LMFDB - Embedded newform 476.3.s.a.341.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(341,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("476.341");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.s (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:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.10
Character	$\chi$	$=$	476.341
Dual form			476.3.s.a.409.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.565149 + 0.326289i) q^{3} +(1.39043 + 0.802767i) q^{5} +(-5.00309 + 4.89583i) q^{7} +(-4.28707 + 7.42543i) q^{9} +O(q^{10})$	\(q+(-0.565149 + 0.326289i) q^{3} +(1.39043 + 0.802767i) q^{5} +(-5.00309 + 4.89583i) q^{7} +(-4.28707 + 7.42543i) q^{9} +(4.70585 + 8.15077i) q^{11} -22.3588i q^{13} -1.04774 q^{15} +(3.57071 - 2.06155i) q^{17} +(-27.5279 - 15.8932i) q^{19} +(1.23003 - 4.39932i) q^{21} +(-11.5096 + 19.9353i) q^{23} +(-11.2111 - 19.4182i) q^{25} -11.4685i q^{27} -29.1784 q^{29} +(12.0407 - 6.95169i) q^{31} +(-5.31901 - 3.07093i) q^{33} +(-10.8867 + 2.79101i) q^{35} +(-24.4444 + 42.3389i) q^{37} +(7.29542 + 12.6360i) q^{39} +44.6306i q^{41} -1.15970 q^{43} +(-11.9218 + 6.88304i) q^{45} +(18.6212 + 10.7509i) q^{47} +(1.06176 - 48.9885i) q^{49} +(-1.34532 + 2.33017i) q^{51} +(-52.4221 - 90.7977i) q^{53} +15.1108i q^{55} +20.7431 q^{57} +(-77.8014 + 44.9186i) q^{59} +(-60.6480 - 35.0152i) q^{61} +(-14.9050 - 58.1388i) q^{63} +(17.9489 - 31.0884i) q^{65} +(35.2883 + 61.1211i) q^{67} -15.0219i q^{69} -22.3327 q^{71} +(-30.2281 + 17.4522i) q^{73} +(12.6719 + 7.31613i) q^{75} +(-63.4485 - 17.7400i) q^{77} +(-10.6769 + 18.4930i) q^{79} +(-34.8416 - 60.3474i) q^{81} -12.2248i q^{83} +6.61979 q^{85} +(16.4902 - 9.52059i) q^{87} +(82.5262 + 47.6465i) q^{89} +(109.465 + 111.863i) q^{91} +(-4.53652 + 7.85748i) q^{93} +(-25.5171 - 44.1970i) q^{95} +95.0498i q^{97} -80.6972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.565149	+	0.326289i	−0.188383	+	0.108763i	−0.591225	−	0.806506i	$-0.701356\pi$
$3$	−0.565149	+	0.326289i	−0.188383	+	0.108763i	0.402842	+	0.915269i	$0.368022\pi$
$4$		0			0
$5$	1.39043	+	0.802767i	0.278087	+	0.160553i	0.632557	−	0.774514i	$-0.282005\pi$
$5$	1.39043	+	0.802767i	0.278087	+	0.160553i	−0.354470	+	0.935067i	$0.615339\pi$
$6$		0			0
$7$	−5.00309	+	4.89583i	−0.714727	+	0.699404i
$7$	−5.00309	+	4.89583i	−0.714727	+	0.699404i
$8$		0			0
$9$	−4.28707	+	7.42543i	−0.476341	+	0.825047i
$10$		0			0
$11$	4.70585	+	8.15077i	0.427804	+	0.740979i	0.996678	−	0.0814463i	$-0.0259539\pi$
$11$	4.70585	+	8.15077i	0.427804	+	0.740979i	−0.568873	+	0.822425i	$0.692621\pi$
$12$		0			0
$13$		−	22.3588i		−	1.71991i	−0.510373	−	0.859953i	$-0.670493\pi$
$13$		−	22.3588i		−	1.71991i	0.510373	−	0.859953i	$-0.329507\pi$
$14$		0			0
$15$	−1.04774			−0.0698490
$16$		0			0
$17$	3.57071	−	2.06155i	0.210042	−	0.121268i
$17$	3.57071	−	2.06155i	0.210042	−	0.121268i
$18$		0			0
$19$	−27.5279	−	15.8932i	−1.44884	−	0.836486i	−0.450424	−	0.892815i	$-0.648727\pi$
$19$	−27.5279	−	15.8932i	−1.44884	−	0.836486i	−0.998412	+	0.0563284i	$0.982061\pi$
$20$		0			0
$21$	1.23003	−	4.39932i	0.0585731	−	0.209491i
$22$		0			0
$23$	−11.5096	+	19.9353i	−0.500419	+	0.866752i	0.499580	+	0.866268i	$0.333488\pi$
$23$	−11.5096	+	19.9353i	−0.500419	+	0.866752i	−1.00000		0.000484459i	$0.999846\pi$
$24$		0			0
$25$	−11.2111	−	19.4182i	−0.448445	−	0.776730i
$26$		0			0
$27$		−	11.4685i		−	0.424759i
$28$		0			0
$29$	−29.1784			−1.00615			−0.503076	−	0.864242i	$-0.667799\pi$
$29$	−29.1784			−1.00615			−0.503076	+	0.864242i	$0.667799\pi$
$30$		0			0
$31$	12.0407	−	6.95169i	0.388409	−	0.224248i	−0.293062	−	0.956094i	$-0.594674\pi$
$31$	12.0407	−	6.95169i	0.388409	−	0.224248i	0.681471	+	0.731846i	$0.261341\pi$
$32$		0			0
$33$	−5.31901	−	3.07093i	−0.161182	−	0.0930585i
$34$		0			0
$35$	−10.8867	+	2.79101i	−0.311048	+	0.0797431i
$36$		0			0
$37$	−24.4444	+	42.3389i	−0.660659	+	1.14429i	0.319784	+	0.947491i	$0.396390\pi$
$37$	−24.4444	+	42.3389i	−0.660659	+	1.14429i	−0.980443	+	0.196804i	$0.936944\pi$
$38$		0			0
$39$	7.29542	+	12.6360i	0.187062	+	0.324001i
$40$		0			0
$41$			44.6306i			1.08855i	0.838906	+	0.544276i	$0.183195\pi$
$41$			44.6306i			1.08855i	−0.838906	+	0.544276i	$0.816805\pi$
$42$		0			0
$43$	−1.15970			−0.0269697			−0.0134849	−	0.999909i	$-0.504292\pi$
$43$	−1.15970			−0.0269697			−0.0134849	+	0.999909i	$0.504292\pi$
$44$		0			0
$45$	−11.9218	+	6.88304i	−0.264928	+	0.152956i
$46$		0			0
$47$	18.6212	+	10.7509i	0.396195	+	0.228743i	0.684841	−	0.728693i	$-0.259872\pi$
$47$	18.6212	+	10.7509i	0.396195	+	0.228743i	−0.288646	+	0.957436i	$0.593205\pi$
$48$		0			0
$49$	1.06176	−	48.9885i	0.0216686	−	0.999765i
$50$		0			0
$51$	−1.34532	+	2.33017i	−0.0263789	+	0.0456896i
$52$		0			0
$53$	−52.4221	−	90.7977i	−0.989095	−	1.71316i	−0.622092	−	0.782944i	$-0.713717\pi$
$53$	−52.4221	−	90.7977i	−0.989095	−	1.71316i	−0.367003	−	0.930220i	$-0.619616\pi$
$54$		0			0
$55$			15.1108i			0.274742i
$56$		0			0
$57$	20.7431			0.363915
$58$		0			0
$59$	−77.8014	+	44.9186i	−1.31867	+	0.761333i	−0.983514	−	0.180831i	$-0.942121\pi$
$59$	−77.8014	+	44.9186i	−1.31867	+	0.761333i	−0.335153	+	0.942164i	$0.608788\pi$
$60$		0			0
$61$	−60.6480	−	35.0152i	−0.994230	−	0.574019i	−0.0876940	−	0.996147i	$-0.527950\pi$
$61$	−60.6480	−	35.0152i	−0.994230	−	0.574019i	−0.906536	+	0.422128i	$0.861283\pi$
$62$		0			0
$63$	−14.9050	−	58.1388i	−0.236587	−	0.922838i
$64$		0			0
$65$	17.9489	−	31.0884i	0.276137	−	0.478283i
$66$		0			0
$67$	35.2883	+	61.1211i	0.526690	+	0.912255i	0.999516	+	0.0310988i	$0.00990064\pi$
$67$	35.2883	+	61.1211i	0.526690	+	0.912255i	−0.472826	+	0.881156i	$0.656766\pi$
$68$		0			0
$69$		−	15.0219i		−	0.217708i
$70$		0			0
$71$	−22.3327			−0.314545			−0.157272	−	0.987555i	$-0.550270\pi$
$71$	−22.3327			−0.314545			−0.157272	+	0.987555i	$0.550270\pi$
$72$		0			0
$73$	−30.2281	+	17.4522i	−0.414084	+	0.239071i	−0.692543	−	0.721377i	$-0.743510\pi$
$73$	−30.2281	+	17.4522i	−0.414084	+	0.239071i	0.278459	+	0.960448i	$0.410176\pi$
$74$		0			0
$75$	12.6719	+	7.31613i	0.168959	+	0.0975484i
$76$		0			0
$77$	−63.4485	−	17.7400i	−0.824007	−	0.230389i
$78$		0			0
$79$	−10.6769	+	18.4930i	−0.135151	+	0.234088i	−0.925655	−	0.378368i	$-0.876485\pi$
$79$	−10.6769	+	18.4930i	−0.135151	+	0.234088i	0.790504	+	0.612457i	$0.209819\pi$
$80$		0			0
$81$	−34.8416	−	60.3474i	−0.430143	−	0.745030i
$82$		0			0
$83$		−	12.2248i		−	0.147287i	−0.997285	−	0.0736433i	$-0.976537\pi$
$83$		−	12.2248i		−	0.147287i	0.997285	−	0.0736433i	$-0.0234626\pi$
$84$		0			0
$85$	6.61979			0.0778799
$86$		0			0
$87$	16.4902	−	9.52059i	0.189542	−	0.109432i
$88$		0			0
$89$	82.5262	+	47.6465i	0.927260	+	0.535354i	0.885944	−	0.463792i	$-0.153512\pi$
$89$	82.5262	+	47.6465i	0.927260	+	0.535354i	0.0413163	+	0.999146i	$0.486845\pi$
$90$		0			0
$91$	109.465	+	111.863i	1.20291	+	1.22926i
$92$		0			0
$93$	−4.53652	+	7.85748i	−0.0487797	+	0.0844890i
$94$		0			0
$95$	−25.5171	−	44.1970i	−0.268602	−	0.465231i
$96$		0			0
$97$			95.0498i			0.979895i	0.871752	+	0.489948i	$0.162984\pi$
$97$			95.0498i			0.979895i	−0.871752	+	0.489948i	$0.837016\pi$
$98$		0			0
$99$	−80.6972			−0.815123
$100$		0			0
$101$	21.7246	−	12.5427i	0.215095	−	0.124185i	−0.388582	−	0.921414i	$-0.627035\pi$
$101$	21.7246	−	12.5427i	0.215095	−	0.124185i	0.603677	+	0.797229i	$0.293702\pi$
$102$		0			0
$103$	104.956	+	60.5961i	1.01899	+	0.588312i	0.913810	−	0.406142i	$-0.133126\pi$
$103$	104.956	+	60.5961i	1.01899	+	0.588312i	0.105176	+	0.994454i	$0.466459\pi$
$104$		0			0
$105$	5.24191	−	5.12953i	0.0499230	−	0.0488527i
$106$		0			0
$107$	33.3788	−	57.8138i	0.311951	−	0.540315i	−0.666833	−	0.745207i	$-0.732351\pi$
$107$	33.3788	−	57.8138i	0.311951	−	0.540315i	0.978785	+	0.204891i	$0.0656841\pi$
$108$		0			0
$109$	−30.9500	−	53.6070i	−0.283945	−	0.491808i	0.688408	−	0.725324i	$-0.258310\pi$
$109$	−30.9500	−	53.6070i	−0.283945	−	0.491808i	−0.972353	+	0.233516i	$0.924977\pi$
$110$		0			0
$111$		−	31.9037i		−	0.287421i
$112$		0			0
$113$	158.008			1.39830			0.699152	−	0.714973i	$-0.253561\pi$
$113$	158.008			1.39830			0.699152	+	0.714973i	$0.253561\pi$
$114$		0			0
$115$	−32.0068	+	18.4791i	−0.278320	+	0.160688i
$116$		0			0
$117$	166.023	+	95.8537i	1.41900	+	0.819262i
$118$		0			0
$119$	−7.77159	+	27.7957i	−0.0653075	+	0.233578i
$120$		0			0
$121$	16.2100	−	28.0765i	0.133967	−	0.232037i
$122$		0			0
$123$	−14.5625	−	25.2229i	−0.118394	−	0.205064i
$124$		0			0
$125$		−	76.1381i		−	0.609105i
$126$		0			0
$127$	−84.0898			−0.662125			−0.331062	−	0.943609i	$-0.607407\pi$
$127$	−84.0898			−0.662125			−0.331062	+	0.943609i	$0.607407\pi$
$128$		0			0
$129$	0.655402	−	0.378397i	0.00508064	−	0.00293331i
$130$		0			0
$131$	85.8981	+	49.5933i	0.655711	+	0.378575i	0.790641	−	0.612280i	$-0.209748\pi$
$131$	85.8981	+	49.5933i	0.655711	+	0.378575i	−0.134930	+	0.990855i	$0.543081\pi$
$132$		0			0
$133$	215.535	−	55.2566i	1.62056	−	0.415463i
$134$		0			0
$135$	9.20653	−	15.9462i	0.0681965	−	0.118120i
$136$		0			0
$137$	−27.0559	−	46.8622i	−0.197488	−	0.342060i	0.750225	−	0.661183i	$-0.229945\pi$
$137$	−27.0559	−	46.8622i	−0.197488	−	0.342060i	−0.947713	+	0.319123i	$0.896612\pi$
$138$		0			0
$139$		−	24.9001i		−	0.179138i	−0.995981	−	0.0895688i	$-0.971451\pi$
$139$		−	24.9001i		−	0.179138i	0.995981	−	0.0895688i	$-0.0285489\pi$
$140$		0			0
$141$	−14.0316			−0.0995151
$142$		0			0
$143$	182.241	−	105.217i	1.27441	−	0.735783i
$144$		0			0
$145$	−40.5707	−	23.4235i	−0.279798	−	0.161541i
$146$		0			0
$147$	15.3843	+	28.0322i	0.104655	+	0.190695i
$148$		0			0
$149$	−93.1009	+	161.255i	−0.624838	+	1.08225i	0.363734	+	0.931503i	$0.381502\pi$
$149$	−93.1009	+	161.255i	−0.624838	+	1.08225i	−0.988572	+	0.150749i	$0.951832\pi$
$150$		0			0
$151$	65.1828	+	112.900i	0.431674	+	0.747682i	0.997018	−	0.0771738i	$-0.0245896\pi$
$151$	65.1828	+	112.900i	0.431674	+	0.747682i	−0.565343	+	0.824856i	$0.691256\pi$
$152$		0			0
$153$			35.3521i			0.231059i
$154$		0			0
$155$	22.3224			0.144015
$156$		0			0
$157$	−13.6820	+	7.89934i	−0.0871468	+	0.0503142i	−0.542940	−	0.839771i	$-0.682689\pi$
$157$	−13.6820	+	7.89934i	−0.0871468	+	0.0503142i	0.455793	+	0.890086i	$0.349356\pi$
$158$		0			0
$159$	59.2525	+	34.2095i	0.372657	+	0.215154i
$160$		0			0
$161$	−40.0160	−	156.087i	−0.248546	−	0.969486i
$162$		0			0
$163$	−132.732	+	229.898i	−0.814304	+	1.41042i	0.0955220	+	0.995427i	$0.469548\pi$
$163$	−132.732	+	229.898i	−0.814304	+	1.41042i	−0.909826	+	0.414989i	$0.863785\pi$
$164$		0			0
$165$	−4.93048	−	8.53985i	−0.0298817	−	0.0517567i
$166$		0			0
$167$			154.238i			0.923584i	0.886988	+	0.461792i	$0.152793\pi$
$167$			154.238i			0.923584i	−0.886988	+	0.461792i	$0.847207\pi$
$168$		0			0
$169$	−330.915			−1.95808
$170$		0			0
$171$	236.028	−	136.271i	1.38028	−	0.796906i
$172$		0			0
$173$	1.35536	+	0.782516i	0.00783444	+	0.00452322i	0.503912	−	0.863755i	$-0.331894\pi$
$173$	1.35536	+	0.782516i	0.00783444	+	0.00452322i	−0.496078	+	0.868278i	$0.665227\pi$
$174$		0			0
$175$	151.159	+	42.2634i	0.863764	+	0.241505i
$176$		0			0
$177$	29.3129	−	50.7714i	0.165610	−	0.286844i
$178$		0			0
$179$	72.4539	+	125.494i	0.404770	+	0.701083i	0.994295	−	0.106668i	$-0.0340181\pi$
$179$	72.4539	+	125.494i	0.404770	+	0.701083i	−0.589524	+	0.807751i	$0.700685\pi$
$180$		0			0
$181$		−	235.279i		−	1.29988i	−0.759985	−	0.649941i	$-0.774794\pi$
$181$		−	235.279i		−	1.29988i	0.759985	−	0.649941i	$-0.225206\pi$
$182$		0			0
$183$	45.7002			0.249728
$184$		0			0
$185$	−67.9766	+	39.2463i	−0.367441	+	0.212142i
$186$		0			0
$187$	33.6065	+	19.4027i	0.179714	+	0.103758i
$188$		0			0
$189$	56.1477	+	57.3779i	0.297078	+	0.303587i
$190$		0			0
$191$	−37.1072	+	64.2716i	−0.194279	+	0.336500i	−0.946664	−	0.322223i	$-0.895570\pi$
$191$	−37.1072	+	64.2716i	−0.194279	+	0.336500i	0.752385	+	0.658723i	$0.228903\pi$
$192$		0			0
$193$	−105.085	−	182.013i	−0.544482	−	0.943071i	−0.998639	−	0.0521494i	$-0.983393\pi$
$193$	−105.085	−	182.013i	−0.544482	−	0.943071i	0.454157	−	0.890922i	$-0.349941\pi$
$194$		0			0
$195$			23.4261i			0.120134i
$196$		0			0
$197$	365.918			1.85745			0.928725	−	0.370769i	$-0.120906\pi$
$197$	365.918			1.85745			0.928725	+	0.370769i	$0.120906\pi$
$198$		0			0
$199$	159.439	−	92.0522i	0.801201	−	0.462574i	−0.0426899	−	0.999088i	$-0.513593\pi$
$199$	159.439	−	92.0522i	0.801201	−	0.462574i	0.843891	+	0.536515i	$0.180259\pi$
$200$		0			0
$201$	−39.8862	−	23.0283i	−0.198439	−	0.114569i
$202$		0			0
$203$	145.982	−	142.853i	0.719124	−	0.703707i
$204$		0			0
$205$	−35.8280	+	62.0559i	−0.174771	+	0.302712i
$206$		0			0
$207$	−98.6854	−	170.928i	−0.476741	−	0.825739i
$208$		0			0
$209$		−	299.165i		−	1.43141i
$210$		0			0
$211$	−72.5011			−0.343607			−0.171804	−	0.985131i	$-0.554959\pi$
$211$	−72.5011			−0.343607			−0.171804	+	0.985131i	$0.554959\pi$
$212$		0			0
$213$	12.6213	−	7.28690i	0.0592548	−	0.0342108i
$214$		0			0
$215$	−1.61248	−	0.930968i	−0.00749993	−	0.00433008i
$216$		0			0
$217$	−26.2063	+	93.7290i	−0.120766	+	0.431931i
$218$		0			0
$219$	11.3889	−	19.7262i	0.0520042	−	0.0900739i
$220$		0			0
$221$	−46.0938	−	79.8368i	−0.208569	−	0.361253i
$222$		0			0
$223$			342.543i			1.53607i	0.640409	+	0.768034i	$0.278765\pi$
$223$			342.543i			1.53607i	−0.640409	+	0.768034i	$0.721235\pi$
$224$		0			0
$225$	192.252			0.854452
$226$		0			0
$227$	−214.126	+	123.626i	−0.943287	+	0.544607i	−0.890989	−	0.454024i	$-0.849988\pi$
$227$	−214.126	+	123.626i	−0.943287	+	0.544607i	−0.0522980	+	0.998632i	$0.516655\pi$
$228$		0			0
$229$	32.0290	+	18.4919i	0.139865	+	0.0807508i	0.568299	−	0.822822i	$-0.307602\pi$
$229$	32.0290	+	18.4919i	0.139865	+	0.0807508i	−0.428435	+	0.903573i	$0.640935\pi$
$230$		0			0
$231$	41.6462	−	10.6768i	0.180287	−	0.0462199i
$232$		0			0
$233$	−94.6039	+	163.859i	−0.406025	+	0.703256i	−0.994440	−	0.105303i	$-0.966419\pi$
$233$	−94.6039	+	163.859i	−0.406025	+	0.703256i	0.588415	+	0.808559i	$0.299752\pi$
$234$		0			0
$235$	17.2610	+	29.8969i	0.0734510	+	0.127221i
$236$		0			0
$237$		−	13.9351i		−	0.0587977i
$238$		0			0
$239$	33.7806			0.141341			0.0706707	−	0.997500i	$-0.477486\pi$
$239$	33.7806			0.141341			0.0706707	+	0.997500i	$0.477486\pi$
$240$		0			0
$241$	−339.439	+	195.975i	−1.40846	+	0.813176i	−0.995240	−	0.0974547i	$-0.968930\pi$
$241$	−339.439	+	195.975i	−1.40846	+	0.813176i	−0.413222	+	0.910630i	$0.635597\pi$
$242$		0			0
$243$	128.769	+	74.3450i	0.529915	+	0.305947i
$244$		0			0
$245$	40.8027	−	67.2629i	0.166542	−	0.274542i
$246$		0			0
$247$	−355.353	+	615.490i	−1.43868	+	2.49186i
$248$		0			0
$249$	3.98881	+	6.90882i	0.0160193	+	0.0277463i
$250$		0			0
$251$		−	196.769i		−	0.783939i	−0.919978	−	0.391970i	$-0.871794\pi$
$251$		−	196.769i		−	0.783939i	0.919978	−	0.391970i	$-0.128206\pi$
$252$		0			0
$253$	−216.651			−0.856327
$254$		0			0
$255$	−3.74116	+	2.15996i	−0.0146712	+	0.00847044i
$256$		0			0
$257$	337.436	+	194.819i	1.31298	+	0.758049i	0.982589	−	0.185795i	$-0.0594859\pi$
$257$	337.436	+	194.819i	1.31298	+	0.758049i	0.330391	+	0.943844i	$0.392819\pi$
$258$		0			0
$259$	−84.9866	−	331.501i	−0.328134	−	1.27993i
$260$		0			0
$261$	125.090	−	216.662i	0.479272	−	0.830124i
$262$		0			0
$263$	−11.9752	−	20.7417i	−0.0455331	−	0.0788656i	0.842361	−	0.538914i	$-0.181165\pi$
$263$	−11.9752	−	20.7417i	−0.0455331	−	0.0788656i	−0.887894	+	0.460049i	$0.847832\pi$
$264$		0			0
$265$		−	168.331i		−	0.635211i
$266$		0			0
$267$	−62.1861			−0.232907
$268$		0			0
$269$	411.431	−	237.540i	1.52948	−	0.883049i	0.530102	−	0.847934i	$-0.322154\pi$
$269$	411.431	−	237.540i	1.52948	−	0.883049i	0.999383	−	0.0351144i	$-0.0111795\pi$
$270$		0			0
$271$	16.2064	+	9.35678i	0.0598023	+	0.0345269i	0.529603	−	0.848246i	$-0.322341\pi$
$271$	16.2064	+	9.35678i	0.0598023	+	0.0345269i	−0.469801	+	0.882772i	$0.655674\pi$
$272$		0			0
$273$	−98.3634	−	27.5021i	−0.360306	−	0.100740i
$274$		0			0
$275$	105.516	−	182.759i	0.383694	−	0.664577i
$276$		0			0
$277$	53.0824	+	91.9414i	0.191633	+	0.331918i	0.945792	−	0.324774i	$-0.105288\pi$
$277$	53.0824	+	91.9414i	0.191633	+	0.331918i	−0.754158	+	0.656693i	$0.771955\pi$
$278$		0			0
$279$			119.210i			0.427274i
$280$		0			0
$281$	−430.607			−1.53241			−0.766205	−	0.642596i	$-0.777858\pi$
$281$	−430.607			−1.53241			−0.766205	+	0.642596i	$0.777858\pi$
$282$		0			0
$283$	−466.875	+	269.550i	−1.64973	+	0.952475i	−0.672559	+	0.740044i	$0.734805\pi$
$283$	−466.875	+	269.550i	−1.64973	+	0.952475i	−0.977176	+	0.212431i	$0.931862\pi$
$284$		0			0
$285$	28.8420	+	16.6519i	0.101200	+	0.0584278i
$286$		0			0
$287$	−218.504	−	223.291i	−0.761337	−	0.778017i
$288$		0			0
$289$	8.50000	−	14.7224i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−31.0137	−	53.7173i	−0.106576	−	0.184595i
$292$		0			0
$293$		−	383.267i		−	1.30808i	−0.756461	−	0.654039i	$-0.773073\pi$
$293$		−	383.267i		−	1.30808i	0.756461	−	0.654039i	$-0.226927\pi$
$294$		0			0
$295$	−144.237			−0.488938
$296$		0			0
$297$	93.4770	−	53.9690i	0.314737	−	0.181714i
$298$		0			0
$299$	445.729	+	257.342i	1.49073	+	0.860675i
$300$		0			0
$301$	5.80207	−	5.67768i	0.0192760	−	0.0188627i
$302$		0			0
$303$	−8.18507	+	14.1770i	−0.0270134	+	0.0467886i
$304$		0			0
$305$	−56.2180	−	97.3725i	−0.184321	−	0.319254i
$306$		0			0
$307$		−	397.955i		−	1.29627i	−0.761526	−	0.648135i	$-0.775549\pi$
$307$		−	397.955i		−	1.29627i	0.761526	−	0.648135i	$-0.224451\pi$
$308$		0			0
$309$	−79.0873			−0.255946
$310$		0			0
$311$	−186.355	+	107.592i	−0.599211	+	0.345955i	−0.768731	−	0.639572i	$-0.779112\pi$
$311$	−186.355	+	107.592i	−0.599211	+	0.345955i	0.169520	+	0.985527i	$0.445778\pi$
$312$		0			0
$313$	152.410	+	87.9940i	0.486933	+	0.281131i	0.723301	−	0.690533i	$-0.242624\pi$
$313$	152.410	+	87.9940i	0.486933	+	0.281131i	−0.236368	+	0.971664i	$0.575957\pi$
$314$		0			0
$315$	25.9475	−	92.8034i	0.0823731	−	0.294614i
$316$		0			0
$317$	−249.944	+	432.917i	−0.788468	+	1.36567i	0.138437	+	0.990371i	$0.455792\pi$
$317$	−249.944	+	432.917i	−0.788468	+	1.36567i	−0.926905	+	0.375296i	$0.877541\pi$
$318$		0			0
$319$	−137.309	−	237.827i	−0.430436	−	0.745538i
$320$		0			0
$321$			43.5645i			0.135715i
$322$		0			0
$323$	−131.059			−0.405755
$324$		0			0
$325$	−434.168	+	250.667i	−1.33590	+	0.771284i
$326$		0			0
$327$	34.9827	+	20.1973i	0.106981	+	0.0617654i
$328$		0			0
$329$	−145.798	+	37.3781i	−0.443155	+	0.113611i
$330$		0			0
$331$	−166.119	+	287.727i	−0.501872	+	0.869267i	0.498126	+	0.867105i	$0.334022\pi$
$331$	−166.119	+	287.727i	−0.501872	+	0.869267i	−0.999998	+	0.00216241i	$0.999312\pi$
$332$		0			0
$333$	−209.590	−	363.020i	−0.629398	−	1.09015i
$334$		0			0
$335$			113.313i			0.338248i
$336$		0			0
$337$	−465.548			−1.38145			−0.690724	−	0.723118i	$-0.742708\pi$
$337$	−465.548			−1.38145			−0.690724	+	0.723118i	$0.742708\pi$
$338$		0			0
$339$	−89.2982	+	51.5564i	−0.263417	+	0.152084i
$340$		0			0
$341$	113.323	+	65.4272i	0.332326	+	0.191869i
$342$		0			0
$343$	234.527	+	250.292i	0.683752	+	0.729714i
$344$		0			0
$345$	12.0591	−	20.8869i	0.0349538	−	0.0605418i
$346$		0			0
$347$	−222.175	−	384.819i	−0.640275	−	1.10899i	−0.985371	−	0.170421i	$-0.945487\pi$
$347$	−222.175	−	384.819i	−0.640275	−	1.10899i	0.345096	−	0.938567i	$-0.387846\pi$
$348$		0			0
$349$		−	231.562i		−	0.663503i	−0.943367	−	0.331751i	$-0.892361\pi$
$349$		−	231.562i		−	0.663503i	0.943367	−	0.331751i	$-0.107639\pi$
$350$		0			0
$351$	−256.421			−0.730545
$352$		0			0
$353$	−464.860	+	268.387i	−1.31688	+	0.760303i	−0.983226	−	0.182392i	$-0.941616\pi$
$353$	−464.860	+	268.387i	−1.31688	+	0.760303i	−0.333657	+	0.942695i	$0.608283\pi$
$354$		0			0
$355$	−31.0521	−	17.9279i	−0.0874707	−	0.0505012i
$356$		0			0
$357$	−4.67733	−	18.2445i	−0.0131018	−	0.0511050i
$358$		0			0
$359$	345.317	−	598.107i	0.961886	−	1.66604i	0.244128	−	0.969743i	$-0.421498\pi$
$359$	345.317	−	598.107i	0.961886	−	1.66604i	0.717758	−	0.696293i	$-0.245168\pi$
$360$		0			0
$361$	324.690	+	562.380i	0.899418	+	1.55784i
$362$		0			0
$363$			21.1566i			0.0582825i
$364$		0			0
$365$	−56.0403			−0.153535
$366$		0			0
$367$	174.308	−	100.637i	0.474954	−	0.274215i	−0.243357	−	0.969937i	$-0.578249\pi$
$367$	174.308	−	100.637i	0.474954	−	0.274215i	0.718311	+	0.695722i	$0.244915\pi$
$368$		0			0
$369$	−331.401	−	191.335i	−0.898106	−	0.518522i
$370$		0			0
$371$	706.802	+	197.619i	1.90513	+	0.532667i
$372$		0			0
$373$	−66.1515	+	114.578i	−0.177350	+	0.307179i	−0.940972	−	0.338485i	$-0.890086\pi$
$373$	−66.1515	+	114.578i	−0.177350	+	0.307179i	0.763622	+	0.645663i	$0.223419\pi$
$374$		0			0
$375$	24.8430	+	43.0293i	0.0662480	+	0.114745i
$376$		0			0
$377$			652.394i			1.73049i
$378$		0			0
$379$	692.358			1.82680			0.913401	−	0.407062i	$-0.133447\pi$
$379$	692.358			1.82680			0.913401	+	0.407062i	$0.133447\pi$
$380$		0			0
$381$	47.5233	−	27.4376i	0.124733	−	0.0720146i
$382$		0			0
$383$	−542.743	−	313.353i	−1.41708	−	0.818153i	−0.421041	−	0.907042i	$-0.638335\pi$
$383$	−542.743	−	313.353i	−1.41708	−	0.818153i	−0.996042	+	0.0888888i	$0.971668\pi$
$384$		0			0
$385$	−73.9799	−	75.6007i	−0.192156	−	0.196365i
$386$		0			0
$387$	4.97171	−	8.61126i	0.0128468	−	0.0222513i
$388$		0			0
$389$	−124.016	−	214.802i	−0.318807	−	0.552190i	0.661432	−	0.750005i	$-0.269949\pi$
$389$	−124.016	−	214.802i	−0.318807	−	0.552190i	−0.980239	+	0.197815i	$0.936615\pi$
$390$		0			0
$391$			94.9110i			0.242739i
$392$		0			0
$393$	−64.7270			−0.164700
$394$		0			0
$395$	−29.6911	+	17.1422i	−0.0751674	+	0.0433979i
$396$		0			0
$397$	216.432	+	124.957i	0.545169	+	0.314754i	0.747171	−	0.664631i	$-0.231411\pi$
$397$	216.432	+	124.957i	0.545169	+	0.314754i	−0.202002	+	0.979385i	$0.564745\pi$
$398$		0			0
$399$	−103.780	+	101.555i	−0.260100	+	0.254523i
$400$		0			0
$401$	−96.9106	+	167.854i	−0.241672	+	0.418589i	−0.961191	−	0.275884i	$-0.911029\pi$
$401$	−96.9106	+	167.854i	−0.241672	+	0.418589i	0.719518	+	0.694473i	$0.244363\pi$
$402$		0			0
$403$	−155.431	−	269.215i	−0.385686	−	0.668027i
$404$		0			0
$405$		−	111.879i		−	0.276244i
$406$		0			0
$407$	−460.126			−1.13053
$408$		0			0
$409$	352.130	−	203.302i	0.860953	−	0.497072i	−0.00337816	−	0.999994i	$-0.501075\pi$
$409$	352.130	−	203.302i	0.860953	−	0.497072i	0.864331	+	0.502923i	$0.167742\pi$
$410$		0			0
$411$	30.5812	+	17.6561i	0.0744069	+	0.0429588i
$412$		0			0
$413$	169.333	−	605.634i	0.410008	−	1.46643i
$414$		0			0
$415$	9.81365	−	16.9977i	0.0236474	−	0.0409584i
$416$		0			0
$417$	8.12463	+	14.0723i	0.0194835	+	0.0337464i
$418$		0			0
$419$		−	102.652i		−	0.244994i	−0.992469	−	0.122497i	$-0.960910\pi$
$419$		−	102.652i		−	0.244994i	0.992469	−	0.122497i	$-0.0390902\pi$
$420$		0			0
$421$	−154.918			−0.367976			−0.183988	−	0.982929i	$-0.558901\pi$
$421$	−154.918			−0.367976			−0.183988	+	0.982929i	$0.558901\pi$
$422$		0			0
$423$	−159.660	+	92.1800i	−0.377448	+	0.217920i
$424$		0			0
$425$	−80.0635	−	46.2247i	−0.188385	−	0.108764i
$426$		0			0
$427$	474.856	−	121.738i	1.11207	−	0.285102i
$428$		0			0
$429$	−68.6622	+	118.927i	−0.160052	+	0.277218i
$430$		0			0
$431$	−343.666	−	595.248i	−0.797370	−	1.38109i	−0.921323	−	0.388797i	$-0.872891\pi$
$431$	−343.666	−	595.248i	−0.797370	−	1.38109i	0.123954	−	0.992288i	$-0.460443\pi$
$432$		0			0
$433$			609.535i			1.40770i	0.710347	+	0.703851i	$0.248538\pi$
$433$			609.535i			1.40770i	−0.710347	+	0.703851i	$0.751462\pi$
$434$		0			0
$435$	30.5713			0.0702788
$436$		0			0
$437$	633.673	−	365.851i	1.45005	−	0.837188i
$438$		0			0
$439$	−384.083	−	221.750i	−0.874904	−	0.505126i	−0.00592922	−	0.999982i	$-0.501887\pi$
$439$	−384.083	−	221.750i	−0.874904	−	0.505126i	−0.868975	+	0.494856i	$0.835221\pi$
$440$		0			0
$441$	359.209	+	217.901i	0.814532	+	0.494107i
$442$		0			0
$443$	−247.787	+	429.180i	−0.559339	+	0.968804i	0.438212	+	0.898871i	$0.355612\pi$
$443$	−247.787	+	429.180i	−0.559339	+	0.968804i	−0.997552	+	0.0699326i	$0.977722\pi$
$444$		0			0
$445$	76.4981	+	132.499i	0.171906	+	0.297750i
$446$		0			0
$447$		−	121.511i		−	0.271837i
$448$		0			0
$449$	50.5812			0.112653			0.0563265	−	0.998412i	$-0.482061\pi$
$449$	50.5812			0.112653			0.0563265	+	0.998412i	$0.482061\pi$
$450$		0			0
$451$	−363.774	+	210.025i	−0.806593	+	0.465687i
$452$		0			0
$453$	−73.6760	−	42.5368i	−0.162640	−	0.0939003i
$454$		0			0
$455$	62.4035	+	243.413i	0.137151	+	0.534973i
$456$		0			0
$457$	−65.7806	+	113.935i	−0.143940	+	0.249311i	−0.928977	−	0.370138i	$-0.879311\pi$
$457$	−65.7806	+	113.935i	−0.143940	+	0.249311i	0.785037	+	0.619449i	$0.212644\pi$
$458$		0			0
$459$	−23.6429	−	40.9507i	−0.0515096	−	0.0892172i
$460$		0			0
$461$		−	732.420i		−	1.58876i	−0.607418	−	0.794382i	$-0.707795\pi$
$461$		−	732.420i		−	1.58876i	0.607418	−	0.794382i	$-0.292205\pi$
$462$		0			0
$463$	562.842			1.21564			0.607821	−	0.794074i	$-0.292044\pi$
$463$	562.842			1.21564			0.607821	+	0.794074i	$0.292044\pi$
$464$		0			0
$465$	−12.6154	+	7.28353i	−0.0271300	+	0.0156635i
$466$		0			0
$467$	266.848	+	154.065i	0.571409	+	0.329903i	0.757712	−	0.652589i	$-0.226317\pi$
$467$	266.848	+	154.065i	0.571409	+	0.329903i	−0.186303	+	0.982492i	$0.559651\pi$
$468$		0			0
$469$	−475.788	−	133.029i	−1.01447	−	0.283643i
$470$		0			0
$471$	5.15493	−	8.92860i	0.0109446	−	0.0189567i
$472$		0			0
$473$	−5.45737	−	9.45243i	−0.0115378	−	0.0199840i
$474$		0			0
$475$			712.725i			1.50047i
$476$		0			0
$477$	898.948			1.88459
$478$		0			0
$479$	−52.2196	+	30.1490i	−0.109018	+	0.0629416i	−0.553518	−	0.832837i	$-0.686715\pi$
$479$	−52.2196	+	30.1490i	−0.109018	+	0.0629416i	0.444500	+	0.895779i	$0.353382\pi$
$480$		0			0
$481$	946.646	+	546.547i	1.96808	+	1.13627i
$482$		0			0
$483$	73.5445	+	75.1557i	0.152266	+	0.155602i
$484$		0			0
$485$	−76.3029	+	132.160i	−0.157326	+	0.272496i
$486$		0			0
$487$	−57.2163	−	99.1016i	−0.117487	−	0.203494i	0.801284	−	0.598284i	$-0.204151\pi$
$487$	−57.2163	−	99.1016i	−0.117487	−	0.203494i	−0.918771	+	0.394790i	$0.870817\pi$
$488$		0			0
$489$		−	173.235i		−	0.354264i
$490$		0			0
$491$	−449.200			−0.914868			−0.457434	−	0.889243i	$-0.651231\pi$
$491$	−449.200			−0.914868			−0.457434	+	0.889243i	$0.651231\pi$
$492$		0			0
$493$	−104.188	+	60.1529i	−0.211334	+	0.122014i
$494$		0			0
$495$	−112.204	−	64.7811i	−0.226675	−	0.130871i
$496$		0			0
$497$	111.732	−	109.337i	0.224814	−	0.219994i
$498$		0			0
$499$	−175.889	+	304.649i	−0.352483	+	0.610519i	−0.986684	−	0.162650i	$-0.947996\pi$
$499$	−175.889	+	304.649i	−0.352483	+	0.610519i	0.634201	+	0.773169i	$0.281329\pi$
$500$		0			0
$501$	−50.3263	−	87.1677i	−0.100452	−	0.173987i
$502$		0			0
$503$		−	7.92809i		−	0.0157616i	−0.999969	−	0.00788081i	$-0.997491\pi$
$503$		−	7.92809i		−	0.0157616i	0.999969	−	0.00788081i	$-0.00250856\pi$
$504$		0			0
$505$	40.2754			0.0797533
$506$		0			0
$507$	187.016	−	107.974i	0.368868	−	0.212966i
$508$		0			0
$509$	−177.317	−	102.374i	−0.348364	−	0.201128i	0.315600	−	0.948892i	$-0.397794\pi$
$509$	−177.317	−	102.374i	−0.348364	−	0.201128i	−0.663965	+	0.747764i	$0.731127\pi$
$510$		0			0
$511$	65.7909	−	235.307i	0.128749	−	0.460483i
$512$		0			0
$513$	−182.271	+	315.703i	−0.355305	+	0.615406i
$514$		0			0
$515$	97.2891	+	168.510i	0.188911	+	0.327203i
$516$		0			0
$517$			202.369i			0.391429i
$518$		0			0
$519$	−1.02130			−0.00196783
$520$		0			0
$521$	91.5230	−	52.8408i	0.175668	−	0.101422i	−0.409588	−	0.912271i	$-0.634327\pi$
$521$	91.5230	−	52.8408i	0.175668	−	0.101422i	0.585256	+	0.810849i	$0.300994\pi$
$522$		0			0
$523$	−393.366	−	227.110i	−0.752134	−	0.434245i	0.0743306	−	0.997234i	$-0.476318\pi$
$523$	−393.366	−	227.110i	−0.752134	−	0.434245i	−0.826464	+	0.562989i	$0.809651\pi$
$524$		0			0
$525$	−99.2172	+	25.4362i	−0.188985	+	0.0484500i
$526$		0			0
$527$	28.6626	−	49.6450i	0.0543881	−	0.0942030i
$528$		0			0
$529$	−0.444012	−	0.769052i	−0.000839343	−	0.00145378i
$530$		0			0
$531$		−	770.278i		−	1.45062i
$532$		0			0
$533$	997.886			1.87221
$534$		0			0
$535$	92.8220	−	53.5908i	0.173499	−	0.100170i
$536$		0			0
$537$	−81.8945	−	47.2818i	−0.152504	−	0.0880480i
$538$		0			0
$539$	404.290	−	221.878i	0.750075	−	0.411648i
$540$		0			0
$541$	181.751	−	314.802i	0.335954	−	0.581889i	−0.647714	−	0.761884i	$-0.724275\pi$
$541$	181.751	−	314.802i	0.335954	−	0.581889i	0.983668	+	0.179995i	$0.0576080\pi$
$542$		0			0
$543$	76.7687	+	132.967i	0.141379	+	0.244875i
$544$		0			0
$545$		−	99.3827i		−	0.182354i
$546$		0			0
$547$	−990.890			−1.81150			−0.905749	−	0.423814i	$-0.860691\pi$
$547$	−990.890			−1.81150			−0.905749	+	0.423814i	$0.860691\pi$
$548$		0			0
$549$	520.005	−	300.225i	0.947186	−	0.546858i
$550$		0			0
$551$	803.221	+	463.740i	1.45775	+	0.841633i
$552$		0			0
$553$	−37.1209	−	144.794i	−0.0671263	−	0.261834i
$554$		0			0
$555$	25.6113	−	44.3600i	0.0461464	−	0.0799279i
$556$		0			0
$557$	462.005	+	800.217i	0.829453	+	1.43666i	0.898468	+	0.439039i	$0.144681\pi$
$557$	462.005	+	800.217i	0.829453	+	1.43666i	−0.0690146	+	0.997616i	$0.521986\pi$
$558$		0			0
$559$			25.9294i			0.0463854i
$560$		0			0
$561$	−25.3235			−0.0451400
$562$		0			0
$563$	380.619	−	219.750i	0.676054	−	0.390320i	−0.122313	−	0.992492i	$-0.539031\pi$
$563$	380.619	−	219.750i	0.676054	−	0.390320i	0.798367	+	0.602172i	$0.205698\pi$
$564$		0			0
$565$	219.700	+	126.844i	0.388850	+	0.224503i
$566$		0			0
$567$	469.766	+	131.345i	0.828512	+	0.231649i
$568$		0			0
$569$	−228.845	+	396.371i	−0.402188	+	0.696609i	−0.993990	−	0.109474i	$-0.965083\pi$
$569$	−228.845	+	396.371i	−0.402188	+	0.696609i	0.591802	+	0.806083i	$0.298417\pi$
$570$		0			0
$571$	239.982	+	415.661i	0.420284	+	0.727953i	0.995967	−	0.0897196i	$-0.0285971\pi$
$571$	239.982	+	415.661i	0.420284	+	0.727953i	−0.575683	+	0.817673i	$0.695264\pi$
$572$		0			0
$573$		−	48.4307i		−	0.0845212i
$574$		0			0
$575$	516.145			0.897643
$576$		0			0
$577$	347.972	−	200.902i	0.603072	−	0.348184i	−0.167177	−	0.985927i	$-0.553465\pi$
$577$	347.972	−	200.902i	0.603072	−	0.348184i	0.770249	+	0.637743i	$0.220132\pi$
$578$		0			0
$579$	118.777	+	68.5762i	0.205142	+	0.118439i
$580$		0			0
$581$	59.8504	+	61.1616i	0.103013	+	0.105270i
$582$		0			0
$583$	493.380	−	854.560i	0.846279	−	1.46580i
$584$		0			0
$585$	153.896	+	266.556i	0.263071	+	0.455652i
$586$		0			0
$587$			430.998i			0.734239i	0.930174	+	0.367119i	$0.119656\pi$
$587$			430.998i			0.734239i	−0.930174	+	0.367119i	$0.880344\pi$
$588$		0			0
$589$	−441.939			−0.750322
$590$		0			0
$591$	−206.798	+	119.395i	−0.349912	+	0.202022i
$592$		0			0
$593$	485.115	+	280.081i	0.818069	+	0.472313i	0.849750	−	0.527185i	$-0.176753\pi$
$593$	485.115	+	280.081i	0.818069	+	0.472313i	−0.0316809	+	0.999498i	$0.510086\pi$
$594$		0			0
$595$	−33.1194	+	32.4093i	−0.0556628	+	0.0544695i
$596$		0			0
$597$	−60.0712	+	104.046i	−0.100622	+	0.174282i
$598$		0			0
$599$	−76.8287	−	133.071i	−0.128262	−	0.222156i	0.794742	−	0.606948i	$-0.207606\pi$
$599$	−76.8287	−	133.071i	−0.128262	−	0.222156i	−0.923003	+	0.384792i	$0.874273\pi$
$600$		0			0
$601$			638.369i			1.06218i	0.847316	+	0.531089i	$0.178217\pi$
$601$			638.369i			1.06218i	−0.847316	+	0.531089i	$0.821783\pi$
$602$		0			0
$603$	−605.133			−1.00354
$604$		0			0
$605$	45.0778	−	26.0257i	0.0745088	−	0.0430177i
$606$		0			0
$607$	379.219	+	218.942i	0.624743	+	0.360695i	0.778713	−	0.627380i	$-0.215873\pi$
$607$	379.219	+	218.942i	0.624743	+	0.360695i	−0.153971	+	0.988075i	$0.549206\pi$
$608$		0			0
$609$	−35.8905	+	128.365i	−0.0589335	+	0.210780i
$610$		0			0
$611$	240.378	−	416.346i	0.393417	−	0.681418i
$612$		0			0
$613$	264.933	+	458.878i	0.432192	+	0.748578i	0.997062	−	0.0766020i	$-0.0244071\pi$
$613$	264.933	+	458.878i	0.432192	+	0.748578i	−0.564870	+	0.825180i	$0.691074\pi$
$614$		0			0
$615$		−	46.7611i		−	0.0760343i
$616$		0			0
$617$	364.474			0.590720			0.295360	−	0.955386i	$-0.404560\pi$
$617$	364.474			0.590720			0.295360	+	0.955386i	$0.404560\pi$
$618$		0			0
$619$	317.687	−	183.417i	0.513226	−	0.296311i	−0.220933	−	0.975289i	$-0.570910\pi$
$619$	317.687	−	183.417i	0.513226	−	0.296311i	0.734159	+	0.678978i	$0.237577\pi$
$620$		0			0
$621$	228.628	+	131.998i	0.368161	+	0.212558i
$622$		0			0
$623$	−646.155	+	165.654i	−1.03717	+	0.265898i
$624$		0			0
$625$	−219.157	+	379.591i	−0.350651	+	0.607346i
$626$		0			0
$627$	97.6140	+	169.072i	0.155684	+	0.269653i
$628$		0			0
$629$			201.574i			0.320467i
$630$		0			0
$631$	−471.873			−0.747817			−0.373909	−	0.927466i	$-0.621983\pi$
$631$	−471.873			−0.747817			−0.373909	+	0.927466i	$0.621983\pi$
$632$		0			0
$633$	40.9739	−	23.6563i	0.0647297	−	0.0373717i
$634$		0			0
$635$	−116.921	−	67.5046i	−0.184128	−	0.106306i
$636$		0			0
$637$	−1095.32	−	23.7397i	−1.71950	−	0.0372679i
$638$		0			0
$639$	95.7418	−	165.830i	0.149831	−	0.259514i
$640$		0			0
$641$	−50.2046	−	86.9569i	−0.0783223	−	0.135658i	0.824204	−	0.566293i	$-0.191623\pi$
$641$	−50.2046	−	86.9569i	−0.0783223	−	0.135658i	−0.902526	+	0.430635i	$0.858290\pi$
$642$		0			0
$643$		−	232.905i		−	0.362216i	−0.983463	−	0.181108i	$-0.942032\pi$
$643$		−	232.905i		−	0.362216i	0.983463	−	0.181108i	$-0.0579683\pi$
$644$		0			0
$645$	1.21506			0.00188381
$646$		0			0
$647$	376.257	−	217.232i	0.581540	−	0.335752i	−0.180205	−	0.983629i	$-0.557676\pi$
$647$	376.257	−	217.232i	0.581540	−	0.335752i	0.761745	+	0.647877i	$0.224343\pi$
$648$		0			0
$649$	−732.243	−	422.761i	−1.12826	−	0.651403i
$650$		0			0
$651$	−15.7723	−	61.5216i	−0.0242277	−	0.0945033i
$652$		0			0
$653$	534.572	−	925.905i	0.818640	−	1.41793i	−0.0880450	−	0.996116i	$-0.528062\pi$
$653$	534.572	−	925.905i	0.818640	−	1.41793i	0.906685	−	0.421809i	$-0.138605\pi$
$654$		0			0
$655$	79.6238	+	137.912i	0.121563	+	0.210553i
$656$		0			0
$657$		−	299.276i		−	0.455518i
$658$		0			0
$659$	−350.638			−0.532076			−0.266038	−	0.963962i	$-0.585715\pi$
$659$	−350.638			−0.532076			−0.266038	+	0.963962i	$0.585715\pi$
$660$		0			0
$661$	−764.881	+	441.605i	−1.15716	+	0.668085i	−0.950621	−	0.310353i	$-0.899553\pi$
$661$	−764.881	+	441.605i	−1.15716	+	0.668085i	−0.206537	+	0.978439i	$0.566219\pi$
$662$		0			0
$663$	52.0997	+	30.0798i	0.0785818	+	0.0453692i
$664$		0			0
$665$	344.045	+	96.1939i	0.517361	+	0.144652i
$666$		0			0
$667$	335.833	−	581.681i	0.503498	−	0.872085i
$668$		0			0
$669$	−111.768	−	193.588i	−0.167067	−	0.289369i
$670$		0			0
$671$		−	659.104i		−	0.982271i
$672$		0			0
$673$	597.831			0.888307			0.444154	−	0.895951i	$-0.353504\pi$
$673$	597.831			0.888307			0.444154	+	0.895951i	$0.353504\pi$
$674$		0			0
$675$	−222.698	+	128.575i	−0.329923	+	0.190481i
$676$		0			0
$677$	718.314	+	414.719i	1.06103	+	0.612584i	0.925716	−	0.378220i	$-0.123464\pi$
$677$	718.314	+	414.719i	1.06103	+	0.612584i	0.135310	+	0.990803i	$0.456797\pi$
$678$		0			0
$679$	−465.348	−	475.543i	−0.685342	−	0.700357i
$680$		0			0
$681$	80.6754	−	139.734i	0.118466	−	0.205189i
$682$		0			0
$683$	−659.630	−	1142.51i	−0.965783	−	1.67279i	−0.707496	−	0.706717i	$-0.750175\pi$
$683$	−659.630	−	1142.51i	−0.965783	−	1.67279i	−0.258287	−	0.966068i	$-0.583158\pi$
$684$		0			0
$685$		−	86.8784i		−	0.126830i
$686$		0			0
$687$	−24.1349			−0.0351308
$688$		0			0
$689$	−2030.12	+	1172.09i	−2.94648	+	1.70115i
$690$		0			0
$691$	87.1812	+	50.3341i	0.126167	+	0.0728424i	0.561755	−	0.827304i	$-0.310126\pi$
$691$	87.1812	+	50.3341i	0.126167	+	0.0728424i	−0.435588	+	0.900146i	$0.643460\pi$
$692$		0			0
$693$	403.735	−	395.080i	0.582590	−	0.570100i
$694$		0			0
$695$	19.9890	−	34.6220i	0.0287611	−	0.0498158i
$696$		0			0
$697$	92.0083	+	159.363i	0.132006	+	0.228642i
$698$		0			0
$699$		−	123.473i		−	0.176642i
$700$		0			0
$701$	1077.13			1.53657			0.768283	−	0.640110i	$-0.221111\pi$
$701$	1077.13			1.53657			0.768283	+	0.640110i	$0.221111\pi$
$702$		0			0
$703$	1345.80	−	777.001i	1.91437	−	1.10526i
$704$		0			0
$705$	−19.5101	−	11.2641i	−0.0276738	−	0.0159775i
$706$		0			0
$707$	−47.2831	+	169.112i	−0.0668785	+	0.239196i
$708$		0			0
$709$	−113.382	+	196.384i	−0.159919	+	0.276987i	−0.934839	−	0.355072i	$-0.884456\pi$
$709$	−113.382	+	196.384i	−0.159919	+	0.276987i	0.774921	+	0.632059i	$0.217790\pi$
$710$		0			0
$711$	−91.5455	−	158.562i	−0.128756	−	0.223012i
$712$		0			0
$713$			320.046i			0.448872i
$714$		0			0
$715$	337.859			0.472530
$716$		0			0
$717$	−19.0910	+	11.0222i	−0.0266263	+	0.0153727i
$718$		0			0
$719$	−804.364	−	464.400i	−1.11873	−	0.645897i	−0.177651	−	0.984094i	$-0.556850\pi$
$719$	−804.364	−	464.400i	−1.11873	−	0.645897i	−0.941076	+	0.338196i	$0.890183\pi$
$720$		0			0
$721$	−821.770	+	210.677i	−1.13976	+	0.292200i
$722$		0			0
$723$	127.889	−	221.510i	0.176887	−	0.306377i
$724$		0			0
$725$	327.123	+	566.594i	0.451204	+	0.781509i
$726$		0			0
$727$			245.965i			0.338329i	0.985588	+	0.169165i	$0.0541069\pi$
$727$			245.965i			0.338329i	−0.985588	+	0.169165i	$0.945893\pi$
$728$		0			0
$729$	530.117			0.727184
$730$		0			0
$731$	−4.14095	+	2.39078i	−0.00566478	+	0.00327056i
$732$		0			0
$733$	−231.999	−	133.945i	−0.316506	−	0.182735i	0.333328	−	0.942811i	$-0.391828\pi$
$733$	−231.999	−	133.945i	−0.316506	−	0.182735i	−0.649834	+	0.760076i	$0.725162\pi$
$734$		0			0
$735$	−1.11244	+	51.3270i	−0.00151353	+	0.0698326i
$736$		0			0
$737$	−332.122	+	575.253i	−0.450641	+	0.780533i
$738$		0			0
$739$	−708.334	−	1226.87i	−0.958504	−	1.66018i	−0.726138	−	0.687549i	$-0.758687\pi$
$739$	−708.334	−	1226.87i	−0.958504	−	1.66018i	−0.232366	−	0.972628i	$-0.574647\pi$
$740$		0			0
$741$		−	463.791i		−	0.625899i
$742$		0			0
$743$	453.331			0.610136			0.305068	−	0.952331i	$-0.401321\pi$
$743$	453.331			0.610136			0.305068	+	0.952331i	$0.401321\pi$
$744$		0			0
$745$	−258.901	+	149.477i	−0.347518	+	0.200640i
$746$		0			0
$747$	90.7742	+	52.4085i	0.121518	+	0.0701586i
$748$		0			0
$749$	116.049	+	452.664i	0.154939	+	0.604358i
$750$		0			0
$751$	−546.932	+	947.315i	−0.728272	+	1.26140i	0.229341	+	0.973346i	$0.426343\pi$
$751$	−546.932	+	947.315i	−0.728272	+	1.26140i	−0.957613	+	0.288058i	$0.906990\pi$
$752$		0			0
$753$	64.2034	+	111.204i	0.0852635	+	0.147681i
$754$		0			0
$755$			209.307i			0.277227i
$756$		0			0
$757$	−175.825			−0.232265			−0.116133	−	0.993234i	$-0.537050\pi$
$757$	−175.825			−0.232265			−0.116133	+	0.993234i	$0.537050\pi$
$758$		0			0
$759$	122.440	−	70.6907i	0.161317	−	0.0931366i
$760$		0			0
$761$	−844.062	−	487.319i	−1.10915	−	0.640367i	−0.170540	−	0.985351i	$-0.554551\pi$
$761$	−844.062	−	487.319i	−1.10915	−	0.640367i	−0.938609	+	0.344984i	$0.887884\pi$
$762$		0			0
$763$	417.297	+	116.675i	0.546915	+	0.152916i
$764$		0			0
$765$	−28.3795	+	49.1547i	−0.0370974	+	0.0642546i
$766$		0			0
$767$	1004.33	+	1739.54i	1.30942	+	2.26798i
$768$		0			0
$769$		−	122.836i		−	0.159735i	−0.996805	−	0.0798674i	$-0.974550\pi$
$769$		−	122.836i		−	0.159735i	0.996805	−	0.0798674i	$-0.0254497\pi$
$770$		0			0
$771$	−254.269			−0.329791
$772$		0			0
$773$	−557.318	+	321.768i	−0.720981	+	0.416259i	−0.815114	−	0.579301i	$-0.803326\pi$
$773$	−557.318	+	321.768i	−0.720981	+	0.416259i	0.0941326	+	0.995560i	$0.469992\pi$
$774$		0			0
$775$	−269.979	−	155.873i	−0.348360	−	0.201126i
$776$		0			0
$777$	156.195	+	159.617i	0.201023	+	0.205427i
$778$		0			0
$779$	709.325	−	1228.59i	0.910558	−	1.57713i
$780$		0			0
$781$	−105.094	−	182.028i	−0.134564	−	0.233071i
$782$		0			0
$783$			334.633i			0.427372i
$784$		0			0
$785$	−25.3653			−0.0323125
$786$		0			0
$787$	−183.750	+	106.088i	−0.233481	+	0.134800i	−0.612177	−	0.790721i	$-0.709706\pi$
$787$	−183.750	+	106.088i	−0.233481	+	0.134800i	0.378696	+	0.925521i	$0.376373\pi$
$788$		0			0
$789$	13.5355	+	7.81475i	0.0171553	+	0.00990462i
$790$		0			0
$791$	−790.530	+	773.582i	−0.999406	+	0.977980i
$792$		0			0
$793$	−782.896	+	1356.02i	−0.987259	+	1.70998i
$794$		0			0
$795$	54.9245	+	95.1320i	0.0690874	+	0.119663i
$796$		0			0
$797$		−	110.168i		−	0.138228i	−0.997609	−	0.0691141i	$-0.977983\pi$
$797$		−	110.168i		−	0.138228i	0.997609	−	0.0691141i	$-0.0220173\pi$
$798$		0			0
$799$	88.6545			0.110957
$800$		0			0
$801$	−707.591	+	408.528i	−0.883385	+	0.510022i
$802$		0			0
$803$	−284.498	−	164.255i	−0.354294	−	0.204552i
$804$		0			0
$805$	69.6622	−	249.153i	0.0865369	−	0.309506i
$806$		0			0
$807$	−155.013	+	268.491i	−0.192086	+	0.332702i
$808$		0			0
$809$	−137.824	−	238.718i	−0.170363	−	0.295078i	0.768184	−	0.640230i	$-0.221161\pi$
$809$	−137.824	−	238.718i	−0.170363	−	0.295078i	−0.938547	+	0.345152i	$0.887827\pi$
$810$		0			0
$811$			1120.65i			1.38181i	0.722944	+	0.690907i	$0.242789\pi$
$811$			1120.65i			1.38181i	−0.722944	+	0.690907i	$0.757211\pi$
$812$		0			0
$813$	−12.2120			−0.0150210
$814$		0			0
$815$	−369.109	+	213.105i	−0.452894	+	0.261479i
$816$		0			0
$817$	31.9241	+	18.4314i	0.0390747	+	0.0225598i
$818$		0			0
$819$	−1299.91	+	333.258i	−1.58720	+	0.406908i
$820$		0			0
$821$	150.811	−	261.212i	0.183692	−	0.318163i	−0.759443	−	0.650574i	$-0.774529\pi$
$821$	150.811	−	261.212i	0.183692	−	0.318163i	0.943135	+	0.332410i	$0.107862\pi$
$822$		0			0
$823$	−503.623	−	872.300i	−0.611935	−	1.05990i	−0.990914	−	0.134498i	$-0.957058\pi$
$823$	−503.623	−	872.300i	−0.611935	−	1.05990i	0.378978	−	0.925405i	$-0.376275\pi$
$824$		0			0
$825$			137.714i			0.166927i
$826$		0			0
$827$	−793.504			−0.959497			−0.479748	−	0.877406i	$-0.659272\pi$
$827$	−793.504			−0.959497			−0.479748	+	0.877406i	$0.659272\pi$
$828$		0			0
$829$	834.186	−	481.618i	1.00626	−	0.580962i	0.0961627	−	0.995366i	$-0.469343\pi$
$829$	834.186	−	481.618i	1.00626	−	0.580962i	0.910093	+	0.414404i	$0.136010\pi$
$830$		0			0
$831$	−59.9989	−	34.6404i	−0.0722008	−	0.0416852i
$832$		0			0
$833$	−97.2011	−	177.113i	−0.116688	−	0.212620i
$834$		0			0
$835$	−123.818	+	214.458i	−0.148285	+	0.256836i
$836$		0			0
$837$	−79.7254	−	138.088i	−0.0952514	−	0.164980i
$838$		0			0
$839$		−	586.454i		−	0.698992i	−0.936938	−	0.349496i	$-0.886353\pi$
$839$		−	586.454i		−	0.698992i	0.936938	−	0.349496i	$-0.113647\pi$
$840$		0			0
$841$	10.3807			0.0123433
$842$		0			0
$843$	243.357	−	140.502i	0.288680	−	0.166669i
$844$		0			0
$845$	−460.115	−	265.648i	−0.544515	−	0.314376i
$846$		0			0
$847$	56.3578	+	219.831i	0.0665382	+	0.259540i
$848$		0			0
$849$	175.903	−	304.672i	0.207188	−	0.358860i
$850$		0			0
$851$	−562.692	−	974.612i	−0.661213	−	1.14525i
$852$		0			0
$853$		−	67.2638i		−	0.0788556i	−0.999222	−	0.0394278i	$-0.987446\pi$
$853$		−	67.2638i		−	0.0788556i	0.999222	−	0.0394278i	$-0.0125535\pi$
$854$		0			0
$855$	437.575			0.511784
$856$		0			0
$857$	871.484	−	503.151i	1.01690	−	0.587108i	0.103696	−	0.994609i	$-0.466933\pi$
$857$	871.484	−	503.151i	1.01690	−	0.587108i	0.913205	+	0.407501i	$0.133600\pi$
$858$		0			0
$859$	−733.642	−	423.569i	−0.854066	−	0.493095i	0.00795499	−	0.999968i	$-0.497468\pi$
$859$	−733.642	−	423.569i	−0.854066	−	0.493095i	−0.862021	+	0.506873i	$0.830801\pi$
$860$		0			0
$861$	196.344	+	54.8972i	0.228042	+	0.0637598i
$862$		0			0
$863$	−64.4462	+	111.624i	−0.0746769	+	0.129344i	−0.900946	−	0.433932i	$-0.857126\pi$
$863$	−64.4462	+	111.624i	−0.0746769	+	0.129344i	0.826269	+	0.563276i	$0.190459\pi$
$864$		0			0
$865$	1.25636	+	2.17607i	0.00145244	+	0.00251569i
$866$		0			0
$867$			11.0938i			0.0127956i
$868$		0			0
$869$	−200.976			−0.231273
$870$		0			0
$871$	1366.59	−	789.002i	1.56899	−	0.905858i
$872$		0			0
$873$	−705.785	−	407.485i	−0.808460	−	0.466765i
$874$		0			0
$875$	372.759	+	380.925i	0.426010	+	0.435343i
$876$		0			0
$877$	506.490	−	877.266i	0.577526	−	1.00030i	−0.418236	−	0.908338i	$-0.637352\pi$
$877$	506.490	−	877.266i	0.577526	−	1.00030i	0.995762	−	0.0919657i	$-0.0293150\pi$
$878$		0			0
$879$	125.056	+	216.603i	0.142270	+	0.246420i
$880$		0			0
$881$		−	526.992i		−	0.598175i	−0.954226	−	0.299087i	$-0.903318\pi$
$881$		−	526.992i		−	0.598175i	0.954226	−	0.299087i	$-0.0966822\pi$
$882$		0			0
$883$	−1138.56			−1.28943			−0.644714	−	0.764424i	$-0.723023\pi$
$883$	−1138.56			−1.28943			−0.644714	+	0.764424i	$0.723023\pi$
$884$		0			0
$885$	81.5153	−	47.0629i	0.0921076	−	0.0531784i
$886$		0			0
$887$	−990.028	−	571.593i	−1.11615	−	0.644412i	−0.175737	−	0.984437i	$-0.556231\pi$
$887$	−990.028	−	571.593i	−1.11615	−	0.644412i	−0.940416	+	0.340026i	$0.889564\pi$
$888$		0			0
$889$	420.709	−	411.689i	0.473238	−	0.463093i
$890$		0			0
$891$	327.919	−	567.972i	0.368034	−	0.637454i
$892$		0			0
$893$	−341.734	−	591.901i	−0.382681	−	0.662823i
$894$		0			0
$895$			232.655i			0.259949i
$896$		0			0
$897$	−335.871			−0.374438
$898$		0			0
$899$	−351.328	+	202.839i	−0.390799	+	0.225628i
$900$		0			0
$901$	−374.368	−	216.142i	−0.415503	−	0.239891i
$902$		0			0
$903$	−1.42647	+	5.10189i	−0.00157970	+	0.00564993i
$904$		0			0
$905$	188.874	−	327.139i	0.208700	−	0.361480i
$906$		0			0
$907$	864.237	+	1496.90i	0.952853	+	1.65039i	0.739208	+	0.673478i	$0.235200\pi$
$907$	864.237	+	1496.90i	0.952853	+	1.65039i	0.213645	+	0.976911i	$0.431466\pi$
$908$		0			0
$909$			215.085i			0.236618i
$910$		0			0
$911$	−1413.93			−1.55207			−0.776034	−	0.630691i	$-0.782772\pi$
$911$	−1413.93			−1.55207			−0.776034	+	0.630691i	$0.782772\pi$
$912$		0			0
$913$	99.6413	−	57.5280i	0.109136	−	0.0630098i
$914$		0			0
$915$	63.5431	+	36.6866i	0.0694460	+	0.0400947i
$916$		0			0
$917$	−672.556	+	172.423i	−0.733431	+	0.188029i
$918$		0			0
$919$	499.479	−	865.124i	0.543503	−	0.941375i	−0.455196	−	0.890391i	$-0.650431\pi$
$919$	499.479	−	865.124i	0.543503	−	0.941375i	0.998699	−	0.0509840i	$-0.0162357\pi$
$920$		0			0
$921$	129.848	+	224.904i	0.140986	+	0.244195i
$922$		0			0
$923$			499.331i			0.540987i
$924$		0			0
$925$	1096.20			1.18508
$926$		0			0
$927$	−899.904	+	519.560i	−0.970770	+	0.560474i
$928$		0			0
$929$	−422.459	−	243.907i	−0.454746	−	0.262548i	0.255087	−	0.966918i	$-0.417896\pi$
$929$	−422.459	−	243.907i	−0.454746	−	0.262548i	−0.709832	+	0.704371i	$0.751229\pi$
$930$		0			0
$931$	−807.814	+	1331.68i	−0.867684	+	1.43037i
$932$		0			0
$933$	70.2121	−	121.611i	0.0752541	−	0.130344i
$934$		0			0
$935$	31.1517	+	53.9564i	0.0333173	+	0.0577073i
$936$		0			0
$937$		−	57.8280i		−	0.0617161i	−0.999524	−	0.0308581i	$-0.990176\pi$
$937$		−	57.8280i		−	0.0617161i	0.999524	−	0.0308581i	$-0.00982399\pi$
$938$		0			0
$939$	−114.846			−0.122306
$940$		0			0
$941$	100.938	−	58.2767i	0.107267	−	0.0619306i	−0.445407	−	0.895328i	$-0.646941\pi$
$941$	100.938	−	58.2767i	0.107267	−	0.0619306i	0.552674	+	0.833398i	$0.313608\pi$
$942$		0			0
$943$	−889.724	−	513.683i	−0.943504	−	0.544732i
$944$		0			0
$945$	32.0086	+	124.854i	0.0338716	+	0.132120i
$946$		0			0
$947$	434.826	−	753.140i	0.459161	−	0.795291i	−0.539756	−	0.841822i	$-0.681483\pi$
$947$	434.826	−	753.140i	0.459161	−	0.795291i	0.998917	+	0.0465312i	$0.0148167\pi$
$948$		0			0
$949$	390.210	+	675.864i	0.411180	+	0.712185i
$950$		0			0
$951$		−	326.216i		−	0.343024i
$952$		0			0
$953$	−1202.68			−1.26199			−0.630996	−	0.775786i	$-0.717354\pi$
$953$	−1202.68			−1.26199			−0.630996	+	0.775786i	$0.717354\pi$
$954$		0			0
$955$	−103.190	+	59.5769i	−0.108053	+	0.0623842i
$956$		0			0
$957$	155.200	+	89.6049i	0.162174	+	0.0936311i
$958$		0			0
$959$	364.792	+	101.995i	0.380388	+	0.106355i
$960$		0			0
$961$	−383.848	+	664.844i	−0.399426	+	0.691825i
$962$		0			0
$963$	286.194	+	495.703i	0.297191	+	0.514749i
$964$		0			0
$965$		−	337.435i		−	0.349674i
$966$		0			0
$967$	1.86433			0.00192796			0.000963978	−	1.00000i	$-0.499693\pi$
$967$	1.86433			0.00192796			0.000963978		1.00000i	$0.499693\pi$
$968$		0			0
$969$	74.0678	−	42.7631i	0.0764374	−	0.0441311i
$970$		0			0
$971$	−699.844	−	404.055i	−0.720745	−	0.416122i	0.0942816	−	0.995546i	$-0.469945\pi$
$971$	−699.844	−	404.055i	−0.720745	−	0.416122i	−0.815027	+	0.579423i	$0.803278\pi$
$972$		0			0
$973$	121.907	+	124.577i	0.125289	+	0.128034i
$974$		0			0
$975$	163.580	−	283.328i	0.167774	−	0.290593i
$976$		0			0
$977$	788.243	+	1365.28i	0.806799	+	1.39742i	0.915070	+	0.403296i	$0.132135\pi$
$977$	788.243	+	1365.28i	0.806799	+	1.39742i	−0.108270	+	0.994121i	$0.534531\pi$
$978$		0			0
$979$			896.869i			0.916107i
$980$		0			0
$981$	530.740			0.541019
$982$		0			0
$983$	115.164	−	66.4900i	0.117156	−	0.0676399i	−0.440277	−	0.897862i	$-0.645120\pi$
$983$	115.164	−	66.4900i	0.117156	−	0.0676399i	0.557433	+	0.830222i	$0.311786\pi$
$984$		0			0
$985$	508.784	+	293.747i	0.516532	+	0.298220i
$986$		0			0
$987$	70.2015	−	68.6964i	0.0711261	−	0.0696013i
$988$		0			0
$989$	13.3477	−	23.1189i	0.0134962	−	0.0233761i
$990$		0			0
$991$	−284.716	−	493.143i	−0.287302	−	0.497621i	0.685863	−	0.727731i	$-0.259425\pi$
$991$	−284.716	−	493.143i	−0.287302	−	0.497621i	−0.973165	+	0.230109i	$0.926092\pi$
$992$		0			0
$993$		−	216.812i		−	0.218340i
$994$		0			0
$995$	295.586			0.297071
$996$		0			0
$997$	735.033	−	424.371i	0.737244	−	0.425648i	−0.0838222	−	0.996481i	$-0.526713\pi$
$997$	735.033	−	424.371i	0.737244	−	0.425648i	0.821067	+	0.570833i	$0.193379\pi$
$998$		0			0
$999$	485.563	+	280.340i	0.486049	+	0.280621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.s.a.341.10	✓	44
7.3	odd	6	inner	476.3.s.a.409.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.s.a.341.10	✓	44	1.1	even	1	trivial
476.3.s.a.409.10	yes	44	7.3	odd	6	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.565149 + 0.326289i) q^{3} +(1.39043 + 0.802767i) q^{5} +(-5.00309 + 4.89583i) q^{7} +(-4.28707 + 7.42543i) q^{9} +O(q^{10})\)	\(q+(-0.565149 + 0.326289i) q^{3} +(1.39043 + 0.802767i) q^{5} +(-5.00309 + 4.89583i) q^{7} +(-4.28707 + 7.42543i) q^{9} +(4.70585 + 8.15077i) q^{11} -22.3588i q^{13} -1.04774 q^{15} +(3.57071 - 2.06155i) q^{17} +(-27.5279 - 15.8932i) q^{19} +(1.23003 - 4.39932i) q^{21} +(-11.5096 + 19.9353i) q^{23} +(-11.2111 - 19.4182i) q^{25} -11.4685i q^{27} -29.1784 q^{29} +(12.0407 - 6.95169i) q^{31} +(-5.31901 - 3.07093i) q^{33} +(-10.8867 + 2.79101i) q^{35} +(-24.4444 + 42.3389i) q^{37} +(7.29542 + 12.6360i) q^{39} +44.6306i q^{41} -1.15970 q^{43} +(-11.9218 + 6.88304i) q^{45} +(18.6212 + 10.7509i) q^{47} +(1.06176 - 48.9885i) q^{49} +(-1.34532 + 2.33017i) q^{51} +(-52.4221 - 90.7977i) q^{53} +15.1108i q^{55} +20.7431 q^{57} +(-77.8014 + 44.9186i) q^{59} +(-60.6480 - 35.0152i) q^{61} +(-14.9050 - 58.1388i) q^{63} +(17.9489 - 31.0884i) q^{65} +(35.2883 + 61.1211i) q^{67} -15.0219i q^{69} -22.3327 q^{71} +(-30.2281 + 17.4522i) q^{73} +(12.6719 + 7.31613i) q^{75} +(-63.4485 - 17.7400i) q^{77} +(-10.6769 + 18.4930i) q^{79} +(-34.8416 - 60.3474i) q^{81} -12.2248i q^{83} +6.61979 q^{85} +(16.4902 - 9.52059i) q^{87} +(82.5262 + 47.6465i) q^{89} +(109.465 + 111.863i) q^{91} +(-4.53652 + 7.85748i) q^{93} +(-25.5171 - 44.1970i) q^{95} +95.0498i q^{97} -80.6972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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