LMFDB - Embedded newform 252.4.x.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +O(q^{10})$	\(q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +(16.1150 - 9.30397i) q^{11} +(44.1430 + 25.4860i) q^{13} +(-12.9980 + 20.5859i) q^{15} -112.833 q^{17} -111.459i q^{19} +(59.8590 - 75.3518i) q^{21} +(-124.503 - 71.8819i) q^{23} +(51.5236 + 89.2414i) q^{25} +(-139.308 - 16.6238i) q^{27} +(206.907 - 119.458i) q^{29} +(-179.999 - 103.923i) q^{31} +(-85.5836 + 44.9928i) q^{33} +(35.0243 + 79.3922i) q^{35} -227.815 q^{37} +(-223.953 - 141.404i) q^{39} +(133.141 - 230.607i) q^{41} +(-170.287 - 294.946i) q^{43} +(71.7202 - 104.211i) q^{45} +(-111.979 - 193.952i) q^{47} +(-103.769 - 326.927i) q^{49} +(585.836 + 23.2053i) q^{51} -547.974i q^{53} -87.1854i q^{55} +(-22.9227 + 578.703i) q^{57} +(-43.9483 + 76.1207i) q^{59} +(-312.398 + 180.363i) q^{61} +(-326.290 + 378.922i) q^{63} +(206.827 - 119.412i) q^{65} +(-372.426 + 645.060i) q^{67} +(631.647 + 398.822i) q^{69} -135.948i q^{71} -467.289i q^{73} +(-249.161 - 473.945i) q^{75} +(-37.1896 + 342.612i) q^{77} +(192.171 + 332.850i) q^{79} +(719.878 + 114.962i) q^{81} +(597.216 + 1034.41i) q^{83} +(-264.332 + 457.836i) q^{85} +(-1098.85 + 577.683i) q^{87} +1385.63 q^{89} +(-863.702 + 381.027i) q^{91} +(913.198 + 576.594i) q^{93} +(-452.262 - 261.114i) q^{95} +(1070.10 - 617.821i) q^{97} +(453.610 - 216.005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.19208	−	0.205661i	−0.999216	−	0.0395795i
$3$	−5.19208	−	0.205661i	−0.999216	−	0.0395795i
$4$		0			0
$5$	2.34269	−	4.05766i	0.209537	−	0.362929i	−0.742032	−	0.670365i	$-0.766138\pi$
$5$	2.34269	−	4.05766i	0.209537	−	0.362929i	0.951569	+	0.307436i	$0.0994710\pi$
$6$		0			0
$7$	−10.9369	+	14.9461i	−0.590536	+	0.807011i
$7$	−10.9369	+	14.9461i	−0.590536	+	0.807011i
$8$		0			0
$9$	26.9154	+	2.13562i	0.996867	+	0.0790970i
$10$		0			0
$11$	16.1150	−	9.30397i	0.441713	−	0.255023i	−0.262611	−	0.964902i	$-0.584584\pi$
$11$	16.1150	−	9.30397i	0.441713	−	0.255023i	0.704324	+	0.709879i	$0.251250\pi$
$12$		0			0
$13$	44.1430	+	25.4860i	0.941775	+	0.543734i	0.890516	−	0.454951i	$-0.150343\pi$
$13$	44.1430	+	25.4860i	0.941775	+	0.543734i	0.0512589	+	0.998685i	$0.483677\pi$
$14$		0			0
$15$	−12.9980	+	20.5859i	−0.223737	+	0.354351i
$16$		0			0
$17$	−112.833			−1.60976			−0.804880	−	0.593438i	$-0.797770\pi$
$17$	−112.833			−1.60976			−0.804880	+	0.593438i	$0.797770\pi$
$18$		0			0
$19$		−	111.459i		−	1.34581i	−0.739729	−	0.672905i	$-0.765046\pi$
$19$		−	111.459i		−	1.34581i	0.739729	−	0.672905i	$-0.234954\pi$
$20$		0			0
$21$	59.8590	−	75.3518i	0.622014	−	0.783006i
$22$		0			0
$23$	−124.503	−	71.8819i	−1.12873	−	0.651671i	−0.185112	−	0.982717i	$-0.559265\pi$
$23$	−124.503	−	71.8819i	−1.12873	−	0.651671i	−0.943614	+	0.331047i	$0.892598\pi$
$24$		0			0
$25$	51.5236	+	89.2414i	0.412189	+	0.713932i
$26$		0			0
$27$	−139.308	−	16.6238i	−0.992955	−	0.118490i
$28$		0			0
$29$	206.907	−	119.458i	1.32489	−	0.764924i	0.340383	−	0.940287i	$-0.389443\pi$
$29$	206.907	−	119.458i	1.32489	−	0.764924i	0.984504	+	0.175363i	$0.0561101\pi$
$30$		0			0
$31$	−179.999	−	103.923i	−1.04287	−	0.602099i	−0.122222	−	0.992503i	$-0.539002\pi$
$31$	−179.999	−	103.923i	−1.04287	−	0.602099i	−0.920644	+	0.390404i	$0.872335\pi$
$32$		0			0
$33$	−85.5836	+	44.9928i	−0.451460	+	0.237340i
$34$		0			0
$35$	35.0243	+	79.3922i	0.169148	+	0.383421i
$36$		0			0
$37$	−227.815			−1.01223			−0.506115	−	0.862466i	$-0.668919\pi$
$37$	−227.815			−1.01223			−0.506115	+	0.862466i	$0.668919\pi$
$38$		0			0
$39$	−223.953	−	141.404i	−0.919517	−	0.580583i
$40$		0			0
$41$	133.141	−	230.607i	0.507149	−	0.878407i	−0.492817	−	0.870133i	$-0.664033\pi$
$41$	133.141	−	230.607i	0.507149	−	0.878407i	0.999966	−	0.00827417i	$-0.00263378\pi$
$42$		0			0
$43$	−170.287	−	294.946i	−0.603920	−	1.04602i	−0.992221	−	0.124488i	$-0.960271\pi$
$43$	−170.287	−	294.946i	−0.603920	−	1.04602i	0.388301	−	0.921533i	$-0.373062\pi$
$44$		0			0
$45$	71.7202	−	104.211i	0.237587	−	0.345218i
$46$		0			0
$47$	−111.979	−	193.952i	−0.347527	−	0.601934i	0.638283	−	0.769802i	$-0.279645\pi$
$47$	−111.979	−	193.952i	−0.347527	−	0.601934i	−0.985809	+	0.167868i	$0.946312\pi$
$48$		0			0
$49$	−103.769	−	326.927i	−0.302534	−	0.953139i
$50$		0			0
$51$	585.836	+	23.2053i	1.60850	+	0.0637135i
$52$		0			0
$53$		−	547.974i		−	1.42019i	−0.704107	−	0.710094i	$-0.748652\pi$
$53$		−	547.974i		−	1.42019i	0.704107	−	0.710094i	$-0.251348\pi$
$54$		0			0
$55$		−	87.1854i		−	0.213747i
$56$		0			0
$57$	−22.9227	+	578.703i	−0.0532665	+	1.34476i
$58$		0			0
$59$	−43.9483	+	76.1207i	−0.0969760	+	0.167967i	−0.910432	−	0.413660i	$-0.864250\pi$
$59$	−43.9483	+	76.1207i	−0.0969760	+	0.167967i	0.813456	+	0.581627i	$0.197584\pi$
$60$		0			0
$61$	−312.398	+	180.363i	−0.655712	+	0.378575i	−0.790641	−	0.612280i	$-0.790253\pi$
$61$	−312.398	+	180.363i	−0.655712	+	0.378575i	0.134929	+	0.990855i	$0.456919\pi$
$62$		0			0
$63$	−326.290	+	378.922i	−0.652518	+	0.757773i
$64$		0			0
$65$	206.827	−	119.412i	0.394673	−	0.227865i
$66$		0			0
$67$	−372.426	+	645.060i	−0.679090	+	1.17622i	0.296165	+	0.955137i	$0.404292\pi$
$67$	−372.426	+	645.060i	−0.679090	+	1.17622i	−0.975255	+	0.221082i	$0.929041\pi$
$68$		0			0
$69$	631.647	+	398.822i	1.10205	+	0.695834i
$70$		0			0
$71$		−	135.948i		−	0.227240i	−0.993524	−	0.113620i	$-0.963755\pi$
$71$		−	135.948i		−	0.227240i	0.993524	−	0.113620i	$-0.0362447\pi$
$72$		0			0
$73$		−	467.289i		−	0.749206i	−0.927185	−	0.374603i	$-0.877779\pi$
$73$		−	467.289i		−	0.749206i	0.927185	−	0.374603i	$-0.122221\pi$
$74$		0			0
$75$	−249.161	−	473.945i	−0.383609	−	0.729686i
$76$		0			0
$77$	−37.1896	+	342.612i	−0.0550409	+	0.507068i
$78$		0			0
$79$	192.171	+	332.850i	0.273683	+	0.474032i	0.969802	−	0.243894i	$-0.0784249\pi$
$79$	192.171	+	332.850i	0.273683	+	0.474032i	−0.696119	+	0.717926i	$0.745092\pi$
$80$		0			0
$81$	719.878	+	114.962i	0.987487	+	0.157698i
$82$		0			0
$83$	597.216	+	1034.41i	0.789795	+	1.36796i	0.926092	+	0.377297i	$0.123146\pi$
$83$	597.216	+	1034.41i	0.789795	+	1.36796i	−0.136297	+	0.990668i	$0.543520\pi$
$84$		0			0
$85$	−264.332	+	457.836i	−0.337304	+	0.584228i
$86$		0			0
$87$	−1098.85	+	577.683i	−1.35412	+	0.711886i
$88$		0			0
$89$	1385.63			1.65030			0.825150	−	0.564914i	$-0.191091\pi$
$89$	1385.63			1.65030			0.825150	+	0.564914i	$0.191091\pi$
$90$		0			0
$91$	−863.702	+	381.027i	−0.994952	+	0.438929i
$92$		0			0
$93$	913.198	+	576.594i	1.01822	+	0.642903i
$94$		0			0
$95$	−452.262	−	261.114i	−0.488433	−	0.281997i
$96$		0			0
$97$	1070.10	−	617.821i	1.12012	−	0.646704i	0.178691	−	0.983905i	$-0.442814\pi$
$97$	1070.10	−	617.821i	1.12012	−	0.646704i	0.941432	+	0.337202i	$0.109480\pi$
$98$		0			0
$99$	453.610	−	216.005i	0.460501	−	0.219286i
$100$		0			0
$101$	−94.1707	−	163.108i	−0.0927756	−	0.160692i	0.815902	−	0.578190i	$-0.196241\pi$
$101$	−94.1707	−	163.108i	−0.0927756	−	0.160692i	−0.908678	+	0.417498i	$0.862907\pi$
$102$		0			0
$103$	687.152	+	396.727i	0.657350	+	0.379521i	0.791267	−	0.611471i	$-0.209422\pi$
$103$	687.152	+	396.727i	0.657350	+	0.379521i	−0.133916	+	0.990993i	$0.542755\pi$
$104$		0			0
$105$	−165.521	−	419.414i	−0.153840	−	0.389815i
$106$		0			0
$107$		−	1399.55i		−	1.26448i	−0.774773	−	0.632240i	$-0.782136\pi$
$107$		−	1399.55i		−	1.26448i	0.774773	−	0.632240i	$-0.217864\pi$
$108$		0			0
$109$	−2137.48			−1.87829			−0.939145	−	0.343521i	$-0.888380\pi$
$109$	−2137.48			−1.87829			−0.939145	+	0.343521i	$0.888380\pi$
$110$		0			0
$111$	1182.83	+	46.8526i	1.01144	+	0.0400635i
$112$		0			0
$113$	−1500.15	−	866.110i	−1.24887	−	0.721034i	−0.277984	−	0.960586i	$-0.589666\pi$
$113$	−1500.15	−	866.110i	−1.24887	−	0.721034i	−0.970884	+	0.239552i	$0.922999\pi$
$114$		0			0
$115$	−583.346	+	336.795i	−0.473020	+	0.273098i
$116$		0			0
$117$	1133.70	+	780.239i	0.895817	+	0.616522i
$118$		0			0
$119$	1234.04	−	1686.40i	0.950621	−	1.29909i
$120$		0			0
$121$	−492.372	+	852.814i	−0.369926	+	0.640731i
$122$		0			0
$123$	−738.704	+	1169.95i	−0.541518	+	0.857646i
$124$		0			0
$125$	1068.49			0.764549
$126$		0			0
$127$	−770.489			−0.538345			−0.269173	−	0.963092i	$-0.586750\pi$
$127$	−770.489			−0.538345			−0.269173	+	0.963092i	$0.586750\pi$
$128$		0			0
$129$	823.487	+	1566.41i	0.562046	+	1.06910i
$130$		0			0
$131$	−489.800	+	848.359i	−0.326672	+	0.565813i	−0.981849	−	0.189662i	$-0.939261\pi$
$131$	−489.800	+	848.359i	−0.326672	+	0.565813i	0.655177	+	0.755475i	$0.272594\pi$
$132$		0			0
$133$	1665.87	+	1219.01i	1.08608	+	0.794750i
$134$		0			0
$135$	−393.809	+	526.320i	−0.251064	+	0.335544i
$136$		0			0
$137$	−182.458	+	105.342i	−0.113784	+	0.0656932i	−0.555812	−	0.831308i	$-0.687593\pi$
$137$	−182.458	+	105.342i	−0.113784	+	0.0656932i	0.442028	+	0.897001i	$0.354259\pi$
$138$		0			0
$139$	−730.515	−	421.763i	−0.445766	−	0.257363i	0.260274	−	0.965535i	$-0.416187\pi$
$139$	−730.515	−	421.763i	−0.445766	−	0.257363i	−0.706040	+	0.708172i	$0.749520\pi$
$140$		0			0
$141$	541.513	+	1030.05i	0.323430	+	0.615217i
$142$		0			0
$143$	948.484			0.554659
$144$		0			0
$145$		−	1119.41i		−	0.641119i
$146$		0			0
$147$	471.542	+	1718.77i	0.264572	+	0.964366i
$148$		0			0
$149$	1137.32	+	656.632i	0.625321	+	0.361029i	0.778938	−	0.627101i	$-0.215759\pi$
$149$	1137.32	+	656.632i	0.625321	+	0.361029i	−0.153617	+	0.988131i	$0.549092\pi$
$150$		0			0
$151$	−1738.76	−	3011.62i	−0.937074	−	1.62306i	−0.770893	−	0.636965i	$-0.780190\pi$
$151$	−1738.76	−	3011.62i	−0.937074	−	1.62306i	−0.166182	−	0.986095i	$-0.553144\pi$
$152$		0			0
$153$	−3036.93	−	240.967i	−1.60472	−	0.127327i
$154$		0			0
$155$	−843.366	+	486.918i	−0.437038	+	0.252324i
$156$		0			0
$157$	499.729	+	288.519i	0.254030	+	0.146664i	0.621608	−	0.783328i	$-0.286480\pi$
$157$	499.729	+	288.519i	0.254030	+	0.146664i	−0.367578	+	0.929993i	$0.619813\pi$
$158$		0			0
$159$	−112.697	+	2845.12i	−0.0562103	+	1.41908i
$160$		0			0
$161$	2436.03	−	1074.67i	1.19246	−	0.526060i
$162$		0			0
$163$	1595.73			0.766794			0.383397	−	0.923584i	$-0.374754\pi$
$163$	1595.73			0.766794			0.383397	+	0.923584i	$0.374754\pi$
$164$		0			0
$165$	−17.9307	+	452.674i	−0.00846000	+	0.213579i
$166$		0			0
$167$	184.918	−	320.287i	0.0856850	−	0.148411i	−0.819998	−	0.572366i	$-0.806025\pi$
$167$	184.918	−	320.287i	0.0856850	−	0.148411i	0.905683	+	0.423956i	$0.139359\pi$
$168$		0			0
$169$	200.572	+	347.402i	0.0912938	+	0.158125i
$170$		0			0
$171$	238.033	−	2999.96i	0.106450	−	1.34159i
$172$		0			0
$173$	−973.579	−	1686.29i	−0.427860	−	0.741076i	0.568822	−	0.822460i	$-0.307399\pi$
$173$	−973.579	−	1686.29i	−0.427860	−	0.741076i	−0.996683	+	0.0813844i	$0.974066\pi$
$174$		0			0
$175$	−1897.31	−	205.949i	−0.819563	−	0.0889615i
$176$		0			0
$177$	243.838	−	386.187i	0.103548	−	0.163997i
$178$		0			0
$179$			851.921i			0.355730i	0.984055	+	0.177865i	$0.0569190\pi$
$179$			851.921i			0.355730i	−0.984055	+	0.177865i	$0.943081\pi$
$180$		0			0
$181$			639.259i			0.262518i	0.991348	+	0.131259i	$0.0419020\pi$
$181$			639.259i			0.262518i	−0.991348	+	0.131259i	$0.958098\pi$
$182$		0			0
$183$	1659.09	−	872.210i	0.670182	−	0.352326i
$184$		0			0
$185$	−533.700	+	924.395i	−0.212099	+	0.367367i
$186$		0			0
$187$	−1818.29	+	1049.79i	−0.711051	+	0.410526i
$188$		0			0
$189$	1772.05	−	1900.29i	0.681999	−	0.731353i
$190$		0			0
$191$	3120.13	−	1801.41i	1.18201	−	0.682435i	0.225533	−	0.974235i	$-0.427588\pi$
$191$	3120.13	−	1801.41i	1.18201	−	0.682435i	0.956479	+	0.291800i	$0.0942542\pi$
$192$		0			0
$193$	−1745.01	+	3022.44i	−0.650821	+	1.12725i	0.332103	+	0.943243i	$0.392242\pi$
$193$	−1745.01	+	3022.44i	−0.650821	+	1.12725i	−0.982924	+	0.184012i	$0.941092\pi$
$194$		0			0
$195$	−1098.42	+	577.459i	−0.403383	+	0.212065i
$196$		0			0
$197$		−	1909.86i		−	0.690719i	−0.938470	−	0.345360i	$-0.887757\pi$
$197$		−	1909.86i		−	0.690719i	0.938470	−	0.345360i	$-0.112243\pi$
$198$		0			0
$199$		−	713.005i		−	0.253988i	−0.991903	−	0.126994i	$-0.959467\pi$
$199$		−	713.005i		−	0.253988i	0.991903	−	0.126994i	$-0.0405329\pi$
$200$		0			0
$201$	2066.33	−	3272.61i	0.725112	−	1.14842i
$202$		0			0
$203$	−477.494	+	4398.94i	−0.165091	+	1.52091i
$204$		0			0
$205$	−623.816	−	1080.48i	−0.212533	−	0.368117i
$206$		0			0
$207$	−3197.54	−	2200.62i	−1.07364	−	0.738908i
$208$		0			0
$209$	−1037.01	−	1796.15i	−0.343213	−	0.594462i
$210$		0			0
$211$	788.596	−	1365.89i	0.257295	−	0.445648i	−0.708221	−	0.705990i	$-0.750502\pi$
$211$	788.596	−	1365.89i	0.257295	−	0.445648i	0.965516	+	0.260343i	$0.0838355\pi$
$212$		0			0
$213$	−27.9592	+	705.853i	−0.00899406	+	0.227062i
$214$		0			0
$215$	−1595.72			−0.506174
$216$		0			0
$217$	3521.86	−	1553.69i	1.10175	−	0.486043i
$218$		0			0
$219$	−96.1031	+	2426.20i	−0.0296532	+	0.748618i
$220$		0			0
$221$	−4980.77	−	2875.65i	−1.51603	−	0.875281i
$222$		0			0
$223$	412.569	−	238.197i	0.123891	−	0.0715284i	−0.436774	−	0.899571i	$-0.643879\pi$
$223$	412.569	−	238.197i	0.123891	−	0.0715284i	0.560665	+	0.828043i	$0.310546\pi$
$224$		0			0
$225$	1196.19	+	2512.00i	0.354427	+	0.744298i
$226$		0			0
$227$	−1386.85	−	2402.10i	−0.405501	−	0.702348i	0.588879	−	0.808221i	$-0.299569\pi$
$227$	−1386.85	−	2402.10i	−0.405501	−	0.702348i	−0.994380	+	0.105873i	$0.966236\pi$
$228$		0			0
$229$	−1698.53	−	980.646i	−0.490139	−	0.282982i	0.234493	−	0.972118i	$-0.424657\pi$
$229$	−1698.53	−	980.646i	−0.490139	−	0.282982i	−0.724632	+	0.689136i	$0.757990\pi$
$230$		0			0
$231$	263.553	−	1771.22i	0.0750673	−	0.504492i
$232$		0			0
$233$			4734.94i			1.33132i	0.746257	+	0.665658i	$0.231849\pi$
$233$			4734.94i			1.33132i	−0.746257	+	0.665658i	$0.768151\pi$
$234$		0			0
$235$	−1049.33			−0.291279
$236$		0			0
$237$	−929.313	−	1767.71i	−0.254706	−	0.484493i
$238$		0			0
$239$	−1055.48	−	609.379i	−0.285661	−	0.164927i	0.350322	−	0.936629i	$-0.386072\pi$
$239$	−1055.48	−	609.379i	−0.285661	−	0.164927i	−0.635984	+	0.771703i	$0.719405\pi$
$240$		0			0
$241$	−1784.77	+	1030.43i	−0.477041	+	0.275420i	−0.719182	−	0.694821i	$-0.755483\pi$
$241$	−1784.77	+	1030.43i	−0.477041	+	0.275420i	0.242142	+	0.970241i	$0.422150\pi$
$242$		0			0
$243$	−3714.02	−	744.943i	−0.980472	−	0.196659i
$244$		0			0
$245$	−1569.66	−	344.828i	−0.409313	−	0.0899193i
$246$		0			0
$247$	2840.64	−	4920.13i	0.731763	−	1.26745i
$248$		0			0
$249$	−2888.06	−	5493.56i	−0.735033	−	1.39815i
$250$		0			0
$251$	−2966.29			−0.745937			−0.372969	−	0.927844i	$-0.621660\pi$
$251$	−2966.29			−0.745937			−0.372969	+	0.927844i	$0.621660\pi$
$252$		0			0
$253$	−2675.15			−0.664764
$254$		0			0
$255$	1466.59	−	2322.76i	0.360163	−	0.570419i
$256$		0			0
$257$	1133.09	−	1962.58i	0.275021	−	0.476351i	−0.695119	−	0.718895i	$-0.744648\pi$
$257$	1133.09	−	1962.58i	0.275021	−	0.476351i	0.970141	+	0.242543i	$0.0779817\pi$
$258$		0			0
$259$	2491.58	−	3404.93i	0.597758	−	0.816880i
$260$		0			0
$261$	5824.11	−	2773.38i	1.38124	−	0.657732i
$262$		0			0
$263$	−1580.16	+	912.308i	−0.370483	+	0.213898i	−0.673669	−	0.739033i	$-0.735283\pi$
$263$	−1580.16	+	912.308i	−0.370483	+	0.213898i	0.303186	+	0.952931i	$0.401950\pi$
$264$		0			0
$265$	−2223.49	−	1283.73i	−0.515427	−	0.297582i
$266$		0			0
$267$	−7194.31	−	284.971i	−1.64901	−	0.0653180i
$268$		0			0
$269$	5616.89			1.27312			0.636558	−	0.771229i	$-0.280358\pi$
$269$	5616.89			1.27312			0.636558	+	0.771229i	$0.280358\pi$
$270$		0			0
$271$			5603.22i			1.25598i	0.778220	+	0.627992i	$0.216123\pi$
$271$			5603.22i			1.25598i	−0.778220	+	0.627992i	$0.783877\pi$
$272$		0			0
$273$	4562.78	−	1800.69i	1.01154	−	0.399205i
$274$		0			0
$275$	1660.60	+	958.748i	0.364138	+	0.210235i
$276$		0			0
$277$	2329.35	+	4034.55i	0.505260	+	0.875137i	0.999981	+	0.00608483i	$0.00193687\pi$
$277$	2329.35	+	4034.55i	0.505260	+	0.875137i	−0.494721	+	0.869052i	$0.664730\pi$
$278$		0			0
$279$	−4622.82	−	3181.53i	−0.991974	−	0.682700i
$280$		0			0
$281$	1939.85	−	1119.97i	0.411820	−	0.237765i	−0.279751	−	0.960073i	$-0.590252\pi$
$281$	1939.85	−	1119.97i	0.411820	−	0.237765i	0.691572	+	0.722308i	$0.256919\pi$
$282$		0			0
$283$	2759.51	+	1593.21i	0.579633	+	0.334651i	0.760987	−	0.648767i	$-0.224715\pi$
$283$	2759.51	+	1593.21i	0.579633	+	0.334651i	−0.181355	+	0.983418i	$0.558048\pi$
$284$		0			0
$285$	2294.48	+	1448.74i	0.476889	+	0.301108i
$286$		0			0
$287$	1990.51	+	4512.05i	0.409395	+	0.928006i
$288$		0			0
$289$	7818.18			1.59132
$290$		0			0
$291$	−5683.10	+	2987.70i	−1.14484	+	0.601863i
$292$		0			0
$293$	−4563.57	+	7904.34i	−0.909921	+	1.57603i	−0.0957489	+	0.995406i	$0.530525\pi$
$293$	−4563.57	+	7904.34i	−0.909921	+	1.57603i	−0.814172	+	0.580624i	$0.802809\pi$
$294$		0			0
$295$	205.915	+	356.655i	0.0406401	+	0.0703907i
$296$		0			0
$297$	−2399.61	+	1028.22i	−0.468819	+	0.200888i
$298$		0			0
$299$	−3663.97	−	6346.18i	−0.708671	−	1.22745i
$300$		0			0
$301$	6270.70	+	680.669i	1.20079	+	0.130342i
$302$		0			0
$303$	455.397	+	866.239i	0.0863428	+	0.164238i
$304$		0			0
$305$			1690.14i			0.317302i
$306$		0			0
$307$		−	4744.58i		−	0.882044i	−0.897496	−	0.441022i	$-0.854616\pi$
$307$		−	4744.58i		−	0.882044i	0.897496	−	0.441022i	$-0.145384\pi$
$308$		0			0
$309$	−3486.16	−	2201.16i	−0.641814	−	0.405242i
$310$		0			0
$311$	−1089.62	+	1887.29i	−0.198672	+	0.344110i	−0.948098	−	0.317978i	$-0.896996\pi$
$311$	−1089.62	+	1887.29i	−0.198672	+	0.344110i	0.749426	+	0.662088i	$0.230329\pi$
$312$		0			0
$313$	−1752.85	+	1012.01i	−0.316540	+	0.182754i	−0.649849	−	0.760063i	$-0.725168\pi$
$313$	−1752.85	+	1012.01i	−0.316540	+	0.182754i	0.333309	+	0.942818i	$0.391835\pi$
$314$		0			0
$315$	773.142	+	2211.67i	0.138291	+	0.395599i
$316$		0			0
$317$	189.948	−	109.666i	0.0336547	−	0.0194305i	−0.483078	−	0.875577i	$-0.660481\pi$
$317$	189.948	−	109.666i	0.0336547	−	0.0194305i	0.516733	+	0.856147i	$0.327148\pi$
$318$		0			0
$319$	2222.87	−	3850.12i	0.390146	−	0.675753i
$320$		0			0
$321$	−287.833	+	7266.56i	−0.0500475	+	1.26349i
$322$		0			0
$323$			12576.2i			2.16643i
$324$		0			0
$325$			5252.52i			0.896484i
$326$		0			0
$327$	11098.0	+	439.597i	1.87682	+	0.0743418i
$328$		0			0
$329$	4123.52	+	447.598i	0.690994	+	0.0750057i
$330$		0			0
$331$	1884.36	+	3263.81i	0.312912	+	0.541980i	0.978991	−	0.203901i	$-0.0653621\pi$
$331$	1884.36	+	3263.81i	0.312912	+	0.541980i	−0.666079	+	0.745881i	$0.732029\pi$
$332$		0			0
$333$	−6131.72	−	486.525i	−1.00906	−	0.0800643i
$334$		0			0
$335$	1744.96	+	3022.36i	0.284589	+	0.492922i
$336$		0			0
$337$	3056.60	−	5294.18i	0.494076	−	0.855764i	−0.505901	−	0.862592i	$-0.668840\pi$
$337$	3056.60	−	5294.18i	0.494076	−	0.855764i	0.999977	+	0.00682736i	$0.00217323\pi$
$338$		0			0
$339$	7610.76	+	4805.44i	1.21935	+	0.769898i
$340$		0			0
$341$	−3867.57			−0.614196
$342$		0			0
$343$	6021.17	+	2024.61i	0.947851	+	0.318714i
$344$		0			0
$345$	3098.04	−	1628.69i	0.483458	−	0.254162i
$346$		0			0
$347$	1143.36	+	660.117i	0.176883	+	0.102124i	0.585828	−	0.810436i	$-0.300770\pi$
$347$	1143.36	+	660.117i	0.176883	+	0.102124i	−0.408944	+	0.912559i	$0.634103\pi$
$348$		0			0
$349$	−2309.07	+	1333.14i	−0.354159	+	0.204474i	−0.666515	−	0.745491i	$-0.732215\pi$
$349$	−2309.07	+	1333.14i	−0.354159	+	0.204474i	0.312357	+	0.949965i	$0.398882\pi$
$350$		0			0
$351$	−5725.80	−	4284.22i	−0.870713	−	0.651495i
$352$		0			0
$353$	−4725.05	−	8184.03i	−0.712434	−	1.23397i	−0.963941	−	0.266116i	$-0.914260\pi$
$353$	−4725.05	−	8184.03i	−0.712434	−	1.23397i	0.251508	−	0.967855i	$-0.419074\pi$
$354$		0			0
$355$	−551.632	−	318.485i	−0.0824720	−	0.0476152i
$356$		0			0
$357$	−6754.04	+	8502.14i	−1.00129	+	1.26045i
$358$		0			0
$359$			6846.88i			1.00659i	0.864116	+	0.503293i	$0.167878\pi$
$359$			6846.88i			1.00659i	−0.864116	+	0.503293i	$0.832122\pi$
$360$		0			0
$361$	−5564.07			−0.811206
$362$		0			0
$363$	2731.83	−	4326.62i	0.394996	−	0.625588i
$364$		0			0
$365$	−1896.10	−	1094.71i	−0.271908	−	0.156986i
$366$		0			0
$367$	5440.63	−	3141.15i	0.773838	−	0.446775i	−0.0604042	−	0.998174i	$-0.519239\pi$
$367$	5440.63	−	3141.15i	0.773838	−	0.446775i	0.834242	+	0.551399i	$0.185906\pi$
$368$		0			0
$369$	4076.02	−	5922.53i	0.575039	−	0.835541i
$370$		0			0
$371$	8190.05	+	5993.12i	1.14611	+	0.838672i
$372$		0			0
$373$	−5253.75	+	9099.76i	−0.729300	+	1.26318i	0.227880	+	0.973689i	$0.426821\pi$
$373$	−5253.75	+	9099.76i	−0.729300	+	1.26318i	−0.957179	+	0.289495i	$0.906513\pi$
$374$		0			0
$375$	−5547.68	−	219.747i	−0.763950	−	0.0302605i
$376$		0			0
$377$	12178.0			1.66366
$378$		0			0
$379$	5904.89			0.800301			0.400150	−	0.916450i	$-0.368958\pi$
$379$	5904.89			0.800301			0.400150	+	0.916450i	$0.368958\pi$
$380$		0			0
$381$	4000.44	+	158.460i	0.537923	+	0.0213074i
$382$		0			0
$383$	−1175.26	+	2035.61i	−0.156797	+	0.271580i	−0.933712	−	0.358026i	$-0.883450\pi$
$383$	−1175.26	+	2035.61i	−0.156797	+	0.271580i	0.776915	+	0.629605i	$0.216783\pi$
$384$		0			0
$385$	1303.08	+	953.537i	0.172496	+	0.126225i
$386$		0			0
$387$	−3953.46	−	8302.27i	−0.519291	−	1.09051i
$388$		0			0
$389$	−11034.6	+	6370.81i	−1.43824	+	0.830368i	−0.997727	−	0.0673794i	$-0.978536\pi$
$389$	−11034.6	+	6370.81i	−1.43824	+	0.830368i	−0.440511	+	0.897747i	$0.645203\pi$
$390$		0			0
$391$	14048.0	+	8110.62i	1.81698	+	1.04903i
$392$		0			0
$393$	2717.56	−	4304.02i	0.348811	−	0.552440i
$394$		0			0
$395$	1800.79			0.229386
$396$		0			0
$397$			13326.3i			1.68470i	0.538930	+	0.842350i	$0.318829\pi$
$397$			13326.3i			1.68470i	−0.538930	+	0.842350i	$0.681171\pi$
$398$		0			0
$399$	−8398.63	−	6671.81i	−1.05378	−	0.837114i
$400$		0			0
$401$	−8090.75	−	4671.20i	−1.00756	−	0.581717i	−0.0970856	−	0.995276i	$-0.530952\pi$
$401$	−8090.75	−	4671.20i	−1.00756	−	0.581717i	−0.910477	+	0.413559i	$0.864285\pi$
$402$		0			0
$403$	−5297.15	−	9174.92i	−0.654763	−	1.13408i
$404$		0			0
$405$	2152.93	−	2651.70i	0.264148	−	0.325344i
$406$		0			0
$407$	−3671.22	+	2119.58i	−0.447115	+	0.258142i
$408$		0			0
$409$	268.033	+	154.749i	0.0324044	+	0.0187087i	0.516115	−	0.856519i	$-0.327378\pi$
$409$	268.033	+	154.749i	0.0324044	+	0.0187087i	−0.483710	+	0.875228i	$0.660711\pi$
$410$		0			0
$411$	968.999	−	509.419i	0.116295	−	0.0611382i
$412$		0			0
$413$	−657.047	−	1489.38i	−0.0782837	−	0.177452i
$414$		0			0
$415$	5596.38			0.661965
$416$		0			0
$417$	3706.15	+	2340.07i	0.435230	+	0.274805i
$418$		0			0
$419$	−3008.72	+	5211.26i	−0.350801	+	0.607605i	−0.986390	−	0.164422i	$-0.947424\pi$
$419$	−3008.72	+	5211.26i	−0.350801	+	0.607605i	0.635589	+	0.772028i	$0.280757\pi$
$420$		0			0
$421$	1920.18	+	3325.85i	0.222289	+	0.385017i	0.955503	−	0.294982i	$-0.0953137\pi$
$421$	1920.18	+	3325.85i	0.222289	+	0.385017i	−0.733213	+	0.679999i	$0.761980\pi$
$422$		0			0
$423$	−2599.74	−	5459.45i	−0.298827	−	0.627536i
$424$		0			0
$425$	−5813.53	−	10069.3i	−0.663524	−	1.14926i
$426$		0			0
$427$	720.942	−	6641.72i	0.0817069	−	0.752729i
$428$		0			0
$429$	−4924.61	−	195.066i	−0.554224	−	0.0219531i
$430$		0			0
$431$			4510.80i			0.504125i	0.967711	+	0.252062i	$0.0811088\pi$
$431$			4510.80i			0.504125i	−0.967711	+	0.252062i	$0.918891\pi$
$432$		0			0
$433$		−	7012.84i		−	0.778328i	−0.921169	−	0.389164i	$-0.872764\pi$
$433$		−	7012.84i		−	0.778328i	0.921169	−	0.389164i	$-0.127236\pi$
$434$		0			0
$435$	−230.220	+	5812.09i	−0.0253752	+	0.640616i
$436$		0			0
$437$	−8011.88	+	13877.0i	−0.877025	+	1.51905i
$438$		0			0
$439$	−3220.45	+	1859.33i	−0.350122	+	0.202143i	−0.664739	−	0.747075i	$-0.731457\pi$
$439$	−3220.45	+	1859.33i	−0.350122	+	0.202143i	0.314617	+	0.949219i	$0.398124\pi$
$440$		0			0
$441$	−2094.80	−	9020.97i	−0.226196	−	0.974082i
$442$		0			0
$443$	5177.61	−	2989.29i	0.555295	−	0.320599i	−0.195960	−	0.980612i	$-0.562782\pi$
$443$	5177.61	−	2989.29i	0.555295	−	0.320599i	0.751255	+	0.660012i	$0.229449\pi$
$444$		0			0
$445$	3246.11	−	5622.43i	0.345799	−	0.598941i
$446$		0			0
$447$	−5770.01	−	3643.19i	−0.610542	−	0.385496i
$448$		0			0
$449$			1188.91i			0.124963i	0.998046	+	0.0624813i	$0.0199014\pi$
$449$			1188.91i			0.124963i	−0.998046	+	0.0624813i	$0.980099\pi$
$450$		0			0
$451$		−	4954.95i		−	0.517338i
$452$		0			0
$453$	8408.41	+	15994.2i	0.872100	+	1.65888i
$454$		0			0
$455$	−477.310	+	4397.24i	−0.0491794	+	0.453068i
$456$		0			0
$457$	2039.30	+	3532.17i	0.208741	+	0.361549i	0.951318	−	0.308211i	$-0.0997302\pi$
$457$	2039.30	+	3532.17i	0.208741	+	0.361549i	−0.742577	+	0.669760i	$0.766397\pi$
$458$		0			0
$459$	15718.4	+	1875.70i	1.59842	+	0.190741i
$460$		0			0
$461$	−3283.79	−	5687.69i	−0.331760	−	0.574625i	0.651097	−	0.758995i	$-0.274309\pi$
$461$	−3283.79	−	5687.69i	−0.331760	−	0.574625i	−0.982857	+	0.184369i	$0.940976\pi$
$462$		0			0
$463$	−4120.60	+	7137.09i	−0.413608	+	0.716390i	−0.995281	−	0.0970322i	$-0.969065\pi$
$463$	−4120.60	+	7137.09i	−0.413608	+	0.716390i	0.581673	+	0.813423i	$0.302398\pi$
$464$		0			0
$465$	4478.97	−	2354.67i	0.446682	−	0.234828i
$466$		0			0
$467$	11330.9			1.12276			0.561382	−	0.827557i	$-0.310270\pi$
$467$	11330.9			1.12276			0.561382	+	0.827557i	$0.310270\pi$
$468$		0			0
$469$	−5567.93	−	12621.2i	−0.548194	−	1.24263i
$470$		0			0
$471$	−2535.30	−	1600.79i	−0.248026	−	0.156604i
$472$		0			0
$473$	−5488.35	−	3168.70i	−0.533519	−	0.308027i
$474$		0			0
$475$	9946.74	−	5742.76i	0.960817	−	0.554728i
$476$		0			0
$477$	1170.26	−	14748.9i	0.112333	−	1.41574i
$478$		0			0
$479$	−4151.12	−	7189.94i	−0.395969	−	0.685839i	0.597255	−	0.802051i	$-0.296258\pi$
$479$	−4151.12	−	7189.94i	−0.395969	−	0.685839i	−0.993224	+	0.116212i	$0.962925\pi$
$480$		0			0
$481$	−10056.4	−	5806.08i	−0.953292	−	0.550384i
$482$		0			0
$483$	−12869.1	+	5078.76i	−1.21235	+	0.478451i
$484$		0			0
$485$		−	5789.46i		−	0.542033i
$486$		0			0
$487$	−76.4693			−0.00711530			−0.00355765	−	0.999994i	$-0.501132\pi$
$487$	−76.4693			−0.00711530			−0.00355765	+	0.999994i	$0.501132\pi$
$488$		0			0
$489$	−8285.17	−	328.180i	−0.766193	−	0.0303493i
$490$		0			0
$491$	6951.74	+	4013.59i	0.638957	+	0.368902i	0.784213	−	0.620492i	$-0.213067\pi$
$491$	6951.74	+	4013.59i	0.638957	+	0.368902i	−0.145256	+	0.989394i	$0.546401\pi$
$492$		0			0
$493$	−23345.9	+	13478.7i	−2.13275	+	1.23134i
$494$		0			0
$495$	186.195	−	2346.63i	0.0169067	−	0.213077i
$496$		0			0
$497$	2031.89	+	1486.85i	0.183386	+	0.134194i
$498$		0			0
$499$	8035.68	−	13918.2i	0.720895	−	1.24863i	−0.239747	−	0.970836i	$-0.577064\pi$
$499$	8035.68	−	13918.2i	0.720895	−	1.24863i	0.960641	−	0.277791i	$-0.0896023\pi$
$500$		0			0
$501$	−1025.98	+	1624.93i	−0.0914918	+	0.144903i
$502$		0			0
$503$	7450.97			0.660481			0.330241	−	0.943897i	$-0.392870\pi$
$503$	7450.97			0.660481			0.330241	+	0.943897i	$0.392870\pi$
$504$		0			0
$505$	−882.452			−0.0777596
$506$		0			0
$507$	−969.941	−	1844.99i	−0.0849637	−	0.161615i
$508$		0			0
$509$	6060.49	−	10497.1i	0.527753	−	0.914095i	−0.471724	−	0.881746i	$-0.656368\pi$
$509$	6060.49	−	10497.1i	0.527753	−	0.914095i	0.999477	−	0.0323486i	$-0.0102987\pi$
$510$		0			0
$511$	6984.12	+	5110.68i	0.604617	+	0.442433i
$512$		0			0
$513$	−1852.86	+	15527.1i	−0.159466	+	1.33633i
$514$		0			0
$515$	3219.57	−	1858.82i	0.275478	−	0.159047i
$516$		0			0
$517$	−3609.06	−	2083.69i	−0.307014	−	0.177255i
$518$		0			0
$519$	4708.10	+	8955.57i	0.398194	+	0.757430i
$520$		0			0
$521$	−10433.7			−0.877371			−0.438685	−	0.898641i	$-0.644556\pi$
$521$	−10433.7			−0.877371			−0.438685	+	0.898641i	$0.644556\pi$
$522$		0			0
$523$			22346.3i			1.86833i	0.356846	+	0.934163i	$0.383852\pi$
$523$			22346.3i			1.86833i	−0.356846	+	0.934163i	$0.616148\pi$
$524$		0			0
$525$	9808.66	+	1459.51i	0.815400	+	0.121330i
$526$		0			0
$527$	20309.8	+	11725.9i	1.67876	+	0.969234i
$528$		0			0
$529$	4250.53	+	7362.13i	0.349349	+	0.605090i
$530$		0			0
$531$	−1345.45	+	1954.96i	−0.109958	+	0.159771i
$532$		0			0
$533$	11754.5	−	6786.45i	0.955240	−	0.551508i
$534$		0			0
$535$	−5678.89	−	3278.71i	−0.458916	−	0.264955i
$536$		0			0
$537$	175.207	−	4423.24i	0.0140796	−	0.355451i
$538$		0			0
$539$	−4713.95	−	4302.94i	−0.376706	−	0.343860i
$540$		0			0
$541$	−13690.0			−1.08794			−0.543972	−	0.839103i	$-0.683080\pi$
$541$	−13690.0			−1.08794			−0.543972	+	0.839103i	$0.683080\pi$
$542$		0			0
$543$	131.471	−	3319.09i	0.0103903	−	0.262312i
$544$		0			0
$545$	−5007.46	+	8673.18i	−0.393571	+	0.681685i
$546$		0			0
$547$	−8042.35	−	13929.8i	−0.628640	−	1.08884i	−0.987825	−	0.155570i	$-0.950279\pi$
$547$	−8042.35	−	13929.8i	−0.628640	−	1.08884i	0.359185	−	0.933266i	$-0.383055\pi$
$548$		0			0
$549$	−8793.49	+	4187.38i	−0.683601	+	0.325524i
$550$		0			0
$551$	−13314.6	−	23061.6i	−1.02944	−	1.78305i
$552$		0			0
$553$	−7076.54	−	768.141i	−0.544169	−	0.0590682i
$554$		0			0
$555$	2961.12	−	4689.77i	0.226473	−	0.358684i
$556$		0			0
$557$		−	9207.28i		−	0.700404i	−0.936674	−	0.350202i	$-0.886113\pi$
$557$		−	9207.28i		−	0.700404i	0.936674	−	0.350202i	$-0.113887\pi$
$558$		0			0
$559$		−	17359.8i		−	1.31349i
$560$		0			0
$561$	9656.61	−	5076.65i	0.726743	−	0.382061i
$562$		0			0
$563$	10095.6	−	17486.0i	0.755732	−	1.30897i	−0.189278	−	0.981924i	$-0.560615\pi$
$563$	10095.6	−	17486.0i	0.755732	−	1.30897i	0.945010	−	0.327042i	$-0.106052\pi$
$564$		0			0
$565$	−7028.77	+	4058.06i	−0.523367	+	0.302166i
$566$		0			0
$567$	−9591.45	+	9502.02i	−0.710411	+	0.703787i
$568$		0			0
$569$	−3118.35	+	1800.38i	−0.229750	+	0.132646i	−0.610457	−	0.792050i	$-0.709014\pi$
$569$	−3118.35	+	1800.38i	−0.229750	+	0.132646i	0.380707	+	0.924696i	$0.375681\pi$
$570$		0			0
$571$	−1111.32	+	1924.86i	−0.0814489	+	0.141074i	−0.903873	−	0.427802i	$-0.859288\pi$
$571$	−1111.32	+	1924.86i	−0.0814489	+	0.141074i	0.822424	+	0.568876i	$0.192621\pi$
$572$		0			0
$573$	−16570.4	+	8711.36i	−1.20810	+	0.635117i
$574$		0			0
$575$		−	14814.5i		−	1.07444i
$576$		0			0
$577$		−	8818.52i		−	0.636256i	−0.948048	−	0.318128i	$-0.896946\pi$
$577$		−	8818.52i		−	0.636256i	0.948048	−	0.318128i	$-0.103054\pi$
$578$		0			0
$579$	9681.82	−	15333.9i	0.694927	−	1.10061i
$580$		0			0
$581$	−21992.0	−	2387.18i	−1.57037	−	0.170459i
$582$		0			0
$583$	−5098.33	−	8830.57i	−0.362181	−	0.627316i
$584$		0			0
$585$	5821.86	−	2772.31i	0.411460	−	0.195933i
$586$		0			0
$587$	9540.65	+	16524.9i	0.670843	+	1.16193i	0.977665	+	0.210167i	$0.0674008\pi$
$587$	9540.65	+	16524.9i	0.670843	+	1.16193i	−0.306823	+	0.951767i	$0.599266\pi$
$588$		0			0
$589$	−11583.1	+	20062.5i	−0.810311	+	1.40350i
$590$		0			0
$591$	−392.783	+	9916.13i	−0.0273383	+	0.690178i
$592$		0			0
$593$	−7386.65			−0.511523			−0.255762	−	0.966740i	$-0.582326\pi$
$593$	−7386.65			−0.511523			−0.255762	+	0.966740i	$0.582326\pi$
$594$		0			0
$595$	−3951.88	−	8958.02i	−0.272288	−	0.617215i
$596$		0			0
$597$	−146.638	+	3701.98i	−0.0100527	+	0.253789i
$598$		0			0
$599$	5442.40	+	3142.17i	0.371236	+	0.214333i	0.673998	−	0.738733i	$-0.264575\pi$
$599$	5442.40	+	3142.17i	0.371236	+	0.214333i	−0.302762	+	0.953066i	$0.597909\pi$
$600$		0			0
$601$	23587.5	−	13618.2i	1.60092	−	0.924291i	0.609615	−	0.792697i	$-0.291324\pi$
$601$	23587.5	−	13618.2i	1.60092	−	0.924291i	0.991304	−	0.131594i	$-0.0420094\pi$
$602$		0			0
$603$	−11401.6	+	16566.7i	−0.769998	+	1.11882i
$604$		0			0
$605$	2306.95	+	3995.76i	0.155026	+	0.268514i
$606$		0			0
$607$	−2294.69	−	1324.84i	−0.153441	−	0.0885891i	0.421314	−	0.906915i	$-0.361569\pi$
$607$	−2294.69	−	1324.84i	−0.153441	−	0.0885891i	−0.574755	+	0.818326i	$0.694902\pi$
$608$		0			0
$609$	3383.88	−	22741.5i	0.225159	−	1.51319i
$610$		0			0
$611$		−	11415.5i		−	0.755848i
$612$		0			0
$613$	19866.5			1.30897			0.654486	−	0.756074i	$-0.272885\pi$
$613$	19866.5			1.30897			0.654486	+	0.756074i	$0.272885\pi$
$614$		0			0
$615$	3016.69	+	5738.24i	0.197796	+	0.376241i
$616$		0			0
$617$	−21498.0	−	12411.9i	−1.40272	−	0.809858i	−0.408044	−	0.912962i	$-0.633789\pi$
$617$	−21498.0	−	12411.9i	−1.40272	−	0.809858i	−0.994671	+	0.103104i	$0.967123\pi$
$618$		0			0
$619$	6535.31	−	3773.16i	0.424356	−	0.245002i	−0.272583	−	0.962132i	$-0.587878\pi$
$619$	6535.31	−	3773.16i	0.424356	−	0.245002i	0.696939	+	0.717130i	$0.254545\pi$
$620$		0			0
$621$	16149.3	+	12083.4i	1.04356	+	0.780823i
$622$		0			0
$623$	−15154.5	+	20709.7i	−0.974562	+	1.33181i
$624$		0			0
$625$	−3937.30	+	6819.61i	−0.251987	+	0.436455i
$626$		0			0
$627$	5014.84	+	9539.05i	0.319415	+	0.607580i
$628$		0			0
$629$	25704.9			1.62944
$630$		0			0
$631$	−10950.1			−0.690837			−0.345418	−	0.938449i	$-0.612263\pi$
$631$	−10950.1			−0.690837			−0.345418	+	0.938449i	$0.612263\pi$
$632$		0			0
$633$	−4375.37	+	6929.62i	−0.274732	+	0.435115i
$634$		0			0
$635$	−1805.02	+	3126.39i	−0.112803	+	0.195381i
$636$		0			0
$637$	3751.36	−	17076.2i	0.233335	−	1.06214i
$638$		0			0
$639$	290.333	−	3659.10i	0.0179740	−	0.226528i
$640$		0			0
$641$	27715.4	−	16001.5i	1.70779	−	0.985994i	0.770504	−	0.637435i	$-0.220004\pi$
$641$	27715.4	−	16001.5i	1.70779	−	0.985994i	0.937287	−	0.348559i	$-0.113329\pi$
$642$		0			0
$643$	−4359.15	−	2516.76i	−0.267353	−	0.154356i	0.360331	−	0.932824i	$-0.382664\pi$
$643$	−4359.15	−	2516.76i	−0.267353	−	0.154356i	−0.627684	+	0.778468i	$0.715997\pi$
$644$		0			0
$645$	8285.13	+	328.178i	0.505778	+	0.0200341i
$646$		0			0
$647$	−5406.97			−0.328547			−0.164274	−	0.986415i	$-0.552528\pi$
$647$	−5406.97			−0.328547			−0.164274	+	0.986415i	$0.552528\pi$
$648$		0			0
$649$			1635.58i			0.0989245i
$650$		0			0
$651$	−18605.3	+	7342.57i	−1.12012	+	0.442056i
$652$		0			0
$653$	−22480.8	−	12979.3i	−1.34723	−	0.777826i	−0.359377	−	0.933193i	$-0.617011\pi$
$653$	−22480.8	−	12979.3i	−1.34723	−	0.777826i	−0.987857	+	0.155367i	$0.950344\pi$
$654$		0			0
$655$	2294.90	+	3974.89i	0.136900	+	0.237117i
$656$		0			0
$657$	997.950	−	12577.3i	0.0592599	−	0.746858i
$658$		0			0
$659$	22849.6	−	13192.2i	1.35067	−	0.779811i	0.362328	−	0.932051i	$-0.381982\pi$
$659$	22849.6	−	13192.2i	1.35067	−	0.779811i	0.988344	+	0.152240i	$0.0486486\pi$
$660$		0			0
$661$	4642.84	+	2680.54i	0.273200	+	0.157732i	0.630341	−	0.776318i	$-0.282915\pi$
$661$	4642.84	+	2680.54i	0.273200	+	0.157732i	−0.357141	+	0.934051i	$0.616248\pi$
$662$		0			0
$663$	25269.2	+	15955.0i	1.48020	+	0.934599i
$664$		0			0
$665$	8848.96	−	3903.77i	0.516012	−	0.227642i
$666$		0			0
$667$	−34347.5			−1.99391
$668$		0			0
$669$	−2191.08	+	1151.89i	−0.126625	+	0.0665688i
$670$		0			0
$671$	−3356.18	+	5813.08i	−0.193091	+	0.334443i
$672$		0			0
$673$	3378.73	+	5852.13i	0.193522	+	0.335190i	0.946415	−	0.322953i	$-0.104676\pi$
$673$	3378.73	+	5852.13i	0.193522	+	0.335190i	−0.752893	+	0.658143i	$0.771342\pi$
$674$		0			0
$675$	−5694.11	−	13288.5i	−0.324691	−	0.757742i
$676$		0			0
$677$	−2962.04	−	5130.41i	−0.168154	−	0.291252i	0.769617	−	0.638506i	$-0.220447\pi$
$677$	−2962.04	−	5130.41i	−0.168154	−	0.291252i	−0.937771	+	0.347254i	$0.887114\pi$
$678$		0			0
$679$	−2469.54	+	22750.8i	−0.139576	+	1.28585i
$680$		0			0
$681$	6706.63	+	12757.1i	0.377384	+	0.717847i
$682$		0			0
$683$		−	8838.52i		−	0.495163i	−0.968867	−	0.247582i	$-0.920364\pi$
$683$		−	8838.52i		−	0.495163i	0.968867	−	0.247582i	$-0.0796358\pi$
$684$		0			0
$685$			987.135i			0.0550606i
$686$		0			0
$687$	8617.21	+	5440.91i	0.478555	+	0.302160i
$688$		0			0
$689$	13965.7	−	24189.2i	0.772205	−	1.33750i
$690$		0			0
$691$	−25392.1	+	14660.1i	−1.39792	+	0.807087i	−0.994174	−	0.107787i	$-0.965624\pi$
$691$	−25392.1	+	14660.1i	−1.39792	+	0.807087i	−0.403741	+	0.914873i	$0.632290\pi$
$692$		0			0
$693$	−1732.66	+	9142.11i	−0.0949760	+	0.501125i
$694$		0			0
$695$	−3422.75	+	1976.12i	−0.186809	+	0.107854i
$696$		0			0
$697$	−15022.6	+	26019.9i	−0.816387	+	1.41402i
$698$		0			0
$699$	973.794	−	24584.2i	0.0526928	−	1.33027i
$700$		0			0
$701$			15890.7i			0.856184i	0.903735	+	0.428092i	$0.140814\pi$
$701$			15890.7i			0.856184i	−0.903735	+	0.428092i	$0.859186\pi$
$702$		0			0
$703$			25391.9i			1.36227i
$704$		0			0
$705$	5448.18	+	215.805i	0.291050	+	0.0115287i
$706$		0			0
$707$	3467.76	+	376.417i	0.184468	+	0.0200235i
$708$		0			0
$709$	1060.77	+	1837.31i	0.0561890	+	0.0973222i	0.892752	−	0.450549i	$-0.148772\pi$
$709$	1060.77	+	1837.31i	0.0561890	+	0.0973222i	−0.836563	+	0.547871i	$0.815438\pi$
$710$		0			0
$711$	4461.52	+	9369.19i	0.235331	+	0.494194i
$712$		0			0
$713$	14940.3	+	25877.4i	0.784740	+	1.35921i
$714$		0			0
$715$	2222.01	−	3848.63i	0.116222	−	0.201302i
$716$		0			0
$717$	5354.79	+	3381.02i	0.278910	+	0.176104i
$718$		0			0
$719$	−23897.3			−1.23953			−0.619764	−	0.784789i	$-0.712772\pi$
$719$	−23897.3			−1.23953			−0.619764	+	0.784789i	$0.712772\pi$
$720$		0			0
$721$	−13444.8	+	5931.25i	−0.694467	+	0.306368i
$722$		0			0
$723$	9478.57	−	4983.04i	0.487568	−	0.256323i
$724$		0			0
$725$	21321.2	+	12309.8i	1.09221	+	0.630586i
$726$		0			0
$727$	−10755.1	+	6209.44i	−0.548670	+	0.316775i	−0.748586	−	0.663038i	$-0.769267\pi$
$727$	−10755.1	+	6209.44i	−0.548670	+	0.316775i	0.199915	+	0.979813i	$0.435933\pi$
$728$		0			0
$729$	19130.3	+	4631.64i	0.971920	+	0.235311i
$730$		0			0
$731$	19213.9	+	33279.5i	0.972166	+	1.68384i
$732$		0			0
$733$	199.317	+	115.076i	0.0100436	+	0.00579865i	0.505013	−	0.863112i	$-0.331488\pi$
$733$	199.317	+	115.076i	0.0100436	+	0.00579865i	−0.494970	+	0.868910i	$0.664821\pi$
$734$		0			0
$735$	8078.87	+	2113.19i	0.405434	+	0.106049i
$736$		0			0
$737$			13860.2i			0.692734i
$738$		0			0
$739$	6421.89			0.319666			0.159833	−	0.987144i	$-0.448904\pi$
$739$	6421.89			0.319666			0.159833	+	0.987144i	$0.448904\pi$
$740$		0			0
$741$	−15760.7	+	24961.5i	−0.781355	+	1.23750i
$742$		0			0
$743$	−693.090	−	400.156i	−0.0342221	−	0.0197581i	0.482791	−	0.875735i	$-0.339623\pi$
$743$	−693.090	−	400.156i	−0.0342221	−	0.0197581i	−0.517013	+	0.855977i	$0.672956\pi$
$744$		0			0
$745$	5328.78	−	3076.58i	0.262056	−	0.151298i
$746$		0			0
$747$	13865.2	+	29117.0i	0.679119	+	1.42615i
$748$		0			0
$749$	20917.7	+	15306.7i	1.02045	+	0.746721i
$750$		0			0
$751$	−971.585	+	1682.83i	−0.0472086	+	0.0817676i	−0.888664	−	0.458559i	$-0.848366\pi$
$751$	−971.585	+	1682.83i	−0.0472086	+	0.0817676i	0.841456	+	0.540326i	$0.181699\pi$
$752$		0			0
$753$	15401.2	+	610.050i	0.745353	+	0.0295238i
$754$		0			0
$755$	−16293.5			−0.785406
$756$		0			0
$757$	16016.6			0.768999			0.384500	−	0.923125i	$-0.374374\pi$
$757$	16016.6			0.768999			0.384500	+	0.923125i	$0.374374\pi$
$758$		0			0
$759$	13889.6	+	550.175i	0.664243	+	0.0263110i
$760$		0			0
$761$	20615.4	−	35706.8i	0.982005	−	1.70088i	0.327450	−	0.944869i	$-0.393811\pi$
$761$	20615.4	−	35706.8i	0.982005	−	1.70088i	0.654555	−	0.756014i	$-0.272856\pi$
$762$		0			0
$763$	23377.4	−	31946.9i	1.10920	−	1.51580i
$764$		0			0
$765$	−8092.37	+	11758.3i	−0.382458	+	0.555717i
$766$		0			0
$767$	−3880.03	+	2240.13i	−0.182659	+	0.105458i
$768$		0			0
$769$	−4147.70	−	2394.68i	−0.194499	−	0.112294i	0.399588	−	0.916695i	$-0.369153\pi$
$769$	−4147.70	−	2394.68i	−0.194499	−	0.112294i	−0.594087	+	0.804401i	$0.702487\pi$
$770$		0			0
$771$	−6286.75	+	9956.83i	−0.293660	+	0.465093i
$772$		0			0
$773$	12950.9			0.602601			0.301301	−	0.953529i	$-0.402579\pi$
$773$	12950.9			0.602601			0.301301	+	0.953529i	$0.402579\pi$
$774$		0			0
$775$		−	21417.9i		−	0.992713i
$776$		0			0
$777$	−13636.7	+	17166.2i	−0.629621	+	0.792581i
$778$		0			0
$779$	−25703.1	−	14839.7i	−1.18217	−	0.682526i
$780$		0			0
$781$	−1264.86	−	2190.80i	−0.0579515	−	0.100375i
$782$		0			0
$783$	−30809.6	+	13201.8i	−1.40619	+	0.602548i
$784$		0			0
$785$	2341.42	−	1351.82i	0.106457	−	0.0614632i
$786$		0			0
$787$	2678.82	+	1546.62i	0.121334	+	0.0700521i	0.559439	−	0.828872i	$-0.311017\pi$
$787$	2678.82	+	1546.62i	0.121334	+	0.0700521i	−0.438105	+	0.898924i	$0.644350\pi$
$788$		0			0
$789$	8391.96	−	4411.80i	0.378659	−	0.199067i
$790$		0			0
$791$	29351.9	−	12948.7i	1.31938	−	0.582053i
$792$		0			0
$793$	−18386.9			−0.823377
$794$		0			0
$795$	11280.5	+	7122.54i	0.503245	+	0.317749i
$796$		0			0
$797$	−5377.34	+	9313.83i	−0.238990	+	0.413943i	−0.960425	−	0.278539i	$-0.910150\pi$
$797$	−5377.34	+	9313.83i	−0.238990	+	0.413943i	0.721434	+	0.692483i	$0.243483\pi$
$798$		0			0
$799$	12634.8	+	21884.1i	0.559434	+	0.968968i
$800$		0			0
$801$	37294.8	+	2959.18i	1.64513	+	0.130534i
$802$		0			0
$803$	−4347.64	−	7530.34i	−0.191065	−	0.330934i
$804$		0			0
$805$	1346.23	−	12402.2i	0.0589420	−	0.543006i
$806$		0			0
$807$	−29163.4	−	1155.18i	−1.27212	−	0.0503893i
$808$		0			0
$809$		−	29409.3i		−	1.27809i	−0.769169	−	0.639045i	$-0.779330\pi$
$809$		−	29409.3i		−	1.27809i	0.769169	−	0.639045i	$-0.220670\pi$
$810$		0			0
$811$		−	8850.91i		−	0.383228i	−0.981470	−	0.191614i	$-0.938628\pi$
$811$		−	8850.91i		−	0.383228i	0.981470	−	0.191614i	$-0.0613721\pi$
$812$		0			0
$813$	1152.36	−	29092.4i	0.0497112	−	1.25500i
$814$		0			0
$815$	3738.31	−	6474.95i	0.160672	−	0.278291i
$816$		0			0
$817$	−32874.4	+	18980.0i	−1.40775	+	0.812763i
$818$		0			0
$819$	−24060.6	+	8410.96i	−1.02655	+	0.358856i
$820$		0			0
$821$	−23750.3	+	13712.2i	−1.00961	+	0.582899i	−0.911078	−	0.412235i	$-0.864748\pi$
$821$	−23750.3	+	13712.2i	−1.00961	+	0.582899i	−0.0985331	+	0.995134i	$0.531415\pi$
$822$		0			0
$823$	12157.4	−	21057.2i	0.514921	−	0.891869i	−0.484929	−	0.874554i	$-0.661155\pi$
$823$	12157.4	−	21057.2i	0.514921	−	0.891869i	0.999850	−	0.0173159i	$-0.00551209\pi$
$824$		0			0
$825$	−8424.79	−	5319.42i	−0.355532	−	0.224483i
$826$		0			0
$827$			14415.0i			0.606119i	0.952972	+	0.303059i	$0.0980081\pi$
$827$			14415.0i			0.606119i	−0.952972	+	0.303059i	$0.901992\pi$
$828$		0			0
$829$		−	8609.61i		−	0.360704i	−0.983602	−	0.180352i	$-0.942276\pi$
$829$		−	8609.61i		−	0.360704i	0.983602	−	0.180352i	$-0.0577238\pi$
$830$		0			0
$831$	−11264.4	−	21426.8i	−0.470227	−	0.894449i
$832$		0			0
$833$	11708.5	+	36887.9i	0.487007	+	1.53432i
$834$		0			0
$835$	−866.413	−	1500.67i	−0.0359083	−	0.0621950i
$836$		0			0
$837$	23347.7	+	17469.5i	0.964176	+	0.721427i
$838$		0			0
$839$	3728.54	+	6458.02i	0.153425	+	0.265740i	0.932484	−	0.361210i	$-0.117636\pi$
$839$	3728.54	+	6458.02i	0.153425	+	0.265740i	−0.779059	+	0.626950i	$0.784303\pi$
$840$		0			0
$841$	16345.9	−	28311.9i	0.670216	−	1.16085i
$842$		0			0
$843$	−10302.2	+	5416.03i	−0.420908	+	0.221279i
$844$		0			0
$845$	1879.52			0.0765177
$846$		0			0
$847$	−7361.18	−	16686.1i	−0.298623	−	0.676910i
$848$		0			0
$849$	−14000.0	−	8839.58i	−0.565933	−	0.357330i
$850$		0			0
$851$	28363.6	+	16375.8i	1.14253	+	0.659640i
$852$		0			0
$853$	29109.8	−	16806.6i	1.16847	−	0.674615i	0.215148	−	0.976581i	$-0.430976\pi$
$853$	29109.8	−	16806.6i	1.16847	−	0.674615i	0.953318	+	0.301967i	$0.0976431\pi$
$854$		0			0
$855$	−11615.2	−	7993.85i	−0.464598	−	0.319747i
$856$		0			0
$857$	−20047.3	−	34723.0i	−0.799071	−	1.38403i	−0.920222	−	0.391397i	$-0.871992\pi$
$857$	−20047.3	−	34723.0i	−0.799071	−	1.38403i	0.121151	−	0.992634i	$-0.461341\pi$
$858$		0			0
$859$	15246.8	+	8802.77i	0.605606	+	0.349647i	0.771244	−	0.636540i	$-0.219635\pi$
$859$	15246.8	+	8802.77i	0.605606	+	0.349647i	−0.165638	+	0.986187i	$0.552968\pi$
$860$		0			0
$861$	−9406.96	−	23836.3i	−0.372344	−	0.943482i
$862$		0			0
$863$		−	36465.5i		−	1.43835i	−0.694827	−	0.719177i	$-0.744519\pi$
$863$		−	36465.5i		−	1.43835i	0.694827	−	0.719177i	$-0.255481\pi$
$864$		0			0
$865$	−9123.19			−0.358610
$866$		0			0
$867$	−40592.6	−	1607.89i	−1.59008	−	0.0629838i
$868$		0			0
$869$	6193.65	+	3575.91i	0.241778	+	0.139591i
$870$		0			0
$871$	−32880.0	+	18983.3i	−1.27910	+	0.738489i
$872$		0			0
$873$	30121.6	−	14343.6i	1.16777	−	0.556079i
$874$		0			0
$875$	−11685.9	+	15969.7i	−0.451494	+	0.616999i
$876$		0			0
$877$	−16637.8	+	28817.5i	−0.640614	+	1.10958i	0.344682	+	0.938719i	$0.387987\pi$
$877$	−16637.8	+	28817.5i	−0.640614	+	1.10958i	−0.985296	+	0.170856i	$0.945347\pi$
$878$		0			0
$879$	25320.1	−	40101.4i	0.971586	−	1.53878i
$880$		0			0
$881$	−11874.3			−0.454091			−0.227045	−	0.973884i	$-0.572907\pi$
$881$	−11874.3			−0.454091			−0.227045	+	0.973884i	$0.572907\pi$
$882$		0			0
$883$	−17571.9			−0.669697			−0.334848	−	0.942272i	$-0.608685\pi$
$883$	−17571.9			−0.669697			−0.334848	+	0.942272i	$0.608685\pi$
$884$		0			0
$885$	−995.777	−	1894.13i	−0.0378222	−	0.0719441i
$886$		0			0
$887$	14706.9	−	25473.1i	0.556719	−	0.964266i	−0.441048	−	0.897483i	$-0.645393\pi$
$887$	14706.9	−	25473.1i	0.556719	−	0.964266i	0.997768	−	0.0667825i	$-0.0212734\pi$
$888$		0			0
$889$	8426.75	−	11515.8i	0.317912	−	0.434451i
$890$		0			0
$891$	12670.4	−	4845.12i	0.476403	−	0.182175i
$892$		0			0
$893$	−21617.7	+	12481.0i	−0.810089	+	0.467705i
$894$		0			0
$895$	3456.81	+	1995.79i	0.129104	+	0.0745385i
$896$		0			0
$897$	17718.4	+	33703.4i	0.659534	+	1.25454i
$898$		0			0
$899$	−49657.5			−1.84224
$900$		0			0
$901$			61829.3i			2.28616i
$902$		0			0
$903$	−32418.0	−	4823.72i	−1.19469	−	0.177767i
$904$		0			0
$905$	2593.90	+	1497.59i	0.0952753	+	0.0550072i
$906$		0			0
$907$	6950.77	+	12039.1i	0.254462	+	0.440740i	0.964749	−	0.263171i	$-0.0847684\pi$
$907$	6950.77	+	12039.1i	0.254462	+	0.440740i	−0.710288	+	0.703912i	$0.751435\pi$
$908$		0			0
$909$	−2186.30	−	4591.24i	−0.0797746	−	0.167527i
$910$		0			0
$911$	−40292.9	+	23263.1i	−1.46538	+	0.846038i	−0.999252	−	0.0386789i	$-0.987685\pi$
$911$	−40292.9	+	23263.1i	−1.46538	+	0.846038i	−0.466129	+	0.884717i	$0.654352\pi$
$912$		0			0
$913$	19248.2	+	11113.0i	0.697725	+	0.402832i
$914$		0			0
$915$	347.596	−	8775.34i	0.0125587	−	0.317053i
$916$		0			0
$917$	−7322.74	−	16599.0i	−0.263706	−	0.597761i
$918$		0			0
$919$	48733.4			1.74926			0.874628	−	0.484794i	$-0.161106\pi$
$919$	48733.4			1.74926			0.874628	+	0.484794i	$0.161106\pi$
$920$		0			0
$921$	−975.776	+	24634.2i	−0.0349109	+	0.881353i
$922$		0			0
$923$	3464.77	−	6001.16i	0.123558	−	0.214009i
$924$		0			0
$925$	−11737.8	−	20330.5i	−0.417229	−	0.722662i
$926$		0			0
$927$	17647.7	+	12145.6i	0.625272	+	0.430327i
$928$		0			0
$929$	−24705.0	−	42790.3i	−0.872491	−	1.51120i	−0.859412	−	0.511284i	$-0.829170\pi$
$929$	−24705.0	−	42790.3i	−0.872491	−	1.51120i	−0.0130789	−	0.999914i	$-0.504163\pi$
$930$		0			0
$931$	−36438.8	+	11566.0i	−1.28274	+	0.407154i
$932$		0			0
$933$	6045.56	−	9574.85i	0.212136	−	0.335977i
$934$		0			0
$935$			9837.35i			0.344081i
$936$		0			0
$937$		−	37596.2i		−	1.31080i	−0.755284	−	0.655398i	$-0.772501\pi$
$937$		−	37596.2i		−	1.31080i	0.755284	−	0.655398i	$-0.227499\pi$
$938$		0			0
$939$	9309.07	−	4893.94i	0.323525	−	0.170083i
$940$		0			0
$941$	−4437.16	+	7685.39i	−0.153717	+	0.266245i	−0.932591	−	0.360935i	$-0.882458\pi$
$941$	−4437.16	+	7685.39i	−0.153717	+	0.266245i	0.778874	+	0.627180i	$0.215791\pi$
$942$		0			0
$943$	−33152.9	+	19140.8i	−1.14486	+	0.660987i
$944$		0			0
$945$	−3559.36	−	11642.2i	−0.122525	−	0.400762i
$946$		0			0
$947$	40026.5	−	23109.3i	1.37348	−	0.792979i	0.382115	−	0.924115i	$-0.375196\pi$
$947$	40026.5	−	23109.3i	1.37348	−	0.792979i	0.991364	+	0.131136i	$0.0418623\pi$
$948$		0			0
$949$	11909.3	−	20627.5i	0.407369	−	0.705583i
$950$		0			0
$951$	−1008.78	+	530.332i	−0.0343974	+	0.0180833i
$952$		0			0
$953$		−	23772.8i		−	0.808054i	−0.914747	−	0.404027i	$-0.867610\pi$
$953$		−	23772.8i		−	0.808054i	0.914747	−	0.404027i	$-0.132390\pi$
$954$		0			0
$955$		−	16880.6i		−	0.571981i
$956$		0			0
$957$	−12333.1	+	19533.0i	−0.416587	+	0.659782i
$958$		0			0
$959$	421.070	−	3879.13i	0.0141784	−	0.130619i
$960$		0			0
$961$	6704.33	+	11612.2i	0.225046	+	0.389790i
$962$		0			0
$963$	2988.90	−	37669.4i	0.100017	−	1.26052i
$964$		0			0
$965$	8176.04	+	14161.3i	0.272742	+	0.472403i
$966$		0			0
$967$	15698.7	−	27190.9i	0.522064	−	0.904242i	−0.477606	−	0.878574i	$-0.658495\pi$
$967$	15698.7	−	27190.9i	0.522064	−	0.904242i	0.999671	−	0.0256679i	$-0.00817125\pi$
$968$		0			0
$969$	2586.43	−	65296.5i	0.0857463	−	2.16473i
$970$		0			0
$971$	−42214.9			−1.39520			−0.697600	−	0.716487i	$-0.745749\pi$
$971$	−42214.9			−1.39520			−0.697600	+	0.716487i	$0.745749\pi$
$972$		0			0
$973$	14293.2	−	6305.55i	0.470936	−	0.207756i
$974$		0			0
$975$	1080.24	−	27271.5i	0.0354824	−	0.895782i
$976$		0			0
$977$	39073.6	+	22559.2i	1.27950	+	0.738722i	0.976757	−	0.214349i	$-0.0687631\pi$
$977$	39073.6	+	22559.2i	1.27950	+	0.738722i	0.302747	+	0.953071i	$0.402096\pi$
$978$		0			0
$979$	22329.4	−	12891.9i	0.728959	−	0.420865i
$980$		0			0
$981$	−57531.2	−	4564.84i	−1.87240	−	0.148567i
$982$		0			0
$983$	17928.1	+	31052.5i	0.581708	+	1.00755i	0.995277	+	0.0970751i	$0.0309487\pi$
$983$	17928.1	+	31052.5i	0.581708	+	1.00755i	−0.413569	+	0.910473i	$0.635718\pi$
$984$		0			0
$985$	−7749.56	−	4474.21i	−0.250682	−	0.144731i
$986$		0			0
$987$	−21317.6	−	3172.01i	−0.687484	−	0.102296i
$988$		0			0
$989$			48962.3i			1.57423i
$990$		0			0
$991$	41167.8			1.31961			0.659807	−	0.751435i	$-0.270638\pi$
$991$	41167.8			1.31961			0.659807	+	0.751435i	$0.270638\pi$
$992$		0			0
$993$	−9112.52	−	17333.5i	−0.291216	−	0.553940i
$994$		0			0
$995$	−2893.14	−	1670.35i	−0.0921795	−	0.0532199i
$996$		0			0
$997$	30797.6	−	17781.0i	0.978304	−	0.564824i	0.0765462	−	0.997066i	$-0.475611\pi$
$997$	30797.6	−	17781.0i	0.978304	−	0.564824i	0.901758	+	0.432242i	$0.142277\pi$
$998$		0			0
$999$	31736.3	+	3787.13i	1.00510	+	0.119940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.1	✓	48
3.2	odd	2		756.4.x.a.125.10		48
7.6	odd	2	inner	252.4.x.a.41.24	yes	48
9.2	odd	6	inner	252.4.x.a.209.24	yes	48
9.4	even	3		2268.4.f.a.1133.19		48
9.5	odd	6		2268.4.f.a.1133.30		48
9.7	even	3		756.4.x.a.629.15		48
21.20	even	2		756.4.x.a.125.15		48
63.13	odd	6		2268.4.f.a.1133.29		48
63.20	even	6	inner	252.4.x.a.209.1	yes	48
63.34	odd	6		756.4.x.a.629.10		48
63.41	even	6		2268.4.f.a.1133.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.1	✓	48	1.1	even	1	trivial
252.4.x.a.41.24	yes	48	7.6	odd	2	inner
252.4.x.a.209.1	yes	48	63.20	even	6	inner
252.4.x.a.209.24	yes	48	9.2	odd	6	inner
756.4.x.a.125.10		48	3.2	odd	2
756.4.x.a.125.15		48	21.20	even	2
756.4.x.a.629.10		48	63.34	odd	6
756.4.x.a.629.15		48	9.7	even	3
2268.4.f.a.1133.19		48	9.4	even	3
2268.4.f.a.1133.20		48	63.41	even	6
2268.4.f.a.1133.29		48	63.13	odd	6
2268.4.f.a.1133.30		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +O(q^{10})\)	\(q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +(16.1150 - 9.30397i) q^{11} +(44.1430 + 25.4860i) q^{13} +(-12.9980 + 20.5859i) q^{15} -112.833 q^{17} -111.459i q^{19} +(59.8590 - 75.3518i) q^{21} +(-124.503 - 71.8819i) q^{23} +(51.5236 + 89.2414i) q^{25} +(-139.308 - 16.6238i) q^{27} +(206.907 - 119.458i) q^{29} +(-179.999 - 103.923i) q^{31} +(-85.5836 + 44.9928i) q^{33} +(35.0243 + 79.3922i) q^{35} -227.815 q^{37} +(-223.953 - 141.404i) q^{39} +(133.141 - 230.607i) q^{41} +(-170.287 - 294.946i) q^{43} +(71.7202 - 104.211i) q^{45} +(-111.979 - 193.952i) q^{47} +(-103.769 - 326.927i) q^{49} +(585.836 + 23.2053i) q^{51} -547.974i q^{53} -87.1854i q^{55} +(-22.9227 + 578.703i) q^{57} +(-43.9483 + 76.1207i) q^{59} +(-312.398 + 180.363i) q^{61} +(-326.290 + 378.922i) q^{63} +(206.827 - 119.412i) q^{65} +(-372.426 + 645.060i) q^{67} +(631.647 + 398.822i) q^{69} -135.948i q^{71} -467.289i q^{73} +(-249.161 - 473.945i) q^{75} +(-37.1896 + 342.612i) q^{77} +(192.171 + 332.850i) q^{79} +(719.878 + 114.962i) q^{81} +(597.216 + 1034.41i) q^{83} +(-264.332 + 457.836i) q^{85} +(-1098.85 + 577.683i) q^{87} +1385.63 q^{89} +(-863.702 + 381.027i) q^{91} +(913.198 + 576.594i) q^{93} +(-452.262 - 261.114i) q^{95} +(1070.10 - 617.821i) q^{97} +(453.610 - 216.005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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