LMFDB - Embedded newform 728.2.c.b.365.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.12
Character	$\chi$	$=$	728.365
Dual form			728.2.c.b.365.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06885 + 0.926043i) q^{2} +2.33171i q^{3} +(0.284890 - 1.97961i) q^{4} -0.889625i q^{5} +(-2.15926 - 2.49225i) q^{6} +1.00000 q^{7} +(1.52869 + 2.37973i) q^{8} -2.43685 q^{9} +(0.823831 + 0.950878i) q^{10} -5.19158i q^{11} +(4.61586 + 0.664280i) q^{12} -1.00000i q^{13} +(-1.06885 + 0.926043i) q^{14} +2.07434 q^{15} +(-3.83768 - 1.12794i) q^{16} +3.21826 q^{17} +(2.60463 - 2.25663i) q^{18} -7.04246i q^{19} +(-1.76111 - 0.253446i) q^{20} +2.33171i q^{21} +(4.80762 + 5.54903i) q^{22} +1.95543 q^{23} +(-5.54882 + 3.56446i) q^{24} +4.20857 q^{25} +(0.926043 + 1.06885i) q^{26} +1.31310i q^{27} +(0.284890 - 1.97961i) q^{28} -3.33778i q^{29} +(-2.21717 + 1.92093i) q^{30} -4.20796 q^{31} +(5.14643 - 2.34825i) q^{32} +12.1052 q^{33} +(-3.43984 + 2.98024i) q^{34} -0.889625i q^{35} +(-0.694235 + 4.82400i) q^{36} -4.89196i q^{37} +(6.52162 + 7.52735i) q^{38} +2.33171 q^{39} +(2.11706 - 1.35996i) q^{40} +7.53924 q^{41} +(-2.15926 - 2.49225i) q^{42} -7.93240i q^{43} +(-10.2773 - 1.47903i) q^{44} +2.16788i q^{45} +(-2.09007 + 1.81082i) q^{46} -5.87744 q^{47} +(2.63003 - 8.94833i) q^{48} +1.00000 q^{49} +(-4.49834 + 3.89731i) q^{50} +7.50403i q^{51} +(-1.97961 - 0.284890i) q^{52} +12.5689i q^{53} +(-1.21599 - 1.40351i) q^{54} -4.61856 q^{55} +(1.52869 + 2.37973i) q^{56} +16.4210 q^{57} +(3.09092 + 3.56759i) q^{58} +10.6544i q^{59} +(0.590960 - 4.10638i) q^{60} -0.855217i q^{61} +(4.49769 - 3.89675i) q^{62} -2.43685 q^{63} +(-3.32619 + 7.27574i) q^{64} -0.889625 q^{65} +(-12.9387 + 11.2100i) q^{66} +0.692832i q^{67} +(0.916850 - 6.37088i) q^{68} +4.55950i q^{69} +(0.823831 + 0.950878i) q^{70} -3.83030 q^{71} +(-3.72519 - 5.79903i) q^{72} +0.715881 q^{73} +(4.53016 + 5.22878i) q^{74} +9.81314i q^{75} +(-13.9413 - 2.00633i) q^{76} -5.19158i q^{77} +(-2.49225 + 2.15926i) q^{78} -1.11892 q^{79} +(-1.00344 + 3.41409i) q^{80} -10.3723 q^{81} +(-8.05833 + 6.98166i) q^{82} +11.4825i q^{83} +(4.61586 + 0.664280i) q^{84} -2.86304i q^{85} +(7.34574 + 8.47856i) q^{86} +7.78271 q^{87} +(12.3545 - 7.93633i) q^{88} -2.19918 q^{89} +(-2.00755 - 2.31715i) q^{90} -1.00000i q^{91} +(0.557084 - 3.87099i) q^{92} -9.81173i q^{93} +(6.28211 - 5.44276i) q^{94} -6.26515 q^{95} +(5.47542 + 12.0000i) q^{96} +14.7605 q^{97} +(-1.06885 + 0.926043i) q^{98} +12.6511i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) $ 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.06885	+	0.926043i	−0.755793	+	0.654811i
$2$	−1.06885	+	0.926043i	−0.755793	+	0.654811i
$3$			2.33171i			1.34621i	0.739547	+	0.673105i	$0.235040\pi$
$3$			2.33171i			1.34621i	−0.739547	+	0.673105i	$0.764960\pi$
$4$	0.284890	−	1.97961i	0.142445	−	0.989803i
$5$		−	0.889625i		−	0.397853i	−0.980014	−	0.198926i	$-0.936255\pi$
$5$		−	0.889625i		−	0.397853i	0.980014	−	0.198926i	$-0.0637454\pi$
$6$	−2.15926	−	2.49225i	−0.881514	−	1.01746i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.52869	+	2.37973i	0.540475	+	0.841360i
$9$	−2.43685			−0.812283
$10$	0.823831	+	0.950878i	0.260518	+	0.300694i
$11$		−	5.19158i		−	1.56532i	−0.622450	−	0.782660i	$-0.713863\pi$
$11$		−	5.19158i		−	1.56532i	0.622450	−	0.782660i	$-0.286137\pi$
$12$	4.61586	+	0.664280i	1.33248	+	0.191761i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−1.06885	+	0.926043i	−0.285663	+	0.247495i
$15$	2.07434			0.535593
$16$	−3.83768	−	1.12794i	−0.959419	−	0.281985i
$17$	3.21826			0.780542			0.390271	−	0.920700i	$-0.372381\pi$
$17$	3.21826			0.780542			0.390271	+	0.920700i	$0.372381\pi$
$18$	2.60463	−	2.25663i	0.613918	−	0.531892i
$19$		−	7.04246i		−	1.61565i	−0.589421	−	0.807826i	$-0.700644\pi$
$19$		−	7.04246i		−	1.61565i	0.589421	−	0.807826i	$-0.299356\pi$
$20$	−1.76111	−	0.253446i	−0.393795	−	0.0566722i
$21$			2.33171i			0.508820i
$22$	4.80762	+	5.54903i	1.02499	+	1.18306i
$23$	1.95543			0.407736			0.203868	−	0.978998i	$-0.434649\pi$
$23$	1.95543			0.407736			0.203868	+	0.978998i	$0.434649\pi$
$24$	−5.54882	+	3.56446i	−1.13265	+	0.727593i
$25$	4.20857			0.841713
$26$	0.926043	+	1.06885i	0.181612	+	0.209619i
$27$			1.31310i			0.252707i
$28$	0.284890	−	1.97961i	0.0538392	−	0.374110i
$29$		−	3.33778i		−	0.619809i	−0.950768	−	0.309905i	$-0.899703\pi$
$29$		−	3.33778i		−	0.619809i	0.950768	−	0.309905i	$-0.100297\pi$
$30$	−2.21717	+	1.92093i	−0.404797	+	0.350712i
$31$	−4.20796			−0.755773			−0.377886	−	0.925852i	$-0.623349\pi$
$31$	−4.20796			−0.755773			−0.377886	+	0.925852i	$0.623349\pi$
$32$	5.14643	−	2.34825i	0.909769	−	0.415116i
$33$	12.1052			2.10725
$34$	−3.43984	+	2.98024i	−0.589928	+	0.511108i
$35$		−	0.889625i		−	0.150374i
$36$	−0.694235	+	4.82400i	−0.115706	+	0.804000i
$37$		−	4.89196i		−	0.804234i	−0.915588	−	0.402117i	$-0.868275\pi$
$37$		−	4.89196i		−	0.804234i	0.915588	−	0.402117i	$-0.131725\pi$
$38$	6.52162	+	7.52735i	1.05795	+	1.22110i
$39$	2.33171			0.373372
$40$	2.11706	−	1.35996i	0.334737	−	0.215029i
$41$	7.53924			1.17743			0.588716	−	0.808340i	$-0.299634\pi$
$41$	7.53924			1.17743			0.588716	+	0.808340i	$0.299634\pi$
$42$	−2.15926	−	2.49225i	−0.333181	−	0.384562i
$43$		−	7.93240i		−	1.20968i	−0.796347	−	0.604840i	$-0.793237\pi$
$43$		−	7.93240i		−	1.20968i	0.796347	−	0.604840i	$-0.206763\pi$
$44$	−10.2773	−	1.47903i	−1.54936	−	0.222972i
$45$			2.16788i			0.323169i
$46$	−2.09007	+	1.81082i	−0.308164	+	0.266990i
$47$	−5.87744			−0.857312			−0.428656	−	0.903468i	$-0.641013\pi$
$47$	−5.87744			−0.857312			−0.428656	+	0.903468i	$0.641013\pi$
$48$	2.63003	−	8.94833i	0.379611	−	1.29158i
$49$	1.00000			0.142857
$50$	−4.49834	+	3.89731i	−0.636161	+	0.551163i
$51$			7.50403i			1.05077i
$52$	−1.97961	−	0.284890i	−0.274522	−	0.0395072i
$53$			12.5689i			1.72647i	0.504805	+	0.863234i	$0.331565\pi$
$53$			12.5689i			1.72647i	−0.504805	+	0.863234i	$0.668435\pi$
$54$	−1.21599	−	1.40351i	−0.165475	−	0.190994i
$55$	−4.61856			−0.622766
$56$	1.52869	+	2.37973i	0.204280	+	0.318004i
$57$	16.4210			2.17501
$58$	3.09092	+	3.56759i	0.405858	+	0.468447i
$59$			10.6544i			1.38708i	0.720417	+	0.693541i	$0.243950\pi$
$59$			10.6544i			1.38708i	−0.720417	+	0.693541i	$0.756050\pi$
$60$	0.590960	−	4.10638i	0.0762927	−	0.530132i
$61$		−	0.855217i		−	0.109499i	−0.998500	−	0.0547496i	$-0.982564\pi$
$61$		−	0.855217i		−	0.109499i	0.998500	−	0.0547496i	$-0.0174361\pi$
$62$	4.49769	−	3.89675i	0.571207	−	0.494888i
$63$	−2.43685			−0.307014
$64$	−3.32619	+	7.27574i	−0.415774	+	0.909468i
$65$	−0.889625			−0.110344
$66$	−12.9387	+	11.2100i	−1.59264	+	1.37985i
$67$			0.692832i			0.0846429i	0.999104	+	0.0423215i	$0.0134754\pi$
$67$			0.692832i			0.0846429i	−0.999104	+	0.0423215i	$0.986525\pi$
$68$	0.916850	−	6.37088i	0.111184	−	0.772583i
$69$			4.55950i			0.548899i
$70$	0.823831	+	0.950878i	0.0984666	+	0.113652i
$71$	−3.83030			−0.454573			−0.227287	−	0.973828i	$-0.572985\pi$
$71$	−3.83030			−0.454573			−0.227287	+	0.973828i	$0.572985\pi$
$72$	−3.72519	−	5.79903i	−0.439018	−	0.683423i
$73$	0.715881			0.0837875			0.0418937	−	0.999122i	$-0.486661\pi$
$73$	0.715881			0.0837875			0.0418937	+	0.999122i	$0.486661\pi$
$74$	4.53016	+	5.22878i	0.526621	+	0.607834i
$75$			9.81314i			1.13312i
$76$	−13.9413	−	2.00633i	−1.59918	−	0.230142i
$77$		−	5.19158i		−	0.591635i
$78$	−2.49225	+	2.15926i	−0.282192	+	0.244488i
$79$	−1.11892			−0.125888			−0.0629441	−	0.998017i	$-0.520049\pi$
$79$	−1.11892			−0.125888			−0.0629441	+	0.998017i	$0.520049\pi$
$80$	−1.00344	+	3.41409i	−0.112189	+	0.381707i
$81$	−10.3723			−1.15248
$82$	−8.05833	+	6.98166i	−0.889894	+	0.770995i
$83$			11.4825i			1.26037i	0.776447	+	0.630183i	$0.217020\pi$
$83$			11.4825i			1.26037i	−0.776447	+	0.630183i	$0.782980\pi$
$84$	4.61586	+	0.664280i	0.503631	+	0.0724789i
$85$		−	2.86304i		−	0.310541i
$86$	7.34574	+	8.47856i	0.792111	+	0.914267i
$87$	7.78271			0.834394
$88$	12.3545	−	7.93633i	1.31700	−	0.846015i
$89$	−2.19918			−0.233113			−0.116556	−	0.993184i	$-0.537186\pi$
$89$	−2.19918			−0.233113			−0.116556	+	0.993184i	$0.537186\pi$
$90$	−2.00755	−	2.31715i	−0.211615	−	0.244249i
$91$		−	1.00000i		−	0.104828i
$92$	0.557084	−	3.87099i	0.0580800	−	0.403578i
$93$		−	9.81173i		−	1.01743i
$94$	6.28211	−	5.44276i	0.647950	−	0.561377i
$95$	−6.26515			−0.642791
$96$	5.47542	+	12.0000i	0.558833	+	1.22474i
$97$	14.7605			1.49870			0.749352	−	0.662172i	$-0.230365\pi$
$97$	14.7605			1.49870			0.749352	+	0.662172i	$0.230365\pi$
$98$	−1.06885	+	0.926043i	−0.107970	+	0.0935444i
$99$			12.6511i			1.27148i
$100$	1.19898	−	8.33130i	0.119898	−	0.833130i
$101$			17.5421i			1.74550i	0.488166	+	0.872751i	$0.337666\pi$
$101$			17.5421i			1.74550i	−0.488166	+	0.872751i	$0.662334\pi$
$102$	−6.94905	−	8.02070i	−0.688058	−	0.794167i
$103$	4.01795			0.395900			0.197950	−	0.980212i	$-0.436572\pi$
$103$	4.01795			0.395900			0.197950	+	0.980212i	$0.436572\pi$
$104$	2.37973	−	1.52869i	0.233351	−	0.149901i
$105$	2.07434			0.202435
$106$	−11.6393	−	13.4343i	−1.13051	−	1.30485i
$107$		−	4.53921i		−	0.438822i	−0.975633	−	0.219411i	$-0.929586\pi$
$107$		−	4.53921i		−	0.438822i	0.975633	−	0.219411i	$-0.0704135\pi$
$108$	2.59942	+	0.374090i	0.250130	+	0.0359968i
$109$		−	13.1578i		−	1.26029i	−0.776478	−	0.630145i	$-0.782995\pi$
$109$		−	13.1578i		−	1.26029i	0.776478	−	0.630145i	$-0.217005\pi$
$110$	4.93656	−	4.27698i	0.470682	−	0.407794i
$111$	11.4066			1.08267
$112$	−3.83768	−	1.12794i	−0.362626	−	0.106580i
$113$	−0.259943			−0.0244534			−0.0122267	−	0.999925i	$-0.503892\pi$
$113$	−0.259943			−0.0244534			−0.0122267	+	0.999925i	$0.503892\pi$
$114$	−17.5516	+	15.2065i	−1.64386	+	1.42422i
$115$		−	1.73960i		−	0.162219i
$116$	−6.60748	−	0.950900i	−0.613489	−	0.0882888i
$117$			2.43685i			0.225287i
$118$	−9.86641	−	11.3880i	−0.908276	−	1.04835i
$119$	3.21826			0.295017
$120$	3.17104	+	4.93637i	0.289475	+	0.450627i
$121$	−15.9525			−1.45022
$122$	0.791967	+	0.914100i	0.0717013	+	0.0827587i
$123$			17.5793i			1.58507i
$124$	−1.19881	+	8.33011i	−0.107656	+	0.748066i
$125$		−	8.19217i		−	0.732730i
$126$	2.60463	−	2.25663i	0.232039	−	0.201036i
$127$	−9.05123			−0.803167			−0.401584	−	0.915822i	$-0.631540\pi$
$127$	−9.05123			−0.803167			−0.401584	+	0.915822i	$0.631540\pi$
$128$	−3.18244	−	10.8569i	−0.281290	−	0.959623i
$129$	18.4960			1.62848
$130$	0.950878	−	0.823831i	0.0833975	−	0.0722547i
$131$		−	19.7801i		−	1.72820i	−0.503321	−	0.864099i	$-0.667889\pi$
$131$		−	19.7801i		−	1.72820i	0.503321	−	0.864099i	$-0.332111\pi$
$132$	3.44866	−	23.9636i	0.300167	−	2.08576i
$133$		−	7.04246i		−	0.610659i
$134$	−0.641592	−	0.740535i	−0.0554251	−	0.0639725i
$135$	1.16817			0.100540
$136$	4.91973	+	7.65857i	0.421863	+	0.656717i
$137$	13.8480			1.18311			0.591556	−	0.806264i	$-0.298514\pi$
$137$	13.8480			1.18311			0.591556	+	0.806264i	$0.298514\pi$
$138$	−4.22229	−	4.87343i	−0.359425	−	0.414854i
$139$		−	6.28021i		−	0.532681i	−0.963879	−	0.266340i	$-0.914185\pi$
$139$		−	6.28021i		−	0.532681i	0.963879	−	0.266340i	$-0.0858145\pi$
$140$	−1.76111	−	0.253446i	−0.148841	−	0.0214201i
$141$		−	13.7044i		−	1.15412i
$142$	4.09403	−	3.54702i	0.343563	−	0.297660i
$143$	−5.19158			−0.434141
$144$	9.35184	+	2.74862i	0.779320	+	0.229052i
$145$	−2.96937			−0.246593
$146$	−0.765171	+	0.662936i	−0.0633260	+	0.0548650i
$147$			2.33171i			0.192316i
$148$	−9.68415	−	1.39367i	−0.796032	−	0.114559i
$149$		−	19.9794i		−	1.63677i	−0.574669	−	0.818386i	$-0.694869\pi$
$149$		−	19.9794i		−	1.63677i	0.574669	−	0.818386i	$-0.305131\pi$
$150$	−9.08738	−	10.4888i	−0.741982	−	0.856406i
$151$	20.1238			1.63765			0.818825	−	0.574043i	$-0.194626\pi$
$151$	20.1238			1.63765			0.818825	+	0.574043i	$0.194626\pi$
$152$	16.7591	−	10.7658i	1.35935	−	0.873219i
$153$	−7.84241			−0.634021
$154$	4.80762	+	5.54903i	0.387409	+	0.447153i
$155$			3.74351i			0.300686i
$156$	0.664280	−	4.61586i	0.0531850	−	0.369564i
$157$		−	6.20998i		−	0.495611i	−0.968810	−	0.247805i	$-0.920291\pi$
$157$		−	6.20998i		−	0.495611i	0.968810	−	0.247805i	$-0.0797093\pi$
$158$	1.19596	−	1.03617i	0.0951454	−	0.0824330i
$159$	−29.3069			−2.32419
$160$	−2.08906	−	4.57839i	−0.165155	−	0.361954i
$161$	1.95543			0.154110
$162$	11.0865	−	9.60520i	0.871035	−	0.754656i
$163$		−	16.5675i		−	1.29767i	−0.760930	−	0.648834i	$-0.775257\pi$
$163$		−	16.5675i		−	1.29767i	0.760930	−	0.648834i	$-0.224743\pi$
$164$	2.14786	−	14.9247i	0.167719	−	1.16542i
$165$		−	10.7691i		−	0.838374i
$166$	−10.6333	−	12.2731i	−0.825301	−	0.952575i
$167$	9.45402			0.731574			0.365787	−	0.930699i	$-0.380800\pi$
$167$	9.45402			0.731574			0.365787	+	0.930699i	$0.380800\pi$
$168$	−5.54882	+	3.56446i	−0.428101	+	0.275004i
$169$	−1.00000			−0.0769231
$170$	2.65130	+	3.06017i	0.203345	+	0.234704i
$171$			17.1614i			1.31237i
$172$	−15.7030	−	2.25986i	−1.19734	−	0.172313i
$173$			25.2077i			1.91650i	0.285924	+	0.958252i	$0.407700\pi$
$173$			25.2077i			1.91650i	−0.285924	+	0.958252i	$0.592300\pi$
$174$	−8.31857	+	7.20712i	−0.630629	+	0.546370i
$175$	4.20857			0.318138
$176$	−5.85579	+	19.9236i	−0.441397	+	1.50180i
$177$	−24.8429			−1.86730
$178$	2.35060	−	2.03654i	0.176185	−	0.152645i
$179$			19.5708i			1.46279i	0.681953	+	0.731396i	$0.261131\pi$
$179$			19.5708i			1.46279i	−0.681953	+	0.731396i	$0.738869\pi$
$180$	4.29155	+	0.617609i	0.319873	+	0.0460338i
$181$			1.93265i			0.143652i	0.997417	+	0.0718262i	$0.0228827\pi$
$181$			1.93265i			0.143652i	−0.997417	+	0.0718262i	$0.977117\pi$
$182$	0.926043	+	1.06885i	0.0686428	+	0.0792286i
$183$	1.99411			0.147409
$184$	2.98926	+	4.65340i	0.220371	+	0.343053i
$185$	−4.35201			−0.319966
$186$	9.08608	+	10.4873i	0.666224	+	0.768965i
$187$		−	16.7078i		−	1.22180i
$188$	−1.67442	+	11.6350i	−0.122120	+	0.848570i
$189$			1.31310i			0.0955141i
$190$	6.69652	−	5.80180i	0.485817	−	0.420907i
$191$	1.58197			0.114468			0.0572338	−	0.998361i	$-0.481772\pi$
$191$	1.58197			0.114468			0.0572338	+	0.998361i	$0.481772\pi$
$192$	−16.9649	−	7.75570i	−1.22434	−	0.559720i
$193$	−17.6386			−1.26966			−0.634829	−	0.772653i	$-0.718929\pi$
$193$	−17.6386			−1.26966			−0.634829	+	0.772653i	$0.718929\pi$
$194$	−15.7768	+	13.6689i	−1.13271	+	0.981368i
$195$		−	2.07434i		−	0.148547i
$196$	0.284890	−	1.97961i	0.0203493	−	0.141400i
$197$		−	3.53842i		−	0.252102i	−0.992024	−	0.126051i	$-0.959770\pi$
$197$		−	3.53842i		−	0.252102i	0.992024	−	0.126051i	$-0.0402304\pi$
$198$	−11.7154	−	13.5221i	−0.832581	−	0.960977i
$199$	1.47725			0.104720			0.0523598	−	0.998628i	$-0.483326\pi$
$199$	1.47725			0.104720			0.0523598	+	0.998628i	$0.483326\pi$
$200$	6.43361	+	10.0152i	0.454925	+	0.708184i
$201$	−1.61548			−0.113947
$202$	−16.2447	−	18.7499i	−1.14297	−	1.31924i
$203$		−	3.33778i		−	0.234266i
$204$	14.8550	+	2.13782i	1.04006	+	0.149678i
$205$		−	6.70710i		−	0.468444i
$206$	−4.29459	+	3.72079i	−0.299218	+	0.259240i
$207$	−4.76510			−0.331197
$208$	−1.12794	+	3.83768i	−0.0782086	+	0.266095i
$209$	−36.5615			−2.52901
$210$	−2.21717	+	1.92093i	−0.152999	+	0.132557i
$211$			21.4365i			1.47575i	0.674939	+	0.737873i	$0.264170\pi$
$211$			21.4365i			1.47575i	−0.674939	+	0.737873i	$0.735830\pi$
$212$	24.8814	+	3.58075i	1.70886	+	0.245927i
$213$		−	8.93114i		−	0.611951i
$214$	4.20350	+	4.85174i	0.287345	+	0.331658i
$215$	−7.05686			−0.481274
$216$	−3.12482	+	2.00733i	−0.212617	+	0.136582i
$217$	−4.20796			−0.285655
$218$	12.1847	+	14.0638i	0.825252	+	0.952518i
$219$			1.66922i			0.112796i
$220$	−1.31578	+	9.14292i	−0.0887100	+	0.616416i
$221$		−	3.21826i		−	0.216483i
$222$	−12.1920	+	10.5630i	−0.818272	+	0.708943i
$223$	−26.4880			−1.77377			−0.886883	−	0.461994i	$-0.847134\pi$
$223$	−26.4880			−1.77377			−0.886883	+	0.461994i	$0.847134\pi$
$224$	5.14643	−	2.34825i	0.343860	−	0.156899i
$225$	−10.2556			−0.683710
$226$	0.277840	−	0.240718i	0.0184817	−	0.0160123i
$227$			13.9068i			0.923027i	0.887133	+	0.461514i	$0.152693\pi$
$227$			13.9068i			0.923027i	−0.887133	+	0.461514i	$0.847307\pi$
$228$	4.67817	−	32.5070i	0.309819	−	2.15283i
$229$		−	8.35469i		−	0.552093i	−0.961144	−	0.276047i	$-0.910976\pi$
$229$		−	8.35469i		−	0.552093i	0.961144	−	0.276047i	$-0.0890244\pi$
$230$	1.61095	+	1.85938i	0.106223	+	0.122604i
$231$	12.1052			0.796465
$232$	7.94299	−	5.10244i	0.521483	−	0.334991i
$233$	6.99448			0.458224			0.229112	−	0.973400i	$-0.426418\pi$
$233$	6.99448			0.458224			0.229112	+	0.973400i	$0.426418\pi$
$234$	−2.25663	−	2.60463i	−0.147520	−	0.170270i
$235$			5.22872i			0.341084i
$236$	21.0915	+	3.03533i	1.37294	+	0.197583i
$237$		−	2.60899i		−	0.169472i
$238$	−3.43984	+	2.98024i	−0.222972	+	0.193181i
$239$	−14.1229			−0.913537			−0.456768	−	0.889586i	$-0.650993\pi$
$239$	−14.1229			−0.913537			−0.456768	+	0.889586i	$0.650993\pi$
$240$	−7.96066	−	2.33974i	−0.513858	−	0.151029i
$241$	26.1438			1.68407			0.842036	−	0.539421i	$-0.181357\pi$
$241$	26.1438			1.68407			0.842036	+	0.539421i	$0.181357\pi$
$242$	17.0508	−	14.7727i	1.09607	−	0.949623i
$243$		−	20.2459i		−	1.29877i
$244$	−1.69299	−	0.243643i	−0.108383	−	0.0155976i
$245$		−	0.889625i		−	0.0568361i
$246$	−16.2792	−	18.7897i	−1.03792	−	1.19799i
$247$	−7.04246			−0.448101
$248$	−6.43269	−	10.0138i	−0.408476	−	0.635877i
$249$	−26.7738			−1.69672
$250$	7.58630	+	8.75622i	0.479800	+	0.553792i
$251$		−	2.70950i		−	0.171022i	−0.996337	−	0.0855112i	$-0.972748\pi$
$251$		−	2.70950i		−	0.171022i	0.996337	−	0.0855112i	$-0.0272523\pi$
$252$	−0.694235	+	4.82400i	−0.0437327	+	0.303883i
$253$		−	10.1518i		−	0.638237i
$254$	9.67443	−	8.38183i	0.607028	−	0.525923i
$255$	6.67577			0.418053
$256$	13.4555	+	8.65734i	0.840969	+	0.541084i
$257$	8.57734			0.535040			0.267520	−	0.963552i	$-0.413796\pi$
$257$	8.57734			0.535040			0.267520	+	0.963552i	$0.413796\pi$
$258$	−19.7695	+	17.1281i	−1.23080	+	1.06635i
$259$		−	4.89196i		−	0.303972i
$260$	−0.253446	+	1.76111i	−0.0157180	+	0.109219i
$261$			8.13366i			0.503461i
$262$	18.3173	+	21.1420i	1.13164	+	1.30616i
$263$	−25.0591			−1.54521			−0.772606	−	0.634886i	$-0.781047\pi$
$263$	−25.0591			−1.54521			−0.772606	+	0.634886i	$0.781047\pi$
$264$	18.5052	+	28.8071i	1.13891	+	1.77296i
$265$	11.1816			0.686879
$266$	6.52162	+	7.52735i	0.399866	+	0.461532i
$267$		−	5.12784i		−	0.313819i
$268$	1.37153	+	0.197381i	0.0837798	+	0.0120570i
$269$		−	13.8889i		−	0.846818i	−0.905939	−	0.423409i	$-0.860833\pi$
$269$		−	13.8889i		−	0.846818i	0.905939	−	0.423409i	$-0.139167\pi$
$270$	−1.24860	+	1.08177i	−0.0759874	+	0.0658347i
$271$	4.50260			0.273513			0.136757	−	0.990605i	$-0.456332\pi$
$271$	4.50260			0.273513			0.136757	+	0.990605i	$0.456332\pi$
$272$	−12.3506	−	3.63000i	−0.748867	−	0.220101i
$273$	2.33171			0.141121
$274$	−14.8014	+	12.8238i	−0.894187	+	0.774714i
$275$		−	21.8491i		−	1.31755i
$276$	9.02600	+	1.29896i	0.543301	+	0.0781880i
$277$			16.9466i			1.01822i	0.860700	+	0.509112i	$0.170026\pi$
$277$			16.9466i			1.01822i	−0.860700	+	0.509112i	$0.829974\pi$
$278$	5.81574	+	6.71262i	0.348805	+	0.402596i
$279$	10.2542			0.613901
$280$	2.11706	−	1.35996i	0.126519	−	0.0812734i
$281$	21.0461			1.25550			0.627751	−	0.778414i	$-0.283976\pi$
$281$	21.0461			1.25550			0.627751	+	0.778414i	$0.283976\pi$
$282$	12.6909	+	14.6480i	0.755732	+	0.872277i
$283$		−	5.29404i		−	0.314698i	−0.987543	−	0.157349i	$-0.949705\pi$
$283$		−	5.29404i		−	0.314698i	0.987543	−	0.157349i	$-0.0502947\pi$
$284$	−1.09122	+	7.58249i	−0.0647518	+	0.449938i
$285$		−	14.6085i		−	0.865332i
$286$	5.54903	−	4.80762i	0.328121	−	0.284281i
$287$	7.53924			0.445027
$288$	−12.5411	+	5.72233i	−0.738990	+	0.337191i
$289$	−6.64282			−0.390754
$290$	3.17382	−	2.74976i	0.186373	−	0.161472i
$291$			34.4172i			2.01757i
$292$	0.203947	−	1.41716i	0.0119351	−	0.0829331i
$293$			5.41703i			0.316466i	0.987402	+	0.158233i	$0.0505797\pi$
$293$			5.41703i			0.316466i	−0.987402	+	0.158233i	$0.949420\pi$
$294$	−2.15926	−	2.49225i	−0.125931	−	0.145351i
$295$	9.47840			0.551854
$296$	11.6415	−	7.47831i	0.676650	−	0.434668i
$297$	6.81707			0.395566
$298$	18.5017	+	21.3550i	1.07178	+	1.23706i
$299$		−	1.95543i		−	0.113086i
$300$	19.4261	+	2.79567i	1.12157	+	0.161408i
$301$		−	7.93240i		−	0.457216i
$302$	−21.5094	+	18.6355i	−1.23772	+	1.07235i
$303$	−40.9029			−2.34981
$304$	−7.94348	+	27.0267i	−0.455590	+	1.55009i
$305$	−0.760822			−0.0435646
$306$	8.38238	−	7.26240i	0.479189	−	0.415164i
$307$			9.90651i			0.565394i	0.959209	+	0.282697i	$0.0912292\pi$
$307$			9.90651i			0.565394i	−0.959209	+	0.282697i	$0.908771\pi$
$308$	−10.2773	−	1.47903i	−0.585602	−	0.0842755i
$309$			9.36866i			0.532965i
$310$	−3.46665	−	4.00126i	−0.196892	−	0.227256i
$311$	16.7956			0.952392			0.476196	−	0.879339i	$-0.342015\pi$
$311$	16.7956			0.952392			0.476196	+	0.879339i	$0.342015\pi$
$312$	3.56446	+	5.54882i	0.201798	+	0.314140i
$313$	9.70069			0.548315			0.274158	−	0.961685i	$-0.411601\pi$
$313$	9.70069			0.548315			0.274158	+	0.961685i	$0.411601\pi$
$314$	5.75071	+	6.63756i	0.324531	+	0.374579i
$315$			2.16788i			0.122146i
$316$	−0.318769	+	2.21502i	−0.0179322	+	0.124604i
$317$		−	9.27094i		−	0.520708i	−0.965513	−	0.260354i	$-0.916161\pi$
$317$		−	9.27094i		−	0.520708i	0.965513	−	0.260354i	$-0.0838392\pi$
$318$	31.3247	−	27.1394i	1.75660	−	1.52190i
$319$	−17.3283			−0.970200
$320$	6.47268	+	2.95907i	0.361834	+	0.165417i
$321$	10.5841			0.590747
$322$	−2.09007	+	1.81082i	−0.116475	+	0.100913i
$323$		−	22.6645i		−	1.26108i
$324$	−2.95497	+	20.5331i	−0.164165	+	1.14073i
$325$		−	4.20857i		−	0.233449i
$326$	15.3422	+	17.7082i	0.849727	+	0.980768i
$327$	30.6801			1.69662
$328$	11.5252	+	17.9413i	0.636372	+	0.990644i
$329$	−5.87744			−0.324034
$330$	9.97266	+	11.5106i	0.548977	+	0.633637i
$331$			6.12891i			0.336875i	0.985712	+	0.168438i	$0.0538722\pi$
$331$			6.12891i			0.336875i	−0.985712	+	0.168438i	$0.946128\pi$
$332$	22.7308	+	3.27125i	1.24751	+	0.179533i
$333$			11.9210i			0.653265i
$334$	−10.1050	+	8.75483i	−0.552918	+	0.479043i
$335$	0.616361			0.0336754
$336$	2.63003	−	8.94833i	0.143480	−	0.488171i
$337$	−12.8282			−0.698794			−0.349397	−	0.936975i	$-0.613614\pi$
$337$	−12.8282			−0.698794			−0.349397	+	0.936975i	$0.613614\pi$
$338$	1.06885	−	0.926043i	0.0581379	−	0.0503701i
$339$		−	0.606110i		−	0.0329194i
$340$	−5.66770	−	0.815653i	−0.307374	−	0.0442350i
$341$			21.8460i			1.18303i
$342$	−15.8922	−	18.3430i	−0.859352	−	0.991877i
$343$	1.00000			0.0539949
$344$	18.8769	−	12.1262i	1.01778	−	0.653801i
$345$	4.05624			0.218381
$346$	−23.3434	−	26.9433i	−1.25495	−	1.44848i
$347$			1.74202i			0.0935163i	0.998906	+	0.0467582i	$0.0148890\pi$
$347$			1.74202i			0.0935163i	−0.998906	+	0.0467582i	$0.985111\pi$
$348$	2.21722	−	15.4067i	0.118855	−	0.825885i
$349$			28.4674i			1.52383i	0.647679	+	0.761914i	$0.275740\pi$
$349$			28.4674i			1.52383i	−0.647679	+	0.761914i	$0.724260\pi$
$350$	−4.49834	+	3.89731i	−0.240446	+	0.208320i
$351$	1.31310			0.0700882
$352$	−12.1911	−	26.7181i	−0.649788	−	1.42408i
$353$	24.2648			1.29149			0.645743	−	0.763554i	$-0.276548\pi$
$353$	24.2648			1.29149			0.645743	+	0.763554i	$0.276548\pi$
$354$	26.5534	−	23.0056i	1.41129	−	1.22273i
$355$			3.40753i			0.180853i
$356$	−0.626526	+	4.35351i	−0.0332058	+	0.230736i
$357$			7.50403i			0.397155i
$358$	−18.1234	−	20.9183i	−0.957852	−	1.10557i
$359$	−10.6867			−0.564023			−0.282012	−	0.959411i	$-0.591002\pi$
$359$	−10.6867			−0.564023			−0.282012	+	0.959411i	$0.591002\pi$
$360$	−5.15897	+	3.31403i	−0.271901	+	0.174665i
$361$	−30.5963			−1.61033
$362$	−1.78971	−	2.06571i	−0.0940652	−	0.108571i
$363$		−	37.1964i		−	1.95231i
$364$	−1.97961	−	0.284890i	−0.103760	−	0.0149323i
$365$		−	0.636866i		−	0.0333351i
$366$	−2.13141	+	1.84663i	−0.111411	+	0.0965251i
$367$	−0.861092			−0.0449486			−0.0224743	−	0.999747i	$-0.507154\pi$
$367$	−0.861092			−0.0449486			−0.0224743	+	0.999747i	$0.507154\pi$
$368$	−7.50432	−	2.20561i	−0.391190	−	0.114976i
$369$	−18.3720			−0.956408
$370$	4.65166	−	4.03015i	0.241828	−	0.209517i
$371$			12.5689i			0.652543i
$372$	−19.4234	−	2.79527i	−1.00705	−	0.144928i
$373$			36.1432i			1.87142i	0.352764	+	0.935712i	$0.385242\pi$
$373$			36.1432i			1.87142i	−0.352764	+	0.935712i	$0.614758\pi$
$374$	15.4722	+	17.8582i	0.800047	+	0.923426i
$375$	19.1017			0.986409
$376$	−8.98480	−	13.9867i	−0.463355	−	0.721308i
$377$	−3.33778			−0.171904
$378$	−1.21599	−	1.40351i	−0.0625437	−	0.0721889i
$379$			7.88623i			0.405088i	0.979273	+	0.202544i	$0.0649210\pi$
$379$			7.88623i			0.405088i	−0.979273	+	0.202544i	$0.935079\pi$
$380$	−1.78488	+	12.4025i	−0.0915625	+	0.636237i
$381$		−	21.1048i		−	1.08123i
$382$	−1.69089	+	1.46497i	−0.0865137	+	0.0749546i
$383$	−25.9897			−1.32801			−0.664006	−	0.747727i	$-0.731145\pi$
$383$	−25.9897			−1.32801			−0.664006	+	0.747727i	$0.731145\pi$
$384$	25.3151	−	7.42051i	1.29185	−	0.378676i
$385$	−4.61856			−0.235383
$386$	18.8531	−	16.3341i	0.959598	−	0.831386i
$387$			19.3301i			0.982602i
$388$	4.20513	−	29.2200i	0.213483	−	1.48342i
$389$		−	31.9104i		−	1.61792i	−0.587862	−	0.808961i	$-0.700030\pi$
$389$		−	31.9104i		−	1.61792i	0.587862	−	0.808961i	$-0.299970\pi$
$390$	1.92093	+	2.21717i	0.0972701	+	0.112271i
$391$	6.29309			0.318255
$392$	1.52869	+	2.37973i	0.0772107	+	0.120194i
$393$	46.1215			2.32652
$394$	3.27673	+	3.78205i	0.165079	+	0.190537i
$395$			0.995418i			0.0500849i
$396$	25.0442	+	3.60417i	1.25852	+	0.181116i
$397$			18.4407i			0.925512i	0.886486	+	0.462756i	$0.153139\pi$
$397$			18.4407i			0.925512i	−0.886486	+	0.462756i	$0.846861\pi$
$398$	−1.57896	+	1.36800i	−0.0791464	+	0.0685716i
$399$	16.4210			0.822076
$400$	−16.1511	−	4.74701i	−0.807556	−	0.237351i
$401$	−29.2421			−1.46028			−0.730140	−	0.683298i	$-0.760545\pi$
$401$	−29.2421			−1.46028			−0.730140	+	0.683298i	$0.760545\pi$
$402$	1.72671	−	1.49600i	0.0861205	−	0.0746139i
$403$			4.20796i			0.209614i
$404$	34.7264	+	4.99757i	1.72770	+	0.248638i
$405$			9.22747i			0.458517i
$406$	3.09092	+	3.56759i	0.153400	+	0.177056i
$407$	−25.3970			−1.25888
$408$	−17.8575	+	11.4714i	−0.884080	+	0.567917i
$409$	−19.6165			−0.969974			−0.484987	−	0.874521i	$-0.661176\pi$
$409$	−19.6165			−0.969974			−0.484987	+	0.874521i	$0.661176\pi$
$410$	6.21106	+	7.16890i	0.306742	+	0.354047i
$411$			32.2894i			1.59272i
$412$	1.14467	−	7.95395i	0.0563940	−	0.391863i
$413$			10.6544i			0.524268i
$414$	5.09319	−	4.41268i	0.250316	−	0.216872i
$415$	10.2151			0.501440
$416$	−2.34825	−	5.14643i	−0.115132	−	0.252324i
$417$	14.6436			0.717100
$418$	39.0788	−	33.8575i	1.91141	−	1.65602i
$419$			24.6034i			1.20195i	0.799266	+	0.600977i	$0.205222\pi$
$419$			24.6034i			1.20195i	−0.799266	+	0.600977i	$0.794778\pi$
$420$	0.590960	−	4.10638i	0.0288359	−	0.200371i
$421$			14.8488i			0.723685i	0.932239	+	0.361842i	$0.117852\pi$
$421$			14.8488i			0.723685i	−0.932239	+	0.361842i	$0.882148\pi$
$422$	−19.8511	−	22.9124i	−0.966335	−	1.11536i
$423$	14.3224			0.696380
$424$	−29.9105	+	19.2139i	−1.45258	+	0.933112i
$425$	13.5443			0.656993
$426$	8.27061	+	9.54607i	0.400713	+	0.462508i
$427$		−	0.855217i		−	0.0413868i
$428$	−8.98584	−	1.29318i	−0.434347	−	0.0625080i
$429$		−	12.1052i		−	0.584446i
$430$	7.54274	−	6.53495i	0.363743	−	0.315143i
$431$	8.96639			0.431896			0.215948	−	0.976405i	$-0.430716\pi$
$431$	8.96639			0.431896			0.215948	+	0.976405i	$0.430716\pi$
$432$	1.48110	−	5.03926i	0.0712595	−	0.242451i
$433$	3.46538			0.166535			0.0832677	−	0.996527i	$-0.473464\pi$
$433$	3.46538			0.166535			0.0832677	+	0.996527i	$0.473464\pi$
$434$	4.49769	−	3.89675i	0.215896	−	0.187050i
$435$		−	6.92369i		−	0.331966i
$436$	−26.0473	−	3.74853i	−1.24744	−	0.179522i
$437$		−	13.7711i		−	0.658760i
$438$	−1.54577	−	1.78415i	−0.0738598	−	0.0852501i
$439$	0.528709			0.0252339			0.0126170	−	0.999920i	$-0.495984\pi$
$439$	0.528709			0.0252339			0.0126170	+	0.999920i	$0.495984\pi$
$440$	−7.06036	−	10.9909i	−0.336589	−	0.523971i
$441$	−2.43685			−0.116040
$442$	2.98024	+	3.43984i	0.141756	+	0.163617i
$443$		−	18.5545i		−	0.881552i	−0.897617	−	0.440776i	$-0.854703\pi$
$443$		−	18.5545i		−	0.881552i	0.897617	−	0.440776i	$-0.145297\pi$
$444$	3.24963	−	22.5806i	0.154221	−	1.07163i
$445$			1.95645i			0.0927445i
$446$	28.3117	−	24.5290i	1.34060	−	1.16148i
$447$	46.5860			2.20344
$448$	−3.32619	+	7.27574i	−0.157148	+	0.343747i
$449$	8.39859			0.396354			0.198177	−	0.980166i	$-0.436498\pi$
$449$	8.39859			0.396354			0.198177	+	0.980166i	$0.436498\pi$
$450$	10.9618	−	9.49716i	0.516743	−	0.447700i
$451$		−	39.1405i		−	1.84306i
$452$	−0.0740552	+	0.514584i	−0.00348326	+	0.0242040i
$453$			46.9227i			2.20462i
$454$	−12.8783	−	14.8643i	−0.604408	−	0.697617i
$455$	−0.889625			−0.0417063
$456$	25.1026	+	39.0774i	1.17554	+	1.82997i
$457$	5.59397			0.261675			0.130837	−	0.991404i	$-0.458233\pi$
$457$	5.59397			0.261675			0.130837	+	0.991404i	$0.458233\pi$
$458$	7.73680	+	8.92993i	0.361517	+	0.417268i
$459$			4.22590i			0.197248i
$460$	−3.44373	−	0.495596i	−0.160565	−	0.0231073i
$461$			12.5828i			0.586039i	0.956106	+	0.293019i	$0.0946601\pi$
$461$			12.5828i			0.586039i	−0.956106	+	0.293019i	$0.905340\pi$
$462$	−12.9387	+	11.2100i	−0.601963	+	0.521534i
$463$	−18.7682			−0.872232			−0.436116	−	0.899890i	$-0.643646\pi$
$463$	−18.7682			−0.872232			−0.436116	+	0.899890i	$0.643646\pi$
$464$	−3.76481	+	12.8093i	−0.174777	+	0.594657i
$465$	−8.72876			−0.404787
$466$	−7.47607	+	6.47719i	−0.346322	+	0.300050i
$467$			21.4368i			0.991978i	0.868329	+	0.495989i	$0.165194\pi$
$467$			21.4368i			0.991978i	−0.868329	+	0.495989i	$0.834806\pi$
$468$	4.82400	+	0.694235i	0.222989	+	0.0320910i
$469$			0.692832i			0.0319920i
$470$	−4.84201	−	5.58872i	−0.223345	−	0.257789i
$471$	14.4799			0.667196
$472$	−25.3545	+	16.2873i	−1.16704	+	0.749683i
$473$	−41.1816			−1.89353
$474$	2.41603	+	2.78862i	0.110972	+	0.128086i
$475$		−	29.6387i		−	1.35992i
$476$	0.916850	−	6.37088i	0.0420238	−	0.292009i
$477$		−	30.6284i		−	1.40238i
$478$	15.0953	−	13.0784i	0.690444	−	0.598194i
$479$	39.9154			1.82378			0.911892	−	0.410431i	$-0.134622\pi$
$479$	39.9154			1.82378			0.911892	+	0.410431i	$0.134622\pi$
$480$	10.6755	−	4.87108i	0.487266	−	0.222333i
$481$	−4.89196			−0.223054
$482$	−27.9439	+	24.2103i	−1.27281	+	1.10275i
$483$			4.55950i			0.207464i
$484$	−4.54470	+	31.5796i	−0.206577	+	1.43544i
$485$		−	13.1313i		−	0.596263i
$486$	18.7485	+	21.6398i	0.850451	+	0.981603i
$487$	−40.5689			−1.83835			−0.919177	−	0.393844i	$-0.871145\pi$
$487$	−40.5689			−1.83835			−0.919177	+	0.393844i	$0.871145\pi$
$488$	2.03518	−	1.30736i	0.0921283	−	0.0591816i
$489$	38.6305			1.74693
$490$	0.823831	+	0.950878i	0.0372169	+	0.0429563i
$491$			29.2954i			1.32208i	0.750349	+	0.661042i	$0.229886\pi$
$491$			29.2954i			1.32208i	−0.750349	+	0.661042i	$0.770114\pi$
$492$	34.8001	+	5.00817i	1.56891	+	0.225786i
$493$		−	10.7418i		−	0.483787i
$494$	7.52735	−	6.52162i	0.338672	−	0.293422i
$495$	11.2547			0.505862
$496$	16.1488	+	4.74633i	0.725102	+	0.213117i
$497$	−3.83030			−0.171813
$498$	28.6172	−	24.7936i	1.28237	−	1.11103i
$499$			2.31819i			0.103776i	0.998653	+	0.0518882i	$0.0165239\pi$
$499$			2.31819i			0.103776i	−0.998653	+	0.0518882i	$0.983476\pi$
$500$	−16.2173	−	2.33387i	−0.725258	−	0.104374i
$501$			22.0440i			0.984853i
$502$	2.50912	+	2.89606i	0.111987	+	0.129257i
$503$	−11.4341			−0.509819			−0.254910	−	0.966965i	$-0.582046\pi$
$503$	−11.4341			−0.509819			−0.254910	+	0.966965i	$0.582046\pi$
$504$	−3.72519	−	5.79903i	−0.165933	−	0.258309i
$505$	15.6059			0.694452
$506$	9.40099	+	10.8508i	0.417925	+	0.482375i
$507$		−	2.33171i		−	0.103555i
$508$	−2.57861	+	17.9179i	−0.114407	+	0.794977i
$509$			33.7643i			1.49658i	0.663374	+	0.748288i	$0.269124\pi$
$509$			33.7643i			1.49658i	−0.663374	+	0.748288i	$0.730876\pi$
$510$	−7.13542	+	6.18205i	−0.315962	+	0.273746i
$511$	0.715881			0.0316687
$512$	−22.3990	+	3.20695i	−0.989906	+	0.141728i
$513$	9.24747			0.408286
$514$	−9.16791	+	7.94298i	−0.404379	+	0.350350i
$515$		−	3.57447i		−	0.157510i
$516$	5.26933	−	36.6148i	0.231969	−	1.61188i
$517$			30.5132i			1.34197i
$518$	4.53016	+	5.22878i	0.199044	+	0.229740i
$519$	−58.7769			−2.58002
$520$	−1.35996	−	2.11706i	−0.0596384	−	0.0928394i
$521$	−18.0635			−0.791378			−0.395689	−	0.918385i	$-0.629494\pi$
$521$	−18.0635			−0.791378			−0.395689	+	0.918385i	$0.629494\pi$
$522$	−7.53211	−	8.69368i	−0.329672	−	0.380512i
$523$		−	22.7221i		−	0.993568i	−0.867874	−	0.496784i	$-0.834514\pi$
$523$		−	22.7221i		−	0.993568i	0.867874	−	0.496784i	$-0.165486\pi$
$524$	−39.1569	−	5.63517i	−1.71058	−	0.246174i
$525$			9.81314i			0.428280i
$526$	26.7845	−	23.2058i	1.16786	−	1.01182i
$527$	−13.5423			−0.589912
$528$	−46.4559	−	13.6540i	−2.02173	−	0.594213i
$529$	−19.1763			−0.833751
$530$	−11.9515	+	10.3546i	−0.519138	+	0.449776i
$531$		−	25.9631i		−	1.12670i
$532$	−13.9413	−	2.00633i	−0.604432	−	0.0869854i
$533$		−	7.53924i		−	0.326561i
$534$	4.74860	+	5.48091i	0.205492	+	0.237182i
$535$	−4.03819			−0.174586
$536$	−1.64875	+	1.05913i	−0.0712152	+	0.0457474i
$537$	−45.6334			−1.96923
$538$	12.8617	+	14.8451i	0.554506	+	0.640019i
$539$		−	5.19158i		−	0.223617i
$540$	0.332800	−	2.31251i	0.0143214	−	0.0995147i
$541$			44.6632i			1.92022i	0.279624	+	0.960110i	$0.409790\pi$
$541$			44.6632i			1.92022i	−0.279624	+	0.960110i	$0.590210\pi$
$542$	−4.81261	+	4.16960i	−0.206719	+	0.179099i
$543$	−4.50636			−0.193386
$544$	16.5625	−	7.55727i	0.710113	−	0.324015i
$545$	−11.7055			−0.501410
$546$	−2.49225	+	2.15926i	−0.106658	+	0.0924077i
$547$		−	29.9883i		−	1.28221i	−0.767455	−	0.641103i	$-0.778477\pi$
$547$		−	29.9883i		−	1.28221i	0.767455	−	0.641103i	$-0.221523\pi$
$548$	3.94515	−	27.4135i	0.168528	−	1.17105i
$549$			2.08403i			0.0889444i
$550$	20.2332	+	23.3535i	0.862746	+	0.995795i
$551$	−23.5062			−1.00140
$552$	−10.8504	+	6.97007i	−0.461822	+	0.296666i
$553$	−1.11892			−0.0475813
$554$	−15.6933	−	18.1134i	−0.666744	−	0.769566i
$555$		−	10.1476i		−	0.430742i
$556$	−12.4323	−	1.78917i	−0.527249	−	0.0758778i
$557$		−	22.5823i		−	0.956843i	−0.878130	−	0.478422i	$-0.841209\pi$
$557$		−	22.5823i		−	0.956843i	0.878130	−	0.478422i	$-0.158791\pi$
$558$	−10.9602	+	9.49580i	−0.463982	+	0.401989i
$559$	−7.93240			−0.335505
$560$	−1.00344	+	3.41409i	−0.0424033	+	0.144272i
$561$	38.9577			1.64480
$562$	−22.4951	+	19.4895i	−0.948899	+	0.822117i
$563$			13.4350i			0.566219i	0.959088	+	0.283110i	$0.0913660\pi$
$563$			13.4350i			0.566219i	−0.959088	+	0.283110i	$0.908634\pi$
$564$	−27.1294	−	3.90426i	−1.14235	−	0.164399i
$565$			0.231252i			0.00972883i
$566$	4.90251	+	5.65855i	0.206068	+	0.237846i
$567$	−10.3723			−0.435596
$568$	−5.85536	−	9.11507i	−0.245685	−	0.382460i
$569$	−0.954464			−0.0400132			−0.0200066	−	0.999800i	$-0.506369\pi$
$569$	−0.954464			−0.0400132			−0.0200066	+	0.999800i	$0.506369\pi$
$570$	13.5281	+	15.6143i	0.566629	+	0.654012i
$571$		−	1.74439i		−	0.0730005i	−0.999334	−	0.0365003i	$-0.988379\pi$
$571$		−	1.74439i		−	0.0730005i	0.999334	−	0.0365003i	$-0.0116210\pi$
$572$	−1.47903	+	10.2773i	−0.0618413	+	0.429714i
$573$			3.68869i			0.154097i
$574$	−8.05833	+	6.98166i	−0.336348	+	0.291409i
$575$	8.22957			0.343197
$576$	8.10543	−	17.7299i	0.337726	−	0.738745i
$577$	10.1146			0.421078			0.210539	−	0.977585i	$-0.432478\pi$
$577$	10.1146			0.421078			0.210539	+	0.977585i	$0.432478\pi$
$578$	7.10019	−	6.15153i	0.295329	−	0.255870i
$579$		−	41.1281i		−	1.70923i
$580$	−0.845945	+	5.87818i	−0.0351259	+	0.244078i
$581$			11.4825i			0.476374i
$582$	−31.8718	−	36.7869i	−1.32113	−	1.52487i
$583$	65.2523			2.70247
$584$	1.09436	+	1.70360i	0.0452850	+	0.0704955i
$585$	2.16788			0.0896309
$586$	−5.01640	−	5.79000i	−0.207226	−	0.239183i
$587$			3.47868i			0.143581i	0.997420	+	0.0717903i	$0.0228712\pi$
$587$			3.47868i			0.143581i	−0.997420	+	0.0717903i	$0.977129\pi$
$588$	4.61586	+	0.664280i	0.190355	+	0.0273945i
$589$			29.6344i			1.22107i
$590$	−10.1310	+	8.77740i	−0.417087	+	0.361360i
$591$	8.25056			0.339383
$592$	−5.51784	+	18.7738i	−0.226782	+	0.771597i
$593$	3.45123			0.141725			0.0708626	−	0.997486i	$-0.477425\pi$
$593$	3.45123			0.141725			0.0708626	+	0.997486i	$0.477425\pi$
$594$	−7.28644	+	6.31290i	−0.298966	+	0.259021i
$595$		−	2.86304i		−	0.117373i
$596$	−39.5512	−	5.69192i	−1.62008	−	0.233150i
$597$			3.44452i			0.140975i
$598$	1.81082	+	2.09007i	0.0740497	+	0.0854693i
$599$	−31.2867			−1.27834			−0.639169	−	0.769066i	$-0.720722\pi$
$599$	−31.2867			−1.27834			−0.639169	+	0.769066i	$0.720722\pi$
$600$	−23.3526	+	15.0013i	−0.953365	+	0.612425i
$601$	8.69289			0.354590			0.177295	−	0.984158i	$-0.443265\pi$
$601$	8.69289			0.354590			0.177295	+	0.984158i	$0.443265\pi$
$602$	7.34574	+	8.47856i	0.299390	+	0.345560i
$603$		−	1.68833i		−	0.0687540i
$604$	5.73307	−	39.8371i	0.233275	−	1.62095i
$605$			14.1917i			0.576975i
$606$	43.7192	−	37.8779i	1.77597	−	1.53868i
$607$	25.9859			1.05473			0.527367	−	0.849638i	$-0.323179\pi$
$607$	25.9859			1.05473			0.527367	+	0.849638i	$0.323179\pi$
$608$	−16.5375	−	36.2435i	−0.670683	−	1.46987i
$609$	7.78271			0.315371
$610$	0.813207	−	0.704554i	0.0329258	−	0.0285266i
$611$			5.87744i			0.237776i
$612$	−2.23423	+	15.5249i	−0.0903132	+	0.627556i
$613$		−	9.59008i		−	0.387340i	−0.981067	−	0.193670i	$-0.937961\pi$
$613$		−	9.59008i		−	0.387340i	0.981067	−	0.193670i	$-0.0620391\pi$
$614$	−9.17385	−	10.5886i	−0.370227	−	0.427321i
$615$	15.6390			0.630624
$616$	12.3545	−	7.93633i	0.497778	−	0.319764i
$617$	−20.9085			−0.841746			−0.420873	−	0.907119i	$-0.638276\pi$
$617$	−20.9085			−0.841746			−0.420873	+	0.907119i	$0.638276\pi$
$618$	−8.67578	−	10.0137i	−0.348991	−	0.402811i
$619$		−	3.42979i		−	0.137855i	−0.997622	−	0.0689274i	$-0.978042\pi$
$619$		−	3.42979i		−	0.137855i	0.997622	−	0.0689274i	$-0.0219577\pi$
$620$	7.41067	+	1.06649i	0.297620	+	0.0428313i
$621$			2.56768i			0.103038i
$622$	−17.9520	+	15.5535i	−0.719811	+	0.623637i
$623$	−2.19918			−0.0881084
$624$	−8.94833	−	2.63003i	−0.358220	−	0.105285i
$625$	13.7549			0.550195
$626$	−10.3686	+	8.98325i	−0.414413	+	0.359043i
$627$		−	85.2506i		−	3.40458i
$628$	−12.2933	−	1.76916i	−0.490557	−	0.0705973i
$629$		−	15.7436i		−	0.627738i
$630$	−2.00755	−	2.31715i	−0.0799828	−	0.0923173i
$631$	20.1897			0.803741			0.401870	−	0.915697i	$-0.368360\pi$
$631$	20.1897			0.803741			0.401870	+	0.915697i	$0.368360\pi$
$632$	−1.71048	−	2.66272i	−0.0680394	−	0.105917i
$633$	−49.9835			−1.98667
$634$	8.58528	+	9.90926i	0.340965	+	0.393547i
$635$			8.05221i			0.319542i
$636$	−8.34925	+	58.0161i	−0.331069	+	2.30049i
$637$		−	1.00000i		−	0.0396214i
$638$	18.5214	−	16.0468i	0.733270	−	0.635297i
$639$	9.33387			0.369242
$640$	−9.65856	+	2.83118i	−0.381788	+	0.111912i
$641$	43.0839			1.70171			0.850855	−	0.525400i	$-0.176084\pi$
$641$	43.0839			1.70171			0.850855	+	0.525400i	$0.176084\pi$
$642$	−11.3128	+	9.80132i	−0.446482	+	0.386827i
$643$		−	40.7613i		−	1.60747i	−0.594988	−	0.803734i	$-0.702843\pi$
$643$		−	40.7613i		−	1.60747i	0.594988	−	0.803734i	$-0.297157\pi$
$644$	0.557084	−	3.87099i	0.0219522	−	0.152538i
$645$		−	16.4545i		−	0.647896i
$646$	20.9883	+	24.2250i	0.825772	+	0.953119i
$647$	−17.0384			−0.669847			−0.334924	−	0.942245i	$-0.608710\pi$
$647$	−17.0384			−0.669847			−0.334924	+	0.942245i	$0.608710\pi$
$648$	−15.8561	−	24.6833i	−0.622886	−	0.969650i
$649$	55.3130			2.17123
$650$	3.89731	+	4.49834i	0.152865	+	0.176439i
$651$		−	9.81173i		−	0.384552i
$652$	−32.7971	−	4.71992i	−1.28443	−	0.184846i
$653$			11.3248i			0.443174i	0.975141	+	0.221587i	$0.0711236\pi$
$653$			11.3248i			0.443174i	−0.975141	+	0.221587i	$0.928876\pi$
$654$	−32.7925	+	28.4111i	−1.28229	+	1.11096i
$655$	−17.5969			−0.687568
$656$	−28.9332	−	8.50382i	−1.12965	−	0.332018i
$657$	−1.74449			−0.0680592
$658$	6.28211	−	5.44276i	0.244902	−	0.212181i
$659$		−	9.05494i		−	0.352730i	−0.984325	−	0.176365i	$-0.943566\pi$
$659$		−	9.05494i		−	0.352730i	0.984325	−	0.176365i	$-0.0564339\pi$
$660$	−21.3186	−	3.06802i	−0.829825	−	0.119422i
$661$		−	5.92208i		−	0.230342i	−0.993346	−	0.115171i	$-0.963258\pi$
$661$		−	5.92208i		−	0.230342i	0.993346	−	0.115171i	$-0.0367416\pi$
$662$	−5.67563	−	6.55090i	−0.220590	−	0.254608i
$663$	7.50403			0.291432
$664$	−27.3252	+	17.5532i	−1.06042	+	0.681196i
$665$	−6.26515			−0.242952
$666$	−11.0393	−	12.7418i	−0.427765	−	0.493733i
$667$		−	6.52680i		−	0.252719i
$668$	2.69336	−	18.7152i	0.104209	−	0.724114i
$669$		−	61.7622i		−	2.38786i
$670$	−0.658799	+	0.570777i	−0.0254516	+	0.0220510i
$671$	−4.43992			−0.171401
$672$	5.47542	+	12.0000i	0.211219	+	0.462908i
$673$	−33.2995			−1.28360			−0.641800	−	0.766872i	$-0.721812\pi$
$673$	−33.2995			−1.28360			−0.641800	+	0.766872i	$0.721812\pi$
$674$	13.7114	−	11.8794i	0.528144	−	0.457578i
$675$			5.52628i			0.212706i
$676$	−0.284890	+	1.97961i	−0.0109573	+	0.0761387i
$677$			23.5539i			0.905249i	0.891701	+	0.452625i	$0.149512\pi$
$677$			23.5539i			0.905249i	−0.891701	+	0.452625i	$0.850488\pi$
$678$	0.561284	+	0.647842i	0.0215560	+	0.0248802i
$679$	14.7605			0.566457
$680$	6.81326	−	4.37672i	0.261277	−	0.167839i
$681$	−32.4266			−1.24259
$682$	−20.2303	−	23.3501i	−0.774658	−	0.894122i
$683$			10.8973i			0.416974i	0.978025	+	0.208487i	$0.0668539\pi$
$683$			10.8973i			0.416974i	−0.978025	+	0.208487i	$0.933146\pi$
$684$	33.9728	+	4.88912i	1.29898	+	0.186940i
$685$		−	12.3195i		−	0.470704i
$686$	−1.06885	+	0.926043i	−0.0408090	+	0.0353565i
$687$	19.4807			0.743234
$688$	−8.94727	+	30.4420i	−0.341112	+	1.16059i
$689$	12.5689			0.478836
$690$	−4.33552	+	3.75625i	−0.165051	+	0.142998i
$691$			18.9351i			0.720325i	0.932889	+	0.360163i	$0.117279\pi$
$691$			18.9351i			0.720325i	−0.932889	+	0.360163i	$0.882721\pi$
$692$	49.9013	+	7.18142i	1.89696	+	0.272997i
$693$			12.6511i			0.480575i
$694$	−1.61318	−	1.86196i	−0.0612355	−	0.0706790i
$695$	−5.58704			−0.211928
$696$	11.8974	+	18.5207i	0.450969	+	0.702026i
$697$	24.2632			0.919035
$698$	−26.3621	−	30.4275i	−0.997819	−	1.15170i
$699$			16.3091i			0.616866i
$700$	1.19898	−	8.33130i	0.0453172	−	0.314894i
$701$		−	42.1055i		−	1.59030i	−0.606411	−	0.795152i	$-0.707391\pi$
$701$		−	42.1055i		−	1.59030i	0.606411	−	0.795152i	$-0.292609\pi$
$702$	−1.40351	+	1.21599i	−0.0529721	+	0.0458945i
$703$	−34.4515			−1.29936
$704$	37.7726	+	17.2682i	1.42361	+	0.650819i
$705$	−12.1918			−0.459171
$706$	−25.9355	+	22.4703i	−0.976096	+	0.845680i
$707$			17.5421i			0.659738i
$708$	−7.07749	+	49.1791i	−0.265988	+	1.84826i
$709$			12.1005i			0.454444i	0.973843	+	0.227222i	$0.0729642\pi$
$709$			12.1005i			0.454444i	−0.973843	+	0.227222i	$0.927036\pi$
$710$	−3.15552	−	3.64215i	−0.118425	−	0.136687i
$711$	2.72664			0.102257
$712$	−3.36187	−	5.23345i	−0.125992	−	0.196132i
$713$	−8.22839			−0.308156
$714$	−6.94905	−	8.02070i	−0.260062	−	0.300167i
$715$			4.61856i			0.172724i
$716$	38.7425	+	5.57554i	1.44788	+	0.208368i
$717$		−	32.9305i		−	1.22981i
$718$	11.4225	−	9.89635i	0.426285	−	0.369329i
$719$	27.1158			1.01125			0.505624	−	0.862754i	$-0.331262\pi$
$719$	27.1158			1.01125			0.505624	+	0.862754i	$0.331262\pi$
$720$	2.44524	−	8.31963i	0.0911288	−	0.310054i
$721$	4.01795			0.149636
$722$	32.7029	−	28.3335i	1.21708	−	1.05446i
$723$			60.9597i			2.26712i
$724$	3.82588	+	0.550592i	0.142188	+	0.0204626i
$725$		−	14.0473i		−	0.521702i
$726$	34.4455	+	39.7575i	1.27839	+	1.47554i
$727$	41.6183			1.54354			0.771769	−	0.635903i	$-0.219372\pi$
$727$	41.6183			1.54354			0.771769	+	0.635903i	$0.219372\pi$
$728$	2.37973	−	1.52869i	0.0881985	−	0.0566571i
$729$	16.0905			0.595943
$730$	0.589765	+	0.680715i	0.0218282	+	0.0251944i
$731$		−	25.5285i		−	0.944206i
$732$	0.568103	−	3.94756i	0.0209977	−	0.145906i
$733$		−	26.7816i		−	0.989202i	−0.869120	−	0.494601i	$-0.835314\pi$
$733$		−	26.7816i		−	0.989202i	0.869120	−	0.494601i	$-0.164686\pi$
$734$	0.920380	−	0.797408i	0.0339719	−	0.0294329i
$735$	2.07434			0.0765133
$736$	10.0635	−	4.59185i	0.370946	−	0.169258i
$737$	3.59689			0.132493
$738$	19.6369	−	17.0132i	0.722846	−	0.626266i
$739$		−	42.7016i		−	1.57080i	−0.618987	−	0.785401i	$-0.712457\pi$
$739$		−	42.7016i		−	1.57080i	0.618987	−	0.785401i	$-0.287543\pi$
$740$	−1.23985	+	8.61527i	−0.0455776	+	0.316704i
$741$		−	16.4210i		−	0.603239i
$742$	−11.6393	−	13.4343i	−0.427293	−	0.493187i
$743$	42.5351			1.56046			0.780230	−	0.625492i	$-0.215102\pi$
$743$	42.5351			1.56046			0.780230	+	0.625492i	$0.215102\pi$
$744$	23.3492	−	14.9991i	0.856024	−	0.549895i
$745$	−17.7741			−0.651194
$746$	−33.4702	−	38.6318i	−1.22543	−	1.41441i
$747$		−	27.9811i		−	1.02377i
$748$	−33.0749	−	4.75990i	−1.20934	−	0.174039i
$749$		−	4.53921i		−	0.165859i
$750$	−20.4169	+	17.6890i	−0.745521	+	0.645912i
$751$	42.8241			1.56267			0.781336	−	0.624110i	$-0.214538\pi$
$751$	42.8241			1.56267			0.781336	+	0.624110i	$0.214538\pi$
$752$	22.5557	+	6.62940i	0.822521	+	0.241749i
$753$	6.31776			0.230232
$754$	3.56759	−	3.09092i	0.129924	−	0.112565i
$755$		−	17.9026i		−	0.651543i
$756$	2.59942	+	0.374090i	0.0945401	+	0.0136055i
$757$			7.20682i			0.261936i	0.991387	+	0.130968i	$0.0418085\pi$
$757$			7.20682i			0.261936i	−0.991387	+	0.130968i	$0.958191\pi$
$758$	−7.30298	−	8.42921i	−0.265256	−	0.306163i
$759$	23.6710			0.859202
$760$	−9.57750	−	14.9094i	−0.347412	−	0.540819i
$761$	−8.67573			−0.314495			−0.157247	−	0.987559i	$-0.550262\pi$
$761$	−8.67573			−0.314495			−0.157247	+	0.987559i	$0.550262\pi$
$762$	19.5440	+	22.5579i	0.708003	+	0.817187i
$763$		−	13.1578i		−	0.476345i
$764$	0.450689	−	3.13168i	0.0163053	−	0.113300i
$765$			6.97680i			0.252247i
$766$	27.7791	−	24.0676i	1.00370	−	0.869596i
$767$	10.6544			0.384707
$768$	−20.1864	+	31.3743i	−0.728413	+	1.13212i
$769$	−37.3169			−1.34568			−0.672840	−	0.739788i	$-0.734926\pi$
$769$	−37.3169			−1.34568			−0.672840	+	0.739788i	$0.734926\pi$
$770$	4.93656	−	4.27698i	0.177901	−	0.154132i
$771$			19.9998i			0.720276i
$772$	−5.02508	+	34.9176i	−0.180857	+	1.25671i
$773$			17.6533i			0.634946i	0.948267	+	0.317473i	$0.102834\pi$
$773$			17.6533i			0.634946i	−0.948267	+	0.317473i	$0.897166\pi$
$774$	−17.9005	−	20.6610i	−0.643418	−	0.742643i
$775$	−17.7095			−0.636144
$776$	22.5643	+	35.1260i	0.810012	+	1.26095i
$777$	11.4066			0.409210
$778$	29.5504	+	34.1075i	1.05943	+	1.22281i
$779$		−	53.0948i		−	1.90232i
$780$	−4.10638	−	0.590960i	−0.147032	−	0.0211598i
$781$			19.8853i			0.711552i
$782$	−6.72638	+	5.82767i	−0.240535	+	0.208397i
$783$	4.38284			0.156630
$784$	−3.83768	−	1.12794i	−0.137060	−	0.0402836i
$785$	−5.52456			−0.197180
$786$	−49.2970	+	42.7104i	−1.75837	+	1.52343i
$787$			36.1972i			1.29029i	0.764059	+	0.645146i	$0.223203\pi$
$787$			36.1972i			1.29029i	−0.764059	+	0.645146i	$0.776797\pi$
$788$	−7.00468	−	1.00806i	−0.249532	−	0.0359108i
$789$		−	58.4305i		−	2.08018i
$790$	−0.921800	−	1.06395i	−0.0327962	−	0.0378538i
$791$	−0.259943			−0.00924250
$792$	−30.1061	+	19.3396i	−1.06977	+	0.687204i
$793$	−0.855217			−0.0303696
$794$	−17.0769	−	19.7104i	−0.606035	−	0.699495i
$795$			26.0722i			0.924684i
$796$	0.420855	−	2.92438i	0.0149168	−	0.103652i
$797$		−	23.4086i		−	0.829174i	−0.910010	−	0.414587i	$-0.863926\pi$
$797$		−	23.4086i		−	0.829174i	0.910010	−	0.414587i	$-0.136074\pi$
$798$	−17.5516	+	15.2065i	−0.621319	+	0.538304i
$799$	−18.9151			−0.669168
$800$	21.6591	−	9.88276i	0.765764	−	0.349408i
$801$	5.35907			0.189354
$802$	31.2555	−	27.0794i	1.10367	−	0.956207i
$803$		−	3.71655i		−	0.131154i
$804$	−0.460235	+	3.19801i	−0.0162312	+	0.112785i
$805$		−	1.73960i		−	0.0613130i
$806$	−3.89675	−	4.49769i	−0.137257	−	0.158424i
$807$	32.3847			1.14000
$808$	−41.7453	+	26.8165i	−1.46860	+	0.943399i
$809$	−40.2721			−1.41589			−0.707946	−	0.706266i	$-0.750378\pi$
$809$	−40.2721			−1.41589			−0.707946	+	0.706266i	$0.750378\pi$
$810$	−8.54503	−	9.86280i	−0.300242	−	0.346544i
$811$		−	42.9222i		−	1.50720i	−0.657331	−	0.753602i	$-0.728315\pi$
$811$		−	42.9222i		−	1.50720i	0.657331	−	0.753602i	$-0.271685\pi$
$812$	−6.60748	−	0.950900i	−0.231877	−	0.0333700i
$813$			10.4987i			0.368206i
$814$	27.1456	−	23.5187i	0.951454	−	0.824330i
$815$	−14.7389			−0.516280
$816$	8.46410	−	28.7980i	0.296303	−	1.00813i
$817$	−55.8636			−1.95442
$818$	20.9671	−	18.1657i	0.733099	−	0.635149i
$819$			2.43685i			0.0851504i
$820$	−13.2774	−	1.91079i	−0.463667	−	0.0667276i
$821$			28.2362i			0.985451i	0.870185	+	0.492726i	$0.163999\pi$
$821$			28.2362i			0.985451i	−0.870185	+	0.492726i	$0.836001\pi$
$822$	−29.9013	−	34.5126i	−1.04293	−	1.20376i
$823$	53.0998			1.85094			0.925471	−	0.378819i	$-0.123670\pi$
$823$	53.0998			1.85094			0.925471	+	0.378819i	$0.123670\pi$
$824$	6.14221	+	9.56161i	0.213974	+	0.333094i
$825$	50.9457			1.77370
$826$	−9.86641	−	11.3880i	−0.343296	−	0.396238i
$827$			42.7395i			1.48620i	0.669182	+	0.743099i	$0.266645\pi$
$827$			42.7395i			1.48620i	−0.669182	+	0.743099i	$0.733355\pi$
$828$	−1.35753	+	9.43301i	−0.0471774	+	0.327820i
$829$			4.07693i			0.141598i	0.997491	+	0.0707989i	$0.0225549\pi$
$829$			4.07693i			0.141598i	−0.997491	+	0.0707989i	$0.977445\pi$
$830$	−10.9184	+	9.45962i	−0.378984	+	0.328348i
$831$	−39.5145			−1.37074
$832$	7.27574	+	3.32619i	0.252241	+	0.115315i
$833$	3.21826			0.111506
$834$	−15.6518	+	13.5606i	−0.541979	+	0.469565i
$835$		−	8.41053i		−	0.291059i
$836$	−10.4160	+	72.3773i	−0.360245	+	2.50322i
$837$		−	5.52548i		−	0.190989i
$838$	−22.7838	−	26.2974i	−0.787053	−	0.908428i
$839$	−26.6733			−0.920864			−0.460432	−	0.887695i	$-0.652306\pi$
$839$	−26.6733			−0.920864			−0.460432	+	0.887695i	$0.652306\pi$
$840$	3.17104	+	4.93637i	0.109411	+	0.170321i
$841$	17.8593			0.615836
$842$	−13.7506	−	15.8711i	−0.473877	−	0.546956i
$843$			49.0732i			1.69017i
$844$	42.4357	+	6.10704i	1.46070	+	0.210213i
$845$			0.889625i			0.0306040i
$846$	−15.3086	+	13.2632i	−0.526319	+	0.455997i
$847$	−15.9525			−0.548133
$848$	14.1769	−	48.2352i	0.486838	−	1.65641i
$849$	12.3441			0.423650
$850$	−14.4768	+	12.5426i	−0.496550	+	0.430206i
$851$		−	9.56591i		−	0.327915i
$852$	−17.6801	−	2.54439i	−0.605711	−	0.0871695i
$853$			31.4793i			1.07783i	0.842360	+	0.538916i	$0.181166\pi$
$853$			31.4793i			1.07783i	−0.842360	+	0.538916i	$0.818834\pi$
$854$	0.791967	+	0.914100i	0.0271006	+	0.0312799i
$855$	15.2672			0.522128
$856$	10.8021	−	6.93906i	0.369207	−	0.237172i
$857$	5.01876			0.171438			0.0857188	−	0.996319i	$-0.472681\pi$
$857$	5.01876			0.171438			0.0857188	+	0.996319i	$0.472681\pi$
$858$	11.2100	+	12.9387i	0.382702	+	0.441720i
$859$			6.90746i			0.235680i	0.993033	+	0.117840i	$0.0375969\pi$
$859$			6.90746i			0.235680i	−0.993033	+	0.117840i	$0.962403\pi$
$860$	−2.01043	+	13.9698i	−0.0685551	+	0.476366i
$861$			17.5793i			0.599101i
$862$	−9.58375	+	8.30326i	−0.326424	+	0.282810i
$863$	−19.0353			−0.647971			−0.323985	−	0.946062i	$-0.605023\pi$
$863$	−19.0353			−0.647971			−0.323985	+	0.946062i	$0.605023\pi$
$864$	3.08349	+	6.75778i	0.104902	+	0.229905i
$865$	22.4254			0.762486
$866$	−3.70398	+	3.20909i	−0.125866	+	0.109049i
$867$		−	15.4891i		−	0.526037i
$868$	−1.19881	+	8.33011i	−0.0406902	+	0.282742i
$869$			5.80895i			0.197055i
$870$	6.41164	+	7.40041i	0.217375	+	0.250897i
$871$	0.692832			0.0234757
$872$	31.3120	−	20.1143i	1.06036	−	0.681155i
$873$	−35.9692			−1.21737
$874$	12.7526	+	14.7192i	0.431363	+	0.497886i
$875$		−	8.19217i		−	0.276946i
$876$	3.30440	+	0.475545i	0.111645	+	0.0160672i
$877$		−	25.1299i		−	0.848576i	−0.905527	−	0.424288i	$-0.860524\pi$
$877$		−	25.1299i		−	0.848576i	0.905527	−	0.424288i	$-0.139476\pi$
$878$	−0.565112	+	0.489607i	−0.0190716	+	0.0165235i
$879$	−12.6309			−0.426030
$880$	17.7245	+	5.20946i	0.597494	+	0.175611i
$881$	−33.4577			−1.12722			−0.563610	−	0.826041i	$-0.690588\pi$
$881$	−33.4577			−1.12722			−0.563610	+	0.826041i	$0.690588\pi$
$882$	2.60463	−	2.25663i	0.0877025	−	0.0759846i
$883$			21.7210i			0.730971i	0.930817	+	0.365485i	$0.119097\pi$
$883$			21.7210i			0.730971i	−0.930817	+	0.365485i	$0.880903\pi$
$884$	−6.37088	−	0.916850i	−0.214276	−	0.0308370i
$885$			22.1008i			0.742912i
$886$	17.1823	+	19.8320i	0.577250	+	0.666270i
$887$	−35.4161			−1.18916			−0.594579	−	0.804037i	$-0.702681\pi$
$887$	−35.4161			−1.18916			−0.594579	+	0.804037i	$0.702681\pi$
$888$	17.4372	+	27.1446i	0.585154	+	0.910914i
$889$	−9.05123			−0.303569
$890$	−1.81175	−	2.09115i	−0.0607301	−	0.0700956i
$891$			53.8487i			1.80400i
$892$	−7.54617	+	52.4357i	−0.252664	+	1.75568i
$893$			41.3916i			1.38512i
$894$	−49.7935	+	43.1406i	−1.66534	+	1.44284i
$895$	17.4107			0.581975
$896$	−3.18244	−	10.8569i	−0.106318	−	0.362703i
$897$	4.55950			0.152237
$898$	−8.97685	+	7.77745i	−0.299561	+	0.259537i
$899$			14.0452i			0.468435i
$900$	−2.92173	+	20.3021i	−0.0973911	+	0.676738i
$901$			40.4499i			1.34758i
$902$	36.2458	+	41.8355i	1.20685	+	1.39297i
$903$	18.4960			0.615509
$904$	−0.397373	−	0.618593i	−0.0132164	−	0.0205741i
$905$	1.71933			0.0571525
$906$	−43.4524	−	50.1535i	−1.44361	−	1.66624i
$907$			46.8717i			1.55635i	0.628047	+	0.778175i	$0.283854\pi$
$907$			46.8717i			1.55635i	−0.628047	+	0.778175i	$0.716146\pi$
$908$	27.5300	+	3.96191i	0.913615	+	0.131481i
$909$		−	42.7474i		−	1.41784i
$910$	0.950878	−	0.823831i	0.0315213	−	0.0273097i
$911$	27.6680			0.916680			0.458340	−	0.888777i	$-0.348444\pi$
$911$	27.6680			0.916680			0.458340	+	0.888777i	$0.348444\pi$
$912$	−63.0183	−	18.5219i	−2.08674	−	0.613320i
$913$	59.6122			1.97288
$914$	−5.97912	+	5.18025i	−0.197772	+	0.171347i
$915$		−	1.77401i		−	0.0586471i
$916$	−16.5390	−	2.38017i	−0.546464	−	0.0786430i
$917$		−	19.7801i		−	0.653198i
$918$	−3.91336	−	4.51686i	−0.129160	−	0.149079i
$919$	−6.79058			−0.224000			−0.112000	−	0.993708i	$-0.535726\pi$
$919$	−6.79058			−0.224000			−0.112000	+	0.993708i	$0.535726\pi$
$920$	4.13978	−	2.65932i	0.136484	−	0.0876752i
$921$	−23.0991			−0.761140
$922$	−11.6522	−	13.4491i	−0.383745	−	0.442924i
$923$			3.83030i			0.126076i
$924$	3.44866	−	23.9636i	0.113453	−	0.788344i
$925$		−	20.5881i		−	0.676934i
$926$	20.0604	−	17.3801i	0.659226	−	0.571147i
$927$	−9.79113			−0.321583
$928$	−7.83793	−	17.1776i	−0.257293	−	0.563883i
$929$	−39.6932			−1.30229			−0.651145	−	0.758953i	$-0.725711\pi$
$929$	−39.6932			−1.30229			−0.651145	+	0.758953i	$0.725711\pi$
$930$	9.32976	−	8.08321i	0.305935	−	0.265059i
$931$		−	7.04246i		−	0.230807i
$932$	1.99266	−	13.8463i	0.0652717	−	0.453551i
$933$			39.1624i			1.28212i
$934$	−19.8514	−	22.9128i	−0.649558	−	0.749730i
$935$	−14.8637			−0.486095
$936$	−5.79903	+	3.72519i	−0.189547	+	0.121762i
$937$	−20.4351			−0.667584			−0.333792	−	0.942647i	$-0.608328\pi$
$937$	−20.4351			−0.667584			−0.333792	+	0.942647i	$0.608328\pi$
$938$	−0.641592	−	0.740535i	−0.0209487	−	0.0241793i
$939$			22.6192i			0.738148i
$940$	10.3508	+	1.48961i	0.337606	+	0.0485857i
$941$		−	36.4344i		−	1.18773i	−0.804566	−	0.593863i	$-0.797602\pi$
$941$		−	36.4344i		−	1.18773i	0.804566	−	0.593863i	$-0.202398\pi$
$942$	−15.4768	+	13.4090i	−0.504262	+	0.436888i
$943$	14.7425			0.480081
$944$	12.0175	−	40.8880i	0.391136	−	1.33079i
$945$	1.16817			0.0380005
$946$	44.0171	−	38.1360i	1.43112	−	1.23991i
$947$		−	26.0051i		−	0.845051i	−0.906351	−	0.422526i	$-0.861144\pi$
$947$		−	26.0051i		−	0.845051i	0.906351	−	0.422526i	$-0.138856\pi$
$948$	−5.16477	−	0.743275i	−0.167744	−	0.0241405i
$949$		−	0.715881i		−	0.0232385i
$950$	27.4467	+	31.6794i	0.890488	+	1.02781i
$951$	21.6171			0.700982
$952$	4.91973	+	7.65857i	0.159449	+	0.248216i
$953$	58.1737			1.88443			0.942216	−	0.335006i	$-0.108738\pi$
$953$	58.1737			1.88443			0.942216	+	0.335006i	$0.108738\pi$
$954$	28.3632	+	32.7373i	0.918294	+	1.05991i
$955$		−	1.40736i		−	0.0455412i
$956$	−4.02349	+	27.9578i	−0.130129	+	0.904221i
$957$		−	40.4045i		−	1.30609i
$958$	−42.6637	+	36.9634i	−1.37840	+	1.19423i
$959$	13.8480			0.447174
$960$	−6.89967	+	15.0924i	−0.222686	+	0.487105i
$961$	−13.2930			−0.428808
$962$	5.22878	−	4.53016i	0.168583	−	0.146058i
$963$			11.0614i			0.356448i
$964$	7.44813	−	51.7545i	0.239888	−	1.66690i
$965$			15.6918i			0.505136i
$966$	−4.22229	−	4.87343i	−0.135850	−	0.156800i
$967$	5.23136			0.168229			0.0841146	−	0.996456i	$-0.473194\pi$
$967$	5.23136			0.168229			0.0841146	+	0.996456i	$0.473194\pi$
$968$	−24.3864	−	37.9625i	−0.783809	−	1.22016i
$969$	52.8469			1.69769
$970$	12.1602	+	14.0355i	0.390440	+	0.450651i
$971$			2.29589i			0.0736787i	0.999321	+	0.0368394i	$0.0117290\pi$
$971$			2.29589i			0.0736787i	−0.999321	+	0.0368394i	$0.988271\pi$
$972$	−40.0788	−	5.76785i	−1.28553	−	0.185004i
$973$		−	6.28021i		−	0.201334i
$974$	43.3622	−	37.5686i	1.38941	−	1.20377i
$975$	9.81314			0.314272
$976$	−0.964634	+	3.28204i	−0.0308772	+	0.105056i
$977$	−17.2924			−0.553233			−0.276617	−	0.960980i	$-0.589213\pi$
$977$	−17.2924			−0.553233			−0.276617	+	0.960980i	$0.589213\pi$
$978$	−41.2903	+	35.7735i	−1.32032	+	1.14391i
$979$			11.4172i			0.364896i
$980$	−1.76111	−	0.253446i	−0.0562565	−	0.00809602i
$981$			32.0636i			1.02371i
$982$	−27.1288	−	31.3125i	−0.865715	−	0.999222i
$983$	−0.377112			−0.0120280			−0.00601400	−	0.999982i	$-0.501914\pi$
$983$	−0.377112			−0.0120280			−0.00601400	+	0.999982i	$0.501914\pi$
$984$	−41.8339	+	26.8733i	−1.33362	+	0.856691i
$985$	−3.14787			−0.100300
$986$	9.94739	+	11.4814i	0.316789	+	0.365643i
$987$		−	13.7044i		−	0.436217i
$988$	−2.00633	+	13.9413i	−0.0638299	+	0.443532i
$989$		−	15.5113i		−	0.493230i
$990$	−12.0296	+	10.4224i	−0.382327	+	0.331244i
$991$	55.7354			1.77049			0.885246	−	0.465122i	$-0.153990\pi$
$991$	55.7354			1.77049			0.885246	+	0.465122i	$0.153990\pi$
$992$	−21.6560	+	9.88134i	−0.687578	+	0.313733i
$993$	−14.2908			−0.453505
$994$	4.09403	−	3.54702i	0.129855	−	0.112505i
$995$		−	1.31420i		−	0.0416630i
$996$	−7.62758	+	53.0015i	−0.241689	+	1.67942i
$997$			58.2737i			1.84555i	0.385345	+	0.922773i	$0.374083\pi$
$997$			58.2737i			1.84555i	−0.385345	+	0.922773i	$0.625917\pi$
$998$	−2.14674	−	2.47780i	−0.0679539	−	0.0784334i
$999$	6.42364			0.203235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.b.365.12	yes	38
4.3	odd	2		2912.2.c.b.1457.7		38
8.3	odd	2		2912.2.c.b.1457.32		38
8.5	even	2	inner	728.2.c.b.365.11	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.b.365.11	✓	38	8.5	even	2	inner
728.2.c.b.365.12	yes	38	1.1	even	1	trivial
2912.2.c.b.1457.7		38	4.3	odd	2
2912.2.c.b.1457.32		38	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06885 + 0.926043i) q^{2} +2.33171i q^{3} +(0.284890 - 1.97961i) q^{4} -0.889625i q^{5} +(-2.15926 - 2.49225i) q^{6} +1.00000 q^{7} +(1.52869 + 2.37973i) q^{8} -2.43685 q^{9} +(0.823831 + 0.950878i) q^{10} -5.19158i q^{11} +(4.61586 + 0.664280i) q^{12} -1.00000i q^{13} +(-1.06885 + 0.926043i) q^{14} +2.07434 q^{15} +(-3.83768 - 1.12794i) q^{16} +3.21826 q^{17} +(2.60463 - 2.25663i) q^{18} -7.04246i q^{19} +(-1.76111 - 0.253446i) q^{20} +2.33171i q^{21} +(4.80762 + 5.54903i) q^{22} +1.95543 q^{23} +(-5.54882 + 3.56446i) q^{24} +4.20857 q^{25} +(0.926043 + 1.06885i) q^{26} +1.31310i q^{27} +(0.284890 - 1.97961i) q^{28} -3.33778i q^{29} +(-2.21717 + 1.92093i) q^{30} -4.20796 q^{31} +(5.14643 - 2.34825i) q^{32} +12.1052 q^{33} +(-3.43984 + 2.98024i) q^{34} -0.889625i q^{35} +(-0.694235 + 4.82400i) q^{36} -4.89196i q^{37} +(6.52162 + 7.52735i) q^{38} +2.33171 q^{39} +(2.11706 - 1.35996i) q^{40} +7.53924 q^{41} +(-2.15926 - 2.49225i) q^{42} -7.93240i q^{43} +(-10.2773 - 1.47903i) q^{44} +2.16788i q^{45} +(-2.09007 + 1.81082i) q^{46} -5.87744 q^{47} +(2.63003 - 8.94833i) q^{48} +1.00000 q^{49} +(-4.49834 + 3.89731i) q^{50} +7.50403i q^{51} +(-1.97961 - 0.284890i) q^{52} +12.5689i q^{53} +(-1.21599 - 1.40351i) q^{54} -4.61856 q^{55} +(1.52869 + 2.37973i) q^{56} +16.4210 q^{57} +(3.09092 + 3.56759i) q^{58} +10.6544i q^{59} +(0.590960 - 4.10638i) q^{60} -0.855217i q^{61} +(4.49769 - 3.89675i) q^{62} -2.43685 q^{63} +(-3.32619 + 7.27574i) q^{64} -0.889625 q^{65} +(-12.9387 + 11.2100i) q^{66} +0.692832i q^{67} +(0.916850 - 6.37088i) q^{68} +4.55950i q^{69} +(0.823831 + 0.950878i) q^{70} -3.83030 q^{71} +(-3.72519 - 5.79903i) q^{72} +0.715881 q^{73} +(4.53016 + 5.22878i) q^{74} +9.81314i q^{75} +(-13.9413 - 2.00633i) q^{76} -5.19158i q^{77} +(-2.49225 + 2.15926i) q^{78} -1.11892 q^{79} +(-1.00344 + 3.41409i) q^{80} -10.3723 q^{81} +(-8.05833 + 6.98166i) q^{82} +11.4825i q^{83} +(4.61586 + 0.664280i) q^{84} -2.86304i q^{85} +(7.34574 + 8.47856i) q^{86} +7.78271 q^{87} +(12.3545 - 7.93633i) q^{88} -2.19918 q^{89} +(-2.00755 - 2.31715i) q^{90} -1.00000i q^{91} +(0.557084 - 3.87099i) q^{92} -9.81173i q^{93} +(6.28211 - 5.44276i) q^{94} -6.26515 q^{95} +(5.47542 + 12.0000i) q^{96} +14.7605 q^{97} +(-1.06885 + 0.926043i) q^{98} +12.6511i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) \) 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

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