LMFDB - Embedded newform 961.2.g.k.547.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			547.1
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.k.448.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.571745 - 1.75965i) q^{2} +(0.334133 + 0.371093i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 - 1.04561i) q^{5} +(0.461954 - 0.800128i) q^{6} +(-0.390209 - 3.71259i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(0.287521 - 2.73558i) q^{9} +(-1.49475 + 1.66009i) q^{10} +(-1.69601 - 0.755111i) q^{11} +(-0.695182 - 0.147765i) q^{12} +(5.07118 - 1.07791i) q^{13} +(-6.30977 + 2.80929i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(-5.17750 + 2.30517i) q^{17} +(-4.97805 + 1.05812i) q^{18} +(1.40705 + 0.299078i) q^{19} +(1.56983 + 0.698933i) q^{20} +(1.24733 - 1.38530i) q^{21} +(-0.359048 + 3.41611i) q^{22} +(2.86762 + 2.08345i) q^{23} +(-0.0556982 - 0.529933i) q^{24} +(1.77114 - 3.06770i) q^{25} +(-4.79617 - 8.30721i) q^{26} +(2.32318 - 1.68789i) q^{27} +(3.55516 + 3.94840i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(7.01650 + 7.79262i) q^{34} +(-3.64635 + 2.64923i) q^{35} +(1.95745 + 3.39040i) q^{36} +(-2.25141 + 3.89955i) q^{37} +(-0.278202 - 2.64692i) q^{38} +(2.09445 + 1.52171i) q^{39} +(-0.134670 + 1.28130i) q^{40} +(-3.15770 + 3.50698i) q^{41} +(-3.15081 - 1.40283i) q^{42} +(-6.41589 - 1.36374i) q^{43} +(2.58456 - 0.549365i) q^{44} +(-3.03391 + 1.35078i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(-2.19919 + 0.979142i) q^{48} +(-6.78405 + 1.44199i) q^{49} +(-6.41073 - 1.36264i) q^{50} +(-2.58541 - 1.15110i) q^{51} +(-4.93742 + 5.48357i) q^{52} +(1.35503 - 12.8923i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(0.234298 + 2.22920i) q^{55} +(-1.99173 + 3.44978i) q^{56} +(0.359157 + 0.622078i) q^{57} +(2.05458 - 1.49274i) q^{58} +(-1.45975 - 1.62121i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(-4.18844 - 4.65174i) q^{65} +(-1.38766 + 1.00820i) q^{66} +(-1.44150 - 2.49675i) q^{67} +(4.03315 - 6.98563i) q^{68} +(0.185015 + 1.76030i) q^{69} +(6.74649 + 4.90161i) q^{70} +(-0.940927 + 8.95232i) q^{71} +(-1.96401 + 2.18125i) q^{72} +(-3.84059 - 1.70994i) q^{73} +(8.14908 + 1.73214i) q^{74} +(1.73020 - 0.367765i) q^{75} +(-1.87034 + 0.832730i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(10.2607 - 4.56834i) q^{79} +(5.69331 - 1.21015i) q^{80} +(-6.66899 - 1.41754i) q^{81} +(7.97647 + 3.55135i) q^{82} +(-7.01077 + 7.78625i) q^{83} +(-0.277327 + 2.63859i) q^{84} +(5.53585 + 4.02203i) q^{85} +(1.26855 + 12.0694i) q^{86} +(-0.342708 + 0.593587i) q^{87} +(0.990524 + 1.71564i) q^{88} +(2.18575 - 1.58804i) q^{89} +(4.11152 + 4.56631i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(2.26723 + 2.51801i) q^{96} +(6.70942 - 4.87468i) q^{97} +(6.41615 + 11.1131i) q^{98} +(-2.55330 + 4.42244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	−0.921491	−	0.388400i	$-0.873028\pi$
$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	0.517206	−	0.855861i	$-0.326972\pi$
$3$	0.334133	+	0.371093i	0.192912	+	0.214250i	0.831839	−	0.555017i	$-0.187288\pi$
$3$	0.334133	+	0.371093i	0.192912	+	0.214250i	−0.638927	+	0.769267i	$0.720621\pi$
$4$	−1.15144	+	0.836573i	−0.575722	+	0.418287i
$5$	−0.603681	−	1.04561i	−0.269974	−	0.467609i	0.698881	−	0.715238i	$-0.253682\pi$
$5$	−0.603681	−	1.04561i	−0.269974	−	0.467609i	−0.968855	+	0.247629i	$0.920349\pi$
$6$	0.461954	−	0.800128i	0.188592	−	0.326651i
$7$	−0.390209	−	3.71259i	−0.147485	−	1.40323i	−0.778591	−	0.627531i	$-0.784065\pi$
$7$	−0.390209	−	3.71259i	−0.147485	−	1.40323i	0.631106	−	0.775697i	$-0.282601\pi$
$8$	−0.863288	−	0.627215i	−0.305218	−	0.221754i
$9$	0.287521	−	2.73558i	0.0958402	−	0.911859i
$10$	−1.49475	+	1.66009i	−0.472681	+	0.524966i
$11$	−1.69601	−	0.755111i	−0.511365	−	0.227674i	0.134799	−	0.990873i	$-0.456961\pi$
$11$	−1.69601	−	0.755111i	−0.511365	−	0.227674i	−0.646164	+	0.763199i	$0.723628\pi$
$12$	−0.695182	−	0.147765i	−0.200682	−	0.0426562i
$13$	5.07118	−	1.07791i	1.40649	−	0.298959i	0.558736	−	0.829346i	$-0.311287\pi$
$13$	5.07118	−	1.07791i	1.40649	−	0.298959i	0.847756	+	0.530387i	$0.177953\pi$
$14$	−6.30977	+	2.80929i	−1.68636	+	0.750814i
$15$	0.186307	−	0.573393i	0.0481042	−	0.148049i
$16$	−1.48972	+	4.58490i	−0.372431	+	1.14622i
$17$	−5.17750	+	2.30517i	−1.25573	+	0.559086i	−0.923313	−	0.384048i	$-0.874530\pi$
$17$	−5.17750	+	2.30517i	−1.25573	+	0.559086i	−0.332414	+	0.943134i	$0.607863\pi$
$18$	−4.97805	+	1.05812i	−1.17334	+	0.249401i
$19$	1.40705	+	0.299078i	0.322800	+	0.0686132i	0.366462	−	0.930433i	$-0.380569\pi$
$19$	1.40705	+	0.299078i	0.322800	+	0.0686132i	−0.0436619	+	0.999046i	$0.513902\pi$
$20$	1.56983	+	0.698933i	0.351025	+	0.156286i
$21$	1.24733	−	1.38530i	0.272191	−	0.302298i
$22$	−0.359048	+	3.41611i	−0.0765492	+	0.728317i
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	0.845147	−	0.534534i	$-0.179513\pi$
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	−0.247207	+	0.968963i	$0.579513\pi$
$24$	−0.0556982	−	0.529933i	−0.0113694	−	0.108172i
$25$	1.77114	−	3.06770i	0.354228	−	0.613541i
$26$	−4.79617	−	8.30721i	−0.940606	−	1.62918i
$27$	2.32318	−	1.68789i	0.447096	−	0.324835i
$28$	3.55516	+	3.94840i	0.671862	+	0.746178i
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	0.982684	−	0.185292i	$-0.0593230\pi$
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	−0.903919	+	0.427703i	$0.859323\pi$
$30$	−1.11549			−0.203660
$31$		0			0
$31$		0			0
$32$	6.78540			1.19950
$33$	−0.286476	−	0.881683i	−0.0498691	−	0.153481i
$34$	7.01650	+	7.79262i	1.20332	+	1.33642i
$35$	−3.64635	+	2.64923i	−0.616345	+	0.447801i
$36$	1.95745	+	3.39040i	0.326241	+	0.565066i
$37$	−2.25141	+	3.89955i	−0.370129	+	0.641082i	−0.989585	−	0.143949i	$-0.954020\pi$
$37$	−2.25141	+	3.89955i	−0.370129	+	0.641082i	0.619456	+	0.785031i	$0.287353\pi$
$38$	−0.278202	−	2.64692i	−0.0451303	−	0.429386i
$39$	2.09445	+	1.52171i	0.335381	+	0.243669i
$40$	−0.134670	+	1.28130i	−0.0212931	+	0.202591i
$41$	−3.15770	+	3.50698i	−0.493150	+	0.547699i	−0.937423	−	0.348193i	$-0.886795\pi$
$41$	−3.15770	+	3.50698i	−0.493150	+	0.547699i	0.444273	+	0.895892i	$0.353462\pi$
$42$	−3.15081	−	1.40283i	−0.486180	−	0.216461i
$43$	−6.41589	−	1.36374i	−0.978413	−	0.207968i	−0.309166	−	0.951008i	$-0.600050\pi$
$43$	−6.41589	−	1.36374i	−0.978413	−	0.207968i	−0.669247	+	0.743040i	$0.733383\pi$
$44$	2.58456	−	0.549365i	0.389637	−	0.0828200i
$45$	−3.03391	+	1.35078i	−0.452268	+	0.201363i
$46$	2.02659	−	6.23721i	0.298805	−	0.919627i
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	−1.00000		0.000618100i	$-0.999803\pi$
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	0.809380	+	0.587285i	$0.199803\pi$
$48$	−2.19919	+	0.979142i	−0.317426	+	0.141327i
$49$	−6.78405	+	1.44199i	−0.969149	+	0.205999i
$50$	−6.41073	−	1.36264i	−0.906614	−	0.192707i
$51$	−2.58541	−	1.15110i	−0.362029	−	0.161186i
$52$	−4.93742	+	5.48357i	−0.684698	+	0.760434i
$53$	1.35503	−	12.8923i	0.186128	−	1.77089i	−0.359770	−	0.933041i	$-0.617145\pi$
$53$	1.35503	−	12.8923i	0.186128	−	1.77089i	0.545899	−	0.837851i	$-0.316188\pi$
$54$	−4.29836	−	3.12294i	−0.584933	−	0.424979i
$55$	0.234298	+	2.22920i	0.0315928	+	0.300585i
$56$	−1.99173	+	3.44978i	−0.266156	+	0.460996i
$57$	0.359157	+	0.622078i	0.0475715	+	0.0823963i
$58$	2.05458	−	1.49274i	0.269779	−	0.196006i
$59$	−1.45975	−	1.62121i	−0.190043	−	0.211064i	0.640592	−	0.767881i	$-0.278689\pi$
$59$	−1.45975	−	1.62121i	−0.190043	−	0.211064i	−0.830635	+	0.556817i	$0.812022\pi$
$60$	0.265164	+	0.816089i	0.0342325	+	0.105357i
$61$	−2.68087			−0.343251			−0.171625	−	0.985162i	$-0.554902\pi$
$61$	−2.68087			−0.343251			−0.171625	+	0.985162i	$0.554902\pi$
$62$		0			0
$63$	−10.2683			−1.29368
$64$	−0.900071	−	2.77013i	−0.112509	−	0.346267i
$65$	−4.18844	−	4.65174i	−0.519512	−	0.576977i
$66$	−1.38766	+	1.00820i	−0.170809	+	0.124100i
$67$	−1.44150	−	2.49675i	−0.176107	−	0.305027i	0.764437	−	0.644699i	$-0.223017\pi$
$67$	−1.44150	−	2.49675i	−0.176107	−	0.305027i	−0.940544	+	0.339672i	$0.889684\pi$
$68$	4.03315	−	6.98563i	0.489092	−	0.847132i
$69$	0.185015	+	1.76030i	0.0222732	+	0.211916i
$70$	6.74649	+	4.90161i	0.806360	+	0.585855i
$71$	−0.940927	+	8.95232i	−0.111667	+	1.06245i	0.784926	+	0.619590i	$0.212701\pi$
$71$	−0.940927	+	8.95232i	−0.111667	+	1.06245i	−0.896593	+	0.442855i	$0.853966\pi$
$72$	−1.96401	+	2.18125i	−0.231461	+	0.257063i
$73$	−3.84059	−	1.70994i	−0.449507	−	0.200134i	0.169481	−	0.985533i	$-0.445791\pi$
$73$	−3.84059	−	1.70994i	−0.449507	−	0.200134i	−0.618989	+	0.785400i	$0.712457\pi$
$74$	8.14908	+	1.73214i	0.947311	+	0.201357i
$75$	1.73020	−	0.367765i	0.199786	−	0.0424659i
$76$	−1.87034	+	0.832730i	−0.214543	+	0.0955207i
$77$	−2.14162	+	6.59123i	−0.244060	+	0.751140i
$78$	1.48018	−	4.55554i	0.167598	−	0.515813i
$79$	10.2607	−	4.56834i	1.15442	−	0.513979i	0.261944	−	0.965083i	$-0.415636\pi$
$79$	10.2607	−	4.56834i	1.15442	−	0.513979i	0.892471	+	0.451104i	$0.148970\pi$
$80$	5.69331	−	1.21015i	0.636532	−	0.135299i
$81$	−6.66899	−	1.41754i	−0.740999	−	0.157504i
$82$	7.97647	+	3.55135i	0.880853	+	0.392181i
$83$	−7.01077	+	7.78625i	−0.769532	+	0.854652i	−0.992760	−	0.120114i	$-0.961674\pi$
$83$	−7.01077	+	7.78625i	−0.769532	+	0.854652i	0.223228	+	0.974766i	$0.428341\pi$
$84$	−0.277327	+	2.63859i	−0.0302588	+	0.287893i
$85$	5.53585	+	4.02203i	0.600448	+	0.436251i
$86$	1.26855	+	12.0694i	0.136791	+	1.30148i
$87$	−0.342708	+	0.593587i	−0.0367421	+	0.0636392i
$88$	0.990524	+	1.71564i	0.105590	+	0.182888i
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	−0.465884	−	0.884846i	$-0.654263\pi$
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	0.697573	+	0.716514i	$0.254263\pi$
$90$	4.11152	+	4.56631i	0.433393	+	0.481331i
$91$	−5.98067	−	18.4066i	−0.626944	−	1.92954i
$92$	−5.04486			−0.525963
$93$		0			0
$94$	7.82446			0.807031
$95$	−0.536692	−	1.65177i	−0.0550635	−	0.169468i
$96$	2.26723	+	2.51801i	0.231398	+	0.256994i
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	−0.192530	−	0.981291i	$-0.561669\pi$
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	0.873768	+	0.486342i	$0.161669\pi$
$98$	6.41615	+	11.1131i	0.648129	+	1.12259i
$99$	−2.55330	+	4.42244i	−0.256616	+	0.444472i
$100$	0.526990	+	5.01398i	0.0526990	+	0.501398i
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	0.521586	−	0.853199i	$-0.325341\pi$
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	−0.650261	+	0.759711i	$0.725341\pi$
$102$	−0.547335	+	5.20755i	−0.0541942	+	0.515624i
$103$	12.2503	−	13.6054i	1.20706	−	1.34058i	0.282631	−	0.959229i	$-0.408793\pi$
$103$	12.2503	−	13.6054i	1.20706	−	1.34058i	0.924431	−	0.381349i	$-0.124540\pi$
$104$	−5.05397	−	2.25017i	−0.495582	−	0.220647i
$105$	−2.20147	−	0.467938i	−0.214842	−	0.0456660i
$106$	−23.4607	+	4.98672i	−2.27870	+	0.484353i
$107$	10.5745	−	4.70809i	1.02228	−	0.455148i	0.174027	−	0.984741i	$-0.444322\pi$
$107$	10.5745	−	4.70809i	1.02228	−	0.455148i	0.848252	+	0.529593i	$0.177655\pi$
$108$	−1.26297	+	3.88702i	−0.121529	+	0.374029i
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	−0.928317	−	0.371789i	$-0.878744\pi$
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	0.969557	+	0.244867i	$0.0787444\pi$
$110$	3.78865	−	1.68682i	0.361234	−	0.160832i
$111$	−2.19936	+	0.467489i	−0.208754	+	0.0443721i
$112$	17.6032	+	3.74167i	1.66334	+	0.353554i
$113$	−2.97411	−	1.32416i	−0.279780	−	0.124566i	0.262050	−	0.965054i	$-0.415602\pi$
$113$	−2.97411	−	1.32416i	−0.279780	−	0.124566i	−0.541830	+	0.840488i	$0.682268\pi$
$114$	0.889294	−	0.987661i	0.0832900	−	0.0925030i
$115$	0.447338	−	4.25614i	0.0417145	−	0.396887i
$116$	−1.58047	−	1.14828i	−0.146743	−	0.106615i
$117$	−1.49064	−	14.1825i	−0.137810	−	1.31117i
$118$	−2.01817	+	3.49557i	−0.185787	+	0.321793i
$119$	10.5785	+	18.3224i	0.969726	+	1.67961i
$120$	−0.520477	+	0.378149i	−0.0475129	+	0.0345201i
$121$	−5.05419	−	5.61325i	−0.459472	−	0.510295i
$122$	1.53278	+	4.71740i	0.138771	+	0.427093i
$123$	−2.35651			−0.212479
$124$		0			0
$125$	−10.3136			−0.922478
$126$	5.87084	+	18.0686i	0.523016	+	1.60968i
$127$	6.41792	+	7.12783i	0.569499	+	0.632492i	0.957247	−	0.289273i	$-0.0934136\pi$
$127$	6.41792	+	7.12783i	0.569499	+	0.632492i	−0.387748	+	0.921765i	$0.626747\pi$
$128$	6.61915	−	4.80909i	0.585056	−	0.425068i
$129$	−1.63769	−	2.83656i	−0.144190	−	0.249745i
$130$	−5.79071	+	10.0298i	−0.507879	+	0.879672i
$131$	1.20126	+	11.4292i	0.104955	+	0.998576i	0.912585	+	0.408887i	$0.134083\pi$
$131$	1.20126	+	11.4292i	0.104955	+	0.998576i	−0.807630	+	0.589689i	$0.799250\pi$
$132$	1.06745	+	0.775550i	0.0929099	+	0.0675030i
$133$	0.561310	−	5.34051i	0.0486718	−	0.463081i
$134$	−3.56924	+	3.96404i	−0.308335	+	0.342441i
$135$	−3.16733	−	1.41018i	−0.272600	−	0.121369i
$136$	5.91551	+	1.25738i	0.507250	+	0.107819i
$137$	15.4427	−	3.28245i	1.31936	−	0.280439i	0.506170	−	0.862434i	$-0.331061\pi$
$137$	15.4427	−	3.28245i	1.31936	−	0.280439i	0.813192	+	0.581995i	$0.197728\pi$
$138$	2.99174	−	1.33201i	0.254674	−	0.113388i
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	0.723521	+	0.690303i	$0.242523\pi$
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	−0.991090	+	0.133192i	$0.957477\pi$
$140$	1.98229	−	6.10087i	0.167534	−	0.515618i
$141$	−1.92918	+	0.858927i	−0.162466	+	0.0723347i
$142$	16.2909	−	3.46274i	1.36710	−	0.290587i
$143$	−9.41469	−	2.00115i	−0.787296	−	0.167345i
$144$	12.1140	+	5.39351i	1.00950	+	0.449459i
$145$	1.10890	−	1.23156i	0.0920893	−	0.102275i
$146$	−0.813060	+	7.73575i	−0.0672893	+	0.640215i
$147$	−2.80189	−	2.03569i	−0.231096	−	0.167901i
$148$	−0.669890	−	6.37358i	−0.0550646	−	0.523905i
$149$	−1.91033	+	3.30879i	−0.156501	+	0.271067i	−0.933604	−	0.358305i	$-0.883355\pi$
$149$	−1.91033	+	3.30879i	−0.156501	+	0.271067i	0.777104	+	0.629372i	$0.216688\pi$
$150$	−1.63637	−	2.83428i	−0.133609	−	0.231418i
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	−0.256283	−	0.966602i	$-0.582498\pi$
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	0.840097	+	0.542436i	$0.182498\pi$
$152$	−1.02710	−	1.14071i	−0.0833091	−	0.0925242i
$153$	4.81733	+	14.8262i	0.389458	+	1.19863i
$154$	12.8227			1.03328
$155$		0			0
$156$	−3.68467			−0.295010
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	0.866701	−	0.498829i	$-0.166236\pi$
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	−0.994380	+	0.105873i	$0.966236\pi$
$158$	−13.9052	−	15.4433i	−1.10624	−	1.22860i
$159$	5.23700	−	3.80490i	0.415321	−	0.301748i
$160$	−4.09621	−	7.09485i	−0.323834	−	0.560897i
$161$	6.61602	−	11.4593i	0.521416	−	0.903119i
$162$	1.31859	+	12.5456i	0.103598	+	0.985673i
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	0.570101	−	0.821574i	$-0.306904\pi$
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	−0.605193	+	0.796079i	$0.706904\pi$
$164$	0.702069	−	6.67974i	0.0548224	−	0.521600i
$165$	−0.748953	+	0.831796i	−0.0583059	+	0.0647552i
$166$	17.7095	+	7.88476i	1.37452	+	0.611976i
$167$	−1.95434	−	0.415409i	−0.151232	−	0.0321453i	0.131674	−	0.991293i	$-0.457965\pi$
$167$	−1.95434	−	0.415409i	−0.151232	−	0.0321453i	−0.282905	+	0.959148i	$0.591298\pi$
$168$	−1.94569	+	0.413570i	−0.150113	+	0.0319076i
$169$	12.6789	−	5.64499i	0.975297	−	0.434230i
$170$	3.91228	−	12.0407i	0.300058	−	0.923483i
$171$	1.22271	−	3.76311i	0.0935028	−	0.287772i
$172$	8.52840	−	3.79709i	0.650284	−	0.289525i
$173$	3.96893	−	0.843621i	0.301752	−	0.0641393i	−0.0545476	−	0.998511i	$-0.517372\pi$
$173$	3.96893	−	0.843621i	0.301752	−	0.0641393i	0.356299	+	0.934372i	$0.384038\pi$
$174$	1.24045	+	0.263665i	0.0940380	+	0.0199884i
$175$	−12.0802	−	5.37847i	−0.913181	−	0.406574i
$176$	5.98869	−	6.65111i	0.451414	−	0.501346i
$177$	0.113870	−	1.08340i	0.00855901	−	0.0814336i
$178$	−4.04409	−	2.93820i	−0.303117	−	0.220227i
$179$	0.414336	+	3.94215i	0.0309690	+	0.294650i	0.999034	+	0.0439498i	$0.0139942\pi$
$179$	0.414336	+	3.94215i	0.0309690	+	0.294650i	−0.968065	+	0.250700i	$0.919339\pi$
$180$	2.36334	−	4.09343i	0.176153	−	0.305106i
$181$	−3.19871	−	5.54033i	−0.237758	−	0.411809i	0.722312	−	0.691567i	$-0.243079\pi$
$181$	−3.19871	−	5.54033i	−0.237758	−	0.411809i	−0.960071	+	0.279757i	$0.909746\pi$
$182$	−28.9698	+	21.0478i	−2.14738	+	1.56016i
$183$	−0.895769	−	0.994853i	−0.0662172	−	0.0735416i
$184$	−1.16881	−	3.59723i	−0.0861659	−	0.265191i
$185$	5.43652			0.399701
$186$		0			0
$187$	10.5217			0.769425
$188$	−1.85995	−	5.72434i	−0.135651	−	0.417491i
$189$	−7.17297	−	7.96640i	−0.521757	−	0.579470i
$190$	−2.59968	+	1.88878i	−0.188601	+	0.137027i
$191$	−5.81282	−	10.0681i	−0.420601	−	0.728502i	0.575398	−	0.817874i	$-0.304847\pi$
$191$	−5.81282	−	10.0681i	−0.420601	−	0.728502i	−0.995998	+	0.0893720i	$0.971514\pi$
$192$	0.727233	−	1.25960i	0.0524835	−	0.0909041i
$193$	−1.41568	−	13.4693i	−0.101903	−	0.969544i	−0.919324	−	0.393503i	$-0.871263\pi$
$193$	−1.41568	−	13.4693i	−0.101903	−	0.969544i	0.817420	−	0.576042i	$-0.195403\pi$
$194$	−12.4138	−	9.01917i	−0.891260	−	0.647538i
$195$	0.326727	−	3.10860i	0.0233974	−	0.222612i
$196$	6.60512	−	7.33572i	0.471794	−	0.523980i
$197$	21.3809	+	9.51939i	1.52333	+	0.678228i	0.986243	−	0.165302i	$-0.0528598\pi$
$197$	21.3809	+	9.51939i	1.52333	+	0.678228i	0.537082	+	0.843530i	$0.319526\pi$
$198$	9.24179	+	1.96440i	0.656786	+	0.139604i
$199$	−6.45379	+	1.37179i	−0.457497	+	0.0972439i	−0.430895	−	0.902402i	$-0.641802\pi$
$199$	−6.45379	+	1.37179i	−0.457497	+	0.0972439i	−0.0266019	+	0.999646i	$0.508469\pi$
$200$	−3.45311	+	1.53742i	−0.244172	+	0.108712i
$201$	0.444873	−	1.36918i	0.0313789	−	0.0965744i
$202$	−0.913902	+	2.81270i	−0.0643019	+	0.197901i
$203$	4.68099	−	2.08411i	0.328541	−	0.146276i
$204$	3.93993	−	0.837457i	0.275850	−	0.0586337i
$205$	5.57316	+	1.18461i	0.389247	+	0.0827369i
$206$	−30.9448	−	13.7775i	−2.15603	−	0.959924i
$207$	6.52393	−	7.24556i	0.453445	−	0.503601i
$208$	−2.61254	+	24.8566i	−0.181147	+	1.72350i
$209$	−2.16053	−	1.56972i	−0.149447	−	0.108580i
$210$	0.435275	+	4.14137i	0.0300368	+	0.285781i
$211$	9.68254	−	16.7707i	0.666574	−	1.15454i	−0.312283	−	0.949989i	$-0.601094\pi$
$211$	9.68254	−	16.7707i	0.666574	−	1.15454i	0.978856	−	0.204550i	$-0.0655731\pi$
$212$	9.22510	+	15.9783i	0.633582	+	1.09740i
$213$	−3.63654	+	2.64210i	−0.249171	+	0.181034i
$214$	−14.3305	−	15.9157i	−0.979615	−	1.08797i
$215$	2.44721	+	7.53175i	0.166899	+	0.513661i
$216$	−3.06424			−0.208495
$217$		0			0
$218$	−2.57788			−0.174596
$219$	−0.648723	−	1.99656i	−0.0438366	−	0.134915i
$220$	−2.13467	−	2.37079i	−0.143919	−	0.159839i
$221$	−23.7712	+	17.2708i	−1.59903	+	1.16176i
$222$	2.08009	+	3.60283i	0.139607	+	0.241806i
$223$	−3.52986	+	6.11389i	−0.236377	+	0.409416i	−0.959672	−	0.281123i	$-0.909293\pi$
$223$	−3.52986	+	6.11389i	−0.236377	+	0.409416i	0.723295	+	0.690539i	$0.242627\pi$
$224$	−2.64773	−	25.1914i	−0.176909	−	1.68317i
$225$	−7.88270	−	5.72712i	−0.525513	−	0.381808i
$226$	−0.629623	+	5.99047i	−0.0418819	+	0.398480i
$227$	−6.03543	+	6.70302i	−0.400586	+	0.444895i	−0.909363	−	0.416003i	$-0.863431\pi$
$227$	−6.03543	+	6.70302i	−0.400586	+	0.444895i	0.508778	+	0.860898i	$0.330097\pi$
$228$	−0.933963	−	0.415827i	−0.0618532	−	0.0275388i
$229$	−17.5615	−	3.73281i	−1.16050	−	0.246671i	−0.412870	−	0.910790i	$-0.635473\pi$
$229$	−17.5615	−	3.73281i	−1.16050	−	0.246671i	−0.747627	+	0.664119i	$0.768807\pi$
$230$	−7.74508	+	1.64627i	−0.510696	+	0.108552i
$231$	−3.16154	+	1.40761i	−0.208014	+	0.0926139i
$232$	0.452611	−	1.39299i	0.0297154	−	0.0914545i
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	−0.712597	−	0.701574i	$-0.752481\pi$
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	0.988878	−	0.148731i	$-0.0475190\pi$
$234$	−24.1040	+	10.7318i	−1.57573	+	0.701559i
$235$	4.99432	−	1.06157i	0.325793	−	0.0692495i
$236$	3.03708	+	0.645552i	0.197697	+	0.0420218i
$237$	5.12371	+	2.28122i	0.332821	+	0.148181i
$238$	26.1929	−	29.0902i	1.69783	−	1.88564i
$239$	1.02973	−	9.79726i	0.0666079	−	0.633732i	−0.909389	−	0.415947i	$-0.863450\pi$
$239$	1.02973	−	9.79726i	0.0666079	−	0.633732i	0.975997	−	0.217785i	$-0.0698832\pi$
$240$	2.35140	+	1.70840i	0.151783	+	0.110276i
$241$	0.697185	+	6.63328i	0.0449097	+	0.427287i	0.993758	+	0.111555i	$0.0355832\pi$
$241$	0.697185	+	6.63328i	0.0449097	+	0.427287i	−0.948849	+	0.315732i	$0.897750\pi$
$242$	−6.98765	+	12.1030i	−0.449183	+	0.778008i
$243$	−6.00971	−	10.4091i	−0.385523	−	0.667746i
$244$	3.08688	−	2.24275i	0.197617	−	0.143577i
$245$	5.60315	+	6.22293i	0.357972	+	0.397569i
$246$	1.34732	+	4.14663i	0.0859021	+	0.264380i
$247$	7.45779			0.474528
$248$		0			0
$249$	−5.23195			−0.331562
$250$	5.89676	+	18.1484i	0.372944	+	1.14780i
$251$	−19.6175	−	21.7875i	−1.23825	−	1.37521i	−0.901012	−	0.433795i	$-0.857174\pi$
$251$	−19.6175	−	21.7875i	−1.23825	−	1.37521i	−0.337237	−	0.941420i	$-0.609492\pi$
$252$	11.8233	−	8.59016i	0.744801	−	0.541129i
$253$	−3.29027	−	5.69891i	−0.206857	−	0.358288i
$254$	8.87307	−	15.3686i	0.556746	−	0.964312i
$255$	0.357166	+	3.39821i	0.0223666	+	0.212804i
$256$	−16.9596	−	12.3219i	−1.05998	−	0.770118i
$257$	2.50330	−	23.8173i	0.156152	−	1.48568i	−0.583181	−	0.812342i	$-0.698192\pi$
$257$	2.50330	−	23.8173i	0.156152	−	1.48568i	0.739333	−	0.673341i	$-0.235141\pi$
$258$	−4.05501	+	4.50355i	−0.252454	+	0.280379i
$259$	15.3560	+	6.83691i	0.954173	+	0.424825i
$260$	8.71428	+	1.85228i	0.540436	+	0.114873i
$261$	3.69304	−	0.784979i	0.228593	−	0.0485890i
$262$	19.4246	−	8.64840i	1.20006	−	0.534300i
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	−0.906420	−	0.422378i	$-0.861196\pi$
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	0.981577	+	0.191070i	$0.0611956\pi$
$264$	−0.305694	+	0.940828i	−0.0188141	+	0.0579040i
$265$	−14.2983	+	6.36600i	−0.878335	+	0.391060i
$266$	−9.71836	+	2.06570i	−0.595871	+	0.126656i
$267$	1.31964	+	0.280498i	0.0807608	+	0.0171662i
$268$	3.74852	+	1.66895i	0.228977	+	0.101947i
$269$	8.53291	−	9.47676i	0.520261	−	0.577808i	−0.424558	−	0.905401i	$-0.639571\pi$
$269$	8.53291	−	9.47676i	0.520261	−	0.577808i	0.944819	+	0.327592i	$0.106237\pi$
$270$	−0.670529	+	6.37966i	−0.0408071	+	0.388254i
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	0.666428	−	0.745569i	$-0.267822\pi$
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	−0.503141	+	0.864204i	$0.667822\pi$
$272$	−2.85593	−	27.1724i	−0.173166	−	1.64757i
$273$	4.83221	−	8.36964i	0.292459	−	0.506554i
$274$	−14.6053	−	25.2971i	−0.882337	−	1.52825i
$275$	−5.32032	+	3.86544i	−0.320827	+	0.233095i
$276$	−1.68566	−	1.87211i	−0.101465	−	0.112688i
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	0.932624	+	0.360849i	$0.117513\pi$
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	−0.542407	+	0.840116i	$0.682487\pi$
$278$	18.8878			1.13282
$279$		0			0
$280$	4.80948			0.287421
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	0.826847	−	0.562426i	$-0.190132\pi$
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	−0.999519	+	0.0309964i	$0.990132\pi$
$282$	2.61441	+	2.90360i	0.155686	+	0.172907i
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	−0.316837	−	0.948480i	$-0.602621\pi$
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	0.804150	+	0.594426i	$0.202621\pi$
$284$	−6.40585	−	11.0953i	−0.380117	−	0.658382i
$285$	0.433632	−	0.751074i	0.0256862	−	0.0444898i
$286$	1.86147	+	17.7107i	0.110071	+	1.04726i
$287$	14.2522	+	10.3548i	0.841278	+	0.611225i
$288$	1.95094	−	18.5620i	0.114960	−	1.09378i
$289$	10.1174	−	11.2366i	0.595144	−	0.660974i
$290$	−2.80112	−	1.24714i	−0.164488	−	0.0732346i
$291$	4.05080	+	0.861024i	0.237462	+	0.0504741i
$292$	5.85272	−	1.24403i	0.342504	−	0.0728016i
$293$	−19.4312	+	8.65133i	−1.13518	+	0.505416i	−0.886297	−	0.463117i	$-0.846731\pi$
$293$	−19.4312	+	8.65133i	−1.13518	+	0.505416i	−0.248886	+	0.968533i	$0.580064\pi$
$294$	−1.98014	+	6.09424i	−0.115484	+	0.355423i
$295$	−0.813929	+	2.50502i	−0.0473888	+	0.145848i
$296$	4.38947	−	1.95432i	0.255133	−	0.113592i
$297$	−5.21467	+	1.10841i	−0.302586	+	0.0643166i
$298$	6.91455	+	1.46973i	0.400549	+	0.0851393i
$299$	16.7880	+	7.47450i	0.970875	+	0.432261i
$300$	−1.68456	+	1.87090i	−0.0972584	+	0.108016i
$301$	−2.55947	+	24.3517i	−0.147525	+	1.40361i
$302$	−13.2734	−	9.64371i	−0.763800	−	0.554933i
$303$	−0.0834335	−	0.793817i	−0.00479313	−	0.0456036i
$304$	−3.46736	+	6.00565i	−0.198867	+	0.344447i
$305$	1.61839	+	2.80314i	0.0926688	+	0.160507i
$306$	23.3347	−	16.9536i	1.33396	−	0.969175i
$307$	10.8675	+	12.0696i	0.620241	+	0.688848i	0.968631	−	0.248502i	$-0.0799382\pi$
$307$	10.8675	+	12.0696i	0.620241	+	0.688848i	−0.348390	+	0.937350i	$0.613272\pi$
$308$	−3.04809	−	9.38105i	−0.173681	−	0.534535i
$309$	9.14210			0.520076
$310$		0			0
$311$	−10.3858			−0.588924			−0.294462	−	0.955663i	$-0.595141\pi$
$311$	−10.3858			−0.588924			−0.294462	+	0.955663i	$0.595141\pi$
$312$	−0.853677	−	2.62735i	−0.0483299	−	0.148744i
$313$	21.4414	+	23.8131i	1.21194	+	1.34600i	0.921149	+	0.389209i	$0.127252\pi$
$313$	21.4414	+	23.8131i	1.21194	+	1.34600i	0.290791	+	0.956787i	$0.406082\pi$
$314$	−7.74935	+	5.63023i	−0.437321	+	0.317732i
$315$	6.19876	+	10.7366i	0.349261	+	0.604937i
$316$	−7.99283	+	13.8440i	−0.449632	+	0.778786i
$317$	−2.64611	−	25.1760i	−0.148620	−	1.41403i	−0.773743	−	0.633500i	$-0.781618\pi$
$317$	−2.64611	−	25.1760i	−0.148620	−	1.41403i	0.625123	−	0.780527i	$-0.285049\pi$
$318$	−9.68952	−	7.03985i	−0.543361	−	0.394775i
$319$	0.266365	−	2.53429i	0.0149136	−	0.141893i
$320$	−2.35311	+	2.61340i	−0.131543	+	0.146093i
$321$	5.28044	+	2.35101i	0.294726	+	0.131220i
$322$	−23.9470	−	5.09010i	−1.33452	−	0.283660i
$323$	−7.97443	+	1.69502i	−0.443709	+	0.0943133i
$324$	8.86485	−	3.94689i	0.492492	−	0.219271i
$325$	5.67505	−	17.4660i	0.314795	−	0.968839i
$326$	−0.316619	+	0.974453i	−0.0175359	+	0.0539700i
$327$	0.635597	−	0.282986i	0.0351486	−	0.0156492i
$328$	4.92564	−	1.04698i	0.271973	−	0.0578096i
$329$	15.4419	+	3.28228i	0.851341	+	0.180958i
$330$	1.89188	+	0.842320i	0.104145	+	0.0463682i
$331$	−22.0247	+	24.4609i	−1.21059	+	1.34449i	−0.288513	+	0.957476i	$0.593161\pi$
$331$	−22.0247	+	24.4609i	−1.21059	+	1.34449i	−0.922073	+	0.387016i	$0.873506\pi$
$332$	1.55874	−	14.8305i	0.0855472	−	0.813927i
$333$	10.0202	+	7.28010i	0.549103	+	0.398947i
$334$	0.386413	+	3.67647i	0.0211436	+	0.201167i
$335$	−1.74041	+	3.01448i	−0.0950888	+	0.164699i
$336$	4.49330	+	7.78262i	0.245130	+	0.424577i
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	−0.671426	−	0.741072i	$-0.734318\pi$
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	0.497319	+	0.867568i	$0.334318\pi$
$338$	−17.1823	−	19.0829i	−0.934593	−	1.03797i
$339$	−0.502363	−	1.54611i	−0.0272846	−	0.0839734i
$340$	−9.73895			−0.528169
$341$		0			0
$342$	−7.32083			−0.395865
$343$	−0.0742848	−	0.228625i	−0.00401100	−	0.0123446i
$344$	4.68340	+	5.20144i	0.252512	+	0.280443i
$345$	1.72889	−	1.25611i	0.0930804	−	0.0676269i
$346$	−3.75369	−	6.50159i	−0.201800	−	0.349527i
$347$	6.84222	−	11.8511i	0.367310	−	0.636199i	−0.621834	−	0.783149i	$-0.713612\pi$
$347$	6.84222	−	11.8511i	0.367310	−	0.636199i	0.989144	+	0.146950i	$0.0469456\pi$
$348$	−0.101970	−	0.970182i	−0.00546618	−	0.0520072i
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	0.665110	−	0.746745i	$-0.268385\pi$
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	−0.504667	+	0.863314i	$0.668385\pi$
$350$	−2.55741	+	24.3321i	−0.136699	+	1.30061i
$351$	9.96187	−	11.0638i	0.531725	−	0.590541i
$352$	−11.5081	−	5.12373i	−0.613383	−	0.273096i
$353$	15.1529	+	3.22086i	0.806510	+	0.171429i	0.592676	−	0.805441i	$-0.298071\pi$
$353$	15.1529	+	3.22086i	0.806510	+	0.171429i	0.213834	+	0.976870i	$0.431405\pi$
$354$	−1.97152	+	0.419059i	−0.104785	+	0.0222727i
$355$	9.92862	−	4.42051i	0.526956	−	0.234616i
$356$	−1.18826	+	3.65708i	−0.0629775	+	0.193825i
$357$	−3.26470	+	10.0477i	−0.172786	+	0.531782i
$358$	6.69991	−	2.98299i	0.354101	−	0.157656i
$359$	5.25204	−	1.11636i	0.277192	−	0.0589190i	−0.0672180	−	0.997738i	$-0.521412\pi$
$359$	5.25204	−	1.11636i	0.277192	−	0.0589190i	0.344410	+	0.938819i	$0.388079\pi$
$360$	3.46636	+	0.736798i	0.182693	+	0.0388327i
$361$	−15.4670	−	6.88636i	−0.814054	−	0.362440i
$362$	−7.92020	+	8.79627i	−0.416276	+	0.462322i
$363$	0.394261	−	3.75115i	0.0206934	−	0.196884i
$364$	22.2849	+	16.1909i	1.16804	+	0.848634i
$365$	0.530567	+	5.04800i	0.0277711	+	0.264225i
$366$	−1.23844	+	2.14504i	−0.0647344	+	0.112123i
$367$	7.36045	+	12.7487i	0.384212	+	0.665475i	0.991660	−	0.128885i	$-0.0411397\pi$
$367$	7.36045	+	12.7487i	0.384212	+	0.665475i	−0.607447	+	0.794360i	$0.707806\pi$
$368$	−13.8244	+	10.0440i	−0.720645	+	0.523579i
$369$	8.68572	+	9.64646i	0.452160	+	0.502175i
$370$	−3.10831	−	9.56638i	−0.161593	−	0.497333i
$371$	−48.3926			−2.51242
$372$		0			0
$373$	23.8449			1.23464			0.617320	−	0.786712i	$-0.288218\pi$
$373$	23.8449			1.23464			0.617320	+	0.786712i	$0.288218\pi$
$374$	−6.01574	−	18.5146i	−0.311067	−	0.957365i
$375$	−3.44612	−	3.82731i	−0.177957	−	0.197641i
$376$	3.65081	−	2.65247i	0.188276	−	0.136791i
$377$	3.55811	+	6.16282i	0.183252	+	0.317402i
$378$	−9.91696	+	17.1767i	−0.510073	+	0.883473i
$379$	2.31291	+	22.0059i	0.118806	+	1.13037i	0.877720	+	0.479174i	$0.159064\pi$
$379$	2.31291	+	22.0059i	0.118806	+	1.13037i	−0.758914	+	0.651191i	$0.774270\pi$
$380$	1.99980	+	1.45294i	0.102587	+	0.0745341i
$381$	−0.500642	+	4.76329i	−0.0256487	+	0.244031i
$382$	−14.3929	+	15.9849i	−0.736404	+	0.817859i
$383$	−21.7411	−	9.67976i	−1.11092	−	0.494613i	−0.232544	−	0.972586i	$-0.574705\pi$
$383$	−21.7411	−	9.67976i	−1.11092	−	0.494613i	−0.878374	+	0.477973i	$0.841372\pi$
$384$	3.99630	+	0.849439i	0.203935	+	0.0433478i
$385$	8.18468	−	1.73971i	0.417130	−	0.0886637i
$386$	−22.8919	+	10.1921i	−1.16517	+	0.518766i
$387$	−5.57531	+	17.1590i	−0.283409	+	0.872243i
$388$	−3.64750	+	11.2258i	−0.185174	+	0.569906i
$389$	15.5800	−	6.93665i	0.789936	−	0.351702i	0.0282107	−	0.999602i	$-0.491019\pi$
$389$	15.5800	−	6.93665i	0.789936	−	0.351702i	0.761726	+	0.647900i	$0.224352\pi$
$390$	−5.65686	+	1.20240i	−0.286446	+	0.0608860i
$391$	−19.6498	−	4.17669i	−0.993733	−	0.211225i
$392$	6.76102	+	3.01020i	0.341483	+	0.152038i
$393$	−3.83992	+	4.26466i	−0.193698	+	0.215124i
$394$	4.52637	−	43.0656i	0.228035	−	2.16961i
$395$	−10.9709	−	7.97079i	−0.552004	−	0.401054i
$396$	−0.759716	−	7.22822i	−0.0381772	−	0.363232i
$397$	5.01075	−	8.67887i	0.251482	−	0.435580i	−0.712452	−	0.701721i	$-0.752415\pi$
$397$	5.01075	−	8.67887i	0.251482	−	0.435580i	0.963934	+	0.266141i	$0.0857486\pi$
$398$	6.10380	+	10.5721i	0.305956	+	0.529931i
$399$	2.16938	−	1.57614i	0.108605	−	0.0789059i
$400$	11.4266	+	12.6905i	0.571330	+	0.634526i
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	−0.887213	−	0.461360i	$-0.847362\pi$
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	0.446590	−	0.894739i	$-0.352638\pi$
$402$	−2.66363			−0.132850
$403$		0			0
$404$	2.27501			0.113186
$405$	2.54376	+	7.82888i	0.126400	+	0.389020i
$406$	−6.34364	−	7.04533i	−0.314830	−	0.349654i
$407$	6.76299	−	4.91360i	0.335229	−	0.243558i
$408$	1.50996	+	2.61533i	0.0747543	+	0.129478i
$409$	11.5051	−	19.9274i	0.568891	−	0.985349i	−0.427785	−	0.903881i	$-0.640706\pi$
$409$	11.5051	−	19.9274i	0.568891	−	0.985349i	0.996676	−	0.0814681i	$-0.0259609\pi$
$410$	−1.10193	−	10.4841i	−0.0544202	−	0.517774i
$411$	6.37803	+	4.63391i	0.314605	+	0.228574i
$412$	−2.72369	+	25.9141i	−0.134186	+	1.27670i
$413$	−5.44930	+	6.05206i	−0.268142	+	0.297802i
$414$	−16.4797	−	7.33723i	−0.809933	−	0.360605i
$415$	12.3736	+	2.63009i	0.607397	+	0.129106i
$416$	34.4100	−	7.31406i	1.68709	−	0.358601i
$417$	−4.65694	+	2.07340i	−0.228051	+	0.101535i
$418$	−1.52688	+	4.69926i	−0.0746822	+	0.229848i
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	−0.292137	−	0.956377i	$-0.594366\pi$
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	0.798488	−	0.602011i	$-0.205634\pi$
$420$	2.92634	−	1.30289i	0.142791	−	0.0635745i
$421$	−8.83000	+	1.87687i	−0.430348	+	0.0914733i	−0.417993	−	0.908450i	$-0.637266\pi$
$421$	−8.83000	+	1.87687i	−0.430348	+	0.0914733i	−0.0123552	+	0.999924i	$0.503933\pi$
$422$	−35.0464	−	7.44935i	−1.70603	−	0.362629i
$423$	10.6267	+	4.73132i	0.516689	+	0.230045i
$424$	−9.25602	+	10.2799i	−0.449512	+	0.499234i
$425$	−2.09849	+	19.9658i	−0.101792	+	0.968484i
$426$	6.72834	+	4.88843i	0.325989	+	0.236845i
$427$	1.04610	+	9.95299i	0.0506244	+	0.481659i
$428$	−8.23733	+	14.2675i	−0.398167	+	0.689645i
$429$	−2.40315	−	4.16237i	−0.116025	−	0.200961i
$430$	11.8541	−	8.61248i	0.571654	−	0.415331i
$431$	7.56570	+	8.40256i	0.364427	+	0.404737i	0.897274	−	0.441475i	$-0.145544\pi$
$431$	7.56570	+	8.40256i	0.364427	+	0.404737i	−0.532847	+	0.846212i	$0.678878\pi$
$432$	4.27791	+	13.1660i	0.205821	+	0.633452i
$433$	9.10433			0.437526			0.218763	−	0.975778i	$-0.429798\pi$
$433$	9.10433			0.437526			0.218763	+	0.975778i	$0.429798\pi$
$434$		0			0
$435$	0.827544			0.0396777
$436$	0.612788	+	1.88597i	0.0293472	+	0.0903215i
$437$	3.41178	+	3.78916i	0.163207	+	0.181260i
$438$	−3.14235	+	2.28305i	−0.150147	+	0.109088i
$439$	19.8026	+	34.2992i	0.945128	+	1.63701i	0.755495	+	0.655155i	$0.227397\pi$
$439$	19.8026	+	34.2992i	0.945128	+	1.63701i	0.189633	+	0.981855i	$0.439270\pi$
$440$	1.19592	−	2.07140i	0.0570133	−	0.0987499i
$441$	1.99413	+	18.9729i	0.0949586	+	0.903470i
$442$	43.9817	+	31.9546i	2.09200	+	1.51992i
$443$	−2.64021	+	25.1199i	−0.125440	+	1.19348i	0.732876	+	0.680363i	$0.238178\pi$
$443$	−2.64021	+	25.1199i	−0.125440	+	1.19348i	−0.858316	+	0.513122i	$0.828489\pi$
$444$	2.14136	−	2.37822i	0.101624	−	0.112865i
$445$	−2.97996	−	1.32676i	−0.141264	−	0.0628946i
$446$	12.7765	+	2.71573i	0.604984	+	0.128593i
$447$	−1.86618	+	0.396668i	−0.0882671	+	0.0187617i
$448$	−9.93316	+	4.42253i	−0.469298	+	0.208945i
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	−0.936810	−	0.349839i	$-0.886236\pi$
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	0.963525	+	0.267617i	$0.0862363\pi$
$450$	−5.57083	+	17.1452i	−0.262611	+	0.808235i
$451$	8.00364	−	3.56345i	0.376877	−	0.167796i
$452$	4.53227	−	0.963364i	0.213180	−	0.0453128i
$453$	4.33130	+	0.920647i	0.203502	+	0.0432558i
$454$	15.2457	+	6.78783i	0.715516	+	0.318568i
$455$	−15.6356	+	17.3651i	−0.733010	+	0.814090i
$456$	0.0801211	−	0.762301i	0.00375201	−	0.0356980i
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.998402	−	0.0565045i	$-0.982004\pi$
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.362262	−	0.932076i	$-0.617996\pi$
$458$	3.47226	+	33.0363i	0.162248	+	1.54369i
$459$	−8.13739	+	14.0944i	−0.379821	+	0.657869i
$460$	3.04549	+	5.27494i	0.141997	+	0.245945i
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	−0.562317	−	0.826922i	$-0.690090\pi$
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	0.612684	+	0.790328i	$0.290090\pi$
$462$	4.28450	+	4.75842i	0.199333	+	0.221382i
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	0.830325	−	0.557280i	$-0.188155\pi$
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	−0.999308	+	0.0372039i	$0.988155\pi$
$464$	−6.61711			−0.307192
$465$		0			0
$466$	−25.2503			−1.16970
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	0.998385	−	0.0568157i	$-0.0180947\pi$
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	−0.841106	+	0.540871i	$0.818095\pi$
$468$	13.5811	+	15.0833i	0.627787	+	0.697228i
$469$	−8.70693	+	6.32596i	−0.402049	+	0.292106i
$470$	−4.72348	−	8.18130i	−0.217878	−	0.377375i
$471$	1.29261	−	2.23886i	0.0595602	−	0.103161i
$472$	0.243332	+	2.31515i	0.0112003	+	0.106563i
$473$	9.85161	+	7.15761i	0.452977	+	0.329107i
$474$	1.08470	−	10.3202i	0.0498219	−	0.474023i
$475$	3.40957	−	3.78671i	0.156442	−	0.173746i
$476$	−27.5086	−	12.2476i	−1.26085	−	0.561368i
$477$	−34.8782	−	7.41360i	−1.59697	−	0.339445i
$478$	−17.8285	+	3.78957i	−0.815457	+	0.173331i
$479$	−0.613679	+	0.273227i	−0.0280397	+	0.0124841i	−0.420709	−	0.907196i	$-0.638219\pi$
$479$	−0.613679	+	0.273227i	−0.0280397	+	0.0124841i	0.392669	+	0.919680i	$0.371552\pi$
$480$	1.26417	−	3.89070i	0.0577010	−	0.177585i
$481$	−7.21391	+	22.2021i	−0.328926	+	1.01233i
$482$	11.2736	−	5.01935i	0.513500	−	0.228625i
$483$	6.46309	−	1.37377i	0.294081	−	0.0625088i
$484$	10.5155	+	2.23514i	0.477978	+	0.101597i
$485$	−9.14734	−	4.07266i	−0.415359	−	0.184930i
$486$	−14.8804	+	16.5264i	−0.674989	+	0.749651i
$487$	2.56884	−	24.4409i	0.116405	−	1.10752i	−0.767886	−	0.640586i	$-0.778691\pi$
$487$	2.56884	−	24.4409i	0.116405	−	1.10752i	0.884291	−	0.466935i	$-0.154642\pi$
$488$	2.31437	+	1.68148i	0.104766	+	0.0761172i
$489$	−0.0289053	−	0.275016i	−0.00130714	−	0.0124366i
$490$	7.74661	−	13.4175i	0.349956	−	0.606142i
$491$	−4.31714	−	7.47751i	−0.194830	−	0.337455i	0.752015	−	0.659146i	$-0.229082\pi$
$491$	−4.31714	−	7.47751i	−0.194830	−	0.337455i	−0.946845	+	0.321691i	$0.895749\pi$
$492$	2.71339	−	1.97139i	0.122329	−	0.0888772i
$493$	−5.20529	−	5.78107i	−0.234435	−	0.260366i
$494$	−4.26395	−	13.1231i	−0.191844	−	0.590436i
$495$	6.16551			0.277119
$496$		0			0
$497$	33.6035			1.50732
$498$	2.99134	+	9.20641i	0.134045	+	0.412549i
$499$	20.8075	+	23.1091i	0.931474	+	1.03451i	0.999322	+	0.0368107i	$0.0117199\pi$
$499$	20.8075	+	23.1091i	0.931474	+	1.03451i	−0.0678486	+	0.997696i	$0.521613\pi$
$500$	11.8756	−	8.62809i	0.531091	−	0.385860i
$501$	−0.498856	−	0.864044i	−0.0222873	−	0.0386027i
$502$	−27.1221	+	46.9769i	−1.21052	+	2.09668i
$503$	1.72936	+	16.4537i	0.0771082	+	0.733635i	0.962956	+	0.269659i	$0.0869110\pi$
$503$	1.72936	+	16.4537i	0.0771082	+	0.733635i	−0.885848	+	0.463976i	$0.846422\pi$
$504$	8.86447	+	6.44042i	0.394855	+	0.286879i
$505$	−0.201729	+	1.91933i	−0.00897684	+	0.0854089i
$506$	−8.14690	+	9.04805i	−0.362174	+	0.402235i
$507$	6.33124	+	2.81885i	0.281180	+	0.125190i
$508$	−13.3528	−	2.83823i	−0.592436	−	0.125926i
$509$	−30.2219	+	6.42386i	−1.33956	+	0.284733i	−0.821304	−	0.570491i	$-0.806753\pi$
$509$	−30.2219	+	6.42386i	−1.33956	+	0.284733i	−0.518259	+	0.855224i	$0.673419\pi$
$510$	5.77545	−	2.57140i	0.255741	−	0.113863i
$511$	−4.84968	+	14.9258i	−0.214537	+	0.660278i
$512$	−6.92906	+	21.3254i	−0.306224	+	0.942460i
$513$	3.77365	−	1.68014i	0.166611	−	0.0741798i
$514$	−43.3414	+	9.21250i	−1.91171	+	0.406346i
$515$	−21.6212	−	4.59572i	−0.952742	−	0.202512i
$516$	4.25869	+	1.89609i	0.187479	+	0.0834708i
$517$	5.25342	−	5.83452i	0.231045	−	0.256602i
$518$	3.25088	−	30.9301i	0.142836	−	1.35899i
$519$	1.63921	+	1.19096i	0.0719534	+	0.0522772i
$520$	0.698191	+	6.64284i	0.0306177	+	0.291308i
$521$	7.36097	−	12.7496i	0.322490	−	0.558569i	−0.658511	−	0.752571i	$-0.728813\pi$
$521$	7.36097	−	12.7496i	0.322490	−	0.558569i	0.981001	+	0.194002i	$0.0621468\pi$
$522$	−3.49277	−	6.04965i	−0.152874	−	0.264786i
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.0973541	−	0.995250i	$-0.468962\pi$
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.976623	+	0.214960i	$0.0689621\pi$
$524$	−10.9446	−	12.1552i	−0.478116	−	0.531001i
$525$	−2.04050	−	6.28002i	−0.0890548	−	0.274082i
$526$	−7.29764			−0.318192
$527$		0			0
$528$	4.46920			0.194497
$529$	−3.22490	−	9.92522i	−0.140213	−	0.431531i
$530$	19.3769	+	21.5202i	0.841678	+	0.934778i
$531$	−4.85466	+	3.52712i	−0.210674	+	0.153064i
$532$	3.82141	+	6.61888i	0.165679	+	0.286965i
$533$	−12.2330	+	21.1883i	−0.529872	+	0.917765i
$534$	−0.260919	−	2.48248i	−0.0112911	−	0.107428i
$535$	−11.3065	−	8.21462i	−0.488821	−	0.355149i
$536$	−0.321571	+	3.05954i	−0.0138898	+	0.132152i
$537$	−1.32446	+	1.47096i	−0.0571546	+	0.0634766i
$538$	−21.5544	−	9.59666i	−0.929278	−	0.413741i
$539$	12.5946	+	2.67707i	0.542490	+	0.115310i
$540$	4.82672	−	1.02595i	0.207709	−	0.0441499i
$541$	−24.7580	+	11.0230i	−1.06443	+	0.473914i	−0.862799	−	0.505548i	$-0.831290\pi$
$541$	−24.7580	+	11.0230i	−1.06443	+	0.473914i	−0.201630	+	0.979462i	$0.564624\pi$
$542$	1.89969	−	5.84664i	0.0815986	−	0.251135i
$543$	0.987180	−	3.03823i	0.0423639	−	0.130383i
$544$	−35.1314	+	15.6415i	−1.50625	+	0.670624i
$545$	−1.64545	+	0.349751i	−0.0704833	+	0.0149817i
$546$	−17.4904	−	3.71771i	−0.748522	−	0.159103i
$547$	30.0215	+	13.3664i	1.28363	+	0.571507i	0.931260	−	0.364356i	$-0.118711\pi$
$547$	30.0215	+	13.3664i	1.28363	+	0.571507i	0.352365	+	0.935863i	$0.385377\pi$
$548$	−15.0354	+	16.6985i	−0.642282	+	0.713326i
$549$	−0.770807	+	7.33374i	−0.0328972	+	0.312996i
$550$	9.84368	+	7.15186i	0.419736	+	0.304956i
$551$	0.206388	+	1.96365i	0.00879243	+	0.0836544i
$552$	0.944367	−	1.63569i	0.0401949	−	0.0696197i
$553$	−20.9642	−	36.3111i	−0.891489	−	1.54410i
$554$	31.4588	−	22.8561i	1.33655	−	0.971064i
$555$	1.81652	+	2.01745i	0.0771071	+	0.0856362i
$556$	−4.48982	−	13.8183i	−0.190411	−	0.586025i
$557$	−3.79343			−0.160733			−0.0803663	−	0.996765i	$-0.525609\pi$
$557$	−3.79343			−0.160733			−0.0803663	+	0.996765i	$0.525609\pi$
$558$		0			0
$559$	−34.0061			−1.43830
$560$	−6.71438	−	20.6647i	−0.283734	−	0.873245i
$561$	3.51566	+	3.90453i	0.148431	+	0.164850i
$562$	−14.0207	+	10.1867i	−0.591429	+	0.429698i
$563$	4.48909	+	7.77534i	0.189193	+	0.327691i	0.944981	−	0.327124i	$-0.106080\pi$
$563$	4.48909	+	7.77534i	0.189193	+	0.327691i	−0.755789	+	0.654816i	$0.772746\pi$
$564$	1.50279	−	2.60291i	0.0632789	−	0.109602i
$565$	0.410864	+	3.90911i	0.0172852	+	0.164457i
$566$	−15.1678	−	11.0200i	−0.637549	−	0.463206i
$567$	−2.66044	+	25.3124i	−0.111728	+	1.06302i
$568$	6.42732	−	7.13826i	0.269684	−	0.299515i
$569$	8.67465	+	3.86220i	0.363660	+	0.161912i	0.580429	−	0.814311i	$-0.302885\pi$
$569$	8.67465	+	3.86220i	0.363660	+	0.161912i	−0.216769	+	0.976223i	$0.569552\pi$
$570$	−1.56955	−	0.333619i	−0.0657414	−	0.0139738i
$571$	−6.26832	+	1.33237i	−0.262321	+	0.0557581i	−0.337195	−	0.941435i	$-0.609478\pi$
$571$	−6.26832	+	1.33237i	−0.262321	+	0.0557581i	0.0748734	+	0.997193i	$0.476145\pi$
$572$	12.5146	−	5.57186i	0.523262	−	0.232971i
$573$	1.79394	−	5.52118i	0.0749429	−	0.230651i
$574$	10.0722	−	30.9991i	0.420407	−	1.29388i
$575$	11.4704	−	5.10693i	0.478347	−	0.212974i
$576$	−7.83670	+	1.66574i	−0.326529	+	0.0694060i
$577$	−7.70309	−	1.63734i	−0.320684	−	0.0681635i	0.0447573	−	0.998998i	$-0.485749\pi$
$577$	−7.70309	−	1.63734i	−0.320684	−	0.0681635i	−0.365441	+	0.930834i	$0.619082\pi$
$578$	−25.5570	−	11.3787i	−1.06303	−	0.473292i
$579$	4.52535	−	5.02591i	0.188067	−	0.208869i
$580$	−0.246548	+	2.34575i	−0.0102374	+	0.0974019i
$581$	31.6428	+	22.9899i	1.31277	+	0.953781i
$582$	−0.800924	−	7.62028i	−0.0331994	−	0.315871i
$583$	−12.0332	+	20.8422i	−0.498366	+	0.863196i
$584$	2.24303	+	3.88505i	0.0928174	+	0.160764i
$585$	−13.9294	+	10.1203i	−0.575912	+	0.418424i
$586$	26.3330	+	29.2458i	1.08781	+	1.20813i
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	0.588144	+	0.808756i	$0.299859\pi$
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	−0.000443412		1.00000i	$0.500141\pi$
$588$	4.92922			0.203278
$589$		0			0
$590$	4.87331			0.200631
$591$	3.61149	+	11.1150i	0.148557	+	0.457211i
$592$	−14.5251	−	16.1317i	−0.596977	−	0.663010i
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	−0.721298	−	0.692625i	$-0.756454\pi$
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	0.435832	+	0.900028i	$0.356454\pi$
$594$	4.93188	+	8.54227i	0.202358	+	0.350494i
$595$	12.7720	−	22.1218i	0.523602	−	0.906905i
$596$	−0.568406	−	5.40803i	−0.0232828	−	0.221521i
$597$	−2.66549	−	1.93659i	−0.109091	−	0.0792594i
$598$	3.55405	−	33.8145i	0.145336	−	1.38278i
$599$	−17.0007	+	18.8812i	−0.694629	+	0.771464i	−0.982511	−	0.186202i	$-0.940382\pi$
$599$	−17.0007	+	18.8812i	−0.694629	+	0.771464i	0.287882	+	0.957666i	$0.407049\pi$
$600$	−1.72433	−	0.767720i	−0.0703954	−	0.0313420i
$601$	24.6156	+	5.23220i	1.00409	+	0.213426i	0.680482	−	0.732765i	$-0.261770\pi$
$601$	24.6156	+	5.23220i	1.00409	+	0.213426i	0.323609	+	0.946191i	$0.395104\pi$
$602$	44.3139	−	9.41920i	1.80610	−	0.383898i
$603$	−7.24452	+	3.22547i	−0.295019	+	0.131351i
$604$	−3.90007	+	12.0032i	−0.158692	+	0.488403i
$605$	−2.81813	+	8.67330i	−0.114573	+	0.352620i
$606$	−1.34914	+	0.600675i	−0.0548050	+	0.0244008i
$607$	−9.18188	+	1.95167i	−0.372681	+	0.0792158i	−0.390445	−	0.920626i	$-0.627679\pi$
$607$	−9.18188	+	1.95167i	−0.372681	+	0.0792158i	0.0177637	+	0.999842i	$0.494345\pi$
$608$	9.54741	+	2.02936i	0.387198	+	0.0823016i
$609$	2.33747	+	1.04071i	0.0947192	+	0.0421717i
$610$	4.00723	−	4.45048i	0.162248	−	0.180195i
$611$	−2.29178	+	21.8048i	−0.0927156	+	0.882130i
$612$	−17.9501	−	13.0415i	−0.725590	−	0.527172i
$613$	−1.20061	−	11.4230i	−0.0484922	−	0.461372i	−0.991643	−	0.129008i	$-0.958821\pi$
$613$	−1.20061	−	11.4230i	−0.0484922	−	0.461372i	0.943151	−	0.332364i	$-0.107846\pi$
$614$	15.0248	−	26.0237i	0.606352	−	1.05023i
$615$	1.42258	+	2.46398i	0.0573639	+	0.0993572i
$616$	5.98295	−	4.34687i	0.241060	−	0.175140i
$617$	−1.50781	−	1.67460i	−0.0607022	−	0.0674167i	0.712029	−	0.702150i	$-0.247777\pi$
$617$	−1.50781	−	1.67460i	−0.0607022	−	0.0674167i	−0.772731	+	0.634734i	$0.781110\pi$
$618$	−5.22695	−	16.0869i	−0.210259	−	0.647110i
$619$	23.6684			0.951314			0.475657	−	0.879631i	$-0.342210\pi$
$619$	23.6684			0.951314			0.475657	+	0.879631i	$0.342210\pi$
$620$		0			0
$621$	10.1786			0.408455
$622$	5.93803	+	18.2754i	0.238093	+	0.732776i
$623$	−6.74864	−	7.49513i	−0.270379	−	0.300286i
$624$	−10.0970	+	7.33594i	−0.404205	+	0.293672i
$625$	−2.62956	−	4.55454i	−0.105183	−	0.182182i
$626$	29.6437	−	51.3444i	1.18480	−	2.05214i
$627$	−0.139395	−	1.32625i	−0.00556689	−	0.0529654i
$628$	5.96115	+	4.33103i	0.237876	+	0.172827i
$629$	2.66752	−	25.3798i	0.106361	−	1.01196i
$630$	15.3485	−	17.0462i	0.611499	−	0.679138i
$631$	−31.7018	−	14.1146i	−1.26203	−	0.561892i	−0.336899	−	0.941541i	$-0.609378\pi$
$631$	−31.7018	−	14.1146i	−1.26203	−	0.561892i	−0.925131	+	0.379649i	$0.876045\pi$
$632$	−11.7232	−	2.49185i	−0.466326	−	0.0991206i
$633$	9.45872	−	2.01051i	0.375951	−	0.0799108i
$634$	−42.7881	+	19.0505i	−1.69933	+	0.756592i
$635$	3.57852	−	11.0136i	0.142009	−	0.437059i
$636$	−2.84703	+	8.76226i	−0.112892	+	0.347446i
$637$	−32.8488	+	14.6252i	−1.30152	+	0.579472i
$638$	−4.61176	+	0.980259i	−0.182581	+	0.0388088i
$639$	24.2192	+	5.14796i	0.958098	+	0.203650i
$640$	−9.02427	−	4.01786i	−0.356716	−	0.158820i
$641$	17.6602	−	19.6136i	0.697536	−	0.774692i	−0.285446	−	0.958395i	$-0.592142\pi$
$641$	17.6602	−	19.6136i	0.697536	−	0.774692i	0.982982	+	0.183702i	$0.0588083\pi$
$642$	1.11788	−	10.6359i	0.0441192	−	0.419766i
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	0.388383	−	0.921498i	$-0.373034\pi$
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	−0.756379	+	0.654133i	$0.773034\pi$
$644$	1.96855	+	18.7295i	0.0775718	+	0.738046i
$645$	−1.97728	+	3.42475i	−0.0778554	+	0.134849i
$646$	7.54198	+	13.0631i	0.296735	+	0.513961i
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.371332	+	0.928500i	$0.621099\pi$
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.997804	+	0.0662355i	$0.978901\pi$
$648$	4.86816	+	5.40664i	0.191239	+	0.212393i
$649$	1.25154	+	3.85186i	0.0491274	+	0.151199i
$650$	−33.9787			−1.33276
$651$		0			0
$652$	0.788169			0.0308671
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	−0.627213	−	0.778848i	$-0.715805\pi$
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	0.0496311	−	0.998768i	$-0.484195\pi$
$654$	−0.861356	−	0.956633i	−0.0336817	−	0.0374073i
$655$	11.2253	−	8.15565i	0.438608	−	0.318668i
$656$	−11.3751	−	19.7022i	−0.444121	−	0.769241i
$657$	−5.78193	+	10.0146i	−0.225574	+	0.390706i
$658$	−3.05318	−	29.0490i	−0.119025	−	1.13245i
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	0.886578	−	0.462579i	$-0.153076\pi$
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	−0.165971	+	0.986131i	$0.553076\pi$
$660$	0.166519	−	1.58432i	0.00648173	−	0.0616696i
$661$	−13.3186	+	14.7918i	−0.518035	+	0.575336i	−0.944226	−	0.329297i	$-0.893188\pi$
$661$	−13.3186	+	14.7918i	−0.518035	+	0.575336i	0.426192	+	0.904633i	$0.359855\pi$
$662$	55.6351	+	24.7703i	2.16232	+	0.962727i
$663$	−14.3518	−	3.05058i	−0.557379	−	0.118475i
$664$	10.9360	−	2.32451i	0.424398	−	0.0902085i
$665$	−5.92292	+	2.63705i	−0.229681	+	0.102261i
$666$	7.08143	−	21.7944i	0.274400	−	0.844516i
$667$	−1.50346	+	4.62717i	−0.0582141	+	0.179165i
$668$	2.59784	−	1.15663i	0.100513	−	0.0447514i
$669$	−3.44826	+	0.732951i	−0.133318	+	0.0283375i
$670$	6.29951	+	1.33900i	0.243371	+	0.0517301i
$671$	4.54678	+	2.02436i	0.175526	+	0.0781494i
$672$	8.46366	−	9.39984i	0.326493	−	0.362607i
$673$	−1.82162	+	17.3316i	−0.0702183	+	0.668083i	0.901635	+	0.432497i	$0.142367\pi$
$673$	−1.82162	+	17.3316i	−0.0702183	+	0.668083i	−0.971854	+	0.235586i	$0.924299\pi$
$674$	5.91359	+	4.29648i	0.227783	+	0.165494i
$675$	−1.06327	−	10.1163i	−0.0409252	−	0.389377i
$676$	−9.87655	+	17.1067i	−0.379867	+	0.657949i
$677$	−15.9129	−	27.5619i	−0.611581	−	1.05929i	−0.990974	−	0.134054i	$-0.957200\pi$
$677$	−15.9129	−	27.5619i	−0.611581	−	1.05929i	0.379393	−	0.925236i	$-0.376133\pi$
$678$	−2.43340	+	1.76797i	−0.0934540	+	0.0678983i
$679$	−20.7158	−	23.0072i	−0.794999	−	0.882936i
$680$	−2.25635	−	6.94434i	−0.0865272	−	0.266303i
$681$	−4.50408			−0.172597
$682$		0			0
$683$	19.9935			0.765031			0.382515	−	0.923949i	$-0.375058\pi$
$683$	19.9935			0.765031			0.382515	+	0.923949i	$0.375058\pi$
$684$	1.74023	+	5.35589i	0.0665395	+	0.204788i
$685$	−12.7546	−	14.1655i	−0.487330	−	0.541234i
$686$	−0.359828	+	0.261431i	−0.0137383	+	0.00998147i
$687$	−4.48266	−	7.76420i	−0.171024	−	0.296223i
$688$	15.8105	−	27.3846i	0.602770	−	1.04403i
$689$	−7.02514	−	66.8397i	−0.267636	−	2.54639i
$690$	−3.19881	−	2.32407i	−0.121777	−	0.0884758i
$691$	1.49053	−	14.1814i	0.0567024	−	0.539487i	−0.928891	−	0.370354i	$-0.879236\pi$
$691$	1.49053	−	14.1814i	0.0567024	−	0.539487i	0.985593	−	0.169133i	$-0.0540969\pi$
$692$	−3.86425	+	4.29168i	−0.146897	+	0.163145i
$693$	17.4151	+	7.75368i	0.661543	+	0.294538i
$694$	−24.7658	−	5.26412i	−0.940095	−	0.199823i
$695$	12.0560	−	2.56258i	0.457310	−	0.0972043i
$696$	0.668162	−	0.297485i	0.0253266	−	0.0112761i
$697$	8.26480	−	25.4364i	0.313052	−	0.963473i
$698$	2.11826	−	6.51934i	0.0801773	−	0.246760i
$699$	6.22566	−	2.77184i	0.235476	−	0.104841i
$700$	18.4092	−	3.91300i	0.695803	−	0.147897i
$701$	45.5280	+	9.67727i	1.71957	+	0.365505i	0.958924	−	0.283664i	$-0.0915499\pi$
$701$	45.5280	+	9.67727i	1.71957	+	0.365505i	0.760644	+	0.649169i	$0.224883\pi$
$702$	−25.1640	−	11.2037i	−0.949755	−	0.422858i
$703$	−4.33412	+	4.81352i	−0.163464	+	0.181545i
$704$	−0.565231	+	5.37782i	−0.0213030	+	0.202684i
$705$	2.06271	+	1.49865i	0.0776861	+	0.0564423i
$706$	−2.99604	−	28.5054i	−0.112757	−	1.07282i
$707$	−2.98353	+	5.16762i	−0.112207	+	0.194348i
$708$	0.775231	+	1.34274i	0.0291350	+	0.0504632i
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	−0.871798	−	0.489866i	$-0.837046\pi$
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	0.196489	+	0.980506i	$0.437046\pi$
$710$	−13.4552	−	14.9435i	−0.504964	−	0.560819i
$711$	−9.54690	−	29.3823i	−0.358037	−	1.10192i
$712$	−2.88297			−0.108044
$713$		0			0
$714$	19.5471			0.731531
$715$	3.59105	+	11.0521i	0.134298	+	0.413326i
$716$	−3.77498	−	4.19254i	−0.141078	−	0.156683i
$717$	3.97976	−	2.89147i	0.148627	−	0.107984i
$718$	−4.96722	−	8.60348i	−0.185375	−	0.321079i
$719$	−22.0457	+	38.1842i	−0.822165	+	1.42403i	0.0819018	+	0.996640i	$0.473901\pi$
$719$	−22.0457	+	38.1842i	−0.822165	+	1.42403i	−0.904067	+	0.427391i	$0.859433\pi$
$720$	−1.67352	−	15.9224i	−0.0623683	−	0.593394i
$721$	−55.2914	−	40.1716i	−2.05916	−	1.49607i
$722$	−3.27440	+	31.1538i	−0.121860	+	1.15942i
$723$	−2.22861	+	2.47512i	−0.0828828	+	0.0920507i
$724$	8.31803	+	3.70342i	0.309137	+	0.137637i
$725$	4.75589	+	1.01090i	0.176629	+	0.0375437i
$726$	−6.82613	+	1.45094i	−0.253341	+	0.0538494i
$727$	35.6376	−	15.8669i	1.32173	−	0.588471i	0.380043	−	0.924969i	$-0.375909\pi$
$727$	35.6376	−	15.8669i	1.32173	−	0.588471i	0.941684	+	0.336498i	$0.109243\pi$
$728$	−6.38186	+	19.6414i	−0.236528	+	0.727957i
$729$	−4.46591	+	13.7447i	−0.165404	+	0.509062i
$730$	8.57937	−	3.81978i	0.317537	−	0.141377i
$731$	36.3619	−	7.72895i	1.34489	−	0.285866i
$732$	1.86370	+	0.396141i	0.0688842	+	0.0146418i
$733$	6.22223	+	2.77031i	0.229823	+	0.102324i	0.518418	−	0.855128i	$-0.326521\pi$
$733$	6.22223	+	2.77031i	0.229823	+	0.102324i	−0.288594	+	0.957451i	$0.593188\pi$
$734$	18.2249	−	20.2408i	0.672694	−	0.747102i
$735$	−0.437084	+	4.15858i	−0.0161221	+	0.153391i
$736$	19.4580	+	14.1370i	0.717230	+	0.521098i
$737$	0.559469	+	5.32300i	0.0206083	+	0.196075i
$738$	12.0084	−	20.7991i	0.442035	−	0.765627i
$739$	16.6002	+	28.7524i	0.610649	+	1.05767i	0.991131	+	0.132887i	$0.0424246\pi$
$739$	16.6002	+	28.7524i	0.610649	+	1.05767i	−0.380482	+	0.924788i	$0.624242\pi$
$740$	−6.25985	+	4.54805i	−0.230117	+	0.167190i
$741$	2.49190	+	2.76753i	0.0915421	+	0.101668i
$742$	27.6682	+	85.1540i	1.01573	+	3.12610i
$743$	22.5011			0.825484			0.412742	−	0.910848i	$-0.364571\pi$
$743$	22.5011			0.825484			0.412742	+	0.910848i	$0.364571\pi$
$744$		0			0
$745$	4.61293			0.169005
$746$	−13.6332	−	41.9586i	−0.499146	−	1.53621i
$747$	19.2841	+	21.4172i	0.705570	+	0.783615i
$748$	−12.1152	+	8.80219i	−0.442975	+	0.321840i
$749$	−21.6055	−	37.4218i	−0.789448	−	1.36736i
$750$	−4.76442	+	8.25222i	−0.173972	+	0.301328i
$751$	−0.670500	−	6.37939i	−0.0244669	−	0.232787i	−0.999921	−	0.0125834i	$-0.995994\pi$
$751$	−0.670500	−	6.37939i	−0.0244669	−	0.232787i	0.975454	−	0.220204i	$-0.0706722\pi$
$752$	−16.4936	−	11.9833i	−0.601460	−	0.436986i
$753$	1.53030	−	14.5599i	0.0557673	−	0.530591i
$754$	8.81009	−	9.78459i	0.320844	−	0.356334i
$755$	−9.78076	−	4.35467i	−0.355958	−	0.158483i
$756$	14.9238	+	3.17214i	0.542772	+	0.115370i
$757$	25.3085	−	5.37948i	0.919852	−	0.195521i	0.276432	−	0.961034i	$-0.410848\pi$
$757$	25.3085	−	5.37948i	0.919852	−	0.195521i	0.643420	+	0.765513i	$0.277515\pi$
$758$	37.4002	−	16.6517i	1.35844	−	0.604816i
$759$	1.01544	−	3.12519i	0.0368580	−	0.113437i
$760$	−0.572695	+	1.76257i	−0.0207738	+	0.0639352i
$761$	−40.8653	+	18.1944i	−1.48136	+	0.659546i	−0.978767	−	0.204975i	$-0.934289\pi$
$761$	−40.8653	+	18.1944i	−1.48136	+	0.659546i	−0.502597	+	0.864521i	$0.667622\pi$
$762$	8.66797	−	1.84243i	0.314007	−	0.0667443i
$763$	−5.08757	−	1.08140i	−0.184182	−	0.0391492i
$764$	15.1158	+	6.73000i	0.546872	+	0.243483i
$765$	12.5943	−	13.9873i	0.455346	−	0.505713i
$766$	−4.60263	+	43.7911i	−0.166300	+	1.58224i
$767$	−9.15016	−	6.64798i	−0.330393	−	0.240045i
$768$	−1.09421	−	10.4107i	−0.0394840	−	0.375665i
$769$	−6.34376	+	10.9877i	−0.228762	+	0.396227i	−0.957441	−	0.288628i	$-0.906801\pi$
$769$	−6.34376	+	10.9877i	−0.228762	+	0.396227i	0.728680	+	0.684855i	$0.240134\pi$
$770$	−7.74083	−	13.4075i	−0.278960	−	0.483173i
$771$	9.67486	−	7.02920i	0.348432	−	0.253150i
$772$	12.8982	+	14.3249i	0.464215	+	0.515563i
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	0.989097	−	0.147265i	$-0.0470471\pi$
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	−0.886757	+	0.462236i	$0.847047\pi$
$774$	33.3816			1.19988
$775$		0			0
$776$	−8.84964			−0.317683
$777$	2.59381	+	7.98293i	0.0930524	+	0.286386i
$778$	−21.1139	−	23.4493i	−0.756969	−	0.840699i
$779$	−5.49191	+	3.99011i	−0.196768	+	0.142960i
$780$	2.22436	+	3.85271i	0.0796450	+	0.137949i
$781$	8.35581	−	14.4727i	0.298994	−	0.517873i
$782$	3.88516	+	36.9648i	0.138933	+	1.32186i
$783$	3.18880	+	2.31680i	0.113959	+	0.0827958i
$784$	3.49496	−	33.2523i	0.124820	−	1.18758i
$785$	−4.18250	+	4.64513i	−0.149280	+	0.165792i
$786$	9.69977	+	4.31862i	0.345980	+	0.154040i
$787$	45.7336	+	9.72098i	1.63023	+	0.346516i	0.930044	−	0.367447i	$-0.119768\pi$
$787$	45.7336	+	9.72098i	1.63023	+	0.346516i	0.700183	+	0.713963i	$0.253102\pi$
$788$	−32.5826	+	6.92564i	−1.16071	+	0.246716i
$789$	1.79929	−	0.801096i	0.0640565	−	0.0285198i
$790$	−7.75328	+	23.8621i	−0.275849	+	0.848977i
$791$	−3.75553	+	11.5583i	−0.133531	+	0.410967i
$792$	4.97806	−	2.21637i	0.176888	−	0.0787554i
$793$	−13.5952	+	2.88975i	−0.482779	+	0.102618i
$794$	−18.1367	−	3.85507i	−0.643646	−	0.136811i
$795$	−7.13990	−	3.17889i	−0.253226	−	0.112744i
$796$	6.28357	−	6.97861i	0.222715	−	0.247350i
$797$	0.0376280	−	0.358007i	0.00133285	−	0.0126813i	−0.993835	−	0.110867i	$-0.964637\pi$
$797$	0.0376280	−	0.358007i	0.00133285	−	0.0126813i	0.995168	+	0.0981857i	$0.0313039\pi$
$798$	−4.01380	−	2.91619i	−0.142087	−	0.103232i
$799$	−2.50529	−	23.8363i	−0.0886309	−	0.843267i
$800$	12.0179	−	20.8156i	0.424896	−	0.735942i
$801$	−3.71576	−	6.43588i	−0.131290	−	0.227401i
$802$	−42.7400	+	31.0525i	−1.50920	+	1.09650i
$803$	5.22247	+	5.80014i	0.184297	+	0.204683i
$804$	0.633171	+	1.94870i	0.0223302	+	0.0687254i
$805$	−15.9759			−0.563075
$806$		0			0
$807$	6.36789			0.224160
$808$	0.527081	+	1.62219i	0.0185426	+	0.0570684i
$809$	−19.2182	−	21.3439i	−0.675674	−	0.750412i	0.303634	−	0.952789i	$-0.401800\pi$
$809$	−19.2182	−	21.3439i	−0.675674	−	0.750412i	−0.979308	+	0.202377i	$0.935133\pi$
$810$	12.3217	−	8.95225i	0.432941	−	0.314550i
$811$	9.95675	+	17.2456i	0.349629	+	0.605575i	0.986183	−	0.165657i	$-0.0529744\pi$
$811$	9.95675	+	17.2456i	0.349629	+	0.605575i	−0.636555	+	0.771232i	$0.719641\pi$
$812$	−3.64639	+	6.31573i	−0.127963	+	0.221639i
$813$	0.173430	+	1.65007i	0.00608244	+	0.0578706i
$814$	−12.5129	−	9.09117i	−0.438578	−	0.318646i
$815$	−0.0698886	+	0.664946i	−0.00244809	+	0.0232920i
$816$	9.12920	−	10.1390i	0.319586	−	0.354936i
$817$	−8.61962	−	3.83770i	−0.301562	−	0.134264i
$818$	−41.6433	−	8.85157i	−1.45603	−	0.309488i
$819$	−52.0722	+	11.0683i	−1.81955	+	0.386758i
$820$	−7.40820	+	3.29834i	−0.258706	+	0.115183i
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	−0.318220	−	0.948017i	$-0.603085\pi$
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	0.814676	−	0.579917i	$-0.196915\pi$
$822$	4.50745	−	13.8725i	0.157216	−	0.483860i
$823$	−12.0866	+	5.38131i	−0.421313	+	0.187581i	−0.606432	−	0.795135i	$-0.707400\pi$
$823$	−12.0866	+	5.38131i	−0.421313	+	0.187581i	0.185119	+	0.982716i	$0.440733\pi$
$824$	−19.1091	+	4.06176i	−0.665696	+	0.141498i
$825$	−3.21213	−	0.682759i	−0.111832	−	0.0237706i
$826$	13.7651	+	6.12863i	0.478950	+	0.213242i
$827$	7.63322	−	8.47755i	0.265433	−	0.294793i	−0.595664	−	0.803234i	$-0.703111\pi$
$827$	7.63322	−	8.47755i	0.265433	−	0.294793i	0.861097	+	0.508440i	$0.169778\pi$
$828$	−1.45050	+	13.8006i	−0.0504084	+	0.479604i
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.214766	−	0.976666i	$-0.568899\pi$
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.995230	+	0.0975520i	$0.968899\pi$
$830$	−2.44651	−	23.2770i	−0.0849196	−	0.807956i
$831$	−5.24738	+	9.08873i	−0.182030	+	0.315285i
$832$	−7.55038	−	13.0776i	−0.261762	−	0.453386i
$833$	31.8003	−	23.1043i	1.10182	−	0.800516i
$834$	6.31105	+	7.00913i	0.218534	+	0.242706i
$835$	0.745446	+	2.29425i	0.0257972	+	0.0793957i
$836$	3.80091			0.131457
$837$		0			0
$838$	−62.0578			−2.14375
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	0.861856	+	0.507153i	$0.169302\pi$
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	−0.399159	+	0.916882i	$0.630698\pi$
$840$	1.60701	+	1.78476i	0.0554470	+	0.0615802i
$841$	21.9373	−	15.9384i	0.756458	−	0.549599i
$842$	8.35115	+	14.4646i	0.287800	+	0.498484i
$843$	2.33868	−	4.05072i	0.0805486	−	0.139514i
$844$	2.88097	+	27.4106i	0.0991671	+	0.943512i
$845$	−13.5564	−	9.84931i	−0.466355	−	0.338827i
$846$	2.24969	−	21.4044i	0.0773461	−	0.735899i
$847$	−18.8675	+	20.9545i	−0.648295	+	0.720005i
$848$	57.0912	+	25.4187i	1.96052	+	0.872880i
$849$	4.94945	+	1.05204i	0.169865	+	0.0361059i
$850$	36.3326	−	7.72274i	1.24620	−	0.264888i
$851$	−14.5807	+	6.49174i	−0.499820	+	0.222534i
$852$	1.97696	−	6.08446i	0.0677295	−	0.208450i
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	−0.908959	−	0.416885i	$-0.863122\pi$
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	0.980402	+	0.197005i	$0.0631217\pi$
$854$	16.9157	−	7.53135i	0.578843	−	0.257717i
$855$	−4.67285	+	0.993245i	−0.159808	+	0.0339683i
$856$	−12.0819	−	2.56808i	−0.412949	−	0.0877751i
$857$	−22.6981	−	10.1058i	−0.775351	−	0.345209i	−0.0193790	−	0.999812i	$-0.506169\pi$
$857$	−22.6981	−	10.1058i	−0.775351	−	0.345209i	−0.755972	+	0.654604i	$0.772836\pi$
$858$	−5.95034	+	6.60852i	−0.203141	+	0.225611i
$859$	−0.167023	+	1.58912i	−0.00569874	+	0.0542199i	−0.997002	−	0.0773797i	$-0.975345\pi$
$859$	−0.167023	+	1.58912i	−0.00569874	+	0.0542199i	0.991303	+	0.131600i	$0.0420113\pi$
$860$	−9.11869	−	6.62511i	−0.310945	−	0.225915i
$861$	0.919531	+	8.74876i	0.0313375	+	0.298157i
$862$	10.4599	−	18.1171i	0.356266	−	0.617072i
$863$	15.3856	+	26.6487i	0.523734	+	0.907133i	0.999618	+	0.0276255i	$0.00879457\pi$
$863$	15.3856	+	26.6487i	0.523734	+	0.907133i	−0.475885	+	0.879508i	$0.657872\pi$
$864$	15.7637	−	11.4530i	0.536292	−	0.389639i
$865$	−3.27806	−	3.64065i	−0.111457	−	0.123786i
$866$	−5.20536	−	16.0204i	−0.176885	−	0.544397i
$867$	7.55038			0.256424
$868$		0			0
$869$	−20.8518			−0.707348
$870$	−0.473144	−	1.45619i	−0.0160411	−	0.0493694i
$871$	−10.0014	−	11.1077i	−0.338884	−	0.376369i
$872$	−1.20281	+	0.873895i	−0.0407324	+	0.0295938i
$873$	−11.4060	−	19.7557i	−0.386033	−	0.668630i
$874$	4.71693	−	8.16997i	0.159553	−	0.276353i
$875$	4.02447	+	38.2903i	0.136052	+	1.29445i
$876$	2.41724	+	1.75623i	0.0816710	+	0.0593374i
$877$	−0.870812	+	8.28522i	−0.0294052	+	0.279772i	0.969932	+	0.243375i	$0.0782547\pi$
$877$	−0.870812	+	8.28522i	−0.0294052	+	0.279772i	−0.999337	+	0.0363968i	$0.988412\pi$
$878$	49.0325	−	54.4561i	1.65477	−	1.83780i
$879$	−9.70305	−	4.32008i	−0.327276	−	0.145713i
$880$	−10.5697	−	2.24666i	−0.356304	−	0.0757348i
$881$	−21.3856	+	4.54565i	−0.720500	+	0.153147i	−0.553547	−	0.832818i	$-0.686726\pi$
$881$	−21.3856	+	4.54565i	−0.720500	+	0.153147i	−0.166953	+	0.985965i	$0.553393\pi$
$882$	32.2455	−	14.3566i	1.08576	−	0.483413i
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	−0.994725	−	0.102576i	$-0.967292\pi$
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	0.865042	+	0.501699i	$0.167292\pi$
$884$	12.9229	−	39.7727i	0.434646	−	1.33770i
$885$	−1.20155	+	0.534966i	−0.0403898	+	0.0179827i
$886$	45.7119	−	9.71636i	1.53572	−	0.326427i
$887$	24.2013	+	5.14414i	0.812599	+	0.172723i	0.595426	−	0.803410i	$-0.296983\pi$
$887$	24.2013	+	5.14414i	0.812599	+	0.172723i	0.217172	+	0.976133i	$0.430317\pi$
$888$	2.19190	+	0.975897i	0.0735554	+	0.0327490i
$889$	23.9584	−	26.6085i	0.803538	−	0.892420i
$890$	−0.630863	+	6.00226i	−0.0211466	+	0.201196i
$891$	10.2403	+	7.43998i	0.343062	+	0.249249i
$892$	−1.05028	−	9.99279i	−0.0351661	−	0.334583i
$893$	−3.04165	+	5.26830i	−0.101785	+	0.176297i
$894$	1.76497	+	3.05702i	0.0590295	+	0.102242i
$895$	3.87181	−	2.81303i	0.129420	−	0.0940293i
$896$	−20.4371	−	22.6977i	−0.682754	−	0.758275i
$897$	2.83570	+	8.72738i	0.0946812	+	0.291399i
$898$	−3.38940			−0.113106
$899$		0			0
$900$	13.8676			0.462255
$901$	22.7032	+	69.8734i	0.756354	+	2.32782i
$902$	−10.8465	−	12.0462i	−0.361148	−	0.401095i
$903$	−9.89194	+	7.18692i	−0.329183	+	0.239166i
$904$	1.73698	+	3.00853i	0.0577710	+	0.100062i
$905$	−3.86200	+	6.68918i	−0.128377	+	0.222356i
$906$	−0.856384	−	8.14795i	−0.0284515	−	0.270698i
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	0.923654	−	0.383227i	$-0.125187\pi$
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	−0.0790457	+	0.996871i	$0.525187\pi$
$908$	1.34189	−	12.7672i	0.0445322	−	0.423696i
$909$	−2.94200	+	3.26742i	−0.0975800	+	0.108374i
$910$	39.4962	+	17.5848i	1.30929	+	0.582931i
$911$	−8.20064	−	1.74310i	−0.271699	−	0.0577514i	0.0700471	−	0.997544i	$-0.477685\pi$
$911$	−8.20064	−	1.74310i	−0.271699	−	0.0577514i	−0.341746	+	0.939792i	$0.611018\pi$
$912$	−3.38721	+	0.719974i	−0.112162	+	0.0238407i
$913$	17.7698	−	7.91162i	0.588094	−	0.261836i
$914$	−20.5567	+	63.2671i	−0.679956	+	2.09269i
$915$	−0.499465	+	1.53719i	−0.0165118	+	0.0508181i
$916$	23.3439	−	10.3934i	0.771303	−	0.343406i
$917$	41.9633	−	8.91958i	1.38575	−	0.294550i
$918$	29.4537	+	6.26057i	0.972117	+	0.206630i
$919$	−36.6679	−	16.3256i	−1.20956	−	0.538531i	−0.299935	−	0.953960i	$-0.596965\pi$
$919$	−36.6679	−	16.3256i	−1.20956	−	0.538531i	−0.909626	+	0.415428i	$0.863632\pi$
$920$	−3.05570	+	3.39369i	−0.100743	+	0.111887i
$921$	−0.847739	+	8.06570i	−0.0279340	+	0.265774i
$922$	−2.00088	−	1.45373i	−0.0658956	−	0.0478759i
$923$	4.87821	+	46.4130i	0.160568	+	1.52770i
$924$	2.46277	−	4.26565i	0.0810193	−	0.140329i
$925$	7.97511	+	13.8133i	0.262220	+	0.454178i
$926$	−17.6128	+	12.7965i	−0.578793	+	0.420518i
$927$	−33.6963	−	37.4236i	−1.10673	−	1.22915i
$928$	2.87808	+	8.85781i	0.0944775	+	0.290772i
$929$	54.6187			1.79198			0.895991	−	0.444072i	$-0.146467\pi$
$929$	54.6187			1.79198			0.895991	+	0.444072i	$0.146467\pi$
$930$		0			0
$931$	−9.97677			−0.326975
$932$	6.00225	+	18.4730i	0.196610	+	0.605104i
$933$	−3.47024	−	3.85409i	−0.113611	−	0.126177i
$934$	16.4636	−	11.9615i	0.538705	−	0.391392i
$935$	−6.35176	−	11.0016i	−0.207725	−	0.359790i
$936$	−7.60864	+	13.1785i	−0.248696	+	0.430754i
$937$	1.39962	+	13.3165i	0.0457237	+	0.435032i	0.993305	+	0.115518i	$0.0368529\pi$
$937$	1.39962	+	13.3165i	0.0457237	+	0.435032i	−0.947582	+	0.319514i	$0.896480\pi$
$938$	16.1096	+	11.7043i	0.525998	+	0.382160i
$939$	−1.67258	+	15.9135i	−0.0545825	+	0.519317i
$940$	−4.86259	+	5.40045i	−0.158600	+	0.176143i
$941$	−35.0360	−	15.5990i	−1.14214	−	0.508514i	−0.253599	−	0.967309i	$-0.581614\pi$
$941$	−35.0360	−	15.5990i	−1.14214	−	0.508514i	−0.888542	+	0.458795i	$0.848281\pi$
$942$	−4.67865	−	0.994479i	−0.152439	−	0.0324019i
$943$	−16.3617	+	3.47779i	−0.532811	+	0.113252i
$944$	9.60772	−	4.27763i	0.312705	−	0.139225i
$945$	−3.99952	+	12.3093i	−0.130104	+	0.400420i
$946$	6.96229	−	21.4277i	0.226363	−	0.696675i
$947$	39.7278	−	17.6880i	1.29098	−	0.574782i	0.357669	−	0.933849i	$-0.383572\pi$
$947$	39.7278	−	17.6880i	1.29098	−	0.574782i	0.933312	+	0.359067i	$0.116905\pi$
$948$	−7.80808	+	1.65966i	−0.253595	+	0.0539032i
$949$	−21.3195	−	4.53160i	−0.692060	−	0.147102i
$950$	−8.61269	−	3.83461i	−0.279432	−	0.124411i
$951$	8.45849	−	9.39410i	0.274285	−	0.304625i
$952$	2.35985	−	22.4525i	0.0764833	−	0.727690i
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.972949	−	0.231018i	$-0.0742057\pi$
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.0809464	+	0.996718i	$0.474206\pi$
$954$	6.89612	+	65.6122i	0.223270	+	2.12427i
$955$	−7.01817	+	12.1558i	−0.227103	+	0.393353i
$956$	7.01045	+	12.1424i	0.226734	+	0.392715i
$957$	1.02946	−	0.747945i	0.0332776	−	0.0241776i
$958$	0.831653	+	0.923644i	0.0268695	+	0.0298416i
$959$	−18.2123	−	56.0517i	−0.588106	−	1.81001i
$960$	−1.75607			−0.0566768
$961$		0			0
$962$	43.1925			1.39258
$963$	−9.83894	−	30.2811i	−0.317055	−	0.975796i
$964$	−6.35199	−	7.05460i	−0.204584	−	0.227213i
$965$	−13.2290	+	9.61143i	−0.425856	+	0.309403i
$966$	−6.11260	−	10.5873i	−0.196670	−	0.340642i
$967$	−21.9360	+	37.9943i	−0.705414	+	1.22181i	0.261128	+	0.965304i	$0.415906\pi$
$967$	−21.9360	+	37.9943i	−0.705414	+	1.22181i	−0.966542	+	0.256509i	$0.917428\pi$
$968$	0.842507	+	8.01591i	0.0270792	+	0.257641i
$969$	−3.29353	−	2.39289i	−0.105803	−	0.0768707i
$970$	−1.93651	+	18.4247i	−0.0621776	+	0.591580i
$971$	34.4726	−	38.2857i	1.10628	−	1.22865i	0.134961	−	0.990851i	$-0.456909\pi$
$971$	34.4726	−	38.2857i	1.10628	−	1.22865i	0.971316	−	0.237794i	$-0.0764244\pi$
$972$	15.6278	+	6.95796i	0.501263	+	0.223177i
$973$	37.2760	+	7.92325i	1.19501	+	0.254008i
$974$	−44.4761	+	9.45369i	−1.42511	+	0.302916i
$975$	8.37773	−	3.73000i	0.268302	−	0.119456i
$976$	3.99376	−	12.2915i	0.127837	−	0.393442i
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	−0.854510	−	0.519435i	$-0.826142\pi$
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	0.996629	+	0.0820365i	$0.0261424\pi$
$978$	−0.467405	+	0.208102i	−0.0149460	+	0.00665438i
$979$	−4.90619	+	1.04284i	−0.156802	+	0.0333294i
$980$	−11.6577	−	2.47791i	−0.372390	−	0.0791540i
$981$	−3.50112	−	1.55880i	−0.111782	−	0.0497687i
$982$	−10.6895	+	11.8719i	−0.341116	+	0.378847i
$983$	5.61048	−	53.3801i	0.178946	−	1.70256i	−0.424721	−	0.905324i	$-0.639628\pi$
$983$	5.61048	−	53.3801i	0.178946	−	1.70256i	0.603667	−	0.797237i	$-0.293706\pi$
$984$	2.03434	+	1.47804i	0.0648525	+	0.0471181i
$985$	−2.95371	−	28.1027i	−0.0941129	−	0.895425i
$986$	−7.19655	+	12.4648i	−0.229185	+	0.396960i
$987$	3.94163	+	6.82711i	0.125464	+	0.217309i
$988$	−8.58723	+	6.23898i	−0.273196	+	0.198489i
$989$	−15.5570	−	17.2779i	−0.494685	−	0.549404i
$990$	−3.52510	−	10.8491i	−0.112035	−	0.344808i
$991$	−35.5382			−1.12891			−0.564453	−	0.825465i	$-0.690913\pi$
$991$	−35.5382			−1.12891			−0.564453	+	0.825465i	$0.690913\pi$
$992$		0			0
$993$	−16.4364			−0.521594
$994$	−19.2126	−	59.1304i	−0.609388	−	1.87550i
$995$	5.33038	+	5.91999i	0.168984	+	0.187676i
$996$	6.02430	−	4.37691i	0.190887	−	0.138688i
$997$	15.2613	+	26.4333i	0.483329	+	0.837151i	0.999817	−	0.0191440i	$-0.00609410\pi$
$997$	15.2613	+	26.4333i	0.483329	+	0.837151i	−0.516488	+	0.856295i	$0.672761\pi$
$998$	28.7674	−	49.8265i	0.910615	−	1.57723i
$999$	1.35159	+	12.8595i	0.0427623	+	0.406856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.547.1		16
31.2	even	5		961.2.g.t.235.2		16
31.3	odd	30		961.2.c.i.521.2		16
31.4	even	5		961.2.g.s.816.2		16
31.5	even	3		961.2.d.o.531.2		16
31.6	odd	6		961.2.g.l.844.1		16
31.7	even	15		961.2.g.t.732.2		16
31.8	even	5		31.2.g.a.9.1	yes	16
31.9	even	15		961.2.d.o.628.2		16
31.10	even	15		961.2.d.p.388.3		16
31.11	odd	30		961.2.d.q.374.3		16
31.12	odd	30		961.2.g.m.338.2		16
31.13	odd	30		961.2.a.j.1.2		8
31.14	even	15	inner	961.2.g.k.448.1		16
31.15	odd	10		961.2.c.i.439.2		16
31.16	even	5		961.2.c.j.439.2		16
31.17	odd	30		961.2.g.j.448.1		16
31.18	even	15		961.2.a.i.1.2		8
31.19	even	15		961.2.g.s.338.2		16
31.20	even	15		961.2.d.p.374.3		16
31.21	odd	30		961.2.d.q.388.3		16
31.22	odd	30		961.2.d.n.628.2		16
31.23	odd	10		961.2.g.l.846.1		16
31.24	odd	30		961.2.g.n.732.2		16
31.25	even	3		31.2.g.a.7.1	✓	16
31.26	odd	6		961.2.d.n.531.2		16
31.27	odd	10		961.2.g.m.816.2		16
31.28	even	15		961.2.c.j.521.2		16
31.29	odd	10		961.2.g.n.235.2		16
31.30	odd	2		961.2.g.j.547.1		16
93.8	odd	10		279.2.y.c.226.2		16
93.44	even	30		8649.2.a.be.1.7		8
93.56	odd	6		279.2.y.c.100.2		16
93.80	odd	30		8649.2.a.bf.1.7		8
124.39	odd	10		496.2.bg.c.257.1		16
124.87	odd	6		496.2.bg.c.193.1		16
155.8	odd	20		775.2.ck.a.474.4		32
155.39	even	10		775.2.bl.a.226.2		16
155.87	odd	12		775.2.ck.a.224.4		32
155.118	odd	12		775.2.ck.a.224.1		32
155.132	odd	20		775.2.ck.a.474.1		32
155.149	even	6		775.2.bl.a.751.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.1	✓	16	31.25	even	3
31.2.g.a.9.1	yes	16	31.8	even	5
279.2.y.c.100.2		16	93.56	odd	6
279.2.y.c.226.2		16	93.8	odd	10
496.2.bg.c.193.1		16	124.87	odd	6
496.2.bg.c.257.1		16	124.39	odd	10
775.2.bl.a.226.2		16	155.39	even	10
775.2.bl.a.751.2		16	155.149	even	6
775.2.ck.a.224.1		32	155.118	odd	12
775.2.ck.a.224.4		32	155.87	odd	12
775.2.ck.a.474.1		32	155.132	odd	20
775.2.ck.a.474.4		32	155.8	odd	20
961.2.a.i.1.2		8	31.18	even	15
961.2.a.j.1.2		8	31.13	odd	30
961.2.c.i.439.2		16	31.15	odd	10
961.2.c.i.521.2		16	31.3	odd	30
961.2.c.j.439.2		16	31.16	even	5
961.2.c.j.521.2		16	31.28	even	15
961.2.d.n.531.2		16	31.26	odd	6
961.2.d.n.628.2		16	31.22	odd	30
961.2.d.o.531.2		16	31.5	even	3
961.2.d.o.628.2		16	31.9	even	15
961.2.d.p.374.3		16	31.20	even	15
961.2.d.p.388.3		16	31.10	even	15
961.2.d.q.374.3		16	31.11	odd	30
961.2.d.q.388.3		16	31.21	odd	30
961.2.g.j.448.1		16	31.17	odd	30
961.2.g.j.547.1		16	31.30	odd	2
961.2.g.k.448.1		16	31.14	even	15	inner
961.2.g.k.547.1		16	1.1	even	1	trivial
961.2.g.l.844.1		16	31.6	odd	6
961.2.g.l.846.1		16	31.23	odd	10
961.2.g.m.338.2		16	31.12	odd	30
961.2.g.m.816.2		16	31.27	odd	10
961.2.g.n.235.2		16	31.29	odd	10
961.2.g.n.732.2		16	31.24	odd	30
961.2.g.s.338.2		16	31.19	even	15
961.2.g.s.816.2		16	31.4	even	5
961.2.g.t.235.2		16	31.2	even	5
961.2.g.t.732.2		16	31.7	even	15
8649.2.a.be.1.7		8	93.44	even	30
8649.2.a.bf.1.7		8	93.80	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+(-0.571745 - 1.75965i) q^{2} +(0.334133 + 0.371093i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 - 1.04561i) q^{5} +(0.461954 - 0.800128i) q^{6} +(-0.390209 - 3.71259i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(0.287521 - 2.73558i) q^{9} +(-1.49475 + 1.66009i) q^{10} +(-1.69601 - 0.755111i) q^{11} +(-0.695182 - 0.147765i) q^{12} +(5.07118 - 1.07791i) q^{13} +(-6.30977 + 2.80929i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(-5.17750 + 2.30517i) q^{17} +(-4.97805 + 1.05812i) q^{18} +(1.40705 + 0.299078i) q^{19} +(1.56983 + 0.698933i) q^{20} +(1.24733 - 1.38530i) q^{21} +(-0.359048 + 3.41611i) q^{22} +(2.86762 + 2.08345i) q^{23} +(-0.0556982 - 0.529933i) q^{24} +(1.77114 - 3.06770i) q^{25} +(-4.79617 - 8.30721i) q^{26} +(2.32318 - 1.68789i) q^{27} +(3.55516 + 3.94840i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(7.01650 + 7.79262i) q^{34} +(-3.64635 + 2.64923i) q^{35} +(1.95745 + 3.39040i) q^{36} +(-2.25141 + 3.89955i) q^{37} +(-0.278202 - 2.64692i) q^{38} +(2.09445 + 1.52171i) q^{39} +(-0.134670 + 1.28130i) q^{40} +(-3.15770 + 3.50698i) q^{41} +(-3.15081 - 1.40283i) q^{42} +(-6.41589 - 1.36374i) q^{43} +(2.58456 - 0.549365i) q^{44} +(-3.03391 + 1.35078i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(-2.19919 + 0.979142i) q^{48} +(-6.78405 + 1.44199i) q^{49} +(-6.41073 - 1.36264i) q^{50} +(-2.58541 - 1.15110i) q^{51} +(-4.93742 + 5.48357i) q^{52} +(1.35503 - 12.8923i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(0.234298 + 2.22920i) q^{55} +(-1.99173 + 3.44978i) q^{56} +(0.359157 + 0.622078i) q^{57} +(2.05458 - 1.49274i) q^{58} +(-1.45975 - 1.62121i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(-4.18844 - 4.65174i) q^{65} +(-1.38766 + 1.00820i) q^{66} +(-1.44150 - 2.49675i) q^{67} +(4.03315 - 6.98563i) q^{68} +(0.185015 + 1.76030i) q^{69} +(6.74649 + 4.90161i) q^{70} +(-0.940927 + 8.95232i) q^{71} +(-1.96401 + 2.18125i) q^{72} +(-3.84059 - 1.70994i) q^{73} +(8.14908 + 1.73214i) q^{74} +(1.73020 - 0.367765i) q^{75} +(-1.87034 + 0.832730i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(10.2607 - 4.56834i) q^{79} +(5.69331 - 1.21015i) q^{80} +(-6.66899 - 1.41754i) q^{81} +(7.97647 + 3.55135i) q^{82} +(-7.01077 + 7.78625i) q^{83} +(-0.277327 + 2.63859i) q^{84} +(5.53585 + 4.02203i) q^{85} +(1.26855 + 12.0694i) q^{86} +(-0.342708 + 0.593587i) q^{87} +(0.990524 + 1.71564i) q^{88} +(2.18575 - 1.58804i) q^{89} +(4.11152 + 4.56631i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(2.26723 + 2.51801i) q^{96} +(6.70942 - 4.87468i) q^{97} +(6.41615 + 11.1131i) q^{98} +(-2.55330 + 4.42244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more