$	0.188054	−	0.578772i	0.0664872	−	0.204627i
$9$	1.05522	+	1.17194i	0.351739	+	0.390645i
$10$	4.44454	−	1.97884i	1.40549	−	0.625764i
$11$	−4.18710	−	0.889995i	−1.26246	−	0.268344i	−0.472405	−	0.881382i	$-0.656614\pi$
$11$	−4.18710	−	0.889995i	−1.26246	−	0.268344i	−0.790053	+	0.613038i	$0.789947\pi$
$12$	−0.512931	+	4.88021i	−0.148070	+	1.40880i
$13$	−0.218172	−	2.07577i	−0.0605099	−	0.575714i	−0.982207	−	0.187803i	$-0.939863\pi$
$13$	−0.218172	−	2.07577i	−0.0605099	−	0.575714i	0.921697	−	0.387911i	$-0.126803\pi$
$14$	7.44771	−	1.58306i	1.99048	−	0.423090i
$15$	−4.06377	+	2.95251i	−1.04926	+	0.762334i
$16$	2.69109	−	1.95519i	0.672773	−	0.488798i
$17$	2.08159	−	0.442455i	0.504859	−	0.107311i	0.0515606	−	0.998670i	$-0.483580\pi$
$17$	2.08159	−	0.442455i	0.504859	−	0.107311i	0.453299	+	0.891359i	$0.350247\pi$
$18$	−0.341570	−	3.24983i	−0.0805089	−	0.765991i
$19$	0.0648092	−	0.616619i	0.0148683	−	0.141462i	−0.984569	−	0.174995i	$-0.944009\pi$
$19$	0.0648092	−	0.616619i	0.0148683	−	0.141462i	0.999438	+	0.0335327i	$0.0106758\pi$
$20$	−5.26769	−	1.11968i	−1.17789	−	0.250369i
$21$	−7.18164	+	3.19747i	−1.56716	+	0.697745i
$22$	5.93519	+	6.59170i	1.26539	+	1.40536i
$23$	1.03640	−	3.18973i	0.216105	−	0.665104i	−0.782968	−	0.622062i	$-0.786295\pi$
$23$	1.03640	−	3.18973i	0.216105	−	0.665104i	0.999073	−	0.0430417i	$-0.0137048\pi$
$24$	0.871168	−	0.967530i	0.177826	−	0.197496i
$25$	−0.256344	−	0.444001i	−0.0512688	−	0.0888002i
$26$	−2.16247	+	3.74550i	−0.424094	+	0.734553i
$27$	−0.940760	−	2.89536i	−0.181049	−	0.557213i
$28$	−7.69959	−	3.42808i	−1.45509	−	0.647846i
$29$	−1.11435	−	0.809625i	−0.206930	−	0.150344i	0.479493	−	0.877545i	$-0.340820\pi$
$29$	−1.11435	−	0.809625i	−0.206930	−	0.150344i	−0.686424	+	0.727202i	$0.740820\pi$
$30$	10.4085			1.90032
$31$		0			0
$31$		0			0
$32$	−8.10976			−1.43362
$33$	−7.40895	−	5.38292i	−1.28973	−	0.937046i
$34$	−4.02843	−	1.79357i	−0.690870	−	0.307595i
$35$	−2.66604	−	8.20524i	−0.450644	−	1.38694i
$36$	−1.80857	+	3.13253i	−0.301428	+	0.522089i
$37$	0.137239	+	0.237704i	0.0225619	+	0.0390783i	0.877086	−	0.480334i	$-0.159484\pi$
$37$	0.137239	+	0.237704i	0.0225619	+	0.0390783i	−0.854524	+	0.519412i	$0.826151\pi$
$38$	−0.859664	+	0.954753i	−0.139456	+	0.154881i
$39$	1.37986	−	4.24679i	0.220955	−	0.680030i
$40$	0.956078	+	1.06183i	0.151169	+	0.167890i
$41$	−3.90807	+	1.73998i	−0.610338	+	0.271740i	−0.688541	−	0.725198i	$-0.741748\pi$
$41$	−3.90807	+	1.73998i	−0.610338	+	0.271740i	0.0782030	+	0.996937i	$0.475082\pi$
$42$	15.9336	+	3.38678i	2.45860	+	0.522592i
$43$	0.0281905	−	0.268215i	0.00429902	−	0.0409024i	−0.992162	−	0.124958i	$-0.960121\pi$
$43$	0.0281905	−	0.268215i	0.00429902	−	0.0409024i	0.996461	+	0.0840552i	$0.0267872\pi$
$44$	−1.02631	−	9.76467i	−0.154722	−	1.47208i
$45$	−3.62173	+	0.769824i	−0.539896	+	0.114759i
$46$	−5.62238	+	4.08489i	−0.828974	+	0.602285i
$47$	−4.35183	+	3.16179i	−0.634780	+	0.461195i	−0.858053	−	0.513561i	$-0.828326\pi$
$47$	−4.35183	+	3.16179i	−0.634780	+	0.461195i	0.223273	+	0.974756i	$0.428326\pi$
$48$	6.96090	−	1.47959i	1.00472	−	0.213560i
$49$	−0.679670	−	6.46663i	−0.0970958	−	0.923805i
$50$	−0.111046	+	1.05653i	−0.0157043	+	0.149416i
$51$	4.45333	+	0.946585i	0.623591	+	0.132548i
$52$	4.37349	−	1.94720i	0.606494	−	0.270029i
$53$	−6.36255	−	7.06633i	−0.873964	−	0.970635i	0.125807	−	0.992055i	$-0.459848\pi$
$53$	−6.36255	−	7.06633i	−0.873964	−	0.970635i	−0.999771	+	0.0214197i	$0.993181\pi$
$54$	−1.94937	+	5.99954i	−0.265276	+	0.816434i
$55$	6.72514	−	7.46903i	0.906818	−	1.00712i
$56$	1.11808	+	1.93658i	0.149410	+	0.258786i
$57$	0.663228	−	1.14874i	0.0878467	−	0.152155i
$58$	0.881988	+	2.71448i	0.115811	+	0.356429i
$59$	−5.32363	−	2.37023i	−0.693078	−	0.308578i	0.0297983	−	0.999556i	$-0.490513\pi$
$59$	−5.32363	−	2.37023i	−0.693078	−	0.308578i	−0.722876	+	0.690978i	$0.757180\pi$
$60$	−9.32103	−	6.77212i	−1.20334	−	0.874278i
$61$	−2.22719			−0.285162			−0.142581	−	0.989783i	$-0.545540\pi$
$61$	−2.22719			−0.285162			−0.142581	+	0.989783i	$0.545540\pi$
$62$		0			0
$63$	−5.79474			−0.730068
$64$	8.21287	+	5.96700i	1.02661	+	0.745875i
$65$	4.47688	+	1.99324i	0.555289	+	0.247231i
$66$	5.86404	+	18.0477i	0.721813	+	2.22151i
$67$	6.80719	−	11.7904i	0.831631	−	1.44043i	−0.0651129	−	0.997878i	$-0.520741\pi$
$67$	6.80719	−	11.7904i	0.831631	−	1.44043i	0.896744	−	0.442550i	$-0.145926\pi$
$68$	2.44059	+	4.22722i	0.295965	+	0.512626i
$69$	4.80118	−	5.33225i	0.577994	−	0.641928i
$70$	−5.52437	+	17.0022i	−0.660288	+	2.03216i
$71$	−0.893908	−	0.992785i	−0.106087	−	0.117822i	0.687762	−	0.725936i	$-0.258593\pi$
$71$	−0.893908	−	0.992785i	−0.106087	−	0.117822i	−0.793850	+	0.608114i	$0.791926\pi$
$72$	0.876721	−	0.390342i	0.103323	−	0.0460022i
$73$	−13.8565	−	2.94528i	−1.62178	−	0.344719i	−0.694615	−	0.719382i	$-0.744425\pi$
$73$	−13.8565	−	2.94528i	−1.62178	−	0.344719i	−0.927161	+	0.374663i	$0.877758\pi$
$74$	0.0594505	−	0.565634i	0.00691099	−	0.0657536i
$75$	−0.114651	−	1.09083i	−0.0132388	−	0.125958i
$76$	1.39104	−	0.295676i	0.159564	−	0.0339163i
$77$	12.7253	−	9.24551i	1.45019	−	1.05362i
$78$	−7.48561	+	5.43861i	−0.847578	+	0.615801i
$79$	8.48701	−	1.80397i	0.954863	−	0.202962i	0.295969	−	0.955198i	$-0.404358\pi$
$79$	8.48701	−	1.80397i	0.954863	−	0.202962i	0.658895	+	0.752235i	$0.271024\pi$
$80$	0.816370	+	7.76724i	0.0912730	+	0.868404i
$81$	1.17533	−	11.1825i	0.130592	−	1.24250i
$82$	8.67065	+	1.84300i	0.957513	+	0.203526i
$83$	4.73717	−	2.10912i	0.519972	−	0.231506i	−0.129932	−	0.991523i	$-0.541476\pi$
$83$	4.73717	−	2.10912i	0.519972	−	0.231506i	0.649904	+	0.760016i	$0.274809\pi$
$84$	−12.0653	−	13.3999i	−1.31643	−	1.46205i
$85$	−1.54403	+	4.75202i	−0.167473	+	0.515429i
$86$	−0.373934	+	0.415296i	−0.0403223	+	0.0447825i
$87$	−1.47342	−	2.55203i	−0.157967	−	0.273607i
$88$	−1.30251	+	2.25601i	−0.138848	+	0.240491i
$89$	−1.54897	−	4.76725i	−0.164191	−	0.505327i	0.834785	−	0.550576i	$-0.185592\pi$
$89$	−1.54897	−	4.76725i	−0.164191	−	0.505327i	−0.998976	+	0.0452489i	$0.985592\pi$
$90$	7.00903	+	3.12062i	0.738816	+	0.328942i
$91$	6.20475	+	4.50802i	0.650435	+	0.472569i
$92$	7.69274			0.802024
$93$		0			0
$94$	11.1463			1.14965
$95$	1.17772	+	0.855663i	0.120831	+	0.0877892i
$96$	−15.8500	−	7.05686i	−1.61768	−	0.720238i
$97$	2.07474	+	6.38538i	0.210657	+	0.648337i	0.999433	+	0.0336562i	$0.0107151\pi$
$97$	2.07474	+	6.38538i	0.210657	+	0.648337i	−0.788776	+	0.614681i	$0.789285\pi$
$98$	−6.73673	+	11.6684i	−0.680512	+	1.17868i
$99$	−3.37528	−	5.84615i	−0.339228	−	0.587560i
$100$	0.786862	−	0.873899i	0.0786862	−	0.0873899i
$101$	−5.58165	+	17.1786i	−0.555395	+	1.70933i	0.139503	+	0.990222i	$0.455450\pi$
$101$	−5.58165	+	17.1786i	−0.555395	+	1.70933i	−0.694898	+	0.719108i	$0.744550\pi$
$102$	−6.31258	−	7.01083i	−0.625038	−	0.694175i
$103$	3.57682	−	1.59250i	0.352435	−	0.156914i	−0.222881	−	0.974846i	$-0.571546\pi$
$103$	3.57682	−	1.59250i	0.352435	−	0.156914i	0.575315	+	0.817932i	$0.304879\pi$
$104$	−1.24242	−	0.264085i	−0.121830	−	0.0258957i
$105$	1.92934	−	18.3565i	0.188285	−	1.79141i
$106$	2.05954	+	19.5952i	0.200040	+	1.90326i
$107$	−10.8727	+	2.31107i	−1.05111	+	0.223419i	−0.700905	−	0.713255i	$-0.747220\pi$
$107$	−10.8727	+	2.31107i	−1.05111	+	0.223419i	−0.350201	+	0.936675i	$0.613887\pi$
$108$	5.64922	−	4.10440i	0.543596	−	0.394946i
$109$	−14.6379	+	10.6350i	−1.40205	+	1.01865i	−0.407633	+	0.913146i	$0.633646\pi$
$109$	−14.6379	+	10.6350i	−1.40205	+	1.01865i	−0.994419	+	0.105505i	$0.966354\pi$
$110$	−20.3709	+	4.32997i	−1.94229	+	0.412846i
$111$	0.0613806	+	0.583997i	0.00582599	+	0.0554306i
$112$	−1.27764	+	12.1559i	−0.120726	+	1.14863i
$113$	−17.1555	−	3.64651i	−1.61385	−	0.343035i	−0.689415	−	0.724367i	$-0.742132\pi$
$113$	−17.1555	−	3.64651i	−1.61385	−	0.343035i	−0.924438	+	0.381332i	$0.875465\pi$
$114$	−2.51095	+	1.11795i	−0.235172	+	0.104705i
$115$	5.26914	+	5.85197i	0.491350	+	0.545699i
$116$	0.976297	−	3.00473i	0.0906469	−	0.278982i
$117$	2.20245	−	2.44606i	0.203616	−	0.226139i
$118$	6.03758	+	10.4574i	0.555804	+	0.962681i
$119$	−3.90988	+	6.77211i	−0.358418	+	0.620798i
$120$	0.944616	+	2.90723i	0.0862312	+	0.265392i
$121$	6.69071	+	2.97890i	0.608246	+	0.270809i
$122$	3.73362	+	2.71263i	0.338026	+	0.245590i
$123$	−9.15213			−0.825220
$124$		0			0
$125$	−10.5358			−0.942352
$126$	9.71419	+	7.05777i	0.865409	+	0.628756i
$127$	12.9708	+	5.77496i	1.15097	+	0.512445i	0.891372	−	0.453272i	$-0.149743\pi$
$127$	12.9708	+	5.77496i	1.15097	+	0.512445i	0.259598	+	0.965717i	$0.416410\pi$
$128$	−1.48821	−	4.58025i	−0.131541	−	0.404841i
$129$	0.288489	−	0.499677i	0.0254000	−	0.0439941i
$130$	−5.07728	−	8.79410i	−0.445307	−	0.771294i
$131$	4.81005	−	5.34211i	0.420256	−	0.466742i	−0.495423	−	0.868652i	$-0.664987\pi$
$131$	4.81005	−	5.34211i	0.420256	−	0.466742i	0.915679	+	0.401910i	$0.131654\pi$
$132$	6.49106	−	19.9774i	0.564974	−	1.73881i
$133$	1.52446	+	1.69309i	0.132188	+	0.146809i
$134$	−25.7717	+	11.4743i	−2.22634	+	0.991230i
$135$	6.99170	+	1.48613i	0.601749	+	0.127906i
$136$	0.135371	−	1.28797i	0.0116080	−	0.110442i
$137$	0.792080	+	7.53614i	0.0676720	+	0.643856i	0.974812	+	0.223027i	$0.0715939\pi$
$137$	0.792080	+	7.53614i	0.0676720	+	0.643856i	−0.907140	+	0.420829i	$0.861739\pi$
$138$	−14.5431	+	3.09123i	−1.23799	+	0.263143i
$139$	−16.2598	+	11.8134i	−1.37914	+	1.00200i	−0.382178	+	0.924089i	$0.624826\pi$
$139$	−16.2598	+	11.8134i	−1.37914	+	1.00200i	−0.996960	+	0.0779138i	$0.975174\pi$
$140$	16.0095	−	11.6316i	1.35305	−	0.983046i
$141$	−11.2567	+	2.39268i	−0.947981	+	0.201500i
$142$	0.289355	+	2.75303i	0.0242822	+	0.231029i
$143$	−0.933915	+	8.88561i	−0.0780979	+	0.743052i
$144$	5.13104	+	1.09064i	0.427587	+	0.0908864i
$145$	2.95445	−	1.31541i	0.245354	−	0.109239i
$146$	19.6415	+	21.8141i	1.62554	+	1.80534i
$147$	4.29869	−	13.2300i	0.354550	−	1.09119i
$148$	−0.421261	+	0.467858i	−0.0346274	+	0.0384577i
$149$	−6.15749	−	10.6651i	−0.504441	−	0.873717i	−0.999987	−	0.00513554i	$-0.998365\pi$
$149$	−6.15749	−	10.6651i	−0.504441	−	0.873717i	0.495546	−	0.868582i	$-0.334968\pi$
$150$	−1.13639	+	1.96829i	−0.0927862	+	0.160710i
$151$	6.14232	+	18.9041i	0.499855	+	1.53840i	0.809252	+	0.587462i	$0.199873\pi$
$151$	6.14232	+	18.9041i	0.499855	+	1.53840i	−0.309397	+	0.950933i	$0.600127\pi$
$152$	−0.344694	−	0.153468i	−0.0279584	−	0.0124479i
$153$	2.71505	+	1.97260i	0.219499	+	0.159475i
$154$	−32.5932			−2.62644
$155$		0			0
$156$	10.2421			0.820023
$157$	4.69603	+	3.41187i	0.374784	+	0.272297i	0.759192	−	0.650867i	$-0.225594\pi$
$157$	4.69603	+	3.41187i	0.374784	+	0.272297i	−0.384408	+	0.923163i	$0.625594\pi$
$158$	−16.4246	−	7.31272i	−1.30667	−	0.581769i
$159$	−6.28627	−	19.3472i	−0.498534	−	1.53433i
$160$	9.52050	−	16.4900i	0.752662	−	1.30365i
$161$	6.16198	+	10.6729i	0.485632	+	0.841139i
$162$	−15.5901	+	17.3146i	−1.22488	+	1.36036i
$163$	5.49535	−	16.9129i	0.430429	−	1.32472i	−0.467270	−	0.884115i	$-0.654762\pi$
$163$	5.49535	−	16.9129i	0.430429	−	1.32472i	0.897699	−	0.440610i	$-0.145238\pi$
$164$	−6.56564	−	7.29188i	−0.512691	−	0.569401i
$165$	19.6431	−	8.74569i	1.52922	−	0.680851i
$166$	−10.5101	−	2.23400i	−0.815745	−	0.173392i
$167$	0.228084	−	2.17008i	0.0176497	−	0.167926i	−0.982146	−	0.188118i	$-0.939761\pi$
$167$	0.228084	−	2.17008i	0.0176497	−	0.167926i	0.999796	+	0.0201925i	$0.00642790\pi$
$168$	0.500068	+	4.75783i	0.0385811	+	0.367074i
$169$	8.45472	−	1.79711i	0.650363	−	0.138239i
$170$	8.37616	−	6.08564i	0.642422	−	0.466747i
$171$	0.791026	−	0.574714i	0.0604912	−	0.0439495i
$172$	0.605072	−	0.128612i	0.0461363	−	0.00980658i
$173$	0.575735	+	5.47775i	0.0437723	+	0.416466i	0.994364	+	0.106021i	$0.0338112\pi$
$173$	0.575735	+	5.47775i	0.0437723	+	0.416466i	−0.950592	+	0.310444i	$0.899522\pi$
$174$	−0.638271	+	6.07275i	−0.0483872	+	0.460374i
$175$	1.84273	+	0.391684i	0.139297	+	0.0296085i
$176$	−13.0080	+	5.79153i	−0.980513	+	0.436553i
$177$	−8.34217	−	9.26491i	−0.627036	−	0.696394i
$178$	−3.20966	+	9.87832i	−0.240574	+	0.740411i
$179$	−8.11916	+	9.01724i	−0.606854	+	0.673980i	−0.965773	−	0.259389i	$-0.916479\pi$
$179$	−8.11916	+	9.01724i	−0.606854	+	0.673980i	0.358919	+	0.933369i	$0.383146\pi$
$180$	−4.24636	−	7.35491i	−0.316505	−	0.548202i
$181$	4.82344	−	8.35444i	0.358523	−	0.620980i	−0.629191	−	0.777251i	$-0.716614\pi$
$181$	4.82344	−	8.35444i	0.358523	−	0.620980i	0.987714	+	0.156270i	$0.0499471\pi$
$182$	−4.91094	−	15.1143i	−0.364023	−	1.12035i
$183$	−4.35289	−	1.93803i	−0.321775	−	0.143263i
$184$	−1.65122	−	1.19968i	−0.121730	−	0.0884418i
$185$	−0.644448			−0.0473808
$186$		0			0
$187$	−9.10960			−0.666160
$188$	−9.98175	−	7.25216i	−0.727994	−	0.528918i
$189$	10.2195	+	4.55002i	0.743359	+	0.330965i
$190$	−0.932141	−	2.86884i	−0.0676246	−	0.208127i
$191$	−5.23270	+	9.06331i	−0.378625	+	0.655798i	−0.990862	−	0.134876i	$-0.956936\pi$
$191$	−5.23270	+	9.06331i	−0.378625	+	0.655798i	0.612237	+	0.790674i	$0.290270\pi$
$192$	10.8592	+	18.8087i	0.783695	+	1.35740i
$193$	−1.19818	+	1.33071i	−0.0862468	+	0.0957868i	−0.784723	−	0.619846i	$-0.787195\pi$
$193$	−1.19818	+	1.33071i	−0.0862468	+	0.0957868i	0.698477	+	0.715633i	$0.253862\pi$
$194$	4.29910	−	13.2313i	0.308658	−	0.949951i
$195$	7.01531	+	7.79129i	0.502377	+	0.557946i
$196$	13.6247	−	6.06613i	0.973196	−	0.433295i
$197$	6.25717	+	1.33000i	0.445805	+	0.0947587i	0.425344	−	0.905032i	$-0.360153\pi$
$197$	6.25717	+	1.33000i	0.445805	+	0.0947587i	0.0204611	+	0.999791i	$0.493487\pi$
$198$	−1.46214	+	13.9113i	−0.103910	+	0.988636i
$199$	0.0969142	+	0.922077i	0.00687007	+	0.0653643i	0.997420	−	0.0717898i	$-0.0228711\pi$
$199$	0.0969142	+	0.922077i	0.00687007	+	0.0653643i	−0.990550	+	0.137154i	$0.956204\pi$
$200$	−0.305182	+	0.0648684i	−0.0215796	+	0.00458689i
$201$	23.5638	−	17.1201i	1.66207	−	1.20756i
$202$	30.2798	−	21.9996i	2.13048	−	1.54788i
$203$	4.95077	−	1.05232i	0.347476	−	0.0738583i
$204$	1.09156	+	10.3855i	0.0764248	+	0.727133i
$205$	1.04990	−	9.98914i	0.0733283	−	0.697672i
$206$	−7.93573	−	1.68679i	−0.552908	−	0.117524i
$207$	4.83179	−	2.15125i	0.335832	−	0.149522i
$208$	−4.64564	−	5.15951i	−0.322117	−	0.357747i
$209$	−0.820151	+	2.52416i	−0.0567310	+	0.174600i
$210$	−25.5918	+	28.4226i	−1.76600	+	1.96135i
$211$	3.09072	+	5.35328i	0.212774	+	0.368535i	0.952582	−	0.304283i	$-0.0984169\pi$
$211$	3.09072	+	5.35328i	0.212774	+	0.368535i	−0.739808	+	0.672818i	$0.765084\pi$
$212$	10.9050	−	18.8880i	0.748957	−	1.29723i
$213$	−0.883191	−	2.71818i	−0.0605152	−	0.186247i
$214$	21.0416	+	9.36833i	1.43838	+	0.640406i
$215$	0.512281	+	0.372194i	0.0349373	+	0.0253834i
$216$	−1.85267			−0.126058
$217$		0			0
$218$	37.4917			2.53926
$219$	−24.5186	−	17.8138i	−1.65681	−	1.20375i
$220$	21.0598	+	9.37644i	1.41985	+	0.632160i
$221$	−1.37258	−	4.22436i	−0.0923295	−	0.284161i
$222$	0.608389	−	1.05376i	0.0408324	−	0.0707238i
$223$	7.94891	+	13.7679i	0.532298	+	0.921968i	0.999289	+	0.0377054i	$0.0120048\pi$
$223$	7.94891	+	13.7679i	0.532298	+	0.921968i	−0.466991	+	0.884262i	$0.654662\pi$
$224$	19.9399	−	22.1455i	1.33229	−	1.47966i
$225$	0.249842	−	0.768936i	0.0166562	−	0.0512624i
$226$	24.3178	+	27.0077i	1.61760	+	1.79652i
$227$	−4.24338	+	1.88927i	−0.281643	+	0.125396i	−0.542697	−	0.839929i	$-0.682597\pi$
$227$	−4.24338	+	1.88927i	−0.281643	+	0.125396i	0.261054	+	0.965324i	$0.415930\pi$
$228$	2.97599	+	0.632566i	0.197090	+	0.0418927i
$229$	−2.02977	+	19.3120i	−0.134131	+	1.27617i	0.695771	+	0.718264i	$0.255063\pi$
$229$	−2.02977	+	19.3120i	−0.134131	+	1.27617i	−0.829902	+	0.557909i	$0.811604\pi$
$230$	−1.70561	−	16.2277i	−0.112464	−	1.07003i
$231$	32.9160	−	6.99650i	2.16571	−	0.460336i
$232$	−0.678147	+	0.492703i	−0.0445225	+	0.0323475i
$233$	11.5273	−	8.37505i	0.755176	−	0.548667i	−0.142251	−	0.989831i	$-0.545434\pi$
$233$	11.5273	−	8.37505i	0.755176	−	0.548667i	0.897427	+	0.441163i	$0.145434\pi$
$234$	−6.67135	+	1.41804i	−0.436120	+	0.0927002i
$235$	−1.32017	−	12.5606i	−0.0861186	−	0.819364i
$236$	1.39716	−	13.2931i	0.0909474	−	0.865307i
$237$	18.1570	+	3.85940i	1.17943	+	0.250695i
$238$	14.8026	−	6.59055i	0.959512	−	0.427202i
$239$	4.55110	+	5.05451i	0.294386	+	0.326949i	0.872135	−	0.489266i	$-0.162735\pi$
$239$	4.55110	+	5.05451i	0.294386	+	0.326949i	−0.577748	+	0.816215i	$0.696068\pi$
$240$	−5.16327	+	15.8909i	−0.333288	+	1.02575i
$241$	7.69843	−	8.54997i	0.495899	−	0.550752i	−0.442291	−	0.896872i	$-0.645834\pi$
$241$	7.69843	−	8.54997i	0.495899	−	0.550752i	0.938190	+	0.346120i	$0.112501\pi$
$242$	−7.58800	−	13.1428i	−0.487775	−	0.844851i
$243$	7.46119	−	12.9232i	0.478636	−	0.829021i
$244$	−1.57861	−	4.85845i	−0.101060	−	0.311030i
$245$	13.9468	+	6.20953i	0.891031	+	0.396712i
$246$	15.3425	+	11.1470i	0.978200	+	0.710704i
$247$	−1.29410			−0.0823413
$248$		0			0
$249$	11.0938			0.703039
$250$	17.6620	+	12.8322i	1.11705	+	0.811581i
$251$	6.66377	+	2.96690i	0.420614	+	0.187269i	0.606119	−	0.795374i	$-0.292726\pi$
$251$	6.66377	+	2.96690i	0.420614	+	0.187269i	−0.185505	+	0.982643i	$0.559392\pi$
$252$	−4.10724	−	12.6408i	−0.258732	−	0.796295i
$253$	−7.17837	+	12.4333i	−0.451300	+	0.781675i
$254$	−14.7103	−	25.4790i	−0.923005	−	1.59869i
$255$	−7.15275	+	7.94394i	−0.447923	+	0.497469i
$256$	3.19031	−	9.81877i	0.199395	−	0.613673i
$257$	−16.4979	−	18.3228i	−1.02911	−	1.14294i	−0.989618	−	0.143722i	$-0.954093\pi$
$257$	−16.4979	−	18.3228i	−1.02911	−	1.14294i	−0.0394914	−	0.999220i	$-0.512574\pi$
$258$	−1.09221	+	0.486281i	−0.0679977	+	0.0302745i
$259$	−0.986537	−	0.209695i	−0.0613005	−	0.0130298i
$260$	−1.17494	+	11.1788i	−0.0728665	+	0.693278i
$261$	−0.227055	−	2.16028i	−0.0140543	−	0.133718i
$262$	−14.5700	+	3.09694i	−0.900136	+	0.191330i
$263$	−21.2666	+	15.4511i	−1.31136	+	0.952757i	−0.311360	+	0.950292i	$0.600785\pi$
$263$	−21.2666	+	15.4511i	−1.31136	+	0.952757i	−0.999997	+	0.00246465i	$0.999215\pi$
$264$	−4.50877	+	3.27581i	−0.277495	+	0.201612i
$265$	21.8377	−	4.64174i	1.34148	−	0.285140i
$266$	−0.493464	−	4.69499i	−0.0302562	−	0.287869i
$267$	1.12095	−	10.6651i	0.0686010	−	0.652695i
$268$	30.5448	+	6.49249i	1.86582	+	0.396592i
$269$	19.0746	−	8.49258i	1.16300	−	0.517802i	0.267805	−	0.963473i	$-0.413702\pi$
$269$	19.0746	−	8.49258i	1.16300	−	0.517802i	0.895197	+	0.445672i	$0.147035\pi$
$270$	−9.91070	−	11.0069i	−0.603146	−	0.669861i
$271$	6.49271	−	19.9825i	0.394404	−	1.21385i	−0.535021	−	0.844839i	$-0.679696\pi$
$271$	6.49271	−	19.9825i	0.394404	−	1.21385i	0.929425	−	0.369012i	$-0.120304\pi$
$272$	4.73666	−	5.26059i	0.287202	−	0.318970i
$273$	8.20403	+	14.2098i	0.496530	+	0.860016i
$274$	7.85091	−	13.5982i	0.474291	−	0.821496i
$275$	0.678179	+	2.08722i	0.0408958	+	0.125864i
$276$	15.0349	+	6.69399i	0.904997	+	0.402931i
$277$	−3.85034	−	2.79744i	−0.231345	−	0.168082i	0.466074	−	0.884746i	$-0.345668\pi$
$277$	−3.85034	−	2.79744i	−0.231345	−	0.168082i	−0.697418	+	0.716664i	$0.745668\pi$
$278$	41.6459			2.49776
$279$		0			0
$280$	−5.25032			−0.313767
$281$	5.38386	+	3.91160i	0.321174	+	0.233347i	0.736676	−	0.676246i	$-0.236394\pi$
$281$	5.38386	+	3.91160i	0.321174	+	0.233347i	−0.415502	+	0.909592i	$0.636394\pi$
$282$	21.7846	+	9.69914i	1.29726	+	0.577576i
$283$	−2.23921	−	6.89159i	−0.133107	−	0.409662i	0.862183	−	0.506596i	$-0.169096\pi$
$283$	−2.23921	−	6.89159i	−0.133107	−	0.409662i	−0.995291	+	0.0969338i	$0.969096\pi$
$284$	1.53210	−	2.65367i	0.0909132	−	0.157466i
$285$	1.55720	+	2.69715i	0.0922406	+	0.159765i
$286$	12.3879	−	13.7582i	0.732514	−	0.813539i
$287$	4.85755	−	14.9500i	0.286732	−	0.882471i
$288$	−8.55755	−	9.50412i	−0.504258	−	0.560036i
$289$	−11.3930	+	5.07250i	−0.670178	+	0.298383i
$290$	−6.55491	−	1.39329i	−0.384917	−	0.0818167i
$291$	−1.50143	+	14.2852i	−0.0880154	+	0.837411i
$292$	−3.39638	−	32.3144i	−0.198758	−	1.89106i
$293$	−13.2163	+	2.80920i	−0.772102	+	0.164115i	−0.577085	−	0.816684i	$-0.695810\pi$
$293$	−13.2163	+	2.80920i	−0.772102	+	0.164115i	−0.195018	+	0.980800i	$0.562476\pi$
$294$	−23.3199	+	16.9429i	−1.36004	+	0.988131i
$295$	11.0692	−	8.04226i	0.644475	−	0.468238i
$296$	0.163385	−	0.0347285i	0.00949654	−	0.00201855i
$297$	1.36220	+	12.9604i	0.0790427	+	0.752041i
$298$	−2.66737	+	25.3783i	−0.154517	+	1.47013i
$299$	−6.84723	−	1.45542i	−0.395986	−	0.0841694i
$300$	2.29831	−	1.02327i	0.132693	−	0.0590786i
$301$	0.663106	+	0.736453i	0.0382208	+	0.0424485i
$302$	12.7276	−	39.1716i	0.732393	−	2.25407i
$303$	−25.8572	+	28.7173i	−1.48546	+	1.64977i
$304$	−1.03120	−	1.78609i	−0.0591434	−	0.102439i
$305$	2.61462	−	4.52866i	0.149713	−	0.259310i
$306$	−2.14891	−	6.61367i	−0.122845	−	0.378078i
$307$	−20.7611	−	9.24343i	−1.18490	−	0.527550i	−0.282840	−	0.959167i	$-0.591277\pi$
$307$	−20.7611	−	9.24343i	−1.18490	−	0.527550i	−0.902057	+	0.431617i	$0.857943\pi$
$308$	29.1880	+	21.2063i	1.66314	+	1.20834i
$309$	8.37640			0.476517
$310$		0			0
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	−2.19843	−	1.59725i	−0.124462	−	0.0904266i
$313$	−25.6679	−	11.4281i	−1.45084	−	0.645954i	−0.478193	−	0.878255i	$-0.658708\pi$
$313$	−25.6679	−	11.4281i	−1.45084	−	0.645954i	−0.972644	+	0.232300i	$0.925375\pi$
$314$	−3.71682	−	11.4392i	−0.209752	−	0.645551i
$315$	6.80276	−	11.7827i	0.383292	−	0.663882i
$316$	9.95072	+	17.2352i	0.559772	+	0.969553i
$317$	−10.5835	+	11.7542i	−0.594430	+	0.660181i	−0.963026	−	0.269408i	$-0.913172\pi$
$317$	−10.5835	+	11.7542i	−0.594430	+	0.660181i	0.368596	+	0.929590i	$0.379839\pi$
$318$	−13.0259	+	40.0896i	−0.730457	+	2.24812i
$319$	3.94535	+	4.38175i	0.220897	+	0.245331i
$320$	−21.7745	+	9.69465i	−1.21723	+	0.541948i
$321$	−23.2610	−	4.94428i	−1.29830	−	0.275963i
$322$	2.66932	−	25.3968i	0.148755	−	1.41531i
$323$	−0.137920	−	1.31222i	−0.00767408	−	0.0730140i
$324$	25.2268	−	5.36212i	1.40149	−	0.297896i
$325$	−0.865715	+	0.628979i	−0.0480212	+	0.0348895i
$326$	−29.8116	+	21.6594i	−1.65111	+	1.19960i
$327$	−37.8629	+	8.04802i	−2.09383	+	0.445056i
$328$	0.272124	+	2.58909i	0.0150256	+	0.142959i
$329$	2.06610	−	19.6577i	0.113908	−	1.08376i
$330$	−43.5813	−	9.26350i	−2.39907	−	0.509939i
$331$	−11.8250	+	5.26485i	−0.649963	+	0.289382i	−0.705112	−	0.709096i	$-0.749103\pi$
$331$	−11.8250	+	5.26485i	−0.649963	+	0.289382i	0.0551489	+	0.998478i	$0.482437\pi$
$332$	7.95855	+	8.83887i	0.436782	+	0.485096i
$333$	−0.133758	+	0.411664i	−0.00732988	+	0.0225591i
$334$	−3.02543	+	3.36008i	−0.165544	+	0.183855i
$335$	15.9827	+	27.6828i	0.873228	+	1.51247i
$336$	−13.0748	+	22.6462i	−0.713287	+	1.23545i
$337$	8.61116	+	26.5024i	0.469080	+	1.44368i	0.853778	+	0.520637i	$0.174306\pi$
$337$	8.61116	+	26.5024i	0.469080	+	1.44368i	−0.384698	+	0.923042i	$0.625694\pi$
$338$	−16.3621	−	7.28489i	−0.889983	−	0.396246i
$339$	−30.3561	−	22.0550i	−1.64872	−	1.19786i
$340$	−11.4606			−0.621537
$341$		0			0
$342$	−2.02604			−0.109556
$343$	−1.47969	−	1.07506i	−0.0798956	−	0.0580476i
$344$	−0.149934	−	0.0667549i	−0.00808389	−	0.00359918i
$345$	5.20597	+	16.0223i	0.280280	+	0.862612i
$346$	5.70655	−	9.88403i	0.306786	−	0.531369i
$347$	2.66175	+	4.61029i	0.142890	+	0.247493i	0.928584	−	0.371123i	$-0.121027\pi$
$347$	2.66175	+	4.61029i	0.142890	+	0.247493i	−0.785693	+	0.618616i	$0.787694\pi$
$348$	4.52273	−	5.02300i	0.242444	−	0.269261i
$349$	−1.26632	+	3.89734i	−0.0677847	+	0.208620i	−0.979211	−	0.202843i	$-0.934982\pi$
$349$	−1.26632	+	3.89734i	−0.0677847	+	0.208620i	0.911427	+	0.411463i	$0.134982\pi$
$350$	−2.61206	−	2.90098i	−0.139620	−	0.155064i
$351$	−5.80484	+	2.58448i	−0.309840	+	0.137949i
$352$	33.9564	+	7.21765i	1.80988	+	0.384702i
$353$	2.27761	−	21.6700i	0.121225	−	1.15338i	−0.749637	−	0.661849i	$-0.769772\pi$
$353$	2.27761	−	21.6700i	0.121225	−	1.15338i	0.870862	−	0.491528i	$-0.163562\pi$
$354$	2.70034	+	25.6920i	0.143521	+	1.36551i
$355$	3.06809	−	0.652142i	0.162837	−	0.0346121i
$356$	9.30151	−	6.75794i	0.492979	−	0.358170i
$357$	−13.5345	+	9.83337i	−0.716320	+	0.520437i
$358$	24.5935	−	5.22750i	1.29980	−	0.276282i
$359$	0.740211	+	7.04264i	0.0390668	+	0.371696i	0.996536	+	0.0831610i	$0.0265016\pi$
$359$	0.740211	+	7.04264i	0.0390668	+	0.371696i	−0.957469	+	0.288535i	$0.906832\pi$
$360$	−0.235531	+	2.24093i	−0.0124136	+	0.118107i
$361$	18.2088	+	3.87040i	0.958357	+	0.203705i
$362$	−18.2613	+	8.13046i	−0.959793	+	0.427327i
$363$	10.4844	+	11.6441i	0.550288	+	0.611156i
$364$	−5.43605	+	16.7304i	−0.284927	+	0.876914i
$365$	22.2557	−	24.7174i	1.16491	−	1.29377i
$366$	4.93665	+	8.55053i	0.258043	+	0.446943i
$367$	−8.05884	+	13.9583i	−0.420668	+	0.728619i	−0.996005	−	0.0892980i	$-0.971538\pi$
$367$	−8.05884	+	13.9583i	−0.420668	+	0.728619i	0.575337	+	0.817917i	$0.304871\pi$
$368$	−3.44747	−	10.6102i	−0.179712	−	0.553096i
$369$	−6.16301	−	2.74395i	−0.320833	−	0.142844i
$370$	1.08034	+	0.784913i	0.0561642	+	0.0408057i
$371$	34.9401			1.81400
$372$		0			0
$373$	−9.81895			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$373$	−9.81895			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$374$	15.2712	+	11.0951i	0.789653	+	0.573716i
$375$	−20.5915	−	9.16793i	−1.06334	−	0.473430i
$376$	1.01157	+	3.11331i	0.0521680	+	0.160557i
$377$	−1.43747	+	2.48977i	−0.0740335	+	0.128230i
$378$	−11.5900	−	20.0745i	−0.596127	−	1.03252i
$379$	−9.24446	+	10.2670i	−0.474856	+	0.527381i	−0.932217	−	0.361900i	$-0.882128\pi$
$379$	−9.24446	+	10.2670i	−0.474856	+	0.527381i	0.457361	+	0.889281i	$0.348795\pi$
$380$	−1.03181	+	3.17559i	−0.0529309	+	0.162904i
$381$	20.3253	+	22.5735i	1.04130	+	1.15648i
$382$	19.8108	−	8.82032i	1.01361	−	0.451287i
$383$	10.0808	+	2.14274i	0.515105	+	0.109489i	0.458128	−	0.888886i	$-0.348520\pi$
$383$	10.0808	+	2.14274i	0.515105	+	0.109489i	0.0569778	+	0.998375i	$0.481854\pi$
$384$	1.07698	−	10.2468i	0.0549594	−	0.522904i
$385$	3.86036	+	36.7289i	0.196742	+	1.87188i
$386$	3.62936	−	0.771445i	0.184730	−	0.0392655i
$387$	0.344078	−	0.249987i	0.0174905	−	0.0127076i
$388$	−12.4587	+	9.05177i	−0.632494	+	0.459534i
$389$	−24.8111	+	5.27377i	−1.25797	+	0.267391i	−0.788213	−	0.615403i	$-0.788993\pi$
$389$	−24.8111	+	5.27377i	−1.25797	+	0.267391i	−0.469761	+	0.882794i	$0.655660\pi$
$390$	−2.27084	−	21.6056i	−0.114988	−	1.09404i
$391$	0.746057	−	7.09826i	0.0377297	−	0.358974i
$392$	−3.87052	−	0.822704i	−0.195491	−	0.0415528i
$393$	14.0495	−	6.25522i	0.708701	−	0.315534i
$394$	−8.86951	−	9.85059i	−0.446839	−	0.496265i
$395$	−6.29527	+	19.3749i	−0.316749	+	0.974855i
$396$	10.3606	−	11.5066i	0.520639	−	0.578229i
$397$	−8.37941	−	14.5136i	−0.420550	−	0.728415i	0.575443	−	0.817842i	$-0.304830\pi$
$397$	−8.37941	−	14.5136i	−0.420550	−	0.728415i	−0.995993	+	0.0894272i	$0.971496\pi$
$398$	0.960590	−	1.66379i	0.0481500	−	0.0833983i
$399$	1.50618	+	4.63556i	0.0754035	+	0.232068i
$400$	−1.55795	−	0.693645i	−0.0778977	−	0.0346823i
$401$	−22.3479	−	16.2367i	−1.11600	−	0.810823i	−0.132404	−	0.991196i	$-0.542270\pi$
$401$	−22.3479	−	16.2367i	−1.11600	−	0.810823i	−0.983598	+	0.180372i	$0.942270\pi$
$402$	−60.3537			−3.01017
$403$		0			0
$404$	−41.4300			−2.06122
$405$	21.3581	+	15.5176i	1.06129	+	0.771075i
$406$	−9.58106	−	4.26576i	−0.475500	−	0.211706i
$407$	−0.363076	−	1.11743i	−0.0179970	−	0.0553891i
$408$	1.38532	−	2.39945i	0.0685838	−	0.118791i
$409$	−11.3053	−	19.5814i	−0.559013	−	0.968239i	−0.997579	−	0.0695399i	$-0.977847\pi$
$409$	−11.3053	−	19.5814i	−0.559013	−	0.968239i	0.438566	−	0.898699i	$-0.355486\pi$
$410$	−13.9264	+	15.4669i	−0.687778	+	0.763854i
$411$	−5.00965	+	15.4181i	−0.247108	+	0.760519i
$412$	6.00914	+	6.67383i	0.296049	+	0.328796i
$413$	19.5619	−	8.70952i	0.962578	−	0.428567i
$414$	−10.7201	−	2.27862i	−0.526862	−	0.111988i
$415$	−1.27264	+	12.1083i	−0.0624714	+	0.594375i
$416$	1.76932	+	16.8340i	0.0867481	+	0.825353i
$417$	−42.0583	+	8.93978i	−2.05961	+	0.437783i
$418$	4.44922	−	3.23255i	0.217619	−	0.158109i
$419$	5.00860	−	3.63896i	0.244686	−	0.177775i	−0.458682	−	0.888600i	$-0.651678\pi$
$419$	5.00860	−	3.63896i	0.244686	−	0.177775i	0.703368	+	0.710825i	$0.251678\pi$
$420$	41.4108	−	8.80214i	2.02064	−	0.429500i
$421$	−0.685637	−	6.52340i	−0.0334159	−	0.317931i	−0.998443	−	0.0557811i	$-0.982235\pi$
$421$	−0.685637	−	6.52340i	−0.0334159	−	0.317931i	0.965027	−	0.262150i	$-0.0844316\pi$
$422$	1.33887	−	12.7385i	0.0651753	−	0.620102i
$423$	−8.29754	−	1.76370i	−0.403440	−	0.0857539i
$424$	−5.28630	+	2.35361i	−0.256725	+	0.114301i
$425$	−0.730053	−	0.810806i	−0.0354128	−	0.0393299i
$426$	−1.83008	+	5.63240i	−0.0886676	+	0.272891i
$427$	5.47609	−	6.08182i	0.265007	−	0.294320i
$428$	−12.7479	−	22.0800i	−0.616192	−	1.06728i
$429$	−9.55725	+	16.5536i	−0.461428	+	0.799217i
$430$	−0.405460	−	1.24788i	−0.0195530	−	0.0601780i
$431$	21.4388	+	9.54518i	1.03267	+	0.459775i	0.851875	−	0.523746i	$-0.175466\pi$
$431$	21.4388	+	9.54518i	1.03267	+	0.459775i	0.180797	+	0.983520i	$0.442132\pi$
$432$	−8.19266	−	5.95232i	−0.394170	−	0.286381i
$433$	−24.3130			−1.16841			−0.584203	−	0.811607i	$-0.698593\pi$
$433$	−24.3130			−1.16841			−0.584203	+	0.811607i	$0.698593\pi$
$434$		0			0
$435$	6.91890			0.331736
$436$	−33.5747	−	24.3934i	−1.60793	−	1.16823i
$437$	−1.89968	−	0.845790i	−0.0908738	−	0.0404596i
$438$	19.4060	+	59.7255i	0.927254	+	2.85379i
$439$	−7.25318	+	12.5629i	−0.346175	+	0.599593i	−0.985567	−	0.169288i	$-0.945853\pi$
$439$	−7.25318	+	12.5629i	−0.346175	+	0.599593i	0.639391	+	0.768881i	$0.279186\pi$
$440$	−3.05817	−	5.29690i	−0.145792	−	0.252520i
$441$	6.86128	−	7.62023i	0.326728	−	0.362868i
$442$	−2.84415	+	8.75338i	−0.135282	+	0.416356i
$443$	−11.0848	−	12.3109i	−0.526655	−	0.584910i	0.419852	−	0.907593i	$-0.362082\pi$
$443$	−11.0848	−	12.3109i	−0.526655	−	0.584910i	−0.946507	+	0.322683i	$0.895415\pi$
$444$	−1.23044	+	0.547828i	−0.0583941	+	0.0259987i
$445$	11.5119	+	2.44693i	0.545717	+	0.115996i
$446$	3.44340	−	32.7617i	0.163050	−	1.55131i
$447$	−2.75396	−	26.2022i	−0.130258	−	1.23932i
$448$	−36.4876	+	7.75567i	−1.72388	+	0.366421i
$449$	5.51532	−	4.00712i	0.260284	−	0.189107i	−0.449988	−	0.893035i	$-0.648572\pi$
$449$	5.51532	−	4.00712i	0.260284	−	0.189107i	0.710272	+	0.703927i	$0.248572\pi$
$450$	−1.35537	+	0.984731i	−0.0638926	+	0.0464207i
$451$	17.9121	−	3.80732i	0.843446	−	0.179280i
$452$	−4.20502	−	40.0080i	−0.197787	−	1.88182i
$453$	−4.44503	+	42.2917i	−0.208846	+	1.98704i
$454$	9.41459	+	2.00113i	0.441849	+	0.0939178i
$455$	−16.4505	+	7.32423i	−0.771211	+	0.343365i
$456$	−0.540138	−	0.599884i	−0.0252943	−	0.0280921i
$457$	−6.62154	+	20.3790i	−0.309742	+	0.953289i	0.668122	+	0.744051i	$0.267098\pi$
$457$	−6.62154	+	20.3790i	−0.309742	+	0.953289i	−0.977865	+	0.209238i	$0.932902\pi$
$458$	26.9240	−	29.9021i	1.25807	−	1.39723i
$459$	−3.23934	−	5.61070i	−0.151200	−	0.261885i
$460$	−9.03094	+	15.6420i	−0.421070	+	0.729314i
$461$	2.68057	+	8.24994i	0.124847	+	0.384238i	0.993873	−	0.110527i	$-0.0352540\pi$
$461$	2.68057	+	8.24994i	0.124847	+	0.384238i	−0.869027	+	0.494766i	$0.835254\pi$
$462$	−63.7012	−	28.3616i	−2.96365	−	1.31950i
$463$	2.95281	+	2.14534i	0.137229	+	0.0997025i	0.654282	−	0.756251i	$-0.272971\pi$
$463$	2.95281	+	2.14534i	0.137229	+	0.0997025i	−0.517053	+	0.855953i	$0.672971\pi$
$464$	−4.58180			−0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	2.49267	+	1.81103i	0.115347	+	0.0838045i	0.643963	−	0.765056i	$-0.277289\pi$
$467$	2.49267	+	1.81103i	0.115347	+	0.0838045i	−0.528616	+	0.848861i	$0.677289\pi$
$468$	6.89698	+	3.07073i	0.318813	+	0.141945i
$469$	15.4591	+	47.5782i	0.713834	+	2.19696i
$470$	−13.0852	+	22.6643i	−0.603577	+	1.04543i
$471$	6.20917	+	10.7546i	0.286104	+	0.495546i
$472$	−2.37295	+	2.63543i	−0.109224	+	0.121306i
$473$	−0.356747	+	1.09795i	−0.0164032	+	0.0504839i
$474$	−25.7375	−	28.5844i	−1.18216	−	1.31293i
$475$	−0.290393	+	0.129291i	−0.0133241	+	0.00593229i
$476$	−17.5441	−	3.72912i	−0.804134	−	0.170924i
$477$	1.56742	−	14.9130i	0.0717673	−	0.682820i
$478$	−1.47318	−	14.0164i	−0.0673817	−	0.641094i
$479$	17.0298	−	3.61979i	0.778110	−	0.165392i	0.198297	−	0.980142i	$-0.436459\pi$
$479$	17.0298	−	3.61979i	0.778110	−	0.165392i	0.579813	+	0.814750i	$0.303126\pi$
$480$	32.9562	−	23.9441i	1.50424	−	1.09289i
$481$	0.463476	−	0.336735i	0.0211327	−	0.0153538i
$482$	−23.3190	+	4.95662i	−1.06215	+	0.225768i
$483$	2.75597	+	26.2213i	0.125401	+	1.19311i
$484$	−1.75594	+	16.7067i	−0.0798157	+	0.759395i
$485$	−15.4194	−	3.27749i	−0.700157	−	0.148823i
$486$	−28.2477	+	12.5767i	−1.28134	+	0.570491i
$487$	−19.2533	−	21.3830i	−0.872451	−	0.968955i	0.127287	−	0.991866i	$-0.459373\pi$
$487$	−19.2533	−	21.3830i	−0.872451	−	0.968955i	−0.999738	+	0.0229112i	$0.992706\pi$
$488$	−0.418832	+	1.28903i	−0.0189596	+	0.0583518i
$489$	25.4574	−	28.2733i	1.15122	−	1.27856i
$490$	−15.8172	−	27.3963i	−0.714550	−	1.23764i
$491$	−4.91284	+	8.50929i	−0.221713	+	0.384019i	−0.955328	−	0.295546i	$-0.904498\pi$
$491$	−4.91284	+	8.50929i	−0.221713	+	0.384019i	0.733615	+	0.679565i	$0.237832\pi$
$492$	−6.48693	−	19.9647i	−0.292453	−	0.900078i
$493$	−2.67785	−	1.19225i	−0.120604	−	0.0536964i
$494$	2.16940	+	1.57616i	0.0976058	+	0.0709148i
$495$	15.8497			0.712391
$496$		0			0
$497$	4.90891			0.220195
$498$	−18.5974	−	13.5118i	−0.833369	−	0.605478i
$499$	9.91015	+	4.41228i	0.443639	+	0.197521i	0.616384	−	0.787446i	$-0.288597\pi$
$499$	9.91015	+	4.41228i	0.443639	+	0.197521i	−0.172745	+	0.984967i	$0.555264\pi$
$500$	−7.46766	−	22.9831i	−0.333964	−	1.02784i
$501$	2.33411	−	4.04280i	0.104280	−	0.180619i
$502$	−7.55745	−	13.0899i	−0.337305	−	0.584230i
$503$	5.72839	−	6.36202i	0.255416	−	0.283669i	−0.601776	−	0.798665i	$-0.705540\pi$
$503$	5.72839	−	6.36202i	0.255416	−	0.283669i	0.857192	+	0.514996i	$0.172207\pi$
$504$	−1.08973	+	3.35383i	−0.0485402	+	0.149391i
$505$	−28.3774	−	31.5163i	−1.26278	−	1.40246i
$506$	27.1770	−	12.1000i	1.20816	−	0.537909i
$507$	18.0879	+	3.84471i	0.803314	+	0.170750i
$508$	−3.40412	+	32.3880i	−0.151033	+	1.43699i
$509$	−4.13748	−	39.3655i	−0.183391	−	1.74484i	−0.569140	−	0.822241i	$-0.692724\pi$
$509$	−4.13748	−	39.3655i	−0.183391	−	1.74484i	0.385749	−	0.922604i	$-0.373943\pi$
$510$	21.6662	−	4.60528i	0.959394	−	0.203925i
$511$	42.1123	−	30.5963i	1.86294	−	1.35350i
$512$	−25.0995	+	18.2358i	−1.10925	+	0.805918i
$513$	−1.84630	+	0.392444i	−0.0815163	+	0.0173268i
$514$	5.34032	+	50.8097i	0.235551	+	2.24112i
$515$	−0.960912	+	9.14246i	−0.0423428	+	0.402865i
$516$	1.29449	+	0.275152i	0.0569866	+	0.0121129i
$517$	21.0355	−	9.36563i	0.925142	−	0.411900i
$518$	1.39841	+	1.55309i	0.0614427	+	0.0682391i
$519$	−3.64134	+	11.2069i	−0.159837	+	0.491927i
$520$	1.99553	−	2.21626i	0.0875096	−	0.0971893i
$521$	0.674660	+	1.16855i	0.0295574	+	0.0511949i	0.880426	−	0.474184i	$-0.157257\pi$
$521$	0.674660	+	1.16855i	0.0295574	+	0.0511949i	−0.850868	+	0.525379i	$0.823924\pi$
$522$	−2.25051	+	3.89800i	−0.0985022	+	0.170611i
$523$	−8.79861	−	27.0793i	−0.384736	−	1.18410i	−0.936671	−	0.350210i	$-0.886110\pi$
$523$	−8.79861	−	27.0793i	−0.384736	−	1.18410i	0.551935	−	0.833887i	$-0.313890\pi$
$524$	15.0627	+	6.70636i	0.658018	+	0.292969i
$525$	3.26065	+	2.36900i	0.142306	+	0.103392i
$526$	54.4699			2.37500
$527$		0			0
$528$	−30.4628			−1.32572
$529$	9.50718	+	6.90737i	0.413356	+	0.300320i
$530$	−42.2618	−	18.8161i	−1.83573	−	0.817321i
$531$	−2.83982	−	8.74006i	−0.123238	−	0.379286i
$532$	−2.61282	+	4.52554i	−0.113280	+	0.196207i
$533$	4.46443	+	7.73262i	0.193376	+	0.334937i
$534$	−14.8689	+	16.5135i	−0.643439	+	0.714611i
$535$	8.06488	−	24.8211i	0.348675	−	1.07311i
$536$	−5.54383	−	6.15705i	−0.239457	−	0.265944i
$537$	−23.7149	+	10.5585i	−1.02337	+	0.455634i
$538$	−42.3200	−	8.99540i	−1.82455	−	0.387819i
$539$	−2.90943	+	27.6813i	−0.125318	+	1.19232i
$540$	1.71375	+	16.3052i	0.0737480	+	0.701665i
$541$	13.9969	−	2.97513i	0.601774	−	0.127911i	0.103056	−	0.994676i	$-0.467138\pi$
$541$	13.9969	−	2.97513i	0.601774	−	0.127911i	0.498718	+	0.866765i	$0.333804\pi$
$542$	−35.2222	+	25.5904i	−1.51292	+	1.09920i
$543$	16.6968	−	12.1310i	0.716530	−	0.520590i
$544$	−16.8812	+	3.58821i	−0.723775	+	0.153843i
$545$	−4.44054	−	42.2489i	−0.190212	−	1.80975i
$546$	3.55391	−	33.8132i	0.152094	−	1.44707i
$547$	−41.4411	−	8.80858i	−1.77189	−	0.376628i	−0.797826	−	0.602887i	$-0.794017\pi$
$547$	−41.4411	−	8.80858i	−1.77189	−	0.376628i	−0.974067	+	0.226260i	$0.927350\pi$
$548$	−15.8781	+	7.06939i	−0.678280	+	0.301990i
$549$	−2.35016	−	2.61012i	−0.100303	−	0.111397i
$550$	1.40527	−	4.32498i	0.0599209	−	0.184418i
$551$	−0.571450	+	0.634660i	−0.0243446	+	0.0270374i
$552$	−2.18327	−	3.78154i	−0.0929263	−	0.160953i
$553$	−15.9413	+	27.6111i	−0.677893	+	1.17414i
$554$	3.04747	+	9.37914i	0.129474	+	0.398481i
$555$	−1.25953	−	0.560779i	−0.0534640	−	0.0238037i
$556$	−37.2949	−	27.0963i	−1.58166	−	1.14914i
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$		0			0
$559$	−0.562902			−0.0238082
$560$	−23.2174	−	16.8684i	−0.981114	−	0.712821i
$561$	−17.8041	−	7.92689i	−0.751689	−	0.334674i
$562$	−4.26122	−	13.1147i	−0.179749	−	0.553209i
$563$	−2.59399	+	4.49293i	−0.109324	+	0.189354i	−0.915497	−	0.402326i	$-0.868202\pi$
$563$	−2.59399	+	4.49293i	−0.109324	+	0.189354i	0.806173	+	0.591680i	$0.201535\pi$
$564$	−13.1980	−	22.8597i	−0.555737	−	0.962565i
$565$	27.5544	−	30.6023i	1.15922	−	1.28745i
$566$	−4.63992	+	14.2802i	−0.195030	+	0.600242i
$567$	27.6463	+	30.7044i	1.16104	+	1.28946i
$568$	−0.742699	+	0.330671i	−0.0311630	+	0.0138746i
$569$	2.31609	+	0.492300i	0.0970954	+	0.0206383i	0.256203	−	0.966623i	$-0.417528\pi$
$569$	2.31609	+	0.492300i	0.0970954	+	0.0206383i	−0.159108	+	0.987261i	$0.550862\pi$
$570$	0.674566	−	6.41806i	0.0282544	−	0.268823i
$571$	2.12840	+	20.2504i	0.0890708	+	0.847452i	0.944274	+	0.329160i	$0.106765\pi$
$571$	2.12840	+	20.2504i	0.0890708	+	0.847452i	−0.855203	+	0.518293i	$0.826568\pi$
$572$	−20.0452	+	4.26075i	−0.838134	+	0.178151i
$573$	−18.1136	+	13.1603i	−0.756705	+	0.549778i
$574$	−26.3517	+	19.1456i	−1.09990	+	0.799122i
$575$	−1.68192	+	0.357503i	−0.0701408	+	0.0149089i
$576$	1.67341	+	15.9214i	0.0697254	+	0.663393i
$577$	−2.67402	+	25.4416i	−0.111321	+	1.05915i	0.786138	+	0.618051i	$0.212077\pi$
$577$	−2.67402	+	25.4416i	−0.111321	+	1.05915i	−0.897459	+	0.441097i	$0.854589\pi$
$578$	25.2772	+	5.37283i	1.05139	+	0.223480i
$579$	−3.49970	+	1.55817i	−0.145443	+	0.0647553i
$580$	4.96355	+	5.51258i	0.206100	+	0.228897i
$581$	−5.88809	+	18.1217i	−0.244279	+	0.751814i
$582$	19.9158	−	22.1187i	0.825534	−	0.916849i
$583$	20.3516	+	35.2501i	0.842879	+	1.45991i
$584$	−4.31041	+	7.46585i	−0.178366	+	0.308939i
$585$	2.38813	+	7.34992i	0.0987371	+	0.303882i
$586$	25.5770	+	11.3876i	1.05658	+	0.470418i
$587$	32.3299	+	23.4890i	1.33440	+	0.969495i	0.999630	+	0.0271941i	$0.00865722\pi$
$587$	32.3299	+	23.4890i	1.33440	+	0.969495i	0.334766	+	0.942301i	$0.391343\pi$
$588$	31.9072			1.31583
$589$		0			0
$590$	−28.3514			−1.16721
$591$	11.0719	+	8.04419i	0.455436	+	0.330894i
$592$	0.834079	+	0.371356i	0.0342804	+	0.0152626i
$593$	−6.48230	−	19.9505i	−0.266196	−	0.819268i	−0.991415	−	0.130750i	$-0.958262\pi$
$593$	−6.48230	−	19.9505i	−0.266196	−	0.819268i	0.725219	−	0.688518i	$-0.241738\pi$
$594$	13.5018	−	23.3857i	0.553984	−	0.959529i
$595$	−9.18005	−	15.9003i	−0.376345	−	0.651849i
$596$	18.9007	−	20.9914i	0.774204	−	0.859841i
$597$	−0.612951	+	1.88647i	−0.0250864	+	0.0772080i
$598$	9.70593	+	10.7795i	0.396905	+	0.440807i
$599$	19.1309	−	8.51762i	0.781667	−	0.348020i	0.0231989	−	0.999731i	$-0.492615\pi$
$599$	19.1309	−	8.51762i	0.781667	−	0.348020i	0.758468	+	0.651710i	$0.225948\pi$
$600$	−0.652903	−	0.138779i	−0.0266547	−	0.00566562i
$601$	−1.73712	+	16.5276i	−0.0708588	+	0.674176i	0.900223	+	0.435429i	$0.143403\pi$
$601$	−1.73712	+	16.5276i	−0.0708588	+	0.674176i	−0.971082	+	0.238747i	$0.923263\pi$
$602$	−0.214645	−	2.04221i	−0.00874829	−	0.0832345i
$603$	21.0007	−	4.46383i	0.855213	−	0.181781i
$604$	−36.8843	+	26.7980i	−1.50080	+	1.09040i
$605$	−13.9117	+	10.1075i	−0.565592	+	0.410927i
$606$	78.3232	−	16.6481i	3.18166	−	0.676283i
$607$	−3.08896	−	29.3895i	−0.125377	−	1.19288i	−0.858510	−	0.512797i	$-0.828610\pi$
$607$	−3.08896	−	29.3895i	−0.125377	−	1.19288i	0.733133	−	0.680085i	$-0.238057\pi$
$608$	−0.525587	+	5.00063i	−0.0213154	+	0.202802i
$609$	10.5916	+	2.25132i	0.429195	+	0.0912282i
$610$	−9.89883	+	4.40724i	−0.400792	+	0.178444i
$611$	7.51259	+	8.34357i	0.303927	+	0.337545i
$612$	−2.37869	+	7.32085i	−0.0961528	+	0.295928i
$613$	−24.8246	+	27.5706i	−1.00266	+	1.11356i	−0.00913195	+	0.999958i	$0.502907\pi$
$613$	−24.8246	+	27.5706i	−1.00266	+	1.11356i	−0.993526	+	0.113606i	$0.963760\pi$
$614$	23.5453	+	40.7817i	0.950212	+	1.64582i
$615$	10.7442	−	18.6095i	0.433248	−	0.750407i
$616$	−2.95798	−	9.10373i	−0.119180	−	0.366800i
$617$	−24.0657	−	10.7147i	−0.968847	−	0.431358i	−0.139580	−	0.990211i	$-0.544575\pi$
$617$	−24.0657	−	10.7147i	−0.968847	−	0.431358i	−0.829267	+	0.558853i	$0.811242\pi$
$618$	−14.0420	−	10.2021i	−0.564854	−	0.410390i
$619$	26.3796			1.06029			0.530144	−	0.847908i	$-0.322138\pi$
$619$	26.3796			1.06029			0.530144	+	0.847908i	$0.322138\pi$
$620$		0			0
$621$	−10.2104			−0.409730
$622$	−15.9144	−	11.5625i	−0.638109	−	0.463613i
$623$	16.8265	+	7.49166i	0.674141	+	0.300147i
$624$	−4.58994	−	14.1264i	−0.183745	−	0.565508i
$625$	13.6503	−	23.6430i	0.546012	−	0.945720i
$626$	29.1103	+	50.4204i	1.16348	+	2.01521i
$627$	−3.79938	+	4.21964i	−0.151733	+	0.168516i
$628$	−4.11425	+	12.6623i	−0.164176	+	0.505283i
$629$	0.390847	+	0.434080i	0.0155841	+	0.0173079i
$630$	−25.7550	+	11.4668i	−1.02610	+	0.456850i
$631$	19.5348	+	4.15226i	0.777669	+	0.165299i	0.579613	−	0.814892i	$-0.303204\pi$
$631$	19.5348	+	4.15226i	0.777669	+	0.165299i	0.198056	+	0.980191i	$0.436537\pi$
$632$	0.551932	−	5.25129i	0.0219547	−	0.208885i
$633$	1.38234	+	13.1521i	0.0549430	+	0.522748i
$634$	32.0582	−	6.81418i	1.27319	−	0.270626i
$635$	−26.9696	+	19.5946i	−1.07026	+	0.777587i
$636$	37.7488	−	27.4261i	1.49684	−	1.08751i
$637$	−13.2749	+	2.82167i	−0.525972	+	0.111799i
$638$	−1.27710	−	12.1508i	−0.0505608	−	0.481053i
$639$	0.220215	−	2.09521i	0.00871157	−	0.0828851i
$640$	11.0604	+	2.35095i	0.437199	+	0.0929295i
$641$	−21.2810	+	9.47491i	−0.840549	+	0.374236i	−0.781414	−	0.624014i	$-0.785501\pi$
$641$	−21.2810	+	9.47491i	−0.840549	+	0.374236i	−0.0591353	+	0.998250i	$0.518834\pi$
$642$	32.9724	+	36.6195i	1.30132	+	1.44526i
$643$	12.0189	−	36.9903i	0.473978	−	1.45875i	−0.373354	−	0.927689i	$-0.621792\pi$
$643$	12.0189	−	36.9903i	0.473978	−	1.45875i	0.847332	−	0.531064i	$-0.178208\pi$
$644$	−18.9145	+	21.0067i	−0.745336	+	0.827780i
$645$	0.677346	+	1.17320i	0.0266705	+	0.0461946i
$646$	−1.36703	+	2.36777i	−0.0537851	+	0.0931585i
$647$	0.689235	+	2.12125i	0.0270966	+	0.0833948i	0.963690	−	0.267022i	$-0.0860398\pi$
$647$	0.689235	+	2.12125i	0.0270966	+	0.0833948i	−0.936594	+	0.350417i	$0.886040\pi$
$648$	−6.25107	−	2.78316i	−0.245565	−	0.109333i
$649$	20.1811	+	14.6624i	0.792176	+	0.575550i
$650$	2.21734			0.0869713
$651$		0			0
$652$	40.7894			1.59744
$653$	23.1162	+	16.7949i	0.904607	+	0.657235i	0.939645	−	0.342151i	$-0.111155\pi$
$653$	23.1162	+	16.7949i	0.904607	+	0.657235i	−0.0350384	+	0.999386i	$0.511155\pi$
$654$	73.2749	+	32.6241i	2.86528	+	1.27570i
$655$	5.21559	+	16.0519i	0.203790	+	0.627201i
$656$	−7.11497	+	12.3235i	−0.277793	+	0.481151i
$657$	−11.1699	−	19.3468i	−0.435778	−	0.754790i
$658$	−27.4059	+	30.4373i	−1.06839	+	1.18657i
$659$	1.58766	−	4.88632i	0.0618466	−	0.190344i	−0.915359	−	0.402638i	$-0.868093\pi$
$659$	1.58766	−	4.88632i	0.0618466	−	0.190344i	0.977206	+	0.212294i	$0.0680934\pi$
$660$	33.0009	+	36.6512i	1.28456	+	1.42665i
$661$	−5.38576	+	2.39789i	−0.209482	+	0.0932673i	−0.508795	−	0.860888i	$-0.669909\pi$
$661$	−5.38576	+	2.39789i	−0.209482	+	0.0932673i	0.299314	+	0.954155i	$0.403242\pi$
$662$	26.2357	+	5.57656i	1.01968	+	0.216739i
$663$	0.993297	−	9.45059i	0.0385765	−	0.367030i
$664$	−0.329856	−	3.13837i	−0.0128009	−	0.121792i
$665$	−5.23229	+	1.11216i	−0.202899	+	0.0431276i
$666$	0.725620	−	0.527194i	0.0281172	−	0.0204284i
$667$	−3.73740	+	2.71538i	−0.144713	+	0.105140i
$668$	4.89553	−	1.04058i	0.189414	−	0.0402611i
$669$	3.55519	+	33.8253i	0.137451	+	1.30776i
$670$	6.92356	−	65.8733i	0.267481	−	2.54491i
$671$	9.32546	+	1.98219i	0.360005	+	0.0765215i
$672$	58.2414	−	25.9307i	2.24671	−	1.00030i
$673$	−18.2427	−	20.2606i	−0.703205	−	0.780988i	0.280678	−	0.959802i	$-0.409441\pi$
$673$	−18.2427	−	20.2606i	−0.703205	−	0.780988i	−0.983883	+	0.178814i	$0.942774\pi$
$674$	17.8434	−	54.9163i	0.687301	−	2.11530i
$675$	−1.04439	+	1.15991i	−0.0401984	+	0.0446448i
$676$	9.91286	+	17.1696i	0.381264	+	0.660368i
$677$	−1.31511	+	2.27784i	−0.0505438	+	0.0875444i	−0.890190	−	0.455589i	$-0.849429\pi$
$677$	−1.31511	+	2.27784i	−0.0505438	+	0.0875444i	0.839647	+	0.543133i	$0.182762\pi$
$678$	24.0263	+	73.9453i	0.922724	+	2.83985i
$679$	−22.5379	−	10.0345i	−0.864925	−	0.385090i
$680$	2.45997	+	1.78728i	0.0943357	+	0.0685389i
$681$	−9.93738			−0.380801
$682$		0			0
$683$	29.5859			1.13207			0.566037	−	0.824380i	$-0.308476\pi$
$683$	29.5859			1.13207			0.566037	+	0.824380i	$0.308476\pi$
$684$	1.81437	+	1.31821i	0.0693740	+	0.0504032i
$685$	−16.2535	−	7.23652i	−0.621014	−	0.276493i
$686$	1.17114	+	3.60441i	0.0447145	+	0.137617i
$687$	−20.7717	+	35.9777i	−0.792492	+	1.37264i
$688$	−0.448549	−	0.776909i	−0.0171008	−	0.0296194i
$689$	−13.2799	+	14.7488i	−0.505924	+	0.561886i
$690$	10.7874	−	33.2002i	0.410669	−	1.26391i
$691$	11.2721	+	12.5189i	0.428809	+	0.476241i	0.918367	−	0.395730i	$-0.129508\pi$
$691$	11.2721	+	12.5189i	0.428809	+	0.476241i	−0.489558	+	0.871971i	$0.662842\pi$
$692$	−11.5412	+	5.13849i	−0.438732	+	0.195336i
$693$	24.2631	+	5.15729i	0.921680	+	0.195909i
$694$	1.15305	−	10.9705i	0.0437691	−	0.416435i
$695$	−4.93258	−	46.9303i	−0.187103	−	1.78017i
$696$	−1.75413	+	0.372851i	−0.0664900	+	0.0141329i
$697$	−7.36512	+	5.35108i	−0.278974	+	0.202686i
$698$	6.86966	−	4.99110i	0.260020	−	0.188916i
$699$	29.8169	−	6.33779i	1.12778	−	0.239717i
$700$	0.451674	+	4.29739i	0.0170717	+	0.162426i
$701$	−2.21855	+	21.1081i	−0.0837933	+	0.797240i	0.869243	+	0.494385i	$0.164607\pi$
$701$	−2.21855	+	21.1081i	−0.0837933	+	0.797240i	−0.953036	+	0.302856i	$0.902060\pi$
$702$	12.8789	+	2.73750i	0.486084	+	0.103320i
$703$	0.155467	−	0.0692184i	0.00586356	−	0.00261062i
$704$	−29.0775	−	32.2938i	−1.09590	−	1.21712i
$705$	8.34966	−	25.6976i	0.314467	−	0.967828i
$706$	−30.2114	+	33.5531i	−1.13702	+	1.26279i
$707$	−33.1859	−	57.4796i	−1.24808	−	2.16174i
$708$	14.2979	−	24.7647i	0.537348	−	0.930714i
$709$	−15.8662	−	48.8313i	−0.595869	−	1.83390i	−0.550352	−	0.834933i	$-0.685506\pi$
$709$	−15.8662	−	48.8313i	−0.595869	−	1.83390i	−0.0455172	−	0.998964i	$-0.514494\pi$
$710$	−5.93757	−	2.64358i	−0.222833	−	0.0992117i
$711$	11.0698	+	8.04266i	0.415149	+	0.301623i
$712$	−3.05044			−0.114320
$713$		0			0
$714$	34.6656			1.29733
$715$	−16.9712	−	12.3303i	−0.634686	−	0.461127i
$716$	−25.4252	−	11.3200i	−0.950185	−	0.423049i
$717$	4.49654	+	13.8389i	0.167926	+	0.516824i
$718$	7.33679	−	12.7077i	0.273807	−	0.474247i
$719$	−20.0999	−	34.8141i	−0.749601	−	1.29835i	−0.948014	−	0.318229i	$-0.896912\pi$
$719$	−20.0999	−	34.8141i	−0.749601	−	1.29835i	0.198413	−	0.980119i	$-0.436421\pi$
$720$	−8.24127	+	9.15285i	−0.307134	+	0.341107i
$721$	−4.44583	+	13.6829i	−0.165571	+	0.509576i
$722$	−25.8109	−	28.6659i	−0.960581	−	1.06683i
$723$	22.4860	−	10.0114i	0.836262	−	0.372328i
$724$	21.6434	+	4.60044i	0.804370	+	0.170974i
$725$	−0.0738164	+	0.702317i	−0.00274147	+	0.0260834i
$726$	−3.39377	−	32.2895i	−0.125954	−	1.19838i
$727$	21.0144	−	4.46674i	0.779380	−	0.165662i	0.198991	−	0.980001i	$-0.436234\pi$
$727$	21.0144	−	4.46674i	0.779380	−	0.165662i	0.580389	+	0.814339i	$0.302900\pi$
$728$	3.77594	−	2.74338i	0.139946	−	0.101677i
$729$	−1.46222	+	1.06236i	−0.0541562	+	0.0393468i
$730$	−67.4139	+	14.3293i	−2.49510	+	0.530350i
$731$	−0.0599920	−	0.570786i	−0.00221889	−	0.0211113i
$732$	1.14239	−	10.8692i	0.0422241	−	0.401736i
$733$	−21.9803	−	4.67205i	−0.811860	−	0.172566i	−0.216767	−	0.976223i	$-0.569551\pi$
$733$	−21.9803	−	4.67205i	−0.811860	−	0.172566i	−0.595093	+	0.803657i	$0.702885\pi$
$734$	30.5104	−	13.5841i	1.12616	−	0.501399i
$735$	21.8548	+	24.2722i	0.806126	+	0.895294i
$736$	−8.40499	+	25.8679i	−0.309812	+	0.953504i
$737$	−38.9958	+	43.3092i	−1.43643	+	1.59532i
$738$	6.98953	+	12.1062i	0.257288	+	0.445636i
$739$	26.2750	−	45.5097i	0.966542	−	1.67410i	0.261129	−	0.965304i	$-0.415905\pi$
$739$	26.2750	−	45.5097i	0.966542	−	1.67410i	0.705413	−	0.708797i	$-0.250762\pi$
$740$	−0.456777	−	1.40582i	−0.0167915	−	0.0516788i
$741$	−2.52922	−	1.12608i	−0.0929132	−	0.0413676i
$742$	−58.5729	−	42.5557i	−2.15028	−	1.56227i
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$		0			0
$745$	28.9145			1.05934
$746$	16.4603	+	11.9591i	0.602655	+	0.437854i
$747$	7.47050	+	3.32608i	0.273331	+	0.121695i
$748$	−6.45678	−	19.8719i	−0.236083	−	0.726589i
$749$	20.4224	−	35.3727i	0.746219	−	1.29249i
$750$	23.3530	+	40.4487i	0.852732	+	1.47698i
$751$	−15.0179	+	16.6791i	−0.548013	+	0.608630i	−0.951986	−	0.306141i	$-0.900962\pi$
$751$	−15.0179	+	16.6791i	−0.548013	+	0.608630i	0.403974	+	0.914771i	$0.367629\pi$
$752$	−5.52927	+	17.0173i	−0.201632	+	0.620559i
$753$	10.4422	+	11.5972i	0.380534	+	0.422626i
$754$	5.44220	−	2.42302i	0.198193	−	0.0882413i
$755$	−45.6495	−	9.70310i	−1.66136	−	0.353132i
$756$	−2.68206	+	25.5181i	−0.0975456	+	0.928084i
$757$	−1.54627	−	14.7118i	−0.0562002	−	0.534709i	−0.986012	−	0.166674i	$-0.946697\pi$
$757$	−1.54627	−	14.7118i	−0.0562002	−	0.534709i	0.929812	−	0.368035i	$-0.119969\pi$
$758$	28.0021	−	5.95202i	1.01708	−	0.216187i
$759$	−24.8487	+	18.0536i	−0.901951	+	0.655306i
$760$	0.716709	−	0.520719i	0.0259978	−	0.0188885i
$761$	−19.4664	+	4.13770i	−0.705655	+	0.149992i	−0.546742	−	0.837301i	$-0.684132\pi$
$761$	−19.4664	+	4.13770i	−0.705655	+	0.149992i	−0.158913	+	0.987293i	$0.550799\pi$
$762$	−6.57924	−	62.5973i	−0.238341	−	2.26766i
$763$	6.94956	−	66.1207i	0.251591	−	2.39373i
$764$	−23.4798	−	4.99079i	−0.849470	−	0.180560i
$765$	−7.19835	+	3.20491i	−0.260257	+	0.115874i
$766$	−14.2895	−	15.8701i	−0.516301	−	0.573410i
$767$	−3.75858	+	11.5677i	−0.135714	+	0.417686i
$768$	14.7792	−	16.4140i	0.533300	−	0.592290i
$769$	−2.09853	−	3.63477i	−0.0756751	−	0.131073i	0.825705	−	0.564103i	$-0.190778\pi$
$769$	−2.09853	−	3.63477i	−0.0756751	−	0.131073i	−0.901380	+	0.433030i	$0.857445\pi$
$770$	38.2630	−	66.2734i	1.37890	−	2.38833i
$771$	−16.3001	−	50.1665i	−0.587033	−	1.80670i
$772$	−3.75211	−	1.67055i	−0.135041	−	0.0601242i
$773$	9.61002	+	6.98209i	0.345648	+	0.251128i	0.747041	−	0.664778i	$-0.231474\pi$
$773$	9.61002	+	6.98209i	0.345648	+	0.251128i	−0.401393	+	0.915906i	$0.631474\pi$
$774$	−0.881281			−0.0316770
$775$		0			0
$776$	4.08584			0.146673
$777$	−1.74565	−	1.26829i	−0.0626248	−	0.0454996i
$778$	48.0161	+	21.3782i	1.72146	+	0.766444i
$779$	0.819628	+	2.52256i	0.0293662	+	0.0903799i
$780$	−12.0238	+	20.8258i	−0.430519	+	0.745682i
$781$	2.85931	+	4.95246i	0.102314	+	0.177213i
$782$	−9.89608	+	10.9907i	−0.353883	+	0.393027i
$783$	−1.29582	+	3.98812i	−0.0463088	+	0.142524i
$784$	−14.4726	−	16.0734i	−0.516877	−	0.574050i
$785$	−12.4505	+	5.54330i	−0.444376	+	0.197849i
$786$	−31.1709	−	6.62557i	−1.11183	−	0.236326i
$787$	0.207388	−	1.97316i	0.00739257	−	0.0703356i	−0.990204	−	0.139631i	$-0.955408\pi$
$787$	0.207388	−	1.97316i	0.00739257	−	0.0703356i	0.997596	+	0.0692953i	$0.0220751\pi$
$788$	1.53371	+	14.5922i	0.0546360	+	0.519827i
$789$	−55.0093	+	11.6926i	−1.95838	+	0.416267i
$790$	34.1511	−	24.8122i	1.21504	−	0.882780i
$791$	52.1386	−	37.8809i	1.85384	−	1.34689i
$792$	−4.01832	+	0.854121i	−0.142785	+	0.0303499i
$793$	0.485909	+	4.62312i	0.0172552	+	0.164172i
$794$	−3.62989	+	34.5361i	−0.128820	+	1.22564i
$795$	46.7194	+	9.93050i	1.65696	+	0.352199i
$796$	−1.94275	+	0.864969i	−0.0688590	+	0.0306580i
$797$	33.7150	+	37.4443i	1.19425	+	1.32635i	0.932482	+	0.361215i	$0.117638\pi$
$797$	33.7150	+	37.4443i	1.19425	+	1.32635i	0.261766	+	0.965131i	$0.415695\pi$
$798$	3.12100	−	9.60544i	0.110482	−	0.340029i
$799$	−7.65977	+	8.50704i	−0.270983	+	0.300957i
$800$	2.07889	+	3.60074i	0.0734998	+	0.127305i
$801$	3.95241	−	6.84577i	0.139652	−	0.241884i
$802$	17.6879	+	54.4379i	0.624583	+	1.92227i
$803$	55.3971	+	24.6644i	1.95492	+	0.870387i
$804$	54.0481	+	39.2682i	1.90613	+	1.38488i
$805$	−28.9356			−1.01984
$806$		0			0
$807$	44.6701			1.57246
$808$	8.89281	+	6.46100i	0.312848	+	0.227297i
$809$	14.2261	+	6.33387i	0.500163	+	0.222687i	0.641282	−	0.767306i	$-0.278403\pi$
$809$	14.2261	+	6.33387i	0.500163	+	0.222687i	−0.141118	+	0.989993i	$0.545070\pi$
$810$	−16.9045	−	52.0268i	−0.593964	−	1.82803i
$811$	−10.3694	+	17.9604i	−0.364119	+	0.630673i	−0.988634	−	0.150340i	$-0.951963\pi$
$811$	−10.3694	+	17.9604i	−0.364119	+	0.630673i	0.624515	+	0.781013i	$0.285297\pi$
$812$	5.80460	+	10.0539i	0.203702	+	0.352822i
$813$	30.0777	−	33.4047i	1.05487	−	1.17155i
$814$	−0.752337	+	2.31546i	−0.0263694	+	0.0811567i
$815$	27.9387	+	31.0290i	0.978649	+	1.08690i
$816$	13.8351	−	6.15977i	0.484325	−	0.215635i
$817$	−0.163559	−	0.0347656i	−0.00572222	−	0.00121630i
$818$	−4.89737	+	46.5954i	−0.171233	+	1.62917i
$819$	1.26425	+	12.0285i	0.0441764	+	0.420310i
$820$	22.5347	−	4.78991i	0.786947	−	0.167271i
$821$	15.8525	−	11.5175i	0.553256	−	0.401964i	−0.275729	−	0.961235i	$-0.588919\pi$
$821$	15.8525	−	11.5175i	0.553256	−	0.401964i	0.828984	+	0.559272i	$0.188919\pi$
$822$	27.1768	−	19.7451i	0.947899	−	0.688689i
$823$	2.05472	−	0.436743i	0.0716229	−	0.0152239i	−0.171961	−	0.985104i	$-0.555010\pi$
$823$	2.05472	−	0.436743i	0.0716229	−	0.0152239i	0.243584	+	0.969880i	$0.421677\pi$
$824$	−0.249059	−	2.36964i	−0.00867639	−	0.0825503i
$825$	−0.490780	+	4.66946i	−0.0170868	+	0.162570i
$826$	−43.4011	−	9.22518i	−1.51012	−	0.320985i
$827$	3.20211	−	1.42567i	0.111348	−	0.0495754i	−0.350307	−	0.936635i	$-0.613923\pi$
$827$	3.20211	−	1.42567i	0.111348	−	0.0495754i	0.461655	+	0.887060i	$0.347256\pi$
$828$	8.11751	+	9.01540i	0.282103	+	0.313307i
$829$	0.645411	−	1.98637i	0.0224161	−	0.0689895i	−0.939223	−	0.343308i	$-0.888452\pi$
$829$	0.645411	−	1.98637i	0.0224161	−	0.0689895i	0.961639	+	0.274319i	$0.0884524\pi$
$830$	16.8809	−	18.7482i	0.585946	−	0.650759i
$831$	−5.09098	−	8.81784i	−0.176604	−	0.305888i
$832$	10.5943	−	18.3498i	0.367290	−	0.636166i
$833$	−4.27599	−	13.1601i	−0.148154	−	0.455972i
$834$	81.3941	+	36.2390i	2.81845	+	1.25485i
$835$	4.14477	+	3.01135i	0.143436	+	0.104212i
$836$	−6.08759			−0.210544
$837$		0			0
$838$	−12.8284			−0.443151
$839$	8.71583	+	6.33242i	0.300904	+	0.218620i	0.727984	−	0.685594i	$-0.240458\pi$
$839$	8.71583	+	6.33242i	0.300904	+	0.218620i	−0.427080	+	0.904214i	$0.640458\pi$
$840$	−10.2614	−	4.56866i	−0.354052	−	0.157634i
$841$	−8.37520	−	25.7762i	−0.288800	−	0.888835i
$842$	−6.79587	+	11.7708i	−0.234201	+	0.405648i
$843$	7.11863	+	12.3298i	0.245178	+	0.424662i
$844$	−9.48712	+	10.5365i	−0.326560	+	0.362682i
$845$	−6.27132	+	19.3011i	−0.215740	+	0.663979i
$846$	11.7617	+	13.0627i	0.404377	+	0.449106i
$847$	−24.5853	+	10.9461i	−0.844760	+	0.376112i
$848$	−30.9382	−	6.57613i	−1.06242	−	0.225825i
$849$	1.62046	−	15.4176i	0.0556140	−	0.529132i
$850$	0.236316	+	2.24840i	0.00810558	+	0.0771194i
$851$	0.900446	−	0.191396i	0.0308669	−	0.00656096i
$852$	5.30352	−	3.85323i	0.181695	−	0.132010i
$853$	−26.4147	+	19.1914i	−0.904423	+	0.657102i	−0.939598	−	0.342280i	$-0.888801\pi$
$853$	−26.4147	+	19.1914i	−0.904423	+	0.657102i	0.0351753	+	0.999381i	$0.488801\pi$
$854$	−16.5875	+	3.52577i	−0.567611	+	0.120649i
$855$	0.239966	+	2.28312i	0.00820666	+	0.0780811i
$856$	−0.707081	+	6.72743i	−0.0241675	+	0.229939i
$857$	42.7781	+	9.09277i	1.46127	+	0.310603i	0.868870	−	0.495040i	$-0.164846\pi$
$857$	42.7781	+	9.09277i	1.46127	+	0.310603i	0.592402	+	0.805643i	$0.298180\pi$
$858$	36.1833	−	16.1099i	1.23528	−	0.549981i
$859$	16.3042	+	18.1077i	0.556294	+	0.617827i	0.954044	−	0.299667i	$-0.0968756\pi$
$859$	16.3042	+	18.1077i	0.556294	+	0.617827i	−0.397750	+	0.917494i	$0.630209\pi$
$860$	−0.448815	+	1.38131i	−0.0153045	+	0.0471023i
$861$	22.5028	−	24.9919i	0.766893	−	0.851721i
$862$	−24.3140	−	42.1130i	−0.828137	−	1.43438i
$863$	−21.7570	+	37.6842i	−0.740616	+	1.28279i	0.211599	+	0.977357i	$0.432133\pi$
$863$	−21.7570	+	37.6842i	−0.740616	+	1.28279i	−0.952215	+	0.305429i	$0.901200\pi$
$864$	7.62934	+	23.4807i	0.259555	+	0.798829i
$865$	−11.8141	−	5.25997i	−0.401691	−	0.178844i
$866$	40.7578	+	29.6123i	1.38501	+	1.00627i
$867$	−26.6808			−0.906129
$868$		0			0
$869$	−37.1415			−1.25994
$870$	−11.5987	−	8.42696i	−0.393233	−	0.285701i
$871$	−25.9593	−	11.5578i	−0.879596	−	0.391621i
$872$	3.40254	+	10.4719i	0.115224	+	0.354625i
$873$	−5.29396	+	9.16941i	−0.179173	+	0.310338i
$874$	2.15444	+	3.73160i	0.0728751	+	0.126223i
$875$	25.9049	−	28.7703i	0.875746	−	0.972614i
$876$	21.4810	−	66.1118i	0.725776	−	2.23371i
$877$	−25.5901	−	28.4207i	−0.864117	−	0.959699i	0.135400	−	0.990791i	$-0.456768\pi$
$877$	−25.5901	−	28.4207i	−0.864117	−	0.959699i	−0.999517	+	0.0310921i	$0.990101\pi$
$878$	27.4602	−	12.2261i	0.926737	−	0.412610i
$879$	−28.2748	−	6.00999i	−0.953684	−	0.202712i
$880$	3.49459	−	33.2488i	0.117803	−	1.12082i
$881$	4.25864	+	40.5182i	0.143477	+	1.36509i	0.795067	+	0.606522i	$0.207436\pi$
$881$	4.25864	+	40.5182i	0.143477	+	1.36509i	−0.651590	+	0.758572i	$0.725898\pi$
$882$	−20.7833	+	4.41762i	−0.699809	+	0.148749i
$883$	26.7914	−	19.4651i	0.901604	−	0.655054i	−0.0372736	−	0.999305i	$-0.511867\pi$
$883$	26.7914	−	19.4651i	0.901604	−	0.655054i	0.938877	+	0.344252i	$0.111867\pi$
$884$	8.24226	−	5.98835i	0.277217	−	0.201410i
$885$	28.6322	−	6.08595i	0.962459	−	0.204577i
$886$	3.58812	+	34.1387i	0.120545	+	1.14691i
$887$	−1.30321	+	12.3992i	−0.0437575	+	0.416325i	0.950614	+	0.310376i	$0.100455\pi$
$887$	−1.30321	+	12.3992i	−0.0437575	+	0.416325i	−0.994372	+	0.105949i	$0.966212\pi$
$888$	0.349544	+	0.0742978i	0.0117299	+	0.00249327i
$889$	−47.6616	+	21.2203i	−1.59852	+	0.711707i
$890$	−16.3181	−	18.1231i	−0.546984	−	0.607487i
$891$	−14.8736	+	45.7761i	−0.498283	+	1.53356i
$892$	−24.3996	+	27.0985i	−0.816959	+	0.907325i
$893$	1.66758	+	2.88834i	0.0558035	+	0.0966545i
$894$	−27.2966	+	47.2791i	−0.912936	+	1.58125i
$895$	−8.80368	−	27.0949i	−0.294274	−	0.905684i
$896$	16.1665	+	7.19780i	0.540085	+	0.240461i
$897$	−12.1160	−	8.80278i	−0.404541	−	0.293916i
$898$	−14.1263			−0.471401
$899$		0			0
$900$	1.85446			0.0618154
$901$	−16.3707	−	11.8940i	−0.545389	−	0.396248i
$902$	−34.6646	−	15.4337i	−1.15421	−	0.513885i
$903$	0.655156	+	2.01636i	0.0218022	+	0.0671003i
$904$	−5.33666	+	9.24337i	−0.177495	+	0.307430i
$905$	11.3250	+	19.6155i	0.376456	+	0.652041i
$906$	58.9612	−	65.4831i	1.95886	−	2.17553i
$907$	5.22278	−	16.0741i	0.173419	−	0.533730i	−0.826138	−	0.563467i	$-0.809467\pi$
$907$	5.22278	−	16.0741i	0.173419	−	0.533730i	0.999558	+	0.0297372i	$0.00946703\pi$
$908$	−7.12897	−	7.91753i	−0.236583	−	0.262752i
$909$	−26.0220	+	11.5857i	−0.863096	+	0.384275i
$910$	36.4979	+	7.75788i	1.20989	+	0.257171i
$911$	−5.69363	+	54.1713i	−0.188638	+	1.79477i	0.334366	+	0.942443i	$0.391478\pi$
$911$	−5.69363	+	54.1713i	−0.188638	+	1.79477i	−0.523004	+	0.852330i	$0.675189\pi$
$912$	−0.461209	−	4.38811i	−0.0152722	−	0.145305i
$913$	−21.7121	+	4.61505i	−0.718566	+	0.152736i
$914$	35.9211	−	26.0982i	1.18816	−	0.863251i
$915$	9.05079	−	6.57578i	0.299210	−	0.217389i
$916$	−43.5664	+	9.26032i	−1.43947	+	0.305970i
$917$	2.76107	+	26.2698i	0.0911784	+	0.867505i
$918$	−1.40325	+	13.3511i	−0.0463143	+	0.440651i
$919$	8.57573	+	1.82283i	0.282887	+	0.0601295i	0.347170	−	0.937802i	$-0.387143\pi$
$919$	8.57573	+	1.82283i	0.282887	+	0.0601295i	−0.0642828	+	0.997932i	$0.520476\pi$
$920$	4.37784	−	1.94914i	0.144333	−	0.0642612i
$921$	−32.5328	−	36.1313i	−1.07199	−	1.19057i
$922$	5.55447	−	17.0949i	0.182927	−	0.562990i
$923$	−1.86576	+	2.07214i	−0.0614123	+	0.0682053i
$924$	38.5928	+	66.8447i	1.26961	+	2.19903i
$925$	0.0703606	−	0.121868i	0.00231344	−	0.00400700i
$926$	−2.33709	−	7.19283i	−0.0768016	−	0.236371i
$927$	5.64063	+	2.51137i	0.185263	+	0.0824843i
$928$	9.03714	+	6.56587i	0.296659	+	0.215535i
$929$	44.2868			1.45300			0.726501	−	0.687165i	$-0.241145\pi$
$929$	44.2868			1.45300			0.726501	+	0.687165i	$0.241145\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	26.4399	+	19.2097i	0.866069	+	0.629236i
$933$	18.5540	+	8.26077i	0.607431	+	0.270445i
$934$	−1.97290	−	6.07196i	−0.0645552	−	0.198681i
$935$	10.6943	−	18.5230i	0.349740	−	0.605767i
$936$	−1.00153	−	1.73471i	−0.0327361	−	0.0567006i
$937$	−34.4713	+	38.2843i	−1.12613	+	1.25069i	−0.161559	+	0.986863i	$0.551652\pi$
$937$	−34.4713	+	38.2843i	−1.12613	+	1.25069i	−0.964569	+	0.263829i	$0.915014\pi$
$938$	32.0331	−	98.5877i	1.04592	−	3.21900i
$939$	−40.2218	−	44.6709i	−1.31259	−	1.45778i
$940$	26.4643	−	11.7827i	0.863171	−	0.384309i
$941$	38.3405	+	8.14952i	1.24986	+	0.265667i	0.784877	−	0.619651i	$-0.212726\pi$
$941$	38.3405	+	8.14952i	1.24986	+	0.265667i	0.464986	+	0.885318i	$0.346059\pi$
$942$	2.68976	−	25.5914i	0.0876371	−	0.833812i
$943$	1.49973	+	14.2690i	0.0488380	+	0.464662i
$944$	−18.9606	+	4.03021i	−0.617116	+	0.131172i
$945$	−21.2490	+	15.4383i	−0.691231	+	0.502208i
$946$	1.93531	−	1.40608i	0.0629223	−	0.0457158i
$947$	55.6726	−	11.8336i	1.80912	−	0.384539i	0.825440	−	0.564490i	$-0.190927\pi$
$947$	55.6726	−	11.8336i	1.80912	−	0.384539i	0.983676	+	0.179951i	$0.0575940\pi$
$948$	4.45051	+	42.3437i	0.144546	+	1.37526i
$949$	−3.09062	+	29.4053i	−0.100326	+	0.954537i
$950$	0.644281	+	0.136946i	0.0209032	+	0.00444312i
$951$	−30.9129	+	13.7633i	−1.00242	+	0.446306i
$952$	3.18424	+	3.53645i	0.103202	+	0.114617i
$953$	4.71987	−	14.5263i	0.152892	−	0.470552i	−0.845050	−	0.534688i	$-0.820429\pi$
$953$	4.71987	−	14.5263i	0.152892	−	0.470552i	0.997941	+	0.0641360i	$0.0204292\pi$
$954$	−20.7911	+	23.0908i	−0.673136	+	0.747593i
$955$	−12.2859	−	21.2798i	−0.397563	−	0.688599i
$956$	−7.80028	+	13.5105i	−0.252279	+	0.436960i
$957$	3.89804	+	11.9969i	0.126006	+	0.387806i
$958$	−32.9572	−	14.6735i	−1.06480	−	0.474078i
$959$	−22.5266	−	16.3665i	−0.727421	−	0.528503i
$960$	−50.9928			−1.64579
$961$		0			0
$962$	−1.18709			−0.0382735
$963$	−14.1815	−	10.3035i	−0.456992	−	0.332024i
$964$	24.1077	+	10.7334i	0.776456	+	0.345701i
$965$	−1.29920	−	3.99852i	−0.0418226	−	0.128717i
$966$	27.3165	−	47.3136i	0.878895	−	1.52229i
$967$	5.64979	+	9.78573i	0.181685	+	0.314688i	0.942455	−	0.334334i	$-0.108511\pi$
$967$	5.64979	+	9.78573i	0.181685	+	0.314688i	−0.760769	+	0.649022i	$0.775178\pi$
$968$	2.98232	−	3.31220i	0.0958553	−	0.106458i
$969$	0.872299	−	2.68466i	0.0280223	−	0.0862437i
$970$	21.8569	+	24.2745i	0.701782	+	0.779408i
$971$	−14.4963	+	6.45418i	−0.465210	+	0.207125i	−0.625936	−	0.779874i	$-0.715283\pi$
$971$	−14.4963	+	6.45418i	−0.465210	+	0.207125i	0.160727	+	0.986999i	$0.448616\pi$
$972$	33.4793	+	7.11625i	1.07385	+	0.228254i
$973$	7.71961	−	73.4472i	0.247479	−	2.35461i
$974$	6.23224	+	59.2958i	0.199694	+	1.89996i
$975$	−2.23930	+	0.475977i	−0.0717149	+	0.0152435i
$976$	−5.99357	+	4.35458i	−0.191849	+	0.139387i
$977$	13.3973	−	9.73371i	0.428617	−	0.311409i	−0.352478	−	0.935820i	$-0.614661\pi$
$977$	13.3973	−	9.73371i	0.428617	−	0.311409i	0.781096	+	0.624411i	$0.214661\pi$
$978$	−77.1122	+	16.3907i	−2.46577	+	0.524117i
$979$	2.24287	+	21.3395i	0.0716826	+	0.682014i
$980$	−3.66028	+	34.8252i	−0.116923	+	1.11245i
$981$	−27.9097	−	5.93238i	−0.891087	−	0.189406i
$982$	18.5998	−	8.28116i	0.593543	−	0.264262i
$983$	−14.4866	−	16.0890i	−0.462049	−	0.513158i	0.466422	−	0.884562i	$-0.345543\pi$
$983$	−14.4866	−	16.0890i	−0.462049	−	0.513158i	−0.928471	+	0.371405i	$0.878876\pi$
$984$	−1.72110	+	5.29699i	−0.0548666	+	0.168862i
$985$	−10.0500	+	11.1617i	−0.320220	+	0.355640i
$986$	3.03697	+	5.26019i	0.0967169	+	0.167519i
$987$	21.1436	−	36.6217i	0.673007	−	1.16568i
$988$	−0.917240	−	2.82297i	−0.0291813	−	0.0898108i
$989$	−0.826315	−	0.367899i	−0.0262753	−	0.0116985i
$990$	−26.5701	−	19.3043i	−0.844455	−	0.613532i
$991$	−32.3028			−1.02613			−0.513066	−	0.858349i	$-0.671490\pi$
$991$	−32.3028			−1.02613			−0.513066	+	0.858349i	$0.671490\pi$
$992$		0			0
$993$	−27.6925			−0.878796
$994$	−8.22920	−	5.97887i	−0.261014	−	0.189638i
$995$	−1.98868	−	0.885417i	−0.0630454	−	0.0280696i
$996$	7.86314	+	24.2002i	0.249153	+	0.766814i
$997$	5.74360	−	9.94821i	0.181902	−	0.315063i	−0.760626	−	0.649190i	$-0.775108\pi$
$997$	5.74360	−	9.94821i	0.181902	−	0.315063i	0.942528	+	0.334127i	$0.108441\pi$
$998$	−11.2392	−	19.4669i	−0.355771	−	0.616213i
$999$	0.559131	−	0.620978i	0.0176901	−	0.0196469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.m.732.1		16
31.2	even	5		961.2.g.l.448.2		16
31.3	odd	30		961.2.d.p.388.1		16
31.4	even	5		961.2.c.i.521.7		16
31.5	even	3		961.2.g.n.816.1		16
31.6	odd	6		961.2.d.p.374.1		16
31.7	even	15		961.2.a.j.1.7		8
31.8	even	5		961.2.g.j.844.2		16
31.9	even	15		961.2.g.l.547.2		16
31.10	even	15		961.2.g.j.846.2		16
31.11	odd	30		961.2.c.j.439.7		16
31.12	odd	30		961.2.d.o.628.4		16
31.13	odd	30		961.2.g.s.235.1		16
31.14	even	15		961.2.d.n.531.4		16
31.15	odd	10		961.2.g.t.338.1		16
31.16	even	5		961.2.g.n.338.1		16
31.17	odd	30		961.2.d.o.531.4		16
31.18	even	15	inner	961.2.g.m.235.1		16
31.19	even	15		961.2.d.n.628.4		16
31.20	even	15		961.2.c.i.439.7		16
31.21	odd	30		961.2.g.k.846.2		16
31.22	odd	30		31.2.g.a.20.2	yes	16
31.23	odd	10		961.2.g.k.844.2		16
31.24	odd	30		961.2.a.i.1.7		8
31.25	even	3		961.2.d.q.374.1		16
31.26	odd	6		961.2.g.t.816.1		16
31.27	odd	10		961.2.c.j.521.7		16
31.28	even	15		961.2.d.q.388.1		16
31.29	odd	10		31.2.g.a.14.2	✓	16
31.30	odd	2		961.2.g.s.732.1		16
93.29	even	10		279.2.y.c.262.1		16
93.38	odd	30		8649.2.a.be.1.2		8
93.53	even	30		279.2.y.c.82.1		16
93.86	even	30		8649.2.a.bf.1.2		8
124.91	even	10		496.2.bg.c.417.2		16
124.115	even	30		496.2.bg.c.113.2		16
155.22	even	60		775.2.ck.a.299.2		32
155.29	odd	10		775.2.bl.a.76.1		16
155.53	even	60		775.2.ck.a.299.3		32
155.84	odd	30		775.2.bl.a.51.1		16
155.122	even	20		775.2.ck.a.324.3		32
155.153	even	20		775.2.ck.a.324.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	31.29	odd	10
31.2.g.a.20.2	yes	16	31.22	odd	30
279.2.y.c.82.1		16	93.53	even	30
279.2.y.c.262.1		16	93.29	even	10
496.2.bg.c.113.2		16	124.115	even	30
496.2.bg.c.417.2		16	124.91	even	10
775.2.bl.a.51.1		16	155.84	odd	30
775.2.bl.a.76.1		16	155.29	odd	10
775.2.ck.a.299.2		32	155.22	even	60
775.2.ck.a.299.3		32	155.53	even	60
775.2.ck.a.324.2		32	155.153	even	20
775.2.ck.a.324.3		32	155.122	even	20
961.2.a.i.1.7		8	31.24	odd	30
961.2.a.j.1.7		8	31.7	even	15
961.2.c.i.439.7		16	31.20	even	15
961.2.c.i.521.7		16	31.4	even	5
961.2.c.j.439.7		16	31.11	odd	30
961.2.c.j.521.7		16	31.27	odd	10
961.2.d.n.531.4		16	31.14	even	15
961.2.d.n.628.4		16	31.19	even	15
961.2.d.o.531.4		16	31.17	odd	30
961.2.d.o.628.4		16	31.12	odd	30
961.2.d.p.374.1		16	31.6	odd	6
961.2.d.p.388.1		16	31.3	odd	30
961.2.d.q.374.1		16	31.25	even	3
961.2.d.q.388.1		16	31.28	even	15
961.2.g.j.844.2		16	31.8	even	5
961.2.g.j.846.2		16	31.10	even	15
961.2.g.k.844.2		16	31.23	odd	10
961.2.g.k.846.2		16	31.21	odd	30
961.2.g.l.448.2		16	31.2	even	5
961.2.g.l.547.2		16	31.9	even	15
961.2.g.m.235.1		16	31.18	even	15	inner
961.2.g.m.732.1		16	1.1	even	1	trivial
961.2.g.n.338.1		16	31.16	even	5
961.2.g.n.816.1		16	31.5	even	3
961.2.g.s.235.1		16	31.13	odd	30
961.2.g.s.732.1		16	31.30	odd	2
961.2.g.t.338.1		16	31.15	odd	10
961.2.g.t.816.1		16	31.26	odd	6
8649.2.a.be.1.2		8	93.38	odd	30
8649.2.a.bf.1.2		8	93.86	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+(-1.67638 - 1.21796i) q^{2} +(1.95443 + 0.870169i) q^{3} +(0.708788 + 2.18143i) q^{4} +(-1.17396 + 2.03335i) q^{5} +(-2.21654 - 3.83916i) q^{6} +(-2.45875 + 2.73072i) q^{7} +(0.188054 - 0.578772i) q^{8} +(1.05522 + 1.17194i) q^{9} +(4.44454 - 1.97884i) q^{10} +(-4.18710 - 0.889995i) q^{11} +(-0.512931 + 4.88021i) q^{12} +(-0.218172 - 2.07577i) q^{13} +(7.44771 - 1.58306i) q^{14} +(-4.06377 + 2.95251i) q^{15} +(2.69109 - 1.95519i) q^{16} +(2.08159 - 0.442455i) q^{17} +(-0.341570 - 3.24983i) q^{18} +(0.0648092 - 0.616619i) q^{19} +(-5.26769 - 1.11968i) q^{20} +(-7.18164 + 3.19747i) q^{21} +(5.93519 + 6.59170i) q^{22} +(1.03640 - 3.18973i) q^{23} +(0.871168 - 0.967530i) q^{24} +(-0.256344 - 0.444001i) q^{25} +(-2.16247 + 3.74550i) q^{26} +(-0.940760 - 2.89536i) q^{27} +(-7.69959 - 3.42808i) q^{28} +(-1.11435 - 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 - 5.38292i) q^{33} +(-4.02843 - 1.79357i) q^{34} +(-2.66604 - 8.20524i) q^{35} +(-1.80857 + 3.13253i) q^{36} +(0.137239 + 0.237704i) q^{37} +(-0.859664 + 0.954753i) q^{38} +(1.37986 - 4.24679i) q^{39} +(0.956078 + 1.06183i) q^{40} +(-3.90807 + 1.73998i) q^{41} +(15.9336 + 3.38678i) q^{42} +(0.0281905 - 0.268215i) q^{43} +(-1.02631 - 9.76467i) q^{44} +(-3.62173 + 0.769824i) q^{45} +(-5.62238 + 4.08489i) q^{46} +(-4.35183 + 3.16179i) q^{47} +(6.96090 - 1.47959i) q^{48} +(-0.679670 - 6.46663i) q^{49} +(-0.111046 + 1.05653i) q^{50} +(4.45333 + 0.946585i) q^{51} +(4.37349 - 1.94720i) q^{52} +(-6.36255 - 7.06633i) q^{53} +(-1.94937 + 5.99954i) q^{54} +(6.72514 - 7.46903i) q^{55} +(1.11808 + 1.93658i) q^{56} +(0.663228 - 1.14874i) q^{57} +(0.881988 + 2.71448i) q^{58} +(-5.32363 - 2.37023i) q^{59} +(-9.32103 - 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 + 5.96700i) q^{64} +(4.47688 + 1.99324i) q^{65} +(5.86404 + 18.0477i) q^{66} +(6.80719 - 11.7904i) q^{67} +(2.44059 + 4.22722i) q^{68} +(4.80118 - 5.33225i) q^{69} +(-5.52437 + 17.0022i) q^{70} +(-0.893908 - 0.992785i) q^{71} +(0.876721 - 0.390342i) q^{72} +(-13.8565 - 2.94528i) q^{73} +(0.0594505 - 0.565634i) q^{74} +(-0.114651 - 1.09083i) q^{75} +(1.39104 - 0.295676i) q^{76} +(12.7253 - 9.24551i) q^{77} +(-7.48561 + 5.43861i) q^{78} +(8.48701 - 1.80397i) q^{79} +(0.816370 + 7.76724i) q^{80} +(1.17533 - 11.1825i) q^{81} +(8.67065 + 1.84300i) q^{82} +(4.73717 - 2.10912i) q^{83} +(-12.0653 - 13.3999i) q^{84} +(-1.54403 + 4.75202i) q^{85} +(-0.373934 + 0.415296i) q^{86} +(-1.47342 - 2.55203i) q^{87} +(-1.30251 + 2.25601i) q^{88} +(-1.54897 - 4.76725i) q^{89} +(7.00903 + 3.12062i) q^{90} +(6.20475 + 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 + 0.855663i) q^{95} +(-15.8500 - 7.05686i) q^{96} +(2.07474 + 6.38538i) q^{97} +(-6.73673 + 11.6684i) q^{98} +(-3.37528 - 5.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} + 2 q^{11} + 20 q^{12} + 27 q^{13} - 6 q^{14} - 4 q^{15} - 2 q^{16} + 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 + 2 * q^11 + 20 * q^12 + 27 * q^13 - 6 * q^14 - 4 * q^15 - 2 * q^16 + 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 - 29 * q^21 - 4 * q^22 - 21 * q^23 + 25 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 40 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 + 51 * q^42 - 8 * q^43 - 4 * q^44 + 25 * q^45 + 16 * q^46 + 4 * q^47 + 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 - 24 * q^52 - 66 * q^53 - 39 * q^54 + 52 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 - 51 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 18 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 - 27 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 + 42 * q^77 + 15 * q^78 - 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 - 4 * q^83 + 27 * q^84 + 63 * q^85 - 34 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 + 57 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 + 62 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more