LMFDB - Embedded newform 28.4.d.b.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,4,Mod(27,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("28.27");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	28.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 $ x^8 - 4x^7 - 30x^6 + 84x^5 + 493x^4 - 464x^3 - 3172x^2 + 1072*x + 8978
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.1
Root			$-2.60656 - 0.736813i$ of defining polynomial
Character	$\chi$	$=$	28.27
Dual form			28.4.d.b.27.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41421 - 1.47363i) q^{2} -4.79890 q^{3} +(3.65685 + 7.11529i) q^{4} +17.0728i q^{5} +(11.5856 + 7.07178i) q^{6} +(-18.3722 - 2.33686i) q^{7} +(1.65685 - 22.5667i) q^{8} -3.97056 q^{9} +O(q^{10})$	\(q+(-2.41421 - 1.47363i) q^{2} -4.79890 q^{3} +(3.65685 + 7.11529i) q^{4} +17.0728i q^{5} +(11.5856 + 7.07178i) q^{6} +(-18.3722 - 2.33686i) q^{7} +(1.65685 - 22.5667i) q^{8} -3.97056 q^{9} +(25.1589 - 41.2174i) q^{10} +41.4710i q^{11} +(-17.5489 - 34.1456i) q^{12} -45.3599i q^{13} +(40.9109 + 32.7155i) q^{14} -81.9306i q^{15} +(-37.2548 + 52.0392i) q^{16} +28.2871i q^{17} +(9.58579 + 5.85112i) q^{18} +41.5434 q^{19} +(-121.478 + 62.4327i) q^{20} +(88.1665 + 11.2143i) q^{21} +(61.1127 - 100.120i) q^{22} +93.9291i q^{23} +(-7.95108 + 108.295i) q^{24} -166.480 q^{25} +(-66.8435 + 109.509i) q^{26} +148.625 q^{27} +(-50.5572 - 139.269i) q^{28} +27.8234 q^{29} +(-120.735 + 197.798i) q^{30} -81.4400 q^{31} +(166.627 - 70.7340i) q^{32} -199.015i q^{33} +(41.6846 - 68.2912i) q^{34} +(39.8967 - 313.665i) q^{35} +(-14.5198 - 28.2517i) q^{36} +94.8040 q^{37} +(-100.295 - 61.2194i) q^{38} +217.678i q^{39} +(385.276 + 28.2871i) q^{40} +227.302i q^{41} +(-196.327 - 156.998i) q^{42} +171.988i q^{43} +(-295.078 + 151.653i) q^{44} -67.7886i q^{45} +(138.416 - 226.765i) q^{46} -286.005 q^{47} +(178.782 - 249.731i) q^{48} +(332.078 + 85.8665i) q^{49} +(401.919 + 245.330i) q^{50} -135.747i q^{51} +(322.749 - 165.875i) q^{52} -575.921 q^{53} +(-358.812 - 219.017i) q^{54} -708.025 q^{55} +(-83.1752 + 410.728i) q^{56} -199.362 q^{57} +(-67.1716 - 41.0012i) q^{58} +411.999 q^{59} +(582.960 - 299.608i) q^{60} +778.987i q^{61} +(196.614 + 120.012i) q^{62} +(72.9481 + 9.27863i) q^{63} +(-506.510 - 74.7794i) q^{64} +774.420 q^{65} +(-293.274 + 480.465i) q^{66} +198.773i q^{67} +(-201.271 + 103.442i) q^{68} -450.756i q^{69} +(-558.544 + 698.463i) q^{70} +197.762i q^{71} +(-6.57864 + 89.6024i) q^{72} -255.589i q^{73} +(-228.877 - 139.706i) q^{74} +798.922 q^{75} +(151.918 + 295.593i) q^{76} +(96.9117 - 761.915i) q^{77} +(320.775 - 525.520i) q^{78} -1178.49i q^{79} +(-888.454 - 636.044i) q^{80} -606.029 q^{81} +(334.958 - 548.756i) q^{82} +938.514 q^{83} +(242.619 + 668.340i) q^{84} -482.940 q^{85} +(253.446 - 415.215i) q^{86} -133.522 q^{87} +(935.862 + 68.7114i) q^{88} -1166.81i q^{89} +(-99.8950 + 163.656i) q^{90} +(-106.000 + 833.363i) q^{91} +(-668.333 + 343.485i) q^{92} +390.823 q^{93} +(690.476 + 421.464i) q^{94} +709.261i q^{95} +(-799.628 + 339.446i) q^{96} +656.635i q^{97} +(-675.173 - 696.659i) q^{98} -164.663i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9	$ 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9} - 152 q^{14} + 64 q^{16} + 88 q^{18} - 64 q^{21} + 240 q^{22} - 472 q^{25} - 48 q^{28} - 592 q^{29} + 256 q^{30} + 1152 q^{32} - 976 q^{36} + 1392 q^{37} - 1024 q^{42} - 1184 q^{44} - 816 q^{46} + 1480 q^{49} + 1688 q^{50} - 1168 q^{53} + 800 q^{56} - 192 q^{57} - 560 q^{58} + 2944 q^{60} - 3328 q^{64} + 448 q^{65} - 3200 q^{70} - 1184 q^{72} - 496 q^{74} + 368 q^{77} + 7680 q^{78} - 4984 q^{81} + 4480 q^{84} + 1024 q^{85} + 240 q^{86} + 3776 q^{88} - 3808 q^{92} - 2304 q^{93} - 3144 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9 - 152 * q^14 + 64 * q^16 + 88 * q^18 - 64 * q^21 + 240 * q^22 - 472 * q^25 - 48 * q^28 - 592 * q^29 + 256 * q^30 + 1152 * q^32 - 976 * q^36 + 1392 * q^37 - 1024 * q^42 - 1184 * q^44 - 816 * q^46 + 1480 * q^49 + 1688 * q^50 - 1168 * q^53 + 800 * q^56 - 192 * q^57 - 560 * q^58 + 2944 * q^60 - 3328 * q^64 + 448 * q^65 - 3200 * q^70 - 1184 * q^72 - 496 * q^74 + 368 * q^77 + 7680 * q^78 - 4984 * q^81 + 4480 * q^84 + 1024 * q^85 + 240 * q^86 + 3776 * q^88 - 3808 * q^92 - 2304 * q^93 - 3144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.41421	−	1.47363i	−0.853553	−	0.521005i
$2$	−2.41421	−	1.47363i	−0.853553	−	0.521005i
$3$	−4.79890			−0.923549			−0.461774	−	0.886997i	$-0.652787\pi$
$3$	−4.79890			−0.923549			−0.461774	+	0.886997i	$0.652787\pi$
$4$	3.65685	+	7.11529i	0.457107	+	0.889412i
$5$			17.0728i			1.52704i	0.645786	+	0.763518i	$0.276530\pi$
$5$			17.0728i			1.52704i	−0.645786	+	0.763518i	$0.723470\pi$
$6$	11.5856	+	7.07178i	0.788298	+	0.481174i
$7$	−18.3722	−	2.33686i	−0.992008	−	0.126178i
$7$	−18.3722	−	2.33686i	−0.992008	−	0.126178i
$8$	1.65685	−	22.5667i	0.0732233	−	0.997316i
$9$	−3.97056			−0.147058
$10$	25.1589	−	41.2174i	0.795594	−	1.30341i
$11$			41.4710i			1.13672i	0.822778	+	0.568362i	$0.192423\pi$
$11$			41.4710i			1.13672i	−0.822778	+	0.568362i	$0.807577\pi$
$12$	−17.5489	−	34.1456i	−0.422160	−	0.821415i
$13$		−	45.3599i		−	0.967737i	−0.875141	−	0.483868i	$-0.839231\pi$
$13$		−	45.3599i		−	0.967737i	0.875141	−	0.483868i	$-0.160769\pi$
$14$	40.9109	+	32.7155i	0.780992	+	0.624541i
$15$		−	81.9306i		−	1.41029i
$16$	−37.2548	+	52.0392i	−0.582107	+	0.813112i
$17$			28.2871i			0.403567i	0.979430	+	0.201783i	$0.0646737\pi$
$17$			28.2871i			0.403567i	−0.979430	+	0.201783i	$0.935326\pi$
$18$	9.58579	+	5.85112i	0.125522	+	0.0766179i
$19$	41.5434			0.501616			0.250808	−	0.968037i	$-0.419304\pi$
$19$	41.5434			0.501616			0.250808	+	0.968037i	$0.419304\pi$
$20$	−121.478	+	62.4327i	−1.35816	+	0.698019i
$21$	88.1665	+	11.2143i	0.916167	+	0.116532i
$22$	61.1127	−	100.120i	0.592240	−	0.970255i
$23$			93.9291i			0.851546i	0.904830	+	0.425773i	$0.139998\pi$
$23$			93.9291i			0.851546i	−0.904830	+	0.425773i	$0.860002\pi$
$24$	−7.95108	+	108.295i	−0.0676253	+	0.921069i
$25$	−166.480			−1.33184
$26$	−66.8435	+	109.509i	−0.504196	+	0.826015i
$27$	148.625			1.05936
$28$	−50.5572	−	139.269i	−0.341229	−	0.939980i
$29$	27.8234			0.178161			0.0890805	−	0.996024i	$-0.471607\pi$
$29$	27.8234			0.178161			0.0890805	+	0.996024i	$0.471607\pi$
$30$	−120.735	+	197.798i	−0.734770	+	1.20376i
$31$	−81.4400			−0.471841			−0.235920	−	0.971772i	$-0.575810\pi$
$31$	−81.4400			−0.471841			−0.235920	+	0.971772i	$0.575810\pi$
$32$	166.627	−	70.7340i	0.920495	−	0.390754i
$33$		−	199.015i		−	1.04982i
$34$	41.6846	−	68.2912i	0.210260	−	0.344466i
$35$	39.8967	−	313.665i	0.192679	−	1.51483i
$36$	−14.5198	−	28.2517i	−0.0672212	−	0.130795i
$37$	94.8040			0.421235			0.210617	−	0.977569i	$-0.432453\pi$
$37$	94.8040			0.421235			0.210617	+	0.977569i	$0.432453\pi$
$38$	−100.295	−	61.2194i	−0.428156	−	0.261345i
$39$			217.678i			0.893752i
$40$	385.276	+	28.2871i	1.52294	+	0.111815i
$41$			227.302i			0.865820i	0.901437	+	0.432910i	$0.142513\pi$
$41$			227.302i			0.865820i	−0.901437	+	0.432910i	$0.857487\pi$
$42$	−196.327	−	156.998i	−0.721284	−	0.576794i
$43$			171.988i			0.609951i	0.952360	+	0.304976i	$0.0986483\pi$
$43$			171.988i			0.609951i	−0.952360	+	0.304976i	$0.901352\pi$
$44$	−295.078	+	151.653i	−1.01102	+	0.519604i
$45$		−	67.7886i		−	0.224563i
$46$	138.416	−	226.765i	0.443660	−	0.726840i
$47$	−286.005			−0.887619			−0.443809	−	0.896121i	$-0.646373\pi$
$47$	−286.005			−0.887619			−0.443809	+	0.896121i	$0.646373\pi$
$48$	178.782	−	249.731i	0.537604	−	0.750949i
$49$	332.078	+	85.8665i	0.968158	+	0.250340i
$50$	401.919	+	245.330i	1.13680	+	0.693897i
$51$		−	135.747i		−	0.372714i
$52$	322.749	−	165.875i	0.860717	−	0.442359i
$53$	−575.921			−1.49262			−0.746310	−	0.665599i	$-0.768176\pi$
$53$	−575.921			−1.49262			−0.746310	+	0.665599i	$0.768176\pi$
$54$	−358.812	−	219.017i	−0.904224	−	0.551934i
$55$	−708.025			−1.73582
$56$	−83.1752	+	410.728i	−0.198478	+	0.980105i
$57$	−199.362			−0.463267
$58$	−67.1716	−	41.0012i	−0.152070	−	0.0928229i
$59$	411.999			0.909114			0.454557	−	0.890718i	$-0.349798\pi$
$59$	411.999			0.909114			0.454557	+	0.890718i	$0.349798\pi$
$60$	582.960	−	299.608i	1.25433	−	0.644654i
$61$			778.987i			1.63507i	0.575881	+	0.817534i	$0.304659\pi$
$61$			778.987i			1.63507i	−0.575881	+	0.817534i	$0.695341\pi$
$62$	196.614	+	120.012i	0.402741	+	0.245832i
$63$	72.9481	+	9.27863i	0.145883	+	0.0185555i
$64$	−506.510	−	74.7794i	−0.989277	−	0.146053i
$65$	774.420			1.47777
$66$	−293.274	+	480.465i	−0.546962	+	0.896078i
$67$			198.773i			0.362448i	0.983442	+	0.181224i	$0.0580060\pi$
$67$			198.773i			0.362448i	−0.983442	+	0.181224i	$0.941994\pi$
$68$	−201.271	+	103.442i	−0.358937	+	0.184473i
$69$		−	450.756i		−	0.786444i
$70$	−558.544	+	698.463i	−0.953698	+	1.19260i
$71$			197.762i			0.330564i	0.986246	+	0.165282i	$0.0528534\pi$
$71$			197.762i			0.330564i	−0.986246	+	0.165282i	$0.947147\pi$
$72$	−6.57864	+	89.6024i	−0.0107681	+	0.146663i
$73$		−	255.589i		−	0.409787i	−0.978784	−	0.204894i	$-0.934315\pi$
$73$		−	255.589i		−	0.409787i	0.978784	−	0.204894i	$-0.0656848\pi$
$74$	−228.877	−	139.706i	−0.359546	−	0.219466i
$75$	798.922			1.23002
$76$	151.918	+	295.593i	0.229292	+	0.446143i
$77$	96.9117	−	761.915i	0.143430	−	1.12764i
$78$	320.775	−	525.520i	0.465650	−	0.762865i
$79$		−	1178.49i		−	1.67836i	−0.543856	−	0.839179i	$-0.683036\pi$
$79$		−	1178.49i		−	1.67836i	0.543856	−	0.839179i	$-0.316964\pi$
$80$	−888.454	−	636.044i	−1.24165	−	0.888899i
$81$	−606.029			−0.831316
$82$	334.958	−	548.756i	0.451097	−	0.739024i
$83$	938.514			1.24115			0.620574	−	0.784148i	$-0.286900\pi$
$83$	938.514			1.24115			0.620574	+	0.784148i	$0.286900\pi$
$84$	242.619	+	668.340i	0.315141	+	0.868117i
$85$	−482.940			−0.616261
$86$	253.446	−	415.215i	0.317788	−	0.520626i
$87$	−133.522			−0.164540
$88$	935.862	+	68.7114i	1.13367	+	0.0832347i
$89$		−	1166.81i		−	1.38968i	−0.719165	−	0.694840i	$-0.755475\pi$
$89$		−	1166.81i		−	1.38968i	0.719165	−	0.694840i	$-0.244525\pi$
$90$	−99.8950	+	163.656i	−0.116998	+	0.191676i
$91$	−106.000	+	833.363i	−0.122107	+	0.960002i
$92$	−668.333	+	343.485i	−0.757375	+	0.389248i
$93$	390.823			0.435768
$94$	690.476	+	421.464i	0.757630	+	0.462454i
$95$			709.261i			0.765986i
$96$	−799.628	+	339.446i	−0.850122	+	0.360880i
$97$			656.635i			0.687332i	0.939092	+	0.343666i	$0.111669\pi$
$97$			656.635i			0.687332i	−0.939092	+	0.343666i	$0.888331\pi$
$98$	−675.173	−	696.659i	−0.695946	−	0.718094i
$99$		−	164.663i		−	0.167164i
$100$	−608.794	−	1184.56i	−0.608794	−	1.18456i
$101$			999.426i			0.984620i	0.870420	+	0.492310i	$0.163847\pi$
$101$			999.426i			0.984620i	−0.870420	+	0.492310i	$0.836153\pi$
$102$	−200.040	+	327.722i	−0.194186	+	0.318131i
$103$	−958.932			−0.917344			−0.458672	−	0.888606i	$-0.651675\pi$
$103$	−958.932			−0.917344			−0.458672	+	0.888606i	$0.651675\pi$
$104$	−1023.62	−	75.1548i	−0.965139	−	0.0708609i
$105$	−191.460	+	1505.25i	−0.177948	+	1.39902i
$106$	1390.40	+	848.692i	1.27403	+	0.777663i
$107$		−	685.893i		−	0.619699i	−0.950786	−	0.309849i	$-0.899721\pi$
$107$		−	685.893i		−	0.619699i	0.950786	−	0.309849i	$-0.100279\pi$
$108$	543.499	+	1057.51i	0.484242	+	0.942211i
$109$	1127.80			0.991045			0.495523	−	0.868595i	$-0.334977\pi$
$109$	1127.80			0.991045			0.495523	+	0.868595i	$0.334977\pi$
$110$	1709.32	+	1043.36i	1.48162	+	0.904372i
$111$	−454.955			−0.389031
$112$	806.063	−	869.017i	0.680052	−	0.733164i
$113$	−10.0488			−0.00836557			−0.00418278	−	0.999991i	$-0.501331\pi$
$113$	−10.0488			−0.00836557			−0.00418278	+	0.999991i	$0.501331\pi$
$114$	481.304	+	293.786i	0.395423	+	0.241364i
$115$	−1603.63			−1.30034
$116$	101.746	+	197.972i	0.0814386	+	0.158459i
$117$			180.104i			0.142313i
$118$	−994.654	−	607.132i	−0.775977	−	0.473653i
$119$	66.1029	−	519.698i	0.0509214	−	0.400341i
$120$	−1848.90	−	135.747i	−1.40651	−	0.103266i
$121$	−388.842			−0.292143
$122$	1147.94	−	1880.64i	0.851879	−	1.39562i
$123$		−	1090.80i		−	0.799627i
$124$	−297.814	−	579.470i	−0.215682	−	0.419661i
$125$		−	708.183i		−	0.506735i
$126$	−162.439	−	129.899i	−0.114851	−	0.0918437i
$127$			1347.06i			0.941198i	0.882347	+	0.470599i	$0.155962\pi$
$127$			1347.06i			0.941198i	−0.882347	+	0.470599i	$0.844038\pi$
$128$	1112.63	+	926.939i	0.768306	+	0.640083i
$129$		−	825.352i		−	0.563320i
$130$	−1869.62	−	1141.21i	−1.26136	−	0.769926i
$131$	−480.265			−0.320313			−0.160156	−	0.987092i	$-0.551200\pi$
$131$	−480.265			−0.320313			−0.160156	+	0.987092i	$0.551200\pi$
$132$	1416.05	−	727.769i	0.933723	−	0.479880i
$133$	−763.245	−	97.0809i	−0.497607	−	0.0632931i
$134$	292.918	−	479.881i	0.188838	−	0.309369i
$135$			2537.44i			1.61769i
$136$	638.346	+	46.8676i	0.402483	+	0.0295505i
$137$	−247.803			−0.154535			−0.0772674	−	0.997010i	$-0.524620\pi$
$137$	−247.803			−0.154535			−0.0772674	+	0.997010i	$0.524620\pi$
$138$	−664.246	+	1088.22i	−0.409742	+	0.671272i
$139$	1842.35			1.12422			0.562109	−	0.827063i	$-0.309990\pi$
$139$	1842.35			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$140$	2377.72	−	863.152i	1.43538	−	0.521069i
$141$	1372.51			0.819759
$142$	291.427	−	477.440i	0.172226	−	0.282154i
$143$	1881.12			1.10005
$144$	147.923	−	206.625i	0.0856034	−	0.119575i
$145$			475.023i			0.272059i
$146$	−376.643	+	617.047i	−0.213501	+	0.349775i
$147$	−1593.61	−	412.065i	−0.894141	−	0.231201i
$148$	346.685	+	674.559i	0.192549	+	0.374651i
$149$	−2200.82			−1.21006			−0.605028	−	0.796204i	$-0.706838\pi$
$149$	−2200.82			−1.21006			−0.605028	+	0.796204i	$0.706838\pi$
$150$	−1928.77	−	1177.31i	−1.04989	−	0.640847i
$151$		−	3208.96i		−	1.72941i	−0.502279	−	0.864706i	$-0.667505\pi$
$151$		−	3208.96i		−	1.72941i	0.502279	−	0.864706i	$-0.332495\pi$
$152$	68.8313	−	937.496i	0.0367300	−	0.500269i
$153$		−	112.316i		−	0.0593477i
$154$	−1356.74	+	1696.61i	−0.709931	+	0.887773i
$155$		−	1390.41i		−	0.720518i
$156$	−1548.84	+	796.016i	−0.794914	+	0.408540i
$157$		−	636.547i		−	0.323579i	−0.986825	−	0.161790i	$-0.948273\pi$
$157$		−	636.547i		−	0.323579i	0.986825	−	0.161790i	$-0.0517266\pi$
$158$	−1736.65	+	2845.12i	−0.874433	+	1.43257i
$159$	2763.79			1.37851
$160$	1207.63	+	2844.80i	0.596696	+	1.40563i
$161$	219.499	−	1725.69i	0.107447	−	0.844740i
$162$	1463.08	+	893.061i	0.709573	+	0.433120i
$163$			2460.38i			1.18228i	0.806568	+	0.591141i	$0.201323\pi$
$163$			2460.38i			1.18228i	−0.806568	+	0.591141i	$0.798677\pi$
$164$	−1617.32	+	831.211i	−0.770071	+	0.395772i
$165$	3397.74			1.60311
$166$	−2265.77	−	1383.02i	−1.05939	−	0.646645i
$167$	−2133.16			−0.988435			−0.494218	−	0.869338i	$-0.664545\pi$
$167$	−2133.16			−0.988435			−0.494218	+	0.869338i	$0.664545\pi$
$168$	399.149	−	1971.04i	0.183304	−	0.905175i
$169$	139.478			0.0634855
$170$	1165.92	+	711.673i	0.526012	+	0.321076i
$171$	−164.951			−0.0737666
$172$	−1223.74	+	628.935i	−0.542498	+	0.278813i
$173$			1462.73i			0.642829i	0.946939	+	0.321415i	$0.104158\pi$
$173$			1462.73i			0.642829i	−0.946939	+	0.321415i	$0.895842\pi$
$174$	322.350	+	196.761i	0.140444	+	0.0857264i
$175$	3058.61	+	389.040i	1.32120	+	0.168050i
$176$	−2158.12	−	1544.99i	−0.924285	−	0.661695i
$177$	−1977.14			−0.839611
$178$	−1719.44	+	2816.92i	−0.724030	+	1.18617i
$179$			3038.97i			1.26896i	0.772941	+	0.634478i	$0.218785\pi$
$179$			3038.97i			1.26896i	−0.772941	+	0.634478i	$0.781215\pi$
$180$	482.336	−	247.893i	0.199729	−	0.102649i
$181$		−	384.978i		−	0.158095i	−0.996871	−	0.0790475i	$-0.974812\pi$
$181$		−	384.978i		−	0.158095i	0.996871	−	0.0790475i	$-0.0251879\pi$
$182$	1483.97	−	1855.71i	0.604392	−	0.755795i
$183$		−	3738.28i		−	1.51006i
$184$	2119.67	+	155.627i	0.849260	+	0.0623530i
$185$			1618.57i			0.643241i
$186$	−943.529	−	575.926i	−0.371951	−	0.227037i
$187$	−1173.09			−0.458744
$188$	−1045.88	−	2035.01i	−0.405736	−	0.789459i
$189$	−2730.57	−	347.314i	−1.05090	−	0.133669i
$190$	1045.19	−	1712.31i	0.399083	−	0.653810i
$191$			505.605i			0.191541i	0.995403	+	0.0957704i	$0.0305314\pi$
$191$			505.605i			0.191541i	−0.995403	+	0.0957704i	$0.969469\pi$
$192$	2430.69	+	358.859i	0.913645	+	0.134887i
$193$	1921.91			0.716798			0.358399	−	0.933569i	$-0.383323\pi$
$193$	1921.91			0.716798			0.358399	+	0.933569i	$0.383323\pi$
$194$	967.634	−	1585.26i	0.358103	−	0.586674i
$195$	−3716.37			−1.36479
$196$	603.396	+	2676.84i	0.219896	+	0.975523i
$197$	1603.63			0.579968			0.289984	−	0.957031i	$-0.406350\pi$
$197$	1603.63			0.579968			0.289984	+	0.957031i	$0.406350\pi$
$198$	−242.652	+	397.532i	−0.0870935	+	0.142684i
$199$	2558.75			0.911484			0.455742	−	0.890112i	$-0.349374\pi$
$199$	2558.75			0.911484			0.455742	+	0.890112i	$0.349374\pi$
$200$	−275.833	+	3756.91i	−0.0975219	+	1.32827i
$201$		−	953.894i		−	0.334739i
$202$	1472.78	−	2412.83i	0.512992	−	0.840426i
$203$	−511.178	−	65.0192i	−0.176737	−	0.0224801i
$204$	965.881	−	496.407i	0.331496	−	0.170370i
$205$	−3880.68			−1.32214
$206$	2315.07	+	1413.11i	0.783002	+	0.477941i
$207$		−	372.951i		−	0.125227i
$208$	2360.49	+	1689.88i	0.786879	+	0.563326i
$209$			1722.84i			0.570199i
$210$	2680.40	−	3351.85i	0.880786	−	1.10143i
$211$			381.389i			0.124436i	0.998063	+	0.0622178i	$0.0198173\pi$
$211$			381.389i			0.124436i	−0.998063	+	0.0622178i	$0.980183\pi$
$212$	−2106.06	−	4097.85i	−0.682286	−	1.32755i
$213$		−	949.040i		−	0.305292i
$214$	−1010.75	+	1655.89i	−0.322866	+	0.528946i
$215$	−2936.31			−0.931418
$216$	246.249	−	3353.96i	0.0775701	−	1.05652i
$217$	1496.24	+	190.314i	0.468070	+	0.0595361i
$218$	−2722.76	−	1661.96i	−0.845910	−	0.516340i
$219$			1226.55i			0.378458i
$220$	−2589.15	−	5037.81i	−0.793455	−	1.54386i
$221$	1283.10			0.390546
$222$	1098.36	+	670.434i	0.332059	+	0.202687i
$223$	2943.88			0.884023			0.442011	−	0.897009i	$-0.354265\pi$
$223$	2943.88			0.884023			0.442011	+	0.897009i	$0.354265\pi$
$224$	−3226.61	+	910.158i	−0.962443	+	0.271484i
$225$	661.020			0.195858
$226$	24.2599	+	14.8081i	0.00714046	+	0.00435851i
$227$	−5786.10			−1.69179			−0.845897	−	0.533346i	$-0.820934\pi$
$227$	−5786.10			−1.69179			−0.845897	+	0.533346i	$0.820934\pi$
$228$	−729.040	−	1418.52i	−0.211762	−	0.412035i
$229$		−	4303.85i		−	1.24195i	−0.783830	−	0.620975i	$-0.786737\pi$
$229$		−	4303.85i		−	1.24195i	0.783830	−	0.620975i	$-0.213263\pi$
$230$	3871.51	+	2363.15i	1.10991	+	0.677486i
$231$	−465.069	+	3656.35i	−0.132465	+	1.04143i
$232$	46.0993	−	627.881i	0.0130455	−	0.177683i
$233$	5133.92			1.44349			0.721747	−	0.692157i	$-0.243340\pi$
$233$	5133.92			1.44349			0.721747	+	0.692157i	$0.243340\pi$
$234$	265.406	−	434.811i	0.0741460	−	0.121472i
$235$		−	4882.90i		−	1.35543i
$236$	1506.62	+	2931.49i	0.415562	+	0.808576i
$237$			5655.44i			1.55004i
$238$	−925.427	+	1157.25i	−0.252044	+	0.315182i
$239$		−	468.448i		−	0.126784i	−0.997989	−	0.0633920i	$-0.979808\pi$
$239$		−	468.448i		−	0.126784i	0.997989	−	0.0633920i	$-0.0201919\pi$
$240$	4263.60	+	3052.31i	1.14673	+	0.820941i
$241$		−	389.501i		−	0.104108i	−0.998644	−	0.0520539i	$-0.983423\pi$
$241$		−	389.501i		−	0.104108i	0.998644	−	0.0520539i	$-0.0165768\pi$
$242$	938.747	+	573.007i	0.249359	+	0.152208i
$243$	−1104.59			−0.291603
$244$	−5542.72	+	2848.64i	−1.45425	+	0.747400i
$245$	−1465.98	+	5669.50i	−0.382278	+	1.47841i
$246$	−1607.43	+	2633.42i	−0.416610	+	0.682525i
$247$		−	1884.40i		−	0.485432i
$248$	−134.934	+	1837.83i	−0.0345497	+	0.470574i
$249$	−4503.83			−1.14626
$250$	−1043.60	+	1709.71i	−0.264012	+	0.432525i
$251$	4690.59			1.17955			0.589776	−	0.807567i	$-0.299216\pi$
$251$	4690.59			1.17955			0.589776	+	0.807567i	$0.299216\pi$
$252$	200.740	+	552.978i	0.0501804	+	0.138232i
$253$	−3895.33			−0.967974
$254$	1985.06	−	3252.09i	0.490369	−	0.803363i
$255$	2317.58			0.569147
$256$	−1320.15	−	3877.42i	−0.322303	−	0.946636i
$257$			5223.27i			1.26778i	0.773425	+	0.633888i	$0.218542\pi$
$257$			5223.27i			1.26778i	−0.773425	+	0.633888i	$0.781458\pi$
$258$	−1216.26	+	1992.58i	−0.293493	+	0.480823i
$259$	−1741.76	−	221.543i	−0.417868	−	0.0531507i
$260$	2831.94	+	5510.23i	0.675499	+	1.31435i
$261$	−110.474			−0.0262000
$262$	1159.46	+	707.731i	0.273404	+	0.166885i
$263$			4704.80i			1.10308i	0.834148	+	0.551541i	$0.185960\pi$
$263$			4704.80i			1.10308i	−0.834148	+	0.551541i	$0.814040\pi$
$264$	−4491.11	−	329.739i	−1.04700	−	0.0768713i
$265$		−	9832.58i		−	2.27928i
$266$	1699.57	+	1359.11i	0.391758	+	0.313280i
$267$			5599.40i			1.28344i
$268$	−1414.33	+	726.885i	−0.322366	+	0.165678i
$269$		−	3444.53i		−	0.780730i	−0.920660	−	0.390365i	$-0.872349\pi$
$269$		−	3444.53i		−	0.780730i	0.920660	−	0.390365i	$-0.127651\pi$
$270$	3739.23	−	6125.92i	0.842824	−	1.38078i
$271$	5251.78			1.17721			0.588603	−	0.808422i	$-0.299678\pi$
$271$	5251.78			1.17721			0.588603	+	0.808422i	$0.299678\pi$
$272$	−1472.04	−	1053.83i	−0.328145	−	0.234919i
$273$	508.681	−	3999.23i	0.112772	−	0.886609i
$274$	598.250	+	365.169i	0.131904	+	0.0805134i
$275$		−	6904.10i		−	1.51394i
$276$	3207.26	−	1648.35i	0.699473	−	0.359489i
$277$	6003.19			1.30215			0.651077	−	0.759012i	$-0.274317\pi$
$277$	6003.19			1.30215			0.651077	+	0.759012i	$0.274317\pi$
$278$	−4447.84	−	2714.94i	−0.959581	−	0.585724i
$279$	323.363			0.0693879
$280$	−7012.28	−	1420.03i	−1.49666	−	0.303083i
$281$	−1870.63			−0.397125			−0.198563	−	0.980088i	$-0.563627\pi$
$281$	−1870.63			−0.397125			−0.198563	+	0.980088i	$0.563627\pi$
$282$	−3313.53	−	2022.56i	−0.699708	−	0.427099i
$283$	3963.42			0.832512			0.416256	−	0.909248i	$-0.363342\pi$
$283$	3963.42			0.832512			0.416256	+	0.909248i	$0.363342\pi$
$284$	−1407.14	+	723.187i	−0.294007	+	0.151103i
$285$		−	3403.67i		−	0.707425i
$286$	−4541.43	−	2772.07i	−0.938952	−	0.573132i
$287$	531.172	−	4176.05i	0.109248	−	0.858900i
$288$	−661.605	+	280.854i	−0.135366	+	0.0574635i
$289$	4112.84			0.837134
$290$	700.006	−	1146.81i	0.141744	−	0.232216i
$291$		−	3151.12i		−	0.634784i
$292$	1818.59	−	934.653i	0.364470	−	0.187317i
$293$		−	4654.67i		−	0.928084i	−0.885813	−	0.464042i	$-0.846399\pi$
$293$		−	4654.67i		−	0.928084i	0.885813	−	0.464042i	$-0.153601\pi$
$294$	3240.09	+	3343.20i	0.642740	+	0.663195i
$295$			7033.97i			1.38825i
$296$	157.076	−	2139.41i	0.0308442	−	0.420104i
$297$			6163.61i			1.20420i
$298$	5313.26	+	3243.19i	1.03285	+	0.630446i
$299$	4260.62			0.824073
$300$	2921.54	+	5684.56i	0.562251	+	1.09399i
$301$	401.911	−	3159.80i	0.0769626	−	0.605076i
$302$	−4728.80	+	7747.10i	−0.901033	+	1.47614i
$303$		−	4796.14i		−	0.909344i
$304$	−1547.69	+	2161.88i	−0.291994	+	0.407870i
$305$	−13299.5			−2.49681
$306$	−165.511	+	271.154i	−0.0309205	+	0.0506564i
$307$	−2828.15			−0.525769			−0.262884	−	0.964827i	$-0.584674\pi$
$307$	−2828.15			−0.525769			−0.262884	+	0.964827i	$0.584674\pi$
$308$	5775.64	−	2096.66i	1.06850	−	0.387883i
$309$	4601.82			0.847212
$310$	−2048.94	+	3356.74i	−0.375394	+	0.615001i
$311$	−6559.10			−1.19592			−0.597962	−	0.801524i	$-0.704023\pi$
$311$	−6559.10			−1.19592			−0.597962	+	0.801524i	$0.704023\pi$
$312$	4912.26	+	360.660i	0.891353	+	0.0654435i
$313$			6217.17i			1.12273i	0.827568	+	0.561366i	$0.189724\pi$
$313$			6217.17i			1.12273i	−0.827568	+	0.561366i	$0.810276\pi$
$314$	−938.031	+	1536.76i	−0.168587	+	0.276192i
$315$	−158.412	+	1245.43i	−0.0283350	+	0.222768i
$316$	8385.29	−	4309.56i	1.49275	−	0.767189i
$317$	3254.84			0.576687			0.288344	−	0.957527i	$-0.406895\pi$
$317$	3254.84			0.576687			0.288344	+	0.957527i	$0.406895\pi$
$318$	−6672.37	−	4072.79i	−1.17663	−	0.718209i
$319$			1153.86i			0.202520i
$320$	1276.69	−	8647.53i	0.223029	−	1.51066i
$321$			3291.53i			0.572322i
$322$	−3072.93	+	3842.72i	−0.531826	+	0.665051i
$323$			1175.14i			0.202436i
$324$	−2216.16	−	4312.08i	−0.380000	−	0.739382i
$325$			7551.53i			1.28887i
$326$	3625.68	−	5939.89i	0.615976	−	1.00914i
$327$	−5412.21			−0.915279
$328$	5129.45	+	376.607i	0.863496	+	0.0633982i
$329$	5254.55	+	668.352i	0.880524	+	0.111998i
$330$	−8202.88	−	5007.00i	−1.36834	−	0.835231i
$331$			4385.31i			0.728212i	0.931357	+	0.364106i	$0.118625\pi$
$331$			4385.31i			0.728212i	−0.931357	+	0.364106i	$0.881375\pi$
$332$	3432.01	+	6677.80i	0.567337	+	1.10389i
$333$	−376.425			−0.0619459
$334$	5149.90	+	3143.48i	0.843682	+	0.514980i
$335$	−3393.62			−0.553472
$336$	−3868.21	+	4170.33i	−0.628061	+	0.677113i
$337$	−9569.41			−1.54682			−0.773411	−	0.633905i	$-0.781451\pi$
$337$	−9569.41			−1.54682			−0.773411	+	0.633905i	$0.781451\pi$
$338$	−336.729	−	205.538i	−0.0541883	−	0.0330763i
$339$	48.2231			0.00772601
$340$	−1766.04	−	3436.26i	−0.281697	−	0.548110i
$341$		−	3377.40i		−	0.536353i
$342$	398.226	+	243.075i	0.0629637	+	0.0384328i
$343$	−5900.36	−	2353.58i	−0.928833	−	0.370500i
$344$	3881.19	+	284.959i	0.608314	+	0.0446626i
$345$	7695.67			1.20093
$346$	2155.52	−	3531.35i	0.334917	−	0.548689i
$347$			10409.6i			1.61043i	0.592985	+	0.805214i	$0.297950\pi$
$347$			10409.6i			1.61043i	−0.592985	+	0.805214i	$0.702050\pi$
$348$	−488.269	−	950.045i	−0.0752125	−	0.146344i
$349$			12612.4i			1.93446i	0.253895	+	0.967232i	$0.418288\pi$
$349$			12612.4i			1.93446i	−0.253895	+	0.967232i	$0.581712\pi$
$350$	−6810.85	−	5446.48i	−1.04016	−	0.831790i
$351$		−	6741.60i		−	1.02519i
$352$	2933.41	+	6910.20i	0.444180	+	1.04635i
$353$		−	10352.1i		−	1.56087i	−0.625236	−	0.780435i	$-0.714997\pi$
$353$		−	10352.1i		−	1.56087i	0.625236	−	0.780435i	$-0.285003\pi$
$354$	4773.24	+	2913.57i	0.716653	+	0.437442i
$355$	−3376.35			−0.504783
$356$	8302.18	−	4266.85i	1.23600	−	0.635232i
$357$	−317.221	+	2493.98i	−0.0470284	+	0.369735i
$358$	4478.30	−	7336.72i	0.661133	−	1.08312i
$359$		−	3721.83i		−	0.547161i	−0.961849	−	0.273580i	$-0.911792\pi$
$359$		−	3721.83i		−	0.547161i	0.961849	−	0.273580i	$-0.0882080\pi$
$360$	−1529.76	−	112.316i	−0.223960	−	0.0164432i
$361$	−5133.15			−0.748381
$362$	−567.313	+	929.419i	−0.0823683	+	0.134942i
$363$	1866.01			0.269808
$364$	−6317.25	+	2293.27i	−0.909653	+	0.330220i
$365$	4363.62			0.625760
$366$	−5508.83	+	9025.01i	−0.786752	+	1.28892i
$367$	−4676.11			−0.665097			−0.332549	−	0.943086i	$-0.607909\pi$
$367$	−4676.11			−0.665097			−0.332549	+	0.943086i	$0.607909\pi$
$368$	−4887.99	−	3499.31i	−0.692403	−	0.495691i
$369$		−	902.518i		−	0.127326i
$370$	2385.17	−	3907.57i	0.335132	−	0.549041i
$371$	10581.0	+	1345.84i	1.48069	+	0.188336i
$372$	1429.18	+	2780.82i	0.199192	+	0.387577i
$373$	−6601.94			−0.916448			−0.458224	−	0.888837i	$-0.651514\pi$
$373$	−6601.94			−0.916448			−0.458224	+	0.888837i	$0.651514\pi$
$374$	2832.10	+	1728.70i	0.391563	+	0.239008i
$375$			3398.50i			0.467994i
$376$	−473.868	+	6454.18i	−0.0649944	+	0.885236i
$377$		−	1262.07i		−	0.172413i
$378$	6080.36	+	4862.32i	0.827354	+	0.661616i
$379$		−	12756.2i		−	1.72887i	−0.502747	−	0.864434i	$-0.667677\pi$
$379$		−	12756.2i		−	1.72887i	0.502747	−	0.864434i	$-0.332323\pi$
$380$	−5046.60	+	2593.67i	−0.681277	+	0.350137i
$381$		−	6464.40i		−	0.869242i
$382$	745.072	−	1220.64i	0.0997938	−	0.163490i
$383$	−1573.51			−0.209929			−0.104965	−	0.994476i	$-0.533473\pi$
$383$	−1573.51			−0.209929			−0.104965	+	0.994476i	$0.533473\pi$
$384$	−5339.38	−	4448.29i	−0.709568	−	0.591148i
$385$	13008.0	+	1654.55i	1.72195	+	0.219023i
$386$	−4639.89	−	2832.17i	−0.611825	−	0.373455i
$387$		−	682.889i		−	0.0896981i
$388$	−4672.15	+	2401.22i	−0.611321	+	0.314184i
$389$	−4022.95			−0.524349			−0.262174	−	0.965021i	$-0.584440\pi$
$389$	−4022.95			−0.524349			−0.262174	+	0.965021i	$0.584440\pi$
$390$	8972.10	+	5476.53i	1.16492	+	0.711064i
$391$	−2656.98			−0.343656
$392$	2487.93	−	7351.63i	0.320559	−	0.947228i
$393$	2304.74			0.295824
$394$	−3871.50	−	2363.15i	−0.495034	−	0.302167i
$395$	20120.1			2.56291
$396$	1171.63	−	602.149i	0.148678	−	0.0764119i
$397$		−	3987.32i		−	0.504075i	−0.967717	−	0.252038i	$-0.918899\pi$
$397$		−	3987.32i		−	0.504075i	0.967717	−	0.252038i	$-0.0811007\pi$
$398$	−6177.38	−	3770.65i	−0.778000	−	0.474888i
$399$	3662.73	+	465.881i	0.459564	+	0.0584542i
$400$	6202.19	−	8663.50i	0.775274	−	1.08294i
$401$	4624.46			0.575897			0.287948	−	0.957646i	$-0.407027\pi$
$401$	4624.46			0.575897			0.287948	+	0.957646i	$0.407027\pi$
$402$	−1405.68	+	2302.90i	−0.174401	+	0.285717i
$403$			3694.11i			0.456618i
$404$	−7111.21	+	3654.76i	−0.875733	+	0.450076i
$405$		−	10346.6i		−	1.26945i
$406$	1138.28	+	910.255i	0.139142	+	0.111269i
$407$			3931.62i			0.478828i
$408$	−3063.36	−	224.913i	−0.371713	−	0.0272913i
$409$		−	633.029i		−	0.0765312i	−0.999268	−	0.0382656i	$-0.987817\pi$
$409$		−	633.029i		−	0.0765312i	0.999268	−	0.0382656i	$-0.0121833\pi$
$410$	9368.80	+	5718.67i	1.12852	+	0.688842i
$411$	1189.18			0.142720
$412$	−3506.68	−	6823.09i	−0.419324	−	0.815896i
$413$	−7569.34	−	962.782i	−0.901848	−	0.114710i
$414$	−549.591	+	900.384i	−0.0652437	+	0.106888i
$415$			16023.1i			1.89528i
$416$	−3208.49	−	7558.21i	−0.378147	−	0.890797i
$417$	−8841.27			−1.03827
$418$	2538.83	−	4159.31i	0.297077	−	0.486695i
$419$	−3197.39			−0.372799			−0.186399	−	0.982474i	$-0.559682\pi$
$419$	−3197.39			−0.372799			−0.186399	+	0.982474i	$0.559682\pi$
$420$	−11410.4	+	4142.18i	−1.32565	+	0.481233i
$421$	−5489.09			−0.635444			−0.317722	−	0.948184i	$-0.602918\pi$
$421$	−5489.09			−0.635444			−0.317722	+	0.948184i	$0.602918\pi$
$422$	562.025	−	920.755i	0.0648316	−	0.106212i
$423$	1135.60			0.130531
$424$	−954.217	+	12996.6i	−0.109295	+	1.48861i
$425$		−	4709.25i		−	0.537487i
$426$	−1398.53	+	2291.19i	−0.159059	+	0.260583i
$427$	1820.38	−	14311.7i	0.206310	−	1.62200i
$428$	4880.33	−	2508.21i	0.551167	−	0.283268i
$429$	−9027.31			−1.01595
$430$	7088.89	+	4327.03i	0.795015	+	0.485274i
$431$		−	4178.34i		−	0.466968i	−0.972361	−	0.233484i	$-0.924987\pi$
$431$		−	4178.34i		−	0.466968i	0.972361	−	0.233484i	$-0.0750127\pi$
$432$	−5536.99	+	7734.30i	−0.616663	+	0.861382i
$433$			9306.18i			1.03286i	0.856331	+	0.516428i	$0.172739\pi$
$433$			9306.18i			1.03286i	−0.856331	+	0.516428i	$0.827261\pi$
$434$	−3331.78	−	2664.35i	−0.368504	−	0.294684i
$435$		−	2279.59i		−	0.251259i
$436$	4124.21	+	8024.65i	0.453014	+	0.881448i
$437$			3902.13i			0.427149i
$438$	1807.47	−	2961.15i	0.197179	−	0.323034i
$439$	−2931.42			−0.318700			−0.159350	−	0.987222i	$-0.550940\pi$
$439$	−2931.42			−0.318700			−0.159350	+	0.987222i	$0.550940\pi$
$440$	−1173.09	+	15977.8i	−0.127103	+	1.73116i
$441$	−1318.54	−	340.938i	−0.142375	−	0.0368144i
$442$	−3097.68	−	1890.81i	−0.333352	−	0.203477i
$443$		−	5884.29i		−	0.631086i	−0.948911	−	0.315543i	$-0.897813\pi$
$443$		−	5884.29i		−	0.631086i	0.948911	−	0.315543i	$-0.102187\pi$
$444$	−1663.70	−	3237.14i	−0.177829	−	0.346009i
$445$	19920.7			2.12209
$446$	−7107.17	−	4338.18i	−0.754561	−	0.460581i
$447$	10561.5			1.11755
$448$	9130.97	+	2557.50i	0.962941	+	0.269711i
$449$	12856.4			1.35129			0.675646	−	0.737227i	$-0.263865\pi$
$449$	12856.4			1.35129			0.675646	+	0.737227i	$0.263865\pi$
$450$	−1595.84	−	974.096i	−0.167175	−	0.102043i
$451$	−9426.44			−0.984199
$452$	−36.7469	−	71.5000i	−0.00382396	−	0.00744043i
$453$			15399.5i			1.59720i
$454$	13968.9	+	8526.55i	1.44404	+	0.881434i
$455$	−14227.8	−	1809.71i	−1.46596	−	0.186463i
$456$	−330.315	+	4498.95i	−0.0339219	+	0.462023i
$457$	1831.12			0.187431			0.0937157	−	0.995599i	$-0.470126\pi$
$457$	1831.12			0.187431			0.0937157	+	0.995599i	$0.470126\pi$
$458$	−6342.27	+	10390.4i	−0.647063	+	1.06007i
$459$			4204.16i			0.427524i
$460$	−5864.25	−	11410.3i	−0.594395	−	1.15654i
$461$		−	609.925i		−	0.0616205i	−0.999525	−	0.0308102i	$-0.990191\pi$
$461$		−	609.925i		−	0.0616205i	0.999525	−	0.0308102i	$-0.00980875\pi$
$462$	6510.87	−	8141.88i	0.655656	−	0.819901i
$463$			7896.96i			0.792663i	0.918107	+	0.396332i	$0.129717\pi$
$463$			7896.96i			0.792663i	−0.918107	+	0.396332i	$0.870283\pi$
$464$	−1036.56	+	1447.91i	−0.103709	+	0.144865i
$465$			6672.43i			0.665434i
$466$	−12394.4	−	7565.47i	−1.23210	−	0.752068i
$467$	14588.0			1.44551			0.722755	−	0.691104i	$-0.242875\pi$
$467$	14588.0			1.44551			0.722755	+	0.691104i	$0.242875\pi$
$468$	−1281.50	+	658.616i	−0.126575	+	0.0650524i
$469$	464.505	−	3651.91i	0.0457331	−	0.359551i
$470$	−7195.57	+	11788.4i	−0.706184	+	1.15693i
$471$			3054.72i			0.298841i
$472$	682.622	−	9297.45i	0.0665683	−	0.906673i
$473$	−7132.50			−0.693347
$474$	8334.01	−	13653.5i	0.807582	−	1.32305i
$475$	−6916.15			−0.668073
$476$	3939.53	−	1430.12i	0.379345	−	0.137709i
$477$	2286.73			0.219501
$478$	−690.317	+	1130.93i	−0.0660552	+	0.108217i
$479$	−18352.1			−1.75058			−0.875289	−	0.483599i	$-0.839329\pi$
$479$	−18352.1			−1.75058			−0.875289	+	0.483599i	$0.839329\pi$
$480$	−5795.28	−	13651.9i	−0.551078	−	1.29817i
$481$		−	4300.30i		−	0.407644i
$482$	−573.979	+	940.339i	−0.0542407	+	0.0888615i
$483$	−1053.35	+	8281.40i	−0.0992323	+	0.780159i
$484$	−1421.94	−	2766.72i	−0.133540	−	0.259835i
$485$	−11210.6			−1.04958
$486$	2666.72	+	1627.75i	0.248899	+	0.151927i
$487$		−	14673.5i		−	1.36534i	−0.730729	−	0.682668i	$-0.760820\pi$
$487$		−	14673.5i		−	1.36534i	0.730729	−	0.682668i	$-0.239180\pi$
$488$	17579.2	+	1290.67i	1.63068	+	0.119725i
$489$		−	11807.1i		−	1.09190i
$490$	11893.9	−	11527.1i	1.09656	−	1.06274i
$491$			3216.95i			0.295680i	0.989011	+	0.147840i	$0.0472321\pi$
$491$			3216.95i			0.295680i	−0.989011	+	0.147840i	$0.952768\pi$
$492$	7761.37	−	3988.90i	0.711198	−	0.365515i
$493$			787.043i			0.0718999i
$494$	−2776.91	+	4549.35i	−0.252913	+	0.414342i
$495$	2811.26			0.255266
$496$	3034.03	−	4238.07i	0.274662	−	0.383659i
$497$	462.141	−	3633.33i	0.0417100	−	0.327922i
$498$	10873.2	+	6636.97i	0.978394	+	0.597208i
$499$			8857.13i			0.794589i	0.917691	+	0.397294i	$0.130051\pi$
$499$			8857.13i			0.794589i	−0.917691	+	0.397294i	$0.869949\pi$
$500$	5038.93	−	2589.72i	0.450696	−	0.231632i
$501$	10236.8			0.912868
$502$	−11324.1	−	6912.18i	−1.00681	−	0.614553i
$503$	5037.58			0.446550			0.223275	−	0.974756i	$-0.428325\pi$
$503$	5037.58			0.446550			0.223275	+	0.974756i	$0.428325\pi$
$504$	330.252	−	1630.82i	0.0291877	−	0.144132i
$505$	−17063.0			−1.50355
$506$	9404.16	+	5740.26i	0.826217	+	0.504319i
$507$	−669.339			−0.0586319
$508$	−9584.72	+	4926.00i	−0.837113	+	0.430228i
$509$			10689.6i			0.930860i	0.885085	+	0.465430i	$0.154100\pi$
$509$			10689.6i			0.930860i	−0.885085	+	0.465430i	$0.845900\pi$
$510$	−5595.14	−	3415.25i	−0.485798	−	0.296529i
$511$	−597.275	+	4695.75i	−0.0517063	+	0.406512i
$512$	−2526.73	+	11306.3i	−0.218100	+	0.975927i
$513$	6174.37			0.531394
$514$	7697.14	−	12610.1i	0.660518	−	1.08212i
$515$		−	16371.7i		−	1.40082i
$516$	5872.63	−	3018.19i	0.501023	−	0.257497i
$517$		−	11860.9i		−	1.00898i
$518$	3878.51	+	3101.56i	0.328981	+	0.263079i
$519$		−	7019.50i		−	0.593684i
$520$	1283.10	−	17476.1i	0.108207	−	1.47380i
$521$			13501.9i			1.13537i	0.823246	+	0.567685i	$0.192161\pi$
$521$			13501.9i			1.13537i	−0.823246	+	0.567685i	$0.807839\pi$
$522$	266.709	+	162.798i	0.0223631	+	0.0136503i
$523$	−13819.9			−1.15546			−0.577728	−	0.816229i	$-0.696061\pi$
$523$	−13819.9			−1.15546			−0.577728	+	0.816229i	$0.696061\pi$
$524$	−1756.26	−	3417.23i	−0.146417	−	0.284890i
$525$	−14678.0	−	1866.97i	−1.22019	−	0.155202i
$526$	6933.12	−	11358.4i	0.574711	−	0.941539i
$527$		−	2303.70i		−	0.190419i
$528$	10356.6	+	7414.27i	0.853622	+	0.611108i
$529$	3344.33			0.274869
$530$	−14489.5	+	23737.9i	−1.18752	+	1.94549i
$531$	−1635.87			−0.133692
$532$	−2100.32	−	5785.72i	−0.171166	−	0.471509i
$533$	10310.4			0.837886
$534$	8251.41	−	13518.1i	0.668677	−	1.09548i
$535$	11710.1			0.946303
$536$	4485.65	+	329.339i	0.361475	+	0.0265397i
$537$		−	14583.7i		−	1.17194i
$538$	−5075.94	+	8315.82i	−0.406765	+	0.666395i
$539$	−3560.97	+	13771.6i	−0.284567	+	1.10053i
$540$	−18054.6	+	9279.04i	−1.43879	+	0.739456i
$541$	−1383.46			−0.109944			−0.0549720	−	0.998488i	$-0.517507\pi$
$541$	−1383.46			−0.109944			−0.0549720	+	0.998488i	$0.517507\pi$
$542$	−12678.9	−	7739.16i	−1.00481	−	0.613331i
$543$			1847.47i			0.146008i
$544$	2000.86	+	4713.41i	0.157695	+	0.371481i
$545$			19254.7i			1.51336i
$546$	−7121.43	+	8905.38i	−0.558185	+	0.698013i
$547$			19306.3i			1.50910i	0.656243	+	0.754550i	$0.272145\pi$
$547$			19306.3i			1.50910i	−0.656243	+	0.754550i	$0.727855\pi$
$548$	−906.180	−	1763.19i	−0.0706389	−	0.137445i
$549$		−	3093.02i		−	0.240450i
$550$	−10174.1	+	16668.0i	−0.788769	+	1.29223i
$551$	1155.88			0.0893684
$552$	−10172.1	−	746.837i	−0.784333	−	0.0575861i
$553$	−2753.96	+	21651.5i	−0.211772	+	1.66494i
$554$	−14493.0	−	8846.46i	−1.11146	−	0.678429i
$555$		−	7767.35i		−	0.594064i
$556$	6737.22	+	13108.9i	0.513888	+	0.999893i
$557$	25149.0			1.91310			0.956551	−	0.291564i	$-0.0941755\pi$
$557$	25149.0			1.91310			0.956551	+	0.291564i	$0.0941755\pi$
$558$	−780.667	−	476.516i	−0.0592263	−	0.0361515i
$559$	7801.36			0.590272
$560$	14836.5	+	13761.7i	1.11957	+	1.03846i
$561$	5629.56			0.423673
$562$	4516.09	+	2756.60i	0.338968	+	0.206904i
$563$	11127.2			0.832956			0.416478	−	0.909146i	$-0.363264\pi$
$563$	11127.2			0.832956			0.416478	+	0.909146i	$0.363264\pi$
$564$	5019.06	+	9765.80i	0.374717	+	0.729103i
$565$		−	171.561i		−	0.0127745i
$566$	−9568.54	−	5840.60i	−0.710593	−	0.433743i
$567$	11134.1	+	1416.20i	0.824672	+	0.104894i
$568$	4462.83	+	327.663i	0.329677	+	0.0242050i
$569$	−2444.10			−0.180074			−0.0900368	−	0.995938i	$-0.528698\pi$
$569$	−2444.10			−0.180074			−0.0900368	+	0.995938i	$0.528698\pi$
$570$	−5015.74	+	8217.20i	−0.368572	+	0.603825i
$571$		−	7744.79i		−	0.567617i	−0.958881	−	0.283809i	$-0.908402\pi$
$571$		−	7744.79i		−	0.567617i	0.958881	−	0.283809i	$-0.0915980\pi$
$572$	6878.98	+	13384.7i	0.502840	+	0.978398i
$573$		−	2426.35i		−	0.176897i
$574$	−7436.30	+	9299.13i	−0.540741	+	0.676199i
$575$		−	15637.3i		−	1.13413i
$576$	2011.13	+	296.916i	0.145481	+	0.0214783i
$577$		−	27283.3i		−	1.96849i	−0.176805	−	0.984246i	$-0.556576\pi$
$577$		−	27283.3i		−	1.96849i	0.176805	−	0.984246i	$-0.443424\pi$
$578$	−9929.27	−	6060.78i	−0.714538	−	0.436151i
$579$	−9223.04			−0.661997
$580$	−3379.93	+	1737.09i	−0.241972	+	0.124360i
$581$	−17242.6	−	2193.17i	−1.23123	−	0.156606i
$582$	−4643.58	+	7607.49i	−0.330726	+	0.541822i
$583$		−	23884.0i		−	1.69670i
$584$	−5767.80	−	423.474i	−0.408687	−	0.0300060i
$585$	−3074.89			−0.217318
$586$	−6859.24	+	11237.4i	−0.483537	+	0.792169i
$587$	−3068.80			−0.215780			−0.107890	−	0.994163i	$-0.534409\pi$
$587$	−3068.80			−0.215780			−0.107890	+	0.994163i	$0.534409\pi$
$588$	−2895.64	−	12845.9i	−0.203085	−	0.900943i
$589$	−3383.29			−0.236683
$590$	10365.4	−	16981.5i	0.723286	−	1.18495i
$591$	−7695.65			−0.535629
$592$	−3531.91	+	4933.53i	−0.245204	+	0.342511i
$593$		−	21823.7i		−	1.51129i	−0.654984	−	0.755643i	$-0.727325\pi$
$593$		−	21823.7i		−	1.51129i	0.654984	−	0.755643i	$-0.272675\pi$
$594$	9082.85	−	14880.3i	0.627397	−	1.02785i
$595$	8872.69	+	1128.56i	0.611336	+	0.0777589i
$596$	−8048.09	−	15659.5i	−0.553125	−	1.07624i
$597$	−12279.2			−0.841800
$598$	−10286.0	−	6278.55i	−0.703390	−	0.429346i
$599$			19352.6i			1.32007i	0.751233	+	0.660037i	$0.229459\pi$
$599$			19352.6i			1.32007i	−0.751233	+	0.660037i	$0.770541\pi$
$600$	1323.70	−	18029.0i	0.0900662	−	1.22672i
$601$			8218.83i			0.557826i	0.960316	+	0.278913i	$0.0899740\pi$
$601$			8218.83i			0.557826i	−0.960316	+	0.278913i	$0.910026\pi$
$602$	−5626.66	+	7036.17i	−0.380940	+	0.476367i
$603$		−	789.242i		−	0.0533009i
$604$	22832.7	−	11734.7i	1.53816	−	0.790526i
$605$		−	6638.62i		−	0.446113i
$606$	−7067.72	+	11578.9i	−0.473773	+	0.776174i
$607$	23793.3			1.59101			0.795503	−	0.605950i	$-0.207207\pi$
$607$	23793.3			1.59101			0.795503	+	0.605950i	$0.207207\pi$
$608$	6922.27	−	2938.53i	0.461735	−	0.196008i
$609$	2453.09	+	312.021i	0.163225	+	0.0207614i
$610$	32107.8	+	19598.5i	2.13116	+	1.30085i
$611$			12973.2i			0.858981i
$612$	799.160	−	410.723i	0.0527845	−	0.0271282i
$613$	19490.1			1.28417			0.642087	−	0.766632i	$-0.278069\pi$
$613$	19490.1			1.28417			0.642087	+	0.766632i	$0.278069\pi$
$614$	6827.76	+	4167.63i	0.448772	+	0.273928i
$615$	18623.0			1.22106
$616$	−17033.3	−	3449.36i	−1.11411	−	0.225614i
$617$	−12532.4			−0.817724			−0.408862	−	0.912596i	$-0.634074\pi$
$617$	−12532.4			−0.817724			−0.408862	+	0.912596i	$0.634074\pi$
$618$	−11109.8	−	6781.36i	−0.723140	−	0.441402i
$619$	−3577.14			−0.232274			−0.116137	−	0.993233i	$-0.537051\pi$
$619$	−3577.14			−0.232274			−0.116137	+	0.993233i	$0.537051\pi$
$620$	9893.17	−	5084.52i	0.640837	−	0.329354i
$621$			13960.2i			0.902097i
$622$	15835.1	+	9665.66i	1.02078	+	0.623083i
$623$	−2726.66	+	21436.9i	−0.175347	+	1.37857i
$624$	−11327.8	−	8109.55i	−0.726721	−	0.520259i
$625$	−8719.36			−0.558039
$626$	9161.78	−	15009.6i	0.584949	−	0.958312i
$627$		−	8267.76i		−	0.526607i
$628$	4529.22	−	2327.76i	0.287795	−	0.147910i
$629$			2681.73i			0.169996i
$630$	2217.74	−	2773.29i	0.140249	−	0.175382i
$631$			2950.67i			0.186156i	0.995659	+	0.0930779i	$0.0296706\pi$
$631$			2950.67i			0.186156i	−0.995659	+	0.0930779i	$0.970329\pi$
$632$	−26594.6	−	1952.58i	−1.67385	−	0.122895i
$633$		−	1830.25i		−	0.114922i
$634$	−7857.87	−	4796.41i	−0.492233	−	0.300457i
$635$	−22998.1			−1.43724
$636$	10106.8	+	19665.2i	0.630125	+	1.22606i
$637$	3894.90	−	15063.0i	0.242263	−	0.936922i
$638$	1700.36	−	2785.67i	0.105514	−	0.172862i
$639$		−	785.227i		−	0.0486120i
$640$	−15825.4	+	18995.6i	−0.977430	+	1.17323i
$641$	−2474.02			−0.152446			−0.0762229	−	0.997091i	$-0.524286\pi$
$641$	−2474.02			−0.152446			−0.0762229	+	0.997091i	$0.524286\pi$
$642$	4850.48	−	7946.46i	0.298183	−	0.488507i
$643$	−20855.1			−1.27907			−0.639537	−	0.768760i	$-0.720874\pi$
$643$	−20855.1			−1.27907			−0.639537	+	0.768760i	$0.720874\pi$
$644$	13081.4	−	4748.79i	0.800437	−	0.290572i
$645$	14091.1			0.860210
$646$	1731.72	−	2837.05i	0.105470	−	0.172790i
$647$	24529.0			1.49047			0.745237	−	0.666800i	$-0.232337\pi$
$647$	24529.0			1.49047			0.745237	+	0.666800i	$0.232337\pi$
$648$	−1004.10	+	13676.1i	−0.0608717	+	0.829084i
$649$			17086.0i			1.03341i
$650$	11128.1	−	18231.0i	0.671509	−	1.10012i
$651$	−7180.28	−	913.296i	−0.432285	−	0.0549845i
$652$	−17506.4	+	8997.26i	−1.05154	+	0.540430i
$653$	8840.01			0.529765			0.264882	−	0.964281i	$-0.414667\pi$
$653$	8840.01			0.529765			0.264882	+	0.964281i	$0.414667\pi$
$654$	13066.2	+	7975.58i	0.781239	+	0.476865i
$655$		−	8199.47i		−	0.489129i
$656$	−11828.6	−	8468.10i	−0.704009	−	0.504000i
$657$			1014.83i			0.0602624i
$658$	−11700.7	−	9356.78i	−0.693223	−	0.554354i
$659$		−	26347.9i		−	1.55746i	−0.627356	−	0.778732i	$-0.715863\pi$
$659$		−	26347.9i		−	1.55746i	0.627356	−	0.778732i	$-0.284137\pi$
$660$	12425.0	+	24175.9i	0.732795	+	1.42583i
$661$			22699.6i			1.33572i	0.744286	+	0.667861i	$0.232790\pi$
$661$			22699.6i			1.33572i	−0.744286	+	0.667861i	$0.767210\pi$
$662$	6462.30	−	10587.1i	0.379403	−	0.621568i
$663$	−6157.48			−0.360689
$664$	1554.98	−	21179.1i	0.0908809	−	1.23782i
$665$	1657.44	−	13030.7i	0.0966509	−	0.759864i
$666$	908.771	+	554.710i	0.0528741	+	0.0322741i
$667$			2613.42i			0.151712i
$668$	−7800.65	−	15178.0i	−0.451820	−	0.879126i
$669$	−14127.4			−0.816438
$670$	8192.92	+	5000.92i	0.472418	+	0.288362i
$671$	−32305.4			−1.85862
$672$	15484.2	−	4367.76i	0.888863	−	0.250729i
$673$	−5208.40			−0.298319			−0.149160	−	0.988813i	$-0.547657\pi$
$673$	−5208.40			−0.298319			−0.149160	+	0.988813i	$0.547657\pi$
$674$	23102.6	+	14101.7i	1.32029	+	0.805902i
$675$	−24743.1			−1.41090
$676$	510.049	+	992.424i	0.0290196	+	0.0564647i
$677$		−	3144.71i		−	0.178524i	−0.996008	−	0.0892622i	$-0.971549\pi$
$677$		−	3144.71i		−	0.178524i	0.996008	−	0.0892622i	$-0.0284509\pi$
$678$	−116.421	−	71.0627i	−0.00659456	−	0.00402529i
$679$	1534.46	−	12063.9i	0.0867264	−	0.681838i
$680$	−800.162	+	10898.4i	−0.0451247	+	0.614607i
$681$	27766.9			1.56245
$682$	−4977.02	+	8153.76i	−0.279443	+	0.457806i
$683$		−	11895.3i		−	0.666415i	−0.942854	−	0.333208i	$-0.891869\pi$
$683$		−	11895.3i		−	0.666415i	0.942854	−	0.333208i	$-0.108131\pi$
$684$	−603.200	−	1173.67i	−0.0337192	−	0.0656089i
$685$		−	4230.69i		−	0.235980i
$686$	10776.4	+	14377.0i	0.599776	+	0.800168i
$687$			20653.8i			1.14700i
$688$	−8950.11	−	6407.38i	−0.495959	−	0.355057i
$689$			26123.7i			1.44446i
$690$	−18579.0	−	11340.5i	−1.02506	−	0.625691i
$691$	24606.5			1.35467			0.677333	−	0.735676i	$-0.263136\pi$
$691$	24606.5			1.35467			0.677333	+	0.735676i	$0.263136\pi$
$692$	−10407.8	+	5349.00i	−0.571740	+	0.293842i
$693$	−384.794	+	3025.23i	−0.0210925	+	0.165828i
$694$	15339.9	−	25131.1i	0.839042	−	1.37459i
$695$			31454.1i			1.71672i
$696$	−221.226	+	3013.14i	−0.0120482	+	0.164099i
$697$	−6429.73			−0.349416
$698$	18586.0	−	30449.1i	1.00787	−	1.65117i
$699$	−24637.1			−1.33314
$700$	8416.77	+	23185.6i	0.454463	+	1.25191i
$701$	−1627.77			−0.0877033			−0.0438516	−	0.999038i	$-0.513963\pi$
$701$	−1627.77			−0.0877033			−0.0438516	+	0.999038i	$0.513963\pi$
$702$	−9934.60	+	16275.7i	−0.534127	+	0.875050i
$703$	3938.48			0.211298
$704$	3101.17	−	21005.5i	0.166023	−	1.12454i
$705$			23432.5i			1.25180i
$706$	−15255.1	+	24992.2i	−0.813222	+	1.33229i
$707$	2335.51	−	18361.7i	0.124238	−	0.976750i
$708$	−7230.12	−	14067.9i	−0.383792	−	0.746760i
$709$	−27634.3			−1.46379			−0.731896	−	0.681416i	$-0.761364\pi$
$709$	−27634.3			−1.46379			−0.731896	+	0.681416i	$0.761364\pi$
$710$	8151.23	+	4975.48i	0.430860	+	0.262995i
$711$			4679.26i			0.246816i
$712$	−26331.0	−	1933.23i	−1.38595	−	0.101757i
$713$		−	7649.59i		−	0.401794i
$714$	4441.03	−	5553.53i	0.232775	−	0.291086i
$715$			32116.0i			1.67982i
$716$	−21623.1	+	11113.1i	−1.12862	+	0.580048i
$717$			2248.04i			0.117091i
$718$	−5484.59	+	8985.30i	−0.285074	+	0.467031i
$719$	−5943.23			−0.308269			−0.154134	−	0.988050i	$-0.549259\pi$
$719$	−5943.23			−0.308269			−0.154134	+	0.988050i	$0.549259\pi$
$720$	3527.66	+	2525.45i	0.182595	+	0.130720i
$721$	17617.7	+	2240.89i	0.910012	+	0.115749i
$722$	12392.5	+	7564.34i	0.638783	+	0.389911i
$723$			1869.18i			0.0961486i
$724$	2739.23	−	1407.81i	0.140612	−	0.0722663i
$725$	−4632.04			−0.237282
$726$	−4504.95	−	2749.80i	−0.230295	−	0.140571i
$727$	20574.9			1.04963			0.524816	−	0.851216i	$-0.324134\pi$
$727$	20574.9			1.04963			0.524816	+	0.851216i	$0.324134\pi$
$728$	18630.6	+	3772.82i	0.948484	+	0.192074i
$729$	21663.6			1.10063
$730$	−10534.7	−	6430.35i	−0.534120	−	0.326024i
$731$	−4865.04			−0.246156
$732$	26599.0	−	13670.4i	1.34307	−	0.690261i
$733$		−	16226.5i		−	0.817655i	−0.912612	−	0.408828i	$-0.865938\pi$
$733$		−	16226.5i		−	0.817655i	0.912612	−	0.408828i	$-0.134062\pi$
$734$	11289.1	+	6890.83i	0.567696	+	0.346519i
$735$	7035.10	−	27207.4i	0.353052	−	1.36539i
$736$	6643.98	+	15651.2i	0.332745	+	0.783844i
$737$	−8243.33			−0.412004
$738$	−1329.97	+	2178.87i	−0.0663374	+	0.108679i
$739$			27285.1i			1.35818i	0.734054	+	0.679092i	$0.237626\pi$
$739$			27285.1i			1.35818i	−0.734054	+	0.679092i	$0.762374\pi$
$740$	−11516.6	+	5918.87i	−0.572106	+	0.294030i
$741$			9043.07i			0.448320i
$742$	−23561.4	−	18841.5i	−1.16572	−	0.932202i
$743$		−	15043.5i		−	0.742791i	−0.928475	−	0.371396i	$-0.878879\pi$
$743$		−	15043.5i		−	0.742791i	0.928475	−	0.371396i	$-0.121121\pi$
$744$	647.536	−	8819.56i	0.0319084	−	0.434598i
$745$		−	37574.2i		−	1.84780i
$746$	15938.5	+	9728.78i	0.782238	+	0.477475i
$747$	−3726.43			−0.182521
$748$	−4289.84	−	8346.92i	−0.209695	−	0.408013i
$749$	−1602.83	+	12601.4i	−0.0781926	+	0.614746i
$750$	5008.12	−	8204.71i	0.243828	−	0.399458i
$751$		−	17941.4i		−	0.871757i	−0.900006	−	0.435879i	$-0.856438\pi$
$751$		−	17941.4i		−	0.871757i	0.900006	−	0.435879i	$-0.143562\pi$
$752$	10655.1	−	14883.5i	0.516689	−	0.721734i
$753$	−22509.7			−1.08937
$754$	−1859.81	+	3046.90i	−0.0898281	+	0.147164i
$755$	54785.8			2.64088
$756$	−7514.04	−	20698.9i	−0.361486	−	0.995781i
$757$	−12961.3			−0.622305			−0.311152	−	0.950360i	$-0.600715\pi$
$757$	−12961.3			−0.622305			−0.311152	+	0.950360i	$0.600715\pi$
$758$	−18797.8	+	30796.1i	−0.900749	+	1.47568i
$759$	18693.3			0.893971
$760$	16005.7	+	1175.14i	0.763930	+	0.0560880i
$761$		−	8866.11i		−	0.422334i	−0.977450	−	0.211167i	$-0.932274\pi$
$761$		−	8866.11i		−	0.422334i	0.977450	−	0.211167i	$-0.0677264\pi$
$762$	−9526.11	+	15606.4i	−0.452880	+	0.741945i
$763$	−20720.3	−	2635.51i	−0.983125	−	0.125048i
$764$	−3597.53	+	1848.92i	−0.170359	+	0.0875546i
$765$	1917.54			0.0906261
$766$	3798.80	+	2318.77i	0.179186	+	0.109374i
$767$		−	18688.2i		−	0.879783i
$768$	6335.29	+	18607.4i	0.297663	+	0.874265i
$769$		−	31664.2i		−	1.48484i	−0.669937	−	0.742418i	$-0.733679\pi$
$769$		−	31664.2i		−	1.48484i	0.669937	−	0.742418i	$-0.266321\pi$
$770$	−28965.9	−	23163.4i	−1.35566	−	1.08409i
$771$		−	25065.9i		−	1.17085i
$772$	7028.14	+	13674.9i	0.327653	+	0.637528i
$773$		−	19253.1i		−	0.895842i	−0.894073	−	0.447921i	$-0.852165\pi$
$773$		−	19253.1i		−	0.895842i	0.894073	−	0.447921i	$-0.147835\pi$
$774$	−1006.32	+	1648.64i	−0.0467332	+	0.0765621i
$775$	13558.2			0.628417
$776$	14818.1	+	1087.95i	0.685487	+	0.0503287i
$777$	8358.54	+	1063.16i	0.385922	+	0.0490873i
$778$	9712.26	+	5928.32i	0.447559	+	0.273188i
$779$			9442.90i			0.434309i
$780$	−13590.2	−	26443.0i	−0.623856	−	1.21386i
$781$	−8201.39			−0.375760
$782$	6414.53	+	3915.40i	0.293329	+	0.179047i
$783$	4135.24			0.188737
$784$	−16839.9	+	14082.1i	−0.767126	+	0.641497i
$785$	10867.6			0.494118
$786$	−5564.15	−	3396.33i	−0.252502	−	0.154126i
$787$	1284.72			0.0581897			0.0290949	−	0.999577i	$-0.490738\pi$
$787$	1284.72			0.0581897			0.0290949	+	0.999577i	$0.490738\pi$
$788$	5864.23	+	11410.3i	0.265108	+	0.515831i
$789$		−	22577.9i		−	1.01875i
$790$	−48574.2	−	29649.5i	−2.18758	−	1.33529i
$791$	184.618	+	23.4825i	0.00829871	+	0.00105555i
$792$	−3715.90	−	272.823i	−0.166716	−	0.0122403i
$793$	35334.8			1.58231
$794$	−5875.82	+	9626.25i	−0.262626	+	0.430255i
$795$			47185.6i			2.10503i
$796$	9356.99	+	18206.3i	0.416645	+	0.810684i
$797$		−	2593.21i		−	0.115253i	−0.998338	−	0.0576263i	$-0.981647\pi$
$797$		−	2593.21i		−	0.115253i	0.998338	−	0.0576263i	$-0.0183532\pi$
$798$	−8156.09	−	6522.24i	−0.361808	−	0.289329i
$799$		−	8090.25i		−	0.358213i
$800$	−27740.2	+	11775.8i	−1.22595	+	0.520423i
$801$			4632.89i			0.204363i
$802$	−11164.4	−	6814.72i	−0.491559	−	0.300045i
$803$	10599.5			0.465815
$804$	6787.23	−	3488.25i	0.297721	−	0.153011i
$805$	29462.3	+	3747.46i	1.28995	+	0.164075i
$806$	5443.74	−	8918.38i	0.237900	−	0.389747i
$807$			16529.9i			0.721042i
$808$	22553.7	+	1655.90i	0.981977	+	0.0720971i
$809$	−11424.8			−0.496508			−0.248254	−	0.968695i	$-0.579857\pi$
$809$	−11424.8			−0.496508			−0.248254	+	0.968695i	$0.579857\pi$
$810$	−15247.0	+	24978.9i	−0.661390	+	1.08354i
$811$	32094.4			1.38962			0.694812	−	0.719191i	$-0.255487\pi$
$811$	32094.4			1.38962			0.694812	+	0.719191i	$0.255487\pi$
$812$	−1406.67	−	3874.95i	−0.0607937	−	0.167468i
$813$	−25202.8			−1.08721
$814$	5793.73	−	9491.76i	0.249472	−	0.408705i
$815$	−42005.6			−1.80539
$816$	7064.17	+	5057.24i	0.303058	+	0.216959i
$817$			7144.96i			0.305961i
$818$	−932.847	+	1528.27i	−0.0398732	+	0.0653234i
$819$	420.878	−	3308.92i	0.0179569	−	0.141176i
$820$	−14191.1	−	27612.2i	−0.604359	−	1.17593i
$821$	3861.07			0.164132			0.0820660	−	0.996627i	$-0.473848\pi$
$821$	3861.07			0.164132			0.0820660	+	0.996627i	$0.473848\pi$
$822$	−2870.94	−	1752.41i	−0.121819	−	0.0743581i
$823$			4840.43i			0.205014i	0.994732	+	0.102507i	$0.0326865\pi$
$823$			4840.43i			0.205014i	−0.994732	+	0.102507i	$0.967314\pi$
$824$	−1588.81	+	21639.9i	−0.0671709	+	0.914881i
$825$			33132.1i			1.39819i
$826$	16855.2	+	13478.7i	0.710010	+	0.567779i
$827$		−	831.897i		−	0.0349793i	−0.999847	−	0.0174897i	$-0.994433\pi$
$827$		−	831.897i		−	0.0349793i	0.999847	−	0.0174897i	$-0.00556741\pi$
$828$	2653.66	−	1363.83i	0.111378	−	0.0572419i
$829$			24696.3i			1.03467i	0.855784	+	0.517333i	$0.173075\pi$
$829$			24696.3i			1.03467i	−0.855784	+	0.517333i	$0.826925\pi$
$830$	23612.0	−	38683.1i	0.987450	−	1.61772i
$831$	−28808.7			−1.20260
$832$	−3391.99	+	22975.2i	−0.141341	+	0.957359i
$833$	−2428.92	+	9393.54i	−0.101029	+	0.390716i
$834$	21344.7	+	13028.7i	0.886219	+	0.540945i
$835$		−	36419.0i		−	1.50938i
$836$	−12258.5	+	6300.19i	−0.507142	+	0.260642i
$837$	−12104.0			−0.499851
$838$	7719.18	+	4711.75i	0.318203	+	0.194230i
$839$	−20023.0			−0.823922			−0.411961	−	0.911202i	$-0.635156\pi$
$839$	−20023.0			−0.823922			−0.411961	+	0.911202i	$0.635156\pi$
$840$	33651.2	+	6814.59i	1.38224	+	0.279912i
$841$	−23614.9			−0.968259
$842$	13251.8	+	8088.87i	0.542385	+	0.331070i
$843$	8976.94			0.366764
$844$	−2713.70	+	1394.68i	−0.110674	+	0.0568803i
$845$			2381.27i			0.0969447i
$846$	−2741.58	−	1673.45i	−0.111415	−	0.0680075i
$847$	7143.89	+	908.667i	0.289808	+	0.0368621i
$848$	21455.8	−	29970.5i	0.868864	−	1.21367i
$849$	−19020.0			−0.768865
$850$	−6939.67	+	11369.1i	−0.280034	+	0.458774i
$851$			8904.86i			0.358701i
$852$	6752.70	−	3470.50i	0.271530	−	0.139551i
$853$			25542.4i			1.02527i	0.858606	+	0.512636i	$0.171331\pi$
$853$			25542.4i			1.02527i	−0.858606	+	0.512636i	$0.828669\pi$
$854$	−25484.9	+	31869.0i	−1.02117	+	1.27697i
$855$		−	2816.17i		−	0.112644i
$856$	−15478.3	−	1136.42i	−0.618035	−	0.0453764i
$857$			25923.2i			1.03328i	0.856204	+	0.516638i	$0.172817\pi$
$857$			25923.2i			1.03328i	−0.856204	+	0.516638i	$0.827183\pi$
$858$	21793.8	+	13302.9i	0.867167	+	0.529315i
$859$	−25807.8			−1.02509			−0.512544	−	0.858661i	$-0.671297\pi$
$859$	−25807.8			−1.02509			−0.512544	+	0.858661i	$0.671297\pi$
$860$	−10737.7	−	20892.7i	−0.425758	−	0.828414i
$861$	−2549.04	+	20040.4i	−0.100896	+	0.793236i
$862$	−6157.30	+	10087.4i	−0.243293	+	0.398582i
$863$		−	1101.05i		−	0.0434302i	−0.999764	−	0.0217151i	$-0.993087\pi$
$863$		−	1101.05i		−	0.0434302i	0.999764	−	0.0217151i	$-0.00691267\pi$
$864$	24764.9	−	10512.8i	0.975139	−	0.413951i
$865$	−24972.9			−0.981624
$866$	13713.8	−	22467.1i	0.538123	−	0.881597i
$867$	−19737.1			−0.773134
$868$	4117.38	+	11342.1i	0.161006	+	0.443521i
$869$	48873.0			1.90783
$870$	−3359.26	+	5503.41i	−0.130907	+	0.214463i
$871$	9016.35			0.350755
$872$	1868.61	−	25450.8i	0.0725676	−	0.988385i
$873$		−	2607.21i		−	0.101078i
$874$	5750.28	−	9420.58i	0.222547	−	0.364595i
$875$	−1654.92	+	13010.9i	−0.0639390	+	0.502685i
$876$	−8727.25	+	4485.31i	−0.336605	+	0.172996i
$877$	43509.3			1.67526			0.837631	−	0.546237i	$-0.183940\pi$
$877$	43509.3			1.67526			0.837631	+	0.546237i	$0.183940\pi$
$878$	7077.08	+	4319.82i	0.272027	+	0.166044i
$879$			22337.3i			0.857131i
$880$	26377.4	−	36845.1i	1.01043	−	1.41142i
$881$		−	39281.4i		−	1.50219i	−0.660197	−	0.751093i	$-0.729527\pi$
$881$		−	39281.4i		−	1.50219i	0.660197	−	0.751093i	$-0.270473\pi$
$882$	2680.82	+	2766.13i	0.102344	+	0.105601i
$883$			4217.95i			0.160754i	0.996765	+	0.0803768i	$0.0256123\pi$
$883$			4217.95i			0.160754i	−0.996765	+	0.0803768i	$0.974388\pi$
$884$	4692.12	+	9129.65i	0.178521	+	0.347357i
$885$		−	33755.3i		−	1.28212i
$886$	−8671.25	+	14205.9i	−0.328799	+	0.538666i
$887$	−7206.54			−0.272798			−0.136399	−	0.990654i	$-0.543553\pi$
$887$	−7206.54			−0.272798			−0.136399	+	0.990654i	$0.543553\pi$
$888$	−753.794	+	10266.8i	−0.0284861	+	0.387987i
$889$	3147.88	−	24748.5i	0.118759	−	0.933675i
$890$	−48092.8	−	29355.6i	−1.81132	−	1.10562i
$891$		−	25132.6i		−	0.944977i
$892$	10765.4	+	20946.6i	0.404093	+	0.786260i
$893$	−11881.6			−0.445244
$894$	−25497.8	−	15563.7i	−0.953885	−	0.582247i
$895$	−51883.7			−1.93774
$896$	−18275.3	−	19630.0i	−0.681401	−	0.731911i
$897$	−20446.3			−0.761071
$898$	−31038.0	−	18945.5i	−1.15340	−	0.704030i
$899$	−2265.94			−0.0840636
$900$	2417.25	+	4703.35i	0.0895279	+	0.174198i
$901$		−	16291.1i		−	0.602372i
$902$	22757.4	+	13891.0i	0.840067	+	0.512773i
$903$	−1928.73	+	15163.6i	−0.0710787	+	0.558817i
$904$	−16.6494	+	226.767i	−0.000612554	+	0.00834311i
$905$	6572.65			0.241417
$906$	22693.0	−	37177.6i	0.832147	−	1.36329i
$907$		−	28116.4i		−	1.02932i	−0.857395	−	0.514659i	$-0.827919\pi$
$907$		−	28116.4i		−	1.02932i	0.857395	−	0.514659i	$-0.172081\pi$
$908$	−21158.9	−	41169.8i	−0.773331	−	1.50470i
$909$		−	3968.28i		−	0.144796i
$910$	31682.2	+	25335.5i	1.15413	+	0.922928i
$911$			36758.1i			1.33683i	0.743790	+	0.668414i	$0.233026\pi$
$911$			36758.1i			1.33683i	−0.743790	+	0.668414i	$0.766974\pi$
$912$	7427.22	−	10374.7i	0.269671	−	0.376688i
$913$			38921.1i			1.41084i
$914$	−4420.71	−	2698.38i	−0.159983	−	0.0976527i
$915$	63822.9			2.30592
$916$	30623.2	−	15738.6i	1.10460	−	0.567704i
$917$	8823.55	+	1122.31i	0.317753	+	0.0404165i
$918$	6195.36	−	10149.7i	0.222742	−	0.364915i
$919$		−	4560.64i		−	0.163702i	−0.996645	−	0.0818508i	$-0.973917\pi$
$919$		−	4560.64i		−	0.163702i	0.996645	−	0.0818508i	$-0.0260831\pi$
$920$	−2656.98	+	36188.6i	−0.0952154	+	1.29685i
$921$	13572.0			0.485573
$922$	−898.801	+	1472.49i	−0.0321046	+	0.0525964i
$923$	8970.47			0.319899
$924$	−27716.7	+	10061.6i	−0.986810	+	0.358229i
$925$	−15783.0			−0.561018
$926$	11637.2	−	19065.0i	0.412982	−	0.676580i
$927$	3807.50			0.134903
$928$	4636.14	−	1968.06i	0.163996	−	0.0696172i
$929$			47031.3i			1.66098i	0.557037	+	0.830488i	$0.311938\pi$
$929$			47031.3i			1.66098i	−0.557037	+	0.830488i	$0.688062\pi$
$930$	9832.67	−	16108.7i	0.346694	−	0.567983i
$931$	13795.6	+	3567.19i	0.485644	+	0.125574i
$932$	18774.0	+	36529.3i	0.659831	+	1.28386i
$933$	31476.5			1.10449
$934$	−35218.6	−	21497.3i	−1.23382	−	0.753119i
$935$		−	20028.0i		−	0.700520i
$936$	4064.36	+	298.407i	0.141931	+	0.0104207i
$937$			958.545i			0.0334197i	0.999860	+	0.0167099i	$0.00531916\pi$
$937$			958.545i			0.0334197i	−0.999860	+	0.0167099i	$0.994681\pi$
$938$	−6502.97	+	8131.99i	−0.226364	+	0.283069i
$939$		−	29835.6i		−	1.03690i
$940$	34743.3	−	17856.1i	1.20553	−	0.619575i
$941$		−	26664.8i		−	0.923748i	−0.886945	−	0.461874i	$-0.847177\pi$
$941$		−	26664.8i		−	0.923748i	0.886945	−	0.461874i	$-0.152823\pi$
$942$	4501.52	−	7374.75i	0.155698	−	0.255077i
$943$	−21350.3			−0.737286
$944$	−15349.0	+	21440.1i	−0.529201	+	0.739212i
$945$	5929.62	−	46618.4i	0.204117	−	1.60476i
$946$	17219.4	+	10510.6i	0.591808	+	0.361237i
$947$		−	3408.56i		−	0.116962i	−0.998289	−	0.0584812i	$-0.981374\pi$
$947$		−	3408.56i		−	0.116962i	0.998289	−	0.0584812i	$-0.0186258\pi$
$948$	−40240.2	+	20681.1i	−1.37863	+	0.708536i
$949$	−11593.5			−0.396566
$950$	16697.1	+	10191.8i	0.570236	+	0.348070i
$951$	−15619.6			−0.532599
$952$	−11618.3	−	2352.79i	−0.395538	−	0.0800990i
$953$	−30025.2			−1.02058			−0.510290	−	0.860002i	$-0.670462\pi$
$953$	−30025.2			−1.02058			−0.510290	+	0.860002i	$0.670462\pi$
$954$	−5520.65	−	3369.78i	−0.187356	−	0.114361i
$955$	−8632.09			−0.292490
$956$	3333.15	−	1713.05i	0.112763	−	0.0579539i
$957$		−	5537.27i		−	0.187037i
$958$	44305.8	+	27044.1i	1.49421	+	0.912061i
$959$	4552.70	+	579.080i	0.153300	+	0.0194989i
$960$	−6126.72	+	41498.6i	−0.205978	+	1.39517i
$961$	−23158.5			−0.777366
$962$	−6337.04	+	10381.9i	−0.212385	+	0.347946i
$963$			2723.38i			0.0911316i
$964$	2771.42	−	1424.35i	0.0925947	−	0.0475884i
$965$			32812.3i			1.09458i
$966$	14746.7	−	18440.8i	0.491167	−	0.614207i
$967$			21764.9i			0.723798i	0.932217	+	0.361899i	$0.117872\pi$
$967$			21764.9i			0.723798i	−0.932217	+	0.361899i	$0.882128\pi$
$968$	−644.254	+	8774.87i	−0.0213916	+	0.291358i
$969$		−	5639.39i		−	0.186959i
$970$	27064.8	+	16520.2i	0.895873	+	0.546837i
$971$	21876.6			0.723021			0.361511	−	0.932368i	$-0.382261\pi$
$971$	21876.6			0.723021			0.361511	+	0.932368i	$0.382261\pi$
$972$	−4039.33	−	7859.49i	−0.133294	−	0.259355i
$973$	−33848.2	−	4305.31i	−1.11523	−	0.141852i
$974$	−21623.2	+	35424.9i	−0.711347	+	1.16539i
$975$		−	36239.0i		−	1.19034i
$976$	−40537.9	−	29021.0i	−1.32949	−	0.951784i
$977$	33945.5			1.11158			0.555789	−	0.831323i	$-0.312416\pi$
$977$	33945.5			1.11158			0.555789	+	0.831323i	$0.312416\pi$
$978$	−17399.3	+	28504.9i	−0.568884	+	0.931991i
$979$	48388.7			1.57968
$980$	−45701.1	+	10301.7i	−1.48966	+	0.335790i
$981$	−4478.01			−0.145741
$982$	4740.58	−	7766.41i	0.154051	−	0.252379i
$983$	23428.5			0.760176			0.380088	−	0.924950i	$-0.375894\pi$
$983$	23428.5			0.760176			0.380088	+	0.924950i	$0.375894\pi$
$984$	−24615.7	−	1807.30i	−0.797481	−	0.0585514i
$985$			27378.4i			0.885633i
$986$	1159.81	−	1900.09i	0.0374602	−	0.0613704i
$987$	−25216.0	−	3207.35i	−0.813207	−	0.103436i
$988$	13408.1	−	6890.99i	0.431749	−	0.221894i
$989$	−16154.7			−0.519402
$990$	−6786.98	−	4142.74i	−0.217883	−	0.132995i
$991$			54992.8i			1.76277i	0.472399	+	0.881385i	$0.343388\pi$
$991$			54992.8i			1.76277i	−0.472399	+	0.881385i	$0.656612\pi$
$992$	−13570.1	+	5760.58i	−0.434327	+	0.184374i
$993$		−	21044.7i		−	0.672540i
$994$	−6469.88	+	8090.61i	−0.206451	+	0.258168i
$995$			43685.1i			1.39187i
$996$	−16469.9	−	32046.1i	−0.523963	−	1.01950i
$997$		−	1381.20i		−	0.0438747i	−0.999759	−	0.0219374i	$-0.993017\pi$
$997$		−	1381.20i		−	0.0438747i	0.999759	−	0.0219374i	$-0.00698344\pi$
$998$	13052.1	−	21383.0i	0.413985	−	0.678224i
$999$	14090.2			0.446241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.d.b.27.1	✓	8
3.2	odd	2		252.4.b.d.55.7		8
4.3	odd	2	inner	28.4.d.b.27.4	yes	8
7.2	even	3		196.4.f.c.31.4		16
7.3	odd	6		196.4.f.c.19.7		16
7.4	even	3		196.4.f.c.19.8		16
7.5	odd	6		196.4.f.c.31.3		16
7.6	odd	2	inner	28.4.d.b.27.2	yes	8
8.3	odd	2		448.4.f.d.447.3		8
8.5	even	2		448.4.f.d.447.5		8
12.11	even	2		252.4.b.d.55.5		8
21.20	even	2		252.4.b.d.55.8		8
28.3	even	6		196.4.f.c.19.4		16
28.11	odd	6		196.4.f.c.19.3		16
28.19	even	6		196.4.f.c.31.8		16
28.23	odd	6		196.4.f.c.31.7		16
28.27	even	2	inner	28.4.d.b.27.3	yes	8
56.13	odd	2		448.4.f.d.447.4		8
56.27	even	2		448.4.f.d.447.6		8
84.83	odd	2		252.4.b.d.55.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.1	✓	8	1.1	even	1	trivial
28.4.d.b.27.2	yes	8	7.6	odd	2	inner
28.4.d.b.27.3	yes	8	28.27	even	2	inner
28.4.d.b.27.4	yes	8	4.3	odd	2	inner
196.4.f.c.19.3		16	28.11	odd	6
196.4.f.c.19.4		16	28.3	even	6
196.4.f.c.19.7		16	7.3	odd	6
196.4.f.c.19.8		16	7.4	even	3
196.4.f.c.31.3		16	7.5	odd	6
196.4.f.c.31.4		16	7.2	even	3
196.4.f.c.31.7		16	28.23	odd	6
196.4.f.c.31.8		16	28.19	even	6
252.4.b.d.55.5		8	12.11	even	2
252.4.b.d.55.6		8	84.83	odd	2
252.4.b.d.55.7		8	3.2	odd	2
252.4.b.d.55.8		8	21.20	even	2
448.4.f.d.447.3		8	8.3	odd	2
448.4.f.d.447.4		8	56.13	odd	2
448.4.f.d.447.5		8	8.5	even	2
448.4.f.d.447.6		8	56.27	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41421 - 1.47363i) q^{2} -4.79890 q^{3} +(3.65685 + 7.11529i) q^{4} +17.0728i q^{5} +(11.5856 + 7.07178i) q^{6} +(-18.3722 - 2.33686i) q^{7} +(1.65685 - 22.5667i) q^{8} -3.97056 q^{9} +O(q^{10})\)	\(q+(-2.41421 - 1.47363i) q^{2} -4.79890 q^{3} +(3.65685 + 7.11529i) q^{4} +17.0728i q^{5} +(11.5856 + 7.07178i) q^{6} +(-18.3722 - 2.33686i) q^{7} +(1.65685 - 22.5667i) q^{8} -3.97056 q^{9} +(25.1589 - 41.2174i) q^{10} +41.4710i q^{11} +(-17.5489 - 34.1456i) q^{12} -45.3599i q^{13} +(40.9109 + 32.7155i) q^{14} -81.9306i q^{15} +(-37.2548 + 52.0392i) q^{16} +28.2871i q^{17} +(9.58579 + 5.85112i) q^{18} +41.5434 q^{19} +(-121.478 + 62.4327i) q^{20} +(88.1665 + 11.2143i) q^{21} +(61.1127 - 100.120i) q^{22} +93.9291i q^{23} +(-7.95108 + 108.295i) q^{24} -166.480 q^{25} +(-66.8435 + 109.509i) q^{26} +148.625 q^{27} +(-50.5572 - 139.269i) q^{28} +27.8234 q^{29} +(-120.735 + 197.798i) q^{30} -81.4400 q^{31} +(166.627 - 70.7340i) q^{32} -199.015i q^{33} +(41.6846 - 68.2912i) q^{34} +(39.8967 - 313.665i) q^{35} +(-14.5198 - 28.2517i) q^{36} +94.8040 q^{37} +(-100.295 - 61.2194i) q^{38} +217.678i q^{39} +(385.276 + 28.2871i) q^{40} +227.302i q^{41} +(-196.327 - 156.998i) q^{42} +171.988i q^{43} +(-295.078 + 151.653i) q^{44} -67.7886i q^{45} +(138.416 - 226.765i) q^{46} -286.005 q^{47} +(178.782 - 249.731i) q^{48} +(332.078 + 85.8665i) q^{49} +(401.919 + 245.330i) q^{50} -135.747i q^{51} +(322.749 - 165.875i) q^{52} -575.921 q^{53} +(-358.812 - 219.017i) q^{54} -708.025 q^{55} +(-83.1752 + 410.728i) q^{56} -199.362 q^{57} +(-67.1716 - 41.0012i) q^{58} +411.999 q^{59} +(582.960 - 299.608i) q^{60} +778.987i q^{61} +(196.614 + 120.012i) q^{62} +(72.9481 + 9.27863i) q^{63} +(-506.510 - 74.7794i) q^{64} +774.420 q^{65} +(-293.274 + 480.465i) q^{66} +198.773i q^{67} +(-201.271 + 103.442i) q^{68} -450.756i q^{69} +(-558.544 + 698.463i) q^{70} +197.762i q^{71} +(-6.57864 + 89.6024i) q^{72} -255.589i q^{73} +(-228.877 - 139.706i) q^{74} +798.922 q^{75} +(151.918 + 295.593i) q^{76} +(96.9117 - 761.915i) q^{77} +(320.775 - 525.520i) q^{78} -1178.49i q^{79} +(-888.454 - 636.044i) q^{80} -606.029 q^{81} +(334.958 - 548.756i) q^{82} +938.514 q^{83} +(242.619 + 668.340i) q^{84} -482.940 q^{85} +(253.446 - 415.215i) q^{86} -133.522 q^{87} +(935.862 + 68.7114i) q^{88} -1166.81i q^{89} +(-99.8950 + 163.656i) q^{90} +(-106.000 + 833.363i) q^{91} +(-668.333 + 343.485i) q^{92} +390.823 q^{93} +(690.476 + 421.464i) q^{94} +709.261i q^{95} +(-799.628 + 339.446i) q^{96} +656.635i q^{97} +(-675.173 - 696.659i) q^{98} -164.663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9	\( 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9} - 152 q^{14} + 64 q^{16} + 88 q^{18} - 64 q^{21} + 240 q^{22} - 472 q^{25} - 48 q^{28} - 592 q^{29} + 256 q^{30} + 1152 q^{32} - 976 q^{36} + 1392 q^{37} - 1024 q^{42} - 1184 q^{44} - 816 q^{46} + 1480 q^{49} + 1688 q^{50} - 1168 q^{53} + 800 q^{56} - 192 q^{57} - 560 q^{58} + 2944 q^{60} - 3328 q^{64} + 448 q^{65} - 3200 q^{70} - 1184 q^{72} - 496 q^{74} + 368 q^{77} + 7680 q^{78} - 4984 q^{81} + 4480 q^{84} + 1024 q^{85} + 240 q^{86} + 3776 q^{88} - 3808 q^{92} - 2304 q^{93} - 3144 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9 - 152 * q^14 + 64 * q^16 + 88 * q^18 - 64 * q^21 + 240 * q^22 - 472 * q^25 - 48 * q^28 - 592 * q^29 + 256 * q^30 + 1152 * q^32 - 976 * q^36 + 1392 * q^37 - 1024 * q^42 - 1184 * q^44 - 816 * q^46 + 1480 * q^49 + 1688 * q^50 - 1168 * q^53 + 800 * q^56 - 192 * q^57 - 560 * q^58 + 2944 * q^60 - 3328 * q^64 + 448 * q^65 - 3200 * q^70 - 1184 * q^72 - 496 * q^74 + 368 * q^77 + 7680 * q^78 - 4984 * q^81 + 4480 * q^84 + 1024 * q^85 + 240 * q^86 + 3776 * q^88 - 3808 * q^92 - 2304 * q^93 - 3144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more