LMFDB - Embedded newform 476.3.x.a.321.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(321,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("476.321");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.x (of order $8$, degree $4$, 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:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			321.19
Character	$\chi$	$=$	476.321
Dual form			476.3.x.a.433.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.58574 - 1.07105i) q^{3} +(2.55560 + 6.16976i) q^{5} +(-4.71280 + 5.17586i) q^{7} +(-0.825039 + 0.825039i) q^{9} +(1.49730 - 3.61481i) q^{11} +17.3201 q^{13} +(13.2162 + 13.2162i) q^{15} +(-16.8940 - 1.89555i) q^{17} +(-6.39261 + 6.39261i) q^{19} +(-6.64249 + 18.4311i) q^{21} +(-16.0718 + 38.8007i) q^{23} +(-13.8572 + 13.8572i) q^{25} +(-10.8891 + 26.2887i) q^{27} +(13.4186 - 5.55816i) q^{29} +(3.06492 - 1.26953i) q^{31} -10.9507i q^{33} +(-43.9778 - 15.8494i) q^{35} +(12.8990 + 31.1409i) q^{37} +(44.7853 - 18.5507i) q^{39} +(28.5624 - 68.9556i) q^{41} +(-38.2049 + 38.2049i) q^{43} +(-7.19876 - 2.98182i) q^{45} +58.8692 q^{47} +(-4.57902 - 48.7856i) q^{49} +(-45.7138 + 13.1929i) q^{51} +(13.5679 + 13.5679i) q^{53} +26.1290 q^{55} +(-9.68285 + 23.3765i) q^{57} +(78.1791 + 78.1791i) q^{59} +(7.04078 - 16.9979i) q^{61} +(-0.382041 - 8.15853i) q^{63} +(44.2631 + 106.861i) q^{65} +99.2537 q^{67} +117.542i q^{69} +(-49.5054 - 119.517i) q^{71} +(-45.9951 - 111.042i) q^{73} +(-20.9894 + 50.6728i) q^{75} +(11.6533 + 24.7857i) q^{77} +(-15.2402 + 36.7932i) q^{79} +69.1376i q^{81} +(-26.4297 + 26.4297i) q^{83} +(-31.4791 - 109.076i) q^{85} +(28.7440 - 28.7440i) q^{87} -43.3144 q^{89} +(-81.6261 + 89.6462i) q^{91} +(6.56536 - 6.56536i) q^{93} +(-55.7778 - 23.1039i) q^{95} +(2.09599 + 5.06017i) q^{97} +(1.74703 + 4.21769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{11} - 16 q^{15} + 72 q^{23} + 72 q^{25} + 32 q^{35} - 256 q^{37} - 88 q^{39} - 32 q^{43} - 20 q^{49} - 120 q^{51} - 80 q^{53} + 492 q^{63} - 104 q^{65} - 144 q^{67} - 64 q^{71} + 84 q^{77}+ \cdots + 560 q^{99}+O(q^{100}) $ 96 * q - 40 * q^11 - 16 * q^15 + 72 * q^23 + 72 * q^25 + 32 * q^35 - 256 * q^37 - 88 * q^39 - 32 * q^43 - 20 * q^49 - 120 * q^51 - 80 * q^53 + 492 * q^63 - 104 * q^65 - 144 * q^67 - 64 * q^71 + 84 * q^77 - 256 * q^79 + 824 * q^85 - 368 * q^91 - 264 * q^93 + 104 * q^95 + 560 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.58574	−	1.07105i	0.861915	−	0.357017i	0.0924586	−	0.995717i	$-0.470527\pi$
$3$	2.58574	−	1.07105i	0.861915	−	0.357017i	0.769456	+	0.638700i	$0.220527\pi$
$4$		0			0
$5$	2.55560	+	6.16976i	0.511120	+	1.23395i	0.943233	+	0.332132i	$0.107768\pi$
$5$	2.55560	+	6.16976i	0.511120	+	1.23395i	−0.432113	+	0.901819i	$0.642232\pi$
$6$		0			0
$7$	−4.71280	+	5.17586i	−0.673257	+	0.739408i
$7$	−4.71280	+	5.17586i	−0.673257	+	0.739408i
$8$		0			0
$9$	−0.825039	+	0.825039i	−0.0916710	+	0.0916710i
$10$		0			0
$11$	1.49730	−	3.61481i	0.136118	−	0.328619i	−0.841092	−	0.540892i	$-0.818087\pi$
$11$	1.49730	−	3.61481i	0.136118	−	0.328619i	0.977210	+	0.212273i	$0.0680867\pi$
$12$		0			0
$13$	17.3201			1.33231			0.666157	−	0.745812i	$-0.267938\pi$
$13$	17.3201			1.33231			0.666157	+	0.745812i	$0.267938\pi$
$14$		0			0
$15$	13.2162	+	13.2162i	0.881083	+	0.881083i
$16$		0			0
$17$	−16.8940	−	1.89555i	−0.993764	−	0.111503i
$17$	−16.8940	−	1.89555i	−0.993764	−	0.111503i
$18$		0			0
$19$	−6.39261	+	6.39261i	−0.336453	+	0.336453i	−0.855031	−	0.518577i	$-0.826462\pi$
$19$	−6.39261	+	6.39261i	−0.336453	+	0.336453i	0.518577	+	0.855031i	$0.326462\pi$
$20$		0			0
$21$	−6.64249	+	18.4311i	−0.316309	+	0.877671i
$22$		0			0
$23$	−16.0718	+	38.8007i	−0.698773	+	1.68699i	0.0275376	+	0.999621i	$0.491233\pi$
$23$	−16.0718	+	38.8007i	−0.698773	+	1.68699i	−0.726311	+	0.687367i	$0.758767\pi$
$24$		0			0
$25$	−13.8572	+	13.8572i	−0.554287	+	0.554287i
$26$		0			0
$27$	−10.8891	+	26.2887i	−0.403301	+	0.973655i
$28$		0			0
$29$	13.4186	−	5.55816i	0.462710	−	0.191661i	−0.139135	−	0.990273i	$-0.544432\pi$
$29$	13.4186	−	5.55816i	0.462710	−	0.191661i	0.601845	+	0.798613i	$0.294432\pi$
$30$		0			0
$31$	3.06492	−	1.26953i	0.0988683	−	0.0409526i	−0.332701	−	0.943032i	$-0.607960\pi$
$31$	3.06492	−	1.26953i	0.0988683	−	0.0409526i	0.431569	+	0.902080i	$0.357960\pi$
$32$		0			0
$33$		−	10.9507i		−	0.331838i
$34$		0			0
$35$	−43.9778	−	15.8494i	−1.25651	−	0.452841i
$36$		0			0
$37$	12.8990	+	31.1409i	0.348621	+	0.841645i	0.996783	+	0.0801431i	$0.0255377\pi$
$37$	12.8990	+	31.1409i	0.348621	+	0.841645i	−0.648163	+	0.761502i	$0.724462\pi$
$38$		0			0
$39$	44.7853	−	18.5507i	1.14834	−	0.475658i
$40$		0			0
$41$	28.5624	−	68.9556i	0.696643	−	1.68184i	−0.0343049	−	0.999411i	$-0.510922\pi$
$41$	28.5624	−	68.9556i	0.696643	−	1.68184i	0.730948	−	0.682433i	$-0.239078\pi$
$42$		0			0
$43$	−38.2049	+	38.2049i	−0.888487	+	0.888487i	−0.994378	−	0.105891i	$-0.966230\pi$
$43$	−38.2049	+	38.2049i	−0.888487	+	0.888487i	0.105891	+	0.994378i	$0.466230\pi$
$44$		0			0
$45$	−7.19876	−	2.98182i	−0.159972	−	0.0662628i
$46$		0			0
$47$	58.8692			1.25254			0.626268	−	0.779608i	$-0.284582\pi$
$47$	58.8692			1.25254			0.626268	+	0.779608i	$0.284582\pi$
$48$		0			0
$49$	−4.57902	−	48.7856i	−0.0934493	−	0.995624i
$50$		0			0
$51$	−45.7138	+	13.1929i	−0.896348	+	0.258684i
$52$		0			0
$53$	13.5679	+	13.5679i	0.255999	+	0.255999i	0.823425	−	0.567426i	$-0.192061\pi$
$53$	13.5679	+	13.5679i	0.255999	+	0.255999i	−0.567426	+	0.823425i	$0.692061\pi$
$54$		0			0
$55$	26.1290			0.475073
$56$		0			0
$57$	−9.68285	+	23.3765i	−0.169875	+	0.410114i
$58$		0			0
$59$	78.1791	+	78.1791i	1.32507	+	1.32507i	0.909613	+	0.415457i	$0.136378\pi$
$59$	78.1791	+	78.1791i	1.32507	+	1.32507i	0.415457	+	0.909613i	$0.363622\pi$
$60$		0			0
$61$	7.04078	−	16.9979i	0.115423	−	0.278655i	−0.855602	−	0.517634i	$-0.826813\pi$
$61$	7.04078	−	16.9979i	0.115423	−	0.278655i	0.971025	+	0.238979i	$0.0768129\pi$
$62$		0			0
$63$	−0.382041	−	8.15853i	−0.00606414	−	0.129500i
$64$		0			0
$65$	44.2631	+	106.861i	0.680971	+	1.64401i
$66$		0			0
$67$	99.2537			1.48140			0.740699	−	0.671837i	$-0.234494\pi$
$67$	99.2537			1.48140			0.740699	+	0.671837i	$0.234494\pi$
$68$		0			0
$69$			117.542i			1.70351i
$70$		0			0
$71$	−49.5054	−	119.517i	−0.697259	−	1.68333i	−0.729616	−	0.683857i	$-0.760301\pi$
$71$	−49.5054	−	119.517i	−0.697259	−	1.68333i	0.0323567	−	0.999476i	$-0.489699\pi$
$72$		0			0
$73$	−45.9951	−	111.042i	−0.630070	−	1.52112i	−0.839534	−	0.543308i	$-0.817172\pi$
$73$	−45.9951	−	111.042i	−0.630070	−	1.52112i	0.209463	−	0.977817i	$-0.432828\pi$
$74$		0			0
$75$	−20.9894	+	50.6728i	−0.279858	+	0.675638i
$76$		0			0
$77$	11.6533	+	24.7857i	0.151341	+	0.321892i
$78$		0			0
$79$	−15.2402	+	36.7932i	−0.192914	+	0.465736i	−0.990507	−	0.137460i	$-0.956106\pi$
$79$	−15.2402	+	36.7932i	−0.192914	+	0.465736i	0.797593	+	0.603196i	$0.206106\pi$
$80$		0			0
$81$			69.1376i			0.853550i
$82$		0			0
$83$	−26.4297	+	26.4297i	−0.318431	+	0.318431i	−0.848164	−	0.529734i	$-0.822292\pi$
$83$	−26.4297	+	26.4297i	−0.318431	+	0.318431i	0.529734	+	0.848164i	$0.322292\pi$
$84$		0			0
$85$	−31.4791	−	109.076i	−0.370343	−	1.28325i
$86$		0			0
$87$	28.7440	−	28.7440i	0.330390	−	0.330390i
$88$		0			0
$89$	−43.3144			−0.486679			−0.243340	−	0.969941i	$-0.578243\pi$
$89$	−43.3144			−0.486679			−0.243340	+	0.969941i	$0.578243\pi$
$90$		0			0
$91$	−81.6261	+	89.6462i	−0.896990	+	0.985124i
$92$		0			0
$93$	6.56536	−	6.56536i	0.0705953	−	0.0705953i
$94$		0			0
$95$	−55.7778	−	23.1039i	−0.587135	−	0.243199i
$96$		0			0
$97$	2.09599	+	5.06017i	0.0216081	+	0.0521667i	0.934315	−	0.356448i	$-0.116012\pi$
$97$	2.09599	+	5.06017i	0.0216081	+	0.0521667i	−0.912707	+	0.408614i	$0.866012\pi$
$98$		0			0
$99$	1.74703	+	4.21769i	0.0176467	+	0.0426030i
$100$		0			0
$101$		−	99.4933i		−	0.985082i	−0.870289	−	0.492541i	$-0.836068\pi$
$101$		−	99.4933i		−	0.985082i	0.870289	−	0.492541i	$-0.163932\pi$
$102$		0			0
$103$		−	41.4904i		−	0.402820i	−0.979507	−	0.201410i	$-0.935448\pi$
$103$		−	41.4904i		−	0.402820i	0.979507	−	0.201410i	$-0.0645523\pi$
$104$		0			0
$105$	−130.691	+	6.11988i	−1.24468	+	0.0582846i
$106$		0			0
$107$	72.1912	−	29.9026i	0.674684	−	0.279463i	−0.0189184	−	0.999821i	$-0.506022\pi$
$107$	72.1912	−	29.9026i	0.674684	−	0.279463i	0.693603	+	0.720358i	$0.256022\pi$
$108$		0			0
$109$	170.148	+	70.4774i	1.56099	+	0.646582i	0.985261	−	0.171061i	$-0.0547194\pi$
$109$	170.148	+	70.4774i	1.56099	+	0.646582i	0.575726	+	0.817642i	$0.304719\pi$
$110$		0			0
$111$	66.7069	+	66.7069i	0.600963	+	0.600963i
$112$		0			0
$113$	42.3216	−	102.173i	0.374528	−	0.904190i	−0.618443	−	0.785830i	$-0.712236\pi$
$113$	42.3216	−	102.173i	0.374528	−	0.904190i	0.992971	−	0.118360i	$-0.0377638\pi$
$114$		0			0
$115$	−280.464			−2.43882
$116$		0			0
$117$	−14.2897	+	14.2897i	−0.122135	+	0.122135i
$118$		0			0
$119$	89.4291	−	78.5075i	0.751505	−	0.659727i
$120$		0			0
$121$	74.7350	+	74.7350i	0.617645	+	0.617645i
$122$		0			0
$123$		−	208.893i		−	1.69832i
$124$		0			0
$125$	33.3352	+	13.8079i	0.266681	+	0.110463i
$126$		0			0
$127$	−122.429	+	122.429i	−0.964006	+	0.964006i	−0.999374	−	0.0353684i	$-0.988740\pi$
$127$	−122.429	+	122.429i	−0.964006	+	0.964006i	0.0353684	+	0.999374i	$0.488740\pi$
$128$		0			0
$129$	−57.8687	+	139.708i	−0.448595	+	1.08300i
$130$		0			0
$131$	−8.15133	−	19.6790i	−0.0622239	−	0.150222i	0.889709	−	0.456528i	$-0.150907\pi$
$131$	−8.15133	−	19.6790i	−0.0622239	−	0.150222i	−0.951933	+	0.306306i	$0.900907\pi$
$132$		0			0
$133$	−2.96015	−	63.2144i	−0.0222567	−	0.475296i
$134$		0			0
$135$	−190.023			−1.40758
$136$		0			0
$137$	−53.0715			−0.387383			−0.193692	−	0.981062i	$-0.562046\pi$
$137$	−53.0715			−0.387383			−0.193692	+	0.981062i	$0.562046\pi$
$138$		0			0
$139$	86.6360	−	35.8858i	0.623281	−	0.258171i	−0.0486144	−	0.998818i	$-0.515481\pi$
$139$	86.6360	−	35.8858i	0.623281	−	0.258171i	0.671895	+	0.740646i	$0.265481\pi$
$140$		0			0
$141$	152.221	−	63.0519i	1.07958	−	0.447176i
$142$		0			0
$143$	25.9334	−	62.6088i	0.181352	−	0.437824i
$144$		0			0
$145$	68.5850	+	68.5850i	0.473000	+	0.473000i
$146$		0			0
$147$	−64.0920	−	121.243i	−0.436000	−	0.824780i
$148$		0			0
$149$		−	189.056i		−	1.26884i	−0.772990	−	0.634418i	$-0.781240\pi$
$149$		−	189.056i		−	1.26884i	0.772990	−	0.634418i	$-0.218760\pi$
$150$		0			0
$151$	−184.770	−	184.770i	−1.22364	−	1.22364i	−0.966328	−	0.257313i	$-0.917163\pi$
$151$	−184.770	−	184.770i	−1.22364	−	1.22364i	−0.257313	−	0.966328i	$-0.582837\pi$
$152$		0			0
$153$	15.5021	−	12.3743i	0.101321	−	0.0808778i
$154$		0			0
$155$	15.6654	+	15.6654i	0.101067	+	0.101067i
$156$		0			0
$157$	48.8230			0.310974			0.155487	−	0.987838i	$-0.450305\pi$
$157$	48.8230			0.310974			0.155487	+	0.987838i	$0.450305\pi$
$158$		0			0
$159$	49.6151	+	20.5513i	0.312045	+	0.129253i
$160$		0			0
$161$	−125.084	−	266.045i	−0.776918	−	1.65246i
$162$		0			0
$163$	70.1040	+	29.0380i	0.430086	+	0.178147i	0.587215	−	0.809431i	$-0.300224\pi$
$163$	70.1040	+	29.0380i	0.430086	+	0.178147i	−0.157130	+	0.987578i	$0.550224\pi$
$164$		0			0
$165$	67.5629	−	27.9855i	0.409472	−	0.169609i
$166$		0			0
$167$	93.6387	−	38.7864i	0.560711	−	0.232254i	−0.0842830	−	0.996442i	$-0.526860\pi$
$167$	93.6387	−	38.7864i	0.560711	−	0.232254i	0.644994	+	0.764188i	$0.276860\pi$
$168$		0			0
$169$	130.985			0.775059
$170$		0			0
$171$		−	10.5483i		−	0.0616860i
$172$		0			0
$173$	18.3009	−	7.58047i	0.105785	−	0.0438177i	−0.329163	−	0.944273i	$-0.606767\pi$
$173$	18.3009	−	7.58047i	0.105785	−	0.0438177i	0.434948	+	0.900455i	$0.356767\pi$
$174$		0			0
$175$	−6.41667	−	137.029i	−0.0366667	−	0.783022i
$176$		0			0
$177$	285.885	+	118.417i	1.61517	+	0.669025i
$178$		0			0
$179$	−236.436	+	236.436i	−1.32087	+	1.32087i	−0.407802	+	0.913070i	$0.633705\pi$
$179$	−236.436	+	236.436i	−1.32087	+	1.32087i	−0.913070	+	0.407802i	$0.866295\pi$
$180$		0			0
$181$	208.563	+	86.3898i	1.15228	+	0.477292i	0.875299	−	0.483582i	$-0.160665\pi$
$181$	208.563	+	86.3898i	1.15228	+	0.477292i	0.276986	+	0.960874i	$0.410665\pi$
$182$		0			0
$183$		−	51.4933i		−	0.281384i
$184$		0			0
$185$	−159.167	+	159.167i	−0.860363	+	0.860363i
$186$		0			0
$187$	−32.1475	+	58.2303i	−0.171912	+	0.311392i
$188$		0			0
$189$	−84.7482	−	180.254i	−0.448403	−	0.953725i
$190$		0			0
$191$		−	311.972i		−	1.63336i	−0.577088	−	0.816682i	$-0.695811\pi$
$191$		−	311.972i		−	1.63336i	0.577088	−	0.816682i	$-0.304189\pi$
$192$		0			0
$193$	−10.2994	+	24.8650i	−0.0533648	+	0.128834i	−0.948313	−	0.317335i	$-0.897212\pi$
$193$	−10.2994	+	24.8650i	−0.0533648	+	0.128834i	0.894949	+	0.446169i	$0.147212\pi$
$194$		0			0
$195$	228.906	+	228.906i	1.17388	+	1.17388i
$196$		0			0
$197$	−188.267	−	77.9828i	−0.955671	−	0.395852i	−0.150311	−	0.988639i	$-0.548028\pi$
$197$	−188.267	−	77.9828i	−0.955671	−	0.395852i	−0.805359	+	0.592787i	$0.798028\pi$
$198$		0			0
$199$	−70.8095	−	170.949i	−0.355827	−	0.859041i	−0.995877	−	0.0907089i	$-0.971087\pi$
$199$	−70.8095	−	170.949i	−0.355827	−	0.859041i	0.640051	−	0.768333i	$-0.278913\pi$
$200$		0			0
$201$	256.645	−	106.306i	1.27684	−	0.528884i
$202$		0			0
$203$	−34.4709	+	95.6472i	−0.169807	+	0.471169i
$204$		0			0
$205$	498.434			2.43138
$206$		0			0
$207$	−18.7523	−	45.2720i	−0.0905906	−	0.218705i
$208$		0			0
$209$	13.5364	+	32.6798i	0.0647675	+	0.156363i
$210$		0			0
$211$	−73.4127	−	30.4085i	−0.347927	−	0.144116i	0.201874	−	0.979411i	$-0.435297\pi$
$211$	−73.4127	−	30.4085i	−0.347927	−	0.144116i	−0.549802	+	0.835295i	$0.685297\pi$
$212$		0			0
$213$	−256.017	−	256.017i	−1.20196	−	1.20196i
$214$		0			0
$215$	−333.352	−	138.079i	−1.55047	−	0.642227i
$216$		0			0
$217$	−7.87344	+	21.8466i	−0.0362831	+	0.100676i
$218$		0			0
$219$	−237.863	−	237.863i	−1.08613	−	1.08613i
$220$		0			0
$221$	−292.605	−	32.8311i	−1.32401	−	0.148557i
$222$		0			0
$223$	10.6723	−	10.6723i	0.0478577	−	0.0478577i	−0.682773	−	0.730631i	$-0.739226\pi$
$223$	10.6723	−	10.6723i	0.0478577	−	0.0478577i	0.730631	+	0.682773i	$0.239226\pi$
$224$		0			0
$225$		−	22.8654i		−	0.101624i
$226$		0			0
$227$	−138.108	−	57.2061i	−0.608404	−	0.252009i	0.0571417	−	0.998366i	$-0.481801\pi$
$227$	−138.108	−	57.2061i	−0.608404	−	0.252009i	−0.665546	+	0.746357i	$0.731801\pi$
$228$		0			0
$229$	152.182	+	152.182i	0.664548	+	0.664548i	0.956449	−	0.291900i	$-0.0942876\pi$
$229$	152.182	+	152.182i	0.664548	+	0.664548i	−0.291900	+	0.956449i	$0.594288\pi$
$230$		0			0
$231$	56.6791	+	51.6083i	0.245364	+	0.223412i
$232$		0			0
$233$	−229.290	+	94.9750i	−0.984077	+	0.407618i	−0.815934	−	0.578145i	$-0.803777\pi$
$233$	−229.290	+	94.9750i	−0.984077	+	0.407618i	−0.168143	+	0.985763i	$0.553777\pi$
$234$		0			0
$235$	150.446	+	363.209i	0.640196	+	1.54557i
$236$		0			0
$237$			111.461i			0.470298i
$238$		0			0
$239$	107.048			0.447901			0.223951	−	0.974600i	$-0.428105\pi$
$239$	107.048			0.447901			0.223951	+	0.974600i	$0.428105\pi$
$240$		0			0
$241$	343.119	−	142.125i	1.42373	−	0.589729i	0.467937	−	0.883762i	$-0.344998\pi$
$241$	343.119	−	142.125i	1.42373	−	0.589729i	0.955795	+	0.294033i	$0.0949976\pi$
$242$		0			0
$243$	−23.9524	−	57.8261i	−0.0985694	−	0.237968i
$244$		0			0
$245$	289.293	−	152.928i	1.18079	−	0.624195i
$246$		0			0
$247$	−110.721	+	110.721i	−0.448261	+	0.448261i
$248$		0			0
$249$	−40.0330	+	96.6481i	−0.160775	+	0.388145i
$250$		0			0
$251$	−93.6181			−0.372981			−0.186490	−	0.982457i	$-0.559711\pi$
$251$	−93.6181			−0.372981			−0.186490	+	0.982457i	$0.559711\pi$
$252$		0			0
$253$	116.193	+	116.193i	0.459260	+	0.459260i
$254$		0			0
$255$	−198.223	−	248.327i	−0.777345	−	0.973832i
$256$		0			0
$257$	97.8788	−	97.8788i	0.380851	−	0.380851i	−0.490557	−	0.871409i	$-0.663207\pi$
$257$	97.8788	−	97.8788i	0.380851	−	0.380851i	0.871409	+	0.490557i	$0.163207\pi$
$258$		0			0
$259$	−221.971	−	79.9975i	−0.857031	−	0.308871i
$260$		0			0
$261$	−6.48516	+	15.6566i	−0.0248474	+	0.0599868i
$262$		0			0
$263$	−35.5784	+	35.5784i	−0.135279	+	0.135279i	−0.771504	−	0.636225i	$-0.780495\pi$
$263$	−35.5784	+	35.5784i	−0.135279	+	0.135279i	0.636225	+	0.771504i	$0.280495\pi$
$264$		0			0
$265$	−49.0367	+	118.385i	−0.185044	+	0.446736i
$266$		0			0
$267$	−112.000	+	46.3919i	−0.419476	+	0.173753i
$268$		0			0
$269$	−117.014	+	48.4687i	−0.434996	+	0.180181i	−0.589426	−	0.807823i	$-0.700646\pi$
$269$	−117.014	+	48.4687i	−0.434996	+	0.180181i	0.154430	+	0.988004i	$0.450646\pi$
$270$		0			0
$271$			494.558i			1.82494i	0.409145	+	0.912469i	$0.365827\pi$
$271$			494.558i			1.82494i	−0.409145	+	0.912469i	$0.634173\pi$
$272$		0			0
$273$	−115.048	+	319.228i	−0.421423	+	1.16933i
$274$		0			0
$275$	29.3427	+	70.8395i	0.106701	+	0.257598i
$276$		0			0
$277$	19.0439	−	7.88824i	0.0687505	−	0.0284774i	−0.348043	−	0.937479i	$-0.613154\pi$
$277$	19.0439	−	7.88824i	0.0687505	−	0.0284774i	0.416794	+	0.909001i	$0.363154\pi$
$278$		0			0
$279$	−1.48126	+	3.57609i	−0.00530919	+	0.0128175i
$280$		0			0
$281$	−118.283	+	118.283i	−0.420937	+	0.420937i	−0.885526	−	0.464589i	$-0.846202\pi$
$281$	−118.283	+	118.283i	−0.420937	+	0.420937i	0.464589	+	0.885526i	$0.346202\pi$
$282$		0			0
$283$	217.112	+	89.9308i	0.767180	+	0.317777i	0.731730	−	0.681595i	$-0.238713\pi$
$283$	217.112	+	89.9308i	0.767180	+	0.317777i	0.0354507	+	0.999371i	$0.488713\pi$
$284$		0			0
$285$	−168.973			−0.592887
$286$		0			0
$287$	222.296	+	472.809i	0.774550	+	1.64742i
$288$		0			0
$289$	281.814	+	64.0469i	0.975134	+	0.221615i
$290$		0			0
$291$	10.8394	+	10.8394i	0.0372487	+	0.0372487i
$292$		0			0
$293$	369.182			1.26001			0.630003	−	0.776593i	$-0.283054\pi$
$293$	369.182			1.26001			0.630003	+	0.776593i	$0.283054\pi$
$294$		0			0
$295$	−282.552	+	682.141i	−0.957803	+	2.31234i
$296$		0			0
$297$	78.7243	+	78.7243i	0.265065	+	0.265065i
$298$		0			0
$299$	−278.364	+	672.031i	−0.930985	+	2.24760i
$300$		0			0
$301$	−17.6911	−	377.795i	−0.0587743	−	1.25513i
$302$		0			0
$303$	−106.562	−	257.264i	−0.351691	−	0.849057i
$304$		0			0
$305$	122.867			0.402841
$306$		0			0
$307$			182.073i			0.593073i	0.955022	+	0.296536i	$0.0958316\pi$
$307$			182.073i			0.593073i	−0.955022	+	0.296536i	$0.904168\pi$
$308$		0			0
$309$	−44.4383	−	107.284i	−0.143813	−	0.347196i
$310$		0			0
$311$	−4.12524	−	9.95921i	−0.0132644	−	0.0320232i	0.917109	−	0.398638i	$-0.130517\pi$
$311$	−4.12524	−	9.95921i	−0.0132644	−	0.0320232i	−0.930373	+	0.366614i	$0.880517\pi$
$312$		0			0
$313$	160.175	−	386.697i	0.511741	−	1.23545i	−0.431129	−	0.902290i	$-0.641884\pi$
$313$	160.175	−	386.697i	0.511741	−	1.23545i	0.942870	−	0.333162i	$-0.108116\pi$
$314$		0			0
$315$	49.3598	−	23.2070i	0.156698	−	0.0736731i
$316$		0			0
$317$	4.68687	−	11.3151i	0.0147851	−	0.0356943i	−0.916315	−	0.400459i	$-0.868851\pi$
$317$	4.68687	−	11.3151i	0.0147851	−	0.0356943i	0.931100	+	0.364765i	$0.118851\pi$
$318$		0			0
$319$		−	56.8279i		−	0.178144i
$320$		0			0
$321$	154.641	−	154.641i	0.481747	−	0.481747i
$322$		0			0
$323$	120.114	−	95.8792i	0.371871	−	0.296840i
$324$		0			0
$325$	−240.007	+	240.007i	−0.738484	+	0.738484i
$326$		0			0
$327$	515.443			1.57628
$328$		0			0
$329$	−277.439	+	304.699i	−0.843279	+	0.926136i
$330$		0			0
$331$	58.9936	−	58.9936i	0.178228	−	0.178228i	−0.612355	−	0.790583i	$-0.709778\pi$
$331$	58.9936	−	58.9936i	0.178228	−	0.178228i	0.790583	+	0.612355i	$0.209778\pi$
$332$		0			0
$333$	−36.3346	−	15.0503i	−0.109113	−	0.0451960i
$334$		0			0
$335$	253.652	+	612.371i	0.757172	+	1.82797i
$336$		0			0
$337$	94.1166	+	227.218i	0.279278	+	0.674236i	0.999816	−	0.0191789i	$-0.00610522\pi$
$337$	94.1166	+	227.218i	0.279278	+	0.674236i	−0.720538	+	0.693415i	$0.756105\pi$
$338$		0			0
$339$		−	309.523i		−	0.913047i
$340$		0			0
$341$		−	12.9800i		−	0.0380644i
$342$		0			0
$343$	274.087	+	206.216i	0.799088	+	0.601214i
$344$		0			0
$345$	−725.208	+	300.391i	−2.10205	+	0.870699i
$346$		0			0
$347$	−94.9204	−	39.3173i	−0.273546	−	0.113306i	0.241694	−	0.970353i	$-0.422297\pi$
$347$	−94.9204	−	39.3173i	−0.273546	−	0.113306i	−0.515240	+	0.857046i	$0.672297\pi$
$348$		0			0
$349$	339.177	+	339.177i	0.971853	+	0.971853i	0.999615	−	0.0277618i	$-0.00883799\pi$
$349$	339.177	+	339.177i	0.971853	+	0.971853i	−0.0277618	+	0.999615i	$0.508838\pi$
$350$		0			0
$351$	−188.601	+	455.322i	−0.537324	+	1.29721i
$352$		0			0
$353$	−385.705			−1.09265			−0.546325	−	0.837573i	$-0.683974\pi$
$353$	−385.705			−1.09265			−0.546325	+	0.837573i	$0.683974\pi$
$354$		0			0
$355$	610.873	−	610.873i	1.72077	−	1.72077i
$356$		0			0
$357$	147.155	−	298.783i	0.412200	−	0.836928i
$358$		0			0
$359$	−206.582	−	206.582i	−0.575436	−	0.575436i	0.358206	−	0.933642i	$-0.383388\pi$
$359$	−206.582	−	206.582i	−0.575436	−	0.575436i	−0.933642	+	0.358206i	$0.883388\pi$
$360$		0			0
$361$			279.269i			0.773598i
$362$		0			0
$363$	273.290	+	113.201i	0.752866	+	0.311847i
$364$		0			0
$365$	567.558	−	567.558i	1.55495	−	1.55495i
$366$		0			0
$367$	130.349	−	314.690i	0.355174	−	0.857467i	−0.640790	−	0.767716i	$-0.721393\pi$
$367$	130.349	−	314.690i	0.355174	−	0.857467i	0.995964	−	0.0897506i	$-0.0286070\pi$
$368$		0			0
$369$	33.3260	+	80.4562i	0.0903145	+	0.218038i
$370$		0			0
$371$	−134.169	+	6.28273i	−0.361641	+	0.0169346i
$372$		0			0
$373$	−344.488			−0.923559			−0.461780	−	0.886995i	$-0.652789\pi$
$373$	−344.488			−0.923559			−0.461780	+	0.886995i	$0.652789\pi$
$374$		0			0
$375$	100.985			0.269294
$376$		0			0
$377$	232.411	−	96.2678i	0.616475	−	0.255352i
$378$		0			0
$379$	214.319	−	88.7738i	0.565485	−	0.234232i	−0.0815795	−	0.996667i	$-0.525996\pi$
$379$	214.319	−	88.7738i	0.565485	−	0.234232i	0.647064	+	0.762435i	$0.275996\pi$
$380$		0			0
$381$	−185.442	+	447.697i	−0.486725	+	1.17506i
$382$		0			0
$383$	21.0363	+	21.0363i	0.0549250	+	0.0549250i	0.734036	−	0.679111i	$-0.237634\pi$
$383$	21.0363	+	21.0363i	0.0549250	+	0.0549250i	−0.679111	+	0.734036i	$0.737634\pi$
$384$		0			0
$385$	−123.141	+	135.240i	−0.319846	+	0.351273i
$386$		0			0
$387$		−	63.0411i		−	0.162897i
$388$		0			0
$389$	10.4921	+	10.4921i	0.0269719	+	0.0269719i	0.720464	−	0.693492i	$-0.243929\pi$
$389$	10.4921	+	10.4921i	0.0269719	+	0.0269719i	−0.693492	+	0.720464i	$0.743929\pi$
$390$		0			0
$391$	345.065	−	625.034i	0.882520	−	1.59855i
$392$		0			0
$393$	−42.1545	−	42.1545i	−0.107263	−	0.107263i
$394$		0			0
$395$	−265.953			−0.673298
$396$		0			0
$397$	−455.888	−	188.835i	−1.14833	−	0.475655i	−0.274358	−	0.961628i	$-0.588465\pi$
$397$	−455.888	−	188.835i	−1.14833	−	0.475655i	−0.873974	+	0.485973i	$0.838465\pi$
$398$		0			0
$399$	−75.3600	−	160.286i	−0.188872	−	0.401719i
$400$		0			0
$401$	−270.847	−	112.189i	−0.675429	−	0.279772i	0.0184854	−	0.999829i	$-0.494116\pi$
$401$	−270.847	−	112.189i	−0.675429	−	0.279772i	−0.693915	+	0.720057i	$0.744116\pi$
$402$		0			0
$403$	53.0846	−	21.9884i	0.131724	−	0.0545617i
$404$		0			0
$405$	−426.562	+	176.688i	−1.05324	+	0.436266i
$406$		0			0
$407$	131.882			0.324034
$408$		0			0
$409$		−	191.151i		−	0.467362i	−0.972313	−	0.233681i	$-0.924923\pi$
$409$		−	191.151i		−	0.467362i	0.972313	−	0.233681i	$-0.0750771\pi$
$410$		0			0
$411$	−137.229	+	56.8423i	−0.333891	+	0.138302i
$412$		0			0
$413$	−773.087	+	36.2014i	−1.87188	+	0.0876548i
$414$		0			0
$415$	−230.609	−	95.5213i	−0.555684	−	0.230172i
$416$		0			0
$417$	185.583	−	185.583i	0.445043	−	0.445043i
$418$		0			0
$419$	467.230	+	193.533i	1.11511	+	0.461893i	0.862694	−	0.505727i	$-0.168776\pi$
$419$	467.230	+	193.533i	1.11511	+	0.461893i	0.252414	+	0.967619i	$0.418776\pi$
$420$		0			0
$421$			556.044i			1.32077i	0.750927	+	0.660385i	$0.229607\pi$
$421$			556.044i			1.32077i	−0.750927	+	0.660385i	$0.770393\pi$
$422$		0			0
$423$	−48.5694	+	48.5694i	−0.114821	+	0.114821i
$424$		0			0
$425$	260.370	−	207.836i	0.612635	−	0.489026i
$426$		0			0
$427$	54.7971	+	116.550i	0.128331	+	0.272951i
$428$		0			0
$429$		−	189.666i		−	0.442112i
$430$		0			0
$431$	65.7682	−	158.779i	0.152595	−	0.368396i	−0.829034	−	0.559198i	$-0.811109\pi$
$431$	65.7682	−	158.779i	0.152595	−	0.368396i	0.981628	+	0.190803i	$0.0611090\pi$
$432$		0			0
$433$	289.547	+	289.547i	0.668700	+	0.668700i	0.957415	−	0.288715i	$-0.0932281\pi$
$433$	289.547	+	289.547i	0.668700	+	0.668700i	−0.288715	+	0.957415i	$0.593228\pi$
$434$		0			0
$435$	250.801	+	103.885i	0.576555	+	0.238817i
$436$		0			0
$437$	−145.297	−	350.779i	−0.332488	−	0.802697i
$438$		0			0
$439$	211.924	−	87.7818i	0.482743	−	0.199959i	−0.128021	−	0.991771i	$-0.540862\pi$
$439$	211.924	−	87.7818i	0.482743	−	0.199959i	0.610764	+	0.791813i	$0.290862\pi$
$440$		0			0
$441$	44.0279	+	36.4721i	0.0998365	+	0.0827033i
$442$		0			0
$443$	56.3433			0.127186			0.0635929	−	0.997976i	$-0.479744\pi$
$443$	56.3433			0.127186			0.0635929	+	0.997976i	$0.479744\pi$
$444$		0			0
$445$	−110.694	−	267.240i	−0.248751	−	0.600539i
$446$		0			0
$447$	−202.489	−	488.852i	−0.452995	−	1.09363i
$448$		0			0
$449$	−156.291	−	64.7377i	−0.348086	−	0.144182i	0.201789	−	0.979429i	$-0.435325\pi$
$449$	−156.291	−	64.7377i	−0.348086	−	0.144182i	−0.549875	+	0.835247i	$0.685325\pi$
$450$		0			0
$451$	−206.495	−	206.495i	−0.457860	−	0.457860i
$452$		0			0
$453$	−675.665	−	279.870i	−1.49153	−	0.617814i
$454$		0			0
$455$	−761.699	−	274.513i	−1.67406	−	0.603326i
$456$		0			0
$457$	516.428	+	516.428i	1.13004	+	1.13004i	0.990170	+	0.139869i	$0.0446681\pi$
$457$	516.428	+	516.428i	1.13004	+	1.13004i	0.139869	+	0.990170i	$0.455332\pi$
$458$		0			0
$459$	233.792	−	423.480i	0.509352	−	0.922614i
$460$		0			0
$461$	−261.847	+	261.847i	−0.567997	+	0.567997i	−0.931567	−	0.363570i	$-0.881558\pi$
$461$	−261.847	+	261.847i	−0.567997	+	0.567997i	0.363570	+	0.931567i	$0.381558\pi$
$462$		0			0
$463$			501.256i			1.08263i	0.840821	+	0.541313i	$0.182072\pi$
$463$			501.256i			1.08263i	−0.840821	+	0.541313i	$0.817928\pi$
$464$		0			0
$465$	57.2851	+	23.7283i	0.123194	+	0.0510285i
$466$		0			0
$467$	349.995	+	349.995i	0.749454	+	0.749454i	0.974377	−	0.224922i	$-0.0722129\pi$
$467$	349.995	+	349.995i	0.749454	+	0.749454i	−0.224922	+	0.974377i	$0.572213\pi$
$468$		0			0
$469$	−467.763	+	513.723i	−0.997362	+	1.09536i
$470$		0			0
$471$	126.244	−	52.2918i	0.268033	−	0.111023i
$472$		0			0
$473$	80.8992	+	195.308i	0.171034	+	0.412913i
$474$		0			0
$475$		−	177.167i		−	0.372983i
$476$		0			0
$477$	−22.3881			−0.0469353
$478$		0			0
$479$	174.744	−	72.3812i	0.364809	−	0.151109i	−0.192746	−	0.981249i	$-0.561739\pi$
$479$	174.744	−	72.3812i	0.364809	−	0.151109i	0.557556	+	0.830140i	$0.311739\pi$
$480$		0			0
$481$	223.411	+	539.362i	0.464472	+	1.12133i
$482$		0			0
$483$	−608.383	−	553.954i	−1.25959	−	1.14690i
$484$		0			0
$485$	−25.8635	+	25.8635i	−0.0533268	+	0.0533268i
$486$		0			0
$487$	177.799	−	429.245i	0.365090	−	0.881406i	−0.629449	−	0.777042i	$-0.716719\pi$
$487$	177.799	−	429.245i	0.365090	−	0.881406i	0.994539	−	0.104364i	$-0.0332807\pi$
$488$		0			0
$489$	212.372			0.434299
$490$		0			0
$491$	−231.549	−	231.549i	−0.471587	−	0.471587i	0.430841	−	0.902428i	$-0.358217\pi$
$491$	−231.549	−	231.549i	−0.471587	−	0.471587i	−0.902428	+	0.430841i	$0.858217\pi$
$492$		0			0
$493$	−237.229	+	68.4639i	−0.481195	+	0.138872i
$494$		0			0
$495$	−21.5575	+	21.5575i	−0.0435504	+	0.0435504i
$496$		0			0
$497$	851.910	+	307.025i	1.71411	+	0.617757i
$498$		0			0
$499$	−68.4857	+	165.339i	−0.137246	+	0.331341i	−0.977527	−	0.210810i	$-0.932390\pi$
$499$	−68.4857	+	165.339i	−0.137246	+	0.331341i	0.840281	+	0.542151i	$0.182390\pi$
$500$		0			0
$501$	200.583	−	200.583i	0.400366	−	0.400366i
$502$		0			0
$503$	−41.8123	+	100.944i	−0.0831259	+	0.200684i	−0.959977	−	0.280078i	$-0.909640\pi$
$503$	−41.8123	+	100.944i	−0.0831259	+	0.200684i	0.876851	+	0.480761i	$0.159640\pi$
$504$		0			0
$505$	613.850	−	254.265i	1.21554	−	0.503495i
$506$		0			0
$507$	338.693	−	140.291i	0.668034	−	0.276709i
$508$		0			0
$509$			259.232i			0.509297i	0.967034	+	0.254648i	$0.0819597\pi$
$509$			259.232i			0.509297i	−0.967034	+	0.254648i	$0.918040\pi$
$510$		0			0
$511$	791.504	+	285.255i	1.54893	+	0.558229i
$512$		0			0
$513$	−98.4434	−	237.663i	−0.191898	−	0.463282i
$514$		0			0
$515$	255.986	−	106.033i	0.497060	−	0.205889i
$516$		0			0
$517$	88.1450	−	212.801i	0.170493	−	0.411607i
$518$		0			0
$519$	39.2023	−	39.2023i	0.0755343	−	0.0755343i
$520$		0			0
$521$	−445.716	−	184.622i	−0.855501	−	0.354360i	−0.0885549	−	0.996071i	$-0.528225\pi$
$521$	−445.716	−	184.622i	−0.855501	−	0.354360i	−0.766947	+	0.641711i	$0.778225\pi$
$522$		0			0
$523$	−642.432			−1.22836			−0.614180	−	0.789166i	$-0.710513\pi$
$523$	−642.432			−1.22836			−0.614180	+	0.789166i	$0.710513\pi$
$524$		0			0
$525$	−163.357	−	347.449i	−0.311156	−	0.661808i
$526$		0			0
$527$	−54.1852	+	15.6377i	−0.102818	+	0.0296731i
$528$		0			0
$529$	−873.134	−	873.134i	−1.65054	−	1.65054i
$530$		0			0
$531$	−129.002			−0.242941
$532$		0			0
$533$	494.702	−	1194.32i	0.928147	−	2.24074i
$534$		0			0
$535$	368.984	+	368.984i	0.689689	+	0.689689i
$536$		0			0
$537$	−358.128	+	864.598i	−0.666906	+	1.61005i
$538$		0			0
$539$	−183.207	−	56.4945i	−0.339901	−	0.104814i
$540$		0			0
$541$	−246.142	−	594.239i	−0.454976	−	1.09841i	−0.970406	−	0.241477i	$-0.922368\pi$
$541$	−246.142	−	594.239i	−0.454976	−	1.09841i	0.515431	−	0.856931i	$-0.327632\pi$
$542$		0			0
$543$	631.820			1.16357
$544$		0			0
$545$			1229.88i			2.25666i
$546$		0			0
$547$	−4.12813	−	9.96620i	−0.00754686	−	0.0182197i	0.920061	−	0.391775i	$-0.128139\pi$
$547$	−4.12813	−	9.96620i	−0.00754686	−	0.0182197i	−0.927608	+	0.373555i	$0.878139\pi$
$548$		0			0
$549$	8.21505	+	19.8329i	0.0149637	+	0.0361255i
$550$		0			0
$551$	−50.2487	+	121.311i	−0.0911954	+	0.220165i
$552$		0			0
$553$	−118.612	−	252.280i	−0.214488	−	0.456203i
$554$		0			0
$555$	−241.089	+	582.041i	−0.434395	+	1.04872i
$556$		0			0
$557$			536.780i			0.963699i	0.876254	+	0.481849i	$0.160035\pi$
$557$			536.780i			0.963699i	−0.876254	+	0.481849i	$0.839965\pi$
$558$		0			0
$559$	−661.712	+	661.712i	−1.18374	+	1.18374i
$560$		0			0
$561$	−20.7575	+	185.000i	−0.0370010	+	0.329769i
$562$		0			0
$563$	764.763	−	764.763i	1.35837	−	1.35837i	0.482444	−	0.875927i	$-0.339749\pi$
$563$	764.763	−	764.763i	1.35837	−	1.35837i	0.875927	−	0.482444i	$-0.160251\pi$
$564$		0			0
$565$	738.543			1.30716
$566$		0			0
$567$	−357.846	−	325.832i	−0.631122	−	0.574659i
$568$		0			0
$569$	619.370	−	619.370i	1.08852	−	1.08852i	0.0928430	−	0.995681i	$-0.470405\pi$
$569$	619.370	−	619.370i	1.08852	−	1.08852i	0.995681	−	0.0928430i	$-0.0295955\pi$
$570$		0			0
$571$	693.882	+	287.415i	1.21521	+	0.503355i	0.895882	−	0.444291i	$-0.146545\pi$
$571$	693.882	+	287.415i	1.21521	+	0.503355i	0.319323	+	0.947646i	$0.396545\pi$
$572$		0			0
$573$	−334.138	−	806.681i	−0.583138	−	1.40782i
$574$		0			0
$575$	−314.959	−	760.378i	−0.547754	−	1.32240i
$576$		0			0
$577$			355.899i			0.616810i	0.951255	+	0.308405i	$0.0997952\pi$
$577$			355.899i			0.616810i	−0.951255	+	0.308405i	$0.900205\pi$
$578$		0			0
$579$			75.3256i			0.130096i
$580$		0			0
$581$	−12.2385	−	261.355i	−0.0210645	−	0.449836i
$582$		0			0
$583$	69.3608	−	28.7302i	0.118972	−	0.0492799i
$584$		0			0
$585$	−124.683	−	51.6454i	−0.213133	−	0.0882828i
$586$		0			0
$587$	−26.6252	−	26.6252i	−0.0453580	−	0.0453580i	0.684064	−	0.729422i	$-0.260211\pi$
$587$	−26.6252	−	26.6252i	−0.0453580	−	0.0453580i	−0.729422	+	0.684064i	$0.760211\pi$
$588$		0			0
$589$	−11.4772	+	27.7085i	−0.0194859	+	0.0470432i
$590$		0			0
$591$	−570.334			−0.965032
$592$		0			0
$593$	441.649	−	441.649i	0.744771	−	0.744771i	−0.228721	−	0.973492i	$-0.573454\pi$
$593$	441.649	−	441.649i	0.744771	−	0.744771i	0.973492	+	0.228721i	$0.0734544\pi$
$594$		0			0
$595$	712.917	+	351.122i	1.19818	+	0.590122i
$596$		0			0
$597$	−366.190	−	366.190i	−0.613384	−	0.613384i
$598$		0			0
$599$		−	399.099i		−	0.666275i	−0.942878	−	0.333138i	$-0.891893\pi$
$599$		−	399.099i		−	0.666275i	0.942878	−	0.333138i	$-0.108107\pi$
$600$		0			0
$601$	−837.008	−	346.700i	−1.39269	−	0.576872i	−0.444848	−	0.895606i	$-0.646742\pi$
$601$	−837.008	−	346.700i	−1.39269	−	0.576872i	−0.947844	+	0.318734i	$0.896742\pi$
$602$		0			0
$603$	−81.8882	+	81.8882i	−0.135801	+	0.135801i
$604$		0			0
$605$	−270.104	+	652.089i	−0.446453	+	1.07783i
$606$		0			0
$607$	−98.3533	−	237.446i	−0.162032	−	0.391179i	0.821923	−	0.569599i	$-0.192901\pi$
$607$	−98.3533	−	237.446i	−0.162032	−	0.391179i	−0.983954	+	0.178420i	$0.942901\pi$
$608$		0			0
$609$	13.3101	+	284.239i	0.0218557	+	0.466731i
$610$		0			0
$611$	1019.62			1.66877
$612$		0			0
$613$	502.826			0.820271			0.410136	−	0.912025i	$-0.365481\pi$
$613$	502.826			0.820271			0.410136	+	0.912025i	$0.365481\pi$
$614$		0			0
$615$	1288.82	−	533.847i	2.09564	−	0.868044i
$616$		0			0
$617$	−815.576	+	337.823i	−1.32184	+	0.547525i	−0.928317	−	0.371790i	$-0.878744\pi$
$617$	−815.576	+	337.823i	−1.32184	+	0.547525i	−0.393524	+	0.919314i	$0.628744\pi$
$618$		0			0
$619$	−248.846	+	600.767i	−0.402013	+	0.970545i	0.585164	+	0.810915i	$0.301030\pi$
$619$	−248.846	+	600.767i	−0.402013	+	0.970545i	−0.987177	+	0.159630i	$0.948970\pi$
$620$		0			0
$621$	−845.012	−	845.012i	−1.36073	−	1.36073i
$622$		0			0
$623$	204.132	−	224.189i	0.327660	−	0.359855i
$624$		0			0
$625$			730.882i			1.16941i
$626$		0			0
$627$	70.0033	+	70.0033i	0.111648	+	0.111648i
$628$		0			0
$629$	−158.886	−	550.544i	−0.252601	−	0.875269i
$630$		0			0
$631$	−114.707	−	114.707i	−0.181787	−	0.181787i	0.610347	−	0.792134i	$-0.291030\pi$
$631$	−114.707	−	114.707i	−0.181787	−	0.181787i	−0.792134	+	0.610347i	$0.791030\pi$
$632$		0			0
$633$	−222.395			−0.351336
$634$		0			0
$635$	−1068.23	−	442.477i	−1.68226	−	0.696815i
$636$		0			0
$637$	−79.3089	−	844.970i	−0.124504	−	1.32648i
$638$		0			0
$639$	139.450	+	57.7620i	0.218231	+	0.0903944i
$640$		0			0
$641$	−874.060	+	362.047i	−1.36359	+	0.564816i	−0.940042	−	0.341058i	$-0.889215\pi$
$641$	−874.060	+	362.047i	−1.36359	+	0.564816i	−0.423545	+	0.905875i	$0.639215\pi$
$642$		0			0
$643$	−512.592	+	212.322i	−0.797188	+	0.330206i	−0.743829	−	0.668370i	$-0.766993\pi$
$643$	−512.592	+	212.322i	−0.797188	+	0.330206i	−0.0533582	+	0.998575i	$0.516993\pi$
$644$		0			0
$645$	−1009.85			−1.56566
$646$		0			0
$647$			101.168i			0.156365i	0.996939	+	0.0781824i	$0.0249116\pi$
$647$			101.168i			0.156365i	−0.996939	+	0.0781824i	$0.975088\pi$
$648$		0			0
$649$	399.661	−	165.545i	0.615810	−	0.255077i
$650$		0			0
$651$	3.04014	+	64.9226i	0.00466995	+	0.0997275i
$652$		0			0
$653$	−906.247	−	375.380i	−1.38782	−	0.574854i	−0.441260	−	0.897379i	$-0.645468\pi$
$653$	−906.247	−	375.380i	−1.38782	−	0.574854i	−0.946561	+	0.322525i	$0.895468\pi$
$654$		0			0
$655$	100.583	−	100.583i	0.153563	−	0.153563i
$656$		0			0
$657$	129.562	+	53.6663i	0.197202	+	0.0816838i
$658$		0			0
$659$		−	539.391i		−	0.818499i	−0.912423	−	0.409249i	$-0.865791\pi$
$659$		−	539.391i		−	0.818499i	0.912423	−	0.409249i	$-0.134209\pi$
$660$		0			0
$661$	−96.5660	+	96.5660i	−0.146091	+	0.146091i	−0.776369	−	0.630278i	$-0.782941\pi$
$661$	−96.5660	+	96.5660i	−0.146091	+	0.146091i	0.630278	+	0.776369i	$0.282941\pi$
$662$		0			0
$663$	−791.766	+	228.502i	−1.19422	+	0.344648i
$664$		0			0
$665$	382.453	−	179.814i	0.575117	−	0.270397i
$666$		0			0
$667$			609.980i			0.914513i
$668$		0			0
$669$	16.1652	−	39.0263i	0.0241633	−	0.0583353i
$670$		0			0
$671$	−50.9021	−	50.9021i	−0.0758601	−	0.0758601i
$672$		0			0
$673$	398.377	+	165.013i	0.591942	+	0.245190i	0.658486	−	0.752593i	$-0.271197\pi$
$673$	398.377	+	165.013i	0.591942	+	0.245190i	−0.0665440	+	0.997783i	$0.521197\pi$
$674$		0			0
$675$	−213.394	−	515.180i	−0.316140	−	0.763229i
$676$		0			0
$677$	1081.60	−	448.015i	1.59764	−	0.661765i	0.606562	−	0.795036i	$-0.292548\pi$
$677$	1081.60	−	448.015i	1.59764	−	0.661765i	0.991080	+	0.133271i	$0.0425481\pi$
$678$		0			0
$679$	−36.0687	−	12.9990i	−0.0531203	−	0.0191443i
$680$		0			0
$681$	−418.382			−0.614364
$682$		0			0
$683$	−259.915	−	627.489i	−0.380548	−	0.918725i	−0.991860	−	0.127335i	$-0.959358\pi$
$683$	−259.915	−	627.489i	−0.380548	−	0.918725i	0.611311	−	0.791390i	$-0.290642\pi$
$684$		0			0
$685$	−135.629	−	327.439i	−0.197999	−	0.478012i
$686$		0			0
$687$	556.497	+	230.508i	0.810039	+	0.335529i
$688$		0			0
$689$	234.998	+	234.998i	0.341070	+	0.341070i
$690$		0			0
$691$	403.939	+	167.317i	0.584571	+	0.242137i	0.655313	−	0.755357i	$-0.272537\pi$
$691$	403.939	+	167.317i	0.584571	+	0.242137i	−0.0707418	+	0.997495i	$0.522537\pi$
$692$		0			0
$693$	−30.0636	−	10.8348i	−0.0433818	−	0.0156346i
$694$		0			0
$695$	442.814	+	442.814i	0.637142	+	0.637142i
$696$		0			0
$697$	−613.241	+	1110.79i	−0.879830	+	1.59368i
$698$		0			0
$699$	−491.162	+	491.162i	−0.702664	+	0.702664i
$700$		0			0
$701$		−	781.470i		−	1.11479i	−0.830246	−	0.557397i	$-0.811800\pi$
$701$		−	781.470i		−	1.11479i	0.830246	−	0.557397i	$-0.188200\pi$
$702$		0			0
$703$	−281.530	−	116.613i	−0.400469	−	0.165880i
$704$		0			0
$705$	778.029	+	778.029i	1.10359	+	1.10359i
$706$		0			0
$707$	514.963	+	468.892i	0.728378	+	0.663214i
$708$		0			0
$709$	260.175	−	107.768i	0.366960	−	0.152000i	−0.191581	−	0.981477i	$-0.561361\pi$
$709$	260.175	−	107.768i	0.366960	−	0.152000i	0.558541	+	0.829477i	$0.311361\pi$
$710$		0			0
$711$	−17.7820	−	42.9296i	−0.0250099	−	0.0603791i
$712$		0			0
$713$			139.325i			0.195406i
$714$		0			0
$715$	452.556			0.632946
$716$		0			0
$717$	276.800	−	114.654i	0.386053	−	0.159908i
$718$		0			0
$719$	30.0257	+	72.4884i	0.0417604	+	0.100818i	0.943383	−	0.331704i	$-0.107624\pi$
$719$	30.0257	+	72.4884i	0.0417604	+	0.100818i	−0.901623	+	0.432523i	$0.857624\pi$
$720$		0			0
$721$	214.749	+	195.536i	0.297848	+	0.271201i
$722$		0			0
$723$	734.996	−	734.996i	1.01659	−	1.01659i
$724$		0			0
$725$	−108.923	+	262.964i	−0.150239	+	0.362709i
$726$		0			0
$727$	204.327			0.281055			0.140528	−	0.990077i	$-0.455120\pi$
$727$	204.327			0.281055			0.140528	+	0.990077i	$0.455120\pi$
$728$		0			0
$729$	−563.858	−	563.858i	−0.773468	−	0.773468i
$730$		0			0
$731$	717.853	−	573.014i	0.982015	−	0.783877i
$732$		0			0
$733$	295.368	−	295.368i	0.402958	−	0.402958i	−0.476316	−	0.879274i	$-0.658028\pi$
$733$	295.368	−	295.368i	0.402958	−	0.402958i	0.879274	+	0.476316i	$0.158028\pi$
$734$		0			0
$735$	584.245	−	705.279i	0.794891	−	0.959564i
$736$		0			0
$737$	148.613	−	358.783i	0.201646	−	0.486816i
$738$		0			0
$739$	−886.691	+	886.691i	−1.19985	+	1.19985i	−0.225643	+	0.974210i	$0.572448\pi$
$739$	−886.691	+	886.691i	−1.19985	+	1.19985i	−0.974210	+	0.225643i	$0.927552\pi$
$740$		0			0
$741$	−167.708	+	404.882i	−0.226326	+	0.546400i
$742$		0			0
$743$	−965.640	+	399.981i	−1.29965	+	0.538332i	−0.921847	−	0.387554i	$-0.873320\pi$
$743$	−965.640	+	399.981i	−1.29965	+	0.538332i	−0.377802	+	0.925886i	$0.623320\pi$
$744$		0			0
$745$	1166.43	−	483.152i	1.56568	−	0.648527i
$746$		0			0
$747$		−	43.6111i		−	0.0583817i
$748$		0			0
$749$	−185.451	+	514.577i	−0.247599	+	0.687018i
$750$		0			0
$751$	290.378	+	701.033i	0.386654	+	0.933467i	0.990644	+	0.136474i	$0.0435770\pi$
$751$	290.378	+	701.033i	0.386654	+	0.933467i	−0.603989	+	0.796993i	$0.706423\pi$
$752$		0			0
$753$	−242.073	+	100.270i	−0.321477	+	0.133160i
$754$		0			0
$755$	667.788	−	1612.18i	0.884487	−	2.13534i
$756$		0			0
$757$	189.952	−	189.952i	0.250928	−	0.250928i	−0.570423	−	0.821351i	$-0.693221\pi$
$757$	189.952	−	189.952i	0.250928	−	0.250928i	0.821351	+	0.570423i	$0.193221\pi$
$758$		0			0
$759$	424.893	+	175.997i	0.559807	+	0.231880i
$760$		0			0
$761$	−270.807			−0.355857			−0.177928	−	0.984043i	$-0.556940\pi$
$761$	−270.807			−0.355857			−0.177928	+	0.984043i	$0.556940\pi$
$762$		0			0
$763$	−1166.65	+	548.514i	−1.52903	+	0.718891i
$764$		0			0
$765$	115.964	+	64.0205i	0.151586	+	0.0836870i
$766$		0			0
$767$	1354.07	+	1354.07i	1.76541	+	1.76541i
$768$		0			0
$769$	780.346			1.01475			0.507377	−	0.861724i	$-0.330615\pi$
$769$	780.346			1.01475			0.507377	+	0.861724i	$0.330615\pi$
$770$		0			0
$771$	148.256	−	357.923i	0.192291	−	0.464232i
$772$		0			0
$773$	587.517	+	587.517i	0.760048	+	0.760048i	0.976331	−	0.216283i	$-0.0693933\pi$
$773$	587.517	+	587.517i	0.760048	+	0.760048i	−0.216283	+	0.976331i	$0.569393\pi$
$774$		0			0
$775$	−24.8790	+	60.0632i	−0.0321019	+	0.0775009i
$776$		0			0
$777$	−659.641	+	30.8891i	−0.848959	+	0.0397543i
$778$		0			0
$779$	258.219	+	623.395i	0.331474	+	0.800250i
$780$		0			0
$781$	−506.155			−0.648085
$782$		0			0
$783$			413.281i			0.527817i
$784$		0			0
$785$	124.772	+	301.226i	0.158945	+	0.383727i
$786$		0			0
$787$	−400.943	−	967.962i	−0.509457	−	1.22994i	−0.944197	−	0.329383i	$-0.893159\pi$
$787$	−400.943	−	967.962i	−0.509457	−	1.22994i	0.434739	−	0.900556i	$-0.356841\pi$
$788$		0			0
$789$	−53.8903	+	130.103i	−0.0683020	+	0.164896i
$790$		0			0
$791$	329.382	+	700.574i	0.416412	+	0.885682i
$792$		0			0
$793$	121.947	−	294.405i	0.153779	−	0.371255i
$794$		0			0
$795$			358.634i			0.451112i
$796$		0			0
$797$	596.320	−	596.320i	0.748205	−	0.748205i	−0.225937	−	0.974142i	$-0.572544\pi$
$797$	596.320	−	596.320i	0.748205	−	0.748205i	0.974142	+	0.225937i	$0.0725443\pi$
$798$		0			0
$799$	−994.536	−	111.590i	−1.24473	−	0.139662i
$800$		0			0
$801$	35.7361	−	35.7361i	0.0446144	−	0.0446144i
$802$		0			0
$803$	−470.265			−0.585635
$804$		0			0
$805$	1321.77	−	1451.64i	1.64195	−	1.80328i
$806$		0			0
$807$	−250.655	+	250.655i	−0.310601	+	0.310601i
$808$		0			0
$809$	−178.015	−	73.7362i	−0.220043	−	0.0911448i	0.269939	−	0.962878i	$-0.412997\pi$
$809$	−178.015	−	73.7362i	−0.220043	−	0.0911448i	−0.489982	+	0.871733i	$0.662997\pi$
$810$		0			0
$811$	245.758	+	593.312i	0.303031	+	0.731581i	0.999897	+	0.0143795i	$0.00457729\pi$
$811$	245.758	+	593.312i	0.303031	+	0.731581i	−0.696866	+	0.717202i	$0.745423\pi$
$812$		0			0
$813$	529.697	+	1278.80i	0.651534	+	1.57294i
$814$		0			0
$815$			506.734i			0.621759i
$816$		0			0
$817$		−	488.459i		−	0.597869i
$818$		0			0
$819$	−6.61697	−	141.306i	−0.00807933	−	0.172535i
$820$		0			0
$821$	527.861	−	218.647i	0.642949	−	0.266318i	−0.0372945	−	0.999304i	$-0.511874\pi$
$821$	527.861	−	218.647i	0.642949	−	0.266318i	0.680244	+	0.732986i	$0.261874\pi$
$822$		0			0
$823$	−453.446	−	187.824i	−0.550967	−	0.228218i	0.0897911	−	0.995961i	$-0.471380\pi$
$823$	−453.446	−	187.824i	−0.550967	−	0.228218i	−0.640759	+	0.767742i	$0.721380\pi$
$824$		0			0
$825$	151.745	+	151.745i	0.183934	+	0.183934i
$826$		0			0
$827$	−213.981	+	516.595i	−0.258743	+	0.624662i	−0.998856	−	0.0478213i	$-0.984772\pi$
$827$	−213.981	+	516.595i	−0.258743	+	0.624662i	0.740113	+	0.672483i	$0.234772\pi$
$828$		0			0
$829$	−1103.21			−1.33077			−0.665384	−	0.746501i	$-0.731732\pi$
$829$	−1103.21			−1.33077			−0.665384	+	0.746501i	$0.731732\pi$
$830$		0			0
$831$	40.7939	−	40.7939i	0.0490902	−	0.0490902i
$832$		0			0
$833$	−15.1177	+	832.863i	−0.0181485	+	0.999835i
$834$		0			0
$835$	478.606	+	478.606i	0.573181	+	0.573181i
$836$		0			0
$837$			94.3968i			0.112780i
$838$		0			0
$839$	−1397.65	−	578.924i	−1.66585	−	0.690017i	−0.667347	−	0.744747i	$-0.732570\pi$
$839$	−1397.65	−	578.924i	−1.66585	−	0.690017i	−0.998501	+	0.0547305i	$0.982570\pi$
$840$		0			0
$841$	−445.511	+	445.511i	−0.529740	+	0.529740i
$842$		0			0
$843$	−179.163	+	432.538i	−0.212530	+	0.513093i
$844$		0			0
$845$	334.745	+	808.145i	0.396148	+	0.956385i
$846$		0			0
$847$	−739.029	+	34.6066i	−0.872525	+	0.0408578i
$848$		0			0
$849$	657.716			0.774695
$850$		0			0
$851$	−1415.60			−1.66345
$852$		0			0
$853$	−1105.75	+	458.016i	−1.29631	+	0.536947i	−0.920859	−	0.389897i	$-0.872511\pi$
$853$	−1105.75	+	458.016i	−1.29631	+	0.536947i	−0.375447	+	0.926844i	$0.622511\pi$
$854$		0			0
$855$	65.0806	−	26.9572i	0.0761176	−	0.0315289i
$856$		0			0
$857$	−386.743	+	933.681i	−0.451276	+	1.08948i	0.520562	+	0.853824i	$0.325723\pi$
$857$	−386.743	+	933.681i	−0.451276	+	1.08948i	−0.971837	+	0.235652i	$0.924277\pi$
$858$		0			0
$859$	−496.780	−	496.780i	−0.578324	−	0.578324i	0.356117	−	0.934441i	$-0.384100\pi$
$859$	−496.780	−	496.780i	−0.578324	−	0.578324i	−0.934441	+	0.356117i	$0.884100\pi$
$860$		0			0
$861$	1081.20	+	984.473i	1.25575	+	1.14341i
$862$		0			0
$863$			1636.78i			1.89662i	0.317346	+	0.948310i	$0.397209\pi$
$863$			1636.78i			1.89662i	−0.317346	+	0.948310i	$0.602791\pi$
$864$		0			0
$865$	93.5393	+	93.5393i	0.108138	+	0.108138i
$866$		0			0
$867$	797.296	−	136.228i	0.919603	−	0.157126i
$868$		0			0
$869$	110.181	+	110.181i	0.126791	+	0.126791i
$870$		0			0
$871$	1719.08			1.97369
$872$		0			0
$873$	−5.90411	−	2.44556i	−0.00676301	−	0.00280133i
$874$		0			0
$875$	−228.570	+	107.464i	−0.261222	+	0.122816i
$876$		0			0
$877$	962.736	+	398.778i	1.09776	+	0.454707i	0.856706	−	0.515805i	$-0.172507\pi$
$877$	962.736	+	398.778i	1.09776	+	0.454707i	0.241054	+	0.970512i	$0.422507\pi$
$878$		0			0
$879$	954.609	−	395.412i	1.08602	−	0.449843i
$880$		0			0
$881$	−1244.74	+	515.587i	−1.41287	+	0.585230i	−0.953058	−	0.302787i	$-0.902083\pi$
$881$	−1244.74	+	515.587i	−1.41287	+	0.585230i	−0.459811	+	0.888017i	$0.652083\pi$
$882$		0			0
$883$	663.854			0.751816			0.375908	−	0.926657i	$-0.377331\pi$
$883$	663.854			0.751816			0.375908	+	0.926657i	$0.377331\pi$
$884$		0			0
$885$			2066.47i			2.33499i
$886$		0			0
$887$	−691.553	+	286.451i	−0.779654	+	0.322943i	−0.736776	−	0.676137i	$-0.763653\pi$
$887$	−691.553	+	286.451i	−0.779654	+	0.322943i	−0.0428784	+	0.999080i	$0.513653\pi$
$888$		0			0
$889$	−56.6915	−	1210.66i	−0.0637700	−	1.36182i
$890$		0			0
$891$	249.919	+	103.520i	0.280493	+	0.116184i
$892$		0			0
$893$	−376.328	+	376.328i	−0.421420	+	0.421420i
$894$		0			0
$895$	−2062.99	−	854.519i	−2.30502	−	0.954769i
$896$		0			0
$897$			2035.84i			2.26961i
$898$		0			0
$899$	34.0706	−	34.0706i	0.0378984	−	0.0378984i
$900$		0			0
$901$	−203.498	−	254.935i	−0.225858	−	0.282947i
$902$		0			0
$903$	−450.382	−	957.934i	−0.498762	−	1.06084i
$904$		0			0
$905$			1507.56i			1.66582i
$906$		0			0
$907$	−640.011	+	1545.12i	−0.705635	+	1.70355i	0.00499432	+	0.999988i	$0.498410\pi$
$907$	−640.011	+	1545.12i	−0.705635	+	1.70355i	−0.710629	+	0.703566i	$0.751590\pi$
$908$		0			0
$909$	82.0859	+	82.0859i	0.0903035	+	0.0903035i
$910$		0			0
$911$	284.622	+	117.894i	0.312428	+	0.129412i	0.533387	−	0.845871i	$-0.320919\pi$
$911$	284.622	+	117.894i	0.312428	+	0.129412i	−0.220959	+	0.975283i	$0.570919\pi$
$912$		0			0
$913$	55.9651	+	135.112i	0.0612981	+	0.147987i
$914$		0			0
$915$	317.701	−	131.596i	0.347215	−	0.143821i
$916$		0			0
$917$	140.272	+	50.5533i	0.152968	+	0.0551290i
$918$		0			0
$919$	−340.694			−0.370722			−0.185361	−	0.982670i	$-0.559345\pi$
$919$	−340.694			−0.370722			−0.185361	+	0.982670i	$0.559345\pi$
$920$		0			0
$921$	195.010	+	470.795i	0.211737	+	0.511178i
$922$		0			0
$923$	−857.438	−	2070.04i	−0.928968	−	2.24273i
$924$		0			0
$925$	−610.268	−	252.781i	−0.659749	−	0.273277i
$926$		0			0
$927$	34.2312	+	34.2312i	0.0369269	+	0.0369269i
$928$		0			0
$929$	−1676.85	−	694.573i	−1.80500	−	0.747657i	−0.984348	−	0.176233i	$-0.943609\pi$
$929$	−1676.85	−	694.573i	−1.80500	−	0.747657i	−0.820655	−	0.571424i	$-0.806391\pi$
$930$		0			0
$931$	341.139	+	282.595i	0.366422	+	0.303540i
$932$		0			0
$933$	−21.3336	−	21.3336i	−0.0228656	−	0.0228656i
$934$		0			0
$935$	−441.423	−	49.5289i	−0.472110	−	0.0529721i
$936$		0			0
$937$	−410.955	+	410.955i	−0.438586	+	0.438586i	−0.891536	−	0.452950i	$-0.850372\pi$
$937$	−410.955	+	410.955i	−0.438586	+	0.438586i	0.452950	+	0.891536i	$0.350372\pi$
$938$		0			0
$939$		−	1171.45i		−	1.24755i
$940$		0			0
$941$	−811.748	−	336.237i	−0.862644	−	0.357319i	−0.0929028	−	0.995675i	$-0.529615\pi$
$941$	−811.748	−	336.237i	−0.862644	−	0.357319i	−0.769741	+	0.638356i	$0.779615\pi$
$942$		0			0
$943$	2216.48	+	2216.48i	2.35046	+	2.35046i
$944$		0			0
$945$	895.541	−	983.533i	0.947663	−	1.04078i
$946$		0			0
$947$	740.167	−	306.587i	0.781591	−	0.323746i	0.0440335	−	0.999030i	$-0.485979\pi$
$947$	740.167	−	306.587i	0.781591	−	0.323746i	0.737557	+	0.675285i	$0.235979\pi$
$948$		0			0
$949$	−796.639	−	1923.26i	−0.839451	−	2.02661i
$950$		0			0
$951$		−	34.2778i		−	0.0360440i
$952$		0			0
$953$	481.411			0.505154			0.252577	−	0.967577i	$-0.418722\pi$
$953$	481.411			0.505154			0.252577	+	0.967577i	$0.418722\pi$
$954$		0			0
$955$	1924.79	−	797.276i	2.01549	−	0.834844i
$956$		0			0
$957$	−60.8655	−	146.942i	−0.0636003	−	0.153545i
$958$		0			0
$959$	250.116	−	274.691i	0.260809	−	0.286435i
$960$		0			0
$961$	−671.748	+	671.748i	−0.699009	+	0.699009i
$962$		0			0
$963$	−34.8898	+	84.2314i	−0.0362303	+	0.0874677i
$964$		0			0
$965$	−179.732			−0.186251
$966$		0			0
$967$	−364.587	−	364.587i	−0.377029	−	0.377029i	0.493000	−	0.870029i	$-0.335900\pi$
$967$	−364.587	−	364.587i	−0.377029	−	0.377029i	−0.870029	+	0.493000i	$0.835900\pi$
$968$		0			0
$969$	207.893	−	376.568i	0.214544	−	0.388615i
$970$		0			0
$971$	404.328	−	404.328i	0.416404	−	0.416404i	−0.467558	−	0.883962i	$-0.654866\pi$
$971$	404.328	−	404.328i	0.416404	−	0.416404i	0.883962	+	0.467558i	$0.154866\pi$
$972$		0			0
$973$	−222.558	+	617.538i	−0.228734	+	0.634675i
$974$		0			0
$975$	−363.538	+	877.657i	−0.372859	+	0.900161i
$976$		0			0
$977$	751.571	−	751.571i	0.769264	−	0.769264i	−0.208713	−	0.977977i	$-0.566927\pi$
$977$	751.571	−	751.571i	0.769264	−	0.769264i	0.977977	+	0.208713i	$0.0669273\pi$
$978$		0			0
$979$	−64.8549	+	156.573i	−0.0662460	+	0.159932i
$980$		0			0
$981$	−198.525	+	82.2318i	−0.202370	+	0.0838244i
$982$		0			0
$983$	564.876	−	233.979i	0.574645	−	0.238026i	−0.0763841	−	0.997078i	$-0.524338\pi$
$983$	564.876	−	233.979i	0.574645	−	0.238026i	0.651029	+	0.759053i	$0.274338\pi$
$984$		0			0
$985$		−	1360.86i		−	1.38158i
$986$		0			0
$987$	−391.038	+	1085.02i	−0.396189	+	1.09931i
$988$		0			0
$989$	−868.357	−	2096.40i	−0.878015	−	2.11972i
$990$		0			0
$991$	278.739	−	115.458i	0.281271	−	0.116506i	−0.237588	−	0.971366i	$-0.576357\pi$
$991$	278.739	−	115.458i	0.281271	−	0.116506i	0.518859	+	0.854860i	$0.326357\pi$
$992$		0			0
$993$	89.3572	−	215.727i	0.0899871	−	0.217248i
$994$		0			0
$995$	873.755	−	873.755i	0.878146	−	0.878146i
$996$		0			0
$997$	88.0306	+	36.4635i	0.0882955	+	0.0365732i	0.426394	−	0.904538i	$-0.359784\pi$
$997$	88.0306	+	36.4635i	0.0882955	+	0.0365732i	−0.338099	+	0.941111i	$0.609784\pi$
$998$		0			0
$999$	−959.111			−0.960071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.x.a.321.19	yes	96
7.6	odd	2	inner	476.3.x.a.321.6	✓	96
17.8	even	8	inner	476.3.x.a.433.6	yes	96
119.76	odd	8	inner	476.3.x.a.433.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.x.a.321.6	✓	96	7.6	odd	2	inner
476.3.x.a.321.19	yes	96	1.1	even	1	trivial
476.3.x.a.433.6	yes	96	17.8	even	8	inner
476.3.x.a.433.19	yes	96	119.76	odd	8	inner

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58574 - 1.07105i) q^{3} +(2.55560 + 6.16976i) q^{5} +(-4.71280 + 5.17586i) q^{7} +(-0.825039 + 0.825039i) q^{9} +(1.49730 - 3.61481i) q^{11} +17.3201 q^{13} +(13.2162 + 13.2162i) q^{15} +(-16.8940 - 1.89555i) q^{17} +(-6.39261 + 6.39261i) q^{19} +(-6.64249 + 18.4311i) q^{21} +(-16.0718 + 38.8007i) q^{23} +(-13.8572 + 13.8572i) q^{25} +(-10.8891 + 26.2887i) q^{27} +(13.4186 - 5.55816i) q^{29} +(3.06492 - 1.26953i) q^{31} -10.9507i q^{33} +(-43.9778 - 15.8494i) q^{35} +(12.8990 + 31.1409i) q^{37} +(44.7853 - 18.5507i) q^{39} +(28.5624 - 68.9556i) q^{41} +(-38.2049 + 38.2049i) q^{43} +(-7.19876 - 2.98182i) q^{45} +58.8692 q^{47} +(-4.57902 - 48.7856i) q^{49} +(-45.7138 + 13.1929i) q^{51} +(13.5679 + 13.5679i) q^{53} +26.1290 q^{55} +(-9.68285 + 23.3765i) q^{57} +(78.1791 + 78.1791i) q^{59} +(7.04078 - 16.9979i) q^{61} +(-0.382041 - 8.15853i) q^{63} +(44.2631 + 106.861i) q^{65} +99.2537 q^{67} +117.542i q^{69} +(-49.5054 - 119.517i) q^{71} +(-45.9951 - 111.042i) q^{73} +(-20.9894 + 50.6728i) q^{75} +(11.6533 + 24.7857i) q^{77} +(-15.2402 + 36.7932i) q^{79} +69.1376i q^{81} +(-26.4297 + 26.4297i) q^{83} +(-31.4791 - 109.076i) q^{85} +(28.7440 - 28.7440i) q^{87} -43.3144 q^{89} +(-81.6261 + 89.6462i) q^{91} +(6.56536 - 6.56536i) q^{93} +(-55.7778 - 23.1039i) q^{95} +(2.09599 + 5.06017i) q^{97} +(1.74703 + 4.21769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{11} - 16 q^{15} + 72 q^{23} + 72 q^{25} + 32 q^{35} - 256 q^{37} - 88 q^{39} - 32 q^{43} - 20 q^{49} - 120 q^{51} - 80 q^{53} + 492 q^{63} - 104 q^{65} - 144 q^{67} - 64 q^{71} + 84 q^{77}+ \cdots + 560 q^{99}+O(q^{100}) \) 96 * q - 40 * q^11 - 16 * q^15 + 72 * q^23 + 72 * q^25 + 32 * q^35 - 256 * q^37 - 88 * q^39 - 32 * q^43 - 20 * q^49 - 120 * q^51 - 80 * q^53 + 492 * q^63 - 104 * q^65 - 144 * q^67 - 64 * q^71 + 84 * q^77 - 256 * q^79 + 824 * q^85 - 368 * q^91 - 264 * q^93 + 104 * q^95 + 560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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