LMFDB - Embedded newform 252.4.x.a.41.2

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			41.2
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +O(q^{10})$	\(q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +(-21.5235 + 12.4266i) q^{11} +(-52.5651 - 30.3485i) q^{13} +(72.7066 - 82.1615i) q^{15} +117.397 q^{17} +104.946i q^{19} +(39.6735 - 87.6756i) q^{21} +(-17.4885 - 10.0970i) q^{23} +(-160.403 - 277.826i) q^{25} +(-115.595 - 79.5029i) q^{27} +(-24.2671 + 14.0106i) q^{29} +(-216.679 - 125.100i) q^{31} +(122.472 - 40.9636i) q^{33} +(-286.729 - 265.891i) q^{35} +18.2279 q^{37} +(236.190 + 209.010i) q^{39} +(153.058 - 265.105i) q^{41} +(74.5402 + 129.107i) q^{43} +(-455.363 + 342.983i) q^{45} +(108.676 + 188.233i) q^{47} +(-309.118 - 148.643i) q^{49} +(-597.755 - 121.683i) q^{51} +116.324i q^{53} -524.754i q^{55} +(108.777 - 534.356i) q^{57} +(-38.3919 + 66.4967i) q^{59} +(493.712 - 285.045i) q^{61} +(-292.883 + 405.298i) q^{63} +(1109.87 - 640.781i) q^{65} +(-33.8430 + 58.6179i) q^{67} +(78.5811 + 69.5382i) q^{69} -796.967i q^{71} +710.481i q^{73} +(528.759 + 1580.87i) q^{75} +(-135.800 - 439.800i) q^{77} +(-40.0640 - 69.3928i) q^{79} +(506.174 + 524.622i) q^{81} +(-57.6203 - 99.8013i) q^{83} +(-1239.37 + 2146.65i) q^{85} +(138.084 - 46.1852i) q^{87} +1055.26 q^{89} +(764.359 - 824.261i) q^{91} +(973.605 + 861.564i) q^{93} +(-1918.98 - 1107.92i) q^{95} +(444.295 - 256.514i) q^{97} +(-666.054 + 81.6319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.09172	−	1.03651i	−0.979903	−	0.199476i
$3$	−5.09172	−	1.03651i	−0.979903	−	0.199476i
$4$		0			0
$5$	−10.5571	+	18.2854i	−0.944252	+	1.63549i	−0.187010	+	0.982358i	$0.559880\pi$
$5$	−10.5571	+	18.2854i	−0.944252	+	1.63549i	−0.757242	+	0.653135i	$0.773454\pi$
$6$		0			0
$7$	−4.11592	+	18.0571i	−0.222239	+	0.974992i
$7$	−4.11592	+	18.0571i	−0.222239	+	0.974992i
$8$		0			0
$9$	24.8513	+	10.5552i	0.920419	+	0.390934i
$10$		0			0
$11$	−21.5235	+	12.4266i	−0.589963	+	0.340615i	−0.765083	−	0.643932i	$-0.777302\pi$
$11$	−21.5235	+	12.4266i	−0.589963	+	0.340615i	0.175120	+	0.984547i	$0.443969\pi$
$12$		0			0
$13$	−52.5651	−	30.3485i	−1.12146	−	0.647473i	−0.179684	−	0.983724i	$-0.557507\pi$
$13$	−52.5651	−	30.3485i	−1.12146	−	0.647473i	−0.941772	+	0.336251i	$0.890841\pi$
$14$		0			0
$15$	72.7066	−	82.1615i	1.25152	−	1.41427i
$16$		0			0
$17$	117.397			1.67489			0.837443	−	0.546525i	$-0.184050\pi$
$17$	117.397			1.67489			0.837443	+	0.546525i	$0.184050\pi$
$18$		0			0
$19$			104.946i			1.26717i	0.773672	+	0.633586i	$0.218418\pi$
$19$			104.946i			1.26717i	−0.773672	+	0.633586i	$0.781582\pi$
$20$		0			0
$21$	39.6735	−	87.6756i	0.412260	−	0.911066i
$22$		0			0
$23$	−17.4885	−	10.0970i	−0.158548	−	0.0915379i	0.418627	−	0.908158i	$-0.362512\pi$
$23$	−17.4885	−	10.0970i	−0.158548	−	0.0915379i	−0.577175	+	0.816621i	$0.695845\pi$
$24$		0			0
$25$	−160.403	−	277.826i	−1.28322	−	2.22261i
$26$		0			0
$27$	−115.595	−	79.5029i	−0.823939	−	0.566679i
$28$		0			0
$29$	−24.2671	+	14.0106i	−0.155390	+	0.0897142i	−0.575679	−	0.817676i	$-0.695262\pi$
$29$	−24.2671	+	14.0106i	−0.155390	+	0.0897142i	0.420289	+	0.907390i	$0.361929\pi$
$30$		0			0
$31$	−216.679	−	125.100i	−1.25538	−	0.724794i	−0.283207	−	0.959059i	$-0.591398\pi$
$31$	−216.679	−	125.100i	−1.25538	−	0.724794i	−0.972173	+	0.234265i	$0.924732\pi$
$32$		0			0
$33$	122.472	−	40.9636i	0.646051	−	0.216086i
$34$		0			0
$35$	−286.729	−	265.891i	−1.38474	−	1.28411i
$36$		0			0
$37$	18.2279			0.0809904			0.0404952	−	0.999180i	$-0.487106\pi$
$37$	18.2279			0.0809904			0.0404952	+	0.999180i	$0.487106\pi$
$38$		0			0
$39$	236.190	+	209.010i	0.969763	+	0.858164i
$40$		0			0
$41$	153.058	−	265.105i	0.583016	−	1.00981i	−0.412103	−	0.911137i	$-0.635206\pi$
$41$	153.058	−	265.105i	0.583016	−	1.00981i	0.995120	−	0.0986769i	$-0.0314610\pi$
$42$		0			0
$43$	74.5402	+	129.107i	0.264355	+	0.457877i	0.967395	−	0.253274i	$-0.0815075\pi$
$43$	74.5402	+	129.107i	0.264355	+	0.457877i	−0.703039	+	0.711151i	$0.748174\pi$
$44$		0			0
$45$	−455.363	+	342.983i	−1.50848	+	1.13620i
$46$		0			0
$47$	108.676	+	188.233i	0.337278	+	0.584182i	0.983920	−	0.178611i	$-0.0571605\pi$
$47$	108.676	+	188.233i	0.337278	+	0.584182i	−0.646642	+	0.762794i	$0.723827\pi$
$48$		0			0
$49$	−309.118	−	148.643i	−0.901220	−	0.433362i
$50$		0			0
$51$	−597.755	−	121.683i	−1.64122	−	0.334099i
$52$		0			0
$53$			116.324i			0.301479i	0.988574	+	0.150739i	$0.0481655\pi$
$53$			116.324i			0.301479i	−0.988574	+	0.150739i	$0.951835\pi$
$54$		0			0
$55$		−	524.754i		−	1.28651i
$56$		0			0
$57$	108.777	−	534.356i	0.252770	−	1.24171i
$58$		0			0
$59$	−38.3919	+	66.4967i	−0.0847153	+	0.146731i	−0.905270	−	0.424837i	$-0.860331\pi$
$59$	−38.3919	+	66.4967i	−0.0847153	+	0.146731i	0.820555	+	0.571568i	$0.193665\pi$
$60$		0			0
$61$	493.712	−	285.045i	1.03629	−	0.598300i	0.117506	−	0.993072i	$-0.462510\pi$
$61$	493.712	−	285.045i	1.03629	−	0.598300i	0.918779	+	0.394773i	$0.129177\pi$
$62$		0			0
$63$	−292.883	+	405.298i	−0.585711	+	0.810520i
$64$		0			0
$65$	1109.87	−	640.781i	2.11787	−	1.22276i
$66$		0			0
$67$	−33.8430	+	58.6179i	−0.0617102	+	0.106885i	−0.895230	−	0.445604i	$-0.852989\pi$
$67$	−33.8430	+	58.6179i	−0.0617102	+	0.106885i	0.833520	+	0.552490i	$0.186322\pi$
$68$		0			0
$69$	78.5811	+	69.5382i	0.137102	+	0.121325i
$70$		0			0
$71$		−	796.967i		−	1.33215i	−0.745886	−	0.666074i	$-0.767973\pi$
$71$		−	796.967i		−	1.33215i	0.745886	−	0.666074i	$-0.232027\pi$
$72$		0			0
$73$			710.481i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$73$			710.481i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$74$		0			0
$75$	528.759	+	1580.87i	0.814077	+	2.43391i
$76$		0			0
$77$	−135.800	−	439.800i	−0.200984	−	0.650907i
$78$		0			0
$79$	−40.0640	−	69.3928i	−0.0570576	−	0.0988266i	0.836086	−	0.548599i	$-0.184839\pi$
$79$	−40.0640	−	69.3928i	−0.0570576	−	0.0988266i	−0.893143	+	0.449772i	$0.851505\pi$
$80$		0			0
$81$	506.174	+	524.622i	0.694341	+	0.719646i
$82$		0			0
$83$	−57.6203	−	99.8013i	−0.0762006	−	0.131983i	0.825407	−	0.564538i	$-0.190946\pi$
$83$	−57.6203	−	99.8013i	−0.0762006	−	0.131983i	−0.901608	+	0.432555i	$0.857612\pi$
$84$		0			0
$85$	−1239.37	+	2146.65i	−1.58151	+	2.73926i
$86$		0			0
$87$	138.084	−	46.1852i	0.170162	−	0.0569147i
$88$		0			0
$89$	1055.26			1.25682			0.628409	−	0.777883i	$-0.283706\pi$
$89$	1055.26			1.25682			0.628409	+	0.777883i	$0.283706\pi$
$90$		0			0
$91$	764.359	−	824.261i	0.880512	−	0.949517i
$92$		0			0
$93$	973.605	+	861.564i	1.08557	+	0.960646i
$94$		0			0
$95$	−1918.98	−	1107.92i	−2.07245	−	1.19653i
$96$		0			0
$97$	444.295	−	256.514i	0.465065	−	0.268505i	−0.249106	−	0.968476i	$-0.580137\pi$
$97$	444.295	−	256.514i	0.465065	−	0.268505i	0.714172	+	0.699971i	$0.246804\pi$
$98$		0			0
$99$	−666.054	+	81.6319i	−0.676171	+	0.0828719i
$100$		0			0
$101$	−83.3542	−	144.374i	−0.0821193	−	0.142235i	0.822041	−	0.569429i	$-0.192836\pi$
$101$	−83.3542	−	144.374i	−0.0821193	−	0.142235i	−0.904160	+	0.427194i	$0.859502\pi$
$102$		0			0
$103$	−1304.16	−	752.955i	−1.24760	−	0.720300i	−0.276967	−	0.960879i	$-0.589329\pi$
$103$	−1304.16	−	752.955i	−1.24760	−	0.720300i	−0.970629	+	0.240579i	$0.922663\pi$
$104$		0			0
$105$	1184.35	+	1651.04i	1.10076	+	1.53452i
$106$		0			0
$107$			776.966i			0.701983i	0.936379	+	0.350991i	$0.114155\pi$
$107$			776.966i			0.701983i	−0.936379	+	0.350991i	$0.885845\pi$
$108$		0			0
$109$	−562.383			−0.494189			−0.247094	−	0.968991i	$-0.579476\pi$
$109$	−562.383			−0.494189			−0.247094	+	0.968991i	$0.579476\pi$
$110$		0			0
$111$	−92.8114	−	18.8934i	−0.0793628	−	0.0161557i
$112$		0			0
$113$	1648.89	+	951.987i	1.37270	+	0.792526i	0.991267	−	0.131872i	$-0.0420989\pi$
$113$	1648.89	+	951.987i	1.37270	+	0.792526i	0.381429	+	0.924398i	$0.375432\pi$
$114$		0			0
$115$	369.255	−	213.189i	0.299419	−	0.172870i
$116$		0			0
$117$	−985.976	−	1309.04i	−0.779090	−	1.03436i
$118$		0			0
$119$	−483.198	+	2119.86i	−0.372225	+	1.63300i
$120$		0			0
$121$	−356.658	+	617.750i	−0.267963	+	0.464125i
$122$		0			0
$123$	−1054.11	+	1191.19i	−0.772733	+	0.873222i
$124$		0			0
$125$	4134.27			2.95824
$126$		0			0
$127$	−2470.46			−1.72612			−0.863062	−	0.505098i	$-0.831456\pi$
$127$	−2470.46			−1.72612			−0.863062	+	0.505098i	$0.831456\pi$
$128$		0			0
$129$	−245.717	−	734.641i	−0.167707	−	0.501407i
$130$		0			0
$131$	199.978	−	346.373i	0.133375	−	0.231013i	−0.791600	−	0.611039i	$-0.790752\pi$
$131$	199.978	−	346.373i	0.133375	−	0.231013i	0.924976	+	0.380026i	$0.124085\pi$
$132$		0			0
$133$	−1895.02	−	431.950i	−1.23548	−	0.281615i
$134$		0			0
$135$	2674.09	−	1274.39i	1.70481	−	0.812458i
$136$		0			0
$137$	−2065.15	+	1192.31i	−1.28787	+	0.743550i	−0.978273	−	0.207320i	$-0.933526\pi$
$137$	−2065.15	+	1192.31i	−1.28787	+	0.743550i	−0.309592	+	0.950869i	$0.600193\pi$
$138$		0			0
$139$	570.066	+	329.128i	0.347859	+	0.200836i	0.663742	−	0.747962i	$-0.268967\pi$
$139$	570.066	+	329.128i	0.347859	+	0.200836i	−0.315883	+	0.948798i	$0.602301\pi$
$140$		0			0
$141$	−358.245	−	1071.07i	−0.213969	−	0.639721i
$142$		0			0
$143$	1508.52			0.882156
$144$		0			0
$145$		−	591.645i		−	0.338851i
$146$		0			0
$147$	1419.88	+	1077.25i	0.796662	+	0.604425i
$148$		0			0
$149$	−1116.26	−	644.476i	−0.613745	−	0.354346i	0.160685	−	0.987006i	$-0.448630\pi$
$149$	−1116.26	−	644.476i	−0.613745	−	0.354346i	−0.774430	+	0.632660i	$0.781963\pi$
$150$		0			0
$151$	−98.0311	−	169.795i	−0.0528322	−	0.0915080i	0.838400	−	0.545056i	$-0.183492\pi$
$151$	−98.0311	−	169.795i	−0.0528322	−	0.0915080i	−0.891232	+	0.453548i	$0.850158\pi$
$152$		0			0
$153$	2917.48	+	1239.16i	1.54160	+	0.654770i
$154$		0			0
$155$	4575.00	−	2641.38i	2.37079	−	1.36878i
$156$		0			0
$157$	−2865.72	−	1654.52i	−1.45675	−	0.841053i	−0.457897	−	0.889005i	$-0.651397\pi$
$157$	−2865.72	−	1654.52i	−1.45675	−	0.841053i	−0.998850	+	0.0479519i	$0.984731\pi$
$158$		0			0
$159$	120.571	−	592.292i	0.0601378	−	0.295420i
$160$		0			0
$161$	254.304	−	274.234i	0.124484	−	0.134240i
$162$		0			0
$163$	−1864.65			−0.896018			−0.448009	−	0.894029i	$-0.647867\pi$
$163$	−1864.65			−0.896018			−0.448009	+	0.894029i	$0.647867\pi$
$164$		0			0
$165$	−543.912	+	2671.90i	−0.256627	+	1.26065i
$166$		0			0
$167$	−1863.24	+	3227.22i	−0.863363	+	1.49539i	0.00530083	+	0.999986i	$0.498313\pi$
$167$	−1863.24	+	3227.22i	−0.863363	+	1.49539i	−0.868664	+	0.495402i	$0.835021\pi$
$168$		0			0
$169$	743.558	+	1287.88i	0.338443	+	0.586200i
$170$		0			0
$171$	−1107.73	+	2608.04i	−0.495381	+	1.16633i
$172$		0			0
$173$	−1798.60	−	3115.26i	−0.790432	−	1.36907i	−0.925700	−	0.378259i	$-0.876523\pi$
$173$	−1798.60	−	3115.26i	−0.790432	−	1.36907i	0.135268	−	0.990809i	$-0.456810\pi$
$174$		0			0
$175$	5676.94	−	1752.90i	2.45221	−	0.757183i
$176$		0			0
$177$	264.405	−	298.790i	0.112282	−	0.126884i
$178$		0			0
$179$		−	598.233i		−	0.249799i	−0.992169	−	0.124899i	$-0.960139\pi$
$179$		−	598.233i		−	0.249799i	0.992169	−	0.124899i	$-0.0398608\pi$
$180$		0			0
$181$		−	1669.69i		−	0.685673i	−0.939395	−	0.342837i	$-0.888612\pi$
$181$		−	1669.69i		−	0.685673i	0.939395	−	0.342837i	$-0.111388\pi$
$182$		0			0
$183$	−2809.30	+	939.634i	−1.13481	+	0.379561i
$184$		0			0
$185$	−192.433	+	333.304i	−0.0764754	+	0.132459i
$186$		0			0
$187$	−2526.81	+	1458.85i	−0.988120	+	0.570491i
$188$		0			0
$189$	1911.37	−	1760.09i	0.735619	−	0.677396i
$190$		0			0
$191$	2927.86	−	1690.40i	1.10918	−	0.640383i	0.170560	−	0.985347i	$-0.445442\pi$
$191$	2927.86	−	1690.40i	1.10918	−	0.640383i	0.938616	+	0.344964i	$0.112109\pi$
$192$		0			0
$193$	476.298	−	824.972i	0.177641	−	0.307683i	−0.763431	−	0.645889i	$-0.776487\pi$
$193$	476.298	−	824.972i	0.177641	−	0.307683i	0.941072	+	0.338206i	$0.109820\pi$
$194$		0			0
$195$	−6315.30	+	2112.30i	−2.31922	+	0.775716i
$196$		0			0
$197$			2192.96i			0.793106i	0.918012	+	0.396553i	$0.129794\pi$
$197$			2192.96i			0.793106i	−0.918012	+	0.396553i	$0.870206\pi$
$198$		0			0
$199$		−	1581.79i		−	0.563469i	−0.959492	−	0.281735i	$-0.909090\pi$
$199$		−	1581.79i		−	0.563469i	0.959492	−	0.281735i	$-0.0909098\pi$
$200$		0			0
$201$	233.077	−	263.387i	0.0817911	−	0.0924275i
$202$		0			0
$203$	−153.110	−	495.861i	−0.0529370	−	0.171442i
$204$		0			0
$205$	3231.69	+	5597.45i	1.10103	+	1.90704i
$206$		0			0
$207$	−328.037	−	435.519i	−0.110145	−	0.146235i
$208$		0			0
$209$	−1304.12	−	2258.81i	−0.431618	−	0.747584i
$210$		0			0
$211$	−1547.26	+	2679.93i	−0.504823	+	0.874379i	0.495161	+	0.868801i	$0.335109\pi$
$211$	−1547.26	+	2679.93i	−0.504823	+	0.874379i	−0.999984	+	0.00557832i	$0.998224\pi$
$212$		0			0
$213$	−826.062	+	4057.93i	−0.265732	+	1.30538i
$214$		0			0
$215$	−3147.70			−0.998472
$216$		0			0
$217$	3150.78	−	3397.70i	0.985663	−	1.06291i
$218$		0			0
$219$	736.419	−	3617.57i	0.227226	−	1.11622i
$220$		0			0
$221$	−6171.00	−	3562.83i	−1.87831	−	1.08444i
$222$		0			0
$223$	−1320.52	+	762.403i	−0.396541	+	0.228943i	−0.684990	−	0.728552i	$-0.740194\pi$
$223$	−1320.52	+	762.403i	−0.396541	+	0.228943i	0.288450	+	0.957495i	$0.406860\pi$
$224$		0			0
$225$	−1053.71	−	8597.43i	−0.312209	−	2.54739i
$226$		0			0
$227$	−836.909	−	1449.57i	−0.244703	−	0.423838i	0.717345	−	0.696718i	$-0.245357\pi$
$227$	−836.909	−	1449.57i	−0.244703	−	0.423838i	−0.962048	+	0.272880i	$0.912024\pi$
$228$		0			0
$229$	2751.35	+	1588.49i	0.793949	+	0.458387i	0.841351	−	0.540489i	$-0.181761\pi$
$229$	2751.35	+	1588.49i	0.793949	+	0.458387i	−0.0474019	+	0.998876i	$0.515094\pi$
$230$		0			0
$231$	235.598	+	2380.10i	0.0671049	+	0.677917i
$232$		0			0
$233$		−	3225.60i		−	0.906936i	−0.891272	−	0.453468i	$-0.850187\pi$
$233$		−	3225.60i		−	0.906936i	0.891272	−	0.453468i	$-0.149813\pi$
$234$		0			0
$235$	−4589.21			−1.27390
$236$		0			0
$237$	132.068	+	394.856i	0.0361973	+	0.108222i
$238$		0			0
$239$	−1535.18	−	886.337i	−0.415492	−	0.239884i	0.277655	−	0.960681i	$-0.410443\pi$
$239$	−1535.18	−	886.337i	−0.415492	−	0.239884i	−0.693147	+	0.720797i	$0.743776\pi$
$240$		0			0
$241$	3202.47	−	1848.95i	0.855972	−	0.494196i	−0.00668945	−	0.999978i	$-0.502129\pi$
$241$	3202.47	−	1848.95i	0.855972	−	0.494196i	0.862661	+	0.505782i	$0.168796\pi$
$242$		0			0
$243$	−2033.53	−	3195.89i	−0.536834	−	0.843688i
$244$		0			0
$245$	5981.38	−	4083.11i	1.55974	−	1.06473i
$246$		0			0
$247$	3184.95	−	5516.49i	0.820460	−	1.42108i
$248$		0			0
$249$	189.942	+	567.885i	0.0483417	+	0.144531i
$250$		0			0
$251$	−2501.61			−0.629084			−0.314542	−	0.949244i	$-0.601851\pi$
$251$	−2501.61			−0.629084			−0.314542	+	0.949244i	$0.601851\pi$
$252$		0			0
$253$	501.887			0.124717
$254$		0			0
$255$	8535.56	−	9645.55i	2.09615	−	2.36874i
$256$		0			0
$257$	472.215	−	817.900i	0.114615	−	0.198518i	−0.803011	−	0.595964i	$-0.796770\pi$
$257$	472.215	−	817.900i	0.114615	−	0.198518i	0.917626	+	0.397446i	$0.130103\pi$
$258$		0			0
$259$	−75.0246	+	329.143i	−0.0179992	+	0.0789651i
$260$		0			0
$261$	−750.956	+	92.0376i	−0.178096	+	0.0218275i
$262$		0			0
$263$	−4896.74	+	2827.13i	−1.14808	+	0.662846i	−0.948420	−	0.317018i	$-0.897318\pi$
$263$	−4896.74	+	2827.13i	−1.14808	+	0.662846i	−0.199664	+	0.979864i	$0.563985\pi$
$264$		0			0
$265$	−2127.03	−	1228.04i	−0.493067	−	0.284672i
$266$		0			0
$267$	−5373.07	−	1093.78i	−1.23156	−	0.250705i
$268$		0			0
$269$	−4010.37			−0.908983			−0.454491	−	0.890751i	$-0.650179\pi$
$269$	−4010.37			−0.908983			−0.454491	+	0.890751i	$0.650179\pi$
$270$		0			0
$271$			3596.81i			0.806239i	0.915147	+	0.403120i	$0.132074\pi$
$271$			3596.81i			0.806239i	−0.915147	+	0.403120i	$0.867926\pi$
$272$		0			0
$273$	−4746.26	+	3404.65i	−1.05222	+	0.754794i
$274$		0			0
$275$	6904.88	+	3986.53i	1.51411	+	0.874171i
$276$		0			0
$277$	−3175.77	−	5500.59i	−0.688856	−	1.19313i	−0.972208	−	0.234118i	$-0.924780\pi$
$277$	−3175.77	−	5500.59i	−0.688856	−	1.19313i	0.283352	−	0.959016i	$-0.408554\pi$
$278$		0			0
$279$	−4064.31	−	5396.00i	−0.872128	−	1.15788i
$280$		0			0
$281$	−1591.00	+	918.563i	−0.337761	+	0.195007i	−0.659282	−	0.751896i	$-0.729140\pi$
$281$	−1591.00	+	918.563i	−0.337761	+	0.195007i	0.321520	+	0.946903i	$0.395806\pi$
$282$		0			0
$283$	2653.87	+	1532.21i	0.557442	+	0.321839i	0.752118	−	0.659028i	$-0.229032\pi$
$283$	2653.87	+	1532.21i	0.557442	+	0.321839i	−0.194676	+	0.980868i	$0.562366\pi$
$284$		0			0
$285$	8622.53	+	7630.26i	1.79212	+	1.58589i
$286$		0			0
$287$	4157.05	+	3854.94i	0.854992	+	0.792856i
$288$		0			0
$289$	8869.15			1.80524
$290$		0			0
$291$	−2528.11	+	845.582i	−0.509279	+	0.170340i
$292$		0			0
$293$	−3473.03	+	6015.47i	−0.692481	+	1.19941i	0.278542	+	0.960424i	$0.410149\pi$
$293$	−3473.03	+	6015.47i	−0.692481	+	1.19941i	−0.971023	+	0.238988i	$0.923184\pi$
$294$		0			0
$295$	−810.611	−	1404.02i	−0.159985	−	0.277102i
$296$		0			0
$297$	3475.97	+	274.723i	0.679112	+	0.0536735i
$298$		0			0
$299$	612.857	+	1061.50i	0.118537	+	0.205311i
$300$		0			0
$301$	−2638.11	+	814.585i	−0.505176	+	0.155986i
$302$		0			0
$303$	274.772	+	821.508i	0.0520965	+	0.155757i
$304$		0			0
$305$			12036.9i			2.25978i
$306$		0			0
$307$			2168.45i			0.403128i	0.979475	+	0.201564i	$0.0646023\pi$
$307$			2168.45i			0.403128i	−0.979475	+	0.201564i	$0.935398\pi$
$308$		0			0
$309$	5859.96	+	5185.61i	1.07884	+	0.954689i
$310$		0			0
$311$	142.507	−	246.830i	0.0259834	−	0.0450046i	−0.852741	−	0.522333i	$-0.825062\pi$
$311$	142.507	−	246.830i	0.0259834	−	0.0450046i	0.878725	+	0.477329i	$0.158395\pi$
$312$		0			0
$313$	−9429.66	+	5444.22i	−1.70286	+	0.983148i	−0.760025	+	0.649894i	$0.774813\pi$
$313$	−9429.66	+	5444.22i	−1.70286	+	0.983148i	−0.942837	+	0.333253i	$0.891854\pi$
$314$		0			0
$315$	−4319.04	−	9634.23i	−0.772541	−	1.72326i
$316$		0			0
$317$	598.240	−	345.394i	0.105995	−	0.0611964i	−0.446065	−	0.895000i	$-0.647175\pi$
$317$	598.240	−	345.394i	0.105995	−	0.0611964i	0.552060	+	0.833804i	$0.313842\pi$
$318$		0			0
$319$	348.210	−	603.117i	0.0611160	−	0.105856i
$320$		0			0
$321$	805.332	−	3956.10i	0.140029	−	0.687875i
$322$		0			0
$323$			12320.4i			2.12237i
$324$		0			0
$325$			19471.9i			3.32341i
$326$		0			0
$327$	2863.50	+	582.915i	0.484257	+	0.0985788i
$328$		0			0
$329$	−3846.24	+	1187.63i	−0.644529	+	0.199015i
$330$		0			0
$331$	−4246.17	−	7354.58i	−0.705108	−	1.22128i	−0.966653	−	0.256091i	$-0.917565\pi$
$331$	−4246.17	−	7354.58i	−0.705108	−	1.22128i	0.261545	−	0.965191i	$-0.415768\pi$
$332$		0			0
$333$	452.987	+	192.399i	0.0745451	+	0.0316619i
$334$		0			0
$335$	−714.566	−	1237.66i	−0.116540	−	0.201853i
$336$		0			0
$337$	1799.53	−	3116.88i	0.290881	−	0.503820i	−0.683138	−	0.730290i	$-0.739385\pi$
$337$	1799.53	−	3116.88i	0.290881	−	0.503820i	0.974018	+	0.226470i	$0.0727184\pi$
$338$		0			0
$339$	−7408.95	−	6556.35i	−1.18702	−	1.05042i
$340$		0			0
$341$	6218.28			0.987503
$342$		0			0
$343$	3956.38	−	4969.98i	0.622811	−	0.782372i
$344$		0			0
$345$	−2101.12	+	702.766i	−0.327885	+	0.109669i
$346$		0			0
$347$	5923.82	+	3420.12i	0.916448	+	0.529112i	0.882500	−	0.470312i	$-0.155859\pi$
$347$	5923.82	+	3420.12i	0.916448	+	0.529112i	0.0339480	+	0.999424i	$0.489192\pi$
$348$		0			0
$349$	5589.41	−	3227.04i	0.857289	−	0.494956i	−0.00581419	−	0.999983i	$-0.501851\pi$
$349$	5589.41	−	3227.04i	0.857289	−	0.494956i	0.863104	+	0.505027i	$0.168517\pi$
$350$		0			0
$351$	3663.49	+	7687.22i	0.557102	+	1.16898i
$352$		0			0
$353$	294.916	+	510.809i	0.0444668	+	0.0770188i	0.887402	−	0.460996i	$-0.152508\pi$
$353$	294.916	+	510.809i	0.0444668	+	0.0770188i	−0.842935	+	0.538015i	$0.819174\pi$
$354$		0			0
$355$	14572.8	+	8413.62i	2.17872	+	1.25788i
$356$		0			0
$357$	4657.56	−	10292.9i	0.690488	−	1.52593i
$358$		0			0
$359$			8812.02i			1.29549i	0.761857	+	0.647745i	$0.224288\pi$
$359$			8812.02i			1.29549i	−0.761857	+	0.647745i	$0.775712\pi$
$360$		0			0
$361$	−4154.66			−0.605724
$362$		0			0
$363$	2456.31	−	2775.73i	0.355159	−	0.401345i
$364$		0			0
$365$	−12991.4	−	7500.59i	−1.86302	−	1.07561i
$366$		0			0
$367$	9716.89	−	5610.05i	1.38206	−	0.797935i	0.389661	−	0.920958i	$-0.372592\pi$
$367$	9716.89	−	5610.05i	1.38206	−	0.797935i	0.992404	+	0.123023i	$0.0392589\pi$
$368$		0			0
$369$	6601.93	−	4972.63i	0.931390	−	0.701531i
$370$		0			0
$371$	−2100.48	−	478.782i	−0.293940	−	0.0670003i
$372$		0			0
$373$	−403.305	+	698.546i	−0.0559849	+	0.0969687i	−0.892660	−	0.450731i	$-0.851163\pi$
$373$	−403.305	+	698.546i	−0.0559849	+	0.0969687i	0.836675	+	0.547700i	$0.184497\pi$
$374$		0			0
$375$	−21050.6	−	4285.21i	−2.89879	−	0.590099i
$376$		0			0
$377$	1700.81			0.232350
$378$		0			0
$379$	7667.10			1.03914			0.519568	−	0.854429i	$-0.326093\pi$
$379$	7667.10			1.03914			0.519568	+	0.854429i	$0.326093\pi$
$380$		0			0
$381$	12578.9	+	2560.65i	1.69143	+	0.344320i
$382$		0			0
$383$	−5599.27	+	9698.23i	−0.747022	+	1.29388i	0.202222	+	0.979340i	$0.435184\pi$
$383$	−5599.27	+	9698.23i	−0.747022	+	1.29388i	−0.949244	+	0.314541i	$0.898149\pi$
$384$		0			0
$385$	9475.54	+	2159.85i	1.25433	+	0.285912i
$386$		0			0
$387$	489.663	+	3995.28i	0.0643178	+	0.524784i
$388$		0			0
$389$	1300.72	−	750.970i	0.169535	−	0.0978810i	−0.412832	−	0.910807i	$-0.635460\pi$
$389$	1300.72	−	750.970i	0.169535	−	0.0978810i	0.582366	+	0.812926i	$0.302127\pi$
$390$		0			0
$391$	−2053.11	−	1185.36i	−0.265550	−	0.153315i
$392$		0			0
$393$	−1377.25	+	1556.35i	−0.176777	+	0.199765i
$394$		0			0
$395$	1691.83			0.215507
$396$		0			0
$397$		−	1509.70i		−	0.190856i	−0.995436	−	0.0954280i	$-0.969578\pi$
$397$		−	1509.70i		−	0.190856i	0.995436	−	0.0954280i	$-0.0304220\pi$
$398$		0			0
$399$	9201.21	+	4163.57i	1.15448	+	0.522404i
$400$		0			0
$401$	−780.767	−	450.776i	−0.0972311	−	0.0561364i	0.450596	−	0.892728i	$-0.351212\pi$
$401$	−780.767	−	450.776i	−0.0972311	−	0.0561364i	−0.547827	+	0.836592i	$0.684545\pi$
$402$		0			0
$403$	7593.18	+	13151.8i	0.938569	+	1.62565i
$404$		0			0
$405$	−14936.6	+	3717.12i	−1.83261	+	0.456062i
$406$		0			0
$407$	−392.329	+	226.511i	−0.0477813	+	0.0275866i
$408$		0			0
$409$	−13891.4	−	8020.20i	−1.67943	−	0.969617i	−0.962027	−	0.272955i	$-0.911999\pi$
$409$	−13891.4	−	8020.20i	−1.67943	−	0.969617i	−0.717399	−	0.696662i	$-0.754668\pi$
$410$		0			0
$411$	11751.0	−	3930.39i	1.41030	−	0.471708i
$412$		0			0
$413$	−1042.72	−	966.942i	−0.124235	−	0.115206i
$414$		0			0
$415$	2433.20			0.287810
$416$		0			0
$417$	−2561.48	−	2266.71i	−0.300806	−	0.266190i
$418$		0			0
$419$	424.053	−	734.482i	0.0494424	−	0.0856367i	−0.840245	−	0.542207i	$-0.817589\pi$
$419$	424.053	−	734.482i	0.0494424	−	0.0856367i	0.889687	+	0.456570i	$0.150922\pi$
$420$		0			0
$421$	−3933.58	−	6813.16i	−0.455370	−	0.788725i	0.543339	−	0.839513i	$-0.317160\pi$
$421$	−3933.58	−	6813.16i	−0.455370	−	0.788725i	−0.998709	+	0.0507886i	$0.983827\pi$
$422$		0			0
$423$	713.907	+	5824.93i	0.0820599	+	0.669546i
$424$		0			0
$425$	−18830.9	−	32616.1i	−2.14925	−	3.72262i
$426$		0			0
$427$	3115.01	+	10088.2i	0.353035	+	1.14334i
$428$		0			0
$429$	−7680.94	−	1563.59i	−0.864427	−	0.175969i
$430$		0			0
$431$		−	9164.19i		−	1.02418i	−0.858930	−	0.512092i	$-0.828871\pi$
$431$		−	9164.19i		−	1.02418i	0.858930	−	0.512092i	$-0.171129\pi$
$432$		0			0
$433$			5634.15i			0.625312i	0.949866	+	0.312656i	$0.101219\pi$
$433$			5634.15i			0.625312i	−0.949866	+	0.312656i	$0.898781\pi$
$434$		0			0
$435$	−613.245	+	3012.49i	−0.0675927	+	0.332041i
$436$		0			0
$437$	1059.64	−	1835.35i	0.115994	−	0.200908i
$438$		0			0
$439$	−11030.6	+	6368.50i	−1.19923	+	0.692373i	−0.960383	−	0.278685i	$-0.910101\pi$
$439$	−11030.6	+	6368.50i	−1.19923	+	0.692373i	−0.238843	+	0.971058i	$0.576768\pi$
$440$		0			0
$441$	−6113.03	−	6956.79i	−0.660083	−	0.751192i
$442$		0			0
$443$	1685.37	−	973.047i	0.180754	−	0.104359i	−0.406893	−	0.913476i	$-0.633388\pi$
$443$	1685.37	−	973.047i	0.180754	−	0.104359i	0.587647	+	0.809117i	$0.300054\pi$
$444$		0			0
$445$	−11140.4	+	19295.7i	−1.18675	+	2.05552i
$446$		0			0
$447$	5015.71	+	4438.51i	0.530727	+	0.469652i
$448$		0			0
$449$		−	7602.87i		−	0.799113i	−0.916709	−	0.399556i	$-0.869164\pi$
$449$		−	7602.87i		−	0.799113i	0.916709	−	0.399556i	$-0.130836\pi$
$450$		0			0
$451$			7607.98i			0.794337i
$452$		0			0
$453$	323.154	+	966.159i	0.0335167	+	0.100208i
$454$		0			0
$455$	7002.53	+	22678.4i	0.721503	+	2.33666i
$456$		0			0
$457$	−102.789	−	178.036i	−0.0105214	−	0.0182236i	0.860717	−	0.509084i	$-0.170016\pi$
$457$	−102.789	−	178.036i	−0.0105214	−	0.0182236i	−0.871238	+	0.490861i	$0.836682\pi$
$458$		0			0
$459$	−13570.6	−	9333.43i	−1.38000	−	0.949122i
$460$		0			0
$461$	9165.82	+	15875.7i	0.926019	+	1.60391i	0.789914	+	0.613218i	$0.210125\pi$
$461$	9165.82	+	15875.7i	0.926019	+	1.60391i	0.136105	+	0.990694i	$0.456542\pi$
$462$		0			0
$463$	6817.76	−	11808.7i	0.684338	−	1.18531i	−0.289307	−	0.957236i	$-0.593425\pi$
$463$	6817.76	−	11808.7i	0.684338	−	1.18531i	0.973644	−	0.228071i	$-0.0732419\pi$
$464$		0			0
$465$	−26032.4	+	8707.13i	−2.59618	+	0.868352i
$466$		0			0
$467$	−15609.8			−1.54676			−0.773378	−	0.633946i	$-0.781434\pi$
$467$	−15609.8			−1.54676			−0.773378	+	0.633946i	$0.781434\pi$
$468$		0			0
$469$	−919.174	−	852.374i	−0.0904979	−	0.0839211i
$470$		0			0
$471$	12876.5	+	11394.7i	1.25970	+	1.11474i
$472$		0			0
$473$	−3208.74	−	1852.57i	−0.311920	−	0.180087i
$474$		0			0
$475$	29156.7	−	16833.7i	2.81643	−	1.62607i
$476$		0			0
$477$	−1227.83	+	2890.81i	−0.117858	+	0.277487i
$478$		0			0
$479$	−7412.67	−	12839.1i	−0.707084	−	1.22471i	−0.965934	−	0.258788i	$-0.916677\pi$
$479$	−7412.67	−	12839.1i	−0.707084	−	1.22471i	0.258850	−	0.965918i	$-0.416657\pi$
$480$		0			0
$481$	−958.150	−	553.188i	−0.0908272	−	0.0524391i
$482$		0			0
$483$	−1579.09	+	1132.73i	−0.148760	+	0.106711i
$484$		0			0
$485$			10832.1i			1.01415i
$486$		0			0
$487$	12830.1			1.19381			0.596906	−	0.802311i	$-0.296396\pi$
$487$	12830.1			1.19381			0.596906	+	0.802311i	$0.296396\pi$
$488$		0			0
$489$	9494.30	+	1932.73i	0.878010	+	0.178734i
$490$		0			0
$491$	−7054.53	−	4072.93i	−0.648404	−	0.374356i	0.139441	−	0.990230i	$-0.455470\pi$
$491$	−7054.53	−	4072.93i	−0.648404	−	0.374356i	−0.787844	+	0.615874i	$0.788803\pi$
$492$		0			0
$493$	−2848.90	+	1644.81i	−0.260260	+	0.150261i
$494$		0			0
$495$	5538.90	−	13040.8i	0.502939	−	1.18412i
$496$		0			0
$497$	14390.9	+	3280.25i	1.29883	+	0.296055i
$498$		0			0
$499$	8727.94	−	15117.2i	0.782999	−	1.35619i	−0.147189	−	0.989108i	$-0.547022\pi$
$499$	8727.94	−	15117.2i	0.782999	−	1.35619i	0.930187	−	0.367085i	$-0.119644\pi$
$500$		0			0
$501$	12832.1	−	14500.9i	1.14431	−	1.29311i
$502$		0			0
$503$	13372.9			1.18543			0.592714	−	0.805413i	$-0.298057\pi$
$503$	13372.9			1.18543			0.592714	+	0.805413i	$0.298057\pi$
$504$		0			0
$505$	3519.90			0.310165
$506$		0			0
$507$	−2451.10	−	7328.24i	−0.214708	−	0.641930i
$508$		0			0
$509$	2910.35	−	5040.87i	0.253436	−	0.438964i	−0.711033	−	0.703158i	$-0.751773\pi$
$509$	2910.35	−	5040.87i	0.253436	−	0.438964i	0.964470	+	0.264194i	$0.0851059\pi$
$510$		0			0
$511$	−12829.2	−	2924.28i	−1.11063	−	0.253156i
$512$		0			0
$513$	8343.51	−	12131.3i	0.718080	−	1.04407i
$514$		0			0
$515$	27536.1	−	15898.0i	2.35609	−	1.36029i
$516$		0			0
$517$	−4678.19	−	2700.96i	−0.397963	−	0.229764i
$518$		0			0
$519$	5928.96	+	17726.3i	0.501450	+	1.49923i
$520$		0			0
$521$	6546.17			0.550466			0.275233	−	0.961378i	$-0.411245\pi$
$521$	6546.17			0.550466			0.275233	+	0.961378i	$0.411245\pi$
$522$		0			0
$523$		−	7475.29i		−	0.624994i	−0.949919	−	0.312497i	$-0.898835\pi$
$523$		−	7475.29i		−	0.624994i	0.949919	−	0.312497i	$-0.101165\pi$
$524$		0			0
$525$	−30722.3	+	3041.11i	−2.55397	+	0.252809i
$526$		0			0
$527$	−25437.6	−	14686.4i	−2.10262	−	1.21395i
$528$		0			0
$529$	−5879.60	−	10183.8i	−0.483242	−	0.836999i
$530$		0			0
$531$	−1655.98	+	1247.30i	−0.135336	+	0.101936i
$532$		0			0
$533$	−16091.0	+	9290.16i	−1.30765	+	0.754975i
$534$		0			0
$535$	−14207.1	−	8202.48i	−1.14809	−	0.662849i
$536$		0			0
$537$	−620.073	+	3046.03i	−0.0498289	+	0.244779i
$538$		0			0
$539$	8500.45	−	641.967i	0.679296	−	0.0513014i
$540$		0			0
$541$	−6578.64			−0.522806			−0.261403	−	0.965230i	$-0.584185\pi$
$541$	−6578.64			−0.522806			−0.261403	+	0.965230i	$0.584185\pi$
$542$		0			0
$543$	−1730.64	+	8501.59i	−0.136775	+	0.671893i
$544$		0			0
$545$	5937.11	−	10283.4i	0.466639	−	0.808242i
$546$		0			0
$547$	−2357.36	−	4083.06i	−0.184266	−	0.319158i	0.759063	−	0.651017i	$-0.225657\pi$
$547$	−2357.36	−	4083.06i	−0.184266	−	0.319158i	−0.943329	+	0.331859i	$0.892324\pi$
$548$		0			0
$549$	15278.1	−	1872.49i	1.18771	−	0.145567i
$550$		0			0
$551$	−1470.36	−	2546.74i	−0.113683	−	0.196905i
$552$		0			0
$553$	1417.93	−	437.824i	0.109036	−	0.0336676i
$554$		0			0
$555$	1325.29	−	1497.63i	0.101361	−	0.114542i
$556$		0			0
$557$			5985.03i			0.455286i	0.973745	+	0.227643i	$0.0731018\pi$
$557$			5985.03i			0.455286i	−0.973745	+	0.227643i	$0.926898\pi$
$558$		0			0
$559$		−	9048.73i		−	0.684652i
$560$		0			0
$561$	14377.9	−	4809.02i	1.08206	−	0.361920i
$562$		0			0
$563$	−10574.8	+	18316.0i	−0.791605	+	1.37110i	0.133368	+	0.991067i	$0.457421\pi$
$563$	−10574.8	+	18316.0i	−0.791605	+	1.37110i	−0.924973	+	0.380033i	$0.875913\pi$
$564$		0			0
$565$	−34814.9	+	20100.4i	−2.59234	+	1.49669i
$566$		0			0
$567$	−11556.5	+	6980.74i	−0.855959	+	0.517044i
$568$		0			0
$569$	9600.92	−	5543.09i	0.707366	−	0.408398i	−0.102719	−	0.994710i	$-0.532754\pi$
$569$	9600.92	−	5543.09i	0.707366	−	0.408398i	0.810085	+	0.586312i	$0.199421\pi$
$570$		0			0
$571$	−889.103	+	1539.97i	−0.0651626	+	0.112865i	−0.896766	−	0.442505i	$-0.854090\pi$
$571$	−889.103	+	1539.97i	−0.0651626	+	0.112865i	0.831604	+	0.555370i	$0.187423\pi$
$572$		0			0
$573$	−16660.0	+	5572.31i	−1.21463	+	0.406259i
$574$		0			0
$575$			6478.36i			0.469854i
$576$		0			0
$577$			9282.23i			0.669713i	0.942269	+	0.334856i	$0.108688\pi$
$577$			9282.23i			0.669713i	−0.942269	+	0.334856i	$0.891312\pi$
$578$		0			0
$579$	−3280.27	+	3706.84i	−0.235446	+	0.266064i
$580$		0			0
$581$	2039.28	−	629.682i	0.145617	−	0.0449632i
$582$		0			0
$583$	−1445.52	−	2503.71i	−0.102688	−	0.177861i
$584$		0			0
$585$	34345.2	−	4209.37i	2.42735	−	0.297497i
$586$		0			0
$587$	12177.5	+	21092.1i	0.856253	+	1.48307i	0.875477	+	0.483259i	$0.160547\pi$
$587$	12177.5	+	21092.1i	0.856253	+	1.48307i	−0.0192240	+	0.999815i	$0.506120\pi$
$588$		0			0
$589$	13128.7	−	22739.6i	0.918439	−	1.59078i
$590$		0			0
$591$	2273.02	−	11165.9i	0.158206	−	0.777167i
$592$		0			0
$593$	3634.37			0.251679			0.125840	−	0.992051i	$-0.459838\pi$
$593$	3634.37			0.251679			0.125840	+	0.992051i	$0.459838\pi$
$594$		0			0
$595$	−33661.2	−	31214.9i	−2.31929	−	2.15073i
$596$		0			0
$597$	−1639.54	+	8054.06i	−0.112399	+	0.552145i
$598$		0			0
$599$	16689.7	+	9635.82i	1.13844	+	0.657277i	0.946043	−	0.324041i	$-0.105041\pi$
$599$	16689.7	+	9635.82i	1.13844	+	0.657277i	0.192394	+	0.981318i	$0.438375\pi$
$600$		0			0
$601$	−9993.33	+	5769.65i	−0.678264	+	0.391596i	−0.799201	−	0.601064i	$-0.794744\pi$
$601$	−9993.33	+	5769.65i	−0.678264	+	0.391596i	0.120937	+	0.992660i	$0.461410\pi$
$602$		0			0
$603$	−1459.77	+	1099.51i	−0.0985844	+	0.0742545i
$604$		0			0
$605$	−7530.53	−	13043.3i	−0.506049	−	0.876502i
$606$		0			0
$607$	−3327.05	−	1920.88i	−0.222473	−	0.128445i	0.384622	−	0.923074i	$-0.374332\pi$
$607$	−3327.05	−	1920.88i	−0.222473	−	0.128445i	−0.607095	+	0.794629i	$0.707665\pi$
$608$		0			0
$609$	265.630	+	2683.49i	0.0176747	+	0.178556i
$610$		0			0
$611$		−	13192.6i		−	0.873513i
$612$		0			0
$613$	−26792.1			−1.76529			−0.882644	−	0.470043i	$-0.844238\pi$
$613$	−26792.1			−1.76529			−0.882644	+	0.470043i	$0.844238\pi$
$614$		0			0
$615$	−10653.1	−	31850.3i	−0.698493	−	2.08834i
$616$		0			0
$617$	−2434.46	−	1405.54i	−0.158846	−	0.0917095i	0.418470	−	0.908231i	$-0.362566\pi$
$617$	−2434.46	−	1405.54i	−0.158846	−	0.0917095i	−0.577316	+	0.816521i	$0.695900\pi$
$618$		0			0
$619$	−2964.61	+	1711.62i	−0.192500	+	0.111140i	−0.593152	−	0.805090i	$-0.702117\pi$
$619$	−2964.61	+	1711.62i	−0.192500	+	0.111140i	0.400652	+	0.916230i	$0.368784\pi$
$620$		0			0
$621$	1218.85	+	2557.56i	0.0787614	+	0.165268i
$622$		0			0
$623$	−4343.35	+	19054.9i	−0.279314	+	1.22539i
$624$		0			0
$625$	−23595.4	+	40868.4i	−1.51010	+	2.61558i
$626$		0			0
$627$	4298.97	+	12853.0i	0.273818	+	0.818657i
$628$		0			0
$629$	2139.91			0.135650
$630$		0			0
$631$	−4476.28			−0.282406			−0.141203	−	0.989981i	$-0.545097\pi$
$631$	−4476.28			−0.282406			−0.141203	+	0.989981i	$0.545097\pi$
$632$		0			0
$633$	10656.0	−	12041.7i	0.669095	−	0.756107i
$634$		0			0
$635$	26080.8	−	45173.2i	1.62990	−	2.82306i
$636$		0			0
$637$	11737.7	+	17194.7i	0.730088	+	1.06951i
$638$		0			0
$639$	8412.16	−	19805.7i	0.520782	−	1.22613i
$640$		0			0
$641$	−15150.6	+	8747.20i	−0.933561	+	0.538992i	−0.887936	−	0.459967i	$-0.847861\pi$
$641$	−15150.6	+	8747.20i	−0.933561	+	0.538992i	−0.0456248	+	0.998959i	$0.514528\pi$
$642$		0			0
$643$	4602.79	+	2657.42i	0.282296	+	0.162984i	0.634462	−	0.772954i	$-0.281222\pi$
$643$	4602.79	+	2657.42i	0.282296	+	0.162984i	−0.352166	+	0.935937i	$0.614555\pi$
$644$		0			0
$645$	16027.2	+	3262.62i	0.978406	+	0.199171i
$646$		0			0
$647$	−4660.14			−0.283167			−0.141584	−	0.989926i	$-0.545219\pi$
$647$	−4660.14			−0.283167			−0.141584	+	0.989926i	$0.545219\pi$
$648$		0			0
$649$		−	1908.33i		−	0.115421i
$650$		0			0
$651$	−19564.6	+	14034.4i	−1.17788	+	0.844931i
$652$		0			0
$653$	−16836.5	−	9720.58i	−1.00898	−	0.582536i	−0.0980880	−	0.995178i	$-0.531273\pi$
$653$	−16836.5	−	9720.58i	−1.00898	−	0.582536i	−0.910893	+	0.412642i	$0.864606\pi$
$654$		0			0
$655$	4222.36	+	7313.35i	0.251880	+	0.436269i
$656$		0			0
$657$	−7499.29	+	17656.4i	−0.445320	+	1.04846i
$658$		0			0
$659$	4244.21	−	2450.39i	0.250881	−	0.144846i	−0.369286	−	0.929316i	$-0.620398\pi$
$659$	4244.21	−	2450.39i	0.250881	−	0.144846i	0.620168	+	0.784469i	$0.287065\pi$
$660$		0			0
$661$	6520.45	+	3764.58i	0.383685	+	0.221521i	0.679420	−	0.733749i	$-0.262231\pi$
$661$	6520.45	+	3764.58i	0.383685	+	0.221521i	−0.295735	+	0.955270i	$0.595565\pi$
$662$		0			0
$663$	27728.1	+	24537.2i	1.62424	+	1.43733i
$664$		0			0
$665$	27904.2	−	30091.0i	1.62719	−	1.75471i
$666$		0			0
$667$	565.862			0.0328490
$668$		0			0
$669$	7513.96	−	2513.21i	0.434240	−	0.145241i
$670$		0			0
$671$	−7084.29	+	12270.4i	−0.407580	+	0.705949i
$672$		0			0
$673$	5380.01	+	9318.45i	0.308149	+	0.533729i	0.977957	−	0.208804i	$-0.0669572\pi$
$673$	5380.01	+	9318.45i	0.308149	+	0.533729i	−0.669809	+	0.742534i	$0.733624\pi$
$674$		0			0
$675$	−3546.13	+	44867.9i	−0.202208	+	2.55847i
$676$		0			0
$677$	7477.31	+	12951.1i	0.424485	+	0.735230i	0.996372	−	0.0851025i	$-0.0271218\pi$
$677$	7477.31	+	12951.1i	0.424485	+	0.735230i	−0.571887	+	0.820332i	$0.693788\pi$
$678$		0			0
$679$	2803.21	+	9078.47i	0.158435	+	0.513107i
$680$		0			0
$681$	2758.82	+	8248.27i	0.155240	+	0.464133i
$682$		0			0
$683$		−	28835.1i		−	1.61544i	−0.589566	−	0.807720i	$-0.700701\pi$
$683$		−	28835.1i		−	1.61544i	0.589566	−	0.807720i	$-0.299299\pi$
$684$		0			0
$685$		−	50349.3i		−	2.80839i
$686$		0			0
$687$	−12362.6	−	10940.0i	−0.686556	−	0.607548i
$688$		0			0
$689$	3530.27	−	6114.60i	0.195199	−	0.338095i
$690$		0			0
$691$	−845.405	+	488.095i	−0.0465423	+	0.0268712i	−0.523091	−	0.852277i	$-0.675221\pi$
$691$	−845.405	+	488.095i	−0.0465423	+	0.0268712i	0.476548	+	0.879148i	$0.341888\pi$
$692$		0			0
$693$	1267.39	−	12363.0i	0.0694720	−	0.677679i
$694$		0			0
$695$	−12036.4	+	6949.24i	−0.656933	+	0.379280i
$696$		0			0
$697$	17968.6	−	31122.6i	0.976486	−	1.69132i
$698$		0			0
$699$	−3343.36	+	16423.9i	−0.180912	+	0.888709i
$700$		0			0
$701$		−	6963.25i		−	0.375176i	−0.982248	−	0.187588i	$-0.939933\pi$
$701$		−	6963.25i		−	0.375176i	0.982248	−	0.187588i	$-0.0600669\pi$
$702$		0			0
$703$			1912.94i			0.102629i
$704$		0			0
$705$	23367.0	+	4756.75i	1.24830	+	0.254113i
$706$		0			0
$707$	2950.05	−	910.905i	0.156928	−	0.0484556i
$708$		0			0
$709$	14914.8	+	25833.2i	0.790039	+	1.36839i	0.925942	+	0.377665i	$0.123273\pi$
$709$	14914.8	+	25833.2i	0.790039	+	1.36839i	−0.135903	+	0.990722i	$0.543394\pi$
$710$		0			0
$711$	−263.185	−	2147.39i	−0.0138821	−	0.113268i
$712$		0			0
$713$	2526.27	+	4375.63i	0.132692	+	0.229830i
$714$		0			0
$715$	−15925.5	+	27583.7i	−0.832978	+	1.44276i
$716$		0			0
$717$	6898.02	+	6104.21i	0.359290	+	0.317944i
$718$		0			0
$719$	−14089.4			−0.730803			−0.365402	−	0.930850i	$-0.619068\pi$
$719$	−14089.4			−0.730803			−0.365402	+	0.930850i	$0.619068\pi$
$720$		0			0
$721$	18964.0	−	20450.2i	0.979551	−	1.05632i
$722$		0			0
$723$	−18222.5	+	6094.94i	−0.937349	+	0.313518i
$724$		0			0
$725$	7785.05	+	4494.70i	0.398799	+	0.230247i
$726$		0			0
$727$	16592.3	−	9579.56i	0.846457	−	0.488702i	−0.0129971	−	0.999916i	$-0.504137\pi$
$727$	16592.3	−	9579.56i	0.846457	−	0.488702i	0.859454	+	0.511214i	$0.170804\pi$
$728$		0			0
$729$	7041.59	+	18380.3i	0.357750	+	0.933817i
$730$		0			0
$731$	8750.83	+	15156.9i	0.442765	+	0.766891i
$732$		0			0
$733$	31099.2	+	17955.1i	1.56709	+	0.904757i	0.996507	+	0.0835145i	$0.0266145\pi$
$733$	31099.2	+	17955.1i	1.56709	+	0.904757i	0.570579	+	0.821243i	$0.306719\pi$
$734$		0			0
$735$	−34687.7	+	14590.3i	−1.74078	+	0.732206i
$736$		0			0
$737$		−	1682.22i		−	0.0840778i
$738$		0			0
$739$	15603.3			0.776694			0.388347	−	0.921513i	$-0.373046\pi$
$739$	15603.3			0.776694			0.388347	+	0.921513i	$0.373046\pi$
$740$		0			0
$741$	−21934.8	+	24787.2i	−1.08744	+	1.22886i
$742$		0			0
$743$	9187.85	+	5304.61i	0.453660	+	0.261921i	0.709375	−	0.704831i	$-0.248977\pi$
$743$	9187.85	+	5304.61i	0.453660	+	0.261921i	−0.255715	+	0.966752i	$0.582311\pi$
$744$		0			0
$745$	23569.0	−	13607.5i	1.15906	−	0.669183i
$746$		0			0
$747$	−378.514	−	3088.39i	−0.0185397	−	0.151269i
$748$		0			0
$749$	−14029.8	−	3197.93i	−0.684428	−	0.156008i
$750$		0			0
$751$	−3593.39	+	6223.93i	−0.174600	+	0.302416i	−0.940023	−	0.341112i	$-0.889197\pi$
$751$	−3593.39	+	6223.93i	−0.174600	+	0.302416i	0.765423	+	0.643528i	$0.222530\pi$
$752$		0			0
$753$	12737.5	+	2592.94i	0.616441	+	0.125487i
$754$		0			0
$755$	4139.68			0.199548
$756$		0			0
$757$	−30230.3			−1.45144			−0.725720	−	0.687990i	$-0.758493\pi$
$757$	−30230.3			−1.45144			−0.725720	+	0.687990i	$0.758493\pi$
$758$		0			0
$759$	−2555.47	−	520.209i	−0.122210	−	0.0248780i
$760$		0			0
$761$	−4067.61	+	7045.32i	−0.193759	+	0.335601i	−0.946493	−	0.322724i	$-0.895401\pi$
$761$	−4067.61	+	7045.32i	−0.193759	+	0.335601i	0.752734	+	0.658325i	$0.228735\pi$
$762$		0			0
$763$	2314.73	−	10155.0i	0.109828	−	0.481830i
$764$		0			0
$765$	−53458.4	+	40265.3i	−2.52653	+	1.90300i
$766$		0			0
$767$	4036.15	−	2330.27i	0.190009	−	0.109702i
$768$		0			0
$769$	−19458.9	−	11234.6i	−0.912490	−	0.526826i	−0.0312583	−	0.999511i	$-0.509951\pi$
$769$	−19458.9	−	11234.6i	−0.912490	−	0.526826i	−0.881231	+	0.472685i	$0.843285\pi$
$770$		0			0
$771$	−3252.15	+	3675.07i	−0.151911	+	0.171666i
$772$		0			0
$773$	18079.1			0.841217			0.420609	−	0.907242i	$-0.361817\pi$
$773$	18079.1			0.841217			0.420609	+	0.907242i	$0.361817\pi$
$774$		0			0
$775$			80265.6i			3.72029i
$776$		0			0
$777$	723.164	−	1598.14i	0.0333891	−	0.0737877i
$778$		0			0
$779$	27821.7	+	16062.8i	1.27961	+	0.738782i
$780$		0			0
$781$	9903.60	+	17153.5i	0.453750	+	0.785918i
$782$		0			0
$783$	3919.06	+	309.742i	0.178871	+	0.0141370i
$784$		0			0
$785$	60507.1	−	34933.8i	2.75107	−	1.58833i
$786$		0			0
$787$	−24672.8	−	14244.8i	−1.11752	−	0.645202i	−0.176755	−	0.984255i	$-0.556560\pi$
$787$	−24672.8	−	14244.8i	−1.11752	−	0.645202i	−0.940767	+	0.339053i	$0.889893\pi$
$788$		0			0
$789$	27863.2	−	9319.48i	1.25723	−	0.420510i
$790$		0			0
$791$	−23976.8	+	25855.9i	−1.07777	+	1.16224i
$792$		0			0
$793$	−34602.7			−1.54953
$794$		0			0
$795$	9557.39	+	8457.54i	0.426372	+	0.377306i
$796$		0			0
$797$	1556.36	−	2695.69i	0.0691708	−	0.119807i	−0.829366	−	0.558706i	$-0.811298\pi$
$797$	1556.36	−	2695.69i	0.0691708	−	0.119807i	0.898537	+	0.438899i	$0.144631\pi$
$798$		0			0
$799$	12758.3	+	22098.0i	0.564902	+	0.978438i
$800$		0			0
$801$	26224.5	+	11138.5i	1.15680	+	0.491333i
$802$		0			0
$803$	−8828.88	−	15292.1i	−0.388000	−	0.672036i
$804$		0			0
$805$	2329.76	+	7545.15i	0.102004	+	0.330350i
$806$		0			0
$807$	20419.7	+	4156.78i	0.890715	+	0.181320i
$808$		0			0
$809$			8901.87i			0.386864i	0.981114	+	0.193432i	$0.0619619\pi$
$809$			8901.87i			0.386864i	−0.981114	+	0.193432i	$0.938038\pi$
$810$		0			0
$811$		−	6818.31i		−	0.295220i	−0.989046	−	0.147610i	$-0.952842\pi$
$811$		−	6818.31i		−	0.295220i	0.989046	−	0.147610i	$-0.0471580\pi$
$812$		0			0
$813$	3728.13	−	18314.0i	0.160825	−	0.790036i
$814$		0			0
$815$	19685.3	−	34095.9i	0.846067	−	1.46543i
$816$		0			0
$817$	−13549.3	+	7822.70i	−0.580209	+	0.334984i
$818$		0			0
$819$	27695.6	−	12416.0i	1.18164	−	0.529731i
$820$		0			0
$821$	−14035.7	+	8103.52i	−0.596650	+	0.344476i	−0.767722	−	0.640783i	$-0.778610\pi$
$821$	−14035.7	+	8103.52i	−0.596650	+	0.344476i	0.171073	+	0.985258i	$0.445277\pi$
$822$		0			0
$823$	−3635.33	+	6296.57i	−0.153973	+	0.266689i	−0.932684	−	0.360693i	$-0.882540\pi$
$823$	−3635.33	+	6296.57i	−0.153973	+	0.266689i	0.778712	+	0.627382i	$0.215873\pi$
$824$		0			0
$825$	−31025.7	−	27455.3i	−1.30930	−	1.15863i
$826$		0			0
$827$		−	7040.86i		−	0.296052i	−0.988983	−	0.148026i	$-0.952708\pi$
$827$		−	7040.86i		−	0.296052i	0.988983	−	0.148026i	$-0.0472919\pi$
$828$		0			0
$829$		−	17047.4i		−	0.714212i	−0.934064	−	0.357106i	$-0.883764\pi$
$829$		−	17047.4i		−	0.714212i	0.934064	−	0.357106i	$-0.116236\pi$
$830$		0			0
$831$	10468.7	+	31299.2i	0.437011	+	1.30657i
$832$		0			0
$833$	−36289.7	−	17450.3i	−1.50944	−	0.725832i
$834$		0			0
$835$	−39340.6	−	68139.9i	−1.63046	−	2.82405i
$836$		0			0
$837$	15101.3	+	31687.6i	0.623631	+	1.30858i
$838$		0			0
$839$	6588.67	+	11411.9i	0.271116	+	0.469587i	0.969148	−	0.246480i	$-0.0792740\pi$
$839$	6588.67	+	11411.9i	0.271116	+	0.469587i	−0.698032	+	0.716067i	$0.745941\pi$
$840$		0			0
$841$	−11801.9	+	20441.5i	−0.483903	+	0.838144i
$842$		0			0
$843$	9053.02	−	3027.99i	0.369872	−	0.123712i
$844$		0			0
$845$	−31399.2			−1.27830
$846$		0			0
$847$	−9686.81	−	8982.83i	−0.392967	−	0.364408i
$848$		0			0
$849$	−11924.6	−	10552.4i	−0.482040	−	0.426568i
$850$		0			0
$851$	−318.779	−	184.047i	−0.0128409	−	0.00741369i
$852$		0			0
$853$	−11459.1	+	6615.91i	−0.459967	+	0.265562i	−0.712030	−	0.702149i	$-0.752224\pi$
$853$	−11459.1	+	6615.91i	−0.459967	+	0.265562i	0.252063	+	0.967711i	$0.418891\pi$
$854$		0			0
$855$	−35994.7	−	47788.5i	−1.43976	−	1.91150i
$856$		0			0
$857$	4162.07	+	7208.91i	0.165897	+	0.287342i	0.936973	−	0.349401i	$-0.113615\pi$
$857$	4162.07	+	7208.91i	0.165897	+	0.287342i	−0.771077	+	0.636742i	$0.780282\pi$
$858$		0			0
$859$	−36607.1	−	21135.1i	−1.45404	−	0.839488i	−0.455329	−	0.890323i	$-0.650478\pi$
$859$	−36607.1	−	21135.1i	−1.45404	−	0.839488i	−0.998707	+	0.0508353i	$0.983812\pi$
$860$		0			0
$861$	−17170.9	−	23937.1i	−0.679653	−	0.947473i
$862$		0			0
$863$		−	4503.10i		−	0.177621i	−0.996049	−	0.0888107i	$-0.971693\pi$
$863$		−	4503.10i		−	0.177621i	0.996049	−	0.0888107i	$-0.0283066\pi$
$864$		0			0
$865$	75951.5			2.98547
$866$		0			0
$867$	−45159.2	−	9192.94i	−1.76896	−	0.360102i
$868$		0			0
$869$	1724.64	+	995.719i	0.0673237	+	0.0388693i
$870$		0			0
$871$	3557.93	−	2054.17i	0.138411	−	0.0799114i
$872$		0			0
$873$	13748.9	−	1685.07i	0.533023	−	0.0653276i
$874$		0			0
$875$	−17016.3	+	74653.0i	−0.657437	+	2.88426i
$876$		0			0
$877$	12266.9	−	21246.9i	0.472320	−	0.818082i	−0.527178	−	0.849755i	$-0.676750\pi$
$877$	12266.9	−	21246.9i	0.472320	−	0.818082i	0.999498	+	0.0316724i	$0.0100833\pi$
$878$		0			0
$879$	23918.8	−	27029.3i	0.917818	−	1.03717i
$880$		0			0
$881$	6446.14			0.246511			0.123255	−	0.992375i	$-0.460667\pi$
$881$	6446.14			0.246511			0.123255	+	0.992375i	$0.460667\pi$
$882$		0			0
$883$	13490.2			0.514136			0.257068	−	0.966393i	$-0.417244\pi$
$883$	13490.2			0.514136			0.257068	+	0.966393i	$0.417244\pi$
$884$		0			0
$885$	2672.13	+	7989.09i	0.101495	+	0.303447i
$886$		0			0
$887$	10349.3	−	17925.5i	0.391765	−	0.678556i	−0.600918	−	0.799311i	$-0.705198\pi$
$887$	10349.3	−	17925.5i	0.391765	−	0.678556i	0.992682	+	0.120755i	$0.0385314\pi$
$888$		0			0
$889$	10168.2	−	44609.3i	0.383612	−	1.68296i
$890$		0			0
$891$	−17413.9	−	5001.69i	−0.654758	−	0.188062i
$892$		0			0
$893$	−19754.3	+	11405.1i	−0.740259	+	0.427389i
$894$		0			0
$895$	10938.9	+	6315.58i	0.408544	+	0.235873i
$896$		0			0
$897$	−2020.25	−	6040.10i	−0.0751996	−	0.224830i
$898$		0			0
$899$	7010.92			0.260097
$900$		0			0
$901$			13656.2i			0.504943i
$902$		0			0
$903$	14276.8	−	1413.22i	0.526139	−	0.0520808i
$904$		0			0
$905$	30530.8	+	17627.0i	1.12141	+	0.647449i
$906$		0			0
$907$	−14361.2	−	24874.3i	−0.525750	−	0.910626i	−0.999550	−	0.0299935i	$-0.990451\pi$
$907$	−14361.2	−	24874.3i	−0.525750	−	0.910626i	0.473800	−	0.880633i	$-0.342882\pi$
$908$		0			0
$909$	−547.563	−	4467.70i	−0.0199797	−	0.163019i
$910$		0			0
$911$	−6255.03	+	3611.35i	−0.227485	+	0.131338i	−0.609411	−	0.792854i	$-0.708594\pi$
$911$	−6255.03	+	3611.35i	−0.227485	+	0.131338i	0.381926	+	0.924193i	$0.375261\pi$
$912$		0			0
$913$	2480.38	+	1432.05i	0.0899110	+	0.0519102i
$914$		0			0
$915$	12476.4	−	61288.8i	0.450773	−	2.21437i
$916$		0			0
$917$	5431.39	+	5036.67i	0.195595	+	0.181380i
$918$		0			0
$919$	−9875.41			−0.354472			−0.177236	−	0.984168i	$-0.556716\pi$
$919$	−9875.41			−0.354472			−0.177236	+	0.984168i	$0.556716\pi$
$920$		0			0
$921$	2247.62	−	11041.2i	0.0804143	−	0.395026i
$922$		0			0
$923$	−24186.7	+	41892.6i	−0.862530	+	1.49395i
$924$		0			0
$925$	−2923.81	−	5064.18i	−0.103929	−	0.180010i
$926$		0			0
$927$	−24462.4	−	32477.6i	−0.866721	−	1.15071i
$928$		0			0
$929$	−22240.7	−	38522.0i	−0.785461	−	1.36046i	−0.928723	−	0.370774i	$-0.879092\pi$
$929$	−22240.7	−	38522.0i	−0.785461	−	1.36046i	0.143262	−	0.989685i	$-0.454241\pi$
$930$		0			0
$931$	15599.5	−	32440.7i	0.549145	−	1.14200i
$932$		0			0
$933$	−981.448	+	1109.08i	−0.0344386	+	0.0389171i
$934$		0			0
$935$		−	61604.8i		−	2.15475i
$936$		0			0
$937$		−	1613.46i		−	0.0562532i	−0.999604	−	0.0281266i	$-0.991046\pi$
$937$		−	1613.46i		−	0.0562532i	0.999604	−	0.0281266i	$-0.00895416\pi$
$938$		0			0
$939$	53656.2	−	17946.5i	1.86475	−	0.623709i
$940$		0			0
$941$	−835.528	+	1447.18i	−0.0289452	+	0.0501345i	−0.880135	−	0.474723i	$-0.842548\pi$
$941$	−835.528	+	1447.18i	−0.0289452	+	0.0501345i	0.851190	+	0.524858i	$0.175881\pi$
$942$		0			0
$943$	−5353.53	+	3090.86i	−0.184872	+	0.106736i
$944$		0			0
$945$	12005.4	+	53531.5i	0.413266	+	1.84273i
$946$		0			0
$947$	−31755.5	+	18334.1i	−1.08967	+	0.629121i	−0.933488	−	0.358608i	$-0.883252\pi$
$947$	−31755.5	+	18334.1i	−1.08967	+	0.629121i	−0.156181	+	0.987729i	$0.549918\pi$
$948$		0			0
$949$	21562.0	−	37346.5i	0.737547	−	1.27747i
$950$		0			0
$951$	−3404.08	+	1138.57i	−0.116072	+	0.0388230i
$952$		0			0
$953$			38341.6i			1.30326i	0.758537	+	0.651629i	$0.225914\pi$
$953$			38341.6i			1.30326i	−0.758537	+	0.651629i	$0.774086\pi$
$954$		0			0
$955$			71382.7i			2.41873i
$956$		0			0
$957$	−2398.12	+	2709.98i	−0.0810035	+	0.0915374i
$958$		0			0
$959$	−13029.8	−	42198.1i	−0.438741	−	1.42090i
$960$		0			0
$961$	16404.5	+	28413.4i	0.550653	+	0.953758i
$962$		0			0
$963$	−8201.05	+	19308.6i	−0.274429	+	0.646118i
$964$		0			0
$965$	10056.6	+	17418.5i	0.335475	+	0.581060i
$966$		0			0
$967$	−24342.3	+	42162.0i	−0.809508	+	1.40211i	0.103697	+	0.994609i	$0.466933\pi$
$967$	−24342.3	+	42162.0i	−0.809508	+	1.40211i	−0.913205	+	0.407501i	$0.866400\pi$
$968$		0			0
$969$	12770.2	−	62732.0i	0.423361	−	2.07971i
$970$		0			0
$971$	−41514.9			−1.37207			−0.686033	−	0.727570i	$-0.740650\pi$
$971$	−41514.9			−1.37207			−0.686033	+	0.727570i	$0.740650\pi$
$972$		0			0
$973$	−8289.44	+	8939.08i	−0.273122	+	0.294526i
$974$		0			0
$975$	20182.8	−	99145.7i	0.662941	−	3.25662i
$976$		0			0
$977$	26952.7	+	15561.1i	0.882592	+	0.509565i	0.871512	−	0.490374i	$-0.163140\pi$
$977$	26952.7	+	15561.1i	0.882592	+	0.509565i	0.0110801	+	0.999939i	$0.496473\pi$
$978$		0			0
$979$	−22712.8	+	13113.3i	−0.741476	+	0.428091i
$980$		0			0
$981$	−13976.0	−	5936.08i	−0.454860	−	0.193195i
$982$		0			0
$983$	−13264.6	−	22974.9i	−0.430391	−	0.745460i	0.566516	−	0.824051i	$-0.308291\pi$
$983$	−13264.6	−	22974.9i	−0.430391	−	0.745460i	−0.996907	+	0.0785914i	$0.974958\pi$
$984$		0			0
$985$	−40099.1	−	23151.2i	−1.29712	−	0.748892i
$986$		0			0
$987$	20815.0	−	2060.41i	0.671275	−	0.0664474i
$988$		0			0
$989$		−	3010.53i		−	0.0967941i
$990$		0			0
$991$	21125.0			0.677153			0.338577	−	0.940939i	$-0.390055\pi$
$991$	21125.0			0.677153			0.338577	+	0.940939i	$0.390055\pi$
$992$		0			0
$993$	13997.2	+	41848.7i	0.447320	+	1.33739i
$994$		0			0
$995$	28923.7	+	16699.1i	0.921550	+	0.532057i
$996$		0			0
$997$	−34141.1	+	19711.4i	−1.08451	+	0.626144i	−0.932110	−	0.362175i	$-0.882034\pi$
$997$	−34141.1	+	19711.4i	−1.08451	+	0.626144i	−0.152403	+	0.988318i	$0.548701\pi$
$998$		0			0
$999$	−2107.06	−	1449.17i	−0.0667312	−	0.0458956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.2	✓	48
3.2	odd	2		756.4.x.a.125.24		48
7.6	odd	2	inner	252.4.x.a.41.23	yes	48
9.2	odd	6	inner	252.4.x.a.209.23	yes	48
9.4	even	3		2268.4.f.a.1133.47		48
9.5	odd	6		2268.4.f.a.1133.2		48
9.7	even	3		756.4.x.a.629.1		48
21.20	even	2		756.4.x.a.125.1		48
63.13	odd	6		2268.4.f.a.1133.1		48
63.20	even	6	inner	252.4.x.a.209.2	yes	48
63.34	odd	6		756.4.x.a.629.24		48
63.41	even	6		2268.4.f.a.1133.48		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.2	✓	48	1.1	even	1	trivial
252.4.x.a.41.23	yes	48	7.6	odd	2	inner
252.4.x.a.209.2	yes	48	63.20	even	6	inner
252.4.x.a.209.23	yes	48	9.2	odd	6	inner
756.4.x.a.125.1		48	21.20	even	2
756.4.x.a.125.24		48	3.2	odd	2
756.4.x.a.629.1		48	9.7	even	3
756.4.x.a.629.24		48	63.34	odd	6
2268.4.f.a.1133.1		48	63.13	odd	6
2268.4.f.a.1133.2		48	9.5	odd	6
2268.4.f.a.1133.47		48	9.4	even	3
2268.4.f.a.1133.48		48	63.41	even	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)

\(f(q)\)	\(=\)	\(q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +O(q^{10})\)	\(q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +(-21.5235 + 12.4266i) q^{11} +(-52.5651 - 30.3485i) q^{13} +(72.7066 - 82.1615i) q^{15} +117.397 q^{17} +104.946i q^{19} +(39.6735 - 87.6756i) q^{21} +(-17.4885 - 10.0970i) q^{23} +(-160.403 - 277.826i) q^{25} +(-115.595 - 79.5029i) q^{27} +(-24.2671 + 14.0106i) q^{29} +(-216.679 - 125.100i) q^{31} +(122.472 - 40.9636i) q^{33} +(-286.729 - 265.891i) q^{35} +18.2279 q^{37} +(236.190 + 209.010i) q^{39} +(153.058 - 265.105i) q^{41} +(74.5402 + 129.107i) q^{43} +(-455.363 + 342.983i) q^{45} +(108.676 + 188.233i) q^{47} +(-309.118 - 148.643i) q^{49} +(-597.755 - 121.683i) q^{51} +116.324i q^{53} -524.754i q^{55} +(108.777 - 534.356i) q^{57} +(-38.3919 + 66.4967i) q^{59} +(493.712 - 285.045i) q^{61} +(-292.883 + 405.298i) q^{63} +(1109.87 - 640.781i) q^{65} +(-33.8430 + 58.6179i) q^{67} +(78.5811 + 69.5382i) q^{69} -796.967i q^{71} +710.481i q^{73} +(528.759 + 1580.87i) q^{75} +(-135.800 - 439.800i) q^{77} +(-40.0640 - 69.3928i) q^{79} +(506.174 + 524.622i) q^{81} +(-57.6203 - 99.8013i) q^{83} +(-1239.37 + 2146.65i) q^{85} +(138.084 - 46.1852i) q^{87} +1055.26 q^{89} +(764.359 - 824.261i) q^{91} +(973.605 + 861.564i) q^{93} +(-1918.98 - 1107.92i) q^{95} +(444.295 - 256.514i) q^{97} +(-666.054 + 81.6319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 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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