LMFDB - Embedded newform 495.3.j.c.298.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(298,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.298"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			298.6
Character	$\chi$	$=$	495.298
Dual form			495.3.j.c.397.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40545 + 1.40545i) q^{2} +0.0494143i q^{4} +(4.99874 - 0.112178i) q^{5} +(1.33355 - 1.33355i) q^{7} +(-5.69125 - 5.69125i) q^{8} +(-6.86783 + 7.18315i) q^{10} +3.31662 q^{11} +(2.52995 + 2.52995i) q^{13} +3.74848i q^{14} +15.7999 q^{16} +(19.6260 - 19.6260i) q^{17} +24.1237i q^{19} +(0.00554322 + 0.247009i) q^{20} +(-4.66135 + 4.66135i) q^{22} +(1.52377 + 1.52377i) q^{23} +(24.9748 - 1.12150i) q^{25} -7.11144 q^{26} +(0.0658964 + 0.0658964i) q^{28} -52.1787i q^{29} -5.66217 q^{31} +(0.559027 - 0.559027i) q^{32} +55.1668i q^{34} +(6.51647 - 6.81567i) q^{35} +(26.1846 - 26.1846i) q^{37} +(-33.9047 - 33.9047i) q^{38} +(-29.0875 - 27.8107i) q^{40} -0.868046 q^{41} +(55.2976 + 55.2976i) q^{43} +0.163889i q^{44} -4.28317 q^{46} +(-7.21510 + 7.21510i) q^{47} +45.4433i q^{49} +(-33.5247 + 36.6771i) q^{50} +(-0.125016 + 0.125016i) q^{52} +(34.7108 + 34.7108i) q^{53} +(16.5789 - 0.372054i) q^{55} -15.1791 q^{56} +(73.3347 + 73.3347i) q^{58} +78.6241i q^{59} -71.8790 q^{61} +(7.95790 - 7.95790i) q^{62} +64.7710i q^{64} +(12.9304 + 12.3628i) q^{65} +(-7.85622 + 7.85622i) q^{67} +(0.969807 + 0.969807i) q^{68} +(0.420498 + 18.7377i) q^{70} +75.2724 q^{71} +(11.5472 + 11.5472i) q^{73} +73.6023i q^{74} -1.19206 q^{76} +(4.42288 - 4.42288i) q^{77} -132.372i q^{79} +(78.9796 - 1.77241i) q^{80} +(1.22000 - 1.22000i) q^{82} +(37.5500 + 37.5500i) q^{83} +(95.9038 - 100.307i) q^{85} -155.436 q^{86} +(-18.8758 - 18.8758i) q^{88} +97.5309i q^{89} +6.74762 q^{91} +(-0.0752961 + 0.0752961i) q^{92} -20.2810i q^{94} +(2.70616 + 120.588i) q^{95} +(-58.4602 + 58.4602i) q^{97} +(-63.8683 - 63.8683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) $ 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.40545	+	1.40545i	−0.702726	+	0.702726i	−0.964995	−	0.262269i	$-0.915529\pi$
$2$	−1.40545	+	1.40545i	−0.702726	+	0.702726i	0.262269	+	0.964995i	$0.415529\pi$
$3$		0			0
$3$		0			0
$4$			0.0494143i			0.0123536i
$5$	4.99874	−	0.112178i	0.999748	−	0.0224357i
$5$	4.99874	−	0.112178i	0.999748	−	0.0224357i
$6$		0			0
$7$	1.33355	−	1.33355i	0.190507	−	0.190507i	−0.605408	−	0.795915i	$-0.706990\pi$
$7$	1.33355	−	1.33355i	0.190507	−	0.190507i	0.795915	+	0.605408i	$0.206990\pi$
$8$	−5.69125	−	5.69125i	−0.711407	−	0.711407i
$9$		0			0
$10$	−6.86783	+	7.18315i	−0.686783	+	0.718315i
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$		0			0
$13$	2.52995	+	2.52995i	0.194611	+	0.194611i	0.797685	−	0.603074i	$-0.206058\pi$
$13$	2.52995	+	2.52995i	0.194611	+	0.194611i	−0.603074	+	0.797685i	$0.706058\pi$
$14$			3.74848i			0.267748i
$15$		0			0
$16$	15.7999			0.987494
$17$	19.6260	−	19.6260i	1.15447	−	1.15447i	0.168826	−	0.985646i	$-0.446002\pi$
$17$	19.6260	−	19.6260i	1.15447	−	1.15447i	0.985646	−	0.168826i	$-0.0539977\pi$
$18$		0			0
$19$			24.1237i			1.26967i	0.772649	+	0.634834i	$0.218931\pi$
$19$			24.1237i			1.26967i	−0.772649	+	0.634834i	$0.781069\pi$
$20$	0.00554322	+	0.247009i	0.000277161	+	0.0123505i
$21$		0			0
$22$	−4.66135	+	4.66135i	−0.211880	+	0.211880i
$23$	1.52377	+	1.52377i	0.0662509	+	0.0662509i	0.739456	−	0.673205i	$-0.235083\pi$
$23$	1.52377	+	1.52377i	0.0662509	+	0.0662509i	−0.673205	+	0.739456i	$0.735083\pi$
$24$		0			0
$25$	24.9748	−	1.12150i	0.998993	−	0.0448601i
$26$	−7.11144			−0.273517
$27$		0			0
$28$	0.0658964	+	0.0658964i	0.00235344	+	0.00235344i
$29$		−	52.1787i		−	1.79927i	−0.436646	−	0.899633i	$-0.643834\pi$
$29$		−	52.1787i		−	1.79927i	0.436646	−	0.899633i	$-0.356166\pi$
$30$		0			0
$31$	−5.66217			−0.182651			−0.0913253	−	0.995821i	$-0.529110\pi$
$31$	−5.66217			−0.182651			−0.0913253	+	0.995821i	$0.529110\pi$
$32$	0.559027	−	0.559027i	0.0174696	−	0.0174696i
$33$		0			0
$34$			55.1668i			1.62255i
$35$	6.51647	−	6.81567i	0.186185	−	0.194733i
$36$		0			0
$37$	26.1846	−	26.1846i	0.707691	−	0.707691i	−0.258358	−	0.966049i	$-0.583181\pi$
$37$	26.1846	−	26.1846i	0.707691	−	0.707691i	0.966049	+	0.258358i	$0.0831815\pi$
$38$	−33.9047	−	33.9047i	−0.892228	−	0.892228i
$39$		0			0
$40$	−29.0875	−	27.8107i	−0.727189	−	0.695267i
$41$	−0.868046			−0.0211719			−0.0105859	−	0.999944i	$-0.503370\pi$
$41$	−0.868046			−0.0211719			−0.0105859	+	0.999944i	$0.503370\pi$
$42$		0			0
$43$	55.2976	+	55.2976i	1.28599	+	1.28599i	0.937201	+	0.348789i	$0.113407\pi$
$43$	55.2976	+	55.2976i	1.28599	+	1.28599i	0.348789	+	0.937201i	$0.386593\pi$
$44$			0.163889i			0.00372474i
$45$		0			0
$46$	−4.28317			−0.0931124
$47$	−7.21510	+	7.21510i	−0.153513	+	0.153513i	−0.779685	−	0.626172i	$-0.784621\pi$
$47$	−7.21510	+	7.21510i	−0.153513	+	0.153513i	0.626172	+	0.779685i	$0.284621\pi$
$48$		0			0
$49$			45.4433i			0.927414i
$50$	−33.5247	+	36.6771i	−0.670494	+	0.733542i
$51$		0			0
$52$	−0.125016	+	0.125016i	−0.00240415	+	0.00240415i
$53$	34.7108	+	34.7108i	0.654921	+	0.654921i	0.954174	−	0.299253i	$-0.0967375\pi$
$53$	34.7108	+	34.7108i	0.654921	+	0.654921i	−0.299253	+	0.954174i	$0.596738\pi$
$54$		0			0
$55$	16.5789	−	0.372054i	0.301435	−	0.00676461i
$56$	−15.1791			−0.271056
$57$		0			0
$58$	73.3347	+	73.3347i	1.26439	+	1.26439i
$59$			78.6241i			1.33261i	0.745679	+	0.666306i	$0.232125\pi$
$59$			78.6241i			1.33261i	−0.745679	+	0.666306i	$0.767875\pi$
$60$		0			0
$61$	−71.8790			−1.17834			−0.589172	−	0.808007i	$-0.700546\pi$
$61$	−71.8790			−1.17834			−0.589172	+	0.808007i	$0.700546\pi$
$62$	7.95790	−	7.95790i	0.128353	−	0.128353i
$63$		0			0
$64$			64.7710i			1.01205i
$65$	12.9304	+	12.3628i	0.198929	+	0.190196i
$66$		0			0
$67$	−7.85622	+	7.85622i	−0.117257	+	0.117257i	−0.763301	−	0.646044i	$-0.776422\pi$
$67$	−7.85622	+	7.85622i	−0.117257	+	0.117257i	0.646044	+	0.763301i	$0.276422\pi$
$68$	0.969807	+	0.969807i	0.0142619	+	0.0142619i
$69$		0			0
$70$	0.420498	+	18.7377i	0.00600712	+	0.267681i
$71$	75.2724			1.06017			0.530087	−	0.847943i	$-0.322159\pi$
$71$	75.2724			1.06017			0.530087	+	0.847943i	$0.322159\pi$
$72$		0			0
$73$	11.5472	+	11.5472i	0.158181	+	0.158181i	0.781760	−	0.623579i	$-0.214322\pi$
$73$	11.5472	+	11.5472i	0.158181	+	0.158181i	−0.623579	+	0.781760i	$0.714322\pi$
$74$			73.6023i			0.994625i
$75$		0			0
$76$	−1.19206			−0.0156849
$77$	4.42288	−	4.42288i	0.0574400	−	0.0574400i
$78$		0			0
$79$		−	132.372i		−	1.67560i	−0.545979	−	0.837799i	$-0.683842\pi$
$79$		−	132.372i		−	1.67560i	0.545979	−	0.837799i	$-0.316158\pi$
$80$	78.9796	−	1.77241i	0.987245	−	0.0221551i
$81$		0			0
$82$	1.22000	−	1.22000i	0.0148780	−	0.0148780i
$83$	37.5500	+	37.5500i	0.452409	+	0.452409i	0.896153	−	0.443744i	$-0.146350\pi$
$83$	37.5500	+	37.5500i	0.452409	+	0.452409i	−0.443744	+	0.896153i	$0.646350\pi$
$84$		0			0
$85$	95.9038	−	100.307i	1.12828	−	1.18008i
$86$	−155.436			−1.80740
$87$		0			0
$88$	−18.8758	−	18.8758i	−0.214497	−	0.214497i
$89$			97.5309i			1.09585i	0.836527	+	0.547926i	$0.184583\pi$
$89$			97.5309i			1.09585i	−0.836527	+	0.547926i	$0.815417\pi$
$90$		0			0
$91$	6.74762			0.0741497
$92$	−0.0752961	+	0.0752961i	−0.000818436	+	0.000818436i
$93$		0			0
$94$		−	20.2810i		−	0.215755i
$95$	2.70616	+	120.588i	0.0284858	+	1.26935i
$96$		0			0
$97$	−58.4602	+	58.4602i	−0.602682	+	0.602682i	−0.941023	−	0.338341i	$-0.890134\pi$
$97$	−58.4602	+	58.4602i	−0.602682	+	0.602682i	0.338341	+	0.941023i	$0.390134\pi$
$98$	−63.8683	−	63.8683i	−0.651718	−	0.651718i
$99$		0			0
$100$	0.0554182	+	1.23411i	0.000554182	+	0.0123411i
$101$	−117.896			−1.16728			−0.583642	−	0.812011i	$-0.698373\pi$
$101$	−117.896			−1.16728			−0.583642	+	0.812011i	$0.698373\pi$
$102$		0			0
$103$	20.3226	+	20.3226i	0.197307	+	0.197307i	0.798844	−	0.601538i	$-0.205445\pi$
$103$	20.3226	+	20.3226i	0.197307	+	0.197307i	−0.601538	+	0.798844i	$0.705445\pi$
$104$		−	28.7972i		−	0.276896i
$105$		0			0
$106$	−97.5686			−0.920459
$107$	55.6174	−	55.6174i	0.519788	−	0.519788i	−0.397719	−	0.917507i	$-0.630198\pi$
$107$	55.6174	−	55.6174i	0.519788	−	0.519788i	0.917507	+	0.397719i	$0.130198\pi$
$108$		0			0
$109$			111.807i			1.02575i	0.858462	+	0.512877i	$0.171420\pi$
$109$			111.807i			1.02575i	−0.858462	+	0.512877i	$0.828580\pi$
$110$	−22.7780	+	23.8238i	−0.207073	+	0.216580i
$111$		0			0
$112$	21.0700	−	21.0700i	0.188125	−	0.188125i
$113$	−108.987	−	108.987i	−0.964490	−	0.964490i	0.0349010	−	0.999391i	$-0.488888\pi$
$113$	−108.987	−	108.987i	−0.964490	−	0.964490i	−0.999391	+	0.0349010i	$0.988888\pi$
$114$		0			0
$115$	7.78787	+	7.44600i	0.0677206	+	0.0647479i
$116$	2.57838			0.0222274
$117$		0			0
$118$	−110.502	−	110.502i	−0.936460	−	0.936460i
$119$		−	52.3446i		−	0.439870i
$120$		0			0
$121$	11.0000			0.0909091
$122$	101.022	−	101.022i	0.828053	−	0.828053i
$123$		0			0
$124$		−	0.279792i		−	0.00225639i
$125$	124.717	−	8.40773i	0.997735	−	0.0672618i
$126$		0			0
$127$	116.304	−	116.304i	0.915776	−	0.915776i	−0.0809431	−	0.996719i	$-0.525793\pi$
$127$	116.304	−	116.304i	0.915776	−	0.915776i	0.996719	+	0.0809431i	$0.0257932\pi$
$128$	−88.7963	−	88.7963i	−0.693721	−	0.693721i
$129$		0			0
$130$	−35.5482	+	0.797750i	−0.273448	+	0.00613654i
$131$	−31.6874			−0.241889			−0.120944	−	0.992659i	$-0.538592\pi$
$131$	−31.6874			−0.241889			−0.120944	+	0.992659i	$0.538592\pi$
$132$		0			0
$133$	32.1701	+	32.1701i	0.241881	+	0.241881i
$134$		−	22.0831i		−	0.164799i
$135$		0			0
$136$	−223.393			−1.64260
$137$	−31.4964	+	31.4964i	−0.229901	+	0.229901i	−0.812651	−	0.582750i	$-0.801977\pi$
$137$	−31.4964	+	31.4964i	−0.229901	+	0.229901i	0.582750	+	0.812651i	$0.301977\pi$
$138$		0			0
$139$		−	140.320i		−	1.00949i	−0.863267	−	0.504747i	$-0.831586\pi$
$139$		−	140.320i		−	1.00949i	0.863267	−	0.504747i	$-0.168414\pi$
$140$	0.336791	+	0.322007i	0.00240565	+	0.00230005i
$141$		0			0
$142$	−105.792	+	105.792i	−0.745011	+	0.745011i
$143$	8.39089	+	8.39089i	0.0586776	+	0.0586776i
$144$		0			0
$145$	−5.85333	−	260.828i	−0.0403678	−	1.79881i
$146$	−32.4580			−0.222315
$147$		0			0
$148$	1.29389	+	1.29389i	0.00874252	+	0.00874252i
$149$			36.3096i			0.243689i	0.992549	+	0.121844i	$0.0388809\pi$
$149$			36.3096i			0.243689i	−0.992549	+	0.121844i	$0.961119\pi$
$150$		0			0
$151$	−68.3892			−0.452909			−0.226454	−	0.974022i	$-0.572713\pi$
$151$	−68.3892			−0.452909			−0.226454	+	0.974022i	$0.572713\pi$
$152$	137.294	−	137.294i	0.903250	−	0.903250i
$153$		0			0
$154$			12.4323i			0.0807292i
$155$	−28.3037	+	0.635173i	−0.182605	+	0.00409789i
$156$		0			0
$157$	176.542	−	176.542i	1.12447	−	1.12447i	0.133411	−	0.991061i	$-0.457407\pi$
$157$	176.542	−	176.542i	1.12447	−	1.12447i	0.991061	−	0.133411i	$-0.0425931\pi$
$158$	186.043	+	186.043i	1.17749	+	1.17749i
$159$		0			0
$160$	2.73172	−	2.85714i	0.0170733	−	0.0178571i
$161$	4.06405			0.0252425
$162$		0			0
$163$	130.555	+	130.555i	0.800949	+	0.800949i	0.983244	−	0.182295i	$-0.0583527\pi$
$163$	130.555	+	130.555i	0.800949	+	0.800949i	−0.182295	+	0.983244i	$0.558353\pi$
$164$		−	0.0428939i		−	0.000261548i
$165$		0			0
$166$	−105.549			−0.635839
$167$	206.060	−	206.060i	1.23389	−	1.23389i	0.271433	−	0.962457i	$-0.412503\pi$
$167$	206.060	−	206.060i	1.23389	−	1.23389i	0.962457	−	0.271433i	$-0.0874975\pi$
$168$		0			0
$169$		−	156.199i		−	0.924253i
$170$	6.18853	+	275.765i	0.0364031	+	1.62215i
$171$		0			0
$172$	−2.73249	+	2.73249i	−0.0158866	+	0.0158866i
$173$	−89.1753	−	89.1753i	−0.515464	−	0.515464i	0.400732	−	0.916196i	$-0.368756\pi$
$173$	−89.1753	−	89.1753i	−0.515464	−	0.515464i	−0.916196	+	0.400732i	$0.868756\pi$
$174$		0			0
$175$	31.8096	−	34.8008i	0.181769	−	0.198861i
$176$	52.4023			0.297741
$177$		0			0
$178$	−137.075	−	137.075i	−0.770084	−	0.770084i
$179$			7.03896i			0.0393238i	0.999807	+	0.0196619i	$0.00625898\pi$
$179$			7.03896i			0.0393238i	−0.999807	+	0.0196619i	$0.993741\pi$
$180$		0			0
$181$	−239.812			−1.32493			−0.662464	−	0.749094i	$-0.730489\pi$
$181$	−239.812			−1.32493			−0.662464	+	0.749094i	$0.730489\pi$
$182$	−9.48346	+	9.48346i	−0.0521069	+	0.0521069i
$183$		0			0
$184$		−	17.3443i		−	0.0942627i
$185$	127.953	−	133.827i	0.691635	−	0.723390i
$186$		0			0
$187$	65.0922	−	65.0922i	0.348086	−	0.348086i
$188$	−0.356529	−	0.356529i	−0.00189643	−	0.00189643i
$189$		0			0
$190$	−173.284	−	165.677i	−0.912021	−	0.871985i
$191$	−245.474			−1.28520			−0.642602	−	0.766200i	$-0.722145\pi$
$191$	−245.474			−1.28520			−0.642602	+	0.766200i	$0.722145\pi$
$192$		0			0
$193$	−87.9946	−	87.9946i	−0.455930	−	0.455930i	0.441387	−	0.897317i	$-0.354487\pi$
$193$	−87.9946	−	87.9946i	−0.455930	−	0.455930i	−0.897317	+	0.441387i	$0.854487\pi$
$194$		−	164.326i		−	0.847040i
$195$		0			0
$196$	−2.24555			−0.0114569
$197$	90.4647	−	90.4647i	0.459212	−	0.459212i	−0.439185	−	0.898397i	$-0.644733\pi$
$197$	90.4647	−	90.4647i	0.459212	−	0.459212i	0.898397	+	0.439185i	$0.144733\pi$
$198$		0			0
$199$			282.576i			1.41998i	0.704213	+	0.709989i	$0.251300\pi$
$199$			282.576i			1.41998i	−0.704213	+	0.709989i	$0.748700\pi$
$200$	−148.521	−	135.755i	−0.742604	−	0.678777i
$201$		0			0
$202$	165.697	−	165.697i	0.820280	−	0.820280i
$203$	−69.5829	−	69.5829i	−0.342773	−	0.342773i
$204$		0			0
$205$	−4.33914	+	0.0973760i	−0.0211665	+	0.000475005i
$206$	−57.1248			−0.277305
$207$		0			0
$208$	39.9729	+	39.9729i	0.192178	+	0.192178i
$209$			80.0092i			0.382819i
$210$		0			0
$211$	238.989			1.13265			0.566324	−	0.824183i	$-0.308365\pi$
$211$	238.989			1.13265			0.566324	+	0.824183i	$0.308365\pi$
$212$	−1.71521	+	1.71521i	−0.00809061	+	0.00809061i
$213$		0			0
$214$			156.335i			0.730537i
$215$	282.622	+	270.215i	1.31452	+	1.25681i
$216$		0			0
$217$	−7.55078	+	7.55078i	−0.0347962	+	0.0347962i
$218$	−157.139	−	157.139i	−0.720823	−	0.720823i
$219$		0			0
$220$	0.0183848	+	0.819237i	8.35671e−5	+	0.00372381i
$221$	99.3057			0.449347
$222$		0			0
$223$	−238.846	−	238.846i	−1.07106	−	1.07106i	−0.997274	−	0.0737832i	$-0.976493\pi$
$223$	−238.846	−	238.846i	−1.07106	−	1.07106i	−0.0737832	−	0.997274i	$-0.523507\pi$
$224$		−	1.49098i		−	0.00665616i
$225$		0			0
$226$	306.353			1.35554
$227$	−24.7070	+	24.7070i	−0.108842	+	0.108842i	−0.759430	−	0.650589i	$-0.774522\pi$
$227$	−24.7070	+	24.7070i	−0.108842	+	0.108842i	0.650589	+	0.759430i	$0.274522\pi$
$228$		0			0
$229$		−	54.8992i		−	0.239734i	−0.992790	−	0.119867i	$-0.961753\pi$
$229$		−	54.8992i		−	0.239734i	0.992790	−	0.119867i	$-0.0382469\pi$
$230$	−21.4105	+	0.480479i	−0.0930890	+	0.00208904i
$231$		0			0
$232$	−296.962	+	296.962i	−1.28001	+	1.28001i
$233$	−290.968	−	290.968i	−1.24879	−	1.24879i	−0.956255	−	0.292535i	$-0.905501\pi$
$233$	−290.968	−	290.968i	−1.24879	−	1.24879i	−0.292535	−	0.956255i	$-0.594499\pi$
$234$		0			0
$235$	−35.2571	+	36.8758i	−0.150030	+	0.156918i
$236$	−3.88515			−0.0164625
$237$		0			0
$238$	73.5677	+	73.5677i	0.309108	+	0.309108i
$239$			260.284i			1.08906i	0.838743	+	0.544528i	$0.183291\pi$
$239$			260.284i			1.08906i	−0.838743	+	0.544528i	$0.816709\pi$
$240$		0			0
$241$	−48.0807			−0.199505			−0.0997525	−	0.995012i	$-0.531805\pi$
$241$	−48.0807			−0.199505			−0.0997525	+	0.995012i	$0.531805\pi$
$242$	−15.4600	+	15.4600i	−0.0638841	+	0.0638841i
$243$		0			0
$244$		−	3.55185i		−	0.0145568i
$245$	5.09775	+	227.159i	0.0208072	+	0.927181i
$246$		0			0
$247$	−61.0317	+	61.0317i	−0.247092	+	0.247092i
$248$	32.2248	+	32.2248i	0.129939	+	0.129939i
$249$		0			0
$250$	−163.467	+	187.100i	−0.653868	+	0.748401i
$251$	−178.672			−0.711841			−0.355920	−	0.934516i	$-0.615833\pi$
$251$	−178.672			−0.711841			−0.355920	+	0.934516i	$0.615833\pi$
$252$		0			0
$253$	5.05378	+	5.05378i	0.0199754	+	0.0199754i
$254$			326.918i			1.28708i
$255$		0			0
$256$	−9.48609			−0.0370551
$257$	46.6324	−	46.6324i	0.181449	−	0.181449i	−0.610538	−	0.791987i	$-0.709047\pi$
$257$	46.6324	−	46.6324i	0.181449	−	0.181449i	0.791987	+	0.610538i	$0.209047\pi$
$258$		0			0
$259$		−	69.8368i		−	0.269640i
$260$	−0.610897	+	0.638945i	−0.00234960	+	0.00245748i
$261$		0			0
$262$	44.5351	−	44.5351i	0.169981	−	0.169981i
$263$	−138.165	−	138.165i	−0.525344	−	0.525344i	0.393837	−	0.919180i	$-0.371148\pi$
$263$	−138.165	−	138.165i	−0.525344	−	0.525344i	−0.919180	+	0.393837i	$0.871148\pi$
$264$		0			0
$265$	177.404	+	169.616i	0.669449	+	0.640062i
$266$	−90.4271			−0.339951
$267$		0			0
$268$	−0.388209	−	0.388209i	−0.00144854	−	0.00144854i
$269$			3.15623i			0.0117332i	0.999983	+	0.00586659i	$0.00186740\pi$
$269$			3.15623i			0.0117332i	−0.999983	+	0.00586659i	$0.998133\pi$
$270$		0			0
$271$	348.973			1.28772			0.643861	−	0.765143i	$-0.277332\pi$
$271$	348.973			1.28772			0.643861	+	0.765143i	$0.277332\pi$
$272$	310.089	−	310.089i	1.14003	−	1.14003i
$273$		0			0
$274$		−	88.5334i		−	0.323115i
$275$	82.8321	−	3.71960i	0.301208	−	0.0135258i
$276$		0			0
$277$	194.912	−	194.912i	0.703655	−	0.703655i	−0.261538	−	0.965193i	$-0.584230\pi$
$277$	194.912	−	194.912i	0.703655	−	0.703655i	0.965193	+	0.261538i	$0.0842297\pi$
$278$	197.212	+	197.212i	0.709397	+	0.709397i
$279$		0			0
$280$	−75.8766	+	1.70277i	−0.270988	+	0.00608133i
$281$	171.567			0.610560			0.305280	−	0.952263i	$-0.401250\pi$
$281$	171.567			0.610560			0.305280	+	0.952263i	$0.401250\pi$
$282$		0			0
$283$	174.449	+	174.449i	0.616428	+	0.616428i	0.944613	−	0.328185i	$-0.106437\pi$
$283$	174.449	+	174.449i	0.616428	+	0.616428i	−0.328185	+	0.944613i	$0.606437\pi$
$284$			3.71953i			0.0130969i
$285$		0			0
$286$	−23.5860			−0.0824684
$287$	−1.15758	+	1.15758i	−0.00403339	+	0.00403339i
$288$		0			0
$289$		−	481.362i		−	1.66561i
$290$	374.808	+	358.354i	1.29244	+	1.23570i
$291$		0			0
$292$	−0.570596	+	0.570596i	−0.00195410	+	0.00195410i
$293$	−207.978	−	207.978i	−0.709823	−	0.709823i	0.256675	−	0.966498i	$-0.417373\pi$
$293$	−207.978	−	207.978i	−0.709823	−	0.709823i	−0.966498	+	0.256675i	$0.917373\pi$
$294$		0			0
$295$	8.81992	+	393.021i	0.0298980	+	1.33228i
$296$	−298.046			−1.00691
$297$		0			0
$298$	−51.0314	−	51.0314i	−0.171246	−	0.171246i
$299$			7.71013i			0.0257864i
$300$		0			0
$301$	147.484			0.489981
$302$	96.1177	−	96.1177i	0.318270	−	0.318270i
$303$		0			0
$304$			381.152i			1.25379i
$305$	−359.305	+	8.06327i	−1.17805	+	0.0264370i
$306$		0			0
$307$	−338.440	+	338.440i	−1.10241	+	1.10241i	−0.108292	+	0.994119i	$0.534538\pi$
$307$	−338.440	+	338.440i	−1.10241	+	1.10241i	−0.994119	+	0.108292i	$0.965462\pi$
$308$	0.218554	+	0.218554i	0.000709590	+	0.000709590i
$309$		0			0
$310$	38.8868	−	40.6722i	0.125441	−	0.131201i
$311$	−179.699			−0.577810			−0.288905	−	0.957358i	$-0.593291\pi$
$311$	−179.699			−0.577810			−0.288905	+	0.957358i	$0.593291\pi$
$312$		0			0
$313$	227.442	+	227.442i	0.726653	+	0.726653i	0.969952	−	0.243298i	$-0.0782294\pi$
$313$	227.442	+	227.442i	0.726653	+	0.726653i	−0.243298	+	0.969952i	$0.578229\pi$
$314$			496.243i			1.58039i
$315$		0			0
$316$	6.54108			0.0206996
$317$	−199.205	+	199.205i	−0.628406	+	0.628406i	−0.947667	−	0.319261i	$-0.896565\pi$
$317$	−199.205	+	199.205i	−0.628406	+	0.628406i	0.319261	+	0.947667i	$0.396565\pi$
$318$		0			0
$319$		−	173.057i		−	0.542499i
$320$	7.26590	+	323.773i	0.0227059	+	1.01179i
$321$		0			0
$322$	−5.71182	+	5.71182i	−0.0177386	+	0.0177386i
$323$	473.452	+	473.452i	1.46580	+	1.46580i
$324$		0			0
$325$	66.0224	+	60.3477i	0.203146	+	0.185685i
$326$	−366.976			−1.12569
$327$		0			0
$328$	4.94027	+	4.94027i	0.0150618	+	0.0150618i
$329$			19.2434i			0.0584906i
$330$		0			0
$331$	230.130			0.695256			0.347628	−	0.937632i	$-0.386987\pi$
$331$	230.130			0.695256			0.347628	+	0.937632i	$0.386987\pi$
$332$	−1.85551	+	1.85551i	−0.00558887	+	0.00558887i
$333$		0			0
$334$			579.214i			1.73417i
$335$	−38.3899	+	40.1525i	−0.114597	+	0.119858i
$336$		0			0
$337$	−208.820	+	208.820i	−0.619644	+	0.619644i	−0.945440	−	0.325796i	$-0.894368\pi$
$337$	−208.820	+	208.820i	−0.619644	+	0.619644i	0.325796	+	0.945440i	$0.394368\pi$
$338$	219.530	+	219.530i	0.649496	+	0.649496i
$339$		0			0
$340$	4.95660	+	4.73902i	0.0145782	+	0.0139383i
$341$	−18.7793			−0.0550712
$342$		0			0
$343$	125.945	+	125.945i	0.367186	+	0.367186i
$344$		−	629.425i		−	1.82972i
$345$		0			0
$346$	250.663			0.724459
$347$	−293.703	+	293.703i	−0.846407	+	0.846407i	−0.989683	−	0.143276i	$-0.954236\pi$
$347$	−293.703	+	293.703i	−0.846407	+	0.846407i	0.143276	+	0.989683i	$0.454236\pi$
$348$		0			0
$349$		−	49.0031i		−	0.140410i	−0.997533	−	0.0702051i	$-0.977635\pi$
$349$		−	49.0031i		−	0.140410i	0.997533	−	0.0702051i	$-0.0223654\pi$
$350$	4.20392	+	93.6176i	0.0120112	+	0.267479i
$351$		0			0
$352$	1.85408	−	1.85408i	0.00526728	−	0.00526728i
$353$	−49.8908	−	49.8908i	−0.141334	−	0.141334i	0.632900	−	0.774234i	$-0.281864\pi$
$353$	−49.8908	−	49.8908i	−0.141334	−	0.141334i	−0.774234	+	0.632900i	$0.781864\pi$
$354$		0			0
$355$	376.267	−	8.44393i	1.05991	−	0.0237857i
$356$	−4.81942			−0.0135377
$357$		0			0
$358$	−9.89291	−	9.89291i	−0.0276338	−	0.0276338i
$359$		−	331.174i		−	0.922491i	−0.887273	−	0.461245i	$-0.847403\pi$
$359$		−	331.174i		−	0.922491i	0.887273	−	0.461245i	$-0.152597\pi$
$360$		0			0
$361$	−220.952			−0.612056
$362$	337.044	−	337.044i	0.931060	−	0.931060i
$363$		0			0
$364$			0.333429i			0.000916014i
$365$	59.0168	+	56.4261i	0.161690	+	0.154592i
$366$		0			0
$367$	−453.490	+	453.490i	−1.23567	+	1.23567i	−0.273913	+	0.961754i	$0.588318\pi$
$367$	−453.490	+	453.490i	−1.23567	+	1.23567i	−0.961754	+	0.273913i	$0.911682\pi$
$368$	24.0754	+	24.0754i	0.0654224	+	0.0654224i
$369$		0			0
$370$	8.25658	+	367.919i	0.0223151	+	0.994375i
$371$	92.5771			0.249534
$372$		0			0
$373$	−66.5519	−	66.5519i	−0.178423	−	0.178423i	0.612245	−	0.790668i	$-0.290267\pi$
$373$	−66.5519	−	66.5519i	−0.178423	−	0.178423i	−0.790668	+	0.612245i	$0.790267\pi$
$374$			182.968i			0.489219i
$375$		0			0
$376$	82.1260			0.218420
$377$	132.010	−	132.010i	0.350158	−	0.350158i
$378$		0			0
$379$			141.758i			0.374031i	0.982357	+	0.187016i	$0.0598815\pi$
$379$			141.758i			0.374031i	−0.982357	+	0.187016i	$0.940118\pi$
$380$	−5.95878	+	0.133723i	−0.0156810	+	0.000351902i
$381$		0			0
$382$	345.002	−	345.002i	0.903146	−	0.903146i
$383$	−376.365	−	376.365i	−0.982675	−	0.982675i	0.0171774	−	0.999852i	$-0.494532\pi$
$383$	−376.365	−	376.365i	−0.982675	−	0.982675i	−0.999852	+	0.0171774i	$0.994532\pi$
$384$		0			0
$385$	21.6127	−	22.6050i	0.0561369	−	0.0587143i
$386$	247.344			0.640788
$387$		0			0
$388$	−2.88877	−	2.88877i	−0.00744528	−	0.00744528i
$389$			628.200i			1.61491i	0.589930	+	0.807455i	$0.299155\pi$
$389$			628.200i			1.61491i	−0.589930	+	0.807455i	$0.700845\pi$
$390$		0			0
$391$	59.8111			0.152970
$392$	258.629	−	258.629i	0.659769	−	0.659769i
$393$		0			0
$394$			254.287i			0.645400i
$395$	−14.8493	−	661.695i	−0.0375932	−	1.67518i
$396$		0			0
$397$	178.574	−	178.574i	0.449809	−	0.449809i	−0.445482	−	0.895291i	$-0.646968\pi$
$397$	178.574	−	178.574i	0.449809	−	0.449809i	0.895291	+	0.445482i	$0.146968\pi$
$398$	−397.146	−	397.146i	−0.997855	−	0.997855i
$399$		0			0
$400$	394.600	−	17.7196i	0.986500	−	0.0442990i
$401$	298.987			0.745603			0.372801	−	0.927911i	$-0.378397\pi$
$401$	298.987			0.745603			0.372801	+	0.927911i	$0.378397\pi$
$402$		0			0
$403$	−14.3250	−	14.3250i	−0.0355459	−	0.0355459i
$404$		−	5.82573i		−	0.0144201i
$405$		0			0
$406$	195.591			0.481751
$407$	86.8444	−	86.8444i	0.213377	−	0.213377i
$408$		0			0
$409$		−	644.153i		−	1.57495i	−0.616349	−	0.787473i	$-0.711389\pi$
$409$		−	644.153i		−	1.57495i	0.616349	−	0.787473i	$-0.288611\pi$
$410$	5.96159	−	6.23531i	0.0145405	−	0.0152081i
$411$		0			0
$412$	−1.00423	+	1.00423i	−0.00243744	+	0.00243744i
$413$	104.849	+	104.849i	0.253872	+	0.253872i
$414$		0			0
$415$	191.915	+	183.490i	0.462445	+	0.442145i
$416$	2.82862			0.00679957
$417$		0			0
$418$	−112.449	−	112.449i	−0.269017	−	0.269017i
$419$			104.231i			0.248760i	0.992235	+	0.124380i	$0.0396942\pi$
$419$			104.231i			0.248760i	−0.992235	+	0.124380i	$0.960306\pi$
$420$		0			0
$421$	−167.469			−0.397788			−0.198894	−	0.980021i	$-0.563735\pi$
$421$	−167.469			−0.397788			−0.198894	+	0.980021i	$0.563735\pi$
$422$	−335.887	+	335.887i	−0.795940	+	0.795940i
$423$		0			0
$424$		−	395.096i		−	0.931830i
$425$	468.146	−	512.167i	1.10152	−	1.20510i
$426$		0			0
$427$	−95.8542	+	95.8542i	−0.224483	+	0.224483i
$428$	2.74829	+	2.74829i	0.00642125	+	0.00642125i
$429$		0			0
$430$	−776.985	+	17.4366i	−1.80694	+	0.0405502i
$431$	−122.966			−0.285304			−0.142652	−	0.989773i	$-0.545563\pi$
$431$	−122.966			−0.285304			−0.142652	+	0.989773i	$0.545563\pi$
$432$		0			0
$433$	−29.8699	−	29.8699i	−0.0689837	−	0.0689837i	0.671773	−	0.740757i	$-0.265533\pi$
$433$	−29.8699	−	29.8699i	−0.0689837	−	0.0689837i	−0.740757	+	0.671773i	$0.765533\pi$
$434$		−	21.2245i		−	0.0489044i
$435$		0			0
$436$	−5.52487			−0.0126717
$437$	−36.7590	+	36.7590i	−0.0841166	+	0.0841166i
$438$		0			0
$439$		−	56.2322i		−	0.128092i	−0.997947	−	0.0640458i	$-0.979600\pi$
$439$		−	56.2322i		−	0.128092i	0.997947	−	0.0640458i	$-0.0204004\pi$
$440$	−96.4725	−	92.2376i	−0.219256	−	0.209631i
$441$		0			0
$442$	−139.569	+	139.569i	−0.315768	+	0.315768i
$443$	−365.717	−	365.717i	−0.825546	−	0.825546i	0.161351	−	0.986897i	$-0.448415\pi$
$443$	−365.717	−	365.717i	−0.825546	−	0.825546i	−0.986897	+	0.161351i	$0.948415\pi$
$444$		0			0
$445$	10.9409	+	487.532i	0.0245862	+	1.09558i
$446$	671.372			1.50532
$447$		0			0
$448$	86.3753	+	86.3753i	0.192802	+	0.192802i
$449$		−	696.270i		−	1.55071i	−0.631524	−	0.775356i	$-0.717570\pi$
$449$		−	696.270i		−	1.55071i	0.631524	−	0.775356i	$-0.282430\pi$
$450$		0			0
$451$	−2.87898			−0.00638356
$452$	5.38553	−	5.38553i	0.0119149	−	0.0119149i
$453$		0			0
$454$		−	69.4491i		−	0.152972i
$455$	33.7296	−	0.756937i	0.0741311	−	0.00166360i
$456$		0			0
$457$	−542.497	+	542.497i	−1.18708	+	1.18708i	−0.209214	+	0.977870i	$0.567091\pi$
$457$	−542.497	+	542.497i	−1.18708	+	1.18708i	−0.977870	+	0.209214i	$0.932909\pi$
$458$	77.1581	+	77.1581i	0.168468	+	0.168468i
$459$		0			0
$460$	−0.367939	+	0.384832i	−0.000799868	+	0.000836592i
$461$	−750.064			−1.62704			−0.813518	−	0.581540i	$-0.802450\pi$
$461$	−750.064			−1.62704			−0.813518	+	0.581540i	$0.802450\pi$
$462$		0			0
$463$	466.490	+	466.490i	1.00754	+	1.00754i	0.999971	+	0.00756558i	$0.00240822\pi$
$463$	466.490	+	466.490i	1.00754	+	1.00754i	0.00756558	+	0.999971i	$0.497592\pi$
$464$		−	824.419i		−	1.77676i
$465$		0			0
$466$	817.883			1.75511
$467$	155.227	−	155.227i	0.332393	−	0.332393i	−0.521102	−	0.853495i	$-0.674479\pi$
$467$	155.227	−	155.227i	0.332393	−	0.332393i	0.853495	+	0.521102i	$0.174479\pi$
$468$		0			0
$469$			20.9533i			0.0446766i
$470$	−2.27508	−	101.379i	−0.00484060	−	0.215701i
$471$		0			0
$472$	447.470	−	447.470i	0.948029	−	0.948029i
$473$	183.401	+	183.401i	0.387741	+	0.387741i
$474$		0			0
$475$	27.0547	+	602.485i	0.0569574	+	1.26839i
$476$	2.58657			0.00543397
$477$		0			0
$478$	−365.817	−	365.817i	−0.765307	−	0.765307i
$479$			100.913i			0.210674i	0.994437	+	0.105337i	$0.0335921\pi$
$479$			100.913i			0.210674i	−0.994437	+	0.105337i	$0.966408\pi$
$480$		0			0
$481$	132.491			0.275450
$482$	67.5751	−	67.5751i	0.140197	−	0.140197i
$483$		0			0
$484$			0.543557i			0.00112305i
$485$	−285.669	+	298.785i	−0.589009	+	0.616052i
$486$		0			0
$487$	113.769	−	113.769i	0.233611	−	0.233611i	−0.580587	−	0.814198i	$-0.697177\pi$
$487$	113.769	−	113.769i	0.233611	−	0.233611i	0.814198	+	0.580587i	$0.197177\pi$
$488$	409.082	+	409.082i	0.838282	+	0.838282i
$489$		0			0
$490$	−326.426	−	312.097i	−0.666175	−	0.636932i
$491$	−732.425			−1.49170			−0.745851	−	0.666113i	$-0.767957\pi$
$491$	−732.425			−1.49170			−0.745851	+	0.666113i	$0.767957\pi$
$492$		0			0
$493$	−1024.06	−	1024.06i	−2.07720	−	2.07720i
$494$		−	171.554i		−	0.347275i
$495$		0			0
$496$	−89.4617			−0.180366
$497$	100.379	−	100.379i	0.201971	−	0.201971i
$498$		0			0
$499$		−	526.800i		−	1.05571i	−0.849334	−	0.527855i	$-0.822996\pi$
$499$		−	526.800i		−	1.05571i	0.849334	−	0.527855i	$-0.177004\pi$
$500$	0.415462	+	6.16280i	0.000830924	+	0.0123256i
$501$		0			0
$502$	251.115	−	251.115i	0.500229	−	0.500229i
$503$	−304.311	−	304.311i	−0.604993	−	0.604993i	0.336641	−	0.941633i	$-0.390709\pi$
$503$	−304.311	−	304.311i	−0.604993	−	0.604993i	−0.941633	+	0.336641i	$0.890709\pi$
$504$		0			0
$505$	−589.330	+	13.2253i	−1.16699	+	0.0261888i
$506$	−14.2057			−0.0280745
$507$		0			0
$508$	5.74706	+	5.74706i	0.0113131	+	0.0113131i
$509$			358.316i			0.703961i	0.936007	+	0.351980i	$0.114492\pi$
$509$			358.316i			0.703961i	−0.936007	+	0.351980i	$0.885508\pi$
$510$		0			0
$511$	30.7975			0.0602691
$512$	368.518	−	368.518i	0.719761	−	0.719761i
$513$		0			0
$514$			131.079i			0.255018i
$515$	103.867	+	99.3076i	0.201684	+	0.192830i
$516$		0			0
$517$	−23.9298	+	23.9298i	−0.0462859	+	0.0462859i
$518$	98.1523	+	98.1523i	0.189483	+	0.189483i
$519$		0			0
$520$	−3.23042	−	143.950i	−0.00621234	−	0.276826i
$521$	676.839			1.29912			0.649558	−	0.760312i	$-0.274954\pi$
$521$	676.839			1.29912			0.649558	+	0.760312i	$0.274954\pi$
$522$		0			0
$523$	−194.779	−	194.779i	−0.372426	−	0.372426i	0.495934	−	0.868360i	$-0.334826\pi$
$523$	−194.779	−	194.779i	−0.372426	−	0.372426i	−0.868360	+	0.495934i	$0.834826\pi$
$524$		−	1.56581i		−	0.00298819i
$525$		0			0
$526$	388.370			0.738345
$527$	−111.126	+	111.126i	−0.210865	+	0.210865i
$528$		0			0
$529$		−	524.356i		−	0.991222i
$530$	−487.720	+	10.9451i	−0.920227	+	0.0206511i
$531$		0			0
$532$	−1.58966	+	1.58966i	−0.00298809	+	0.00298809i
$533$	−2.19611	−	2.19611i	−0.00412029	−	0.00412029i
$534$		0			0
$535$	271.778	−	284.256i	0.507996	−	0.531319i
$536$	89.4234			0.166835
$537$		0			0
$538$	−4.43592	−	4.43592i	−0.00824521	−	0.00824521i
$539$			150.718i			0.279626i
$540$		0			0
$541$	−324.984			−0.600710			−0.300355	−	0.953827i	$-0.597105\pi$
$541$	−324.984			−0.600710			−0.300355	+	0.953827i	$0.597105\pi$
$542$	−490.464	+	490.464i	−0.904915	+	0.904915i
$543$		0			0
$544$		−	21.9430i		−	0.0403363i
$545$	12.5423	+	558.895i	0.0230135	+	1.02550i
$546$		0			0
$547$	−155.506	+	155.506i	−0.284290	+	0.284290i	−0.834817	−	0.550527i	$-0.814427\pi$
$547$	−155.506	+	155.506i	−0.284290	+	0.284290i	0.550527	+	0.834817i	$0.314427\pi$
$548$	−1.55637	−	1.55637i	−0.00284010	−	0.00284010i
$549$		0			0
$550$	−111.189	+	121.644i	−0.202161	+	0.221171i
$551$	1258.74			2.28447
$552$		0			0
$553$	−176.525	−	176.525i	−0.319213	−	0.319213i
$554$			547.880i			0.988953i
$555$		0			0
$556$	6.93380			0.0124709
$557$	−290.973	+	290.973i	−0.522393	+	0.522393i	−0.918294	−	0.395900i	$-0.870433\pi$
$557$	−290.973	+	290.973i	−0.522393	+	0.522393i	0.395900	+	0.918294i	$0.370433\pi$
$558$		0			0
$559$			279.800i			0.500537i
$560$	102.960	−	107.687i	0.183857	−	0.192298i
$561$		0			0
$562$	−241.129	+	241.129i	−0.429056	+	0.429056i
$563$	−401.485	−	401.485i	−0.713116	−	0.713116i	0.254069	−	0.967186i	$-0.418231\pi$
$563$	−401.485	−	401.485i	−0.713116	−	0.713116i	−0.967186	+	0.254069i	$0.918231\pi$
$564$		0			0
$565$	−557.026	−	532.574i	−0.985886	−	0.942608i
$566$	−490.359			−0.866359
$567$		0			0
$568$	−428.394	−	428.394i	−0.754215	−	0.754215i
$569$			988.685i			1.73758i	0.495178	+	0.868792i	$0.335103\pi$
$569$			988.685i			1.73758i	−0.495178	+	0.868792i	$0.664897\pi$
$570$		0			0
$571$	101.891			0.178442			0.0892211	−	0.996012i	$-0.471562\pi$
$571$	101.891			0.178442			0.0892211	+	0.996012i	$0.471562\pi$
$572$	−0.414630	+	0.414630i	−0.000724878	+	0.000724878i
$573$		0			0
$574$		−	3.25385i		−	0.00566873i
$575$	39.7648	+	36.3470i	0.0691562	+	0.0632122i
$576$		0			0
$577$	205.643	−	205.643i	0.356401	−	0.356401i	−0.506084	−	0.862484i	$-0.668907\pi$
$577$	205.643	−	205.643i	0.356401	−	0.356401i	0.862484	+	0.506084i	$0.168907\pi$
$578$	676.531	+	676.531i	1.17047	+	1.17047i
$579$		0			0
$580$	12.8886	−	0.289238i	0.0222218	−	0.000498686i
$581$	100.149			0.172374
$582$		0			0
$583$	115.123	+	115.123i	0.197466	+	0.197466i
$584$		−	131.436i		−	0.225062i
$585$		0			0
$586$	584.606			0.997622
$587$	66.4402	−	66.4402i	0.113186	−	0.113186i	−0.648245	−	0.761431i	$-0.724497\pi$
$587$	66.4402	−	66.4402i	0.113186	−	0.113186i	0.761431	+	0.648245i	$0.224497\pi$
$588$		0			0
$589$		−	136.592i		−	0.231906i
$590$	−564.768	−	539.976i	−0.957234	−	0.915214i
$591$		0			0
$592$	413.714	−	413.714i	0.698841	−	0.698841i
$593$	623.997	+	623.997i	1.05227	+	1.05227i	0.998556	+	0.0537156i	$0.0171064\pi$
$593$	623.997	+	623.997i	1.05227	+	1.05227i	0.0537156	+	0.998556i	$0.482894\pi$
$594$		0			0
$595$	−5.87193	−	261.657i	−0.00986879	−	0.439760i
$596$	−1.79421			−0.00301043
$597$		0			0
$598$	−10.8362	−	10.8362i	−0.0181207	−	0.0181207i
$599$			26.0024i			0.0434096i	0.999764	+	0.0217048i	$0.00690940\pi$
$599$			26.0024i			0.0434096i	−0.999764	+	0.0217048i	$0.993091\pi$
$600$		0			0
$601$	−816.931			−1.35929			−0.679643	−	0.733543i	$-0.737865\pi$
$601$	−816.931			−1.35929			−0.679643	+	0.733543i	$0.737865\pi$
$602$	−207.282	+	207.282i	−0.344322	+	0.344322i
$603$		0			0
$604$		−	3.37940i		−	0.00559504i
$605$	54.9862	−	1.23396i	0.0908862	−	0.00203961i
$606$		0			0
$607$	−154.340	+	154.340i	−0.254267	+	0.254267i	−0.822718	−	0.568450i	$-0.807543\pi$
$607$	−154.340	+	154.340i	−0.254267	+	0.254267i	0.568450	+	0.822718i	$0.307543\pi$
$608$	13.4858	+	13.4858i	0.0221806	+	0.0221806i
$609$		0			0
$610$	493.653	−	516.318i	0.809266	−	0.846422i
$611$	−36.5077			−0.0597507
$612$		0			0
$613$	−124.979	−	124.979i	−0.203882	−	0.203882i	0.597779	−	0.801661i	$-0.296050\pi$
$613$	−124.979	−	124.979i	−0.203882	−	0.203882i	−0.801661	+	0.597779i	$0.796050\pi$
$614$		−	951.322i		−	1.54939i
$615$		0			0
$616$	−50.3435			−0.0817265
$617$	−415.755	+	415.755i	−0.673832	+	0.673832i	−0.958597	−	0.284765i	$-0.908084\pi$
$617$	−415.755	+	415.755i	−0.673832	+	0.673832i	0.284765	+	0.958597i	$0.408084\pi$
$618$		0			0
$619$			1103.71i			1.78305i	0.452967	+	0.891527i	$0.350366\pi$
$619$			1103.71i			1.78305i	−0.452967	+	0.891527i	$0.649634\pi$
$620$	−0.0313866	−	1.39861i	−5.06236e−5	−	0.00225582i
$621$		0			0
$622$	252.558	−	252.558i	0.406042	−	0.406042i
$623$	130.062	+	130.062i	0.208768	+	0.208768i
$624$		0			0
$625$	622.484	−	56.0186i	0.995975	−	0.0896298i
$626$	−639.318			−1.02128
$627$		0			0
$628$	8.72371	+	8.72371i	0.0138913	+	0.0138913i
$629$		−	1027.80i		−	1.63402i
$630$		0			0
$631$	−633.834			−1.00449			−0.502246	−	0.864725i	$-0.667493\pi$
$631$	−633.834			−1.00449			−0.502246	+	0.864725i	$0.667493\pi$
$632$	−753.364	+	753.364i	−1.19203	+	1.19203i
$633$		0			0
$634$		−	559.945i		−	0.883194i
$635$	568.324	−	594.418i	0.894999	−	0.936091i
$636$		0			0
$637$	−114.969	+	114.969i	−0.180485	+	0.180485i
$638$	243.224	+	243.224i	0.381228	+	0.381228i
$639$		0			0
$640$	−453.831	−	433.909i	−0.709111	−	0.677983i
$641$	1051.56			1.64049			0.820247	−	0.572009i	$-0.193836\pi$
$641$	1051.56			1.64049			0.820247	+	0.572009i	$0.193836\pi$
$642$		0			0
$643$	−341.723	−	341.723i	−0.531451	−	0.531451i	0.389553	−	0.921004i	$-0.372629\pi$
$643$	−341.723	−	341.723i	−0.531451	−	0.531451i	−0.921004	+	0.389553i	$0.872629\pi$
$644$			0.200822i			0.000311836i
$645$		0			0
$646$	−1330.83			−2.06010
$647$	49.3114	−	49.3114i	0.0762155	−	0.0762155i	−0.667971	−	0.744187i	$-0.732837\pi$
$647$	49.3114	−	49.3114i	0.0762155	−	0.0762155i	0.744187	+	0.667971i	$0.232837\pi$
$648$		0			0
$649$			260.767i			0.401797i
$650$	−177.607	+	7.97549i	−0.273242	+	0.0122700i
$651$		0			0
$652$	−6.45127	+	6.45127i	−0.00989458	+	0.00989458i
$653$	186.993	+	186.993i	0.286360	+	0.286360i	0.835639	−	0.549279i	$-0.185098\pi$
$653$	186.993	+	186.993i	0.286360	+	0.286360i	−0.549279	+	0.835639i	$0.685098\pi$
$654$		0			0
$655$	−158.397	+	3.55464i	−0.241828	+	0.00542694i
$656$	−13.7150			−0.0209071
$657$		0			0
$658$	−27.0457	−	27.0457i	−0.0411028	−	0.0411028i
$659$			550.468i			0.835308i	0.908606	+	0.417654i	$0.137148\pi$
$659$			550.468i			0.835308i	−0.908606	+	0.417654i	$0.862852\pi$
$660$		0			0
$661$	393.621			0.595494			0.297747	−	0.954645i	$-0.403765\pi$
$661$	393.621			0.595494			0.297747	+	0.954645i	$0.403765\pi$
$662$	−323.436	+	323.436i	−0.488574	+	0.488574i
$663$		0			0
$664$		−	427.413i		−	0.643694i
$665$	164.419	+	157.201i	0.247247	+	0.236393i
$666$		0			0
$667$	79.5084	−	79.5084i	0.119203	−	0.119203i
$668$	10.1823	+	10.1823i	0.0152430	+	0.0152430i
$669$		0			0
$670$	−2.47724	−	110.387i	−0.00369737	−	0.164757i
$671$	−238.396			−0.355284
$672$		0			0
$673$	127.506	+	127.506i	0.189459	+	0.189459i	0.795462	−	0.606003i	$-0.207228\pi$
$673$	127.506	+	127.506i	0.189459	+	0.189459i	−0.606003	+	0.795462i	$0.707228\pi$
$674$		−	586.973i		−	0.870879i
$675$		0			0
$676$	7.71845			0.0114178
$677$	−812.543	+	812.543i	−1.20021	+	1.20021i	−0.226109	+	0.974102i	$0.572601\pi$
$677$	−812.543	+	812.543i	−1.20021	+	1.20021i	−0.974102	+	0.226109i	$0.927399\pi$
$678$		0			0
$679$			155.919i			0.229630i
$680$	−1116.69	+	25.0599i	−1.64219	+	0.0368528i
$681$		0			0
$682$	26.3934	−	26.3934i	0.0387000	−	0.0387000i
$683$	−286.806	−	286.806i	−0.419920	−	0.419920i	0.465256	−	0.885176i	$-0.345962\pi$
$683$	−286.806	−	286.806i	−0.419920	−	0.419920i	−0.885176	+	0.465256i	$0.845962\pi$
$684$		0			0
$685$	−153.909	+	160.976i	−0.224685	+	0.235001i
$686$	−354.019			−0.516062
$687$		0			0
$688$	873.696	+	873.696i	1.26991	+	1.26991i
$689$			175.633i			0.254910i
$690$		0			0
$691$	−828.622			−1.19916			−0.599582	−	0.800313i	$-0.704666\pi$
$691$	−828.622			−1.19916			−0.599582	+	0.800313i	$0.704666\pi$
$692$	4.40653	−	4.40653i	0.00636782	−	0.00636782i
$693$		0			0
$694$		−	825.571i		−	1.18958i
$695$	−15.7408	−	701.421i	−0.0226487	−	1.00924i
$696$		0			0
$697$	−17.0363	+	17.0363i	−0.0244423	+	0.0244423i
$698$	68.8715	+	68.8715i	0.0986698	+	0.0986698i
$699$		0			0
$700$	1.71966	+	1.57185i	0.00245665	+	0.00224550i
$701$	−377.097			−0.537942			−0.268971	−	0.963148i	$-0.586684\pi$
$701$	−377.097			−0.537942			−0.268971	+	0.963148i	$0.586684\pi$
$702$		0			0
$703$	631.668	+	631.668i	0.898532	+	0.898532i
$704$			214.821i			0.305143i
$705$		0			0
$706$	140.238			0.198638
$707$	−157.220	+	157.220i	−0.222376	+	0.222376i
$708$		0			0
$709$		−	701.021i		−	0.988746i	−0.869250	−	0.494373i	$-0.835398\pi$
$709$		−	701.021i		−	0.988746i	0.869250	−	0.494373i	$-0.164602\pi$
$710$	−516.957	+	540.693i	−0.728109	+	0.761539i
$711$		0			0
$712$	555.073	−	555.073i	0.779597	−	0.779597i
$713$	−8.62785	−	8.62785i	−0.0121008	−	0.0121008i
$714$		0			0
$715$	42.8852	+	41.0026i	0.0599793	+	0.0573463i
$716$	−0.347825			−0.000485789
$717$		0			0
$718$	465.449	+	465.449i	0.648258	+	0.648258i
$719$			856.257i			1.19090i	0.803393	+	0.595450i	$0.203026\pi$
$719$			856.257i			1.19090i	−0.803393	+	0.595450i	$0.796974\pi$
$720$		0			0
$721$	54.2024			0.0751766
$722$	310.537	−	310.537i	0.430107	−	0.430107i
$723$		0			0
$724$		−	11.8501i		−	0.0163676i
$725$	−58.5185	−	1303.16i	−0.0807152	−	1.79746i
$726$		0			0
$727$	76.4618	−	76.4618i	0.105174	−	0.105174i	−0.652561	−	0.757736i	$-0.726306\pi$
$727$	76.4618	−	76.4618i	0.105174	−	0.105174i	0.757736	+	0.652561i	$0.226306\pi$
$728$	−38.4024	−	38.4024i	−0.0527506	−	0.0527506i
$729$		0			0
$730$	−162.249	+	3.64109i	−0.222259	+	0.00498779i
$731$	2170.54			2.96928
$732$		0			0
$733$	−289.170	−	289.170i	−0.394502	−	0.394502i	0.481786	−	0.876289i	$-0.339988\pi$
$733$	−289.170	−	289.170i	−0.394502	−	0.394502i	−0.876289	+	0.481786i	$0.839988\pi$
$734$		−	1274.72i		−	1.73667i
$735$		0			0
$736$	1.70366			0.00231475
$737$	−26.0561	+	26.0561i	−0.0353543	+	0.0353543i
$738$		0			0
$739$			1351.93i			1.82940i	0.404133	+	0.914700i	$0.367573\pi$
$739$			1351.93i			1.82940i	−0.404133	+	0.914700i	$0.632427\pi$
$740$	6.61298	+	6.32269i	0.00893646	+	0.00854417i
$741$		0			0
$742$	−130.113	+	130.113i	−0.175354	+	0.175354i
$743$	141.927	+	141.927i	0.191018	+	0.191018i	0.796136	−	0.605118i	$-0.206874\pi$
$743$	141.927	+	141.927i	0.191018	+	0.191018i	−0.605118	+	0.796136i	$0.706874\pi$
$744$		0			0
$745$	4.07315	+	181.502i	0.00546732	+	0.243627i
$746$	187.071			0.250765
$747$		0			0
$748$	3.21648	+	3.21648i	0.00430011	+	0.00430011i
$749$		−	148.337i		−	0.198047i
$750$		0			0
$751$	−1058.20			−1.40906			−0.704530	−	0.709674i	$-0.748842\pi$
$751$	−1058.20			−1.40906			−0.704530	+	0.709674i	$0.748842\pi$
$752$	−113.998	+	113.998i	−0.151593	+	0.151593i
$753$		0			0
$754$			371.066i			0.492130i
$755$	−341.860	+	7.67179i	−0.452795	+	0.0101613i
$756$		0			0
$757$	643.998	−	643.998i	0.850725	−	0.850725i	−0.139498	−	0.990222i	$-0.544549\pi$
$757$	643.998	−	643.998i	0.850725	−	0.850725i	0.990222	+	0.139498i	$0.0445488\pi$
$758$	−199.234	−	199.234i	−0.262841	−	0.262841i
$759$		0			0
$760$	670.896	−	701.699i	0.882758	−	0.923288i
$761$	895.219			1.17637			0.588186	−	0.808726i	$-0.299842\pi$
$761$	895.219			1.17637			0.588186	+	0.808726i	$0.299842\pi$
$762$		0			0
$763$	149.100	+	149.100i	0.195413	+	0.195413i
$764$		−	12.1299i		−	0.0158769i
$765$		0			0
$766$	1057.92			1.38110
$767$	−198.915	+	198.915i	−0.259341	+	0.259341i
$768$		0			0
$769$		−	684.424i		−	0.890019i	−0.895526	−	0.445009i	$-0.853200\pi$
$769$		−	684.424i		−	0.890019i	0.895526	−	0.445009i	$-0.146800\pi$
$770$	1.39463	+	62.1458i	0.00181121	+	0.0807089i
$771$		0			0
$772$	4.34819	−	4.34819i	0.00563237	−	0.00563237i
$773$	−362.906	−	362.906i	−0.469477	−	0.469477i	0.432268	−	0.901745i	$-0.357713\pi$
$773$	−362.906	−	362.906i	−0.469477	−	0.469477i	−0.901745	+	0.432268i	$0.857713\pi$
$774$		0			0
$775$	−141.412	+	6.35013i	−0.182467	+	0.00819372i
$776$	665.423			0.857504
$777$		0			0
$778$	−882.904	−	882.904i	−1.13484	−	1.13484i
$779$		−	20.9405i		−	0.0268812i
$780$		0			0
$781$	249.650			0.319655
$782$	−84.0616	+	84.0616i	−0.107496	+	0.107496i
$783$		0			0
$784$			717.999i			0.915816i
$785$	862.684	−	902.292i	1.09896	−	1.14942i
$786$		0			0
$787$	−606.535	+	606.535i	−0.770692	+	0.770692i	−0.978227	−	0.207535i	$-0.933456\pi$
$787$	−606.535	+	606.535i	−0.770692	+	0.770692i	0.207535	+	0.978227i	$0.433456\pi$
$788$	4.47025	+	4.47025i	0.00567291	+	0.00567291i
$789$		0			0
$790$	950.849	+	909.109i	1.20361	+	1.15077i
$791$	−290.680			−0.367484
$792$		0			0
$793$	−181.850	−	181.850i	−0.229319	−	0.229319i
$794$			501.955i			0.632185i
$795$		0			0
$796$	−13.9633			−0.0175418
$797$	−408.289	+	408.289i	−0.512283	+	0.512283i	−0.915225	−	0.402943i	$-0.867987\pi$
$797$	−408.289	+	408.289i	−0.512283	+	0.512283i	0.402943	+	0.915225i	$0.367987\pi$
$798$		0			0
$799$			283.208i			0.354453i
$800$	13.3347	−	14.5886i	0.0166683	−	0.0182357i
$801$		0			0
$802$	−420.211	+	420.211i	−0.523954	+	0.523954i
$803$	38.2977	+	38.2977i	0.0476933	+	0.0476933i
$804$		0			0
$805$	20.3151	−	0.455898i	0.0252362	−	0.000566333i
$806$	40.2662			0.0499580
$807$		0			0
$808$	670.974	+	670.974i	0.830413	+	0.830413i
$809$		−	755.271i		−	0.933586i	−0.884367	−	0.466793i	$-0.845409\pi$
$809$		−	755.271i		−	0.933586i	0.884367	−	0.466793i	$-0.154591\pi$
$810$		0			0
$811$	832.082			1.02600			0.512998	−	0.858390i	$-0.328535\pi$
$811$	832.082			1.02600			0.512998	+	0.858390i	$0.328535\pi$
$812$	3.43839	−	3.43839i	0.00423447	−	0.00423447i
$813$		0			0
$814$			244.111i			0.299891i
$815$	667.254	+	637.963i	0.818717	+	0.782777i
$816$		0			0
$817$	−1333.98	+	1333.98i	−1.63278	+	1.63278i
$818$	905.325	+	905.325i	1.10675	+	1.10675i
$819$		0			0
$820$	−0.00481177	−	0.214416i	−5.86801e−6	−	0.000261482i
$821$	−342.502			−0.417177			−0.208589	−	0.978003i	$-0.566887\pi$
$821$	−342.502			−0.417177			−0.208589	+	0.978003i	$0.566887\pi$
$822$		0			0
$823$	995.836	+	995.836i	1.21001	+	1.21001i	0.971024	+	0.238983i	$0.0768142\pi$
$823$	995.836	+	995.836i	1.21001	+	1.21001i	0.238983	+	0.971024i	$0.423186\pi$
$824$		−	231.322i		−	0.280731i
$825$		0			0
$826$	−294.721			−0.356805
$827$	−105.216	+	105.216i	−0.127226	+	0.127226i	−0.767853	−	0.640627i	$-0.778675\pi$
$827$	−105.216	+	105.216i	−0.127226	+	0.127226i	0.640627	+	0.767853i	$0.278675\pi$
$828$		0			0
$829$			859.801i			1.03715i	0.855031	+	0.518577i	$0.173538\pi$
$829$			859.801i			1.03715i	−0.855031	+	0.518577i	$0.826462\pi$
$830$	−527.614	+	11.8403i	−0.635679	+	0.0142655i
$831$		0			0
$832$	−163.867	+	163.867i	−0.196956	+	0.196956i
$833$	891.871	+	891.871i	1.07067	+	1.07067i
$834$		0			0
$835$	1006.92	−	1053.15i	1.20590	−	1.26126i
$836$	−3.95360			−0.00472919
$837$		0			0
$838$	−146.491	−	146.491i	−0.174810	−	0.174810i
$839$			43.7687i			0.0521677i	0.999660	+	0.0260838i	$0.00830369\pi$
$839$			43.7687i			0.0521677i	−0.999660	+	0.0260838i	$0.991696\pi$
$840$		0			0
$841$	−1881.62			−2.23736
$842$	235.369	−	235.369i	0.279536	−	0.279536i
$843$		0			0
$844$			11.8095i			0.0139922i
$845$	−17.5221	−	780.797i	−0.0207362	−	0.924020i
$846$		0			0
$847$	14.6690	−	14.6690i	0.0173188	−	0.0173188i
$848$	548.427	+	548.427i	0.646730	+	0.646730i
$849$		0			0
$850$	61.8697	+	1377.78i	0.0727879	+	1.62092i
$851$	79.7986			0.0937704
$852$		0			0
$853$	493.411	+	493.411i	0.578442	+	0.578442i	0.934474	−	0.356032i	$-0.115870\pi$
$853$	493.411	+	493.411i	0.578442	+	0.578442i	−0.356032	+	0.934474i	$0.615870\pi$
$854$		−	269.437i		−	0.315500i
$855$		0			0
$856$	−633.065			−0.739562
$857$	496.151	−	496.151i	0.578939	−	0.578939i	−0.355672	−	0.934611i	$-0.615748\pi$
$857$	496.151	−	496.151i	0.578939	−	0.578939i	0.934611	+	0.355672i	$0.115748\pi$
$858$		0			0
$859$		−	420.510i		−	0.489535i	−0.969582	−	0.244767i	$-0.921288\pi$
$859$		−	420.510i		−	0.489535i	0.969582	−	0.244767i	$-0.0787116\pi$
$860$	−13.3525	+	13.9655i	−0.0155262	+	0.0162390i
$861$		0			0
$862$	172.823	−	172.823i	0.200490	−	0.200490i
$863$	−857.573	−	857.573i	−0.993711	−	0.993711i	0.00626898	−	0.999980i	$-0.498005\pi$
$863$	−857.573	−	857.573i	−0.993711	−	0.993711i	−0.999980	+	0.00626898i	$0.998005\pi$
$864$		0			0
$865$	−455.768	−	435.761i	−0.526899	−	0.503769i
$866$	83.9615			0.0969532
$867$		0			0
$868$	−0.373117	−	0.373117i	−0.000429858	−	0.000429858i
$869$		−	439.029i		−	0.505212i
$870$		0			0
$871$	−39.7516			−0.0456391
$872$	636.323	−	636.323i	0.729728	−	0.729728i
$873$		0			0
$874$		−	103.326i		−	0.118222i
$875$	155.104	−	177.528i	0.177262	−	0.202890i
$876$		0			0
$877$	530.997	−	530.997i	0.605470	−	0.605470i	−0.336289	−	0.941759i	$-0.609172\pi$
$877$	530.997	−	530.997i	0.605470	−	0.605470i	0.941759	+	0.336289i	$0.109172\pi$
$878$	79.0316	+	79.0316i	0.0900132	+	0.0900132i
$879$		0			0
$880$	261.946	−	5.87841i	0.297666	−	0.00668001i
$881$	−353.287			−0.401007			−0.200504	−	0.979693i	$-0.564258\pi$
$881$	−353.287			−0.401007			−0.200504	+	0.979693i	$0.564258\pi$
$882$		0			0
$883$	815.306	+	815.306i	0.923336	+	0.923336i	0.997264	−	0.0739272i	$-0.0235533\pi$
$883$	815.306	+	815.306i	0.923336	+	0.923336i	−0.0739272	+	0.997264i	$0.523553\pi$
$884$			4.90712i			0.00555104i
$885$		0			0
$886$	1027.99			1.16026
$887$	−49.0535	+	49.0535i	−0.0553027	+	0.0553027i	−0.734217	−	0.678915i	$-0.762451\pi$
$887$	−49.0535	+	49.0535i	−0.0553027	+	0.0553027i	0.678915	+	0.734217i	$0.262451\pi$
$888$		0			0
$889$		−	310.193i		−	0.348923i
$890$	−700.579	−	669.825i	−0.787167	−	0.752613i
$891$		0			0
$892$	11.8024	−	11.8024i	0.0132314	−	0.0132314i
$893$	−174.055	−	174.055i	−0.194910	−	0.194910i
$894$		0			0
$895$	0.789619	+	35.1859i	0.000882255	+	0.0393139i
$896$	−236.829			−0.264318
$897$		0			0
$898$	978.573	+	978.573i	1.08973	+	1.08973i
$899$			295.445i			0.328637i
$900$		0			0
$901$	1362.47			1.51218
$902$	4.04627	−	4.04627i	0.00448589	−	0.00448589i
$903$		0			0
$904$			1240.55i			1.37229i
$905$	−1198.76	+	26.9017i	−1.32459	+	0.0297256i
$906$		0			0
$907$	1237.12	−	1237.12i	1.36396	−	1.36396i	0.495167	−	0.868798i	$-0.335107\pi$
$907$	1237.12	−	1237.12i	1.36396	−	1.36396i	0.868798	−	0.495167i	$-0.164893\pi$
$908$	−1.22088	−	1.22088i	−0.00134458	−	0.00134458i
$909$		0			0
$910$	−46.3415	+	48.4692i	−0.0509247	+	0.0532628i
$911$	−318.606			−0.349732			−0.174866	−	0.984592i	$-0.555949\pi$
$911$	−318.606			−0.349732			−0.174866	+	0.984592i	$0.555949\pi$
$912$		0			0
$913$	124.539	+	124.539i	0.136407	+	0.136407i
$914$		−	1524.91i		−	1.66839i
$915$		0			0
$916$	2.71281			0.00296158
$917$	−42.2568	+	42.2568i	−0.0460815	+	0.0460815i
$918$		0			0
$919$			902.066i			0.981573i	0.871280	+	0.490787i	$0.163291\pi$
$919$			902.066i			0.981573i	−0.871280	+	0.490787i	$0.836709\pi$
$920$	−1.94566	−	86.6999i	−0.00211485	−	0.0942390i
$921$		0			0
$922$	1054.18	−	1054.18i	1.14336	−	1.14336i
$923$	190.435	+	190.435i	0.206322	+	0.206322i
$924$		0			0
$925$	624.589	−	683.321i	0.675232	−	0.738726i
$926$	−1311.26			−1.41604
$927$		0			0
$928$	−29.1693	−	29.1693i	−0.0314325	−	0.0314325i
$929$		−	1607.96i		−	1.73085i	−0.501039	−	0.865425i	$-0.667049\pi$
$929$		−	1607.96i		−	1.73085i	0.501039	−	0.865425i	$-0.332951\pi$
$930$		0			0
$931$	−1096.26			−1.17751
$932$	14.3780	−	14.3780i	0.0154270	−	0.0154270i
$933$		0			0
$934$			436.329i			0.467162i
$935$	318.077	−	332.681i	0.340189	−	0.355808i
$936$		0			0
$937$	−1230.00	+	1230.00i	−1.31270	+	1.31270i	−0.393289	+	0.919415i	$0.628663\pi$
$937$	−1230.00	+	1230.00i	−1.31270	+	1.31270i	−0.919415	+	0.393289i	$0.871337\pi$
$938$	−29.4488	−	29.4488i	−0.0313954	−	0.0313954i
$939$		0			0
$940$	−1.82219	−	1.74220i	−0.00193850	−	0.00185341i
$941$	1176.40			1.25016			0.625078	−	0.780562i	$-0.285067\pi$
$941$	1176.40			1.25016			0.625078	+	0.780562i	$0.285067\pi$
$942$		0			0
$943$	−1.32270	−	1.32270i	−0.00140266	−	0.00140266i
$944$			1242.25i			1.31595i
$945$		0			0
$946$	−515.523			−0.544951
$947$	−899.613	+	899.613i	−0.949961	+	0.949961i	−0.998806	−	0.0488452i	$-0.984446\pi$
$947$	−899.613	+	899.613i	−0.949961	+	0.949961i	0.0488452	+	0.998806i	$0.484446\pi$
$948$		0			0
$949$			58.4276i			0.0615675i
$950$	−884.787	−	808.739i	−0.931355	−	0.851304i
$951$		0			0
$952$	−297.906	+	297.906i	−0.312927	+	0.312927i
$953$	−660.652	−	660.652i	−0.693234	−	0.693234i	0.269708	−	0.962942i	$-0.413073\pi$
$953$	−660.652	−	660.652i	−0.693234	−	0.693234i	−0.962942	+	0.269708i	$0.913073\pi$
$954$		0			0
$955$	−1227.06	+	27.5369i	−1.28488	+	0.0288344i
$956$	−12.8618			−0.0134537
$957$		0			0
$958$	−141.828	−	141.828i	−0.148046	−	0.148046i
$959$			84.0041i			0.0875955i
$960$		0			0
$961$	−928.940			−0.966639
$962$	−186.210	+	186.210i	−0.193565	+	0.193565i
$963$		0			0
$964$		−	2.37587i		−	0.00246460i
$965$	−449.733	−	429.991i	−0.466045	−	0.445587i
$966$		0			0
$967$	−702.503	+	702.503i	−0.726476	+	0.726476i	−0.969916	−	0.243440i	$-0.921724\pi$
$967$	−702.503	+	702.503i	−0.726476	+	0.726476i	0.243440	+	0.969916i	$0.421724\pi$
$968$	−62.6038	−	62.6038i	−0.0646733	−	0.0646733i
$969$		0			0
$970$	−18.4338	−	821.422i	−0.0190039	−	0.846827i
$971$	323.426			0.333086			0.166543	−	0.986034i	$-0.446740\pi$
$971$	323.426			0.333086			0.166543	+	0.986034i	$0.446740\pi$
$972$		0			0
$973$	−187.123	−	187.123i	−0.192316	−	0.192316i
$974$			319.793i			0.328329i
$975$		0			0
$976$	−1135.68			−1.16361
$977$	−80.1080	+	80.1080i	−0.0819939	+	0.0819939i	−0.746914	−	0.664920i	$-0.768465\pi$
$977$	−80.1080	+	80.1080i	−0.0819939	+	0.0819939i	0.664920	+	0.746914i	$0.268465\pi$
$978$		0			0
$979$			323.473i			0.330412i
$980$	−11.2249	+	0.251902i	−0.0114540	+	0.000257043i
$981$		0			0
$982$	1029.39	−	1029.39i	1.04826	−	1.04826i
$983$	399.699	+	399.699i	0.406612	+	0.406612i	0.880555	−	0.473943i	$-0.157170\pi$
$983$	399.699	+	399.699i	0.406612	+	0.406612i	−0.473943	+	0.880555i	$0.657170\pi$
$984$		0			0
$985$	442.062	−	462.358i	0.448793	−	0.469399i
$986$	2878.54			2.91941
$987$		0			0
$988$	−3.01584	−	3.01584i	−0.00305247	−	0.00305247i
$989$			168.522i			0.170396i
$990$		0			0
$991$	1426.48			1.43943			0.719716	−	0.694268i	$-0.244272\pi$
$991$	1426.48			1.43943			0.719716	+	0.694268i	$0.244272\pi$
$992$	−3.16531	+	3.16531i	−0.00319083	+	0.00319083i
$993$		0			0
$994$			282.157i			0.283860i
$995$	31.6989	+	1412.52i	0.0318582	+	1.41962i
$996$		0			0
$997$	968.762	−	968.762i	0.971677	−	0.971677i	−0.0279332	−	0.999610i	$-0.508893\pi$
$997$	968.762	−	968.762i	0.971677	−	0.971677i	0.999610	+	0.0279332i	$0.00889256\pi$
$998$	740.391	+	740.391i	0.741875	+	0.741875i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.c.298.6	✓	40
3.2	odd	2	inner	495.3.j.c.298.15	yes	40
5.2	odd	4	inner	495.3.j.c.397.6	yes	40
15.2	even	4	inner	495.3.j.c.397.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.3.j.c.298.6	✓	40	1.1	even	1	trivial
495.3.j.c.298.15	yes	40	3.2	odd	2	inner
495.3.j.c.397.6	yes	40	5.2	odd	4	inner
495.3.j.c.397.15	yes	40	15.2	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40545 + 1.40545i) q^{2} +0.0494143i q^{4} +(4.99874 - 0.112178i) q^{5} +(1.33355 - 1.33355i) q^{7} +(-5.69125 - 5.69125i) q^{8} +(-6.86783 + 7.18315i) q^{10} +3.31662 q^{11} +(2.52995 + 2.52995i) q^{13} +3.74848i q^{14} +15.7999 q^{16} +(19.6260 - 19.6260i) q^{17} +24.1237i q^{19} +(0.00554322 + 0.247009i) q^{20} +(-4.66135 + 4.66135i) q^{22} +(1.52377 + 1.52377i) q^{23} +(24.9748 - 1.12150i) q^{25} -7.11144 q^{26} +(0.0658964 + 0.0658964i) q^{28} -52.1787i q^{29} -5.66217 q^{31} +(0.559027 - 0.559027i) q^{32} +55.1668i q^{34} +(6.51647 - 6.81567i) q^{35} +(26.1846 - 26.1846i) q^{37} +(-33.9047 - 33.9047i) q^{38} +(-29.0875 - 27.8107i) q^{40} -0.868046 q^{41} +(55.2976 + 55.2976i) q^{43} +0.163889i q^{44} -4.28317 q^{46} +(-7.21510 + 7.21510i) q^{47} +45.4433i q^{49} +(-33.5247 + 36.6771i) q^{50} +(-0.125016 + 0.125016i) q^{52} +(34.7108 + 34.7108i) q^{53} +(16.5789 - 0.372054i) q^{55} -15.1791 q^{56} +(73.3347 + 73.3347i) q^{58} +78.6241i q^{59} -71.8790 q^{61} +(7.95790 - 7.95790i) q^{62} +64.7710i q^{64} +(12.9304 + 12.3628i) q^{65} +(-7.85622 + 7.85622i) q^{67} +(0.969807 + 0.969807i) q^{68} +(0.420498 + 18.7377i) q^{70} +75.2724 q^{71} +(11.5472 + 11.5472i) q^{73} +73.6023i q^{74} -1.19206 q^{76} +(4.42288 - 4.42288i) q^{77} -132.372i q^{79} +(78.9796 - 1.77241i) q^{80} +(1.22000 - 1.22000i) q^{82} +(37.5500 + 37.5500i) q^{83} +(95.9038 - 100.307i) q^{85} -155.436 q^{86} +(-18.8758 - 18.8758i) q^{88} +97.5309i q^{89} +6.74762 q^{91} +(-0.0752961 + 0.0752961i) q^{92} -20.2810i q^{94} +(2.70616 + 120.588i) q^{95} +(-58.4602 + 58.4602i) q^{97} +(-63.8683 - 63.8683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) \) 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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