LMFDB - Embedded newform 961.2.g.s.846.1

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			846.1
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.s.844.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.213065 + 0.655747i) q^{2} +(0.882681 + 0.187620i) q^{3} +(1.23343 + 0.896137i) q^{4} +(-1.85376 - 3.21080i) q^{5} +(-0.311099 + 0.538840i) q^{6} +(0.697395 - 0.310500i) q^{7} +(-1.96606 + 1.42843i) q^{8} +(-1.99671 - 0.888993i) q^{9} +(2.50044 - 0.531486i) q^{10} +(0.430200 - 4.09308i) q^{11} +(0.920590 + 1.02242i) q^{12} +(-1.94700 + 2.16237i) q^{13} +(0.0550190 + 0.523471i) q^{14} +(-1.03387 - 3.18192i) q^{15} +(0.424467 + 1.30637i) q^{16} +(-0.136778 - 1.30136i) q^{17} +(1.00838 - 1.11992i) q^{18} +(-2.54239 - 2.82361i) q^{19} +(0.590845 - 5.62151i) q^{20} +(0.673833 - 0.143228i) q^{21} +(2.59236 + 1.15419i) q^{22} +(2.65597 - 1.92967i) q^{23} +(-2.00341 + 0.891974i) q^{24} +(-4.37284 + 7.57398i) q^{25} +(-1.00313 - 1.73747i) q^{26} +(-3.78584 - 2.75057i) q^{27} +(1.13844 + 0.241982i) q^{28} +(1.51283 - 4.65602i) q^{29} +2.30681 q^{30} -5.80746 q^{32} +(1.14767 - 3.53217i) q^{33} +(0.882502 + 0.187582i) q^{34} +(-2.28976 - 1.66361i) q^{35} +(-1.66614 - 2.88584i) q^{36} +(5.20639 - 9.01773i) q^{37} +(2.39327 - 1.06555i) q^{38} +(-2.12429 + 1.54338i) q^{39} +(8.23100 + 3.66468i) q^{40} +(-0.739427 + 0.157170i) q^{41} +(-0.0496492 + 0.472381i) q^{42} +(-4.78889 - 5.31861i) q^{43} +(4.19858 - 4.66299i) q^{44} +(0.847038 + 8.05903i) q^{45} +(0.699483 + 2.15279i) q^{46} +(-0.270719 - 0.833189i) q^{47} +(0.129567 + 1.23275i) q^{48} +(-4.29396 + 4.76893i) q^{49} +(-4.03491 - 4.48122i) q^{50} +(0.123429 - 1.17434i) q^{51} +(-4.33926 + 0.922339i) q^{52} +(3.26657 + 1.45437i) q^{53} +(2.61031 - 1.89650i) q^{54} +(-13.9396 + 6.20629i) q^{55} +(-0.927595 + 1.60664i) q^{56} +(-1.71435 - 2.96935i) q^{57} +(2.73084 + 1.98407i) q^{58} +(-0.907007 - 0.192790i) q^{59} +(1.57623 - 4.85115i) q^{60} +2.31704 q^{61} -1.66853 q^{63} +(0.388433 - 1.19547i) q^{64} +(10.5522 + 2.24294i) q^{65} +(2.07168 + 1.50516i) q^{66} +(1.04345 + 1.80731i) q^{67} +(0.997488 - 1.72770i) q^{68} +(2.70642 - 1.20498i) q^{69} +(1.57877 - 1.14704i) q^{70} +(-7.06726 - 3.14655i) q^{71} +(5.19552 - 1.10434i) q^{72} +(0.591367 - 5.62649i) q^{73} +(4.80405 + 5.33544i) q^{74} +(-5.28085 + 5.86498i) q^{75} +(-0.605510 - 5.76105i) q^{76} +(-0.970882 - 2.98807i) q^{77} +(-0.559458 - 1.72183i) q^{78} +(1.47330 + 14.0175i) q^{79} +(3.40765 - 3.78458i) q^{80} +(1.56187 + 1.73464i) q^{81} +(0.0544822 - 0.518364i) q^{82} +(13.7994 - 2.93316i) q^{83} +(0.959476 + 0.427186i) q^{84} +(-3.92484 + 2.85157i) q^{85} +(4.50800 - 2.00709i) q^{86} +(2.20891 - 3.82595i) q^{87} +(5.00086 + 8.66175i) q^{88} +(3.58784 + 2.60672i) q^{89} +(-5.46515 - 1.16165i) q^{90} +(-0.686415 + 2.11257i) q^{91} +5.00520 q^{92} +0.604042 q^{94} +(-4.35308 + 13.3974i) q^{95} +(-5.12614 - 1.08959i) q^{96} +(4.26970 + 3.10212i) q^{97} +(-2.21232 - 3.83184i) q^{98} +(-4.49770 + 7.79025i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−0.213065	+	0.655747i	−0.150660	+	0.463683i	−0.997695	−	0.0678533i	$-0.978385\pi$
$2$	−0.213065	+	0.655747i	−0.150660	+	0.463683i	0.847036	+	0.531536i	$0.178385\pi$
$3$	0.882681	+	0.187620i	0.509616	+	0.108322i	0.455541	−	0.890215i	$-0.349446\pi$
$3$	0.882681	+	0.187620i	0.509616	+	0.108322i	0.0540749	+	0.998537i	$0.482779\pi$
$4$	1.23343	+	0.896137i	0.616714	+	0.448069i
$5$	−1.85376	−	3.21080i	−0.829026	−	1.43591i	−0.898803	−	0.438352i	$-0.855562\pi$
$5$	−1.85376	−	3.21080i	−0.829026	−	1.43591i	0.0697774	−	0.997563i	$-0.477771\pi$
$6$	−0.311099	+	0.538840i	−0.127006	+	0.219981i
$7$	0.697395	−	0.310500i	0.263591	−	0.117358i	−0.270686	−	0.962668i	$-0.587251\pi$
$7$	0.697395	−	0.310500i	0.263591	−	0.117358i	0.534277	+	0.845310i	$0.320584\pi$
$8$	−1.96606	+	1.42843i	−0.695108	+	0.505025i
$9$	−1.99671	−	0.888993i	−0.665570	−	0.296331i
$10$	2.50044	−	0.531486i	0.790710	−	0.168071i
$11$	0.430200	−	4.09308i	0.129710	−	1.23411i	−0.715092	−	0.699030i	$-0.753615\pi$
$11$	0.430200	−	4.09308i	0.129710	−	1.23411i	0.844802	−	0.535079i	$-0.179718\pi$
$12$	0.920590	+	1.02242i	0.265751	+	0.295147i
$13$	−1.94700	+	2.16237i	−0.540002	+	0.599733i	−0.949960	−	0.312372i	$-0.898877\pi$
$13$	−1.94700	+	2.16237i	−0.540002	+	0.599733i	0.409958	+	0.912104i	$0.365543\pi$
$14$	0.0550190	+	0.523471i	0.0147045	+	0.139904i
$15$	−1.03387	−	3.18192i	−0.266943	−	0.821568i
$16$	0.424467	+	1.30637i	0.106117	+	0.326594i
$17$	−0.136778	−	1.30136i	−0.0331735	−	0.315625i	−0.998508	−	0.0546085i	$-0.982609\pi$
$17$	−0.136778	−	1.30136i	−0.0331735	−	0.315625i	0.965334	−	0.261017i	$-0.0840577\pi$
$18$	1.00838	−	1.11992i	0.237678	−	0.263968i
$19$	−2.54239	−	2.82361i	−0.583264	−	0.647781i	0.377217	−	0.926125i	$-0.376881\pi$
$19$	−2.54239	−	2.82361i	−0.583264	−	0.647781i	−0.960481	+	0.278344i	$0.910214\pi$
$20$	0.590845	−	5.62151i	0.132117	−	1.25701i
$21$	0.673833	−	0.143228i	0.147043	−	0.0312549i
$22$	2.59236	+	1.15419i	0.552693	+	0.246075i
$23$	2.65597	−	1.92967i	0.553808	−	0.402365i	−0.275380	−	0.961336i	$-0.588804\pi$
$23$	2.65597	−	1.92967i	0.553808	−	0.402365i	0.829187	+	0.558971i	$0.188804\pi$
$24$	−2.00341	+	0.891974i	−0.408944	+	0.182073i
$25$	−4.37284	+	7.57398i	−0.874568	+	1.51480i
$26$	−1.00313	−	1.73747i	−0.196729	−	0.340745i
$27$	−3.78584	−	2.75057i	−0.728585	−	0.529348i
$28$	1.13844	+	0.241982i	0.215144	+	0.0457303i
$29$	1.51283	−	4.65602i	0.280926	−	0.864602i	−0.706664	−	0.707549i	$-0.749801\pi$
$29$	1.51283	−	4.65602i	0.280926	−	0.864602i	0.987590	−	0.157052i	$-0.0501992\pi$
$30$	2.30681			0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	1.14767	−	3.53217i	0.199784	−	0.614872i
$34$	0.882502	+	0.187582i	0.151348	+	0.0321700i
$35$	−2.28976	−	1.66361i	−0.387040	−	0.281201i
$36$	−1.66614	−	2.88584i	−0.277690	−	0.480973i
$37$	5.20639	−	9.01773i	0.855925	−	1.48251i	−0.0198583	−	0.999803i	$-0.506321\pi$
$37$	5.20639	−	9.01773i	0.855925	−	1.48251i	0.875784	−	0.482704i	$-0.160345\pi$
$38$	2.39327	−	1.06555i	0.388239	−	0.172855i
$39$	−2.12429	+	1.54338i	−0.340158	+	0.247139i
$40$	8.23100	+	3.66468i	1.30144	+	0.579437i
$41$	−0.739427	+	0.157170i	−0.115479	+	0.0245458i	−0.265289	−	0.964169i	$-0.585467\pi$
$41$	−0.739427	+	0.157170i	−0.115479	+	0.0245458i	0.149810	+	0.988715i	$0.452134\pi$
$42$	−0.0496492	+	0.472381i	−0.00766104	+	0.0728899i
$43$	−4.78889	−	5.31861i	−0.730299	−	0.811080i	0.257588	−	0.966255i	$-0.417072\pi$
$43$	−4.78889	−	5.31861i	−0.730299	−	0.811080i	−0.987887	+	0.155175i	$0.950406\pi$
$44$	4.19858	−	4.66299i	0.632960	−	0.702973i
$45$	0.847038	+	8.05903i	0.126269	+	1.20137i
$46$	0.699483	+	2.15279i	0.103133	+	0.317411i
$47$	−0.270719	−	0.833189i	−0.0394885	−	0.121533i	0.929369	−	0.369152i	$-0.120352\pi$
$47$	−0.270719	−	0.833189i	−0.0394885	−	0.121533i	−0.968857	+	0.247619i	$0.920352\pi$
$48$	0.129567	+	1.23275i	0.0187014	+	0.177932i
$49$	−4.29396	+	4.76893i	−0.613424	+	0.681276i
$50$	−4.03491	−	4.48122i	−0.570623	−	0.633741i
$51$	0.123429	−	1.17434i	0.0172835	−	0.164441i
$52$	−4.33926	+	0.922339i	−0.601748	+	0.127905i
$53$	3.26657	+	1.45437i	0.448698	+	0.199773i	0.618630	−	0.785683i	$-0.287688\pi$
$53$	3.26657	+	1.45437i	0.448698	+	0.199773i	−0.169932	+	0.985456i	$0.554355\pi$
$54$	2.61031	−	1.89650i	0.355218	−	0.258081i
$55$	−13.9396	+	6.20629i	−1.87961	+	0.836856i
$56$	−0.927595	+	1.60664i	−0.123955	+	0.214696i
$57$	−1.71435	−	2.96935i	−0.227072	−	0.393300i
$58$	2.73084	+	1.98407i	0.358577	+	0.260521i
$59$	−0.907007	−	0.192790i	−0.118082	−	0.0250992i	0.148491	−	0.988914i	$-0.452558\pi$
$59$	−0.907007	−	0.192790i	−0.118082	−	0.0250992i	−0.266574	+	0.963815i	$0.585892\pi$
$60$	1.57623	−	4.85115i	0.203491	−	0.626281i
$61$	2.31704			0.296666			0.148333	−	0.988937i	$-0.452609\pi$
$61$	2.31704			0.296666			0.148333	+	0.988937i	$0.452609\pi$
$62$		0			0
$63$	−1.66853			−0.210215
$64$	0.388433	−	1.19547i	0.0485541	−	0.149434i
$65$	10.5522	+	2.24294i	1.30884	+	0.278203i
$66$	2.07168	+	1.50516i	0.255006	+	0.185273i
$67$	1.04345	+	1.80731i	0.127478	+	0.220798i	0.922699	−	0.385522i	$-0.125979\pi$
$67$	1.04345	+	1.80731i	0.127478	+	0.220798i	−0.795221	+	0.606320i	$0.792645\pi$
$68$	0.997488	−	1.72770i	0.120963	−	0.209514i
$69$	2.70642	−	1.20498i	0.325815	−	0.145062i
$70$	1.57877	−	1.14704i	0.188699	−	0.137098i
$71$	−7.06726	−	3.14655i	−0.838730	−	0.373427i	−0.0580164	−	0.998316i	$-0.518478\pi$
$71$	−7.06726	−	3.14655i	−0.838730	−	0.373427i	−0.780714	+	0.624889i	$0.785144\pi$
$72$	5.19552	−	1.10434i	0.612298	−	0.130148i
$73$	0.591367	−	5.62649i	0.0692143	−	0.658530i	−0.903827	−	0.427899i	$-0.859254\pi$
$73$	0.591367	−	5.62649i	0.0692143	−	0.658530i	0.973041	−	0.230632i	$-0.0740793\pi$
$74$	4.80405	+	5.33544i	0.558459	+	0.620232i
$75$	−5.28085	+	5.86498i	−0.609780	+	0.677229i
$76$	−0.605510	−	5.76105i	−0.0694568	−	0.660837i
$77$	−0.970882	−	2.98807i	−0.110642	−	0.340522i
$78$	−0.559458	−	1.72183i	−0.0633461	−	0.194959i
$79$	1.47330	+	14.0175i	0.165759	+	1.57709i	0.688906	+	0.724850i	$0.258091\pi$
$79$	1.47330	+	14.0175i	0.165759	+	1.57709i	−0.523147	+	0.852242i	$0.675242\pi$
$80$	3.40765	−	3.78458i	0.380987	−	0.423129i
$81$	1.56187	+	1.73464i	0.173541	+	0.192737i
$82$	0.0544822	−	0.518364i	0.00601656	−	0.0572437i
$83$	13.7994	−	2.93316i	1.51468	−	0.321956i	0.625762	−	0.780014i	$-0.284788\pi$
$83$	13.7994	−	2.93316i	1.51468	−	0.321956i	0.888922	+	0.458058i	$0.151455\pi$
$84$	0.959476	+	0.427186i	0.104687	+	0.0466098i
$85$	−3.92484	+	2.85157i	−0.425709	+	0.309296i
$86$	4.50800	−	2.00709i	0.486110	−	0.216430i
$87$	2.20891	−	3.82595i	0.236820	−	0.410184i
$88$	5.00086	+	8.66175i	0.533094	+	0.923346i
$89$	3.58784	+	2.60672i	0.380310	+	0.276311i	0.761473	−	0.648196i	$-0.224476\pi$
$89$	3.58784	+	2.60672i	0.380310	+	0.276311i	−0.381163	+	0.924508i	$0.624476\pi$
$90$	−5.46515	−	1.16165i	−0.576078	−	0.122449i
$91$	−0.686415	+	2.11257i	−0.0719559	+	0.221457i
$92$	5.00520			0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	−4.35308	+	13.3974i	−0.446617	+	1.37454i
$96$	−5.12614	−	1.08959i	−0.523184	−	0.111206i
$97$	4.26970	+	3.10212i	0.433522	+	0.314972i	0.783056	−	0.621951i	$-0.213660\pi$
$97$	4.26970	+	3.10212i	0.433522	+	0.314972i	−0.349533	+	0.936924i	$0.613660\pi$
$98$	−2.21232	−	3.83184i	−0.223478	−	0.387075i
$99$	−4.49770	+	7.79025i	−0.452036	+	0.782949i
$100$	−12.1809	+	5.42329i	−1.21809	+	0.542329i
$101$	−3.08028	+	2.23795i	−0.306499	+	0.222684i	−0.730393	−	0.683027i	$-0.760663\pi$
$101$	−3.08028	+	2.23795i	−0.306499	+	0.222684i	0.423894	+	0.905712i	$0.360663\pi$
$102$	0.743774	+	0.331150i	0.0736446	+	0.0327887i
$103$	6.10921	−	1.29855i	0.601958	−	0.127950i	0.103155	−	0.994665i	$-0.467106\pi$
$103$	6.10921	−	1.29855i	0.601958	−	0.127950i	0.498804	+	0.866715i	$0.333773\pi$
$104$	0.739145	−	7.03250i	0.0724792	−	0.689593i
$105$	−1.70900	−	1.89804i	−0.166781	−	0.185229i
$106$	−1.64969	+	1.83217i	−0.160232	+	0.177956i
$107$	−0.243278	−	2.31464i	−0.0235186	−	0.223764i	−0.999968	−	0.00801720i	$-0.997448\pi$
$107$	−0.243278	−	2.31464i	−0.0235186	−	0.223764i	0.976449	−	0.215747i	$-0.0692186\pi$
$108$	−2.20467	−	6.78526i	−0.212144	−	0.652912i
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	0.970531	−	0.240978i	$-0.0774680\pi$
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	−0.926819	+	0.375509i	$0.877468\pi$
$110$	−1.09972	−	10.4632i	−0.104854	−	0.997623i
$111$	6.28749	−	6.98296i	0.596782	−	0.662794i
$112$	0.701651	+	0.779262i	0.0662998	+	0.0736334i
$113$	−0.666949	+	6.34559i	−0.0627413	+	0.596943i	0.917307	+	0.398182i	$0.130359\pi$
$113$	−0.666949	+	6.34559i	−0.0627413	+	0.596943i	−0.980048	+	0.198762i	$0.936308\pi$
$114$	2.31241	−	0.491518i	0.216577	−	0.0460349i
$115$	−11.1193	−	4.95064i	−1.03688	−	0.461650i
$116$	6.03840	−	4.38716i	0.560652	−	0.407337i
$117$	5.80993	−	2.58675i	0.537128	−	0.239145i
$118$	0.319673	−	0.553690i	0.0294283	−	0.0509713i
$119$	−0.499460	−	0.865089i	−0.0457854	−	0.0793026i
$120$	6.57779	+	4.77904i	0.600467	+	0.436265i
$121$	−5.80858	−	1.23465i	−0.528053	−	0.112241i
$122$	−0.493680	+	1.51939i	−0.0446957	+	0.137559i
$123$	−0.682166			−0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	0.355505	−	1.09413i	0.0316709	−	0.0974730i
$127$	1.40072	+	0.297732i	0.124294	+	0.0264195i	0.269639	−	0.962962i	$-0.413096\pi$
$127$	1.40072	+	0.297732i	0.124294	+	0.0264195i	−0.145345	+	0.989381i	$0.546429\pi$
$128$	−8.69550	−	6.31765i	−0.768581	−	0.558407i
$129$	−3.22919	−	5.59312i	−0.284314	−	0.492447i
$130$	−3.71911	+	6.44168i	−0.326187	+	0.564973i
$131$	5.74885	−	2.55955i	0.502279	−	0.223629i	−0.139926	−	0.990162i	$-0.544686\pi$
$131$	5.74885	−	2.55955i	0.502279	−	0.223629i	0.642205	+	0.766533i	$0.278020\pi$
$132$	4.58088	−	3.32820i	0.398714	−	0.289683i
$133$	−2.64978	−	1.17976i	−0.229765	−	0.102298i
$134$	−1.40746	+	0.299164i	−0.121586	+	0.0258439i
$135$	−1.81352	+	17.2545i	−0.156083	+	1.48503i
$136$	2.12781	+	2.36317i	0.182458	+	0.202640i
$137$	8.53135	−	9.47503i	0.728883	−	0.809506i	−0.258808	−	0.965929i	$-0.583330\pi$
$137$	8.53135	−	9.47503i	0.728883	−	0.809506i	0.987690	+	0.156423i	$0.0499962\pi$
$138$	0.213515	+	2.03146i	0.0181756	+	0.172930i
$139$	5.78287	+	17.7978i	0.490496	+	1.50959i	0.823860	+	0.566794i	$0.191816\pi$
$139$	5.78287	+	17.7978i	0.490496	+	1.50959i	−0.333363	+	0.942798i	$0.608184\pi$
$140$	−1.33343	−	4.10387i	−0.112695	−	0.346841i
$141$	−0.0826364	−	0.786233i	−0.00695924	−	0.0662127i
$142$	3.56913	−	3.96392i	0.299514	−	0.332644i
$143$	8.01313	+	8.89948i	0.670092	+	0.744212i
$144$	0.313820	−	2.98580i	0.0261517	−	0.248817i
$145$	−17.7540	+	3.77373i	−1.47439	+	0.313391i
$146$	3.56355	+	1.58659i	0.294921	+	0.131307i
$147$	−4.68495	+	3.40381i	−0.386408	+	0.280742i
$148$	14.5028	−	6.45708i	1.19213	−	0.530768i
$149$	10.0677	−	17.4377i	0.824774	−	1.42855i	−0.0773172	−	0.997007i	$-0.524635\pi$
$149$	10.0677	−	17.4377i	0.824774	−	1.42855i	0.902092	−	0.431545i	$-0.142031\pi$
$150$	−2.72078	−	4.71252i	−0.222150	−	0.384776i
$151$	−12.4366	−	9.03571i	−1.01207	−	0.735315i	−0.0474314	−	0.998874i	$-0.515104\pi$
$151$	−12.4366	−	9.03571i	−1.01207	−	0.735315i	−0.964643	+	0.263559i	$0.915104\pi$
$152$	9.03182	+	1.91977i	0.732577	+	0.155714i
$153$	−0.883790	+	2.72003i	−0.0714502	+	0.219901i
$154$	2.16628			0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	4.68076	−	14.4059i	0.373566	−	1.14972i	−0.570876	−	0.821037i	$-0.693396\pi$
$157$	4.68076	−	14.4059i	0.373566	−	1.14972i	0.944441	−	0.328680i	$-0.106604\pi$
$158$	−9.50584	−	2.02053i	−0.756244	−	0.160745i
$159$	2.61047	+	1.89662i	0.207024	+	0.150412i
$160$	10.7656	+	18.6466i	0.851098	+	1.47414i
$161$	1.25310	−	2.17042i	0.0987577	−	0.171053i
$162$	−1.47026	+	0.654603i	−0.115515	+	0.0514305i
$163$	0.845317	−	0.614159i	0.0662103	−	0.0481046i	−0.554188	−	0.832392i	$-0.686971\pi$
$163$	0.845317	−	0.614159i	0.0662103	−	0.0481046i	0.620398	+	0.784287i	$0.286971\pi$
$164$	−1.05287	−	0.468770i	−0.0822157	−	0.0366048i
$165$	−13.4686	+	2.86284i	−1.04853	+	0.222872i
$166$	−1.01677	+	9.67388i	−0.0789163	+	0.750839i
$167$	−7.55409	−	8.38966i	−0.584553	−	0.649212i	0.376226	−	0.926528i	$-0.377222\pi$
$167$	−7.55409	−	8.38966i	−0.584553	−	0.649212i	−0.960779	+	0.277316i	$0.910555\pi$
$168$	−1.12021	+	1.24412i	−0.0864259	+	0.0959857i
$169$	0.473864	+	4.50851i	0.0364511	+	0.346809i
$170$	−1.03366	−	3.18127i	−0.0792779	−	0.243992i
$171$	2.56625	+	7.89810i	0.196246	+	0.603983i
$172$	−1.14055	−	10.8516i	−0.0869662	−	0.827428i
$173$	−13.8193	+	15.3479i	−1.05067	+	1.16688i	−0.0650489	+	0.997882i	$0.520720\pi$
$173$	−13.8193	+	15.3479i	−1.05067	+	1.16688i	−0.985616	+	0.169000i	$0.945946\pi$
$174$	2.03821	+	2.26366i	0.154516	+	0.171608i
$175$	−0.697873	+	6.63982i	−0.0527543	+	0.501923i
$176$	5.52970	−	1.17537i	0.416817	−	0.0885971i
$177$	−0.764427	−	0.340345i	−0.0574578	−	0.0255819i
$178$	−2.47379	+	1.79731i	−0.185418	+	0.134714i
$179$	−0.120280	+	0.0535519i	−0.00899012	+	0.00400266i	−0.411227	−	0.911533i	$-0.634900\pi$
$179$	−0.120280	+	0.0535519i	−0.00899012	+	0.00400266i	0.402237	+	0.915536i	$0.368233\pi$
$180$	−6.17723	+	10.6993i	−0.460424	+	0.797477i
$181$	−3.86599	−	6.69610i	−0.287357	−	0.497717i	0.685821	−	0.727770i	$-0.259443\pi$
$181$	−3.86599	−	6.69610i	−0.287357	−	0.497717i	−0.973178	+	0.230053i	$0.926110\pi$
$182$	−1.23906	−	0.900229i	−0.0918451	−	0.0667294i
$183$	2.04521	+	0.434722i	0.151186	+	0.0321356i
$184$	−2.46540	+	7.58772i	−0.181752	+	0.559374i
$185$	−38.6056			−2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	0.412739	−	1.27028i	0.0301021	−	0.0926447i
$189$	−3.49428	−	0.742732i	−0.254171	−	0.0540258i
$190$	−7.85781	−	5.70903i	−0.570066	−	0.414177i
$191$	10.5513	+	18.2755i	0.763468	+	1.32237i	0.941053	+	0.338260i	$0.109838\pi$
$191$	10.5513	+	18.2755i	0.763468	+	1.32237i	−0.177585	+	0.984106i	$0.556828\pi$
$192$	0.567157	−	0.982344i	0.0409310	−	0.0708946i
$193$	5.17362	−	2.30345i	0.372406	−	0.165806i	−0.211995	−	0.977271i	$-0.567996\pi$
$193$	5.17362	−	2.30345i	0.372406	−	0.165806i	0.584401	+	0.811465i	$0.301330\pi$
$194$	−2.94393	+	2.13889i	−0.211362	+	0.153563i
$195$	8.89342	+	3.95960i	0.636871	+	0.283553i
$196$	−9.56991	+	2.03415i	−0.683565	+	0.145296i
$197$	−1.66355	+	15.8276i	−0.118523	+	1.12767i	0.759984	+	0.649942i	$0.225207\pi$
$197$	−1.66355	+	15.8276i	−0.118523	+	1.12767i	−0.878507	+	0.477729i	$0.841460\pi$
$198$	−4.15013	−	4.60918i	−0.294937	−	0.327560i
$199$	−2.85147	+	3.16688i	−0.202135	+	0.224494i	−0.835686	−	0.549207i	$-0.814930\pi$
$199$	−2.85147	+	3.16688i	−0.202135	+	0.224494i	0.633551	+	0.773701i	$0.281597\pi$
$200$	−2.22161	−	21.1372i	−0.157091	−	1.49463i
$201$	0.581946	+	1.79105i	0.0410473	+	0.126331i
$202$	−0.811230	−	2.49671i	−0.0570779	−	0.175668i
$203$	−0.390654	−	3.71682i	−0.0274185	−	0.260870i
$204$	1.20461	−	1.33786i	0.0843399	−	0.0936689i
$205$	1.87536	+	2.08280i	0.130981	+	0.145469i
$206$	−0.450137	+	4.28277i	−0.0313625	+	0.298395i
$207$	−7.01867	+	1.49186i	−0.487831	+	0.103692i
$208$	−3.65130	−	1.62566i	−0.253172	−	0.112719i
$209$	−12.6510	+	9.19148i	−0.875087	+	0.635788i
$210$	1.60876	−	0.716266i	0.111015	−	0.0494270i
$211$	5.75414	−	9.96646i	0.396131	−	0.686120i	−0.597113	−	0.802157i	$-0.703686\pi$
$211$	5.75414	−	9.96646i	0.396131	−	0.686120i	0.993245	+	0.116037i	$0.0370191\pi$
$212$	2.72576	+	4.72115i	0.187206	+	0.324250i
$213$	−5.64779	−	4.10336i	−0.386980	−	0.281157i
$214$	1.56965	+	0.333639i	0.107299	+	0.0228071i
$215$	−8.19954	+	25.2356i	−0.559204	+	1.72105i
$216$	11.3722			0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	1.57763	−	4.85544i	0.106606	−	0.328100i
$220$	−22.7551	−	4.83675i	−1.53415	−	0.326093i
$221$	3.08032	+	2.23798i	0.207204	+	0.150543i
$222$	3.23941	+	5.61082i	0.217415	+	0.376574i
$223$	−4.71196	+	8.16135i	−0.315536	+	0.546524i	−0.979551	−	0.201195i	$-0.935518\pi$
$223$	−4.71196	+	8.16135i	−0.315536	+	0.546524i	0.664015	+	0.747719i	$0.268851\pi$
$224$	−4.05010	+	1.80322i	−0.270608	+	0.120483i
$225$	15.4645	−	11.2356i	1.03097	−	0.749042i
$226$	−4.01900	−	1.78937i	−0.267340	−	0.119027i
$227$	−21.2875	+	4.52479i	−1.41290	+	0.300321i	−0.850251	−	0.526377i	$-0.823550\pi$
$227$	−21.2875	+	4.52479i	−1.41290	+	0.300321i	−0.562646	+	0.826698i	$0.690217\pi$
$228$	0.546413	−	5.19877i	0.0361871	−	0.344297i
$229$	11.3457	+	12.6007i	0.749745	+	0.832677i	0.990443	−	0.137924i	$-0.0440428\pi$
$229$	11.3457	+	12.6007i	0.749745	+	0.832677i	−0.240697	+	0.970600i	$0.577376\pi$
$230$	5.61551	−	6.23665i	0.370276	−	0.411233i
$231$	−0.296359	−	2.81967i	−0.0194990	−	0.185521i
$232$	3.67647	+	11.3150i	0.241372	+	0.742866i
$233$	−3.03952	−	9.35469i	−0.199126	−	0.612846i	−0.999904	−	0.0138848i	$-0.995580\pi$
$233$	−3.03952	−	9.35469i	−0.199126	−	0.612846i	0.800778	−	0.598962i	$-0.204420\pi$
$234$	0.458358	+	4.36099i	0.0299638	+	0.285087i
$235$	−2.17336	+	2.41376i	−0.141774	+	0.157456i
$236$	−0.945960	−	1.05060i	−0.0615768	−	0.0683879i
$237$	−1.32951	+	12.6494i	−0.0863607	+	0.821667i
$238$	0.673697	−	0.143199i	0.0436693	−	0.00928219i
$239$	0.539572	+	0.240233i	0.0349020	+	0.0155394i	0.424113	−	0.905609i	$-0.360586\pi$
$239$	0.539572	+	0.240233i	0.0349020	+	0.0155394i	−0.389211	+	0.921148i	$0.627252\pi$
$240$	3.71793	−	2.70124i	0.239992	−	0.174364i
$241$	14.0416	−	6.25172i	0.904499	−	0.402709i	0.0988501	−	0.995102i	$-0.468484\pi$
$241$	14.0416	−	6.25172i	0.904499	−	0.402709i	0.805649	+	0.592393i	$0.201817\pi$
$242$	2.04722	−	3.54590i	0.131601	−	0.227939i
$243$	8.07252	+	13.9820i	0.517852	+	0.896946i
$244$	2.85790	+	2.07639i	0.182958	+	0.132927i
$245$	23.2721	+	4.94663i	1.48680	+	0.316029i
$246$	0.145346	−	0.447328i	0.00926690	−	0.0285206i
$247$	11.0557			0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	−2.95887	+	9.10646i	−0.187135	+	0.575943i
$251$	5.91926	+	1.25818i	0.373621	+	0.0794155i	0.390895	−	0.920435i	$-0.372166\pi$
$251$	5.91926	+	1.25818i	0.373621	+	0.0794155i	−0.0172744	+	0.999851i	$0.505499\pi$
$252$	−2.05801	−	1.49523i	−0.129642	−	0.0941907i
$253$	−6.75571	−	11.7012i	−0.424728	−	0.735650i
$254$	−0.493682	+	0.855082i	−0.0309763	+	0.0536526i
$255$	−3.99940	+	1.78065i	−0.250452	+	0.111508i
$256$	8.02935	−	5.83366i	0.501834	−	0.364604i
$257$	−4.13639	−	1.84164i	−0.258021	−	0.114878i	0.273650	−	0.961829i	$-0.411769\pi$
$257$	−4.13639	−	1.84164i	−0.258021	−	0.114878i	−0.531671	+	0.846951i	$0.678436\pi$
$258$	4.35570	−	0.925833i	0.271174	−	0.0576398i
$259$	0.830903	−	7.90551i	0.0516298	−	0.491224i
$260$	11.0054	+	12.2227i	0.682526	+	0.758022i
$261$	−7.15986	+	7.95183i	−0.443184	+	0.492206i
$262$	0.453539	+	4.31514i	0.0280198	+	0.266590i
$263$	−0.775281	−	2.38607i	−0.0478059	−	0.147131i	0.924304	−	0.381657i	$-0.124646\pi$
$263$	−0.775281	−	2.38607i	−0.0478059	−	0.147131i	−0.972110	+	0.234525i	$0.924646\pi$
$264$	2.78905	+	8.58383i	0.171654	+	0.528298i
$265$	−1.38573	−	13.1844i	−0.0851248	−	0.809909i
$266$	1.33820	−	1.48622i	0.0820502	−	0.0911260i
$267$	2.67785	+	2.97405i	0.163882	+	0.182009i
$268$	−0.332576	+	3.16425i	−0.0203153	+	0.193288i
$269$	−13.0483	+	2.77349i	−0.795567	+	0.169103i	−0.587726	−	0.809060i	$-0.699977\pi$
$269$	−13.0483	+	2.77349i	−0.795567	+	0.169103i	−0.207840	+	0.978163i	$0.566643\pi$
$270$	−10.9282	−	4.86554i	−0.665067	−	0.296107i
$271$	−11.1840	+	8.12564i	−0.679379	+	0.493598i	−0.873152	−	0.487449i	$-0.837928\pi$
$271$	−11.1840	+	8.12564i	−0.679379	+	0.493598i	0.193773	+	0.981046i	$0.437928\pi$
$272$	1.64200	−	0.731066i	0.0995609	−	0.0443274i
$273$	−1.00225	+	1.73594i	−0.0606586	+	0.105064i
$274$	4.39548	+	7.61320i	0.265541	+	0.459930i
$275$	29.1197	+	21.1567i	1.75598	+	1.27580i
$276$	4.41799	+	0.939074i	0.265932	+	0.0565256i
$277$	3.57556	−	11.0044i	0.214834	−	0.661192i	−0.784331	−	0.620343i	$-0.786994\pi$
$277$	3.57556	−	11.0044i	0.214834	−	0.661192i	0.999165	−	0.0408496i	$-0.0130065\pi$
$278$	−12.9030			−0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	0.702855	+	0.711333i	$0.251908\pi$
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	−0.986733	+	0.162353i	$0.948092\pi$
$282$	0.533176	+	0.113330i	0.0317502	+	0.00674871i
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.979645	−	0.200736i	$-0.0643333\pi$
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.111816	+	0.993729i	$0.464333\pi$
$284$	−5.89722	−	10.2143i	−0.349935	−	0.606106i
$285$	−6.35600	+	11.0089i	−0.376497	+	0.652112i
$286$	−7.54312	+	3.35842i	−0.446034	+	0.198587i
$287$	−0.466871	+	0.339202i	−0.0275585	+	0.0200224i
$288$	11.5958	+	5.16279i	0.683291	+	0.304221i
$289$	14.9537	−	3.17851i	0.879629	−	0.186971i
$290$	1.30815	−	12.4462i	0.0768169	−	0.730864i
$291$	3.18677	+	3.53926i	0.186812	+	0.207475i
$292$	5.77151	−	6.40991i	0.337752	−	0.375112i
$293$	−1.29624	−	12.3329i	−0.0757273	−	0.720497i	−0.964845	−	0.262819i	$-0.915348\pi$
$293$	−1.29624	−	12.3329i	−0.0757273	−	0.720497i	0.889118	−	0.457678i	$-0.151319\pi$
$294$	−1.23384	−	3.79737i	−0.0719591	−	0.221467i
$295$	1.06236	+	3.26961i	0.0618530	+	0.190364i
$296$	2.64509	+	25.1664i	0.153743	+	1.46277i
$297$	−12.8870	+	14.3124i	−0.747778	+	0.830492i
$298$	9.28964	+	10.3172i	0.538134	+	0.597659i
$299$	−0.998518	+	9.50026i	−0.0577458	+	0.549414i
$300$	−11.7694	+	2.50166i	−0.679505	+	0.144433i
$301$	−4.99118	−	2.22222i	−0.287687	−	0.128086i
$302$	8.57493	−	6.23005i	0.493432	−	0.358499i
$303$	−3.13878	+	1.39748i	−0.180318	+	0.0802830i
$304$	2.60953	−	4.51984i	0.149667	−	0.259231i
$305$	−4.29523	−	7.43956i	−0.245944	−	0.425988i
$306$	−1.59534	−	1.15908i	−0.0911997	−	0.0662605i
$307$	−30.0487	−	6.38704i	−1.71497	−	0.364528i	−0.757449	−	0.652894i	$-0.773554\pi$
$307$	−30.0487	−	6.38704i	−1.71497	−	0.364528i	−0.957520	+	0.288367i	$0.906888\pi$
$308$	1.48021	−	4.55561i	0.0843426	−	0.259580i
$309$	5.63612			0.320628
$310$		0			0
$311$	2.38141			0.135037			0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141			0.135037			0.0675187	+	0.997718i	$0.478492\pi$
$312$	1.97187	−	6.06878i	0.111635	−	0.343577i
$313$	−10.5108	−	2.23413i	−0.594104	−	0.126281i	−0.0989597	−	0.995091i	$-0.531551\pi$
$313$	−10.5108	−	2.23413i	−0.594104	−	0.126281i	−0.495144	+	0.868811i	$0.664885\pi$
$314$	8.44932	+	6.13879i	0.476823	+	0.346432i
$315$	3.09305	+	5.35732i	0.174274	+	0.301851i
$316$	−10.7444	+	18.6098i	−0.604420	+	1.04689i
$317$	7.99019	−	3.55746i	0.448774	−	0.199807i	−0.169890	−	0.985463i	$-0.554341\pi$
$317$	7.99019	−	3.55746i	0.448774	−	0.199807i	0.618663	+	0.785656i	$0.287674\pi$
$318$	−1.79990	+	1.30770i	−0.100933	+	0.0733324i
$319$	−18.4066	−	8.19516i	−1.03057	−	0.458841i
$320$	−4.55849	+	0.968937i	−0.254827	+	0.0541652i
$321$	0.219534	−	2.08873i	0.0122532	−	0.116581i
$322$	1.15626	+	1.28415i	0.0644357	+	0.0715631i
$323$	−3.32678	+	3.69476i	−0.185107	+	0.205582i
$324$	0.371985	+	3.53920i	0.0206658	+	0.196622i
$325$	−7.86379	−	24.2022i	−0.436204	−	1.34250i
$326$	0.222625	+	0.685170i	0.0123301	+	0.0379480i
$327$	0.139304	+	1.32539i	0.00770353	+	0.0732942i
$328$	1.22925	−	1.36522i	0.0678741	−	0.0753818i
$329$	−0.447504	−	0.497003i	−0.0246717	−	0.0274007i
$330$	0.992390	−	9.44196i	0.0546293	−	0.519763i
$331$	31.6618	−	6.72991i	1.74029	−	0.369910i	0.775175	−	0.631746i	$-0.217661\pi$
$331$	31.6618	−	6.72991i	1.74029	−	0.369910i	0.965112	+	0.261837i	$0.0843281\pi$
$332$	19.6491	+	8.74834i	1.07838	+	0.480128i
$333$	−18.4124	+	13.3774i	−1.00899	+	0.733075i
$334$	7.11100	−	3.16602i	0.389097	−	0.173237i
$335$	3.86860	−	6.70062i	0.211364	−	0.366094i
$336$	0.473129	+	0.819484i	0.0258113	+	0.0447065i
$337$	−22.4371	−	16.3015i	−1.22223	−	0.888000i	−0.225944	−	0.974140i	$-0.572547\pi$
$337$	−22.4371	−	16.3015i	−1.22223	−	0.888000i	−0.996283	+	0.0861400i	$0.972547\pi$
$338$	−3.05741	−	0.649872i	−0.166301	−	0.0353484i
$339$	−1.77926	+	5.47600i	−0.0966362	+	0.297416i
$340$	−7.39640			−0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	−3.16515	+	9.74132i	−0.170902	+	0.525982i
$344$	17.0125	+	3.61612i	0.917253	+	0.194968i
$345$	−8.88598	−	6.45605i	−0.478405	−	0.347582i
$346$	−7.11994	−	12.3321i	−0.382770	−	0.662977i
$347$	12.9580	−	22.4440i	0.695624	−	1.20486i	−0.274347	−	0.961631i	$-0.588462\pi$
$347$	12.9580	−	22.4440i	0.695624	−	1.20486i	0.969970	−	0.243224i	$-0.0782051\pi$
$348$	6.15310	−	2.73954i	0.329841	−	0.146855i
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	−0.702285	−	0.711896i	$-0.747837\pi$
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	0.460036	+	0.887900i	$0.347837\pi$
$350$	−4.20535	−	1.87234i	−0.224785	−	0.100081i
$351$	13.3188	−	2.83100i	0.710905	−	0.151107i
$352$	−2.49837	+	23.7704i	−0.133163	+	1.26697i
$353$	7.80807	+	8.67174i	0.415582	+	0.461550i	0.914195	−	0.405274i	$-0.132824\pi$
$353$	7.80807	+	8.67174i	0.415582	+	0.461550i	−0.498614	+	0.866824i	$0.666157\pi$
$354$	0.386052	−	0.428755i	0.0205185	−	0.0227881i
$355$	2.99805	+	28.5245i	0.159120	+	1.51393i
$356$	2.08936	+	6.43039i	0.110736	+	0.340810i
$357$	−0.278556	−	0.857307i	−0.0147427	−	0.0453735i
$358$	−0.00948912	−	0.0902830i	−0.000501516	−	0.00477160i
$359$	17.5311	−	19.4703i	0.925257	−	1.02760i	−0.0742818	−	0.997237i	$-0.523666\pi$
$359$	17.5311	−	19.4703i	0.925257	−	1.02760i	0.999539	−	0.0303649i	$-0.00966692\pi$
$360$	−13.1771	−	14.6346i	−0.694492	−	0.771312i
$361$	0.477014	−	4.53848i	0.0251060	−	0.238868i
$362$	5.21465	−	1.10841i	0.274076	−	0.0582566i
$363$	−4.89548	−	2.17961i	−0.256946	−	0.114400i
$364$	−2.73979	+	1.99058i	−0.143604	+	0.104335i
$365$	−19.1618	+	8.53138i	−1.00297	+	0.446553i
$366$	−0.720830	+	1.24851i	−0.0376784	+	0.0652608i
$367$	−13.5073	−	23.3953i	−0.705076	−	1.22123i	−0.966664	−	0.256047i	$-0.917580\pi$
$367$	−13.5073	−	23.3953i	−0.705076	−	1.22123i	0.261589	−	0.965179i	$-0.415754\pi$
$368$	3.64825	+	2.65061i	0.190178	+	0.138173i
$369$	1.61614	+	0.343522i	0.0841331	+	0.0178830i
$370$	8.22549	−	25.3155i	0.427623	−	1.31609i
$371$	2.72967			0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$	1.14744	−	3.53145i	0.0593326	−	0.182607i
$375$	12.2579	+	2.60550i	0.632997	+	0.134548i
$376$	1.72240	+	1.25140i	0.0888261	+	0.0645359i
$377$	7.12253	+	12.3366i	0.366829	+	0.635367i
$378$	1.23155	−	2.13311i	0.0633442	−	0.109715i
$379$	−4.23795	+	1.88686i	−0.217689	+	0.0969213i	−0.512684	−	0.858577i	$-0.671349\pi$
$379$	−4.23795	+	1.88686i	−0.217689	+	0.0969213i	0.294995	+	0.955499i	$0.404682\pi$
$380$	−17.3751	+	12.6238i	−0.891325	+	0.647585i
$381$	1.18053	+	0.525606i	0.0604804	+	0.0269276i
$382$	−14.2322	+	3.02514i	−0.728182	+	0.154780i
$383$	0.524872	−	4.99383i	0.0268197	−	0.255173i	−0.972894	−	0.231251i	$-0.925718\pi$
$383$	0.524872	−	4.99383i	0.0268197	−	0.255173i	0.999714	−	0.0239216i	$-0.00761520\pi$
$384$	−6.49004	−	7.20792i	−0.331194	−	0.367828i
$385$	−7.79432	+	8.65647i	−0.397235	+	0.441175i
$386$	0.408159	+	3.88337i	0.0207747	+	0.197658i
$387$	4.83383	+	14.8770i	0.245718	+	0.756241i
$388$	2.48644	+	7.65247i	0.126230	+	0.388496i
$389$	−1.94442	−	18.4999i	−0.0985861	−	0.937984i	−0.926288	−	0.376816i	$-0.877019\pi$
$389$	−1.94442	−	18.4999i	−0.0985861	−	0.937984i	0.827702	−	0.561168i	$-0.189648\pi$
$390$	−4.49137	+	4.98817i	−0.227429	+	0.252586i
$391$	−2.87447	−	3.19242i	−0.145368	−	0.161448i
$392$	1.63013	−	15.5096i	0.0823339	−	0.783355i
$393$	5.55462	−	1.18067i	0.280194	−	0.0595570i
$394$	−10.0245	−	4.46318i	−0.505025	−	0.224852i
$395$	42.2763	−	30.7155i	2.12715	−	1.54547i
$396$	−12.5287	+	5.57815i	−0.629592	+	0.280312i
$397$	−16.2794	+	28.1968i	−0.817040	+	1.41515i	0.0908142	+	0.995868i	$0.471053\pi$
$397$	−16.2794	+	28.1968i	−0.817040	+	1.41515i	−0.907854	+	0.419287i	$0.862280\pi$
$398$	−1.46912	−	2.54459i	−0.0736404	−	0.127549i
$399$	−2.11757	−	1.53850i	−0.106011	−	0.0770214i
$400$	−11.7506	−	2.49766i	−0.587529	−	0.124883i
$401$	−3.82880	+	11.7838i	−0.191201	+	0.588457i	0.808799	+	0.588086i	$0.200118\pi$
$401$	−3.82880	+	11.7838i	−0.191201	+	0.588457i	−1.00000		0.000371451i	$0.999882\pi$
$402$	−1.29847			−0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	2.67424	−	8.23046i	0.132884	−	0.408975i
$406$	2.52053	+	0.535755i	0.125092	+	0.0265891i
$407$	−34.6705	−	25.1896i	−1.71855	−	1.24860i
$408$	1.43480	+	2.48514i	0.0710331	+	0.123033i
$409$	1.72404	−	2.98613i	0.0852484	−	0.147654i	−0.820249	−	0.572007i	$-0.806165\pi$
$409$	1.72404	−	2.98613i	0.0852484	−	0.147654i	0.905497	+	0.424353i	$0.139498\pi$
$410$	−1.76536	+	0.785989i	−0.0871850	+	0.0388173i
$411$	9.30817	−	6.76278i	0.459138	−	0.333583i
$412$	8.69895	+	3.87302i	0.428566	+	0.190810i
$413$	−0.692404	+	0.147175i	−0.0340709	+	0.00724200i
$414$	0.517148	−	4.92033i	0.0254164	−	0.241821i
$415$	−34.9986	−	38.8699i	−1.71801	−	1.90805i
$416$	11.3071	−	12.5579i	0.554379	−	0.615700i
$417$	1.76520	+	16.7948i	0.0864424	+	0.822444i
$418$	−3.33180	−	10.2542i	−0.162964	−	0.501550i
$419$	−12.3752	−	38.0871i	−0.604570	−	1.86068i	−0.499717	−	0.866189i	$-0.666563\pi$
$419$	−12.3752	−	38.0871i	−0.604570	−	1.86068i	−0.104854	−	0.994488i	$-0.533437\pi$
$420$	−0.407026	−	3.87259i	−0.0198608	−	0.188963i
$421$	14.5097	−	16.1147i	0.707160	−	0.785381i	−0.277339	−	0.960772i	$-0.589452\pi$
$421$	14.5097	−	16.1147i	0.707160	−	0.785381i	0.984499	+	0.175392i	$0.0561191\pi$
$422$	5.30947	+	5.89676i	0.258461	+	0.287050i
$423$	−0.200151	+	1.90431i	−0.00973165	+	0.0925905i
$424$	−8.49974	+	1.80667i	−0.412784	+	0.0877399i
$425$	10.4545	+	4.65467i	0.507120	+	0.225784i
$426$	3.89411	−	2.82924i	0.188670	−	0.137077i
$427$	1.61589	−	0.719441i	0.0781985	−	0.0348162i
$428$	1.77417	−	3.07294i	0.0857575	−	0.148536i
$429$	5.40332	+	9.35883i	0.260875	+	0.451849i
$430$	−14.8011	−	10.7536i	−0.713774	−	0.518587i
$431$	11.3667	+	2.41607i	0.547516	+	0.116378i	0.473361	−	0.880869i	$-0.343041\pi$
$431$	11.3667	+	2.41607i	0.547516	+	0.116378i	0.0741552	+	0.997247i	$0.476374\pi$
$432$	1.98632	−	6.11325i	0.0955667	−	0.294124i
$433$	24.5964			1.18203			0.591015	−	0.806661i	$-0.298728\pi$
$433$	24.5964			1.18203			0.591015	+	0.806661i	$0.298728\pi$
$434$		0			0
$435$	−16.3791			−0.785320
$436$	−0.695773	+	2.14137i	−0.0333215	+	0.102553i
$437$	−12.2012	−	2.59344i	−0.583660	−	0.124061i
$438$	2.84780	+	2.06905i	0.136073	+	0.0988630i
$439$	−9.09662	−	15.7558i	−0.434158	−	0.751984i	0.563068	−	0.826410i	$-0.309621\pi$
$439$	−9.09662	−	15.7558i	−0.434158	−	0.751984i	−0.997227	+	0.0744265i	$0.976287\pi$
$440$	18.5408	−	32.1136i	0.883897	−	1.53096i
$441$	12.8134	−	5.70487i	0.610160	−	0.271661i
$442$	−2.12386	+	1.54307i	−0.101021	+	0.0733964i
$443$	16.2249	+	7.22378i	0.770867	+	0.343212i	0.754196	−	0.656649i	$-0.228027\pi$
$443$	16.2249	+	7.22378i	0.770867	+	0.343212i	0.0166706	+	0.999861i	$0.494693\pi$
$444$	14.0129	−	2.97852i	0.665021	−	0.141354i
$445$	1.71867	−	16.3521i	0.0814728	−	0.775162i
$446$	−4.34782	−	4.82875i	−0.205875	−	0.228648i
$447$	12.1582	−	13.5030i	0.575062	−	0.638671i
$448$	−0.100304	−	0.954326i	−0.00473890	−	0.0450876i
$449$	−2.84252	−	8.74836i	−0.134147	−	0.412861i	0.861310	−	0.508080i	$-0.169645\pi$
$449$	−2.84252	−	8.74836i	−0.134147	−	0.412861i	−0.995456	+	0.0952196i	$0.969645\pi$
$450$	4.07278	+	12.5347i	0.191993	+	0.590892i
$451$	0.325208	+	3.09414i	0.0153134	+	0.145698i
$452$	−6.50915	+	7.22915i	−0.306165	+	0.340031i
$453$	−9.28226	−	10.3090i	−0.436119	−	0.484359i
$454$	1.56850	−	14.9232i	0.0736132	−	0.700383i
$455$	8.05549	−	1.71225i	0.377647	−	0.0802714i
$456$	7.61203	+	3.38909i	0.356466	+	0.158709i
$457$	25.2412	−	18.3388i	1.18074	−	0.857855i	0.188481	−	0.982077i	$-0.439644\pi$
$457$	25.2412	−	18.3388i	1.18074	−	0.857855i	0.992254	+	0.124222i	$0.0396436\pi$
$458$	−10.6802	+	4.75514i	−0.499054	+	0.222193i
$459$	−3.06166	+	5.30294i	−0.142906	+	0.247520i
$460$	−9.27842	−	16.0707i	−0.432609	−	0.749300i
$461$	5.39491	+	3.91963i	0.251266	+	0.182555i	0.706288	−	0.707925i	$-0.250369\pi$
$461$	5.39491	+	3.91963i	0.251266	+	0.182555i	−0.455022	+	0.890480i	$0.650369\pi$
$462$	1.91213	+	0.406436i	0.0889604	+	0.0189091i
$463$	10.9140	−	33.5899i	0.507217	−	1.56105i	−0.289795	−	0.957089i	$-0.593587\pi$
$463$	10.9140	−	33.5899i	0.507217	−	1.56105i	0.797011	−	0.603964i	$-0.206413\pi$
$464$	6.72466			0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	−0.271159	−	0.962535i	$-0.587407\pi$
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	0.785136	−	0.619324i	$-0.212593\pi$
$468$	9.48421	+	2.01593i	0.438408	+	0.0931865i
$469$	1.28886	+	0.936415i	0.0595143	+	0.0432396i
$470$	−1.11975	−	1.93946i	−0.0516501	−	0.0894606i
$471$	6.83446	−	11.8376i	0.314915	−	0.545449i
$472$	2.05862	−	0.916556i	0.0947556	−	0.0421879i
$473$	−23.8296	+	17.3132i	−1.09569	+	0.796064i
$474$	−8.01154	−	3.56697i	−0.367982	−	0.163836i
$475$	32.5034	−	6.90882i	1.49136	−	0.316998i
$476$	0.159192	−	1.51461i	0.00729655	−	0.0694220i
$477$	−5.22947	−	5.80791i	−0.239441	−	0.265926i
$478$	−0.272496	+	0.302637i	−0.0124637	+	0.0138423i
$479$	−3.47499	−	33.0623i	−0.158776	−	1.51065i	−0.726346	−	0.687329i	$-0.758783\pi$
$479$	−3.47499	−	33.0623i	−0.158776	−	1.51065i	0.567570	−	0.823325i	$-0.307884\pi$
$480$	6.00415	+	18.4789i	0.274051	+	0.843441i
$481$	9.36278	+	28.8157i	0.426906	+	1.31388i
$482$	1.10777	+	10.5398i	0.0504577	+	0.480073i
$483$	1.51330	−	1.68069i	0.0688574	−	0.0764739i
$484$	−6.05805	−	6.72814i	−0.275366	−	0.305825i
$485$	2.04530	−	19.4597i	0.0928724	−	0.883621i
$486$	−10.8886	+	2.31445i	−0.493918	+	0.104986i
$487$	26.0501	+	11.5982i	1.18044	+	0.525566i	0.900672	−	0.434501i	$-0.143075\pi$
$487$	26.0501	+	11.5982i	1.18044	+	0.525566i	0.279770	+	0.960067i	$0.409742\pi$
$488$	−4.55544	+	3.30972i	−0.206215	+	0.149824i
$489$	0.861374	−	0.383508i	0.0389527	−	0.0173428i
$490$	−8.20220	+	14.2066i	−0.370538	+	0.641790i
$491$	13.9818	+	24.2172i	0.630991	+	1.09291i	0.987350	+	0.158559i	$0.0506848\pi$
$491$	13.9818	+	24.2172i	0.630991	+	1.09291i	−0.356359	+	0.934349i	$0.615982\pi$
$492$	−0.841402	−	0.611315i	−0.0379333	−	0.0275602i
$493$	−6.26606	−	1.33189i	−0.282209	−	0.0599854i
$494$	−2.35559	+	7.24975i	−0.105983	+	0.326182i
$495$	33.3506			1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	−2.71249	+	8.34819i	−0.121550	+	0.374091i
$499$	40.4024	+	8.58778i	1.80866	+	0.384442i	0.983565	−	0.180555i	$-0.0577895\pi$
$499$	40.4024	+	8.58778i	1.80866	+	0.384442i	0.825093	+	0.564997i	$0.191123\pi$
$500$	17.1288	+	12.4448i	0.766023	+	0.556548i
$501$	−5.09378	−	8.82269i	−0.227573	−	0.394169i
$502$	−2.08623	+	3.61346i	−0.0931132	+	0.161277i
$503$	−23.3740	+	10.4068i	−1.04220	+	0.464015i	−0.855174	−	0.518341i	$-0.826550\pi$
$503$	−23.3740	+	10.4068i	−1.04220	+	0.464015i	−0.187021	+	0.982356i	$0.559883\pi$
$504$	3.28043	−	2.38337i	0.146122	−	0.106164i
$505$	12.8957	+	5.74154i	0.573851	+	0.255495i
$506$	9.11245	−	1.93691i	0.405098	−	0.0861062i
$507$	−0.427615	+	4.06849i	−0.0189911	+	0.180688i
$508$	1.46088	+	1.62247i	0.0648160	+	0.0719855i
$509$	−16.3721	+	18.1831i	−0.725683	+	0.805952i	−0.987241	−	0.159236i	$-0.949097\pi$
$509$	−16.3721	+	18.1831i	−0.725683	+	0.805952i	0.261558	+	0.965188i	$0.415764\pi$
$510$	−0.315521	−	3.00198i	−0.0139715	−	0.132930i
$511$	−1.33461	−	4.10750i	−0.0590396	−	0.181705i
$512$	−4.52814	−	13.9362i	−0.200118	−	0.615898i
$513$	1.85853	+	17.6828i	0.0820563	+	0.780713i
$514$	2.08897	−	2.32003i	0.0921404	−	0.102332i
$515$	−15.4944	−	17.2083i	−0.682765	−	0.758287i
$516$	1.02923	−	9.79251i	0.0453095	−	0.431091i
$517$	−3.52677	+	0.749638i	−0.155107	+	0.0329690i
$518$	5.00697	+	2.22925i	0.219994	+	0.0979476i
$519$	−15.0776	+	10.9546i	−0.661835	+	0.480851i
$520$	−23.9502	+	10.6633i	−1.05028	+	0.467617i
$521$	−7.48279	+	12.9606i	−0.327827	+	0.567813i	−0.982080	−	0.188462i	$-0.939650\pi$
$521$	−7.48279	+	12.9606i	−0.327827	+	0.567813i	0.654253	+	0.756275i	$0.272983\pi$
$522$	−3.68887	−	6.38931i	−0.161458	−	0.279653i
$523$	16.9615	+	12.3233i	0.741677	+	0.538860i	0.893236	−	0.449589i	$-0.148429\pi$
$523$	16.9615	+	12.3233i	0.741677	+	0.538860i	−0.151559	+	0.988448i	$0.548429\pi$
$524$	9.38450	+	1.99474i	0.409964	+	0.0871405i
$525$	−1.86176	+	5.72991i	−0.0812539	+	0.250074i
$526$	1.72984			0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	−3.77686	+	11.6240i	−0.164211	+	0.505391i
$530$	8.94085	+	1.90044i	0.388366	+	0.0825497i
$531$	1.63964	+	1.19127i	0.0711544	+	0.0516967i
$532$	−2.21109	−	3.82971i	−0.0958628	−	0.166039i
$533$	1.09981	−	1.90492i	0.0476379	−	0.0825113i
$534$	−2.52078	+	1.12232i	−0.109085	+	0.0485676i
$535$	−6.98086	+	5.07189i	−0.301809	+	0.219277i
$536$	−4.63309	−	2.06278i	−0.200119	−	0.0890987i
$537$	−0.116216	+	0.0247025i	−0.00501509	+	0.00106599i
$538$	0.961419	−	9.14729i	0.0414497	−	0.394368i
$539$	17.6723	+	19.6271i	0.761202	+	0.845400i
$540$	−17.6992	+	19.6570i	−0.761654	+	0.845902i
$541$	−0.180970	−	1.72182i	−0.00778052	−	0.0740267i	0.989943	−	0.141469i	$-0.0451827\pi$
$541$	−0.180970	−	1.72182i	−0.00778052	−	0.0740267i	−0.997723	+	0.0674427i	$0.978516\pi$
$542$	−2.94545	−	9.06515i	−0.126518	−	0.389382i
$543$	−2.15612	−	6.63586i	−0.0925280	−	0.284772i
$544$	0.794333	+	7.55757i	0.0340567	+	0.324028i
$545$	3.66373	−	4.06898i	0.156937	−	0.174296i
$546$	−0.924793	−	1.02709i	−0.0395775	−	0.0439553i
$547$	1.37156	−	13.0495i	0.0586438	−	0.557958i	−0.925269	−	0.379311i	$-0.876161\pi$
$547$	1.37156	−	13.0495i	0.0586438	−	0.557958i	0.983913	−	0.178648i	$-0.0571722\pi$
$548$	19.0137	−	4.04149i	0.812226	−	0.172644i
$549$	−4.62646	−	2.05983i	−0.197452	−	0.0879115i
$550$	−20.0778	+	14.5874i	−0.856121	+	0.622008i
$551$	−16.9930	+	7.56577i	−0.723926	+	0.322313i
$552$	−3.59977	+	6.23498i	−0.153216	+	0.265378i
$553$	5.37991	+	9.31828i	0.228777	+	0.396254i
$554$	6.45429	+	4.68932i	0.274217	+	0.199230i
$555$	−34.0764	−	7.24316i	−1.44646	−	0.307455i
$556$	−8.81656	+	27.1346i	−0.373905	+	1.15076i
$557$	−28.0246			−1.18744			−0.593721	−	0.804671i	$-0.702342\pi$
$557$	−28.0246			−1.18744			−0.593721	+	0.804671i	$0.702342\pi$
$558$		0			0
$559$	20.8248			0.880794
$560$	1.20137	−	3.69743i	0.0507670	−	0.156245i
$561$	−4.75358	−	1.01041i	−0.200696	−	0.0426594i
$562$	−8.58993	−	6.24095i	−0.362344	−	0.263259i
$563$	−11.3259	−	19.6171i	−0.477331	−	0.826762i	0.522331	−	0.852743i	$-0.325062\pi$
$563$	−11.3259	−	19.6171i	−0.477331	−	0.826762i	−0.999662	+	0.0259808i	$0.991729\pi$
$564$	0.602646	−	1.04381i	0.0253760	−	0.0439525i
$565$	21.6108	−	9.62175i	0.909174	−	0.404790i
$566$	−12.6599	+	9.19798i	−0.532136	+	0.386620i
$567$	1.62785	+	0.724764i	0.0683632	+	0.0304372i
$568$	18.3893	−	3.90877i	0.771598	−	0.164008i
$569$	4.85451	−	46.1876i	0.203512	−	1.93629i	−0.125783	−	0.992058i	$-0.540144\pi$
$569$	4.85451	−	46.1876i	0.203512	−	1.93629i	0.329294	−	0.944227i	$-0.393189\pi$
$570$	−5.86482	−	6.51354i	−0.245650	−	0.272822i
$571$	−8.36303	+	9.28809i	−0.349982	+	0.388694i	−0.892273	−	0.451496i	$-0.850890\pi$
$571$	−8.36303	+	9.28809i	−0.349982	+	0.388694i	0.542291	+	0.840191i	$0.317557\pi$
$572$	1.90845	+	18.1577i	0.0797965	+	0.759213i
$573$	5.88463	+	18.1110i	0.245834	+	0.756600i
$574$	−0.122956	−	0.378421i	−0.00513210	−	0.0157950i
$575$	3.00119	+	28.5544i	0.125158	+	1.19080i
$576$	−1.83836	+	2.04170i	−0.0765982	+	0.0850709i
$577$	−20.3980	−	22.6542i	−0.849179	−	0.943109i	0.149780	−	0.988719i	$-0.452143\pi$
$577$	−20.3980	−	22.6542i	−0.849179	−	0.943109i	−0.998959	+	0.0456107i	$0.985477\pi$
$578$	−1.10181	+	10.4831i	−0.0458294	+	0.436038i
$579$	4.99883	−	1.06253i	0.207744	−	0.0441574i
$580$	−25.2800	−	11.2554i	−1.04970	−	0.467355i
$581$	8.71290	−	6.33030i	0.361472	−	0.262625i
$582$	−2.99985	+	1.33562i	−0.124348	+	0.0553631i
$583$	7.35812	−	12.7446i	0.304742	−	0.527829i
$584$	6.87436	+	11.9067i	0.284463	+	0.492705i
$585$	−19.0758	−	13.8593i	−0.788685	−	0.573013i
$586$	8.36346	+	1.77771i	0.345491	+	0.0734364i
$587$	10.4009	−	32.0107i	0.429292	−	1.32123i	−0.469532	−	0.882915i	$-0.655577\pi$
$587$	10.4009	−	32.0107i	0.429292	−	1.32123i	0.898824	−	0.438310i	$-0.144423\pi$
$588$	−8.82883			−0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	−4.43796	+	13.6586i	−0.182553	+	0.561841i
$592$	13.9905	+	2.97377i	0.575005	+	0.122221i
$593$	36.3151	+	26.3844i	1.49128	+	1.08348i	0.973697	+	0.227847i	$0.0731687\pi$
$593$	36.3151	+	26.3844i	1.49128	+	1.08348i	0.517585	+	0.855632i	$0.326831\pi$
$594$	−6.63957	−	11.5001i	−0.272425	−	0.471854i
$595$	−1.85175	+	3.20733i	−0.0759145	+	0.131488i
$596$	28.0443	−	12.4861i	1.14874	−	0.511451i
$597$	−3.11111	+	2.26035i	−0.127329	+	0.0925100i
$598$	−6.01701	−	2.67895i	−0.246054	−	0.109550i
$599$	19.1566	−	4.07187i	0.782719	−	0.166372i	0.200815	−	0.979629i	$-0.435641\pi$
$599$	19.1566	−	4.07187i	0.782719	−	0.166372i	0.581905	+	0.813257i	$0.302308\pi$
$600$	2.00478	−	19.0742i	0.0818449	−	0.778702i
$601$	20.3814	+	22.6358i	0.831373	+	0.923333i	0.998034	−	0.0626811i	$-0.0199651\pi$
$601$	20.3814	+	22.6358i	0.831373	+	0.923333i	−0.166661	+	0.986014i	$0.553298\pi$
$602$	2.52066	−	2.79947i	0.102734	−	0.114098i
$603$	−0.476783	−	4.53629i	−0.0194161	−	0.184732i
$604$	−7.24238	−	22.2898i	−0.294688	−	0.906958i
$605$	6.80348	+	20.9390i	0.276601	+	0.851290i
$606$	−0.247626	−	2.35600i	−0.0100591	−	0.0957060i
$607$	−8.94933	+	9.93924i	−0.363242	+	0.403421i	−0.896867	−	0.442300i	$-0.854163\pi$
$607$	−8.94933	+	9.93924i	−0.363242	+	0.403421i	0.533625	+	0.845721i	$0.320829\pi$
$608$	14.7648	+	16.3980i	0.598793	+	0.665027i
$609$	0.352526	−	3.35406i	0.0142851	−	0.135914i
$610$	5.79363	−	1.23147i	0.234577	−	0.0498609i
$611$	2.32875	+	1.03683i	0.0942112	+	0.0419455i
$612$	−3.52761	+	2.56296i	−0.142595	+	0.103601i
$613$	−4.74606	+	2.11308i	−0.191691	+	0.0853465i	−0.500338	−	0.865830i	$-0.666791\pi$
$613$	−4.74606	+	2.11308i	−0.191691	+	0.0853465i	0.308646	+	0.951177i	$0.400124\pi$
$614$	10.5906	−	18.3435i	0.427402	−	0.740282i
$615$	1.26457	+	2.19030i	0.0509924	+	0.0883215i
$616$	6.17705	+	4.48789i	0.248881	+	0.180822i
$617$	29.3572	+	6.24007i	1.18188	+	0.251216i	0.756619	−	0.653856i	$-0.226850\pi$
$617$	29.3572	+	6.24007i	1.18188	+	0.251216i	0.425258	+	0.905072i	$0.360183\pi$
$618$	−1.20086	+	3.69587i	−0.0483057	+	0.148670i
$619$	18.3260			0.736584			0.368292	−	0.929710i	$-0.379943\pi$
$619$	18.3260			0.736584			0.368292	+	0.929710i	$0.379943\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$	−0.507396	+	1.56160i	−0.0203447	+	0.0626146i
$623$	3.31153	+	0.703887i	0.132674	+	0.0282006i
$624$	−2.91793	−	2.12000i	−0.116811	−	0.0848679i
$625$	−3.87924	−	6.71905i	−0.155170	−	0.268762i
$626$	3.70450	−	6.41639i	0.148062	−	0.256450i
$627$	−12.8913	+	5.73957i	−0.514829	+	0.229216i
$628$	18.6831	−	13.5740i	0.745535	−	0.541663i
$629$	−12.4474	−	5.54194i	−0.496310	−	0.220972i
$630$	−4.17206	+	0.886800i	−0.166219	+	0.0353309i
$631$	−1.08032	+	10.2786i	−0.0430070	+	0.409184i	0.951747	+	0.306885i	$0.0992867\pi$
$631$	−1.08032	+	10.2786i	−0.0430070	+	0.409184i	−0.994754	+	0.102299i	$0.967380\pi$
$632$	−22.9196	−	25.4548i	−0.911692	−	1.01254i
$633$	6.94898	−	7.71762i	0.276197	−	0.306748i
$634$	0.630363	+	5.99751i	0.0250349	+	0.238191i
$635$	−1.64064	−	5.04936i	−0.0651067	−	0.200378i
$636$	1.52020	+	4.67868i	0.0602797	+	0.185522i
$637$	−1.95181	−	18.5703i	−0.0773336	−	0.735780i
$638$	9.29576	−	10.3240i	0.368023	−	0.408731i
$639$	11.3140	+	12.5655i	0.447576	+	0.497083i
$640$	−4.16538	+	39.6310i	−0.164651	+	1.56655i
$641$	−0.0990394	+	0.0210515i	−0.00391182	+	0.000831483i	−0.209867	−	0.977730i	$-0.567303\pi$
$641$	−0.0990394	+	0.0210515i	−0.00391182	+	0.000831483i	0.205955	+	0.978561i	$0.433970\pi$
$642$	1.32290	+	0.588994i	0.0522108	+	0.0232457i
$643$	11.0931	−	8.05961i	0.437469	−	0.317840i	−0.347159	−	0.937806i	$-0.612854\pi$
$643$	11.0931	−	8.05961i	0.437469	−	0.317840i	0.784629	+	0.619966i	$0.212854\pi$
$644$	3.49060	−	1.55412i	0.137549	−	0.0612407i
$645$	−11.9723	+	20.7366i	−0.471408	+	0.816503i
$646$	−1.71401	−	2.96875i	−0.0674367	−	0.116804i
$647$	8.76519	+	6.36828i	0.344595	+	0.250363i	0.746598	−	0.665275i	$-0.231686\pi$
$647$	8.76519	+	6.36828i	0.344595	+	0.250363i	−0.402003	+	0.915638i	$0.631686\pi$
$648$	−5.54854	−	1.17938i	−0.217967	−	0.0463304i
$649$	−1.17930	+	3.62951i	−0.0462916	+	0.142471i
$650$	17.5460			0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	−7.49434	+	23.0652i	−0.293276	+	0.902611i	0.690519	+	0.723314i	$0.257382\pi$
$653$	−7.49434	+	23.0652i	−0.293276	+	0.902611i	−0.983795	+	0.179297i	$0.942618\pi$
$654$	−0.898800	−	0.191046i	−0.0351459	−	0.00747049i
$655$	−18.8752	−	13.7136i	−0.737515	−	0.535836i
$656$	−0.519185	−	0.899255i	−0.0202708	−	0.0351100i
$657$	−6.18270	+	10.7087i	−0.241210	+	0.417788i
$658$	0.421256	−	0.187555i	0.0164223	−	0.00731166i
$659$	6.90374	−	5.01586i	0.268932	−	0.195390i	−0.445144	−	0.895459i	$-0.646847\pi$
$659$	6.90374	−	5.01586i	0.268932	−	0.195390i	0.714075	+	0.700069i	$0.246847\pi$
$660$	−19.1780	−	8.53861i	−0.746504	−	0.332365i
$661$	−37.0563	+	7.87657i	−1.44132	+	0.306363i	−0.861242	−	0.508195i	$-0.830313\pi$
$661$	−37.0563	+	7.87657i	−1.44132	+	0.306363i	−0.580083	+	0.814558i	$0.696980\pi$
$662$	−2.33289	+	22.1960i	−0.0906705	+	0.862672i
$663$	2.29905	+	2.55335i	0.0892876	+	0.0991639i
$664$	−22.9407	+	25.4783i	−0.890273	+	0.988748i
$665$	1.12408	+	10.6949i	0.0435900	+	0.414731i
$666$	−4.84913	−	14.9241i	−0.187900	−	0.578297i
$667$	−4.96657	−	15.2855i	−0.192306	−	0.591858i
$668$	−1.79913	−	17.1175i	−0.0696102	−	0.662297i
$669$	−5.69038	+	6.31981i	−0.220003	+	0.244338i
$670$	3.56964	+	3.96449i	0.137907	+	0.153162i
$671$	0.996790	−	9.48382i	0.0384806	−	0.366119i
$672$	−3.91326	+	0.831790i	−0.150957	+	0.0320870i
$673$	6.50454	+	2.89601i	0.250732	+	0.111633i	0.528254	−	0.849086i	$-0.322847\pi$
$673$	6.50454	+	2.89601i	0.250732	+	0.111633i	−0.277523	+	0.960719i	$0.589513\pi$
$674$	15.4702	−	11.2398i	0.595891	−	0.432940i
$675$	37.3877	−	16.6461i	1.43905	−	0.640707i
$676$	−3.45577	+	5.98557i	−0.132914	+	0.230214i
$677$	−24.0305	−	41.6220i	−0.923567	−	1.59966i	−0.793850	−	0.608113i	$-0.791927\pi$
$677$	−24.0305	−	41.6220i	−0.923567	−	1.59966i	−0.129716	−	0.991551i	$-0.541407\pi$
$678$	−3.21177	−	2.33349i	−0.123347	−	0.0896171i
$679$	3.94088	+	0.837659i	0.151237	+	0.0321464i
$680$	3.64323	−	11.2127i	0.139712	−	0.429988i
$681$	−19.6390			−0.752567
$682$		0			0
$683$	32.5731			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$684$	−3.91250	+	12.0414i	−0.149598	+	0.460416i
$685$	−46.2375	−	9.82809i	−1.76664	−	0.375512i
$686$	−5.71346	−	4.15107i	−0.218141	−	0.158489i
$687$	7.65051	+	13.2511i	0.291885	+	0.505560i
$688$	4.91537	−	8.51366i	0.187397	−	0.324580i
$689$	−9.50490	+	4.23185i	−0.362108	+	0.161221i
$690$	6.12682	−	4.45140i	0.233244	−	0.169462i
$691$	24.8969	+	11.0848i	0.947124	+	0.421687i	0.821383	−	0.570376i	$-0.193203\pi$
$691$	24.8969	+	11.0848i	0.947124	+	0.421687i	0.125740	+	0.992063i	$0.459869\pi$
$692$	−30.7990	+	6.54653i	−1.17080	+	0.248862i
$693$	−0.717801	+	6.82942i	−0.0272670	+	0.259428i
$694$	11.9567	+	13.2792i	0.453868	+	0.504072i
$695$	46.4253	−	51.5605i	1.76101	−	1.95580i
$696$	1.12223	+	10.6773i	0.0425381	+	0.404723i
$697$	0.305671	+	0.940760i	0.0115781	+	0.0356338i
$698$	−1.19187	−	3.66820i	−0.0451130	−	0.138844i
$699$	−0.927806	−	8.82749i	−0.0350929	−	0.333886i
$700$	−6.81097	+	7.56435i	−0.257430	+	0.285905i
$701$	5.68035	+	6.30867i	0.214544	+	0.238275i	0.840805	−	0.541338i	$-0.182082\pi$
$701$	5.68035	+	6.30867i	0.214544	+	0.238275i	−0.626261	+	0.779614i	$0.715416\pi$
$702$	−0.981352	+	9.33694i	−0.0370387	+	0.352400i
$703$	−38.6992	+	8.22578i	−1.45957	+	0.310241i
$704$	−4.72606	−	2.10418i	−0.178120	−	0.0793042i
$705$	−2.37125	+	1.72281i	−0.0893065	+	0.0648849i
$706$	−7.35009	+	3.27247i	−0.276624	+	0.123161i
$707$	−1.45328	+	2.51716i	−0.0546564	+	0.0946676i
$708$	−0.637869	−	1.10482i	−0.0239726	−	0.0415217i
$709$	18.9198	+	13.7460i	0.710546	+	0.516242i	0.883350	−	0.468714i	$-0.155283\pi$
$709$	18.9198	+	13.7460i	0.710546	+	0.516242i	−0.172804	+	0.984956i	$0.555283\pi$
$710$	−19.3436	−	4.11162i	−0.725954	−	0.154306i
$711$	9.51971	−	29.2987i	0.357017	−	1.09879i
$712$	−10.7774			−0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	13.7201	−	42.2261i	0.513102	−	1.57917i
$716$	−0.196346	−	0.0417346i	−0.00733779	−	0.00155970i
$717$	0.431198	+	0.313283i	0.0161034	+	0.0116998i
$718$	9.03230	+	15.6444i	0.337083	+	0.583844i
$719$	−6.48843	+	11.2383i	−0.241978	+	0.419118i	−0.961278	−	0.275582i	$-0.911129\pi$
$719$	−6.48843	+	11.2383i	−0.241978	+	0.419118i	0.719300	+	0.694700i	$0.244463\pi$
$720$	−10.1686	+	4.52734i	−0.378960	+	0.168724i
$721$	3.85733	−	2.80252i	0.143655	−	0.104371i
$722$	2.87446	+	1.27979i	0.106976	+	0.0476289i
$723$	13.5672	−	2.88380i	0.504570	−	0.107250i
$724$	1.23220	−	11.7236i	0.0457944	−	0.435704i
$725$	28.6492	+	31.8182i	1.06401	+	1.18170i
$726$	2.47233	−	2.74580i	0.0917567	−	0.101906i
$727$	1.29856	+	12.3550i	0.0481609	+	0.458220i	0.991852	+	0.127393i	$0.0406610\pi$
$727$	1.29856	+	12.3550i	0.0481609	+	0.458220i	−0.943691	+	0.330827i	$0.892672\pi$
$728$	−1.66812	−	5.13393i	−0.0618245	−	0.190276i
$729$	2.33825	+	7.19640i	0.0866020	+	0.266533i
$730$	−1.51172	−	14.3830i	−0.0559511	−	0.532339i
$731$	−6.26638	+	6.95952i	−0.231771	+	0.257407i
$732$	2.13304	+	2.36898i	0.0788395	+	0.0875602i
$733$	3.57041	−	33.9702i	0.131876	−	1.25472i	−0.705744	−	0.708467i	$-0.749387\pi$
$733$	3.57041	−	33.9702i	0.131876	−	1.25472i	0.837621	−	0.546252i	$-0.183946\pi$
$734$	18.2193	−	3.87264i	0.672488	−	0.142942i
$735$	19.6137	+	8.73260i	0.723464	+	0.322107i
$736$	−15.4244	+	11.2065i	−0.568552	+	0.413077i
$737$	7.84633	−	3.49341i	0.289023	−	0.128682i
$738$	−0.569607	+	0.986589i	−0.0209675	+	0.0363168i
$739$	6.18747	+	10.7170i	0.227610	+	0.394231i	0.957099	−	0.289761i	$-0.0935757\pi$
$739$	6.18747	+	10.7170i	0.227610	+	0.394231i	−0.729490	+	0.683992i	$0.760242\pi$
$740$	−47.6171	−	34.5959i	−1.75044	−	1.27177i
$741$	9.75868	+	2.07427i	0.358494	+	0.0762002i
$742$	−0.581597	+	1.78997i	−0.0213511	+	0.0657119i
$743$	−16.2455			−0.595990			−0.297995	−	0.954567i	$-0.596318\pi$
$743$	−16.2455			−0.595990			−0.297995	+	0.954567i	$0.596318\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$	2.64325	−	8.13509i	0.0967763	−	0.297847i
$747$	−30.1610	−	6.41092i	−1.10353	−	0.234563i
$748$	−6.64249	−	4.82605i	−0.242873	−	0.176458i
$749$	−0.888356	−	1.53868i	−0.0324598	−	0.0562220i
$750$	−4.32029	+	7.48296i	−0.157755	+	0.273239i
$751$	−9.85558	+	4.38799i	−0.359635	+	0.160120i	−0.578597	−	0.815614i	$-0.696400\pi$
$751$	−9.85558	+	4.38799i	−0.359635	+	0.160120i	0.218962	+	0.975733i	$0.429733\pi$
$752$	0.973546	−	0.707322i	0.0355016	−	0.0257934i
$753$	4.98876	+	2.22114i	0.181801	+	0.0809429i
$754$	−9.60724	+	2.04208i	−0.349875	+	0.0743682i
$755$	−5.95746	+	56.6814i	−0.216814	+	2.06285i
$756$	−3.64435	−	4.04746i	−0.132544	−	0.147205i
$757$	27.5024	−	30.5445i	0.999591	−	1.11016i	0.00567884	−	0.999984i	$-0.498192\pi$
$757$	27.5024	−	30.5445i	0.999591	−	1.11016i	0.993912	−	0.110175i	$-0.0351410\pi$
$758$	−0.334341	−	3.18104i	−0.0121438	−	0.115541i
$759$	−3.76776	−	11.5960i	−0.136761	−	0.420907i
$760$	−10.5788	−	32.5582i	−0.383733	−	1.18101i
$761$	−2.05508	−	19.5528i	−0.0744967	−	0.708789i	−0.966484	−	0.256728i	$-0.917356\pi$
$761$	−2.05508	−	19.5528i	−0.0744967	−	0.708789i	0.891987	−	0.452061i	$-0.149311\pi$
$762$	−0.596194	+	0.662140i	−0.0215978	+	0.0239868i
$763$	0.754378	+	0.837822i	0.0273103	+	0.0303312i
$764$	−3.36301	+	31.9969i	−0.121669	+	1.15761i
$765$	10.3718	−	2.20459i	0.374993	−	0.0797073i
$766$	3.16285	+	1.40819i	0.114279	+	0.0508801i
$767$	2.18283	−	1.58592i	0.0788174	−	0.0572642i
$768$	8.18186	−	3.64280i	0.295238	−	0.131448i
$769$	−1.89417	+	3.28080i	−0.0683055	+	0.118309i	−0.898155	−	0.439678i	$-0.855093\pi$
$769$	−1.89417	+	3.28080i	−0.0683055	+	0.118309i	0.829850	+	0.557986i	$0.188426\pi$
$770$	−4.01575	−	6.95549i	−0.144718	−	0.250658i
$771$	−3.30558	−	2.40165i	−0.119048	−	0.0864932i
$772$	8.44549	+	1.79514i	0.303960	+	0.0646087i
$773$	−7.83963	+	24.1279i	−0.281972	+	0.867820i	0.705318	+	0.708891i	$0.250804\pi$
$773$	−7.83963	+	24.1279i	−0.281972	+	0.867820i	−0.987290	+	0.158929i	$0.949196\pi$
$774$	−10.7855			−0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	2.21665	−	6.82215i	0.0795219	−	0.244743i
$778$	12.5456	+	2.66664i	0.449780	+	0.0956037i
$779$	2.32370	+	1.68826i	0.0832551	+	0.0604884i
$780$	7.42103	+	12.8536i	0.265716	+	0.460233i
$781$	−15.9194	+	27.5732i	−0.569641	+	0.986647i
$782$	2.70587	−	1.20473i	0.0967617	−	0.0430811i
$783$	−18.5341	+	13.4658i	−0.662354	+	0.481228i
$784$	−8.05266	−	3.58527i	−0.287595	−	0.128046i
$785$	−54.9316	+	11.6761i	−1.96059	+	0.416737i
$786$	−0.409274	+	3.89399i	−0.0145983	+	0.138894i
$787$	−17.3617	−	19.2821i	−0.618876	−	0.687332i	0.349469	−	0.936948i	$-0.386362\pi$
$787$	−17.3617	−	19.2821i	−0.618876	−	0.687332i	−0.968345	+	0.249616i	$0.919695\pi$
$788$	−16.2356	+	18.0314i	−0.578369	+	0.642344i
$789$	−0.236653	−	2.25160i	−0.00842505	−	0.0801590i
$790$	11.1340	+	34.2670i	0.396130	+	1.21916i
$791$	1.50518	+	4.63247i	0.0535181	+	0.164712i
$792$	−2.28504	−	21.7408i	−0.0811955	−	0.772524i
$793$	−4.51128	+	5.01029i	−0.160200	+	0.177921i
$794$	−15.0214	−	16.6829i	−0.533088	−	0.592054i
$795$	1.25049	−	11.8976i	0.0443502	−	0.421964i
$796$	−6.35504	+	1.35080i	−0.225248	+	0.0478780i
$797$	−16.9030	−	7.52569i	−0.598734	−	0.266574i	0.0849105	−	0.996389i	$-0.472940\pi$
$797$	−16.9030	−	7.52569i	−0.598734	−	0.266574i	−0.683645	+	0.729815i	$0.739606\pi$
$798$	1.46005	−	1.06079i	0.0516851	−	0.0375514i
$799$	−1.04725	+	0.466264i	−0.0370489	+	0.0164952i
$800$	25.3951	−	43.9856i	0.897852	−	1.55513i
$801$	−4.84652	−	8.39442i	−0.171243	−	0.296602i
$802$	−6.91143	−	5.02145i	−0.244051	−	0.177314i
$803$	−22.7752	−	4.84102i	−0.803720	−	0.170836i
$804$	−0.887235	+	2.73063i	−0.0312904	+	0.0963019i
$805$	−9.29174			−0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	2.85926	−	8.79990i	0.100588	−	0.309579i
$809$	−35.9448	−	7.64030i	−1.26375	−	0.268619i	−0.473168	−	0.880972i	$-0.656890\pi$
$809$	−35.9448	−	7.64030i	−1.26375	−	0.268619i	−0.790584	+	0.612353i	$0.790223\pi$
$810$	4.82731	+	3.50725i	0.169614	+	0.123232i
$811$	19.7151	+	34.1475i	0.692289	+	1.19908i	0.971086	+	0.238730i	$0.0767310\pi$
$811$	19.7151	+	34.1475i	0.692289	+	1.19908i	−0.278797	+	0.960350i	$0.589936\pi$
$812$	2.84894	−	4.93451i	0.0999782	−	0.173167i
$813$	−11.3964	+	5.07402i	−0.399690	+	0.177954i
$814$	23.9051	−	17.3680i	0.837872	−	0.608749i
$815$	−3.53896	−	1.57565i	−0.123964	−	0.0551924i
$816$	1.58653	−	0.337226i	0.0555395	−	0.0118053i
$817$	−2.84243	+	27.0439i	−0.0994441	+	0.946147i
$818$	1.59081	+	1.76677i	0.0556214	+	0.0617738i
$819$	3.24863	−	3.60797i	0.113516	−	0.126073i
$820$	0.446647	+	4.24956i	0.0155976	+	0.148401i
$821$	0.457525	+	1.40812i	0.0159677	+	0.0491436i	0.958723	−	0.284342i	$-0.0917751\pi$
$821$	0.457525	+	1.40812i	0.0159677	+	0.0491436i	−0.942755	+	0.333486i	$0.891775\pi$
$822$	2.45142	+	7.54471i	0.0855032	+	0.263152i
$823$	4.06252	+	38.6523i	0.141611	+	1.34733i	0.802410	+	0.596773i	$0.203551\pi$
$823$	4.06252	+	38.6523i	0.141611	+	1.34733i	−0.660800	+	0.750562i	$0.729783\pi$
$824$	−10.1562	+	11.2796i	−0.353808	+	0.392943i
$825$	21.7340	+	24.1380i	0.756680	+	0.840379i
$826$	0.0510175	−	0.485399i	0.00177513	−	0.0168892i
$827$	−33.1947	+	7.05575i	−1.15429	+	0.245352i	−0.745009	−	0.667055i	$-0.767555\pi$
$827$	−33.1947	+	7.05575i	−1.15429	+	0.245352i	−0.409284	+	0.912407i	$0.634221\pi$
$828$	−9.99393	−	4.44959i	−0.347313	−	0.154634i
$829$	−13.3736	+	9.71650i	−0.464485	+	0.337468i	−0.795288	−	0.606232i	$-0.792680\pi$
$829$	−13.3736	+	9.71650i	−0.464485	+	0.337468i	0.330803	+	0.943700i	$0.392680\pi$
$830$	32.9458	−	14.6684i	1.14356	−	0.509148i
$831$	5.22073	−	9.04256i	0.181105	−	0.313683i
$832$	1.82877	+	3.16752i	0.0634012	+	0.109814i
$833$	6.79340	+	4.93569i	0.235377	+	0.171012i
$834$	−11.3892	−	2.42086i	−0.394377	−	0.0838274i
$835$	−12.9341	+	39.8071i	−0.447603	+	1.37758i
$836$	−23.8409			−0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	−16.7110	+	51.4313i	−0.576929	+	1.77561i	0.0525843	+	0.998616i	$0.483254\pi$
$839$	−16.7110	+	51.4313i	−0.576929	+	1.77561i	−0.629514	+	0.776989i	$0.716746\pi$
$840$	6.07121	+	1.29048i	0.209477	+	0.0445256i
$841$	4.07162	+	2.95820i	0.140401	+	0.102007i
$842$	7.47562	+	12.9482i	0.257627	+	0.446223i
$843$	−6.94819	+	12.0346i	−0.239308	+	0.414494i
$844$	16.0286	−	7.13641i	0.551728	−	0.245645i
$845$	13.5975	−	9.87918i	0.467769	−	0.339854i
$846$	−1.20610	−	0.536989i	−0.0414665	−	0.0184621i
$847$	−4.43424	+	0.942526i	−0.152362	+	0.0323856i
$848$	−0.513402	+	4.88470i	−0.0176303	+	0.167741i
$849$	13.7042	+	15.2201i	0.470328	+	0.522352i
$850$	−5.27978	+	5.86379i	−0.181095	+	0.201126i
$851$	−3.57328	−	33.9975i	−0.122490	−	1.16542i
$852$	−3.28896	−	10.1224i	−0.112678	−	0.346787i
$853$	12.2297	+	37.6392i	0.418738	+	1.28874i	0.908865	+	0.417091i	$0.136950\pi$
$853$	12.2297	+	37.6392i	0.418738	+	1.28874i	−0.490127	+	0.871651i	$0.663050\pi$
$854$	0.127481	+	1.21290i	0.00436232	+	0.0415047i
$855$	20.6020	−	22.8809i	0.704575	−	0.782510i
$856$	3.78459	+	4.20321i	0.129355	+	0.143663i
$857$	−1.33013	+	12.6553i	−0.0454363	+	0.432298i	0.948031	+	0.318179i	$0.103071\pi$
$857$	−1.33013	+	12.6553i	−0.0454363	+	0.432298i	−0.993467	+	0.114119i	$0.963595\pi$
$858$	−7.28828	+	1.54917i	−0.248818	+	0.0528878i
$859$	−19.3255	−	8.60425i	−0.659376	−	0.293573i	0.0496383	−	0.998767i	$-0.484193\pi$
$859$	−19.3255	−	8.60425i	−0.659376	−	0.293573i	−0.709014	+	0.705194i	$0.750860\pi$
$860$	−32.7281	+	23.7784i	−1.11602	+	0.810835i
$861$	−0.475739	+	0.211813i	−0.0162132	+	0.00721856i
$862$	−4.00618	+	6.93891i	−0.136451	+	0.236340i
$863$	−4.66987	−	8.08845i	−0.158964	−	0.275334i	0.775531	−	0.631309i	$-0.217482\pi$
$863$	−4.66987	−	8.08845i	−0.158964	−	0.275334i	−0.934495	+	0.355975i	$0.884149\pi$
$864$	21.9861	+	15.9739i	0.747983	+	0.543441i
$865$	74.8969	+	15.9198i	2.54657	+	0.541290i
$866$	−5.24064	+	16.1290i	−0.178084	+	0.548087i
$867$	13.7957			0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	3.48982	−	10.7406i	0.118316	−	0.364139i
$871$	−5.93966	−	1.26251i	−0.201258	−	0.0427786i
$872$	−2.90353	−	2.10954i	−0.0983260	−	0.0714380i
$873$	−5.76760	−	9.98977i	−0.195204	−	0.338102i
$874$	4.30028	−	7.44830i	0.145459	−	0.251942i
$875$	9.68484	−	4.31197i	0.327407	−	0.145771i
$876$	6.29703	−	4.57506i	0.212757	−	0.154577i
$877$	20.4956	+	9.12524i	0.692088	+	0.308137i	0.722471	−	0.691401i	$-0.243006\pi$
$877$	20.4956	+	9.12524i	0.692088	+	0.308137i	−0.0303833	+	0.999538i	$0.509673\pi$
$878$	12.2700	−	2.60807i	0.414092	−	0.0880180i
$879$	1.16973	−	11.1292i	0.0394540	−	0.375380i
$880$	−14.0246	−	15.5759i	−0.472770	−	0.525064i
$881$	−31.0687	+	34.5053i	−1.04673	+	1.16251i	−0.0603272	+	0.998179i	$0.519214\pi$
$881$	−31.0687	+	34.5053i	−1.04673	+	1.16251i	−0.986405	+	0.164335i	$0.947452\pi$
$882$	1.01087	+	9.61782i	0.0340379	+	0.323849i
$883$	11.2913	+	34.7512i	0.379984	+	1.16947i	0.940054	+	0.341026i	$0.110774\pi$
$883$	11.2913	+	34.7512i	0.379984	+	1.16947i	−0.560070	+	0.828445i	$0.689226\pi$
$884$	1.79381	+	5.52077i	0.0603323	+	0.185684i
$885$	0.324282	+	3.08534i	0.0109006	+	0.103713i
$886$	−8.19392	+	9.10027i	−0.275280	+	0.305730i
$887$	19.1940	+	21.3171i	0.644473	+	0.715760i	0.973532	−	0.228550i	$-0.0733983\pi$
$887$	19.1940	+	21.3171i	0.644473	+	0.715760i	−0.329059	+	0.944309i	$0.606732\pi$
$888$	−2.38693	+	22.7102i	−0.0801003	+	0.762103i
$889$	1.06930	−	0.227287i	0.0358632	−	0.00762297i
$890$	10.3566	+	4.61107i	0.347155	+	0.154563i
$891$	7.77192	−	5.64663i	0.260369	−	0.189169i
$892$	−13.1255	+	5.84387i	−0.439476	+	0.195667i
$893$	−1.66433	+	2.88270i	−0.0556945	+	0.0964658i
$894$	6.26408	+	10.8497i	0.209502	+	0.362869i
$895$	0.394914	+	0.286922i	0.0132005	+	0.00959074i
$896$	−8.02583	−	1.70594i	−0.268124	−	0.0569916i
$897$	−2.66381	+	8.19836i	−0.0889420	+	0.273735i
$898$	6.34235			0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	1.44586	−	4.44989i	0.0481685	−	0.148247i
$902$	−2.09826	−	0.446000i	−0.0698646	−	0.0148502i
$903$	−3.98869	−	2.89795i	−0.132735	−	0.0964378i
$904$	−7.75296	−	13.4285i	−0.257860	−	0.446626i
$905$	−14.3332	+	24.8259i	−0.476453	+	0.825240i
$906$	8.73781	−	3.89032i	0.290294	−	0.129247i
$907$	17.9518	−	13.0427i	0.596079	−	0.433077i	−0.248406	−	0.968656i	$-0.579907\pi$
$907$	17.9518	−	13.0427i	0.596079	−	0.433077i	0.844485	+	0.535579i	$0.179907\pi$
$908$	−30.3113	−	13.4955i	−1.00592	−	0.447863i
$909$	8.13994	−	1.73020i	0.269985	−	0.0573871i
$910$	−0.593543	+	5.64718i	−0.0196757	+	0.187202i
$911$	−19.2927	−	21.4267i	−0.639194	−	0.709897i	0.333301	−	0.942821i	$-0.391838\pi$
$911$	−19.2927	−	21.4267i	−0.639194	−	0.709897i	−0.972495	+	0.232923i	$0.925171\pi$
$912$	3.15140	−	3.49998i	0.104353	−	0.115896i
$913$	−6.06913	−	57.7440i	−0.200859	−	1.91105i
$914$	6.64760	+	20.4592i	0.219883	+	0.676731i
$915$	−2.39551	−	7.37263i	−0.0791932	−	0.243732i
$916$	2.70216	+	25.7093i	0.0892819	+	0.849460i
$917$	3.21448	−	3.57004i	0.106151	−	0.117893i
$918$	−2.82505	−	3.13754i	−0.0932407	−	0.103554i
$919$	−5.02388	+	47.7990i	−0.165723	+	1.57675i	0.523392	+	0.852092i	$0.324667\pi$
$919$	−5.02388	+	47.7990i	−0.165723	+	1.57675i	−0.689114	+	0.724653i	$0.742000\pi$
$920$	28.9329	−	6.14988i	0.953890	−	0.202756i
$921$	−25.3251	−	11.2754i	−0.834490	−	0.371539i
$922$	−3.71975	+	2.70256i	−0.122503	+	0.0890039i
$923$	20.5640	−	9.15567i	0.676872	−	0.301363i
$924$	2.16127	−	3.74343i	0.0711007	−	0.123150i
$925$	45.5334	+	78.8662i	1.49713	+	2.59310i
$926$	19.7010	+	14.3136i	0.647416	+	0.470376i
$927$	−13.3527	−	2.83821i	−0.438561	−	0.0932191i
$928$	−8.78572	+	27.0397i	−0.288405	+	0.887621i
$929$	7.01617			0.230193			0.115097	−	0.993354i	$-0.463282\pi$
$929$	7.01617			0.230193			0.115097	+	0.993354i	$0.463282\pi$
$930$		0			0
$931$	24.3825			0.799105
$932$	4.63406	−	14.2622i	0.151794	−	0.467173i
$933$	2.10203	+	0.446800i	0.0688173	+	0.0146276i
$934$	20.0497	+	14.5669i	0.656045	+	0.476644i
$935$	9.98321	+	17.2914i	0.326486	+	0.565490i
$936$	−7.72770	+	13.3848i	−0.252588	+	0.437495i
$937$	−11.7671	+	5.23903i	−0.384413	+	0.171152i	−0.589839	−	0.807521i	$-0.700809\pi$
$937$	−11.7671	+	5.23903i	−0.384413	+	0.171152i	0.205426	+	0.978673i	$0.434142\pi$
$938$	−0.888663	+	0.645651i	−0.0290159	+	0.0210813i
$939$	−8.85850	−	3.94406i	−0.289086	−	0.128709i
$940$	−4.84374	+	1.02957i	−0.157985	+	0.0335808i
$941$	5.23053	−	49.7651i	0.170510	−	1.62230i	−0.490168	−	0.871628i	$-0.663065\pi$
$941$	5.23053	−	49.7651i	0.170510	−	1.62230i	0.660679	−	0.750669i	$-0.270269\pi$
$942$	6.30630	+	7.00385i	0.205470	+	0.228198i
$943$	−1.66061	+	1.84429i	−0.0540768	+	0.0600584i
$944$	−0.133138	−	1.26672i	−0.00433328	−	0.0412284i
$945$	4.09278	+	12.5963i	0.133138	+	0.409757i
$946$	−6.27584	−	19.3151i	−0.204045	−	0.627987i
$947$	−5.42168	−	51.5838i	−0.176181	−	1.67625i	−0.623461	−	0.781854i	$-0.714274\pi$
$947$	−5.42168	−	51.5838i	−0.176181	−	1.67625i	0.447280	−	0.894394i	$-0.352393\pi$
$948$	−12.9755	+	14.4107i	−0.421423	+	0.468038i
$949$	11.0151	+	12.2335i	0.357566	+	0.397118i
$950$	−2.39491	+	22.7860i	−0.0777011	+	0.739277i
$951$	7.72024	−	1.64099i	0.250346	−	0.0532127i
$952$	2.21769	+	0.987377i	0.0718756	+	0.0320011i
$953$	−15.1571	+	11.0123i	−0.490987	+	0.356723i	−0.805564	−	0.592509i	$-0.798137\pi$
$953$	−15.1571	+	11.0123i	−0.490987	+	0.356723i	0.314577	+	0.949232i	$0.398137\pi$
$954$	4.92274	−	2.19174i	0.159379	−	0.0709603i
$955$	39.1193	−	67.7565i	1.26587	−	2.19255i
$956$	0.450241	+	0.779840i	0.0145618	+	0.0252218i
$957$	−14.7096	−	10.6872i	−0.475494	−	0.345467i
$958$	22.4209	+	4.76571i	0.724386	+	0.153973i
$959$	3.00772	−	9.25682i	0.0971245	−	0.298918i
$960$	−4.20549			−0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	−1.57194	+	4.83793i	−0.0506550	+	0.155900i
$964$	22.9217	+	4.87216i	0.738258	+	0.156922i
$965$	−16.9866	−	12.3415i	−0.546817	−	0.397285i
$966$	0.779674	+	1.35044i	0.0250856	+	0.0434496i
$967$	23.8923	−	41.3827i	0.768324	−	1.33078i	−0.170146	−	0.985419i	$-0.554424\pi$
$967$	23.8923	−	41.3827i	0.768324	−	1.33078i	0.938471	−	0.345358i	$-0.112243\pi$
$968$	13.1836	−	5.86974i	0.423738	−	0.188660i
$969$	−3.62969	+	2.63713i	−0.116603	+	0.0847167i
$970$	12.3249	+	5.48739i	0.395728	+	0.176189i
$971$	30.4210	−	6.46619i	0.976257	−	0.207510i	0.307956	−	0.951401i	$-0.400355\pi$
$971$	30.4210	−	6.46619i	0.976257	−	0.207510i	0.668301	+	0.743891i	$0.267022\pi$
$972$	−2.57294	+	24.4799i	−0.0825270	+	0.785192i
$973$	9.55917	+	10.6165i	0.306453	+	0.340351i
$974$	−13.1559	+	14.6111i	−0.421541	+	0.468169i
$975$	−2.40040	−	22.8383i	−0.0768743	−	0.731410i
$976$	0.983507	+	3.02692i	0.0314813	+	0.0968894i
$977$	−6.82283	−	20.9985i	−0.218282	−	0.671802i	−0.998904	−	0.0467994i	$-0.985098\pi$
$977$	−6.82283	−	20.9985i	−0.218282	−	0.671802i	0.780623	−	0.625003i	$-0.214902\pi$
$978$	0.0679557	+	0.646555i	0.00217298	+	0.0206746i
$979$	12.2130	−	13.5639i	0.390329	−	0.433504i
$980$	24.2715	+	26.9563i	0.775326	+	0.861087i
$981$	0.337403	−	3.21018i	0.0107725	−	0.102493i
$982$	−18.8594	+	4.00869i	−0.601828	+	0.127922i
$983$	−34.3282	−	15.2839i	−1.09490	−	0.487480i	−0.221834	−	0.975084i	$-0.571204\pi$
$983$	−34.3282	−	15.2839i	−1.09490	−	0.487480i	−0.873065	+	0.487604i	$0.837871\pi$
$984$	1.34118	−	0.974425i	0.0427553	−	0.0310635i
$985$	53.9032	−	23.9992i	1.71750	−	0.764679i
$986$	2.20846	−	3.82517i	0.0703318	−	0.121818i
$987$	−0.301756	−	0.522656i	−0.00960499	−	0.0166363i
$988$	13.6364	+	9.90744i	0.433832	+	0.315198i
$989$	−22.9823	−	4.88504i	−0.730796	−	0.155335i
$990$	−7.10585	+	21.8695i	−0.225839	+	0.695060i
$991$	−6.77397			−0.215182			−0.107591	−	0.994195i	$-0.534314\pi$
$991$	−6.77397			−0.215182			−0.107591	+	0.994195i	$0.534314\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$	1.25829	−	3.87263i	0.0399106	−	0.122832i
$995$	15.4542	+	3.28488i	0.489930	+	0.104138i
$996$	15.7025	+	11.4086i	0.497554	+	0.361494i
$997$	14.7866	+	25.6112i	0.468298	+	0.811115i	0.999344	−	0.0362278i	$-0.0115342\pi$
$997$	14.7866	+	25.6112i	0.468298	+	0.811115i	−0.531046	+	0.847343i	$0.678201\pi$
$998$	−14.2397	+	24.6639i	−0.450751	+	0.780724i
$999$	−44.5145	+	19.8191i	−1.40838	+	0.627050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.s.846.1		16
31.2	even	5		961.2.c.j.439.3		16
31.3	odd	30		961.2.g.l.732.2		16
31.4	even	5		961.2.g.t.547.1		16
31.5	even	3		961.2.d.p.628.1		16
31.6	odd	6		961.2.g.n.448.1		16
31.7	even	15	inner	961.2.g.s.844.1		16
31.8	even	5		31.2.g.a.18.2	✓	16
31.9	even	15		961.2.d.o.388.4		16
31.10	even	15		961.2.a.i.1.3		8
31.11	odd	30		961.2.d.q.531.1		16
31.12	odd	30		961.2.c.i.521.3		16
31.13	odd	30		961.2.d.n.374.4		16
31.14	even	15		961.2.g.k.338.2		16
31.15	odd	10		961.2.g.j.816.2		16
31.16	even	5		961.2.g.k.816.2		16
31.17	odd	30		961.2.g.j.338.2		16
31.18	even	15		961.2.d.o.374.4		16
31.19	even	15		961.2.c.j.521.3		16
31.20	even	15		961.2.d.p.531.1		16
31.21	odd	30		961.2.a.j.1.3		8
31.22	odd	30		961.2.d.n.388.4		16
31.23	odd	10		961.2.g.l.235.2		16
31.24	odd	30		961.2.g.m.844.1		16
31.25	even	3		961.2.g.t.448.1		16
31.26	odd	6		961.2.d.q.628.1		16
31.27	odd	10		961.2.g.n.547.1		16
31.28	even	15		31.2.g.a.19.2	yes	16
31.29	odd	10		961.2.c.i.439.3		16
31.30	odd	2		961.2.g.m.846.1		16
93.8	odd	10		279.2.y.c.235.1		16
93.41	odd	30		8649.2.a.bf.1.6		8
93.59	odd	30		279.2.y.c.19.1		16
93.83	even	30		8649.2.a.be.1.6		8
124.39	odd	10		496.2.bg.c.49.1		16
124.59	odd	30		496.2.bg.c.81.1		16
155.8	odd	20		775.2.ck.a.49.2		32
155.28	odd	60		775.2.ck.a.174.3		32
155.39	even	10		775.2.bl.a.576.1		16
155.59	even	30		775.2.bl.a.701.1		16
155.132	odd	20		775.2.ck.a.49.3		32
155.152	odd	60		775.2.ck.a.174.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.8	even	5
31.2.g.a.19.2	yes	16	31.28	even	15
279.2.y.c.19.1		16	93.59	odd	30
279.2.y.c.235.1		16	93.8	odd	10
496.2.bg.c.49.1		16	124.39	odd	10
496.2.bg.c.81.1		16	124.59	odd	30
775.2.bl.a.576.1		16	155.39	even	10
775.2.bl.a.701.1		16	155.59	even	30
775.2.ck.a.49.2		32	155.8	odd	20
775.2.ck.a.49.3		32	155.132	odd	20
775.2.ck.a.174.2		32	155.152	odd	60
775.2.ck.a.174.3		32	155.28	odd	60
961.2.a.i.1.3		8	31.10	even	15
961.2.a.j.1.3		8	31.21	odd	30
961.2.c.i.439.3		16	31.29	odd	10
961.2.c.i.521.3		16	31.12	odd	30
961.2.c.j.439.3		16	31.2	even	5
961.2.c.j.521.3		16	31.19	even	15
961.2.d.n.374.4		16	31.13	odd	30
961.2.d.n.388.4		16	31.22	odd	30
961.2.d.o.374.4		16	31.18	even	15
961.2.d.o.388.4		16	31.9	even	15
961.2.d.p.531.1		16	31.20	even	15
961.2.d.p.628.1		16	31.5	even	3
961.2.d.q.531.1		16	31.11	odd	30
961.2.d.q.628.1		16	31.26	odd	6
961.2.g.j.338.2		16	31.17	odd	30
961.2.g.j.816.2		16	31.15	odd	10
961.2.g.k.338.2		16	31.14	even	15
961.2.g.k.816.2		16	31.16	even	5
961.2.g.l.235.2		16	31.23	odd	10
961.2.g.l.732.2		16	31.3	odd	30
961.2.g.m.844.1		16	31.24	odd	30
961.2.g.m.846.1		16	31.30	odd	2
961.2.g.n.448.1		16	31.6	odd	6
961.2.g.n.547.1		16	31.27	odd	10
961.2.g.s.844.1		16	31.7	even	15	inner
961.2.g.s.846.1		16	1.1	even	1	trivial
961.2.g.t.448.1		16	31.25	even	3
961.2.g.t.547.1		16	31.4	even	5
8649.2.a.be.1.6		8	93.83	even	30
8649.2.a.bf.1.6		8	93.41	odd	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+(-0.213065 + 0.655747i) q^{2} +(0.882681 + 0.187620i) q^{3} +(1.23343 + 0.896137i) q^{4} +(-1.85376 - 3.21080i) q^{5} +(-0.311099 + 0.538840i) q^{6} +(0.697395 - 0.310500i) q^{7} +(-1.96606 + 1.42843i) q^{8} +(-1.99671 - 0.888993i) q^{9} +(2.50044 - 0.531486i) q^{10} +(0.430200 - 4.09308i) q^{11} +(0.920590 + 1.02242i) q^{12} +(-1.94700 + 2.16237i) q^{13} +(0.0550190 + 0.523471i) q^{14} +(-1.03387 - 3.18192i) q^{15} +(0.424467 + 1.30637i) q^{16} +(-0.136778 - 1.30136i) q^{17} +(1.00838 - 1.11992i) q^{18} +(-2.54239 - 2.82361i) q^{19} +(0.590845 - 5.62151i) q^{20} +(0.673833 - 0.143228i) q^{21} +(2.59236 + 1.15419i) q^{22} +(2.65597 - 1.92967i) q^{23} +(-2.00341 + 0.891974i) q^{24} +(-4.37284 + 7.57398i) q^{25} +(-1.00313 - 1.73747i) q^{26} +(-3.78584 - 2.75057i) q^{27} +(1.13844 + 0.241982i) q^{28} +(1.51283 - 4.65602i) q^{29} +2.30681 q^{30} -5.80746 q^{32} +(1.14767 - 3.53217i) q^{33} +(0.882502 + 0.187582i) q^{34} +(-2.28976 - 1.66361i) q^{35} +(-1.66614 - 2.88584i) q^{36} +(5.20639 - 9.01773i) q^{37} +(2.39327 - 1.06555i) q^{38} +(-2.12429 + 1.54338i) q^{39} +(8.23100 + 3.66468i) q^{40} +(-0.739427 + 0.157170i) q^{41} +(-0.0496492 + 0.472381i) q^{42} +(-4.78889 - 5.31861i) q^{43} +(4.19858 - 4.66299i) q^{44} +(0.847038 + 8.05903i) q^{45} +(0.699483 + 2.15279i) q^{46} +(-0.270719 - 0.833189i) q^{47} +(0.129567 + 1.23275i) q^{48} +(-4.29396 + 4.76893i) q^{49} +(-4.03491 - 4.48122i) q^{50} +(0.123429 - 1.17434i) q^{51} +(-4.33926 + 0.922339i) q^{52} +(3.26657 + 1.45437i) q^{53} +(2.61031 - 1.89650i) q^{54} +(-13.9396 + 6.20629i) q^{55} +(-0.927595 + 1.60664i) q^{56} +(-1.71435 - 2.96935i) q^{57} +(2.73084 + 1.98407i) q^{58} +(-0.907007 - 0.192790i) q^{59} +(1.57623 - 4.85115i) q^{60} +2.31704 q^{61} -1.66853 q^{63} +(0.388433 - 1.19547i) q^{64} +(10.5522 + 2.24294i) q^{65} +(2.07168 + 1.50516i) q^{66} +(1.04345 + 1.80731i) q^{67} +(0.997488 - 1.72770i) q^{68} +(2.70642 - 1.20498i) q^{69} +(1.57877 - 1.14704i) q^{70} +(-7.06726 - 3.14655i) q^{71} +(5.19552 - 1.10434i) q^{72} +(0.591367 - 5.62649i) q^{73} +(4.80405 + 5.33544i) q^{74} +(-5.28085 + 5.86498i) q^{75} +(-0.605510 - 5.76105i) q^{76} +(-0.970882 - 2.98807i) q^{77} +(-0.559458 - 1.72183i) q^{78} +(1.47330 + 14.0175i) q^{79} +(3.40765 - 3.78458i) q^{80} +(1.56187 + 1.73464i) q^{81} +(0.0544822 - 0.518364i) q^{82} +(13.7994 - 2.93316i) q^{83} +(0.959476 + 0.427186i) q^{84} +(-3.92484 + 2.85157i) q^{85} +(4.50800 - 2.00709i) q^{86} +(2.20891 - 3.82595i) q^{87} +(5.00086 + 8.66175i) q^{88} +(3.58784 + 2.60672i) q^{89} +(-5.46515 - 1.16165i) q^{90} +(-0.686415 + 2.11257i) q^{91} +5.00520 q^{92} +0.604042 q^{94} +(-4.35308 + 13.3974i) q^{95} +(-5.12614 - 1.08959i) q^{96} +(4.26970 + 3.10212i) q^{97} +(-2.21232 - 3.83184i) q^{98} +(-4.49770 + 7.79025i) 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