LMFDB - Embedded newform 128.4.g.a.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	128.113
Dual form			128.4.g.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.729459 - 1.76107i) q^{3} +(4.29822 + 1.78038i) q^{5} +(-1.47807 - 1.47807i) q^{7} +(16.5226 - 16.5226i) q^{9} +O(q^{10})$	\(q+(-0.729459 - 1.76107i) q^{3} +(4.29822 + 1.78038i) q^{5} +(-1.47807 - 1.47807i) q^{7} +(16.5226 - 16.5226i) q^{9} +(-0.854325 + 2.06252i) q^{11} +(40.9706 - 16.9706i) q^{13} -8.86818i q^{15} -73.1063i q^{17} +(18.2478 - 7.55849i) q^{19} +(-1.52480 + 3.68119i) q^{21} +(144.221 - 144.221i) q^{23} +(-73.0834 - 73.0834i) q^{25} +(-88.6990 - 36.7403i) q^{27} +(80.7690 + 194.994i) q^{29} +168.830 q^{31} +4.25544 q^{33} +(-3.72155 - 8.98462i) q^{35} +(-72.0103 - 29.8277i) q^{37} +(-59.7727 - 59.7727i) q^{39} +(-141.297 + 141.297i) q^{41} +(-161.344 + 389.519i) q^{43} +(100.434 - 41.6013i) q^{45} +239.015i q^{47} -338.631i q^{49} +(-128.745 + 53.3280i) q^{51} +(-59.8701 + 144.539i) q^{53} +(-7.34415 + 7.34415i) q^{55} +(-26.6221 - 26.6221i) q^{57} +(-582.808 - 241.407i) q^{59} +(238.297 + 575.301i) q^{61} -48.8433 q^{63} +206.315 q^{65} +(156.090 + 376.834i) q^{67} +(-359.185 - 148.780i) q^{69} +(-411.945 - 411.945i) q^{71} +(-642.439 + 642.439i) q^{73} +(-75.3937 + 182.016i) q^{75} +(4.31132 - 1.78581i) q^{77} +800.261i q^{79} -447.890i q^{81} +(1345.29 - 557.236i) q^{83} +(130.157 - 314.227i) q^{85} +(284.480 - 284.480i) q^{87} +(340.094 + 340.094i) q^{89} +(-85.6413 - 35.4738i) q^{91} +(-123.155 - 297.321i) q^{93} +91.8900 q^{95} +632.602 q^{97} +(19.9626 + 48.1940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.729459	−	1.76107i	−0.140384	−	0.338918i	0.838013	−	0.545650i	$-0.183717\pi$
$3$	−0.729459	−	1.76107i	−0.140384	−	0.338918i	−0.978398	+	0.206732i	$0.933717\pi$
$4$		0			0
$5$	4.29822	+	1.78038i	0.384444	+	0.159242i	0.566531	−	0.824040i	$-0.308285\pi$
$5$	4.29822	+	1.78038i	0.384444	+	0.159242i	−0.182087	+	0.983282i	$0.558285\pi$
$6$		0			0
$7$	−1.47807	−	1.47807i	−0.0798085	−	0.0798085i	0.666076	−	0.745884i	$-0.267973\pi$
$7$	−1.47807	−	1.47807i	−0.0798085	−	0.0798085i	−0.745884	+	0.666076i	$0.767973\pi$
$8$		0			0
$9$	16.5226	−	16.5226i	0.611949	−	0.611949i
$10$		0			0
$11$	−0.854325	+	2.06252i	−0.0234172	+	0.0565340i	−0.935156	−	0.354237i	$-0.884741\pi$
$11$	−0.854325	+	2.06252i	−0.0234172	+	0.0565340i	0.911738	+	0.410771i	$0.134741\pi$
$12$		0			0
$13$	40.9706	−	16.9706i	0.874092	−	0.362061i	0.0998893	−	0.994999i	$-0.468151\pi$
$13$	40.9706	−	16.9706i	0.874092	−	0.362061i	0.774203	+	0.632938i	$0.218151\pi$
$14$		0			0
$15$		−	8.86818i		−	0.152650i
$16$		0			0
$17$		−	73.1063i		−	1.04299i	−0.853253	−	0.521496i	$-0.825374\pi$
$17$		−	73.1063i		−	1.04299i	0.853253	−	0.521496i	$-0.174626\pi$
$18$		0			0
$19$	18.2478	−	7.55849i	0.220333	−	0.0912650i	−0.269786	−	0.962920i	$-0.586953\pi$
$19$	18.2478	−	7.55849i	0.220333	−	0.0912650i	0.490120	+	0.871655i	$0.336953\pi$
$20$		0			0
$21$	−1.52480	+	3.68119i	−0.0158447	+	0.0382524i
$22$		0			0
$23$	144.221	−	144.221i	1.30748	−	1.30748i	0.384253	−	0.923228i	$-0.374459\pi$
$23$	144.221	−	144.221i	1.30748	−	1.30748i	0.923228	−	0.384253i	$-0.125541\pi$
$24$		0			0
$25$	−73.0834	−	73.0834i	−0.584667	−	0.584667i
$26$		0			0
$27$	−88.6990	−	36.7403i	−0.632227	−	0.261877i
$28$		0			0
$29$	80.7690	+	194.994i	0.517187	+	1.24860i	0.939624	+	0.342208i	$0.111175\pi$
$29$	80.7690	+	194.994i	0.517187	+	1.24860i	−0.422437	+	0.906392i	$0.638825\pi$
$30$		0			0
$31$	168.830			0.978153			0.489077	−	0.872241i	$-0.337334\pi$
$31$	168.830			0.978153			0.489077	+	0.872241i	$0.337334\pi$
$32$		0			0
$33$	4.25544			0.0224478
$34$		0			0
$35$	−3.72155	−	8.98462i	−0.0179731	−	0.0433908i
$36$		0			0
$37$	−72.0103	−	29.8277i	−0.319958	−	0.132531i	0.216924	−	0.976189i	$-0.430398\pi$
$37$	−72.0103	−	29.8277i	−0.319958	−	0.132531i	−0.536881	+	0.843658i	$0.680398\pi$
$38$		0			0
$39$	−59.7727	−	59.7727i	−0.245418	−	0.245418i
$40$		0			0
$41$	−141.297	+	141.297i	−0.538215	+	0.538215i	−0.923005	−	0.384789i	$-0.874274\pi$
$41$	−141.297	+	141.297i	−0.538215	+	0.538215i	0.384789	+	0.923005i	$0.374274\pi$
$42$		0			0
$43$	−161.344	+	389.519i	−0.572203	+	1.38142i	0.327472	+	0.944861i	$0.393803\pi$
$43$	−161.344	+	389.519i	−0.572203	+	1.38142i	−0.899675	+	0.436560i	$0.856197\pi$
$44$		0			0
$45$	100.434	−	41.6013i	0.332708	−	0.137812i
$46$		0			0
$47$			239.015i			0.741787i	0.928675	+	0.370893i	$0.120948\pi$
$47$			239.015i			0.741787i	−0.928675	+	0.370893i	$0.879052\pi$
$48$		0			0
$49$		−	338.631i		−	0.987261i
$50$		0			0
$51$	−128.745	+	53.3280i	−0.353489	+	0.146420i
$52$		0			0
$53$	−59.8701	+	144.539i	−0.155166	+	0.374604i	−0.982277	−	0.187435i	$-0.939983\pi$
$53$	−59.8701	+	144.539i	−0.155166	+	0.374604i	0.827111	+	0.562038i	$0.189983\pi$
$54$		0			0
$55$	−7.34415	+	7.34415i	−0.0180052	+	0.0180052i
$56$		0			0
$57$	−26.6221	−	26.6221i	−0.0618627	−	0.0618627i
$58$		0			0
$59$	−582.808	−	241.407i	−1.28602	−	0.532686i	−0.368222	−	0.929738i	$-0.620033\pi$
$59$	−582.808	−	241.407i	−1.28602	−	0.532686i	−0.917796	+	0.397051i	$0.870033\pi$
$60$		0			0
$61$	238.297	+	575.301i	0.500178	+	1.20754i	0.949387	+	0.314110i	$0.101706\pi$
$61$	238.297	+	575.301i	0.500178	+	1.20754i	−0.449209	+	0.893427i	$0.648294\pi$
$62$		0			0
$63$	−48.8433			−0.0976775
$64$		0			0
$65$	206.315			0.393695
$66$		0			0
$67$	156.090	+	376.834i	0.284618	+	0.687129i	0.999932	−	0.0116744i	$-0.00371618\pi$
$67$	156.090	+	376.834i	0.284618	+	0.687129i	−0.715314	+	0.698804i	$0.753716\pi$
$68$		0			0
$69$	−359.185	−	148.780i	−0.626679	−	0.259579i
$70$		0			0
$71$	−411.945	−	411.945i	−0.688577	−	0.688577i	0.273341	−	0.961917i	$-0.411871\pi$
$71$	−411.945	−	411.945i	−0.688577	−	0.688577i	−0.961917	+	0.273341i	$0.911871\pi$
$72$		0			0
$73$	−642.439	+	642.439i	−1.03003	+	1.03003i	−0.0304901	+	0.999535i	$0.509707\pi$
$73$	−642.439	+	642.439i	−1.03003	+	1.03003i	−0.999535	+	0.0304901i	$0.990293\pi$
$74$		0			0
$75$	−75.3937	+	182.016i	−0.116076	+	0.280233i
$76$		0			0
$77$	4.31132	−	1.78581i	0.00638078	−	0.00264301i
$78$		0			0
$79$			800.261i			1.13970i	0.821748	+	0.569850i	$0.192999\pi$
$79$			800.261i			1.13970i	−0.821748	+	0.569850i	$0.807001\pi$
$80$		0			0
$81$		−	447.890i		−	0.614390i
$82$		0			0
$83$	1345.29	−	557.236i	1.77909	−	0.736923i	0.786187	−	0.617989i	$-0.212052\pi$
$83$	1345.29	−	557.236i	1.77909	−	0.736923i	0.992902	−	0.118933i	$-0.0379475\pi$
$84$		0			0
$85$	130.157	−	314.227i	0.166088	−	0.400973i
$86$		0			0
$87$	284.480	−	284.480i	0.350568	−	0.350568i
$88$		0			0
$89$	340.094	+	340.094i	0.405055	+	0.405055i	0.880010	−	0.474955i	$-0.157536\pi$
$89$	340.094	+	340.094i	0.405055	+	0.405055i	−0.474955	+	0.880010i	$0.657536\pi$
$90$		0			0
$91$	−85.6413	−	35.4738i	−0.0986555	−	0.0408644i
$92$		0			0
$93$	−123.155	−	297.321i	−0.137317	−	0.331514i
$94$		0			0
$95$	91.8900			0.0992391
$96$		0			0
$97$	632.602			0.662175			0.331088	−	0.943600i	$-0.392584\pi$
$97$	632.602			0.662175			0.331088	+	0.943600i	$0.392584\pi$
$98$		0			0
$99$	19.9626	+	48.1940i	0.0202658	+	0.0489261i
$100$		0			0
$101$	−1069.17	−	442.863i	−1.05333	−	0.436303i	−0.212249	−	0.977216i	$-0.568079\pi$
$101$	−1069.17	−	442.863i	−1.05333	−	0.436303i	−0.841078	+	0.540913i	$0.818079\pi$
$102$		0			0
$103$	−251.287	−	251.287i	−0.240389	−	0.240389i	0.576622	−	0.817011i	$-0.304371\pi$
$103$	−251.287	−	251.287i	−0.240389	−	0.240389i	−0.817011	+	0.576622i	$0.804371\pi$
$104$		0			0
$105$	−13.1078	+	13.1078i	−0.0121828	+	0.0121828i
$106$		0			0
$107$	539.593	−	1302.69i	0.487518	−	1.17697i	−0.468447	−	0.883492i	$-0.655186\pi$
$107$	539.593	−	1302.69i	0.487518	−	1.17697i	0.955965	−	0.293481i	$-0.0948138\pi$
$108$		0			0
$109$	723.084	−	299.511i	0.635403	−	0.263192i	−0.0416440	−	0.999133i	$-0.513260\pi$
$109$	723.084	−	299.511i	0.635403	−	0.263192i	0.677047	+	0.735940i	$0.263260\pi$
$110$		0			0
$111$			148.573i			0.127045i
$112$		0			0
$113$			118.490i			0.0986425i	0.998783	+	0.0493213i	$0.0157058\pi$
$113$			118.490i			0.0986425i	−0.998783	+	0.0493213i	$0.984294\pi$
$114$		0			0
$115$	876.659	−	363.124i	0.710860	−	0.294448i
$116$		0			0
$117$	396.543	−	957.340i	0.313337	−	0.756463i
$118$		0			0
$119$	−108.056	+	108.056i	−0.0832397	+	0.0832397i
$120$		0			0
$121$	937.635	+	937.635i	0.704459	+	0.704459i
$122$		0			0
$123$	351.903	+	145.763i	0.257968	+	0.106854i
$124$		0			0
$125$	−406.560	−	981.522i	−0.290910	−	0.702320i
$126$		0			0
$127$	−842.166			−0.588427			−0.294213	−	0.955740i	$-0.595058\pi$
$127$	−842.166			−0.588427			−0.294213	+	0.955740i	$0.595058\pi$
$128$		0			0
$129$	803.664			0.548517
$130$		0			0
$131$	−488.895	−	1180.30i	−0.326069	−	0.787199i	−0.998877	−	0.0473823i	$-0.984912\pi$
$131$	−488.895	−	1180.30i	−0.326069	−	0.787199i	0.672808	−	0.739817i	$-0.265088\pi$
$132$		0			0
$133$	−38.1436	−	15.7996i	−0.0248682	−	0.0103007i
$134$		0			0
$135$	−315.836	−	315.836i	−0.201354	−	0.201354i
$136$		0			0
$137$	354.278	−	354.278i	0.220934	−	0.220934i	−0.587958	−	0.808892i	$-0.700068\pi$
$137$	354.278	−	354.278i	0.220934	−	0.220934i	0.808892	+	0.587958i	$0.200068\pi$
$138$		0			0
$139$	−506.903	+	1223.77i	−0.309316	+	0.746756i	0.690411	+	0.723417i	$0.257430\pi$
$139$	−506.903	+	1223.77i	−0.309316	+	0.746756i	−0.999728	+	0.0233385i	$0.992570\pi$
$140$		0			0
$141$	420.923	−	174.352i	0.251405	−	0.104135i
$142$		0			0
$143$			99.0012i			0.0578944i
$144$		0			0
$145$			981.925i			0.562375i
$146$		0			0
$147$	−596.352	+	247.017i	−0.334601	+	0.138596i
$148$		0			0
$149$	263.786	−	636.836i	0.145035	−	0.350145i	−0.834623	−	0.550822i	$-0.814314\pi$
$149$	263.786	−	636.836i	0.145035	−	0.350145i	0.979657	+	0.200677i	$0.0643142\pi$
$150$		0			0
$151$	−963.930	+	963.930i	−0.519493	+	0.519493i	−0.917418	−	0.397925i	$-0.869731\pi$
$151$	−963.930	+	963.930i	−0.519493	+	0.519493i	0.397925	+	0.917418i	$0.369731\pi$
$152$		0			0
$153$	−1207.91	−	1207.91i	−0.638259	−	0.638259i
$154$		0			0
$155$	725.668	+	300.581i	0.376045	+	0.155763i
$156$		0			0
$157$	439.451	+	1060.93i	0.223389	+	0.539308i	0.995346	−	0.0963665i	$-0.0307221\pi$
$157$	439.451	+	1060.93i	0.223389	+	0.539308i	−0.771957	+	0.635674i	$0.780722\pi$
$158$		0			0
$159$	298.217			0.148743
$160$		0			0
$161$	−426.337			−0.208696
$162$		0			0
$163$	437.870	+	1057.11i	0.210409	+	0.507972i	0.993486	−	0.113953i	$-0.0363512\pi$
$163$	437.870	+	1057.11i	0.210409	+	0.507972i	−0.783077	+	0.621924i	$0.786351\pi$
$164$		0			0
$165$	18.2908	+	7.57631i	0.00862993	+	0.00357464i
$166$		0			0
$167$	856.325	+	856.325i	0.396793	+	0.396793i	0.877100	−	0.480307i	$-0.159475\pi$
$167$	856.325	+	856.325i	0.396793	+	0.396793i	−0.480307	+	0.877100i	$0.659475\pi$
$168$		0			0
$169$	−162.925	+	162.925i	−0.0741580	+	0.0741580i
$170$		0			0
$171$	176.616	−	426.388i	0.0789832	−	0.190682i
$172$		0			0
$173$	−2410.30	+	998.380i	−1.05926	+	0.438760i	−0.843189	−	0.537618i	$-0.819324\pi$
$173$	−2410.30	+	998.380i	−1.05926	+	0.438760i	−0.216071	+	0.976378i	$0.569324\pi$
$174$		0			0
$175$			216.045i			0.0933228i
$176$		0			0
$177$			1202.46i			0.510636i
$178$		0			0
$179$	−1526.52	+	632.305i	−0.637415	+	0.264026i	−0.677900	−	0.735154i	$-0.737110\pi$
$179$	−1526.52	+	632.305i	−0.637415	+	0.264026i	0.0404847	+	0.999180i	$0.487110\pi$
$180$		0			0
$181$	−1487.44	+	3590.99i	−0.610831	+	1.47468i	0.251258	+	0.967920i	$0.419156\pi$
$181$	−1487.44	+	3590.99i	−0.610831	+	1.47468i	−0.862089	+	0.506756i	$0.830844\pi$
$182$		0			0
$183$	839.317	−	839.317i	0.339039	−	0.339039i
$184$		0			0
$185$	−256.412	−	256.412i	−0.101901	−	0.101901i
$186$		0			0
$187$	150.783	+	62.4565i	0.0589646	+	0.0244239i
$188$		0			0
$189$	76.7987	+	185.409i	0.0295571	+	0.0713571i
$190$		0			0
$191$	−1908.11			−0.722858			−0.361429	−	0.932400i	$-0.617711\pi$
$191$	−1908.11			−0.722858			−0.361429	+	0.932400i	$0.617711\pi$
$192$		0			0
$193$	−3674.63			−1.37049			−0.685247	−	0.728310i	$-0.740306\pi$
$193$	−3674.63			−1.37049			−0.685247	+	0.728310i	$0.740306\pi$
$194$		0			0
$195$	−150.498	−	363.334i	−0.0552687	−	0.133430i
$196$		0			0
$197$	2539.28	+	1051.80i	0.918356	+	0.380395i	0.791249	−	0.611494i	$-0.209431\pi$
$197$	2539.28	+	1051.80i	0.918356	+	0.380395i	0.127107	+	0.991889i	$0.459431\pi$
$198$		0			0
$199$	1751.18	+	1751.18i	0.623809	+	0.623809i	0.946503	−	0.322694i	$-0.104589\pi$
$199$	1751.18	+	1751.18i	0.623809	+	0.623809i	−0.322694	+	0.946503i	$0.604589\pi$
$200$		0			0
$201$	549.771	−	549.771i	0.192924	−	0.192924i
$202$		0			0
$203$	168.832	−	407.597i	0.0583730	−	0.140925i
$204$		0			0
$205$	−858.886	+	355.762i	−0.292620	+	0.121207i
$206$		0			0
$207$		−	4765.80i		−	1.60022i
$208$		0			0
$209$			44.0939i			0.0145935i
$210$		0			0
$211$	−4123.79	+	1708.13i	−1.34547	+	0.557311i	−0.935027	−	0.354577i	$-0.884625\pi$
$211$	−4123.79	+	1708.13i	−1.34547	+	0.557311i	−0.410440	+	0.911887i	$0.634625\pi$
$212$		0			0
$213$	−424.967	+	1025.96i	−0.136706	+	0.330036i
$214$		0			0
$215$	−1386.98	+	1386.98i	−0.439961	+	0.439961i
$216$		0			0
$217$	−249.543	−	249.543i	−0.0780649	−	0.0780649i
$218$		0			0
$219$	1600.01	+	662.747i	0.493694	+	0.204495i
$220$		0			0
$221$	−1240.66	−	2995.21i	−0.377627	−	0.911672i
$222$		0			0
$223$	4869.99			1.46242			0.731208	−	0.682155i	$-0.238957\pi$
$223$	4869.99			1.46242			0.731208	+	0.682155i	$0.238957\pi$
$224$		0			0
$225$	−2415.06			−0.715573
$226$		0			0
$227$	−11.2187	−	27.0843i	−0.00328022	−	0.00791916i	0.922231	−	0.386639i	$-0.126364\pi$
$227$	−11.2187	−	27.0843i	−0.00328022	−	0.00791916i	−0.925511	+	0.378720i	$0.876364\pi$
$228$		0			0
$229$	4258.86	+	1764.08i	1.22897	+	0.509054i	0.900250	−	0.435374i	$-0.143384\pi$
$229$	4258.86	+	1764.08i	1.22897	+	0.509054i	0.328716	+	0.944429i	$0.393384\pi$
$230$		0			0
$231$	−6.28986	−	6.28986i	−0.00179153	−	0.00179153i
$232$		0			0
$233$	4653.94	−	4653.94i	1.30854	−	1.30854i	0.386069	−	0.922470i	$-0.373833\pi$
$233$	4653.94	−	4653.94i	1.30854	−	1.30854i	0.922470	−	0.386069i	$-0.126167\pi$
$234$		0			0
$235$	−425.538	+	1027.34i	−0.118124	+	0.285176i
$236$		0			0
$237$	1409.32	−	583.757i	0.386265	−	0.159996i
$238$		0			0
$239$		−	630.197i		−	0.170561i	−0.996357	−	0.0852805i	$-0.972821\pi$
$239$		−	630.197i		−	0.170561i	0.996357	−	0.0852805i	$-0.0271786\pi$
$240$		0			0
$241$		−	1523.56i		−	0.407224i	−0.979052	−	0.203612i	$-0.934732\pi$
$241$		−	1523.56i		−	0.407224i	0.979052	−	0.203612i	$-0.0652681\pi$
$242$		0			0
$243$	−3183.64	+	1318.71i	−0.840455	+	0.348128i
$244$		0			0
$245$	602.891	−	1455.51i	0.157214	−	0.379547i
$246$		0			0
$247$	619.351	−	619.351i	0.159548	−	0.159548i
$248$		0			0
$249$	−1962.66	−	1962.66i	−0.499513	−	0.499513i
$250$		0			0
$251$	−2943.19	−	1219.11i	−0.740129	−	0.306572i	−0.0194224	−	0.999811i	$-0.506183\pi$
$251$	−2943.19	−	1219.11i	−0.740129	−	0.306572i	−0.720707	+	0.693240i	$0.756183\pi$
$252$		0			0
$253$	174.247	+	420.670i	0.0432997	+	0.104535i
$254$		0			0
$255$	−648.320			−0.159213
$256$		0			0
$257$	3355.93			0.814541			0.407270	−	0.913308i	$-0.366481\pi$
$257$	3355.93			0.814541			0.407270	+	0.913308i	$0.366481\pi$
$258$		0			0
$259$	62.3491	+	150.524i	0.0149582	+	0.0361124i
$260$		0			0
$261$	4556.32	+	1887.29i	1.08057	+	0.447588i
$262$		0			0
$263$	3273.56	+	3273.56i	0.767514	+	0.767514i	0.977668	−	0.210154i	$-0.0673966\pi$
$263$	3273.56	+	3273.56i	0.767514	+	0.767514i	−0.210154	+	0.977668i	$0.567397\pi$
$264$		0			0
$265$	−514.670	+	514.670i	−0.119305	+	0.119305i
$266$		0			0
$267$	350.845	−	847.014i	0.0804170	−	0.194144i
$268$		0			0
$269$	−1523.46	+	631.037i	−0.345304	+	0.143030i	−0.548594	−	0.836089i	$-0.684837\pi$
$269$	−1523.46	+	631.037i	−0.345304	+	0.143030i	0.203290	+	0.979119i	$0.434837\pi$
$270$		0			0
$271$		−	6024.40i		−	1.35039i	−0.737639	−	0.675196i	$-0.764059\pi$
$271$		−	6024.40i		−	1.35039i	0.737639	−	0.675196i	$-0.235941\pi$
$272$		0			0
$273$			176.697i			0.0391729i
$274$		0			0
$275$	213.173	−	88.2993i	0.0467448	−	0.0193623i
$276$		0			0
$277$	631.310	−	1524.12i	0.136938	−	0.330597i	−0.840503	−	0.541807i	$-0.817740\pi$
$277$	631.310	−	1524.12i	0.136938	−	0.330597i	0.977441	+	0.211210i	$0.0677404\pi$
$278$		0			0
$279$	2789.51	−	2789.51i	0.598580	−	0.598580i
$280$		0			0
$281$	185.259	+	185.259i	0.0393296	+	0.0393296i	0.726498	−	0.687168i	$-0.241147\pi$
$281$	185.259	+	185.259i	0.0393296	+	0.0393296i	−0.687168	+	0.726498i	$0.741147\pi$
$282$		0			0
$283$	5010.11	+	2075.25i	1.05237	+	0.435905i	0.840736	−	0.541445i	$-0.182123\pi$
$283$	5010.11	+	2075.25i	1.05237	+	0.435905i	0.211631	+	0.977350i	$0.432123\pi$
$284$		0			0
$285$	−67.0300	−	161.825i	−0.0139316	−	0.0336339i
$286$		0			0
$287$	417.694			0.0859083
$288$		0			0
$289$	−431.529			−0.0878340
$290$		0			0
$291$	−461.457	−	1114.06i	−0.0929591	−	0.224423i
$292$		0			0
$293$	−3670.99	−	1520.58i	−0.731951	−	0.303184i	−0.0145978	−	0.999893i	$-0.504647\pi$
$293$	−3670.99	−	1520.58i	−0.731951	−	0.303184i	−0.717354	+	0.696709i	$0.754647\pi$
$294$		0			0
$295$	−2075.24	−	2075.24i	−0.409577	−	0.409577i
$296$		0			0
$297$	151.556	−	151.556i	0.0296099	−	0.0296099i
$298$		0			0
$299$	3461.30	−	8356.31i	0.669471	−	1.61625i
$300$		0			0
$301$	814.216	−	337.259i	0.155916	−	0.0645824i
$302$		0			0
$303$			2205.93i			0.418242i
$304$		0			0
$305$			2897.03i			0.543880i
$306$		0			0
$307$	5184.84	−	2147.63i	0.963890	−	0.399256i	0.155456	−	0.987843i	$-0.450315\pi$
$307$	5184.84	−	2147.63i	0.963890	−	0.399256i	0.808434	+	0.588586i	$0.200315\pi$
$308$		0			0
$309$	−259.231	+	625.838i	−0.0477253	+	0.115219i
$310$		0			0
$311$	−4758.86	+	4758.86i	−0.867685	+	0.867685i	−0.992216	−	0.124531i	$-0.960257\pi$
$311$	−4758.86	+	4758.86i	−0.867685	+	0.867685i	0.124531	+	0.992216i	$0.460257\pi$
$312$		0			0
$313$	1629.22	+	1629.22i	0.294214	+	0.294214i	0.838742	−	0.544529i	$-0.183291\pi$
$313$	1629.22	+	1629.22i	0.294214	+	0.294214i	−0.544529	+	0.838742i	$0.683291\pi$
$314$		0			0
$315$	−209.939	−	86.9597i	−0.0375515	−	0.0155544i
$316$		0			0
$317$	−1717.07	−	4145.38i	−0.304228	−	0.734472i	−0.999871	−	0.0160838i	$-0.994880\pi$
$317$	−1717.07	−	4145.38i	−0.304228	−	0.734472i	0.695642	−	0.718388i	$-0.255120\pi$
$318$		0			0
$319$	−471.182			−0.0826994
$320$		0			0
$321$	−2687.74			−0.467337
$322$		0			0
$323$	−552.573	−	1334.03i	−0.0951888	−	0.229806i
$324$		0			0
$325$	−4234.54	−	1754.00i	−0.722738	−	0.299368i
$326$		0			0
$327$	−1054.92	−	1054.92i	−0.178401	−	0.178401i
$328$		0			0
$329$	353.282	−	353.282i	0.0592009	−	0.0592009i
$330$		0			0
$331$	−3512.87	+	8480.82i	−0.583338	+	1.40830i	0.306432	+	0.951893i	$0.400865\pi$
$331$	−3512.87	+	8480.82i	−0.583338	+	1.40830i	−0.889770	+	0.456410i	$0.849135\pi$
$332$		0			0
$333$	−1682.63	+	696.969i	−0.276900	+	0.114696i
$334$		0			0
$335$			1897.62i			0.309486i
$336$		0			0
$337$			967.017i			0.156311i	0.996941	+	0.0781555i	$0.0249031\pi$
$337$			967.017i			0.156311i	−0.996941	+	0.0781555i	$0.975097\pi$
$338$		0			0
$339$	208.669	−	86.4336i	0.0334317	−	0.0138479i
$340$		0			0
$341$	−144.236	+	348.216i	−0.0229056	+	0.0552989i
$342$		0			0
$343$	−1007.50	+	1007.50i	−0.158600	+	0.158600i
$344$		0			0
$345$	−1278.97	−	1278.97i	−0.199587	−	0.199587i
$346$		0			0
$347$	6675.62	+	2765.13i	1.03276	+	0.427781i	0.833706	−	0.552208i	$-0.186215\pi$
$347$	6675.62	+	2765.13i	1.03276	+	0.427781i	0.199049	+	0.979990i	$0.436215\pi$
$348$		0			0
$349$	1025.92	+	2476.80i	0.157354	+	0.379885i	0.982820	−	0.184566i	$-0.0590878\pi$
$349$	1025.92	+	2476.80i	0.157354	+	0.379885i	−0.825466	+	0.564451i	$0.809088\pi$
$350$		0			0
$351$	−4257.55			−0.647440
$352$		0			0
$353$	4340.88			0.654509			0.327254	−	0.944936i	$-0.393877\pi$
$353$	4340.88			0.654509			0.327254	+	0.944936i	$0.393877\pi$
$354$		0			0
$355$	−1037.21	−	2504.05i	−0.155069	−	0.374370i
$356$		0			0
$357$	269.118	+	111.472i	0.0398970	+	0.0165259i
$358$		0			0
$359$	2662.28	+	2662.28i	0.391392	+	0.391392i	0.875183	−	0.483792i	$-0.160741\pi$
$359$	2662.28	+	2662.28i	0.391392	+	0.391392i	−0.483792	+	0.875183i	$0.660741\pi$
$360$		0			0
$361$	−4574.19	+	4574.19i	−0.666889	+	0.666889i
$362$		0			0
$363$	967.274	−	2335.21i	0.139859	−	0.337649i
$364$		0			0
$365$	−3905.13	+	1617.56i	−0.560011	+	0.231964i
$366$		0			0
$367$			11287.0i			1.60539i	0.596389	+	0.802695i	$0.296601\pi$
$367$			11287.0i			1.60539i	−0.596389	+	0.802695i	$0.703399\pi$
$368$		0			0
$369$			4669.18i			0.658721i
$370$		0			0
$371$	302.132	−	125.147i	0.0422801	−	0.0175130i
$372$		0			0
$373$	16.5243	−	39.8932i	0.00229382	−	0.00553778i	−0.922728	−	0.385451i	$-0.874046\pi$
$373$	16.5243	−	39.8932i	0.00229382	−	0.00553778i	0.925022	+	0.379913i	$0.124046\pi$
$374$		0			0
$375$	−1431.96	+	1431.96i	−0.197190	+	0.197190i
$376$		0			0
$377$	6618.31	+	6618.31i	0.904138	+	0.904138i
$378$		0			0
$379$	−10994.6	−	4554.09i	−1.49011	−	0.617224i	−0.518770	−	0.854914i	$-0.673610\pi$
$379$	−10994.6	−	4554.09i	−1.49011	−	0.617224i	−0.971341	+	0.237689i	$0.923610\pi$
$380$		0			0
$381$	614.326	+	1483.11i	0.0826060	+	0.199428i
$382$		0			0
$383$	−11220.8			−1.49701			−0.748506	−	0.663128i	$-0.769229\pi$
$383$	−11220.8			−1.49701			−0.748506	+	0.663128i	$0.769229\pi$
$384$		0			0
$385$	21.7104			0.00287393
$386$		0			0
$387$	3770.05	+	9101.71i	0.495200	+	1.19552i
$388$		0			0
$389$	−7872.36	−	3260.84i	−1.02608	−	0.425016i	−0.194783	−	0.980846i	$-0.562400\pi$
$389$	−7872.36	−	3260.84i	−1.02608	−	0.425016i	−0.831296	+	0.555831i	$0.812400\pi$
$390$		0			0
$391$	−10543.4	−	10543.4i	−1.36369	−	1.36369i
$392$		0			0
$393$	−1721.96	+	1721.96i	−0.221021	+	0.221021i
$394$		0			0
$395$	−1424.77	+	3439.70i	−0.181488	+	0.438152i
$396$		0			0
$397$	12780.9	−	5294.04i	1.61576	−	0.669270i	0.622230	−	0.782835i	$-0.286227\pi$
$397$	12780.9	−	5294.04i	1.61576	−	0.669270i	0.993531	+	0.113565i	$0.0362269\pi$
$398$		0			0
$399$			78.6987i			0.00987434i
$400$		0			0
$401$			1951.13i			0.242979i	0.992593	+	0.121490i	$0.0387671\pi$
$401$			1951.13i			0.242979i	−0.992593	+	0.121490i	$0.961233\pi$
$402$		0			0
$403$	6917.06	−	2865.14i	0.854996	−	0.354151i
$404$		0			0
$405$	797.415	−	1925.13i	0.0978368	−	0.236199i
$406$		0			0
$407$	123.041	−	123.041i	0.0149850	−	0.0149850i
$408$		0			0
$409$	3631.15	+	3631.15i	0.438995	+	0.438995i	0.891674	−	0.452679i	$-0.149532\pi$
$409$	3631.15	+	3631.15i	0.438995	+	0.438995i	−0.452679	+	0.891674i	$0.649532\pi$
$410$		0			0
$411$	−882.339	−	365.477i	−0.105894	−	0.0438629i
$412$		0			0
$413$	504.616	+	1218.25i	0.0601223	+	0.145148i
$414$		0			0
$415$	6774.43			0.801310
$416$		0			0
$417$	2524.91			0.296512
$418$		0			0
$419$	−1055.57	−	2548.38i	−0.123074	−	0.297128i	0.850319	−	0.526267i	$-0.176409\pi$
$419$	−1055.57	−	2548.38i	−0.123074	−	0.297128i	−0.973394	+	0.229139i	$0.926409\pi$
$420$		0			0
$421$	−9547.06	−	3954.52i	−1.10521	−	0.457795i	−0.245927	−	0.969288i	$-0.579092\pi$
$421$	−9547.06	−	3954.52i	−1.10521	−	0.457795i	−0.859287	+	0.511493i	$0.829092\pi$
$422$		0			0
$423$	3949.16	+	3949.16i	0.453936	+	0.453936i
$424$		0			0
$425$	−5342.86	+	5342.86i	−0.609804	+	0.609804i
$426$		0			0
$427$	498.116	−	1202.56i	0.0564532	−	0.136290i
$428$		0			0
$429$	174.348	−	72.2173i	0.0196214	−	0.00812747i
$430$		0			0
$431$			14341.1i			1.60275i	0.598162	+	0.801375i	$0.295898\pi$
$431$			14341.1i			1.60275i	−0.598162	+	0.801375i	$0.704102\pi$
$432$		0			0
$433$		−	16123.8i		−	1.78951i	−0.446554	−	0.894757i	$-0.647349\pi$
$433$		−	16123.8i		−	1.78951i	0.446554	−	0.894757i	$-0.352651\pi$
$434$		0			0
$435$	1729.24	−	716.274i	0.190599	−	0.0789487i
$436$		0			0
$437$	1541.62	−	3721.80i	0.168754	−	0.407409i
$438$		0			0
$439$	8026.57	−	8026.57i	0.872637	−	0.872637i	−0.120123	−	0.992759i	$-0.538329\pi$
$439$	8026.57	−	8026.57i	0.872637	−	0.872637i	0.992759	+	0.120123i	$0.0383288\pi$
$440$		0			0
$441$	−5595.07	−	5595.07i	−0.604154	−	0.604154i
$442$		0			0
$443$	−5998.55	−	2484.68i	−0.643340	−	0.266480i	0.0370688	−	0.999313i	$-0.488198\pi$
$443$	−5998.55	−	2484.68i	−0.643340	−	0.266480i	−0.680409	+	0.732832i	$0.738198\pi$
$444$		0			0
$445$	856.302	+	2067.29i	0.0912193	+	0.220223i
$446$		0			0
$447$	−1313.93			−0.139031
$448$		0			0
$449$	10135.3			1.06529			0.532646	−	0.846338i	$-0.321198\pi$
$449$	10135.3			1.06529			0.532646	+	0.846338i	$0.321198\pi$
$450$		0			0
$451$	−170.714	−	412.141i	−0.0178240	−	0.0430310i
$452$		0			0
$453$	2400.70	+	994.401i	0.248995	+	0.103137i
$454$		0			0
$455$	−304.948	−	304.948i	−0.0314202	−	0.0314202i
$456$		0			0
$457$	−2946.68	+	2946.68i	−0.301619	+	0.301619i	−0.841647	−	0.540028i	$-0.818414\pi$
$457$	−2946.68	+	2946.68i	−0.301619	+	0.301619i	0.540028	+	0.841647i	$0.318414\pi$
$458$		0			0
$459$	−2685.95	+	6484.45i	−0.273136	+	0.659408i
$460$		0			0
$461$	−10176.1	+	4215.08i	−1.02809	+	0.425847i	−0.832021	−	0.554743i	$-0.812816\pi$
$461$	−10176.1	+	4215.08i	−1.02809	+	0.425847i	−0.196065	+	0.980591i	$0.562816\pi$
$462$		0			0
$463$		−	11097.1i		−	1.11388i	−0.830552	−	0.556941i	$-0.811975\pi$
$463$		−	11097.1i		−	1.11388i	0.830552	−	0.556941i	$-0.188025\pi$
$464$		0			0
$465$		−	1497.21i		−	0.149315i
$466$		0			0
$467$	9665.86	−	4003.73i	0.957779	−	0.396725i	0.151630	−	0.988437i	$-0.451548\pi$
$467$	9665.86	−	4003.73i	0.957779	−	0.396725i	0.806149	+	0.591712i	$0.201548\pi$
$468$		0			0
$469$	326.277	−	787.701i	0.0321238	−	0.0775537i
$470$		0			0
$471$	1547.81	−	1547.81i	0.151421	−	0.151421i
$472$		0			0
$473$	−665.552	−	665.552i	−0.0646979	−	0.0646979i
$474$		0			0
$475$	−1886.01	−	781.212i	−0.182181	−	0.0754620i
$476$		0			0
$477$	1398.96	+	3377.38i	0.134285	+	0.324192i
$478$		0			0
$479$	19410.2			1.85151			0.925757	−	0.378119i	$-0.123429\pi$
$479$	19410.2			1.85151			0.925757	+	0.378119i	$0.123429\pi$
$480$		0			0
$481$	−3456.50			−0.327656
$482$		0			0
$483$	310.996	+	750.810i	0.0292977	+	0.0707309i
$484$		0			0
$485$	2719.06	+	1126.27i	0.254570	+	0.105446i
$486$		0			0
$487$	−10505.7	−	10505.7i	−0.977530	−	0.977530i	0.0222232	−	0.999753i	$-0.492926\pi$
$487$	−10505.7	−	10505.7i	−0.977530	−	0.977530i	−0.999753	+	0.0222232i	$0.992926\pi$
$488$		0			0
$489$	1542.24	−	1542.24i	0.142623	−	0.142623i
$490$		0			0
$491$	5195.37	−	12542.7i	0.477523	−	1.15284i	−0.483243	−	0.875486i	$-0.660541\pi$
$491$	5195.37	−	12542.7i	0.477523	−	1.15284i	0.960767	−	0.277357i	$-0.0894586\pi$
$492$		0			0
$493$	14255.3	−	5904.72i	1.30228	−	0.539422i
$494$		0			0
$495$			242.689i			0.0220365i
$496$		0			0
$497$			1217.77i			0.109908i
$498$		0			0
$499$	7506.94	−	3109.48i	0.673461	−	0.278957i	−0.0196297	−	0.999807i	$-0.506249\pi$
$499$	7506.94	−	3109.48i	0.673461	−	0.278957i	0.693090	+	0.720851i	$0.256249\pi$
$500$		0			0
$501$	883.395	−	2132.70i	0.0787768	−	0.190184i
$502$		0			0
$503$	2849.72	−	2849.72i	0.252610	−	0.252610i	−0.569430	−	0.822040i	$-0.692836\pi$
$503$	2849.72	−	2849.72i	0.252610	−	0.252610i	0.822040	+	0.569430i	$0.192836\pi$
$504$		0			0
$505$	−3807.05	−	3807.05i	−0.335468	−	0.335468i
$506$		0			0
$507$	405.770	+	168.075i	0.0355441	+	0.0147229i
$508$		0			0
$509$	5853.53	+	14131.7i	0.509731	+	1.23060i	0.944039	+	0.329834i	$0.106993\pi$
$509$	5853.53	+	14131.7i	0.509731	+	1.23060i	−0.434308	+	0.900764i	$0.643007\pi$
$510$		0			0
$511$	1899.15			0.164409
$512$		0			0
$513$	−1896.26			−0.163201
$514$		0			0
$515$	−632.701	−	1527.47i	−0.0541362	−	0.130696i
$516$		0			0
$517$	−492.975	−	204.197i	−0.0419362	−	0.0173705i
$518$		0			0
$519$	3516.44	+	3516.44i	0.297407	+	0.297407i
$520$		0			0
$521$	−108.330	+	108.330i	−0.00910949	+	0.00910949i	−0.711647	−	0.702537i	$-0.752050\pi$
$521$	−108.330	+	108.330i	−0.00910949	+	0.00910949i	0.702537	+	0.711647i	$0.252050\pi$
$522$		0			0
$523$	−7209.17	+	17404.5i	−0.602744	+	1.45515i	0.268001	+	0.963419i	$0.413637\pi$
$523$	−7209.17	+	17404.5i	−0.602744	+	1.45515i	−0.870745	+	0.491734i	$0.836363\pi$
$524$		0			0
$525$	380.471	−	157.596i	0.0316288	−	0.0131011i
$526$		0			0
$527$		−	12342.5i		−	1.02021i
$528$		0			0
$529$		−	29432.1i		−	2.41901i
$530$		0			0
$531$	−13618.2	+	5640.84i	−1.11296	+	0.461001i
$532$		0			0
$533$	−3391.12	+	8186.89i	−0.275583	+	0.665317i
$534$		0			0
$535$	4638.58	−	4638.58i	0.374847	−	0.374847i
$536$		0			0
$537$	2227.07	+	2227.07i	0.178966	+	0.178966i
$538$		0			0
$539$	698.434	+	289.301i	0.0558138	+	0.0231189i
$540$		0			0
$541$	−1014.09	−	2448.22i	−0.0805895	−	0.194560i	0.878449	−	0.477836i	$-0.158579\pi$
$541$	−1014.09	−	2448.22i	−0.0805895	−	0.194560i	−0.959038	+	0.283276i	$0.908579\pi$
$542$		0			0
$543$	7409.02			0.585546
$544$		0			0
$545$	3641.22			0.286188
$546$		0			0
$547$	430.820	+	1040.09i	0.0336755	+	0.0813000i	0.939823	−	0.341663i	$-0.110990\pi$
$547$	430.820	+	1040.09i	0.0336755	+	0.0813000i	−0.906147	+	0.422963i	$0.860990\pi$
$548$		0			0
$549$	13442.8	+	5568.18i	1.04503	+	0.432868i
$550$		0			0
$551$	2947.71	+	2947.71i	0.227907	+	0.227907i
$552$		0			0
$553$	1182.84	−	1182.84i	0.0909578	−	0.0909578i
$554$		0			0
$555$	−264.517	+	638.601i	−0.0202309	+	0.0488416i
$556$		0			0
$557$	388.391	−	160.877i	0.0295452	−	0.0122380i	−0.367862	−	0.929880i	$-0.619910\pi$
$557$	388.391	−	160.877i	0.0295452	−	0.0122380i	0.397407	+	0.917642i	$0.369910\pi$
$558$		0			0
$559$			18696.9i			1.41466i
$560$		0			0
$561$		−	311.100i		−	0.0234129i
$562$		0			0
$563$	−12187.4	+	5048.19i	−0.912323	+	0.377897i	−0.788946	−	0.614463i	$-0.789373\pi$
$563$	−12187.4	+	5048.19i	−0.912323	+	0.377897i	−0.123378	+	0.992360i	$0.539373\pi$
$564$		0			0
$565$	−210.957	+	509.296i	−0.0157080	+	0.0379226i
$566$		0			0
$567$	−662.015	+	662.015i	−0.0490335	+	0.0490335i
$568$		0			0
$569$	−7590.98	−	7590.98i	−0.559280	−	0.559280i	0.369822	−	0.929102i	$-0.379418\pi$
$569$	−7590.98	−	7590.98i	−0.559280	−	0.559280i	−0.929102	+	0.369822i	$0.879418\pi$
$570$		0			0
$571$	−19882.0	−	8235.38i	−1.45715	−	0.603573i	−0.493265	−	0.869879i	$-0.664197\pi$
$571$	−19882.0	−	8235.38i	−1.45715	−	0.603573i	−0.963888	+	0.266306i	$0.914197\pi$
$572$		0			0
$573$	1391.89	+	3360.31i	0.101478	+	0.244990i
$574$		0			0
$575$	−21080.3			−1.52888
$576$		0			0
$577$	−4301.60			−0.310361			−0.155180	−	0.987886i	$-0.549596\pi$
$577$	−4301.60			−0.310361			−0.155180	+	0.987886i	$0.549596\pi$
$578$		0			0
$579$	2680.49	+	6471.28i	0.192396	+	0.464485i
$580$		0			0
$581$	−2812.07	−	1164.80i	−0.200799	−	0.0831737i
$582$		0			0
$583$	−246.967	−	246.967i	−0.0175443	−	0.0175443i
$584$		0			0
$585$	3408.86	−	3408.86i	0.240921	−	0.240921i
$586$		0			0
$587$	−1724.60	+	4163.55i	−0.121264	+	0.292756i	−0.972842	−	0.231471i	$-0.925646\pi$
$587$	−1724.60	+	4163.55i	−0.121264	+	0.292756i	0.851578	+	0.524228i	$0.175646\pi$
$588$		0			0
$589$	3080.77	−	1276.10i	0.215520	−	0.0892712i
$590$		0			0
$591$		−	5239.10i		−	0.364649i
$592$		0			0
$593$			19409.8i			1.34412i	0.740495	+	0.672062i	$0.234591\pi$
$593$			19409.8i			1.34412i	−0.740495	+	0.672062i	$0.765409\pi$
$594$		0			0
$595$	−656.832	+	272.069i	−0.0452563	+	0.0187458i
$596$		0			0
$597$	1806.54	−	4361.37i	0.123847	−	0.298993i
$598$		0			0
$599$	182.514	−	182.514i	0.0124496	−	0.0124496i	−0.700855	−	0.713304i	$-0.747198\pi$
$599$	182.514	−	182.514i	0.0124496	−	0.0124496i	0.713304	+	0.700855i	$0.247198\pi$
$600$		0			0
$601$	−2102.19	−	2102.19i	−0.142679	−	0.142679i	0.632159	−	0.774838i	$-0.282169\pi$
$601$	−2102.19	−	2102.19i	−0.142679	−	0.142679i	−0.774838	+	0.632159i	$0.782169\pi$
$602$		0			0
$603$	8805.31	+	3647.28i	0.594660	+	0.246316i
$604$		0			0
$605$	2360.81	+	5699.51i	0.158646	+	0.383005i
$606$		0			0
$607$	13085.1			0.874974			0.437487	−	0.899225i	$-0.355869\pi$
$607$	13085.1			0.874974			0.437487	+	0.899225i	$0.355869\pi$
$608$		0			0
$609$	−840.964			−0.0559566
$610$		0			0
$611$	4056.23	+	9792.60i	0.268572	+	0.648390i
$612$		0			0
$613$	−8687.78	−	3598.60i	−0.572424	−	0.237106i	0.0776446	−	0.996981i	$-0.475260\pi$
$613$	−8687.78	−	3598.60i	−0.572424	−	0.237106i	−0.650069	+	0.759875i	$0.725260\pi$
$614$		0			0
$615$	1253.04	+	1253.04i	0.0821587	+	0.0821587i
$616$		0			0
$617$	−3141.32	+	3141.32i	−0.204967	+	0.204967i	−0.802124	−	0.597157i	$-0.796297\pi$
$617$	−3141.32	+	3141.32i	−0.204967	+	0.204967i	0.597157	+	0.802124i	$0.296297\pi$
$618$		0			0
$619$	808.300	−	1951.41i	0.0524852	−	0.126710i	−0.895462	−	0.445138i	$-0.853155\pi$
$619$	808.300	−	1951.41i	0.0524852	−	0.126710i	0.947947	+	0.318427i	$0.103155\pi$
$620$		0			0
$621$	−18090.9	+	7493.51i	−1.16902	+	0.484226i
$622$		0			0
$623$		−	1005.37i		−	0.0646536i
$624$		0			0
$625$			7976.82i			0.510516i
$626$		0			0
$627$	77.6525	−	32.1647i	0.00494600	−	0.00204870i
$628$		0			0
$629$	−2180.59	+	5264.41i	−0.138229	+	0.333713i
$630$		0			0
$631$	−4291.77	+	4291.77i	−0.270765	+	0.270765i	−0.829408	−	0.558643i	$-0.811322\pi$
$631$	−4291.77	+	4291.77i	−0.270765	+	0.270765i	0.558643	+	0.829408i	$0.311322\pi$
$632$		0			0
$633$	6016.28	+	6016.28i	0.377765	+	0.377765i
$634$		0			0
$635$	−3619.81	−	1499.38i	−0.226217	−	0.0937023i
$636$		0			0
$637$	−5746.75	−	13873.9i	−0.357449	−	0.862957i
$638$		0			0
$639$	−13612.8			−0.842748
$640$		0			0
$641$	−14676.8			−0.904365			−0.452182	−	0.891925i	$-0.649354\pi$
$641$	−14676.8			−0.904365			−0.452182	+	0.891925i	$0.649354\pi$
$642$		0			0
$643$	−11364.5	−	27436.3i	−0.697001	−	1.68271i	−0.730175	−	0.683260i	$-0.760562\pi$
$643$	−11364.5	−	27436.3i	−0.697001	−	1.68271i	0.0331742	−	0.999450i	$-0.489438\pi$
$644$		0			0
$645$	3454.32	+	1430.83i	0.210874	+	0.0873470i
$646$		0			0
$647$	10214.4	+	10214.4i	0.620661	+	0.620661i	0.945701	−	0.325039i	$-0.105378\pi$
$647$	10214.4	+	10214.4i	0.620661	+	0.620661i	−0.325039	+	0.945701i	$0.605378\pi$
$648$		0			0
$649$	995.815	−	995.815i	0.0602298	−	0.0602298i
$650$		0			0
$651$	−257.431	+	621.494i	−0.0154985	+	0.0374167i
$652$		0			0
$653$	−3089.13	+	1279.56i	−0.185125	+	0.0766814i	−0.473321	−	0.880890i	$-0.656945\pi$
$653$	−3089.13	+	1279.56i	−0.185125	+	0.0766814i	0.288195	+	0.957572i	$0.406945\pi$
$654$		0			0
$655$		−	5943.60i		−	0.354558i
$656$		0			0
$657$			21229.6i			1.26065i
$658$		0			0
$659$	−12234.1	+	5067.54i	−0.723178	+	0.299550i	−0.713745	−	0.700405i	$-0.753003\pi$
$659$	−12234.1	+	5067.54i	−0.723178	+	0.299550i	−0.00943266	+	0.999956i	$0.503003\pi$
$660$		0			0
$661$	−8849.67	+	21365.0i	−0.520745	+	1.25719i	0.416696	+	0.909046i	$0.363188\pi$
$661$	−8849.67	+	21365.0i	−0.520745	+	1.25719i	−0.937441	+	0.348144i	$0.886812\pi$
$662$		0			0
$663$	−4369.76	+	4369.76i	−0.255969	+	0.255969i
$664$		0			0
$665$	−135.820	−	135.820i	−0.00792012	−	0.00792012i
$666$		0			0
$667$	39770.6	+	16473.5i	2.30873	+	0.956309i
$668$		0			0
$669$	−3552.46	−	8576.39i	−0.205300	−	0.495639i
$670$		0			0
$671$	−1390.16			−0.0799797
$672$		0			0
$673$	−11132.3			−0.637621			−0.318811	−	0.947818i	$-0.603283\pi$
$673$	−11132.3			−0.637621			−0.318811	+	0.947818i	$0.603283\pi$
$674$		0			0
$675$	3797.32	+	9167.53i	0.216532	+	0.522753i
$676$		0			0
$677$	19266.1	+	7980.30i	1.09373	+	0.453040i	0.855307	−	0.518121i	$-0.173368\pi$
$677$	19266.1	+	7980.30i	1.09373	+	0.453040i	0.238427	+	0.971160i	$0.423368\pi$
$678$		0			0
$679$	−935.033	−	935.033i	−0.0528472	−	0.0528472i
$680$		0			0
$681$	−39.5138	+	39.5138i	−0.00222345	+	0.00222345i
$682$		0			0
$683$	6152.93	−	14854.5i	0.344708	−	0.832199i	−0.652519	−	0.757773i	$-0.726288\pi$
$683$	6152.93	−	14854.5i	0.344708	−	0.832199i	0.997227	−	0.0744258i	$-0.0237124\pi$
$684$		0			0
$685$	2153.51	−	892.014i	0.120119	−	0.0497549i
$686$		0			0
$687$		−	8786.97i		−	0.487982i
$688$		0			0
$689$			6937.89i			0.383618i
$690$		0			0
$691$	3264.16	−	1352.06i	0.179703	−	0.0744353i	−0.291018	−	0.956718i	$-0.593994\pi$
$691$	3264.16	−	1352.06i	0.179703	−	0.0744353i	0.470721	+	0.882282i	$0.343994\pi$
$692$		0			0
$693$	41.7281	−	100.740i	0.00228733	−	0.00552210i
$694$		0			0
$695$	−4357.56	+	4357.56i	−0.237830	+	0.237830i
$696$		0			0
$697$	10329.7	+	10329.7i	0.561355	+	0.561355i
$698$		0			0
$699$	−11590.8	−	4801.05i	−0.627186	−	0.259789i
$700$		0			0
$701$	−9617.29	−	23218.2i	−0.518174	−	1.25098i	−0.939024	−	0.343852i	$-0.888268\pi$
$701$	−9617.29	−	23218.2i	−0.518174	−	1.25098i	0.420850	−	0.907130i	$-0.361732\pi$
$702$		0			0
$703$	−1539.48			−0.0825927
$704$		0			0
$705$	2119.63			0.113234
$706$		0			0
$707$	925.723	+	2234.89i	0.0492438	+	0.118885i
$708$		0			0
$709$	−16496.9	−	6833.23i	−0.873841	−	0.361957i	−0.0997360	−	0.995014i	$-0.531800\pi$
$709$	−16496.9	−	6833.23i	−0.873841	−	0.361957i	−0.774105	+	0.633057i	$0.781800\pi$
$710$		0			0
$711$	13222.4	+	13222.4i	0.697439	+	0.697439i
$712$		0			0
$713$	24348.7	−	24348.7i	1.27892	−	1.27892i
$714$		0			0
$715$	−176.260	+	425.529i	−0.00921922	+	0.0222572i
$716$		0			0
$717$	−1109.82	+	459.703i	−0.0578062	+	0.0239441i
$718$		0			0
$719$		−	8307.83i		−	0.430918i	−0.976513	−	0.215459i	$-0.930875\pi$
$719$		−	8307.83i		−	0.430918i	0.976513	−	0.215459i	$-0.0691247\pi$
$720$		0			0
$721$			742.842i			0.0383702i
$722$		0			0
$723$	−2683.09	+	1111.37i	−0.138015	+	0.0571679i
$724$		0			0
$725$	8347.93	−	20153.7i	0.427633	−	1.03240i
$726$		0			0
$727$	−18455.8	+	18455.8i	−0.941524	+	0.941524i	−0.998382	−	0.0568585i	$-0.981892\pi$
$727$	−18455.8	+	18455.8i	−0.941524	+	0.941524i	0.0568585	+	0.998382i	$0.481892\pi$
$728$		0			0
$729$	−3906.40	−	3906.40i	−0.198466	−	0.198466i
$730$		0			0
$731$	28476.3	+	11795.3i	1.44081	+	0.596804i
$732$		0			0
$733$	1663.72	+	4016.59i	0.0838350	+	0.202396i	0.960238	−	0.279183i	$-0.0900636\pi$
$733$	1663.72	+	4016.59i	0.0838350	+	0.202396i	−0.876403	+	0.481579i	$0.840064\pi$
$734$		0			0
$735$	−3003.04			−0.150706
$736$		0			0
$737$	−910.581			−0.0455111
$738$		0			0
$739$	−5023.53	−	12127.9i	−0.250059	−	0.603695i	0.748149	−	0.663530i	$-0.230943\pi$
$739$	−5023.53	−	12127.9i	−0.250059	−	0.603695i	−0.998208	+	0.0598348i	$0.980943\pi$
$740$		0			0
$741$	−1542.51	−	638.930i	−0.0764718	−	0.0316757i
$742$		0			0
$743$	−2091.87	−	2091.87i	−0.103289	−	0.103289i	0.653574	−	0.756863i	$-0.273269\pi$
$743$	−2091.87	−	2091.87i	−0.103289	−	0.103289i	−0.756863	+	0.653574i	$0.773269\pi$
$744$		0			0
$745$	2267.62	−	2267.62i	0.111516	−	0.111516i
$746$		0			0
$747$	13020.7	−	31434.7i	0.637753	−	1.53967i
$748$		0			0
$749$	−2723.03	+	1127.92i	−0.132840	+	0.0550243i
$750$		0			0
$751$		−	24.8821i		−	0.00120900i	−1.00000		0.000604502i	$-0.999808\pi$
$751$		−	24.8821i		−	0.00120900i	1.00000		0.000604502i	$-0.000192419\pi$
$752$		0			0
$753$			6072.45i			0.293881i
$754$		0			0
$755$	−5859.34	+	2427.02i	−0.282442	+	0.116991i
$756$		0			0
$757$	8933.37	−	21567.1i	0.428915	−	1.03549i	−0.550717	−	0.834692i	$-0.685646\pi$
$757$	8933.37	−	21567.1i	0.428915	−	1.03549i	0.979632	−	0.200801i	$-0.0643544\pi$
$758$		0			0
$759$	613.722	−	613.722i	0.0293501	−	0.0293501i
$760$		0			0
$761$	−11741.7	−	11741.7i	−0.559311	−	0.559311i	0.369800	−	0.929111i	$-0.379426\pi$
$761$	−11741.7	−	11741.7i	−0.559311	−	0.559311i	−0.929111	+	0.369800i	$0.879426\pi$
$762$		0			0
$763$	−1511.47	−	626.072i	−0.0717155	−	0.0297055i
$764$		0			0
$765$	−3041.32	−	7342.39i	−0.143737	−	0.347012i
$766$		0			0
$767$	−27974.8			−1.31696
$768$		0			0
$769$	31635.5			1.48349			0.741745	−	0.670682i	$-0.233998\pi$
$769$	31635.5			1.48349			0.741745	+	0.670682i	$0.233998\pi$
$770$		0			0
$771$	−2448.01	−	5910.02i	−0.114349	−	0.276063i
$772$		0			0
$773$	36991.4	+	15322.3i	1.72120	+	0.712944i	0.999791	+	0.0204334i	$0.00650462\pi$
$773$	36991.4	+	15322.3i	1.72120	+	0.712944i	0.721408	+	0.692511i	$0.243495\pi$
$774$		0			0
$775$	−12338.7	−	12338.7i	−0.571894	−	0.571894i
$776$		0			0
$777$	219.602	−	219.602i	0.0101392	−	0.0101392i
$778$		0			0
$779$	−1510.36	+	3646.34i	−0.0694665	+	0.167707i
$780$		0			0
$781$	1201.58	−	497.712i	0.0550525	−	0.0228035i
$782$		0			0
$783$		−	20263.2i		−	0.924838i
$784$		0			0
$785$			5342.49i			0.242907i
$786$		0			0
$787$	26589.7	−	11013.8i	1.20435	−	0.498857i	0.311946	−	0.950100i	$-0.399019\pi$
$787$	26589.7	−	11013.8i	1.20435	−	0.498857i	0.892401	+	0.451243i	$0.149019\pi$
$788$		0			0
$789$	3377.04	−	8152.89i	0.152377	−	0.367871i
$790$		0			0
$791$	175.137	−	175.137i	0.00787251	−	0.00787251i
$792$		0			0
$793$	19526.4	+	19526.4i	0.874403	+	0.874403i
$794$		0			0
$795$	1281.80	+	530.939i	0.0571833	+	0.0236861i
$796$		0			0
$797$	−14859.3	−	35873.5i	−0.660406	−	1.59436i	−0.797168	−	0.603757i	$-0.793670\pi$
$797$	−14859.3	−	35873.5i	−0.660406	−	1.59436i	0.136763	−	0.990604i	$-0.456330\pi$
$798$		0			0
$799$	17473.5			0.773678
$800$		0			0
$801$	11238.5			0.495746
$802$		0			0
$803$	−776.194	−	1873.90i	−0.0341112	−	0.0823517i
$804$		0			0
$805$	−1832.49	−	759.042i	−0.0802321	−	0.0332332i
$806$		0			0
$807$	2222.60	+	2222.60i	0.0969507	+	0.0969507i
$808$		0			0
$809$	11376.3	−	11376.3i	0.494401	−	0.494401i	−0.415288	−	0.909690i	$-0.636319\pi$
$809$	11376.3	−	11376.3i	0.494401	−	0.494401i	0.909690	+	0.415288i	$0.136319\pi$
$810$		0			0
$811$	5636.60	−	13608.0i	0.244054	−	0.589199i	−0.753624	−	0.657306i	$-0.771696\pi$
$811$	5636.60	−	13608.0i	0.244054	−	0.589199i	0.997678	+	0.0681071i	$0.0216960\pi$
$812$		0			0
$813$	−10609.4	+	4394.55i	−0.457672	+	0.189574i
$814$		0			0
$815$			5323.27i			0.228793i
$816$		0			0
$817$			8327.39i			0.356595i
$818$		0			0
$819$	−2001.14	+	828.899i	−0.0853791	+	0.0353652i
$820$		0			0
$821$	−919.197	+	2219.14i	−0.0390745	+	0.0943343i	−0.942212	−	0.335017i	$-0.891258\pi$
$821$	−919.197	+	2219.14i	−0.0390745	+	0.0943343i	0.903137	+	0.429352i	$0.141258\pi$
$822$		0			0
$823$	−11701.5	+	11701.5i	−0.495612	+	0.495612i	−0.910069	−	0.414457i	$-0.863971\pi$
$823$	−11701.5	+	11701.5i	−0.495612	+	0.495612i	0.414457	+	0.910069i	$0.363971\pi$
$824$		0			0
$825$	−311.002	−	311.002i	−0.0131245	−	0.0131245i
$826$		0			0
$827$	12650.0	+	5239.79i	0.531901	+	0.220321i	0.632436	−	0.774613i	$-0.282055\pi$
$827$	12650.0	+	5239.79i	0.531901	+	0.220321i	−0.100534	+	0.994934i	$0.532055\pi$
$828$		0			0
$829$	6993.42	+	16883.6i	0.292993	+	0.707349i	1.00000		0.000141685i	$4.50997e-5\pi$
$829$	6993.42	+	16883.6i	0.292993	+	0.707349i	−0.707007	+	0.707207i	$0.749955\pi$
$830$		0			0
$831$	−3144.59			−0.131269
$832$		0			0
$833$	−24756.0			−1.02971
$834$		0			0
$835$	2156.09	+	5205.26i	0.0893587	+	0.215731i
$836$		0			0
$837$	−14975.0	−	6202.86i	−0.618415	−	0.256156i
$838$		0			0
$839$	8472.75	+	8472.75i	0.348643	+	0.348643i	0.859604	−	0.510961i	$-0.170710\pi$
$839$	8472.75	+	8472.75i	0.348643	+	0.348643i	−0.510961	+	0.859604i	$0.670710\pi$
$840$		0			0
$841$	−14253.2	+	14253.2i	−0.584413	+	0.584413i
$842$		0			0
$843$	191.115	−	461.393i	0.00780825	−	0.0188508i
$844$		0			0
$845$	−990.357	+	410.219i	−0.0403187	+	0.0167006i
$846$		0			0
$847$		−	2771.79i		−	0.112444i
$848$		0			0
$849$		−	10337.0i		−	0.417861i
$850$		0			0
$851$	−14687.1	+	6083.61i	−0.591620	+	0.245057i
$852$		0			0
$853$	−9905.44	+	23913.8i	−0.397603	+	0.959900i	0.590629	+	0.806943i	$0.298879\pi$
$853$	−9905.44	+	23913.8i	−0.397603	+	0.959900i	−0.988233	+	0.152957i	$0.951121\pi$
$854$		0			0
$855$	1518.26	−	1518.26i	0.0607293	−	0.0607293i
$856$		0			0
$857$	−918.681	−	918.681i	−0.0366179	−	0.0366179i	0.688561	−	0.725179i	$-0.258243\pi$
$857$	−918.681	−	918.681i	−0.0366179	−	0.0366179i	−0.725179	+	0.688561i	$0.758243\pi$
$858$		0			0
$859$	−16817.5	−	6966.03i	−0.667992	−	0.276691i	0.0228054	−	0.999740i	$-0.492740\pi$
$859$	−16817.5	−	6966.03i	−0.667992	−	0.276691i	−0.690797	+	0.723049i	$0.742740\pi$
$860$		0			0
$861$	−304.691	−	735.588i	−0.0120602	−	0.0291159i
$862$		0			0
$863$	30735.4			1.21233			0.606167	−	0.795338i	$-0.292706\pi$
$863$	30735.4			1.21233			0.606167	+	0.795338i	$0.292706\pi$
$864$		0			0
$865$	−12137.5			−0.477096
$866$		0			0
$867$	314.782	+	759.952i	0.0123305	+	0.0297685i
$868$		0			0
$869$	−1650.56	−	683.683i	−0.0644319	−	0.0266886i
$870$		0			0
$871$	12790.2	+	12790.2i	0.497565	+	0.497565i
$872$		0			0
$873$	10452.2	−	10452.2i	0.405218	−	0.405218i
$874$		0			0
$875$	−849.837	+	2051.69i	−0.0328340	+	0.0792682i
$876$		0			0
$877$	15138.1	−	6270.40i	0.582870	−	0.241433i	−0.0717100	−	0.997426i	$-0.522846\pi$
$877$	15138.1	−	6270.40i	0.582870	−	0.241433i	0.654580	+	0.755993i	$0.272846\pi$
$878$		0			0
$879$			7574.08i			0.290634i
$880$		0			0
$881$		−	8980.66i		−	0.343435i	−0.985146	−	0.171717i	$-0.945068\pi$
$881$		−	8980.66i		−	0.343435i	0.985146	−	0.171717i	$-0.0549316\pi$
$882$		0			0
$883$	−16480.5	+	6826.45i	−0.628101	+	0.260168i	−0.673946	−	0.738780i	$-0.735402\pi$
$883$	−16480.5	+	6826.45i	−0.628101	+	0.260168i	0.0458448	+	0.998949i	$0.485402\pi$
$884$		0			0
$885$	−2140.84	+	5168.44i	−0.0813147	+	0.196311i
$886$		0			0
$887$	12126.2	−	12126.2i	0.459029	−	0.459029i	−0.439308	−	0.898337i	$-0.644776\pi$
$887$	12126.2	−	12126.2i	0.459029	−	0.459029i	0.898337	+	0.439308i	$0.144776\pi$
$888$		0			0
$889$	1244.78	+	1244.78i	0.0469614	+	0.0469614i
$890$		0			0
$891$	923.785	+	382.644i	0.0347339	+	0.0143873i
$892$		0			0
$893$	1806.59	+	4361.51i	0.0676992	+	0.163440i
$894$		0			0
$895$	−7687.05			−0.287095
$896$		0			0
$897$	−17240.9			−0.641758
$898$		0			0
$899$	13636.2	+	32920.8i	0.505888	+	1.22132i
$900$		0			0
$901$	10566.7	+	4376.88i	0.390709	+	0.161837i
$902$		0			0
$903$	−1187.88	−	1187.88i	−0.0437763	−	0.0437763i
$904$		0			0
$905$	−12786.7	+	12786.7i	−0.469661	+	0.469661i
$906$		0			0
$907$	−11478.3	+	27711.2i	−0.420212	+	1.01448i	0.562073	+	0.827087i	$0.310004\pi$
$907$	−11478.3	+	27711.2i	−0.420212	+	1.01448i	−0.982285	+	0.187393i	$0.939996\pi$
$908$		0			0
$909$	−24982.7	+	10348.2i	−0.911578	+	0.377588i
$910$		0			0
$911$		−	29181.6i		−	1.06128i	−0.847596	−	0.530642i	$-0.821951\pi$
$911$		−	29181.6i		−	1.06128i	0.847596	−	0.530642i	$-0.178049\pi$
$912$		0			0
$913$			3250.75i			0.117836i
$914$		0			0
$915$	5101.87	−	2113.26i	0.184331	−	0.0763523i
$916$		0			0
$917$	−1021.94	+	2467.19i	−0.0368021	+	0.0888482i
$918$		0			0
$919$	17444.3	−	17444.3i	0.626151	−	0.626151i	−0.320946	−	0.947097i	$-0.604001\pi$
$919$	17444.3	−	17444.3i	0.626151	−	0.626151i	0.947097	+	0.320946i	$0.104001\pi$
$920$		0			0
$921$	−7564.25	−	7564.25i	−0.270630	−	0.270630i
$922$		0			0
$923$	−23868.6	−	9886.70i	−0.851186	−	0.352573i
$924$		0			0
$925$	3082.85	+	7442.67i	0.109582	+	0.264555i
$926$		0			0
$927$	−8303.85			−0.294212
$928$		0			0
$929$	−2760.78			−0.0975009			−0.0487505	−	0.998811i	$-0.515524\pi$
$929$	−2760.78			−0.0975009			−0.0487505	+	0.998811i	$0.515524\pi$
$930$		0			0
$931$	−2559.54	−	6179.26i	−0.0901024	−	0.217527i
$932$		0			0
$933$	11852.1	+	4909.29i	0.415884	+	0.172265i
$934$		0			0
$935$	536.904	+	536.904i	0.0187793	+	0.0187793i
$936$		0			0
$937$	−20708.4	+	20708.4i	−0.721998	+	0.721998i	−0.969012	−	0.247014i	$-0.920551\pi$
$937$	−20708.4	+	20708.4i	−0.721998	+	0.721998i	0.247014	+	0.969012i	$0.420551\pi$
$938$		0			0
$939$	1680.72	−	4057.62i	0.0584113	−	0.141017i
$940$		0			0
$941$	11292.0	−	4677.30i	0.391189	−	0.162036i	−0.178415	−	0.983955i	$-0.557097\pi$
$941$	11292.0	−	4677.30i	0.391189	−	0.162036i	0.569603	+	0.821920i	$0.307097\pi$
$942$		0			0
$943$			40755.8i			1.40741i
$944$		0			0
$945$			933.657i			0.0321395i
$946$		0			0
$947$	−9860.15	+	4084.21i	−0.338344	+	0.140147i	−0.545385	−	0.838186i	$-0.683617\pi$
$947$	−9860.15	+	4084.21i	−0.338344	+	0.140147i	0.207041	+	0.978332i	$0.433617\pi$
$948$		0			0
$949$	−15418.6	+	37223.7i	−0.527405	+	1.27327i
$950$		0			0
$951$	−6047.77	+	6047.77i	−0.206217	+	0.206217i
$952$		0			0
$953$	−18343.1	−	18343.1i	−0.623497	−	0.623497i	0.322927	−	0.946424i	$-0.395333\pi$
$953$	−18343.1	−	18343.1i	−0.623497	−	0.623497i	−0.946424	+	0.322927i	$0.895333\pi$
$954$		0			0
$955$	−8201.47	−	3397.16i	−0.277899	−	0.115109i
$956$		0			0
$957$	343.708	+	829.784i	0.0116097	+	0.0280283i
$958$		0			0
$959$	−1047.30			−0.0352649
$960$		0			0
$961$	−1287.46			−0.0432165
$962$		0			0
$963$	−12608.4	−	30439.4i	−0.421911	−	1.01858i
$964$		0			0
$965$	−15794.4	−	6542.23i	−0.526879	−	0.218240i
$966$		0			0
$967$	−31549.6	−	31549.6i	−1.04919	−	1.04919i	−0.998726	−	0.0504630i	$-0.983930\pi$
$967$	−31549.6	−	31549.6i	−1.04919	−	1.04919i	−0.0504630	−	0.998726i	$-0.516070\pi$
$968$		0			0
$969$	−1946.24	+	1946.24i	−0.0645224	+	0.0645224i
$970$		0			0
$971$	−14733.2	+	35569.2i	−0.486934	+	1.17556i	0.469322	+	0.883027i	$0.344499\pi$
$971$	−14733.2	+	35569.2i	−0.486934	+	1.17556i	−0.956255	+	0.292534i	$0.905501\pi$
$972$		0			0
$973$	2558.07	−	1059.59i	0.0842835	−	0.0349114i
$974$		0			0
$975$			8736.79i			0.286976i
$976$		0			0
$977$		−	15596.5i		−	0.510724i	−0.966845	−	0.255362i	$-0.917805\pi$
$977$		−	15596.5i		−	0.510724i	0.966845	−	0.255362i	$-0.0821947\pi$
$978$		0			0
$979$	−992.003	+	410.901i	−0.0323846	+	0.0134141i
$980$		0			0
$981$	6998.54	−	16896.0i	0.227774	−	0.549894i
$982$		0			0
$983$	8671.68	−	8671.68i	0.281367	−	0.281367i	−0.552287	−	0.833654i	$-0.686245\pi$
$983$	8671.68	−	8671.68i	0.281367	−	0.281367i	0.833654	+	0.552287i	$0.186245\pi$
$984$		0			0
$985$	9041.76	+	9041.76i	0.292482	+	0.292482i
$986$		0			0
$987$	−879.860	−	364.450i	−0.0283751	−	0.0117534i
$988$		0			0
$989$	32907.5	+	79445.8i	1.05804	+	2.55433i
$990$		0			0
$991$	25010.6			0.801705			0.400852	−	0.916143i	$-0.368714\pi$
$991$	25010.6			0.801705			0.400852	+	0.916143i	$0.368714\pi$
$992$		0			0
$993$	17497.8			0.559191
$994$		0			0
$995$	4409.19	+	10644.7i	0.140483	+	0.339156i
$996$		0			0
$997$	−24578.9	−	10180.9i	−0.780763	−	0.323403i	−0.0435398	−	0.999052i	$-0.513864\pi$
$997$	−24578.9	−	10180.9i	−0.780763	−	0.323403i	−0.737223	+	0.675649i	$0.763864\pi$
$998$		0			0
$999$	5291.37	+	5291.37i	0.167579	+	0.167579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.113.5		44
4.3	odd	2		32.4.g.a.5.7	✓	44
8.3	odd	2		256.4.g.b.225.5		44
8.5	even	2		256.4.g.a.225.7		44
32.3	odd	8		256.4.g.b.33.5		44
32.13	even	8	inner	128.4.g.a.17.5		44
32.19	odd	8		32.4.g.a.13.7	yes	44
32.29	even	8		256.4.g.a.33.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.7	✓	44	4.3	odd	2
32.4.g.a.13.7	yes	44	32.19	odd	8
128.4.g.a.17.5		44	32.13	even	8	inner
128.4.g.a.113.5		44	1.1	even	1	trivial
256.4.g.a.33.7		44	32.29	even	8
256.4.g.a.225.7		44	8.5	even	2
256.4.g.b.33.5		44	32.3	odd	8
256.4.g.b.225.5		44	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.729459 - 1.76107i) q^{3} +(4.29822 + 1.78038i) q^{5} +(-1.47807 - 1.47807i) q^{7} +(16.5226 - 16.5226i) q^{9} +O(q^{10})\)	\(q+(-0.729459 - 1.76107i) q^{3} +(4.29822 + 1.78038i) q^{5} +(-1.47807 - 1.47807i) q^{7} +(16.5226 - 16.5226i) q^{9} +(-0.854325 + 2.06252i) q^{11} +(40.9706 - 16.9706i) q^{13} -8.86818i q^{15} -73.1063i q^{17} +(18.2478 - 7.55849i) q^{19} +(-1.52480 + 3.68119i) q^{21} +(144.221 - 144.221i) q^{23} +(-73.0834 - 73.0834i) q^{25} +(-88.6990 - 36.7403i) q^{27} +(80.7690 + 194.994i) q^{29} +168.830 q^{31} +4.25544 q^{33} +(-3.72155 - 8.98462i) q^{35} +(-72.0103 - 29.8277i) q^{37} +(-59.7727 - 59.7727i) q^{39} +(-141.297 + 141.297i) q^{41} +(-161.344 + 389.519i) q^{43} +(100.434 - 41.6013i) q^{45} +239.015i q^{47} -338.631i q^{49} +(-128.745 + 53.3280i) q^{51} +(-59.8701 + 144.539i) q^{53} +(-7.34415 + 7.34415i) q^{55} +(-26.6221 - 26.6221i) q^{57} +(-582.808 - 241.407i) q^{59} +(238.297 + 575.301i) q^{61} -48.8433 q^{63} +206.315 q^{65} +(156.090 + 376.834i) q^{67} +(-359.185 - 148.780i) q^{69} +(-411.945 - 411.945i) q^{71} +(-642.439 + 642.439i) q^{73} +(-75.3937 + 182.016i) q^{75} +(4.31132 - 1.78581i) q^{77} +800.261i q^{79} -447.890i q^{81} +(1345.29 - 557.236i) q^{83} +(130.157 - 314.227i) q^{85} +(284.480 - 284.480i) q^{87} +(340.094 + 340.094i) q^{89} +(-85.6413 - 35.4738i) q^{91} +(-123.155 - 297.321i) q^{93} +91.8900 q^{95} +632.602 q^{97} +(19.9626 + 48.1940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more