LMFDB - Embedded newform 252.4.bm.a.173.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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			173.3
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.84961 - 1.86582i) q^{3} -21.0452 q^{5} +(9.48976 + 15.9042i) q^{7} +(20.0374 + 18.0970i) q^{9} +O(q^{10})$	\(q+(-4.84961 - 1.86582i) q^{3} -21.0452 q^{5} +(9.48976 + 15.9042i) q^{7} +(20.0374 + 18.0970i) q^{9} +33.5753i q^{11} +(-38.7042 + 22.3459i) q^{13} +(102.061 + 39.2666i) q^{15} +(-60.7921 - 105.295i) q^{17} +(11.4313 + 6.59986i) q^{19} +(-16.3471 - 94.8355i) q^{21} -183.391i q^{23} +317.900 q^{25} +(-63.4076 - 125.150i) q^{27} +(17.1663 + 9.91099i) q^{29} +(6.16954 + 3.56198i) q^{31} +(62.6456 - 162.827i) q^{33} +(-199.714 - 334.707i) q^{35} +(82.0019 - 142.031i) q^{37} +(229.394 - 36.1535i) q^{39} +(181.934 + 315.120i) q^{41} +(-86.9180 + 150.546i) q^{43} +(-421.691 - 380.855i) q^{45} +(78.1664 + 135.388i) q^{47} +(-162.889 + 301.855i) q^{49} +(98.3559 + 624.067i) q^{51} +(133.285 - 76.9522i) q^{53} -706.598i q^{55} +(-43.1231 - 53.3355i) q^{57} +(389.435 - 674.522i) q^{59} +(141.115 - 81.4730i) q^{61} +(-97.6692 + 490.416i) q^{63} +(814.538 - 470.274i) q^{65} +(58.7568 - 101.770i) q^{67} +(-342.175 + 889.373i) q^{69} -163.420i q^{71} +(711.897 - 411.014i) q^{73} +(-1541.69 - 593.145i) q^{75} +(-533.989 + 318.621i) q^{77} +(-275.591 - 477.337i) q^{79} +(73.9944 + 725.235i) q^{81} +(-188.265 + 326.085i) q^{83} +(1279.38 + 2215.95i) q^{85} +(-64.7578 - 80.0938i) q^{87} +(35.7337 - 61.8925i) q^{89} +(-722.689 - 403.504i) q^{91} +(-23.2738 - 28.7855i) q^{93} +(-240.574 - 138.895i) q^{95} +(1173.81 + 677.697i) q^{97} +(-607.613 + 672.761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.84961	−	1.86582i	−0.933307	−	0.359078i
$3$	−4.84961	−	1.86582i	−0.933307	−	0.359078i
$4$		0			0
$5$	−21.0452			−1.88234			−0.941169	−	0.337936i	$-0.890271\pi$
$5$	−21.0452			−1.88234			−0.941169	+	0.337936i	$0.890271\pi$
$6$		0			0
$7$	9.48976	+	15.9042i	0.512399	+	0.858747i
$7$	9.48976	+	15.9042i	0.512399	+	0.858747i
$8$		0			0
$9$	20.0374	+	18.0970i	0.742126	+	0.670261i
$10$		0			0
$11$			33.5753i			0.920302i	0.887841	+	0.460151i	$0.152205\pi$
$11$			33.5753i			0.920302i	−0.887841	+	0.460151i	$0.847795\pi$
$12$		0			0
$13$	−38.7042	+	22.3459i	−0.825740	+	0.476741i	−0.852392	−	0.522903i	$-0.824849\pi$
$13$	−38.7042	+	22.3459i	−0.825740	+	0.476741i	0.0266515	+	0.999645i	$0.491516\pi$
$14$		0			0
$15$	102.061	+	39.2666i	1.75680	+	0.675907i
$16$		0			0
$17$	−60.7921	−	105.295i	−0.867309	−	1.50222i	−0.864736	−	0.502227i	$-0.832514\pi$
$17$	−60.7921	−	105.295i	−0.867309	−	1.50222i	−0.00257377	−	0.999997i	$-0.500819\pi$
$18$		0			0
$19$	11.4313	+	6.59986i	0.138027	+	0.0796901i	0.567423	−	0.823426i	$-0.307940\pi$
$19$	11.4313	+	6.59986i	0.138027	+	0.0796901i	−0.429396	+	0.903116i	$0.641274\pi$
$20$		0			0
$21$	−16.3471	−	94.8355i	−0.169868	−	0.985467i
$22$		0			0
$23$		−	183.391i		−	1.66259i	−0.555831	−	0.831295i	$-0.687600\pi$
$23$		−	183.391i		−	1.66259i	0.555831	−	0.831295i	$-0.312400\pi$
$24$		0			0
$25$	317.900			2.54320
$26$		0			0
$27$	−63.4076	−	125.150i	−0.451956	−	0.892040i
$28$		0			0
$29$	17.1663	+	9.91099i	0.109921	+	0.0634629i	0.553953	−	0.832548i	$-0.313119\pi$
$29$	17.1663	+	9.91099i	0.109921	+	0.0634629i	−0.444032	+	0.896011i	$0.646452\pi$
$30$		0			0
$31$	6.16954	+	3.56198i	0.0357446	+	0.0206371i	0.517766	−	0.855522i	$-0.326764\pi$
$31$	6.16954	+	3.56198i	0.0357446	+	0.0206371i	−0.482021	+	0.876160i	$0.660097\pi$
$32$		0			0
$33$	62.6456	−	162.827i	0.330460	−	0.858925i
$34$		0			0
$35$	−199.714	−	334.707i	−0.964509	−	1.61645i
$36$		0			0
$37$	82.0019	−	142.031i	0.364352	−	0.631077i	−0.624320	−	0.781169i	$-0.714624\pi$
$37$	82.0019	−	142.031i	0.364352	−	0.631077i	0.988672	+	0.150092i	$0.0479571\pi$
$38$		0			0
$39$	229.394	−	36.1535i	0.941857	−	0.148441i
$40$		0			0
$41$	181.934	+	315.120i	0.693009	+	1.20033i	0.970847	+	0.239699i	$0.0770488\pi$
$41$	181.934	+	315.120i	0.693009	+	1.20033i	−0.277838	+	0.960628i	$0.589618\pi$
$42$		0			0
$43$	−86.9180	+	150.546i	−0.308253	+	0.533909i	−0.977980	−	0.208698i	$-0.933078\pi$
$43$	−86.9180	+	150.546i	−0.308253	+	0.533909i	0.669727	+	0.742607i	$0.266411\pi$
$44$		0			0
$45$	−421.691	−	380.855i	−1.39693	−	1.26166i
$46$		0			0
$47$	78.1664	+	135.388i	0.242590	+	0.420179i	0.961451	−	0.274975i	$-0.0886696\pi$
$47$	78.1664	+	135.388i	0.242590	+	0.420179i	−0.718861	+	0.695154i	$0.755336\pi$
$48$		0			0
$49$	−162.889	+	301.855i	−0.474894	+	0.880043i
$50$		0			0
$51$	98.3559	+	624.067i	0.270051	+	1.71347i
$52$		0			0
$53$	133.285	−	76.9522i	0.345436	−	0.199438i	−0.317237	−	0.948346i	$-0.602755\pi$
$53$	133.285	−	76.9522i	0.345436	−	0.199438i	0.662673	+	0.748909i	$0.269422\pi$
$54$		0			0
$55$		−	706.598i		−	1.73232i
$56$		0			0
$57$	−43.1231	−	53.3355i	−0.100207	−	0.123938i
$58$		0			0
$59$	389.435	−	674.522i	0.859325	−	1.48839i	−0.0132485	−	0.999912i	$-0.504217\pi$
$59$	389.435	−	674.522i	0.859325	−	1.48839i	0.872574	−	0.488483i	$-0.162449\pi$
$60$		0			0
$61$	141.115	−	81.4730i	0.296196	−	0.171009i	−0.344537	−	0.938773i	$-0.611964\pi$
$61$	141.115	−	81.4730i	0.296196	−	0.171009i	0.640733	+	0.767764i	$0.278631\pi$
$62$		0			0
$63$	−97.6692	+	490.416i	−0.195320	+	0.980740i
$64$		0			0
$65$	814.538	−	470.274i	1.55432	−	0.897389i
$66$		0			0
$67$	58.7568	−	101.770i	0.107139	−	0.185570i	−0.807471	−	0.589907i	$-0.799164\pi$
$67$	58.7568	−	101.770i	0.107139	−	0.185570i	0.914610	+	0.404337i	$0.132498\pi$
$68$		0			0
$69$	−342.175	+	889.373i	−0.597000	+	1.55171i
$70$		0			0
$71$		−	163.420i		−	0.273160i	−0.990629	−	0.136580i	$-0.956389\pi$
$71$		−	163.420i		−	0.273160i	0.990629	−	0.136580i	$-0.0436111\pi$
$72$		0			0
$73$	711.897	−	411.014i	1.14139	−	0.658980i	0.194613	−	0.980880i	$-0.437655\pi$
$73$	711.897	−	411.014i	1.14139	−	0.658980i	0.946774	+	0.321900i	$0.104321\pi$
$74$		0			0
$75$	−1541.69	−	593.145i	−2.37359	−	0.913207i
$76$		0			0
$77$	−533.989	+	318.621i	−0.790307	+	0.471562i
$78$		0			0
$79$	−275.591	−	477.337i	−0.392486	−	0.679805i	0.600291	−	0.799782i	$-0.295051\pi$
$79$	−275.591	−	477.337i	−0.392486	−	0.679805i	−0.992777	+	0.119977i	$0.961718\pi$
$80$		0			0
$81$	73.9944	+	725.235i	0.101501	+	0.994835i
$82$		0			0
$83$	−188.265	+	326.085i	−0.248974	+	0.431235i	−0.963241	−	0.268638i	$-0.913427\pi$
$83$	−188.265	+	326.085i	−0.248974	+	0.431235i	0.714268	+	0.699873i	$0.246760\pi$
$84$		0			0
$85$	1279.38	+	2215.95i	1.63257	+	2.82769i
$86$		0			0
$87$	−64.7578	−	80.0938i	−0.0798019	−	0.0987006i
$88$		0			0
$89$	35.7337	−	61.8925i	0.0425591	−	0.0737146i	−0.843961	−	0.536404i	$-0.819782\pi$
$89$	35.7337	−	61.8925i	0.0425591	−	0.0737146i	0.886520	+	0.462690i	$0.153116\pi$
$90$		0			0
$91$	−722.689	−	403.504i	−0.832509	−	0.464821i
$92$		0			0
$93$	−23.2738	−	28.7855i	−0.0259503	−	0.0320959i
$94$		0			0
$95$	−240.574	−	138.895i	−0.259814	−	0.150004i
$96$		0			0
$97$	1173.81	+	677.697i	1.22868	+	0.709379i	0.966754	−	0.255709i	$-0.0823090\pi$
$97$	1173.81	+	677.697i	1.22868	+	0.709379i	0.261926	+	0.965088i	$0.415642\pi$
$98$		0			0
$99$	−607.613	+	672.761i	−0.616842	+	0.682980i
$100$		0			0
$101$	−1616.55			−1.59260			−0.796300	−	0.604902i	$-0.793212\pi$
$101$	−1616.55			−1.59260			−0.796300	+	0.604902i	$0.793212\pi$
$102$		0			0
$103$		−	1884.25i		−	1.80253i	−0.433271	−	0.901264i	$-0.642641\pi$
$103$		−	1884.25i		−	1.80253i	0.433271	−	0.901264i	$-0.357359\pi$
$104$		0			0
$105$	344.029	+	1995.83i	0.319750	+	1.85498i
$106$		0			0
$107$	−533.466	−	307.997i	−0.481982	−	0.278273i	0.239260	−	0.970956i	$-0.423095\pi$
$107$	−533.466	−	307.997i	−0.481982	−	0.278273i	−0.721242	+	0.692683i	$0.756429\pi$
$108$		0			0
$109$	343.685	+	595.279i	0.302009	+	0.523096i	0.976591	−	0.215105i	$-0.0690092\pi$
$109$	343.685	+	595.279i	0.302009	+	0.523096i	−0.674582	+	0.738200i	$0.735676\pi$
$110$		0			0
$111$	−662.683	+	535.796i	−0.566658	+	0.458158i
$112$		0			0
$113$	213.577	−	123.309i	0.177802	−	0.102654i	−0.408458	−	0.912777i	$-0.633933\pi$
$113$	213.577	−	123.309i	0.177802	−	0.102654i	0.586259	+	0.810123i	$0.300600\pi$
$114$		0			0
$115$			3859.49i			3.12956i
$116$		0			0
$117$	−1179.93	−	252.678i	−0.932344	−	0.199659i
$118$		0			0
$119$	1097.73	−	1966.08i	0.845622	−	1.51454i
$120$		0			0
$121$	203.701			0.153044
$122$		0			0
$123$	−294.352	−	1867.66i	−0.215779	−	1.36912i
$124$		0			0
$125$	−4059.61			−2.90482
$126$		0			0
$127$	842.198			0.588449			0.294224	−	0.955736i	$-0.404939\pi$
$127$	842.198			0.588449			0.294224	+	0.955736i	$0.404939\pi$
$128$		0			0
$129$	702.411	−	567.917i	0.479410	−	0.387615i
$130$		0			0
$131$	1754.19			1.16996			0.584978	−	0.811049i	$-0.301103\pi$
$131$	1754.19			1.16996			0.584978	+	0.811049i	$0.301103\pi$
$132$		0			0
$133$	3.51463	+	244.437i	0.00229140	+	0.159364i
$134$		0			0
$135$	1334.42	+	2633.80i	0.850733	+	1.67912i
$136$		0			0
$137$			1227.65i			0.765588i	0.923834	+	0.382794i	$0.125038\pi$
$137$			1227.65i			0.765588i	−0.923834	+	0.382794i	$0.874962\pi$
$138$		0			0
$139$	12.8249	−	7.40447i	0.00782587	−	0.00451827i	−0.496082	−	0.868276i	$-0.665228\pi$
$139$	12.8249	−	7.40447i	0.00782587	−	0.00451827i	0.503908	+	0.863757i	$0.331895\pi$
$140$		0			0
$141$	−126.466	−	802.425i	−0.0755343	−	0.479265i
$142$		0			0
$143$	−750.270	−	1299.51i	−0.438746	−	0.759931i
$144$		0			0
$145$	−361.269	−	208.579i	−0.206908	−	0.119459i
$146$		0			0
$147$	1353.15	−	1159.96i	0.759227	−	0.650826i
$148$		0			0
$149$		−	3227.59i		−	1.77459i	−0.461200	−	0.887296i	$-0.652581\pi$
$149$		−	3227.59i		−	1.77459i	0.461200	−	0.887296i	$-0.347419\pi$
$150$		0			0
$151$	−2552.89			−1.37584			−0.687918	−	0.725788i	$-0.741475\pi$
$151$	−2552.89			−1.37584			−0.687918	+	0.725788i	$0.741475\pi$
$152$		0			0
$153$	687.413	−	3210.00i	0.363229	−	1.69616i
$154$		0			0
$155$	−129.839	−	74.9626i	−0.0672833	−	0.0388461i
$156$		0			0
$157$	1221.42	+	705.187i	0.620891	+	0.358472i	0.777216	−	0.629234i	$-0.216631\pi$
$157$	1221.42	+	705.187i	0.620891	+	0.358472i	−0.156325	+	0.987706i	$0.549965\pi$
$158$		0			0
$159$	−789.960	+	124.501i	−0.394012	+	0.0620981i
$160$		0			0
$161$	2916.69	−	1740.33i	1.42775	−	0.851910i
$162$		0			0
$163$	−148.525	+	257.254i	−0.0713706	+	0.123618i	−0.899502	−	0.436916i	$-0.856071\pi$
$163$	−148.525	+	257.254i	−0.0713706	+	0.123618i	0.828132	+	0.560534i	$0.189404\pi$
$164$		0			0
$165$	−1318.39	+	3426.72i	−0.622038	+	1.61679i
$166$		0			0
$167$	432.425	+	748.982i	0.200372	+	0.347054i	0.948648	−	0.316333i	$-0.102452\pi$
$167$	432.425	+	748.982i	0.200372	+	0.347054i	−0.748277	+	0.663387i	$0.769118\pi$
$168$		0			0
$169$	−99.8209	+	172.895i	−0.0454351	+	0.0786959i
$170$		0			0
$171$	109.615	+	339.117i	0.0490205	+	0.151654i
$172$		0			0
$173$	469.499	+	813.197i	0.206332	+	0.357377i	0.950556	−	0.310553i	$-0.100514\pi$
$173$	469.499	+	813.197i	0.206332	+	0.357377i	−0.744225	+	0.667930i	$0.767181\pi$
$174$		0			0
$175$	3016.79	+	5055.95i	1.30313	+	2.18396i
$176$		0			0
$177$	−3147.15	+	2544.55i	−1.33646	+	1.08057i
$178$		0			0
$179$	−2563.24	+	1479.89i	−1.07031	+	0.617944i	−0.928266	−	0.371916i	$-0.878701\pi$
$179$	−2563.24	+	1479.89i	−1.07031	+	0.617944i	−0.142045	+	0.989860i	$0.545368\pi$
$180$		0			0
$181$			2771.25i			1.13804i	0.822324	+	0.569020i	$0.192677\pi$
$181$			2771.25i			1.13804i	−0.822324	+	0.569020i	$0.807323\pi$
$182$		0			0
$183$	−836.369	+	131.816i	−0.337848	+	0.0532464i
$184$		0			0
$185$	−1725.75	+	2989.08i	−0.685834	+	1.18790i
$186$		0			0
$187$	3535.31	−	2041.11i	1.38250	−	0.798187i
$188$		0			0
$189$	1388.69	−	2196.09i	0.534456	−	0.845196i
$190$		0			0
$191$	2400.22	−	1385.77i	0.909286	−	0.524976i	0.0290845	−	0.999577i	$-0.490741\pi$
$191$	2400.22	−	1385.77i	0.909286	−	0.524976i	0.880201	+	0.474601i	$0.157407\pi$
$192$		0			0
$193$	2269.59	−	3931.04i	0.846469	−	1.46613i	−0.0378701	−	0.999283i	$-0.512057\pi$
$193$	2269.59	−	3931.04i	0.846469	−	1.46613i	0.884339	−	0.466845i	$-0.154609\pi$
$194$		0			0
$195$	−4827.64	+	760.858i	−1.77289	+	0.279416i
$196$		0			0
$197$			504.256i			0.182369i	0.995834	+	0.0911847i	$0.0290654\pi$
$197$			504.256i			0.182369i	−0.995834	+	0.0911847i	$0.970935\pi$
$198$		0			0
$199$	399.083	−	230.411i	0.142162	−	0.0820772i	−0.427232	−	0.904142i	$-0.640511\pi$
$199$	399.083	−	230.411i	0.142162	−	0.0820772i	0.569394	+	0.822065i	$0.307178\pi$
$200$		0			0
$201$	−474.832	+	383.914i	−0.166627	+	0.134722i
$202$		0			0
$203$	5.27790	+	367.070i	0.00182481	+	0.126913i
$204$		0			0
$205$	−3828.84	−	6631.75i	−1.30448	−	2.25942i
$206$		0			0
$207$	3318.83	−	3674.67i	1.11437	−	1.23385i
$208$		0			0
$209$	−221.592	+	383.809i	−0.0733390	+	0.127027i
$210$		0			0
$211$	−1133.85	−	1963.88i	−0.369939	−	0.640754i	0.619616	−	0.784905i	$-0.287288\pi$
$211$	−1133.85	−	1963.88i	−0.369939	−	0.640754i	−0.989556	+	0.144151i	$0.953955\pi$
$212$		0			0
$213$	−304.913	+	792.522i	−0.0980858	+	0.254942i
$214$		0			0
$215$	1829.20	−	3168.28i	0.580236	−	1.00500i
$216$		0			0
$217$	1.89686	+	131.924i	0.000593399	+	0.0412700i
$218$		0			0
$219$	−4219.30	+	664.981i	−1.30189	+	0.205184i
$220$		0			0
$221$	4705.83	+	2716.91i	1.43235	+	0.826965i
$222$		0			0
$223$	−3338.01	−	1927.20i	−1.00237	−	0.578721i	−0.0934245	−	0.995626i	$-0.529781\pi$
$223$	−3338.01	−	1927.20i	−1.00237	−	0.578721i	−0.908950	+	0.416905i	$0.863115\pi$
$224$		0			0
$225$	6369.88	+	5753.04i	1.88737	+	1.70461i
$226$		0			0
$227$	1439.86			0.420999			0.210499	−	0.977594i	$-0.432491\pi$
$227$	1439.86			0.420999			0.210499	+	0.977594i	$0.432491\pi$
$228$		0			0
$229$		−	4964.54i		−	1.43260i	−0.697792	−	0.716301i	$-0.745834\pi$
$229$		−	4964.54i		−	1.43260i	0.697792	−	0.716301i	$-0.254166\pi$
$230$		0			0
$231$	3184.13	−	548.860i	0.906927	−	0.156330i
$232$		0			0
$233$	94.5829	+	54.6075i	0.0265937	+	0.0153539i	0.513238	−	0.858246i	$-0.328446\pi$
$233$	94.5829	+	54.6075i	0.0265937	+	0.0153539i	−0.486644	+	0.873600i	$0.661779\pi$
$234$		0			0
$235$	−1645.03	−	2849.27i	−0.456637	−	0.790918i
$236$		0			0
$237$	445.879	+	2829.10i	0.122207	+	0.775400i
$238$		0			0
$239$	434.585	−	250.908i	0.117619	−	0.0679075i	−0.440036	−	0.897980i	$-0.645034\pi$
$239$	434.585	−	250.908i	0.117619	−	0.0679075i	0.557655	+	0.830073i	$0.311701\pi$
$240$		0			0
$241$		−	3529.85i		−	0.943475i	−0.881739	−	0.471737i	$-0.843627\pi$
$241$		−	3529.85i		−	0.943475i	0.881739	−	0.471737i	$-0.156373\pi$
$242$		0			0
$243$	994.318	−	3655.17i	0.262492	−	0.964934i
$244$		0			0
$245$	3428.02	−	6352.59i	0.893912	−	1.65654i
$246$		0			0
$247$	−589.919			−0.151966
$248$		0			0
$249$	1521.43	−	1230.12i	0.387216	−	0.313074i
$250$		0			0
$251$	−1766.40			−0.444200			−0.222100	−	0.975024i	$-0.571291\pi$
$251$	−1766.40			−0.444200			−0.222100	+	0.975024i	$0.571291\pi$
$252$		0			0
$253$	6157.39			1.53009
$254$		0			0
$255$	−2069.92	−	13133.6i	−0.508326	−	3.22533i
$256$		0			0
$257$	−2630.73			−0.638523			−0.319261	−	0.947667i	$-0.603435\pi$
$257$	−2630.73			−0.638523			−0.319261	+	0.947667i	$0.603435\pi$
$258$		0			0
$259$	3037.08	−	43.6685i	0.728629	−	0.0104766i
$260$		0			0
$261$	164.609	+	509.250i	0.0390385	+	0.120773i
$262$		0			0
$263$		−	6434.38i		−	1.50860i	−0.656532	−	0.754298i	$-0.727977\pi$
$263$		−	6434.38i		−	1.50860i	0.656532	−	0.754298i	$-0.272023\pi$
$264$		0			0
$265$	−2805.01	+	1619.47i	−0.650228	+	0.375409i
$266$		0			0
$267$	−288.775	+	233.482i	−0.0661900	+	0.0535163i
$268$		0			0
$269$	−1990.20	−	3447.13i	−0.451095	−	0.781320i	0.547359	−	0.836898i	$-0.315633\pi$
$269$	−1990.20	−	3447.13i	−0.451095	−	0.781320i	−0.998454	+	0.0555781i	$0.982300\pi$
$270$		0			0
$271$	4543.45	+	2623.16i	1.01843	+	0.587992i	0.913649	−	0.406503i	$-0.133252\pi$
$271$	4543.45	+	2623.16i	1.01843	+	0.587992i	0.104782	+	0.994495i	$0.466585\pi$
$272$		0			0
$273$	2751.89	+	3305.24i	0.610080	+	0.732756i
$274$		0			0
$275$			10673.6i			2.34051i
$276$		0			0
$277$	3550.52			0.770146			0.385073	−	0.922886i	$-0.374176\pi$
$277$	3550.52			0.770146			0.385073	+	0.922886i	$0.374176\pi$
$278$		0			0
$279$	59.1601	+	183.023i	0.0126947	+	0.0392735i
$280$		0			0
$281$	1480.16	+	854.571i	0.314231	+	0.181422i	0.648818	−	0.760943i	$-0.275263\pi$
$281$	1480.16	+	854.571i	0.314231	+	0.181422i	−0.334587	+	0.942365i	$0.608597\pi$
$282$		0			0
$283$	−6366.49	−	3675.70i	−1.33727	−	0.772076i	−0.350872	−	0.936423i	$-0.614115\pi$
$283$	−6366.49	−	3675.70i	−1.33727	−	0.772076i	−0.986403	+	0.164347i	$0.947448\pi$
$284$		0			0
$285$	907.533	+	1122.46i	0.188623	+	0.233293i
$286$		0			0
$287$	−3285.22	+	5883.94i	−0.675680	+	1.21017i
$288$		0			0
$289$	−4934.87	+	8547.44i	−1.00445	+	1.73976i
$290$		0			0
$291$	−4428.04	−	5476.68i	−0.892014	−	1.10326i
$292$		0			0
$293$	90.0474	+	155.967i	0.0179544	+	0.0310979i	0.874863	−	0.484370i	$-0.160951\pi$
$293$	90.0474	+	155.967i	0.0179544	+	0.0310979i	−0.856909	+	0.515468i	$0.827618\pi$
$294$		0			0
$295$	−8195.74	+	14195.4i	−1.61754	+	2.80166i
$296$		0			0
$297$	4201.94	−	2128.93i	0.820947	−	0.415936i
$298$		0			0
$299$	4098.03	+	7098.00i	0.792626	+	1.37287i
$300$		0			0
$301$	−3219.15	+	46.2865i	−0.616442	+	0.00886348i
$302$		0			0
$303$	7839.63	+	3016.20i	1.48639	+	0.571868i
$304$		0			0
$305$	−2969.80	+	1714.61i	−0.557542	+	0.321897i
$306$		0			0
$307$		−	5424.63i		−	1.00847i	−0.863567	−	0.504235i	$-0.831775\pi$
$307$		−	5424.63i		−	1.00847i	0.863567	−	0.504235i	$-0.168225\pi$
$308$		0			0
$309$	−3515.67	+	9137.86i	−0.647248	+	1.68231i
$310$		0			0
$311$	−2924.83	+	5065.95i	−0.533286	+	0.923678i	0.465958	+	0.884807i	$0.345710\pi$
$311$	−2924.83	+	5065.95i	−0.533286	+	0.923678i	−0.999244	+	0.0388715i	$0.987624\pi$
$312$		0			0
$313$	−77.1160	+	44.5229i	−0.0139261	+	0.00804021i	−0.506947	−	0.861977i	$-0.669226\pi$
$313$	−77.1160	+	44.5229i	−0.0139261	+	0.00804021i	0.493021	+	0.870018i	$0.335893\pi$
$314$		0			0
$315$	2055.47	−	10320.9i	0.367658	−	1.84608i
$316$		0			0
$317$	−4667.33	+	2694.69i	−0.826951	+	0.477440i	−0.852808	−	0.522225i	$-0.825102\pi$
$317$	−4667.33	+	2694.69i	−0.826951	+	0.477440i	0.0258565	+	0.999666i	$0.491769\pi$
$318$		0			0
$319$	−332.764	+	576.364i	−0.0584050	+	0.101161i
$320$		0			0
$321$	2012.43	+	2489.02i	0.349916	+	0.432783i
$322$		0			0
$323$		−	1604.88i		−	0.276464i
$324$		0			0
$325$	−12304.1	+	7103.76i	−2.10002	+	1.21245i
$326$		0			0
$327$	−556.049	−	3528.13i	−0.0940354	−	0.596654i
$328$		0			0
$329$	−1411.46	+	2527.98i	−0.236524	+	0.423623i
$330$		0			0
$331$	629.237	+	1089.87i	0.104489	+	0.180981i	0.913529	−	0.406773i	$-0.133346\pi$
$331$	629.237	+	1089.87i	0.104489	+	0.180981i	−0.809040	+	0.587753i	$0.800013\pi$
$332$		0			0
$333$	4213.45	−	1361.95i	0.693381	−	0.224127i
$334$		0			0
$335$	−1236.55	+	2141.76i	−0.201671	+	0.349305i
$336$		0			0
$337$	−663.239	−	1148.76i	−0.107207	−	0.185689i	0.807431	−	0.589963i	$-0.200858\pi$
$337$	−663.239	−	1148.76i	−0.107207	−	0.185689i	−0.914638	+	0.404274i	$0.867524\pi$
$338$		0			0
$339$	−1265.83	+	199.501i	−0.202804	+	0.0319629i
$340$		0			0
$341$	−119.595	+	207.144i	−0.0189924	+	0.0328958i
$342$		0			0
$343$	−6346.54	+	273.911i	−0.999070	+	0.0431190i
$344$		0			0
$345$	7201.13	−	18717.0i	1.12376	−	2.92084i
$346$		0			0
$347$	459.599	+	265.350i	0.0711025	+	0.0410510i	0.535130	−	0.844770i	$-0.320263\pi$
$347$	459.599	+	265.350i	0.0711025	+	0.0410510i	−0.464027	+	0.885821i	$0.653596\pi$
$348$		0			0
$349$	3675.13	+	2121.83i	0.563682	+	0.325442i	0.754622	−	0.656160i	$-0.227820\pi$
$349$	3675.13	+	2121.83i	0.563682	+	0.325442i	−0.190940	+	0.981602i	$0.561154\pi$
$350$		0			0
$351$	5250.73	+	3426.93i	0.798471	+	0.521128i
$352$		0			0
$353$	12389.6			1.86807			0.934036	−	0.357179i	$-0.116261\pi$
$353$	12389.6			1.86807			0.934036	+	0.357179i	$0.116261\pi$
$354$		0			0
$355$			3439.20i			0.514180i
$356$		0			0
$357$	−8991.93	+	7486.53i	−1.33306	+	1.10989i
$358$		0			0
$359$	−4395.22	−	2537.58i	−0.646158	−	0.373060i	0.140824	−	0.990035i	$-0.455025\pi$
$359$	−4395.22	−	2537.58i	−0.646158	−	0.373060i	−0.786983	+	0.616975i	$0.788358\pi$
$360$		0			0
$361$	−3342.38	−	5789.18i	−0.487299	−	0.844027i
$362$		0			0
$363$	−987.870	−	380.071i	−0.142837	−	0.0549546i
$364$		0			0
$365$	−14982.0	+	8649.86i	−2.14848	+	1.24042i
$366$		0			0
$367$		−	4431.94i		−	0.630369i	−0.949030	−	0.315184i	$-0.897934\pi$
$367$		−	4431.94i		−	0.630369i	0.949030	−	0.315184i	$-0.102066\pi$
$368$		0			0
$369$	−2057.24	+	9606.65i	−0.290232	+	1.35529i
$370$		0			0
$371$	2488.71	+	1389.54i	0.348268	+	0.194451i
$372$		0			0
$373$	6224.86			0.864105			0.432052	−	0.901849i	$-0.357790\pi$
$373$	6224.86			0.864105			0.432052	+	0.901849i	$0.357790\pi$
$374$		0			0
$375$	19687.5	+	7574.52i	2.71109	+	1.04306i
$376$		0			0
$377$	−885.880			−0.121022
$378$		0			0
$379$	9661.21			1.30940			0.654701	−	0.755888i	$-0.272795\pi$
$379$	9661.21			1.30940			0.654701	+	0.755888i	$0.272795\pi$
$380$		0			0
$381$	−4084.33	−	1571.39i	−0.549204	−	0.211299i
$382$		0			0
$383$	−3363.33			−0.448716			−0.224358	−	0.974507i	$-0.572028\pi$
$383$	−3363.33			−0.448716			−0.224358	+	0.974507i	$0.572028\pi$
$384$		0			0
$385$	11237.9	−	6705.45i	1.48763	−	0.887639i
$386$		0			0
$387$	−4466.05	+	1443.60i	−0.586621	+	0.189618i
$388$		0			0
$389$		−	2959.10i		−	0.385688i	−0.981229	−	0.192844i	$-0.938229\pi$
$389$		−	2959.10i		−	0.385688i	0.981229	−	0.192844i	$-0.0617711\pi$
$390$		0			0
$391$	−19310.1	+	11148.7i	−2.49758	+	1.44198i
$392$		0			0
$393$	−8507.12	−	3273.01i	−1.09193	−	0.420105i
$394$		0			0
$395$	5799.85	+	10045.6i	0.738791	+	1.27962i
$396$		0			0
$397$	−7666.47	−	4426.24i	−0.969191	−	0.559563i	−0.0702018	−	0.997533i	$-0.522364\pi$
$397$	−7666.47	−	4426.24i	−0.969191	−	0.559563i	−0.898990	+	0.437970i	$0.855698\pi$
$398$		0			0
$399$	439.032	−	1191.98i	0.0550854	−	0.149558i
$400$		0			0
$401$			8566.60i			1.06682i	0.845856	+	0.533411i	$0.179090\pi$
$401$			8566.60i			1.06682i	−0.845856	+	0.533411i	$0.820910\pi$
$402$		0			0
$403$	−318.383			−0.0393543
$404$		0			0
$405$	−1557.22	−	15262.7i	−0.191060	−	1.87262i
$406$		0			0
$407$	4768.75	+	2753.24i	0.580781	+	0.335314i
$408$		0			0
$409$	−6576.84	−	3797.14i	−0.795119	−	0.459062i	0.0466427	−	0.998912i	$-0.485148\pi$
$409$	−6576.84	−	3797.14i	−0.795119	−	0.459062i	−0.841762	+	0.539850i	$0.818481\pi$
$410$		0			0
$411$	2290.59	−	5953.64i	0.274906	−	0.714529i
$412$		0			0
$413$	14423.4	−	207.386i	1.71847	−	0.0247090i
$414$		0			0
$415$	3962.08	−	6862.53i	0.468653	−	0.811731i
$416$		0			0
$417$	−76.0113	+	11.9797i	−0.00892635	+	0.00140683i
$418$		0			0
$419$	5864.21	+	10157.1i	0.683736	+	1.18427i	0.973832	+	0.227268i	$0.0729794\pi$
$419$	5864.21	+	10157.1i	0.683736	+	1.18427i	−0.290096	+	0.956997i	$0.593687\pi$
$420$		0			0
$421$	7252.37	−	12561.5i	0.839570	−	1.45418i	−0.0506842	−	0.998715i	$-0.516140\pi$
$421$	7252.37	−	12561.5i	0.839570	−	1.45418i	0.890254	−	0.455464i	$-0.150526\pi$
$422$		0			0
$423$	−883.874	+	4127.41i	−0.101597	+	0.474424i
$424$		0			0
$425$	−19325.8	−	33473.3i	−2.20574	−	3.82045i
$426$		0			0
$427$	2634.92	+	1471.17i	0.298624	+	0.166733i
$428$		0			0
$429$	1213.86	+	7701.96i	0.136611	+	0.866793i
$430$		0			0
$431$	−4370.77	+	2523.46i	−0.488475	+	0.282021i	−0.723941	−	0.689861i	$-0.757671\pi$
$431$	−4370.77	+	2523.46i	−0.488475	+	0.282021i	0.235467	+	0.971882i	$0.424338\pi$
$432$		0			0
$433$		−	12311.9i		−	1.36645i	−0.730207	−	0.683226i	$-0.760576\pi$
$433$		−	12311.9i		−	1.36645i	0.730207	−	0.683226i	$-0.239424\pi$
$434$		0			0
$435$	1362.84	+	1685.59i	0.150214	+	0.185788i
$436$		0			0
$437$	1210.35	−	2096.39i	0.132492	−	0.229483i
$438$		0			0
$439$	−9548.16	+	5512.63i	−1.03806	+	0.599325i	−0.919284	−	0.393596i	$-0.871231\pi$
$439$	−9548.16	+	5512.63i	−1.03806	+	0.599325i	−0.118778	+	0.992921i	$0.537898\pi$
$440$		0			0
$441$	−8726.54	+	3100.58i	−0.942289	+	0.334800i
$442$		0			0
$443$	4120.54	−	2379.00i	0.441925	−	0.255146i	−0.262489	−	0.964935i	$-0.584543\pi$
$443$	4120.54	−	2379.00i	0.441925	−	0.255146i	0.704414	+	0.709789i	$0.251210\pi$
$444$		0			0
$445$	−752.022	+	1302.54i	−0.0801107	+	0.138756i
$446$		0			0
$447$	−6022.11	+	15652.5i	−0.637218	+	1.65624i
$448$		0			0
$449$			17394.1i			1.82824i	0.405445	+	0.914120i	$0.367117\pi$
$449$			17394.1i			1.82824i	−0.405445	+	0.914120i	$0.632883\pi$
$450$		0			0
$451$	−10580.2	+	6108.50i	−1.10466	+	0.637778i
$452$		0			0
$453$	12380.5	+	4763.25i	1.28408	+	0.494033i
$454$		0			0
$455$	15209.1	+	8491.81i	1.56706	+	0.874950i
$456$		0			0
$457$	−79.1908	−	137.162i	−0.00810588	−	0.0140398i	0.861944	−	0.507003i	$-0.169247\pi$
$457$	−79.1908	−	137.162i	−0.00810588	−	0.0140398i	−0.870050	+	0.492964i	$0.835914\pi$
$458$		0			0
$459$	−9322.98	+	14284.6i	−0.948059	+	1.45261i
$460$		0			0
$461$	862.510	−	1493.91i	0.0871391	−	0.150929i	−0.819162	−	0.573563i	$-0.805561\pi$
$461$	862.510	−	1493.91i	0.0871391	−	0.150929i	0.906301	+	0.422633i	$0.138894\pi$
$462$		0			0
$463$	−8072.56	−	13982.1i	−0.810289	−	1.40346i	−0.912662	−	0.408716i	$-0.865977\pi$
$463$	−8072.56	−	13982.1i	−0.810289	−	1.40346i	0.102373	−	0.994746i	$-0.467357\pi$
$464$		0			0
$465$	489.801	+	605.796i	0.0488473	+	0.0604153i
$466$		0			0
$467$	4915.93	−	8514.64i	0.487114	−	0.843706i	−0.512776	−	0.858522i	$-0.671383\pi$
$467$	4915.93	−	8514.64i	0.487114	−	0.843706i	0.999890	+	0.0148163i	$0.00471634\pi$
$468$		0			0
$469$	2176.16	−	31.2898i	0.214255	−	0.00308066i
$470$		0			0
$471$	−4607.65	−	5698.84i	−0.450763	−	0.557513i
$472$		0			0
$473$	−5054.64	−	2918.29i	−0.491358	−	0.283686i
$474$		0			0
$475$	3634.00	+	2098.09i	0.351031	+	0.202668i
$476$		0			0
$477$	4063.29	+	870.145i	0.390032	+	0.0835245i
$478$		0			0
$479$	18181.6			1.73431			0.867157	−	0.498035i	$-0.165945\pi$
$479$	18181.6			1.73431			0.867157	+	0.498035i	$0.165945\pi$
$480$		0			0
$481$			7329.63i			0.694807i
$482$		0			0
$483$	−17391.9	+	2997.91i	−1.63843	+	0.282422i
$484$		0			0
$485$	−24703.0	−	14262.3i	−2.31279	−	1.33529i
$486$		0			0
$487$	−4399.69	−	7620.49i	−0.409382	−	0.709071i	0.585438	−	0.810717i	$-0.300922\pi$
$487$	−4399.69	−	7620.49i	−0.409382	−	0.709071i	−0.994821	+	0.101646i	$0.967589\pi$
$488$		0			0
$489$	1200.28	−	970.457i	0.110999	−	0.0897455i
$490$		0			0
$491$	15609.4	−	9012.11i	1.43471	−	0.828331i	0.437237	−	0.899347i	$-0.355957\pi$
$491$	15609.4	−	9012.11i	1.43471	−	0.828331i	0.997475	+	0.0710153i	$0.0226239\pi$
$492$		0			0
$493$		−	2410.04i		−	0.220168i
$494$		0			0
$495$	12787.3	−	14158.4i	1.16111	−	1.28560i
$496$		0			0
$497$	2599.07	−	1550.82i	0.234576	−	0.139967i
$498$		0			0
$499$	7063.79			0.633705			0.316852	−	0.948475i	$-0.397374\pi$
$499$	7063.79			0.633705			0.316852	+	0.948475i	$0.397374\pi$
$500$		0			0
$501$	−699.623	−	4439.10i	−0.0623889	−	0.395857i
$502$		0			0
$503$	−3634.87			−0.322208			−0.161104	−	0.986937i	$-0.551505\pi$
$503$	−3634.87			−0.322208			−0.161104	+	0.986937i	$0.551505\pi$
$504$		0			0
$505$	34020.6			2.99781
$506$		0			0
$507$	806.684	−	652.224i	0.0706629	−	0.0571327i
$508$		0			0
$509$	4562.67			0.397322			0.198661	−	0.980068i	$-0.436341\pi$
$509$	4562.67			0.397322			0.198661	+	0.980068i	$0.436341\pi$
$510$		0			0
$511$	13292.6	+	7421.75i	1.15074	+	0.642502i
$512$		0			0
$513$	101.140	−	1849.11i	0.00870459	−	0.159142i
$514$		0			0
$515$			39654.3i			3.39297i
$516$		0			0
$517$	−4545.70	+	2624.46i	−0.386691	+	0.223256i
$518$		0			0
$519$	−759.605	−	4819.69i	−0.0642446	−	0.407632i
$520$		0			0
$521$	8703.46	+	15074.8i	0.731873	+	1.26764i	0.956082	+	0.293100i	$0.0946868\pi$
$521$	8703.46	+	15074.8i	0.731873	+	1.26764i	−0.224209	+	0.974541i	$0.571980\pi$
$522$		0			0
$523$	8236.41	+	4755.29i	0.688629	+	0.397580i	0.803098	−	0.595846i	$-0.203183\pi$
$523$	8236.41	+	4755.29i	0.688629	+	0.397580i	−0.114469	+	0.993427i	$0.536517\pi$
$524$		0			0
$525$	−5196.75	−	30148.2i	−0.432009	−	2.50624i
$526$		0			0
$527$		−	866.162i		−	0.0715951i
$528$		0			0
$529$	−21465.1			−1.76421
$530$		0			0
$531$	20010.1	−	6468.04i	1.63534	−	0.528604i
$532$		0			0
$533$	−14083.3	−	8130.98i	−1.14449	−	0.660772i
$534$		0			0
$535$	11226.9	+	6481.85i	0.907254	+	0.523803i
$536$		0			0
$537$	15191.9	−	2394.32i	1.22082	−	0.192407i
$538$		0			0
$539$	−10134.9	−	5469.03i	−0.809905	−	0.437046i
$540$		0			0
$541$	2258.33	−	3911.55i	0.179470	−	0.310851i	−0.762229	−	0.647307i	$-0.775895\pi$
$541$	2258.33	−	3911.55i	0.179470	−	0.310851i	0.941699	+	0.336456i	$0.109228\pi$
$542$		0			0
$543$	5170.66	−	13439.5i	0.408645	−	1.06214i
$544$		0			0
$545$	−7232.91	−	12527.8i	−0.568484	−	0.984643i
$546$		0			0
$547$	−2534.85	+	4390.49i	−0.198140	+	0.343188i	−0.947925	−	0.318493i	$-0.896823\pi$
$547$	−2534.85	+	4390.49i	−0.198140	+	0.343188i	0.749786	+	0.661681i	$0.230157\pi$
$548$		0			0
$549$	4302.01	+	921.264i	0.334436	+	0.0716186i
$550$		0			0
$551$	130.822	+	226.591i	0.0101147	+	0.0175192i
$552$		0			0
$553$	4976.38	−	8912.87i	0.382671	−	0.685377i
$554$		0			0
$555$	13946.3	−	11275.9i	1.06664	−	0.862407i
$556$		0			0
$557$	−9472.25	+	5468.81i	−0.720560	+	0.416016i	−0.814959	−	0.579519i	$-0.803241\pi$
$557$	−9472.25	+	5468.81i	−0.720560	+	0.416016i	0.0943986	+	0.995534i	$0.469907\pi$
$558$		0			0
$559$		−	7769.04i		−	0.587828i
$560$		0			0
$561$	−20953.2	+	3302.33i	−1.57691	+	0.248528i
$562$		0			0
$563$	11388.7	−	19725.9i	0.852537	−	1.47664i	−0.0263735	−	0.999652i	$-0.508396\pi$
$563$	11388.7	−	19725.9i	0.852537	−	1.47664i	0.878911	−	0.476986i	$-0.158271\pi$
$564$		0			0
$565$	−4494.76	+	2595.05i	−0.334683	+	0.193229i
$566$		0			0
$567$	−10832.1	+	8059.13i	−0.802303	+	0.596917i
$568$		0			0
$569$	−5379.02	+	3105.58i	−0.396310	+	0.228810i	−0.684890	−	0.728646i	$-0.740150\pi$
$569$	−5379.02	+	3105.58i	−0.396310	+	0.228810i	0.288581	+	0.957456i	$0.406817\pi$
$570$		0			0
$571$	2860.04	−	4953.73i	0.209613	−	0.363060i	−0.741980	−	0.670422i	$-0.766113\pi$
$571$	2860.04	−	4953.73i	0.209613	−	0.363060i	0.951593	+	0.307362i	$0.0994463\pi$
$572$		0			0
$573$	−14225.7	+	2242.04i	−1.03715	+	0.163460i
$574$		0			0
$575$		−	58299.8i		−	4.22830i
$576$		0			0
$577$	−12581.9	+	7264.16i	−0.907783	+	0.524109i	−0.879717	−	0.475497i	$-0.842268\pi$
$577$	−12581.9	+	7264.16i	−0.907783	+	0.524109i	−0.0280660	+	0.999606i	$0.508935\pi$
$578$		0			0
$579$	−18341.2	+	14829.4i	−1.31647	+	1.06440i
$580$		0			0
$581$	−6972.73	+	100.257i	−0.497896	+	0.00715897i
$582$		0			0
$583$	2583.69	+	4475.08i	0.183543	+	0.317906i
$584$		0			0
$585$	24831.8	+	5317.67i	1.75499	+	0.375826i
$586$		0			0
$587$	9662.68	−	16736.3i	0.679423	−	1.17680i	−0.295731	−	0.955271i	$-0.595563\pi$
$587$	9662.68	−	16736.3i	0.679423	−	1.17680i	0.975155	−	0.221525i	$-0.0711033\pi$
$588$		0			0
$589$	47.0172	+	81.4361i	0.00328915	+	0.00569697i
$590$		0			0
$591$	940.854	−	2445.44i	0.0654848	−	0.170207i
$592$		0			0
$593$	3983.96	−	6900.42i	0.275888	−	0.477852i	−0.694471	−	0.719521i	$-0.744361\pi$
$593$	3983.96	−	6900.42i	0.275888	−	0.477852i	0.970359	+	0.241669i	$0.0776948\pi$
$594$		0			0
$595$	−23102.0	+	41376.5i	−1.59175	+	2.85087i
$596$		0			0
$597$	−2365.30	+	372.782i	−0.162153	+	0.0255560i
$598$		0			0
$599$	−4251.49	−	2454.60i	−0.290002	−	0.167433i	0.347941	−	0.937516i	$-0.386881\pi$
$599$	−4251.49	−	2454.60i	−0.290002	−	0.167433i	−0.637943	+	0.770084i	$0.720214\pi$
$600$		0			0
$601$	23649.5	+	13654.1i	1.60513	+	0.926724i	0.990438	+	0.137958i	$0.0440540\pi$
$601$	23649.5	+	13654.1i	1.60513	+	0.926724i	0.614694	+	0.788765i	$0.289279\pi$
$602$		0			0
$603$	3019.07	−	975.877i	0.203890	−	0.0659051i
$604$		0			0
$605$	−4286.93			−0.288080
$606$		0			0
$607$			3152.97i			0.210832i	0.994428	+	0.105416i	$0.0336175\pi$
$607$			3152.97i			0.210832i	−0.994428	+	0.105416i	$0.966383\pi$
$608$		0			0
$609$	659.293	−	1789.99i	0.0438685	−	0.119104i
$610$		0			0
$611$	−6050.74	−	3493.40i	−0.400633	−	0.231306i
$612$		0			0
$613$	8441.91	+	14621.8i	0.556224	+	0.963409i	0.997807	+	0.0661884i	$0.0210838\pi$
$613$	8441.91	+	14621.8i	0.556224	+	0.963409i	−0.441583	+	0.897221i	$0.645583\pi$
$614$		0			0
$615$	6194.70	+	39305.3i	0.406170	+	2.57714i
$616$		0			0
$617$	16517.0	−	9536.08i	1.07771	−	0.622217i	0.147433	−	0.989072i	$-0.452899\pi$
$617$	16517.0	−	9536.08i	1.07771	−	0.622217i	0.930278	+	0.366855i	$0.119565\pi$
$618$		0			0
$619$		−	18974.3i		−	1.23205i	−0.787725	−	0.616027i	$-0.788741\pi$
$619$		−	18974.3i		−	1.23205i	0.787725	−	0.616027i	$-0.211259\pi$
$620$		0			0
$621$	−22951.3	+	11628.4i	−1.48310	+	0.751417i
$622$		0			0
$623$	1323.46	−	19.0293i	0.0851095	−	0.00122374i
$624$		0			0
$625$	45697.8			2.92466
$626$		0			0
$627$	1790.75	−	1447.87i	0.114060	−	0.0922207i
$628$		0			0
$629$	−19940.3			−1.26402
$630$		0			0
$631$	−4831.10			−0.304791			−0.152395	−	0.988320i	$-0.548699\pi$
$631$	−4831.10			−0.304791			−0.152395	+	0.988320i	$0.548699\pi$
$632$		0			0
$633$	1834.45	+	11639.6i	0.115186	+	0.730857i
$634$		0			0
$635$	−17724.2			−1.10766
$636$		0			0
$637$	−440.732	−	15323.0i	−0.0274136	−	0.953089i
$638$		0			0
$639$	2957.42	−	3274.51i	0.183088	−	0.202719i
$640$		0			0
$641$		−	3950.16i		−	0.243404i	−0.992567	−	0.121702i	$-0.961165\pi$
$641$		−	3950.16i		−	0.243404i	0.992567	−	0.121702i	$-0.0388352\pi$
$642$		0			0
$643$	19298.7	−	11142.1i	1.18362	−	0.683362i	0.226769	−	0.973949i	$-0.427184\pi$
$643$	19298.7	−	11142.1i	1.18362	−	0.683362i	0.956849	+	0.290587i	$0.0938504\pi$
$644$		0			0
$645$	−14782.4	+	11951.9i	−0.902412	+	0.729622i
$646$		0			0
$647$	6793.26	+	11766.3i	0.412783	+	0.714962i	0.995193	−	0.0979339i	$-0.0312234\pi$
$647$	6793.26	+	11766.3i	0.412783	+	0.714962i	−0.582410	+	0.812895i	$0.697890\pi$
$648$		0			0
$649$	22647.3	+	13075.4i	1.36977	+	0.790839i
$650$		0			0
$651$	236.948	−	643.319i	0.0142653	−	0.0387307i
$652$		0			0
$653$			10088.3i			0.604572i	0.953217	+	0.302286i	$0.0977498\pi$
$653$			10088.3i			0.604572i	−0.953217	+	0.302286i	$0.902250\pi$
$654$		0			0
$655$	−36917.2			−2.20225
$656$		0			0
$657$	21702.7	+	4647.58i	1.28874	+	0.275981i
$658$		0			0
$659$	−9993.24	−	5769.60i	−0.590715	−	0.341050i	0.174665	−	0.984628i	$-0.444116\pi$
$659$	−9993.24	−	5769.60i	−0.590715	−	0.341050i	−0.765380	+	0.643578i	$0.777449\pi$
$660$		0			0
$661$	−5776.45	−	3335.03i	−0.339906	−	0.196245i	0.320324	−	0.947308i	$-0.396208\pi$
$661$	−5776.45	−	3335.03i	−0.339906	−	0.196245i	−0.660230	+	0.751063i	$0.729541\pi$
$662$		0			0
$663$	−17752.1	−	21956.2i	−1.03987	−	1.28614i
$664$		0			0
$665$	−73.9659	−	5144.22i	−0.00431320	−	0.299976i
$666$		0			0
$667$	1817.58	−	3148.14i	0.105513	−	0.182754i
$668$		0			0
$669$	12592.2	+	15574.3i	0.727717	+	0.900056i
$670$		0			0
$671$	2735.48	+	4737.99i	0.157380	+	0.272590i
$672$		0			0
$673$	−3279.71	+	5680.62i	−0.187851	+	0.325367i	−0.944533	−	0.328415i	$-0.893485\pi$
$673$	−3279.71	+	5680.62i	−0.187851	+	0.325367i	0.756683	+	0.653782i	$0.226819\pi$
$674$		0			0
$675$	−20157.3	−	39785.1i	−1.14941	−	2.26864i
$676$		0			0
$677$	10506.7	+	18198.1i	0.596463	+	1.03310i	0.993339	+	0.115232i	$0.0367610\pi$
$677$	10506.7	+	18198.1i	0.596463	+	1.03310i	−0.396876	+	0.917872i	$0.629906\pi$
$678$		0			0
$679$	360.894	+	25099.7i	0.0203974	+	1.41861i
$680$		0			0
$681$	−6982.75	−	2686.52i	−0.392921	−	0.151172i
$682$		0			0
$683$	102.587	−	59.2288i	0.00574729	−	0.00331820i	−0.497124	−	0.867680i	$-0.665610\pi$
$683$	102.587	−	59.2288i	0.00574729	−	0.00331820i	0.502871	+	0.864362i	$0.332277\pi$
$684$		0			0
$685$		−	25836.2i		−	1.44109i
$686$		0			0
$687$	−9262.96	+	24076.1i	−0.514416	+	1.33706i
$688$		0			0
$689$	−3439.13	+	5956.75i	−0.190160	+	0.329368i
$690$		0			0
$691$	−3067.94	+	1771.27i	−0.168900	+	0.0975144i	−0.582067	−	0.813141i	$-0.697756\pi$
$691$	−3067.94	+	1771.27i	−0.168900	+	0.0975144i	0.413167	+	0.910655i	$0.364423\pi$
$692$		0			0
$693$	−16465.8	−	3279.27i	−0.902577	−	0.179754i
$694$		0			0
$695$	−269.903	+	155.828i	−0.0147309	+	0.00850490i
$696$		0			0
$697$	22120.4	−	38313.6i	1.20211	−	2.08211i
$698$		0			0
$699$	−356.802	−	441.300i	−0.0193069	−	0.0238791i
$700$		0			0
$701$		−	4777.24i		−	0.257395i	−0.991684	−	0.128697i	$-0.958920\pi$
$701$		−	4777.24i		−	0.257395i	0.991684	−	0.128697i	$-0.0410796\pi$
$702$		0			0
$703$	1874.78	−	1082.40i	0.100581	−	0.0580705i
$704$		0			0
$705$	2661.50	+	16887.2i	0.142181	+	0.902138i
$706$		0			0
$707$	−15340.7	−	25709.9i	−0.816047	−	1.36764i
$708$		0			0
$709$	−9090.74	−	15745.6i	−0.481537	−	0.834047i	0.518238	−	0.855236i	$-0.326588\pi$
$709$	−9090.74	−	15745.6i	−0.481537	−	0.834047i	−0.999775	+	0.0211896i	$0.993255\pi$
$710$		0			0
$711$	3116.27	−	14552.0i	0.164373	−	0.767568i
$712$		0			0
$713$	653.234	−	1131.43i	0.0343111	−	0.0594286i
$714$		0			0
$715$	15789.6	+	27348.3i	0.825869	+	1.43045i
$716$		0			0
$717$	−2575.72	+	405.945i	−0.134159	+	0.0211441i
$718$		0			0
$719$	−9552.20	+	16544.9i	−0.495462	+	0.858165i	−0.999986	−	0.00523231i	$-0.998334\pi$
$719$	−9552.20	+	16544.9i	−0.495462	+	0.858165i	0.504524	+	0.863397i	$0.331668\pi$
$720$		0			0
$721$	29967.5	−	17881.1i	1.54792	−	0.923614i
$722$		0			0
$723$	−6586.08	+	17118.4i	−0.338781	+	0.880552i
$724$		0			0
$725$	5457.17	+	3150.70i	0.279551	+	0.161399i
$726$		0			0
$727$	−12203.8	−	7045.88i	−0.622579	−	0.359446i	0.155293	−	0.987868i	$-0.450368\pi$
$727$	−12203.8	−	7045.88i	−0.622579	−	0.359446i	−0.777872	+	0.628422i	$0.783701\pi$
$728$		0			0
$729$	−11642.0	+	15870.9i	−0.591472	+	0.806325i
$730$		0			0
$731$	21135.7			1.06940
$732$		0			0
$733$			2218.46i			0.111788i	0.998437	+	0.0558940i	$0.0178009\pi$
$733$			2218.46i			0.111788i	−0.998437	+	0.0558940i	$0.982199\pi$
$734$		0			0
$735$	−28477.4	+	24411.5i	−1.42912	+	1.22508i
$736$		0			0
$737$	3416.95	+	1972.78i	0.170780	+	0.0985999i
$738$		0			0
$739$	−7935.97	−	13745.5i	−0.395033	−	0.684217i	0.598072	−	0.801442i	$-0.295934\pi$
$739$	−7935.97	−	13745.5i	−0.395033	−	0.684217i	−0.993105	+	0.117225i	$0.962600\pi$
$740$		0			0
$741$	2860.88	+	1100.69i	0.141831	+	0.0545678i
$742$		0			0
$743$	−21671.3	+	12511.9i	−1.07004	+	0.617790i	−0.928193	−	0.372098i	$-0.878638\pi$
$743$	−21671.3	+	12511.9i	−1.07004	+	0.617790i	−0.141850	+	0.989888i	$0.545305\pi$
$744$		0			0
$745$			67925.2i			3.34038i
$746$		0			0
$747$	−9673.53	+	3126.85i	−0.473810	+	0.153153i
$748$		0			0
$749$	−164.018	−	11407.2i	−0.00800143	−	0.556488i
$750$		0			0
$751$	8494.13			0.412723			0.206362	−	0.978476i	$-0.433838\pi$
$751$	8494.13			0.412723			0.206362	+	0.978476i	$0.433838\pi$
$752$		0			0
$753$	8566.36	+	3295.80i	0.414576	+	0.159503i
$754$		0			0
$755$	53726.1			2.58979
$756$		0			0
$757$	−18632.8			−0.894611			−0.447306	−	0.894381i	$-0.647616\pi$
$757$	−18632.8			−0.894611			−0.447306	+	0.894381i	$0.647616\pi$
$758$		0			0
$759$	−29860.9	−	11488.6i	−1.42804	−	0.549421i
$760$		0			0
$761$	14617.8			0.696313			0.348156	−	0.937437i	$-0.386808\pi$
$761$	14617.8			0.696313			0.348156	+	0.937437i	$0.386808\pi$
$762$		0			0
$763$	−6205.97	+	11115.1i	−0.294458	+	0.527384i
$764$		0			0
$765$	−14466.7	+	67555.0i	−0.683720	+	3.19275i
$766$		0			0
$767$			34809.2i			1.63870i
$768$		0			0
$769$	−21048.4	+	12152.3i	−0.987027	+	0.569861i	−0.904384	−	0.426719i	$-0.859669\pi$
$769$	−21048.4	+	12152.3i	−0.987027	+	0.569861i	−0.0826431	+	0.996579i	$0.526336\pi$
$770$		0			0
$771$	12758.0	+	4908.48i	0.595938	+	0.229280i
$772$		0			0
$773$	3868.78	+	6700.93i	0.180013	+	0.311792i	0.941885	−	0.335936i	$-0.109053\pi$
$773$	3868.78	+	6700.93i	0.180013	+	0.311792i	−0.761871	+	0.647728i	$0.775719\pi$
$774$		0			0
$775$	1961.29	+	1132.35i	0.0909055	+	0.0524843i
$776$		0			0
$777$	−14810.1	−	5454.88i	−0.683797	−	0.251857i
$778$		0			0
$779$			4802.96i			0.220904i
$780$		0			0
$781$	5486.87			0.251390
$782$		0			0
$783$	151.882	−	2776.79i	0.00693209	−	0.126736i
$784$		0			0
$785$	−25705.0	−	14840.8i	−1.16873	−	0.674765i
$786$		0			0
$787$	14372.4	+	8297.94i	0.650981	+	0.375844i	0.788832	−	0.614609i	$-0.210686\pi$
$787$	14372.4	+	8297.94i	0.650981	+	0.375844i	−0.137851	+	0.990453i	$0.544019\pi$
$788$		0			0
$789$	−12005.4	+	31204.2i	−0.541704	+	1.40798i
$790$		0			0
$791$	3987.92	+	2226.60i	0.179259	+	0.100087i
$792$		0			0
$793$	−3641.18	+	6306.71i	−0.163054	+	0.282418i
$794$		0			0
$795$	16624.9	−	2620.15i	0.741664	−	0.116890i
$796$		0			0
$797$	−13705.0	−	23737.7i	−0.609104	−	1.05500i	−0.991388	−	0.130954i	$-0.958196\pi$
$797$	−13705.0	−	23737.7i	−0.609104	−	1.05500i	0.382285	−	0.924045i	$-0.375137\pi$
$798$		0			0
$799$	9503.81	−	16461.1i	0.420802	−	0.728850i
$800$		0			0
$801$	1836.08	−	593.492i	0.0809922	−	0.0261798i
$802$		0			0
$803$	13799.9	+	23902.1i	0.606461	+	1.05042i
$804$		0			0
$805$	−61382.2	+	36625.6i	−2.68750	+	1.60358i
$806$		0			0
$807$	3219.95	+	20430.6i	0.140456	+	0.891190i
$808$		0			0
$809$	1683.36	−	971.887i	0.0731566	−	0.0422370i	−0.462975	−	0.886371i	$-0.653218\pi$
$809$	1683.36	−	971.887i	0.0731566	−	0.0422370i	0.536132	+	0.844134i	$0.319885\pi$
$810$		0			0
$811$		−	19877.7i		−	0.860664i	−0.902671	−	0.430332i	$-0.858396\pi$
$811$		−	19877.7i		−	0.860664i	0.902671	−	0.430332i	$-0.141604\pi$
$812$		0			0
$813$	−17139.6	−	21198.6i	−0.739375	−	0.914474i
$814$		0			0
$815$	3125.74	−	5413.95i	0.134344	−	0.232690i
$816$		0			0
$817$	−1987.17	+	1147.29i	−0.0850946	+	0.0491294i
$818$		0			0
$819$	−7178.57	−	21163.7i	−0.306276	−	0.902954i
$820$		0			0
$821$	3992.85	−	2305.27i	0.169734	−	0.0979959i	−0.412726	−	0.910855i	$-0.635423\pi$
$821$	3992.85	−	2305.27i	0.169734	−	0.0979959i	0.582460	+	0.812859i	$0.302090\pi$
$822$		0			0
$823$	16563.9	−	28689.6i	0.701558	−	1.21513i	−0.266361	−	0.963873i	$-0.585821\pi$
$823$	16563.9	−	28689.6i	0.701558	−	1.21513i	0.967919	−	0.251261i	$-0.0808453\pi$
$824$		0			0
$825$	19915.0	−	51762.6i	0.840426	−	2.18442i
$826$		0			0
$827$			1937.80i			0.0814800i	0.999170	+	0.0407400i	$0.0129715\pi$
$827$			1937.80i			0.0814800i	−0.999170	+	0.0407400i	$0.987028\pi$
$828$		0			0
$829$	−10237.2	+	5910.44i	−0.428893	+	0.247622i	−0.698875	−	0.715244i	$-0.746316\pi$
$829$	−10237.2	+	5910.44i	−0.428893	+	0.247622i	0.269982	+	0.962865i	$0.412982\pi$
$830$		0			0
$831$	−17218.7	−	6624.66i	−0.718783	−	0.276542i
$832$		0			0
$833$	41686.2	−	1199.01i	1.73390	−	0.0498720i
$834$		0			0
$835$	−9100.47	−	15762.5i	−0.377167	−	0.653273i
$836$		0			0
$837$	54.5861	−	997.973i	0.00225421	−	0.0412127i
$838$		0			0
$839$	−14192.1	+	24581.4i	−0.583986	+	1.01149i	0.411015	+	0.911629i	$0.365174\pi$
$839$	−14192.1	+	24581.4i	−0.583986	+	1.01149i	−0.995001	+	0.0998651i	$0.968159\pi$
$840$		0			0
$841$	−11998.0	−	20781.2i	−0.491945	−	0.852074i
$842$		0			0
$843$	−5583.72	−	6906.06i	−0.228130	−	0.282156i
$844$		0			0
$845$	2100.75	−	3638.60i	0.0855242	−	0.148132i
$846$		0			0
$847$	1933.08	+	3239.71i	0.0784194	+	0.131426i
$848$		0			0
$849$	24016.8	+	29704.5i	0.970853	+	1.20077i
$850$		0			0
$851$	−26047.2	−	15038.4i	−1.04922	−	0.605769i
$852$		0			0
$853$	37002.9	+	21363.6i	1.48529	+	0.857533i	0.999860	−	0.0167411i	$-0.00532912\pi$
$853$	37002.9	+	21363.6i	1.48529	+	0.857533i	0.485432	+	0.874275i	$0.338662\pi$
$854$		0			0
$855$	−2306.88	−	7136.77i	−0.0922731	−	0.285465i
$856$		0			0
$857$	−15237.6			−0.607360			−0.303680	−	0.952774i	$-0.598215\pi$
$857$	−15237.6			−0.607360			−0.303680	+	0.952774i	$0.598215\pi$
$858$		0			0
$859$			34867.3i			1.38493i	0.721451	+	0.692465i	$0.243475\pi$
$859$			34867.3i			1.38493i	−0.721451	+	0.692465i	$0.756525\pi$
$860$		0			0
$861$	26910.4	−	22405.1i	1.06516	−	0.886835i
$862$		0			0
$863$	−5873.12	−	3390.85i	−0.231661	−	0.133749i	0.379677	−	0.925119i	$-0.376035\pi$
$863$	−5873.12	−	3390.85i	−0.231661	−	0.133749i	−0.611338	+	0.791370i	$0.709368\pi$
$864$		0			0
$865$	−9880.70	−	17113.9i	−0.388386	−	0.672704i
$866$		0			0
$867$	39880.2	−	32244.2i	1.56217	−	1.26306i
$868$		0			0
$869$	16026.7	−	9253.03i	0.625626	−	0.361205i
$870$		0			0
$871$			5251.90i			0.204310i
$872$		0			0
$873$	11255.7	+	34821.7i	0.436366	+	1.34998i
$874$		0			0
$875$	−38524.7	−	64564.9i	−1.48843	−	2.49451i
$876$		0			0
$877$	−35127.3			−1.35253			−0.676263	−	0.736661i	$-0.736402\pi$
$877$	−35127.3			−1.35253			−0.676263	+	0.736661i	$0.736402\pi$
$878$		0			0
$879$	−145.688	−	924.390i	−0.00559037	−	0.0354709i
$880$		0			0
$881$	6961.66			0.266225			0.133112	−	0.991101i	$-0.457503\pi$
$881$	6961.66			0.266225			0.133112	+	0.991101i	$0.457503\pi$
$882$		0			0
$883$	29695.3			1.13174			0.565870	−	0.824494i	$-0.308540\pi$
$883$	29695.3			1.13174			0.565870	+	0.824494i	$0.308540\pi$
$884$		0			0
$885$	66232.3	−	53550.5i	2.51568	−	2.03399i
$886$		0			0
$887$	5644.18			0.213656			0.106828	−	0.994278i	$-0.465931\pi$
$887$	5644.18			0.213656			0.106828	+	0.994278i	$0.465931\pi$
$888$		0			0
$889$	7992.26	+	13394.5i	0.301521	+	0.505329i
$890$		0			0
$891$	−24350.0	+	2484.38i	−0.915549	+	0.0934118i
$892$		0			0
$893$			2063.55i			0.0773282i
$894$		0			0
$895$	53943.9	−	31144.5i	2.01469	−	1.16318i
$896$		0			0
$897$	−6630.22	−	42068.7i	−0.246797	−	1.56592i
$898$		0			0
$899$	70.6055	+	122.292i	0.00261938	+	0.00453691i
$900$		0			0
$901$	−16205.4	−	9356.18i	−0.599200	−	0.345948i
$902$		0			0
$903$	15698.0	+	5781.91i	0.578512	+	0.213078i
$904$		0			0
$905$		−	58321.4i		−	2.14218i
$906$		0			0
$907$	18011.9			0.659398			0.329699	−	0.944086i	$-0.393053\pi$
$907$	18011.9			0.659398			0.329699	+	0.944086i	$0.393053\pi$
$908$		0			0
$909$	−32391.4	−	29254.7i	−1.18191	−	1.06746i
$910$		0			0
$911$	−40124.8	−	23166.1i	−1.45927	−	0.842510i	−0.460295	−	0.887766i	$-0.652256\pi$
$911$	−40124.8	−	23166.1i	−1.45927	−	0.842510i	−0.998975	+	0.0452562i	$0.985590\pi$
$912$		0			0
$913$	−10948.4	−	6321.06i	−0.396867	−	0.229131i
$914$		0			0
$915$	17601.5	−	2774.08i	0.635944	−	0.100228i
$916$		0			0
$917$	16646.8	+	27899.0i	0.599484	+	1.00470i
$918$		0			0
$919$	3387.56	−	5867.43i	0.121595	−	0.210608i	−0.798802	−	0.601594i	$-0.794533\pi$
$919$	3387.56	−	5867.43i	0.121595	−	0.210608i	0.920397	+	0.390986i	$0.127866\pi$
$920$		0			0
$921$	−10121.4	+	26307.3i	−0.362119	+	0.941212i
$922$		0			0
$923$	3651.76	+	6325.04i	0.130227	+	0.225559i
$924$		0			0
$925$	26068.4	−	45151.8i	0.926620	−	1.60495i
$926$		0			0
$927$	34099.3	−	37755.4i	1.20816	−	1.33770i
$928$		0			0
$929$	20448.9	+	35418.5i	0.722180	+	1.25085i	0.960124	+	0.279573i	$0.0901930\pi$
$929$	20448.9	+	35418.5i	0.722180	+	1.25085i	−0.237944	+	0.971279i	$0.576474\pi$
$930$		0			0
$931$	−3854.23	+	2375.55i	−0.135679	+	0.0836256i
$932$		0			0
$933$	23636.5	−	19110.7i	0.829392	−	0.670584i
$934$		0			0
$935$	−74401.3	+	42955.6i	−2.60233	+	1.50246i
$936$		0			0
$937$			45677.6i			1.59255i	0.604933	+	0.796277i	$0.293200\pi$
$937$			45677.6i			1.59255i	−0.604933	+	0.796277i	$0.706800\pi$
$938$		0			0
$939$	457.054	−	72.0339i	0.0158844	−	0.00250345i
$940$		0			0
$941$	14013.9	−	24272.8i	0.485485	−	0.840884i	−0.514376	−	0.857565i	$-0.671976\pi$
$941$	14013.9	−	24272.8i	0.485485	−	0.840884i	0.999861	+	0.0166805i	$0.00530982\pi$
$942$		0			0
$943$	57790.0	−	33365.1i	1.99565	−	1.15219i
$944$		0			0
$945$	−29225.2	+	46217.1i	−1.00603	+	1.59095i
$946$		0			0
$947$	780.984	−	450.901i	0.0267989	−	0.0154724i	−0.486541	−	0.873658i	$-0.661741\pi$
$947$	780.984	−	450.901i	0.0267989	−	0.0154724i	0.513340	+	0.858186i	$0.328408\pi$
$948$		0			0
$949$	−18369.0	+	31816.0i	−0.628326	+	1.08829i
$950$		0			0
$951$	27662.5	−	4359.74i	0.943238	−	0.148659i
$952$		0			0
$953$		−	27310.4i		−	0.928302i	−0.885756	−	0.464151i	$-0.846359\pi$
$953$		−	27310.4i		−	0.928302i	0.885756	−	0.464151i	$-0.153641\pi$
$954$		0			0
$955$	−50513.0	+	29163.7i	−1.71158	+	0.988183i
$956$		0			0
$957$	2689.17	−	2174.26i	0.0908344	−	0.0734419i
$958$		0			0
$959$	−19524.9	+	11650.1i	−0.657446	+	0.392286i
$960$		0			0
$961$	−14870.1	−	25755.8i	−0.499148	−	0.864550i
$962$		0			0
$963$	−5115.44	−	15825.6i	−0.171176	−	0.529567i
$964$		0			0
$965$	−47763.9	+	82729.5i	−1.59334	+	2.75975i
$966$		0			0
$967$	−10422.3	−	18052.0i	−0.346597	−	0.600323i	0.639046	−	0.769169i	$-0.279329\pi$
$967$	−10422.3	−	18052.0i	−0.346597	−	0.600323i	−0.985643	+	0.168846i	$0.945996\pi$
$968$		0			0
$969$	−2994.42	+	7783.03i	−0.0992721	+	0.258026i
$970$		0			0
$971$	17075.9	−	29576.4i	0.564359	−	0.977499i	−0.432750	−	0.901514i	$-0.642457\pi$
$971$	17075.9	−	29576.4i	0.564359	−	0.977499i	0.997109	−	0.0759847i	$-0.0242100\pi$
$972$		0			0
$973$	239.468	+	133.704i	0.00789002	+	0.00440529i
$974$		0			0
$975$	72924.3	−	11493.2i	2.39533	−	0.377515i
$976$		0			0
$977$	41325.7	+	23859.4i	1.35325	+	0.781300i	0.988704	−	0.149884i	$-0.0478901\pi$
$977$	41325.7	+	23859.4i	1.35325	+	0.781300i	0.364548	+	0.931185i	$0.381223\pi$
$978$		0			0
$979$	2078.06	+	1199.77i	0.0678397	+	0.0391673i
$980$		0			0
$981$	−3886.25	+	18147.5i	−0.126482	+	0.590628i
$982$		0			0
$983$	−1110.83			−0.0360427			−0.0180214	−	0.999838i	$-0.505737\pi$
$983$	−1110.83			−0.0360427			−0.0180214	+	0.999838i	$0.505737\pi$
$984$		0			0
$985$		−	10612.2i		−	0.343281i
$986$		0			0
$987$	11561.8	−	9626.16i	0.372864	−	0.310440i
$988$		0			0
$989$	27608.8	+	15939.9i	0.887673	+	0.512498i
$990$		0			0
$991$	−21000.5	−	36373.9i	−0.673160	−	1.16595i	−0.977003	−	0.213226i	$-0.931603\pi$
$991$	−21000.5	−	36373.9i	−0.673160	−	1.16595i	0.303843	−	0.952722i	$-0.401730\pi$
$992$		0			0
$993$	−1018.04	−	6459.49i	−0.0325344	−	0.206431i
$994$		0			0
$995$	−8398.77	+	4849.03i	−0.267597	+	0.154497i
$996$		0			0
$997$			56175.6i			1.78445i	0.451590	+	0.892225i	$0.350857\pi$
$997$			56175.6i			1.78445i	−0.451590	+	0.892225i	$0.649143\pi$
$998$		0			0
$999$	−22974.8	−	1256.65i	−0.727617	−	0.0397984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.3	yes	48
3.2	odd	2		756.4.bm.a.89.24		48
7.3	odd	6		252.4.w.a.101.11	yes	48
9.4	even	3		756.4.w.a.341.24		48
9.5	odd	6		252.4.w.a.5.11	✓	48
21.17	even	6		756.4.w.a.521.24		48
63.31	odd	6		756.4.bm.a.17.24		48
63.59	even	6	inner	252.4.bm.a.185.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.11	✓	48	9.5	odd	6
252.4.w.a.101.11	yes	48	7.3	odd	6
252.4.bm.a.173.3	yes	48	1.1	even	1	trivial
252.4.bm.a.185.3	yes	48	63.59	even	6	inner
756.4.w.a.341.24		48	9.4	even	3
756.4.w.a.521.24		48	21.17	even	6
756.4.bm.a.17.24		48	63.31	odd	6
756.4.bm.a.89.24		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-4.84961 - 1.86582i) q^{3} -21.0452 q^{5} +(9.48976 + 15.9042i) q^{7} +(20.0374 + 18.0970i) q^{9} +O(q^{10})\)	\(q+(-4.84961 - 1.86582i) q^{3} -21.0452 q^{5} +(9.48976 + 15.9042i) q^{7} +(20.0374 + 18.0970i) q^{9} +33.5753i q^{11} +(-38.7042 + 22.3459i) q^{13} +(102.061 + 39.2666i) q^{15} +(-60.7921 - 105.295i) q^{17} +(11.4313 + 6.59986i) q^{19} +(-16.3471 - 94.8355i) q^{21} -183.391i q^{23} +317.900 q^{25} +(-63.4076 - 125.150i) q^{27} +(17.1663 + 9.91099i) q^{29} +(6.16954 + 3.56198i) q^{31} +(62.6456 - 162.827i) q^{33} +(-199.714 - 334.707i) q^{35} +(82.0019 - 142.031i) q^{37} +(229.394 - 36.1535i) q^{39} +(181.934 + 315.120i) q^{41} +(-86.9180 + 150.546i) q^{43} +(-421.691 - 380.855i) q^{45} +(78.1664 + 135.388i) q^{47} +(-162.889 + 301.855i) q^{49} +(98.3559 + 624.067i) q^{51} +(133.285 - 76.9522i) q^{53} -706.598i q^{55} +(-43.1231 - 53.3355i) q^{57} +(389.435 - 674.522i) q^{59} +(141.115 - 81.4730i) q^{61} +(-97.6692 + 490.416i) q^{63} +(814.538 - 470.274i) q^{65} +(58.7568 - 101.770i) q^{67} +(-342.175 + 889.373i) q^{69} -163.420i q^{71} +(711.897 - 411.014i) q^{73} +(-1541.69 - 593.145i) q^{75} +(-533.989 + 318.621i) q^{77} +(-275.591 - 477.337i) q^{79} +(73.9944 + 725.235i) q^{81} +(-188.265 + 326.085i) q^{83} +(1279.38 + 2215.95i) q^{85} +(-64.7578 - 80.0938i) q^{87} +(35.7337 - 61.8925i) q^{89} +(-722.689 - 403.504i) q^{91} +(-23.2738 - 28.7855i) q^{93} +(-240.574 - 138.895i) q^{95} +(1173.81 + 677.697i) q^{97} +(-607.613 + 672.761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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