LMFDB - Embedded newform 380.2.y.b.373.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(217,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("380.217");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.y (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.9
Character	$\chi$	$=$	380.373
Dual form			380.2.y.b.217.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.09534 + 0.829395i) q^{3} +(1.17655 - 1.90150i) q^{5} +(0.137224 - 0.137224i) q^{7} +(6.29517 + 3.63452i) q^{9} +O(q^{10})$	\(q+(3.09534 + 0.829395i) q^{3} +(1.17655 - 1.90150i) q^{5} +(0.137224 - 0.137224i) q^{7} +(6.29517 + 3.63452i) q^{9} -5.43860 q^{11} +(0.695043 + 2.59394i) q^{13} +(5.21894 - 4.90998i) q^{15} +(-4.69368 - 1.25767i) q^{17} +(-1.07234 - 4.22494i) q^{19} +(0.538567 - 0.310942i) q^{21} +(3.03445 - 0.813079i) q^{23} +(-2.23144 - 4.47445i) q^{25} +(9.67343 + 9.67343i) q^{27} +(-4.80457 + 8.32175i) q^{29} -0.448018i q^{31} +(-16.8343 - 4.51074i) q^{33} +(-0.0994805 - 0.422383i) q^{35} +(4.78673 + 4.78673i) q^{37} +8.60559i q^{39} +(-2.57531 + 1.48686i) q^{41} +(0.798608 - 2.98045i) q^{43} +(14.3177 - 7.69409i) q^{45} +(-1.29577 - 4.83587i) q^{47} +6.96234i q^{49} +(-13.4854 - 7.78582i) q^{51} +(1.18983 + 4.44051i) q^{53} +(-6.39880 + 10.3415i) q^{55} +(0.184873 - 13.9670i) q^{57} +(1.38677 + 2.40196i) q^{59} +(5.58710 - 9.67713i) q^{61} +(1.36259 - 0.365105i) q^{63} +(5.75014 + 1.73028i) q^{65} +(-2.96306 + 0.793949i) q^{67} +10.0670 q^{69} +(10.2220 - 5.90170i) q^{71} +(-0.500400 + 1.86752i) q^{73} +(-3.19599 - 15.7007i) q^{75} +(-0.746305 + 0.746305i) q^{77} +(-1.88680 - 3.26803i) q^{79} +(11.0159 + 19.0801i) q^{81} +(-10.6496 - 10.6496i) q^{83} +(-7.91383 + 7.44534i) q^{85} +(-21.7738 + 21.7738i) q^{87} +(2.07573 - 3.59527i) q^{89} +(0.451326 + 0.260573i) q^{91} +(0.371583 - 1.38677i) q^{93} +(-9.29540 - 2.93180i) q^{95} +(2.00868 - 7.49651i) q^{97} +(-34.2369 - 19.7667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{3} - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 36 * q - 6 * q^3 - 4 * q^5 + 4 * q^7	$ 36 q - 6 q^{3} - 4 q^{5} + 4 q^{7} - 12 q^{11} - 6 q^{13} - 12 q^{15} + 6 q^{17} + 48 q^{21} + 16 q^{23} + 4 q^{25} - 54 q^{33} + 16 q^{35} - 2 q^{43} + 100 q^{45} + 24 q^{47} - 108 q^{51} + 14 q^{55} - 30 q^{57} + 34 q^{61} - 26 q^{63} - 78 q^{67} - 42 q^{71} + 16 q^{73} - 20 q^{77} + 14 q^{81} - 28 q^{83} + 10 q^{85} - 124 q^{87} + 96 q^{91} - 26 q^{93} - 32 q^{95} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^3 - 4 * q^5 + 4 * q^7 - 12 * q^11 - 6 * q^13 - 12 * q^15 + 6 * q^17 + 48 * q^21 + 16 * q^23 + 4 * q^25 - 54 * q^33 + 16 * q^35 - 2 * q^43 + 100 * q^45 + 24 * q^47 - 108 * q^51 + 14 * q^55 - 30 * q^57 + 34 * q^61 - 26 * q^63 - 78 * q^67 - 42 * q^71 + 16 * q^73 - 20 * q^77 + 14 * q^81 - 28 * q^83 + 10 * q^85 - 124 * q^87 + 96 * q^91 - 26 * q^93 - 32 * q^95 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.09534	+	0.829395i	1.78710	+	0.478851i	0.991847	−	0.127431i	$-0.0406732\pi$
$3$	3.09534	+	0.829395i	1.78710	+	0.478851i	0.795249	+	0.606282i	$0.207340\pi$
$4$		0			0
$5$	1.17655	−	1.90150i	0.526171	−	0.850379i
$5$	1.17655	−	1.90150i	0.526171	−	0.850379i
$6$		0			0
$7$	0.137224	−	0.137224i	0.0518657	−	0.0518657i	−0.680698	−	0.732564i	$-0.738323\pi$
$7$	0.137224	−	0.137224i	0.0518657	−	0.0518657i	0.732564	+	0.680698i	$0.238323\pi$
$8$		0			0
$9$	6.29517	+	3.63452i	2.09839	+	1.21151i
$10$		0			0
$11$	−5.43860			−1.63980			−0.819899	−	0.572508i	$-0.805971\pi$
$11$	−5.43860			−1.63980			−0.819899	+	0.572508i	$0.805971\pi$
$12$		0			0
$13$	0.695043	+	2.59394i	0.192770	+	0.719429i	0.992833	+	0.119512i	$0.0381330\pi$
$13$	0.695043	+	2.59394i	0.192770	+	0.719429i	−0.800062	+	0.599917i	$0.795200\pi$
$14$		0			0
$15$	5.21894	−	4.90998i	1.34752	−	1.26775i
$16$		0			0
$17$	−4.69368	−	1.25767i	−1.13838	−	0.305029i	−0.360083	−	0.932920i	$-0.617252\pi$
$17$	−4.69368	−	1.25767i	−1.13838	−	0.305029i	−0.778301	+	0.627891i	$0.783918\pi$
$18$		0			0
$19$	−1.07234	−	4.22494i	−0.246012	−	0.969267i
$19$	−1.07234	−	4.22494i	−0.246012	−	0.969267i
$20$		0			0
$21$	0.538567	−	0.310942i	0.117525	−	0.0678531i
$22$		0			0
$23$	3.03445	−	0.813079i	0.632727	−	0.169539i	0.0718201	−	0.997418i	$-0.477119\pi$
$23$	3.03445	−	0.813079i	0.632727	−	0.169539i	0.560907	+	0.827879i	$0.310453\pi$
$24$		0			0
$25$	−2.23144	−	4.47445i	−0.446288	−	0.894889i
$26$		0			0
$27$	9.67343	+	9.67343i	1.86165	+	1.86165i
$28$		0			0
$29$	−4.80457	+	8.32175i	−0.892186	+	1.54531i	−0.0549362	+	0.998490i	$0.517496\pi$
$29$	−4.80457	+	8.32175i	−0.892186	+	1.54531i	−0.837249	+	0.546821i	$0.815838\pi$
$30$		0			0
$31$		−	0.448018i		−	0.0804664i	−0.999190	−	0.0402332i	$-0.987190\pi$
$31$		−	0.448018i		−	0.0804664i	0.999190	−	0.0402332i	$-0.0128101\pi$
$32$		0			0
$33$	−16.8343	−	4.51074i	−2.93048	−	0.785220i
$34$		0			0
$35$	−0.0994805	−	0.422383i	−0.0168153	−	0.0713957i
$36$		0			0
$37$	4.78673	+	4.78673i	0.786933	+	0.786933i	0.980990	−	0.194057i	$-0.0621648\pi$
$37$	4.78673	+	4.78673i	0.786933	+	0.786933i	−0.194057	+	0.980990i	$0.562165\pi$
$38$		0			0
$39$			8.60559i			1.37800i
$40$		0			0
$41$	−2.57531	+	1.48686i	−0.402196	+	0.232208i	−0.687431	−	0.726250i	$-0.741262\pi$
$41$	−2.57531	+	1.48686i	−0.402196	+	0.232208i	0.285235	+	0.958458i	$0.407928\pi$
$42$		0			0
$43$	0.798608	−	2.98045i	0.121787	−	0.454514i	−0.877918	−	0.478811i	$-0.841068\pi$
$43$	0.798608	−	2.98045i	0.121787	−	0.454514i	0.999705	+	0.0242968i	$0.00773467\pi$
$44$		0			0
$45$	14.3177	−	7.69409i	2.13435	−	1.14697i
$46$		0			0
$47$	−1.29577	−	4.83587i	−0.189007	−	0.705384i	−0.993737	−	0.111743i	$-0.964357\pi$
$47$	−1.29577	−	4.83587i	−0.189007	−	0.705384i	0.804730	−	0.593641i	$-0.202310\pi$
$48$		0			0
$49$			6.96234i			0.994620i
$50$		0			0
$51$	−13.4854	−	7.78582i	−1.88834	−	1.09023i
$52$		0			0
$53$	1.18983	+	4.44051i	0.163436	+	0.609950i	0.998235	+	0.0593952i	$0.0189172\pi$
$53$	1.18983	+	4.44051i	0.163436	+	0.609950i	−0.834799	+	0.550555i	$0.814416\pi$
$54$		0			0
$55$	−6.39880	+	10.3415i	−0.862814	+	1.39445i
$56$		0			0
$57$	0.184873	−	13.9670i	0.0244870	−	1.84998i
$58$		0			0
$59$	1.38677	+	2.40196i	0.180543	+	0.312709i	0.942065	−	0.335429i	$-0.108881\pi$
$59$	1.38677	+	2.40196i	0.180543	+	0.312709i	−0.761523	+	0.648138i	$0.775548\pi$
$60$		0			0
$61$	5.58710	−	9.67713i	0.715354	−	1.23903i	−0.247468	−	0.968896i	$-0.579599\pi$
$61$	5.58710	−	9.67713i	0.715354	−	1.23903i	0.962823	−	0.270134i	$-0.0870680\pi$
$62$		0			0
$63$	1.36259	−	0.365105i	0.171670	−	0.0459989i
$64$		0			0
$65$	5.75014	+	1.73028i	0.713217	+	0.214615i
$66$		0			0
$67$	−2.96306	+	0.793949i	−0.361995	+	0.0969963i	−0.435232	−	0.900318i	$-0.643334\pi$
$67$	−2.96306	+	0.793949i	−0.361995	+	0.0969963i	0.0732371	+	0.997315i	$0.476667\pi$
$68$		0			0
$69$	10.0670			1.21193
$70$		0			0
$71$	10.2220	−	5.90170i	1.21313	−	0.700403i	0.249692	−	0.968325i	$-0.419670\pi$
$71$	10.2220	−	5.90170i	1.21313	−	0.700403i	0.963440	+	0.267923i	$0.0863372\pi$
$72$		0			0
$73$	−0.500400	+	1.86752i	−0.0585673	+	0.218576i	−0.989007	−	0.147869i	$-0.952759\pi$
$73$	−0.500400	+	1.86752i	−0.0585673	+	0.218576i	0.930440	+	0.366445i	$0.119425\pi$
$74$		0			0
$75$	−3.19599	−	15.7007i	−0.369042	−	1.81296i
$76$		0			0
$77$	−0.746305	+	0.746305i	−0.0850493	+	0.0850493i
$78$		0			0
$79$	−1.88680	−	3.26803i	−0.212281	−	0.367682i	0.740147	−	0.672445i	$-0.234756\pi$
$79$	−1.88680	−	3.26803i	−0.212281	−	0.367682i	−0.952428	+	0.304763i	$0.901423\pi$
$80$		0			0
$81$	11.0159	+	19.0801i	1.22399	+	2.12001i
$82$		0			0
$83$	−10.6496	−	10.6496i	−1.16894	−	1.16894i	−0.982458	−	0.186485i	$-0.940290\pi$
$83$	−10.6496	−	10.6496i	−1.16894	−	1.16894i	−0.186485	−	0.982458i	$-0.559710\pi$
$84$		0			0
$85$	−7.91383	+	7.44534i	−0.858375	+	0.807561i
$86$		0			0
$87$	−21.7738	+	21.7738i	−2.33440	+	2.33440i
$88$		0			0
$89$	2.07573	−	3.59527i	0.220027	−	0.381098i	−0.734789	−	0.678296i	$-0.762719\pi$
$89$	2.07573	−	3.59527i	0.220027	−	0.381098i	0.954816	+	0.297198i	$0.0960522\pi$
$90$		0			0
$91$	0.451326	+	0.260573i	0.0473118	+	0.0273155i
$92$		0			0
$93$	0.371583	−	1.38677i	0.0385314	−	0.143801i
$94$		0			0
$95$	−9.29540	−	2.93180i	−0.953688	−	0.300796i
$96$		0			0
$97$	2.00868	−	7.49651i	0.203951	−	0.761155i	−0.785816	−	0.618460i	$-0.787757\pi$
$97$	2.00868	−	7.49651i	0.203951	−	0.761155i	0.989767	−	0.142695i	$-0.0455767\pi$
$98$		0			0
$99$	−34.2369	−	19.7667i	−3.44094	−	1.98663i
$100$		0			0
$101$	−0.547865	+	0.948930i	−0.0545146	+	0.0944221i	−0.891995	−	0.452045i	$-0.850694\pi$
$101$	−0.547865	+	0.948930i	−0.0545146	+	0.0944221i	0.837480	+	0.546468i	$0.184028\pi$
$102$		0			0
$103$	−3.72076	+	3.72076i	−0.366617	+	0.366617i	−0.866242	−	0.499625i	$-0.833471\pi$
$103$	−3.72076	+	3.72076i	−0.366617	+	0.366617i	0.499625	+	0.866242i	$0.333471\pi$
$104$		0			0
$105$	0.0423958	−	1.38993i	0.00413741	−	0.135643i
$106$		0			0
$107$	−6.65809	−	6.65809i	−0.643662	−	0.643662i	0.307792	−	0.951454i	$-0.400410\pi$
$107$	−6.65809	−	6.65809i	−0.643662	−	0.643662i	−0.951454	+	0.307792i	$0.900410\pi$
$108$		0			0
$109$	4.65411	+	8.06116i	0.445783	+	0.772119i	0.998106	−	0.0615111i	$-0.0195920\pi$
$109$	4.65411	+	8.06116i	0.445783	+	0.772119i	−0.552323	+	0.833630i	$0.686259\pi$
$110$		0			0
$111$	10.8465	+	18.7866i	1.02950	+	1.78315i
$112$		0			0
$113$	−13.3083	+	13.3083i	−1.25194	+	1.25194i	−0.297091	+	0.954849i	$0.596016\pi$
$113$	−13.3083	+	13.3083i	−1.25194	+	1.25194i	−0.954849	+	0.297091i	$0.903984\pi$
$114$		0			0
$115$	2.02412	−	6.72666i	0.188750	−	0.627264i
$116$		0			0
$117$	−5.05230	+	18.8554i	−0.467085	+	1.74319i
$118$		0			0
$119$	−0.816666	+	0.471503i	−0.0748637	+	0.0432226i
$120$		0			0
$121$	18.5783			1.68894
$122$		0			0
$123$	−9.20466	+	2.46638i	−0.829956	+	0.222386i
$124$		0			0
$125$	−11.1336	−	1.02133i	−0.995819	−	0.0913506i
$126$		0			0
$127$	8.53177	−	2.28608i	0.757072	−	0.202857i	0.140419	−	0.990092i	$-0.455155\pi$
$127$	8.53177	−	2.28608i	0.757072	−	0.202857i	0.616653	+	0.787235i	$0.288488\pi$
$128$		0			0
$129$	4.94393	−	8.56314i	0.435289	−	0.753943i
$130$		0			0
$131$	−0.720576	−	1.24808i	−0.0629571	−	0.109045i	0.832829	−	0.553531i	$-0.186720\pi$
$131$	−0.720576	−	1.24808i	−0.0629571	−	0.109045i	−0.895786	+	0.444486i	$0.853386\pi$
$132$		0			0
$133$	−0.726913	−	0.432611i	−0.0630313	−	0.0375121i
$134$		0			0
$135$	29.7754	−	7.01276i	2.56266	−	0.603562i
$136$		0			0
$137$	−3.61726	−	13.4998i	−0.309043	−	1.15337i	−0.929408	−	0.369053i	$-0.879682\pi$
$137$	−3.61726	−	13.4998i	−0.309043	−	1.15337i	0.620365	−	0.784313i	$-0.286984\pi$
$138$		0			0
$139$	10.8105	+	6.24144i	0.916933	+	0.529392i	0.882655	−	0.470021i	$-0.155754\pi$
$139$	10.8105	+	6.24144i	0.916933	+	0.529392i	0.0342778	+	0.999412i	$0.489087\pi$
$140$		0			0
$141$		−	16.0434i		−	1.35109i
$142$		0			0
$143$	−3.78006	−	14.1074i	−0.316104	−	1.17972i
$144$		0			0
$145$	10.1710	+	18.9269i	0.844658	+	1.57179i
$146$		0			0
$147$	−5.77453	+	21.5508i	−0.476275	+	1.77748i
$148$		0			0
$149$	14.2418	−	8.22251i	1.16673	−	0.673614i	0.213825	−	0.976872i	$-0.431408\pi$
$149$	14.2418	−	8.22251i	1.16673	−	0.673614i	0.952909	+	0.303258i	$0.0980744\pi$
$150$		0			0
$151$			8.67696i			0.706121i	0.935600	+	0.353061i	$0.114859\pi$
$151$			8.67696i			0.706121i	−0.935600	+	0.353061i	$0.885141\pi$
$152$		0			0
$153$	−24.9765	−	24.9765i	−2.01923	−	2.01923i
$154$		0			0
$155$	−0.851908	−	0.527117i	−0.0684269	−	0.0423391i
$156$		0			0
$157$	−4.82253	−	1.29219i	−0.384880	−	0.103128i	0.0611904	−	0.998126i	$-0.480510\pi$
$157$	−4.82253	−	1.29219i	−0.384880	−	0.103128i	−0.446071	+	0.894998i	$0.647177\pi$
$158$		0			0
$159$			14.7317i			1.16830i
$160$		0			0
$161$	0.304825	−	0.527973i	0.0240236	−	0.0416101i
$162$		0			0
$163$	−4.34827	−	4.34827i	−0.340583	−	0.340583i	0.516004	−	0.856586i	$-0.327419\pi$
$163$	−4.34827	−	4.34827i	−0.340583	−	0.340583i	−0.856586	+	0.516004i	$0.827419\pi$
$164$		0			0
$165$	−28.3837	+	26.7034i	−2.20967	+	2.07886i
$166$		0			0
$167$	−14.5472	+	3.89791i	−1.12570	+	0.301630i	−0.773187	−	0.634178i	$-0.781339\pi$
$167$	−14.5472	+	3.89791i	−1.12570	+	0.301630i	−0.352510	+	0.935808i	$0.614672\pi$
$168$		0			0
$169$	5.01291	−	2.89420i	0.385608	−	0.222631i
$170$		0			0
$171$	8.60504	−	30.4942i	0.658044	−	2.33195i
$172$		0			0
$173$	−3.92353	−	1.05131i	−0.298301	−	0.0799295i	0.106565	−	0.994306i	$-0.466015\pi$
$173$	−3.92353	−	1.05131i	−0.298301	−	0.0799295i	−0.404865	+	0.914376i	$0.632682\pi$
$174$		0			0
$175$	−0.920207	−	0.307794i	−0.0695611	−	0.0232670i
$176$		0			0
$177$	2.30037	+	8.58508i	0.172906	+	0.645294i
$178$		0			0
$179$	25.6525			1.91736			0.958679	−	0.284491i	$-0.0918245\pi$
$179$	25.6525			1.91736			0.958679	+	0.284491i	$0.0918245\pi$
$180$		0			0
$181$	16.6402	+	9.60723i	1.23686	+	0.714099i	0.968450	−	0.249206i	$-0.0801698\pi$
$181$	16.6402	+	9.60723i	1.23686	+	0.714099i	0.268406	+	0.963306i	$0.413503\pi$
$182$		0			0
$183$	25.3201	−	25.3201i	1.87172	−	1.87172i
$184$		0			0
$185$	14.7338	−	3.47014i	1.08325	−	0.255130i
$186$		0			0
$187$	25.5270	+	6.83995i	1.86672	+	0.500186i
$188$		0			0
$189$	2.65485			0.193112
$190$		0			0
$191$	−0.00947247			−0.000685404			−0.000342702	−	1.00000i	$-0.500109\pi$
$191$	−0.00947247			−0.000685404			−0.000342702		1.00000i	$0.500109\pi$
$192$		0			0
$193$	22.2989	+	5.97497i	1.60511	+	0.430087i	0.946580	−	0.322469i	$-0.104513\pi$
$193$	22.2989	+	5.97497i	1.60511	+	0.430087i	0.658528	+	0.752556i	$0.271179\pi$
$194$		0			0
$195$	16.3636	+	10.1249i	1.17182	+	0.725062i
$196$		0			0
$197$	12.1359	−	12.1359i	0.864645	−	0.864645i	−0.127228	−	0.991873i	$-0.540608\pi$
$197$	12.1359	−	12.1359i	0.864645	−	0.864645i	0.991873	+	0.127228i	$0.0406081\pi$
$198$		0			0
$199$	−14.7454	−	8.51325i	−1.04527	−	0.603488i	−0.123950	−	0.992288i	$-0.539556\pi$
$199$	−14.7454	−	8.51325i	−1.04527	−	0.603488i	−0.921322	+	0.388800i	$0.872890\pi$
$200$		0			0
$201$	−9.83017			−0.693367
$202$		0			0
$203$	0.482642	+	1.80124i	0.0338748	+	0.126423i
$204$		0			0
$205$	−0.202728	+	6.64633i	−0.0141591	+	0.464200i
$206$		0			0
$207$	22.0576	+	5.91030i	1.53311	+	0.410795i
$208$		0			0
$209$	5.83204	+	22.9777i	0.403410	+	1.58940i
$210$		0			0
$211$	−0.665546	+	0.384253i	−0.0458181	+	0.0264531i	−0.522734	−	0.852496i	$-0.675088\pi$
$211$	−0.665546	+	0.384253i	−0.0458181	+	0.0264531i	0.476916	+	0.878949i	$0.341755\pi$
$212$		0			0
$213$	36.5355	−	9.78967i	2.50337	−	0.670777i
$214$		0			0
$215$	−4.72773	−	5.02522i	−0.322428	−	0.342717i
$216$		0			0
$217$	−0.0614787	−	0.0614787i	−0.00417345	−	0.00417345i
$218$		0			0
$219$	−3.09782	+	5.36558i	−0.209331	+	0.362572i
$220$		0			0
$221$		−	13.0492i		−	0.877787i
$222$		0			0
$223$	−1.39954	−	0.375005i	−0.0937199	−	0.0251122i	0.211654	−	0.977345i	$-0.432115\pi$
$223$	−1.39954	−	0.375005i	−0.0937199	−	0.0251122i	−0.305374	+	0.952232i	$0.598782\pi$
$224$		0			0
$225$	2.21515	−	36.2776i	0.147677	−	2.41851i
$226$		0			0
$227$	4.20077	+	4.20077i	0.278815	+	0.278815i	0.832636	−	0.553821i	$-0.186831\pi$
$227$	4.20077	+	4.20077i	0.278815	+	0.278815i	−0.553821	+	0.832636i	$0.686831\pi$
$228$		0			0
$229$			24.6251i			1.62727i	0.581376	+	0.813635i	$0.302514\pi$
$229$			24.6251i			1.62727i	−0.581376	+	0.813635i	$0.697486\pi$
$230$		0			0
$231$	−2.92905	+	1.69109i	−0.192717	+	0.111265i
$232$		0			0
$233$	−4.10662	+	15.3261i	−0.269034	+	1.00405i	0.690701	+	0.723140i	$0.257302\pi$
$233$	−4.10662	+	15.3261i	−0.269034	+	1.00405i	−0.959735	+	0.280907i	$0.909365\pi$
$234$		0			0
$235$	−10.7200	−	3.22575i	−0.699293	−	0.210425i
$236$		0			0
$237$	−3.12980	−	11.6806i	−0.203302	−	0.758734i
$238$		0			0
$239$		−	4.41162i		−	0.285364i	−0.989769	−	0.142682i	$-0.954427\pi$
$239$		−	4.41162i		−	0.285364i	0.989769	−	0.142682i	$-0.0455726\pi$
$240$		0			0
$241$	−10.2452	−	5.91506i	−0.659950	−	0.381022i	0.132308	−	0.991209i	$-0.457761\pi$
$241$	−10.2452	−	5.91506i	−0.659950	−	0.381022i	−0.792258	+	0.610186i	$0.791095\pi$
$242$		0			0
$243$	7.65093	+	28.5536i	0.490807	+	1.83172i
$244$		0			0
$245$	13.2389	+	8.19157i	0.845804	+	0.523340i
$246$		0			0
$247$	10.2139	−	5.71810i	0.649894	−	0.363834i
$248$		0			0
$249$	−24.1314	−	41.7968i	−1.52926	−	2.64876i
$250$		0			0
$251$	−13.0182	+	22.5483i	−0.821704	+	1.42323i	0.0827086	+	0.996574i	$0.473643\pi$
$251$	−13.0182	+	22.5483i	−0.821704	+	1.42323i	−0.904412	+	0.426659i	$0.859690\pi$
$252$		0			0
$253$	−16.5032	+	4.42201i	−1.03754	+	0.278009i
$254$		0			0
$255$	−30.6711	+	16.4822i	−1.92070	+	1.03215i
$256$		0			0
$257$	−10.7548	+	2.88174i	−0.670866	+	0.179758i	−0.578145	−	0.815934i	$-0.696223\pi$
$257$	−10.7548	+	2.88174i	−0.670866	+	0.179758i	−0.0927211	+	0.995692i	$0.529557\pi$
$258$		0			0
$259$	1.31371			0.0816297
$260$		0			0
$261$	−60.4912	+	34.9246i	−3.74431	+	2.16178i
$262$		0			0
$263$	1.73817	−	6.48694i	0.107180	−	0.400002i	−0.891403	−	0.453211i	$-0.850278\pi$
$263$	1.73817	−	6.48694i	0.107180	−	0.400002i	0.998583	+	0.0532094i	$0.0169451\pi$
$264$		0			0
$265$	9.84354	+	2.96203i	0.604684	+	0.181956i
$266$		0			0
$267$	9.40699	−	9.40699i	0.575698	−	0.575698i
$268$		0			0
$269$	−8.70299	−	15.0740i	−0.530631	−	0.919079i	−0.999361	−	0.0357382i	$-0.988622\pi$
$269$	−8.70299	−	15.0740i	−0.530631	−	0.919079i	0.468730	−	0.883341i	$-0.344712\pi$
$270$		0			0
$271$	2.07341	+	3.59125i	0.125951	+	0.218153i	0.922104	−	0.386942i	$-0.126469\pi$
$271$	2.07341	+	3.59125i	0.125951	+	0.218153i	−0.796154	+	0.605095i	$0.793135\pi$
$272$		0			0
$273$	1.18089	+	1.18089i	0.0714708	+	0.0714708i
$274$		0			0
$275$	12.1359	+	24.3347i	0.731823	+	1.46744i
$276$		0			0
$277$	−3.11564	+	3.11564i	−0.187201	+	0.187201i	−0.794485	−	0.607284i	$-0.792259\pi$
$277$	−3.11564	+	3.11564i	−0.187201	+	0.187201i	0.607284	+	0.794485i	$0.292259\pi$
$278$		0			0
$279$	1.62833	−	2.82035i	0.0974855	−	0.168850i
$280$		0			0
$281$	4.01060	+	2.31552i	0.239252	+	0.138132i	0.614833	−	0.788657i	$-0.289223\pi$
$281$	4.01060	+	2.31552i	0.239252	+	0.138132i	−0.375581	+	0.926790i	$0.622557\pi$
$282$		0			0
$283$	−5.76161	+	21.5026i	−0.342492	+	1.27820i	0.553023	+	0.833166i	$0.313474\pi$
$283$	−5.76161	+	21.5026i	−0.342492	+	1.27820i	−0.895515	+	0.445032i	$0.853192\pi$
$284$		0			0
$285$	−26.3408	−	16.7845i	−1.56030	−	0.994227i
$286$		0			0
$287$	−0.149362	+	0.557426i	−0.00881655	+	0.0329038i
$288$		0			0
$289$	5.72647	+	3.30618i	0.336851	+	0.194481i
$290$		0			0
$291$	12.4351	−	21.5383i	0.728960	−	1.26260i
$292$		0			0
$293$	4.76693	−	4.76693i	0.278487	−	0.278487i	−0.554018	−	0.832505i	$-0.686906\pi$
$293$	4.76693	−	4.76693i	0.278487	−	0.278487i	0.832505	+	0.554018i	$0.186906\pi$
$294$		0			0
$295$	6.19896	+	0.189082i	0.360917	+	0.0110088i
$296$		0			0
$297$	−52.6099	−	52.6099i	−3.05273	−	3.05273i
$298$		0			0
$299$	4.21815	+	7.30605i	0.243942	+	0.422520i
$300$		0			0
$301$	−0.299400	−	0.518576i	−0.0172571	−	0.0298902i
$302$		0			0
$303$	−2.48287	+	2.48287i	−0.142637	+	0.142637i
$304$		0			0
$305$	−11.8276	−	22.0096i	−0.677246	−	1.26026i
$306$		0			0
$307$	0.849827	−	3.17160i	0.0485022	−	0.181013i	−0.937425	−	0.348187i	$-0.886798\pi$
$307$	0.849827	−	3.17160i	0.0485022	−	0.181013i	0.985927	+	0.167174i	$0.0534642\pi$
$308$		0			0
$309$	−14.6030	+	8.43105i	−0.830736	+	0.479626i
$310$		0			0
$311$	13.7106			0.777458			0.388729	−	0.921352i	$-0.372914\pi$
$311$	13.7106			0.777458			0.388729	+	0.921352i	$0.372914\pi$
$312$		0			0
$313$	12.5642	−	3.36656i	0.710169	−	0.190289i	0.114388	−	0.993436i	$-0.463509\pi$
$313$	12.5642	−	3.36656i	0.710169	−	0.190289i	0.595781	+	0.803147i	$0.296843\pi$
$314$		0			0
$315$	0.908912	−	3.02054i	0.0512114	−	0.170188i
$316$		0			0
$317$	13.7666	−	3.68876i	0.773211	−	0.207181i	0.149421	−	0.988774i	$-0.452259\pi$
$317$	13.7666	−	3.68876i	0.773211	−	0.207181i	0.623790	+	0.781592i	$0.285592\pi$
$318$		0			0
$319$	26.1301	−	45.2587i	1.46300	−	2.53400i
$320$		0			0
$321$	−15.0869	−	26.1313i	−0.842068	−	1.45850i
$322$		0			0
$323$	−0.280335	+	21.1791i	−0.0155983	+	1.17844i
$324$		0			0
$325$	10.0555	−	8.89815i	0.557778	−	0.493581i
$326$		0			0
$327$	7.72019	+	28.8121i	0.426927	+	1.59331i
$328$		0			0
$329$	−0.841406	−	0.485786i	−0.0463882	−	0.0267822i
$330$		0			0
$331$		−	12.1888i		−	0.669956i	−0.942226	−	0.334978i	$-0.891271\pi$
$331$		−	12.1888i		−	0.669956i	0.942226	−	0.334978i	$-0.108729\pi$
$332$		0			0
$333$	12.7358	+	47.5307i	0.697919	+	2.60467i
$334$		0			0
$335$	−1.97650	+	6.56839i	−0.107988	+	0.358869i
$336$		0			0
$337$	2.67726	−	9.99167i	0.145840	−	0.544281i	−0.853877	−	0.520475i	$-0.825755\pi$
$337$	2.67726	−	9.99167i	0.145840	−	0.544281i	0.999717	−	0.0238059i	$-0.00757837\pi$
$338$		0			0
$339$	−52.2316	+	30.1559i	−2.83683	+	1.63785i
$340$		0			0
$341$			2.43659i			0.131949i
$342$		0			0
$343$	1.91597	+	1.91597i	0.103452	+	0.103452i
$344$		0			0
$345$	11.8444	−	19.1425i	0.637681	−	1.03060i
$346$		0			0
$347$	11.6801	+	3.12967i	0.627020	+	0.168010i	0.558317	−	0.829628i	$-0.311447\pi$
$347$	11.6801	+	3.12967i	0.627020	+	0.168010i	0.0687031	+	0.997637i	$0.478114\pi$
$348$		0			0
$349$			26.3286i			1.40934i	0.709536	+	0.704670i	$0.248905\pi$
$349$			26.3286i			1.40934i	−0.709536	+	0.704670i	$0.751095\pi$
$350$		0			0
$351$	−18.3688	+	31.8157i	−0.980454	+	1.69820i
$352$		0			0
$353$	−19.1514	−	19.1514i	−1.01933	−	1.01933i	−0.999810	−	0.0195178i	$-0.993787\pi$
$353$	−19.1514	−	19.1514i	−1.01933	−	1.01933i	−0.0195178	−	0.999810i	$-0.506213\pi$
$354$		0			0
$355$	0.804676	−	26.3809i	0.0427077	−	1.40015i
$356$		0			0
$357$	−2.91892	+	0.782123i	−0.154486	+	0.0413944i
$358$		0			0
$359$	2.59548	−	1.49850i	0.136984	−	0.0790878i	−0.429942	−	0.902857i	$-0.641466\pi$
$359$	2.59548	−	1.49850i	0.136984	−	0.0790878i	0.566926	+	0.823769i	$0.308133\pi$
$360$		0			0
$361$	−16.7002	+	9.06115i	−0.878956	+	0.476903i
$362$		0			0
$363$	57.5063	+	15.4088i	3.01830	+	0.808751i
$364$		0			0
$365$	2.96235	+	3.14875i	0.155056	+	0.164813i
$366$		0			0
$367$	−3.31372	−	12.3670i	−0.172975	−	0.645551i	−0.996888	−	0.0788343i	$-0.974880\pi$
$367$	−3.31372	−	12.3670i	−0.172975	−	0.645551i	0.823913	−	0.566716i	$-0.191786\pi$
$368$		0			0
$369$	−21.6160			−1.12529
$370$		0			0
$371$	0.772616	+	0.446070i	0.0401122	+	0.0231588i
$372$		0			0
$373$	−21.5902	+	21.5902i	−1.11790	+	1.11790i	−0.125848	+	0.992050i	$0.540165\pi$
$373$	−21.5902	+	21.5902i	−1.11790	+	1.11790i	−0.992050	+	0.125848i	$0.959835\pi$
$374$		0			0
$375$	−33.6152	−	12.3955i	−1.73588	−	0.640101i
$376$		0			0
$377$	−24.9255	−	6.67876i	−1.28373	−	0.343974i
$378$		0			0
$379$	−1.40439			−0.0721386			−0.0360693	−	0.999349i	$-0.511484\pi$
$379$	−1.40439			−0.0721386			−0.0360693	+	0.999349i	$0.511484\pi$
$380$		0			0
$381$	28.3048			1.45010
$382$		0			0
$383$	27.0289	+	7.24237i	1.38111	+	0.370068i	0.871525	−	0.490352i	$-0.163132\pi$
$383$	27.0289	+	7.24237i	1.38111	+	0.370068i	0.509587	+	0.860419i	$0.329798\pi$
$384$		0			0
$385$	0.541034	+	2.29717i	0.0275737	+	0.117075i
$386$		0			0
$387$	15.8599	−	15.8599i	0.806203	−	0.806203i
$388$		0			0
$389$	15.8300	+	9.13946i	0.802613	+	0.463389i	0.844384	−	0.535738i	$-0.179967\pi$
$389$	15.8300	+	9.13946i	0.802613	+	0.463389i	−0.0417711	+	0.999127i	$0.513300\pi$
$390$		0			0
$391$	−15.2653			−0.772001
$392$		0			0
$393$	−1.19528	−	4.46086i	−0.0602941	−	0.225021i
$394$		0			0
$395$	−8.43408	−	0.257258i	−0.424365	−	0.0129441i
$396$		0			0
$397$	12.4712	+	3.34165i	0.625911	+	0.167712i	0.557814	−	0.829966i	$-0.311640\pi$
$397$	12.4712	+	3.34165i	0.625911	+	0.167712i	0.0680976	+	0.997679i	$0.478307\pi$
$398$		0			0
$399$	−1.89124	−	1.94198i	−0.0946803	−	0.0972204i
$400$		0			0
$401$	−12.9309	+	7.46568i	−0.645740	+	0.372818i	−0.786822	−	0.617180i	$-0.788275\pi$
$401$	−12.9309	+	7.46568i	−0.645740	+	0.372818i	0.141082	+	0.989998i	$0.454942\pi$
$402$		0			0
$403$	1.16213	−	0.311392i	0.0578898	−	0.0155115i
$404$		0			0
$405$	49.2418	+	1.50198i	2.44684	+	0.0746341i
$406$		0			0
$407$	−26.0331	−	26.0331i	−1.29041	−	1.29041i
$408$		0			0
$409$	3.17563	−	5.50035i	0.157025	−	0.271975i	−0.776770	−	0.629785i	$-0.783143\pi$
$409$	3.17563	−	5.50035i	0.157025	−	0.271975i	0.933794	+	0.357810i	$0.116476\pi$
$410$		0			0
$411$		−	44.7866i		−	2.20916i
$412$		0			0
$413$	0.519905	+	0.139308i	0.0255829	+	0.00685490i
$414$		0			0
$415$	−32.7800	+	7.72042i	−1.60911	+	0.378981i
$416$		0			0
$417$	28.2855	+	28.2855i	1.38515	+	1.38515i
$418$		0			0
$419$			32.1321i			1.56975i	0.619651	+	0.784877i	$0.287274\pi$
$419$			32.1321i			1.56975i	−0.619651	+	0.784877i	$0.712726\pi$
$420$		0			0
$421$	18.2090	−	10.5130i	0.887451	−	0.512370i	0.0143432	−	0.999897i	$-0.495434\pi$
$421$	18.2090	−	10.5130i	0.887451	−	0.512370i	0.873108	+	0.487527i	$0.162101\pi$
$422$		0			0
$423$	9.41898	−	35.1521i	0.457966	−	1.70915i
$424$		0			0
$425$	4.84630	+	23.8080i	0.235080	+	1.15486i
$426$		0			0
$427$	−0.561250	−	2.09462i	−0.0271608	−	0.101366i
$428$		0			0
$429$		−	46.8023i		−	2.25964i
$430$		0			0
$431$	−21.9521	−	12.6741i	−1.05740	−	0.610488i	−0.132686	−	0.991158i	$-0.542360\pi$
$431$	−21.9521	−	12.6741i	−1.05740	−	0.610488i	−0.924711	+	0.380670i	$0.875693\pi$
$432$		0			0
$433$	−4.89308	−	18.2612i	−0.235147	−	0.877579i	−0.978083	−	0.208217i	$-0.933234\pi$
$433$	−4.89308	−	18.2612i	−0.235147	−	0.877579i	0.742936	−	0.669362i	$-0.233433\pi$
$434$		0			0
$435$	15.7849	+	67.0210i	0.756830	+	3.21341i
$436$		0			0
$437$	−6.68918	−	11.9485i	−0.319987	−	0.571573i
$438$		0			0
$439$	3.60234	+	6.23944i	0.171930	+	0.297792i	0.939095	−	0.343658i	$-0.111666\pi$
$439$	3.60234	+	6.23944i	0.171930	+	0.297792i	−0.767164	+	0.641451i	$0.778333\pi$
$440$		0			0
$441$	−25.3048	+	43.8291i	−1.20499	+	2.08710i
$442$		0			0
$443$	6.14747	−	1.64721i	0.292075	−	0.0782612i	−0.109806	−	0.993953i	$-0.535023\pi$
$443$	6.14747	−	1.64721i	0.292075	−	0.0782612i	0.401881	+	0.915692i	$0.368356\pi$
$444$		0			0
$445$	−4.39421	−	8.17703i	−0.208306	−	0.387629i
$446$		0			0
$447$	50.9030	−	13.6394i	2.40763	−	0.645122i
$448$		0			0
$449$	11.8083			0.557268			0.278634	−	0.960397i	$-0.410118\pi$
$449$	11.8083			0.557268			0.278634	+	0.960397i	$0.410118\pi$
$450$		0			0
$451$	14.0061	−	8.08641i	0.659520	−	0.380774i
$452$		0			0
$453$	−7.19663	+	26.8582i	−0.338127	+	1.26191i
$454$		0			0
$455$	1.02649	−	0.551620i	0.0481227	−	0.0258604i
$456$		0			0
$457$	1.13144	−	1.13144i	0.0529263	−	0.0529263i	−0.680148	−	0.733075i	$-0.738085\pi$
$457$	1.13144	−	1.13144i	0.0529263	−	0.0529263i	0.733075	+	0.680148i	$0.238085\pi$
$458$		0			0
$459$	−33.2380	−	57.5699i	−1.55142	−	2.68713i
$460$		0			0
$461$	3.99545	+	6.92032i	0.186087	+	0.322311i	0.943942	−	0.330111i	$-0.107086\pi$
$461$	3.99545	+	6.92032i	0.186087	+	0.322311i	−0.757856	+	0.652422i	$0.773753\pi$
$462$		0			0
$463$	−7.17804	−	7.17804i	−0.333592	−	0.333592i	0.520357	−	0.853949i	$-0.325799\pi$
$463$	−7.17804	−	7.17804i	−0.333592	−	0.333592i	−0.853949	+	0.520357i	$0.825799\pi$
$464$		0			0
$465$	−2.19976	−	2.33818i	−0.102011	−	0.108430i
$466$		0			0
$467$	13.3434	−	13.3434i	0.617457	−	0.617457i	−0.327421	−	0.944878i	$-0.606180\pi$
$467$	13.3434	−	13.3434i	0.617457	−	0.617457i	0.944878	+	0.327421i	$0.106180\pi$
$468$		0			0
$469$	−0.297653	+	0.515550i	−0.0137443	+	0.0238059i
$470$		0			0
$471$	−13.8557	−	7.99957i	−0.638435	−	0.368601i
$472$		0			0
$473$	−4.34331	+	16.2095i	−0.199706	+	0.745311i
$474$		0			0
$475$	−16.5114	+	14.2258i	−0.757594	+	0.652726i
$476$		0			0
$477$	−8.64892	+	32.2782i	−0.396007	+	1.47792i
$478$		0			0
$479$	15.3649	+	8.87094i	0.702041	+	0.405324i	0.808107	−	0.589035i	$-0.200492\pi$
$479$	15.3649	+	8.87094i	0.702041	+	0.405324i	−0.106066	+	0.994359i	$0.533825\pi$
$480$		0			0
$481$	−9.08948	+	15.7434i	−0.414445	+	0.717839i
$482$		0			0
$483$	1.38144	−	1.38144i	0.0628575	−	0.0628575i
$484$		0			0
$485$	−11.8913	−	12.6396i	−0.539957	−	0.573933i
$486$		0			0
$487$	−24.7545	−	24.7545i	−1.12174	−	1.12174i	−0.991481	−	0.130255i	$-0.958420\pi$
$487$	−24.7545	−	24.7545i	−1.12174	−	1.12174i	−0.130255	−	0.991481i	$-0.541580\pi$
$488$		0			0
$489$	−9.85296	−	17.0658i	−0.445566	−	0.771743i
$490$		0			0
$491$	0.433880	+	0.751503i	0.0195808	+	0.0339149i	0.875650	−	0.482947i	$-0.160434\pi$
$491$	0.433880	+	0.751503i	0.0195808	+	0.0339149i	−0.856069	+	0.516862i	$0.827100\pi$
$492$		0			0
$493$	33.0171	−	33.0171i	1.48702	−	1.48702i
$494$		0			0
$495$	−77.8680	+	41.8451i	−3.49991	+	1.88080i
$496$		0			0
$497$	0.592854	−	2.21256i	0.0265931	−	0.0992469i
$498$		0			0
$499$	−22.8568	+	13.1964i	−1.02321	+	0.590750i	−0.915032	−	0.403381i	$-0.867835\pi$
$499$	−22.8568	+	13.1964i	−1.02321	+	0.590750i	−0.108178	+	0.994132i	$0.534502\pi$
$500$		0			0
$501$	−48.2615			−2.15617
$502$		0			0
$503$	−42.4701	+	11.3798i	−1.89365	+	0.507401i	−0.895606	+	0.444849i	$0.853257\pi$
$503$	−42.4701	+	11.3798i	−1.89365	+	0.507401i	−0.998042	+	0.0625524i	$0.980076\pi$
$504$		0			0
$505$	1.15980	+	2.15824i	0.0516105	+	0.0960402i
$506$		0			0
$507$	17.9171	−	4.80087i	0.795727	−	0.213214i
$508$		0			0
$509$	−9.13718	+	15.8261i	−0.404998	+	0.701478i	−0.994321	−	0.106420i	$-0.966061\pi$
$509$	−9.13718	+	15.8261i	−0.404998	+	0.701478i	0.589323	+	0.807898i	$0.299395\pi$
$510$		0			0
$511$	0.187601	+	0.324934i	0.00829898	+	0.0143743i
$512$		0			0
$513$	30.4964	−	51.2428i	1.34645	−	2.26243i
$514$		0			0
$515$	2.69737	+	11.4527i	0.118860	+	0.504667i
$516$		0			0
$517$	7.04715	+	26.3003i	0.309933	+	1.15669i
$518$		0			0
$519$	−11.2727	−	6.50832i	−0.494818	−	0.285683i
$520$		0			0
$521$		−	0.452896i		−	0.0198417i	−0.999951	−	0.00992087i	$-0.996842\pi$
$521$		−	0.452896i		−	0.0198417i	0.999951	−	0.00992087i	$-0.00315796\pi$
$522$		0			0
$523$	−2.21323	−	8.25991i	−0.0967780	−	0.361180i	0.900505	−	0.434846i	$-0.143197\pi$
$523$	−2.21323	−	8.25991i	−0.0967780	−	0.361180i	−0.997283	+	0.0736652i	$0.976530\pi$
$524$		0			0
$525$	−2.59307	−	1.71594i	−0.113171	−	0.0748898i
$526$		0			0
$527$	−0.563457	+	2.10285i	−0.0245446	+	0.0916016i
$528$		0			0
$529$	−11.3718	+	6.56550i	−0.494425	+	0.285457i
$530$		0			0
$531$			20.1610i			0.874915i
$532$		0			0
$533$	−5.64676	−	5.64676i	−0.244588	−	0.244588i
$534$		0			0
$535$	−20.4940	+	4.82679i	−0.886033	+	0.208680i
$536$		0			0
$537$	79.4033	+	21.2760i	3.42650	+	0.918129i
$538$		0			0
$539$		−	37.8654i		−	1.63098i
$540$		0			0
$541$	7.98899	−	13.8373i	0.343474	−	0.594914i	−0.641602	−	0.767038i	$-0.721730\pi$
$541$	7.98899	−	13.8373i	0.343474	−	0.594914i	0.985075	+	0.172124i	$0.0550631\pi$
$542$		0			0
$543$	43.5389	+	43.5389i	1.86844	+	1.86844i
$544$		0			0
$545$	20.8041	+	0.634572i	0.891152	+	0.0271821i
$546$		0			0
$547$	−30.2233	+	8.09830i	−1.29225	+	0.346258i	−0.838516	−	0.544877i	$-0.816576\pi$
$547$	−30.2233	+	8.09830i	−1.29225	+	0.346258i	−0.453737	+	0.891135i	$0.649910\pi$
$548$		0			0
$549$	70.3435	−	40.6128i	3.00219	−	1.73331i
$550$		0			0
$551$	40.3110	+	11.3752i	1.71731	+	0.484601i
$552$		0			0
$553$	−0.707364	−	0.189538i	−0.0300802	−	0.00805996i
$554$		0			0
$555$	48.4843	+	1.47888i	2.05805	+	0.0627749i
$556$		0			0
$557$	−6.57002	−	24.5196i	−0.278381	−	1.03893i	−0.953542	−	0.301260i	$-0.902593\pi$
$557$	−6.57002	−	24.5196i	−0.278381	−	1.03893i	0.675161	−	0.737670i	$-0.264074\pi$
$558$		0			0
$559$	8.28616			0.350467
$560$		0			0
$561$	73.3419	+	42.3440i	3.09650	+	1.78776i
$562$		0			0
$563$	−10.1647	+	10.1647i	−0.428392	+	0.428392i	−0.888080	−	0.459689i	$-0.847961\pi$
$563$	−10.1647	+	10.1647i	−0.428392	+	0.428392i	0.459689	+	0.888080i	$0.347961\pi$
$564$		0			0
$565$	9.64787	+	40.9637i	0.405889	+	1.72336i
$566$		0			0
$567$	4.12989	+	1.10660i	0.173439	+	0.0464729i
$568$		0			0
$569$	−17.6738			−0.740926			−0.370463	−	0.928847i	$-0.620801\pi$
$569$	−17.6738			−0.740926			−0.370463	+	0.928847i	$0.620801\pi$
$570$		0			0
$571$	7.14972			0.299207			0.149603	−	0.988746i	$-0.452200\pi$
$571$	7.14972			0.299207			0.149603	+	0.988746i	$0.452200\pi$
$572$		0			0
$573$	−0.0293205	−	0.00785641i	−0.00122488	−	0.000328206i
$574$		0			0
$575$	−10.4093	−	11.7632i	−0.434097	−	0.490557i
$576$		0			0
$577$	−33.4182	+	33.4182i	−1.39122	+	1.39122i	−0.568614	+	0.822605i	$0.692520\pi$
$577$	−33.4182	+	33.4182i	−1.39122	+	1.39122i	−0.822605	+	0.568614i	$0.807480\pi$
$578$		0			0
$579$	64.0671	+	36.9891i	2.66254	+	1.53722i
$580$		0			0
$581$	−2.92275			−0.121256
$582$		0			0
$583$	−6.47100	−	24.1501i	−0.268002	−	1.00020i
$584$		0			0
$585$	29.9094	+	31.7914i	1.23660	+	1.31441i
$586$		0			0
$587$	−35.9945	−	9.64470i	−1.48565	−	0.398079i	−0.577385	−	0.816472i	$-0.695927\pi$
$587$	−35.9945	−	9.64470i	−1.48565	−	0.398079i	−0.908266	+	0.418393i	$0.862594\pi$
$588$		0			0
$589$	−1.89285	+	0.480428i	−0.0779934	+	0.0197957i
$590$		0			0
$591$	47.6301	−	27.4993i	1.95924	−	1.13117i
$592$		0			0
$593$	10.3910	−	2.78425i	0.426705	−	0.114335i	−0.0390739	−	0.999236i	$-0.512441\pi$
$593$	10.3910	−	2.78425i	0.426705	−	0.114335i	0.465779	+	0.884901i	$0.345774\pi$
$594$		0			0
$595$	−0.0642877	+	2.10764i	−0.00263554	+	0.0864050i
$596$		0			0
$597$	−38.5812	−	38.5812i	−1.57902	−	1.57902i
$598$		0			0
$599$	16.8693	−	29.2185i	0.689261	−	1.19384i	−0.282816	−	0.959174i	$-0.591269\pi$
$599$	16.8693	−	29.2185i	0.689261	−	1.19384i	0.972077	−	0.234661i	$-0.0753980\pi$
$600$		0			0
$601$		−	43.0890i		−	1.75764i	−0.477157	−	0.878818i	$-0.658333\pi$
$601$		−	43.0890i		−	1.75764i	0.477157	−	0.878818i	$-0.341667\pi$
$602$		0			0
$603$	−21.5386	−	5.77124i	−0.877119	−	0.235023i
$604$		0			0
$605$	21.8584	−	35.3268i	0.888671	−	1.43624i
$606$		0			0
$607$	−26.7620	−	26.7620i	−1.08624	−	1.08624i	−0.995912	−	0.0903240i	$-0.971210\pi$
$607$	−26.7620	−	26.7620i	−1.08624	−	1.08624i	−0.0903240	−	0.995912i	$-0.528790\pi$
$608$		0			0
$609$			5.97577i			0.242150i
$610$		0			0
$611$	11.6433	−	6.72227i	0.471038	−	0.271954i
$612$		0			0
$613$	−9.50543	+	35.4747i	−0.383921	+	1.43281i	0.455941	+	0.890010i	$0.349303\pi$
$613$	−9.50543	+	35.4747i	−0.383921	+	1.43281i	−0.839861	+	0.542801i	$0.817364\pi$
$614$		0			0
$615$	−6.13994	+	20.4045i	−0.247586	+	0.822790i
$616$		0			0
$617$	2.11734	+	7.90202i	0.0852409	+	0.318123i	0.995360	−	0.0962240i	$-0.0306765\pi$
$617$	2.11734	+	7.90202i	0.0852409	+	0.318123i	−0.910119	+	0.414347i	$0.864010\pi$
$618$		0			0
$619$		−	2.04139i		−	0.0820503i	−0.999158	−	0.0410251i	$-0.986938\pi$
$619$		−	2.04139i		−	0.0820503i	0.999158	−	0.0410251i	$-0.0130624\pi$
$620$		0			0
$621$	37.2188	+	21.4883i	1.49354	+	0.862295i
$622$		0			0
$623$	−0.208517	−	0.778196i	−0.00835405	−	0.0311777i
$624$		0			0
$625$	−15.0413	+	19.9689i	−0.601654	+	0.798757i
$626$		0			0
$627$	−1.00545	+	75.9610i	−0.0401537	+	3.03359i
$628$		0			0
$629$	−16.4472	−	28.4875i	−0.655795	−	1.13587i
$630$		0			0
$631$	14.2095	−	24.6116i	0.565672	−	0.979772i	−0.431315	−	0.902201i	$-0.641950\pi$
$631$	14.2095	−	24.6116i	0.565672	−	0.979772i	0.996987	−	0.0775707i	$-0.0247163\pi$
$632$		0			0
$633$	−2.37879	+	0.637395i	−0.0945485	+	0.0253342i
$634$		0			0
$635$	5.69110	−	18.9129i	0.225844	−	0.750536i
$636$		0			0
$637$	−18.0599	+	4.83913i	−0.715558	+	0.191733i
$638$		0			0
$639$	85.7994			3.39417
$640$		0			0
$641$	16.2760	−	9.39696i	0.642864	−	0.371158i	−0.142853	−	0.989744i	$-0.545628\pi$
$641$	16.2760	−	9.39696i	0.642864	−	0.371158i	0.785717	+	0.618586i	$0.212294\pi$
$642$		0			0
$643$	10.8538	−	40.5068i	0.428030	−	1.59743i	−0.329185	−	0.944266i	$-0.606774\pi$
$643$	10.8538	−	40.5068i	0.428030	−	1.59743i	0.757215	−	0.653166i	$-0.226559\pi$
$644$		0			0
$645$	−10.4661	−	19.4759i	−0.412101	−	0.766863i
$646$		0			0
$647$	21.3988	−	21.3988i	0.841272	−	0.841272i	−0.147752	−	0.989024i	$-0.547204\pi$
$647$	21.3988	−	21.3988i	0.841272	−	0.841272i	0.989024	+	0.147752i	$0.0472039\pi$
$648$		0			0
$649$	−7.54211	−	13.0633i	−0.296054	−	0.512780i
$650$		0			0
$651$	−0.139308	−	0.241288i	−0.00545989	−	0.00945681i
$652$		0			0
$653$	20.8237	+	20.8237i	0.814895	+	0.814895i	0.985363	−	0.170468i	$-0.0545279\pi$
$653$	20.8237	+	20.8237i	0.814895	+	0.814895i	−0.170468	+	0.985363i	$0.554528\pi$
$654$		0			0
$655$	−3.22102	−	0.0982481i	−0.125856	−	0.00383887i
$656$		0			0
$657$	−9.93763	+	9.93763i	−0.387704	+	0.387704i
$658$		0			0
$659$	−12.3111	+	21.3235i	−0.479573	+	0.830645i	−0.999726	−	0.0234286i	$-0.992542\pi$
$659$	−12.3111	+	21.3235i	−0.479573	+	0.830645i	0.520153	+	0.854073i	$0.325875\pi$
$660$		0			0
$661$	−40.5364	−	23.4037i	−1.57668	−	0.910298i	−0.995318	−	0.0966557i	$-0.969185\pi$
$661$	−40.5364	−	23.4037i	−1.57668	−	0.910298i	−0.581365	−	0.813643i	$-0.697481\pi$
$662$		0			0
$663$	10.8230	−	40.3919i	0.420329	−	1.56869i
$664$		0			0
$665$	−1.67786	+	0.873238i	−0.0650648	+	0.0338627i
$666$		0			0
$667$	−7.81298	+	29.1585i	−0.302520	+	1.12902i
$668$		0			0
$669$	−4.02102	−	2.32154i	−0.155462	−	0.0897558i
$670$		0			0
$671$	−30.3860	+	52.6300i	−1.17304	+	2.03176i
$672$		0			0
$673$	14.0886	−	14.0886i	0.543077	−	0.543077i	−0.381353	−	0.924430i	$-0.624542\pi$
$673$	14.0886	−	14.0886i	0.543077	−	0.543077i	0.924430	+	0.381353i	$0.124542\pi$
$674$		0			0
$675$	21.6975	−	64.8689i	0.835139	−	2.49681i
$676$		0			0
$677$	−6.44919	−	6.44919i	−0.247862	−	0.247862i	0.572230	−	0.820093i	$-0.306078\pi$
$677$	−6.44919	−	6.44919i	−0.247862	−	0.247862i	−0.820093	+	0.572230i	$0.806078\pi$
$678$		0			0
$679$	−0.753060	−	1.30434i	−0.0288998	−	0.0500559i
$680$		0			0
$681$	9.51873	+	16.4869i	0.364759	+	0.631780i
$682$		0			0
$683$	−28.3296	+	28.3296i	−1.08400	+	1.08400i	−0.0878690	+	0.996132i	$0.528006\pi$
$683$	−28.3296	+	28.3296i	−1.08400	+	1.08400i	−0.996132	+	0.0878690i	$0.971994\pi$
$684$		0			0
$685$	−29.9258	−	9.00501i	−1.14341	−	0.344064i
$686$		0			0
$687$	−20.4239	+	76.2230i	−0.779220	+	2.90809i
$688$		0			0
$689$	−10.6914	+	6.17269i	−0.407310	+	0.235161i
$690$		0			0
$691$	7.67458			0.291955			0.145977	−	0.989288i	$-0.453367\pi$
$691$	7.67458			0.291955			0.145977	+	0.989288i	$0.453367\pi$
$692$		0			0
$693$	−7.41058	+	1.98566i	−0.281505	+	0.0754289i
$694$		0			0
$695$	24.5872	−	13.2128i	0.932647	−	0.501190i
$696$		0			0
$697$	13.9576	−	3.73994i	0.528684	−	0.141660i
$698$		0			0
$699$	−25.4228	+	44.0336i	−0.961578	+	1.66550i
$700$		0			0
$701$	21.9736	+	38.0593i	0.829930	+	1.43748i	0.898093	+	0.439806i	$0.144953\pi$
$701$	21.9736	+	38.0593i	0.829930	+	1.43748i	−0.0681632	+	0.997674i	$0.521714\pi$
$702$		0			0
$703$	15.0906	−	25.3566i	0.569153	−	0.956343i
$704$		0			0
$705$	−30.5065	−	18.8759i	−1.14894	−	0.710907i
$706$		0			0
$707$	0.0550357	+	0.205396i	0.00206983	+	0.00772471i
$708$		0			0
$709$	−20.3338	−	11.7398i	−0.763654	−	0.440896i	0.0669523	−	0.997756i	$-0.478672\pi$
$709$	−20.3338	−	11.7398i	−0.763654	−	0.440896i	−0.830606	+	0.556861i	$0.812006\pi$
$710$		0			0
$711$		−	27.4304i		−	1.02872i
$712$		0			0
$713$	−0.364274	−	1.35949i	−0.0136422	−	0.0509132i
$714$		0			0
$715$	−31.2727	−	9.41029i	−1.16953	−	0.351925i
$716$		0			0
$717$	3.65897	−	13.6555i	0.136647	−	0.509973i
$718$		0			0
$719$	−8.64356	+	4.99036i	−0.322350	+	0.186109i	−0.652440	−	0.757841i	$-0.726254\pi$
$719$	−8.64356	+	4.99036i	−0.322350	+	0.186109i	0.330089	+	0.943950i	$0.392921\pi$
$720$		0			0
$721$			1.02115i			0.0380298i
$722$		0			0
$723$	−26.8064	−	26.8064i	−0.996941	−	0.996941i
$724$		0			0
$725$	47.9564	+	2.92827i	1.78105	+	0.108753i
$726$		0			0
$727$	31.8614	+	8.53725i	1.18168	+	0.316629i	0.795591	−	0.605834i	$-0.207161\pi$
$727$	31.8614	+	8.53725i	1.18168	+	0.316629i	0.386085	+	0.922463i	$0.373827\pi$
$728$		0			0
$729$			28.6334i			1.06050i
$730$		0			0
$731$	−7.49682	+	12.9849i	−0.277280	+	0.480263i
$732$		0			0
$733$	−26.2388	−	26.2388i	−0.969153	−	0.969153i	0.0303850	−	0.999538i	$-0.490327\pi$
$733$	−26.2388	−	26.2388i	−0.969153	−	0.969153i	−0.999538	+	0.0303850i	$0.990327\pi$
$734$		0			0
$735$	34.1850	+	36.3360i	1.26093	+	1.34027i
$736$		0			0
$737$	16.1149	−	4.31797i	0.593599	−	0.159054i
$738$		0			0
$739$	2.68922	−	1.55262i	0.0989246	−	0.0571141i	−0.449722	−	0.893169i	$-0.648477\pi$
$739$	2.68922	−	1.55262i	0.0989246	−	0.0571141i	0.548646	+	0.836055i	$0.315143\pi$
$740$		0			0
$741$	36.3581	−	9.22813i	1.33565	−	0.339004i
$742$		0			0
$743$	3.85631	+	1.03330i	0.141474	+	0.0379079i	0.328861	−	0.944378i	$-0.393335\pi$
$743$	3.85631	+	1.03330i	0.141474	+	0.0379079i	−0.187387	+	0.982286i	$0.560002\pi$
$744$		0			0
$745$	1.12111	−	36.7551i	0.0410743	−	1.34660i
$746$		0			0
$747$	−28.3348	−	105.747i	−1.03672	−	3.86908i
$748$		0			0
$749$	−1.82730			−0.0667680
$750$		0			0
$751$	−2.62250	−	1.51410i	−0.0956963	−	0.0552503i	0.451388	−	0.892328i	$-0.350929\pi$
$751$	−2.62250	−	1.51410i	−0.0956963	−	0.0552503i	−0.547084	+	0.837077i	$0.684262\pi$
$752$		0			0
$753$	−58.9973	+	58.9973i	−2.14998	+	2.14998i
$754$		0			0
$755$	16.4993	+	10.2089i	0.600471	+	0.371540i
$756$		0			0
$757$	31.8121	+	8.52402i	1.15623	+	0.309811i	0.785459	−	0.618914i	$-0.212427\pi$
$757$	31.8121	+	8.52402i	1.15623	+	0.309811i	0.370771	+	0.928724i	$0.379094\pi$
$758$		0			0
$759$	−54.7505			−1.98732
$760$		0			0
$761$	−15.3941			−0.558037			−0.279018	−	0.960286i	$-0.590009\pi$
$761$	−15.3941			−0.558037			−0.279018	+	0.960286i	$0.590009\pi$
$762$		0			0
$763$	1.74484	+	0.467528i	0.0631674	+	0.0169256i
$764$		0			0
$765$	−76.8792	+	18.1067i	−2.77957	+	0.654651i
$766$		0			0
$767$	−5.26667	+	5.26667i	−0.190169	+	0.190169i
$768$		0			0
$769$	−30.9201	−	17.8517i	−1.11501	−	0.643749i	−0.174885	−	0.984589i	$-0.555955\pi$
$769$	−30.9201	−	17.8517i	−1.11501	−	0.643749i	−0.940121	+	0.340840i	$0.889289\pi$
$770$		0			0
$771$	−35.6799			−1.28498
$772$		0			0
$773$	−2.62537	−	9.79800i	−0.0944279	−	0.352410i	0.902504	−	0.430681i	$-0.141727\pi$
$773$	−2.62537	−	9.79800i	−0.0944279	−	0.352410i	−0.996932	+	0.0782714i	$0.975060\pi$
$774$		0			0
$775$	−2.00463	+	0.999725i	−0.0720085	+	0.0359112i
$776$		0			0
$777$	4.06637	+	1.08958i	0.145880	+	0.0390885i
$778$		0			0
$779$	9.04348	+	9.28610i	0.324016	+	0.332709i
$780$		0			0
$781$	−55.5936	+	32.0970i	−1.98929	+	1.14852i
$782$		0			0
$783$	−126.976	+	34.0232i	−4.53777	+	1.21589i
$784$		0			0
$785$	−8.13109	+	7.64974i	−0.290211	+	0.273031i
$786$		0			0
$787$	27.0647	+	27.0647i	0.964752	+	0.964752i	0.999400	−	0.0346473i	$-0.0110308\pi$
$787$	27.0647	+	27.0647i	0.964752	+	0.964752i	−0.0346473	+	0.999400i	$0.511031\pi$
$788$		0			0
$789$	10.7605	−	18.6377i	0.383082	−	0.663518i
$790$		0			0
$791$			3.65243i			0.129866i
$792$		0			0
$793$	28.9851	+	7.76655i	1.02929	+	0.275798i
$794$		0			0
$795$	28.0124	+	17.3327i	0.993499	+	0.614726i
$796$		0			0
$797$	−13.4978	−	13.4978i	−0.478116	−	0.478116i	0.426413	−	0.904529i	$-0.359777\pi$
$797$	−13.4978	−	13.4978i	−0.478116	−	0.478116i	−0.904529	+	0.426413i	$0.859777\pi$
$798$		0			0
$799$			24.3276i			0.860650i
$800$		0			0
$801$	26.1341	−	15.0886i	0.923405	−	0.533128i
$802$		0			0
$803$	2.72147	−	10.1567i	0.0960387	−	0.358421i
$804$		0			0
$805$	−0.645299	−	1.20082i	−0.0227438	−	0.0423232i
$806$		0			0
$807$	−14.4364	−	53.8775i	−0.508186	−	1.89658i
$808$		0			0
$809$		−	30.1477i		−	1.05994i	−0.848018	−	0.529968i	$-0.822204\pi$
$809$		−	30.1477i		−	1.05994i	0.848018	−	0.529968i	$-0.177796\pi$
$810$		0			0
$811$	−14.5538	−	8.40263i	−0.511052	−	0.295056i	0.222214	−	0.974998i	$-0.428672\pi$
$811$	−14.5538	−	8.40263i	−0.511052	−	0.295056i	−0.733266	+	0.679942i	$0.762005\pi$
$812$		0			0
$813$	3.43935	+	12.8358i	0.120623	+	0.450172i
$814$		0			0
$815$	−13.3842	+	3.15228i	−0.468829	+	0.110420i
$816$		0			0
$817$	−13.4486	−	0.178011i	−0.470506	−	0.00622780i
$818$		0			0
$819$	1.89412	+	3.28071i	0.0661859	+	0.114637i
$820$		0			0
$821$	−7.47522	+	12.9475i	−0.260887	+	0.451869i	−0.966478	−	0.256750i	$-0.917348\pi$
$821$	−7.47522	+	12.9475i	−0.260887	+	0.451869i	0.705591	+	0.708619i	$0.250682\pi$
$822$		0			0
$823$	20.6122	−	5.52303i	0.718496	−	0.192521i	0.118996	−	0.992895i	$-0.462033\pi$
$823$	20.6122	−	5.52303i	0.718496	−	0.192521i	0.599501	+	0.800374i	$0.295366\pi$
$824$		0			0
$825$	17.3817	+	85.3897i	0.605154	+	2.97289i
$826$		0			0
$827$	40.5797	−	10.8733i	1.41109	−	0.378101i	0.528778	−	0.848760i	$-0.322650\pi$
$827$	40.5797	−	10.8733i	1.41109	−	0.378101i	0.882315	+	0.470658i	$0.155984\pi$
$828$		0			0
$829$	8.24412			0.286330			0.143165	−	0.989699i	$-0.454272\pi$
$829$	8.24412			0.286330			0.143165	+	0.989699i	$0.454272\pi$
$830$		0			0
$831$	−12.2281	+	7.05987i	−0.424187	+	0.244904i
$832$		0			0
$833$	8.75631	−	32.6790i	0.303388	−	1.13226i
$834$		0			0
$835$	−9.70368	+	32.2477i	−0.335810	+	1.11598i
$836$		0			0
$837$	4.33387	−	4.33387i	0.149800	−	0.149800i
$838$		0			0
$839$	12.2792	+	21.2683i	0.423927	+	0.734262i	0.996320	−	0.0857171i	$-0.0273181\pi$
$839$	12.2792	+	21.2683i	0.423927	+	0.734262i	−0.572393	+	0.819979i	$0.693985\pi$
$840$		0			0
$841$	−31.6677	−	54.8501i	−1.09199	−	1.89138i
$842$		0			0
$843$	10.4937	+	10.4937i	0.361422	+	0.361422i
$844$		0			0
$845$	0.394614	−	12.9373i	0.0135752	−	0.445055i
$846$		0			0
$847$	2.54939	−	2.54939i	0.0875981	−	0.0875981i
$848$		0			0
$849$	−35.6683	+	61.7793i	−1.22413	+	2.12026i
$850$		0			0
$851$	18.4171	+	10.6331i	0.631329	+	0.364498i
$852$		0			0
$853$	−5.22484	+	19.4994i	−0.178895	+	0.667646i	0.816960	+	0.576694i	$0.195658\pi$
$853$	−5.22484	+	19.4994i	−0.178895	+	0.667646i	−0.995855	+	0.0909519i	$0.971009\pi$
$854$		0			0
$855$	−47.8605	−	52.2405i	−1.63679	−	1.78659i
$856$		0			0
$857$	−1.17256	+	4.37606i	−0.0400539	+	0.149483i	−0.983057	−	0.183301i	$-0.941322\pi$
$857$	−1.17256	+	4.37606i	−0.0400539	+	0.149483i	0.943003	+	0.332785i	$0.107988\pi$
$858$		0			0
$859$	−27.2399	−	15.7270i	−0.929413	−	0.536597i	−0.0427871	−	0.999084i	$-0.513624\pi$
$859$	−27.2399	−	15.7270i	−0.929413	−	0.536597i	−0.886626	+	0.462487i	$0.846957\pi$
$860$		0			0
$861$	−0.924652	+	1.60154i	−0.0315120	+	0.0545805i
$862$		0			0
$863$	−21.9717	+	21.9717i	−0.747926	+	0.747926i	−0.974089	−	0.226163i	$-0.927382\pi$
$863$	−21.9717	+	21.9717i	−0.747926	+	0.747926i	0.226163	+	0.974089i	$0.427382\pi$
$864$		0			0
$865$	−6.61532	+	6.22370i	−0.224928	+	0.211612i
$866$		0			0
$867$	14.9832	+	14.9832i	0.508858	+	0.508858i
$868$		0			0
$869$	10.2615	+	17.7735i	0.348098	+	0.602924i
$870$		0			0
$871$	−4.11890	−	7.13415i	−0.139564	−	0.241732i
$872$		0			0
$873$	39.8912	−	39.8912i	1.35011	−	1.35011i
$874$		0			0
$875$	−1.66794	+	1.38764i	−0.0563868	+	0.0469109i
$876$		0			0
$877$	−2.72321	+	10.1632i	−0.0919564	+	0.343186i	−0.996540	−	0.0831094i	$-0.973515\pi$
$877$	−2.72321	+	10.1632i	−0.0919564	+	0.343186i	0.904584	+	0.426295i	$0.140182\pi$
$878$		0			0
$879$	18.7089	−	10.8016i	0.631037	−	0.364329i
$880$		0			0
$881$	−23.2625			−0.783733			−0.391867	−	0.920022i	$-0.628171\pi$
$881$	−23.2625			−0.783733			−0.391867	+	0.920022i	$0.628171\pi$
$882$		0			0
$883$	−19.7192	+	5.28376i	−0.663605	+	0.177813i	−0.574873	−	0.818243i	$-0.694948\pi$
$883$	−19.7192	+	5.28376i	−0.663605	+	0.177813i	−0.0887328	+	0.996055i	$0.528282\pi$
$884$		0			0
$885$	19.0311	+	5.72666i	0.639723	+	0.192499i
$886$		0			0
$887$	−44.7684	+	11.9957i	−1.50318	+	0.402775i	−0.914163	−	0.405348i	$-0.867150\pi$
$887$	−44.7684	+	11.9957i	−1.50318	+	0.402775i	−0.589014	+	0.808123i	$0.700484\pi$
$888$		0			0
$889$	0.857057	−	1.48447i	0.0287448	−	0.0497874i
$890$		0			0
$891$	−59.9111	−	103.769i	−2.00710	−	3.47640i
$892$		0			0
$893$	−19.0417	+	10.6602i	−0.637207	+	0.356731i
$894$		0			0
$895$	30.1815	−	48.7783i	1.00886	−	1.63048i
$896$		0			0
$897$	6.99702	+	26.1132i	0.233624	+	0.871896i
$898$		0			0
$899$	3.72829	+	2.15253i	0.124346	+	0.0717909i
$900$		0			0
$901$		−	22.3387i		−	0.744211i
$902$		0			0
$903$	−0.496642	−	1.85349i	−0.0165272	−	0.0616804i
$904$		0			0
$905$	37.8463	−	20.3380i	1.25805	−	0.676058i
$906$		0			0
$907$	−8.67420	+	32.3725i	−0.288022	+	1.07491i	0.658581	+	0.752510i	$0.271157\pi$
$907$	−8.67420	+	32.3725i	−0.288022	+	1.07491i	−0.946603	+	0.322403i	$0.895510\pi$
$908$		0			0
$909$	−6.89781	+	3.98245i	−0.228786	+	0.132090i
$910$		0			0
$911$			15.8550i			0.525301i	0.964891	+	0.262651i	$0.0845966\pi$
$911$			15.8550i			0.525301i	−0.964891	+	0.262651i	$0.915403\pi$
$912$		0			0
$913$	57.9188	+	57.9188i	1.91683	+	1.91683i
$914$		0			0
$915$	−18.3559	−	77.9369i	−0.606826	−	2.57651i
$916$		0			0
$917$	−0.270146	−	0.0723854i	−0.00892100	−	0.00239038i
$918$		0			0
$919$			20.8285i			0.687070i	0.939140	+	0.343535i	$0.111624\pi$
$919$			20.8285i			0.687070i	−0.939140	+	0.343535i	$0.888376\pi$
$920$		0			0
$921$	5.26101	−	9.11234i	0.173356	−	0.300262i
$922$		0			0
$923$	22.4134	+	22.4134i	0.737746	+	0.737746i
$924$		0			0
$925$	10.7366	−	32.0992i	0.353019	−	1.05542i
$926$		0			0
$927$	−36.9460	+	9.89965i	−1.21347	+	0.325147i
$928$		0			0
$929$	−18.6425	+	10.7633i	−0.611641	+	0.353131i	−0.773608	−	0.633665i	$-0.781550\pi$
$929$	−18.6425	+	10.7633i	−0.611641	+	0.353131i	0.161966	+	0.986796i	$0.448216\pi$
$930$		0			0
$931$	29.4154	−	7.46601i	0.964052	−	0.244689i
$932$		0			0
$933$	42.4391	+	11.3715i	1.38939	+	0.372287i
$934$		0			0
$935$	43.0401	−	40.4922i	1.40756	−	1.32424i
$936$		0			0
$937$	3.37812	+	12.6073i	0.110358	+	0.411863i	0.998898	−	0.0469373i	$-0.0149461\pi$
$937$	3.37812	+	12.6073i	0.110358	+	0.411863i	−0.888540	+	0.458800i	$0.848279\pi$
$938$		0			0
$939$	41.6826			1.36026
$940$		0			0
$941$	−7.26556	−	4.19477i	−0.236850	−	0.136746i	0.376878	−	0.926263i	$-0.376998\pi$
$941$	−7.26556	−	4.19477i	−0.236850	−	0.136746i	−0.613728	+	0.789517i	$0.710331\pi$
$942$		0			0
$943$	−6.60572	+	6.60572i	−0.215112	+	0.215112i
$944$		0			0
$945$	3.12357	−	5.04821i	0.101610	−	0.164218i
$946$		0			0
$947$	−23.6501	−	6.33703i	−0.768526	−	0.205926i	−0.146806	−	0.989165i	$-0.546899\pi$
$947$	−23.6501	−	6.33703i	−0.768526	−	0.205926i	−0.621720	+	0.783240i	$0.713566\pi$
$948$		0			0
$949$	−5.19202			−0.168540
$950$		0			0
$951$	45.6719			1.48101
$952$		0			0
$953$	−39.4672	−	10.5752i	−1.27847	−	0.342565i	−0.445199	−	0.895432i	$-0.646867\pi$
$953$	−39.4672	−	10.5752i	−1.27847	−	0.342565i	−0.833270	+	0.552867i	$0.813534\pi$
$954$		0			0
$955$	−0.0111449	+	0.0180119i	−0.000360640	+	0.000582853i
$956$		0			0
$957$	118.419	−	118.419i	3.82794	−	3.82794i
$958$		0			0
$959$	−2.34887	−	1.35612i	−0.0758489	−	0.0437914i
$960$		0			0
$961$	30.7993			0.993525
$962$		0			0
$963$	−17.7149	−	66.1128i	−0.570854	−	2.13046i
$964$		0			0
$965$	37.5973	−	35.3716i	1.21030	−	1.13865i
$966$		0			0
$967$	31.0768	+	8.32700i	0.999362	+	0.267778i	0.721178	−	0.692750i	$-0.243601\pi$
$967$	31.0768	+	8.32700i	0.999362	+	0.267778i	0.278184	+	0.960528i	$0.410268\pi$
$968$		0			0
$969$	−18.4336	+	65.3242i	−0.592173	+	2.09852i
$970$		0			0
$971$	−9.21708	+	5.32148i	−0.295790	+	0.170775i	−0.640550	−	0.767916i	$-0.721294\pi$
$971$	−9.21708	+	5.32148i	−0.295790	+	0.170775i	0.344760	+	0.938691i	$0.387960\pi$
$972$		0			0
$973$	2.33993	−	0.626982i	0.0750147	−	0.0201001i
$974$		0			0
$975$	38.5052	−	19.2029i	1.23315	−	0.614984i
$976$		0			0
$977$	10.2263	+	10.2263i	0.327168	+	0.327168i	0.851509	−	0.524341i	$-0.175688\pi$
$977$	10.2263	+	10.2263i	0.327168	+	0.327168i	−0.524341	+	0.851509i	$0.675688\pi$
$978$		0			0
$979$	−11.2891	+	19.5532i	−0.360800	+	0.624923i
$980$		0			0
$981$			67.6619i			2.16028i
$982$		0			0
$983$	44.2533	+	11.8576i	1.41146	+	0.378200i	0.882446	−	0.470413i	$-0.155895\pi$
$983$	44.2533	+	11.8576i	1.41146	+	0.378200i	0.529014	+	0.848613i	$0.322562\pi$
$984$		0			0
$985$	−8.79791	−	37.3549i	−0.280325	−	1.19023i
$986$		0			0
$987$	−2.20153	−	2.20153i	−0.0700755	−	0.0700755i
$988$		0			0
$989$		−	9.69336i		−	0.308231i
$990$		0			0
$991$	−33.7903	+	19.5088i	−1.07338	+	0.619718i	−0.929104	−	0.369819i	$-0.879420\pi$
$991$	−33.7903	+	19.5088i	−1.07338	+	0.619718i	−0.144280	+	0.989537i	$0.546086\pi$
$992$		0			0
$993$	10.1093	−	37.7285i	0.320809	−	1.19728i
$994$		0			0
$995$	−33.5367	+	18.0221i	−1.06319	+	0.571339i
$996$		0			0
$997$	8.91198	+	33.2600i	0.282245	+	1.05335i	0.950829	+	0.309717i	$0.100234\pi$
$997$	8.91198	+	33.2600i	0.282245	+	1.05335i	−0.668584	+	0.743637i	$0.733099\pi$
$998$		0			0
$999$			92.6081i			2.92999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.y.b.373.9	yes	36
5.2	odd	4	inner	380.2.y.b.297.9	yes	36
19.8	odd	6	inner	380.2.y.b.293.9	yes	36
95.27	even	12	inner	380.2.y.b.217.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.y.b.217.9	✓	36	95.27	even	12	inner
380.2.y.b.293.9	yes	36	19.8	odd	6	inner
380.2.y.b.297.9	yes	36	5.2	odd	4	inner
380.2.y.b.373.9	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.09534 + 0.829395i) q^{3} +(1.17655 - 1.90150i) q^{5} +(0.137224 - 0.137224i) q^{7} +(6.29517 + 3.63452i) q^{9} +O(q^{10})\)	\(q+(3.09534 + 0.829395i) q^{3} +(1.17655 - 1.90150i) q^{5} +(0.137224 - 0.137224i) q^{7} +(6.29517 + 3.63452i) q^{9} -5.43860 q^{11} +(0.695043 + 2.59394i) q^{13} +(5.21894 - 4.90998i) q^{15} +(-4.69368 - 1.25767i) q^{17} +(-1.07234 - 4.22494i) q^{19} +(0.538567 - 0.310942i) q^{21} +(3.03445 - 0.813079i) q^{23} +(-2.23144 - 4.47445i) q^{25} +(9.67343 + 9.67343i) q^{27} +(-4.80457 + 8.32175i) q^{29} -0.448018i q^{31} +(-16.8343 - 4.51074i) q^{33} +(-0.0994805 - 0.422383i) q^{35} +(4.78673 + 4.78673i) q^{37} +8.60559i q^{39} +(-2.57531 + 1.48686i) q^{41} +(0.798608 - 2.98045i) q^{43} +(14.3177 - 7.69409i) q^{45} +(-1.29577 - 4.83587i) q^{47} +6.96234i q^{49} +(-13.4854 - 7.78582i) q^{51} +(1.18983 + 4.44051i) q^{53} +(-6.39880 + 10.3415i) q^{55} +(0.184873 - 13.9670i) q^{57} +(1.38677 + 2.40196i) q^{59} +(5.58710 - 9.67713i) q^{61} +(1.36259 - 0.365105i) q^{63} +(5.75014 + 1.73028i) q^{65} +(-2.96306 + 0.793949i) q^{67} +10.0670 q^{69} +(10.2220 - 5.90170i) q^{71} +(-0.500400 + 1.86752i) q^{73} +(-3.19599 - 15.7007i) q^{75} +(-0.746305 + 0.746305i) q^{77} +(-1.88680 - 3.26803i) q^{79} +(11.0159 + 19.0801i) q^{81} +(-10.6496 - 10.6496i) q^{83} +(-7.91383 + 7.44534i) q^{85} +(-21.7738 + 21.7738i) q^{87} +(2.07573 - 3.59527i) q^{89} +(0.451326 + 0.260573i) q^{91} +(0.371583 - 1.38677i) q^{93} +(-9.29540 - 2.93180i) q^{95} +(2.00868 - 7.49651i) q^{97} +(-34.2369 - 19.7667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{3} - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 36 * q - 6 * q^3 - 4 * q^5 + 4 * q^7	\( 36 q - 6 q^{3} - 4 q^{5} + 4 q^{7} - 12 q^{11} - 6 q^{13} - 12 q^{15} + 6 q^{17} + 48 q^{21} + 16 q^{23} + 4 q^{25} - 54 q^{33} + 16 q^{35} - 2 q^{43} + 100 q^{45} + 24 q^{47} - 108 q^{51} + 14 q^{55} - 30 q^{57} + 34 q^{61} - 26 q^{63} - 78 q^{67} - 42 q^{71} + 16 q^{73} - 20 q^{77} + 14 q^{81} - 28 q^{83} + 10 q^{85} - 124 q^{87} + 96 q^{91} - 26 q^{93} - 32 q^{95} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^3 - 4 * q^5 + 4 * q^7 - 12 * q^11 - 6 * q^13 - 12 * q^15 + 6 * q^17 + 48 * q^21 + 16 * q^23 + 4 * q^25 - 54 * q^33 + 16 * q^35 - 2 * q^43 + 100 * q^45 + 24 * q^47 - 108 * q^51 + 14 * q^55 - 30 * q^57 + 34 * q^61 - 26 * q^63 - 78 * q^67 - 42 * q^71 + 16 * q^73 - 20 * q^77 + 14 * q^81 - 28 * q^83 + 10 * q^85 - 124 * q^87 + 96 * q^91 - 26 * q^93 - 32 * q^95 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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