LMFDB - Embedded newform 961.2.g.h.235.1

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 = [8,4,4,-4,-4,12,3] 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:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	961.235
Dual form			961.2.g.h.732.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.363271i) q^{2} +(1.12920 - 0.502754i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.381966 - 0.661585i) q^{6} +(-2.83448 - 3.14801i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.985051 + 1.09401i) q^{9} +(-0.564602 - 0.251377i) q^{10} +(-1.95630 + 0.415823i) q^{11} +(0.209057 + 1.98904i) q^{12} +(-0.129204 + 1.22930i) q^{13} +(-2.56082 - 0.544320i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(-5.12165 - 1.08864i) q^{17} +(-0.0951031 + 0.904846i) q^{18} +(-0.233733 - 2.22382i) q^{19} +(1.58268 - 0.336408i) q^{20} +(-4.78339 - 2.12970i) q^{21} +(-0.827091 + 0.918578i) q^{22} +(-2.38197 - 7.33094i) q^{23} +(1.84943 + 2.05400i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.381966 + 0.661585i) q^{26} +(-1.70820 + 5.25731i) q^{27} +(6.26153 - 2.78781i) q^{28} +(-5.85410 + 4.25325i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(-2.00000 + 1.45309i) q^{33} +(-2.95630 + 1.31623i) q^{34} +(-1.30902 + 4.02874i) q^{35} +(-1.19098 - 2.06284i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-0.924716 - 1.02700i) q^{38} +(0.472136 + 1.45309i) q^{39} +(1.49622 - 1.66172i) q^{40} +(6.39482 + 2.84716i) q^{41} +(-3.16535 + 0.672816i) q^{42} +(0.338261 + 3.21834i) q^{43} +(0.338261 - 3.21834i) q^{44} +(1.43997 + 0.306074i) q^{45} +(-3.85410 - 2.80017i) q^{46} +(5.23607 + 3.80423i) q^{47} +(-2.24171 - 0.476491i) q^{48} +(-1.14399 + 10.8843i) q^{49} +(-0.258409 - 2.45859i) q^{50} +(-6.33070 + 1.34563i) q^{51} +(-1.82709 - 0.813473i) q^{52} +(-1.02234 + 1.13542i) q^{53} +(1.05573 + 3.24920i) q^{54} +(1.33826 + 1.48629i) q^{55} +(4.73607 - 8.20311i) q^{56} +(-1.38197 - 2.39364i) q^{57} +(-1.38197 + 4.25325i) q^{58} +(-2.04275 + 0.909491i) q^{59} +(1.61803 - 1.17557i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(0.190983 - 0.138757i) q^{64} +(1.12920 - 0.502754i) q^{65} +(-0.472136 + 1.45309i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-6.37539 - 7.08058i) q^{69} +(0.809017 + 2.48990i) q^{70} +(8.81937 - 9.79490i) q^{71} +(-3.00721 - 1.33889i) q^{72} +(0.461819 - 0.0981626i) q^{73} +(-0.129204 - 1.22930i) q^{74} +(0.516817 - 4.91719i) q^{75} +(3.53897 + 0.752232i) q^{76} +(6.85410 + 4.97980i) q^{77} +(0.763932 + 0.555029i) q^{78} +(-1.67088 - 0.355156i) q^{79} +(-0.193806 + 1.84395i) q^{80} +(0.252583 + 2.40317i) q^{81} +(4.23170 - 0.899475i) q^{82} +(2.68973 + 1.19754i) q^{83} +(5.66897 - 6.29602i) q^{84} +(1.61803 + 4.97980i) q^{85} +(1.33826 + 1.48629i) q^{86} +(-4.47214 + 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(-0.527864 + 1.62460i) q^{89} +(0.831171 - 0.370061i) q^{90} +(4.23607 - 3.07768i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(-1.80902 + 1.31433i) q^{95} +(-6.34391 + 2.82449i) q^{96} +(0.600813 - 1.84911i) q^{97} +(3.38197 + 5.85774i) q^{98} +(1.47214 - 2.54981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 8 q^{15} - 12 q^{16} - 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 8 * q^15 - 12 * q^16 - 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 - 8 * q^21 + 6 * q^22 - 28 * q^23 + 10 * q^24 + 16 * q^25 + 12 * q^26 + 40 * q^27 + 11 * q^28 - 20 * q^29 - 24 * q^30 - 36 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 14 * q^36 + 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 + 13 * q^45 - 4 * q^46 + 24 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^52 - 16 * q^53 + 80 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 - 20 * q^58 - 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 + 6 * q^64 + 4 * q^65 + 32 * q^66 - 32 * q^67 + 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 + 28 * q^77 + 24 * q^78 - 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 + 14 * q^83 - 6 * q^84 + 4 * q^85 + 2 * q^86 - 40 * q^89 - 6 * q^90 + 16 * q^91 + 64 * q^92 + 32 * q^94 - 10 * q^95 - 18 * q^96 + 54 * q^97 + 36 * q^98 - 24 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

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 $

$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	−0.396805	−	0.917903i	$-0.629881\pi$
$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	0.750358	+	0.661031i	$0.229881\pi$
$3$	1.12920	−	0.502754i	0.651946	−	0.290265i	−0.0539889	−	0.998542i	$-0.517194\pi$
$3$	1.12920	−	0.502754i	0.651946	−	0.290265i	0.705935	+	0.708276i	$0.250527\pi$
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	0.381966	−	0.661585i	0.155937	−	0.270091i
$7$	−2.83448	−	3.14801i	−1.07133	−	1.18984i	−0.981017	−	0.193924i	$-0.937879\pi$
$7$	−2.83448	−	3.14801i	−1.07133	−	1.18984i	−0.0903171	−	0.995913i	$-0.528788\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−0.985051	+	1.09401i	−0.328350	+	0.364670i
$10$	−0.564602	−	0.251377i	−0.178543	−	0.0794924i
$11$	−1.95630	+	0.415823i	−0.589845	+	0.125375i	−0.493159	−	0.869939i	$-0.664158\pi$
$11$	−1.95630	+	0.415823i	−0.589845	+	0.125375i	−0.0966866	+	0.995315i	$0.530824\pi$
$12$	0.209057	+	1.98904i	0.0603495	+	0.574187i
$13$	−0.129204	+	1.22930i	−0.0358348	+	0.340946i	0.961885	+	0.273454i	$0.0881662\pi$
$13$	−0.129204	+	1.22930i	−0.0358348	+	0.340946i	−0.997720	+	0.0674914i	$0.978500\pi$
$14$	−2.56082	−	0.544320i	−0.684409	−	0.145476i
$15$	−1.00000	−	0.726543i	−0.258199	−	0.187592i
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	−5.12165	−	1.08864i	−1.24218	−	0.264034i	−0.460471	−	0.887675i	$-0.652319\pi$
$17$	−5.12165	−	1.08864i	−1.24218	−	0.264034i	−0.781711	+	0.623641i	$0.785653\pi$
$18$	−0.0951031	+	0.904846i	−0.0224160	+	0.213274i
$19$	−0.233733	−	2.22382i	−0.0536220	−	0.510179i	−0.988062	−	0.154058i	$-0.950766\pi$
$19$	−0.233733	−	2.22382i	−0.0536220	−	0.510179i	0.934440	−	0.356121i	$-0.115901\pi$
$20$	1.58268	−	0.336408i	0.353897	−	0.0752232i
$21$	−4.78339	−	2.12970i	−1.04382	−	0.464739i
$22$	−0.827091	+	0.918578i	−0.176336	+	0.195841i
$23$	−2.38197	−	7.33094i	−0.496674	−	1.52861i	−0.814331	−	0.580400i	$-0.802896\pi$
$23$	−2.38197	−	7.33094i	−0.496674	−	1.52861i	0.317657	−	0.948206i	$-0.397104\pi$
$24$	1.84943	+	2.05400i	0.377514	+	0.419271i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	0.381966	+	0.661585i	0.0749097	+	0.129747i
$27$	−1.70820	+	5.25731i	−0.328744	+	1.01177i
$28$	6.26153	−	2.78781i	1.18332	−	0.526847i
$29$	−5.85410	+	4.25325i	−1.08708	+	0.789809i	−0.978904	−	0.204322i	$-0.934501\pi$
$29$	−5.85410	+	4.25325i	−1.08708	+	0.789809i	−0.108176	+	0.994132i	$0.534501\pi$
$30$	−0.763932			−0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	−2.00000	+	1.45309i	−0.348155	+	0.252950i
$34$	−2.95630	+	1.31623i	−0.507000	+	0.225731i
$35$	−1.30902	+	4.02874i	−0.221264	+	0.680981i
$36$	−1.19098	−	2.06284i	−0.198497	−	0.343807i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−0.924716	−	1.02700i	−0.150009	−	0.166602i
$39$	0.472136	+	1.45309i	0.0756023	+	0.232680i
$40$	1.49622	−	1.66172i	0.236573	−	0.262741i
$41$	6.39482	+	2.84716i	0.998703	+	0.444651i	0.839948	−	0.542667i	$-0.182585\pi$
$41$	6.39482	+	2.84716i	0.998703	+	0.444651i	0.158755	+	0.987318i	$0.449252\pi$
$42$	−3.16535	+	0.672816i	−0.488424	+	0.103818i
$43$	0.338261	+	3.21834i	0.0515844	+	0.490792i	0.989563	+	0.144100i	$0.0460286\pi$
$43$	0.338261	+	3.21834i	0.0515844	+	0.490792i	−0.937979	+	0.346693i	$0.887305\pi$
$44$	0.338261	−	3.21834i	0.0509948	−	0.485183i
$45$	1.43997	+	0.306074i	0.214657	+	0.0456269i
$46$	−3.85410	−	2.80017i	−0.568256	−	0.412862i
$47$	5.23607	+	3.80423i	0.763759	+	0.554903i	0.900061	−	0.435764i	$-0.143522\pi$
$47$	5.23607	+	3.80423i	0.763759	+	0.554903i	−0.136302	+	0.990667i	$0.543522\pi$
$48$	−2.24171	−	0.476491i	−0.323564	−	0.0687756i
$49$	−1.14399	+	10.8843i	−0.163427	+	1.55490i
$50$	−0.258409	−	2.45859i	−0.0365445	−	0.347698i
$51$	−6.33070	+	1.34563i	−0.886476	+	0.188426i
$52$	−1.82709	−	0.813473i	−0.253372	−	0.112808i
$53$	−1.02234	+	1.13542i	−0.140429	+	0.155963i	−0.809257	−	0.587455i	$-0.800130\pi$
$53$	−1.02234	+	1.13542i	−0.140429	+	0.155963i	0.668827	+	0.743418i	$0.266797\pi$
$54$	1.05573	+	3.24920i	0.143666	+	0.442160i
$55$	1.33826	+	1.48629i	0.180451	+	0.200411i
$56$	4.73607	−	8.20311i	0.632884	−	1.09619i
$57$	−1.38197	−	2.39364i	−0.183046	−	0.317045i
$58$	−1.38197	+	4.25325i	−0.181461	+	0.558480i
$59$	−2.04275	+	0.909491i	−0.265943	+	0.118406i	−0.535377	−	0.844613i	$-0.679830\pi$
$59$	−2.04275	+	0.909491i	−0.265943	+	0.118406i	0.269433	+	0.963019i	$0.413164\pi$
$60$	1.61803	−	1.17557i	0.208887	−	0.151765i
$61$	−14.1803			−1.81561			−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803			−1.81561			−0.907803	+	0.419396i	$0.862242\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	1.12920	−	0.502754i	0.140061	−	0.0623590i
$66$	−0.472136	+	1.45309i	−0.0581159	+	0.178862i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	4.23607	−	7.33708i	0.513699	−	0.889752i
$69$	−6.37539	−	7.08058i	−0.767506	−	0.852402i
$70$	0.809017	+	2.48990i	0.0966960	+	0.297600i
$71$	8.81937	−	9.79490i	1.04667	−	1.16244i	0.0602490	−	0.998183i	$-0.480811\pi$
$71$	8.81937	−	9.79490i	1.04667	−	1.16244i	0.986417	−	0.164258i	$-0.0525228\pi$
$72$	−3.00721	−	1.33889i	−0.354403	−	0.157790i
$73$	0.461819	−	0.0981626i	0.0540518	−	0.0114891i	−0.180806	−	0.983519i	$-0.557871\pi$
$73$	0.461819	−	0.0981626i	0.0540518	−	0.0114891i	0.234858	+	0.972030i	$0.424537\pi$
$74$	−0.129204	−	1.22930i	−0.0150197	−	0.142903i
$75$	0.516817	−	4.91719i	0.0596769	−	0.567788i
$76$	3.53897	+	0.752232i	0.405948	+	0.0862869i
$77$	6.85410	+	4.97980i	0.781097	+	0.567500i
$78$	0.763932	+	0.555029i	0.0864983	+	0.0628447i
$79$	−1.67088	−	0.355156i	−0.187988	−	0.0399581i	0.112955	−	0.993600i	$-0.463968\pi$
$79$	−1.67088	−	0.355156i	−0.187988	−	0.0399581i	−0.300944	+	0.953642i	$0.597302\pi$
$80$	−0.193806	+	1.84395i	−0.0216682	+	0.206159i
$81$	0.252583	+	2.40317i	0.0280648	+	0.267019i
$82$	4.23170	−	0.899475i	0.467313	−	0.0993304i
$83$	2.68973	+	1.19754i	0.295236	+	0.131447i	0.549009	−	0.835816i	$-0.315005\pi$
$83$	2.68973	+	1.19754i	0.295236	+	0.131447i	−0.253774	+	0.967264i	$0.581672\pi$
$84$	5.66897	−	6.29602i	0.618535	−	0.686953i
$85$	1.61803	+	4.97980i	0.175500	+	0.540135i
$86$	1.33826	+	1.48629i	0.144308	+	0.160271i
$87$	−4.47214	+	7.74597i	−0.479463	+	0.830455i
$88$	−2.23607	−	3.87298i	−0.238366	−	0.412861i
$89$	−0.527864	+	1.62460i	−0.0559535	+	0.172207i	−0.975128	−	0.221644i	$-0.928858\pi$
$89$	−0.527864	+	1.62460i	−0.0559535	+	0.172207i	0.919174	+	0.393852i	$0.128858\pi$
$90$	0.831171	−	0.370061i	0.0876131	−	0.0390079i
$91$	4.23607	−	3.07768i	0.444061	−	0.322629i
$92$	12.4721			1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	−1.80902	+	1.31433i	−0.185601	+	0.134847i
$96$	−6.34391	+	2.82449i	−0.647472	+	0.288273i
$97$	0.600813	−	1.84911i	0.0610033	−	0.187749i	−0.915911	−	0.401382i	$-0.868530\pi$
$97$	0.600813	−	1.84911i	0.0610033	−	0.187749i	0.976914	+	0.213634i	$0.0685298\pi$
$98$	3.38197	+	5.85774i	0.341630	+	0.591721i
$99$	1.47214	−	2.54981i	0.147955	−	0.256266i
$100$	4.33070	+	4.80973i	0.433070	+	0.480973i
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	0.894281	−	0.447506i	$-0.147688\pi$
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	−0.986526	+	0.163605i	$0.947688\pi$
$102$	−2.67652	+	2.97258i	−0.265015	+	0.294329i
$103$	1.61143	+	0.717456i	0.158779	+	0.0706930i	0.484587	−	0.874743i	$-0.338970\pi$
$103$	1.61143	+	0.717456i	0.158779	+	0.0706930i	−0.325808	+	0.945436i	$0.605636\pi$
$104$	−2.70353	+	0.574654i	−0.265103	+	0.0563494i
$105$	0.547318	+	5.20738i	0.0534128	+	0.508189i
$106$	−0.0987033	+	0.939099i	−0.00958691	+	0.0912134i
$107$	−10.0124	−	2.12820i	−0.967934	−	0.205741i	−0.303288	−	0.952899i	$-0.598084\pi$
$107$	−10.0124	−	2.12820i	−0.967934	−	0.205741i	−0.664646	+	0.747158i	$0.731418\pi$
$108$	−7.23607	−	5.25731i	−0.696291	−	0.505885i
$109$	−3.19098	−	2.31838i	−0.305641	−	0.222061i	0.424383	−	0.905483i	$-0.360491\pi$
$109$	−3.19098	−	2.31838i	−0.305641	−	0.222061i	−0.730024	+	0.683422i	$0.760491\pi$
$110$	1.20906	+	0.256993i	0.115279	+	0.0245033i
$111$	0.258409	−	2.45859i	0.0245271	−	0.233359i
$112$	0.820977	+	7.81108i	0.0775751	+	0.738077i
$113$	5.35256	−	1.13772i	0.503526	−	0.107028i	0.0508563	−	0.998706i	$-0.483805\pi$
$113$	5.35256	−	1.13772i	0.503526	−	0.107028i	0.452670	+	0.891678i	$0.350472\pi$
$114$	−1.56052	−	0.694789i	−0.146156	−	0.0650730i
$115$	−5.15780	+	5.72831i	−0.480967	+	0.534168i
$116$	−3.61803	−	11.1352i	−0.335926	−	1.03387i
$117$	−1.21759	−	1.35227i	−0.112566	−	0.125017i
$118$	−0.690983	+	1.19682i	−0.0636101	+	0.110176i
$119$	11.0902	+	19.2087i	1.01663	+	1.76086i
$120$	0.854102	−	2.62866i	0.0779685	−	0.239962i
$121$	−6.39482	+	2.84716i	−0.581347	+	0.258832i
$122$	−7.09017	+	5.15131i	−0.641914	+	0.466378i
$123$	8.65248			0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	3.11803	−	2.26538i	0.277777	−	0.201816i
$127$	3.22286	−	1.43491i	0.285983	−	0.127328i	−0.258732	−	0.965949i	$-0.583305\pi$
$127$	3.22286	−	1.43491i	0.285983	−	0.127328i	0.544715	+	0.838621i	$0.316638\pi$
$128$	3.51722	−	10.8249i	0.310881	−	0.956794i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	0.381966	−	0.661585i	0.0335006	−	0.0580248i
$131$	8.02957	+	8.91774i	0.701547	+	0.779146i	0.983622	−	0.180246i	$-0.0576894\pi$
$131$	8.02957	+	8.91774i	0.701547	+	0.779146i	−0.282075	+	0.959392i	$0.591023\pi$
$132$	−1.23607	−	3.80423i	−0.107586	−	0.331115i
$133$	−6.33810	+	7.03917i	−0.549583	+	0.610373i
$134$	−4.51682	−	2.01102i	−0.390194	−	0.173725i
$135$	5.40707	−	1.14931i	0.465366	−	0.0989166i
$136$	−1.22384	−	11.6441i	−0.104943	−	0.998470i
$137$	−2.06007	+	19.6002i	−0.176004	+	1.67456i	0.448687	+	0.893689i	$0.351892\pi$
$137$	−2.06007	+	19.6002i	−0.176004	+	1.67456i	−0.624690	+	0.780873i	$0.714775\pi$
$138$	−5.75987	−	1.22430i	−0.490312	−	0.104219i
$139$	10.8541	+	7.88597i	0.920633	+	0.668879i	0.943681	−	0.330855i	$-0.107337\pi$
$139$	10.8541	+	7.88597i	0.920633	+	0.668879i	−0.0230486	+	0.999734i	$0.507337\pi$
$140$	−5.54508	−	4.02874i	−0.468645	−	0.340491i
$141$	7.82518	+	1.66329i	0.658999	+	0.140075i
$142$	0.851478	−	8.10127i	0.0714545	−	0.679844i
$143$	−0.258409	−	2.45859i	−0.0216092	−	0.205598i
$144$	2.66984	−	0.567493i	0.222487	−	0.0472911i
$145$	6.61048	+	2.94317i	0.548970	+	0.244417i
$146$	0.195250	−	0.216847i	0.0161590	−	0.0179464i
$147$	4.18034	+	12.8658i	0.344789	+	1.06115i
$148$	2.16535	+	2.40487i	0.177991	+	0.197679i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−1.52786	−	2.64634i	−0.124750	−	0.216073i
$151$	2.52786	−	7.77997i	0.205715	−	0.633125i	−0.793969	−	0.607959i	$-0.791989\pi$
$151$	2.52786	−	7.77997i	0.205715	−	0.633125i	0.999683	−	0.0251659i	$-0.00801140\pi$
$152$	4.56773	−	2.03368i	0.370492	−	0.164953i
$153$	6.23607	−	4.53077i	0.504156	−	0.366291i
$154$	5.23607			0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	12.0451	−	8.75127i	0.961302	−	0.698427i	0.00784957	−	0.999969i	$-0.497501\pi$
$157$	12.0451	−	8.75127i	0.961302	−	0.698427i	0.953453	+	0.301542i	$0.0975014\pi$
$158$	−0.964456	+	0.429403i	−0.0767280	+	0.0341615i
$159$	−0.583592	+	1.79611i	−0.0462819	+	0.142441i
$160$	2.80902	+	4.86536i	0.222072	+	0.384640i
$161$	−16.3262	+	28.2779i	−1.28669	+	2.22861i
$162$	0.999294	+	1.10983i	0.0785120	+	0.0871964i
$163$	−0.836881	−	2.57565i	−0.0655496	−	0.201741i	0.912917	−	0.408144i	$-0.133824\pi$
$163$	−0.836881	−	2.57565i	−0.0655496	−	0.201741i	−0.978467	+	0.206404i	$0.933824\pi$
$164$	−7.57873	+	8.41704i	−0.591800	+	0.657260i
$165$	2.25841	+	1.00551i	0.175817	+	0.0782787i
$166$	1.77990	−	0.378329i	0.138147	−	0.0293640i
$167$	−0.258409	−	2.45859i	−0.0199963	−	0.190252i	0.979964	−	0.199175i	$-0.0638262\pi$
$167$	−0.258409	−	2.45859i	−0.0199963	−	0.190252i	−0.999960	+	0.00892337i	$0.997160\pi$
$168$	1.22384	−	11.6441i	0.0944213	−	0.898359i
$169$	11.2214	+	2.38519i	0.863188	+	0.183476i
$170$	2.61803	+	1.90211i	0.200794	+	0.145885i
$171$	2.66312	+	1.93487i	0.203654	+	0.147963i
$172$	−5.12165	−	1.08864i	−0.390522	−	0.0830080i
$173$	1.56210	−	14.8624i	0.118764	−	1.12997i	−0.759072	−	0.651007i	$-0.774347\pi$
$173$	1.56210	−	14.8624i	0.118764	−	1.12997i	0.877836	−	0.478961i	$-0.158986\pi$
$174$	0.577819	+	5.49758i	0.0438044	+	0.416771i
$175$	−16.5740	+	3.52291i	−1.25288	+	0.266307i
$176$	3.38761	+	1.50826i	0.255351	+	0.113690i
$177$	−1.84943	+	2.05400i	−0.139012	+	0.154388i
$178$	0.326238	+	1.00406i	0.0244526	+	0.0752573i
$179$	−7.83432	−	8.70089i	−0.585564	−	0.650335i	0.375447	−	0.926844i	$-0.377489\pi$
$179$	−7.83432	−	8.70089i	−0.585564	−	0.650335i	−0.961011	+	0.276509i	$0.910823\pi$
$180$	−1.19098	+	2.06284i	−0.0887706	+	0.153755i
$181$	−9.09017	−	15.7446i	−0.675667	−	1.17029i	−0.976273	−	0.216541i	$-0.930522\pi$
$181$	−9.09017	−	15.7446i	−0.675667	−	1.17029i	0.300606	−	0.953748i	$-0.402811\pi$
$182$	1.00000	−	3.07768i	0.0741249	−	0.228133i
$183$	−16.0125	+	7.12922i	−1.18368	+	0.527007i
$184$	13.9443	−	10.1311i	1.02799	−	0.746875i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	−8.47214	+	6.15537i	−0.617894	+	0.448926i
$189$	21.3920	−	9.52431i	1.55604	−	0.692792i
$190$	−0.427051	+	1.31433i	−0.0309815	+	0.0953514i
$191$	−1.59017	−	2.75426i	−0.115061	−	0.199291i	0.802743	−	0.596325i	$-0.203373\pi$
$191$	−1.59017	−	2.75426i	−0.115061	−	0.199291i	−0.917804	+	0.397034i	$0.870040\pi$
$192$	0.145898	−	0.252703i	0.0105293	−	0.0182373i
$193$	−3.66157	−	4.06659i	−0.263566	−	0.292720i	0.596807	−	0.802385i	$-0.296436\pi$
$193$	−3.66157	−	4.06659i	−0.263566	−	0.292720i	−0.860373	+	0.509665i	$0.829769\pi$
$194$	−0.371323	−	1.14281i	−0.0266594	−	0.0820493i
$195$	1.02234	−	1.13542i	0.0732113	−	0.0813094i
$196$	−16.1772	−	7.20258i	−1.15552	−	0.514470i
$197$	15.0795	−	3.20525i	1.07437	−	0.228365i	0.363434	−	0.931620i	$-0.381604\pi$
$197$	15.0795	−	3.20525i	1.07437	−	0.228365i	0.710937	+	0.703255i	$0.248271\pi$
$198$	−0.190206	−	1.80969i	−0.0135174	−	0.128609i
$199$	0.110354	−	1.04994i	0.00782276	−	0.0744286i	−0.989914	−	0.141670i	$-0.954753\pi$
$199$	0.110354	−	1.04994i	0.00782276	−	0.0744286i	0.997737	+	0.0672410i	$0.0214196\pi$
$200$	8.74882	+	1.85962i	0.618635	+	0.131495i
$201$	−8.00000	−	5.81234i	−0.564276	−	0.409971i
$202$	−1.50000	−	1.08981i	−0.105540	−	0.0766790i
$203$	29.9826	+	6.37301i	2.10437	+	0.447297i
$204$	1.09464	−	10.4148i	0.0766399	−	0.729180i
$205$	−0.731699	−	6.96165i	−0.0511041	−	0.486223i
$206$	1.06635	−	0.226659i	0.0742959	−	0.0157921i
$207$	10.3665	+	4.61545i	0.720520	+	0.320796i
$208$	1.53351	−	1.70314i	0.106330	−	0.118091i
$209$	1.38197	+	4.25325i	0.0955926	+	0.294204i
$210$	2.16535	+	2.40487i	0.149423	+	0.165952i
$211$	−0.409830	+	0.709846i	−0.0282139	+	0.0488678i	−0.879788	−	0.475367i	$-0.842315\pi$
$211$	−0.409830	+	0.709846i	−0.0282139	+	0.0488678i	0.851574	+	0.524235i	$0.175649\pi$
$212$	−1.23607	−	2.14093i	−0.0848935	−	0.147040i
$213$	5.03444	−	15.4944i	0.344954	−	1.06166i
$214$	−5.77931	+	2.57311i	−0.395065	+	0.175894i
$215$	2.61803	−	1.90211i	0.178548	−	0.129723i
$216$	−12.3607			−0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	0.472136	−	0.343027i	0.0319040	−	0.0231796i
$220$	−2.95630	+	1.31623i	−0.199313	+	0.0887400i
$221$	2.00000	−	6.15537i	0.134535	−	0.414055i
$222$	−0.763932	−	1.32317i	−0.0512718	−	0.0888053i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	15.9242	+	17.6856i	1.06398	+	1.18167i
$225$	1.81966	+	5.60034i	0.121311	+	0.373356i
$226$	2.26298	−	2.51329i	0.150531	−	0.167182i
$227$	2.25841	+	1.00551i	0.149896	+	0.0667379i	0.480313	−	0.877097i	$-0.340523\pi$
$227$	2.25841	+	1.00551i	0.149896	+	0.0667379i	−0.330418	+	0.943835i	$0.607190\pi$
$228$	4.37441	−	0.929809i	0.289702	−	0.0615781i
$229$	−1.40240	−	13.3429i	−0.0926730	−	0.881724i	−0.937804	−	0.347165i	$-0.887144\pi$
$229$	−1.40240	−	13.3429i	−0.0926730	−	0.881724i	0.845131	−	0.534559i	$-0.179522\pi$
$230$	−0.497966	+	4.73783i	−0.0328349	+	0.312404i
$231$	10.2433	+	2.17728i	0.673959	+	0.143254i
$232$	−13.0902	−	9.51057i	−0.859412	−	0.624399i
$233$	−0.0450850	−	0.0327561i	−0.00295361	−	0.00214593i	0.586307	−	0.810089i	$-0.300581\pi$
$233$	−0.0450850	−	0.0327561i	−0.00295361	−	0.00214593i	−0.589261	+	0.807943i	$0.700581\pi$
$234$	−1.10004	−	0.233820i	−0.0719116	−	0.0152853i
$235$	0.676522	−	6.43668i	0.0441315	−	0.419883i
$236$	−0.378188	−	3.59821i	−0.0246179	−	0.234224i
$237$	−2.06532	+	0.438996i	−0.134157	+	0.0285159i
$238$	12.5231	+	5.57563i	0.811750	+	0.361414i
$239$	1.14301	−	1.26944i	0.0739353	−	0.0821134i	−0.705042	−	0.709165i	$-0.749072\pi$
$239$	1.14301	−	1.26944i	0.0739353	−	0.0821134i	0.778977	+	0.627052i	$0.215739\pi$
$240$	0.708204	+	2.17963i	0.0457144	+	0.140694i
$241$	−20.3153	−	22.5624i	−1.30862	−	1.45337i	−0.809850	−	0.586637i	$-0.800452\pi$
$241$	−20.3153	−	22.5624i	−1.30862	−	1.45337i	−0.498771	−	0.866734i	$-0.666215\pi$
$242$	−2.16312	+	3.74663i	−0.139051	+	0.240843i
$243$	−6.79837	−	11.7751i	−0.436116	−	0.755375i
$244$	7.09017	−	21.8213i	0.453902	−	1.39697i
$245$	9.99809	−	4.45144i	0.638755	−	0.284392i
$246$	4.32624	−	3.14320i	0.275831	−	0.200403i
$247$	2.76393			0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	−4.50000	+	3.26944i	−0.284605	+	0.206778i
$251$	−22.0898	+	9.83503i	−1.39430	+	0.620782i	−0.960003	−	0.279989i	$-0.909669\pi$
$251$	−22.0898	+	9.83503i	−1.39430	+	0.620782i	−0.434295	+	0.900771i	$0.643002\pi$
$252$	−3.11803	+	9.59632i	−0.196418	+	0.604511i
$253$	7.70820	+	13.3510i	0.484611	+	0.839370i
$254$	1.09017	−	1.88823i	0.0684033	−	0.118478i
$255$	4.33070	+	4.80973i	0.271199	+	0.301197i
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	−10.6688	+	11.8489i	−0.665501	+	0.739114i	−0.977492	−	0.210971i	$-0.932337\pi$
$257$	−10.6688	+	11.8489i	−0.665501	+	0.739114i	0.311991	+	0.950085i	$0.399004\pi$
$258$	2.25841	+	1.00551i	0.140602	+	0.0626002i
$259$	−8.28700	+	1.76146i	−0.514929	+	0.109452i
$260$	0.209057	+	1.98904i	0.0129652	+	0.123355i
$261$	1.11349	−	10.5941i	0.0689231	−	0.655760i
$262$	7.25434	+	1.54196i	0.448175	+	0.0952625i
$263$	15.1803	+	11.0292i	0.936060	+	0.680087i	0.947469	−	0.319848i	$-0.103632\pi$
$263$	15.1803	+	11.0292i	0.936060	+	0.680087i	−0.0114091	+	0.999935i	$0.503632\pi$
$264$	−4.47214	−	3.24920i	−0.275241	−	0.199974i
$265$	1.49448	+	0.317661i	0.0918050	+	0.0195137i
$266$	−0.611920	+	5.82203i	−0.0375192	+	0.356972i
$267$	0.220707	+	2.09989i	0.0135071	+	0.128511i
$268$	12.6614	−	2.69127i	0.773419	−	0.164395i
$269$	−26.4419	−	11.7727i	−1.61219	−	0.717794i	−0.614712	−	0.788751i	$-0.710728\pi$
$269$	−26.4419	−	11.7727i	−1.61219	−	0.717794i	−0.997479	+	0.0709575i	$0.977395\pi$
$270$	2.28602	−	2.53889i	0.139123	−	0.154512i
$271$	2.52786	+	7.77997i	0.153557	+	0.472599i	0.998012	−	0.0630273i	$-0.0200755\pi$
$271$	2.52786	+	7.77997i	0.153557	+	0.472599i	−0.844455	+	0.535627i	$0.820076\pi$
$272$	6.49606	+	7.21460i	0.393881	+	0.437449i
$273$	3.23607	−	5.60503i	0.195856	−	0.339232i
$274$	6.09017	+	10.5485i	0.367921	+	0.637257i
$275$	−2.47214	+	7.60845i	−0.149075	+	0.458807i
$276$	14.0836	−	6.27042i	0.847732	−	0.377435i
$277$	−15.0902	+	10.9637i	−0.906680	+	0.658742i	−0.940173	−	0.340697i	$-0.889337\pi$
$277$	−15.0902	+	10.9637i	−0.906680	+	0.658742i	0.0334927	+	0.999439i	$0.489337\pi$
$278$	8.29180			0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	−0.916842	−	0.399250i	$-0.869271\pi$
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	0.0963896	+	0.995344i	$0.469271\pi$
$282$	4.51682	−	2.01102i	0.268973	−	0.119754i
$283$	6.76393	−	20.8172i	0.402074	−	1.23746i	−0.521240	−	0.853410i	$-0.674530\pi$
$283$	6.76393	−	20.8172i	0.402074	−	1.23746i	0.923314	−	0.384046i	$-0.125470\pi$
$284$	10.6631	+	18.4691i	0.632740	+	1.09594i
$285$	−1.38197	+	2.39364i	−0.0818606	+	0.141787i
$286$	−1.02234	−	1.13542i	−0.0604523	−	0.0671390i
$287$	−9.16312	−	28.2012i	−0.540882	−	1.66466i
$288$	5.53405	−	6.14619i	0.326097	−	0.362168i
$289$	9.51586	+	4.23673i	0.559757	+	0.249220i
$290$	4.37441	−	0.929809i	0.256874	−	0.0546003i
$291$	−0.251208	−	2.39009i	−0.0147261	−	0.140109i
$292$	−0.0798526	+	0.759747i	−0.00467302	+	0.0444608i
$293$	−8.28700	−	1.76146i	−0.484132	−	0.102905i	−0.0406213	−	0.999175i	$-0.512934\pi$
$293$	−8.28700	−	1.76146i	−0.484132	−	0.102905i	−0.443510	+	0.896269i	$0.646267\pi$
$294$	6.76393	+	4.91428i	0.394481	+	0.286607i
$295$	1.80902	+	1.31433i	0.105325	+	0.0765231i
$296$	4.37441	+	0.929809i	0.254257	+	0.0540441i
$297$	1.15564	−	10.9952i	0.0670569	−	0.638004i
$298$	0.646021	+	6.14648i	0.0374230	+	0.356056i
$299$	9.31966	−	1.98095i	0.538970	−	0.114562i
$300$	7.30836	+	3.25389i	0.421949	+	0.187864i
$301$	9.17258	−	10.1872i	0.528699	−	0.587179i
$302$	−1.56231	−	4.80828i	−0.0899006	−	0.276686i
$303$	−2.48127	−	2.75573i	−0.142545	−	0.158313i
$304$	−2.07295	+	3.59045i	−0.118892	+	0.205927i
$305$	7.09017	+	12.2805i	0.405982	+	0.703181i
$306$	1.47214	−	4.53077i	0.0841564	−	0.259007i
$307$	−13.9698	+	6.21973i	−0.797296	+	0.354979i	−0.764615	−	0.644487i	$-0.777071\pi$
$307$	−13.9698	+	6.21973i	−0.797296	+	0.354979i	−0.0326804	+	0.999466i	$0.510404\pi$
$308$	−11.0902	+	8.05748i	−0.631921	+	0.459118i
$309$	2.18034			0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	−2.76393	+	2.00811i	−0.156477	+	0.113687i
$313$	19.4001	−	8.63749i	1.09656	−	0.488220i	0.222941	−	0.974832i	$-0.428434\pi$
$313$	19.4001	−	8.63749i	1.09656	−	0.488220i	0.873618	+	0.486612i	$0.161768\pi$
$314$	2.84346	−	8.75127i	0.160466	−	0.493863i
$315$	−3.11803	−	5.40059i	−0.175681	−	0.304289i
$316$	1.38197	−	2.39364i	0.0777417	−	0.134653i
$317$	14.6836	+	16.3078i	0.824712	+	0.915936i	0.997616	−	0.0690029i	$-0.0219818\pi$
$317$	14.6836	+	16.3078i	0.824712	+	0.915936i	−0.172904	+	0.984939i	$0.555315\pi$
$318$	0.360680	+	1.11006i	0.0202259	+	0.0622490i
$319$	9.68375	−	10.7549i	0.542186	−	0.602158i
$320$	−0.215659	−	0.0960175i	−0.0120557	−	0.00536754i
$321$	−12.3760	+	2.63060i	−0.690760	+	0.146826i
$322$	2.10942	+	20.0698i	0.117553	+	1.11845i
$323$	−1.22384	+	11.6441i	−0.0680963	+	0.647893i
$324$	−3.82439	−	0.812899i	−0.212466	−	0.0451611i
$325$	4.00000	+	2.90617i	0.221880	+	0.161205i
$326$	−1.35410	−	0.983813i	−0.0749968	−	0.0544883i
$327$	−4.76885	−	1.01365i	−0.263718	−	0.0560550i
$328$	−1.63613	+	15.5667i	−0.0903401	+	0.859529i
$329$	−2.86579	−	27.2662i	−0.157996	−	1.50324i
$330$	1.49448	−	0.317661i	0.0822682	−	0.0174867i
$331$	1.82709	+	0.813473i	0.100426	+	0.0447125i	0.456335	−	0.889808i	$-0.349162\pi$
$331$	1.82709	+	0.813473i	0.100426	+	0.0447125i	−0.355909	+	0.934521i	$0.615829\pi$
$332$	−3.18769	+	3.54029i	−0.174947	+	0.194299i
$333$	0.909830	+	2.80017i	0.0498584	+	0.153448i
$334$	−1.02234	−	1.13542i	−0.0559400	−	0.0621277i
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$	4.85410	+	8.40755i	0.264813	+	0.458670i
$337$	−5.94427	+	18.2946i	−0.323805	+	0.996570i	0.648172	+	0.761494i	$0.275534\pi$
$337$	−5.94427	+	18.2946i	−0.323805	+	0.996570i	−0.971977	+	0.235076i	$0.924466\pi$
$338$	6.47719	−	2.88383i	0.352313	−	0.156860i
$339$	5.47214	−	3.97574i	0.297206	−	0.215933i
$340$	−8.47214			−0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	13.5172	−	9.82084i	0.729861	−	0.530275i
$344$	−6.61048	+	2.94317i	−0.356413	+	0.158685i
$345$	−2.94427	+	9.06154i	−0.158514	+	0.487857i
$346$	−4.61803	−	7.99867i	−0.248267	−	0.430011i
$347$	−0.909830	+	1.57587i	−0.0488422	+	0.0845972i	−0.889413	−	0.457105i	$-0.848886\pi$
$347$	−0.909830	+	1.57587i	−0.0488422	+	0.0845972i	0.840571	+	0.541702i	$0.182220\pi$
$348$	−9.68375	−	10.7549i	−0.519103	−	0.576523i
$349$	8.61803	+	26.5236i	0.461313	+	1.41977i	0.863561	+	0.504244i	$0.168229\pi$
$349$	8.61803	+	26.5236i	0.461313	+	1.41977i	−0.402248	+	0.915531i	$0.631771\pi$
$350$	−7.00723	+	7.78231i	−0.374552	+	0.415982i
$351$	−6.24209	−	2.77916i	−0.333178	−	0.148340i
$352$	10.9905	−	2.33611i	0.585797	−	0.124515i
$353$	2.02957	+	19.3100i	0.108023	+	1.02777i	0.905478	+	0.424392i	$0.139512\pi$
$353$	2.02957	+	19.3100i	0.108023	+	1.02777i	−0.797456	+	0.603378i	$0.793821\pi$
$354$	−0.178556	+	1.69885i	−0.00949014	+	0.0902927i
$355$	−12.8923	−	2.74035i	−0.684253	−	0.145443i
$356$	−2.23607	−	1.62460i	−0.118511	−	0.0861035i
$357$	22.1803	+	16.1150i	1.17391	+	0.852894i
$358$	−7.07794	−	1.50446i	−0.374081	−	0.0795133i
$359$	−1.85684	+	17.6666i	−0.0980001	+	0.932409i	0.829480	+	0.558536i	$0.188637\pi$
$359$	−1.85684	+	17.6666i	−0.0980001	+	0.932409i	−0.927480	+	0.373872i	$0.878030\pi$
$360$	0.344086	+	3.27376i	0.0181349	+	0.172542i
$361$	13.6941	−	2.91076i	0.720740	−	0.153198i
$362$	−10.2647	−	4.57012i	−0.539498	−	0.240200i
$363$	−5.78964	+	6.43004i	−0.303877	+	0.337490i
$364$	2.61803	+	8.05748i	0.137222	+	0.422327i
$365$	−0.315921	−	0.350865i	−0.0165360	−	0.0183651i
$366$	−5.41641	+	9.38149i	−0.283120	+	0.490379i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−4.41641	+	13.5923i	−0.230221	+	0.708548i
$369$	−9.41404	+	4.19140i	−0.490075	+	0.218196i
$370$	−1.00000	+	0.726543i	−0.0519875	+	0.0377711i
$371$	6.47214			0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	5.23607	−	3.80423i	0.270751	−	0.196712i
$375$	−10.1628	+	4.52479i	−0.524807	+	0.233659i
$376$	−4.47214	+	13.7638i	−0.230633	+	0.709815i
$377$	−4.47214	−	7.74597i	−0.230327	−	0.398938i
$378$	7.23607	−	12.5332i	0.372183	−	0.644640i
$379$	−25.3524	−	28.1567i	−1.30226	−	1.44631i	−0.822334	−	0.569005i	$-0.807329\pi$
$379$	−25.3524	−	28.1567i	−1.30226	−	1.44631i	−0.479930	−	0.877307i	$-0.659338\pi$
$380$	−1.11803	−	3.44095i	−0.0573539	−	0.176517i
$381$	2.91786	−	3.24062i	0.149487	−	0.166022i
$382$	−1.79563	−	0.799465i	−0.0918723	−	0.0409042i
$383$	−11.6288	+	2.47177i	−0.594201	+	0.126301i	−0.495190	−	0.868785i	$-0.664901\pi$
$383$	−11.6288	+	2.47177i	−0.594201	+	0.126301i	−0.0990117	+	0.995086i	$0.531568\pi$
$384$	−1.47060	−	13.9918i	−0.0750462	−	0.714017i
$385$	0.885579	−	8.42572i	0.0451333	−	0.429415i
$386$	−3.30806	−	0.703150i	−0.168376	−	0.0357894i
$387$	−3.85410	−	2.80017i	−0.195915	−	0.142341i
$388$	2.54508	+	1.84911i	0.129207	+	0.0938745i
$389$	−17.4976	−	3.71924i	−0.887165	−	0.188573i	−0.258279	−	0.966070i	$-0.583155\pi$
$389$	−17.4976	−	3.71924i	−0.887165	−	0.188573i	−0.628886	+	0.777497i	$0.716489\pi$
$390$	0.0987033	−	0.939099i	0.00499804	−	0.0475531i
$391$	4.21884	+	40.1396i	0.213356	+	2.02995i
$392$	−23.9374	+	5.08804i	−1.20902	+	0.256985i
$393$	13.5505	+	6.03305i	0.683530	+	0.304327i
$394$	6.37539	−	7.08058i	0.321187	−	0.356715i
$395$	0.527864	+	1.62460i	0.0265597	+	0.0817424i
$396$	3.18769	+	3.54029i	0.160188	+	0.177906i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	−0.326238	−	0.565061i	−0.0163528	−	0.0283239i
$399$	−3.61803	+	11.1352i	−0.181128	+	0.557455i
$400$	−6.77523	+	3.01652i	−0.338761	+	0.150826i
$401$	−12.7984	+	9.29856i	−0.639120	+	0.464348i	−0.859548	−	0.511055i	$-0.829255\pi$
$401$	−12.7984	+	9.29856i	−0.639120	+	0.464348i	0.220428	+	0.975403i	$0.429255\pi$
$402$	−6.11146			−0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	1.95492	−	1.42033i	0.0971405	−	0.0705767i
$406$	17.3065	−	7.70533i	0.858905	−	0.382409i
$407$	−1.23607	+	3.80423i	−0.0612696	+	0.188568i
$408$	−7.23607	−	12.5332i	−0.358239	−	0.620488i
$409$	13.0902	−	22.6728i	0.647267	−	1.12110i	−0.336506	−	0.941681i	$-0.609245\pi$
$409$	13.0902	−	22.6728i	0.647267	−	1.12110i	0.983773	−	0.179418i	$-0.0574216\pi$
$410$	−2.89482	−	3.21502i	−0.142965	−	0.158779i
$411$	7.52786	+	23.1684i	0.371322	+	1.14281i
$412$	−1.90977	+	2.12101i	−0.0940875	+	0.104495i
$413$	8.65323	+	3.85266i	0.425797	+	0.189577i
$414$	6.85990	−	1.45812i	0.337146	−	0.0716625i
$415$	−0.307760	−	2.92814i	−0.0151074	−	0.143737i
$416$	0.725874	−	6.90623i	0.0355889	−	0.338606i
$417$	16.2212	+	3.44792i	0.794356	+	0.168846i
$418$	2.23607	+	1.62460i	0.109370	+	0.0794617i
$419$	−24.3713	−	17.7068i	−1.19062	−	0.865034i	−0.197288	−	0.980346i	$-0.563213\pi$
$419$	−24.3713	−	17.7068i	−1.19062	−	0.865034i	−0.993329	+	0.115312i	$0.963213\pi$
$420$	−8.28700	−	1.76146i	−0.404364	−	0.0859503i
$421$	1.60563	−	15.2765i	0.0782535	−	0.744533i	−0.883094	−	0.469196i	$-0.844544\pi$
$421$	1.60563	−	15.2765i	0.0782535	−	0.744533i	0.961348	−	0.275337i	$-0.0887894\pi$
$422$	0.0529518	+	0.503803i	0.00257765	+	0.0245247i
$423$	−9.31966	+	1.98095i	−0.453137	+	0.0963173i
$424$	−3.12104	−	1.38958i	−0.151571	−	0.0674839i
$425$	−14.0145	+	15.5646i	−0.679801	+	0.754995i
$426$	−3.11146	−	9.57608i	−0.150751	−	0.463962i
$427$	40.1939	+	44.6399i	1.94512	+	2.16028i
$428$	8.28115	−	14.3434i	0.400285	−	0.693313i
$429$	−1.52786	−	2.64634i	−0.0737660	−	0.127766i
$430$	0.618034	−	1.90211i	0.0298042	−	0.0917280i
$431$	10.9625	−	4.88084i	0.528047	−	0.235102i	−0.125356	−	0.992112i	$-0.540007\pi$
$431$	10.9625	−	4.88084i	0.528047	−	0.235102i	0.653403	+	0.757010i	$0.273341\pi$
$432$	8.29180	−	6.02434i	0.398939	−	0.289846i
$433$	−12.1803			−0.585350			−0.292675	−	0.956212i	$-0.594545\pi$
$433$	−12.1803			−0.585350			−0.292675	+	0.956212i	$0.594545\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	5.16312	−	3.75123i	0.247269	−	0.179651i
$437$	−15.7459	+	7.01054i	−0.753230	+	0.335360i
$438$	0.111456	−	0.343027i	0.00532558	−	0.0163905i
$439$	−10.5902	−	18.3427i	−0.505441	−	0.875450i	−0.999980	−	0.00629443i	$-0.997996\pi$
$439$	−10.5902	−	18.3427i	−0.505441	−	0.875450i	0.494539	−	0.869155i	$-0.335337\pi$
$440$	−2.23607	+	3.87298i	−0.106600	+	0.184637i
$441$	−10.7807	−	11.9731i	−0.513365	−	0.570150i
$442$	−1.23607	−	3.80423i	−0.0587938	−	0.180949i
$443$	11.5705	−	12.8503i	0.549730	−	0.610537i	−0.402686	−	0.915338i	$-0.631923\pi$
$443$	11.5705	−	12.8503i	0.549730	−	0.610537i	0.952416	+	0.304801i	$0.0985901\pi$
$444$	3.65418	+	1.62695i	0.173420	+	0.0772115i
$445$	1.67088	−	0.355156i	0.0792071	−	0.0168360i
$446$	0.258409	+	2.45859i	0.0122360	+	0.116418i
$447$	−1.29204	+	12.2930i	−0.0611115	+	0.581437i
$448$	−0.978148	−	0.207912i	−0.0462131	−	0.00982290i
$449$	−25.3262	−	18.4006i	−1.19522	−	0.868377i	−0.201413	−	0.979506i	$-0.564553\pi$
$449$	−25.3262	−	18.4006i	−1.19522	−	0.868377i	−0.993806	+	0.111129i	$0.964553\pi$
$450$	2.94427	+	2.13914i	0.138794	+	0.100840i
$451$	−13.6941	−	2.91076i	−0.644828	−	0.137063i
$452$	−0.925506	+	8.80560i	−0.0435321	+	0.414181i
$453$	−1.05693	−	10.0561i	−0.0496591	−	0.472475i
$454$	1.49448	−	0.317661i	0.0701393	−	0.0149086i
$455$	−4.78339	−	2.12970i	−0.224249	−	0.0998419i
$456$	4.13545	−	4.59289i	0.193660	−	0.215082i
$457$	−6.47214	−	19.9192i	−0.302754	−	0.931780i	−0.980506	−	0.196490i	$-0.937046\pi$
$457$	−6.47214	−	19.9192i	−0.302754	−	0.931780i	0.677752	−	0.735290i	$-0.262954\pi$
$458$	−5.54829	−	6.16201i	−0.259255	−	0.287932i
$459$	14.4721	−	25.0665i	0.675501	−	1.17000i
$460$	−6.23607	−	10.8012i	−0.290758	−	0.503608i
$461$	−3.20163	+	9.85359i	−0.149115	+	0.458928i	−0.997517	−	0.0704241i	$-0.977565\pi$
$461$	−3.20163	+	9.85359i	−0.149115	+	0.458928i	0.848403	+	0.529352i	$0.177565\pi$
$462$	5.91259	−	2.63245i	0.275079	−	0.122473i
$463$	23.7984	−	17.2905i	1.10600	−	0.803559i	0.123975	−	0.992285i	$-0.460436\pi$
$463$	23.7984	−	17.2905i	1.10600	−	0.803559i	0.982030	+	0.188726i	$0.0604359\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	7.04508	−	5.11855i	0.326008	−	0.236858i	−0.412727	−	0.910855i	$-0.635424\pi$
$467$	7.04508	−	5.11855i	0.326008	−	0.236858i	0.738735	+	0.673996i	$0.235424\pi$
$468$	2.68973	−	1.19754i	0.124333	−	0.0553565i
$469$	−10.4721	+	32.2299i	−0.483558	+	1.48824i
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	9.20163	−	15.9377i	0.423989	−	0.734370i
$472$	−3.34565	−	3.71572i	−0.153996	−	0.171030i
$473$	−2.00000	−	6.15537i	−0.0919601	−	0.283024i
$474$	−0.873183	+	0.969768i	−0.0401066	+	0.0445429i
$475$	−8.17100	−	3.63796i	−0.374911	−	0.166921i
$476$	−35.1043	+	7.46165i	−1.60900	+	0.342004i
$477$	−0.235108	−	2.23690i	−0.0107649	−	0.102421i
$478$	0.110354	−	1.04994i	0.00504746	−	0.0480234i
$479$	−35.9060	−	7.63206i	−1.64059	−	0.348718i	−0.707042	−	0.707172i	$-0.749971\pi$
$479$	−35.9060	−	7.63206i	−1.64059	−	0.348718i	−0.933547	+	0.358454i	$0.883304\pi$
$480$	5.61803	+	4.08174i	0.256427	+	0.186305i
$481$	2.00000	+	1.45309i	0.0911922	+	0.0662550i
$482$	−18.3539	−	3.90124i	−0.835997	−	0.177697i
$483$	−4.21884	+	40.1396i	−0.191964	+	1.82641i
$484$	−1.18391	−	11.2642i	−0.0538143	−	0.512009i
$485$	−1.90178	+	0.404237i	−0.0863556	+	0.0183555i
$486$	−7.67675	−	3.41791i	−0.348225	−	0.155040i
$487$	−9.87900	+	10.9717i	−0.447660	+	0.497177i	−0.924164	−	0.381995i	$-0.875237\pi$
$487$	−9.87900	+	10.9717i	−0.447660	+	0.497177i	0.476504	+	0.879172i	$0.341904\pi$
$488$	−9.79837	−	30.1563i	−0.443552	−	1.36511i
$489$	−2.23993	−	2.48770i	−0.101293	−	0.112497i
$490$	3.38197	−	5.85774i	0.152782	−	0.264626i
$491$	20.1803	+	34.9534i	0.910726	+	1.57742i	0.813041	+	0.582206i	$0.197810\pi$
$491$	20.1803	+	34.9534i	0.910726	+	1.57742i	0.0976849	+	0.995217i	$0.468856\pi$
$492$	−4.32624	+	13.3148i	−0.195042	+	0.600277i
$493$	34.6129	−	15.4107i	1.55889	−	0.694061i
$494$	1.38197	−	1.00406i	0.0621776	−	0.0451747i
$495$	−2.94427			−0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	1.81966	−	1.32206i	0.0815409	−	0.0592429i
$499$	−30.5274	+	13.5917i	−1.36659	+	0.608447i	−0.953265	−	0.302135i	$-0.902301\pi$
$499$	−30.5274	+	13.5917i	−1.36659	+	0.608447i	−0.413329	+	0.910582i	$0.635634\pi$
$500$	4.50000	−	13.8496i	0.201246	−	0.619372i
$501$	−1.52786	−	2.64634i	−0.0682599	−	0.118230i
$502$	−7.47214	+	12.9421i	−0.333498	+	0.577635i
$503$	−1.10572	−	1.22803i	−0.0493017	−	0.0547551i	0.717990	−	0.696054i	$-0.245063\pi$
$503$	−1.10572	−	1.22803i	−0.0493017	−	0.0547551i	−0.767291	+	0.641299i	$0.778396\pi$
$504$	4.30902	+	13.2618i	0.191939	+	0.590727i
$505$	−2.00739	+	2.22943i	−0.0893278	+	0.0992085i
$506$	8.70414	+	3.87533i	0.386946	+	0.172279i
$507$	13.8705	−	2.94826i	0.616009	−	0.130937i
$508$	0.596670	+	5.67693i	0.0264729	+	0.251873i
$509$	2.04842	−	19.4894i	0.0907945	−	0.863852i	−0.850434	−	0.526082i	$-0.823661\pi$
$509$	2.04842	−	19.4894i	0.0907945	−	0.863852i	0.941229	−	0.337770i	$-0.109673\pi$
$510$	3.91259	+	0.831647i	0.173252	+	0.0368259i
$511$	−1.61803	−	1.17557i	−0.0715776	−	0.0520042i
$512$	15.1353	+	10.9964i	0.668890	+	0.485977i
$513$	12.0906	+	2.56993i	0.533812	+	0.113465i
$514$	−1.03003	+	9.80012i	−0.0454329	+	0.432265i
$515$	−0.184381	−	1.75427i	−0.00812480	−	0.0773023i
$516$	−6.33070	+	1.34563i	−0.278694	+	0.0592382i
$517$	−11.8252	−	5.26491i	−0.520071	−	0.231550i
$518$	−3.50361	+	3.89116i	−0.153940	+	0.170968i
$519$	−5.70820	−	17.5680i	−0.250562	−	0.771152i
$520$	1.84943	+	2.05400i	0.0811029	+	0.0900739i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	−3.29180	−	5.70156i	−0.144078	−	0.249550i
$523$	−1.32624	+	4.08174i	−0.0579923	+	0.178482i	−0.975857	−	0.218413i	$-0.929912\pi$
$523$	−1.32624	+	4.08174i	−0.0579923	+	0.178482i	0.917864	+	0.396895i	$0.129912\pi$
$524$	−17.7378	+	7.89736i	−0.774878	+	0.344998i
$525$	−16.9443	+	12.3107i	−0.739509	+	0.537284i
$526$	11.5967			0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	−29.4615	+	21.4050i	−1.28093	+	0.930653i
$530$	0.862635	−	0.384070i	0.0374705	−	0.0166829i
$531$	1.01722	−	3.13068i	0.0441436	−	0.135860i
$532$	−7.66312	−	13.2729i	−0.332238	−	0.575454i
$533$	−4.32624	+	7.49326i	−0.187390	+	0.324569i
$534$	0.873183	+	0.969768i	0.0377863	+	0.0419660i
$535$	3.16312	+	9.73508i	0.136754	+	0.420884i
$536$	11.9698	−	13.2938i	0.517015	−	0.574204i
$537$	−13.2210	−	5.88635i	−0.570526	−	0.254015i
$538$	−17.4976	+	3.71924i	−0.754377	+	0.160348i
$539$	−2.28798	−	21.7686i	−0.0985501	−	0.937642i
$540$	−0.934931	+	8.89527i	−0.0402330	+	0.382792i
$541$	−18.9376	−	4.02531i	−0.814191	−	0.173062i	−0.218046	−	0.975938i	$-0.569968\pi$
$541$	−18.9376	−	4.02531i	−0.814191	−	0.173062i	−0.596145	+	0.802877i	$0.703302\pi$
$542$	4.09017	+	2.97168i	0.175688	+	0.127645i
$543$	−18.1803	−	13.2088i	−0.780193	−	0.566843i
$544$	28.7736	+	6.11602i	1.23366	+	0.262222i
$545$	−0.412289	+	3.92266i	−0.0176605	+	0.168028i
$546$	−0.418114	−	3.97809i	−0.0178936	−	0.170246i
$547$	−27.5100	+	5.84744i	−1.17624	+	0.250018i	−0.754254	−	0.656582i	$-0.772001\pi$
$547$	−27.5100	+	5.84744i	−1.17624	+	0.250018i	−0.421989	+	0.906601i	$0.638668\pi$
$548$	−29.1316	−	12.9702i	−1.24444	−	0.554061i
$549$	13.9684	−	15.5134i	0.596155	−	0.662097i
$550$	1.52786	+	4.70228i	0.0651483	+	0.200506i
$551$	10.8268	+	12.0243i	0.461236	+	0.512254i
$552$	10.6525	−	18.4506i	0.453399	−	0.785311i
$553$	3.61803	+	6.26662i	0.153854	+	0.266484i
$554$	−3.56231	+	10.9637i	−0.151348	+	0.465801i
$555$	−2.25841	+	1.00551i	−0.0958641	+	0.0426814i
$556$	−17.5623	+	12.7598i	−0.744808	+	0.541134i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	6.35410	−	4.61653i	0.268510	−	0.195084i
$561$	11.8252	−	5.26491i	0.499260	−	0.222285i
$562$	−3.24671	+	9.99235i	−0.136954	+	0.421502i
$563$	19.7705	+	34.2435i	0.833228	+	1.44319i	0.895465	+	0.445131i	$0.146843\pi$
$563$	19.7705	+	34.2435i	0.833228	+	1.44319i	−0.0622377	+	0.998061i	$0.519824\pi$
$564$	−6.47214	+	11.2101i	−0.272526	+	0.472029i
$565$	−3.66157	−	4.06659i	−0.154044	−	0.171083i
$566$	−4.18034	−	12.8658i	−0.175713	−	0.540788i
$567$	6.84927	−	7.60688i	0.287642	−	0.319459i
$568$	26.9241	+	11.9874i	1.12971	+	0.502980i
$569$	−14.1559	+	3.00893i	−0.593446	+	0.126141i	−0.494837	−	0.868986i	$-0.664772\pi$
$569$	−14.1559	+	3.00893i	−0.593446	+	0.126141i	−0.0986082	+	0.995126i	$0.531439\pi$
$570$	0.178556	+	1.69885i	0.00747888	+	0.0711568i
$571$	−0.608320	+	5.78778i	−0.0254574	+	0.242211i	0.974392	+	0.224856i	$0.0721912\pi$
$571$	−0.608320	+	5.78778i	−0.0254574	+	0.242211i	−0.999849	+	0.0173549i	$0.994475\pi$
$572$	3.91259	+	0.831647i	0.163594	+	0.0347729i
$573$	−3.18034	−	2.31065i	−0.132861	−	0.0965289i
$574$	−14.8262	−	10.7719i	−0.618835	−	0.449610i
$575$	−30.1590	−	6.41050i	−1.25772	−	0.267336i
$576$	−0.0363262	+	0.345620i	−0.00151359	+	0.0144008i
$577$	−2.59574	−	24.6968i	−0.108062	−	1.02814i	−0.905386	−	0.424589i	$-0.860419\pi$
$577$	−2.59574	−	24.6968i	−0.108062	−	1.02814i	0.797324	−	0.603551i	$-0.206248\pi$
$578$	6.29702	−	1.33847i	0.261921	−	0.0556731i
$579$	−6.17916	−	2.75114i	−0.256797	−	0.114333i
$580$	−7.83432	+	8.70089i	−0.325302	+	0.361285i
$581$	−3.85410	−	11.8617i	−0.159895	−	0.492106i
$582$	−0.993854	−	1.10379i	−0.0411966	−	0.0457534i
$583$	1.52786	−	2.64634i	0.0632777	−	0.109600i
$584$	0.527864	+	0.914287i	0.0218432	+	0.0378335i
$585$	−0.562306	+	1.73060i	−0.0232485	+	0.0715515i
$586$	−4.78339	+	2.12970i	−0.197600	+	0.0879771i
$587$	−2.00000	+	1.45309i	−0.0825488	+	0.0599752i	−0.628294	−	0.777976i	$-0.716247\pi$
$587$	−2.00000	+	1.45309i	−0.0825488	+	0.0599752i	0.545745	+	0.837951i	$0.316247\pi$
$588$	−21.8885			−0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	15.4164	−	11.2007i	0.634146	−	0.460734i
$592$	−3.38761	+	1.50826i	−0.139230	+	0.0619892i
$593$	−4.78115	+	14.7149i	−0.196338	+	0.604268i	0.803620	+	0.595143i	$0.202905\pi$
$593$	−4.78115	+	14.7149i	−0.196338	+	0.604268i	−0.999958	+	0.00912470i	$0.997095\pi$
$594$	−3.41641	−	5.91739i	−0.140177	−	0.242794i
$595$	11.0902	−	19.2087i	0.454653	−	0.787481i
$596$	−10.8268	−	12.0243i	−0.443481	−	0.492536i
$597$	−0.403252	−	1.24108i	−0.0165040	−	0.0507941i
$598$	3.94020	−	4.37604i	0.161127	−	0.178950i
$599$	31.6057	+	14.0718i	1.29137	+	0.574957i	0.933421	−	0.358783i	$-0.116808\pi$
$599$	31.6057	+	14.0718i	1.29137	+	0.574957i	0.357953	+	0.933740i	$0.383475\pi$
$600$	10.8141	−	2.29862i	0.441485	−	0.0938406i
$601$	3.81958	+	36.3408i	0.155804	+	1.48237i	0.741012	+	0.671491i	$0.234346\pi$
$601$	3.81958	+	36.3408i	0.155804	+	1.48237i	−0.585209	+	0.810883i	$0.698987\pi$
$602$	0.885579	−	8.42572i	0.0360935	−	0.343407i
$603$	11.5197	+	2.44859i	0.469120	+	0.0997145i
$604$	10.7082	+	7.77997i	0.435711	+	0.316562i
$605$	5.66312	+	4.11450i	0.230239	+	0.167278i
$606$	−2.24171	−	0.476491i	−0.0910634	−	0.0193561i
$607$	−1.41405	+	13.4538i	−0.0573944	+	0.546071i	0.927611	+	0.373548i	$0.121859\pi$
$607$	−1.41405	+	13.4538i	−0.0573944	+	0.546071i	−0.985005	+	0.172524i	$0.944808\pi$
$608$	1.31312	+	12.4935i	0.0532540	+	0.506678i
$609$	37.0606	−	7.87747i	1.50177	−	0.319211i
$610$	8.00625	+	3.56461i	0.324164	+	0.144327i
$611$	−5.35304	+	5.94516i	−0.216561	+	0.240515i
$612$	3.85410	+	11.8617i	0.155793	+	0.479481i
$613$	−5.42762	−	6.02799i	−0.219220	−	0.243468i	0.623497	−	0.781826i	$-0.285712\pi$
$613$	−5.42762	−	6.02799i	−0.219220	−	0.243468i	−0.842716	+	0.538358i	$0.819045\pi$
$614$	−4.72542	+	8.18468i	−0.190703	+	0.330307i
$615$	−4.32624	−	7.49326i	−0.174451	−	0.302158i
$616$	−5.85410	+	18.0171i	−0.235868	+	0.725929i
$617$	21.4938	−	9.56964i	0.865307	−	0.385259i	0.0744237	−	0.997227i	$-0.476288\pi$
$617$	21.4938	−	9.56964i	0.865307	−	0.385259i	0.790883	+	0.611967i	$0.209622\pi$
$618$	1.09017	−	0.792055i	0.0438531	−	0.0318611i
$619$	−16.1803			−0.650343			−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803			−0.650343			−0.325171	+	0.945655i	$0.605422\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	−3.40983	+	2.47739i	−0.136722	+	0.0993342i
$623$	6.61048	−	2.94317i	0.264843	−	0.117916i
$624$	0.875388	−	2.69417i	0.0350436	−	0.107853i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	6.56231	−	11.3662i	0.262282	−	0.454287i
$627$	3.69886	+	4.10800i	0.147718	+	0.164058i
$628$	7.44427	+	22.9111i	0.297059	+	0.914253i
$629$	−7.00723	+	7.78231i	−0.279396	+	0.310301i
$630$	−3.52090	−	1.56760i	−0.140276	−	0.0624549i
$631$	10.1343	−	2.15411i	0.403439	−	0.0857536i	−0.00172296	−	0.999999i	$-0.500548\pi$
$631$	10.1343	−	2.15411i	0.403439	−	0.0857536i	0.405162	+	0.914245i	$0.367215\pi$
$632$	−0.399263	−	3.79874i	−0.0158818	−	0.151106i
$633$	−0.105904	+	1.00761i	−0.00420929	+	0.0400487i
$634$	13.2659	+	2.81976i	0.526858	+	0.111987i
$635$	−2.85410	−	2.07363i	−0.113262	−	0.0822894i
$636$	−2.47214	−	1.79611i	−0.0980266	−	0.0712205i
$637$	−13.2322	−	2.81260i	−0.524281	−	0.111439i
$638$	0.934931	−	8.89527i	0.0370143	−	0.352167i
$639$	2.02819	+	19.2970i	0.0802340	+	0.763376i
$640$	−11.1332	+	2.36644i	−0.440080	+	0.0935419i
$641$	10.9625	+	4.88084i	0.432995	+	0.192782i	0.611647	−	0.791131i	$-0.290507\pi$
$641$	10.9625	+	4.88084i	0.432995	+	0.192782i	−0.178653	+	0.983912i	$0.557174\pi$
$642$	−5.23237	+	5.81114i	−0.206505	+	0.229347i
$643$	8.79837	+	27.0786i	0.346974	+	1.06788i	0.960519	+	0.278216i	$0.0897431\pi$
$643$	8.79837	+	27.0786i	0.346974	+	1.06788i	−0.613545	+	0.789660i	$0.710257\pi$
$644$	−35.3521	−	39.2624i	−1.39307	−	1.54716i
$645$	2.00000	−	3.46410i	0.0787499	−	0.136399i
$646$	3.61803	+	6.26662i	0.142350	+	0.246557i
$647$	5.23607	−	16.1150i	0.205851	−	0.633544i	−0.793826	−	0.608145i	$-0.791914\pi$
$647$	5.23607	−	16.1150i	0.205851	−	0.633544i	0.999677	−	0.0253999i	$-0.00808591\pi$
$648$	−4.93612	+	2.19770i	−0.193909	+	0.0863338i
$649$	3.61803	−	2.62866i	0.142020	−	0.103184i
$650$	3.05573			0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	−12.3820	+	8.99602i	−0.484544	+	0.352042i	−0.803082	−	0.595868i	$-0.796808\pi$
$653$	−12.3820	+	8.99602i	−0.484544	+	0.352042i	0.318538	+	0.947910i	$0.396808\pi$
$654$	−2.75265	+	1.22556i	−0.107637	+	0.0479232i
$655$	3.70820	−	11.4127i	0.144892	−	0.445930i
$656$	−6.48936	−	11.2399i	−0.253367	−	0.438844i
$657$	−0.347524	+	0.601929i	−0.0135582	+	0.0234835i
$658$	−11.3379	−	12.5920i	−0.441999	−	0.490889i
$659$	−1.74671	−	5.37582i	−0.0680422	−	0.209412i	0.911254	−	0.411845i	$-0.135115\pi$
$659$	−1.74671	−	5.37582i	−0.0680422	−	0.209412i	−0.979296	+	0.202432i	$0.935115\pi$
$660$	−2.67652	+	2.97258i	−0.104183	+	0.115707i
$661$	−41.4390	−	18.4499i	−1.61179	−	0.717616i	−0.614346	−	0.789037i	$-0.710580\pi$
$661$	−41.4390	−	18.4499i	−1.61179	−	0.717616i	−0.997446	+	0.0714210i	$0.977247\pi$
$662$	1.20906	−	0.256993i	0.0469913	−	0.00998832i
$663$	−0.836228	−	7.95618i	−0.0324764	−	0.308992i
$664$	−0.688173	+	6.54753i	−0.0267063	+	0.254093i
$665$	9.26515	+	1.96937i	0.359287	+	0.0763688i
$666$	1.47214	+	1.06957i	0.0570441	+	0.0414450i
$667$	45.1246	+	32.7849i	1.74723	+	1.26944i
$668$	3.91259	+	0.831647i	0.151383	+	0.0321774i
$669$	−0.516817	+	4.91719i	−0.0199813	+	0.190109i
$670$	0.516817	+	4.91719i	0.0199664	+	0.189967i
$671$	27.7409	−	5.89652i	1.07093	−	0.227633i
$672$	26.8732	+	11.9647i	1.03666	+	0.461550i
$673$	31.4579	−	34.9376i	1.21261	−	1.34674i	0.291929	−	0.956440i	$-0.405703\pi$
$673$	31.4579	−	34.9376i	1.21261	−	1.34674i	0.920686	−	0.390305i	$-0.127630\pi$
$674$	3.67376	+	11.3067i	0.141508	+	0.435517i
$675$	14.7955	+	16.4320i	0.569477	+	0.632469i
$676$	−9.28115	+	16.0754i	−0.356967	+	0.618286i
$677$	−21.3607	−	36.9978i	−0.820958	−	1.42194i	−0.904970	−	0.425476i	$-0.860107\pi$
$677$	−21.3607	−	36.9978i	−0.820958	−	1.42194i	0.0840123	−	0.996465i	$-0.473226\pi$
$678$	1.29180	−	3.97574i	0.0496111	−	0.152687i
$679$	−7.52402	+	3.34991i	−0.288745	+	0.128558i
$680$	−9.47214	+	6.88191i	−0.363240	+	0.263909i
$681$	3.05573			0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	−4.30902	+	3.13068i	−0.164759	+	0.119705i
$685$	18.0043	−	8.01605i	0.687910	−	0.306277i
$686$	3.19098	−	9.82084i	0.121832	−	0.374961i
$687$	−8.29180	−	14.3618i	−0.316352	−	0.547937i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−1.26368	−	1.40346i	−0.0481425	−	0.0534676i
$690$	1.81966	+	5.60034i	0.0692733	+	0.213201i
$691$	−12.8342	+	14.2538i	−0.488234	+	0.542239i	−0.936041	−	0.351891i	$-0.885539\pi$
$691$	−12.8342	+	14.2538i	−0.488234	+	0.542239i	0.447807	+	0.894130i	$0.352205\pi$
$692$	22.0898	+	9.83503i	0.839730	+	0.373872i
$693$	−12.1996	+	2.59310i	−0.463424	+	0.0985038i
$694$	0.117554	+	1.11845i	0.00446229	+	0.0424558i
$695$	1.40240	−	13.3429i	0.0531959	−	0.506125i
$696$	−19.5630	−	4.15823i	−0.741532	−	0.157617i
$697$	−29.6525	−	21.5438i	−1.12317	−	0.816029i
$698$	13.9443	+	10.1311i	0.527798	+	0.383468i
$699$	−0.0673784	−	0.0143217i	−0.00254849	−	0.000541698i
$700$	2.86579	−	27.2662i	0.108317	−	1.03057i
$701$	−0.731699	−	6.96165i	−0.0276359	−	0.262938i	−0.999612	−	0.0278579i	$-0.991131\pi$
$701$	−0.731699	−	6.96165i	−0.0276359	−	0.262938i	0.971976	−	0.235080i	$-0.0755353\pi$
$702$	−4.13063	+	0.877993i	−0.155901	+	0.0331377i
$703$	−4.08550	−	1.81898i	−0.154088	−	0.0686042i
$704$	−0.315921	+	0.350865i	−0.0119067	+	0.0132237i
$705$	−2.47214	−	7.60845i	−0.0931060	−	0.286551i
$706$	8.02957	+	8.91774i	0.302197	+	0.335623i
$707$	−6.35410	+	11.0056i	−0.238971	+	0.413909i
$708$	−2.23607	−	3.87298i	−0.0840366	−	0.145556i
$709$	10.6525	−	32.7849i	0.400062	−	1.23126i	−0.524886	−	0.851172i	$-0.675892\pi$
$709$	10.6525	−	32.7849i	0.400062	−	1.23126i	0.924949	−	0.380092i	$-0.124108\pi$
$710$	−7.44165	+	3.31324i	−0.279280	+	0.124344i
$711$	2.03444	−	1.47811i	0.0762975	−	0.0554334i
$712$	−3.81966			−0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	−2.00000	+	1.45309i	−0.0747958	+	0.0543423i
$716$	17.3065	−	7.70533i	0.646773	−	0.287962i
$717$	0.652476	−	2.00811i	0.0243672	−	0.0749944i
$718$	5.48936	+	9.50785i	0.204861	+	0.354830i
$719$	18.0902	−	31.3331i	0.674649	−	1.16853i	−0.301922	−	0.953333i	$-0.597628\pi$
$719$	18.0902	−	31.3331i	0.674649	−	1.16853i	0.976571	−	0.215194i	$-0.0690385\pi$
$720$	−1.82639	−	2.02841i	−0.0680654	−	0.0755942i
$721$	−2.30902	−	7.10642i	−0.0859923	−	0.264657i
$722$	5.78964	−	6.43004i	0.215468	−	0.239301i
$723$	−34.2834	−	15.2640i	−1.27501	−	0.567673i
$724$	28.7736	−	6.11602i	1.06936	−	0.227300i
$725$	3.02550	+	28.7857i	0.112364	+	1.06907i
$726$	−0.558968	+	5.31823i	−0.0207453	+	0.197378i
$727$	38.8950	+	8.26739i	1.44254	+	0.306620i	0.861707	−	0.507406i	$-0.169395\pi$
$727$	38.8950	+	8.26739i	1.44254	+	0.306620i	0.580828	+	0.814026i	$0.302729\pi$
$728$	9.47214	+	6.88191i	0.351061	+	0.255061i
$729$	−19.4615	−	14.1396i	−0.720796	−	0.523689i
$730$	−0.285420	−	0.0606678i	−0.0105639	−	0.00224542i
$731$	1.77116	−	16.8514i	0.0655087	−	0.623273i
$732$	−2.96450	−	28.2053i	−0.109571	−	1.04250i
$733$	5.35256	−	1.13772i	0.197701	−	0.0420227i	−0.107997	−	0.994151i	$-0.534444\pi$
$733$	5.35256	−	1.13772i	0.197701	−	0.0420227i	0.305698	+	0.952129i	$0.401110\pi$
$734$	−10.1628	−	4.52479i	−0.375117	−	0.167013i
$735$	9.05191	−	10.0532i	0.333885	−	0.370816i
$736$	13.3820	+	41.1855i	0.493266	+	1.51812i
$737$	10.7061	+	11.8903i	0.394364	+	0.437985i
$738$	−3.18441	+	5.51555i	−0.117220	+	0.203030i
$739$	8.09017	+	14.0126i	0.297602	+	0.515461i	0.975587	−	0.219614i	$-0.0704799\pi$
$739$	8.09017	+	14.0126i	0.297602	+	0.515461i	−0.677985	+	0.735076i	$0.737147\pi$
$740$	1.00000	−	3.07768i	0.0367607	−	0.113138i
$741$	3.12104	−	1.38958i	0.114654	−	0.0510474i
$742$	3.23607	−	2.35114i	0.118800	−	0.0863131i
$743$	27.8197			1.02060			0.510302	−	0.859995i	$-0.329534\pi$
$743$	27.8197			1.02060			0.510302	+	0.859995i	$0.329534\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	9.50000	−	6.90215i	0.347820	−	0.252706i
$747$	−3.95964	+	1.76295i	−0.144876	+	0.0645028i
$748$	−5.23607	+	16.1150i	−0.191450	+	0.589221i
$749$	21.6803	+	37.5515i	0.792182	+	1.37210i
$750$	−3.43769	+	5.95426i	−0.125527	+	0.217419i
$751$	30.4729	+	33.8436i	1.11197	+	1.23497i	0.969479	+	0.245174i	$0.0788450\pi$
$751$	30.4729	+	33.8436i	1.11197	+	1.23497i	0.142492	+	0.989796i	$0.454488\pi$
$752$	−3.70820	−	11.4127i	−0.135224	−	0.416178i
$753$	−19.9993	+	22.2115i	−0.728816	+	0.809433i
$754$	−5.04996	−	2.24838i	−0.183909	−	0.0818813i
$755$	−8.00158	+	1.70079i	−0.291207	+	0.0618980i
$756$	3.96043	+	37.6810i	0.144039	+	1.37044i
$757$	2.36783	−	22.5284i	0.0860602	−	0.818808i	−0.863315	−	0.504665i	$-0.831616\pi$
$757$	2.36783	−	22.5284i	0.0860602	−	0.818808i	0.949376	−	0.314143i	$-0.101717\pi$
$758$	−22.9047	−	4.86854i	−0.831936	−	0.176834i
$759$	15.4164	+	11.2007i	0.559580	+	0.406559i
$760$	−4.04508	−	2.93893i	−0.146731	−	0.106606i
$761$	−1.95630	−	0.415823i	−0.0709156	−	0.0150736i	0.172317	−	0.985042i	$-0.444875\pi$
$761$	−1.95630	−	0.415823i	−0.0709156	−	0.0150736i	−0.243233	+	0.969968i	$0.578208\pi$
$762$	0.281709	−	2.68028i	0.0102052	−	0.0970965i
$763$	1.74648	+	16.6167i	0.0632269	+	0.601564i
$764$	5.03345	−	1.06989i	0.182104	−	0.0387073i
$765$	−7.04179	−	3.13521i	−0.254597	−	0.113354i
$766$	−4.91645	+	5.46027i	−0.177639	+	0.197288i
$767$	−0.854102	−	2.62866i	−0.0308398	−	0.0949153i
$768$	−5.42762	−	6.02799i	−0.195852	−	0.217516i
$769$	1.31966	−	2.28572i	0.0475882	−	0.0824251i	−0.841250	−	0.540646i	$-0.818180\pi$
$769$	1.31966	−	2.28572i	0.0475882	−	0.0824251i	0.888838	+	0.458221i	$0.151513\pi$
$770$	−2.61803	−	4.53457i	−0.0943474	−	0.163414i
$771$	−6.09017	+	18.7436i	−0.219332	+	0.675035i
$772$	8.08862	−	3.60129i	0.291116	−	0.129613i
$773$	−23.5623	+	17.1190i	−0.847477	+	0.615728i	−0.924449	−	0.381305i	$-0.875475\pi$
$773$	−23.5623	+	17.1190i	−0.847477	+	0.615728i	0.0769721	+	0.997033i	$0.475475\pi$
$774$	−2.94427			−0.105830
$775$		0			0
$776$	4.34752			0.156067
$777$	−8.47214	+	6.15537i	−0.303936	+	0.220823i
$778$	−10.0999	+	4.49677i	−0.362099	+	0.161217i
$779$	4.83688	−	14.8864i	0.173299	−	0.533360i
$780$	1.23607	+	2.14093i	0.0442583	+	0.0766577i
$781$	−13.1803	+	22.8290i	−0.471630	+	0.816887i
$782$	16.6910	+	18.5372i	0.596868	+	0.662889i
$783$	−12.3607	−	38.0423i	−0.441735	−	1.35952i
$784$	13.5779	−	15.0797i	0.484924	−	0.538562i
$785$	−13.6014	−	6.05572i	−0.485453	−	0.216138i
$786$	8.96686	−	1.90596i	0.319837	−	0.0679835i
$787$	−4.04028	−	38.4407i	−0.144021	−	1.37026i	−0.792890	−	0.609365i	$-0.791425\pi$
$787$	−4.04028	−	38.4407i	−0.144021	−	1.37026i	0.648870	−	0.760900i	$-0.275242\pi$
$788$	−2.60739	+	24.8076i	−0.0928843	+	0.883735i
$789$	22.6867	+	4.82220i	0.807667	+	0.171675i
$790$	0.854102	+	0.620541i	0.0303876	+	0.0220779i
$791$	−18.7533	−	13.6251i	−0.666790	−	0.484451i
$792$	6.43972	+	1.36881i	0.228826	+	0.0486384i
$793$	1.83216	−	17.4318i	0.0650619	−	0.619023i
$794$	−0.452215	−	4.30254i	−0.0160485	−	0.152691i
$795$	1.84727	−	0.392650i	0.0655161	−	0.0139259i
$796$	1.56052	+	0.694789i	0.0553112	+	0.0246261i
$797$	−19.1262	+	21.2417i	−0.677483	+	0.752421i	−0.979624	−	0.200842i	$-0.935632\pi$
$797$	−19.1262	+	21.2417i	−0.677483	+	0.752421i	0.302140	+	0.953263i	$0.402299\pi$
$798$	2.23607	+	6.88191i	0.0791559	+	0.243617i
$799$	−22.6759	−	25.1841i	−0.802214	−	0.890949i
$800$	−11.2361	+	19.4614i	−0.397255	+	0.688066i
$801$	−1.25735	−	2.17780i	−0.0444264	−	0.0769488i
$802$	−3.02129	+	9.29856i	−0.106685	+	0.328344i
$803$	−0.862635	+	0.384070i	−0.0304417	+	0.0135535i
$804$	12.9443	−	9.40456i	0.456509	−	0.331673i
$805$	32.6525			1.15085
$806$		0			0
$807$	−35.7771			−1.25941
$808$	5.42705	−	3.94298i	0.190923	−	0.138714i
$809$	−3.12104	+	1.38958i	−0.109730	+	0.0488550i	−0.460867	−	0.887469i	$-0.652462\pi$
$809$	−3.12104	+	1.38958i	−0.109730	+	0.0488550i	0.351137	+	0.936324i	$0.385795\pi$
$810$	0.461493	−	1.42033i	0.0162152	−	0.0499053i
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	0.999953	−	0.00966502i	$-0.00307652\pi$
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	−0.508347	+	0.861152i	$0.669743\pi$
$812$	−24.7984	+	42.9520i	−0.870252	+	1.50732i
$813$	6.76588	+	7.51428i	0.237290	+	0.263537i
$814$	0.763932	+	2.35114i	0.0267758	+	0.0824074i
$815$	−1.81214	+	2.01259i	−0.0634766	+	0.0704979i
$816$	10.9625	+	4.88084i	0.383766	+	0.170864i
$817$	7.07794	−	1.50446i	0.247626	−	0.0526345i
$818$	−1.69131	−	16.0917i	−0.0591351	−	0.562633i
$819$	−0.805727	+	7.66598i	−0.0281544	+	0.267871i
$820$	11.0787	+	2.35486i	0.386886	+	0.0822352i
$821$	29.5623	+	21.4783i	1.03173	+	0.749597i	0.968655	−	0.248412i	$-0.0799086\pi$
$821$	29.5623	+	21.4783i	1.03173	+	0.749597i	0.0630771	+	0.998009i	$0.479909\pi$
$822$	12.1803	+	8.84953i	0.424838	+	0.308663i
$823$	27.1027	+	5.76086i	0.944741	+	0.200811i	0.654431	−	0.756122i	$-0.272908\pi$
$823$	27.1027	+	5.76086i	0.944741	+	0.200811i	0.290310	+	0.956933i	$0.406242\pi$
$824$	−0.412289	+	3.92266i	−0.0143628	+	0.136653i
$825$	1.03363	+	9.83437i	0.0359865	+	0.342389i
$826$	5.72618	−	1.21714i	0.199239	−	0.0423496i
$827$	44.4462	+	19.7887i	1.54555	+	0.688122i	0.989699	−	0.143162i	$-0.0457269\pi$
$827$	44.4462	+	19.7887i	1.54555	+	0.688122i	0.555848	+	0.831284i	$0.312394\pi$
$828$	−12.2857	+	13.6446i	−0.426957	+	0.474184i
$829$	−11.3820	−	35.0301i	−0.395312	−	1.21665i	−0.928718	−	0.370786i	$-0.879088\pi$
$829$	−11.3820	−	35.0301i	−0.395312	−	1.21665i	0.533406	−	0.845859i	$-0.320912\pi$
$830$	−1.21759	−	1.35227i	−0.0422632	−	0.0469380i
$831$	−11.5279	+	19.9668i	−0.399897	+	0.692642i
$832$	0.145898	+	0.252703i	0.00505810	+	0.00876089i
$833$	17.7082	−	54.5002i	0.613553	−	1.88832i
$834$	9.36313	−	4.16873i	0.324219	−	0.144351i
$835$	−2.00000	+	1.45309i	−0.0692129	+	0.0502861i
$836$	−7.23607			−0.250265
$837$		0			0
$838$	−18.6180			−0.643149
$839$	−8.94427	+	6.49839i	−0.308791	+	0.224349i	−0.731377	−	0.681973i	$-0.761122\pi$
$839$	−8.94427	+	6.49839i	−0.308791	+	0.224349i	0.422587	+	0.906322i	$0.361122\pi$
$840$	−10.6960	+	4.76216i	−0.369046	+	0.164310i
$841$	7.21885	−	22.2173i	0.248926	−	0.766115i
$842$	−4.74671	−	8.22154i	−0.163582	−	0.283333i
$843$	−10.5066	+	18.1979i	−0.361866	+	0.626770i
$844$	−0.887426	−	0.985587i	−0.0305465	−	0.0339253i
$845$	−3.54508	−	10.9106i	−0.121955	−	0.375338i
$846$	−3.94020	+	4.37604i	−0.135467	+	0.150451i
$847$	27.0889	+	12.0607i	0.930785	+	0.414412i
$848$	2.77091	−	0.588976i	0.0951535	−	0.0202255i
$849$	−2.82809	−	26.9075i	−0.0970599	−	0.923463i
$850$	−1.35304	+	12.8734i	−0.0464091	+	0.441553i
$851$	−15.0795	−	3.20525i	−0.516919	−	0.109875i
$852$	21.3262	+	15.4944i	0.730625	+	0.530830i
$853$	−30.2705	−	21.9928i	−1.03644	−	0.753020i	−0.0668546	−	0.997763i	$-0.521296\pi$
$853$	−30.2705	−	21.9928i	−1.03644	−	0.753020i	−0.969588	+	0.244743i	$0.921296\pi$
$854$	36.3133	+	7.71864i	1.24262	+	0.264126i
$855$	0.344086	−	3.27376i	0.0117675	−	0.111960i
$856$	−2.39250	−	22.7632i	−0.0817741	−	0.778029i
$857$	−50.5366	+	10.7419i	−1.72630	+	0.366936i	−0.960959	−	0.276691i	$-0.910762\pi$
$857$	−50.5366	+	10.7419i	−1.72630	+	0.366936i	−0.765339	+	0.643627i	$0.777429\pi$
$858$	−1.72527	−	0.768140i	−0.0588998	−	0.0262239i
$859$	25.3524	−	28.1567i	0.865012	−	0.960693i	−0.134531	−	0.990909i	$-0.542953\pi$
$859$	25.3524	−	28.1567i	0.865012	−	0.960693i	0.999543	+	0.0302160i	$0.00961951\pi$
$860$	1.61803	+	4.97980i	0.0551745	+	0.169810i
$861$	−24.5253	−	27.2381i	−0.835820	−	0.928272i
$862$	3.70820	−	6.42280i	0.126302	−	0.218761i
$863$	16.0902	+	27.8690i	0.547716	+	0.948672i	0.998431	+	0.0560035i	$0.0178358\pi$
$863$	16.0902	+	27.8690i	0.547716	+	0.948672i	−0.450715	+	0.892668i	$0.648831\pi$
$864$	9.59675	−	29.5358i	0.326488	−	1.00483i
$865$	−13.6523	+	6.07838i	−0.464191	+	0.206671i
$866$	−6.09017	+	4.42477i	−0.206952	+	0.150360i
$867$	12.8754			0.437271
$868$		0			0
$869$	3.41641			0.115894
$870$	4.47214	−	3.24920i	0.151620	−	0.110158i
$871$	9.03363	−	4.02203i	0.306093	−	0.136281i
$872$	2.72542	−	8.38800i	0.0922945	−	0.284053i
$873$	1.43112	+	2.47877i	0.0484359	+	0.0838935i
$874$	−5.32624	+	9.22531i	−0.180163	+	0.312051i
$875$	25.5103	+	28.3321i	0.862407	+	0.957800i
$876$	0.291796	+	0.898056i	0.00985888	+	0.0303425i
$877$	−24.0514	+	26.7118i	−0.812158	+	0.901993i	−0.996728	−	0.0808260i	$-0.974244\pi$
$877$	−24.0514	+	26.7118i	−0.812158	+	0.901993i	0.184570	+	0.982819i	$0.440911\pi$
$878$	−11.9585	−	5.32425i	−0.403579	−	0.179685i
$879$	−10.2433	+	2.17728i	−0.345498	+	0.0734378i
$880$	−0.387613	−	3.68789i	−0.0130664	−	0.124319i
$881$	−2.54638	+	24.2272i	−0.0857899	+	0.816236i	0.864030	+	0.503440i	$0.167932\pi$
$881$	−2.54638	+	24.2272i	−0.0857899	+	0.816236i	−0.949820	+	0.312796i	$0.898734\pi$
$882$	−9.73983	−	2.07027i	−0.327957	−	0.0697095i
$883$	−32.1803	−	23.3804i	−1.08295	−	0.786813i	−0.104759	−	0.994498i	$-0.533407\pi$
$883$	−32.1803	−	23.3804i	−1.08295	−	0.786813i	−0.978196	+	0.207685i	$0.933407\pi$
$884$	8.47214	+	6.15537i	0.284949	+	0.207027i
$885$	2.70353	+	0.574654i	0.0908783	+	0.0193168i
$886$	1.11709	−	10.6284i	0.0375293	−	0.357067i
$887$	3.24758	+	30.8987i	0.109043	+	1.03748i	0.903041	+	0.429555i	$0.141330\pi$
$887$	3.24758	+	30.8987i	0.109043	+	1.03748i	−0.793997	+	0.607921i	$0.792004\pi$
$888$	5.40707	−	1.14931i	0.181449	−	0.0385682i
$889$	−13.6523	−	6.07838i	−0.457882	−	0.203862i
$890$	0.706420	−	0.784559i	0.0236793	−	0.0262985i
$891$	−1.49342	−	4.59628i	−0.0500315	−	0.153981i
$892$	−4.33070	−	4.80973i	−0.145003	−	0.161042i
$893$	7.23607	−	12.5332i	0.242146	−	0.419409i
$894$	3.81966	+	6.61585i	0.127749	+	0.221267i
$895$	−3.61803	+	11.1352i	−0.120938	+	0.372207i
$896$	−44.0464	+	19.6107i	−1.47149	+	0.655148i
$897$	9.52786	−	6.92240i	0.318126	−	0.231132i
$898$	−19.3475			−0.645635
$899$		0			0
$900$	−9.52786			−0.317595
$901$	6.47214	−	4.70228i	0.215618	−	0.156656i
$902$	−7.90443	+	3.51928i	−0.263189	+	0.117179i
$903$	5.23607	−	16.1150i	0.174245	−	0.536272i
$904$	6.11803	+	10.5967i	0.203483	+	0.352443i
$905$	−9.09017	+	15.7446i	−0.302167	+	0.523369i
$906$	−4.18155	−	4.64408i	−0.138923	−	0.154289i
$907$	−6.10739	−	18.7966i	−0.202793	−	0.624131i	−0.999797	−	0.0201577i	$-0.993583\pi$
$907$	−6.10739	−	18.7966i	−0.202793	−	0.624131i	0.797004	−	0.603974i	$-0.206417\pi$
$908$	−2.67652	+	2.97258i	−0.0888235	+	0.0986485i
$909$	4.03459	+	1.79631i	0.133819	+	0.0595800i
$910$	−3.16535	+	0.672816i	−0.104930	+	0.0223036i
$911$	0.436965	+	4.15744i	0.0144773	+	0.137742i	0.999373	−	0.0354065i	$-0.0112726\pi$
$911$	0.436965	+	4.15744i	0.0144773	+	0.137742i	−0.984896	+	0.173149i	$0.944606\pi$
$912$	−0.535668	+	5.09654i	−0.0177377	+	0.168763i
$913$	−5.75987	−	1.22430i	−0.190624	−	0.0405183i
$914$	−10.4721	−	7.60845i	−0.346387	−	0.251665i
$915$	14.1803	+	10.3026i	0.468788	+	0.340594i
$916$	21.2338	+	4.51339i	0.701585	+	0.149127i
$917$	5.31348	−	50.5543i	0.175466	−	1.66945i
$918$	−1.86986	−	17.7905i	−0.0617146	−	0.587176i
$919$	5.40707	−	1.14931i	0.178363	−	0.0379122i	−0.117864	−	0.993030i	$-0.537605\pi$
$919$	5.40707	−	1.14931i	0.178363	−	0.0379122i	0.296227	+	0.955118i	$0.404271\pi$
$920$	−15.7459	−	7.01054i	−0.519128	−	0.231131i
$921$	−12.6477	+	14.0467i	−0.416756	+	0.462855i
$922$	1.97871	+	6.08985i	0.0651655	+	0.200559i
$923$	10.9013	+	12.1072i	0.358822	+	0.398512i
$924$	−8.47214	+	14.6742i	−0.278713	+	0.482745i
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	5.61803	−	17.2905i	0.184620	−	0.568202i
$927$	−2.37225	+	1.05619i	−0.0779148	+	0.0346899i
$928$	32.8885	−	23.8949i	1.07962	−	0.784389i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	24.4721			0.802042
$932$	0.0729490	−	0.0530006i	0.00238952	−	0.00173609i
$933$	−7.70079	+	3.42861i	−0.252113	+	0.112248i
$934$	1.66312	−	5.11855i	0.0544189	−	0.167484i
$935$	−5.23607	−	9.06914i	−0.171238	−	0.296592i
$936$	2.03444	−	3.52376i	0.0664978	−	0.115178i
$937$	18.0292	+	20.0235i	0.588989	+	0.654139i	0.961795	−	0.273770i	$-0.0882708\pi$
$937$	18.0292	+	20.0235i	0.588989	+	0.654139i	−0.372806	+	0.927909i	$0.621604\pi$
$938$	6.47214	+	19.9192i	0.211323	+	0.650384i
$939$	17.5642	−	19.5070i	0.573185	−	0.636586i
$940$	9.56677	+	4.25940i	0.312034	+	0.138926i
$941$	37.1696	−	7.90064i	1.21169	−	0.257554i	0.442618	−	0.896710i	$-0.354050\pi$
$941$	37.1696	−	7.90064i	1.21169	−	0.257554i	0.769077	+	0.639157i	$0.220716\pi$
$942$	−1.18889	−	11.3115i	−0.0387361	−	0.368550i
$943$	5.64009	−	53.6618i	0.183667	−	1.74747i
$944$	4.05530	+	0.861981i	0.131989	+	0.0280551i
$945$	−18.9443	−	13.7638i	−0.616257	−	0.447737i
$946$	−3.23607	−	2.35114i	−0.105214	−	0.0764422i
$947$	30.2681	+	6.43368i	0.983580	+	0.209066i	0.671512	−	0.740993i	$-0.265645\pi$
$947$	30.2681	+	6.43368i	0.983580	+	0.209066i	0.312068	+	0.950060i	$0.398978\pi$
$948$	0.357112	−	3.39769i	0.0115985	−	0.110352i
$949$	0.0610020	+	0.580395i	0.00198021	+	0.0188404i
$950$	−5.40707	+	1.14931i	−0.175428	+	0.0372885i
$951$	24.7796	+	11.0326i	0.803532	+	0.357756i
$952$	−33.1867	+	36.8576i	−1.07559	+	1.19456i
$953$	9.97871	+	30.7113i	0.323242	+	0.994837i	0.972228	+	0.234037i	$0.0751936\pi$
$953$	9.97871	+	30.7113i	0.323242	+	0.994837i	−0.648986	+	0.760801i	$0.724806\pi$
$954$	−0.930156	−	1.03304i	−0.0301149	−	0.0334460i
$955$	−1.59017	+	2.75426i	−0.0514567	+	0.0891256i
$956$	1.38197	+	2.39364i	0.0446960	+	0.0774157i
$957$	5.52786	−	17.0130i	0.178690	−	0.549953i
$958$	−20.7255	+	9.22760i	−0.669611	+	0.298130i
$959$	67.5410	−	49.0714i	2.18101	−	1.58460i
$960$	−0.291796			−0.00941768
$961$		0			0
$962$	1.52786			0.0492603
$963$	12.1910	−	8.85727i	0.392849	−	0.285421i
$964$	44.8776	−	19.9808i	1.44541	−	0.643538i
$965$	−1.69098	+	5.20431i	−0.0544347	+	0.167533i
$966$	12.4721	+	21.6024i	0.401284	+	0.695045i
$967$	−7.81966	+	13.5440i	−0.251463	+	0.435547i	−0.963929	−	0.266160i	$-0.914245\pi$
$967$	−7.81966	+	13.5440i	−0.251463	+	0.435547i	0.712466	+	0.701707i	$0.247578\pi$
$968$	−10.4736	−	11.6321i	−0.336633	−	0.373868i
$969$	4.47214	+	13.7638i	0.143666	+	0.442158i
$970$	−0.804045	+	0.892982i	−0.0258163	+	0.0286719i
$971$	−25.5793	−	11.3886i	−0.820878	−	0.365478i	−0.0470644	−	0.998892i	$-0.514987\pi$
$971$	−25.5793	−	11.3886i	−0.820878	−	0.365478i	−0.773814	+	0.633413i	$0.781653\pi$
$972$	21.5192	−	4.57406i	0.690230	−	0.146713i
$973$	−5.94065	−	56.5215i	−0.190448	−	1.81200i
$974$	−0.953782	+	9.07463i	−0.0305611	+	0.290770i
$975$	5.97791	+	1.27064i	0.191446	+	0.0406931i
$976$	21.2705	+	15.4539i	0.680852	+	0.494668i
$977$	−26.8992	−	19.5434i	−0.860581	−	0.625249i	0.0674618	−	0.997722i	$-0.478510\pi$
$977$	−26.8992	−	19.5434i	−0.860581	−	0.625249i	−0.928043	+	0.372473i	$0.878510\pi$
$978$	−2.02367	−	0.430145i	−0.0647099	−	0.0137545i
$979$	0.357112	−	3.39769i	0.0114133	−	0.108591i
$980$	1.85101	+	17.6112i	0.0591284	+	0.562569i
$981$	5.67962	−	1.20724i	0.181336	−	0.0385442i
$982$	22.7877	+	10.1457i	0.727186	+	0.323764i
$983$	32.4342	−	36.0218i	1.03449	−	1.14892i	0.0457990	−	0.998951i	$-0.485417\pi$
$983$	32.4342	−	36.0218i	1.03449	−	1.14892i	0.988691	−	0.149967i	$-0.0479167\pi$
$984$	5.97871	+	18.4006i	0.190594	+	0.586589i
$985$	−10.3156	−	11.4566i	−0.328682	−	0.365038i
$986$	11.7082	−	20.2792i	0.372865	−	0.645821i
$987$	−16.9443	−	29.3483i	−0.539342	−	0.934168i
$988$	−1.38197	+	4.25325i	−0.0439662	+	0.135314i
$989$	22.7877	−	10.1457i	0.724608	−	0.322616i
$990$	−1.47214	+	1.06957i	−0.0467876	+	0.0339931i
$991$	50.5410			1.60549			0.802744	−	0.596324i	$-0.203372\pi$
$991$	50.5410			1.60549			0.802744	+	0.596324i	$0.203372\pi$
$992$		0			0
$993$	2.47214			0.0784509
$994$	−27.9164	+	20.2825i	−0.885455	+	0.643320i
$995$	−0.964456	+	0.429403i	−0.0305753	+	0.0136130i
$996$	−1.81966	+	5.60034i	−0.0576581	+	0.177453i
$997$	−7.68034	−	13.3027i	−0.243239	−	0.421302i	0.718396	−	0.695634i	$-0.244877\pi$
$997$	−7.68034	−	13.3027i	−0.243239	−	0.421302i	−0.961635	+	0.274332i	$0.911543\pi$
$998$	−10.3262	+	17.8856i	−0.326871	+	0.566158i
$999$	7.39773	+	8.21601i	0.234054	+	0.259943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.h.235.1		8
31.2	even	5	inner	961.2.g.h.816.1		8
31.3	odd	30		961.2.g.d.844.1		8
31.4	even	5		961.2.g.a.846.1		8
31.5	even	3		961.2.d.d.388.1		4
31.6	odd	6		961.2.g.e.338.1		8
31.7	even	15		961.2.g.a.448.1		8
31.8	even	5		961.2.c.e.439.1		4
31.9	even	15		31.2.a.a.1.1	✓	2
31.10	even	15		961.2.d.d.374.1		4
31.11	odd	30		961.2.d.a.628.1		4
31.12	odd	30		961.2.g.e.732.1		8
31.13	odd	30		961.2.d.a.531.1		4
31.14	even	15		961.2.c.e.521.1		4
31.15	odd	10		961.2.g.d.547.1		8
31.16	even	5		961.2.g.a.547.1		8
31.17	odd	30		961.2.c.c.521.1		4
31.18	even	15		961.2.d.c.531.1		4
31.19	even	15	inner	961.2.g.h.732.1		8
31.20	even	15		961.2.d.c.628.1		4
31.21	odd	30		961.2.d.g.374.1		4
31.22	odd	30		961.2.a.f.1.1		2
31.23	odd	10		961.2.c.c.439.1		4
31.24	odd	30		961.2.g.d.448.1		8
31.25	even	3	inner	961.2.g.h.338.1		8
31.26	odd	6		961.2.d.g.388.1		4
31.27	odd	10		961.2.g.d.846.1		8
31.28	even	15		961.2.g.a.844.1		8
31.29	odd	10		961.2.g.e.816.1		8
31.30	odd	2		961.2.g.e.235.1		8
93.53	even	30		8649.2.a.c.1.2		2
93.71	odd	30		279.2.a.a.1.2		2
124.71	odd	30		496.2.a.i.1.1		2
155.9	even	30		775.2.a.d.1.2		2
155.102	odd	60		775.2.b.d.249.2		4
155.133	odd	60		775.2.b.d.249.3		4
217.195	odd	30		1519.2.a.a.1.1		2
248.133	even	30		1984.2.a.r.1.1		2
248.195	odd	30		1984.2.a.n.1.2		2
341.164	odd	30		3751.2.a.b.1.2		2
372.71	even	30		4464.2.a.bf.1.2		2
403.350	even	30		5239.2.a.f.1.2		2
465.164	odd	30		6975.2.a.y.1.1		2
527.288	even	30		8959.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	31.9	even	15
279.2.a.a.1.2		2	93.71	odd	30
496.2.a.i.1.1		2	124.71	odd	30
775.2.a.d.1.2		2	155.9	even	30
775.2.b.d.249.2		4	155.102	odd	60
775.2.b.d.249.3		4	155.133	odd	60
961.2.a.f.1.1		2	31.22	odd	30
961.2.c.c.439.1		4	31.23	odd	10
961.2.c.c.521.1		4	31.17	odd	30
961.2.c.e.439.1		4	31.8	even	5
961.2.c.e.521.1		4	31.14	even	15
961.2.d.a.531.1		4	31.13	odd	30
961.2.d.a.628.1		4	31.11	odd	30
961.2.d.c.531.1		4	31.18	even	15
961.2.d.c.628.1		4	31.20	even	15
961.2.d.d.374.1		4	31.10	even	15
961.2.d.d.388.1		4	31.5	even	3
961.2.d.g.374.1		4	31.21	odd	30
961.2.d.g.388.1		4	31.26	odd	6
961.2.g.a.448.1		8	31.7	even	15
961.2.g.a.547.1		8	31.16	even	5
961.2.g.a.844.1		8	31.28	even	15
961.2.g.a.846.1		8	31.4	even	5
961.2.g.d.448.1		8	31.24	odd	30
961.2.g.d.547.1		8	31.15	odd	10
961.2.g.d.844.1		8	31.3	odd	30
961.2.g.d.846.1		8	31.27	odd	10
961.2.g.e.235.1		8	31.30	odd	2
961.2.g.e.338.1		8	31.6	odd	6
961.2.g.e.732.1		8	31.12	odd	30
961.2.g.e.816.1		8	31.29	odd	10
961.2.g.h.235.1		8	1.1	even	1	trivial
961.2.g.h.338.1		8	31.25	even	3	inner
961.2.g.h.732.1		8	31.19	even	15	inner
961.2.g.h.816.1		8	31.2	even	5	inner
1519.2.a.a.1.1		2	217.195	odd	30
1984.2.a.n.1.2		2	248.195	odd	30
1984.2.a.r.1.1		2	248.133	even	30
3751.2.a.b.1.2		2	341.164	odd	30
4464.2.a.bf.1.2		2	372.71	even	30
5239.2.a.f.1.2		2	403.350	even	30
6975.2.a.y.1.1		2	465.164	odd	30
8649.2.a.c.1.2		2	93.53	even	30
8959.2.a.b.1.1		2	527.288	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.363271i) q^{2} +(1.12920 - 0.502754i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.381966 - 0.661585i) q^{6} +(-2.83448 - 3.14801i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.985051 + 1.09401i) q^{9} +(-0.564602 - 0.251377i) q^{10} +(-1.95630 + 0.415823i) q^{11} +(0.209057 + 1.98904i) q^{12} +(-0.129204 + 1.22930i) q^{13} +(-2.56082 - 0.544320i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(-5.12165 - 1.08864i) q^{17} +(-0.0951031 + 0.904846i) q^{18} +(-0.233733 - 2.22382i) q^{19} +(1.58268 - 0.336408i) q^{20} +(-4.78339 - 2.12970i) q^{21} +(-0.827091 + 0.918578i) q^{22} +(-2.38197 - 7.33094i) q^{23} +(1.84943 + 2.05400i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.381966 + 0.661585i) q^{26} +(-1.70820 + 5.25731i) q^{27} +(6.26153 - 2.78781i) q^{28} +(-5.85410 + 4.25325i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(-2.00000 + 1.45309i) q^{33} +(-2.95630 + 1.31623i) q^{34} +(-1.30902 + 4.02874i) q^{35} +(-1.19098 - 2.06284i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-0.924716 - 1.02700i) q^{38} +(0.472136 + 1.45309i) q^{39} +(1.49622 - 1.66172i) q^{40} +(6.39482 + 2.84716i) q^{41} +(-3.16535 + 0.672816i) q^{42} +(0.338261 + 3.21834i) q^{43} +(0.338261 - 3.21834i) q^{44} +(1.43997 + 0.306074i) q^{45} +(-3.85410 - 2.80017i) q^{46} +(5.23607 + 3.80423i) q^{47} +(-2.24171 - 0.476491i) q^{48} +(-1.14399 + 10.8843i) q^{49} +(-0.258409 - 2.45859i) q^{50} +(-6.33070 + 1.34563i) q^{51} +(-1.82709 - 0.813473i) q^{52} +(-1.02234 + 1.13542i) q^{53} +(1.05573 + 3.24920i) q^{54} +(1.33826 + 1.48629i) q^{55} +(4.73607 - 8.20311i) q^{56} +(-1.38197 - 2.39364i) q^{57} +(-1.38197 + 4.25325i) q^{58} +(-2.04275 + 0.909491i) q^{59} +(1.61803 - 1.17557i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(0.190983 - 0.138757i) q^{64} +(1.12920 - 0.502754i) q^{65} +(-0.472136 + 1.45309i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-6.37539 - 7.08058i) q^{69} +(0.809017 + 2.48990i) q^{70} +(8.81937 - 9.79490i) q^{71} +(-3.00721 - 1.33889i) q^{72} +(0.461819 - 0.0981626i) q^{73} +(-0.129204 - 1.22930i) q^{74} +(0.516817 - 4.91719i) q^{75} +(3.53897 + 0.752232i) q^{76} +(6.85410 + 4.97980i) q^{77} +(0.763932 + 0.555029i) q^{78} +(-1.67088 - 0.355156i) q^{79} +(-0.193806 + 1.84395i) q^{80} +(0.252583 + 2.40317i) q^{81} +(4.23170 - 0.899475i) q^{82} +(2.68973 + 1.19754i) q^{83} +(5.66897 - 6.29602i) q^{84} +(1.61803 + 4.97980i) q^{85} +(1.33826 + 1.48629i) q^{86} +(-4.47214 + 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(-0.527864 + 1.62460i) q^{89} +(0.831171 - 0.370061i) q^{90} +(4.23607 - 3.07768i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(-1.80902 + 1.31433i) q^{95} +(-6.34391 + 2.82449i) q^{96} +(0.600813 - 1.84911i) q^{97} +(3.38197 + 5.85774i) q^{98} +(1.47214 - 2.54981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 8 q^{15} - 12 q^{16} - 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 8 * q^15 - 12 * q^16 - 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 - 8 * q^21 + 6 * q^22 - 28 * q^23 + 10 * q^24 + 16 * q^25 + 12 * q^26 + 40 * q^27 + 11 * q^28 - 20 * q^29 - 24 * q^30 - 36 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 14 * q^36 + 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 + 13 * q^45 - 4 * q^46 + 24 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^52 - 16 * q^53 + 80 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 - 20 * q^58 - 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 + 6 * q^64 + 4 * q^65 + 32 * q^66 - 32 * q^67 + 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 + 28 * q^77 + 24 * q^78 - 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 + 14 * q^83 - 6 * q^84 + 4 * q^85 + 2 * q^86 - 40 * q^89 - 6 * q^90 + 16 * q^91 + 64 * q^92 + 32 * q^94 - 10 * q^95 - 18 * q^96 + 54 * q^97 + 36 * q^98 - 24 * q^99

Introduction

L-functions

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