LMFDB - Embedded newform 130.2.p.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(7,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("130.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.p (of order $12$, degree $4$, 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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 192x^{8} + 680x^{6} + 1104x^{4} + 672x^{2} + 4 $ x^12 + 24x^10 + 192x^8 + 680x^6 + 1104x^4 + 672*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Root			$-1.32083i$ of defining polynomial
Character	$\chi$	$=$	130.37
Dual form			130.2.p.a.123.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.660414 + 0.176957i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.483457 + 2.18318i) q^{5} +(0.660414 - 0.176957i) q^{6} +(0.189447 - 0.328132i) q^{7} -1.00000i q^{8} +(-2.19324 - 1.26627i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.660414 + 0.176957i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.483457 + 2.18318i) q^{5} +(0.660414 - 0.176957i) q^{6} +(0.189447 - 0.328132i) q^{7} -1.00000i q^{8} +(-2.19324 - 1.26627i) q^{9} +(1.51028 + 1.64896i) q^{10} +(0.895058 + 0.239830i) q^{11} +(0.483457 - 0.483457i) q^{12} +(-3.16145 - 1.73356i) q^{13} -0.378894i q^{14} +(-0.0670481 + 1.52735i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.589312 - 2.19934i) q^{17} -2.53254 q^{18} +(-0.0311497 - 0.116252i) q^{19} +(2.13242 + 0.672904i) q^{20} +(0.183179 - 0.183179i) q^{21} +(0.895058 - 0.239830i) q^{22} +(-2.32731 + 8.68563i) q^{23} +(0.176957 - 0.660414i) q^{24} +(-4.53254 + 2.11094i) q^{25} +(-3.60468 + 0.0794160i) q^{26} +(-2.67474 - 2.67474i) q^{27} +(-0.189447 - 0.328132i) q^{28} +(5.31003 - 3.06575i) q^{29} +(0.705611 + 1.35625i) q^{30} +(2.45303 + 2.45303i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.548669 + 0.316774i) q^{33} +(-1.61003 - 1.61003i) q^{34} +(0.807960 + 0.254959i) q^{35} +(-2.19324 + 1.26627i) q^{36} +(-1.07176 - 1.85634i) q^{37} +(-0.0851026 - 0.0851026i) q^{38} +(-1.78110 - 1.70431i) q^{39} +(2.18318 - 0.483457i) q^{40} +(0.855872 - 3.19416i) q^{41} +(0.0670481 - 0.250227i) q^{42} +(-7.67535 + 2.05660i) q^{43} +(0.655228 - 0.655228i) q^{44} +(1.70415 - 5.40043i) q^{45} +(2.32731 + 8.68563i) q^{46} +4.99481 q^{47} +(-0.176957 - 0.660414i) q^{48} +(3.42822 + 5.93785i) q^{49} +(-2.86982 + 4.09440i) q^{50} -1.55676i q^{51} +(-3.08203 + 1.87111i) q^{52} +(-0.286513 + 0.286513i) q^{53} +(-3.65377 - 0.979024i) q^{54} +(-0.0908702 + 2.07002i) q^{55} +(-0.328132 - 0.189447i) q^{56} -0.0822868i q^{57} +(3.06575 - 5.31003i) q^{58} +(13.2458 - 3.54920i) q^{59} +(1.28920 + 0.821742i) q^{60} +(4.60338 - 7.97329i) q^{61} +(3.35090 + 0.897870i) q^{62} +(-0.831007 + 0.479782i) q^{63} -1.00000 q^{64} +(2.25625 - 7.74011i) q^{65} +0.633549 q^{66} +(-7.24548 + 4.18318i) q^{67} +(-2.19934 - 0.589312i) q^{68} +(-3.07397 + 5.32428i) q^{69} +(0.827193 - 0.183179i) q^{70} +(8.69557 - 2.32997i) q^{71} +(-1.26627 + 2.19324i) q^{72} -11.2294i q^{73} +(-1.85634 - 1.07176i) q^{74} +(-3.36690 + 0.592031i) q^{75} +(-0.116252 - 0.0311497i) q^{76} +(0.248262 - 0.248262i) q^{77} +(-2.39463 - 0.585427i) q^{78} +6.19564i q^{79} +(1.64896 - 1.51028i) q^{80} +(2.50569 + 4.33998i) q^{81} +(-0.855872 - 3.19416i) q^{82} +10.8523 q^{83} +(-0.0670481 - 0.250227i) q^{84} +(4.51665 - 2.34986i) q^{85} +(-5.61875 + 5.61875i) q^{86} +(4.04933 - 1.08501i) q^{87} +(0.239830 - 0.895058i) q^{88} +(-0.273792 + 1.02180i) q^{89} +(-1.22437 - 5.52899i) q^{90} +(-1.16776 + 0.708954i) q^{91} +(6.35832 + 6.35832i) q^{92} +(1.18593 + 2.05409i) q^{93} +(4.32564 - 2.49741i) q^{94} +(0.238740 - 0.124208i) q^{95} +(-0.483457 - 0.483457i) q^{96} +(-10.4433 - 6.02947i) q^{97} +(5.93785 + 3.42822i) q^{98} +(-1.65939 - 1.65939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 24 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 24 * q^9	$ 12 q + 6 q^{4} - 24 q^{9} + 6 q^{11} - 12 q^{13} - 6 q^{15} - 6 q^{16} + 12 q^{17} + 12 q^{18} + 36 q^{19} - 6 q^{20} - 24 q^{21} + 6 q^{22} + 6 q^{23} - 12 q^{25} + 6 q^{26} - 12 q^{27} + 6 q^{29} + 6 q^{30} - 24 q^{31} - 6 q^{33} - 12 q^{34} - 12 q^{35} - 24 q^{36} - 6 q^{38} + 6 q^{39} + 18 q^{41} + 6 q^{42} + 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 24 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} - 24 q^{55} + 6 q^{56} + 6 q^{58} + 18 q^{59} + 24 q^{60} + 18 q^{61} + 12 q^{62} + 30 q^{63} - 12 q^{64} + 30 q^{65} - 36 q^{66} + 12 q^{67} - 42 q^{69} + 24 q^{70} + 18 q^{71} + 6 q^{72} + 6 q^{74} - 12 q^{75} + 30 q^{76} + 30 q^{77} + 30 q^{78} - 6 q^{80} + 30 q^{81} - 18 q^{82} - 48 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{87} + 6 q^{89} - 12 q^{90} - 6 q^{91} - 42 q^{93} + 24 q^{94} + 30 q^{95} - 102 q^{97} - 48 q^{98} + 54 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 24 * q^9 + 6 * q^11 - 12 * q^13 - 6 * q^15 - 6 * q^16 + 12 * q^17 + 12 * q^18 + 36 * q^19 - 6 * q^20 - 24 * q^21 + 6 * q^22 + 6 * q^23 - 12 * q^25 + 6 * q^26 - 12 * q^27 + 6 * q^29 + 6 * q^30 - 24 * q^31 - 6 * q^33 - 12 * q^34 - 12 * q^35 - 24 * q^36 - 6 * q^38 + 6 * q^39 + 18 * q^41 + 6 * q^42 + 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 - 24 * q^55 + 6 * q^56 + 6 * q^58 + 18 * q^59 + 24 * q^60 + 18 * q^61 + 12 * q^62 + 30 * q^63 - 12 * q^64 + 30 * q^65 - 36 * q^66 + 12 * q^67 - 42 * q^69 + 24 * q^70 + 18 * q^71 + 6 * q^72 + 6 * q^74 - 12 * q^75 + 30 * q^76 + 30 * q^77 + 30 * q^78 - 6 * q^80 + 30 * q^81 - 18 * q^82 - 48 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^87 + 6 * q^89 - 12 * q^90 - 6 * q^91 - 42 * q^93 + 24 * q^94 + 30 * q^95 - 102 * q^97 - 48 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.660414	+	0.176957i	0.381290	+	0.102166i	0.444373	−	0.895842i	$-0.353427\pi$
$3$	0.660414	+	0.176957i	0.381290	+	0.102166i	−0.0630827	+	0.998008i	$0.520093\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.483457	+	2.18318i	0.216208	+	0.976347i
$5$	0.483457	+	2.18318i	0.216208	+	0.976347i
$6$	0.660414	−	0.176957i	0.269613	−	0.0722426i
$7$	0.189447	−	0.328132i	0.0716042	−	0.124022i	−0.828000	−	0.560728i	$-0.810521\pi$
$7$	0.189447	−	0.328132i	0.0716042	−	0.124022i	0.899605	+	0.436705i	$0.143855\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.19324	−	1.26627i	−0.731081	−	0.422090i
$10$	1.51028	+	1.64896i	0.477591	+	0.521447i
$11$	0.895058	+	0.239830i	0.269870	+	0.0723115i	0.391216	−	0.920299i	$-0.372054\pi$
$11$	0.895058	+	0.239830i	0.269870	+	0.0723115i	−0.121346	+	0.992610i	$0.538721\pi$
$12$	0.483457	−	0.483457i	0.139562	−	0.139562i
$13$	−3.16145	−	1.73356i	−0.876828	−	0.480804i
$13$	−3.16145	−	1.73356i	−0.876828	−	0.480804i
$14$		−	0.378894i		−	0.101264i
$15$	−0.0670481	+	1.52735i	−0.0173117	+	0.394361i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.589312	−	2.19934i	−0.142929	−	0.533419i	−0.999839	−	0.0179524i	$-0.994285\pi$
$17$	−0.589312	−	2.19934i	−0.142929	−	0.533419i	0.856910	−	0.515467i	$-0.172381\pi$
$18$	−2.53254			−0.596925
$19$	−0.0311497	−	0.116252i	−0.00714623	−	0.0266701i	0.962261	−	0.272129i	$-0.0877279\pi$
$19$	−0.0311497	−	0.116252i	−0.00714623	−	0.0266701i	−0.969407	+	0.245459i	$0.921061\pi$
$20$	2.13242	+	0.672904i	0.476823	+	0.150466i
$21$	0.183179	−	0.183179i	0.0399729	−	0.0399729i
$22$	0.895058	−	0.239830i	0.190827	−	0.0511320i
$23$	−2.32731	+	8.68563i	−0.485277	+	1.81108i	0.0935330	+	0.995616i	$0.470184\pi$
$23$	−2.32731	+	8.68563i	−0.485277	+	1.81108i	−0.578810	+	0.815462i	$0.696483\pi$
$24$	0.176957	−	0.660414i	0.0361213	−	0.134806i
$25$	−4.53254	+	2.11094i	−0.906508	+	0.422189i
$26$	−3.60468	+	0.0794160i	−0.706935	+	0.0155748i
$27$	−2.67474	−	2.67474i	−0.514755	−	0.514755i
$28$	−0.189447	−	0.328132i	−0.0358021	−	0.0620111i
$29$	5.31003	−	3.06575i	0.986048	−	0.569295i	0.0819573	−	0.996636i	$-0.473883\pi$
$29$	5.31003	−	3.06575i	0.986048	−	0.569295i	0.904091	+	0.427341i	$0.140550\pi$
$30$	0.705611	+	1.35625i	0.128826	+	0.247616i
$31$	2.45303	+	2.45303i	0.440577	+	0.440577i	0.892206	−	0.451629i	$-0.149157\pi$
$31$	2.45303	+	2.45303i	0.440577	+	0.440577i	−0.451629	+	0.892206i	$0.649157\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.548669	+	0.316774i	0.0955111	+	0.0551433i
$34$	−1.61003	−	1.61003i	−0.276118	−	0.276118i
$35$	0.807960	+	0.254959i	0.136570	+	0.0430960i
$36$	−2.19324	+	1.26627i	−0.365541	+	0.211045i
$37$	−1.07176	−	1.85634i	−0.176196	−	0.305180i	0.764379	−	0.644768i	$-0.223046\pi$
$37$	−1.07176	−	1.85634i	−0.176196	−	0.305180i	−0.940575	+	0.339587i	$0.889713\pi$
$38$	−0.0851026	−	0.0851026i	−0.0138055	−	0.0138055i
$39$	−1.78110	−	1.70431i	−0.285204	−	0.272908i
$40$	2.18318	−	0.483457i	0.345191	−	0.0764412i
$41$	0.855872	−	3.19416i	0.133665	−	0.498844i	−0.866335	−	0.499463i	$-0.833531\pi$
$41$	0.855872	−	3.19416i	0.133665	−	0.498844i	1.00000		0.000619694i	$0.000197255\pi$
$42$	0.0670481	−	0.250227i	0.0103457	−	0.0386108i
$43$	−7.67535	+	2.05660i	−1.17048	+	0.313629i	−0.791144	−	0.611630i	$-0.790514\pi$
$43$	−7.67535	+	2.05660i	−1.17048	+	0.313629i	−0.379336	+	0.925259i	$0.623848\pi$
$44$	0.655228	−	0.655228i	0.0987794	−	0.0987794i
$45$	1.70415	−	5.40043i	0.254040	−	0.805048i
$46$	2.32731	+	8.68563i	0.343143	+	1.28063i
$47$	4.99481			0.728568			0.364284	−	0.931288i	$-0.381314\pi$
$47$	4.99481			0.728568			0.364284	+	0.931288i	$0.381314\pi$
$48$	−0.176957	−	0.660414i	−0.0255416	−	0.0953226i
$49$	3.42822	+	5.93785i	0.489746	+	0.848264i
$50$	−2.86982	+	4.09440i	−0.405854	+	0.579036i
$51$		−	1.55676i		−	0.217990i
$52$	−3.08203	+	1.87111i	−0.427401	+	0.259477i
$53$	−0.286513	+	0.286513i	−0.0393555	+	0.0393555i	−0.726511	−	0.687155i	$-0.758859\pi$
$53$	−0.286513	+	0.286513i	−0.0393555	+	0.0393555i	0.687155	+	0.726511i	$0.258859\pi$
$54$	−3.65377	−	0.979024i	−0.497215	−	0.133228i
$55$	−0.0908702	+	2.07002i	−0.0122529	+	0.279121i
$56$	−0.328132	−	0.189447i	−0.0438485	−	0.0253159i
$57$		−	0.0822868i		−	0.0108992i
$58$	3.06575	−	5.31003i	0.402552	−	0.697241i
$59$	13.2458	−	3.54920i	1.72446	−	0.462067i	0.745563	−	0.666435i	$-0.232180\pi$
$59$	13.2458	−	3.54920i	1.72446	−	0.462067i	0.978894	+	0.204368i	$0.0655138\pi$
$60$	1.28920	+	0.821742i	0.166435	+	0.106086i
$61$	4.60338	−	7.97329i	0.589403	−	1.02088i	−0.404908	−	0.914357i	$-0.632696\pi$
$61$	4.60338	−	7.97329i	0.589403	−	1.02088i	0.994311	−	0.106518i	$-0.0339703\pi$
$62$	3.35090	+	0.897870i	0.425564	+	0.114030i
$63$	−0.831007	+	0.479782i	−0.104697	+	0.0604468i
$64$	−1.00000			−0.125000
$65$	2.25625	−	7.74011i	0.279854	−	0.960043i
$66$	0.633549			0.0779845
$67$	−7.24548	+	4.18318i	−0.885176	+	0.511057i	−0.872362	−	0.488861i	$-0.837412\pi$
$67$	−7.24548	+	4.18318i	−0.885176	+	0.511057i	−0.0128145	+	0.999918i	$0.504079\pi$
$68$	−2.19934	−	0.589312i	−0.266710	−	0.0714646i
$69$	−3.07397	+	5.32428i	−0.370063	+	0.640968i
$70$	0.827193	−	0.183179i	0.0988685	−	0.0218941i
$71$	8.69557	−	2.32997i	1.03197	−	0.276517i	0.297191	−	0.954818i	$-0.403950\pi$
$71$	8.69557	−	2.32997i	1.03197	−	0.276517i	0.734784	+	0.678301i	$0.237284\pi$
$72$	−1.26627	+	2.19324i	−0.149231	+	0.258476i
$73$		−	11.2294i		−	1.31430i	−0.753760	−	0.657150i	$-0.771762\pi$
$73$		−	11.2294i		−	1.31430i	0.753760	−	0.657150i	$-0.228238\pi$
$74$	−1.85634	−	1.07176i	−0.215795	−	0.124589i
$75$	−3.36690	+	0.592031i	−0.388776	+	0.0683619i
$76$	−0.116252	−	0.0311497i	−0.0133351	−	0.00357312i
$77$	0.248262	−	0.248262i	0.0282921	−	0.0282921i
$78$	−2.39463	−	0.585427i	−0.271139	−	0.0662865i
$79$			6.19564i			0.697064i	0.937297	+	0.348532i	$0.113320\pi$
$79$			6.19564i			0.697064i	−0.937297	+	0.348532i	$0.886680\pi$
$80$	1.64896	−	1.51028i	0.184359	−	0.168854i
$81$	2.50569	+	4.33998i	0.278410	+	0.482220i
$82$	−0.855872	−	3.19416i	−0.0945152	−	0.352736i
$83$	10.8523			1.19120			0.595599	−	0.803282i	$-0.296915\pi$
$83$	10.8523			1.19120			0.595599	+	0.803282i	$0.296915\pi$
$84$	−0.0670481	−	0.250227i	−0.00731555	−	0.0273020i
$85$	4.51665	−	2.34986i	0.489900	−	0.254878i
$86$	−5.61875	+	5.61875i	−0.605885	+	0.605885i
$87$	4.04933	−	1.08501i	0.434133	−	0.116326i
$88$	0.239830	−	0.895058i	0.0255660	−	0.0954135i
$89$	−0.273792	+	1.02180i	−0.0290218	+	0.108311i	−0.978917	−	0.204256i	$-0.934522\pi$
$89$	−0.273792	+	1.02180i	−0.0290218	+	0.108311i	0.949896	+	0.312567i	$0.101189\pi$
$90$	−1.22437	−	5.52899i	−0.129060	−	0.582806i
$91$	−1.16776	+	0.708954i	−0.122415	+	0.0743186i
$92$	6.35832	+	6.35832i	0.662901	+	0.662901i
$93$	1.18593	+	2.05409i	0.122975	+	0.213000i
$94$	4.32564	−	2.49741i	0.446155	−	0.257588i
$95$	0.238740	−	0.124208i	0.0244942	−	0.0127435i
$96$	−0.483457	−	0.483457i	−0.0493426	−	0.0493426i
$97$	−10.4433	−	6.02947i	−1.06036	−	0.612200i	−0.134829	−	0.990869i	$-0.543049\pi$
$97$	−10.4433	−	6.02947i	−1.06036	−	0.612200i	−0.925532	+	0.378669i	$0.876382\pi$
$98$	5.93785	+	3.42822i	0.599813	+	0.346302i
$99$	−1.65939	−	1.65939i	−0.166775	−	0.166775i
$100$	−0.438138	+	4.98077i	−0.0438138	+	0.498077i
$101$	−12.8481	+	7.41785i	−1.27843	+	0.738103i	−0.976560	−	0.215245i	$-0.930945\pi$
$101$	−12.8481	+	7.41785i	−1.27843	+	0.738103i	−0.301872	+	0.953348i	$0.597612\pi$
$102$	−0.778380	−	1.34819i	−0.0770711	−	0.133491i
$103$	7.14285	+	7.14285i	0.703806	+	0.703806i	0.965225	−	0.261420i	$-0.0841906\pi$
$103$	7.14285	+	7.14285i	0.703806	+	0.703806i	−0.261420	+	0.965225i	$0.584191\pi$
$104$	−1.73356	+	3.16145i	−0.169990	+	0.310006i
$105$	0.488471	+	0.311353i	0.0476699	+	0.0303849i
$106$	−0.104871	+	0.391383i	−0.0101860	+	0.0380145i
$107$	−2.03922	+	7.61047i	−0.197139	+	0.735732i	0.794564	+	0.607180i	$0.207699\pi$
$107$	−2.03922	+	7.61047i	−0.197139	+	0.735732i	−0.991703	+	0.128552i	$0.958967\pi$
$108$	−3.65377	+	0.979024i	−0.351584	+	0.0942066i
$109$	−3.45987	+	3.45987i	−0.331395	+	0.331395i	−0.853116	−	0.521721i	$-0.825290\pi$
$109$	−3.45987	+	3.45987i	−0.331395	+	0.331395i	0.521721	+	0.853116i	$0.325290\pi$
$110$	0.956314	+	1.83812i	0.0911810	+	0.175258i
$111$	−0.379311	−	1.41561i	−0.0360026	−	0.134364i
$112$	−0.378894			−0.0358021
$113$	0.340609	+	1.27117i	0.0320418	+	0.119582i	0.980094	−	0.198532i	$-0.0636173\pi$
$113$	0.340609	+	1.27117i	0.0320418	+	0.119582i	−0.948053	+	0.318114i	$0.896951\pi$
$114$	−0.0411434	−	0.0712625i	−0.00385343	−	0.00667434i
$115$	−20.0874	−	0.881802i	−1.87316	−	0.0822285i
$116$		−	6.13150i		−	0.569295i
$117$	4.73867	+	7.80537i	0.438090	+	0.721607i
$118$	9.69661	−	9.69661i	0.892645	−	0.892645i
$119$	−0.833318	−	0.223287i	−0.0763901	−	0.0204687i
$120$	1.52735	+	0.0670481i	0.139428	+	0.00612063i
$121$	−8.78267	−	5.07068i	−0.798424	−	0.460971i
$122$		−	9.20677i		−	0.833542i
$123$	1.13046	−	1.95801i	0.101930	−	0.176548i
$124$	3.35090	−	0.897870i	0.300919	−	0.0806311i
$125$	−6.79986	−	8.87479i	−0.608198	−	0.793786i
$126$	−0.479782	+	0.831007i	−0.0427424	+	0.0740319i
$127$	6.73263	+	1.80400i	0.597425	+	0.160079i	0.544844	−	0.838537i	$-0.316589\pi$
$127$	6.73263	+	1.80400i	0.597425	+	0.160079i	0.0525803	+	0.998617i	$0.483255\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.43284			−0.478335
$130$	−1.91608	−	7.83126i	−0.168052	−	0.686847i
$131$	−13.8836			−1.21301			−0.606507	−	0.795078i	$-0.707430\pi$
$131$	−13.8836			−1.21301			−0.606507	+	0.795078i	$0.707430\pi$
$132$	0.548669	−	0.316774i	0.0477555	−	0.0275717i
$133$	−0.0440473	−	0.0118024i	−0.00381938	−	0.00102340i
$134$	−4.18318	+	7.24548i	−0.361372	+	0.625914i
$135$	4.54632	−	7.13256i	0.391285	−	0.613873i
$136$	−2.19934	+	0.589312i	−0.188592	+	0.0505331i
$137$	−6.27687	+	10.8719i	−0.536269	+	0.928845i	0.462832	+	0.886446i	$0.346833\pi$
$137$	−6.27687	+	10.8719i	−0.536269	+	0.928845i	−0.999101	+	0.0423991i	$0.986500\pi$
$138$			6.14795i			0.523348i
$139$	−17.9255	−	10.3493i	−1.52042	−	0.877815i	−0.999710	−	0.0240818i	$-0.992334\pi$
$139$	−17.9255	−	10.3493i	−1.52042	−	0.877815i	−0.520710	−	0.853733i	$-0.674333\pi$
$140$	0.624781	−	0.572234i	0.0528036	−	0.0483626i
$141$	3.29865	+	0.883869i	0.277796	+	0.0744352i
$142$	6.36560	−	6.36560i	0.534189	−	0.534189i
$143$	−2.41392	−	2.30985i	−0.201862	−	0.193159i
$144$			2.53254i			0.211045i
$145$	9.26024	+	10.1106i	0.769021	+	0.839639i
$146$	−5.61469	−	9.72494i	−0.464675	−	0.804841i
$147$	1.21330	+	4.52809i	0.100071	+	0.373471i
$148$	−2.14352			−0.176196
$149$	3.51501	+	13.1182i	0.287961	+	1.07468i	0.946648	+	0.322268i	$0.104445\pi$
$149$	3.51501	+	13.1182i	0.287961	+	1.07468i	−0.658687	+	0.752417i	$0.728888\pi$
$150$	−2.61981	+	2.19616i	−0.213906	+	0.179316i
$151$	8.29184	−	8.29184i	0.674780	−	0.674780i	−0.284034	−	0.958814i	$-0.591673\pi$
$151$	8.29184	−	8.29184i	0.674780	−	0.674780i	0.958814	+	0.284034i	$0.0916729\pi$
$152$	−0.116252	+	0.0311497i	−0.00942931	+	0.00252657i
$153$	−1.49246	+	5.56992i	−0.120658	+	0.450302i
$154$	0.0908702	−	0.339132i	0.00732253	−	0.0273280i
$155$	−4.16946	+	6.54133i	−0.334899	+	0.525412i
$156$	−2.36653	+	0.690322i	−0.189474	+	0.0552700i
$157$	−11.2602	−	11.2602i	−0.898665	−	0.898665i	0.0966528	−	0.995318i	$-0.469186\pi$
$157$	−11.2602	−	11.2602i	−0.898665	−	0.898665i	−0.995318	+	0.0966528i	$0.969186\pi$
$158$	3.09782	+	5.36558i	0.246449	+	0.426863i
$159$	−0.239917	+	0.138516i	−0.0190267	+	0.0109851i
$160$	0.672904	−	2.13242i	0.0531977	−	0.168582i
$161$	2.40913	+	2.40913i	0.189866	+	0.189866i
$162$	4.33998	+	2.50569i	0.340981	+	0.196865i
$163$	−1.75029	−	1.01053i	−0.137094	−	0.0791510i	0.429885	−	0.902884i	$-0.358554\pi$
$163$	−1.75029	−	1.01053i	−0.137094	−	0.0791510i	−0.566978	+	0.823733i	$0.691888\pi$
$164$	−2.33829	−	2.33829i	−0.182589	−	0.182589i
$165$	−0.426317	+	1.35099i	−0.0331888	+	0.105174i
$166$	9.39839	−	5.42616i	0.729456	−	0.421152i
$167$	9.35196	+	16.1981i	0.723676	+	1.25344i	0.959517	+	0.281652i	$0.0908824\pi$
$167$	9.35196	+	16.1981i	0.723676	+	1.25344i	−0.235841	+	0.971792i	$0.575784\pi$
$168$	−0.183179	−	0.183179i	−0.0141326	−	0.0141326i
$169$	6.98953	+	10.9611i	0.537656	+	0.843164i
$170$	2.73661	−	4.29337i	0.209888	−	0.329286i
$171$	−0.0788879	+	0.294413i	−0.00603271	+	0.0225144i
$172$	−2.05660	+	7.67535i	−0.156815	+	0.585240i
$173$	17.1102	−	4.58467i	1.30086	−	0.348566i	0.459088	−	0.888391i	$-0.348176\pi$
$173$	17.1102	−	4.58467i	1.30086	−	0.348566i	0.841777	+	0.539825i	$0.181510\pi$
$174$	2.96431	−	2.96431i	0.224724	−	0.224724i
$175$	−0.166008	+	1.88718i	−0.0125490	+	0.142658i
$176$	−0.239830	−	0.895058i	−0.0180779	−	0.0674676i
$177$	9.37578			0.704727
$178$	0.273792	+	1.02180i	0.0205215	+	0.0765875i
$179$	−12.1322	−	21.0135i	−0.906801	−	1.57063i	−0.818481	−	0.574534i	$-0.805183\pi$
$179$	−12.1322	−	21.0135i	−0.906801	−	1.57063i	−0.0883206	−	0.996092i	$-0.528150\pi$
$180$	−3.82483	−	4.17606i	−0.285086	−	0.311265i
$181$			8.47489i			0.629934i	0.949103	+	0.314967i	$0.101993\pi$
$181$			8.47489i			0.629934i	−0.949103	+	0.314967i	$0.898007\pi$
$182$	−0.656836	+	1.19785i	−0.0486879	+	0.0887908i
$183$	4.45107	−	4.45107i	0.329033	−	0.329033i
$184$	8.68563	+	2.32731i	0.640313	+	0.171571i
$185$	3.53457	−	3.23730i	0.259867	−	0.238011i
$186$	2.05409	+	1.18593i	0.150614	+	0.0869568i
$187$		−	2.10988i		−	0.154289i
$188$	2.49741	−	4.32564i	0.182142	−	0.315479i
$189$	−1.38439	+	0.370946i	−0.100700	+	0.0269824i
$190$	0.144651	−	0.226938i	0.0104941	−	0.0164638i
$191$	9.02643	−	15.6342i	0.653130	−	1.13125i	−0.329230	−	0.944250i	$-0.606789\pi$
$191$	9.02643	−	15.6342i	0.653130	−	1.13125i	0.982359	−	0.187004i	$-0.0598777\pi$
$192$	−0.660414	−	0.176957i	−0.0476613	−	0.0127708i
$193$	5.93606	−	3.42718i	0.427287	−	0.246694i	−0.270903	−	0.962607i	$-0.587322\pi$
$193$	5.93606	−	3.42718i	0.427287	−	0.246694i	0.698190	+	0.715912i	$0.253989\pi$
$194$	−12.0589			−0.865781
$195$	2.85973	−	4.71242i	0.204790	−	0.337463i
$196$	6.85644			0.489746
$197$	11.1979	−	6.46509i	0.797815	−	0.460619i	−0.0448917	−	0.998992i	$-0.514294\pi$
$197$	11.1979	−	6.46509i	0.797815	−	0.460619i	0.842706	+	0.538373i	$0.180961\pi$
$198$	−2.26677	−	0.607379i	−0.161092	−	0.0431646i
$199$	−4.21853	+	7.30671i	−0.299044	+	0.517959i	−0.975917	−	0.218140i	$-0.930001\pi$
$199$	−4.21853	+	7.30671i	−0.299044	+	0.517959i	0.676874	+	0.736099i	$0.263334\pi$
$200$	2.11094	+	4.53254i	0.149266	+	0.320499i
$201$	−5.52526	+	1.48049i	−0.389722	+	0.104426i
$202$	−7.41785	+	12.8481i	−0.521918	+	0.903988i
$203$		−	2.32319i		−	0.163056i
$204$	−1.34819	−	0.778380i	−0.0943925	−	0.0544975i
$205$	7.38719	+	0.324285i	0.515944	+	0.0226490i
$206$	9.75731	+	2.61446i	0.679824	+	0.182158i
$207$	16.1027	−	16.1027i	1.11921	−	1.11921i
$208$	0.0794160	+	3.60468i	0.00550651	+	0.249939i
$209$		−	0.111523i		−	0.00771422i
$210$	0.578705	+	0.0254041i	0.0399344	+	0.00175305i
$211$	6.29684	+	10.9064i	0.433492	+	0.750830i	0.997171	−	0.0751634i	$-0.0239478\pi$
$211$	6.29684	+	10.9064i	0.433492	+	0.750830i	−0.563679	+	0.825994i	$0.690615\pi$
$212$	0.104871	+	0.391383i	0.00720256	+	0.0268803i
$213$	6.15498			0.421733
$214$	2.03922	+	7.61047i	0.139398	+	0.520241i
$215$	−8.20064	−	15.7624i	−0.559279	−	1.07499i
$216$	−2.67474	+	2.67474i	−0.181993	+	0.181993i
$217$	1.26963	−	0.340197i	0.0861884	−	0.0230941i
$218$	−1.26640	+	4.72627i	−0.0857714	+	0.320103i
$219$	1.98712	−	7.41605i	0.134277	−	0.501130i
$220$	1.74725	+	1.11371i	0.117800	+	0.0750860i
$221$	−1.94962	+	7.97472i	−0.131145	+	0.536438i
$222$	−1.03630	−	1.03630i	−0.0695517	−	0.0695517i
$223$	−5.76572	−	9.98652i	−0.386101	−	0.668747i	0.605820	−	0.795602i	$-0.292845\pi$
$223$	−5.76572	−	9.98652i	−0.386101	−	0.668747i	−0.991921	+	0.126855i	$0.959512\pi$
$224$	−0.328132	+	0.189447i	−0.0219242	+	0.0126580i
$225$	12.6140	+	1.10960i	0.840932	+	0.0739734i
$226$	0.930561	+	0.930561i	0.0619000	+	0.0619000i
$227$	−8.87817	−	5.12582i	−0.589265	−	0.340212i	0.175542	−	0.984472i	$-0.443832\pi$
$227$	−8.87817	−	5.12582i	−0.589265	−	0.340212i	−0.764807	+	0.644260i	$0.777166\pi$
$228$	−0.0712625	−	0.0411434i	−0.00471947	−	0.00272479i
$229$	10.0876	+	10.0876i	0.666607	+	0.666607i	0.956929	−	0.290322i	$-0.0937624\pi$
$229$	10.0876	+	10.0876i	0.666607	+	0.666607i	−0.290322	+	0.956929i	$0.593762\pi$
$230$	−17.8371	+	9.28005i	−1.17615	+	0.611909i
$231$	0.207887	−	0.120024i	0.0136780	−	0.00789699i
$232$	−3.06575	−	5.31003i	−0.201276	−	0.348621i
$233$	3.31418	+	3.31418i	0.217119	+	0.217119i	0.807283	−	0.590164i	$-0.200937\pi$
$233$	3.31418	+	3.31418i	0.217119	+	0.217119i	−0.590164	+	0.807283i	$0.700937\pi$
$234$	8.00650	+	4.39031i	0.523401	+	0.287004i
$235$	2.41478	+	10.9046i	0.157523	+	0.711336i
$236$	3.54920	−	13.2458i	0.231034	−	0.862229i
$237$	−1.09636	+	4.09169i	−0.0712165	+	0.265784i
$238$	−0.833318	+	0.223287i	−0.0540160	+	0.0144735i
$239$	−3.70335	+	3.70335i	−0.239550	+	0.239550i	−0.816664	−	0.577114i	$-0.804179\pi$
$239$	−3.70335	+	3.70335i	−0.239550	+	0.239550i	0.577114	+	0.816664i	$0.304179\pi$
$240$	1.35625	−	0.705611i	0.0875456	−	0.0455470i
$241$	−3.75780	−	14.0243i	−0.242061	−	0.903385i	−0.974838	−	0.222915i	$-0.928443\pi$
$241$	−3.75780	−	14.0243i	−0.242061	−	0.903385i	0.732777	−	0.680469i	$-0.238224\pi$
$242$	−10.1414			−0.651911
$243$	3.82387	+	14.2709i	0.245301	+	0.915478i
$244$	−4.60338	−	7.97329i	−0.294701	−	0.510438i
$245$	−11.3060	+	10.3551i	−0.722313	+	0.661564i
$246$		−	2.26092i		−	0.144151i
$247$	−0.103052	+	0.421526i	−0.00655706	+	0.0268210i
$248$	2.45303	−	2.45303i	0.155767	−	0.155767i
$249$	7.16703	+	1.92040i	0.454192	+	0.121700i
$250$	−10.3262	−	4.28587i	−0.653089	−	0.271062i
$251$	−7.75590	−	4.47787i	−0.489548	−	0.282641i	0.234839	−	0.972034i	$-0.424544\pi$
$251$	−7.75590	−	4.47787i	−0.489548	−	0.282641i	−0.724387	+	0.689394i	$0.757877\pi$
$252$			0.959564i			0.0604468i
$253$	−4.16615	+	7.21598i	−0.261924	+	0.453665i
$254$	6.73263	−	1.80400i	0.422443	−	0.113193i
$255$	3.39869	−	0.752626i	0.212834	−	0.0471313i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.68822	−	2.06005i	−0.479578	−	0.128503i	0.0109281	−	0.999940i	$-0.496521\pi$
$257$	−7.68822	−	2.06005i	−0.479578	−	0.128503i	−0.490506	+	0.871438i	$0.663188\pi$
$258$	−4.70498	+	2.71642i	−0.292919	+	0.169117i
$259$	−0.812165			−0.0504655
$260$	−5.57501	−	5.82403i	−0.345747	−	0.361191i
$261$	−15.5283			−0.961175
$262$	−12.0235	+	6.94179i	−0.742816	+	0.428865i
$263$	−27.1991	−	7.28798i	−1.67717	−	0.449396i	−0.710139	−	0.704061i	$-0.751368\pi$
$263$	−27.1991	−	7.28798i	−1.67717	−	0.449396i	−0.967029	+	0.254665i	$0.918035\pi$
$264$	0.316774	−	0.548669i	0.0194961	−	0.0337683i
$265$	−0.764025	−	0.486992i	−0.0469337	−	0.0299157i
$266$	−0.0440473	+	0.0118024i	−0.00270071	+	0.000723654i
$267$	−0.361632	+	0.626364i	−0.0221315	+	0.0383329i
$268$			8.36636i			0.511057i
$269$	−10.9664	−	6.33147i	−0.668634	−	0.386036i	0.126925	−	0.991912i	$-0.459489\pi$
$269$	−10.9664	−	6.33147i	−0.668634	−	0.386036i	−0.795559	+	0.605876i	$0.792823\pi$
$270$	0.370946	−	8.45014i	0.0225751	−	0.514259i
$271$	26.6019	+	7.12796i	1.61595	+	0.432993i	0.949808	−	0.312832i	$-0.101278\pi$
$271$	26.6019	+	7.12796i	1.61595	+	0.432993i	0.666142	+	0.745825i	$0.267944\pi$
$272$	−1.61003	+	1.61003i	−0.0976225	+	0.0976225i
$273$	−0.896662	+	0.261559i	−0.0542685	+	0.0158303i
$274$			12.5537i			0.758399i
$275$	−4.56315	+	0.802379i	−0.275169	+	0.0483853i
$276$	3.07397	+	5.32428i	0.185031	+	0.320484i
$277$	−4.93665	−	18.4238i	−0.296614	−	1.10698i	−0.939927	−	0.341376i	$-0.889107\pi$
$277$	−4.93665	−	18.4238i	−0.296614	−	1.10698i	0.643312	−	0.765604i	$-0.277560\pi$
$278$	−20.6986			−1.24142
$279$	−2.27389	−	8.48628i	−0.136134	−	0.508060i
$280$	0.254959	−	0.807960i	0.0152367	−	0.0482848i
$281$	−22.0054	+	22.0054i	−1.31273	+	1.31273i	−0.393337	+	0.919394i	$0.628680\pi$
$281$	−22.0054	+	22.0054i	−1.31273	+	1.31273i	−0.919394	+	0.393337i	$0.871320\pi$
$282$	3.29865	−	0.883869i	0.196431	−	0.0526337i
$283$	4.77227	−	17.8104i	0.283682	−	1.05872i	−0.666115	−	0.745849i	$-0.732044\pi$
$283$	4.77227	−	17.8104i	0.283682	−	1.05872i	0.949797	−	0.312867i	$-0.101289\pi$
$284$	2.32997	−	8.69557i	0.138258	−	0.515987i
$285$	0.179647	−	0.0397821i	0.0106414	−	0.00235649i
$286$	−3.24544	−	0.793428i	−0.191907	−	0.0469164i
$287$	−0.885962	−	0.885962i	−0.0522967	−	0.0522967i
$288$	1.26627	+	2.19324i	0.0746157	+	0.129238i
$289$	10.2326	−	5.90780i	0.601918	−	0.347518i
$290$	13.0749	+	4.12591i	0.767785	+	0.242282i
$291$	−5.82998	−	5.82998i	−0.341759	−	0.341759i
$292$	−9.72494	−	5.61469i	−0.569109	−	0.328575i
$293$	−21.2147	−	12.2483i	−1.23938	−	0.715555i	−0.270411	−	0.962745i	$-0.587160\pi$
$293$	−21.2147	−	12.2483i	−1.23938	−	0.715555i	−0.968967	+	0.247190i	$0.920493\pi$
$294$	3.31479	+	3.31479i	0.193323	+	0.193323i
$295$	14.1523	+	27.2021i	0.823980	+	1.58377i
$296$	−1.85634	+	1.07176i	−0.107898	+	0.0622947i
$297$	−1.75257	−	3.03553i	−0.101694	−	0.176140i
$298$	9.60319	+	9.60319i	0.556298	+	0.556298i
$299$	22.4147	−	23.4246i	1.29628	−	1.35468i
$300$	−1.17074	+	3.21184i	−0.0675925	+	0.185435i
$301$	−0.779235	+	2.90814i	−0.0449144	+	0.167623i
$302$	3.03502	−	11.3269i	0.174646	−	0.651788i
$303$	−9.79770	+	2.62529i	−0.562863	+	0.150819i
$304$	−0.0851026	+	0.0851026i	−0.00488097	+	0.00488097i
$305$	19.6327	+	6.19527i	1.12416	+	0.354740i
$306$	1.49246	+	5.56992i	0.0853181	+	0.318411i
$307$	−4.06480			−0.231990			−0.115995	−	0.993250i	$-0.537006\pi$
$307$	−4.06480			−0.231990			−0.115995	+	0.993250i	$0.537006\pi$
$308$	−0.0908702	−	0.339132i	−0.00517781	−	0.0193238i
$309$	3.45326	+	5.98122i	0.196449	+	0.340260i
$310$	−0.340197	+	7.74969i	−0.0193219	+	0.440153i
$311$			17.7947i			1.00904i	0.863399	+	0.504522i	$0.168331\pi$
$311$			17.7947i			1.00904i	−0.863399	+	0.504522i	$0.831669\pi$
$312$	−1.70431	+	1.78110i	−0.0964876	+	0.100835i
$313$	−7.24706	+	7.24706i	−0.409628	+	0.409628i	−0.881609	−	0.471981i	$-0.843539\pi$
$313$	−7.24706	+	7.24706i	−0.409628	+	0.409628i	0.471981	+	0.881609i	$0.343539\pi$
$314$	−15.3818	−	4.12154i	−0.868044	−	0.232592i
$315$	−1.44921	−	1.58228i	−0.0816535	−	0.0891515i
$316$	5.36558	+	3.09782i	0.301837	+	0.174266i
$317$			13.4590i			0.755932i	0.925819	+	0.377966i	$0.123376\pi$
$317$			13.4590i			0.755932i	−0.925819	+	0.377966i	$0.876624\pi$
$318$	−0.138516	+	0.239917i	−0.00776761	+	0.0134539i
$319$	5.48805	−	1.47052i	0.307272	−	0.0823332i
$320$	−0.483457	−	2.18318i	−0.0270260	−	0.122043i
$321$	−2.69346	+	4.66521i	−0.150334	+	0.260386i
$322$	3.29093	+	0.881802i	0.183396	+	0.0491409i
$323$	−0.237322	+	0.137018i	−0.0132049	+	0.00762387i
$324$	5.01137			0.278410
$325$	17.9888	+	1.18379i	0.997842	+	0.0656650i
$326$	−2.02107			−0.111936
$327$	−2.89719	+	1.67270i	−0.160215	+	0.0925003i
$328$	−3.19416	−	0.855872i	−0.176368	−	0.0472576i
$329$	0.946252	−	1.63896i	0.0521686	−	0.0903586i
$330$	0.306293	+	1.38315i	0.0168609	+	0.0761399i
$331$	−17.6915	+	4.74042i	−0.972412	+	0.260557i	−0.709846	−	0.704357i	$-0.751235\pi$
$331$	−17.6915	+	4.74042i	−0.972412	+	0.260557i	−0.262566	+	0.964914i	$0.584569\pi$
$332$	5.42616	−	9.39839i	0.297799	−	0.515803i
$333$			5.42854i			0.297482i
$334$	16.1981	+	9.35196i	0.886319	+	0.511716i
$335$	−12.6355	−	13.7958i	−0.690351	−	0.753744i
$336$	−0.250227	−	0.0670481i	−0.0136510	−	0.00365777i
$337$	5.76560	−	5.76560i	0.314072	−	0.314072i	−0.532413	−	0.846485i	$-0.678715\pi$
$337$	5.76560	−	5.76560i	0.314072	−	0.314072i	0.846485	+	0.532413i	$0.178715\pi$
$338$	11.5337	+	5.99786i	0.627349	+	0.326241i
$339$			0.899772i			0.0488689i
$340$	0.223287	−	5.08647i	0.0121094	−	0.275852i
$341$	1.60729	+	2.78391i	0.0870397	+	0.150757i
$342$	0.0788879	+	0.294413i	0.00426577	+	0.0159201i
$343$	5.25012			0.283480
$344$	2.05660	+	7.67535i	0.110885	+	0.413827i
$345$	−13.1100	−	4.13697i	−0.705818	−	0.222727i
$346$	12.5255	−	12.5255i	0.673377	−	0.673377i
$347$	18.6232	−	4.99008i	0.999747	−	0.267881i	0.278407	−	0.960463i	$-0.410193\pi$
$347$	18.6232	−	4.99008i	0.999747	−	0.267881i	0.721339	+	0.692582i	$0.243527\pi$
$348$	1.08501	−	4.04933i	0.0581628	−	0.217067i
$349$	8.27437	−	30.8804i	0.442917	−	1.65299i	−0.278462	−	0.960447i	$-0.589825\pi$
$349$	8.27437	−	30.8804i	0.442917	−	1.65299i	0.721379	−	0.692541i	$-0.243509\pi$
$350$	0.799824	+	1.71735i	0.0427524	+	0.0917963i
$351$	3.81923	+	13.0929i	0.203856	+	0.698847i
$352$	−0.655228	−	0.655228i	−0.0349238	−	0.0349238i
$353$	−4.53267	−	7.85082i	−0.241250	−	0.417857i	0.719821	−	0.694160i	$-0.244224\pi$
$353$	−4.53267	−	7.85082i	−0.241250	−	0.417857i	−0.961071	+	0.276303i	$0.910891\pi$
$354$	8.11966	−	4.68789i	0.431555	−	0.249158i
$355$	9.29068	+	17.8575i	0.493098	+	0.947780i
$356$	0.748013	+	0.748013i	0.0396446	+	0.0396446i
$357$	−0.510823	−	0.294924i	−0.0270356	−	0.0156090i
$358$	−21.0135	−	12.1322i	−1.11060	−	0.641205i
$359$	6.31399	+	6.31399i	0.333240	+	0.333240i	0.853816	−	0.520576i	$-0.174283\pi$
$359$	6.31399	+	6.31399i	0.333240	+	0.333240i	−0.520576	+	0.853816i	$0.674283\pi$
$360$	−5.40043	−	1.70415i	−0.284628	−	0.0898168i
$361$	16.4419	−	9.49276i	0.865365	−	0.499619i
$362$	4.23745	+	7.33947i	0.222715	+	0.385754i
$363$	−4.90290	−	4.90290i	−0.257336	−	0.257336i
$364$	0.0300903	+	1.36579i	0.00157716	+	0.0715868i
$365$	24.5158	−	5.42892i	1.28321	−	0.284163i
$366$	1.62921	−	6.08028i	0.0851600	−	0.317821i
$367$	−2.68725	+	10.0289i	−0.140273	+	0.523506i	0.859647	+	0.510888i	$0.170683\pi$
$367$	−2.68725	+	10.0289i	−0.140273	+	0.523506i	−0.999920	+	0.0126182i	$0.995983\pi$
$368$	8.68563	−	2.32731i	0.452770	−	0.121319i
$369$	−5.92180	+	5.92180i	−0.308277	+	0.308277i
$370$	1.44238	−	4.57087i	0.0749858	−	0.237628i
$371$	0.0397349	+	0.148293i	0.00206294	+	0.00769898i
$372$	2.37186			0.122975
$373$	3.24216	+	12.0999i	0.167873	+	0.626509i	0.997656	+	0.0684241i	$0.0217971\pi$
$373$	3.24216	+	12.0999i	0.167873	+	0.626509i	−0.829784	+	0.558085i	$0.811536\pi$
$374$	−1.05494	−	1.82721i	−0.0545495	−	0.0944825i
$375$	−2.92026	−	7.06432i	−0.150802	−	0.364800i
$376$		−	4.99481i		−	0.257588i
$377$	−22.1021	+	0.486939i	−1.13831	+	0.0250786i
$378$	−1.01344	+	1.01344i	−0.0521259	+	0.0521259i
$379$	−25.1554	−	6.74037i	−1.29215	−	0.346230i	−0.453671	−	0.891169i	$-0.649886\pi$
$379$	−25.1554	−	6.74037i	−1.29215	−	0.346230i	−0.838475	+	0.544939i	$0.816553\pi$
$380$	0.0118024	−	0.268859i	0.000605452	−	0.0137922i
$381$	4.12709	+	2.38278i	0.211437	+	0.122073i
$382$		−	18.0529i		−	0.923665i
$383$	−0.602501	+	1.04356i	−0.0307863	+	0.0533235i	−0.881008	−	0.473101i	$-0.843134\pi$
$383$	−0.602501	+	1.04356i	−0.0307863	+	0.0533235i	0.850222	+	0.526425i	$0.176468\pi$
$384$	−0.660414	+	0.176957i	−0.0337016	+	0.00903032i
$385$	0.662024	+	0.421976i	0.0337399	+	0.0215059i
$386$	3.42718	−	5.93606i	0.174439	−	0.302137i
$387$	19.4381	+	5.20843i	0.988096	+	0.264759i
$388$	−10.4433	+	6.02947i	−0.530181	+	0.306100i
$389$	−28.4152			−1.44071			−0.720354	−	0.693606i	$-0.756021\pi$
$389$	−28.4152			−1.44071			−0.720354	+	0.693606i	$0.756021\pi$
$390$	0.120390	−	5.51094i	0.00609620	−	0.279057i
$391$	20.4742			1.03542
$392$	5.93785	−	3.42822i	0.299907	−	0.173151i
$393$	−9.16891	−	2.45680i	−0.462510	−	0.123929i
$394$	6.46509	−	11.1979i	0.325707	−	0.564140i
$395$	−13.5262	+	2.99532i	−0.680576	+	0.150711i
$396$	−2.26677	+	0.607379i	−0.113909	+	0.0305220i
$397$	−6.64275	+	11.5056i	−0.333390	+	0.577449i	−0.983174	−	0.182670i	$-0.941526\pi$
$397$	−6.64275	+	11.5056i	−0.333390	+	0.577449i	0.649784	+	0.760119i	$0.274859\pi$
$398$			8.43706i			0.422912i
$399$	−0.0270009	−	0.0155890i	−0.00135174	−	0.000780426i
$400$	4.09440	+	2.86982i	0.204720	+	0.143491i
$401$	24.6586	+	6.60726i	1.23139	+	0.329951i	0.815122	−	0.579290i	$-0.196670\pi$
$401$	24.6586	+	6.60726i	1.23139	+	0.329951i	0.416271	+	0.909241i	$0.363337\pi$
$402$	−4.04477	+	4.04477i	−0.201735	+	0.201735i
$403$	−3.50265	−	12.0076i	−0.174479	−	0.598141i
$404$			14.8357i			0.738103i
$405$	−8.26355	+	7.56855i	−0.410619	+	0.376084i
$406$	−1.16159	−	2.01194i	−0.0576489	−	0.0998508i
$407$	−0.514080	−	1.91857i	−0.0254820	−	0.0951001i
$408$	−1.55676			−0.0770711
$409$	7.00448	+	26.1411i	0.346349	+	1.29259i	0.891028	+	0.453948i	$0.149985\pi$
$409$	7.00448	+	26.1411i	0.346349	+	1.29259i	−0.544679	+	0.838645i	$0.683348\pi$
$410$	6.55964	−	3.41276i	0.323957	−	0.168544i
$411$	−6.06919	+	6.06919i	−0.299371	+	0.299371i
$412$	9.75731	−	2.61446i	0.480708	−	0.128805i
$413$	1.34477	−	5.01876i	0.0661719	−	0.246957i
$414$	5.89400	−	21.9967i	0.289674	−	1.08108i
$415$	5.24663	+	23.6926i	0.257547	+	1.16302i
$416$	1.87111	+	3.08203i	0.0917389	+	0.151109i
$417$	−10.0069	−	10.0069i	−0.490038	−	0.490038i
$418$	−0.0557616	−	0.0965819i	−0.00272739	−	0.00472398i
$419$	17.3895	−	10.0398i	0.849531	−	0.490477i	−0.0109618	−	0.999940i	$-0.503489\pi$
$419$	17.3895	−	10.0398i	0.849531	−	0.490477i	0.860492	+	0.509463i	$0.170156\pi$
$420$	0.513875	−	0.267352i	0.0250745	−	0.0130454i
$421$	−25.0166	−	25.0166i	−1.21923	−	1.21923i	−0.967900	−	0.251334i	$-0.919131\pi$
$421$	−25.0166	−	25.0166i	−1.21923	−	1.21923i	−0.251334	−	0.967900i	$-0.580869\pi$
$422$	10.9064	+	6.29684i	0.530917	+	0.306525i
$423$	−10.9548	−	6.32478i	−0.532643	−	0.307521i
$424$	0.286513	+	0.286513i	0.0139143	+	0.0139143i
$425$	7.31377	+	8.72460i	0.354770	+	0.423205i
$426$	5.33037	−	3.07749i	0.258257	−	0.149105i
$427$	−1.74419	−	3.02103i	−0.0844075	−	0.146198i
$428$	5.57125	+	5.57125i	0.269297	+	0.269297i
$429$	−1.18544	−	1.95262i	−0.0572337	−	0.0942733i
$430$	−14.9832	−	9.55031i	−0.722552	−	0.460557i
$431$	−0.975777	+	3.64165i	−0.0470015	+	0.175412i	−0.985436	−	0.170044i	$-0.945609\pi$
$431$	−0.975777	+	3.64165i	−0.0470015	+	0.175412i	0.938435	+	0.345456i	$0.112276\pi$
$432$	−0.979024	+	3.65377i	−0.0471033	+	0.175792i
$433$	38.1793	−	10.2301i	1.83478	−	0.491628i	0.836381	−	0.548149i	$-0.184667\pi$
$433$	38.1793	−	10.2301i	1.83478	−	0.491628i	0.998401	+	0.0565202i	$0.0180005\pi$
$434$	0.929437	−	0.929437i	0.0446144	−	0.0446144i
$435$	4.32645	+	8.31585i	0.207438	+	0.398714i
$436$	1.26640	+	4.72627i	0.0606495	+	0.226347i
$437$	1.08222			0.0517696
$438$	−1.98712	−	7.41605i	−0.0949484	−	0.354352i
$439$	−2.45915	−	4.25937i	−0.117369	−	0.203289i	0.801355	−	0.598189i	$-0.204113\pi$
$439$	−2.45915	−	4.25937i	−0.117369	−	0.203289i	−0.918724	+	0.394900i	$0.870779\pi$
$440$	2.07002	+	0.0908702i	0.0986843	+	0.00433207i
$441$		−	17.3642i		−	0.826867i
$442$	2.29894	+	7.88112i	0.109350	+	0.374867i
$443$	−18.9234	+	18.9234i	−0.899080	+	0.899080i	−0.995355	−	0.0962751i	$-0.969307\pi$
$443$	−18.9234	+	18.9234i	−0.899080	+	0.899080i	0.0962751	+	0.995355i	$0.469307\pi$
$444$	−1.41561	−	0.379311i	−0.0671818	−	0.0180013i
$445$	−2.36315	−	0.103738i	−0.112024	−	0.00491765i
$446$	−9.98652	−	5.76572i	−0.472876	−	0.273015i
$447$			9.28545i			0.439187i
$448$	−0.189447	+	0.328132i	−0.00895053	+	0.0155028i
$449$	−2.34340	+	0.627913i	−0.110592	+	0.0296330i	−0.313691	−	0.949525i	$-0.601565\pi$
$449$	−2.34340	+	0.627913i	−0.110592	+	0.0296330i	0.203099	+	0.979158i	$0.434899\pi$
$450$	11.4788	−	5.34605i	0.541117	−	0.252015i
$451$	1.53211	−	2.65369i	0.0721443	−	0.124958i
$452$	1.27117	+	0.340609i	0.0597908	+	0.0160209i
$453$	6.94335	−	4.00874i	0.326227	−	0.188347i
$454$	−10.2516			−0.481133
$455$	−2.11234	−	2.20669i	−0.0990279	−	0.103451i
$456$	−0.0822868			−0.00385343
$457$	9.29603	−	5.36707i	0.434850	−	0.251061i	−0.266561	−	0.963818i	$-0.585887\pi$
$457$	9.29603	−	5.36707i	0.434850	−	0.251061i	0.701411	+	0.712757i	$0.252554\pi$
$458$	13.7799	+	3.69232i	0.643893	+	0.172531i
$459$	−4.30642	+	7.45894i	−0.201006	+	0.348153i
$460$	−10.8074	+	16.9553i	−0.503897	+	0.790546i
$461$	−4.50275	+	1.20651i	−0.209714	+	0.0561926i	−0.362146	−	0.932121i	$-0.617956\pi$
$461$	−4.50275	+	1.20651i	−0.209714	+	0.0561926i	0.152433	+	0.988314i	$0.451289\pi$
$462$	0.120024	−	0.207887i	0.00558402	−	0.00967180i
$463$			17.2033i			0.799507i	0.916623	+	0.399753i	$0.130904\pi$
$463$			17.2033i			0.799507i	−0.916623	+	0.399753i	$0.869096\pi$
$464$	−5.31003	−	3.06575i	−0.246512	−	0.142324i
$465$	−3.91111	+	3.58217i	−0.181373	+	0.166119i
$466$	4.52726	+	1.21307i	0.209721	+	0.0561946i
$467$	4.23868	−	4.23868i	0.196142	−	0.196142i	−0.602202	−	0.798344i	$-0.705710\pi$
$467$	4.23868	−	4.23868i	0.196142	−	0.196142i	0.798344	+	0.602202i	$0.205710\pi$
$468$	9.12898	−	0.201124i	0.421987	−	0.00929697i
$469$			3.16996i			0.146375i
$470$	7.54354	+	8.23625i	0.347958	+	0.379910i
$471$	−5.44384	−	9.42901i	−0.250839	−	0.434466i
$472$	−3.54920	−	13.2458i	−0.163365	−	0.609688i
$473$	−7.36312			−0.338557
$474$	1.09636	+	4.09169i	0.0503577	+	0.187937i
$475$	0.386589	+	0.461163i	0.0177379	+	0.0211596i
$476$	−0.610031	+	0.610031i	−0.0279607	+	0.0279607i
$477$	0.991194	−	0.265590i	0.0453837	−	0.0121605i
$478$	−1.35552	+	5.05886i	−0.0620000	+	0.231387i
$479$	0.292924	−	1.09321i	0.0133841	−	0.0499500i	−0.958911	−	0.283708i	$-0.908436\pi$
$479$	0.292924	−	1.09321i	0.0133841	−	0.0499500i	0.972295	+	0.233758i	$0.0751022\pi$
$480$	0.821742	−	1.28920i	0.0375072	−	0.0588438i
$481$	0.170230	+	7.72668i	0.00776180	+	0.352306i
$482$	−10.2665	−	10.2665i	−0.467626	−	0.467626i
$483$	1.16471	+	2.01734i	0.0529961	+	0.0917920i
$484$	−8.78267	+	5.07068i	−0.399212	+	0.230485i
$485$	8.11450	−	25.7147i	0.368461	−	1.16764i
$486$	10.4470	+	10.4470i	0.473886	+	0.473886i
$487$	−29.0241	−	16.7570i	−1.31521	−	0.759334i	−0.332252	−	0.943191i	$-0.607809\pi$
$487$	−29.0241	−	16.7570i	−1.31521	−	0.759334i	−0.982953	+	0.183856i	$0.941142\pi$
$488$	−7.97329	−	4.60338i	−0.360934	−	0.208385i
$489$	−0.977097	−	0.977097i	−0.0441859	−	0.0441859i
$490$	−4.61372	+	14.6208i	−0.208427	+	0.660500i
$491$	11.2257	−	6.48115i	0.506608	−	0.292490i	−0.224831	−	0.974398i	$-0.572183\pi$
$491$	11.2257	−	6.48115i	0.506608	−	0.292490i	0.731438	+	0.681908i	$0.238850\pi$
$492$	−1.13046	−	1.95801i	−0.0509651	−	0.0882741i
$493$	−9.87190	−	9.87190i	−0.444608	−	0.444608i
$494$	0.121517	+	0.416578i	0.00546730	+	0.0187427i
$495$	2.82050	−	4.42499i	0.126772	−	0.198889i
$496$	0.897870	−	3.35090i	0.0403156	−	0.150460i
$497$	0.882812	−	3.29470i	0.0395995	−	0.147787i
$498$	7.16703	−	1.92040i	0.321162	−	0.0860551i
$499$	−12.5606	+	12.5606i	−0.562290	+	0.562290i	−0.929957	−	0.367667i	$-0.880157\pi$
$499$	−12.5606	+	12.5606i	−0.562290	+	0.562290i	0.367667	+	0.929957i	$0.380157\pi$
$500$	−11.0857	+	1.45145i	−0.495769	+	0.0649109i
$501$	3.30980	+	12.3523i	0.147871	+	0.551861i
$502$	−8.95574			−0.399714
$503$	8.65691	+	32.3080i	0.385993	+	1.44054i	0.836596	+	0.547820i	$0.184542\pi$
$503$	8.65691	+	32.3080i	0.385993	+	1.44054i	−0.450604	+	0.892724i	$0.648791\pi$
$504$	0.479782	+	0.831007i	0.0213712	+	0.0370160i
$505$	−22.4060	−	24.4635i	−0.997053	−	1.08861i
$506$			8.33230i			0.370416i
$507$	2.67633	+	8.47574i	0.118860	+	0.376421i
$508$	4.92863	−	4.92863i	0.218673	−	0.218673i
$509$	30.6906	+	8.22352i	1.36034	+	0.364501i	0.863940	−	0.503595i	$-0.167990\pi$
$509$	30.6906	+	8.22352i	1.36034	+	0.364501i	0.496396	+	0.868096i	$0.334656\pi$
$510$	2.56704	−	2.35114i	0.113670	−	0.104110i
$511$	−3.68472	−	2.12737i	−0.163002	−	0.0941095i
$512$			1.00000i			0.0441942i
$513$	−0.227628	+	0.394262i	−0.0100500	+	0.0174071i
$514$	−7.68822	+	2.06005i	−0.339113	+	0.0908650i
$515$	−12.1409	+	19.0474i	−0.534990	+	0.839327i
$516$	−2.71642	+	4.70498i	−0.119584	+	0.207125i
$517$	4.47065	+	1.19791i	0.196619	+	0.0526839i
$518$	−0.703356	+	0.406083i	−0.0309037	+	0.0178422i
$519$	12.1111			0.531619
$520$	−7.74011	−	2.25625i	−0.339426	−	0.0989432i
$521$	11.2898			0.494614			0.247307	−	0.968937i	$-0.420454\pi$
$521$	11.2898			0.494614			0.247307	+	0.968937i	$0.420454\pi$
$522$	−13.4479	+	7.76413i	−0.588597	+	0.339827i
$523$	32.7918	+	8.78653i	1.43389	+	0.384208i	0.890388	−	0.455203i	$-0.150433\pi$
$523$	32.7918	+	8.78653i	1.43389	+	0.384208i	0.543497	+	0.839411i	$0.317100\pi$
$524$	−6.94179	+	12.0235i	−0.303254	+	0.525251i
$525$	−0.443585	+	1.21695i	−0.0193596	+	0.0531119i
$526$	−27.1991	+	7.28798i	−1.18594	+	0.317771i
$527$	3.94945	−	6.84065i	0.172041	−	0.297983i
$528$		−	0.633549i		−	0.0275717i
$529$	−50.1052	−	28.9282i	−2.17849	−	1.25775i
$530$	−0.905161	−	0.0397349i	−0.0393177	−	0.00172598i
$531$	−33.5455	−	8.98850i	−1.45575	−	0.390068i
$532$	−0.0322449	+	0.0322449i	−0.00139799	+	0.00139799i
$533$	−8.24306	+	8.61446i	−0.357047	+	0.373134i
$534$			0.723263i			0.0312987i
$535$	−17.6009	−	0.772648i	−0.760953	−	0.0334045i
$536$	4.18318	+	7.24548i	0.180686	+	0.312957i
$537$	−4.29376	−	16.0245i	−0.185289	−	0.691509i
$538$	−12.6629			−0.545938
$539$	1.64438	+	6.13691i	0.0708285	+	0.264336i
$540$	−3.90382	−	7.50351i	−0.167994	−	0.322900i
$541$	11.8553	−	11.8553i	0.509700	−	0.509700i	−0.404734	−	0.914434i	$-0.632636\pi$
$541$	11.8553	−	11.8553i	0.509700	−	0.509700i	0.914434	+	0.404734i	$0.132636\pi$
$542$	26.6019	−	7.12796i	1.14265	−	0.306172i
$543$	−1.49970	+	5.59694i	−0.0643581	+	0.240188i
$544$	−0.589312	+	2.19934i	−0.0252666	+	0.0942961i
$545$	−9.22621	−	5.88081i	−0.395207	−	0.251906i
$546$	−0.645753	+	0.674848i	−0.0276357	+	0.0288808i
$547$	7.28174	+	7.28174i	0.311345	+	0.311345i	0.845430	−	0.534086i	$-0.179344\pi$
$547$	7.28174	+	7.28174i	0.311345	+	0.311345i	−0.534086	+	0.845430i	$0.679344\pi$
$548$	6.27687	+	10.8719i	0.268135	+	0.464423i
$549$	−20.1927	+	11.6583i	−0.861803	+	0.497562i
$550$	−3.55062	+	2.97646i	−0.151399	+	0.126917i
$551$	−0.521806	−	0.521806i	−0.0222297	−	0.0222297i
$552$	5.32428	+	3.07397i	0.226616	+	0.130837i
$553$	2.03299	+	1.17374i	0.0864513	+	0.0499127i
$554$	−13.4872	−	13.4872i	−0.573015	−	0.573015i
$555$	2.90715	−	1.51249i	0.123401	−	0.0642016i
$556$	−17.9255	+	10.3493i	−0.760210	+	0.438908i
$557$	14.2300	+	24.6471i	0.602944	+	1.04433i	0.992373	+	0.123274i	$0.0393393\pi$
$557$	14.2300	+	24.6471i	0.602944	+	1.04433i	−0.389428	+	0.921057i	$0.627327\pi$
$558$	−6.21239	−	6.21239i	−0.262991	−	0.262991i
$559$	27.8305	+	6.80385i	1.17710	+	0.287772i
$560$	−0.183179	−	0.827193i	−0.00774072	−	0.0349553i
$561$	0.373358	−	1.39339i	0.0157632	−	0.0588290i
$562$	−8.05453	+	30.0599i	−0.339760	+	1.26800i
$563$	14.4243	−	3.86499i	0.607913	−	0.162890i	0.0582861	−	0.998300i	$-0.481436\pi$
$563$	14.4243	−	3.86499i	0.607913	−	0.162890i	0.549627	+	0.835410i	$0.314770\pi$
$564$	2.41478	−	2.41478i	0.101680	−	0.101680i
$565$	−2.61052	+	1.35817i	−0.109825	+	0.0571385i
$566$	−4.77227	−	17.8104i	−0.200594	−	0.748625i
$567$	1.89878			0.0797412
$568$	−2.32997	−	8.69557i	−0.0977634	−	0.364858i
$569$	9.41820	+	16.3128i	0.394831	+	0.683868i	0.993080	−	0.117443i	$-0.0374697\pi$
$569$	9.41820	+	16.3128i	0.394831	+	0.683868i	−0.598248	+	0.801311i	$0.704136\pi$
$570$	0.135688	−	0.124276i	0.00568333	−	0.00520534i
$571$		−	31.7460i		−	1.32853i	−0.747497	−	0.664265i	$-0.768745\pi$
$571$		−	31.7460i		−	1.32853i	0.747497	−	0.664265i	$-0.231255\pi$
$572$	−3.20735	+	0.935592i	−0.134106	+	0.0391191i
$573$	8.72778	−	8.72778i	0.364608	−	0.364608i
$574$	−1.21025	−	0.324285i	−0.0505147	−	0.0135354i
$575$	−7.78627	−	44.2808i	−0.324710	−	1.84664i
$576$	2.19324	+	1.26627i	0.0913851	+	0.0527612i
$577$			0.818818i			0.0340879i	0.999855	+	0.0170439i	$0.00542551\pi$
$577$			0.818818i			0.0340879i	−0.999855	+	0.0170439i	$0.994574\pi$
$578$	5.90780	−	10.2326i	0.245732	−	0.425620i
$579$	4.52672	−	1.21293i	0.188124	−	0.0504077i
$580$	13.3861	−	2.96431i	0.555830	−	0.123086i
$581$	2.05594	−	3.56099i	0.0852947	−	0.147735i
$582$	−7.96389	−	2.13392i	−0.330114	−	0.0884538i
$583$	−0.325160	+	0.187731i	−0.0134667	+	0.00777503i
$584$	−11.2294			−0.464675
$585$	−14.7496	+	14.1189i	−0.609820	+	0.583746i
$586$	−24.4967			−1.01195
$587$	17.1038	−	9.87490i	0.705951	−	0.407581i	−0.103609	−	0.994618i	$-0.533039\pi$
$587$	17.1038	−	9.87490i	0.705951	−	0.407581i	0.809560	+	0.587037i	$0.199706\pi$
$588$	4.52809	+	1.21330i	0.186735	+	0.0500356i
$589$	0.208759	−	0.361581i	0.00860176	−	0.0148987i
$590$	25.8573	+	16.4815i	1.06453	+	0.678534i
$591$	8.53927	−	2.28809i	0.351259	−	0.0941195i
$592$	−1.07176	+	1.85634i	−0.0440490	+	0.0762951i
$593$		−	21.6010i		−	0.887049i	−0.896262	−	0.443524i	$-0.853728\pi$
$593$		−	21.6010i		−	0.887049i	0.896262	−	0.443524i	$-0.146272\pi$
$594$	−3.03553	−	1.75257i	−0.124550	−	0.0719087i
$595$	0.0846020	−	1.92723i	0.00346834	−	0.0790088i
$596$	13.1182	+	3.51501i	0.537342	+	0.143980i
$597$	−4.07895	+	4.07895i	−0.166940	+	0.166940i
$598$	7.69941	−	31.4937i	0.314852	−	1.28787i
$599$			19.5073i			0.797046i	0.917158	+	0.398523i	$0.130477\pi$
$599$			19.5073i			0.797046i	−0.917158	+	0.398523i	$0.869523\pi$
$600$	0.592031	+	3.36690i	0.0241696	+	0.137453i
$601$	−4.51855	−	7.82635i	−0.184315	−	0.319244i	0.759030	−	0.651055i	$-0.225673\pi$
$601$	−4.51855	−	7.82635i	−0.184315	−	0.319244i	−0.943346	+	0.331812i	$0.892340\pi$
$602$	0.779235	+	2.90814i	0.0317592	+	0.118527i
$603$	21.1881			0.862847
$604$	−3.03502	−	11.3269i	−0.123493	−	0.460883i
$605$	6.82415	−	21.6256i	0.277441	−	0.879205i
$606$	−7.17242	+	7.17242i	−0.291359	+	0.291359i
$607$	−18.3696	+	4.92213i	−0.745601	+	0.199783i	−0.611566	−	0.791194i	$-0.709460\pi$
$607$	−18.3696	+	4.92213i	−0.745601	+	0.199783i	−0.134035	+	0.990977i	$0.542793\pi$
$608$	−0.0311497	+	0.116252i	−0.00126329	+	0.00471465i
$609$	0.411105	−	1.53426i	0.0166588	−	0.0621716i
$610$	20.1000	−	4.45107i	0.813826	−	0.180219i
$611$	−15.7908	−	8.65882i	−0.638829	−	0.350298i
$612$	4.07747	+	4.07747i	0.164822	+	0.164822i
$613$	0.0195779	+	0.0339099i	0.000790744	+	0.00136961i	0.866421	−	0.499315i	$-0.166415\pi$
$613$	0.0195779	+	0.0339099i	0.000790744	+	0.00136961i	−0.865630	+	0.500685i	$0.833082\pi$
$614$	−3.52022	+	2.03240i	−0.142064	+	0.0820210i
$615$	4.82122	+	1.52138i	0.194410	+	0.0613480i
$616$	−0.248262	−	0.248262i	−0.0100028	−	0.0100028i
$617$	37.4537	+	21.6239i	1.50783	+	0.870546i	0.999958	+	0.00911390i	$0.00290108\pi$
$617$	37.4537	+	21.6239i	1.50783	+	0.870546i	0.507872	+	0.861432i	$0.330432\pi$
$618$	5.98122	+	3.45326i	0.240600	+	0.138910i
$619$	8.43247	+	8.43247i	0.338930	+	0.338930i	0.855964	−	0.517035i	$-0.172964\pi$
$619$	8.43247	+	8.43247i	0.338930	+	0.338930i	−0.517035	+	0.855964i	$0.672964\pi$
$620$	3.58022	+	6.88152i	0.143785	+	0.276369i
$621$	29.4568	−	17.0069i	1.18206	−	0.682462i
$622$	8.89734	+	15.4106i	0.356751	+	0.617911i
$623$	0.283417	+	0.283417i	0.0113549	+	0.0113549i
$624$	−0.585427	+	2.39463i	−0.0234358	+	0.0958620i
$625$	16.0878	−	19.1359i	0.643513	−	0.765435i
$626$	−2.65261	+	9.89967i	−0.106020	+	0.395670i
$627$	0.0197349	−	0.0736515i	0.000788134	−	0.00294136i
$628$	−15.3818	+	4.12154i	−0.613800	+	0.164467i
$629$	−3.45113	+	3.45113i	−0.137605	+	0.137605i
$630$	−2.04619	−	0.645694i	−0.0815221	−	0.0257251i
$631$	12.9011	+	48.1475i	0.513584	+	1.91672i	0.377441	+	0.926034i	$0.376804\pi$
$631$	12.9011	+	48.1475i	0.513584	+	1.91672i	0.136143	+	0.990689i	$0.456529\pi$
$632$	6.19564			0.246449
$633$	2.22854	+	8.31704i	0.0885767	+	0.330573i
$634$	6.72949	+	11.6558i	0.267262	+	0.462912i
$635$	−0.683526	+	15.5707i	−0.0271249	+	0.617904i
$636$			0.277033i			0.0109851i
$637$	−0.544511	−	24.7152i	−0.0215743	−	0.979254i
$638$	4.01753	−	4.01753i	0.159055	−	0.159055i
$639$	−22.0219	−	5.90074i	−0.871172	−	0.233430i
$640$	−1.51028	−	1.64896i	−0.0596989	−	0.0651809i
$641$	−7.81678	−	4.51302i	−0.308744	−	0.178254i	0.337620	−	0.941282i	$-0.390378\pi$
$641$	−7.81678	−	4.51302i	−0.308744	−	0.178254i	−0.646364	+	0.763029i	$0.723711\pi$
$642$			5.38692i			0.212605i
$643$	11.9124	−	20.6328i	0.469778	−	0.813679i	−0.529625	−	0.848232i	$-0.677667\pi$
$643$	11.9124	−	20.6328i	0.469778	−	0.813679i	0.999403	+	0.0345529i	$0.0110007\pi$
$644$	3.29093	−	0.881802i	0.129681	−	0.0347479i
$645$	−2.62654	−	11.8609i	−0.103420	−	0.467021i
$646$	−0.137018	+	0.237322i	−0.00539089	+	0.00933730i
$647$	−19.3954	−	5.19697i	−0.762510	−	0.204314i	−0.143450	−	0.989658i	$-0.545820\pi$
$647$	−19.3954	−	5.19697i	−0.762510	−	0.204314i	−0.619060	+	0.785344i	$0.712486\pi$
$648$	4.33998	−	2.50569i	0.170490	−	0.0984327i
$649$	12.7070			0.498793
$650$	16.1707	−	7.96923i	0.634267	−	0.312579i
$651$	0.898685			0.0352222
$652$	−1.75029	+	1.01053i	−0.0685468	+	0.0395755i
$653$	−1.56901	−	0.420415i	−0.0614001	−	0.0164521i	0.227988	−	0.973664i	$-0.426785\pi$
$653$	−1.56901	−	0.420415i	−0.0614001	−	0.0164521i	−0.289388	+	0.957212i	$0.593452\pi$
$654$	−1.67270	+	2.89719i	−0.0654076	+	0.113289i
$655$	−6.71211	−	30.3103i	−0.262264	−	1.18432i
$656$	−3.19416	+	0.855872i	−0.124711	+	0.0334162i
$657$	−14.2194	+	24.6288i	−0.554753	+	0.960860i
$658$		−	1.89250i		−	0.0737775i
$659$	20.8830	+	12.0568i	0.813484	+	0.469665i	0.848164	−	0.529733i	$-0.177708\pi$
$659$	20.8830	+	12.0568i	0.813484	+	0.469665i	−0.0346800	+	0.999398i	$0.511041\pi$
$660$	0.956833	+	1.04470i	0.0372447	+	0.0406648i
$661$	−5.06284	−	1.35658i	−0.196922	−	0.0527650i	0.159010	−	0.987277i	$-0.449170\pi$
$661$	−5.06284	−	1.35658i	−0.196922	−	0.0527650i	−0.355932	+	0.934512i	$0.615836\pi$
$662$	−12.9511	+	12.9511i	−0.503358	+	0.503358i
$663$	−2.69874	+	4.92162i	−0.104810	+	0.191140i
$664$		−	10.8523i		−	0.421152i
$665$	0.00447187	−	0.101869i	0.000173412	−	0.00395031i
$666$	2.71427	+	4.70125i	0.105176	+	0.182170i
$667$	14.2699	+	53.2559i	0.552532	+	2.06208i
$668$	18.7039			0.723676
$669$	−2.04057	−	7.61553i	−0.0788932	−	0.294433i
$670$	−17.8406	−	5.62975i	−0.689241	−	0.217496i
$671$	6.03253	−	6.03253i	0.232883	−	0.232883i
$672$	−0.250227	+	0.0670481i	−0.00965271	+	0.00258644i
$673$	3.79961	−	14.1804i	0.146464	−	0.546612i	−0.853222	−	0.521549i	$-0.825354\pi$
$673$	3.79961	−	14.1804i	0.146464	−	0.546612i	0.999686	−	0.0250637i	$-0.00797884\pi$
$674$	2.11036	−	7.87595i	0.0812878	−	0.303370i
$675$	17.7696	+	6.47714i	0.683953	+	0.249305i
$676$	12.9874	−	0.572538i	0.499515	−	0.0220207i
$677$	−5.86651	−	5.86651i	−0.225468	−	0.225468i	0.585328	−	0.810796i	$-0.300966\pi$
$677$	−5.86651	−	5.86651i	−0.225468	−	0.225468i	−0.810796	+	0.585328i	$0.800966\pi$
$678$	0.449886	+	0.779225i	0.0172778	+	0.0299260i
$679$	−3.95692	+	2.28453i	−0.151853	+	0.0876722i
$680$	−2.34986	−	4.51665i	−0.0901131	−	0.173206i
$681$	−4.95622	−	4.95622i	−0.189923	−	0.189923i
$682$	2.78391	+	1.60729i	0.106601	+	0.0615464i
$683$	41.3278	+	23.8606i	1.58137	+	0.913002i	0.994660	+	0.103202i	$0.0329087\pi$
$683$	41.3278	+	23.8606i	1.58137	+	0.913002i	0.586705	+	0.809800i	$0.300425\pi$
$684$	0.215526	+	0.215526i	0.00824083	+	0.00824083i
$685$	−26.7698	−	8.44746i	−1.02282	−	0.322761i
$686$	4.54674	−	2.62506i	0.173595	−	0.100225i
$687$	4.87692	+	8.44707i	0.186066	+	0.322276i
$688$	5.61875	+	5.61875i	0.214213	+	0.214213i
$689$	1.40248	−	0.409108i	0.0534303	−	0.0155858i
$690$	−13.4221	+	2.97227i	−0.510969	+	0.113152i
$691$	1.28539	−	4.79712i	0.0488984	−	0.182491i	−0.937157	−	0.348907i	$-0.886553\pi$
$691$	1.28539	−	4.79712i	0.0488984	−	0.182491i	0.986056	+	0.166416i	$0.0532195\pi$
$692$	4.58467	−	17.1102i	0.174283	−	0.650432i
$693$	−0.858865	+	0.230132i	−0.0326256	+	0.00874200i
$694$	13.6331	−	13.6331i	0.517507	−	0.517507i
$695$	13.9281	−	44.1380i	0.528325	−	1.67425i
$696$	−1.08501	−	4.04933i	−0.0411273	−	0.153489i
$697$	−7.52942			−0.285197
$698$	−8.27437	−	30.8804i	−0.313190	−	1.16884i
$699$	1.60226	+	2.77520i	0.0606032	+	0.104968i
$700$	1.55134	+	1.08736i	0.0586353	+	0.0410983i
$701$			17.7217i			0.669338i	0.942336	+	0.334669i	$0.108625\pi$
$701$			17.7217i			0.669338i	−0.942336	+	0.334669i	$0.891375\pi$
$702$	9.85400	+	9.42917i	0.371915	+	0.355881i
$703$	−0.182419	+	0.182419i	−0.00688006	+	0.00688006i
$704$	−0.895058	−	0.239830i	−0.0337338	−	0.00903894i
$705$	−0.334893	+	7.62884i	−0.0126128	+	0.287319i
$706$	−7.85082	−	4.53267i	−0.295470	−	0.170589i
$707$			5.62115i			0.211405i
$708$	4.68789	−	8.11966i	0.176182	−	0.305156i
$709$	16.4056	−	4.39588i	0.616127	−	0.165091i	0.0627605	−	0.998029i	$-0.480010\pi$
$709$	16.4056	−	4.39588i	0.616127	−	0.165091i	0.553366	+	0.832938i	$0.313343\pi$
$710$	16.9747	+	10.8198i	0.637050	+	0.406058i
$711$	7.84535	−	13.5885i	0.294224	−	0.509610i
$712$	1.02180	+	0.273792i	0.0382937	+	0.0102608i
$713$	−27.0150	+	15.5971i	−1.01172	+	0.584117i
$714$	−0.589847			−0.0220745
$715$	3.87579	−	6.38673i	0.144946	−	0.238850i
$716$	−24.2644			−0.906801
$717$	−3.10108	+	1.79041i	−0.115812	+	0.0668640i
$718$	8.62508	+	2.31108i	0.321885	+	0.0862488i
$719$	−23.3128	+	40.3790i	−0.869422	+	1.50588i	−0.00683386	+	0.999977i	$0.502175\pi$
$719$	−23.3128	+	40.3790i	−0.869422	+	1.50588i	−0.862588	+	0.505907i	$0.831158\pi$
$720$	−5.52899	+	1.22437i	−0.206053	+	0.0456297i
$721$	3.69699	−	0.990604i	0.137683	−	0.0368920i
$722$	9.49276	−	16.4419i	0.353284	−	0.611906i
$723$		−	9.92682i		−	0.369182i
$724$	7.33947	+	4.23745i	0.272769	+	0.157483i
$725$	−17.5963	+	25.1048i	−0.653510	+	0.932369i
$726$	−6.69749	−	1.79459i	−0.248567	−	0.0666034i
$727$	14.6028	−	14.6028i	0.541588	−	0.541588i	−0.382407	−	0.923994i	$-0.624905\pi$
$727$	14.6028	−	14.6028i	0.541588	−	0.541588i	0.923994	+	0.382407i	$0.124905\pi$
$728$	0.708954	+	1.16776i	0.0262756	+	0.0432802i
$729$		−	4.93276i		−	0.182695i
$730$	18.5168	−	16.9595i	0.685338	−	0.627698i
$731$	9.04636	+	15.6688i	0.334592	+	0.579530i
$732$	−1.62921	−	6.08028i	−0.0602172	−	0.224734i
$733$	29.7961			1.10054			0.550271	−	0.834986i	$-0.314524\pi$
$733$	29.7961			1.10054			0.550271	+	0.834986i	$0.314524\pi$
$734$	2.68725	+	10.0289i	0.0991880	+	0.370175i
$735$	−9.29905	+	4.83798i	−0.343001	+	0.178452i
$736$	6.35832	−	6.35832i	0.234371	−	0.234371i
$737$	−7.48838	+	2.00650i	−0.275838	+	0.0739106i
$738$	−2.16753	+	8.08933i	−0.0797878	+	0.297772i
$739$	−1.54742	+	5.77503i	−0.0569226	+	0.212438i	−0.988529	−	0.151030i	$-0.951741\pi$
$739$	−1.54742	+	5.77503i	−0.0569226	+	0.212438i	0.931607	+	0.363468i	$0.118408\pi$
$740$	−1.03630	−	4.67968i	−0.0380951	−	0.172028i
$741$	−0.142649	+	0.260146i	−0.00524035	+	0.00955669i
$742$	0.108558	+	0.108558i	0.00398528	+	0.00398528i
$743$	−7.05718	−	12.2234i	−0.258903	−	0.448433i	0.707045	−	0.707168i	$-0.250028\pi$
$743$	−7.05718	−	12.2234i	−0.258903	−	0.448433i	−0.965948	+	0.258735i	$0.916694\pi$
$744$	2.05409	−	1.18593i	0.0753068	−	0.0434784i
$745$	−26.9400	+	14.0160i	−0.987006	+	0.513506i
$746$	8.85774	+	8.85774i	0.324305	+	0.324305i
$747$	−23.8018	−	13.7420i	−0.870862	−	0.502792i
$748$	−1.82721	−	1.05494i	−0.0668092	−	0.0385723i
$749$	2.11091	+	2.11091i	0.0771311	+	0.0771311i
$750$	−6.06118	−	4.65775i	−0.221323	−	0.170077i
$751$	−46.4374	+	26.8106i	−1.69452	+	0.978334i	−0.743747	+	0.668462i	$0.766953\pi$
$751$	−46.4374	+	26.8106i	−1.69452	+	0.978334i	−0.950778	+	0.309873i	$0.899714\pi$
$752$	−2.49741	−	4.32564i	−0.0910710	−	0.157740i
$753$	−4.32971	−	4.32971i	−0.157784	−	0.157784i
$754$	−18.8975	+	11.4727i	−0.688205	+	0.417812i
$755$	22.1113	+	14.0938i	0.804713	+	0.512927i
$756$	−0.370946	+	1.38439i	−0.0134912	+	0.0503498i
$757$	−0.164516	+	0.613984i	−0.00597945	+	0.0223156i	−0.968851	−	0.247644i	$-0.920344\pi$
$757$	−0.164516	+	0.613984i	−0.00597945	+	0.0223156i	0.962872	+	0.269960i	$0.0870103\pi$
$758$	−25.1554	+	6.74037i	−0.913686	+	0.244821i
$759$	−4.02831	+	4.02831i	−0.146218	+	0.146218i
$760$	−0.124208	−	0.238740i	−0.00450551	−	0.00866001i
$761$	2.75617	+	10.2861i	0.0999109	+	0.372873i	0.997718	−	0.0675160i	$-0.0215074\pi$
$761$	2.75617	+	10.2861i	0.0999109	+	0.372873i	−0.897807	+	0.440389i	$0.854841\pi$
$762$	4.76556			0.172638
$763$	0.479831	+	1.79075i	0.0173711	+	0.0648296i
$764$	−9.02643	−	15.6342i	−0.326565	−	0.565627i
$765$	−12.8817	−	0.565483i	−0.465738	−	0.0204451i
$766$			1.20500i			0.0435385i
$767$	−48.0287	−	11.7418i	−1.73422	−	0.423972i
$768$	−0.483457	+	0.483457i	−0.0174452	+	0.0174452i
$769$	15.6194	+	4.18521i	0.563251	+	0.150923i	0.529199	−	0.848498i	$-0.322492\pi$
$769$	15.6194	+	4.18521i	0.563251	+	0.150923i	0.0340513	+	0.999420i	$0.489159\pi$
$770$	0.784318	+	0.0344302i	0.0282649	+	0.00124078i
$771$	−4.71287	−	2.72098i	−0.169730	−	0.0979935i
$772$		−	6.85437i		−	0.246694i
$773$	−11.5537	+	20.0115i	−0.415557	+	0.719765i	−0.995487	−	0.0949012i	$-0.969746\pi$
$773$	−11.5537	+	20.0115i	−0.415557	+	0.719765i	0.579930	+	0.814666i	$0.303080\pi$
$774$	19.4381	−	5.20843i	0.698689	−	0.187213i
$775$	−16.2966	−	5.94024i	−0.585393	−	0.213380i
$776$	−6.02947	+	10.4433i	−0.216445	+	0.374894i
$777$	−0.536365	−	0.143719i	−0.0192420	−	0.00515588i
$778$	−24.6083	+	14.2076i	−0.882250	+	0.509367i
$779$	−0.397988			−0.0142594
$780$	−2.65121	−	4.83281i	−0.0949285	−	0.173042i
$781$	8.34184			0.298494
$782$	17.7312	−	10.2371i	0.634065	−	0.366078i
$783$	−22.4031	−	6.00288i	−0.800620	−	0.214525i
$784$	3.42822	−	5.93785i	0.122436	−	0.212066i
$785$	19.1393	−	30.0270i	0.683110	−	1.07171i
$786$	−9.16891	+	2.45680i	−0.327044	+	0.0876313i
$787$	4.08383	−	7.07340i	0.145573	−	0.252140i	−0.784014	−	0.620744i	$-0.786831\pi$
$787$	4.08383	−	7.07340i	0.145573	−	0.252140i	0.929587	+	0.368604i	$0.120164\pi$
$788$		−	12.9302i		−	0.460619i
$789$	−16.6730	−	9.62617i	−0.593575	−	0.342701i
$790$	−10.2164	+	9.35712i	−0.363482	+	0.332911i
$791$	0.481639	+	0.129055i	0.0171251	+	0.00458866i
$792$	−1.65939	+	1.65939i	−0.0589639	+	0.0589639i
$793$	−28.3756	+	17.2269i	−1.00765	+	0.611746i
$794$			13.2855i			0.471485i
$795$	−0.418396	−	0.456816i	−0.0148390	−	0.0162016i
$796$	4.21853	+	7.30671i	0.149522	+	0.258979i
$797$	−3.84123	−	14.3357i	−0.136063	−	0.507795i	−0.999991	−	0.00417991i	$-0.998669\pi$
$797$	−3.84123	−	14.3357i	−0.136063	−	0.507795i	0.863928	−	0.503616i	$-0.167997\pi$
$798$	−0.0311780			−0.00110369
$799$	−2.94350	−	10.9853i	−0.104134	−	0.388632i
$800$	4.98077	+	0.438138i	0.176097	+	0.0154905i
$801$	1.89437	−	1.89437i	0.0669343	−	0.0669343i
$802$	24.6586	−	6.60726i	0.870726	−	0.233310i
$803$	2.69315	−	10.0510i	0.0950391	−	0.354691i
$804$	−1.48049	+	5.52526i	−0.0522128	+	0.194861i
$805$	−4.09485	+	6.42427i	−0.144324	+	0.226426i
$806$	−9.03718	−	8.64756i	−0.318321	−	0.304597i
$807$	−6.12198	−	6.12198i	−0.215504	−	0.215504i
$808$	7.41785	+	12.8481i	0.260959	+	0.451994i
$809$	5.87478	−	3.39181i	0.206546	−	0.119250i	−0.393159	−	0.919471i	$-0.628618\pi$
$809$	5.87478	−	3.39181i	0.206546	−	0.119250i	0.599705	+	0.800221i	$0.295284\pi$
$810$	−3.37217	+	10.6863i	−0.118486	+	0.375480i
$811$	−4.03955	−	4.03955i	−0.141848	−	0.141848i	0.632617	−	0.774465i	$-0.281981\pi$
$811$	−4.03955	−	4.03955i	−0.141848	−	0.141848i	−0.774465	+	0.632617i	$0.781981\pi$
$812$	−2.01194	−	1.16159i	−0.0706052	−	0.0407639i
$813$	16.3069	+	9.41481i	0.571909	+	0.330192i
$814$	−1.40449	−	1.40449i	−0.0492274	−	0.0492274i
$815$	1.35998	−	4.30975i	0.0476381	−	0.150964i
$816$	−1.34819	+	0.778380i	−0.0471962	+	0.0272488i
$817$	0.478170	+	0.828215i	0.0167290	+	0.0289756i
$818$	19.1366	+	19.1366i	0.669095	+	0.669095i
$819$	3.45892	−	0.0762047i	0.120864	−	0.00266281i
$820$	3.97444	−	6.23535i	0.138793	−	0.217748i
$821$	1.80562	−	6.73865i	0.0630164	−	0.235180i	−0.927233	−	0.374484i	$-0.877820\pi$
$821$	1.80562	−	6.73865i	0.0630164	−	0.235180i	0.990250	+	0.139304i	$0.0444864\pi$
$822$	−2.22148	+	8.29067i	−0.0774829	+	0.289170i
$823$	−45.1605	+	12.1007i	−1.57419	+	0.421804i	−0.937123	−	0.349000i	$-0.886521\pi$
$823$	−45.1605	+	12.1007i	−1.57419	+	0.421804i	−0.637072	+	0.770804i	$0.719855\pi$
$824$	7.14285	−	7.14285i	0.248833	−	0.248833i
$825$	−3.15556	−	0.277582i	−0.109862	−	0.00966416i
$826$	−1.34477	−	5.01876i	−0.0467906	−	0.174625i
$827$	−42.2620			−1.46959			−0.734797	−	0.678287i	$-0.762723\pi$
$827$	−42.2620			−1.46959			−0.734797	+	0.678287i	$0.762723\pi$
$828$	−5.89400	−	21.9967i	−0.204831	−	0.764438i
$829$	1.11016	+	1.92285i	0.0385574	+	0.0667833i	0.884660	−	0.466237i	$-0.154390\pi$
$829$	1.11016	+	1.92285i	0.0385574	+	0.0667833i	−0.846103	+	0.533020i	$0.821057\pi$
$830$	16.3900	+	17.8950i	0.568905	+	0.621146i
$831$		−	13.0409i		−	0.452385i
$832$	3.16145	+	1.73356i	0.109604	+	0.0601004i
$833$	11.0391	−	11.0391i	0.382481	−	0.382481i
$834$	−13.6696	−	3.66277i	−0.473341	−	0.126831i
$835$	−30.8420	+	28.2481i	−1.06733	+	0.977564i
$836$	−0.0965819	−	0.0557616i	−0.00334036	−	0.00192856i
$837$		−	13.1224i		−	0.453578i
$838$	10.0398	−	17.3895i	0.346819	−	0.600709i
$839$	12.5298	−	3.35734i	0.432575	−	0.115908i	−0.0359595	−	0.999353i	$-0.511449\pi$
$839$	12.5298	−	3.35734i	0.432575	−	0.115908i	0.468535	+	0.883445i	$0.344782\pi$
$840$	0.311353	−	0.488471i	0.0107427	−	0.0168539i
$841$	4.29762	−	7.44369i	0.148194	−	0.256679i
$842$	−34.1733	−	9.15671i	−1.17769	−	0.315561i
$843$	−18.4267	+	10.6387i	−0.634649	+	0.366415i
$844$	12.5937			0.433492
$845$	−20.5510	+	20.5586i	−0.706976	+	0.707238i
$846$	−12.6496			−0.434901
$847$	−3.32770	+	1.92125i	−0.114341	+	0.0660149i
$848$	0.391383	+	0.104871i	0.0134402	+	0.00360128i
$849$	6.30335	−	10.9177i	0.216330	−	0.374695i
$850$	10.6962	+	3.89884i	0.366877	+	0.133729i
$851$	18.6178	−	4.98862i	0.638210	−	0.171008i
$852$	3.07749	−	5.33037i	0.105433	−	0.182616i
$853$			14.7877i			0.506322i	0.967424	+	0.253161i	$0.0814703\pi$
$853$			14.7877i			0.506322i	−0.967424	+	0.253161i	$0.918530\pi$
$854$	−3.02103	−	1.74419i	−0.103378	−	0.0596851i
$855$	−0.680896	−	0.0298901i	−0.0232862	−	0.00102222i
$856$	7.61047	+	2.03922i	0.260120	+	0.0696991i
$857$	−26.0242	+	26.0242i	−0.888970	+	0.888970i	−0.994424	−	0.105454i	$-0.966370\pi$
$857$	−26.0242	+	26.0242i	−0.888970	+	0.888970i	0.105454	+	0.994424i	$0.466370\pi$
$858$	−2.00293	−	1.09830i	−0.0683790	−	0.0374952i
$859$		−	7.74966i		−	0.264415i	−0.991222	−	0.132207i	$-0.957794\pi$
$859$		−	7.74966i		−	0.264415i	0.991222	−	0.132207i	$-0.0422065\pi$
$860$	−17.7509	−	0.779235i	−0.605302	−	0.0265717i
$861$	−0.428324	−	0.741879i	−0.0145973	−	0.0252832i
$862$	0.975777	+	3.64165i	0.0332351	+	0.124035i
$863$	9.27091			0.315585			0.157793	−	0.987472i	$-0.449562\pi$
$863$	9.27091			0.315585			0.157793	+	0.987472i	$0.449562\pi$
$864$	0.979024	+	3.65377i	0.0333071	+	0.124304i
$865$	18.2812	+	35.1381i	0.621579	+	1.19473i
$866$	27.9492	−	27.9492i	0.949753	−	0.949753i
$867$	7.80319	−	2.09086i	0.265010	−	0.0710093i
$868$	0.340197	−	1.26963i	0.0115471	−	0.0430942i
$869$	−1.48590	+	5.54546i	−0.0504057	+	0.188117i
$870$	7.90474	+	5.03851i	0.267996	+	0.170821i
$871$	30.1580	−	0.664423i	1.02187	−	0.0225131i
$872$	3.45987	+	3.45987i	0.117166	+	0.117166i
$873$	15.2699	+	26.4482i	0.516807	+	0.895136i
$874$	0.937229	−	0.541110i	0.0317023	−	0.0183033i
$875$	−4.20031	+	0.549946i	−0.141997	+	0.0185916i
$876$	−5.42892	−	5.42892i	−0.183426	−	0.183426i
$877$	29.8962	+	17.2606i	1.00952	+	0.582848i	0.911052	−	0.412292i	$-0.135272\pi$
$877$	29.8962	+	17.2606i	1.00952	+	0.582848i	0.0984709	+	0.995140i	$0.468605\pi$
$878$	−4.25937	−	2.45915i	−0.143747	−	0.0829923i
$879$	−11.8431	−	11.8431i	−0.399457	−	0.399457i
$880$	1.83812	−	0.956314i	0.0619632	−	0.0322373i
$881$	−8.59813	+	4.96413i	−0.289678	+	0.167246i	−0.637797	−	0.770205i	$-0.720154\pi$
$881$	−8.59813	+	4.96413i	−0.289678	+	0.167246i	0.348118	+	0.937451i	$0.386821\pi$
$882$	−8.68210	−	15.0378i	−0.292342	−	0.506350i
$883$	−20.3915	−	20.3915i	−0.686228	−	0.686228i	0.275168	−	0.961396i	$-0.411267\pi$
$883$	−20.3915	−	20.3915i	−0.686228	−	0.686228i	−0.961396	+	0.275168i	$0.911267\pi$
$884$	5.93150	+	5.67578i	0.199498	+	0.190897i
$885$	4.53278	+	20.4690i	0.152368	+	0.688058i
$886$	−6.92646	+	25.8499i	−0.232699	+	0.868444i
$887$	9.15170	−	34.1546i	0.307284	−	1.14680i	−0.623677	−	0.781682i	$-0.714362\pi$
$887$	9.15170	−	34.1546i	0.307284	−	1.14680i	0.930961	−	0.365118i	$-0.118971\pi$
$888$	−1.41561	+	0.379311i	−0.0475047	+	0.0127288i
$889$	1.86743	−	1.86743i	0.0626315	−	0.0626315i
$890$	−2.09841	+	1.09173i	−0.0703390	+	0.0365950i
$891$	1.20188	+	4.48547i	0.0402644	+	0.150269i
$892$	−11.5314			−0.386101
$893$	−0.155587	−	0.580658i	−0.00520652	−	0.0194310i
$894$	4.64273	+	8.04144i	0.155276	+	0.268946i
$895$	40.0109	−	36.6458i	1.33742	−	1.22494i
$896$			0.378894i			0.0126580i
$897$	18.9482	−	11.5035i	0.632661	−	0.384091i
$898$	−1.71549	+	1.71549i	−0.0572467	+	0.0572467i
$899$	20.5460	+	5.50529i	0.685248	+	0.183612i
$900$	7.26794	−	10.3692i	0.242265	−	0.345641i
$901$	0.798985	+	0.461294i	0.0266180	+	0.0153679i
$902$		−	3.06422i		−	0.102027i
$903$	−1.02924	+	1.78269i	−0.0342508	+	0.0593241i
$904$	1.27117	−	0.340609i	0.0422785	−	0.0113285i
$905$	−18.5022	+	4.09724i	−0.615034	+	0.136197i
$906$	4.00874	−	6.94335i	0.133182	−	0.230677i
$907$	22.0047	+	5.89615i	0.730655	+	0.195779i	0.604921	−	0.796285i	$-0.293205\pi$
$907$	22.0047	+	5.89615i	0.730655	+	0.195779i	0.125734	+	0.992064i	$0.459871\pi$
$908$	−8.87817	+	5.12582i	−0.294633	+	0.170106i
$909$	37.5720			1.24618
$910$	−2.93268	−	0.854880i	−0.0972174	−	0.0283390i
$911$	25.9630			0.860192			0.430096	−	0.902783i	$-0.358480\pi$
$911$	25.9630			0.860192			0.430096	+	0.902783i	$0.358480\pi$
$912$	−0.0712625	+	0.0411434i	−0.00235974	+	0.00136239i
$913$	9.71346	+	2.60271i	0.321469	+	0.0861373i
$914$	5.36707	−	9.29603i	0.177527	−	0.307485i
$915$	11.8694	+	7.56559i	0.392390	+	0.250111i
$916$	13.7799	−	3.69232i	0.455301	−	0.121998i
$917$	−2.63020	+	4.55564i	−0.0868569	+	0.150441i
$918$			8.61284i			0.284266i
$919$	−17.4334	−	10.0652i	−0.575076	−	0.332020i	0.184098	−	0.982908i	$-0.441064\pi$
$919$	−17.4334	−	10.0652i	−0.575076	−	0.332020i	−0.759174	+	0.650887i	$0.774397\pi$
$920$	−0.881802	+	20.0874i	−0.0290722	+	0.662263i
$921$	−2.68445	−	0.719296i	−0.0884557	−	0.0237016i
$922$	−3.29624	+	3.29624i	−0.108556	+	0.108556i
$923$	−31.5298	−	7.70822i	−1.03781	−	0.253719i
$924$		−	0.240048i		−	0.00789699i
$925$	8.77642	+	6.15151i	0.288567	+	0.202260i
$926$	8.60167	+	14.8985i	0.282668	+	0.489596i
$927$	−6.62123	−	24.7108i	−0.217470	−	0.811608i
$928$	−6.13150			−0.201276
$929$	−12.3780	−	46.1954i	−0.406110	−	1.51562i	−0.802000	−	0.597324i	$-0.796230\pi$
$929$	−12.3780	−	46.1954i	−0.406110	−	1.51562i	0.395890	−	0.918298i	$-0.370436\pi$
$930$	−1.59604	+	5.05780i	−0.0523361	+	0.165852i
$931$	0.583501	−	0.583501i	0.0191235	−	0.0191235i
$932$	4.52726	−	1.21307i	0.148295	−	0.0397356i
$933$	−3.14890	+	11.7519i	−0.103090	+	0.384739i
$934$	1.55146	−	5.79014i	0.0507654	−	0.189459i
$935$	4.60623	−	1.02003i	0.150640	−	0.0333587i
$936$	7.80537	−	4.73867i	0.255127	−	0.154888i
$937$	19.3391	+	19.3391i	0.631781	+	0.631781i	0.948514	−	0.316734i	$-0.102586\pi$
$937$	19.3391	+	19.3391i	0.631781	+	0.631781i	−0.316734	+	0.948514i	$0.602586\pi$
$938$	1.58498	+	2.74527i	0.0517515	+	0.0896362i
$939$	−6.06848	+	3.50364i	−0.198037	+	0.114337i
$940$	10.6510	+	3.36103i	0.347398	+	0.109625i
$941$	20.1027	+	20.1027i	0.655330	+	0.655330i	0.954271	−	0.298942i	$-0.0966336\pi$
$941$	20.1027	+	20.1027i	0.655330	+	0.655330i	−0.298942	+	0.954271i	$0.596634\pi$
$942$	−9.42901	−	5.44384i	−0.307214	−	0.177370i
$943$	25.7514	+	14.8676i	0.838580	+	0.484155i
$944$	−9.69661	−	9.69661i	−0.315598	−	0.315598i
$945$	−1.47913	−	2.84303i	−0.0481162	−	0.0924839i
$946$	−6.37665	+	3.68156i	−0.207323	+	0.119698i
$947$	19.5492	+	33.8602i	0.635264	+	1.10031i	0.986459	+	0.164007i	$0.0524419\pi$
$947$	19.5492	+	33.8602i	0.635264	+	1.10031i	−0.351196	+	0.936302i	$0.614225\pi$
$948$	2.99532	+	2.99532i	0.0972835	+	0.0972835i
$949$	−19.4668	+	35.5011i	−0.631920	+	1.15242i
$950$	0.565378	+	0.206084i	0.0183433	+	0.00668625i
$951$	−2.38167	+	8.88851i	−0.0772309	+	0.288230i
$952$	−0.223287	+	0.833318i	−0.00723677	+	0.0270080i
$953$	−5.71690	+	1.53184i	−0.185189	+	0.0496211i	−0.350221	−	0.936667i	$-0.613894\pi$
$953$	−5.71690	+	1.53184i	−0.185189	+	0.0496211i	0.165033	+	0.986288i	$0.447227\pi$
$954$	0.725604	−	0.725604i	0.0234923	−	0.0234923i
$955$	38.4962	+	12.1478i	1.24571	+	0.393095i
$956$	1.35552	+	5.05886i	0.0438406	+	0.163615i
$957$	3.88460			0.125571
$958$	−0.292924	−	1.09321i	−0.00946396	−	0.0353200i
$959$	2.37827	+	4.11928i	0.0767983	+	0.133018i
$960$	0.0670481	−	1.52735i	0.00216397	−	0.0492951i
$961$		−	18.9653i		−	0.611785i
$962$	4.01077	+	6.60639i	0.129312	+	0.212999i
$963$	14.1094	−	14.1094i	0.454669	−	0.454669i
$964$	−14.0243	−	3.75780i	−0.451692	−	0.121031i
$965$	10.3520	+	11.3026i	0.333242	+	0.363843i
$966$	2.01734	+	1.16471i	0.0649067	+	0.0374739i
$967$		−	24.4096i		−	0.784959i	−0.919761	−	0.392479i	$-0.871617\pi$
$967$		−	24.4096i		−	0.784959i	0.919761	−	0.392479i	$-0.128383\pi$
$968$	−5.07068	+	8.78267i	−0.162978	+	0.282286i
$969$	−0.180977	+	0.0484926i	−0.00581382	+	0.00155781i
$970$	−5.82998	−	26.3268i	−0.187189	−	0.845303i
$971$	13.0566	−	22.6147i	0.419006	−	0.725739i	−0.576834	−	0.816861i	$-0.695712\pi$
$971$	13.0566	−	22.6147i	0.419006	−	0.725739i	0.995840	+	0.0911224i	$0.0290454\pi$
$972$	14.2709	+	3.82387i	0.457739	+	0.122651i
$973$	−6.79186	+	3.92128i	−0.217737	+	0.125711i
$974$	−33.5141			−1.07386
$975$	11.6706	+	3.96505i	0.373759	+	0.126983i
$976$	−9.20677			−0.294701
$977$	42.1031	−	24.3082i	1.34700	−	0.777689i	0.359173	−	0.933271i	$-0.383059\pi$
$977$	42.1031	−	24.3082i	1.34700	−	0.777689i	0.987823	+	0.155582i	$0.0497254\pi$
$978$	−1.33474	−	0.357642i	−0.0426803	−	0.0114361i
$979$	−0.490119	+	0.848911i	−0.0156643	+	0.0271313i
$980$	3.31479	+	14.9688i	0.105887	+	0.478162i
$981$	11.9695	−	3.20721i	0.382155	−	0.102398i
$982$	6.48115	−	11.2257i	0.206822	−	0.358226i
$983$		−	43.9991i		−	1.40335i	−0.712496	−	0.701676i	$-0.752435\pi$
$983$		−	43.9991i		−	1.40335i	0.712496	−	0.701676i	$-0.247565\pi$
$984$	−1.95801	−	1.13046i	−0.0624192	−	0.0360377i
$985$	19.5281	+	21.3213i	0.622218	+	0.679355i
$986$	−13.4853	−	3.61336i	−0.429458	−	0.115073i
$987$	0.914944	−	0.914944i	0.0291230	−	0.0291230i
$988$	0.313526	+	0.300009i	0.00997458	+	0.00954455i
$989$		−	71.4516i		−	2.27203i
$990$	0.230132	−	5.24241i	0.00731408	−	0.166615i
$991$	−5.90956	−	10.2357i	−0.187723	−	0.325147i	0.756767	−	0.653684i	$-0.226778\pi$
$991$	−5.90956	−	10.2357i	−0.187723	−	0.325147i	−0.944491	+	0.328538i	$0.893444\pi$
$992$	−0.897870	−	3.35090i	−0.0285074	−	0.106391i
$993$	−12.5226			−0.397391
$994$	−0.882812	−	3.29470i	−0.0280011	−	0.104502i
$995$	−17.9913	−	5.67733i	−0.570363	−	0.179983i
$996$	5.24663	−	5.24663i	0.166246	−	0.166246i
$997$	7.59691	−	2.03559i	0.240597	−	0.0644677i	−0.136506	−	0.990639i	$-0.543587\pi$
$997$	7.59691	−	2.03559i	0.240597	−	0.0644677i	0.377102	+	0.926172i	$0.376921\pi$
$998$	−4.59750	+	17.1581i	−0.145531	+	0.543131i
$999$	−2.09855	+	7.83191i	−0.0663953	+	0.247791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.p.a.37.2	✓	12
5.2	odd	4		650.2.w.e.193.2		12
5.3	odd	4		130.2.s.a.63.2	yes	12
5.4	even	2		650.2.t.e.557.2		12
13.6	odd	12		130.2.s.a.97.2	yes	12
65.19	odd	12		650.2.w.e.357.2		12
65.32	even	12		650.2.t.e.643.2		12
65.58	even	12	inner	130.2.p.a.123.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.a.37.2	✓	12	1.1	even	1	trivial
130.2.p.a.123.2	yes	12	65.58	even	12	inner
130.2.s.a.63.2	yes	12	5.3	odd	4
130.2.s.a.97.2	yes	12	13.6	odd	12
650.2.t.e.557.2		12	5.4	even	2
650.2.t.e.643.2		12	65.32	even	12
650.2.w.e.193.2		12	5.2	odd	4
650.2.w.e.357.2		12	65.19	odd	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.660414 + 0.176957i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.483457 + 2.18318i) q^{5} +(0.660414 - 0.176957i) q^{6} +(0.189447 - 0.328132i) q^{7} -1.00000i q^{8} +(-2.19324 - 1.26627i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.660414 + 0.176957i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.483457 + 2.18318i) q^{5} +(0.660414 - 0.176957i) q^{6} +(0.189447 - 0.328132i) q^{7} -1.00000i q^{8} +(-2.19324 - 1.26627i) q^{9} +(1.51028 + 1.64896i) q^{10} +(0.895058 + 0.239830i) q^{11} +(0.483457 - 0.483457i) q^{12} +(-3.16145 - 1.73356i) q^{13} -0.378894i q^{14} +(-0.0670481 + 1.52735i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.589312 - 2.19934i) q^{17} -2.53254 q^{18} +(-0.0311497 - 0.116252i) q^{19} +(2.13242 + 0.672904i) q^{20} +(0.183179 - 0.183179i) q^{21} +(0.895058 - 0.239830i) q^{22} +(-2.32731 + 8.68563i) q^{23} +(0.176957 - 0.660414i) q^{24} +(-4.53254 + 2.11094i) q^{25} +(-3.60468 + 0.0794160i) q^{26} +(-2.67474 - 2.67474i) q^{27} +(-0.189447 - 0.328132i) q^{28} +(5.31003 - 3.06575i) q^{29} +(0.705611 + 1.35625i) q^{30} +(2.45303 + 2.45303i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.548669 + 0.316774i) q^{33} +(-1.61003 - 1.61003i) q^{34} +(0.807960 + 0.254959i) q^{35} +(-2.19324 + 1.26627i) q^{36} +(-1.07176 - 1.85634i) q^{37} +(-0.0851026 - 0.0851026i) q^{38} +(-1.78110 - 1.70431i) q^{39} +(2.18318 - 0.483457i) q^{40} +(0.855872 - 3.19416i) q^{41} +(0.0670481 - 0.250227i) q^{42} +(-7.67535 + 2.05660i) q^{43} +(0.655228 - 0.655228i) q^{44} +(1.70415 - 5.40043i) q^{45} +(2.32731 + 8.68563i) q^{46} +4.99481 q^{47} +(-0.176957 - 0.660414i) q^{48} +(3.42822 + 5.93785i) q^{49} +(-2.86982 + 4.09440i) q^{50} -1.55676i q^{51} +(-3.08203 + 1.87111i) q^{52} +(-0.286513 + 0.286513i) q^{53} +(-3.65377 - 0.979024i) q^{54} +(-0.0908702 + 2.07002i) q^{55} +(-0.328132 - 0.189447i) q^{56} -0.0822868i q^{57} +(3.06575 - 5.31003i) q^{58} +(13.2458 - 3.54920i) q^{59} +(1.28920 + 0.821742i) q^{60} +(4.60338 - 7.97329i) q^{61} +(3.35090 + 0.897870i) q^{62} +(-0.831007 + 0.479782i) q^{63} -1.00000 q^{64} +(2.25625 - 7.74011i) q^{65} +0.633549 q^{66} +(-7.24548 + 4.18318i) q^{67} +(-2.19934 - 0.589312i) q^{68} +(-3.07397 + 5.32428i) q^{69} +(0.827193 - 0.183179i) q^{70} +(8.69557 - 2.32997i) q^{71} +(-1.26627 + 2.19324i) q^{72} -11.2294i q^{73} +(-1.85634 - 1.07176i) q^{74} +(-3.36690 + 0.592031i) q^{75} +(-0.116252 - 0.0311497i) q^{76} +(0.248262 - 0.248262i) q^{77} +(-2.39463 - 0.585427i) q^{78} +6.19564i q^{79} +(1.64896 - 1.51028i) q^{80} +(2.50569 + 4.33998i) q^{81} +(-0.855872 - 3.19416i) q^{82} +10.8523 q^{83} +(-0.0670481 - 0.250227i) q^{84} +(4.51665 - 2.34986i) q^{85} +(-5.61875 + 5.61875i) q^{86} +(4.04933 - 1.08501i) q^{87} +(0.239830 - 0.895058i) q^{88} +(-0.273792 + 1.02180i) q^{89} +(-1.22437 - 5.52899i) q^{90} +(-1.16776 + 0.708954i) q^{91} +(6.35832 + 6.35832i) q^{92} +(1.18593 + 2.05409i) q^{93} +(4.32564 - 2.49741i) q^{94} +(0.238740 - 0.124208i) q^{95} +(-0.483457 - 0.483457i) q^{96} +(-10.4433 - 6.02947i) q^{97} +(5.93785 + 3.42822i) q^{98} +(-1.65939 - 1.65939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 24 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 24 * q^9	\( 12 q + 6 q^{4} - 24 q^{9} + 6 q^{11} - 12 q^{13} - 6 q^{15} - 6 q^{16} + 12 q^{17} + 12 q^{18} + 36 q^{19} - 6 q^{20} - 24 q^{21} + 6 q^{22} + 6 q^{23} - 12 q^{25} + 6 q^{26} - 12 q^{27} + 6 q^{29} + 6 q^{30} - 24 q^{31} - 6 q^{33} - 12 q^{34} - 12 q^{35} - 24 q^{36} - 6 q^{38} + 6 q^{39} + 18 q^{41} + 6 q^{42} + 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 24 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} - 24 q^{55} + 6 q^{56} + 6 q^{58} + 18 q^{59} + 24 q^{60} + 18 q^{61} + 12 q^{62} + 30 q^{63} - 12 q^{64} + 30 q^{65} - 36 q^{66} + 12 q^{67} - 42 q^{69} + 24 q^{70} + 18 q^{71} + 6 q^{72} + 6 q^{74} - 12 q^{75} + 30 q^{76} + 30 q^{77} + 30 q^{78} - 6 q^{80} + 30 q^{81} - 18 q^{82} - 48 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{87} + 6 q^{89} - 12 q^{90} - 6 q^{91} - 42 q^{93} + 24 q^{94} + 30 q^{95} - 102 q^{97} - 48 q^{98} + 54 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 24 * q^9 + 6 * q^11 - 12 * q^13 - 6 * q^15 - 6 * q^16 + 12 * q^17 + 12 * q^18 + 36 * q^19 - 6 * q^20 - 24 * q^21 + 6 * q^22 + 6 * q^23 - 12 * q^25 + 6 * q^26 - 12 * q^27 + 6 * q^29 + 6 * q^30 - 24 * q^31 - 6 * q^33 - 12 * q^34 - 12 * q^35 - 24 * q^36 - 6 * q^38 + 6 * q^39 + 18 * q^41 + 6 * q^42 + 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 - 24 * q^55 + 6 * q^56 + 6 * q^58 + 18 * q^59 + 24 * q^60 + 18 * q^61 + 12 * q^62 + 30 * q^63 - 12 * q^64 + 30 * q^65 - 36 * q^66 + 12 * q^67 - 42 * q^69 + 24 * q^70 + 18 * q^71 + 6 * q^72 + 6 * q^74 - 12 * q^75 + 30 * q^76 + 30 * q^77 + 30 * q^78 - 6 * q^80 + 30 * q^81 - 18 * q^82 - 48 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^87 + 6 * q^89 - 12 * q^90 - 6 * q^91 - 42 * q^93 + 24 * q^94 + 30 * q^95 - 102 * q^97 - 48 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more