LMFDB - Embedded newform 128.4.g.a.17.7

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			17.7
Character	$\chi$	$=$	128.17
Dual form			128.4.g.a.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +O(q^{10})$	\(q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +(-11.7977 - 28.4821i) q^{11} +(-12.9230 - 5.35288i) q^{13} -49.1278i q^{15} -72.9239i q^{17} +(143.136 + 59.2889i) q^{19} +(6.17043 + 14.8967i) q^{21} +(-83.6411 - 83.6411i) q^{23} +(162.441 - 162.441i) q^{25} +(113.737 - 47.1114i) q^{27} +(-39.6554 + 95.7367i) q^{29} +29.0324 q^{31} -80.4149 q^{33} +(-44.5534 + 107.562i) q^{35} +(-267.681 + 110.877i) q^{37} +(-25.7996 + 25.7996i) q^{39} +(-124.918 - 124.918i) q^{41} +(27.0156 + 65.2215i) q^{43} +(351.421 + 145.564i) q^{45} +282.627i q^{47} +304.789i q^{49} +(-175.738 - 72.7931i) q^{51} +(-51.4343 - 124.173i) q^{53} +(-410.570 - 410.570i) q^{55} +(285.759 - 285.759i) q^{57} +(222.476 - 92.1524i) q^{59} +(-226.809 + 547.566i) q^{61} -124.842 q^{63} -263.447 q^{65} +(-356.015 + 859.496i) q^{67} +(-285.056 + 118.074i) q^{69} +(-690.837 + 690.837i) q^{71} +(223.345 + 223.345i) q^{73} +(-229.314 - 553.612i) q^{75} +(176.062 + 72.9275i) q^{77} -698.000i q^{79} +224.174i q^{81} +(915.116 + 379.053i) q^{83} +(-525.601 - 1268.91i) q^{85} +(191.130 + 191.130i) q^{87} +(-163.738 + 163.738i) q^{89} +(79.8837 - 33.0889i) q^{91} +(28.9803 - 69.9647i) q^{93} +2917.97 q^{95} -839.460 q^{97} +(238.266 - 575.225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	0.998206	−	2.40988i	0.192105	−	0.463782i	−0.798252	−	0.602324i	$-0.794242\pi$
$3$	0.998206	−	2.40988i	0.192105	−	0.463782i	0.990357	+	0.138542i	$0.0442415\pi$
$4$		0			0
$5$	17.4005	−	7.20752i	1.55635	−	0.644661i	0.571898	−	0.820325i	$-0.306207\pi$
$5$	17.4005	−	7.20752i	1.55635	−	0.644661i	0.984450	+	0.175664i	$0.0562073\pi$
$6$		0			0
$7$	−4.37099	+	4.37099i	−0.236012	+	0.236012i	−0.815196	−	0.579185i	$-0.803371\pi$
$7$	−4.37099	+	4.37099i	−0.236012	+	0.236012i	0.579185	+	0.815196i	$0.303371\pi$
$8$		0			0
$9$	14.2808	+	14.2808i	0.528917	+	0.528917i
$10$		0			0
$11$	−11.7977	−	28.4821i	−0.323375	−	0.780697i	−0.999053	−	0.0435002i	$-0.986149\pi$
$11$	−11.7977	−	28.4821i	−0.323375	−	0.780697i	0.675678	−	0.737197i	$-0.263851\pi$
$12$		0			0
$13$	−12.9230	−	5.35288i	−0.275707	−	0.114202i	0.240546	−	0.970638i	$-0.422674\pi$
$13$	−12.9230	−	5.35288i	−0.275707	−	0.114202i	−0.516253	+	0.856436i	$0.672674\pi$
$14$		0			0
$15$		−	49.1278i		−	0.845649i
$16$		0			0
$17$		−	72.9239i		−	1.04039i	−0.854047	−	0.520195i	$-0.825859\pi$
$17$		−	72.9239i		−	1.04039i	0.854047	−	0.520195i	$-0.174141\pi$
$18$		0			0
$19$	143.136	+	59.2889i	1.72830	+	0.715884i	0.999515	+	0.0311397i	$0.00991368\pi$
$19$	143.136	+	59.2889i	1.72830	+	0.715884i	0.728783	+	0.684745i	$0.240086\pi$
$20$		0			0
$21$	6.17043	+	14.8967i	0.0641190	+	0.154797i
$22$		0			0
$23$	−83.6411	−	83.6411i	−0.758278	−	0.758278i	0.217731	−	0.976009i	$-0.430134\pi$
$23$	−83.6411	−	83.6411i	−0.758278	−	0.758278i	−0.976009	+	0.217731i	$0.930134\pi$
$24$		0			0
$25$	162.441	−	162.441i	1.29953	−	1.29953i
$26$		0			0
$27$	113.737	−	47.1114i	0.810692	−	0.335800i
$28$		0			0
$29$	−39.6554	+	95.7367i	−0.253925	+	0.613030i	−0.998514	−	0.0544937i	$-0.982646\pi$
$29$	−39.6554	+	95.7367i	−0.253925	+	0.613030i	0.744589	+	0.667523i	$0.232646\pi$
$30$		0			0
$31$	29.0324			0.168206			0.0841029	−	0.996457i	$-0.473198\pi$
$31$	29.0324			0.168206			0.0841029	+	0.996457i	$0.473198\pi$
$32$		0			0
$33$	−80.4149			−0.424195
$34$		0			0
$35$	−44.5534	+	107.562i	−0.215169	+	0.519463i
$36$		0			0
$37$	−267.681	+	110.877i	−1.18936	+	0.492650i	−0.887547	−	0.460716i	$-0.847593\pi$
$37$	−267.681	+	110.877i	−1.18936	+	0.492650i	−0.301815	+	0.953366i	$0.597593\pi$
$38$		0			0
$39$	−25.7996	+	25.7996i	−0.105929	+	0.105929i
$40$		0			0
$41$	−124.918	−	124.918i	−0.475827	−	0.475827i	0.427968	−	0.903794i	$-0.359230\pi$
$41$	−124.918	−	124.918i	−0.475827	−	0.475827i	−0.903794	+	0.427968i	$0.859230\pi$
$42$		0			0
$43$	27.0156	+	65.2215i	0.0958103	+	0.231306i	0.964517	−	0.264020i	$-0.0850485\pi$
$43$	27.0156	+	65.2215i	0.0958103	+	0.231306i	−0.868707	+	0.495326i	$0.835048\pi$
$44$		0			0
$45$	351.421	+	145.564i	1.16415	+	0.482207i
$46$		0			0
$47$			282.627i			0.877136i	0.898698	+	0.438568i	$0.144514\pi$
$47$			282.627i			0.877136i	−0.898698	+	0.438568i	$0.855486\pi$
$48$		0			0
$49$			304.789i			0.888597i
$50$		0			0
$51$	−175.738	−	72.7931i	−0.482515	−	0.199864i
$52$		0			0
$53$	−51.4343	−	124.173i	−0.133303	−	0.321821i	0.843107	−	0.537745i	$-0.180724\pi$
$53$	−51.4343	−	124.173i	−0.133303	−	0.321821i	−0.976410	+	0.215924i	$0.930724\pi$
$54$		0			0
$55$	−410.570	−	410.570i	−1.00657	−	1.00657i
$56$		0			0
$57$	285.759	−	285.759i	0.664029	−	0.664029i
$58$		0			0
$59$	222.476	−	92.1524i	0.490913	−	0.203343i	−0.123474	−	0.992348i	$-0.539404\pi$
$59$	222.476	−	92.1524i	0.490913	−	0.203343i	0.614387	+	0.789005i	$0.289404\pi$
$60$		0			0
$61$	−226.809	+	547.566i	−0.476065	+	1.14932i	0.485374	+	0.874306i	$0.338683\pi$
$61$	−226.809	+	547.566i	−0.476065	+	1.14932i	−0.961440	+	0.275016i	$0.911317\pi$
$62$		0			0
$63$	−124.842			−0.249661
$64$		0			0
$65$	−263.447			−0.502717
$66$		0			0
$67$	−356.015	+	859.496i	−0.649166	+	1.56723i	0.164808	+	0.986326i	$0.447299\pi$
$67$	−356.015	+	859.496i	−0.649166	+	1.56723i	−0.813975	+	0.580900i	$0.802701\pi$
$68$		0			0
$69$	−285.056	+	118.074i	−0.497344	+	0.206007i
$70$		0			0
$71$	−690.837	+	690.837i	−1.15475	+	1.15475i	−0.169163	+	0.985588i	$0.554106\pi$
$71$	−690.837	+	690.837i	−1.15475	+	1.15475i	−0.985588	+	0.169163i	$0.945894\pi$
$72$		0			0
$73$	223.345	+	223.345i	0.358089	+	0.358089i	0.863108	−	0.505019i	$-0.168515\pi$
$73$	223.345	+	223.345i	0.358089	+	0.358089i	−0.505019	+	0.863108i	$0.668515\pi$
$74$		0			0
$75$	−229.314	−	553.612i	−0.353052	−	0.852342i
$76$		0			0
$77$	176.062	+	72.9275i	0.260574	+	0.107933i
$78$		0			0
$79$		−	698.000i		−	0.994065i	−0.867732	−	0.497033i	$-0.834423\pi$
$79$		−	698.000i		−	0.994065i	0.867732	−	0.497033i	$-0.165577\pi$
$80$		0			0
$81$			224.174i			0.307509i
$82$		0			0
$83$	915.116	+	379.053i	1.21020	+	0.501283i	0.894283	−	0.447502i	$-0.147686\pi$
$83$	915.116	+	379.053i	1.21020	+	0.501283i	0.315922	+	0.948785i	$0.397686\pi$
$84$		0			0
$85$	−525.601	−	1268.91i	−0.670699	−	1.61921i
$86$		0			0
$87$	191.130	+	191.130i	0.235532	+	0.235532i
$88$		0			0
$89$	−163.738	+	163.738i	−0.195014	+	0.195014i	−0.797859	−	0.602845i	$-0.794034\pi$
$89$	−163.738	+	163.738i	−0.195014	+	0.195014i	0.602845	+	0.797859i	$0.294034\pi$
$90$		0			0
$91$	79.8837	−	33.0889i	0.0920229	−	0.0381171i
$92$		0			0
$93$	28.9803	−	69.9647i	0.0323131	−	0.0780108i
$94$		0			0
$95$	2917.97			3.15134
$96$		0			0
$97$	−839.460			−0.878704			−0.439352	−	0.898315i	$-0.644792\pi$
$97$	−839.460			−0.878704			−0.439352	+	0.898315i	$0.644792\pi$
$98$		0			0
$99$	238.266	−	575.225i	0.241885	−	0.583963i
$100$		0			0
$101$	1561.02	−	646.594i	1.53789	−	0.637015i	0.556814	−	0.830637i	$-0.312024\pi$
$101$	1561.02	−	646.594i	1.53789	−	0.637015i	0.981076	+	0.193622i	$0.0620235\pi$
$102$		0			0
$103$	80.1481	−	80.1481i	0.0766721	−	0.0766721i	−0.667731	−	0.744403i	$-0.732734\pi$
$103$	80.1481	−	80.1481i	0.0766721	−	0.0766721i	0.744403	+	0.667731i	$0.232734\pi$
$104$		0			0
$105$	214.737	+	214.737i	0.199583	+	0.199583i
$106$		0			0
$107$	−552.814	−	1334.61i	−0.499463	−	1.20581i	−0.949773	−	0.312939i	$-0.898687\pi$
$107$	−552.814	−	1334.61i	−0.499463	−	1.20581i	0.450310	−	0.892872i	$-0.351313\pi$
$108$		0			0
$109$	490.666	+	203.241i	0.431168	+	0.178596i	0.587703	−	0.809077i	$-0.300032\pi$
$109$	490.666	+	203.241i	0.431168	+	0.178596i	−0.156535	+	0.987672i	$0.550032\pi$
$110$		0			0
$111$			755.757i			0.646246i
$112$		0			0
$113$			109.197i			0.0909060i	0.998966	+	0.0454530i	$0.0144731\pi$
$113$			109.197i			0.0909060i	−0.998966	+	0.0454530i	$0.985527\pi$
$114$		0			0
$115$	−2058.24	−	852.552i	−1.66898	−	0.691312i
$116$		0			0
$117$	−108.107	−	260.993i	−0.0854230	−	0.206229i
$118$		0			0
$119$	318.750	+	318.750i	0.245544	+	0.245544i
$120$		0			0
$121$	269.116	−	269.116i	0.202191	−	0.202191i
$122$		0			0
$123$	−425.731	+	176.344i	−0.312088	+	0.129271i
$124$		0			0
$125$	754.814	−	1822.28i	0.540101	−	1.30392i
$126$		0			0
$127$	−1519.49			−1.06167			−0.530837	−	0.847474i	$-0.678122\pi$
$127$	−1519.49			−1.06167			−0.530837	+	0.847474i	$0.678122\pi$
$128$		0			0
$129$	184.143			0.125681
$130$		0			0
$131$	−386.047	+	932.000i	−0.257474	+	0.621597i	−0.998770	−	0.0495811i	$-0.984211\pi$
$131$	−386.047	+	932.000i	−0.257474	+	0.621597i	0.741296	+	0.671178i	$0.234211\pi$
$132$		0			0
$133$	−884.798	+	366.495i	−0.576855	+	0.238941i
$134$		0			0
$135$	1639.52	−	1639.52i	1.04524	−	1.04524i
$136$		0			0
$137$	121.798	+	121.798i	0.0759557	+	0.0759557i	0.744064	−	0.668108i	$-0.232896\pi$
$137$	121.798	+	121.798i	0.0759557	+	0.0759557i	−0.668108	+	0.744064i	$0.732896\pi$
$138$		0			0
$139$	2.36667	+	5.71364i	0.00144416	+	0.00348651i	0.924600	−	0.380939i	$-0.124399\pi$
$139$	2.36667	+	5.71364i	0.00144416	+	0.00348651i	−0.923156	+	0.384426i	$0.874399\pi$
$140$		0			0
$141$	681.098	+	282.120i	0.406800	+	0.168502i
$142$		0			0
$143$			431.225i			0.252174i
$144$		0			0
$145$			1951.68i			1.11778i
$146$		0			0
$147$	734.505	+	304.242i	0.412115	+	0.170704i
$148$		0			0
$149$	311.513	+	752.060i	0.171276	+	0.413497i	0.986087	−	0.166229i	$-0.0531592\pi$
$149$	311.513	+	752.060i	0.171276	+	0.413497i	−0.814811	+	0.579727i	$0.803159\pi$
$150$		0			0
$151$	−571.254	−	571.254i	−0.307868	−	0.307868i	0.536214	−	0.844082i	$-0.319854\pi$
$151$	−571.254	−	571.254i	−0.307868	−	0.307868i	−0.844082	+	0.536214i	$0.819854\pi$
$152$		0			0
$153$	1041.41	−	1041.41i	0.550281	−	0.550281i
$154$		0			0
$155$	505.179	−	209.252i	0.261787	−	0.108436i
$156$		0			0
$157$	−219.641	+	530.260i	−0.111651	+	0.269550i	−0.969822	−	0.243814i	$-0.921601\pi$
$157$	−219.641	+	530.260i	−0.111651	+	0.269550i	0.858171	+	0.513365i	$0.171601\pi$
$158$		0			0
$159$	−350.585			−0.174863
$160$		0			0
$161$	731.190			0.357924
$162$		0			0
$163$	570.638	−	1377.64i	0.274207	−	0.661995i	−0.725447	−	0.688278i	$-0.758367\pi$
$163$	570.638	−	1377.64i	0.274207	−	0.661995i	0.999655	+	0.0262826i	$0.00836698\pi$
$164$		0			0
$165$	−1399.26	+	579.593i	−0.660196	+	0.273462i
$166$		0			0
$167$	−642.374	+	642.374i	−0.297655	+	0.297655i	−0.840095	−	0.542440i	$-0.817501\pi$
$167$	−642.374	+	642.374i	−0.297655	+	0.297655i	0.542440	+	0.840095i	$0.317501\pi$
$168$		0			0
$169$	−1415.16	−	1415.16i	−0.644134	−	0.644134i
$170$		0			0
$171$	1197.40	+	2890.78i	0.535483	+	1.29277i
$172$		0			0
$173$	−1861.21	−	770.937i	−0.817948	−	0.338805i	−0.0658275	−	0.997831i	$-0.520969\pi$
$173$	−1861.21	−	770.937i	−0.817948	−	0.338805i	−0.752120	+	0.659026i	$0.770969\pi$
$174$		0			0
$175$			1420.06i			0.613406i
$176$		0			0
$177$		−	628.127i		−	0.266740i
$178$		0			0
$179$	317.221	+	131.397i	0.132459	+	0.0548664i	0.447928	−	0.894069i	$-0.352162\pi$
$179$	317.221	+	131.397i	0.132459	+	0.0548664i	−0.315469	+	0.948936i	$0.602162\pi$
$180$		0			0
$181$	532.578	+	1285.76i	0.218708	+	0.528008i	0.994710	−	0.102722i	$-0.0327553\pi$
$181$	532.578	+	1285.76i	0.218708	+	0.528008i	−0.776002	+	0.630731i	$0.782755\pi$
$182$		0			0
$183$	1093.17	+	1093.17i	0.441581	+	0.441581i
$184$		0			0
$185$	−3858.63	+	3858.63i	−1.53347	+	1.53347i
$186$		0			0
$187$	−2077.02	+	860.331i	−0.812230	+	0.336437i
$188$		0			0
$189$	−291.220	+	703.067i	−0.112080	+	0.270585i
$190$		0			0
$191$	−3161.63			−1.19773			−0.598867	−	0.800848i	$-0.704382\pi$
$191$	−3161.63			−1.19773			−0.598867	+	0.800848i	$0.704382\pi$
$192$		0			0
$193$	−1428.55			−0.532796			−0.266398	−	0.963863i	$-0.585834\pi$
$193$	−1428.55			−0.532796			−0.266398	+	0.963863i	$0.585834\pi$
$194$		0			0
$195$	−262.975	+	634.877i	−0.0965744	+	0.233151i
$196$		0			0
$197$	1377.48	−	570.573i	0.498181	−	0.206353i	−0.119421	−	0.992844i	$-0.538104\pi$
$197$	1377.48	−	570.573i	0.498181	−	0.206353i	0.617603	+	0.786490i	$0.288104\pi$
$198$		0			0
$199$	−1207.72	+	1207.72i	−0.430217	+	0.430217i	−0.888702	−	0.458485i	$-0.848392\pi$
$199$	−1207.72	+	1207.72i	−0.430217	+	0.430217i	0.458485	+	0.888702i	$0.348392\pi$
$200$		0			0
$201$	1715.91	+	1715.91i	0.602143	+	0.602143i
$202$		0			0
$203$	−245.131	−	591.798i	−0.0847528	−	0.204611i
$204$		0			0
$205$	−3073.98	−	1273.28i	−1.04730	−	0.433805i
$206$		0			0
$207$		−	2388.92i		−	0.802132i
$208$		0			0
$209$		−	4776.28i		−	1.58078i
$210$		0			0
$211$	627.654	+	259.983i	0.204784	+	0.0848245i	0.482718	−	0.875776i	$-0.339650\pi$
$211$	627.654	+	259.983i	0.204784	+	0.0848245i	−0.277934	+	0.960600i	$0.589650\pi$
$212$		0			0
$213$	975.239	+	2354.43i	0.313720	+	0.757386i
$214$		0			0
$215$	940.170	+	940.170i	0.298228	+	0.298228i
$216$		0			0
$217$	−126.901	+	126.901i	−0.0396985	+	0.0396985i
$218$		0			0
$219$	761.178	−	315.290i	0.234866	−	0.0972846i
$220$		0			0
$221$	−390.353	+	942.394i	−0.118814	+	0.286843i
$222$		0			0
$223$	−1684.85			−0.505946			−0.252973	−	0.967473i	$-0.581408\pi$
$223$	−1684.85			−0.505946			−0.252973	+	0.967473i	$0.581408\pi$
$224$		0			0
$225$	4639.56			1.37468
$226$		0			0
$227$	1751.96	−	4229.60i	0.512254	−	1.23669i	−0.430315	−	0.902679i	$-0.641598\pi$
$227$	1751.96	−	4229.60i	0.512254	−	1.23669i	0.942569	−	0.334011i	$-0.108402\pi$
$228$		0			0
$229$	1072.62	−	444.292i	0.309521	−	0.128208i	−0.222515	−	0.974929i	$-0.571427\pi$
$229$	1072.62	−	444.292i	0.309521	−	0.128208i	0.532037	+	0.846721i	$0.321427\pi$
$230$		0			0
$231$	351.493	−	351.493i	0.100115	−	0.100115i
$232$		0			0
$233$	−224.008	−	224.008i	−0.0629840	−	0.0629840i	0.674913	−	0.737897i	$-0.264181\pi$
$233$	−224.008	−	224.008i	−0.0629840	−	0.0629840i	−0.737897	+	0.674913i	$0.764181\pi$
$234$		0			0
$235$	2037.04	+	4917.85i	0.565455	+	1.36513i
$236$		0			0
$237$	−1682.10	−	696.748i	−0.461030	−	0.190965i
$238$		0			0
$239$		−	5695.35i		−	1.54143i	−0.637181	−	0.770714i	$-0.719899\pi$
$239$		−	5695.35i		−	1.54143i	0.637181	−	0.770714i	$-0.280101\pi$
$240$		0			0
$241$		−	5864.62i		−	1.56752i	−0.621061	−	0.783762i	$-0.713298\pi$
$241$		−	5864.62i		−	1.56752i	0.621061	−	0.783762i	$-0.286702\pi$
$242$		0			0
$243$	3611.13	+	1495.78i	0.953309	+	0.394874i
$244$		0			0
$245$	2196.77	+	5303.48i	0.572844	+	1.38297i
$246$		0			0
$247$	−1532.38	−	1532.38i	−0.394749	−	0.394749i
$248$		0			0
$249$	1826.95	−	1826.95i	0.464972	−	0.464972i
$250$		0			0
$251$	−1284.55	+	532.079i	−0.323029	+	0.133803i	−0.538305	−	0.842750i	$-0.680935\pi$
$251$	−1284.55	+	532.079i	−0.323029	+	0.133803i	0.215276	+	0.976553i	$0.430935\pi$
$252$		0			0
$253$	−1395.50	+	3369.04i	−0.346777	+	0.837193i
$254$		0			0
$255$	−3582.59			−0.879805
$256$		0			0
$257$	6068.35			1.47289			0.736446	−	0.676497i	$-0.236503\pi$
$257$	6068.35			1.47289			0.736446	+	0.676497i	$0.236503\pi$
$258$		0			0
$259$	685.388	−	1654.67i	0.164432	−	0.396974i
$260$		0			0
$261$	−1933.50	+	800.883i	−0.458547	+	0.189937i
$262$		0			0
$263$	1919.51	−	1919.51i	0.450046	−	0.450046i	−0.445324	−	0.895370i	$-0.646911\pi$
$263$	1919.51	−	1919.51i	0.450046	−	0.450046i	0.895370	+	0.445324i	$0.146911\pi$
$264$		0			0
$265$	−1789.97	−	1789.97i	−0.414931	−	0.414931i
$266$		0			0
$267$	231.146	+	558.035i	0.0529808	+	0.127907i
$268$		0			0
$269$	3969.40	+	1644.18i	0.899697	+	0.372667i	0.784103	−	0.620630i	$-0.213123\pi$
$269$	3969.40	+	1644.18i	0.899697	+	0.372667i	0.115593	+	0.993297i	$0.463123\pi$
$270$		0			0
$271$			4538.69i			1.01736i	0.860954	+	0.508682i	$0.169867\pi$
$271$			4538.69i			1.01736i	−0.860954	+	0.508682i	$0.830133\pi$
$272$		0			0
$273$		−	225.540i		−	0.0500011i
$274$		0			0
$275$	−6543.07	−	2710.23i	−1.43477	−	0.594301i
$276$		0			0
$277$	−1889.91	−	4562.63i	−0.409940	−	0.989683i	−0.985153	−	0.171679i	$-0.945081\pi$
$277$	−1889.91	−	4562.63i	−0.409940	−	0.989683i	0.575213	−	0.818004i	$-0.304919\pi$
$278$		0			0
$279$	414.605	+	414.605i	0.0889669	+	0.0889669i
$280$		0			0
$281$	−30.7223	+	30.7223i	−0.00652220	+	0.00652220i	−0.710360	−	0.703838i	$-0.751468\pi$
$281$	−30.7223	+	30.7223i	−0.00652220	+	0.00652220i	0.703838	+	0.710360i	$0.251468\pi$
$282$		0			0
$283$	5549.45	−	2298.66i	1.16565	−	0.482830i	0.285901	−	0.958259i	$-0.407707\pi$
$283$	5549.45	−	2298.66i	1.16565	−	0.482830i	0.879754	+	0.475429i	$0.157707\pi$
$284$		0			0
$285$	2912.73	−	7031.95i	0.605387	−	1.46153i
$286$		0			0
$287$	1092.03			0.224601
$288$		0			0
$289$	−404.895			−0.0824130
$290$		0			0
$291$	−837.954	+	2023.00i	−0.168803	+	0.407527i
$292$		0			0
$293$	2663.79	−	1103.38i	0.531128	−	0.220000i	−0.100969	−	0.994890i	$-0.532194\pi$
$293$	2663.79	−	1103.38i	0.531128	−	0.220000i	0.632097	+	0.774889i	$0.282194\pi$
$294$		0			0
$295$	3207.00	−	3207.00i	0.632944	−	0.632944i
$296$		0			0
$297$	−2683.66	−	2683.66i	−0.524316	−	0.524316i
$298$		0			0
$299$	633.173	+	1528.61i	0.122466	+	0.295659i
$300$		0			0
$301$	−403.168	−	166.998i	−0.0772033	−	0.0319787i
$302$		0			0
$303$		−	4407.30i		−	0.835620i
$304$		0			0
$305$			11162.7i			2.09565i
$306$		0			0
$307$	−401.539	−	166.323i	−0.0746484	−	0.0309204i	0.345047	−	0.938585i	$-0.387863\pi$
$307$	−401.539	−	166.323i	−0.0746484	−	0.0309204i	−0.419695	+	0.907665i	$0.637863\pi$
$308$		0			0
$309$	−113.143	−	273.152i	−0.0208301	−	0.0502883i
$310$		0			0
$311$	5345.11	+	5345.11i	0.974577	+	0.974577i	0.999685	−	0.0251081i	$-0.00799300\pi$
$311$	5345.11	+	5345.11i	0.974577	+	0.974577i	−0.0251081	+	0.999685i	$0.507993\pi$
$312$		0			0
$313$	−1787.53	+	1787.53i	−0.322803	+	0.322803i	−0.849841	−	0.527039i	$-0.823302\pi$
$313$	−1787.53	+	1787.53i	−0.322803	+	0.322803i	0.527039	+	0.849841i	$0.323302\pi$
$314$		0			0
$315$	−2172.32	+	899.804i	−0.388560	+	0.160947i
$316$		0			0
$317$	2370.77	−	5723.55i	0.420050	−	1.01409i	−0.562282	−	0.826945i	$-0.690077\pi$
$317$	2370.77	−	5723.55i	0.420050	−	1.01409i	0.982332	−	0.187145i	$-0.0599234\pi$
$318$		0			0
$319$	3194.62			0.560703
$320$		0			0
$321$	−3768.08			−0.655183
$322$		0			0
$323$	4323.58	−	10438.0i	0.744800	−	1.79811i
$324$		0			0
$325$	−2968.74	+	1229.69i	−0.506696	+	0.209880i
$326$		0			0
$327$	979.572	−	979.572i	0.165659	−	0.165659i
$328$		0			0
$329$	−1235.36	−	1235.36i	−0.207014	−	0.207014i
$330$		0			0
$331$	−1696.86	−	4096.57i	−0.281775	−	0.680265i	0.718102	−	0.695938i	$-0.245011\pi$
$331$	−1696.86	−	4096.57i	−0.281775	−	0.680265i	−0.999877	+	0.0156724i	$0.995011\pi$
$332$		0			0
$333$	−5406.09	−	2239.28i	−0.889646	−	0.368503i
$334$		0			0
$335$			17521.6i			2.85764i
$336$		0			0
$337$		−	927.470i		−	0.149918i	−0.997187	−	0.0749592i	$-0.976117\pi$
$337$		−	927.470i		−	0.149918i	0.997187	−	0.0749592i	$-0.0238826\pi$
$338$		0			0
$339$	263.152	+	109.001i	0.0421606	+	0.0174635i
$340$		0			0
$341$	−342.515	−	826.904i	−0.0543936	−	0.131318i
$342$		0			0
$343$	−2831.48	−	2831.48i	−0.445731	−	0.445731i
$344$		0			0
$345$	−4109.10	+	4109.10i	−0.641237	+	0.641237i
$346$		0			0
$347$	−3765.13	+	1559.57i	−0.582487	+	0.241274i	−0.654415	−	0.756136i	$-0.727085\pi$
$347$	−3765.13	+	1559.57i	−0.582487	+	0.241274i	0.0719277	+	0.997410i	$0.477085\pi$
$348$		0			0
$349$	−1631.14	+	3937.93i	−0.250181	+	0.603990i	−0.998218	−	0.0596662i	$-0.980996\pi$
$349$	−1631.14	+	3937.93i	−0.250181	+	0.603990i	0.748037	+	0.663657i	$0.230996\pi$
$350$		0			0
$351$	−1722.00			−0.261862
$352$		0			0
$353$	−11289.2			−1.70216			−0.851080	−	0.525037i	$-0.824052\pi$
$353$	−11289.2			−1.70216			−0.851080	+	0.525037i	$0.824052\pi$
$354$		0			0
$355$	−7041.69	+	17000.1i	−1.05277	+	2.54162i
$356$		0			0
$357$	1086.33	−	449.972i	0.161049	−	0.0667088i
$358$		0			0
$359$	−2970.97	+	2970.97i	−0.436774	+	0.436774i	−0.890925	−	0.454151i	$-0.849943\pi$
$359$	−2970.97	+	2970.97i	−0.436774	+	0.436774i	0.454151	+	0.890925i	$0.349943\pi$
$360$		0			0
$361$	12122.7	+	12122.7i	1.76742	+	1.76742i
$362$		0			0
$363$	−379.904	−	917.170i	−0.0549306	−	0.132614i
$364$		0			0
$365$	5496.07	+	2276.55i	0.788157	+	0.326465i
$366$		0			0
$367$		−	12266.5i		−	1.74470i	−0.488882	−	0.872350i	$-0.662595\pi$
$367$		−	12266.5i		−	1.74470i	0.488882	−	0.872350i	$-0.337405\pi$
$368$		0			0
$369$		−	3567.84i		−	0.503346i
$370$		0			0
$371$	767.581	+	317.942i	0.107415	+	0.0444926i
$372$		0			0
$373$	−905.804	−	2186.80i	−0.125739	−	0.303561i	0.848457	−	0.529265i	$-0.177532\pi$
$373$	−905.804	−	2186.80i	−0.125739	−	0.303561i	−0.974196	+	0.225703i	$0.927532\pi$
$374$		0			0
$375$	−3638.03	−	3638.03i	−0.500979	−	0.500979i
$376$		0			0
$377$	1024.93	−	1024.93i	0.140018	−	0.140018i
$378$		0			0
$379$	−6881.62	+	2850.46i	−0.932679	+	0.386328i	−0.796694	−	0.604383i	$-0.793420\pi$
$379$	−6881.62	+	2850.46i	−0.932679	+	0.386328i	−0.135985	+	0.990711i	$0.543420\pi$
$380$		0			0
$381$	−1516.76	+	3661.78i	−0.203953	+	0.492385i
$382$		0			0
$383$	2433.37			0.324645			0.162323	−	0.986738i	$-0.448101\pi$
$383$	2433.37			0.324645			0.162323	+	0.986738i	$0.448101\pi$
$384$		0			0
$385$	3589.20			0.475124
$386$		0			0
$387$	−545.609	+	1317.22i	−0.0716663	+	0.173018i
$388$		0			0
$389$	4253.32	−	1761.78i	0.554375	−	0.229630i	−0.0878663	−	0.996132i	$-0.528005\pi$
$389$	4253.32	−	1761.78i	0.554375	−	0.229630i	0.642241	+	0.766503i	$0.278005\pi$
$390$		0			0
$391$	−6099.44	+	6099.44i	−0.788905	+	0.788905i
$392$		0			0
$393$	1860.66	+	1860.66i	0.238824	+	0.238824i
$394$		0			0
$395$	−5030.85	−	12145.6i	−0.640835	−	1.54711i
$396$		0			0
$397$	−306.541	−	126.974i	−0.0387528	−	0.0160519i	0.363223	−	0.931702i	$-0.381676\pi$
$397$	−306.541	−	126.974i	−0.0387528	−	0.0160519i	−0.401976	+	0.915650i	$0.631676\pi$
$398$		0			0
$399$			2498.10i			0.313437i
$400$		0			0
$401$			10975.6i			1.36682i	0.730036	+	0.683409i	$0.239503\pi$
$401$			10975.6i			1.36682i	−0.730036	+	0.683409i	$0.760497\pi$
$402$		0			0
$403$	−375.186	−	155.407i	−0.0463755	−	0.0192094i
$404$		0			0
$405$	1615.74	+	3900.74i	0.198239	+	0.478591i
$406$		0			0
$407$	6316.01	+	6316.01i	0.769221	+	0.769221i
$408$		0			0
$409$	8384.88	−	8384.88i	1.01371	−	1.01371i	0.0138007	−	0.999905i	$-0.495607\pi$
$409$	8384.88	−	8384.88i	1.01371	−	1.01371i	0.999905	−	0.0138007i	$-0.00439304\pi$
$410$		0			0
$411$	415.100	−	171.940i	0.0498184	−	0.0206355i
$412$		0			0
$413$	−569.642	+	1375.24i	−0.0678698	+	0.163852i
$414$		0			0
$415$	18655.5			2.20666
$416$		0			0
$417$	16.1316			0.00189441
$418$		0			0
$419$	−533.639	+	1288.32i	−0.0622195	+	0.150211i	−0.951931	−	0.306311i	$-0.900905\pi$
$419$	−533.639	+	1288.32i	−0.0622195	+	0.150211i	0.889712	+	0.456522i	$0.150905\pi$
$420$		0			0
$421$	1963.49	−	813.303i	0.227303	−	0.0941520i	−0.266125	−	0.963938i	$-0.585744\pi$
$421$	1963.49	−	813.303i	0.227303	−	0.0941520i	0.493428	+	0.869786i	$0.335744\pi$
$422$		0			0
$423$	−4036.13	+	4036.13i	−0.463932	+	0.463932i
$424$		0			0
$425$	−11845.8	−	11845.8i	−1.35201	−	1.35201i
$426$		0			0
$427$	−1402.03	−	3384.79i	−0.158897	−	0.383610i
$428$		0			0
$429$	1039.20	+	430.451i	0.116954	+	0.0484438i
$430$		0			0
$431$		−	4521.29i		−	0.505297i	−0.967558	−	0.252649i	$-0.918698\pi$
$431$		−	4521.29i		−	0.505297i	0.967558	−	0.252649i	$-0.0813016\pi$
$432$		0			0
$433$			2122.80i			0.235601i	0.993037	+	0.117801i	$0.0375844\pi$
$433$			2122.80i			0.235601i	−0.993037	+	0.117801i	$0.962416\pi$
$434$		0			0
$435$	4703.33	+	1948.18i	0.518408	+	0.214732i
$436$		0			0
$437$	−7013.07	−	16931.1i	−0.767691	−	1.85337i
$438$		0			0
$439$	−8028.12	−	8028.12i	−0.872805	−	0.872805i	0.119972	−	0.992777i	$-0.461719\pi$
$439$	−8028.12	−	8028.12i	−0.872805	−	0.872805i	−0.992777	+	0.119972i	$0.961719\pi$
$440$		0			0
$441$	−4352.62	+	4352.62i	−0.469994	+	0.469994i
$442$		0			0
$443$	−3136.09	+	1299.01i	−0.336343	+	0.139318i	−0.544462	−	0.838786i	$-0.683266\pi$
$443$	−3136.09	+	1299.01i	−0.336343	+	0.139318i	0.208119	+	0.978104i	$0.433266\pi$
$444$		0			0
$445$	−1668.98	+	4029.28i	−0.177792	+	0.429227i
$446$		0			0
$447$	2123.33			0.224676
$448$		0			0
$449$	−16955.9			−1.78218			−0.891088	−	0.453832i	$-0.850057\pi$
$449$	−16955.9			−1.78218			−0.891088	+	0.453832i	$0.850057\pi$
$450$		0			0
$451$	−2084.18	+	5031.66i	−0.217606	+	0.525347i
$452$		0			0
$453$	−1946.88	+	806.426i	−0.201926	+	0.0836406i
$454$		0			0
$455$	1151.53	−	1151.53i	0.118647	−	0.118647i
$456$		0			0
$457$	6223.46	+	6223.46i	0.637027	+	0.637027i	0.949821	−	0.312794i	$-0.101265\pi$
$457$	6223.46	+	6223.46i	0.637027	+	0.637027i	−0.312794	+	0.949821i	$0.601265\pi$
$458$		0			0
$459$	−3435.55	−	8294.14i	−0.349363	−	0.843437i
$460$		0			0
$461$	10872.5	+	4503.54i	1.09844	+	0.454991i	0.856944	−	0.515410i	$-0.172360\pi$
$461$	10872.5	+	4503.54i	1.09844	+	0.454991i	0.241501	+	0.970401i	$0.422360\pi$
$462$		0			0
$463$			13182.5i			1.32320i	0.749858	+	0.661599i	$0.230122\pi$
$463$			13182.5i			1.32320i	−0.749858	+	0.661599i	$0.769878\pi$
$464$		0			0
$465$		−	1426.30i		−	0.142243i
$466$		0			0
$467$	−7043.25	−	2917.41i	−0.697907	−	0.289083i	0.00538305	−	0.999986i	$-0.498287\pi$
$467$	−7043.25	−	2917.41i	−0.697907	−	0.289083i	−0.703290	+	0.710903i	$0.748287\pi$
$468$		0			0
$469$	−2200.71	−	5312.99i	−0.216673	−	0.523094i
$470$		0			0
$471$	1058.62	+	1058.62i	0.103564	+	0.103564i
$472$		0			0
$473$	1538.92	−	1538.92i	0.149598	−	0.149598i
$474$		0			0
$475$	32882.1	−	13620.2i	3.17628	−	1.31566i
$476$		0			0
$477$	1038.77	−	2507.81i	0.0997107	−	0.240723i
$478$		0			0
$479$	−4612.37			−0.439968			−0.219984	−	0.975503i	$-0.570601\pi$
$479$	−4612.37			−0.439968			−0.219984	+	0.975503i	$0.570601\pi$
$480$		0			0
$481$	4052.74			0.384177
$482$		0			0
$483$	729.878	−	1762.08i	0.0687590	−	0.165999i
$484$		0			0
$485$	−14607.0	+	6050.43i	−1.36757	+	0.566466i
$486$		0			0
$487$	10988.9	−	10988.9i	1.02249	−	1.02249i	0.0227515	−	0.999741i	$-0.492757\pi$
$487$	10988.9	−	10988.9i	1.02249	−	1.02249i	0.999741	−	0.0227515i	$-0.00724266\pi$
$488$		0			0
$489$	−2750.34	−	2750.34i	−0.254345	−	0.254345i
$490$		0			0
$491$	7836.91	+	18920.0i	0.720316	+	1.73900i	0.672451	+	0.740142i	$0.265242\pi$
$491$	7836.91	+	18920.0i	0.720316	+	1.73900i	0.0478645	+	0.998854i	$0.484758\pi$
$492$		0			0
$493$	6981.49	+	2891.83i	0.637790	+	0.264181i
$494$		0			0
$495$		−	11726.5i		−	1.06478i
$496$		0			0
$497$		−	6039.29i		−	0.545069i
$498$		0			0
$499$	6404.45	+	2652.81i	0.574554	+	0.237988i	0.650990	−	0.759086i	$-0.274354\pi$
$499$	6404.45	+	2652.81i	0.574554	+	0.237988i	−0.0764356	+	0.997075i	$0.524354\pi$
$500$		0			0
$501$	906.824	+	2189.27i	0.0808661	+	0.195228i
$502$		0			0
$503$	−2553.60	−	2553.60i	−0.226361	−	0.226361i	0.584810	−	0.811171i	$-0.301169\pi$
$503$	−2553.60	−	2553.60i	−0.226361	−	0.226361i	−0.811171	+	0.584810i	$0.801169\pi$
$504$		0			0
$505$	22502.1	−	22502.1i	1.98283	−	1.98283i
$506$		0			0
$507$	−4823.00	+	1997.75i	−0.422479	+	0.174997i
$508$		0			0
$509$	3141.82	−	7585.02i	0.273593	−	0.660511i	−0.726039	−	0.687654i	$-0.758641\pi$
$509$	3141.82	−	7585.02i	0.273593	−	0.660511i	0.999632	+	0.0271425i	$0.00864080\pi$
$510$		0			0
$511$	−1952.48			−0.169026
$512$		0			0
$513$	19073.0			1.64151
$514$		0			0
$515$	816.948	−	1972.29i	0.0699010	−	0.168756i
$516$		0			0
$517$	8049.80	−	3334.34i	0.684777	−	0.283644i
$518$		0			0
$519$	−3715.74	+	3715.74i	−0.314263	+	0.314263i
$520$		0			0
$521$	−7065.05	−	7065.05i	−0.594099	−	0.594099i	0.344637	−	0.938736i	$-0.388002\pi$
$521$	−7065.05	−	7065.05i	−0.594099	−	0.594099i	−0.938736	+	0.344637i	$0.888002\pi$
$522$		0			0
$523$	111.041	+	268.077i	0.00928391	+	0.0224134i	0.928454	−	0.371449i	$-0.121139\pi$
$523$	111.041	+	268.077i	0.00928391	+	0.0224134i	−0.919170	+	0.393862i	$0.871139\pi$
$524$		0			0
$525$	3422.17	+	1417.51i	0.284487	+	0.117838i
$526$		0			0
$527$		−	2117.16i		−	0.175000i
$528$		0			0
$529$			1824.68i			0.149970i
$530$		0			0
$531$	4493.13	+	1861.11i	0.367204	+	0.152101i
$532$		0			0
$533$	945.642	+	2282.98i	0.0768486	+	0.185529i
$534$		0			0
$535$	−19238.5	−	19238.5i	−1.55468	−	1.55468i
$536$		0			0
$537$	633.304	−	633.304i	0.0508921	−	0.0508921i
$538$		0			0
$539$	8681.02	−	3595.79i	0.693725	−	0.287350i
$540$		0			0
$541$	−8420.37	+	20328.6i	−0.669168	+	1.61552i	0.113837	+	0.993499i	$0.463686\pi$
$541$	−8420.37	+	20328.6i	−0.669168	+	1.61552i	−0.783005	+	0.622016i	$0.786314\pi$
$542$		0			0
$543$	3630.14			0.286896
$544$		0			0
$545$	10002.7			0.786181
$546$		0			0
$547$	−646.357	+	1560.44i	−0.0505233	+	0.121974i	−0.947126	−	0.320862i	$-0.896028\pi$
$547$	−646.357	+	1560.44i	−0.0505233	+	0.121974i	0.896603	+	0.442836i	$0.146028\pi$
$548$		0			0
$549$	−11058.7	+	4580.65i	−0.859696	+	0.356098i
$550$		0			0
$551$	−11352.2	+	11352.2i	−0.877717	+	0.877717i
$552$		0			0
$553$	3050.95	+	3050.95i	0.234611	+	0.234611i
$554$		0			0
$555$	5447.14	+	13150.5i	0.416609	+	1.00578i
$556$		0			0
$557$	−6482.01	−	2684.93i	−0.493091	−	0.204245i	0.122260	−	0.992498i	$-0.460986\pi$
$557$	−6482.01	−	2684.93i	−0.493091	−	0.204245i	−0.615351	+	0.788253i	$0.710986\pi$
$558$		0			0
$559$		−	987.467i		−	0.0747145i
$560$		0			0
$561$			5864.17i			0.441329i
$562$		0			0
$563$	945.289	+	391.551i	0.0707623	+	0.0293107i	0.417784	−	0.908546i	$-0.362807\pi$
$563$	945.289	+	391.551i	0.0707623	+	0.0293107i	−0.347022	+	0.937857i	$0.612807\pi$
$564$		0			0
$565$	787.039	+	1900.08i	0.0586035	+	0.141481i
$566$		0			0
$567$	−979.862	−	979.862i	−0.0725756	−	0.0725756i
$568$		0			0
$569$	−3760.45	+	3760.45i	−0.277058	+	0.277058i	−0.831934	−	0.554875i	$-0.812766\pi$
$569$	−3760.45	+	3760.45i	−0.277058	+	0.277058i	0.554875	+	0.831934i	$0.312766\pi$
$570$		0			0
$571$	−2056.20	+	851.705i	−0.150699	+	0.0624216i	−0.456758	−	0.889591i	$-0.650990\pi$
$571$	−2056.20	+	851.705i	−0.150699	+	0.0624216i	0.306059	+	0.952013i	$0.400990\pi$
$572$		0			0
$573$	−3155.95	+	7619.15i	−0.230091	+	0.555488i
$574$		0			0
$575$	−27173.5			−1.97080
$576$		0			0
$577$	−23621.3			−1.70427			−0.852137	−	0.523318i	$-0.824694\pi$
$577$	−23621.3			−1.70427			−0.852137	+	0.523318i	$0.824694\pi$
$578$		0			0
$579$	−1425.99	+	3442.65i	−0.102353	+	0.247101i
$580$		0			0
$581$	−5656.80	+	2343.13i	−0.403931	+	0.167314i
$582$		0			0
$583$	−2929.91	+	2929.91i	−0.208138	+	0.208138i
$584$		0			0
$585$	−3762.23	−	3762.23i	−0.265896	−	0.265896i
$586$		0			0
$587$	−7316.12	−	17662.7i	−0.514427	−	1.24194i	−0.941283	−	0.337617i	$-0.890379\pi$
$587$	−7316.12	−	17662.7i	−0.514427	−	1.24194i	0.426857	−	0.904319i	$-0.359621\pi$
$588$		0			0
$589$	4155.59	+	1721.30i	0.290710	+	0.120416i
$590$		0			0
$591$		−	3889.13i		−	0.270689i
$592$		0			0
$593$		−	16542.0i		−	1.14553i	−0.819720	−	0.572764i	$-0.805871\pi$
$593$		−	16542.0i		−	1.14553i	0.819720	−	0.572764i	$-0.194129\pi$
$594$		0			0
$595$	7843.81	+	3249.01i	0.540445	+	0.223860i
$596$		0			0
$597$	1704.91	+	4116.02i	0.116880	+	0.282174i
$598$		0			0
$599$	8579.81	+	8579.81i	0.585244	+	0.585244i	0.936340	−	0.351095i	$-0.114191\pi$
$599$	8579.81	+	8579.81i	0.585244	+	0.585244i	−0.351095	+	0.936340i	$0.614191\pi$
$600$		0			0
$601$	−13633.8	+	13633.8i	−0.925346	+	0.925346i	−0.997401	−	0.0720542i	$-0.977045\pi$
$601$	−13633.8	+	13633.8i	−0.925346	+	0.925346i	0.0720542	+	0.997401i	$0.477045\pi$
$602$		0			0
$603$	−17358.4	+	7190.09i	−1.17229	+	0.485578i
$604$		0			0
$605$	2743.09	−	6622.41i	0.184335	−	0.445023i
$606$		0			0
$607$	23984.1			1.60376			0.801881	−	0.597484i	$-0.203833\pi$
$607$	23984.1			1.60376			0.801881	+	0.597484i	$0.203833\pi$
$608$		0			0
$609$	−1670.86			−0.111176
$610$		0			0
$611$	1512.87	−	3652.38i	0.100170	−	0.241833i
$612$		0			0
$613$	18072.9	−	7486.04i	1.19080	−	0.493244i	0.302782	−	0.953060i	$-0.402085\pi$
$613$	18072.9	−	7486.04i	1.19080	−	0.493244i	0.888014	+	0.459816i	$0.152085\pi$
$614$		0			0
$615$	−6136.93	+	6136.93i	−0.402382	+	0.402382i
$616$		0			0
$617$	18674.2	+	18674.2i	1.21847	+	1.21847i	0.968168	+	0.250301i	$0.0805297\pi$
$617$	18674.2	+	18674.2i	1.21847	+	1.21847i	0.250301	+	0.968168i	$0.419470\pi$
$618$		0			0
$619$	−3214.09	−	7759.51i	−0.208700	−	0.503846i	0.784519	−	0.620105i	$-0.212910\pi$
$619$	−3214.09	−	7759.51i	−0.208700	−	0.503846i	−0.993219	+	0.116258i	$0.962910\pi$
$620$		0			0
$621$	−13453.5	−	5572.64i	−0.869359	−	0.360100i
$622$		0			0
$623$		−	1431.40i		−	0.0920511i
$624$		0			0
$625$		−	8433.25i		−	0.539728i
$626$		0			0
$627$	−11510.3	−	4767.71i	−0.733136	−	0.303675i
$628$		0			0
$629$	8085.58	+	19520.3i	0.512549	+	1.23740i
$630$		0			0
$631$	20023.0	+	20023.0i	1.26324	+	1.26324i	0.949515	+	0.313722i	$0.101576\pi$
$631$	20023.0	+	20023.0i	1.26324	+	1.26324i	0.313722	+	0.949515i	$0.398424\pi$
$632$		0			0
$633$	1253.06	−	1253.06i	0.0786801	−	0.0786801i
$634$		0			0
$635$	−26439.8	+	10951.7i	−1.65233	+	0.684419i
$636$		0			0
$637$	1631.50	−	3938.78i	0.101479	−	0.244992i
$638$		0			0
$639$	−19731.4			−1.22154
$640$		0			0
$641$	8637.88			0.532255			0.266128	−	0.963938i	$-0.414256\pi$
$641$	8637.88			0.532255			0.266128	+	0.963938i	$0.414256\pi$
$642$		0			0
$643$	−5274.73	+	12734.3i	−0.323507	+	0.781015i	0.675538	+	0.737325i	$0.263911\pi$
$643$	−5274.73	+	12734.3i	−0.323507	+	0.781015i	−0.999045	+	0.0436901i	$0.986089\pi$
$644$		0			0
$645$	3204.18	−	1327.22i	0.195604	−	0.0810219i
$646$		0			0
$647$	14785.3	−	14785.3i	0.898406	−	0.898406i	−0.0968891	−	0.995295i	$-0.530889\pi$
$647$	14785.3	−	14785.3i	0.898406	−	0.898406i	0.995295	+	0.0968891i	$0.0308892\pi$
$648$		0			0
$649$	−5249.38	−	5249.38i	−0.317498	−	0.317498i
$650$		0			0
$651$	179.143	+	432.488i	0.0107852	+	0.0260377i
$652$		0			0
$653$	−25046.7	−	10374.7i	−1.50100	−	0.621733i	−0.527321	−	0.849666i	$-0.676803\pi$
$653$	−25046.7	−	10374.7i	−1.50100	−	0.621733i	−0.973677	+	0.227933i	$0.926803\pi$
$654$		0			0
$655$			18999.7i			1.13340i
$656$		0			0
$657$			6379.06i			0.378799i
$658$		0			0
$659$	23962.3	+	9925.50i	1.41645	+	0.586711i	0.953965	−	0.299918i	$-0.0969594\pi$
$659$	23962.3	+	9925.50i	1.41645	+	0.586711i	0.462481	+	0.886629i	$0.346959\pi$
$660$		0			0
$661$	−398.063	−	961.010i	−0.0234234	−	0.0565491i	0.911735	−	0.410779i	$-0.134743\pi$
$661$	−398.063	−	961.010i	−0.0234234	−	0.0565491i	−0.935158	+	0.354230i	$0.884743\pi$
$662$		0			0
$663$	1881.41	+	1881.41i	0.110208	+	0.110208i
$664$		0			0
$665$	−12754.4	+	12754.4i	−0.743752	+	0.743752i
$666$		0			0
$667$	11324.4	−	4690.70i	0.657392	−	0.272301i
$668$		0			0
$669$	−1681.83	+	4060.30i	−0.0971948	+	0.234649i
$670$		0			0
$671$	18271.6			1.05122
$672$		0			0
$673$	−15307.7			−0.876775			−0.438387	−	0.898786i	$-0.644450\pi$
$673$	−15307.7			−0.876775			−0.438387	+	0.898786i	$0.644450\pi$
$674$		0			0
$675$	10822.7	−	26128.3i	0.617135	−	1.48990i
$676$		0			0
$677$	−1043.10	+	432.068i	−0.0592168	+	0.0245284i	−0.412095	−	0.911141i	$-0.635203\pi$
$677$	−1043.10	+	432.068i	−0.0592168	+	0.0245284i	0.352878	+	0.935669i	$0.385203\pi$
$678$		0			0
$679$	3669.28	−	3669.28i	0.207384	−	0.207384i
$680$		0			0
$681$	−8444.03	−	8444.03i	−0.475148	−	0.475148i
$682$		0			0
$683$	8946.40	+	21598.5i	0.501207	+	1.21002i	0.948827	+	0.315797i	$0.102272\pi$
$683$	8946.40	+	21598.5i	0.501207	+	1.21002i	−0.447619	+	0.894224i	$0.647728\pi$
$684$		0			0
$685$	2997.22	+	1241.49i	0.167179	+	0.0692479i
$686$		0			0
$687$		−	3028.37i		−	0.168180i
$688$		0			0
$689$			1880.01i			0.103952i
$690$		0			0
$691$	−19676.4	−	8150.22i	−1.08325	−	0.448696i	−0.231600	−	0.972811i	$-0.574396\pi$
$691$	−19676.4	−	8150.22i	−1.08325	−	0.448696i	−0.851647	+	0.524115i	$0.824396\pi$
$692$		0			0
$693$	1472.85	+	3555.77i	0.0807342	+	0.194910i
$694$		0			0
$695$	82.3624	+	82.3624i	0.00449523	+	0.00449523i
$696$		0			0
$697$	−9109.50	+	9109.50i	−0.495046	+	0.495046i
$698$		0			0
$699$	−763.440	+	316.227i	−0.0413104	+	0.0171113i
$700$		0			0
$701$	2739.27	−	6613.19i	0.147591	−	0.356315i	−0.832744	−	0.553658i	$-0.813231\pi$
$701$	2739.27	−	6613.19i	0.147591	−	0.356315i	0.980334	+	0.197343i	$0.0632313\pi$
$702$		0			0
$703$	−44888.5			−2.40825
$704$		0			0
$705$	13884.8			0.741749
$706$		0			0
$707$	−3996.93	+	9649.45i	−0.212617	+	0.513303i
$708$		0			0
$709$	−2388.26	+	989.248i	−0.126506	+	0.0524005i	−0.445039	−	0.895511i	$-0.646810\pi$
$709$	−2388.26	+	989.248i	−0.126506	+	0.0524005i	0.318532	+	0.947912i	$0.396810\pi$
$710$		0			0
$711$	9967.97	−	9967.97i	0.525778	−	0.525778i
$712$		0			0
$713$	−2428.31	−	2428.31i	−0.127547	−	0.127547i
$714$		0			0
$715$	3108.06	+	7503.53i	0.162566	+	0.392470i
$716$		0			0
$717$	−13725.1	−	5685.13i	−0.714887	−	0.296116i
$718$		0			0
$719$		−	11843.1i		−	0.614288i	−0.951663	−	0.307144i	$-0.900627\pi$
$719$		−	11843.1i		−	0.614288i	0.951663	−	0.307144i	$-0.0993734\pi$
$720$		0			0
$721$			700.654i			0.0361910i
$722$		0			0
$723$	−14133.0	−	5854.10i	−0.726990	−	0.301129i
$724$		0			0
$725$	9109.88	+	21993.2i	0.466665	+	1.12663i
$726$		0			0
$727$	4691.36	+	4691.36i	0.239330	+	0.239330i	0.816573	−	0.577243i	$-0.195871\pi$
$727$	4691.36	+	4691.36i	0.239330	+	0.239330i	−0.577243	+	0.816573i	$0.695871\pi$
$728$		0			0
$729$	2929.40	−	2929.40i	0.148829	−	0.148829i
$730$		0			0
$731$	4756.20	−	1970.08i	0.240649	−	0.0996801i
$732$		0			0
$733$	13224.6	−	31927.0i	0.666386	−	1.60880i	−0.121224	−	0.992625i	$-0.538682\pi$
$733$	13224.6	−	31927.0i	0.666386	−	1.60880i	0.787610	−	0.616174i	$-0.211318\pi$
$734$		0			0
$735$	14973.6			0.751441
$736$		0			0
$737$	28680.4			1.43345
$738$		0			0
$739$	13199.0	−	31865.1i	0.657012	−	1.58617i	−0.145383	−	0.989375i	$-0.546442\pi$
$739$	13199.0	−	31865.1i	0.657012	−	1.58617i	0.802396	−	0.596793i	$-0.203558\pi$
$740$		0			0
$741$	−5222.48	+	2163.22i	−0.258911	+	0.107244i
$742$		0			0
$743$	14307.6	−	14307.6i	0.706452	−	0.706452i	−0.259335	−	0.965787i	$-0.583503\pi$
$743$	14307.6	−	14307.6i	0.706452	−	0.706452i	0.965787	+	0.259335i	$0.0835035\pi$
$744$		0			0
$745$	10841.0	+	10841.0i	0.533131	+	0.533131i
$746$		0			0
$747$	7655.38	+	18481.7i	0.374961	+	0.905235i
$748$		0			0
$749$	8249.93	+	3417.23i	0.402464	+	0.166706i
$750$		0			0
$751$			15781.7i			0.766820i	0.923578	+	0.383410i	$0.125250\pi$
$751$			15781.7i			0.766820i	−0.923578	+	0.383410i	$0.874750\pi$
$752$		0			0
$753$			3626.75i			0.175519i
$754$		0			0
$755$	−14057.4	−	5822.78i	−0.677619	−	0.280679i
$756$		0			0
$757$	−15069.9	−	36382.0i	−0.723548	−	1.74680i	−0.662983	−	0.748635i	$-0.730710\pi$
$757$	−15069.9	−	36382.0i	−0.723548	−	1.74680i	−0.0605650	−	0.998164i	$-0.519290\pi$
$758$		0			0
$759$	6726.00	+	6726.00i	0.321658	+	0.321658i
$760$		0			0
$761$	−12120.7	+	12120.7i	−0.577363	+	0.577363i	−0.934176	−	0.356813i	$-0.883863\pi$
$761$	−12120.7	+	12120.7i	−0.577363	+	0.577363i	0.356813	+	0.934176i	$0.383863\pi$
$762$		0			0
$763$	−3033.06	+	1256.34i	−0.143911	+	0.0596100i
$764$		0			0
$765$	10615.1	−	25627.0i	0.501684	−	1.21117i
$766$		0			0
$767$	−3368.33			−0.158570
$768$		0			0
$769$	5213.88			0.244496			0.122248	−	0.992500i	$-0.460990\pi$
$769$	5213.88			0.244496			0.122248	+	0.992500i	$0.460990\pi$
$770$		0			0
$771$	6057.46	−	14624.0i	0.282950	−	0.683101i
$772$		0			0
$773$	25960.5	−	10753.2i	1.20793	−	0.500343i	0.314380	−	0.949297i	$-0.398203\pi$
$773$	25960.5	−	10753.2i	1.20793	−	0.500343i	0.893555	+	0.448954i	$0.148203\pi$
$774$		0			0
$775$	4716.05	−	4716.05i	0.218588	−	0.218588i
$776$		0			0
$777$	−3303.41	−	3303.41i	−0.152521	−	0.152521i
$778$		0			0
$779$	−10474.0	−	25286.5i	−0.481733	−	1.16301i
$780$		0			0
$781$	27826.7	+	11526.2i	1.27493	+	0.528093i
$782$		0			0
$783$			12757.0i			0.582246i
$784$		0			0
$785$			10809.9i			0.491491i
$786$		0			0
$787$	−31369.3	−	12993.6i	−1.42083	−	0.588528i	−0.465762	−	0.884910i	$-0.654220\pi$
$787$	−31369.3	−	12993.6i	−1.42083	−	0.588528i	−0.955069	+	0.296382i	$0.904220\pi$
$788$		0			0
$789$	−2709.73	−	6541.86i	−0.122267	−	0.295179i
$790$		0			0
$791$	−477.299	−	477.299i	−0.0214549	−	0.0214549i
$792$		0			0
$793$	5862.11	−	5862.11i	0.262509	−	0.262509i
$794$		0			0
$795$	−6100.36	+	2526.85i	−0.272148	+	0.112727i
$796$		0			0
$797$	8986.32	−	21694.9i	0.399387	−	0.964207i	−0.588424	−	0.808552i	$-0.700251\pi$
$797$	8986.32	−	21694.9i	0.399387	−	0.964207i	0.987812	−	0.155654i	$-0.0497485\pi$
$798$		0			0
$799$	20610.3			0.912564
$800$		0			0
$801$	−4676.62			−0.206292
$802$		0			0
$803$	3726.37	−	8996.26i	0.163762	−	0.395356i
$804$		0			0
$805$	12723.1	−	5270.07i	0.557055	−	0.230740i
$806$		0			0
$807$	7924.55	−	7924.55i	0.345672	−	0.345672i
$808$		0			0
$809$	−13193.6	−	13193.6i	−0.573376	−	0.573376i	0.359694	−	0.933070i	$-0.382881\pi$
$809$	−13193.6	−	13193.6i	−0.573376	−	0.573376i	−0.933070	+	0.359694i	$0.882881\pi$
$810$		0			0
$811$	−140.367	−	338.877i	−0.00607764	−	0.0146727i	0.920812	−	0.390008i	$-0.127528\pi$
$811$	−140.367	−	338.877i	−0.00607764	−	0.0146727i	−0.926889	+	0.375335i	$0.877528\pi$
$812$		0			0
$813$	10937.7	+	4530.55i	0.471835	+	0.195441i
$814$		0			0
$815$		−	28084.5i		−	1.20707i
$816$		0			0
$817$			10937.3i			0.468356i
$818$		0			0
$819$	1613.33	+	668.265i	0.0688333	+	0.0285117i
$820$		0			0
$821$	6304.96	+	15221.5i	0.268020	+	0.647058i	0.999390	−	0.0349231i	$-0.0111186\pi$
$821$	6304.96	+	15221.5i	0.268020	+	0.647058i	−0.731370	+	0.681981i	$0.761119\pi$
$822$		0			0
$823$	769.291	+	769.291i	0.0325830	+	0.0325830i	0.723211	−	0.690628i	$-0.242666\pi$
$823$	769.291	+	769.291i	0.0325830	+	0.0325830i	−0.690628	+	0.723211i	$0.742666\pi$
$824$		0			0
$825$	−13062.7	+	13062.7i	−0.551253	+	0.551253i
$826$		0			0
$827$	−22898.4	+	9484.82i	−0.962823	+	0.398815i	−0.808036	−	0.589133i	$-0.799469\pi$
$827$	−22898.4	+	9484.82i	−0.962823	+	0.398815i	−0.154788	+	0.987948i	$0.549469\pi$
$828$		0			0
$829$	−10844.8	+	26181.7i	−0.454350	+	1.09690i	0.516301	+	0.856407i	$0.327309\pi$
$829$	−10844.8	+	26181.7i	−0.454350	+	1.09690i	−0.970651	+	0.240492i	$0.922691\pi$
$830$		0			0
$831$	−12881.9			−0.537749
$832$		0			0
$833$	22226.4			0.924488
$834$		0			0
$835$	−6547.70	+	15807.5i	−0.271368	+	0.655141i
$836$		0			0
$837$	3302.06	−	1367.76i	0.136363	−	0.0564834i
$838$		0			0
$839$	−23945.5	+	23945.5i	−0.985327	+	0.985327i	−0.999894	−	0.0145666i	$-0.995363\pi$
$839$	−23945.5	+	23945.5i	−0.985327	+	0.985327i	0.0145666	+	0.999894i	$0.495363\pi$
$840$		0			0
$841$	9652.67	+	9652.67i	0.395779	+	0.395779i
$842$		0			0
$843$	43.3699	+	104.704i	0.00177193	+	0.00427783i
$844$		0			0
$845$	−34824.4	−	14424.7i	−1.41775	−	0.587249i
$846$		0			0
$847$			2352.61i			0.0954386i
$848$		0			0
$849$		−	15668.0i		−	0.633364i
$850$		0			0
$851$	31663.0	+	13115.2i	1.27543	+	0.528302i
$852$		0			0
$853$	8663.21	+	20914.8i	0.347740	+	0.839520i	0.996886	+	0.0788554i	$0.0251266\pi$
$853$	8663.21	+	20914.8i	0.347740	+	0.839520i	−0.649146	+	0.760664i	$0.724873\pi$
$854$		0			0
$855$	41670.8	+	41670.8i	1.66680	+	1.66680i
$856$		0			0
$857$	−9119.55	+	9119.55i	−0.363498	+	0.363498i	−0.865099	−	0.501601i	$-0.832745\pi$
$857$	−9119.55	+	9119.55i	−0.363498	+	0.363498i	0.501601	+	0.865099i	$0.332745\pi$
$858$		0			0
$859$	30582.3	−	12667.6i	1.21473	−	0.503159i	0.319002	−	0.947754i	$-0.396652\pi$
$859$	30582.3	−	12667.6i	1.21473	−	0.503159i	0.895732	+	0.444595i	$0.146652\pi$
$860$		0			0
$861$	1090.07	−	2631.66i	0.0431470	−	0.104166i
$862$		0			0
$863$	−1210.85			−0.0477612			−0.0238806	−	0.999715i	$-0.507602\pi$
$863$	−1210.85			−0.0477612			−0.0238806	+	0.999715i	$0.507602\pi$
$864$		0			0
$865$	−37942.5			−1.49143
$866$		0			0
$867$	−404.169	+	975.749i	−0.0158319	+	0.0382217i
$868$		0			0
$869$	−19880.5	+	8234.77i	−0.776064	+	0.321456i
$870$		0			0
$871$	9201.55	−	9201.55i	0.357959	−	0.357959i
$872$		0			0
$873$	−11988.1	−	11988.1i	−0.464762	−	0.464762i
$874$		0			0
$875$	4665.90	+	11264.5i	0.180270	+	0.435210i
$876$		0			0
$877$	−36421.4	−	15086.2i	−1.40235	−	0.580873i	−0.451990	−	0.892023i	$-0.649286\pi$
$877$	−36421.4	−	15086.2i	−1.40235	−	0.580873i	−0.950361	+	0.311150i	$0.899286\pi$
$878$		0			0
$879$		−	7520.83i		−	0.288591i
$880$		0			0
$881$		−	39286.1i		−	1.50236i	−0.660095	−	0.751182i	$-0.729484\pi$
$881$		−	39286.1i		−	1.50236i	0.660095	−	0.751182i	$-0.270516\pi$
$882$		0			0
$883$	234.092	+	96.9642i	0.00892167	+	0.00369548i	0.387140	−	0.922021i	$-0.373463\pi$
$883$	234.092	+	96.9642i	0.00892167	+	0.00369548i	−0.378218	+	0.925717i	$0.623463\pi$
$884$		0			0
$885$	−4527.24	−	10929.7i	−0.171957	−	0.415140i
$886$		0			0
$887$	−13552.8	−	13552.8i	−0.513032	−	0.513032i	0.402422	−	0.915454i	$-0.368168\pi$
$887$	−13552.8	−	13552.8i	−0.513032	−	0.513032i	−0.915454	+	0.402422i	$0.868168\pi$
$888$		0			0
$889$	6641.66	−	6641.66i	0.250567	−	0.250567i
$890$		0			0
$891$	6384.93	−	2644.73i	0.240071	−	0.0994407i
$892$		0			0
$893$	−16756.6	+	40454.1i	−0.627928	+	1.51595i
$894$		0			0
$895$	6466.85			0.241523
$896$		0			0
$897$	4315.82			0.160648
$898$		0			0
$899$	−1151.29	+	2779.47i	−0.0427117	+	0.103115i
$900$		0			0
$901$	−9055.21	+	3750.79i	−0.334820	+	0.138687i
$902$		0			0
$903$	−804.889	+	804.889i	−0.0296623	+	0.0296623i
$904$		0			0
$905$	18534.2	+	18534.2i	0.680772	+	0.680772i
$906$		0			0
$907$	2600.00	+	6276.95i	0.0951835	+	0.229793i	0.964299	−	0.264816i	$-0.0853112\pi$
$907$	2600.00	+	6276.95i	0.0951835	+	0.229793i	−0.869115	+	0.494609i	$0.835311\pi$
$908$		0			0
$909$	31526.4	+	13058.6i	1.15034	+	0.476488i
$910$		0			0
$911$		−	22984.1i		−	0.835891i	−0.908472	−	0.417946i	$-0.862750\pi$
$911$		−	22984.1i		−	0.835891i	0.908472	−	0.417946i	$-0.137250\pi$
$912$		0			0
$913$		−	30536.3i		−	1.10691i
$914$		0			0
$915$	26900.7	+	11142.6i	0.971924	+	0.402584i
$916$		0			0
$917$	−2386.36	−	5761.17i	−0.0859372	−	0.207471i
$918$		0			0
$919$	−38048.0	−	38048.0i	−1.36571	−	1.36571i	−0.866453	−	0.499258i	$-0.833606\pi$
$919$	−38048.0	−	38048.0i	−1.36571	−	1.36571i	−0.499258	−	0.866453i	$-0.666394\pi$
$920$		0			0
$921$	−801.638	+	801.638i	−0.0286806	+	0.0286806i
$922$		0			0
$923$	12625.6	−	5229.71i	0.450247	−	0.186499i
$924$		0			0
$925$	−25471.3	+	61493.2i	−0.905396	+	2.18582i
$926$		0			0
$927$	2289.15			0.0811064
$928$		0			0
$929$	28435.1			1.00423			0.502113	−	0.864802i	$-0.332556\pi$
$929$	28435.1			1.00423			0.502113	+	0.864802i	$0.332556\pi$
$930$		0			0
$931$	−18070.6	+	43626.3i	−0.636133	+	1.53576i
$932$		0			0
$933$	18216.6	−	7545.57i	0.639212	−	0.264770i
$934$		0			0
$935$	−29940.4	+	29940.4i	−1.04723	+	1.04723i
$936$		0			0
$937$	10599.3	+	10599.3i	0.369546	+	0.369546i	0.867311	−	0.497766i	$-0.165846\pi$
$937$	10599.3	+	10599.3i	0.369546	+	0.369546i	−0.497766	+	0.867311i	$0.665846\pi$
$938$		0			0
$939$	2523.42	+	6092.07i	0.0876982	+	0.211722i
$940$		0			0
$941$	−17446.0	−	7226.38i	−0.604383	−	0.250344i	0.0594418	−	0.998232i	$-0.481068\pi$
$941$	−17446.0	−	7226.38i	−0.604383	−	0.250344i	−0.663825	+	0.747888i	$0.731068\pi$
$942$		0			0
$943$			20896.5i			0.721617i
$944$		0			0
$945$			14332.7i			0.493378i
$946$		0			0
$947$	8125.64	+	3365.75i	0.278826	+	0.115493i	0.517714	−	0.855554i	$-0.326783\pi$
$947$	8125.64	+	3365.75i	0.278826	+	0.115493i	−0.238889	+	0.971047i	$0.576783\pi$
$948$		0			0
$949$	−1690.74	−	4081.81i	−0.0578333	−	0.139622i
$950$		0			0
$951$	−11426.6	−	11426.6i	−0.389623	−	0.389623i
$952$		0			0
$953$	20053.9	−	20053.9i	0.681648	−	0.681648i	−0.278723	−	0.960371i	$-0.589911\pi$
$953$	20053.9	−	20053.9i	0.681648	−	0.681648i	0.960371	+	0.278723i	$0.0899113\pi$
$954$		0			0
$955$	−55013.9	+	22787.5i	−1.86409	+	0.772132i
$956$		0			0
$957$	3188.89	−	7698.66i	0.107714	−	0.260044i
$958$		0			0
$959$	−1064.76			−0.0358529
$960$		0			0
$961$	−28948.1			−0.971707
$962$		0			0
$963$	11164.7	−	26953.9i	0.373599	−	0.901949i
$964$		0			0
$965$	−24857.6	+	10296.3i	−0.829216	+	0.343473i
$966$		0			0
$967$	−17483.6	+	17483.6i	−0.581421	+	0.581421i	−0.935294	−	0.353872i	$-0.884865\pi$
$967$	−17483.6	+	17483.6i	−0.581421	+	0.581421i	0.353872	+	0.935294i	$0.384865\pi$
$968$		0			0
$969$	−20838.6	−	20838.6i	−0.690849	−	0.690849i
$970$		0			0
$971$	−2567.45	−	6198.36i	−0.0848540	−	0.204856i	0.875757	−	0.482752i	$-0.160363\pi$
$971$	−2567.45	−	6198.36i	−0.0848540	−	0.204856i	−0.960611	+	0.277896i	$0.910363\pi$
$972$		0			0
$973$	−35.3190	−	14.6296i	−0.00116369	−	0.000482018i
$974$		0			0
$975$			8381.81i			0.275316i
$976$		0			0
$977$			31111.6i			1.01878i	0.860536	+	0.509390i	$0.170129\pi$
$977$			31111.6i			1.01878i	−0.860536	+	0.509390i	$0.829871\pi$
$978$		0			0
$979$	6595.34	+	2731.88i	0.215309	+	0.0891841i
$980$		0			0
$981$	4104.66	+	9909.52i	0.133590	+	0.322514i
$982$		0			0
$983$	−17048.2	−	17048.2i	−0.553156	−	0.553156i	0.374194	−	0.927350i	$-0.377919\pi$
$983$	−17048.2	−	17048.2i	−0.553156	−	0.553156i	−0.927350	+	0.374194i	$0.877919\pi$
$984$		0			0
$985$	19856.5	−	19856.5i	0.642316	−	0.642316i
$986$		0			0
$987$	−4210.22	+	1743.93i	−0.135778	+	0.0562410i
$988$		0			0
$989$	3195.58	−	7714.81i	0.102744	−	0.248045i
$990$		0			0
$991$	−32857.3			−1.05323			−0.526613	−	0.850105i	$-0.676538\pi$
$991$	−32857.3			−1.05323			−0.526613	+	0.850105i	$0.676538\pi$
$992$		0			0
$993$	−11566.1			−0.369625
$994$		0			0
$995$	−12310.3	+	29719.7i	−0.392223	+	0.946911i
$996$		0			0
$997$	−30160.2	+	12492.8i	−0.958057	+	0.396840i	−0.806253	−	0.591570i	$-0.798508\pi$
$997$	−30160.2	+	12492.8i	−0.958057	+	0.396840i	−0.151804	+	0.988411i	$0.548508\pi$
$998$		0			0
$999$	−25221.6	+	25221.6i	−0.798775	+	0.798775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.17.7		44
4.3	odd	2		32.4.g.a.13.2	yes	44
8.3	odd	2		256.4.g.b.33.7		44
8.5	even	2		256.4.g.a.33.5		44
32.5	even	8	inner	128.4.g.a.113.7		44
32.11	odd	8		256.4.g.b.225.7		44
32.21	even	8		256.4.g.a.225.5		44
32.27	odd	8		32.4.g.a.5.2	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.2	✓	44	32.27	odd	8
32.4.g.a.13.2	yes	44	4.3	odd	2
128.4.g.a.17.7		44	1.1	even	1	trivial
128.4.g.a.113.7		44	32.5	even	8	inner
256.4.g.a.33.5		44	8.5	even	2
256.4.g.a.225.5		44	32.21	even	8
256.4.g.b.33.7		44	8.3	odd	2
256.4.g.b.225.7		44	32.11	odd	8

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)

\(f(q)\)	\(=\)	\(q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +O(q^{10})\)	\(q+(0.998206 - 2.40988i) q^{3} +(17.4005 - 7.20752i) q^{5} +(-4.37099 + 4.37099i) q^{7} +(14.2808 + 14.2808i) q^{9} +(-11.7977 - 28.4821i) q^{11} +(-12.9230 - 5.35288i) q^{13} -49.1278i q^{15} -72.9239i q^{17} +(143.136 + 59.2889i) q^{19} +(6.17043 + 14.8967i) q^{21} +(-83.6411 - 83.6411i) q^{23} +(162.441 - 162.441i) q^{25} +(113.737 - 47.1114i) q^{27} +(-39.6554 + 95.7367i) q^{29} +29.0324 q^{31} -80.4149 q^{33} +(-44.5534 + 107.562i) q^{35} +(-267.681 + 110.877i) q^{37} +(-25.7996 + 25.7996i) q^{39} +(-124.918 - 124.918i) q^{41} +(27.0156 + 65.2215i) q^{43} +(351.421 + 145.564i) q^{45} +282.627i q^{47} +304.789i q^{49} +(-175.738 - 72.7931i) q^{51} +(-51.4343 - 124.173i) q^{53} +(-410.570 - 410.570i) q^{55} +(285.759 - 285.759i) q^{57} +(222.476 - 92.1524i) q^{59} +(-226.809 + 547.566i) q^{61} -124.842 q^{63} -263.447 q^{65} +(-356.015 + 859.496i) q^{67} +(-285.056 + 118.074i) q^{69} +(-690.837 + 690.837i) q^{71} +(223.345 + 223.345i) q^{73} +(-229.314 - 553.612i) q^{75} +(176.062 + 72.9275i) q^{77} -698.000i q^{79} +224.174i q^{81} +(915.116 + 379.053i) q^{83} +(-525.601 - 1268.91i) q^{85} +(191.130 + 191.130i) q^{87} +(-163.738 + 163.738i) q^{89} +(79.8837 - 33.0889i) q^{91} +(28.9803 - 69.9647i) q^{93} +2917.97 q^{95} -839.460 q^{97} +(238.266 - 575.225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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