LMFDB - Embedded newform 252.4.x.a.41.16

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			41.16
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +O(q^{10})$	\(q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +(0.00221312 - 0.00127775i) q^{11} +(6.06841 + 3.50360i) q^{13} +(-34.8386 - 52.1602i) q^{15} -28.3143 q^{17} +49.1973i q^{19} +(-80.9069 - 52.1064i) q^{21} +(44.4689 + 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(-137.615 + 27.2951i) q^{27} +(97.9469 - 56.5497i) q^{29} +(-28.4271 - 16.4124i) q^{31} +(-0.000866054 - 0.0132505i) q^{33} +(-179.663 - 133.052i) q^{35} -101.961 q^{37} +(30.2779 - 20.2230i) q^{39} +(-11.2449 + 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(-323.155 + 42.4243i) q^{45} +(231.260 + 400.554i) q^{47} +(-334.149 - 77.4179i) q^{49} +(-65.0960 + 131.941i) q^{51} -567.586i q^{53} -0.0308484i q^{55} +(229.253 + 113.107i) q^{57} +(-145.654 + 252.280i) q^{59} +(592.003 - 341.793i) q^{61} +(-428.818 + 257.220i) q^{63} +(73.2542 - 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} +(221.874 - 148.193i) q^{69} +307.517i q^{71} -495.192i q^{73} +(-107.429 + 7.02162i) q^{75} +(-0.0188553 - 0.0434103i) q^{77} +(-324.865 - 562.683i) q^{79} +(-189.193 + 704.022i) q^{81} +(565.581 + 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} +(-38.3293 - 586.430i) q^{87} +130.217 q^{89} +(77.2337 - 104.291i) q^{91} +(-141.835 + 94.7337i) q^{93} +(514.315 + 296.940i) q^{95} +(1260.41 - 727.696i) q^{97} +(-0.0637365 - 0.0264277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.29905	−	4.65987i	0.442452	−	0.896792i
$3$	2.29905	−	4.65987i	0.442452	−	0.896792i
$4$		0			0
$5$	6.03570	−	10.4541i	0.539850	−	0.935047i	−0.459062	−	0.888404i	$-0.651814\pi$
$5$	6.03570	−	10.4541i	0.539850	−	0.935047i	0.998912	−	0.0466430i	$-0.0148523\pi$
$6$		0			0
$7$	2.10370	−	18.4004i	0.113589	−	0.993528i
$7$	2.10370	−	18.4004i	0.113589	−	0.993528i
$8$		0			0
$9$	−16.4287	−	21.4265i	−0.608472	−	0.793575i
$10$		0			0
$11$	0.00221312	−	0.00127775i	6.06619e−5	−	3.50232e-5i	−0.499970	−	0.866043i	$-0.666656\pi$
$11$	0.00221312	−	0.00127775i	6.06619e−5	−	3.50232e-5i	0.500030	+	0.866008i	$0.333322\pi$
$12$		0			0
$13$	6.06841	+	3.50360i	0.129467	+	0.0747479i	0.563335	−	0.826229i	$-0.309518\pi$
$13$	6.06841	+	3.50360i	0.129467	+	0.0747479i	−0.433868	+	0.900977i	$0.642851\pi$
$14$		0			0
$15$	−34.8386	−	52.1602i	−0.599685	−	0.897847i
$16$		0			0
$17$	−28.3143			−0.403955			−0.201977	−	0.979390i	$-0.564737\pi$
$17$	−28.3143			−0.403955			−0.201977	+	0.979390i	$0.564737\pi$
$18$		0			0
$19$			49.1973i			0.594033i	0.954872	+	0.297016i	$0.0959916\pi$
$19$			49.1973i			0.594033i	−0.954872	+	0.297016i	$0.904008\pi$
$20$		0			0
$21$	−80.9069	−	52.1064i	−0.840730	−	0.541455i
$22$		0			0
$23$	44.4689	+	25.6741i	0.403148	+	0.232758i	0.687841	−	0.725861i	$-0.258558\pi$
$23$	44.4689	+	25.6741i	0.403148	+	0.232758i	−0.284693	+	0.958619i	$0.591892\pi$
$24$		0			0
$25$	−10.3594	−	17.9431i	−0.0828756	−	0.143545i
$26$		0			0
$27$	−137.615	+	27.2951i	−0.980892	+	0.194554i
$28$		0			0
$29$	97.9469	−	56.5497i	0.627182	−	0.362104i	−0.152478	−	0.988307i	$-0.548725\pi$
$29$	97.9469	−	56.5497i	0.627182	−	0.362104i	0.779660	+	0.626203i	$0.215392\pi$
$30$		0			0
$31$	−28.4271	−	16.4124i	−0.164699	−	0.0950889i	0.415385	−	0.909646i	$-0.363647\pi$
$31$	−28.4271	−	16.4124i	−0.164699	−	0.0950889i	−0.580084	+	0.814557i	$0.696980\pi$
$32$		0			0
$33$	−0.000866054	−	0.0132505i	−4.56850e−6	−	6.98972e-5i
$34$		0			0
$35$	−179.663	−	133.052i	−0.867674	−	0.642567i
$36$		0			0
$37$	−101.961			−0.453034			−0.226517	−	0.974007i	$-0.572734\pi$
$37$	−101.961			−0.453034			−0.226517	+	0.974007i	$0.572734\pi$
$38$		0			0
$39$	30.2779	−	20.2230i	0.124316	−	0.0830328i
$40$		0			0
$41$	−11.2449	+	19.4767i	−0.0428331	+	0.0741891i	−0.886647	−	0.462447i	$-0.846972\pi$
$41$	−11.2449	+	19.4767i	−0.0428331	+	0.0741891i	0.843814	+	0.536636i	$0.180305\pi$
$42$		0			0
$43$	−227.203	−	393.527i	−0.805771	−	1.39564i	−0.915769	−	0.401705i	$-0.868418\pi$
$43$	−227.203	−	393.527i	−0.805771	−	1.39564i	0.109998	−	0.993932i	$-0.464916\pi$
$44$		0			0
$45$	−323.155	+	42.4243i	−1.07051	+	0.140539i
$46$		0			0
$47$	231.260	+	400.554i	0.717717	+	1.24312i	0.961902	+	0.273394i	$0.0881464\pi$
$47$	231.260	+	400.554i	0.717717	+	1.24312i	−0.244185	+	0.969729i	$0.578520\pi$
$48$		0			0
$49$	−334.149	−	77.4179i	−0.974195	−	0.225708i
$50$		0			0
$51$	−65.0960	+	131.941i	−0.178731	+	0.362263i
$52$		0			0
$53$		−	567.586i		−	1.47102i	−0.677515	−	0.735509i	$-0.736943\pi$
$53$		−	567.586i		−	1.47102i	0.677515	−	0.735509i	$-0.263057\pi$
$54$		0			0
$55$		−	0.0308484i		−	7.56290e-5i
$56$		0			0
$57$	229.253	+	113.107i	0.532724	+	0.262831i
$58$		0			0
$59$	−145.654	+	252.280i	−0.321399	+	0.556680i	−0.980777	−	0.195132i	$-0.937486\pi$
$59$	−145.654	+	252.280i	−0.321399	+	0.556680i	0.659378	+	0.751812i	$0.270820\pi$
$60$		0			0
$61$	592.003	−	341.793i	1.24259	−	0.717412i	0.272972	−	0.962022i	$-0.411993\pi$
$61$	592.003	−	341.793i	1.24259	−	0.717412i	0.969621	+	0.244610i	$0.0786601\pi$
$62$		0			0
$63$	−428.818	+	257.220i	−0.857555	+	0.514392i
$64$		0			0
$65$	73.2542	−	42.2933i	0.139786	−	0.0807053i
$66$		0			0
$67$	269.780	−	467.273i	0.491924	−	0.852037i	−0.508033	−	0.861338i	$-0.669627\pi$
$67$	269.780	−	467.273i	0.491924	−	0.852037i	0.999957	+	0.00930051i	$0.00296049\pi$
$68$		0			0
$69$	221.874	−	148.193i	0.387109	−	0.258556i
$70$		0			0
$71$			307.517i			0.514022i	0.966408	+	0.257011i	$0.0827377\pi$
$71$			307.517i			0.514022i	−0.966408	+	0.257011i	$0.917262\pi$
$72$		0			0
$73$		−	495.192i		−	0.793943i	−0.917831	−	0.396971i	$-0.870061\pi$
$73$		−	495.192i		−	0.793943i	0.917831	−	0.396971i	$-0.129939\pi$
$74$		0			0
$75$	−107.429	+	7.02162i	−0.165398	+	0.0108105i
$76$		0			0
$77$	−0.0188553	−	0.0434103i	−2.79060e−5	−	6.42476e-5i
$78$		0			0
$79$	−324.865	−	562.683i	−0.462661	−	0.801352i	0.536432	−	0.843944i	$-0.319772\pi$
$79$	−324.865	−	562.683i	−0.462661	−	0.801352i	−0.999093	+	0.0425920i	$0.986438\pi$
$80$		0			0
$81$	−189.193	+	704.022i	−0.259524	+	0.965737i
$82$		0			0
$83$	565.581	+	979.615i	0.747959	+	1.29550i	0.948800	+	0.315879i	$0.102299\pi$
$83$	565.581	+	979.615i	0.747959	+	1.29550i	−0.200841	+	0.979624i	$0.564367\pi$
$84$		0			0
$85$	−170.897	+	296.002i	−0.218075	+	0.377717i
$86$		0			0
$87$	−38.3293	−	586.430i	−0.0472336	−	0.722665i
$88$		0			0
$89$	130.217			0.155089			0.0775447	−	0.996989i	$-0.475292\pi$
$89$	130.217			0.155089			0.0775447	+	0.996989i	$0.475292\pi$
$90$		0			0
$91$	77.2337	−	104.291i	0.0889702	−	0.120139i
$92$		0			0
$93$	−141.835	+	94.7337i	−0.158146	+	0.105628i
$94$		0			0
$95$	514.315	+	296.940i	0.555449	+	0.320688i
$96$		0			0
$97$	1260.41	−	727.696i	1.31933	−	0.761715i	0.335709	−	0.941966i	$-0.391024\pi$
$97$	1260.41	−	727.696i	1.31933	−	0.761715i	0.983621	+	0.180251i	$0.0576909\pi$
$98$		0			0
$99$	−0.0637365	−	0.0264277i	−6.47046e−5	−	2.68292e-5i
$100$		0			0
$101$	197.600	+	342.254i	0.194673	+	0.337183i	0.946793	−	0.321842i	$-0.104302\pi$
$101$	197.600	+	342.254i	0.194673	+	0.337183i	−0.752120	+	0.659026i	$0.770969\pi$
$102$		0			0
$103$	545.260	+	314.806i	0.521612	+	0.301153i	0.737594	−	0.675244i	$-0.235962\pi$
$103$	545.260	+	314.806i	0.521612	+	0.301153i	−0.215982	+	0.976397i	$0.569295\pi$
$104$		0			0
$105$	−1033.06	+	531.314i	−0.960154	+	0.493818i
$106$		0			0
$107$			515.616i			0.465855i	0.972494	+	0.232927i	$0.0748305\pi$
$107$			515.616i			0.465855i	−0.972494	+	0.232927i	$0.925170\pi$
$108$		0			0
$109$	794.011			0.697729			0.348864	−	0.937173i	$-0.386567\pi$
$109$	794.011			0.697729			0.348864	+	0.937173i	$0.386567\pi$
$110$		0			0
$111$	−234.413	+	475.124i	−0.200446	+	0.406277i
$112$		0			0
$113$	1782.31	+	1029.02i	1.48377	+	0.856654i	0.999830	−	0.0184476i	$-0.00587238\pi$
$113$	1782.31	+	1029.02i	1.48377	+	0.856654i	0.483939	+	0.875102i	$0.339206\pi$
$114$		0			0
$115$	536.802	−	309.923i	0.435279	−	0.251308i
$116$		0			0
$117$	−24.6264	−	187.585i	−0.0194591	−	0.148224i
$118$		0			0
$119$	−59.5649	+	520.994i	−0.0458849	+	0.401340i
$120$		0			0
$121$	−665.500	+	1152.68i	−0.500000	+	0.866025i
$122$		0			0
$123$	64.9064	+	97.1776i	0.0475806	+	0.0712375i
$124$		0			0
$125$	1258.82			0.900738
$126$		0			0
$127$	−2071.63			−1.44746			−0.723729	−	0.690084i	$-0.757573\pi$
$127$	−2071.63			−1.44746			−0.723729	+	0.690084i	$0.757573\pi$
$128$		0			0
$129$	−2356.14	+	153.998i	−1.60811	+	0.105107i
$130$		0			0
$131$	−467.210	+	809.232i	−0.311606	+	0.539717i	−0.978710	−	0.205247i	$-0.934200\pi$
$131$	−467.210	+	809.232i	−0.311606	+	0.539717i	0.667104	+	0.744964i	$0.267533\pi$
$132$		0			0
$133$	905.249	+	103.496i	0.590188	+	0.0674758i
$134$		0			0
$135$	−545.258	+	1603.40i	−0.347617	+	1.02221i
$136$		0			0
$137$	2320.59	−	1339.79i	1.44716	−	0.835521i	0.448853	−	0.893606i	$-0.351833\pi$
$137$	2320.59	−	1339.79i	1.44716	−	0.835521i	0.998312	+	0.0580849i	$0.0184994\pi$
$138$		0			0
$139$	794.727	+	458.836i	0.484949	+	0.279985i	0.722476	−	0.691395i	$-0.243004\pi$
$139$	794.727	+	458.836i	0.484949	+	0.279985i	−0.237528	+	0.971381i	$0.576337\pi$
$140$		0			0
$141$	2398.21	−	156.748i	1.43238	−	0.0936207i
$142$		0			0
$143$	0.0179068			1.04716e−5
$144$		0			0
$145$		−	1365.27i		−	0.781926i
$146$		0			0
$147$	−1128.98	+	1379.10i	−0.633448	+	0.773785i
$148$		0			0
$149$	1187.44	+	685.572i	0.652881	+	0.376941i	0.789559	−	0.613674i	$-0.210309\pi$
$149$	1187.44	+	685.572i	0.652881	+	0.376941i	−0.136678	+	0.990616i	$0.543643\pi$
$150$		0			0
$151$	127.186	+	220.292i	0.0685445	+	0.118723i	0.898261	−	0.439463i	$-0.144831\pi$
$151$	127.186	+	220.292i	0.0685445	+	0.118723i	−0.829716	+	0.558185i	$0.811498\pi$
$152$		0			0
$153$	465.169	+	606.678i	0.245795	+	0.320568i
$154$		0			0
$155$	−343.155	+	198.121i	−0.177825	+	0.102667i
$156$		0			0
$157$	511.747	+	295.457i	0.260139	+	0.150191i	0.624398	−	0.781106i	$-0.285344\pi$
$157$	511.747	+	295.457i	0.260139	+	0.150191i	−0.364259	+	0.931298i	$0.618678\pi$
$158$		0			0
$159$	−2644.87	−	1304.91i	−1.31920	−	0.650855i
$160$		0			0
$161$	565.963	−	764.234i	0.277044	−	0.374100i
$162$		0			0
$163$	−2197.17			−1.05580			−0.527901	−	0.849306i	$-0.677021\pi$
$163$	−2197.17			−1.05580			−0.527901	+	0.849306i	$0.677021\pi$
$164$		0			0
$165$	−0.143749	−	0.0709220i	−6.78235e−5	−	3.34622e-5i
$166$		0			0
$167$	210.903	−	365.295i	0.0977256	−	0.169266i	−0.813017	−	0.582240i	$-0.802177\pi$
$167$	210.903	−	365.295i	0.0977256	−	0.169266i	0.910743	+	0.412974i	$0.135510\pi$
$168$		0			0
$169$	−1073.95	−	1860.14i	−0.488826	−	0.846671i
$170$		0			0
$171$	1054.13	−	808.249i	0.471410	−	0.361452i
$172$		0			0
$173$	872.428	+	1511.09i	0.383407	+	0.664081i	0.991547	−	0.129749i	$-0.0414172\pi$
$173$	872.428	+	1511.09i	0.383407	+	0.664081i	−0.608139	+	0.793830i	$0.708084\pi$
$174$		0			0
$175$	−351.953	+	152.871i	−0.152029	+	0.0660341i
$176$		0			0
$177$	840.727	+	1258.73i	0.357022	+	0.534532i
$178$		0			0
$179$		−	4311.61i		−	1.80036i	−0.435518	−	0.900180i	$-0.643435\pi$
$179$		−	4311.61i		−	1.80036i	0.435518	−	0.900180i	$-0.356565\pi$
$180$		0			0
$181$		−	1307.99i		−	0.537141i	−0.963260	−	0.268570i	$-0.913449\pi$
$181$		−	1307.99i		−	0.537141i	0.963260	−	0.268570i	$-0.0865512\pi$
$182$		0			0
$183$	−231.667	−	3544.45i	−0.0935808	−	1.43177i
$184$		0			0
$185$	−615.405	+	1065.91i	−0.244570	+	0.423608i
$186$		0			0
$187$	−0.0626630	+	0.0361785i	−2.45047e−5	+	1.41478e-5i
$188$		0			0
$189$	212.739	+	2589.60i	0.0818757	+	0.996643i
$190$		0			0
$191$	−3495.99	+	2018.41i	−1.32440	+	0.764644i	−0.984428	−	0.175791i	$-0.943752\pi$
$191$	−3495.99	+	2018.41i	−1.32440	+	0.764644i	−0.339975	+	0.940435i	$0.610419\pi$
$192$		0			0
$193$	2209.64	−	3827.21i	0.824112	−	1.42740i	−0.0784849	−	0.996915i	$-0.525008\pi$
$193$	2209.64	−	3827.21i	0.824112	−	1.42740i	0.902596	−	0.430488i	$-0.141658\pi$
$194$		0			0
$195$	−28.6663	−	438.589i	−0.0105274	−	0.161067i
$196$		0			0
$197$		−	151.673i		−	0.0548540i	−0.999624	−	0.0274270i	$-0.991269\pi$
$197$		−	151.673i		−	0.0548540i	0.999624	−	0.0274270i	$-0.00873138\pi$
$198$		0			0
$199$		−	1838.65i		−	0.654966i	−0.944857	−	0.327483i	$-0.893800\pi$
$199$		−	1838.65i		−	0.654966i	0.944857	−	0.327483i	$-0.106200\pi$
$200$		0			0
$201$	−1557.19	−	2331.42i	−0.546447	−	0.818139i
$202$		0			0
$203$	−834.485	−	1921.22i	−0.288519	−	0.664254i
$204$		0			0
$205$	135.742	+	235.111i	0.0462468	+	0.0801019i
$206$		0			0
$207$	−180.461	−	1374.61i	−0.0605936	−	0.461555i
$208$		0			0
$209$	0.0628616	+	0.108879i	2.08049e−5	+	3.60352e-5i
$210$		0			0
$211$	1229.27	−	2129.15i	0.401072	−	0.694678i	−0.592783	−	0.805362i	$-0.701971\pi$
$211$	1229.27	−	2129.15i	0.401072	−	0.694678i	0.993856	+	0.110684i	$0.0353042\pi$
$212$		0			0
$213$	1432.99	+	706.997i	0.460971	+	0.227430i
$214$		0			0
$215$	−5485.32			−1.73998
$216$		0			0
$217$	−361.797	+	488.543i	−0.113181	+	0.152832i
$218$		0			0
$219$	−2307.53	−	1138.47i	−0.712002	−	0.351282i
$220$		0			0
$221$	−171.823	−	99.2019i	−0.0522989	−	0.0301948i
$222$		0			0
$223$	−4491.19	+	2592.99i	−1.34867	+	0.778653i	−0.988061	−	0.154066i	$-0.950763\pi$
$223$	−4491.19	+	2592.99i	−1.34867	+	0.778653i	−0.360606	+	0.932718i	$0.617430\pi$
$224$		0			0
$225$	−214.266	+	516.750i	−0.0634861	+	0.153111i
$226$		0			0
$227$	497.531	+	861.749i	0.145473	+	0.251966i	0.929549	−	0.368698i	$-0.120196\pi$
$227$	497.531	+	861.749i	0.145473	+	0.251966i	−0.784077	+	0.620664i	$0.786863\pi$
$228$		0			0
$229$	101.864	+	58.8111i	0.0293946	+	0.0169710i	0.514625	−	0.857415i	$-0.327931\pi$
$229$	101.864	+	58.8111i	0.0293946	+	0.0169710i	−0.485231	+	0.874386i	$0.661264\pi$
$230$		0			0
$231$	−0.245635	−	0.0119393i	−6.99637e−5	−	3.40064e-6i
$232$		0			0
$233$		−	1484.08i		−	0.417276i	−0.977993	−	0.208638i	$-0.933097\pi$
$233$		−	1484.08i		−	0.417276i	0.977993	−	0.208638i	$-0.0669030\pi$
$234$		0			0
$235$	5583.26			1.54984
$236$		0			0
$237$	−3368.91	+	220.193i	−0.923351	+	0.0603505i
$238$		0			0
$239$	2392.08	+	1381.07i	0.647409	+	0.373782i	0.787463	−	0.616362i	$-0.211394\pi$
$239$	2392.08	+	1381.07i	0.647409	+	0.373782i	−0.140054	+	0.990144i	$0.544728\pi$
$240$		0			0
$241$	−3362.99	+	1941.62i	−0.898877	+	0.518967i	−0.876836	−	0.480790i	$-0.840350\pi$
$241$	−3362.99	+	1941.62i	−0.898877	+	0.518967i	−0.0220413	+	0.999757i	$0.507017\pi$
$242$		0			0
$243$	2845.69	+	2500.19i	0.751238	+	0.660031i
$244$		0			0
$245$	−2826.16	+	3025.97i	−0.736967	+	0.789070i
$246$		0			0
$247$	−172.367	+	298.549i	−0.0444027	+	0.0769078i
$248$		0			0
$249$	5865.18	−	383.350i	1.49273	−	0.0975655i
$250$		0			0
$251$	−5549.57			−1.39556			−0.697780	−	0.716312i	$-0.745829\pi$
$251$	−5549.57			−1.39556			−0.697780	+	0.716312i	$0.745829\pi$
$252$		0			0
$253$	0.131220			3.26076e−5
$254$		0			0
$255$	986.430	+	1476.88i	0.242246	+	0.362689i
$256$		0			0
$257$	809.585	−	1402.24i	0.196500	−	0.340348i	−0.750891	−	0.660426i	$-0.770376\pi$
$257$	809.585	−	1402.24i	0.196500	−	0.340348i	0.947391	+	0.320078i	$0.103709\pi$
$258$		0			0
$259$	−214.495	+	1876.12i	−0.0514598	+	0.450102i
$260$		0			0
$261$	−2820.81	−	1169.62i	−0.668979	−	0.277386i
$262$		0			0
$263$	−594.813	+	343.415i	−0.139459	+	0.0805167i	−0.568106	−	0.822955i	$-0.692324\pi$
$263$	−594.813	+	343.415i	−0.139459	+	0.0805167i	0.428647	+	0.903472i	$0.358990\pi$
$264$		0			0
$265$	−5933.62	−	3425.78i	−1.37547	−	0.794128i
$266$		0			0
$267$	299.375	−	606.793i	0.0686196	−	0.139083i
$268$		0			0
$269$	−1805.03			−0.409124			−0.204562	−	0.978854i	$-0.565577\pi$
$269$	−1805.03			−0.409124			−0.204562	+	0.978854i	$0.565577\pi$
$270$		0			0
$271$			6726.19i			1.50770i	0.657046	+	0.753851i	$0.271806\pi$
$271$			6726.19i			1.50770i	−0.657046	+	0.753851i	$0.728194\pi$
$272$		0			0
$273$	−308.416	−	599.668i	−0.0683743	−	0.132943i
$274$		0			0
$275$	−0.0458534	−	0.0264735i	−1.00548e−5	−	5.80513e-6i
$276$		0			0
$277$	−336.124	−	582.184i	−0.0729088	−	0.126282i	0.827266	−	0.561810i	$-0.189895\pi$
$277$	−336.124	−	582.184i	−0.0729088	−	0.126282i	−0.900175	+	0.435528i	$0.856562\pi$
$278$		0			0
$279$	115.361	+	878.730i	0.0247544	+	0.188560i
$280$		0			0
$281$	−2007.12	+	1158.81i	−0.426102	+	0.246010i	−0.697685	−	0.716405i	$-0.745786\pi$
$281$	−2007.12	+	1158.81i	−0.426102	+	0.246010i	0.271583	+	0.962415i	$0.412453\pi$
$282$		0			0
$283$	8014.87	+	4627.39i	1.68352	+	0.971978i	0.959294	+	0.282411i	$0.0911342\pi$
$283$	8014.87	+	4627.39i	1.68352	+	0.971978i	0.724222	+	0.689567i	$0.242199\pi$
$284$		0			0
$285$	2566.14	−	1713.96i	0.533350	−	0.356233i
$286$		0			0
$287$	334.723	+	247.883i	0.0688435	+	0.0509829i
$288$		0			0
$289$	−4111.30			−0.836821
$290$		0			0
$291$	−493.231	−	7546.34i	−0.0993599	−	1.52019i
$292$		0			0
$293$	4392.72	−	7608.42i	0.875855	−	1.51703i	0.0200056	−	0.999800i	$-0.493632\pi$
$293$	4392.72	−	7608.42i	0.875855	−	1.51703i	0.855849	−	0.517225i	$-0.173035\pi$
$294$		0			0
$295$	1758.25	+	3045.38i	0.347015	+	0.601047i
$296$		0			0
$297$	−0.269683	+	0.236245i	−5.26889e−5	+	4.61559e-5i
$298$		0			0
$299$	179.904	+	311.602i	0.0347963	+	0.0602689i
$300$		0			0
$301$	−7719.03	+	3352.76i	−1.47813	+	0.642027i
$302$		0			0
$303$	2049.15	−	133.933i	0.388517	−	0.0253936i
$304$		0			0
$305$		−	8251.85i		−	1.54918i
$306$		0			0
$307$		−	599.516i		−	0.111453i	−0.998446	−	0.0557267i	$-0.982252\pi$
$307$		−	599.516i		−	0.111453i	0.998446	−	0.0557267i	$-0.0177476\pi$
$308$		0			0
$309$	2720.53	−	1817.08i	0.500860	−	0.334532i
$310$		0			0
$311$	4494.29	−	7784.34i	0.819447	−	1.41932i	−0.0866437	−	0.996239i	$-0.527614\pi$
$311$	4494.29	−	7784.34i	0.819447	−	1.41932i	0.906090	−	0.423084i	$-0.139052\pi$
$312$		0			0
$313$	7102.69	−	4100.74i	1.28264	−	0.740535i	0.305314	−	0.952252i	$-0.401239\pi$
$313$	7102.69	−	4100.74i	1.28264	−	0.740535i	0.977331	+	0.211717i	$0.0679054\pi$
$314$		0			0
$315$	100.801	+	6035.43i	0.0180301	+	1.07955i
$316$		0			0
$317$	−5894.42	+	3403.15i	−1.04436	+	0.602964i	−0.921066	−	0.389405i	$-0.872681\pi$
$317$	−5894.42	+	3403.15i	−1.04436	+	0.602964i	−0.123298	+	0.992370i	$0.539347\pi$
$318$		0			0
$319$	0.144512	−	0.250302i	2.53640e−5	−	4.39318e-5i
$320$		0			0
$321$	2402.70	+	1185.43i	0.417775	+	0.206118i
$322$		0			0
$323$		−	1392.99i		−	0.239962i
$324$		0			0
$325$		−	145.181i		−	0.0247791i
$326$		0			0
$327$	1825.47	−	3699.99i	0.308712	−	0.625718i
$328$		0			0
$329$	7856.85	−	3412.63i	1.31660	−	0.571867i
$330$		0			0
$331$	3875.41	+	6712.41i	0.643540	+	1.11464i	0.984637	+	0.174616i	$0.0558684\pi$
$331$	3875.41	+	6712.41i	0.643540	+	1.11464i	−0.341097	+	0.940028i	$0.610798\pi$
$332$		0			0
$333$	1675.09	+	2184.67i	0.275658	+	0.359517i
$334$		0			0
$335$	−3256.63	−	5640.64i	−0.531130	−	0.919944i
$336$		0			0
$337$	−1544.24	+	2674.70i	−0.249614	+	0.432344i	−0.963419	−	0.268001i	$-0.913637\pi$
$337$	−1544.24	+	2674.70i	−0.249614	+	0.432344i	0.713805	+	0.700345i	$0.246970\pi$
$338$		0			0
$339$	8892.72	−	5939.58i	1.42474	−	0.951603i
$340$		0			0
$341$	−0.0838835			−1.33213e−5
$342$		0			0
$343$	−2127.47	+	5985.61i	−0.334906	+	0.942252i
$344$		0			0
$345$	−210.065	−	3213.95i	−0.0327812	−	0.501546i
$346$		0			0
$347$	10112.9	+	5838.71i	1.56453	+	0.903281i	0.996789	+	0.0800721i	$0.0255151\pi$
$347$	10112.9	+	5838.71i	1.56453	+	0.903281i	0.567739	+	0.823209i	$0.307818\pi$
$348$		0			0
$349$	−6683.19	+	3858.54i	−1.02505	+	0.591814i	−0.915563	−	0.402174i	$-0.868255\pi$
$349$	−6683.19	+	3858.54i	−1.02505	+	0.591814i	−0.109489	+	0.993988i	$0.534921\pi$
$350$		0			0
$351$	−930.737	−	316.511i	−0.141536	−	0.0481313i
$352$		0			0
$353$	2760.12	+	4780.66i	0.416165	+	0.720818i	0.995550	−	0.0942355i	$-0.0300407\pi$
$353$	2760.12	+	4780.66i	0.416165	+	0.720818i	−0.579385	+	0.815054i	$0.696707\pi$
$354$		0			0
$355$	3214.83	+	1856.08i	0.480635	+	0.277495i
$356$		0			0
$357$	2290.82	+	1475.36i	0.339617	+	0.218723i
$358$		0			0
$359$			6290.95i			0.924857i	0.886657	+	0.462429i	$0.153022\pi$
$359$			6290.95i			0.924857i	−0.886657	+	0.462429i	$0.846978\pi$
$360$		0			0
$361$	4438.63			0.647125
$362$		0			0
$363$	3841.32	+	5751.21i	0.555419	+	0.831571i
$364$		0			0
$365$	−5176.81	−	2988.83i	−0.742374	−	0.428610i
$366$		0			0
$367$	−3342.42	+	1929.75i	−0.475404	+	0.274474i	−0.718499	−	0.695528i	$-0.755171\pi$
$367$	−3342.42	+	1929.75i	−0.475404	+	0.274474i	0.243095	+	0.970002i	$0.421837\pi$
$368$		0			0
$369$	602.058	−	79.0390i	0.0849373	−	0.0111507i
$370$		0			0
$371$	−10443.8	−	1194.03i	−1.46150	−	0.167092i
$372$		0			0
$373$	−4308.29	+	7462.17i	−0.598055	+	1.03586i	0.395052	+	0.918659i	$0.370726\pi$
$373$	−4308.29	+	7462.17i	−0.598055	+	1.03586i	−0.993108	+	0.117204i	$0.962607\pi$
$374$		0			0
$375$	2894.09	−	5865.93i	0.398534	−	0.807775i
$376$		0			0
$377$	792.509			0.108266
$378$		0			0
$379$	11100.5			1.50447			0.752237	−	0.658893i	$-0.228975\pi$
$379$	11100.5			1.50447			0.752237	+	0.658893i	$0.228975\pi$
$380$		0			0
$381$	−4762.77	+	9653.51i	−0.640431	+	1.29807i
$382$		0			0
$383$	−3294.29	+	5705.87i	−0.439505	+	0.761244i	−0.997651	−	0.0684980i	$-0.978179\pi$
$383$	−3294.29	+	5705.87i	−0.439505	+	0.761244i	0.558147	+	0.829742i	$0.311513\pi$
$384$		0			0
$385$	−0.567622	−	0.0648959i	−7.51395e−5	−	8.59065e-6i
$386$		0			0
$387$	−4699.27	+	11333.3i	−0.617253	+	1.48865i
$388$		0			0
$389$	−6913.20	+	3991.34i	−0.901062	+	0.520228i	−0.877545	−	0.479495i	$-0.840820\pi$
$389$	−6913.20	+	3991.34i	−0.901062	+	0.520228i	−0.0235174	+	0.999723i	$0.507487\pi$
$390$		0			0
$391$	−1259.11	−	726.945i	−0.162854	−	0.0940235i
$392$		0			0
$393$	2696.77	+	4037.60i	0.346143	+	0.518245i
$394$		0			0
$395$	−7843.16			−0.999069
$396$		0			0
$397$			9040.06i			1.14284i	0.820658	+	0.571420i	$0.193607\pi$
$397$			9040.06i			1.14284i	−0.820658	+	0.571420i	$0.806393\pi$
$398$		0			0
$399$	2563.49	−	3980.40i	0.321642	−	0.499421i
$400$		0			0
$401$	−836.173	−	482.765i	−0.104131	−	0.0601200i	0.447030	−	0.894519i	$-0.352482\pi$
$401$	−836.173	−	482.765i	−0.104131	−	0.0601200i	−0.551161	+	0.834399i	$0.685815\pi$
$402$		0			0
$403$	−115.005	−	199.194i	−0.0142154	−	0.0246218i
$404$		0			0
$405$	6218.04	+	6227.12i	0.762906	+	0.764020i
$406$		0			0
$407$	−0.225652	+	0.130280i	−2.74819e−5	+	1.58667e-5i
$408$		0			0
$409$	−2868.77	−	1656.28i	−0.346825	−	0.200240i	0.316461	−	0.948606i	$-0.397505\pi$
$409$	−2868.77	−	1656.28i	−0.346825	−	0.200240i	−0.663286	+	0.748366i	$0.730839\pi$
$410$		0			0
$411$	−908.110	−	13893.9i	−0.108987	−	1.66748i
$412$		0			0
$413$	4335.64	+	3210.82i	0.516569	+	0.382552i
$414$		0			0
$415$	13654.7			1.61514
$416$		0			0
$417$	3965.23	−	2648.44i	0.465655	−	0.311018i
$418$		0			0
$419$	4172.32	−	7226.67i	0.486470	−	0.842591i	−0.513409	−	0.858144i	$-0.671618\pi$
$419$	4172.32	−	7226.67i	0.486470	−	0.842591i	0.999879	+	0.0155530i	$0.00495087\pi$
$420$		0			0
$421$	3350.59	+	5803.38i	0.387880	+	0.671828i	0.992164	−	0.124941i	$-0.0398741\pi$
$421$	3350.59	+	5803.38i	0.387880	+	0.671828i	−0.604284	+	0.796769i	$0.706541\pi$
$422$		0			0
$423$	4783.17	−	11535.7i	0.549801	−	1.32597i
$424$		0			0
$425$	293.321	+	508.046i	0.0334780	+	0.0579856i
$426$		0			0
$427$	−5043.73	−	11612.1i	−0.571623	−	1.31604i
$428$		0			0
$429$	0.0411687	−	0.0834434i	4.63320e−6	−	9.39088e-6i
$430$		0			0
$431$			9168.55i			1.02467i	0.858785	+	0.512336i	$0.171220\pi$
$431$			9168.55i			1.02467i	−0.858785	+	0.512336i	$0.828780\pi$
$432$		0			0
$433$			1346.90i			0.149487i	0.997203	+	0.0747436i	$0.0238138\pi$
$433$			1346.90i			0.149487i	−0.997203	+	0.0747436i	$0.976186\pi$
$434$		0			0
$435$	−6361.97	−	3138.82i	−0.701225	−	0.345965i
$436$		0			0
$437$	−1263.10	+	2187.75i	−0.138266	+	0.239483i
$438$		0			0
$439$	4892.07	−	2824.44i	0.531858	−	0.307069i	−0.209914	−	0.977720i	$-0.567319\pi$
$439$	4892.07	−	2824.44i	0.531858	−	0.307069i	0.741773	+	0.670651i	$0.233985\pi$
$440$		0			0
$441$	3830.85	+	8431.53i	0.413654	+	0.910434i
$442$		0			0
$443$	−7525.68	+	4344.95i	−0.807124	+	0.465993i	−0.845956	−	0.533253i	$-0.820970\pi$
$443$	−7525.68	+	4344.95i	−0.807124	+	0.465993i	0.0388322	+	0.999246i	$0.487636\pi$
$444$		0			0
$445$	785.950	−	1361.31i	0.0837249	−	0.145016i
$446$		0			0
$447$	5924.67	−	3957.17i	0.626906	−	0.418720i
$448$		0			0
$449$		−	14492.3i		−	1.52324i	−0.648026	−	0.761618i	$-0.724405\pi$
$449$		−	14492.3i		−	1.52324i	0.648026	−	0.761618i	$-0.275595\pi$
$450$		0			0
$451$			0.0574724i			6.00060e-6i
$452$		0			0
$453$	1318.94	−	86.2062i	0.136797	−	0.00894111i
$454$		0			0
$455$	−624.109	−	1436.88i	−0.0643048	−	0.148048i
$456$		0			0
$457$	−4131.68	−	7156.27i	−0.422914	−	0.732508i	0.573309	−	0.819339i	$-0.305659\pi$
$457$	−4131.68	−	7156.27i	−0.422914	−	0.732508i	−0.996223	+	0.0868308i	$0.972326\pi$
$458$		0			0
$459$	3896.48	−	772.843i	0.396236	−	0.0785909i
$460$		0			0
$461$	4948.33	+	8570.75i	0.499928	+	0.865900i	1.00000		8.36677e-5i	$-2.66323e-5\pi$
$461$	4948.33	+	8570.75i	0.499928	+	0.865900i	−0.500072	+	0.865984i	$0.666693\pi$
$462$		0			0
$463$	1987.79	−	3442.95i	0.199525	−	0.345588i	−0.748849	−	0.662740i	$-0.769393\pi$
$463$	1987.79	−	3442.95i	0.199525	−	0.345588i	0.948375	+	0.317152i	$0.102727\pi$
$464$		0			0
$465$	134.286	+	2054.55i	0.0133922	+	0.204898i
$466$		0			0
$467$	−17044.5			−1.68892			−0.844460	−	0.535619i	$-0.820079\pi$
$467$	−17044.5			−1.68892			−0.844460	+	0.535619i	$0.820079\pi$
$468$		0			0
$469$	−8030.47	−	5947.07i	−0.790645	−	0.585522i
$470$		0			0
$471$	2553.32	−	1705.40i	0.249790	−	0.166838i
$472$		0			0
$473$	−1.00566	−	0.580616i	−9.77592e−5	−	5.64413e-5i
$474$		0			0
$475$	882.751	−	509.656i	0.0852703	−	0.0492308i
$476$		0			0
$477$	−12161.4	+	9324.72i	−1.16736	+	0.895073i
$478$		0			0
$479$	−5364.93	−	9292.33i	−0.511753	−	0.886383i	−0.999907	−	0.0136250i	$-0.995663\pi$
$479$	−5364.93	−	9292.33i	−0.511753	−	0.886383i	0.488154	−	0.872758i	$-0.337670\pi$
$480$		0			0
$481$	−618.740	−	357.230i	−0.0586530	−	0.0338633i
$482$		0			0
$483$	−2260.05	−	4394.33i	−0.212911	−	0.413973i
$484$		0			0
$485$		−	17568.6i		−	1.64485i
$486$		0			0
$487$	−12461.1			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$487$	−12461.1			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$488$		0			0
$489$	−5051.40	+	10238.5i	−0.467142	+	0.946834i
$490$		0			0
$491$	−4052.21	−	2339.55i	−0.372452	−	0.215035i	0.302077	−	0.953283i	$-0.402320\pi$
$491$	−4052.21	−	2339.55i	−0.372452	−	0.215035i	−0.674529	+	0.738248i	$0.735653\pi$
$492$		0			0
$493$	−2773.30	+	1601.16i	−0.253353	+	0.146273i
$494$		0			0
$495$	−0.660974	+	0.506800i	−6.00173e−5	+	4.60181e-5i
$496$		0			0
$497$	5658.43	+	646.925i	0.510695	+	0.0583874i
$498$		0			0
$499$	2685.54	−	4651.49i	0.240924	−	0.417293i	−0.720054	−	0.693918i	$-0.755883\pi$
$499$	2685.54	−	4651.49i	0.240924	−	0.417293i	0.960978	+	0.276625i	$0.0892161\pi$
$500$		0			0
$501$	−1217.35	−	1822.61i	−0.108557	−	0.162532i
$502$		0			0
$503$	22263.9			1.97355			0.986777	−	0.162086i	$-0.0518222\pi$
$503$	22263.9			1.97355			0.986777	+	0.162086i	$0.0518222\pi$
$504$		0			0
$505$	4770.63			0.420376
$506$		0			0
$507$	−11137.0	+	727.921i	−0.975569	+	0.0637635i
$508$		0			0
$509$	−7249.76	+	12556.9i	−0.631316	+	1.09347i	0.355967	+	0.934498i	$0.384152\pi$
$509$	−7249.76	+	12556.9i	−0.631316	+	1.09347i	−0.987283	+	0.158973i	$0.949182\pi$
$510$		0			0
$511$	−9111.72	−	1041.74i	−0.788804	−	0.0901834i
$512$		0			0
$513$	−1342.85	−	6770.30i	−0.115571	−	0.582682i
$514$		0			0
$515$	6582.05	−	3800.15i	0.563184	−	0.325155i
$516$		0			0
$517$	1.02361	+	0.590983i	8.70762e−5	+	5.02735e-5i
$518$		0			0
$519$	9047.24	−	591.330i	0.765182	−	0.0500126i
$520$		0			0
$521$	−7009.79			−0.589452			−0.294726	−	0.955582i	$-0.595228\pi$
$521$	−7009.79			−0.589452			−0.294726	+	0.955582i	$0.595228\pi$
$522$		0			0
$523$			3631.76i			0.303644i	0.988408	+	0.151822i	$0.0485141\pi$
$523$			3631.76i			0.303644i	−0.988408	+	0.151822i	$0.951486\pi$
$524$		0			0
$525$	−96.7990	+	1991.51i	−0.00804696	+	0.165556i
$526$		0			0
$527$	804.894	+	464.706i	0.0665308	+	0.0384116i
$528$		0			0
$529$	−4765.18	−	8253.53i	−0.391648	−	0.678354i
$530$		0			0
$531$	7798.41	−	1023.79i	0.637330	−	0.0836696i
$532$		0			0
$533$	−136.477	+	78.7951i	−0.0110910	+	0.00640336i
$534$		0			0
$535$	5390.32	+	3112.10i	0.435596	+	0.251492i
$536$		0			0
$537$	−20091.5	−	9912.59i	−1.61455	−	0.796573i
$538$		0			0
$539$	−0.838432	+	0.255622i	−6.70015e−5	+	2.04275e-5i
$540$		0			0
$541$	−12760.4			−1.01407			−0.507037	−	0.861925i	$-0.669259\pi$
$541$	−12760.4			−1.01407			−0.507037	+	0.861925i	$0.669259\pi$
$542$		0			0
$543$	−6095.08	−	3007.14i	−0.481704	−	0.237659i
$544$		0			0
$545$	4792.42	−	8300.71i	0.376669	−	0.652410i
$546$		0			0
$547$	−3919.62	−	6788.98i	−0.306382	−	0.530669i	0.671186	−	0.741289i	$-0.265785\pi$
$547$	−3919.62	−	6788.98i	−0.306382	−	0.530669i	−0.977568	+	0.210620i	$0.932452\pi$
$548$		0			0
$549$	−17049.3	−	7069.34i	−1.32540	−	0.549566i
$550$		0			0
$551$	2782.09	+	4818.72i	0.215101	+	0.372567i
$552$		0			0
$553$	−11037.0	+	4793.93i	−0.848718	+	0.368641i
$554$		0			0
$555$	3552.17	+	5318.29i	0.271678	+	0.406755i
$556$		0			0
$557$		−	9443.19i		−	0.718350i	−0.933270	−	0.359175i	$-0.883058\pi$
$557$		−	9443.19i		−	0.718350i	0.933270	−	0.359175i	$-0.116942\pi$
$558$		0			0
$559$		−	3184.11i		−	0.240919i
$560$		0			0
$561$	0.0245217	+	0.375177i	1.84547e−6	+	2.82353e-5i
$562$		0			0
$563$	−8022.13	+	13894.7i	−0.600519	+	1.04013i	0.392223	+	0.919870i	$0.371706\pi$
$563$	−8022.13	+	13894.7i	−0.600519	+	1.04013i	−0.992742	+	0.120260i	$0.961627\pi$
$564$		0			0
$565$	21515.0	−	12421.7i	1.60202	−	0.924929i
$566$		0			0
$567$	12556.3	+	4962.27i	0.930007	+	0.367541i
$568$		0			0
$569$	19213.9	−	11093.2i	1.41562	−	0.817310i	0.419712	−	0.907657i	$-0.362131\pi$
$569$	19213.9	−	11093.2i	1.41562	−	0.817310i	0.995910	+	0.0903469i	$0.0287976\pi$
$570$		0			0
$571$	−3211.11	+	5561.80i	−0.235343	+	0.407625i	−0.959372	−	0.282144i	$-0.908955\pi$
$571$	−3211.11	+	5561.80i	−0.235343	+	0.407625i	0.724030	+	0.689769i	$0.242288\pi$
$572$		0			0
$573$	1368.07	+	20931.3i	0.0997419	+	1.52603i
$574$		0			0
$575$		−	1063.88i		−	0.0771597i
$576$		0			0
$577$		−	21441.1i		−	1.54697i	−0.633813	−	0.773486i	$-0.718511\pi$
$577$		−	21441.1i		−	1.54697i	0.633813	−	0.773486i	$-0.281489\pi$
$578$		0			0
$579$	−12754.2	−	19095.6i	−0.915454	−	1.37061i
$580$		0			0
$581$	19215.1	−	8346.09i	1.37208	−	0.595963i
$582$		0			0
$583$	−0.725230	−	1.25614i	−5.15197e−5	−	8.92347e-5i
$584$		0			0
$585$	−2109.67	−	874.757i	−0.149101	−	0.0618235i
$586$		0			0
$587$	342.762	+	593.681i	0.0241010	+	0.0417442i	0.877824	−	0.478983i	$-0.158994\pi$
$587$	342.762	+	593.681i	0.0241010	+	0.0417442i	−0.853723	+	0.520727i	$0.825661\pi$
$588$		0			0
$589$	807.445	−	1398.54i	0.0564859	−	0.0978365i
$590$		0			0
$591$	−706.775	−	348.703i	−0.0491926	−	0.0242703i
$592$		0			0
$593$	−11503.8			−0.796635			−0.398317	−	0.917248i	$-0.630406\pi$
$593$	−11503.8			−0.796635			−0.398317	+	0.917248i	$0.630406\pi$
$594$		0			0
$595$	5087.04	+	3767.27i	0.350501	+	0.259568i
$596$		0			0
$597$	−8567.85	−	4227.14i	−0.587368	−	0.289791i
$598$		0			0
$599$	5124.45	+	2958.60i	0.349548	+	0.201812i	0.664486	−	0.747300i	$-0.268650\pi$
$599$	5124.45	+	2958.60i	0.349548	+	0.201812i	−0.314938	+	0.949112i	$0.601984\pi$
$600$		0			0
$601$	−10168.3	+	5870.67i	−0.690139	+	0.398452i	−0.803664	−	0.595083i	$-0.797119\pi$
$601$	−10168.3	+	5870.67i	−0.690139	+	0.398452i	0.113525	+	0.993535i	$0.463786\pi$
$602$		0			0
$603$	−14444.2	+	1896.25i	−0.975478	+	0.128062i
$604$		0			0
$605$	8033.52	+	13914.5i	0.539850	+	0.935047i
$606$		0			0
$607$	24018.0	+	13866.8i	1.60603	+	0.927241i	0.990247	+	0.139325i	$0.0444933\pi$
$607$	24018.0	+	13866.8i	1.60603	+	0.927241i	0.615782	+	0.787916i	$0.288840\pi$
$608$		0			0
$609$	−10871.2	−	528.402i	−0.723353	−	0.0351591i
$610$		0			0
$611$			3240.96i			0.214592i
$612$		0			0
$613$	−19338.2			−1.27416			−0.637081	−	0.770797i	$-0.719858\pi$
$613$	−19338.2			−1.27416			−0.637081	+	0.770797i	$0.719858\pi$
$614$		0			0
$615$	1407.66	−	92.0054i	0.0922968	−	0.00603255i
$616$		0			0
$617$	9927.33	+	5731.55i	0.647746	+	0.373976i	0.787592	−	0.616197i	$-0.211327\pi$
$617$	9927.33	+	5731.55i	0.647746	+	0.373976i	−0.139846	+	0.990173i	$0.544661\pi$
$618$		0			0
$619$	−3429.59	+	1980.07i	−0.222693	+	0.128572i	−0.607196	−	0.794552i	$-0.707706\pi$
$619$	−3429.59	+	1980.07i	−0.222693	+	0.128572i	0.384504	+	0.923123i	$0.374373\pi$
$620$		0			0
$621$	−6820.38	−	2319.37i	−0.440728	−	0.149876i
$622$		0			0
$623$	273.937	−	2396.04i	0.0176165	−	0.154086i
$624$		0			0
$625$	8892.79	−	15402.8i	0.569139	−	0.985777i
$626$		0			0
$627$	0.651886	−	0.0426075i	4.15212e−5	−	2.71384e-6i
$628$		0			0
$629$	2886.95			0.183005
$630$		0			0
$631$	−5409.20			−0.341263			−0.170631	−	0.985335i	$-0.554581\pi$
$631$	−5409.20			−0.341263			−0.170631	+	0.985335i	$0.554581\pi$
$632$		0			0
$633$	−7095.43	−	10623.3i	−0.445526	−	0.667040i
$634$		0			0
$635$	−12503.7	+	21657.1i	−0.781410	+	1.35344i
$636$		0			0
$637$	−1756.51	−	1640.53i	−0.109255	−	0.102041i
$638$		0			0
$639$	6589.02	−	5052.12i	0.407915	−	0.312768i
$640$		0			0
$641$	−20809.6	+	12014.4i	−1.28226	+	0.740313i	−0.977261	−	0.212040i	$-0.931989\pi$
$641$	−20809.6	+	12014.4i	−1.28226	+	0.740313i	−0.304999	+	0.952353i	$0.598656\pi$
$642$		0			0
$643$	−3581.87	−	2068.00i	−0.219682	−	0.126833i	0.386121	−	0.922448i	$-0.373815\pi$
$643$	−3581.87	−	2068.00i	−0.219682	−	0.126833i	−0.605803	+	0.795615i	$0.707148\pi$
$644$		0			0
$645$	−12611.0	+	25560.9i	−0.769859	+	1.56040i
$646$		0			0
$647$	1393.75			0.0846895			0.0423447	−	0.999103i	$-0.486517\pi$
$647$	1393.75			0.0846895			0.0423447	+	0.999103i	$0.486517\pi$
$648$		0			0
$649$			0.744436i			4.50257e-5i
$650$		0			0
$651$	1444.76	+	2809.11i	0.0869809	+	0.169121i
$652$		0			0
$653$	7846.10	+	4529.95i	0.470202	+	0.271471i	0.716324	−	0.697768i	$-0.245823\pi$
$653$	7846.10	+	4529.95i	0.470202	+	0.271471i	−0.246122	+	0.969239i	$0.579157\pi$
$654$		0			0
$655$	5639.89	+	9768.57i	0.336441	+	0.582732i
$656$		0			0
$657$	−10610.2	+	8135.38i	−0.630053	+	0.483092i
$658$		0			0
$659$	14018.1	−	8093.34i	0.828629	−	0.478409i	−0.0247539	−	0.999694i	$-0.507880\pi$
$659$	14018.1	−	8093.34i	0.828629	−	0.478409i	0.853383	+	0.521284i	$0.174547\pi$
$660$		0			0
$661$	24821.5	+	14330.7i	1.46058	+	0.843269i	0.999038	−	0.0438473i	$-0.0139615\pi$
$661$	24821.5	+	14330.7i	1.46058	+	0.843269i	0.461546	+	0.887116i	$0.347295\pi$
$662$		0			0
$663$	−857.297	+	572.601i	−0.0502182	+	0.0335415i
$664$		0			0
$665$	6545.78	−	8838.93i	0.381706	−	0.515427i
$666$		0			0
$667$	5807.45			0.337130
$668$		0			0
$669$	1757.53	+	26889.8i	0.101569	+	1.55399i
$670$		0			0
$671$	0.873449	−	1.51286i	5.02521e−5	−	8.70391e-5i
$672$		0			0
$673$	3670.88	+	6358.15i	0.210255	+	0.364173i	0.951794	−	0.306737i	$-0.0992371\pi$
$673$	3670.88	+	6358.15i	0.210255	+	0.364173i	−0.741539	+	0.670910i	$0.765904\pi$
$674$		0			0
$675$	1915.38	+	2186.48i	0.109219	+	0.124678i
$676$		0			0
$677$	16478.4	+	28541.4i	0.935474	+	1.62029i	0.773787	+	0.633446i	$0.218360\pi$
$677$	16478.4	+	28541.4i	0.935474	+	1.62029i	0.161687	+	0.986842i	$0.448307\pi$
$678$		0			0
$679$	−10738.4	−	24722.8i	−0.606924	−	1.39731i
$680$		0			0
$681$	5159.48	−	337.226i	0.290326	−	0.0189758i
$682$		0			0
$683$			22213.0i			1.24444i	0.782841	+	0.622222i	$0.213770\pi$
$683$			22213.0i			1.24444i	−0.782841	+	0.622222i	$0.786230\pi$
$684$		0			0
$685$		−	32346.4i		−	1.80422i
$686$		0			0
$687$	508.242	−	339.463i	0.0282251	−	0.0188520i
$688$		0			0
$689$	1988.59	−	3444.34i	0.109955	−	0.190448i
$690$		0			0
$691$	22072.1	−	12743.3i	1.21514	−	0.701563i	0.251267	−	0.967918i	$-0.419153\pi$
$691$	22072.1	−	12743.3i	1.21514	−	0.701563i	0.963875	+	0.266355i	$0.0858194\pi$
$692$		0			0
$693$	−0.620364	+	1.11718i	−3.40053e−5	+	6.12383e-5i
$694$		0			0
$695$	9593.47	−	5538.79i	0.523599	−	0.302300i
$696$		0			0
$697$	318.391	−	551.470i	0.0173026	−	0.0299690i
$698$		0			0
$699$	−6915.61	−	3411.97i	−0.374209	−	0.184625i
$700$		0			0
$701$			22316.4i			1.20239i	0.799101	+	0.601197i	$0.205309\pi$
$701$			22316.4i			1.20239i	−0.799101	+	0.601197i	$0.794691\pi$
$702$		0			0
$703$		−	5016.19i		−	0.269117i
$704$		0			0
$705$	12836.2	−	26017.3i	0.685729	−	1.38988i
$706$		0			0
$707$	6713.29	−	2915.92i	0.357114	−	0.155113i
$708$		0			0
$709$	−620.251	−	1074.31i	−0.0328547	−	0.0569061i	0.849130	−	0.528183i	$-0.177127\pi$
$709$	−620.251	−	1074.31i	−0.0328547	−	0.0569061i	−0.881985	+	0.471277i	$0.843793\pi$
$710$		0			0
$711$	−6719.22	+	16204.9i	−0.354417	+	0.854756i
$712$		0			0
$713$	−842.748	−	1459.68i	−0.0442653	−	0.0766698i
$714$		0			0
$715$	0.108080	−	0.187201i	5.65311e−6	−	9.79147e-6i
$716$		0			0
$717$	11935.1	−	7971.63i	0.621652	−	0.415211i
$718$		0			0
$719$	1718.52			0.0891374			0.0445687	−	0.999006i	$-0.485809\pi$
$719$	1718.52			0.0891374			0.0445687	+	0.999006i	$0.485809\pi$
$720$		0			0
$721$	6939.62	−	9370.74i	0.358453	−	0.484028i
$722$		0			0
$723$	1316.03	+	20135.0i	0.0676952	+	1.03572i
$724$		0			0
$725$	−2029.35	−	1171.65i	−0.103956	−	0.0600191i
$726$		0			0
$727$	2204.74	−	1272.91i	0.112475	−	0.0649376i	−0.442707	−	0.896666i	$-0.645982\pi$
$727$	2204.74	−	1272.91i	0.112475	−	0.0649376i	0.555182	+	0.831729i	$0.312649\pi$
$728$		0			0
$729$	18193.0	−	7512.46i	0.924298	−	0.381672i
$730$		0			0
$731$	6433.10	+	11142.5i	0.325495	+	0.563774i
$732$		0			0
$733$	19126.0	+	11042.4i	0.963761	+	0.556427i	0.897328	−	0.441363i	$-0.145505\pi$
$733$	19126.0	+	11042.4i	0.963761	+	0.556427i	0.0664323	+	0.997791i	$0.478838\pi$
$734$		0			0
$735$	7603.13	+	20126.4i	0.381559	+	1.01003i
$736$		0			0
$737$		−	1.37884i		−	6.89149e-5i
$738$		0			0
$739$	−5401.50			−0.268873			−0.134437	−	0.990922i	$-0.542922\pi$
$739$	−5401.50			−0.268873			−0.134437	+	0.990922i	$0.542922\pi$
$740$		0			0
$741$	994.918	+	1489.59i	0.0493242	+	0.0738480i
$742$		0			0
$743$	−26971.1	−	15571.7i	−1.33173	−	0.768872i	−0.346161	−	0.938175i	$-0.612515\pi$
$743$	−26971.1	−	15571.7i	−1.33173	−	0.768872i	−0.985564	+	0.169303i	$0.945848\pi$
$744$		0			0
$745$	14334.1	−	8275.82i	0.704915	−	0.406983i
$746$		0			0
$747$	11698.0	−	28212.3i	0.572967	−	1.38184i
$748$		0			0
$749$	9487.53	+	1084.70i	0.462840	+	0.0529161i
$750$		0			0
$751$	−2644.61	+	4580.61i	−0.128500	+	0.222568i	−0.923096	−	0.384571i	$-0.874350\pi$
$751$	−2644.61	+	4580.61i	−0.128500	+	0.222568i	0.794596	+	0.607139i	$0.207683\pi$
$752$		0			0
$753$	−12758.7	+	25860.2i	−0.617468	+	1.25153i
$754$		0			0
$755$	3070.62			0.148015
$756$		0			0
$757$	−20794.2			−0.998384			−0.499192	−	0.866491i	$-0.666370\pi$
$757$	−20794.2			−0.998384			−0.499192	+	0.866491i	$0.666370\pi$
$758$		0			0
$759$	0.301681	−	0.611468i	1.44273e−5	−	2.92423e-5i
$760$		0			0
$761$	−9126.94	+	15808.3i	−0.434759	+	0.753024i	−0.997276	−	0.0737616i	$-0.976500\pi$
$761$	−9126.94	+	15808.3i	−0.434759	+	0.753024i	0.562517	+	0.826785i	$0.309833\pi$
$762$		0			0
$763$	1670.36	−	14610.1i	0.0792546	−	0.693213i
$764$		0			0
$765$	9149.92	−	1201.21i	0.432439	−	0.0567712i
$766$		0			0
$767$	−1767.78	+	1020.63i	−0.0832213	+	0.0480478i
$768$		0			0
$769$	−28098.3	−	16222.6i	−1.31762	−	0.760730i	−0.334278	−	0.942475i	$-0.608492\pi$
$769$	−28098.3	−	16222.6i	−1.31762	−	0.760730i	−0.983346	+	0.181745i	$0.941826\pi$
$770$		0			0
$771$	−4672.99	−	6996.39i	−0.218280	−	0.326808i
$772$		0			0
$773$	20600.1			0.958519			0.479259	−	0.877673i	$-0.340905\pi$
$773$	20600.1			0.958519			0.479259	+	0.877673i	$0.340905\pi$
$774$		0			0
$775$			680.094i			0.0315222i
$776$		0			0
$777$	8249.33	+	5312.81i	0.380879	+	0.245297i
$778$		0			0
$779$	−958.201	−	553.217i	−0.0440707	−	0.0254442i
$780$		0			0
$781$	0.392929	+	0.680572i	1.80027e−5	+	3.11816e-5i
$782$		0			0
$783$	−11935.5	+	10455.6i	−0.544749	+	0.477205i
$784$		0			0
$785$	6177.51	−	3566.59i	0.280872	−	0.162162i
$786$		0			0
$787$	12253.1	+	7074.35i	0.554990	+	0.320424i	0.751132	−	0.660152i	$-0.229508\pi$
$787$	12253.1	+	7074.35i	0.554990	+	0.320424i	−0.196142	+	0.980575i	$0.562841\pi$
$788$		0			0
$789$	232.766	+	3561.28i	0.0105028	+	0.160691i
$790$		0			0
$791$	22683.8	−	30630.5i	1.01965	−	1.37686i
$792$		0			0
$793$	4790.02			0.214500
$794$		0			0
$795$	−29605.4	+	19773.9i	−1.32075	+	0.882147i
$796$		0			0
$797$	9980.73	−	17287.1i	0.443583	−	0.768308i	−0.554369	−	0.832271i	$-0.687041\pi$
$797$	9980.73	−	17287.1i	0.443583	−	0.768308i	0.997952	+	0.0639626i	$0.0203739\pi$
$798$		0			0
$799$	−6547.96	−	11341.4i	−0.289925	−	0.502165i
$800$		0			0
$801$	−2139.30	−	2790.09i	−0.0943675	−	0.123075i
$802$		0			0
$803$	−0.632729	−	1.09592i	−2.78064e−5	−	4.81621e-5i
$804$		0			0
$805$	−4573.43	−	10529.4i	−0.200239	−	0.461007i
$806$		0			0
$807$	−4149.84	+	8411.18i	−0.181018	+	0.366899i
$808$		0			0
$809$		−	13027.7i		−	0.566169i	−0.959095	−	0.283085i	$-0.908642\pi$
$809$		−	13027.7i		−	0.566169i	0.959095	−	0.283085i	$-0.0913578\pi$
$810$		0			0
$811$			2467.58i			0.106841i	0.998572	+	0.0534207i	$0.0170124\pi$
$811$			2467.58i			0.106841i	−0.998572	+	0.0534207i	$0.982988\pi$
$812$		0			0
$813$	31343.2	+	15463.8i	1.35209	+	0.667086i
$814$		0			0
$815$	−13261.5	+	22969.5i	−0.569974	+	0.987224i
$816$		0			0
$817$	19360.5	−	11177.8i	0.829054	−	0.478654i
$818$		0			0
$819$	−3503.44	+	58.5127i	−0.149475	+	0.00249646i
$820$		0			0
$821$	17302.8	−	9989.80i	0.735534	−	0.424661i	−0.0849092	−	0.996389i	$-0.527060\pi$
$821$	17302.8	−	9989.80i	0.735534	−	0.424661i	0.820443	+	0.571728i	$0.193727\pi$
$822$		0			0
$823$	−20481.8	+	35475.5i	−0.867497	+	1.50255i	−0.00295098	+	0.999996i	$0.500939\pi$
$823$	−20481.8	+	35475.5i	−0.867497	+	1.50255i	−0.864546	+	0.502553i	$0.832394\pi$
$824$		0			0
$825$	−0.228782	+	0.152807i	−9.65476e−6	+	6.44856e-6i
$826$		0			0
$827$			38066.2i			1.60059i	0.599604	+	0.800297i	$0.295325\pi$
$827$			38066.2i			1.60059i	−0.599604	+	0.800297i	$0.704675\pi$
$828$		0			0
$829$		−	5157.09i		−	0.216059i	−0.994148	−	0.108030i	$-0.965546\pi$
$829$		−	5157.09i		−	0.216059i	0.994148	−	0.108030i	$-0.0344542\pi$
$830$		0			0
$831$	−3485.67	+	227.824i	−0.145507	+	0.00951039i
$832$		0			0
$833$	9461.19	+	2192.04i	0.393531	+	0.0911759i
$834$		0			0
$835$	−2545.90	−	4409.62i	−0.105514	−	0.182756i
$836$		0			0
$837$	4359.99	+	1482.68i	0.180052	+	0.0612291i
$838$		0			0
$839$	−12192.2	−	21117.5i	−0.501695	−	0.868960i	−0.999998	−	0.00195781i	$-0.999377\pi$
$839$	−12192.2	−	21117.5i	−0.501695	−	0.868960i	0.498304	−	0.867003i	$-0.333957\pi$
$840$		0			0
$841$	−5798.77	+	10043.8i	−0.237762	+	0.411816i
$842$		0			0
$843$	785.439	+	12017.1i	0.0320901	+	0.490972i
$844$		0			0
$845$	−25928.2			−1.05557
$846$		0			0
$847$	19809.7	+	14670.4i	0.803626	+	0.595135i
$848$		0			0
$849$	39989.6	−	26709.7i	1.61654	−	1.07971i
$850$		0			0
$851$	−4534.08	−	2617.75i	−0.182640	−	0.105447i
$852$		0			0
$853$	−35213.6	+	20330.6i	−1.41347	+	0.816068i	−0.995714	−	0.0924912i	$-0.970517\pi$
$853$	−35213.6	+	20330.6i	−1.41347	+	0.816068i	−0.417757	+	0.908559i	$0.637184\pi$
$854$		0			0
$855$	−2087.16	−	15898.3i	−0.0834846	−	0.635920i
$856$		0			0
$857$	−5424.95	−	9396.29i	−0.216234	−	0.374529i	0.737419	−	0.675435i	$-0.236044\pi$
$857$	−5424.95	−	9396.29i	−0.216234	−	0.374529i	−0.953654	+	0.300906i	$0.902711\pi$
$858$		0			0
$859$	29442.4	+	16998.6i	1.16945	+	0.675184i	0.953551	−	0.301230i	$-0.0973974\pi$
$859$	29442.4	+	16998.6i	1.16945	+	0.675184i	0.215902	+	0.976415i	$0.430731\pi$
$860$		0			0
$861$	1924.65	−	989.870i	0.0761810	−	0.0391808i
$862$		0			0
$863$			21617.2i			0.852675i	0.904564	+	0.426337i	$0.140196\pi$
$863$			21617.2i			0.852675i	−0.904564	+	0.426337i	$0.859804\pi$
$864$		0			0
$865$	21062.9			0.827930
$866$		0			0
$867$	−9452.08	+	19158.1i	−0.370253	+	0.750454i
$868$		0			0
$869$	−1.43793	−	0.830190i	−5.61317e−5	−	3.24077e-5i
$870$		0			0
$871$	3274.27	−	1890.40i	0.127376	−	0.0735406i
$872$		0			0
$873$	−36298.9	−	15051.0i	−1.40725	−	0.583505i
$874$		0			0
$875$	2648.18	−	23162.8i	0.102314	−	0.894908i
$876$		0			0
$877$	7452.42	−	12908.0i	0.286945	−	0.497003i	−0.686134	−	0.727475i	$-0.740694\pi$
$877$	7452.42	−	12908.0i	0.286945	−	0.497003i	0.973079	+	0.230472i	$0.0740271\pi$
$878$		0			0
$879$	−25355.1	−	37961.6i	−0.972932	−	1.45667i
$880$		0			0
$881$	18956.5			0.724928			0.362464	−	0.931998i	$-0.381936\pi$
$881$	18956.5			0.724928			0.362464	+	0.931998i	$0.381936\pi$
$882$		0			0
$883$	−35931.1			−1.36940			−0.684700	−	0.728825i	$-0.740067\pi$
$883$	−35931.1			−1.36940			−0.684700	+	0.728825i	$0.740067\pi$
$884$		0			0
$885$	18233.4	−	1191.74i	0.692551	−	0.0452654i
$886$		0			0
$887$	−19322.4	+	33467.3i	−0.731434	+	1.26688i	0.224837	+	0.974396i	$0.427815\pi$
$887$	−19322.4	+	33467.3i	−0.731434	+	1.26688i	−0.956270	+	0.292484i	$0.905518\pi$
$888$		0			0
$889$	−4358.09	+	38118.7i	−0.164416	+	1.43809i
$890$		0			0
$891$	0.480855	+	1.79983i	1.80800e−5	+	6.76728e-5i
$892$		0			0
$893$	−19706.1	+	11377.3i	−0.738456	+	0.426348i
$894$		0			0
$895$	−45074.2	−	26023.6i	−1.68342	−	0.971924i
$896$		0			0
$897$	1865.63	−	121.938i	0.0694444	−	0.00453891i
$898$		0			0
$899$	−3712.46			−0.137728
$900$		0			0
$901$			16070.8i			0.594224i
$902$		0			0
$903$	−2122.99	+	43677.8i	−0.0782378	+	1.60964i
$904$		0			0
$905$	−13674.0	−	7894.67i	−0.502252	−	0.289975i
$906$		0			0
$907$	−286.156	−	495.636i	−0.0104759	−	0.0181448i	0.860740	−	0.509045i	$-0.170001\pi$
$907$	−286.156	−	495.636i	−0.0104759	−	0.0181448i	−0.871216	+	0.490900i	$0.836668\pi$
$908$		0			0
$909$	4086.99	−	9856.69i	0.149127	−	0.359654i
$910$		0			0
$911$	24634.1	−	14222.5i	0.895901	−	0.517248i	0.0200327	−	0.999799i	$-0.493623\pi$
$911$	24634.1	−	14222.5i	0.895901	−	0.517248i	0.875868	+	0.482551i	$0.160290\pi$
$912$		0			0
$913$	2.50340	+	1.44534i	9.07452e−5	+	5.23918e-5i
$914$		0			0
$915$	−38452.5	−	18971.4i	−1.38929	−	0.685437i
$916$		0			0
$917$	13907.3	+	10299.2i	0.500829	+	0.370895i
$918$		0			0
$919$	20019.4			0.718585			0.359292	−	0.933225i	$-0.383018\pi$
$919$	20019.4			0.718585			0.359292	+	0.933225i	$0.383018\pi$
$920$		0			0
$921$	−2793.67	−	1378.32i	−0.0999506	−	0.0493128i
$922$		0			0
$923$	−1077.42	+	1866.14i	−0.0384221	+	0.0665490i
$924$		0			0
$925$	1056.26	+	1829.49i	0.0375455	+	0.0650306i
$926$		0			0
$927$	−2212.74	−	16854.9i	−0.0783989	−	0.597182i
$928$		0			0
$929$	−15791.3	−	27351.3i	−0.557690	−	0.965948i	−0.997689	−	0.0679494i	$-0.978354\pi$
$929$	−15791.3	−	27351.3i	−0.557690	−	0.965948i	0.439999	−	0.897999i	$-0.354979\pi$
$930$		0			0
$931$	3808.75	−	16439.2i	0.134078	−	0.578704i
$932$		0			0
$933$	−25941.4	−	38839.4i	−0.910272	−	1.36286i
$934$		0			0
$935$			0.873451i			3.05507e-5i
$936$		0			0
$937$			39841.1i			1.38906i	0.719463	+	0.694531i	$0.244388\pi$
$937$			39841.1i			1.38906i	−0.719463	+	0.694531i	$0.755612\pi$
$938$		0			0
$939$	−2779.47	−	42525.4i	−0.0965971	−	1.47792i
$940$		0			0
$941$	−5443.60	+	9428.59i	−0.188583	+	0.326635i	−0.944778	−	0.327711i	$-0.893723\pi$
$941$	−5443.60	+	9428.59i	−0.188583	+	0.326635i	0.756195	+	0.654346i	$0.227056\pi$
$942$		0			0
$943$	−1000.09	+	577.405i	−0.0345361	+	0.0199394i
$944$		0			0
$945$	28356.1	+	13406.0i	0.976108	+	0.461480i
$946$		0			0
$947$	19780.5	−	11420.3i	0.678755	−	0.391879i	−0.120631	−	0.992697i	$-0.538492\pi$
$947$	19780.5	−	11420.3i	0.678755	−	0.391879i	0.799386	+	0.600818i	$0.205158\pi$
$948$		0			0
$949$	1734.95	−	3005.03i	0.0593456	−	0.102790i
$950$		0			0
$951$	2306.65	+	35291.2i	0.0786521	+	1.20336i
$952$		0			0
$953$			51243.3i			1.74180i	0.491462	+	0.870899i	$0.336463\pi$
$953$			51243.3i			1.74180i	−0.491462	+	0.870899i	$0.663537\pi$
$954$		0			0
$955$			48730.1i			1.65117i
$956$		0			0
$957$	−0.834136	−	1.24887i	−2.81753e−5	−	4.21840e-5i
$958$		0			0
$959$	−19770.9	−	45518.3i	−0.665731	−	1.53270i
$960$		0			0
$961$	−14356.8	−	24866.6i	−0.481916	−	0.834703i
$962$		0			0
$963$	11047.9	−	8470.92i	0.369691	−	0.283460i
$964$		0			0
$965$	−26673.5	−	46199.8i	−0.889793	−	1.54117i
$966$		0			0
$967$	−7489.56	+	12972.3i	−0.249067	+	0.431397i	−0.963267	−	0.268544i	$-0.913457\pi$
$967$	−7489.56	+	12972.3i	−0.249067	+	0.431397i	0.714200	+	0.699942i	$0.246791\pi$
$968$		0			0
$969$	−6491.13	−	3202.54i	−0.215196	−	0.106172i
$970$		0			0
$971$	−12705.2			−0.419908			−0.209954	−	0.977711i	$-0.567331\pi$
$971$	−12705.2			−0.419908			−0.209954	+	0.977711i	$0.567331\pi$
$972$		0			0
$973$	10114.6	−	13658.0i	0.333258	−	0.450007i
$974$		0			0
$975$	−676.526	−	333.779i	−0.0222217	−	0.0109636i
$976$		0			0
$977$	−17602.3	−	10162.7i	−0.576405	−	0.332788i	0.183298	−	0.983057i	$-0.441323\pi$
$977$	−17602.3	−	10162.7i	−0.576405	−	0.332788i	−0.759703	+	0.650270i	$0.774656\pi$
$978$		0			0
$979$	0.288185	−	0.166384i	9.40802e−6	−	5.43172e-6i
$980$		0			0
$981$	−13044.6	−	17012.9i	−0.424549	−	0.553700i
$982$		0			0
$983$	−20257.1	−	35086.3i	−0.657274	−	1.13843i	−0.981318	−	0.192390i	$-0.938376\pi$
$983$	−20257.1	−	35086.3i	−0.657274	−	1.13843i	0.324044	−	0.946042i	$-0.394957\pi$
$984$		0			0
$985$	−1585.61	−	915.452i	−0.0512911	−	0.0296129i
$986$		0			0
$987$	2160.90	−	44457.7i	0.0696881	−	1.43374i
$988$		0			0
$989$		−	23333.0i		−	0.750197i
$990$		0			0
$991$	−5083.59			−0.162952			−0.0814761	−	0.996675i	$-0.525963\pi$
$991$	−5083.59			−0.162952			−0.0814761	+	0.996675i	$0.525963\pi$
$992$		0			0
$993$	40188.7	−	2626.75i	1.28434	−	0.0839449i
$994$		0			0
$995$	−19221.5	−	11097.5i	−0.612424	−	0.353583i
$996$		0			0
$997$	15996.3	−	9235.49i	0.508133	−	0.293371i	−0.223933	−	0.974605i	$-0.571890\pi$
$997$	15996.3	−	9235.49i	0.508133	−	0.293371i	0.732066	+	0.681234i	$0.238556\pi$
$998$		0			0
$999$	14031.4	−	2783.03i	0.444377	−	0.0881394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.16	yes	48
3.2	odd	2		756.4.x.a.125.5		48
7.6	odd	2	inner	252.4.x.a.41.9	✓	48
9.2	odd	6	inner	252.4.x.a.209.9	yes	48
9.4	even	3		2268.4.f.a.1133.9		48
9.5	odd	6		2268.4.f.a.1133.40		48
9.7	even	3		756.4.x.a.629.20		48
21.20	even	2		756.4.x.a.125.20		48
63.13	odd	6		2268.4.f.a.1133.39		48
63.20	even	6	inner	252.4.x.a.209.16	yes	48
63.34	odd	6		756.4.x.a.629.5		48
63.41	even	6		2268.4.f.a.1133.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.9	✓	48	7.6	odd	2	inner
252.4.x.a.41.16	yes	48	1.1	even	1	trivial
252.4.x.a.209.9	yes	48	9.2	odd	6	inner
252.4.x.a.209.16	yes	48	63.20	even	6	inner
756.4.x.a.125.5		48	3.2	odd	2
756.4.x.a.125.20		48	21.20	even	2
756.4.x.a.629.5		48	63.34	odd	6
756.4.x.a.629.20		48	9.7	even	3
2268.4.f.a.1133.9		48	9.4	even	3
2268.4.f.a.1133.10		48	63.41	even	6
2268.4.f.a.1133.39		48	63.13	odd	6
2268.4.f.a.1133.40		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)

\(f(q)\)	\(=\)	\(q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +O(q^{10})\)	\(q+(2.29905 - 4.65987i) q^{3} +(6.03570 - 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-16.4287 - 21.4265i) q^{9} +(0.00221312 - 0.00127775i) q^{11} +(6.06841 + 3.50360i) q^{13} +(-34.8386 - 52.1602i) q^{15} -28.3143 q^{17} +49.1973i q^{19} +(-80.9069 - 52.1064i) q^{21} +(44.4689 + 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(-137.615 + 27.2951i) q^{27} +(97.9469 - 56.5497i) q^{29} +(-28.4271 - 16.4124i) q^{31} +(-0.000866054 - 0.0132505i) q^{33} +(-179.663 - 133.052i) q^{35} -101.961 q^{37} +(30.2779 - 20.2230i) q^{39} +(-11.2449 + 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(-323.155 + 42.4243i) q^{45} +(231.260 + 400.554i) q^{47} +(-334.149 - 77.4179i) q^{49} +(-65.0960 + 131.941i) q^{51} -567.586i q^{53} -0.0308484i q^{55} +(229.253 + 113.107i) q^{57} +(-145.654 + 252.280i) q^{59} +(592.003 - 341.793i) q^{61} +(-428.818 + 257.220i) q^{63} +(73.2542 - 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} +(221.874 - 148.193i) q^{69} +307.517i q^{71} -495.192i q^{73} +(-107.429 + 7.02162i) q^{75} +(-0.0188553 - 0.0434103i) q^{77} +(-324.865 - 562.683i) q^{79} +(-189.193 + 704.022i) q^{81} +(565.581 + 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} +(-38.3293 - 586.430i) q^{87} +130.217 q^{89} +(77.2337 - 104.291i) q^{91} +(-141.835 + 94.7337i) q^{93} +(514.315 + 296.940i) q^{95} +(1260.41 - 727.696i) q^{97} +(-0.0637365 - 0.0264277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more