LMFDB - Embedded newform 370.2.o.b.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			181.2
Root			$0.206805 - 0.358197i$ of defining polynomial
Character	$\chi$	$=$	370.181
Dual form			370.2.o.b.231.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.0718226 - 0.407326i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.413610 q^{6} +(1.40064 - 1.17528i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.65832 - 0.967550i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.0718226 - 0.407326i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.413610 q^{6} +(1.40064 - 1.17528i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.65832 - 0.967550i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.38981 - 2.40722i) q^{11} +(-0.0718226 + 0.407326i) q^{12} +(-1.46474 - 0.533123i) q^{13} +(0.914204 + 1.58345i) q^{14} +(0.316844 + 0.265863i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.42780 - 1.24762i) q^{17} +(0.491238 + 2.78595i) q^{18} +(1.36723 + 7.75395i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-0.579320 - 0.486107i) q^{21} +(2.12931 + 1.78670i) q^{22} +(1.17391 + 2.03327i) q^{23} +(-0.388666 - 0.141463i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.779374 - 1.34991i) q^{26} +(-1.20545 - 2.08790i) q^{27} +(-1.71814 + 0.625353i) q^{28} +(2.26877 - 3.92963i) q^{29} +(-0.316844 + 0.265863i) q^{30} +10.2681 q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.08034 - 0.393213i) q^{33} +(0.633432 + 3.59237i) q^{34} +(-0.317500 + 1.80063i) q^{35} -2.82893 q^{36} +(5.23041 - 3.10530i) q^{37} -7.87357 q^{38} +(-0.111953 + 0.634919i) q^{39} +(0.173648 + 0.984808i) q^{40} +(-6.81323 - 2.47981i) q^{41} +(0.579320 - 0.486107i) q^{42} -7.55904 q^{43} +(-2.12931 + 1.78670i) q^{44} +(-1.41446 + 2.44992i) q^{45} +(-2.20622 + 0.803000i) q^{46} +(-1.50187 - 2.60131i) q^{47} +(0.206805 - 0.358197i) q^{48} +(-0.635018 + 3.60137i) q^{49} +(0.939693 + 0.342020i) q^{50} +(-0.754381 - 1.30663i) q^{51} +(1.19407 + 1.00194i) q^{52} +(-4.46406 - 3.74579i) q^{53} +(2.26551 - 0.824577i) q^{54} +(0.482676 + 2.73739i) q^{55} +(-0.317500 - 1.80063i) q^{56} +(3.06019 - 1.11382i) q^{57} +(3.47596 + 2.91668i) q^{58} +(-8.83996 - 7.41760i) q^{59} +(-0.206805 - 0.358197i) q^{60} +(8.16439 + 2.97159i) q^{61} +(-1.78303 + 10.1121i) q^{62} +(2.58622 - 4.47946i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.46474 - 0.533123i) q^{65} +(0.574839 - 0.995651i) q^{66} +(-10.2097 + 8.56694i) q^{67} -3.64779 q^{68} +(0.743890 - 0.624198i) q^{69} +(-1.71814 - 0.625353i) q^{70} +(0.720391 + 4.08554i) q^{71} +(0.491238 - 2.78595i) q^{72} -7.76993 q^{73} +(2.14987 + 5.69017i) q^{74} -0.413610 q^{75} +(1.36723 - 7.75395i) q^{76} +(-0.882528 - 5.00507i) q^{77} +(-0.605833 - 0.220505i) q^{78} +(4.38034 - 3.67554i) q^{79} -1.00000 q^{80} +(5.73737 - 4.81423i) q^{81} +(3.62524 - 6.27911i) q^{82} +(-13.2686 + 4.82937i) q^{83} +(0.378124 + 0.654930i) q^{84} +(-1.82389 + 3.15908i) q^{85} +(1.31261 - 7.44420i) q^{86} +(-1.76359 - 0.641894i) q^{87} +(-1.38981 - 2.40722i) q^{88} +(8.95509 + 7.51421i) q^{89} +(-2.16708 - 1.81840i) q^{90} +(-2.67815 + 0.974767i) q^{91} +(-0.407694 - 2.31215i) q^{92} +(-0.737480 - 4.18246i) q^{93} +(2.82259 - 1.02734i) q^{94} +(-6.03150 - 5.06103i) q^{95} +(0.316844 + 0.265863i) q^{96} +(-5.92534 - 10.2630i) q^{97} +(-3.43638 - 1.25074i) q^{98} +(1.36545 - 7.74388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.0718226	−	0.407326i	−0.0414668	−	0.235170i	0.957029	−	0.289991i	$-0.0936523\pi$
$3$	−0.0718226	−	0.407326i	−0.0414668	−	0.235170i	−0.998496	+	0.0548209i	$0.982541\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	0.413610			0.168856
$7$	1.40064	−	1.17528i	0.529393	−	0.444213i	−0.338499	−	0.940967i	$-0.609919\pi$
$7$	1.40064	−	1.17528i	0.529393	−	0.444213i	0.867892	+	0.496753i	$0.165475\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.65832	−	0.967550i	0.886107	−	0.322517i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.38981	−	2.40722i	0.419043	−	0.725804i	−0.576800	−	0.816885i	$-0.695699\pi$
$11$	1.38981	−	2.40722i	0.419043	−	0.725804i	0.995843	+	0.0910810i	$0.0290322\pi$
$12$	−0.0718226	+	0.407326i	−0.0207334	+	0.117585i
$13$	−1.46474	−	0.533123i	−0.406247	−	0.147862i	0.130811	−	0.991407i	$-0.458242\pi$
$13$	−1.46474	−	0.533123i	−0.406247	−	0.147862i	−0.537058	+	0.843546i	$0.680464\pi$
$14$	0.914204	+	1.58345i	0.244331	+	0.423194i
$15$	0.316844	+	0.265863i	0.0818087	+	0.0686456i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.42780	−	1.24762i	0.831363	−	0.302592i	0.108945	−	0.994048i	$-0.465253\pi$
$17$	3.42780	−	1.24762i	0.831363	−	0.302592i	0.722418	+	0.691456i	$0.243031\pi$
$18$	0.491238	+	2.78595i	0.115786	+	0.656654i
$19$	1.36723	+	7.75395i	0.313664	+	1.77888i	0.579613	+	0.814892i	$0.303204\pi$
$19$	1.36723	+	7.75395i	0.313664	+	1.77888i	−0.265949	+	0.963987i	$0.585685\pi$
$20$	0.939693	−	0.342020i	0.210122	−	0.0764780i
$21$	−0.579320	−	0.486107i	−0.126418	−	0.106077i
$22$	2.12931	+	1.78670i	0.453971	+	0.380927i
$23$	1.17391	+	2.03327i	0.244777	+	0.423965i	0.962069	−	0.272807i	$-0.0879520\pi$
$23$	1.17391	+	2.03327i	0.244777	+	0.423965i	−0.717292	+	0.696772i	$0.754619\pi$
$24$	−0.388666	−	0.141463i	−0.0793362	−	0.0288760i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	0.779374	−	1.34991i	0.152848	−	0.264740i
$27$	−1.20545	−	2.08790i	−0.231989	−	0.401817i
$28$	−1.71814	+	0.625353i	−0.324698	+	0.118181i
$29$	2.26877	−	3.92963i	0.421300	−	0.729713i	−0.574767	−	0.818317i	$-0.694907\pi$
$29$	2.26877	−	3.92963i	0.421300	−	0.729713i	0.996067	+	0.0886039i	$0.0282405\pi$
$30$	−0.316844	+	0.265863i	−0.0578475	+	0.0485398i
$31$	10.2681			1.84420			0.922100	−	0.386952i	$-0.126472\pi$
$31$	10.2681			1.84420			0.922100	+	0.386952i	$0.126472\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−1.08034	−	0.393213i	−0.188064	−	0.0684496i
$34$	0.633432	+	3.59237i	0.108633	+	0.616086i
$35$	−0.317500	+	1.80063i	−0.0536673	+	0.304362i
$36$	−2.82893			−0.471488
$37$	5.23041	−	3.10530i	0.859873	−	0.510508i
$37$	5.23041	−	3.10530i	0.859873	−	0.510508i
$38$	−7.87357			−1.27726
$39$	−0.111953	+	0.634919i	−0.0179269	+	0.101668i
$40$	0.173648	+	0.984808i	0.0274562	+	0.155712i
$41$	−6.81323	−	2.47981i	−1.06405	−	0.387282i	−0.250100	−	0.968220i	$-0.580464\pi$
$41$	−6.81323	−	2.47981i	−1.06405	−	0.387282i	−0.813948	+	0.580938i	$0.802686\pi$
$42$	0.579320	−	0.486107i	0.0893910	−	0.0750079i
$43$	−7.55904			−1.15274			−0.576371	−	0.817188i	$-0.695532\pi$
$43$	−7.55904			−1.15274			−0.576371	+	0.817188i	$0.695532\pi$
$44$	−2.12931	+	1.78670i	−0.321006	+	0.269356i
$45$	−1.41446	+	2.44992i	−0.210856	+	0.365213i
$46$	−2.20622	+	0.803000i	−0.325290	+	0.118396i
$47$	−1.50187	−	2.60131i	−0.219070	−	0.379441i	0.735454	−	0.677575i	$-0.236969\pi$
$47$	−1.50187	−	2.60131i	−0.219070	−	0.379441i	−0.954524	+	0.298134i	$0.903636\pi$
$48$	0.206805	−	0.358197i	0.0298497	−	0.0517013i
$49$	−0.635018	+	3.60137i	−0.0907168	+	0.514481i
$50$	0.939693	+	0.342020i	0.132893	+	0.0483690i
$51$	−0.754381	−	1.30663i	−0.105634	−	0.182964i
$52$	1.19407	+	1.00194i	0.165588	+	0.138945i
$53$	−4.46406	−	3.74579i	−0.613186	−	0.514524i	0.282468	−	0.959277i	$-0.408847\pi$
$53$	−4.46406	−	3.74579i	−0.613186	−	0.514524i	−0.895653	+	0.444753i	$0.853291\pi$
$54$	2.26551	−	0.824577i	0.308297	−	0.112211i
$55$	0.482676	+	2.73739i	0.0650840	+	0.369110i
$56$	−0.317500	−	1.80063i	−0.0424277	−	0.240619i
$57$	3.06019	−	1.11382i	0.405332	−	0.147529i
$58$	3.47596	+	2.91668i	0.456416	+	0.382978i
$59$	−8.83996	−	7.41760i	−1.15086	−	0.965690i	−0.151125	−	0.988515i	$-0.548289\pi$
$59$	−8.83996	−	7.41760i	−1.15086	−	0.965690i	−0.999739	+	0.0228250i	$0.992734\pi$
$60$	−0.206805	−	0.358197i	−0.0266984	−	0.0462430i
$61$	8.16439	+	2.97159i	1.04534	+	0.380474i	0.806903	−	0.590684i	$-0.201142\pi$
$61$	8.16439	+	2.97159i	1.04534	+	0.380474i	0.238439	+	0.971157i	$0.423364\pi$
$62$	−1.78303	+	10.1121i	−0.226445	+	1.28423i
$63$	2.58622	−	4.47946i	0.325833	−	0.564359i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.46474	−	0.533123i	0.181679	−	0.0661258i
$66$	0.574839	−	0.995651i	0.0707578	−	0.122556i
$67$	−10.2097	+	8.56694i	−1.24731	+	1.04662i	−0.250396	+	0.968144i	$0.580561\pi$
$67$	−10.2097	+	8.56694i	−1.24731	+	1.04662i	−0.996916	+	0.0784753i	$0.974995\pi$
$68$	−3.64779			−0.442359
$69$	0.743890	−	0.624198i	0.0895539	−	0.0751446i
$70$	−1.71814	−	0.625353i	−0.205357	−	0.0747439i
$71$	0.720391	+	4.08554i	0.0854947	+	0.484865i	0.997249	+	0.0741279i	$0.0236173\pi$
$71$	0.720391	+	4.08554i	0.0854947	+	0.484865i	−0.911754	+	0.410737i	$0.865272\pi$
$72$	0.491238	−	2.78595i	0.0578929	−	0.328327i
$73$	−7.76993			−0.909402			−0.454701	−	0.890644i	$-0.650254\pi$
$73$	−7.76993			−0.909402			−0.454701	+	0.890644i	$0.650254\pi$
$74$	2.14987	+	5.69017i	0.249917	+	0.661469i
$75$	−0.413610			−0.0477596
$76$	1.36723	−	7.75395i	0.156832	−	0.889439i
$77$	−0.882528	−	5.00507i	−0.100573	−	0.570380i
$78$	−0.605833	−	0.220505i	−0.0685971	−	0.0249673i
$79$	4.38034	−	3.67554i	0.492826	−	0.413530i	−0.362212	−	0.932096i	$-0.617978\pi$
$79$	4.38034	−	3.67554i	0.492826	−	0.413530i	0.855038	+	0.518566i	$0.173534\pi$
$80$	−1.00000			−0.111803
$81$	5.73737	−	4.81423i	0.637486	−	0.534914i
$82$	3.62524	−	6.27911i	0.400341	−	0.693411i
$83$	−13.2686	+	4.82937i	−1.45642	+	0.530093i	−0.944376	−	0.328868i	$-0.893333\pi$
$83$	−13.2686	+	4.82937i	−1.45642	+	0.530093i	−0.512042	+	0.858961i	$0.671111\pi$
$84$	0.378124	+	0.654930i	0.0412567	+	0.0714587i
$85$	−1.82389	+	3.15908i	−0.197829	+	0.342650i
$86$	1.31261	−	7.44420i	0.141543	−	0.802729i
$87$	−1.76359	−	0.641894i	−0.189077	−	0.0688183i
$88$	−1.38981	−	2.40722i	−0.148154	−	0.256611i
$89$	8.95509	+	7.51421i	0.949237	+	0.796505i	0.979169	−	0.203047i	$-0.0650845\pi$
$89$	8.95509	+	7.51421i	0.949237	+	0.796505i	−0.0299315	+	0.999552i	$0.509529\pi$
$90$	−2.16708	−	1.81840i	−0.228431	−	0.191676i
$91$	−2.67815	+	0.974767i	−0.280746	+	0.102183i
$92$	−0.407694	−	2.31215i	−0.0425050	−	0.241058i
$93$	−0.737480	−	4.18246i	−0.0764731	−	0.433700i
$94$	2.82259	−	1.02734i	0.291128	−	0.105962i
$95$	−6.03150	−	5.06103i	−0.618819	−	0.519251i
$96$	0.316844	+	0.265863i	0.0323377	+	0.0271346i
$97$	−5.92534	−	10.2630i	−0.601627	−	1.04205i	−0.992575	−	0.121636i	$-0.961186\pi$
$97$	−5.92534	−	10.2630i	−0.601627	−	1.04205i	0.390948	−	0.920413i	$-0.372147\pi$
$98$	−3.43638	−	1.25074i	−0.347127	−	0.126344i
$99$	1.36545	−	7.74388i	0.137233	−	0.778289i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.87950	+	4.98744i	0.286521	+	0.496268i	0.972977	−	0.230903i	$-0.0741679\pi$
$101$	2.87950	+	4.98744i	0.286521	+	0.496268i	−0.686456	+	0.727171i	$0.740835\pi$
$102$	1.41777	−	0.516027i	0.140380	−	0.0510943i
$103$	−7.71393	+	13.3609i	−0.760076	+	1.31649i	0.182734	+	0.983162i	$0.441505\pi$
$103$	−7.71393	+	13.3609i	−0.760076	+	1.31649i	−0.942811	+	0.333329i	$0.891828\pi$
$104$	−1.19407	+	1.00194i	−0.117088	+	0.0982487i
$105$	0.756248			0.0738023
$106$	4.46406	−	3.74579i	0.433588	−	0.363823i
$107$	2.53244	+	0.921734i	0.244821	+	0.0891074i	0.461516	−	0.887132i	$-0.347306\pi$
$107$	2.53244	+	0.921734i	0.244821	+	0.0891074i	−0.216695	+	0.976239i	$0.569528\pi$
$108$	0.418649	+	2.37428i	0.0402845	+	0.228465i
$109$	1.08181	−	6.13524i	0.103618	−	0.587650i	−0.888145	−	0.459564i	$-0.848006\pi$
$109$	1.08181	−	6.13524i	0.103618	−	0.587650i	0.991763	−	0.128086i	$-0.0408832\pi$
$110$	−2.77962			−0.265026
$111$	−1.64053	−	1.90745i	−0.155712	−	0.181047i
$112$	1.82841			0.172768
$113$	2.01929	−	11.4519i	0.189958	−	1.07731i	−0.729459	−	0.684025i	$-0.760228\pi$
$113$	2.01929	−	11.4519i	0.189958	−	1.07731i	0.919417	−	0.393283i	$-0.128661\pi$
$114$	0.565501	+	3.20711i	0.0529640	+	0.300374i
$115$	−2.20622	−	0.803000i	−0.205731	−	0.0748801i
$116$	−3.47596	+	2.91668i	−0.322735	+	0.270807i
$117$	−4.40958			−0.407666
$118$	8.83996	−	7.41760i	0.813784	−	0.682846i
$119$	3.33482	−	5.77608i	0.305703	−	0.529493i
$120$	0.388666	−	0.141463i	0.0354802	−	0.0129137i
$121$	1.63686	+	2.83512i	0.148805	+	0.257739i
$122$	−4.34418	+	7.52434i	−0.393304	+	0.681222i
$123$	−0.520749	+	2.95332i	−0.0469544	+	0.266291i
$124$	−9.64883	−	3.51189i	−0.866490	−	0.315377i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	3.96231	+	3.32478i	0.352991	+	0.296195i
$127$	2.19112	+	1.83857i	0.194431	+	0.163147i	0.734806	−	0.678278i	$-0.237273\pi$
$127$	2.19112	+	1.83857i	0.194431	+	0.163147i	−0.540375	+	0.841424i	$0.681718\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	0.542910	+	3.07900i	0.0478006	+	0.271090i
$130$	0.270674	+	1.53507i	0.0237397	+	0.134634i
$131$	−4.23730	+	1.54225i	−0.370215	+	0.134747i	−0.520426	−	0.853907i	$-0.674227\pi$
$131$	−4.23730	+	1.54225i	−0.370215	+	0.134747i	0.150211	+	0.988654i	$0.452005\pi$
$132$	0.880705	+	0.738999i	0.0766555	+	0.0643216i
$133$	11.0281	+	9.25364i	0.956254	+	0.802392i
$134$	−6.66390	−	11.5422i	−0.575673	−	0.997095i
$135$	2.26551	+	0.824577i	0.194984	+	0.0709683i
$136$	0.633432	−	3.59237i	0.0543163	−	0.308043i
$137$	2.93307	−	5.08023i	0.250590	−	0.434034i	−0.713099	−	0.701064i	$-0.752709\pi$
$137$	2.93307	−	5.08023i	0.250590	−	0.434034i	0.963688	+	0.267030i	$0.0860422\pi$
$138$	0.485540	+	0.840980i	0.0413319	+	0.0715890i
$139$	−2.04952	+	0.745966i	−0.173838	+	0.0632720i	−0.427473	−	0.904028i	$-0.640596\pi$
$139$	−2.04952	+	0.745966i	−0.173838	+	0.0632720i	0.253635	+	0.967300i	$0.418374\pi$
$140$	0.914204	−	1.58345i	0.0772644	−	0.133826i
$141$	−0.951716	+	0.798584i	−0.0801489	+	0.0672529i
$142$	−4.14857			−0.348140
$143$	−3.31906	+	2.78502i	−0.277554	+	0.232895i
$144$	2.65832	+	0.967550i	0.221527	+	0.0806292i
$145$	0.787936	+	4.46861i	0.0654345	+	0.371098i
$146$	1.34923	−	7.65189i	0.111663	−	0.633275i
$147$	1.51254			0.124752
$148$	−5.97705	+	1.12912i	−0.491310	+	0.0928131i
$149$	−15.1996			−1.24520			−0.622600	−	0.782540i	$-0.713924\pi$
$149$	−15.1996			−1.24520			−0.622600	+	0.782540i	$0.713924\pi$
$150$	0.0718226	−	0.407326i	0.00586429	−	0.0332581i
$151$	2.57812	+	14.6212i	0.209804	+	1.18986i	0.889698	+	0.456549i	$0.150915\pi$
$151$	2.57812	+	14.6212i	0.209804	+	1.18986i	−0.679894	+	0.733310i	$0.737974\pi$
$152$	7.39874	+	2.69292i	0.600117	+	0.218425i
$153$	7.90506	−	6.63313i	0.639086	−	0.536257i
$154$	5.08228			0.409542
$155$	−7.86580	+	6.60019i	−0.631796	+	0.530140i
$156$	0.322357	−	0.558338i	0.0258092	−	0.0447029i
$157$	8.31290	−	3.02565i	0.663442	−	0.241473i	0.0117200	−	0.999931i	$-0.496269\pi$
$157$	8.31290	−	3.02565i	0.663442	−	0.241473i	0.651722	+	0.758458i	$0.274047\pi$
$158$	2.85906	+	4.95204i	0.227455	+	0.393963i
$159$	−1.20514	+	2.08736i	−0.0955738	+	0.165539i
$160$	0.173648	−	0.984808i	0.0137281	−	0.0778559i
$161$	4.03388	+	1.46821i	0.317914	+	0.115711i
$162$	3.74480	+	6.48619i	0.294220	+	0.509603i
$163$	13.9904	+	11.7393i	1.09581	+	0.919494i	0.997136	−	0.0756261i	$-0.0240955\pi$
$163$	13.9904	+	11.7393i	1.09581	+	0.919494i	0.0986738	+	0.995120i	$0.468540\pi$
$164$	5.55420	+	4.66052i	0.433710	+	0.363926i
$165$	1.08034	−	0.393213i	0.0841047	−	0.0306116i
$166$	−2.45194	−	13.9056i	−0.190307	−	1.07929i
$167$	2.16795	+	12.2951i	0.167761	+	0.951422i	0.946171	+	0.323666i	$0.104915\pi$
$167$	2.16795	+	12.2951i	0.167761	+	0.951422i	−0.778410	+	0.627756i	$0.783974\pi$
$168$	−0.710641	+	0.258652i	−0.0548271	+	0.0199554i
$169$	−8.09732	−	6.79446i	−0.622871	−	0.522651i
$170$	−2.79437	−	2.34475i	−0.214318	−	0.179834i
$171$	11.1369	+	19.2896i	0.851658	+	1.47512i
$172$	7.10317	+	2.58534i	0.541612	+	0.197131i
$173$	−3.01768	+	17.1141i	−0.229430	+	1.30116i	0.624604	+	0.780942i	$0.285260\pi$
$173$	−3.01768	+	17.1141i	−0.229430	+	1.30116i	−0.854033	+	0.520218i	$0.825851\pi$
$174$	0.938387	−	1.62533i	0.0711389	−	0.123216i
$175$	−0.914204	−	1.58345i	−0.0691073	−	0.119697i
$176$	2.61199	−	0.950686i	0.196886	−	0.0716606i
$177$	−2.38648	+	4.13350i	−0.179379	+	0.310693i
$178$	−8.95509	+	7.51421i	−0.671212	+	0.563214i
$179$	−5.27399			−0.394196			−0.197098	−	0.980384i	$-0.563152\pi$
$179$	−5.27399			−0.394196			−0.197098	+	0.980384i	$0.563152\pi$
$180$	2.16708	−	1.81840i	0.161525	−	0.135535i
$181$	18.5847	+	6.76426i	1.38139	+	0.502784i	0.922598	−	0.385762i	$-0.126061\pi$
$181$	18.5847	+	6.76426i	1.38139	+	0.502784i	0.458788	+	0.888546i	$0.348284\pi$
$182$	−0.494902	−	2.80673i	−0.0366846	−	0.208049i
$183$	0.624021	−	3.53900i	0.0461290	−	0.261610i
$184$	2.34781			0.173083
$185$	−2.01068	+	5.74083i	−0.147828	+	0.422075i
$186$	4.24698			0.311403
$187$	1.76070	−	9.98542i	0.128755	−	0.730206i
$188$	0.521594	+	2.95811i	0.0380411	+	0.215742i
$189$	−4.14227	−	1.50766i	−0.301306	−	0.109666i
$190$	6.03150	−	5.06103i	0.437571	−	0.367166i
$191$	−12.7894			−0.925405			−0.462703	−	0.886514i	$-0.653120\pi$
$191$	−12.7894			−0.925405			−0.462703	+	0.886514i	$0.653120\pi$
$192$	−0.316844	+	0.265863i	−0.0228662	+	0.0191870i
$193$	−4.86936	+	8.43398i	−0.350504	+	0.607091i	−0.986338	−	0.164735i	$-0.947323\pi$
$193$	−4.86936	+	8.43398i	−0.350504	+	0.607091i	0.635834	+	0.771826i	$0.280656\pi$
$194$	11.1360	−	4.05317i	0.799518	−	0.291001i
$195$	−0.322357	−	0.558338i	−0.0230845	−	0.0399834i
$196$	1.82846	−	3.16699i	0.130604	−	0.226213i
$197$	2.17105	−	12.3127i	0.154681	−	0.877241i	−0.804396	−	0.594094i	$-0.797511\pi$
$197$	2.17105	−	12.3127i	0.154681	−	0.877241i	0.959077	−	0.283146i	$-0.0913782\pi$
$198$	7.38912	+	2.68942i	0.525122	+	0.191129i
$199$	−1.68858	−	2.92471i	−0.119700	−	0.207327i	0.799948	−	0.600069i	$-0.204860\pi$
$199$	−1.68858	−	2.92471i	−0.119700	−	0.207327i	−0.919649	+	0.392741i	$0.871527\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	4.22283	+	3.54337i	0.297855	+	0.249930i
$202$	−5.41169	+	1.96969i	−0.380765	+	0.138587i
$203$	−1.44067	−	8.17044i	−0.101115	−	0.573452i
$204$	0.261994	+	1.48584i	0.0183432	+	0.104030i
$205$	6.81323	−	2.47981i	0.475857	−	0.173198i
$206$	−11.8184	−	9.91684i	−0.823429	−	0.690939i
$207$	5.08791	+	4.26926i	0.353634	+	0.296734i
$208$	−0.779374	−	1.34991i	−0.0540398	−	0.0935998i
$209$	20.5657	+	7.48529i	1.42256	+	0.517768i
$210$	−0.131321	+	0.744759i	−0.00906202	+	0.0513933i
$211$	0.225587	−	0.390728i	0.0155300	−	0.0268988i	−0.858156	−	0.513389i	$-0.828390\pi$
$211$	0.225587	−	0.390728i	0.0155300	−	0.0268988i	0.873686	+	0.486490i	$0.161723\pi$
$212$	2.91371	+	5.04669i	0.200114	+	0.346608i
$213$	1.61241	−	0.586869i	0.110480	−	0.0402116i
$214$	−1.34749	+	2.33391i	−0.0921122	+	0.159543i
$215$	5.79056	−	4.85886i	0.394913	−	0.331371i
$216$	−2.41090			−0.164041
$217$	14.3819	−	12.0678i	0.976306	−	0.819218i
$218$	5.85418	+	2.13075i	0.396495	+	0.144312i
$219$	0.558057	+	3.16490i	0.0377100	+	0.213864i
$220$	0.482676	−	2.73739i	0.0325420	−	0.184555i
$221$	−5.68598			−0.382480
$222$	2.16335	−	1.28438i	0.145194	−	0.0862021i
$223$	−2.28366			−0.152925			−0.0764624	−	0.997072i	$-0.524363\pi$
$223$	−2.28366			−0.152925			−0.0764624	+	0.997072i	$0.524363\pi$
$224$	−0.317500	+	1.80063i	−0.0212138	+	0.120310i
$225$	−0.491238	−	2.78595i	−0.0327492	−	0.185730i
$226$	10.9273	+	3.97722i	0.726874	+	0.264561i
$227$	−10.3080	+	8.64946i	−0.684168	+	0.574085i	−0.917221	−	0.398379i	$-0.869573\pi$
$227$	−10.3080	+	8.64946i	−0.684168	+	0.574085i	0.233053	+	0.972464i	$0.425128\pi$
$228$	−3.25659			−0.215673
$229$	−15.5912	+	13.0826i	−1.03030	+	0.864523i	−0.990886	−	0.134700i	$-0.956993\pi$
$229$	−15.5912	+	13.0826i	−1.03030	+	0.864523i	−0.0394118	+	0.999223i	$0.512548\pi$
$230$	1.17391	−	2.03327i	0.0774052	−	0.134070i
$231$	−1.97531	+	0.718954i	−0.129966	+	0.0473037i
$232$	−2.26877	−	3.92963i	−0.148952	−	0.257993i
$233$	8.10911	−	14.0454i	0.531246	−	0.920144i	−0.468089	−	0.883681i	$-0.655057\pi$
$233$	8.10911	−	14.0454i	0.531246	−	0.920144i	0.999335	−	0.0364633i	$-0.0116092\pi$
$234$	0.765716	−	4.34259i	0.0500564	−	0.283884i
$235$	2.82259	+	1.02734i	0.184126	+	0.0670162i
$236$	5.76987	+	9.99371i	0.375587	+	0.650535i
$237$	−1.81175	−	1.52024i	−0.117686	−	0.0987502i
$238$	5.10925	+	4.28717i	0.331183	+	0.277896i
$239$	−8.79514	+	3.20117i	−0.568910	+	0.207066i	−0.610429	−	0.792071i	$-0.709003\pi$
$239$	−8.79514	+	3.20117i	−0.568910	+	0.207066i	0.0415182	+	0.999138i	$0.486781\pi$
$240$	0.0718226	+	0.407326i	0.00463613	+	0.0262928i
$241$	0.817231	+	4.63475i	0.0526425	+	0.298550i	0.999750	−	0.0223666i	$-0.00712010\pi$
$241$	0.817231	+	4.63475i	0.0526425	+	0.298550i	−0.947107	+	0.320917i	$0.896009\pi$
$242$	−3.07629	+	1.11968i	−0.197751	+	0.0719756i
$243$	−7.91361	−	6.64031i	−0.507658	−	0.425976i
$244$	−6.65567	−	5.58477i	−0.426086	−	0.357528i
$245$	−1.82846	−	3.16699i	−0.116816	−	0.202331i
$246$	−2.81802	−	1.02568i	−0.179670	−	0.0653947i
$247$	2.13117	−	12.0865i	0.135603	−	0.769043i
$248$	5.13403	−	8.89241i	0.326011	−	0.564668i
$249$	2.92012	+	5.05779i	0.185055	+	0.320525i
$250$	−0.939693	+	0.342020i	−0.0594314	+	0.0216313i
$251$	−9.53379	+	16.5130i	−0.601768	+	1.04229i	0.390786	+	0.920482i	$0.372203\pi$
$251$	−9.53379	+	16.5130i	−0.601768	+	1.04229i	−0.992553	+	0.121810i	$0.961130\pi$
$252$	−3.96231	+	3.32478i	−0.249602	+	0.209441i
$253$	6.52603			0.410288
$254$	−2.19112	+	1.83857i	−0.137483	+	0.115362i
$255$	1.41777	+	0.516027i	0.0887844	+	0.0323149i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.46680	+	13.9899i	−0.153875	+	0.872668i	0.805932	+	0.592008i	$0.201664\pi$
$257$	−2.46680	+	13.9899i	−0.153875	+	0.872668i	−0.959807	+	0.280660i	$0.909447\pi$
$258$	−3.12649			−0.194647
$259$	3.67634	−	10.4966i	0.228437	−	0.652226i
$260$	−1.55875			−0.0966694
$261$	2.22901	−	12.6414i	0.137972	−	0.782481i
$262$	−0.783022	−	4.44074i	−0.0483753	−	0.274350i
$263$	1.81016	+	0.658845i	0.111619	+	0.0406261i	0.397226	−	0.917721i	$-0.369973\pi$
$263$	1.81016	+	0.658845i	0.111619	+	0.0406261i	−0.285607	+	0.958347i	$0.592195\pi$
$264$	−0.880705	+	0.738999i	−0.0542036	+	0.0454822i
$265$	5.82742			0.357975
$266$	−11.0281	+	9.25364i	−0.676173	+	0.567377i
$267$	2.41756	−	4.18733i	0.147952	−	0.256261i
$268$	12.5240	−	4.55838i	0.765027	−	0.278447i
$269$	−9.92942	−	17.1983i	−0.605407	−	1.04860i	−0.991987	−	0.126340i	$-0.959677\pi$
$269$	−9.92942	−	17.1983i	−0.605407	−	1.04860i	0.386580	−	0.922256i	$-0.373656\pi$
$270$	−1.20545	+	2.08790i	−0.0733614	+	0.127066i
$271$	3.44637	−	19.5454i	0.209352	−	1.18730i	−0.681090	−	0.732200i	$-0.738494\pi$
$271$	3.44637	−	19.5454i	0.209352	−	1.18730i	0.890442	−	0.455096i	$-0.150395\pi$
$272$	3.42780	+	1.24762i	0.207841	+	0.0756479i
$273$	0.589400	+	1.02087i	0.0356721	+	0.0617859i
$274$	4.49373	+	3.77069i	0.271476	+	0.227796i
$275$	−2.12931	−	1.78670i	−0.128402	−	0.107742i
$276$	−0.912517	+	0.332129i	−0.0549270	+	0.0199918i
$277$	3.14599	+	17.8418i	0.189024	+	1.07201i	0.920675	+	0.390330i	$0.127639\pi$
$277$	3.14599	+	17.8418i	0.189024	+	1.07201i	−0.731651	+	0.681679i	$0.761250\pi$
$278$	−0.378737	−	2.14792i	−0.0227151	−	0.128824i
$279$	27.2958	−	9.93487i	1.63416	−	0.594785i
$280$	1.40064	+	1.17528i	0.0837044	+	0.0702363i
$281$	−19.8454	−	16.6523i	−1.18388	−	0.993391i	−0.999945	−	0.0104514i	$-0.996673\pi$
$281$	−19.8454	−	16.6523i	−1.18388	−	0.993391i	−0.183931	−	0.982939i	$-0.558882\pi$
$282$	−0.621188	−	1.07593i	−0.0369912	−	0.0640707i
$283$	−16.1238	−	5.86857i	−0.958459	−	0.348851i	−0.185030	−	0.982733i	$-0.559238\pi$
$283$	−16.1238	−	5.86857i	−0.958459	−	0.348851i	−0.773429	+	0.633882i	$0.781460\pi$
$284$	0.720391	−	4.08554i	0.0427474	−	0.242432i
$285$	−1.62829	+	2.82029i	−0.0964518	+	0.167059i
$286$	−2.16636	−	3.75225i	−0.128100	−	0.221875i
$287$	−12.4574	+	4.53411i	−0.735335	+	0.267640i
$288$	−1.41446	+	2.44992i	−0.0833481	+	0.144363i
$289$	−2.82949	+	2.37423i	−0.166441	+	0.139660i
$290$	−4.53754			−0.266454
$291$	−3.75481	+	3.15066i	−0.220111	+	0.184695i
$292$	7.30135	+	2.65747i	0.427279	+	0.155517i
$293$	−0.855631	−	4.85253i	−0.0499865	−	0.283488i	0.949560	−	0.313584i	$-0.101530\pi$
$293$	−0.855631	−	4.85253i	−0.0499865	−	0.283488i	−0.999547	+	0.0300963i	$0.990419\pi$
$294$	−0.262650	+	1.48956i	−0.0153180	+	0.0868730i
$295$	11.5397			0.671870
$296$	−0.0740626	−	6.08231i	−0.00430480	−	0.353527i
$297$	−6.70139			−0.388854
$298$	2.63938	−	14.9687i	0.152895	−	0.867113i
$299$	−0.635492	−	3.60405i	−0.0367514	−	0.208428i
$300$	0.388666	+	0.141463i	0.0224397	+	0.00816737i
$301$	−10.5875	+	8.88397i	−0.610254	+	0.512064i
$302$	−14.8468			−0.854337
$303$	1.82470	−	1.53111i	0.104826	−	0.0879598i
$304$	−3.93679	+	6.81871i	−0.225790	+	0.391080i
$305$	−8.16439	+	2.97159i	−0.467491	+	0.170153i
$306$	5.15966	+	8.93680i	0.294958	+	0.510883i
$307$	13.2229	−	22.9028i	0.754672	−	1.30713i	−0.190866	−	0.981616i	$-0.561129\pi$
$307$	13.2229	−	22.9028i	0.754672	−	1.30713i	0.945537	−	0.325514i	$-0.105537\pi$
$308$	−0.882528	+	5.00507i	−0.0502867	+	0.285190i
$309$	5.99629	+	2.18247i	0.341117	+	0.124157i
$310$	−5.13403	−	8.89241i	−0.291594	−	0.505055i
$311$	6.98331	+	5.85970i	0.395987	+	0.332273i	0.818940	−	0.573879i	$-0.194562\pi$
$311$	6.98331	+	5.85970i	0.395987	+	0.332273i	−0.422953	+	0.906152i	$0.639006\pi$
$312$	0.493879	+	0.414414i	0.0279604	+	0.0234616i
$313$	−0.246169	+	0.0895982i	−0.0139143	+	0.00506439i	−0.348968	−	0.937135i	$-0.613468\pi$
$313$	−0.246169	+	0.0895982i	−0.0139143	+	0.00506439i	0.335054	+	0.942199i	$0.391246\pi$
$314$	1.53616	+	8.71200i	0.0866906	+	0.491647i
$315$	0.898184	+	5.09385i	0.0506069	+	0.287006i
$316$	−5.37328	+	1.95571i	−0.302270	+	0.110017i
$317$	−10.3019	−	8.64434i	−0.578613	−	0.485514i	0.305878	−	0.952071i	$-0.401050\pi$
$317$	−10.3019	−	8.64434i	−0.578613	−	0.485514i	−0.884491	+	0.466556i	$0.845494\pi$
$318$	−1.84638	−	1.54930i	−0.103540	−	0.0868803i
$319$	−6.30632	−	10.9229i	−0.353086	−	0.611563i
$320$	0.939693	+	0.342020i	0.0525304	+	0.0191195i
$321$	0.193560	−	1.09773i	0.0108035	−	0.0612695i
$322$	−2.14638	+	3.71764i	−0.119613	+	0.207176i
$323$	14.3606	+	24.8732i	0.799043	+	1.38398i
$324$	−7.03793	+	2.56160i	−0.390996	+	0.142311i
$325$	−0.779374	+	1.34991i	−0.0432319	+	0.0748798i
$326$	−13.9904	+	11.7393i	−0.774855	+	0.650180i
$327$	−2.57674			−0.142494
$328$	−5.55420	+	4.66052i	−0.306679	+	0.257334i
$329$	−5.16085	−	1.87840i	−0.284527	−	0.103559i
$330$	0.199640	+	1.13221i	0.0109898	+	0.0623262i
$331$	−0.423905	+	2.40409i	−0.0232999	+	0.132141i	−0.994239	−	0.107187i	$-0.965816\pi$
$331$	−0.423905	+	2.40409i	−0.0232999	+	0.132141i	0.970939	+	0.239327i	$0.0769269\pi$
$332$	14.1201			0.774944
$333$	10.8996	−	13.3156i	0.597293	−	0.729688i
$334$	−12.4848			−0.683135
$335$	2.31435	−	13.1253i	0.126446	−	0.717113i
$336$	−0.131321	−	0.744759i	−0.00716415	−	0.0406299i
$337$	−23.2370	−	8.45759i	−1.26580	−	0.460714i	−0.380090	−	0.924950i	$-0.624107\pi$
$337$	−23.2370	−	8.45759i	−1.26580	−	0.460714i	−0.885712	+	0.464236i	$0.846329\pi$
$338$	8.09732	−	6.79446i	0.440436	−	0.369570i
$339$	−4.80971			−0.261228
$340$	2.79437	−	2.34475i	0.151546	−	0.127162i
$341$	14.2707	−	24.7175i	0.772799	−	1.33853i
$342$	−20.9305	+	7.61807i	−1.13179	+	0.411938i
$343$	9.74260	+	16.8747i	0.526051	+	0.911147i
$344$	−3.77952	+	6.54632i	−0.203778	+	0.352954i
$345$	−0.168626	+	0.956327i	−0.00907853	+	0.0514869i
$346$	−16.3301	−	5.94366i	−0.877910	−	0.319533i
$347$	−3.54376	−	6.13797i	−0.190239	−	0.329503i	0.755090	−	0.655621i	$-0.227593\pi$
$347$	−3.54376	−	6.13797i	−0.190239	−	0.329503i	−0.945329	+	0.326117i	$0.894260\pi$
$348$	1.43769	+	1.20637i	0.0770684	+	0.0646680i
$349$	9.26221	+	7.77192i	0.495795	+	0.416021i	0.856098	−	0.516814i	$-0.172882\pi$
$349$	9.26221	+	7.77192i	0.495795	+	0.416021i	−0.360303	+	0.932835i	$0.617327\pi$
$350$	1.71814	−	0.625353i	0.0918386	−	0.0334265i
$351$	0.652568	+	3.70090i	0.0348315	+	0.197539i
$352$	0.482676	+	2.73739i	0.0257267	+	0.145903i
$353$	30.1327	−	10.9674i	1.60380	−	0.583736i	0.623601	−	0.781742i	$-0.285669\pi$
$353$	30.1327	−	10.9674i	1.60380	−	0.583736i	0.980201	+	0.198006i	$0.0634466\pi$
$354$	−3.65629	−	3.06800i	−0.194330	−	0.163062i
$355$	−3.17799	−	2.66665i	−0.168670	−	0.141531i
$356$	−5.84502	−	10.1239i	−0.309785	−	0.536564i
$357$	−2.59227	−	0.943508i	−0.137197	−	0.0499357i
$358$	0.915818	−	5.19386i	0.0484025	−	0.274504i
$359$	10.9698	−	19.0002i	0.578962	−	1.00279i	−0.416637	−	0.909073i	$-0.636791\pi$
$359$	10.9698	−	19.0002i	0.578962	−	1.00279i	0.995599	−	0.0937185i	$-0.0298754\pi$
$360$	1.41446	+	2.44992i	0.0745488	+	0.129122i
$361$	−40.4003	+	14.7045i	−2.12633	+	0.773921i
$362$	−9.88869	+	17.1277i	−0.519738	+	0.900212i
$363$	1.03726	−	0.870362i	0.0544419	−	0.0456822i
$364$	2.85003			0.149382
$365$	5.95211	−	4.99442i	0.311548	−	0.261420i
$366$	3.37687	+	1.22908i	0.176512	+	0.0642451i
$367$	1.21498	+	6.89050i	0.0634215	+	0.359681i	0.999958	+	0.00911241i	$0.00290061\pi$
$367$	1.21498	+	6.89050i	0.0634215	+	0.359681i	−0.936537	+	0.350569i	$0.885988\pi$
$368$	−0.407694	+	2.31215i	−0.0212525	+	0.120529i
$369$	−20.5111			−1.06776
$370$	−5.30447	−	2.97702i	−0.275766	−	0.154768i
$371$	−10.6549			−0.553175
$372$	−0.737480	+	4.18246i	−0.0382365	+	0.216850i
$373$	−4.85662	−	27.5433i	−0.251467	−	1.42614i	−0.804982	−	0.593299i	$-0.797825\pi$
$373$	−4.85662	−	27.5433i	−0.251467	−	1.42614i	0.553516	−	0.832839i	$-0.313286\pi$
$374$	9.52798	+	3.46790i	0.492680	+	0.179321i
$375$	0.316844	−	0.265863i	0.0163617	−	0.0137291i
$376$	−3.00374			−0.154906
$377$	−5.41814	+	4.54636i	−0.279049	+	0.234150i
$378$	2.20406	−	3.81754i	0.113364	−	0.196353i
$379$	−26.0708	+	9.48901i	−1.33917	+	0.487418i	−0.909551	−	0.415593i	$-0.863574\pi$
$379$	−26.0708	+	9.48901i	−1.33917	+	0.487418i	−0.429619	+	0.903010i	$0.641352\pi$
$380$	3.93679	+	6.81871i	0.201953	+	0.349793i
$381$	0.591526	−	1.02455i	0.0303048	−	0.0524894i
$382$	2.22085	−	12.5951i	0.113628	−	0.644419i
$383$	21.1308	+	7.69098i	1.07973	+	0.392991i	0.819808	−	0.572638i	$-0.194080\pi$
$383$	21.1308	+	7.69098i	1.07973	+	0.392991i	0.259925	+	0.965629i	$0.416302\pi$
$384$	−0.206805	−	0.358197i	−0.0105535	−	0.0182792i
$385$	3.89325	+	3.26683i	0.198418	+	0.166493i
$386$	−7.46030	−	6.25993i	−0.379719	−	0.318622i
$387$	−20.0944	+	7.31375i	−1.02145	+	0.371779i
$388$	2.05785	+	11.6706i	0.104471	+	0.592487i
$389$	4.07147	+	23.0904i	0.206432	+	1.17073i	0.895171	+	0.445723i	$0.147053\pi$
$389$	4.07147	+	23.0904i	0.206432	+	1.17073i	−0.688739	+	0.725009i	$0.741836\pi$
$390$	0.605833	−	0.220505i	0.0306775	−	0.0111657i
$391$	6.56066	+	5.50504i	0.331787	+	0.278402i
$392$	2.80137	+	2.35062i	0.141490	+	0.118724i
$393$	0.932535	+	1.61520i	0.0470402	+	0.0814759i
$394$	11.7486	+	4.27614i	0.591886	+	0.215429i
$395$	−0.992942	+	5.63125i	−0.0499603	+	0.283339i
$396$	−3.93167	+	6.80985i	−0.197574	+	0.342208i
$397$	13.9389	+	24.1429i	0.699573	+	1.21170i	0.968614	+	0.248568i	$0.0799599\pi$
$397$	13.9389	+	24.1429i	0.699573	+	1.21170i	−0.269041	+	0.963129i	$0.586707\pi$
$398$	3.17350	−	1.15506i	0.159073	−	0.0578979i
$399$	2.97719	−	5.15664i	0.149046	−	0.258155i
$400$	0.766044	−	0.642788i	0.0383022	−	0.0321394i
$401$	−6.90843			−0.344991			−0.172495	−	0.985010i	$-0.555183\pi$
$401$	−6.90843			−0.344991			−0.172495	+	0.985010i	$0.555183\pi$
$402$	−4.22283	+	3.54337i	−0.210616	+	0.176727i
$403$	−15.0401	−	5.47414i	−0.749200	−	0.272687i
$404$	−1.00004	−	5.67150i	−0.0497538	−	0.282168i
$405$	−1.30056	+	7.37582i	−0.0646252	+	0.366508i
$406$	8.29648			0.411747
$407$	−0.205866	−	16.9065i	−0.0102044	−	0.838024i
$408$	−1.50876			−0.0746948
$409$	−4.74780	+	26.9261i	−0.234764	+	1.33141i	0.608347	+	0.793671i	$0.291833\pi$
$409$	−4.74780	+	26.9261i	−0.234764	+	1.33141i	−0.843111	+	0.537740i	$0.819278\pi$
$410$	1.25903	+	7.14034i	0.0621792	+	0.352636i
$411$	−2.27998	−	0.829843i	−0.112463	−	0.0409331i
$412$	11.8184	−	9.91684i	0.582252	−	0.488568i
$413$	−21.0994			−1.03823
$414$	−5.08791	+	4.26926i	−0.250057	+	0.209823i
$415$	7.06007	−	12.2284i	0.346565	−	0.600269i
$416$	1.46474	−	0.533123i	0.0718150	−	0.0261385i
$417$	0.451054	+	0.781248i	0.0220882	+	0.0382579i
$418$	−10.9428	+	18.9534i	−0.535228	+	0.927042i
$419$	3.00104	−	17.0198i	0.146611	−	0.831470i	−0.819449	−	0.573152i	$-0.805721\pi$
$419$	3.00104	−	17.0198i	0.146611	−	0.831470i	0.966060	−	0.258318i	$-0.0831683\pi$
$420$	−0.710641	−	0.258652i	−0.0346757	−	0.0126209i
$421$	−9.44964	−	16.3673i	−0.460547	−	0.797691i	0.538441	−	0.842663i	$-0.319013\pi$
$421$	−9.44964	−	16.3673i	−0.460547	−	0.797691i	−0.998988	+	0.0449721i	$0.985680\pi$
$422$	0.345619	+	0.290009i	0.0168245	+	0.0141174i
$423$	−6.50935	−	5.46200i	−0.316496	−	0.265571i
$424$	−5.47598	+	1.99309i	−0.265937	+	0.0967932i
$425$	−0.633432	−	3.59237i	−0.0307260	−	0.174256i
$426$	0.297961	+	1.68982i	0.0144363	+	0.0818721i
$427$	14.9278	−	5.43329i	0.722409	−	0.262935i
$428$	−2.06447	−	1.73229i	−0.0997898	−	0.0837336i
$429$	1.37280	+	1.15191i	0.0662792	+	0.0556149i
$430$	3.77952	+	6.54632i	0.182265	+	0.315691i
$431$	−11.0313	−	4.01505i	−0.531357	−	0.193398i	0.0623872	−	0.998052i	$-0.480129\pi$
$431$	−11.0313	−	4.01505i	−0.531357	−	0.193398i	−0.593744	+	0.804654i	$0.702351\pi$
$432$	0.418649	−	2.37428i	0.0201423	−	0.114232i
$433$	16.4183	−	28.4373i	0.789012	−	1.36661i	−0.137561	−	0.990493i	$-0.543926\pi$
$433$	16.4183	−	28.4373i	0.789012	−	1.36661i	0.926573	−	0.376115i	$-0.122740\pi$
$434$	9.38711	+	16.2590i	0.450596	+	0.780455i
$435$	1.76359	−	0.641894i	0.0845577	−	0.0307765i
$436$	−3.11494	+	5.39524i	−0.149179	+	0.258385i
$437$	−14.1609	+	11.8824i	−0.677406	+	0.568411i
$438$	−3.21372			−0.153558
$439$	16.9441	−	14.2178i	0.808699	−	0.678579i	−0.141598	−	0.989924i	$-0.545224\pi$
$439$	16.9441	−	14.2178i	0.808699	−	0.678579i	0.950297	+	0.311345i	$0.100780\pi$
$440$	2.61199	+	0.950686i	0.124522	+	0.0453222i
$441$	1.79642	+	10.1880i	0.0855438	+	0.485143i
$442$	0.987360	−	5.59960i	0.0469639	−	0.266346i
$443$	33.4209			1.58787			0.793937	−	0.608000i	$-0.208028\pi$
$443$	33.4209			1.58787			0.793937	+	0.608000i	$0.208028\pi$
$444$	0.889208	+	2.35351i	0.0421999	+	0.111693i
$445$	−11.6900			−0.554161
$446$	0.396553	−	2.24896i	0.0187773	−	0.106491i
$447$	1.09168	+	6.19120i	0.0516345	+	0.292834i
$448$	−1.71814	−	0.625353i	−0.0811746	−	0.0295451i
$449$	6.20585	−	5.20732i	0.292872	−	0.245749i	−0.484498	−	0.874792i	$-0.660998\pi$
$449$	6.20585	−	5.20732i	0.292872	−	0.245749i	0.777370	+	0.629044i	$0.216553\pi$
$450$	2.82893			0.133357
$451$	−15.4385	+	12.9545i	−0.726973	+	0.610003i
$452$	−5.81430	+	10.0707i	−0.273482	+	0.473684i
$453$	5.77045	−	2.10027i	0.271119	−	0.0986794i
$454$	−6.72809	−	11.6534i	−0.315765	−	0.546921i
$455$	1.42501	−	2.46820i	0.0668057	−	0.115711i
$456$	0.565501	−	3.20711i	0.0264820	−	0.150187i
$457$	21.4170	+	7.79517i	1.00185	+	0.364643i	0.790297	−	0.612724i	$-0.209926\pi$
$457$	21.4170	+	7.79517i	1.00185	+	0.364643i	0.211551	+	0.977367i	$0.432149\pi$
$458$	−10.1765	−	17.6261i	−0.475515	−	0.823616i
$459$	−6.73695	−	5.65297i	−0.314454	−	0.263858i
$460$	1.79853	+	1.50915i	0.0838569	+	0.0703643i
$461$	34.5043	−	12.5585i	1.60702	−	0.584909i	0.626175	−	0.779682i	$-0.284619\pi$
$461$	34.5043	−	12.5585i	1.60702	−	0.584909i	0.980848	+	0.194774i	$0.0623973\pi$
$462$	−0.365023	−	2.07015i	−0.0169824	−	0.0963119i
$463$	−1.29322	−	7.33423i	−0.0601011	−	0.340850i	0.939899	−	0.341453i	$-0.110919\pi$
$463$	−1.29322	−	7.33423i	−0.0601011	−	0.340850i	−1.00000		0.000603012i	$0.999808\pi$
$464$	4.26390	−	1.55193i	0.197946	−	0.0720466i
$465$	3.25337	+	2.72990i	0.150872	+	0.126596i
$466$	12.4239	+	10.4249i	0.575525	+	0.482923i
$467$	8.67123	+	15.0190i	0.401257	+	0.694997i	0.993878	−	0.110484i	$-0.0352402\pi$
$467$	8.67123	+	15.0190i	0.401257	+	0.694997i	−0.592621	+	0.805481i	$0.701907\pi$
$468$	4.14365	+	1.50817i	0.191540	+	0.0697150i
$469$	−4.23157	+	23.9984i	−0.195396	+	1.10815i
$470$	−1.50187	+	2.60131i	−0.0692761	+	0.119990i
$471$	−1.82948	−	3.16875i	−0.0842980	−	0.146008i
$472$	−10.8438	+	3.94682i	−0.499127	+	0.181667i
$473$	−10.5056	+	18.1963i	−0.483049	+	0.836665i
$474$	1.81175	−	1.52024i	0.0832165	−	0.0698269i
$475$	7.87357			0.361264
$476$	−5.10925	+	4.28717i	−0.234182	+	0.196502i
$477$	−15.4911	−	5.63832i	−0.709291	−	0.258161i
$478$	−1.62528	−	9.21740i	−0.0743384	−	0.421594i
$479$	−4.11002	+	23.3091i	−0.187792	+	1.06502i	0.734524	+	0.678583i	$0.237405\pi$
$479$	−4.11002	+	23.3091i	−0.187792	+	1.06502i	−0.922316	+	0.386437i	$0.873706\pi$
$480$	−0.413610			−0.0188786
$481$	−9.31671	+	1.76001i	−0.424805	+	0.0802497i
$482$	−4.70625			−0.214364
$483$	0.308318	−	1.74856i	0.0140289	−	0.0795621i
$484$	−0.568475	−	3.22398i	−0.0258398	−	0.146545i
$485$	11.1360	+	4.05317i	0.505659	+	0.184045i
$486$	7.91361	−	6.64031i	0.358969	−	0.301211i
$487$	−19.7695			−0.895843			−0.447921	−	0.894073i	$-0.647836\pi$
$487$	−19.7695			−0.895843			−0.447921	+	0.894073i	$0.647836\pi$
$488$	6.65567	−	5.58477i	0.301288	−	0.252811i
$489$	3.77691	−	6.54179i	0.170798	−	0.295830i
$490$	3.43638	−	1.25074i	0.155240	−	0.0565027i
$491$	10.6049	+	18.3682i	0.478592	+	0.828945i	0.999699	−	0.0245461i	$-0.00781405\pi$
$491$	10.6049	+	18.3682i	0.478592	+	0.828945i	−0.521107	+	0.853491i	$0.674481\pi$
$492$	1.49944	−	2.59710i	0.0675999	−	0.117086i
$493$	2.87422	−	16.3005i	0.129449	−	0.734139i
$494$	11.5328	+	4.19758i	0.518883	+	0.188858i
$495$	3.93167	+	6.80985i	0.176715	+	0.306080i
$496$	7.86580	+	6.60019i	0.353185	+	0.296357i
$497$	5.81066	+	4.87572i	0.260644	+	0.218706i
$498$	−5.48803	+	1.99748i	−0.245924	+	0.0895091i
$499$	−1.85214	−	10.5040i	−0.0829132	−	0.470224i	−0.997787	−	0.0664850i	$-0.978822\pi$
$499$	−1.85214	−	10.5040i	−0.0829132	−	0.470224i	0.914874	−	0.403739i	$-0.132290\pi$
$500$	−0.173648	−	0.984808i	−0.00776578	−	0.0440419i
$501$	4.85240	−	1.76613i	0.216789	−	0.0789049i
$502$	−14.6066	−	12.2564i	−0.651925	−	0.547030i
$503$	−12.3408	−	10.3552i	−0.550249	−	0.461714i	0.324776	−	0.945791i	$-0.394711\pi$
$503$	−12.3408	−	10.3552i	−0.550249	−	0.461714i	−0.875025	+	0.484077i	$0.839155\pi$
$504$	−2.58622	−	4.47946i	−0.115199	−	0.199531i
$505$	−5.41169	−	1.96969i	−0.240817	−	0.0876502i
$506$	−1.13323	+	6.42688i	−0.0503784	+	0.285710i
$507$	−2.18599	+	3.78625i	−0.0970833	+	0.168153i
$508$	−1.43015	−	2.47710i	−0.0634528	−	0.109903i
$509$	9.59007	−	3.49050i	0.425072	−	0.154714i	−0.120621	−	0.992699i	$-0.538489\pi$
$509$	9.59007	−	3.49050i	0.425072	−	0.154714i	0.545693	+	0.837985i	$0.316266\pi$
$510$	−0.754381	+	1.30663i	−0.0334046	+	0.0578584i
$511$	−10.8829	+	9.13183i	−0.481431	+	0.403968i
$512$	−1.00000			−0.0441942
$513$	14.5414	−	12.2017i	0.642017	−	0.538716i
$514$	−13.3490	−	4.85865i	−0.588801	−	0.214306i
$515$	−2.67902	−	15.1935i	−0.118052	−	0.669505i
$516$	0.542910	−	3.07900i	0.0239003	−	0.135545i
$517$	−8.34925			−0.367200
$518$	9.69873	+	5.44320i	0.426138	+	0.239161i
$519$	7.18776			0.315508
$520$	0.270674	−	1.53507i	0.0118698	−	0.0673171i
$521$	−1.79848	−	10.1997i	−0.0787929	−	0.446857i	−0.998524	−	0.0543082i	$-0.982705\pi$
$521$	−1.79848	−	10.1997i	−0.0787929	−	0.446857i	0.919731	−	0.392548i	$-0.128406\pi$
$522$	12.0622	+	4.39030i	0.527950	+	0.192158i
$523$	−1.56380	+	1.31218i	−0.0683800	+	0.0573777i	−0.676337	−	0.736592i	$-0.736434\pi$
$523$	−1.56380	+	1.31218i	−0.0683800	+	0.0573777i	0.607957	+	0.793970i	$0.291989\pi$
$524$	4.50925			0.196987
$525$	−0.579320	+	0.486107i	−0.0252836	+	0.0212154i
$526$	−0.963167	+	1.66825i	−0.0419961	+	0.0727393i
$527$	35.1969	−	12.8106i	1.53320	−	0.558039i
$528$	−0.574839	−	0.995651i	−0.0250167	−	0.0433301i
$529$	8.74388	−	15.1449i	0.380169	−	0.658472i
$530$	−1.01192	+	5.73888i	−0.0439550	+	0.249281i
$531$	−30.6763	−	11.1653i	−1.33124	−	0.484532i
$532$	−7.19805	−	12.4674i	−0.312075	−	0.540530i
$533$	8.65759	+	7.26458i	0.375002	+	0.314664i
$534$	3.70392	+	3.10795i	0.160284	+	0.134494i
$535$	−2.53244	+	0.921734i	−0.109487	+	0.0398501i
$536$	2.31435	+	13.1253i	0.0999646	+	0.566928i
$537$	0.378792	+	2.14823i	0.0163461	+	0.0927032i
$538$	18.6612	−	6.79212i	0.804541	−	0.292829i
$539$	7.78673	+	6.53384i	0.335398	+	0.281432i
$540$	−1.84686	−	1.54970i	−0.0794762	−	0.0666884i
$541$	−7.41917	−	12.8504i	−0.318975	−	0.552481i	0.661299	−	0.750122i	$-0.270005\pi$
$541$	−7.41917	−	12.8504i	−0.318975	−	0.552481i	−0.980274	+	0.197641i	$0.936672\pi$
$542$	18.6500	+	6.78803i	0.801085	+	0.291571i
$543$	1.42046	−	8.05585i	0.0609579	−	0.345710i
$544$	−1.82389	+	3.15908i	−0.0781988	+	0.135444i
$545$	3.11494	+	5.39524i	0.133430	+	0.231107i
$546$	−1.10771	+	0.403173i	−0.0474056	+	0.0172542i
$547$	8.98627	−	15.5647i	0.384225	−	0.665498i	−0.607436	−	0.794369i	$-0.707802\pi$
$547$	8.98627	−	15.5647i	0.384225	−	0.665498i	0.991661	+	0.128871i	$0.0411353\pi$
$548$	−4.49373	+	3.77069i	−0.191963	+	0.161076i
$549$	24.5787			1.04899
$550$	2.12931	−	1.78670i	0.0907941	−	0.0761853i
$551$	33.5721	+	12.2192i	1.43022	+	0.520557i
$552$	−0.168626	−	0.956327i	−0.00717721	−	0.0407040i
$553$	1.81550	−	10.2962i	0.0772030	−	0.437840i
$554$	−18.1170			−0.769719
$555$	2.48281	+	0.406680i	0.105389	+	0.0172626i
$556$	2.18106			0.0924975
$557$	−1.05198	+	5.96609i	−0.0445740	+	0.252791i	−0.998950	−	0.0458163i	$-0.985411\pi$
$557$	−1.05198	+	5.96609i	−0.0445740	+	0.252791i	0.954376	+	0.298608i	$0.0965222\pi$
$558$	5.04406	+	28.6063i	0.213532	+	1.21100i
$559$	11.0721	+	4.02990i	0.468298	+	0.170446i
$560$	−1.40064	+	1.17528i	−0.0591879	+	0.0496646i
$561$	−4.19378			−0.177062
$562$	19.8454	−	16.6523i	0.837127	−	0.702433i
$563$	14.8753	−	25.7648i	0.626920	−	1.08586i	−0.361246	−	0.932471i	$-0.617648\pi$
$563$	14.8753	−	25.7648i	0.626920	−	1.08586i	0.988166	−	0.153387i	$-0.0490183\pi$
$564$	1.16745	−	0.424918i	0.0491586	−	0.0178923i
$565$	5.81430	+	10.0707i	0.244610	+	0.423676i
$566$	8.57928	−	14.8598i	0.360614	−	0.624602i
$567$	2.37795	−	13.4860i	0.0998644	−	0.566359i
$568$	3.89838	+	1.41889i	0.163572	+	0.0595355i
$569$	−6.07347	−	10.5196i	−0.254613	−	0.441003i	0.710177	−	0.704023i	$-0.248615\pi$
$569$	−6.07347	−	10.5196i	−0.254613	−	0.441003i	−0.964790	+	0.263020i	$0.915281\pi$
$570$	−2.49469	−	2.09329i	−0.104491	−	0.0876785i
$571$	10.7079	+	8.98503i	0.448113	+	0.376012i	0.838735	−	0.544539i	$-0.183296\pi$
$571$	10.7079	+	8.98503i	0.448113	+	0.376012i	−0.390622	+	0.920551i	$0.627740\pi$
$572$	4.07143	−	1.48188i	0.170235	−	0.0619605i
$573$	0.918565	+	5.20944i	0.0383736	+	0.217628i
$574$	−2.30203	−	13.0555i	−0.0960848	−	0.544924i
$575$	2.20622	−	0.803000i	0.0920059	−	0.0334874i
$576$	−2.16708	−	1.81840i	−0.0902951	−	0.0757666i
$577$	−8.78368	−	7.37038i	−0.365669	−	0.306833i	0.441376	−	0.897322i	$-0.354490\pi$
$577$	−8.78368	−	7.37038i	−0.365669	−	0.306833i	−0.807046	+	0.590489i	$0.798935\pi$
$578$	−1.84682	−	3.19879i	−0.0768177	−	0.133052i
$579$	3.78511	+	1.37767i	0.157304	+	0.0572540i
$580$	0.787936	−	4.46861i	0.0327173	−	0.185549i
$581$	−12.9087	+	22.3585i	−0.535543	+	0.927588i
$582$	−2.45078	−	4.24488i	−0.101588	−	0.175956i
$583$	−15.2211	+	5.54004i	−0.630395	+	0.229445i
$584$	−3.88497	+	6.72896i	−0.160761	+	0.278446i
$585$	3.37794	−	2.83442i	0.139660	−	0.117189i
$586$	4.92738			0.203548
$587$	−18.6741	+	15.6694i	−0.770763	+	0.646747i	−0.940904	−	0.338673i	$-0.890022\pi$
$587$	−18.6741	+	15.6694i	−0.770763	+	0.646747i	0.170141	+	0.985420i	$0.445578\pi$
$588$	−1.42132	−	0.517319i	−0.0586144	−	0.0213339i
$589$	14.0388	+	79.6181i	0.578460	+	3.28061i
$590$	−2.00386	+	11.3644i	−0.0824974	+	0.467866i
$591$	−5.17120			−0.212715
$592$	6.00277	+	0.983245i	0.246712	+	0.0404111i
$593$	13.8629			0.569279			0.284640	−	0.958635i	$-0.408126\pi$
$593$	13.8629			0.569279			0.284640	+	0.958635i	$0.408126\pi$
$594$	1.16368	−	6.59958i	0.0477465	−	0.270784i
$595$	1.15817	+	6.56832i	0.0474804	+	0.269275i
$596$	14.2830	+	5.19857i	0.585053	+	0.212942i
$597$	−1.07003	+	0.897865i	−0.0437936	+	0.0367472i
$598$	3.65965			0.149654
$599$	16.5446	−	13.8826i	0.675993	−	0.567226i	−0.238839	−	0.971059i	$-0.576767\pi$
$599$	16.5446	−	13.8826i	0.675993	−	0.567226i	0.914833	+	0.403833i	$0.132322\pi$
$600$	−0.206805	+	0.358197i	−0.00844278	+	0.0146233i
$601$	−0.844866	+	0.307506i	−0.0344628	+	0.0125434i	−0.359194	−	0.933263i	$-0.616948\pi$
$601$	−0.844866	+	0.307506i	−0.0344628	+	0.0125434i	0.324731	+	0.945806i	$0.394726\pi$
$602$	−6.91050	−	11.9693i	−0.281651	−	0.487834i
$603$	−18.8517	+	32.6521i	−0.767700	+	1.32970i
$604$	2.57812	−	14.6212i	0.104902	−	0.594930i
$605$	−3.07629	−	1.11968i	−0.125069	−	0.0455214i
$606$	1.19099	+	2.06285i	0.0483806	+	0.0837977i
$607$	6.00849	+	5.04172i	0.243877	+	0.204637i	0.756530	−	0.653959i	$-0.226893\pi$
$607$	6.00849	+	5.04172i	0.243877	+	0.204637i	−0.512653	+	0.858596i	$0.671337\pi$
$608$	−6.03150	−	5.06103i	−0.244610	−	0.205252i
$609$	−3.22456	+	1.17365i	−0.130666	+	0.0475585i
$610$	−1.50872	−	8.55636i	−0.0610862	−	0.346437i
$611$	0.813033	+	4.61094i	0.0328918	+	0.186539i
$612$	−9.69699	+	3.52942i	−0.391978	+	0.142668i
$613$	−8.07775	−	6.77804i	−0.326257	−	0.273762i	0.464916	−	0.885355i	$-0.346085\pi$
$613$	−8.07775	−	6.77804i	−0.326257	−	0.273762i	−0.791173	+	0.611593i	$0.790529\pi$
$614$	20.2587	+	16.9991i	0.817574	+	0.686026i
$615$	−1.49944	−	2.59710i	−0.0604632	−	0.104725i
$616$	−4.77578	−	1.73824i	−0.192422	−	0.0700358i
$617$	0.665771	−	3.77577i	0.0268029	−	0.152007i	−0.968469	−	0.249134i	$-0.919854\pi$
$617$	0.665771	−	3.77577i	0.0268029	−	0.152007i	0.995272	+	0.0971268i	$0.0309652\pi$
$618$	−3.19056	+	5.52621i	−0.128343	+	0.222297i
$619$	11.8734	+	20.5653i	0.477231	+	0.826589i	0.999659	−	0.0260946i	$-0.00830712\pi$
$619$	11.8734	+	20.5653i	0.477231	+	0.826589i	−0.522428	+	0.852683i	$0.674974\pi$
$620$	9.64883	−	3.51189i	0.387506	−	0.141041i
$621$	2.83018	−	4.90201i	0.113571	−	0.196711i
$622$	−6.98331	+	5.85970i	−0.280005	+	0.234952i
$623$	21.3742			0.856338
$624$	−0.493879	+	0.414414i	−0.0197710	+	0.0165898i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−0.0454902	−	0.257988i	−0.00181815	−	0.0103113i
$627$	1.57188	−	8.91455i	0.0627747	−	0.356013i
$628$	−8.84640			−0.353010
$629$	14.0546	−	17.1699i	0.560392	−	0.684608i
$630$	−5.17243			−0.206075
$631$	7.52300	−	42.6650i	0.299486	−	1.69847i	−0.348903	−	0.937159i	$-0.613446\pi$
$631$	7.52300	−	42.6650i	0.299486	−	1.69847i	0.648389	−	0.761309i	$-0.275443\pi$
$632$	−0.992942	−	5.63125i	−0.0394971	−	0.223999i
$633$	−0.175356	−	0.0638244i	−0.00696978	−	0.00253679i
$634$	10.3019	−	8.64434i	0.409141	−	0.343310i
$635$	−2.86031			−0.113508
$636$	1.84638	−	1.54930i	0.0732137	−	0.0614336i
$637$	2.85011	−	4.93653i	0.112925	−	0.195593i
$638$	11.8520	−	4.31378i	0.469225	−	0.170784i
$639$	5.86800	+	10.1637i	0.232134	+	0.402068i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	4.62036	−	26.2034i	0.182493	−	1.03497i	−0.746640	−	0.665228i	$-0.768334\pi$
$641$	4.62036	−	26.2034i	0.182493	−	1.03497i	0.929134	−	0.369744i	$-0.120554\pi$
$642$	1.04744	+	0.381239i	0.0413393	+	0.0150463i
$643$	8.84717	+	15.3238i	0.348899	+	0.604310i	0.986054	−	0.166425i	$-0.0532225\pi$
$643$	8.84717	+	15.3238i	0.348899	+	0.604310i	−0.637156	+	0.770735i	$0.719889\pi$
$644$	−3.28845	−	2.75934i	−0.129583	−	0.108733i
$645$	−2.39503	−	2.00967i	−0.0943043	−	0.0791307i
$646$	−26.9890	+	9.82320i	−1.06187	+	0.386489i
$647$	1.52652	+	8.65732i	0.0600136	+	0.340354i	1.00000		0.000858769i	$-0.000273355\pi$
$647$	1.52652	+	8.65732i	0.0600136	+	0.340354i	−0.939986	+	0.341213i	$0.889162\pi$
$648$	−1.30056	−	7.37582i	−0.0510907	−	0.289750i
$649$	−30.1417	+	10.9707i	−1.18316	+	0.430636i
$650$	−1.19407	−	1.00194i	−0.0468353	−	0.0392995i
$651$	−5.94849	−	4.99138i	−0.233140	−	0.195628i
$652$	−9.13156	−	15.8163i	−0.357620	−	0.619415i
$653$	−21.0592	−	7.66492i	−0.824110	−	0.299952i	−0.104671	−	0.994507i	$-0.533379\pi$
$653$	−21.0592	−	7.66492i	−0.824110	−	0.299952i	−0.719439	+	0.694555i	$0.755601\pi$
$654$	0.447447	−	2.53760i	0.0174966	−	0.0992279i
$655$	2.25462	−	3.90512i	0.0880954	−	0.152586i
$656$	−3.62524	−	6.27911i	−0.141542	−	0.245158i
$657$	−20.6550	+	7.51780i	−0.805827	+	0.293297i
$658$	2.74603	−	4.75626i	0.107051	−	0.185418i
$659$	−12.8085	+	10.7476i	−0.498947	+	0.418666i	−0.857220	−	0.514951i	$-0.827810\pi$
$659$	−12.8085	+	10.7476i	−0.498947	+	0.418666i	0.358273	+	0.933617i	$0.383366\pi$
$660$	−1.14968			−0.0447512
$661$	−34.7346	+	29.1458i	−1.35102	+	1.13364i	−0.372373	+	0.928083i	$0.621456\pi$
$661$	−34.7346	+	29.1458i	−1.35102	+	1.13364i	−0.978645	+	0.205556i	$0.934100\pi$
$662$	−2.29395	−	0.834930i	−0.0891570	−	0.0324505i
$663$	0.408382	+	2.31605i	0.0158602	+	0.0899479i
$664$	−2.45194	+	13.9056i	−0.0951536	+	0.539643i
$665$	−14.3961			−0.558257
$666$	11.2206	+	13.0462i	0.434788	+	0.505530i
$667$	10.6533			0.412498
$668$	2.16795	−	12.2951i	0.0838807	−	0.475711i
$669$	0.164018	+	0.930193i	0.00634131	+	0.0359633i
$670$	12.5240	+	4.55838i	0.483846	+	0.176105i
$671$	18.5002	−	15.5235i	0.714193	−	0.599279i
$672$	0.756248			0.0291729
$673$	−32.1728	+	26.9962i	−1.24017	+	1.04063i	−0.242659	+	0.970112i	$0.578020\pi$
$673$	−32.1728	+	26.9962i	−1.24017	+	1.04063i	−0.997511	+	0.0705148i	$0.977536\pi$
$674$	12.3642	−	21.4154i	0.476250	−	0.824889i
$675$	−2.26551	+	0.824577i	−0.0871994	+	0.0317380i
$676$	5.28515	+	9.15415i	0.203275	+	0.352083i
$677$	−21.6467	+	37.4933i	−0.831952	+	1.44098i	0.0645359	+	0.997915i	$0.479443\pi$
$677$	−21.6467	+	37.4933i	−0.831952	+	1.44098i	−0.896488	+	0.443068i	$0.853890\pi$
$678$	0.835197	−	4.73664i	0.0320756	−	0.181910i
$679$	−20.3611	−	7.41085i	−0.781389	−	0.284402i
$680$	1.82389	+	3.15908i	0.0699431	+	0.121145i
$681$	4.26351	+	3.57751i	0.163378	+	0.137090i
$682$	21.8639	+	18.3460i	0.837213	+	0.702505i
$683$	−3.19231	+	1.16191i	−0.122150	+	0.0444591i	−0.402372	−	0.915476i	$-0.631814\pi$
$683$	−3.19231	+	1.16191i	−0.122150	+	0.0444591i	0.280222	+	0.959935i	$0.409592\pi$
$684$	−3.86780	−	21.9354i	−0.147889	−	0.838720i
$685$	1.01865	+	5.77703i	0.0389205	+	0.220729i
$686$	−18.3101	+	6.66433i	−0.699083	+	0.254445i
$687$	6.44869	+	5.41110i	0.246033	+	0.206446i
$688$	−5.79056	−	4.85886i	−0.220763	−	0.185242i
$689$	4.54174	+	7.86652i	0.173026	+	0.299690i
$690$	−0.912517	−	0.332129i	−0.0347389	−	0.0126439i
$691$	5.76746	−	32.7089i	0.219404	−	1.24430i	−0.653694	−	0.756759i	$-0.726781\pi$
$691$	5.76746	−	32.7089i	0.219404	−	1.24430i	0.873098	−	0.487545i	$-0.162107\pi$
$692$	8.68905	−	15.0499i	0.330308	−	0.572110i
$693$	−7.18870	−	12.4512i	−0.273076	−	0.472982i
$694$	6.66008	−	2.42407i	0.252813	−	0.0920165i
$695$	1.09053	−	1.88885i	0.0413661	−	0.0716483i
$696$	−1.43769	+	1.20637i	−0.0544956	+	0.0457272i
$697$	−26.4482			−1.00180
$698$	−9.26221	+	7.77192i	−0.350580	+	0.294172i
$699$	−6.30348	−	2.29428i	−0.238419	−	0.0867776i
$700$	0.317500	+	1.80063i	0.0120004	+	0.0680574i
$701$	0.728325	−	4.13054i	0.0275085	−	0.156008i	−0.967959	−	0.251107i	$-0.919205\pi$
$701$	0.728325	−	4.13054i	0.0275085	−	0.156008i	0.995468	+	0.0950985i	$0.0303166\pi$
$702$	−3.75799			−0.141836
$703$	31.2295	+	36.3107i	1.17784	+	1.36948i
$704$	−2.77962			−0.104761
$705$	0.215736	−	1.22350i	0.00812510	−	0.0460798i
$706$	5.56830	+	31.5794i	0.209566	+	1.18851i
$707$	9.89477	+	3.60140i	0.372131	+	0.135445i
$708$	3.65629	−	3.06800i	0.137412	−	0.115302i
$709$	−37.5333			−1.40959			−0.704797	−	0.709409i	$-0.748962\pi$
$709$	−37.5333			−1.40959			−0.704797	+	0.709409i	$0.748962\pi$
$710$	3.17799	−	2.66665i	0.119268	−	0.100078i
$711$	8.08807	−	14.0090i	0.303326	−	0.525377i
$712$	10.9850	−	3.99823i	0.411682	−	0.149840i
$713$	12.0538	+	20.8777i	0.451417	+	0.781877i
$714$	1.37932	−	2.38905i	0.0516196	−	0.0894078i
$715$	0.752370	−	4.26690i	0.0281370	−	0.159573i
$716$	4.95593	+	1.80381i	0.185212	+	0.0674115i
$717$	1.93561	+	3.35258i	0.0722867	+	0.125204i
$718$	16.8067	+	14.1025i	0.627219	+	0.526299i
$719$	−14.2132	−	11.9263i	−0.530063	−	0.444775i	0.338060	−	0.941124i	$-0.390229\pi$
$719$	−14.2132	−	11.9263i	−0.530063	−	0.444775i	−0.868123	+	0.496349i	$0.834674\pi$
$720$	−2.65832	+	0.967550i	−0.0990698	+	0.0360585i
$721$	4.89834	+	27.7799i	0.182424	+	1.03458i
$722$	−7.46567	−	42.3399i	−0.277844	−	1.57573i
$723$	1.82916	−	0.665760i	0.0680272	−	0.0247599i
$724$	−15.1503	−	12.7127i	−0.563058	−	0.472462i
$725$	−3.47596	−	2.91668i	−0.129094	−	0.108323i
$726$	0.677022	+	1.17264i	0.0251266	+	0.0435206i
$727$	34.7849	+	12.6607i	1.29010	+	0.469558i	0.893760	−	0.448546i	$-0.148058\pi$
$727$	34.7849	+	12.6607i	1.29010	+	0.469558i	0.396339	+	0.918104i	$0.370280\pi$
$728$	−0.494902	+	2.80673i	−0.0183423	+	0.104024i
$729$	9.09801	−	15.7582i	0.336963	−	0.583638i
$730$	3.88497	+	6.72896i	0.143789	+	0.249050i
$731$	−25.9109	+	9.43078i	−0.958348	+	0.348810i
$732$	−1.79680	+	3.11214i	−0.0664115	+	0.115028i
$733$	−26.3621	+	22.1204i	−0.973706	+	0.817036i	−0.983128	−	0.182920i	$-0.941445\pi$
$733$	−26.3621	+	22.1204i	−0.973706	+	0.817036i	0.00942230	+	0.999956i	$0.497001\pi$
$734$	−6.99680			−0.258257
$735$	−1.15867	+	0.972242i	−0.0427383	+	0.0358617i
$736$	−2.20622	−	0.803000i	−0.0813225	−	0.0295990i
$737$	6.43301	+	36.4834i	0.236963	+	1.34388i
$738$	3.56171	−	20.1995i	0.131109	−	0.743553i
$739$	−11.9503			−0.439600			−0.219800	−	0.975545i	$-0.570541\pi$
$739$	−11.9503			−0.439600			−0.219800	+	0.975545i	$0.570541\pi$
$740$	3.85290	−	4.70693i	0.141635	−	0.173030i
$741$	−5.07620			−0.186479
$742$	1.85020	−	10.4930i	0.0679231	−	0.385211i
$743$	0.600992	+	3.40840i	0.0220483	+	0.125042i	0.993845	−	0.110777i	$-0.0353339\pi$
$743$	0.600992	+	3.40840i	0.0220483	+	0.125042i	−0.971797	+	0.235819i	$0.924223\pi$
$744$	−3.99085	−	1.45255i	−0.146312	−	0.0532531i
$745$	11.6436	−	9.77012i	0.426587	−	0.357949i
$746$	27.9682			1.02399
$747$	−30.5995	+	25.6761i	−1.11958	+	0.939438i
$748$	−5.06973	+	8.78103i	−0.185368	+	0.321066i
$749$	4.63034	−	1.68531i	0.169189	−	0.0615798i
$750$	0.206805	+	0.358197i	0.00755145	+	0.0130795i
$751$	18.6027	−	32.2208i	0.678821	−	1.17575i	−0.296516	−	0.955028i	$-0.595825\pi$
$751$	18.6027	−	32.2208i	0.678821	−	1.17575i	0.975336	−	0.220724i	$-0.0708420\pi$
$752$	0.521594	−	2.95811i	0.0190206	−	0.107871i
$753$	7.41093	+	2.69736i	0.270069	+	0.0982972i
$754$	−3.53644	−	6.12530i	−0.128790	−	0.223070i
$755$	−11.3733	−	9.54333i	−0.413917	−	0.347317i
$756$	3.37681	+	2.83348i	0.122813	+	0.103053i
$757$	20.3450	−	7.40498i	0.739452	−	0.269139i	0.0552919	−	0.998470i	$-0.482391\pi$
$757$	20.3450	−	7.40498i	0.739452	−	0.269139i	0.684160	+	0.729332i	$0.260169\pi$
$758$	−4.81770	−	27.3225i	−0.174987	−	0.992399i
$759$	−0.468717	−	2.65822i	−0.0170133	−	0.0964874i
$760$	−7.39874	+	2.69292i	−0.268380	+	0.0976825i
$761$	−10.5813	−	8.87877i	−0.383572	−	0.321855i	0.430531	−	0.902576i	$-0.358326\pi$
$761$	−10.5813	−	8.87877i	−0.383572	−	0.321855i	−0.814103	+	0.580721i	$0.802771\pi$
$762$	0.906270	+	0.760451i	0.0328307	+	0.0275482i
$763$	−5.69539	−	9.86471i	−0.206187	−	0.357126i
$764$	12.0181	+	4.37422i	0.434798	+	0.158254i
$765$	−1.79193	+	10.1626i	−0.0647874	+	0.367428i
$766$	−11.2435	+	19.4742i	−0.406243	+	0.703633i
$767$	8.99377	+	15.5777i	0.324746	+	0.562477i
$768$	0.388666	−	0.141463i	0.0140248	−	0.00510461i
$769$	−26.0393	+	45.1013i	−0.938999	+	1.62639i	−0.171658	+	0.985157i	$0.554912\pi$
$769$	−26.0393	+	45.1013i	−0.938999	+	1.62639i	−0.767342	+	0.641238i	$0.778421\pi$
$770$	−3.89325	+	3.26683i	−0.140303	+	0.117728i
$771$	5.87564			0.211606
$772$	7.46030	−	6.25993i	0.268502	−	0.225300i
$773$	−35.3134	−	12.8530i	−1.27013	−	0.462291i	−0.382976	−	0.923758i	$-0.625101\pi$
$773$	−35.3134	−	12.8530i	−1.27013	−	0.462291i	−0.887157	+	0.461467i	$0.847323\pi$
$774$	−3.71329	−	21.0591i	−0.133471	−	0.756953i
$775$	1.78303	−	10.1121i	0.0640484	−	0.363236i
$776$	−11.8507			−0.425415
$777$	−4.53958	−	0.743577i	−0.162857	−	0.0266757i
$778$	−23.4467			−0.840603
$779$	9.91309	−	56.2199i	0.355173	−	2.01429i
$780$	0.111953	+	0.634919i	0.00400857	+	0.0227338i
$781$	10.8360	+	3.94398i	0.387743	+	0.141127i
$782$	−6.56066	+	5.50504i	−0.234609	+	0.196860i
$783$	−10.9396			−0.390949
$784$	−2.80137	+	2.35062i	−0.100049	+	0.0839509i
$785$	−4.42320	+	7.66121i	−0.157871	+	0.273440i
$786$	−1.75259	+	0.637891i	−0.0625129	+	0.0227528i
$787$	0.190390	+	0.329765i	0.00678667	+	0.0117549i	0.869399	−	0.494111i	$-0.164506\pi$
$787$	0.190390	+	0.329765i	0.00678667	+	0.0117549i	−0.862612	+	0.505866i	$0.831173\pi$
$788$	−6.25130	+	10.8276i	−0.222693	+	0.385716i
$789$	0.138354	−	0.784647i	0.00492555	−	0.0279342i
$790$	−5.37328	−	1.95571i	−0.191173	−	0.0695811i
$791$	−10.6309	−	18.4133i	−0.377992	−	0.654701i
$792$	−6.02367	−	5.05446i	−0.214042	−	0.179602i
$793$	−10.3745	−	8.70525i	−0.368410	−	0.309132i
$794$	−26.1966	+	9.53477i	−0.929681	+	0.338376i
$795$	−0.418540	−	2.37366i	−0.0148441	−	0.0841851i
$796$	0.586439	+	3.32586i	0.0207858	+	0.117882i
$797$	45.5026	−	16.5616i	1.61178	−	0.586642i	0.629993	−	0.776601i	$-0.283058\pi$
$797$	45.5026	−	16.5616i	1.61178	−	0.586642i	0.981792	+	0.189960i	$0.0608357\pi$
$798$	4.56131	+	3.82740i	0.161469	+	0.135488i
$799$	−8.39355	−	7.04302i	−0.296942	−	0.249164i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	31.0759	+	11.3107i	1.09801	+	0.399644i
$802$	1.19964	−	6.80348i	0.0423606	−	0.240239i
$803$	−10.7987	+	18.7039i	−0.381079	+	0.660048i
$804$	−2.75626	−	4.77398i	−0.0972057	−	0.168365i
$805$	−4.03388	+	1.46821i	−0.142176	+	0.0517477i
$806$	8.00266	−	13.8610i	0.281882	−	0.488234i
$807$	−6.29215	+	5.27974i	−0.221494	+	0.185856i
$808$	5.75899			0.202601
$809$	−27.5903	+	23.1510i	−0.970023	+	0.813946i	−0.982554	−	0.185976i	$-0.940455\pi$
$809$	−27.5903	+	23.1510i	−0.970023	+	0.813946i	0.0125316	+	0.999921i	$0.496011\pi$
$810$	−7.03793	−	2.56160i	−0.247288	−	0.0900053i
$811$	2.63290	+	14.9319i	0.0924535	+	0.524330i	0.995498	+	0.0947827i	$0.0302156\pi$
$811$	2.63290	+	14.9319i	0.0924535	+	0.524330i	−0.903045	+	0.429547i	$0.858673\pi$
$812$	−1.44067	+	8.17044i	−0.0505576	+	0.286726i
$813$	−8.20887			−0.287898
$814$	16.6854	+	2.73305i	0.584823	+	0.0957932i
$815$	−18.2631			−0.639729
$816$	0.261994	−	1.48584i	0.00917162	−	0.0520148i
$817$	−10.3350	−	58.6124i	−0.361574	−	2.05059i
$818$	−25.6926	−	9.35135i	−0.898321	−	0.326962i
$819$	−6.17625	+	5.18249i	−0.215816	+	0.181091i
$820$	−7.25049			−0.253198
$821$	5.27847	−	4.42916i	0.184220	−	0.154579i	−0.546014	−	0.837776i	$-0.683855\pi$
$821$	5.27847	−	4.42916i	0.184220	−	0.154579i	0.730234	+	0.683197i	$0.239411\pi$
$822$	1.21315	−	2.10124i	0.0423134	−	0.0732890i
$823$	−9.49631	+	3.45638i	−0.331021	+	0.120482i	−0.502183	−	0.864761i	$-0.667470\pi$
$823$	−9.49631	+	3.45638i	−0.331021	+	0.120482i	0.171163	+	0.985243i	$0.445248\pi$
$824$	7.71393	+	13.3609i	0.268728	+	0.465450i
$825$	−0.574839	+	0.995651i	−0.0200133	+	0.0346641i
$826$	3.66387	−	20.7788i	0.127482	−	0.722987i
$827$	5.57923	+	2.03067i	0.194009	+	0.0706134i	0.437197	−	0.899366i	$-0.355971\pi$
$827$	5.57923	+	2.03067i	0.194009	+	0.0706134i	−0.243188	+	0.969979i	$0.578193\pi$
$828$	−3.32090	−	5.75196i	−0.115409	−	0.199895i
$829$	−32.3986	−	27.1856i	−1.12525	−	0.944195i	−0.126391	−	0.991981i	$-0.540339\pi$
$829$	−32.3986	−	27.1856i	−1.12525	−	0.944195i	−0.998858	+	0.0477851i	$0.984784\pi$
$830$	10.8167	+	9.07625i	0.375452	+	0.315041i
$831$	7.04148	−	2.56289i	0.244266	−	0.0889056i
$832$	0.270674	+	1.53507i	0.00938392	+	0.0532189i
$833$	2.31641	+	13.1370i	0.0802589	+	0.455171i
$834$	−0.847704	+	0.308539i	−0.0293536	+	0.0106838i
$835$	−9.56387	−	8.02504i	−0.330971	−	0.277718i
$836$	−16.7653	−	14.0677i	−0.579839	−	0.486543i
$837$	−12.3777	−	21.4387i	−0.427834	−	0.741031i
$838$	16.2401	+	5.91090i	0.561004	+	0.204189i
$839$	1.64846	−	9.34889i	0.0569112	−	0.322759i	−0.943040	−	0.332681i	$-0.892047\pi$
$839$	1.64846	−	9.34889i	0.0569112	−	0.322759i	0.999951	+	0.00992110i	$0.00315803\pi$
$840$	0.378124	−	0.654930i	0.0130465	−	0.0225972i
$841$	4.20535	+	7.28389i	0.145012	+	0.251169i
$842$	17.7595	−	6.46393i	0.612033	−	0.222762i
$843$	−5.35756	+	9.27956i	−0.184524	+	0.319605i
$844$	−0.345619	+	0.290009i	−0.0118967	+	0.00998252i
$845$	10.5703			0.363630
$846$	6.50935	−	5.46200i	0.223796	−	0.187787i
$847$	5.62471	+	2.04723i	0.193267	+	0.0703436i
$848$	−1.01192	−	5.73888i	−0.0347495	−	0.197074i
$849$	−1.23237	+	6.98914i	−0.0422949	+	0.239867i
$850$	3.64779			0.125118
$851$	12.4539	+	6.98948i	0.426914	+	0.239596i
$852$	−1.71589			−0.0587854
$853$	−1.11899	+	6.34609i	−0.0383134	+	0.217286i	−0.997953	−	0.0639452i	$-0.979632\pi$
$853$	−1.11899	+	6.34609i	−0.0383134	+	0.217286i	0.959640	+	0.281231i	$0.0907428\pi$
$854$	2.75855	+	15.6445i	0.0943957	+	0.535345i
$855$	−20.9305	−	7.61807i	−0.715807	−	0.260533i
$856$	2.06447	−	1.73229i	0.0705620	−	0.0592086i
$857$	29.2469			0.999055			0.499528	−	0.866298i	$-0.333507\pi$
$857$	29.2469			0.999055			0.499528	+	0.866298i	$0.333507\pi$
$858$	−1.37280	+	1.15191i	−0.0468665	+	0.0393257i
$859$	−9.41213	+	16.3023i	−0.321138	+	0.556227i	−0.980723	−	0.195403i	$-0.937399\pi$
$859$	−9.41213	+	16.3023i	−0.321138	+	0.556227i	0.659585	+	0.751630i	$0.270732\pi$
$860$	−7.10317	+	2.58534i	−0.242216	+	0.0881595i
$861$	2.74158	+	4.74856i	0.0934329	+	0.161831i
$862$	5.86961	−	10.1665i	0.199920	−	0.346271i
$863$	−8.32732	+	47.2266i	−0.283465	+	1.60761i	0.427251	+	0.904133i	$0.359482\pi$
$863$	−8.32732	+	47.2266i	−0.283465	+	1.60761i	−0.710716	+	0.703479i	$0.751629\pi$
$864$	2.26551	+	0.824577i	0.0770741	+	0.0280527i
$865$	−8.68905	−	15.0499i	−0.295437	−	0.511711i
$866$	25.1542	+	21.1069i	0.854776	+	0.717242i
$867$	1.17031	+	0.982005i	0.0397457	+	0.0333506i
$868$	−17.6420	+	6.42116i	−0.598808	+	0.217948i
$869$	−2.76000	−	15.6527i	−0.0936265	−	0.530983i
$870$	0.325898	+	1.84826i	0.0110490	+	0.0626619i
$871$	19.5218	−	7.10536i	0.661471	−	0.240756i
$872$	−4.77237	−	4.00449i	−0.161613	−	0.135609i
$873$	−25.6814	−	21.5493i	−0.869184	−	0.729332i
$874$	−9.24284	−	16.0091i	−0.312644	−	0.541515i
$875$	1.71814	+	0.625353i	0.0580838	+	0.0211408i
$876$	0.558057	−	3.16490i	0.0188550	−	0.106932i
$877$	21.5577	−	37.3390i	0.727952	−	1.26085i	−0.229795	−	0.973239i	$-0.573806\pi$
$877$	21.5577	−	37.3390i	0.727952	−	1.26085i	0.957747	−	0.287611i	$-0.0928610\pi$
$878$	11.0595	+	19.1556i	0.373240	+	0.646470i
$879$	−1.91511	+	0.697043i	−0.0645950	+	0.0235107i
$880$	−1.38981	+	2.40722i	−0.0468505	+	0.0811474i
$881$	38.6564	−	32.4366i	1.30237	−	1.09282i	0.312637	−	0.949873i	$-0.398788\pi$
$881$	38.6564	−	32.4366i	1.30237	−	1.09282i	0.989731	−	0.142944i	$-0.0456567\pi$
$882$	−10.3452			−0.348340
$883$	7.78030	−	6.52844i	0.261828	−	0.219700i	−0.502418	−	0.864625i	$-0.667556\pi$
$883$	7.78030	−	6.52844i	0.261828	−	0.219700i	0.764246	+	0.644925i	$0.223112\pi$
$884$	5.34307	+	1.94472i	0.179707	+	0.0654080i
$885$	−0.828815	−	4.70044i	−0.0278603	−	0.158004i
$886$	−5.80348	+	32.9131i	−0.194972	+	1.10574i
$887$	−39.2378			−1.31748			−0.658738	−	0.752372i	$-0.728910\pi$
$887$	−39.2378			−1.31748			−0.658738	+	0.752372i	$0.728910\pi$
$888$	−2.47217	+	0.467015i	−0.0829605	+	0.0156720i
$889$	5.22981			0.175402
$890$	2.02995	−	11.5124i	0.0680442	−	0.385898i
$891$	−3.61505	−	20.5020i	−0.121109	−	0.686842i
$892$	2.14593	+	0.781056i	0.0718512	+	0.0261517i
$893$	18.1171	−	15.2020i	0.606264	−	0.508716i
$894$	−6.28671			−0.210259
$895$	4.04011	−	3.39005i	0.135046	−	0.113317i
$896$	0.914204	−	1.58345i	0.0305414	−	0.0528993i
$897$	−1.42238	+	0.517705i	−0.0474920	+	0.0172857i
$898$	4.05058	+	7.01581i	0.135170	+	0.234121i
$899$	23.2959	−	40.3497i	0.776962	−	1.34574i
$900$	−0.491238	+	2.78595i	−0.0163746	+	0.0928650i
$901$	−19.9752	−	7.27038i	−0.665471	−	0.242212i
$902$	−10.0768	−	17.4535i	−0.335521	−	0.581139i
$903$	4.37910	+	3.67450i	0.145727	+	0.122280i
$904$	−8.90803	−	7.47472i	−0.296277	−	0.248606i
$905$	−18.5847	+	6.76426i	−0.617775	+	0.224852i
$906$	1.06634	+	6.04749i	0.0354266	+	0.200914i
$907$	−5.67369	−	32.1771i	−0.188392	−	1.06842i	−0.921520	−	0.388331i	$-0.873052\pi$
$907$	−5.67369	−	32.1771i	−0.188392	−	1.06842i	0.733128	−	0.680091i	$-0.238060\pi$
$908$	12.6447	−	4.60228i	0.419628	−	0.152732i
$909$	12.4802	+	10.4722i	0.413943	+	0.347339i
$910$	2.18325	+	1.83196i	0.0723739	+	0.0607290i
$911$	16.5439	+	28.6549i	0.548124	+	0.949379i	0.998403	+	0.0564907i	$0.0179911\pi$
$911$	16.5439	+	28.6549i	0.548124	+	0.949379i	−0.450279	+	0.892888i	$0.648676\pi$
$912$	3.06019	+	1.11382i	0.101333	+	0.0368822i
$913$	−6.81545	+	38.6523i	−0.225559	+	1.27921i
$914$	−11.3958	+	19.7381i	−0.376939	+	0.652877i
$915$	1.79680	+	3.11214i	0.0594003	+	0.102884i
$916$	19.1255	−	6.96111i	0.631924	−	0.230001i
$917$	−4.12237	+	7.14016i	−0.136133	+	0.235789i
$918$	6.73695	−	5.65297i	0.222352	−	0.186576i
$919$	34.4460			1.13627			0.568135	−	0.822936i	$-0.307665\pi$
$919$	34.4460			1.13627			0.568135	+	0.822936i	$0.307665\pi$
$920$	−1.79853	+	1.50915i	−0.0592958	+	0.0497551i
$921$	−10.2786	−	3.74111i	−0.338692	−	0.123274i
$922$	6.37613	+	36.1608i	0.209987	+	1.19089i
$923$	1.12291	−	6.36833i	0.0369610	−	0.209616i
$924$	2.10208			0.0691534
$925$	−2.14987	−	5.69017i	−0.0706873	−	0.187092i
$926$	7.44737			0.244736
$927$	−7.57875	+	42.9812i	−0.248919	+	1.41169i
$928$	0.787936	+	4.46861i	0.0258653	+	0.146689i
$929$	20.8781	+	7.59900i	0.684987	+	0.249315i	0.660987	−	0.750397i	$-0.270138\pi$
$929$	20.8781	+	7.59900i	0.684987	+	0.249315i	0.0239998	+	0.999712i	$0.492360\pi$
$930$	−3.25337	+	2.72990i	−0.106682	+	0.0895171i
$931$	−28.7930			−0.943654
$932$	−12.4239	+	10.4249i	−0.406958	+	0.341478i
$933$	1.88525	−	3.26535i	0.0617203	−	0.106903i
$934$	−16.2966	+	5.93147i	−0.533240	+	0.194084i
$935$	5.06973	+	8.78103i	0.165798	+	0.287170i
$936$	−2.20479	+	3.81881i	−0.0720659	+	0.124822i
$937$	−6.06956	+	34.4222i	−0.198284	+	1.12452i	0.709380	+	0.704826i	$0.248975\pi$
$937$	−6.06956	+	34.4222i	−0.198284	+	1.12452i	−0.907664	+	0.419697i	$0.862136\pi$
$938$	−22.8991	−	8.33457i	−0.747681	−	0.272133i
$939$	0.0541762	+	0.0938359i	0.00176797	+	0.00306222i
$940$	−2.30100	−	1.93077i	−0.0750503	−	0.0629746i
$941$	−34.4998	−	28.9488i	−1.12466	−	0.943704i	−0.125832	−	0.992052i	$-0.540160\pi$
$941$	−34.4998	−	28.9488i	−1.12466	−	0.943704i	−0.998831	+	0.0483480i	$0.984604\pi$
$942$	3.43830	−	1.25144i	0.112026	−	0.0407741i
$943$	−2.95598	−	16.7642i	−0.0962599	−	0.545917i
$944$	−2.00386	−	11.3644i	−0.0652199	−	0.369881i
$945$	4.14227	−	1.50766i	0.134748	−	0.0490443i
$946$	−16.0955	−	13.5058i	−0.523311	−	0.439110i
$947$	11.0855	+	9.30188i	0.360232	+	0.302270i	0.804883	−	0.593433i	$-0.202228\pi$
$947$	11.0855	+	9.30188i	0.360232	+	0.302270i	−0.444651	+	0.895704i	$0.646672\pi$
$948$	1.18254	+	2.04821i	0.0384070	+	0.0665229i
$949$	11.3810	+	4.14233i	0.369442	+	0.134466i
$950$	−1.36723	+	7.75395i	−0.0443588	+	0.251571i
$951$	−2.78116	+	4.81710i	−0.0901852	+	0.156205i
$952$	−3.33482	−	5.77608i	−0.108082	−	0.187204i
$953$	−22.2045	+	8.08179i	−0.719276	+	0.261795i	−0.675618	−	0.737252i	$-0.736123\pi$
$953$	−22.2045	+	8.08179i	−0.719276	+	0.261795i	−0.0436574	+	0.999047i	$0.513901\pi$
$954$	8.24267	−	14.2767i	0.266866	−	0.462226i
$955$	9.79721	−	8.22084i	0.317030	−	0.266020i
$956$	9.35959			0.302711
$957$	−3.99624	+	3.35324i	−0.129180	+	0.108395i
$958$	−22.2413	−	8.09516i	−0.718583	−	0.261543i
$959$	−1.86250	−	10.5628i	−0.0601433	−	0.341090i
$960$	0.0718226	−	0.407326i	0.00231807	−	0.0131464i
$961$	74.4332			2.40107
$962$	−0.115445	−	9.48079i	−0.00372209	−	0.305673i
$963$	7.62388			0.245676
$964$	0.817231	−	4.63475i	0.0263212	−	0.149275i
$965$	−1.69111	−	9.59077i	−0.0544388	−	0.308738i
$966$	1.66845	+	0.607267i	0.0536816	+	0.0195385i
$967$	−35.2545	+	29.5821i	−1.13371	+	0.951295i	−0.999215	−	0.0396197i	$-0.987385\pi$
$967$	−35.2545	+	29.5821i	−1.13371	+	0.951295i	−0.134494	+	0.990914i	$0.542941\pi$
$968$	3.27372			0.105221
$969$	9.10010	−	7.63589i	0.292337	−	0.245300i
$970$	−5.92534	+	10.2630i	−0.190251	+	0.329525i
$971$	−45.8400	+	16.6844i	−1.47107	+	0.535427i	−0.948392	−	0.317101i	$-0.897291\pi$
$971$	−45.8400	+	16.6844i	−1.47107	+	0.535427i	−0.522682	+	0.852528i	$0.675069\pi$
$972$	5.16524	+	8.94646i	0.165675	+	0.286958i
$973$	−1.99393	+	3.45359i	−0.0639226	+	0.110717i
$974$	3.43294	−	19.4692i	0.109999	−	0.623833i
$975$	0.605833	+	0.220505i	0.0194022	+	0.00706181i
$976$	4.34418	+	7.52434i	0.139054	+	0.240848i
$977$	42.9094	+	36.0053i	1.37279	+	1.15191i	0.971794	+	0.235833i	$0.0757819\pi$
$977$	42.9094	+	36.0053i	1.37279	+	1.15191i	0.401001	+	0.916078i	$0.368663\pi$
$978$	5.78656	+	4.85550i	0.185034	+	0.155262i
$979$	30.5342	−	11.1136i	0.975878	−	0.355191i
$980$	0.635018	+	3.60137i	0.0202849	+	0.115041i
$981$	−3.06036	−	17.3562i	−0.0977097	−	0.554139i
$982$	−19.9307	+	7.25417i	−0.636013	+	0.231490i
$983$	5.44988	+	4.57299i	0.173824	+	0.145856i	0.725549	−	0.688170i	$-0.241586\pi$
$983$	5.44988	+	4.57299i	0.173824	+	0.145856i	−0.551725	+	0.834026i	$0.686030\pi$
$984$	2.29727	+	1.92764i	0.0732343	+	0.0614509i
$985$	6.25130	+	10.8276i	0.199183	+	0.344995i
$986$	15.5538	+	5.66111i	0.495333	+	0.180287i
$987$	−0.394454	+	2.23706i	−0.0125556	+	0.0712065i
$988$	−6.13645	+	10.6286i	−0.195227	+	0.338142i
$989$	−8.87361	−	15.3695i	−0.282164	−	0.488723i
$990$	−7.38912	+	2.68942i	−0.234842	+	0.0854754i
$991$	29.4034	−	50.9283i	0.934031	−	1.61779i	0.157679	−	0.987490i	$-0.449599\pi$
$991$	29.4034	−	50.9283i	0.934031	−	1.61779i	0.776352	−	0.630299i	$-0.217068\pi$
$992$	−7.86580	+	6.60019i	−0.249739	+	0.209556i
$993$	1.00969			0.0320417
$994$	−5.81066	+	4.87572i	−0.184303	+	0.154648i
$995$	3.17350	+	1.15506i	0.100607	+	0.0366178i
$996$	−1.01415	−	5.75151i	−0.0321345	−	0.182244i
$997$	−4.35725	+	24.7112i	−0.137996	+	0.782612i	0.834731	+	0.550658i	$0.185623\pi$
$997$	−4.35725	+	24.7112i	−0.137996	+	0.782612i	−0.972727	+	0.231954i	$0.925488\pi$
$998$	10.6660			0.337628
$999$	−12.7886	−	7.17730i	−0.404612	−	0.227080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.181.2	✓	18
37.9	even	9	inner	370.2.o.b.231.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.181.2	✓	18	1.1	even	1	trivial
370.2.o.b.231.2	yes	18	37.9	even	9	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.0718226 - 0.407326i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.413610 q^{6} +(1.40064 - 1.17528i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.65832 - 0.967550i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.0718226 - 0.407326i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.413610 q^{6} +(1.40064 - 1.17528i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.65832 - 0.967550i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.38981 - 2.40722i) q^{11} +(-0.0718226 + 0.407326i) q^{12} +(-1.46474 - 0.533123i) q^{13} +(0.914204 + 1.58345i) q^{14} +(0.316844 + 0.265863i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.42780 - 1.24762i) q^{17} +(0.491238 + 2.78595i) q^{18} +(1.36723 + 7.75395i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-0.579320 - 0.486107i) q^{21} +(2.12931 + 1.78670i) q^{22} +(1.17391 + 2.03327i) q^{23} +(-0.388666 - 0.141463i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.779374 - 1.34991i) q^{26} +(-1.20545 - 2.08790i) q^{27} +(-1.71814 + 0.625353i) q^{28} +(2.26877 - 3.92963i) q^{29} +(-0.316844 + 0.265863i) q^{30} +10.2681 q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.08034 - 0.393213i) q^{33} +(0.633432 + 3.59237i) q^{34} +(-0.317500 + 1.80063i) q^{35} -2.82893 q^{36} +(5.23041 - 3.10530i) q^{37} -7.87357 q^{38} +(-0.111953 + 0.634919i) q^{39} +(0.173648 + 0.984808i) q^{40} +(-6.81323 - 2.47981i) q^{41} +(0.579320 - 0.486107i) q^{42} -7.55904 q^{43} +(-2.12931 + 1.78670i) q^{44} +(-1.41446 + 2.44992i) q^{45} +(-2.20622 + 0.803000i) q^{46} +(-1.50187 - 2.60131i) q^{47} +(0.206805 - 0.358197i) q^{48} +(-0.635018 + 3.60137i) q^{49} +(0.939693 + 0.342020i) q^{50} +(-0.754381 - 1.30663i) q^{51} +(1.19407 + 1.00194i) q^{52} +(-4.46406 - 3.74579i) q^{53} +(2.26551 - 0.824577i) q^{54} +(0.482676 + 2.73739i) q^{55} +(-0.317500 - 1.80063i) q^{56} +(3.06019 - 1.11382i) q^{57} +(3.47596 + 2.91668i) q^{58} +(-8.83996 - 7.41760i) q^{59} +(-0.206805 - 0.358197i) q^{60} +(8.16439 + 2.97159i) q^{61} +(-1.78303 + 10.1121i) q^{62} +(2.58622 - 4.47946i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.46474 - 0.533123i) q^{65} +(0.574839 - 0.995651i) q^{66} +(-10.2097 + 8.56694i) q^{67} -3.64779 q^{68} +(0.743890 - 0.624198i) q^{69} +(-1.71814 - 0.625353i) q^{70} +(0.720391 + 4.08554i) q^{71} +(0.491238 - 2.78595i) q^{72} -7.76993 q^{73} +(2.14987 + 5.69017i) q^{74} -0.413610 q^{75} +(1.36723 - 7.75395i) q^{76} +(-0.882528 - 5.00507i) q^{77} +(-0.605833 - 0.220505i) q^{78} +(4.38034 - 3.67554i) q^{79} -1.00000 q^{80} +(5.73737 - 4.81423i) q^{81} +(3.62524 - 6.27911i) q^{82} +(-13.2686 + 4.82937i) q^{83} +(0.378124 + 0.654930i) q^{84} +(-1.82389 + 3.15908i) q^{85} +(1.31261 - 7.44420i) q^{86} +(-1.76359 - 0.641894i) q^{87} +(-1.38981 - 2.40722i) q^{88} +(8.95509 + 7.51421i) q^{89} +(-2.16708 - 1.81840i) q^{90} +(-2.67815 + 0.974767i) q^{91} +(-0.407694 - 2.31215i) q^{92} +(-0.737480 - 4.18246i) q^{93} +(2.82259 - 1.02734i) q^{94} +(-6.03150 - 5.06103i) q^{95} +(0.316844 + 0.265863i) q^{96} +(-5.92534 - 10.2630i) q^{97} +(-3.43638 - 1.25074i) q^{98} +(1.36545 - 7.74388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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