LMFDB - Embedded newform 280.2.br.a.107.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	280.107
Dual form			280.2.br.a.123.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950661 + 1.04702i) q^{2} +(1.52971 + 0.409884i) q^{3} +(-0.192487 - 1.99072i) q^{4} +(0.934747 + 2.03132i) q^{5} +(-1.88339 + 1.21197i) q^{6} +(1.62314 + 2.08935i) q^{7} +(2.26730 + 1.69096i) q^{8} +(-0.426076 - 0.245995i) q^{9} +O(q^{10})$	\(q+(-0.950661 + 1.04702i) q^{2} +(1.52971 + 0.409884i) q^{3} +(-0.192487 - 1.99072i) q^{4} +(0.934747 + 2.03132i) q^{5} +(-1.88339 + 1.21197i) q^{6} +(1.62314 + 2.08935i) q^{7} +(2.26730 + 1.69096i) q^{8} +(-0.426076 - 0.245995i) q^{9} +(-3.01545 - 0.952398i) q^{10} +(-1.76127 - 3.05061i) q^{11} +(0.521514 - 3.12411i) q^{12} +(1.68796 + 1.68796i) q^{13} +(-3.73065 - 0.286809i) q^{14} +(0.597286 + 3.49046i) q^{15} +(-3.92590 + 0.766373i) q^{16} +(0.335857 - 1.25343i) q^{17} +(0.662615 - 0.212251i) q^{18} +(6.62328 + 3.82395i) q^{19} +(3.86385 - 2.25182i) q^{20} +(1.62654 + 3.86140i) q^{21} +(4.86841 + 1.05602i) q^{22} +(-3.50951 + 0.940371i) q^{23} +(2.77521 + 3.51600i) q^{24} +(-3.25250 + 3.79754i) q^{25} +(-3.37200 + 0.162644i) q^{26} +(-3.91041 - 3.91041i) q^{27} +(3.84688 - 3.63339i) q^{28} -5.07439 q^{29} +(-4.22238 - 2.69287i) q^{30} +(2.42122 - 1.39789i) q^{31} +(2.92979 - 4.83904i) q^{32} +(-1.44383 - 5.38846i) q^{33} +(0.993080 + 1.54324i) q^{34} +(-2.72691 + 5.25014i) q^{35} +(-0.407692 + 0.895547i) q^{36} +(-0.340662 - 1.27137i) q^{37} +(-10.3002 + 3.29940i) q^{38} +(1.89022 + 3.27395i) q^{39} +(-1.31552 + 6.18623i) q^{40} -4.50117 q^{41} +(-5.58924 - 1.96787i) q^{42} +(7.05995 - 7.05995i) q^{43} +(-5.73387 + 4.09339i) q^{44} +(0.101421 - 1.09544i) q^{45} +(2.35177 - 4.56849i) q^{46} +(2.14078 + 7.98948i) q^{47} +(-6.31960 - 0.436835i) q^{48} +(-1.73080 + 6.78265i) q^{49} +(-0.884061 - 7.01559i) q^{50} +(1.02752 - 1.77973i) q^{51} +(3.03534 - 3.68516i) q^{52} +(3.15330 - 11.7683i) q^{53} +(7.81174 - 0.376789i) q^{54} +(4.55041 - 6.42925i) q^{55} +(0.147146 + 7.48187i) q^{56} +(8.56430 + 8.56430i) q^{57} +(4.82403 - 5.31297i) q^{58} +(10.7678 - 6.21679i) q^{59} +(6.83354 - 1.86089i) q^{60} +(-11.1830 - 6.45654i) q^{61} +(-0.838145 + 3.86398i) q^{62} +(-0.177612 - 1.28951i) q^{63} +(2.28132 + 7.66783i) q^{64} +(-1.85096 + 5.00660i) q^{65} +(7.01440 + 3.61088i) q^{66} +(0.866858 - 3.23516i) q^{67} +(-2.55988 - 0.427325i) q^{68} -5.75397 q^{69} +(-2.90461 - 7.84622i) q^{70} -2.60984i q^{71} +(-0.550075 - 1.27822i) q^{72} +(1.56766 + 0.420053i) q^{73} +(1.65500 + 0.851962i) q^{74} +(-6.53191 + 4.47597i) q^{75} +(6.33751 - 13.9211i) q^{76} +(3.51501 - 8.63150i) q^{77} +(-5.22484 - 1.13333i) q^{78} +(3.66367 - 6.34566i) q^{79} +(-5.22647 - 7.25838i) q^{80} +(-3.64099 - 6.30638i) q^{81} +(4.27909 - 4.71280i) q^{82} +(4.94034 - 4.94034i) q^{83} +(7.37386 - 3.98125i) q^{84} +(2.86006 - 0.489413i) q^{85} +(0.680264 + 14.1035i) q^{86} +(-7.76234 - 2.07991i) q^{87} +(1.16512 - 9.89489i) q^{88} +(-4.71065 - 2.71969i) q^{89} +(1.05053 + 1.14758i) q^{90} +(-0.786943 + 6.26655i) q^{91} +(2.54755 + 6.80543i) q^{92} +(4.27674 - 1.14595i) q^{93} +(-10.4003 - 5.35386i) q^{94} +(-1.57657 + 17.0284i) q^{95} +(6.46517 - 6.20144i) q^{96} +(-5.73033 - 5.73033i) q^{97} +(-5.45614 - 8.26018i) q^{98} +1.73306i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.950661	+	1.04702i	−0.672219	+	0.740352i
$2$	−0.950661	+	1.04702i	−0.672219	+	0.740352i
$3$	1.52971	+	0.409884i	0.883177	+	0.236647i	0.671777	−	0.740753i	$-0.265531\pi$
$3$	1.52971	+	0.409884i	0.883177	+	0.236647i	0.211400	+	0.977400i	$0.432198\pi$
$4$	−0.192487	−	1.99072i	−0.0962435	−	0.995358i
$5$	0.934747	+	2.03132i	0.418032	+	0.908432i
$5$	0.934747	+	2.03132i	0.418032	+	0.908432i
$6$	−1.88339	+	1.21197i	−0.768890	+	0.494784i
$7$	1.62314	+	2.08935i	0.613491	+	0.789702i
$7$	1.62314	+	2.08935i	0.613491	+	0.789702i
$8$	2.26730	+	1.69096i	0.801612	+	0.597844i
$9$	−0.426076	−	0.245995i	−0.142025	−	0.0819984i
$10$	−3.01545	−	0.952398i	−0.953569	−	0.301175i
$11$	−1.76127	−	3.05061i	−0.531043	−	0.919793i	−0.999344	−	0.0362243i	$-0.988467\pi$
$11$	−1.76127	−	3.05061i	−0.531043	−	0.919793i	0.468301	−	0.883569i	$-0.344866\pi$
$12$	0.521514	−	3.12411i	0.150548	−	0.901853i
$13$	1.68796	+	1.68796i	0.468156	+	0.468156i	0.901317	−	0.433161i	$-0.142602\pi$
$13$	1.68796	+	1.68796i	0.468156	+	0.468156i	−0.433161	+	0.901317i	$0.642602\pi$
$14$	−3.73065	−	0.286809i	−0.997058	−	0.0766529i
$15$	0.597286	+	3.49046i	0.154219	+	0.901232i
$16$	−3.92590	+	0.766373i	−0.981474	+	0.191593i
$17$	0.335857	−	1.25343i	0.0814572	−	0.304002i	−0.913163	−	0.407596i	$-0.866367\pi$
$17$	0.335857	−	1.25343i	0.0814572	−	0.304002i	0.994620	+	0.103593i	$0.0330340\pi$
$18$	0.662615	−	0.212251i	0.156180	−	0.0500280i
$19$	6.62328	+	3.82395i	1.51948	+	0.877275i	0.999736	+	0.0229553i	$0.00730755\pi$
$19$	6.62328	+	3.82395i	1.51948	+	0.877275i	0.519748	+	0.854320i	$0.326026\pi$
$20$	3.86385	−	2.25182i	0.863983	−	0.503522i
$21$	1.62654	+	3.86140i	0.354941	+	0.842627i
$22$	4.86841	+	1.05602i	1.03795	+	0.225144i
$23$	−3.50951	+	0.940371i	−0.731784	+	0.196081i	−0.605424	−	0.795903i	$-0.706996\pi$
$23$	−3.50951	+	0.940371i	−0.731784	+	0.196081i	−0.126360	+	0.991984i	$0.540330\pi$
$24$	2.77521	+	3.51600i	0.566488	+	0.717701i
$25$	−3.25250	+	3.79754i	−0.650499	+	0.759507i
$26$	−3.37200	+	0.162644i	−0.661303	+	0.0318971i
$27$	−3.91041	−	3.91041i	−0.752559	−	0.752559i
$28$	3.84688	−	3.63339i	0.726991	−	0.686647i
$29$	−5.07439			−0.942291			−0.471146	−	0.882055i	$-0.656159\pi$
$29$	−5.07439			−0.942291			−0.471146	+	0.882055i	$0.656159\pi$
$30$	−4.22238	−	2.69287i	−0.770898	−	0.491649i
$31$	2.42122	−	1.39789i	0.434864	−	0.251069i	−0.266552	−	0.963820i	$-0.585885\pi$
$31$	2.42122	−	1.39789i	0.434864	−	0.251069i	0.701417	+	0.712751i	$0.252551\pi$
$32$	2.92979	−	4.83904i	0.517919	−	0.855430i
$33$	−1.44383	−	5.38846i	−0.251339	−	0.938010i
$34$	0.993080	+	1.54324i	0.170312	+	0.264663i
$35$	−2.72691	+	5.25014i	−0.460932	+	0.887435i
$36$	−0.407692	+	0.895547i	−0.0679487	+	0.149258i
$37$	−0.340662	−	1.27137i	−0.0560045	−	0.209012i	0.932254	−	0.361806i	$-0.117840\pi$
$37$	−0.340662	−	1.27137i	−0.0560045	−	0.209012i	−0.988258	+	0.152794i	$0.951173\pi$
$38$	−10.3002	+	3.29940i	−1.67092	+	0.535233i
$39$	1.89022	+	3.27395i	0.302677	+	0.524252i
$40$	−1.31552	+	6.18623i	−0.208002	+	0.978128i
$41$	−4.50117			−0.702965			−0.351483	−	0.936194i	$-0.614322\pi$
$41$	−4.50117			−0.702965			−0.351483	+	0.936194i	$0.614322\pi$
$42$	−5.58924	−	1.96787i	−0.862439	−	0.303648i
$43$	7.05995	−	7.05995i	1.07663	−	1.07663i	0.0798234	−	0.996809i	$-0.474564\pi$
$43$	7.05995	−	7.05995i	1.07663	−	1.07663i	0.996809	−	0.0798234i	$-0.0254357\pi$
$44$	−5.73387	+	4.09339i	−0.864414	+	0.617102i
$45$	0.101421	−	1.09544i	0.0151189	−	0.163298i
$46$	2.35177	−	4.56849i	0.346750	−	0.673587i
$47$	2.14078	+	7.98948i	0.312264	+	1.16539i	0.926510	+	0.376271i	$0.122794\pi$
$47$	2.14078	+	7.98948i	0.312264	+	1.16539i	−0.614246	+	0.789115i	$0.710540\pi$
$48$	−6.31960	−	0.436835i	−0.912156	−	0.0630517i
$49$	−1.73080	+	6.78265i	−0.247258	+	0.968950i
$50$	−0.884061	−	7.01559i	−0.125025	−	0.992154i
$51$	1.02752	−	1.77973i	0.143882	−	0.249211i
$52$	3.03534	−	3.68516i	0.420926	−	0.511039i
$53$	3.15330	−	11.7683i	0.433139	−	1.61650i	−0.312340	−	0.949970i	$-0.601113\pi$
$53$	3.15330	−	11.7683i	0.433139	−	1.61650i	0.745480	−	0.666528i	$-0.232220\pi$
$54$	7.81174	−	0.376789i	1.06304	−	0.0512745i
$55$	4.55041	−	6.42925i	0.613577	−	0.866919i
$56$	0.147146	+	7.48187i	0.0196632	+	0.999807i
$57$	8.56430	+	8.56430i	1.13437	+	1.13437i
$58$	4.82403	−	5.31297i	0.633426	−	0.697628i
$59$	10.7678	−	6.21679i	1.40185	−	0.809357i	0.407265	−	0.913310i	$-0.366482\pi$
$59$	10.7678	−	6.21679i	1.40185	−	0.809357i	0.994582	+	0.103953i	$0.0331492\pi$
$60$	6.83354	−	1.86089i	0.882206	−	0.240240i
$61$	−11.1830	−	6.45654i	−1.43184	−	0.826675i	−0.434581	−	0.900633i	$-0.643104\pi$
$61$	−11.1830	−	6.45654i	−1.43184	−	0.826675i	−0.997261	+	0.0739580i	$0.976437\pi$
$62$	−0.838145	+	3.86398i	−0.106444	+	0.490726i
$63$	−0.177612	−	1.28951i	−0.0223770	−	0.162463i
$64$	2.28132	+	7.66783i	0.285164	+	0.958479i
$65$	−1.85096	+	5.00660i	−0.229584	+	0.620992i
$66$	7.01440	+	3.61088i	0.863413	+	0.444469i
$67$	0.866858	−	3.23516i	0.105904	−	0.395238i	−0.892543	−	0.450963i	$-0.851081\pi$
$67$	0.866858	−	3.23516i	0.105904	−	0.395238i	0.998446	+	0.0557257i	$0.0177472\pi$
$68$	−2.55988	−	0.427325i	−0.310431	−	0.0518208i
$69$	−5.75397			−0.692697
$70$	−2.90461	−	7.84622i	−0.347168	−	0.937803i
$71$		−	2.60984i		−	0.309731i	−0.987936	−	0.154865i	$-0.950506\pi$
$71$		−	2.60984i		−	0.309731i	0.987936	−	0.154865i	$-0.0494944\pi$
$72$	−0.550075	−	1.27822i	−0.0648270	−	0.150640i
$73$	1.56766	+	0.420053i	0.183481	+	0.0491635i	0.349389	−	0.936978i	$-0.386389\pi$
$73$	1.56766	+	0.420053i	0.183481	+	0.0491635i	−0.165909	+	0.986141i	$0.553056\pi$
$74$	1.65500	+	0.851962i	0.192390	+	0.0990386i
$75$	−6.53191	+	4.47597i	−0.754241	+	0.516841i
$76$	6.33751	−	13.9211i	0.726962	−	1.59686i
$77$	3.51501	−	8.63150i	0.400572	−	0.983651i
$78$	−5.22484	−	1.13333i	−0.591596	−	0.128324i
$79$	3.66367	−	6.34566i	0.412195	−	0.713942i	−0.582935	−	0.812519i	$-0.698096\pi$
$79$	3.66367	−	6.34566i	0.412195	−	0.713942i	0.995129	+	0.0985767i	$0.0314290\pi$
$80$	−5.22647	−	7.25838i	−0.584337	−	0.811511i
$81$	−3.64099	−	6.30638i	−0.404554	−	0.700708i
$82$	4.27909	−	4.71280i	0.472547	−	0.520442i
$83$	4.94034	−	4.94034i	0.542273	−	0.542273i	−0.381921	−	0.924195i	$-0.624738\pi$
$83$	4.94034	−	4.94034i	0.542273	−	0.542273i	0.924195	+	0.381921i	$0.124738\pi$
$84$	7.37386	−	3.98125i	0.804555	−	0.434391i
$85$	2.86006	−	0.489413i	0.310217	−	0.0530843i
$86$	0.680264	+	14.1035i	0.0733548	+	1.52082i
$87$	−7.76234	−	2.07991i	−0.832210	−	0.222990i
$88$	1.16512	−	9.89489i	0.124203	−	1.05480i
$89$	−4.71065	−	2.71969i	−0.499328	−	0.288287i	0.229108	−	0.973401i	$-0.426419\pi$
$89$	−4.71065	−	2.71969i	−0.499328	−	0.288287i	−0.728436	+	0.685114i	$0.759752\pi$
$90$	1.05053	+	1.14758i	0.110735	+	0.120966i
$91$	−0.786943	+	6.26655i	−0.0824941	+	0.656913i
$92$	2.54755	+	6.80543i	0.265600	+	0.709515i
$93$	4.27674	−	1.14595i	0.443477	−	0.118829i
$94$	−10.4003	−	5.35386i	−1.07271	−	0.552209i
$95$	−1.57657	+	17.0284i	−0.161752	+	1.74708i
$96$	6.46517	−	6.20144i	0.659849	−	0.632932i
$97$	−5.73033	−	5.73033i	−0.581827	−	0.581827i	0.353578	−	0.935405i	$-0.384965\pi$
$97$	−5.73033	−	5.73033i	−0.581827	−	0.581827i	−0.935405	+	0.353578i	$0.884965\pi$
$98$	−5.45614	−	8.26018i	−0.551153	−	0.834404i
$99$			1.73306i			0.174179i
$100$	8.18588	+	5.74382i	0.818588	+	0.574382i
$101$	−1.55648	+	0.898635i	−0.154876	+	0.0894175i	−0.575435	−	0.817848i	$-0.695167\pi$
$101$	−1.55648	+	0.898635i	−0.154876	+	0.0894175i	0.420559	+	0.907265i	$0.361834\pi$
$102$	0.886574	+	2.76775i	0.0877839	+	0.274048i
$103$	0.396755	−	0.106310i	0.0390934	−	0.0104751i	−0.239219	−	0.970966i	$-0.576891\pi$
$103$	0.396755	−	0.106310i	0.0390934	−	0.0104751i	0.278313	+	0.960491i	$0.410225\pi$
$104$	0.972843	+	6.68138i	0.0953951	+	0.655164i
$105$	−6.32332	+	6.91346i	−0.617093	+	0.674685i
$106$	9.32387	+	14.4892i	0.905614	+	1.40732i
$107$	2.19245	−	0.587465i	0.211952	−	0.0567924i	−0.151281	−	0.988491i	$-0.548340\pi$
$107$	2.19245	−	0.587465i	0.211952	−	0.0567924i	0.363233	+	0.931698i	$0.381673\pi$
$108$	−7.03182	+	8.53722i	−0.676637	+	0.821495i
$109$	1.42491	+	2.46801i	0.136481	+	0.236392i	0.926162	−	0.377125i	$-0.123087\pi$
$109$	1.42491	+	2.46801i	0.136481	+	0.236392i	−0.789681	+	0.613517i	$0.789754\pi$
$110$	2.40563	+	10.8764i	0.229368	+	1.03702i
$111$		−	2.08445i		−	0.197848i
$112$	−7.97352	−	6.95866i	−0.753427	−	0.657531i
$113$	−6.70606	+	6.70606i	−0.630853	+	0.630853i	−0.948282	−	0.317429i	$-0.897180\pi$
$113$	−6.70606	+	6.70606i	−0.630853	+	0.630853i	0.317429	+	0.948282i	$0.397180\pi$
$114$	−17.1087	+	0.825216i	−1.60238	+	0.0772886i
$115$	−5.19070	−	6.24992i	−0.484035	−	0.582808i
$116$	0.976754	+	10.1017i	0.0906894	+	0.937917i
$117$	−0.303969	−	1.13443i	−0.0281020	−	0.104878i
$118$	−3.72744	+	17.1841i	−0.343139	+	1.58193i
$119$	3.16401	−	1.33278i	0.290045	−	0.122176i
$120$	−4.54799	+	8.92391i	−0.415173	+	0.814638i
$121$	−0.704146	+	1.21962i	−0.0640133	+	0.110874i
$122$	17.3914	−	5.57086i	1.57454	−	0.504362i
$123$	−6.88548	−	1.84496i	−0.620843	−	0.166354i
$124$	−3.24886	−	4.55089i	−0.291756	−	0.408682i
$125$	−10.7543	−	3.05711i	−0.961890	−	0.273436i
$126$	1.51899	+	1.03992i	0.135322	+	0.0926438i
$127$	1.37573	−	1.37573i	0.122076	−	0.122076i	−0.643429	−	0.765506i	$-0.722489\pi$
$127$	1.37573	−	1.37573i	0.122076	−	0.122076i	0.765506	+	0.643429i	$0.222489\pi$
$128$	−10.1971	−	4.90093i	−0.901305	−	0.433185i
$129$	13.6934	−	7.90590i	1.20564	−	0.696076i
$130$	−3.48235	−	6.69757i	−0.305422	−	0.587415i
$131$	2.04335	−	3.53919i	0.178528	−	0.309220i	−0.762848	−	0.646578i	$-0.776200\pi$
$131$	2.04335	−	3.53919i	0.178528	−	0.309220i	0.941377	+	0.337357i	$0.109533\pi$
$132$	−10.4490	+	3.91147i	−0.909466	+	0.340450i
$133$	2.76095	+	20.0452i	0.239405	+	1.73814i
$134$	2.56318	+	3.98315i	0.221425	+	0.344092i
$135$	4.28804	−	11.5985i	0.369056	−	0.998243i
$136$	2.88099	−	2.27399i	0.247043	−	0.194993i
$137$	−4.92103	+	18.3655i	−0.420432	+	1.56907i	0.353268	+	0.935522i	$0.385070\pi$
$137$	−4.92103	+	18.3655i	−0.420432	+	1.56907i	−0.773700	+	0.633552i	$0.781596\pi$
$138$	5.47008	−	6.02450i	0.465644	−	0.512840i
$139$		−	4.28772i		−	0.363680i	−0.983328	−	0.181840i	$-0.941795\pi$
$139$		−	4.28772i		−	0.363680i	0.983328	−	0.181840i	$-0.0582052\pi$
$140$	10.9764	+	4.41792i	0.927677	+	0.373382i
$141$			13.0990i			1.10314i
$142$	2.73254	+	2.48107i	0.229310	+	0.208207i
$143$	2.17635	−	8.12226i	0.181996	−	0.679217i
$144$	1.86126	+	0.639218i	0.155105	+	0.0532682i
$145$	−4.74328	−	10.3077i	−0.393908	−	0.856008i
$146$	−1.93011	+	1.24204i	−0.159737	+	0.102792i
$147$	−5.42772	+	9.66604i	−0.447671	+	0.797241i
$148$	−2.46536	+	0.922884i	−0.202651	+	0.0758606i
$149$	−1.06581	+	1.84604i	−0.0873149	+	0.151234i	−0.906375	−	0.422473i	$-0.861162\pi$
$149$	−1.06581	+	1.84604i	−0.0873149	+	0.151234i	0.819060	+	0.573707i	$0.194495\pi$
$150$	1.52322	−	11.0942i	0.124370	−	0.905834i
$151$	−13.8226	+	7.98046i	−1.12486	+	0.649441i	−0.942638	−	0.333816i	$-0.891664\pi$
$151$	−13.8226	+	7.98046i	−1.12486	+	0.649441i	−0.182226	+	0.983257i	$0.558330\pi$
$152$	8.55083	+	19.8697i	0.693564	+	1.61165i
$153$	−0.451439	+	0.451439i	−0.0364967	+	0.0364967i
$154$	5.69574	+	11.8859i	0.458976	+	0.957793i
$155$	5.10279	+	3.61159i	0.409866	+	0.290090i
$156$	6.15366	−	4.39308i	0.492687	−	0.351728i
$157$	−0.299000	−	0.0801167i	−0.0238628	−	0.00639401i	0.246868	−	0.969049i	$-0.420599\pi$
$157$	−0.299000	−	0.0801167i	−0.0238628	−	0.00639401i	−0.270731	+	0.962655i	$0.587265\pi$
$158$	3.16110	+	9.86849i	0.251484	+	0.785095i
$159$	9.64726	−	16.7095i	0.765078	−	1.32515i
$160$	12.5682	+	1.42806i	0.993607	+	0.112898i
$161$	−7.66121	−	5.80626i	−0.603788	−	0.457597i
$162$	10.0642	+	2.18305i	0.790720	+	0.171517i
$163$	4.73174	+	17.6591i	0.370618	+	1.38317i	0.859643	+	0.510896i	$0.170686\pi$
$163$	4.73174	+	17.6591i	0.370618	+	1.38317i	−0.489024	+	0.872270i	$0.662647\pi$
$164$	0.866417	+	8.96056i	0.0676558	+	0.699702i
$165$	9.59604	−	7.96973i	0.747051	−	0.620442i
$166$	0.476029	+	9.86922i	0.0369470	+	0.766000i
$167$	−11.0028	+	11.0028i	−0.851425	+	0.851425i	−0.990309	−	0.138884i	$-0.955649\pi$
$167$	−11.0028	+	11.0028i	−0.851425	+	0.851425i	0.138884	+	0.990309i	$0.455649\pi$
$168$	−2.84161	+	11.5054i	−0.219235	+	0.887659i
$169$		−	7.30159i		−	0.561660i
$170$	−2.20653	+	3.45980i	−0.169233	+	0.265354i
$171$	−1.88135	−	3.25859i	−0.143870	−	0.249191i
$172$	−15.4133	−	12.6954i	−1.17525	−	0.968016i
$173$	−4.03885	+	1.08221i	−0.307068	+	0.0822786i	−0.409063	−	0.912506i	$-0.634144\pi$
$173$	−4.03885	+	1.08221i	−0.307068	+	0.0822786i	0.101995	+	0.994785i	$0.467478\pi$
$174$	9.55706	−	6.15000i	0.724518	−	0.466231i
$175$	−13.2137	−	0.631667i	−0.998859	−	0.0477495i
$176$	9.25247	+	10.6266i	0.697431	+	0.801009i
$177$	19.0197	−	5.09632i	1.42961	−	0.383063i
$178$	7.32579	−	2.34662i	0.549091	−	0.175886i
$179$	−17.6513	+	10.1910i	−1.31932	+	0.761711i	−0.983619	−	0.180257i	$-0.942307\pi$
$179$	−17.6513	+	10.1910i	−1.31932	+	0.761711i	−0.335702	+	0.941968i	$0.608974\pi$
$180$	−2.20023	+	0.00895801i	−0.163995	+	0.000667691i
$181$			17.3870i			1.29237i	0.763182	+	0.646183i	$0.223636\pi$
$181$			17.3870i			1.29237i	−0.763182	+	0.646183i	$0.776364\pi$
$182$	−5.81306	−	6.78131i	−0.430893	−	0.502664i
$183$	−14.4604	−	14.4604i	−1.06894	−	1.06894i
$184$	−9.54725	−	3.80234i	−0.703833	−	0.280312i
$185$	2.26412	−	1.88040i	0.166461	−	0.138250i
$186$	−2.86590	+	5.56722i	−0.210138	+	0.408208i
$187$	−4.41527	+	1.18307i	−0.322877	+	0.0865146i
$188$	15.4927	−	5.79955i	1.12992	−	0.422975i
$189$	1.82307	−	14.5174i	0.132609	−	1.05599i
$190$	−16.3302	−	17.8389i	−1.18472	−	1.29417i
$191$	−2.18647	−	1.26236i	−0.158208	−	0.0913412i	0.418806	−	0.908076i	$-0.362449\pi$
$191$	−2.18647	−	1.26236i	−0.158208	−	0.0913412i	−0.577014	+	0.816735i	$0.695782\pi$
$192$	0.346826	+	12.6646i	0.0250300	+	0.913989i
$193$	26.5441	+	7.11247i	1.91069	+	0.511967i	0.993550	+	0.113396i	$0.0361730\pi$
$193$	26.5441	+	7.11247i	1.91069	+	0.511967i	0.917138	+	0.398571i	$0.130494\pi$
$194$	11.4474	−	0.552148i	0.821872	−	0.0396419i
$195$	−4.88356	+	6.89995i	−0.349719	+	0.494115i
$196$	13.8355	+	2.13997i	0.988249	+	0.152855i
$197$	16.1289	−	16.1289i	1.14913	−	1.14913i	0.162412	−	0.986723i	$-0.448073\pi$
$197$	16.1289	−	16.1289i	1.14913	−	1.14913i	0.986723	−	0.162412i	$-0.0519273\pi$
$198$	−1.81454	−	1.64755i	−0.128954	−	0.117086i
$199$	2.41828	+	4.18858i	0.171427	+	0.296921i	0.938919	−	0.344138i	$-0.111829\pi$
$199$	2.41828	+	4.18858i	0.171427	+	0.296921i	−0.767492	+	0.641059i	$0.778495\pi$
$200$	−13.7959	+	3.11032i	−0.975515	+	0.219933i
$201$	2.65208	−	4.59353i	0.187063	−	0.324003i
$202$	0.538801	−	2.48396i	0.0379099	−	0.174771i
$203$	−8.23647	−	10.6022i	−0.578087	−	0.744129i
$204$	−3.74071	−	1.70294i	−0.261902	−	0.119229i
$205$	−4.20746	−	9.14331i	−0.293862	−	0.638596i
$206$	−0.265871	+	0.516474i	−0.0185241	+	0.0359845i
$207$	1.72665	+	0.462653i	0.120010	+	0.0321566i
$208$	−7.92036	−	5.33315i	−0.549178	−	0.369787i
$209$		−	26.9401i		−	1.86348i
$210$	−1.22717	−	13.1930i	−0.0846827	−	0.910402i
$211$	−8.85681			−0.609728			−0.304864	−	0.952396i	$-0.598611\pi$
$211$	−8.85681			−0.609728			−0.304864	+	0.952396i	$0.598611\pi$
$212$	−24.0343	−	4.01209i	−1.65068	−	0.275551i
$213$	1.06973	−	3.99229i	0.0732967	−	0.273547i
$214$	−1.46919	+	2.85401i	−0.100432	+	0.195096i
$215$	20.9403	+	7.74173i	1.42811	+	0.527981i
$216$	−2.25374	−	15.4784i	−0.153347	−	1.05317i
$217$	6.85069	+	2.78981i	0.465055	+	0.189385i
$218$	−3.93865	−	0.854340i	−0.266759	−	0.0578632i
$219$	2.22589	+	1.28512i	0.150411	+	0.0868401i
$220$	−13.6747	−	7.82103i	−0.921948	−	0.527294i
$221$	2.68266	−	1.54883i	0.180455	−	0.104186i
$222$	2.18246	+	1.98161i	0.146477	+	0.132997i
$223$	0.581823	+	0.581823i	0.0389618	+	0.0389618i	0.726319	−	0.687358i	$-0.241229\pi$
$223$	0.581823	+	0.581823i	0.0389618	+	0.0389618i	−0.687358	+	0.726319i	$0.741229\pi$
$224$	14.8659	−	1.73309i	0.993273	−	0.115797i
$225$	2.31999	−	0.817941i	0.154666	−	0.0545294i
$226$	−0.646164	−	13.3965i	−0.0429822	−	0.891125i
$227$	−2.52248	+	9.41401i	−0.167423	+	0.624829i	0.830296	+	0.557322i	$0.188171\pi$
$227$	−2.52248	+	9.41401i	−0.167423	+	0.624829i	−0.997719	+	0.0675072i	$0.978495\pi$
$228$	15.4006	−	18.6976i	1.01993	−	1.23828i
$229$	−5.21707	+	9.03624i	−0.344754	+	0.597131i	−0.985309	−	0.170781i	$-0.945371\pi$
$229$	−5.21707	+	9.03624i	−0.344754	+	0.597131i	0.640555	+	0.767912i	$0.278704\pi$
$230$	11.4784	+	0.506811i	0.756861	+	0.0334181i
$231$	8.91485	−	11.7629i	0.586554	−	0.773943i
$232$	−11.5052	−	8.58059i	−0.755352	−	0.563343i
$233$	3.47955	+	12.9859i	0.227953	+	0.850732i	0.981200	+	0.192994i	$0.0618199\pi$
$233$	3.47955	+	12.9859i	0.227953	+	0.850732i	−0.753247	+	0.657738i	$0.771513\pi$
$234$	1.47674	+	0.760197i	0.0965374	+	0.0496956i
$235$	−14.2281	+	11.8167i	−0.928138	+	0.770839i
$236$	−14.4485	−	20.2390i	−0.940518	−	1.31744i
$237$	8.20532	−	8.20532i	0.532993	−	0.532993i
$238$	−1.61246	+	4.57980i	−0.104520	+	0.296864i
$239$	−26.1978			−1.69460			−0.847298	−	0.531118i	$-0.821772\pi$
$239$	−26.1978			−1.69460			−0.847298	+	0.531118i	$0.821772\pi$
$240$	−5.01988	−	13.2454i	−0.324032	−	0.854989i
$241$	−10.5712	−	18.3099i	−0.680953	−	1.17945i	−0.974690	−	0.223559i	$-0.928232\pi$
$241$	−10.5712	−	18.3099i	−0.680953	−	1.17945i	0.293737	−	0.955886i	$-0.405101\pi$
$242$	−0.607555	−	1.89669i	−0.0390551	−	0.121924i
$243$	1.30917	+	4.88588i	0.0839831	+	0.313429i
$244$	−10.7005	+	23.5051i	−0.685032	+	1.50476i
$245$	−15.3956	+	2.82425i	−0.983587	+	0.180435i
$246$	8.47746	−	5.45528i	0.540503	−	0.347816i
$247$	4.72515	+	17.6345i	0.300654	+	1.12206i
$248$	7.85342	+	0.924741i	0.498693	+	0.0587211i
$249$	9.58225	−	5.53231i	0.607250	−	0.350596i
$250$	13.4245	−	8.35361i	0.849040	−	0.528328i
$251$	12.3678			0.780648			0.390324	−	0.920677i	$-0.372363\pi$
$251$	12.3678			0.780648			0.390324	+	0.920677i	$0.372363\pi$
$252$	−2.53286	+	0.601789i	−0.159555	+	0.0379091i
$253$	9.04991	+	9.04991i	0.568963	+	0.568963i
$254$	0.132559	+	2.74827i	0.00831749	+	0.172442i
$255$	4.57566	+	0.423635i	0.286539	+	0.0265291i
$256$	14.8253	−	6.01741i	0.926584	−	0.376088i
$257$	7.05835	−	1.89128i	0.440288	−	0.117975i	−0.0318637	−	0.999492i	$-0.510144\pi$
$257$	7.05835	−	1.89128i	0.440288	−	0.117975i	0.472151	+	0.881517i	$0.343478\pi$
$258$	−4.74019	+	21.8531i	−0.295112	+	1.36051i
$259$	2.10340	−	2.77538i	0.130699	−	0.172454i
$260$	10.3230	+	2.72104i	0.640205	+	0.168752i
$261$	2.16208	+	1.24828i	0.133829	+	0.0772664i
$262$	1.76305	+	5.50399i	0.108922	+	0.340038i
$263$	−0.181866	+	0.678733i	−0.0112143	+	0.0418524i	−0.971306	−	0.237832i	$-0.923563\pi$
$263$	−0.181866	+	0.678733i	−0.0112143	+	0.0418524i	0.960092	+	0.279685i	$0.0902299\pi$
$264$	5.83805	−	14.6587i	0.359307	−	0.902182i
$265$	26.8527	−	4.59502i	1.64955	−	0.282270i
$266$	−23.6124	−	16.1654i	−1.44777	−	0.991167i
$267$	−6.09115	−	6.09115i	−0.372773	−	0.372773i
$268$	−6.60714	−	1.10294i	−0.403595	−	0.0673729i
$269$	13.5648	+	23.4949i	0.827059	+	1.43251i	0.900335	+	0.435197i	$0.143321\pi$
$269$	13.5648	+	23.4949i	0.827059	+	1.43251i	−0.0732765	+	0.997312i	$0.523346\pi$
$270$	8.06738	+	15.5159i	0.490965	+	0.944269i
$271$	−8.49993	−	4.90744i	−0.516334	−	0.298106i	0.219100	−	0.975703i	$-0.429688\pi$
$271$	−8.49993	−	4.90744i	−0.516334	−	0.298106i	−0.735433	+	0.677597i	$0.763021\pi$
$272$	−0.357940	+	5.17825i	−0.0217033	+	0.313977i
$273$	−3.77235	+	9.26343i	−0.228313	+	0.560648i
$274$	−14.5508	−	22.6118i	−0.879045	−	1.36603i
$275$	17.3133	+	3.23361i	1.04403	+	0.194994i
$276$	1.10756	+	11.4545i	0.0666675	+	0.689481i
$277$	9.72480	+	2.60575i	0.584306	+	0.156564i	0.538850	−	0.842402i	$-0.318859\pi$
$277$	9.72480	+	2.60575i	0.584306	+	0.156564i	0.0454566	+	0.998966i	$0.485526\pi$
$278$	4.48931	+	4.07617i	0.269251	+	0.244472i
$279$	−1.37550			−0.0823490
$280$	−15.0605	+	7.29256i	−0.900037	+	0.435814i
$281$	−18.5208			−1.10486			−0.552429	−	0.833560i	$-0.686299\pi$
$281$	−18.5208			−1.10486			−0.552429	+	0.833560i	$0.686299\pi$
$282$	−13.7149	−	12.4527i	−0.816711	−	0.741550i
$283$	5.38049	+	1.44170i	0.319837	+	0.0857000i	0.415166	−	0.909746i	$-0.363724\pi$
$283$	5.38049	+	1.44170i	0.319837	+	0.0857000i	−0.0953290	+	0.995446i	$0.530390\pi$
$284$	−5.19544	+	0.502359i	−0.308293	+	0.0298095i
$285$	−9.39135	+	25.4023i	−0.556296	+	1.50470i
$286$	6.43516	+	10.0002i	0.380519	+	0.591324i
$287$	−7.30606	−	9.40455i	−0.431263	−	0.555133i
$288$	−2.43870	+	1.34108i	−0.143701	+	0.0790242i
$289$	13.2641	+	7.65805i	0.780243	+	0.450474i
$290$	15.3016	+	4.83284i	0.898540	+	0.283794i
$291$	−6.41696	−	11.1145i	−0.376169	−	0.651543i
$292$	0.534452	−	3.20162i	0.0312764	−	0.187360i
$293$	−3.56250	−	3.56250i	−0.208123	−	0.208123i	0.595346	−	0.803469i	$-0.297015\pi$
$293$	−3.56250	−	3.56250i	−0.208123	−	0.208123i	−0.803469	+	0.595346i	$0.797015\pi$
$294$	−4.96058	−	14.8720i	−0.289307	−	0.867355i
$295$	22.6934	+	16.0617i	1.32126	+	0.935147i
$296$	1.37745	−	3.45862i	0.0800626	−	0.201028i
$297$	−5.04185	+	18.8164i	−0.292558	+	1.09184i
$298$	−0.919610	−	2.87089i	−0.0532716	−	0.166306i
$299$	−7.51122	−	4.33661i	−0.434385	−	0.250792i
$300$	10.1677	+	12.1416i	0.587032	+	0.700997i
$301$	26.2101	+	3.29142i	1.51072	+	0.189714i
$302$	4.78490	−	22.0592i	0.275340	−	1.26936i
$303$	−2.74930	+	0.736672i	−0.157943	+	0.0423207i
$304$	−28.9329	−	9.93654i	−1.65942	−	0.569900i
$305$	2.66195	−	28.7515i	0.152423	−	1.64631i
$306$	−0.0434986	−	0.901830i	−0.00248665	−	0.0515542i
$307$	−1.49192	−	1.49192i	−0.0851481	−	0.0851481i	0.663250	−	0.748398i	$-0.269177\pi$
$307$	−1.49192	−	1.49192i	−0.0851481	−	0.0851481i	−0.748398	+	0.663250i	$0.769177\pi$
$308$	−17.8595	−	5.33593i	−1.01764	−	0.304043i
$309$	0.650494			0.0370053
$310$	−8.63243	+	1.90931i	−0.490289	+	0.108442i
$311$	12.4858	−	7.20869i	0.708006	−	0.408767i	−0.102316	−	0.994752i	$-0.532625\pi$
$311$	12.4858	−	7.20869i	0.708006	−	0.408767i	0.810322	+	0.585985i	$0.199292\pi$
$312$	−1.25043	+	10.6193i	−0.0707914	+	0.601200i
$313$	1.56812	+	5.85232i	0.0886356	+	0.330793i	0.995978	−	0.0896003i	$-0.0285589\pi$
$313$	1.56812	+	5.85232i	0.0886356	+	0.330793i	−0.907342	+	0.420393i	$0.861892\pi$
$314$	0.368131	−	0.236894i	0.0207748	−	0.0133687i
$315$	2.45338	−	1.56615i	0.138232	−	0.0882427i
$316$	−13.3376	−	6.07186i	−0.750299	−	0.341569i
$317$	4.39736	+	16.4112i	0.246981	+	0.921744i	0.972378	+	0.233413i	$0.0749895\pi$
$317$	4.39736	+	16.4112i	0.246981	+	0.921744i	−0.725397	+	0.688331i	$0.758344\pi$
$318$	8.32390	+	25.9860i	0.466781	+	1.45722i
$319$	8.93738	+	15.4800i	0.500397	+	0.866713i
$320$	−13.4433	+	11.8016i	−0.751505	+	0.659727i
$321$	3.59460			0.200631
$322$	13.3625	−	2.50163i	0.744661	−	0.139411i
$323$	7.01755	−	7.01755i	0.390467	−	0.390467i
$324$	−11.8534	+	8.46207i	−0.658520	+	0.470115i
$325$	−11.9002	+	0.920005i	−0.660102	+	0.0510327i
$326$	−22.9876	−	11.8336i	−1.27317	−	0.655402i
$327$	1.16809	+	4.35938i	0.0645956	+	0.241074i
$328$	−10.2055	−	7.61130i	−0.563506	−	0.420264i
$329$	−13.2181	+	17.4409i	−0.728736	+	0.961549i
$330$	−0.778151	+	17.6237i	−0.0428358	+	0.970154i
$331$	9.87135	−	17.0977i	0.542578	−	0.939773i	−0.456177	−	0.889889i	$-0.650782\pi$
$331$	9.87135	−	17.0977i	0.542578	−	0.939773i	0.998755	−	0.0498839i	$-0.0158851\pi$
$332$	−10.7858	−	8.88387i	−0.591946	−	0.487566i
$333$	−0.167603	+	0.625501i	−0.00918456	+	0.0342773i
$334$	−1.06018	−	21.9801i	−0.0580106	−	1.20270i
$335$	7.38192	−	1.26319i	0.403318	−	0.0690156i
$336$	−9.34492	−	13.9129i	−0.509807	−	0.759012i
$337$	−16.0087	−	16.0087i	−0.872050	−	0.872050i	0.120646	−	0.992696i	$-0.461503\pi$
$337$	−16.0087	−	16.0087i	−0.872050	−	0.872050i	−0.992696	+	0.120646i	$0.961503\pi$
$338$	7.64488	+	6.94133i	0.415827	+	0.377559i
$339$	−13.0070	+	7.50960i	−0.706444	+	0.407866i
$340$	−1.52481	−	5.59937i	−0.0826942	−	0.303668i
$341$	−8.52885	−	4.92414i	−0.461863	−	0.266657i
$342$	5.20032	+	1.12801i	0.281201	+	0.0609959i
$343$	−16.9807	+	7.39296i	−0.916872	+	0.399182i
$344$	27.9451	−	4.06895i	1.50670	−	0.219383i
$345$	−5.37851	−	11.6881i	−0.289569	−	0.629268i
$346$	2.70649	−	5.25755i	0.145502	−	0.282648i
$347$	−0.976243	+	3.64339i	−0.0524075	+	0.195587i	−0.987166	−	0.159695i	$-0.948949\pi$
$347$	−0.976243	+	3.64339i	−0.0524075	+	0.195587i	0.934759	+	0.355283i	$0.115615\pi$
$348$	−2.64637	+	15.8530i	−0.141860	+	0.849808i
$349$	−24.7370			−1.32414			−0.662069	−	0.749443i	$-0.730322\pi$
$349$	−24.7370			−1.32414			−0.662069	+	0.749443i	$0.730322\pi$
$350$	13.2231	−	13.2344i	0.706804	−	0.707410i
$351$		−	13.2012i		−	0.704630i
$352$	−19.9222	−	0.414795i	−1.06186	−	0.0221086i
$353$	−21.1337	−	5.66275i	−1.12483	−	0.301398i	−0.351995	−	0.936002i	$-0.614497\pi$
$353$	−21.1337	−	5.66275i	−1.12483	−	0.301398i	−0.772838	+	0.634604i	$0.781163\pi$
$354$	−12.7454	+	24.7589i	−0.677410	+	1.31592i
$355$	5.30140	−	2.43954i	0.281369	−	0.129477i
$356$	−4.50740	+	9.90106i	−0.238892	+	0.524755i
$357$	5.38630	−	0.741888i	0.285073	−	0.0392649i
$358$	6.11029	−	28.1694i	0.322939	−	1.48880i
$359$	10.7425	−	18.6065i	0.566967	−	0.982016i	−0.429897	−	0.902878i	$-0.641450\pi$
$359$	10.7425	−	18.6065i	0.566967	−	0.982016i	0.996864	−	0.0791378i	$-0.0252167\pi$
$360$	2.08229	−	2.31219i	0.109746	−	0.121863i
$361$	19.7452	+	34.1997i	1.03922	+	1.79999i
$362$	−18.2045	−	16.5292i	−0.956807	−	0.868753i
$363$	−1.57704	+	1.57704i	−0.0827731	+	0.0827731i
$364$	12.6264	+	0.360352i	0.661803	+	0.0188876i
$365$	0.612104	+	3.57705i	0.0320390	+	0.187232i
$366$	28.8871	−	1.39333i	1.50995	−	0.0728307i
$367$	−35.8558	−	9.60753i	−1.87166	−	0.501509i	−0.999934	−	0.0115121i	$-0.996336\pi$
$367$	−35.8558	−	9.60753i	−1.87166	−	0.501509i	−0.871724	−	0.489997i	$-0.836998\pi$
$368$	13.0573	−	6.38140i	0.680659	−	0.332653i
$369$	1.91784	+	1.10727i	0.0998389	+	0.0576420i
$370$	−0.183599	+	4.15820i	−0.00954487	+	0.216174i
$371$	29.7064	−	12.5133i	1.54228	−	0.649656i
$372$	−3.10447	−	8.29318i	−0.160959	−	0.429982i
$373$	−3.81547	+	1.02235i	−0.197557	+	0.0529354i	−0.356241	−	0.934394i	$-0.615942\pi$
$373$	−3.81547	+	1.02235i	−0.197557	+	0.0529354i	0.158683	+	0.987330i	$0.449275\pi$
$374$	2.95874	−	5.74756i	0.152993	−	0.297199i
$375$	−15.1978	−	9.08448i	−0.784811	−	0.469121i
$376$	−8.65610	+	21.7345i	−0.446404	+	1.12087i
$377$	−8.56537	−	8.56537i	−0.441139	−	0.441139i
$378$	13.4668	+	15.7099i	0.692659	+	0.808031i
$379$			19.2397i			0.988279i	0.869383	+	0.494140i	$0.164517\pi$
$379$			19.2397i			0.988279i	−0.869383	+	0.494140i	$0.835483\pi$
$380$	34.2022	−	0.139251i	1.75454	−	0.00714341i
$381$	2.66835	−	1.54058i	0.136704	−	0.0789261i
$382$	3.40031	−	1.08920i	0.173975	−	0.0557281i
$383$	35.8097	−	9.59518i	1.82979	−	0.490291i	0.831883	−	0.554951i	$-0.187263\pi$
$383$	35.8097	−	9.59518i	1.82979	−	0.490291i	0.997907	+	0.0646604i	$0.0205964\pi$
$384$	−13.5898	−	11.6766i	−0.693500	−	0.595870i
$385$	20.8190	−	0.928173i	1.06103	−	0.0473041i
$386$	−32.6813	+	21.0306i	−1.66344	+	1.07043i
$387$	−4.74479	+	1.27136i	−0.241191	+	0.0646270i
$388$	−10.3044	+	12.5105i	−0.523129	+	0.635123i
$389$	−15.3735	−	26.6277i	−0.779467	−	1.35008i	−0.932249	−	0.361817i	$-0.882157\pi$
$389$	−15.3735	−	26.6277i	−0.779467	−	1.35008i	0.152782	−	0.988260i	$-0.451177\pi$
$390$	−2.58175	−	11.6727i	−0.130732	−	0.591069i
$391$			4.71477i			0.238436i
$392$	−15.3934	+	12.4516i	−0.777486	+	0.628900i
$393$	4.57639	−	4.57639i	0.230848	−	0.230848i
$394$	1.55410	+	32.2203i	0.0782946	+	1.62324i
$395$	16.3146	+	1.51048i	0.820879	+	0.0760006i
$396$	3.45002	−	0.333591i	0.173370	−	0.0167636i
$397$	1.41993	+	5.29926i	0.0712643	+	0.265962i	0.992360	−	0.123373i	$-0.0393713\pi$
$397$	1.41993	+	5.29926i	0.0712643	+	0.265962i	−0.921096	+	0.389336i	$0.872705\pi$
$398$	−6.68448	−	1.44994i	−0.335063	−	0.0726791i
$399$	−3.99276	+	31.7950i	−0.199888	+	1.59174i
$400$	9.85863	−	17.4014i	0.492932	−	0.870068i
$401$	−6.76757	+	11.7218i	−0.337956	+	0.585357i	−0.984048	−	0.177902i	$-0.943069\pi$
$401$	−6.76757	+	11.7218i	−0.337956	+	0.585357i	0.646092	+	0.763260i	$0.276402\pi$
$402$	2.28828	+	7.14367i	0.114129	+	0.356294i
$403$	6.44651	+	1.72734i	0.321124	+	0.0860448i
$404$	2.08853	+	2.92554i	0.103908	+	0.145551i
$405$	9.40684	−	13.2909i	0.467430	−	0.660428i
$406$	18.9308	+	1.45538i	0.939519	+	0.0722294i
$407$	−3.27845	+	3.27845i	−0.162507	+	0.162507i
$408$	5.33915	−	2.29767i	0.264327	−	0.113752i
$409$	−22.6003	+	13.0483i	−1.11751	+	0.645197i	−0.940765	−	0.339058i	$-0.889892\pi$
$409$	−22.6003	+	13.0483i	−1.11751	+	0.645197i	−0.176750	+	0.984256i	$0.556558\pi$
$410$	13.5731	+	4.28691i	0.670326	+	0.211715i
$411$	−15.0555	+	26.0768i	−0.742632	+	1.28628i
$412$	−0.288004	−	0.769363i	−0.0141889	−	0.0379038i
$413$	30.4668	+	12.4070i	1.49917	+	0.610508i
$414$	−2.12586	+	1.36800i	−0.104480	+	0.0672335i
$415$	14.6534	+	5.41743i	0.719306	+	0.265931i
$416$	13.1135	−	3.22273i	0.642941	−	0.158007i
$417$	1.75747	−	6.55896i	0.0860635	−	0.321193i
$418$	28.2067	+	25.6109i	1.37963	+	1.25267i
$419$		−	12.8847i		−	0.629460i	−0.949181	−	0.314730i	$-0.898086\pi$
$419$		−	12.8847i		−	0.629460i	0.949181	−	0.314730i	$-0.101914\pi$
$420$	14.9799	+	11.2572i	0.730944	+	0.549295i
$421$			23.7295i			1.15650i	0.815858	+	0.578252i	$0.196265\pi$
$421$			23.7295i			1.15650i	−0.815858	+	0.578252i	$0.803735\pi$
$422$	8.41982	−	9.27322i	0.409871	−	0.451413i
$423$	1.05324	−	3.93075i	0.0512103	−	0.191119i
$424$	27.0492	−	21.3502i	1.31362	−	1.03686i
$425$	3.66759	+	5.35222i	0.177904	+	0.259621i
$426$	3.16304	+	4.91534i	0.153250	+	0.238149i
$427$	−4.66171	−	33.8452i	−0.225596	−	1.63789i
$428$	−1.59149	−	4.25147i	−0.0769278	−	0.205502i
$429$	6.65837	−	11.5326i	0.321469	−	0.556800i
$430$	−28.0128	+	14.5650i	−1.35090	+	0.702389i
$431$	−1.42359	+	0.821912i	−0.0685721	+	0.0395901i	−0.533894	−	0.845551i	$-0.679272\pi$
$431$	−1.42359	+	0.821912i	−0.0685721	+	0.0395901i	0.465322	+	0.885141i	$0.345939\pi$
$432$	18.3487	+	12.3550i	0.882803	+	0.594432i
$433$	−2.40313	+	2.40313i	−0.115487	+	0.115487i	−0.762489	−	0.647002i	$-0.776023\pi$
$433$	−2.40313	+	2.40313i	−0.115487	+	0.115487i	0.647002	+	0.762489i	$0.276023\pi$
$434$	−9.43366	+	4.52062i	−0.452830	+	0.216997i
$435$	−3.03086	−	17.7120i	−0.145319	−	0.849223i
$436$	4.63883	−	3.31164i	0.222160	−	0.158599i
$437$	−26.8404	−	7.19187i	−1.28395	−	0.344034i
$438$	−3.46160	+	1.10883i	−0.165402	+	0.0529819i
$439$	−3.15999	+	5.47326i	−0.150818	+	0.261225i	−0.931528	−	0.363668i	$-0.881524\pi$
$439$	−3.15999	+	5.47326i	−0.150818	+	0.261225i	0.780710	+	0.624893i	$0.214857\pi$
$440$	21.1887	−	6.88248i	1.01013	−	0.328110i
$441$	2.40595	−	2.46415i	0.114569	−	0.117341i
$442$	−0.928645	+	4.28120i	−0.0441711	+	0.203636i
$443$	7.35101	+	27.4343i	0.349257	+	1.30344i	0.887559	+	0.460693i	$0.152399\pi$
$443$	7.35101	+	27.4343i	0.349257	+	1.30344i	−0.538303	+	0.842752i	$0.680934\pi$
$444$	−4.14956	+	0.401230i	−0.196929	+	0.0190415i
$445$	1.12129	−	12.1110i	0.0531544	−	0.574118i
$446$	−1.16229	+	0.0560618i	−0.0550363	+	0.00265460i
$447$	−2.38705	+	2.38705i	−0.112903	+	0.112903i
$448$	−12.3179	+	17.2125i	−0.581966	+	0.813213i
$449$		−	3.54938i		−	0.167506i	−0.996487	−	0.0837528i	$-0.973309\pi$
$449$		−	3.54938i		−	0.167506i	0.996487	−	0.0837528i	$-0.0266906\pi$
$450$	−1.34912	+	3.20665i	−0.0635982	+	0.151163i
$451$	7.92778	+	13.7313i	0.373305	+	0.646583i
$452$	14.6407	+	12.0590i	0.688640	+	0.567209i
$453$	−24.4155	+	6.54213i	−1.14714	+	0.307376i
$454$	−7.45860	−	11.5906i	−0.350049	−	0.543974i
$455$	−13.4649	+	4.25911i	−0.631246	+	0.199670i
$456$	4.93598	+	33.8998i	0.231148	+	1.58750i
$457$	2.41330	−	0.646641i	0.112889	−	0.0302486i	−0.201932	−	0.979400i	$-0.564722\pi$
$457$	2.41330	−	0.646641i	0.112889	−	0.0302486i	0.314821	+	0.949151i	$0.398055\pi$
$458$	−4.50142	−	14.0528i	−0.210338	−	0.656642i
$459$	−6.21478	+	3.58811i	−0.290081	+	0.167478i
$460$	−11.4427	+	11.5362i	−0.533518	+	0.537880i
$461$		−	23.6985i		−	1.10375i	−0.833928	−	0.551874i	$-0.813913\pi$
$461$		−	23.6985i		−	1.10375i	0.833928	−	0.551874i	$-0.186087\pi$
$462$	3.84097	+	20.5165i	0.178698	+	0.954516i
$463$	−13.4785	−	13.4785i	−0.626398	−	0.626398i	0.320762	−	0.947160i	$-0.396061\pi$
$463$	−13.4785	−	13.4785i	−0.626398	−	0.626398i	−0.947160	+	0.320762i	$0.896061\pi$
$464$	19.9216	−	3.88888i	0.924835	−	0.180537i
$465$	6.32545	+	7.61623i	0.293336	+	0.353194i
$466$	−16.9043	−	8.70201i	−0.783076	−	0.403113i
$467$	−2.43441	+	0.652297i	−0.112651	+	0.0301847i	−0.314704	−	0.949190i	$-0.601905\pi$
$467$	−2.43441	+	0.652297i	−0.112651	+	0.0301847i	0.202053	+	0.979375i	$0.435239\pi$
$468$	−2.19982	+	0.823479i	−0.101687	+	0.0380653i
$469$	8.16643	−	3.43996i	0.377091	−	0.158842i
$470$	1.15377	−	26.1308i	0.0532193	−	1.20532i
$471$	−0.424544	−	0.245110i	−0.0195619	−	0.0112941i
$472$	34.9262	+	4.11256i	1.60761	+	0.189296i
$473$	−33.9716	−	9.10267i	−1.56202	−	0.418541i
$474$	0.790627	+	16.3916i	0.0363147	+	0.752891i
$475$	−36.0638	+	12.7148i	−1.65472	+	0.583393i
$476$	−3.26222	−	6.04211i	−0.149524	−	0.276939i
$477$	−4.23849	+	4.23849i	−0.194067	+	0.194067i
$478$	24.9052	−	27.4295i	1.13914	−	1.25460i
$479$	9.15394	+	15.8551i	0.418254	+	0.724437i	0.995764	−	0.0919464i	$-0.0293088\pi$
$479$	9.15394	+	15.8551i	0.418254	+	0.724437i	−0.577510	+	0.816384i	$0.695976\pi$
$480$	18.6404	+	7.33603i	0.850814	+	0.334842i
$481$	1.57099	−	2.72104i	0.0716312	−	0.124069i
$482$	29.2204	+	6.33827i	1.33095	+	0.288700i
$483$	−9.33953	−	12.0221i	−0.424963	−	0.547024i
$484$	2.56345	+	1.16699i	0.116520	+	0.0530452i
$485$	6.28370	−	16.9965i	0.285328	−	0.771772i
$486$	−6.36017	−	3.27410i	−0.288503	−	0.148516i
$487$	27.4262	+	7.34883i	1.24280	+	0.333007i	0.819551	−	0.573006i	$-0.194223\pi$
$487$	27.4262	+	7.34883i	1.24280	+	0.333007i	0.423249	+	0.906013i	$0.360890\pi$
$488$	−14.4376	−	33.5490i	−0.653560	−	1.51869i
$489$			28.9527i			1.30929i
$490$	11.6789	−	18.8043i	0.527600	−	0.849493i
$491$	11.3959			0.514290			0.257145	−	0.966373i	$-0.417218\pi$
$491$	11.3959			0.514290			0.257145	+	0.966373i	$0.417218\pi$
$492$	−2.34742	+	14.0622i	−0.105830	+	0.633971i
$493$	−1.70427	+	6.36042i	−0.0767564	+	0.286459i
$494$	−22.9556	−	11.8171i	−1.03282	−	0.531678i
$495$	−3.52039	+	1.61997i	−0.158230	+	0.0728122i
$496$	−8.43416	+	7.34355i	−0.378705	+	0.329735i
$497$	5.45287	−	4.23614i	0.244595	−	0.190017i
$498$	−3.31705	+	15.2921i	−0.148640	+	0.685257i
$499$	−23.4689	−	13.5498i	−1.05061	−	0.606572i	−0.127793	−	0.991801i	$-0.540789\pi$
$499$	−23.4689	−	13.5498i	−1.05061	−	0.606572i	−0.922821	+	0.385228i	$0.874123\pi$
$500$	−4.01579	+	21.9971i	−0.179591	+	0.983741i
$501$	−21.3410	+	12.3212i	−0.953446	+	0.550472i
$502$	−11.7576	+	12.9493i	−0.524767	+	0.577955i
$503$	16.1198	+	16.1198i	0.718748	+	0.718748i	0.968349	−	0.249601i	$-0.0802995\pi$
$503$	16.1198	+	16.1198i	0.718748	+	0.718748i	−0.249601	+	0.968349i	$0.580300\pi$
$504$	1.77781	−	3.22404i	0.0791899	−	0.143610i
$505$	−3.28033	−	2.32171i	−0.145973	−	0.103315i
$506$	−18.0788	+	0.872007i	−0.803700	+	0.0387654i
$507$	2.99280	−	11.1693i	0.132915	−	0.496046i
$508$	−3.00350	−	2.47388i	−0.133259	−	0.109761i
$509$	14.2916	−	24.7538i	0.633464	−	1.09719i	−0.353374	−	0.935482i	$-0.614966\pi$
$509$	14.2916	−	24.7538i	0.633464	−	1.09719i	0.986838	−	0.161710i	$-0.0517011\pi$
$510$	−4.79346	+	4.38806i	−0.212258	+	0.194307i
$511$	1.66690	+	3.95720i	0.0737392	+	0.175056i
$512$	−7.79355	+	21.2429i	−0.344430	+	0.938812i
$513$	−10.9465	−	40.8530i	−0.483301	−	1.80370i
$514$	−4.72990	+	9.18817i	−0.208627	+	0.405273i
$515$	0.586815	+	0.706562i	0.0258582	+	0.0311348i
$516$	−18.3742	−	25.7379i	−0.808879	−	1.13305i
$517$	20.6023	−	20.6023i	0.906088	−	0.906088i
$518$	0.906251	+	4.84074i	0.0398184	+	0.212690i
$519$	−6.62183			−0.290666
$520$	−12.6626	+	8.22156i	−0.555294	+	0.360539i
$521$	19.3140	+	33.4528i	0.846160	+	1.46559i	0.884610	+	0.466332i	$0.154425\pi$
$521$	19.3140	+	33.4528i	0.846160	+	1.46559i	−0.0384496	+	0.999261i	$0.512242\pi$
$522$	−3.36237	+	1.07704i	−0.147167	+	0.0471409i
$523$	−6.30604	−	23.5345i	−0.275744	−	1.02909i	−0.955341	−	0.295505i	$-0.904512\pi$
$523$	−6.30604	−	23.5345i	−0.275744	−	1.02909i	0.679597	−	0.733585i	$-0.262155\pi$
$524$	−7.43884	−	3.38649i	−0.324967	−	0.147939i
$525$	−19.9541	−	6.38233i	−0.870870	−	0.278548i
$526$	−0.537751	−	0.835661i	−0.0234471	−	0.0364366i
$527$	−0.938984	−	3.50433i	−0.0409028	−	0.152651i
$528$	9.79791	+	20.0480i	0.426399	+	0.872478i
$529$	−8.48620	+	4.89951i	−0.368965	+	0.213022i
$530$	−20.7167	+	32.4835i	−0.899877	+	1.41099i
$531$	−6.11720			−0.265464
$532$	39.3729	−	9.35470i	1.70703	−	0.405578i
$533$	−7.59780	−	7.59780i	−0.329097	−	0.329097i
$534$	12.1682	−	0.586915i	0.526568	−	0.0253983i
$535$	3.24271	+	3.90443i	0.140195	+	0.168803i
$536$	7.43595	−	5.86926i	0.321184	−	0.253513i
$537$	−31.1785	+	8.35425i	−1.34545	+	0.360512i
$538$	−37.4950	−	8.13313i	−1.61653	−	0.350644i
$539$	23.7396	−	6.66607i	1.02254	−	0.287128i
$540$	−23.9148	−	6.30370i	−1.02913	−	0.271268i
$541$	−23.7632	−	13.7197i	−1.02166	−	0.589855i	−0.107075	−	0.994251i	$-0.534148\pi$
$541$	−23.7632	−	13.7197i	−1.02166	−	0.589855i	−0.914584	+	0.404396i	$0.867482\pi$
$542$	13.2187	−	4.23426i	0.567793	−	0.181877i
$543$	−7.12666	+	26.5971i	−0.305834	+	1.14139i
$544$	−5.08143	−	5.29753i	−0.217864	−	0.227130i
$545$	−3.68138	+	5.20140i	−0.157693	+	0.222803i
$546$	−6.11274	−	12.7561i	−0.261601	−	0.545910i
$547$	−15.9557	−	15.9557i	−0.682215	−	0.682215i	0.278284	−	0.960499i	$-0.410234\pi$
$547$	−15.9557	−	15.9557i	−0.682215	−	0.682215i	−0.960499	+	0.278284i	$0.910234\pi$
$548$	37.5078	+	6.26125i	1.60225	+	0.267467i
$549$	3.17655	+	5.50195i	0.135572	+	0.234818i
$550$	−19.8447	+	15.0533i	−0.846183	+	0.641873i
$551$	−33.6091	−	19.4042i	−1.43180	−	0.826648i
$552$	−13.0460	−	9.72973i	−0.555274	−	0.414125i
$553$	19.2050	−	2.64522i	0.816679	−	0.112486i
$554$	−11.9733	+	7.70484i	−0.508695	+	0.327347i
$555$	4.23419	−	1.94844i	0.179731	−	0.0827066i
$556$	−8.53563	+	0.825330i	−0.361991	+	0.0350018i
$557$	−2.31677	−	0.620777i	−0.0981647	−	0.0263032i	0.209402	−	0.977830i	$-0.432848\pi$
$557$	−2.31677	−	0.620777i	−0.0981647	−	0.0263032i	−0.307567	+	0.951526i	$0.599515\pi$
$558$	1.30763	−	1.44017i	0.0553566	−	0.0609673i
$559$	23.8338			1.00806
$560$	6.68201	−	22.7013i	0.282366	−	0.959307i
$561$	−7.23900			−0.305631
$562$	17.6070	−	19.3916i	0.742706	−	0.817984i
$563$	12.5729	+	3.36890i	0.529884	+	0.141982i	0.513835	−	0.857889i	$-0.328224\pi$
$563$	12.5729	+	3.36890i	0.529884	+	0.141982i	0.0160495	+	0.999871i	$0.494891\pi$
$564$	26.0765	−	2.52139i	1.09802	−	0.106170i
$565$	−19.8906	−	7.35366i	−0.836804	−	0.309371i
$566$	−6.62450	+	4.26289i	−0.278448	+	0.179183i
$567$	7.26640	−	17.8435i	0.305160	−	0.749355i
$568$	4.41313	−	5.91729i	0.185171	−	0.248284i
$569$	−1.55807	−	0.899553i	−0.0653177	−	0.0377112i	0.466985	−	0.884265i	$-0.345340\pi$
$569$	−1.55807	−	0.899553i	−0.0653177	−	0.0377112i	−0.532303	+	0.846554i	$0.678673\pi$
$570$	−17.6686	−	33.9819i	−0.740056	−	1.42334i
$571$	7.71307	+	13.3594i	0.322782	+	0.559075i	0.981061	−	0.193699i	$-0.0620486\pi$
$571$	7.71307	+	13.3594i	0.322782	+	0.559075i	−0.658279	+	0.752774i	$0.728715\pi$
$572$	−16.5880	−	2.76907i	−0.693580	−	0.115781i
$573$	−2.82724	−	2.82724i	−0.118110	−	0.118110i
$574$	16.7923	+	1.29098i	0.700897	+	0.0538843i
$575$	7.84358	−	16.3861i	0.327100	−	0.683346i
$576$	0.914235	−	3.82827i	0.0380931	−	0.159511i
$577$	0.365364	−	1.36356i	0.0152103	−	0.0567656i	−0.957904	−	0.287090i	$-0.907312\pi$
$577$	0.365364	−	1.36356i	0.0152103	−	0.0567656i	0.973114	+	0.230324i	$0.0739788\pi$
$578$	−20.6278	+	6.60756i	−0.858003	+	0.274838i
$579$	37.6894	+	21.7600i	1.56632	+	0.904315i
$580$	−19.6067	+	11.4266i	−0.814123	+	0.474464i
$581$	18.3410	+	2.30324i	0.760914	+	0.0955544i
$582$	17.7374	+	3.84746i	0.735239	+	0.159482i
$583$	−41.4543	+	11.1076i	−1.71686	+	0.460031i
$584$	2.84406	+	3.60323i	0.117688	+	0.149103i
$585$	2.02025	−	1.67786i	0.0835271	−	0.0693711i
$586$	7.11673	−	0.343266i	0.293989	−	0.0141802i
$587$	24.9675	+	24.9675i	1.03052	+	1.03052i	0.999519	+	0.0310004i	$0.00986931\pi$
$587$	24.9675	+	24.9675i	1.03052	+	1.03052i	0.0310004	+	0.999519i	$0.490131\pi$
$588$	20.2871	+	8.94446i	0.836626	+	0.368864i
$589$	21.3819			0.881026
$590$	−38.3906	+	8.49119i	−1.58052	+	0.349577i
$591$	31.2834	−	18.0615i	1.28683	−	0.742951i
$592$	2.31175	+	4.73019i	0.0950123	+	0.194410i
$593$	2.10106	+	7.84125i	0.0862800	+	0.322001i	0.995554	−	0.0941977i	$-0.0300286\pi$
$593$	2.10106	+	7.84125i	0.0862800	+	0.322001i	−0.909273	+	0.416199i	$0.863362\pi$
$594$	−14.9080	−	23.1670i	−0.611684	−	0.950552i
$595$	5.66485	+	5.18130i	0.232236	+	0.212412i
$596$	3.88010	+	1.76639i	0.158935	+	0.0723543i
$597$	1.98243	+	7.39852i	0.0811353	+	0.302801i
$598$	11.6811	−	3.74173i	0.477677	−	0.153011i
$599$	−7.24397	−	12.5469i	−0.295981	−	0.512654i	0.679232	−	0.733924i	$-0.262313\pi$
$599$	−7.24397	−	12.5469i	−0.295981	−	0.512654i	−0.975213	+	0.221270i	$0.928980\pi$
$600$	−22.3785	−	0.896819i	−0.913599	−	0.0366125i
$601$	29.4757			1.20234			0.601169	−	0.799122i	$-0.294702\pi$
$601$	29.4757			1.20234			0.601169	+	0.799122i	$0.294702\pi$
$602$	−28.3631	+	24.3133i	−1.15599	+	0.990938i
$603$	−1.16518	+	1.16518i	−0.0474498	+	0.0474498i
$604$	18.5475	+	25.9807i	0.754687	+	1.05714i
$605$	−3.13563	−	0.290310i	−0.127481	−	0.0118028i
$606$	1.84234	−	3.57889i	0.0748401	−	0.145382i
$607$	−8.28409	−	30.9167i	−0.336241	−	1.25487i	−0.902517	−	0.430653i	$-0.858283\pi$
$607$	−8.28409	−	30.9167i	−0.336241	−	1.25487i	0.566276	−	0.824215i	$-0.308383\pi$
$608$	37.9091	−	20.8469i	1.53742	−	0.845455i
$609$	−8.25372	−	19.5943i	−0.334458	−	0.794000i
$610$	27.5727	+	30.1201i	1.11639	+	1.21953i
$611$	−9.87238	+	17.0995i	−0.399394	+	0.691770i
$612$	0.985583	+	0.811791i	0.0398398	+	0.0328147i
$613$	7.57810	−	28.2818i	0.306076	−	1.14229i	−0.625938	−	0.779873i	$-0.715284\pi$
$613$	7.57810	−	28.2818i	0.306076	−	1.14229i	0.932015	−	0.362420i	$-0.118049\pi$
$614$	2.98037	−	0.143754i	0.120278	−	0.00580144i
$615$	−2.68849	−	15.7112i	−0.108410	−	0.633535i
$616$	22.5651	−	13.6265i	0.909174	−	0.549026i
$617$	27.7291	+	27.7291i	1.11633	+	1.11633i	0.992275	+	0.124055i	$0.0395900\pi$
$617$	27.7291	+	27.7291i	1.11633	+	1.11633i	0.124055	+	0.992275i	$0.460410\pi$
$618$	−0.618399	+	0.681078i	−0.0248757	+	0.0273970i
$619$	−12.3075	+	7.10575i	−0.494681	+	0.285604i	−0.726514	−	0.687151i	$-0.758861\pi$
$619$	−12.3075	+	7.10575i	−0.494681	+	0.285604i	0.231833	+	0.972756i	$0.425528\pi$
$620$	6.20743	−	10.8534i	0.249296	−	0.435883i
$621$	17.4009	+	10.0464i	0.698273	+	0.403148i
$622$	−4.32216	+	19.9259i	−0.173303	+	0.798955i
$623$	−1.96366	−	14.2567i	−0.0786723	−	0.571181i
$624$	−9.92987	−	11.4046i	−0.397513	−	0.456549i
$625$	−3.84255	−	24.7029i	−0.153702	−	0.988117i
$626$	−7.61823	−	3.92172i	−0.304486	−	0.156743i
$627$	11.0423	−	41.2104i	0.440987	−	1.64579i
$628$	−0.101936	+	0.610645i	−0.00406769	+	0.0243674i
$629$	−1.70799			−0.0681021
$630$	−0.692546	+	4.05761i	−0.0275917	+	0.161659i
$631$		−	24.0239i		−	0.956377i	−0.878257	−	0.478188i	$-0.841294\pi$
$631$		−	24.0239i		−	0.956377i	0.878257	−	0.478188i	$-0.158706\pi$
$632$	19.0369	−	8.19241i	0.757247	−	0.325877i
$633$	−13.5483	−	3.63026i	−0.538498	−	0.144290i
$634$	−21.3632	−	10.9974i	−0.848440	−	0.436761i
$635$	4.08050	+	1.50858i	0.161930	+	0.0598663i
$636$	−35.1209	−	15.9886i	−1.39264	−	0.633989i
$637$	−14.3704	+	8.52731i	−0.569374	+	0.337864i
$638$	−24.7042	−	5.35865i	−0.978050	−	0.212151i
$639$	−0.642007	+	1.11199i	−0.0253974	+	0.0439896i
$640$	0.423634	−	25.2947i	0.0167456	−	0.999860i
$641$	−7.36105	−	12.7497i	−0.290744	−	0.503583i	0.683242	−	0.730192i	$-0.260569\pi$
$641$	−7.36105	−	12.7497i	−0.290744	−	0.503583i	−0.973986	+	0.226609i	$0.927236\pi$
$642$	−3.41725	+	3.76361i	−0.134868	+	0.148538i
$643$	−8.54124	+	8.54124i	−0.336833	+	0.336833i	−0.855174	−	0.518341i	$-0.826550\pi$
$643$	−8.54124	+	8.54124i	−0.336833	+	0.336833i	0.518341	+	0.855174i	$0.326550\pi$
$644$	−10.0839	+	16.3689i	−0.397362	+	0.645026i
$645$	28.8593	+	20.4257i	1.13633	+	0.804259i
$646$	0.676178	+	14.0188i	0.0266039	+	0.551562i
$647$	−1.68511	−	0.451523i	−0.0662484	−	0.0177512i	0.225543	−	0.974233i	$-0.427585\pi$
$647$	−1.68511	−	0.451523i	−0.0662484	−	0.0177512i	−0.291791	+	0.956482i	$0.594251\pi$
$648$	2.40860	−	20.4552i	0.0946189	−	0.803557i
$649$	−37.9300	−	21.8989i	−1.48888	−	0.859607i
$650$	10.3498	−	13.3343i	0.405951	−	0.523014i
$651$	9.33605	+	7.07558i	0.365909	+	0.277314i
$652$	34.2434	−	12.8187i	1.34108	−	0.502018i
$653$	−29.7355	+	7.96761i	−1.16364	+	0.311797i	−0.788419	−	0.615138i	$-0.789100\pi$
$653$	−29.7355	+	7.96761i	−1.16364	+	0.311797i	−0.375222	+	0.926935i	$0.622433\pi$
$654$	−5.67480	−	2.92128i	−0.221902	−	0.114231i
$655$	9.09923	+	0.842448i	0.355536	+	0.0329172i
$656$	17.6711	−	3.44958i	0.689942	−	0.134683i
$657$	−0.564611	−	0.564611i	−0.0220276	−	0.0220276i
$658$	−5.69502	−	30.4199i	−0.222015	−	1.18589i
$659$		−	32.5051i		−	1.26622i	−0.774062	−	0.633110i	$-0.781778\pi$
$659$		−	32.5051i		−	1.26622i	0.774062	−	0.633110i	$-0.218222\pi$
$660$	−17.7126	−	17.5689i	−0.689461	−	0.683870i
$661$	30.3385	−	17.5159i	1.18003	−	0.681290i	0.224008	−	0.974587i	$-0.428086\pi$
$661$	30.3385	−	17.5159i	1.18003	−	0.681290i	0.956021	+	0.293297i	$0.0947524\pi$
$662$	8.51724	+	26.5896i	0.331032	+	1.03343i
$663$	4.73852	−	1.26968i	0.184029	−	0.0493104i
$664$	19.5552	−	2.84733i	0.758888	−	0.110498i
$665$	−38.1374	+	24.3456i	−1.47890	+	0.944080i
$666$	−0.495577	−	0.770122i	−0.0192032	−	0.0298416i
$667$	17.8086	−	4.77181i	0.689554	−	0.184765i
$668$	24.0214	+	19.7856i	0.929416	+	0.765528i
$669$	0.651539	+	1.12850i	0.0251900	+	0.0436303i
$670$	−5.69513	+	8.92986i	−0.220022	+	0.344991i
$671$			45.4868i			1.75600i
$672$	23.4509	+	3.44220i	0.904639	+	0.132786i
$673$	−18.8090	+	18.8090i	−0.725032	+	0.725032i	−0.969626	−	0.244594i	$-0.921345\pi$
$673$	−18.8090	+	18.8090i	−0.725032	+	0.725032i	0.244594	+	0.969626i	$0.421345\pi$
$674$	31.9802	−	1.54252i	1.23183	−	0.0594158i
$675$	27.5685	−	2.13133i	1.06111	−	0.0820350i
$676$	−14.5354	+	1.40546i	−0.559053	+	0.0540561i
$677$	0.635085	+	2.37017i	0.0244083	+	0.0910930i	0.977056	−	0.212985i	$-0.0683184\pi$
$677$	0.635085	+	2.37017i	0.0244083	+	0.0910930i	−0.952647	+	0.304078i	$0.901652\pi$
$678$	4.50258	−	20.7576i	0.172921	−	0.797192i
$679$	2.67154	−	21.2738i	0.102524	−	0.816415i
$680$	7.31220	+	3.72660i	0.280410	+	0.142909i
$681$	−7.71730	+	13.3668i	−0.295727	+	0.512215i
$682$	13.2637	−	4.24867i	0.507893	−	0.162690i
$683$	−21.6049	−	5.78900i	−0.826687	−	0.221510i	−0.179419	−	0.983773i	$-0.557422\pi$
$683$	−21.6049	−	5.78900i	−0.826687	−	0.221510i	−0.647268	+	0.762263i	$0.724088\pi$
$684$	−6.12479	+	4.37246i	−0.234187	+	0.167185i
$685$	−41.9061	+	7.17096i	−1.60115	+	0.273988i
$686$	8.40235	−	24.8073i	0.320803	−	0.947146i
$687$	−11.6844	+	11.6844i	−0.445788	+	0.445788i
$688$	−22.3061	+	33.1272i	−0.850412	+	1.26296i
$689$	25.1870	−	14.5417i	0.959550	−	0.553996i
$690$	17.3508	+	5.48007i	0.660534	+	0.208623i
$691$	−3.35719	+	5.81482i	−0.127714	+	0.221206i	−0.922790	−	0.385302i	$-0.874097\pi$
$691$	−3.35719	+	5.81482i	−0.127714	+	0.221206i	0.795077	+	0.606509i	$0.207430\pi$
$692$	2.93179	+	7.83189i	0.111450	+	0.297724i
$693$	−3.62097	+	2.81300i	−0.137549	+	0.106857i
$694$	−2.88661	−	4.48577i	−0.109574	−	0.170278i
$695$	8.70972	−	4.00793i	0.330378	−	0.152030i
$696$	−14.0825	−	17.8416i	−0.533796	−	0.676284i
$697$	−1.51175	+	5.64192i	−0.0572616	+	0.213703i
$698$	23.5165	−	25.9000i	0.890111	−	0.980329i
$699$			21.2908i			0.805291i
$700$	1.28599	+	26.4262i	0.0486058	+	0.998818i
$701$		−	31.2839i		−	1.18158i	−0.806826	−	0.590789i	$-0.798817\pi$
$701$		−	31.2839i		−	1.18158i	0.806826	−	0.590789i	$-0.201183\pi$
$702$	13.8219	+	12.5499i	0.521674	+	0.473666i
$703$	2.60535	−	9.72331i	0.0982627	−	0.366722i
$704$	19.3735	−	20.4645i	0.730168	−	0.771286i
$705$	−26.6083	+	12.2443i	−1.00213	+	0.461147i
$706$	26.0200	−	16.7440i	0.979275	−	0.630167i
$707$	−4.40396	−	1.79343i	−0.165628	−	0.0674488i
$708$	−13.8064	−	36.8819i	−0.518876	−	1.38611i
$709$	−20.9688	+	36.3190i	−0.787499	+	1.36399i	0.139996	+	0.990152i	$0.455291\pi$
$709$	−20.9688	+	36.3190i	−0.787499	+	1.36399i	−0.927495	+	0.373836i	$0.878042\pi$
$710$	−2.48560	+	7.86983i	−0.0932830	+	0.295350i
$711$	−3.12200	+	1.80249i	−0.117084	+	0.0675986i
$712$	−6.08157	−	14.1319i	−0.227916	−	0.529614i
$713$	−7.18277	+	7.18277i	−0.268997	+	0.268997i
$714$	−4.34378	+	6.34483i	−0.162562	+	0.237449i
$715$	18.5332	−	3.17140i	0.693103	−	0.118604i
$716$	23.6850	+	33.1771i	0.885151	+	1.23989i
$717$	−40.0750	−	10.7381i	−1.49663	−	0.401020i
$718$	9.26889	+	28.9361i	0.345912	+	1.07989i
$719$	−5.97764	+	10.3536i	−0.222928	+	0.386123i	−0.955696	−	0.294356i	$-0.904895\pi$
$719$	−5.97764	+	10.3536i	−0.222928	+	0.386123i	0.732768	+	0.680479i	$0.238228\pi$
$720$	0.441348	+	4.37831i	0.0164481	+	0.163170i
$721$	0.866111	+	0.656405i	0.0322556	+	0.0244458i
$722$	−54.5787	−	11.8388i	−2.03121	−	0.440594i
$723$	−8.66596	−	32.3418i	−0.322290	−	1.20280i
$724$	34.6126	−	3.34677i	1.28637	−	0.124382i
$725$	16.5044	−	19.2702i	0.612960	−	0.715677i
$726$	−0.151956	−	3.15042i	−0.00563962	−	0.116923i
$727$	−5.77933	+	5.77933i	−0.214344	+	0.214344i	−0.806110	−	0.591766i	$-0.798431\pi$
$727$	−5.77933	+	5.77933i	−0.214344	+	0.214344i	0.591766	+	0.806110i	$0.298431\pi$
$728$	−12.3807	+	12.8775i	−0.458860	+	0.477271i
$729$			29.8565i			1.10580i
$730$	−4.32714	−	2.75968i	−0.160155	−	0.102140i
$731$	−6.47805	−	11.2203i	−0.239599	−	0.414998i
$732$	−26.0030	+	31.5699i	−0.961100	+	1.16686i
$733$	37.9041	−	10.1564i	1.40002	−	0.375134i	0.521668	−	0.853149i	$-0.325310\pi$
$733$	37.9041	−	10.1564i	1.40002	−	0.375134i	0.878352	+	0.478015i	$0.158643\pi$
$734$	44.1460	−	28.4081i	1.62946	−	1.04856i
$735$	−24.7083	−	1.99012i	−0.911381	−	0.0734066i
$736$	−5.73165	+	19.7378i	−0.211271	+	0.727544i
$737$	−11.3960	+	3.05354i	−0.419776	+	0.112479i
$738$	−2.98254	+	0.955377i	−0.109789	+	0.0351679i
$739$	16.3667	−	9.44933i	0.602060	−	0.347599i	−0.167792	−	0.985822i	$-0.553664\pi$
$739$	16.3667	−	9.44933i	0.602060	−	0.347599i	0.769851	+	0.638223i	$0.220330\pi$
$740$	−4.17916	−	4.14527i	−0.153629	−	0.152383i
$741$			28.9124i			1.06212i
$742$	−15.1391	+	42.9990i	−0.555774	+	1.57854i
$743$	15.0864	+	15.0864i	0.553466	+	0.553466i	0.927439	−	0.373973i	$-0.122005\pi$
$743$	15.0864	+	15.0864i	0.553466	+	0.553466i	−0.373973	+	0.927439i	$0.622005\pi$
$744$	11.6344	+	4.63358i	0.426538	+	0.169875i
$745$	−4.74617	−	0.439421i	−0.173886	−	0.0160991i
$746$	2.55680	−	4.96677i	0.0936110	−	0.181846i
$747$	−3.32026	+	0.889662i	−0.121482	+	0.0325510i
$748$	3.20504	+	8.56183i	0.117188	+	0.313051i
$749$	4.78609	+	3.62726i	0.174880	+	0.132537i
$750$	23.9596	−	7.27609i	0.874880	−	0.265685i
$751$	34.8309	+	20.1096i	1.27100	+	0.733811i	0.975176	−	0.221432i	$-0.0710732\pi$
$751$	34.8309	+	20.1096i	1.27100	+	0.733811i	0.295822	+	0.955243i	$0.404407\pi$
$752$	−14.5274	−	29.7253i	−0.529759	−	1.08397i
$753$	18.9191	+	5.06936i	0.689451	+	0.184738i
$754$	17.1108	−	0.825319i	0.623140	−	0.0300564i
$755$	−29.1315	−	20.6183i	−1.06020	−	0.750377i
$756$	−29.2509	−	0.834811i	−1.06385	−	0.0303618i
$757$	−25.8937	+	25.8937i	−0.941123	+	0.941123i	−0.998361	−	0.0572373i	$-0.981771\pi$
$757$	−25.8937	+	25.8937i	−0.941123	+	0.941123i	0.0572373	+	0.998361i	$0.481771\pi$
$758$	−20.1443	−	18.2905i	−0.731675	−	0.664340i
$759$	10.1343	+	17.5531i	0.367852	+	0.637138i
$760$	−32.3689	+	35.9426i	−1.17414	+	1.30378i
$761$	11.7952	−	20.4299i	0.427577	−	0.740585i	−0.569080	−	0.822282i	$-0.692701\pi$
$761$	11.7952	−	20.4299i	0.427577	−	0.740585i	0.996657	+	0.0816972i	$0.0260340\pi$
$762$	−0.923693	+	4.25838i	−0.0334619	+	0.154265i
$763$	−2.84372	+	6.98307i	−0.102949	+	0.252804i
$764$	−2.09213	+	4.59563i	−0.0756907	+	0.166264i
$765$	−1.33900	−	0.495034i	−0.0484116	−	0.0178980i
$766$	−23.9966	+	46.6151i	−0.867032	+	1.68427i
$767$	28.6693	+	7.68191i	1.03519	+	0.277378i
$768$	25.1449	−	3.12820i	0.907338	−	0.112879i
$769$			52.0526i			1.87707i	0.345191	+	0.938533i	$0.387814\pi$
$769$			52.0526i			1.87707i	−0.345191	+	0.938533i	$0.612186\pi$
$770$	−18.8200	+	22.6802i	−0.678224	+	0.817336i
$771$	11.5724			0.416770
$772$	9.04952	−	54.2108i	0.325699	−	1.95109i
$773$	2.99897	−	11.1923i	0.107866	−	0.402560i	−0.890789	−	0.454417i	$-0.849848\pi$
$773$	2.99897	−	11.1923i	0.107866	−	0.402560i	0.998654	+	0.0518576i	$0.0165142\pi$
$774$	3.17955	−	6.17651i	0.114287	−	0.222010i
$775$	−2.56646	+	13.7413i	−0.0921901	+	0.493603i
$776$	−3.30263	−	22.6821i	−0.118558	−	0.814241i
$777$	4.35516	−	3.38337i	0.156241	−	0.121378i
$778$	42.4946	+	9.21759i	1.52350	+	0.330467i
$779$	−29.8125	−	17.2123i	−1.06814	−	0.616694i
$780$	14.6759	+	8.39363i	0.525480	+	0.300540i
$781$	−7.96159	+	4.59663i	−0.284888	+	0.164480i
$782$	−4.93644	−	4.48215i	−0.176527	−	0.160281i
$783$	19.8430	+	19.8430i	0.709130	+	0.709130i
$784$	1.59692	−	27.9544i	0.0570328	−	0.998372i
$785$	−0.116747	−	0.682252i	−0.00416687	−	0.0243506i
$786$	0.440959	+	9.14215i	0.0157285	+	0.326090i
$787$	−4.88402	+	18.2274i	−0.174097	+	0.649737i	0.822607	+	0.568610i	$0.192519\pi$
$787$	−4.88402	+	18.2274i	−0.174097	+	0.649737i	−0.996704	+	0.0811272i	$0.974148\pi$
$788$	−35.2126	−	29.0034i	−1.25440	−	1.03320i
$789$	−0.556403	+	0.963718i	−0.0198085	+	0.0343093i
$790$	−17.0912	+	15.6457i	−0.608078	+	0.556651i
$791$	−24.8962	−	3.12643i	−0.885208	−	0.111163i
$792$	−2.93053	+	3.92936i	−0.104132	+	0.139624i
$793$	−7.97816	−	29.7749i	−0.283313	−	1.05734i
$794$	−6.89829	−	3.55111i	−0.244811	−	0.126024i
$795$	42.9601	+	3.97744i	1.52364	+	0.141065i
$796$	7.87279	−	5.62035i	0.279044	−	0.199208i
$797$	21.9699	−	21.9699i	0.778215	−	0.778215i	−0.201312	−	0.979527i	$-0.564521\pi$
$797$	21.9699	−	21.9699i	0.778215	−	0.778215i	0.979527	+	0.201312i	$0.0645206\pi$
$798$	−29.4941	−	34.4067i	−1.04408	−	1.21799i
$799$	10.7333			0.379716
$800$	8.84729	+	26.8649i	0.312799	+	0.949819i
$801$	1.33806	+	2.31759i	0.0472781	+	0.0818881i
$802$	−5.83923	−	18.2292i	−0.206190	−	0.643695i
$803$	−1.47965	−	5.52214i	−0.0522158	−	0.194872i
$804$	−9.65491	−	4.39534i	−0.340503	−	0.155012i
$805$	4.63305	−	20.9897i	0.163294	−	0.739791i
$806$	−7.93700	+	5.10749i	−0.279569	+	0.179904i
$807$	11.1200	+	41.5003i	0.391441	+	1.46088i
$808$	−5.04857	−	0.594470i	−0.177608	−	0.0209134i
$809$	35.4170	−	20.4480i	1.24519	−	0.718913i	0.275047	−	0.961431i	$-0.411307\pi$
$809$	35.4170	−	20.4480i	1.24519	−	0.718913i	0.970147	+	0.242518i	$0.0779732\pi$
$810$	4.97304	+	22.4842i	0.174735	+	0.790015i
$811$	5.00467			0.175738			0.0878689	−	0.996132i	$-0.471994\pi$
$811$	5.00467			0.175738			0.0878689	+	0.996132i	$0.471994\pi$
$812$	−19.5206	+	18.4373i	−0.685038	+	0.647021i
$813$	−10.9909	−	10.9909i	−0.385469	−	0.385469i
$814$	−0.315896	−	6.54929i	−0.0110722	−	0.229552i
$815$	−31.4482	+	26.1184i	−1.10158	+	0.914889i
$816$	−2.67002	+	7.77449i	−0.0934695	+	0.272161i
$817$	73.7570	−	19.7631i	2.58043	−	0.691424i
$818$	7.82347	−	36.0674i	0.273541	−	1.26107i
$819$	1.87684	−	2.47644i	0.0655820	−	0.0865339i
$820$	−17.3918	+	10.1358i	−0.607350	+	0.353958i
$821$	15.0739	+	8.70295i	0.526084	+	0.303735i	0.739420	−	0.673244i	$-0.235100\pi$
$821$	15.0739	+	8.70295i	0.526084	+	0.303735i	−0.213336	+	0.976979i	$0.568433\pi$
$822$	−12.9902	−	40.5536i	−0.453086	−	1.41447i
$823$	4.16440	−	15.5418i	0.145162	−	0.541751i	−0.854586	−	0.519309i	$-0.826189\pi$
$823$	4.16440	−	15.5418i	0.145162	−	0.541751i	0.999748	−	0.0224420i	$-0.00714411\pi$
$824$	1.07933	+	0.429859i	0.0376002	+	0.0149749i
$825$	25.1589	+	12.0429i	0.875921	+	0.419281i
$826$	−41.9539	+	20.1044i	−1.45976	+	0.699520i
$827$	31.7551	+	31.7551i	1.10423	+	1.10423i	0.993894	+	0.110339i	$0.0351937\pi$
$827$	31.7551	+	31.7551i	1.10423	+	1.10423i	0.110339	+	0.993894i	$0.464806\pi$
$828$	0.588655	−	3.52632i	0.0204572	−	0.122548i
$829$	17.4297	+	30.1891i	0.605359	+	1.04851i	0.991995	+	0.126280i	$0.0403037\pi$
$829$	17.4297	+	30.1891i	0.605359	+	1.04851i	−0.386636	+	0.922232i	$0.626363\pi$
$830$	−19.6025	+	10.1922i	−0.680414	+	0.353776i
$831$	13.8080	+	7.97207i	0.478996	+	0.276548i
$832$	−9.09222	+	16.7938i	−0.315216	+	0.582219i
$833$	7.92030	+	4.44745i	0.274422	+	0.154095i
$834$	5.19658	+	8.07544i	0.179943	+	0.279630i
$835$	−32.6351	−	12.0654i	−1.12938	−	0.417539i
$836$	−53.6300	+	5.18561i	−1.85483	+	0.179348i
$837$	−14.9343	−	4.00164i	−0.516206	−	0.138317i
$838$	13.4905	+	12.2490i	0.466022	+	0.423135i
$839$	−3.57010			−0.123253			−0.0616267	−	0.998099i	$-0.519629\pi$
$839$	−3.57010			−0.123253			−0.0616267	+	0.998099i	$0.519629\pi$
$840$	−26.0273	+	4.98242i	−0.898026	+	0.171910i
$841$	−3.25053			−0.112087
$842$	−24.8451	−	22.5587i	−0.856220	−	0.777423i
$843$	−28.3314	−	7.59137i	−0.975785	−	0.261461i
$844$	1.70482	+	17.6314i	0.0586823	+	0.606897i
$845$	14.8318	−	6.82514i	0.510231	−	0.234792i
$846$	3.11428	+	4.83957i	0.107071	+	0.166388i
$847$	−3.69114	+	0.508404i	−0.126829	+	0.0174690i
$848$	−3.36064	+	48.6177i	−0.115405	+	1.66954i
$849$	7.63964	+	4.41075i	0.262192	+	0.151376i
$850$	−9.09049	−	1.24812i	−0.311801	−	0.0428101i
$851$	2.39112	+	4.14154i	0.0819664	+	0.141970i
$852$	−8.15342	−	1.36107i	−0.279331	−	0.0466293i
$853$	14.3301	+	14.3301i	0.490652	+	0.490652i	0.908512	−	0.417859i	$-0.137220\pi$
$853$	14.3301	+	14.3301i	0.490652	+	0.490652i	−0.417859	+	0.908512i	$0.637220\pi$
$854$	39.8682	+	27.2945i	1.36426	+	0.933997i
$855$	4.86064	−	6.86757i	0.166230	−	0.234866i
$856$	5.96433	+	2.37538i	0.203856	+	0.0811889i
$857$	6.45005	−	24.0719i	0.220330	−	0.822281i	−0.763893	−	0.645343i	$-0.776714\pi$
$857$	6.45005	−	24.0719i	0.220330	−	0.822281i	0.984222	−	0.176938i	$-0.0566191\pi$
$858$	5.74500	+	17.9350i	0.196131	+	0.612292i
$859$	33.7707	+	19.4975i	1.15224	+	0.665246i	0.949432	−	0.313972i	$-0.101660\pi$
$859$	33.7707	+	19.4975i	1.15224	+	0.665246i	0.202808	+	0.979218i	$0.434993\pi$
$860$	11.3809	−	43.1763i	0.388084	−	1.47230i
$861$	−7.32136	−	17.3808i	−0.249511	−	0.592337i
$862$	0.492799	−	2.27188i	0.0167848	−	0.0773807i
$863$	−14.0466	+	3.76378i	−0.478152	+	0.128121i	−0.489842	−	0.871811i	$-0.662946\pi$
$863$	−14.0466	+	3.76378i	−0.478152	+	0.128121i	0.0116897	+	0.999932i	$0.496279\pi$
$864$	−30.3793	+	7.46595i	−1.03353	+	0.253997i
$865$	−5.97360	−	7.19259i	−0.203109	−	0.244555i
$866$	−0.231554	−	4.80068i	−0.00786854	−	0.163134i
$867$	17.1513	+	17.1513i	0.582490	+	0.582490i
$868$	4.23505	−	14.1748i	0.143747	−	0.481123i
$869$	−25.8108			−0.875573
$870$	21.4260	+	13.6647i	0.726411	+	0.463277i
$871$	6.92404	−	3.99759i	0.234612	−	0.135453i
$872$	−0.942610	+	8.00518i	−0.0319208	+	0.271089i
$873$	1.03192	+	3.85119i	0.0349253	+	0.130343i
$874$	33.0461	−	21.2653i	1.11780	−	0.719311i
$875$	−11.0683	−	27.4316i	−0.374178	−	0.927357i
$876$	2.12985	−	4.67847i	0.0719608	−	0.158071i
$877$	5.32190	+	19.8616i	0.179708	+	0.670678i	0.995702	+	0.0926180i	$0.0295235\pi$
$877$	5.32190	+	19.8616i	0.179708	+	0.670678i	−0.815994	+	0.578060i	$0.803810\pi$
$878$	−2.72652	−	8.51178i	−0.0920155	−	0.287259i
$879$	−3.98937	−	6.90979i	−0.134558	−	0.233062i
$880$	−12.9372	+	28.7279i	−0.436115	+	0.968417i
$881$	−19.0415			−0.641523			−0.320761	−	0.947160i	$-0.603939\pi$
$881$	−19.0415			−0.641523			−0.320761	+	0.947160i	$0.603939\pi$
$882$	0.292765	+	4.86165i	0.00985791	+	0.163700i
$883$	−2.84748	+	2.84748i	−0.0958254	+	0.0958254i	−0.753394	−	0.657569i	$-0.771585\pi$
$883$	−2.84748	+	2.84748i	−0.0958254	+	0.0958254i	0.657569	+	0.753394i	$0.271585\pi$
$884$	−3.59966	−	5.04228i	−0.121070	−	0.169590i
$885$	28.1309	+	33.8713i	0.945610	+	1.13857i
$886$	−35.7125	−	18.3841i	−1.19979	−	0.617627i
$887$	12.8098	+	47.8070i	0.430112	+	1.60520i	0.752499	+	0.658593i	$0.228848\pi$
$887$	12.8098	+	47.8070i	0.430112	+	1.60520i	−0.322387	+	0.946608i	$0.604485\pi$
$888$	3.52473	−	4.72609i	0.118282	−	0.158597i
$889$	5.10740	+	0.641379i	0.171297	+	0.0215112i
$890$	11.6145	+	12.6875i	0.389319	+	0.425286i
$891$	−12.8255	+	22.2145i	−0.429671	+	0.744212i
$892$	1.04625	−	1.27024i	0.0350311	−	0.0425307i
$893$	−16.3724	+	61.1028i	−0.547883	+	2.04473i
$894$	−0.230005	−	4.76855i	−0.00769251	−	0.159484i
$895$	−37.2007	−	26.3294i	−1.24348	−	0.880096i
$896$	−6.31158	−	29.2603i	−0.210855	−	0.977517i
$897$	−9.71247	−	9.71247i	−0.324290	−	0.324290i
$898$	3.71626	+	3.37426i	0.124013	+	0.112600i
$899$	−12.2862	+	7.09346i	−0.409769	+	0.236580i
$900$	−2.07485	−	4.46099i	−0.0691618	−	0.148700i
$901$	−13.6917	−	7.90492i	−0.456137	−	0.263351i
$902$	−21.9136	−	4.75332i	−0.729642	−	0.158268i
$903$	38.7446	+	15.7780i	1.28934	+	0.525059i
$904$	−26.5443	+	3.86499i	−0.882851	+	0.128548i
$905$	−35.3185	+	16.2525i	−1.17403	+	0.540250i
$906$	16.3612	−	31.7828i	0.543564	−	1.05591i
$907$	2.16896	−	8.09467i	0.0720191	−	0.268779i	−0.920522	−	0.390691i	$-0.872236\pi$
$907$	2.16896	−	8.09467i	0.0720191	−	0.268779i	0.992541	+	0.121912i	$0.0389027\pi$
$908$	19.2262	+	3.20946i	0.638042	+	0.106510i
$909$	0.884240			0.0293284
$910$	8.34124	−	18.1470i	0.276509	−	0.601566i
$911$			35.9285i			1.19036i	0.803591	+	0.595182i	$0.202920\pi$
$911$			35.9285i			1.19036i	−0.803591	+	0.595182i	$0.797080\pi$
$912$	−40.1860	−	27.0591i	−1.33069	−	0.896017i
$913$	−23.7723	−	6.36978i	−0.786750	−	0.210809i
$914$	−1.61718	+	3.14150i	−0.0534917	+	0.103911i
$915$	15.8568	−	42.8904i	0.524209	−	1.41791i
$916$	18.9928	+	8.64635i	0.627540	+	0.285684i
$917$	10.7113	−	1.47533i	0.353718	−	0.0487197i
$918$	2.15135	−	9.91805i	0.0710050	−	0.327345i
$919$	6.88039	−	11.9172i	0.226963	−	0.393112i	−0.729943	−	0.683508i	$-0.760454\pi$
$919$	6.88039	−	11.9172i	0.226963	−	0.393112i	0.956907	+	0.290396i	$0.0937870\pi$
$920$	−1.20052	−	22.9477i	−0.0395799	−	0.756564i
$921$	−1.67068	−	2.89371i	−0.0550508	−	0.0953509i
$922$	24.8127	+	22.5292i	0.817162	+	0.741960i
$923$	4.40530	−	4.40530i	0.145002	−	0.145002i
$924$	−25.1326	−	15.4827i	−0.826803	−	0.509344i
$925$	5.93607	+	2.84144i	0.195177	+	0.0934261i
$926$	26.9256	−	1.29872i	0.884831	−	0.0426787i
$927$	−0.195200	−	0.0523036i	−0.00641120	−	0.00171788i
$928$	−14.8669	+	24.5552i	−0.488031	+	0.806064i
$929$	−11.8867	−	6.86276i	−0.389989	−	0.225160i	0.292167	−	0.956367i	$-0.405624\pi$
$929$	−11.8867	−	6.86276i	−0.389989	−	0.225160i	−0.682155	+	0.731207i	$0.738957\pi$
$930$	−13.9877	−	0.617607i	−0.458674	−	0.0202521i
$931$	−37.4001	+	38.3049i	−1.22574	+	1.25539i
$932$	25.1814	−	9.42641i	0.824844	−	0.308772i
$933$	22.0544	−	5.90945i	0.722028	−	0.193467i
$934$	1.63133	−	3.16898i	0.0533787	−	0.103692i
$935$	−6.53035	−	7.86295i	−0.213565	−	0.257146i
$936$	1.22908	−	3.08609i	0.0401738	−	0.100872i
$937$	−28.0706	−	28.0706i	−0.917028	−	0.917028i	0.0797841	−	0.996812i	$-0.474577\pi$
$937$	−28.0706	−	28.0706i	−0.917028	−	0.917028i	−0.996812	+	0.0797841i	$0.974577\pi$
$938$	−4.16182	+	11.8206i	−0.135888	+	0.385957i
$939$			9.59508i			0.313124i
$940$	26.2625	+	26.0495i	0.856588	+	0.849641i
$941$	5.44393	−	3.14306i	0.177467	−	0.102461i	−0.408635	−	0.912698i	$-0.633995\pi$
$941$	5.44393	−	3.14306i	0.177467	−	0.102461i	0.586102	+	0.810237i	$0.300662\pi$
$942$	0.660232	−	0.211487i	0.0215115	−	0.00689063i
$943$	15.7969	−	4.23277i	0.514419	−	0.137838i
$944$	−37.5089	+	32.6586i	−1.22081	+	1.06295i
$945$	31.1936	−	9.86686i	1.01473	−	0.320969i
$946$	41.8262	−	26.9153i	1.35989	−	0.875092i
$947$	−0.711568	+	0.190664i	−0.0231229	+	0.00619575i	−0.270362	−	0.962759i	$-0.587143\pi$
$947$	−0.711568	+	0.190664i	−0.0231229	+	0.00619575i	0.247239	+	0.968955i	$0.420477\pi$
$948$	−17.9139	−	14.7550i	−0.581816	−	0.479222i
$949$	1.93711	+	3.35518i	0.0628813	+	0.108914i
$950$	20.9719	−	49.8468i	0.680418	−	1.61724i
$951$			26.9067i			0.872510i
$952$	9.42745	+	2.32840i	0.305545	+	0.0754638i
$953$	−2.24676	+	2.24676i	−0.0727798	+	0.0727798i	−0.742560	−	0.669780i	$-0.766388\pi$
$953$	−2.24676	+	2.24676i	−0.0727798	+	0.0727798i	0.669780	+	0.742560i	$0.266388\pi$
$954$	−0.408401	−	8.46713i	−0.0132225	−	0.274134i
$955$	0.520455	−	5.62140i	0.0168415	−	0.181904i
$956$	5.04274	+	52.1524i	0.163094	+	1.68673i
$957$	7.32658	+	27.3432i	0.236835	+	0.883879i
$958$	−25.3028	−	5.48849i	−0.817497	−	0.177325i
$959$	−46.3597	+	19.5281i	−1.49703	+	0.630597i
$960$	−25.4016	+	12.5427i	−0.819834	+	0.404815i
$961$	−11.5918	+	20.0776i	−0.373929	+	0.647663i
$962$	1.35549	+	4.23165i	0.0437029	+	0.136434i
$963$	−1.07866	−	0.289027i	−0.0347595	−	0.00931377i
$964$	−34.4150	+	24.5687i	−1.10843	+	0.791306i
$965$	10.3644	+	60.5679i	0.333640	+	1.94975i
$966$	21.4660	+	1.65029i	0.690659	+	0.0530972i
$967$	19.3131	−	19.3131i	0.621067	−	0.621067i	−0.324738	−	0.945804i	$-0.605276\pi$
$967$	19.3131	−	19.3131i	0.621067	−	0.621067i	0.945804	+	0.324738i	$0.105276\pi$
$968$	−3.65883	+	1.57456i	−0.117599	+	0.0506082i
$969$	13.6112	−	7.85841i	0.437254	−	0.252449i
$970$	11.8220	+	22.7371i	0.379580	+	0.730044i
$971$	1.81116	−	3.13703i	0.0581230	−	0.100672i	−0.835500	−	0.549491i	$-0.814822\pi$
$971$	1.81116	−	3.13703i	0.0581230	−	0.100672i	0.893623	+	0.448819i	$0.148155\pi$
$972$	9.47440	−	3.54665i	0.303892	−	0.113759i
$973$	8.95857	−	6.95959i	0.287198	−	0.223114i
$974$	−33.7674	+	21.7294i	−1.08198	+	0.696256i
$975$	−18.5809	−	3.47035i	−0.595064	−	0.111140i
$976$	48.8516	+	16.7773i	1.56370	+	0.537029i
$977$	0.648307	−	2.41951i	0.0207412	−	0.0774071i	−0.954780	−	0.297315i	$-0.903909\pi$
$977$	0.648307	−	2.41951i	0.0207412	−	0.0774071i	0.975521	+	0.219908i	$0.0705756\pi$
$978$	−30.3139	−	27.5242i	−0.969333	−	0.880127i
$979$			19.1605i			0.612371i
$980$	8.58573	+	30.1046i	0.274261	+	0.961655i
$981$		−	1.40208i		−	0.0447649i
$982$	−10.8336	+	11.9317i	−0.345716	+	0.380756i
$983$	0.464575	−	1.73382i	0.0148176	−	0.0553002i	−0.958121	−	0.286363i	$-0.907554\pi$
$983$	0.464575	−	1.73382i	0.0148176	−	0.0553002i	0.972939	+	0.231063i	$0.0742203\pi$
$984$	−12.4917	−	15.8261i	−0.398221	−	0.504519i
$985$	47.8393	+	17.6864i	1.52429	+	0.563537i
$986$	−5.03928	−	7.83100i	−0.160483	−	0.249390i
$987$	−27.3685	+	21.2616i	−0.871150	+	0.676765i
$988$	34.1958	−	12.8008i	1.08791	−	0.407249i
$989$	−18.1380	+	31.4160i	−0.576755	+	0.998969i
$990$	1.65056	−	5.22594i	0.0524582	−	0.166091i
$991$	−4.15586	+	2.39939i	−0.132015	+	0.0762190i	−0.564553	−	0.825397i	$-0.690951\pi$
$991$	−4.15586	+	2.39939i	−0.132015	+	0.0762190i	0.432538	+	0.901616i	$0.357618\pi$
$992$	0.329216	−	15.8119i	0.0104526	−	0.502029i
$993$	22.1083	−	22.1083i	0.701587	−	0.701587i
$994$	−0.748525	+	9.73638i	−0.0237418	+	0.308819i
$995$	−6.24786	+	8.82755i	−0.198070	+	0.279852i
$996$	−12.8577	−	18.0106i	−0.407413	−	0.570689i
$997$	24.9653	+	6.68943i	0.790659	+	0.211856i	0.631479	−	0.775393i	$-0.282448\pi$
$997$	24.9653	+	6.68943i	0.790659	+	0.211856i	0.159180	+	0.987250i	$0.449115\pi$
$998$	36.4979	−	11.6911i	1.15532	−	0.370075i
$999$	−3.63945	+	6.30371i	−0.115147	+	0.199440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.107.13	yes	176
5.3	odd	4	inner	280.2.br.a.163.34	yes	176
7.4	even	3	inner	280.2.br.a.67.17	✓	176
8.3	odd	2	inner	280.2.br.a.107.5	yes	176
35.18	odd	12	inner	280.2.br.a.123.5	yes	176
40.3	even	4	inner	280.2.br.a.163.17	yes	176
56.11	odd	6	inner	280.2.br.a.67.34	yes	176
280.123	even	12	inner	280.2.br.a.123.13	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.17	✓	176	7.4	even	3	inner
280.2.br.a.67.34	yes	176	56.11	odd	6	inner
280.2.br.a.107.5	yes	176	8.3	odd	2	inner
280.2.br.a.107.13	yes	176	1.1	even	1	trivial
280.2.br.a.123.5	yes	176	35.18	odd	12	inner
280.2.br.a.123.13	yes	176	280.123	even	12	inner
280.2.br.a.163.17	yes	176	40.3	even	4	inner
280.2.br.a.163.34	yes	176	5.3	odd	4	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.950661 + 1.04702i) q^{2} +(1.52971 + 0.409884i) q^{3} +(-0.192487 - 1.99072i) q^{4} +(0.934747 + 2.03132i) q^{5} +(-1.88339 + 1.21197i) q^{6} +(1.62314 + 2.08935i) q^{7} +(2.26730 + 1.69096i) q^{8} +(-0.426076 - 0.245995i) q^{9} +O(q^{10})\)	\(q+(-0.950661 + 1.04702i) q^{2} +(1.52971 + 0.409884i) q^{3} +(-0.192487 - 1.99072i) q^{4} +(0.934747 + 2.03132i) q^{5} +(-1.88339 + 1.21197i) q^{6} +(1.62314 + 2.08935i) q^{7} +(2.26730 + 1.69096i) q^{8} +(-0.426076 - 0.245995i) q^{9} +(-3.01545 - 0.952398i) q^{10} +(-1.76127 - 3.05061i) q^{11} +(0.521514 - 3.12411i) q^{12} +(1.68796 + 1.68796i) q^{13} +(-3.73065 - 0.286809i) q^{14} +(0.597286 + 3.49046i) q^{15} +(-3.92590 + 0.766373i) q^{16} +(0.335857 - 1.25343i) q^{17} +(0.662615 - 0.212251i) q^{18} +(6.62328 + 3.82395i) q^{19} +(3.86385 - 2.25182i) q^{20} +(1.62654 + 3.86140i) q^{21} +(4.86841 + 1.05602i) q^{22} +(-3.50951 + 0.940371i) q^{23} +(2.77521 + 3.51600i) q^{24} +(-3.25250 + 3.79754i) q^{25} +(-3.37200 + 0.162644i) q^{26} +(-3.91041 - 3.91041i) q^{27} +(3.84688 - 3.63339i) q^{28} -5.07439 q^{29} +(-4.22238 - 2.69287i) q^{30} +(2.42122 - 1.39789i) q^{31} +(2.92979 - 4.83904i) q^{32} +(-1.44383 - 5.38846i) q^{33} +(0.993080 + 1.54324i) q^{34} +(-2.72691 + 5.25014i) q^{35} +(-0.407692 + 0.895547i) q^{36} +(-0.340662 - 1.27137i) q^{37} +(-10.3002 + 3.29940i) q^{38} +(1.89022 + 3.27395i) q^{39} +(-1.31552 + 6.18623i) q^{40} -4.50117 q^{41} +(-5.58924 - 1.96787i) q^{42} +(7.05995 - 7.05995i) q^{43} +(-5.73387 + 4.09339i) q^{44} +(0.101421 - 1.09544i) q^{45} +(2.35177 - 4.56849i) q^{46} +(2.14078 + 7.98948i) q^{47} +(-6.31960 - 0.436835i) q^{48} +(-1.73080 + 6.78265i) q^{49} +(-0.884061 - 7.01559i) q^{50} +(1.02752 - 1.77973i) q^{51} +(3.03534 - 3.68516i) q^{52} +(3.15330 - 11.7683i) q^{53} +(7.81174 - 0.376789i) q^{54} +(4.55041 - 6.42925i) q^{55} +(0.147146 + 7.48187i) q^{56} +(8.56430 + 8.56430i) q^{57} +(4.82403 - 5.31297i) q^{58} +(10.7678 - 6.21679i) q^{59} +(6.83354 - 1.86089i) q^{60} +(-11.1830 - 6.45654i) q^{61} +(-0.838145 + 3.86398i) q^{62} +(-0.177612 - 1.28951i) q^{63} +(2.28132 + 7.66783i) q^{64} +(-1.85096 + 5.00660i) q^{65} +(7.01440 + 3.61088i) q^{66} +(0.866858 - 3.23516i) q^{67} +(-2.55988 - 0.427325i) q^{68} -5.75397 q^{69} +(-2.90461 - 7.84622i) q^{70} -2.60984i q^{71} +(-0.550075 - 1.27822i) q^{72} +(1.56766 + 0.420053i) q^{73} +(1.65500 + 0.851962i) q^{74} +(-6.53191 + 4.47597i) q^{75} +(6.33751 - 13.9211i) q^{76} +(3.51501 - 8.63150i) q^{77} +(-5.22484 - 1.13333i) q^{78} +(3.66367 - 6.34566i) q^{79} +(-5.22647 - 7.25838i) q^{80} +(-3.64099 - 6.30638i) q^{81} +(4.27909 - 4.71280i) q^{82} +(4.94034 - 4.94034i) q^{83} +(7.37386 - 3.98125i) q^{84} +(2.86006 - 0.489413i) q^{85} +(0.680264 + 14.1035i) q^{86} +(-7.76234 - 2.07991i) q^{87} +(1.16512 - 9.89489i) q^{88} +(-4.71065 - 2.71969i) q^{89} +(1.05053 + 1.14758i) q^{90} +(-0.786943 + 6.26655i) q^{91} +(2.54755 + 6.80543i) q^{92} +(4.27674 - 1.14595i) q^{93} +(-10.4003 - 5.35386i) q^{94} +(-1.57657 + 17.0284i) q^{95} +(6.46517 - 6.20144i) q^{96} +(-5.73033 - 5.73033i) q^{97} +(-5.45614 - 8.26018i) q^{98} +1.73306i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more