LMFDB - Embedded newform 380.2.y.b.297.9

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			297.9
Character	$\chi$	$=$	380.297
Dual form			380.2.y.b.293.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.829395 - 3.09534i) q^{3} +(-2.23503 + 0.0681732i) q^{5} +(0.137224 + 0.137224i) q^{7} +(-6.29517 - 3.63452i) q^{9} +O(q^{10})$	\(q+(0.829395 - 3.09534i) q^{3} +(-2.23503 + 0.0681732i) q^{5} +(0.137224 + 0.137224i) q^{7} +(-6.29517 - 3.63452i) q^{9} -5.43860 q^{11} +(2.59394 - 0.695043i) q^{13} +(-1.64270 + 6.97472i) q^{15} +(1.25767 - 4.69368i) q^{17} +(1.07234 + 4.22494i) q^{19} +(0.538567 - 0.310942i) q^{21} +(-0.813079 - 3.03445i) q^{23} +(4.99070 - 0.304738i) q^{25} +(-9.67343 + 9.67343i) q^{27} +(4.80457 - 8.32175i) q^{29} -0.448018i q^{31} +(-4.51074 + 16.8343i) q^{33} +(-0.316054 - 0.297344i) q^{35} +(-4.78673 + 4.78673i) q^{37} -8.60559i q^{39} +(-2.57531 + 1.48686i) q^{41} +(-2.98045 - 0.798608i) q^{43} +(14.3177 + 7.69409i) q^{45} +(4.83587 - 1.29577i) q^{47} -6.96234i q^{49} +(-13.4854 - 7.78582i) q^{51} +(4.44051 - 1.18983i) q^{53} +(12.1554 - 0.370767i) q^{55} +(13.9670 + 0.184873i) q^{57} +(-1.38677 - 2.40196i) q^{59} +(5.58710 - 9.67713i) q^{61} +(-0.365105 - 1.36259i) q^{63} +(-5.75014 + 1.73028i) q^{65} +(-0.793949 - 2.96306i) q^{67} -10.0670 q^{69} +(10.2220 - 5.90170i) q^{71} +(1.86752 + 0.500400i) q^{73} +(3.19599 - 15.7007i) q^{75} +(-0.746305 - 0.746305i) q^{77} +(1.88680 + 3.26803i) q^{79} +(11.0159 + 19.0801i) q^{81} +(-10.6496 + 10.6496i) q^{83} +(-2.49094 + 10.5762i) q^{85} +(-21.7738 - 21.7738i) q^{87} +(-2.07573 + 3.59527i) q^{89} +(0.451326 + 0.260573i) q^{91} +(-1.38677 - 0.371583i) q^{93} +(-2.68474 - 9.36975i) q^{95} +(7.49651 + 2.00868i) q^{97} +(34.2369 + 19.7667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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
$3$	0.829395	−	3.09534i	0.478851	−	1.78710i	−0.127431	−	0.991847i	$-0.540673\pi$
$3$	0.829395	−	3.09534i	0.478851	−	1.78710i	0.606282	−	0.795249i	$-0.292660\pi$
$4$		0			0
$5$	−2.23503	+	0.0681732i	−0.999535	+	0.0304880i
$5$	−2.23503	+	0.0681732i	−0.999535	+	0.0304880i
$6$		0			0
$7$	0.137224	+	0.137224i	0.0518657	+	0.0518657i	0.732564	−	0.680698i	$-0.238323\pi$
$7$	0.137224	+	0.137224i	0.0518657	+	0.0518657i	−0.680698	+	0.732564i	$0.738323\pi$
$8$		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
$13$	2.59394	−	0.695043i	0.719429	−	0.192770i	0.119512	−	0.992833i	$-0.461867\pi$
$13$	2.59394	−	0.695043i	0.719429	−	0.192770i	0.599917	+	0.800062i	$0.295200\pi$
$14$		0			0
$15$	−1.64270	+	6.97472i	−0.424144	+	1.80087i
$16$		0			0
$17$	1.25767	−	4.69368i	0.305029	−	1.13838i	−0.627891	−	0.778301i	$-0.716082\pi$
$17$	1.25767	−	4.69368i	0.305029	−	1.13838i	0.932920	−	0.360083i	$-0.117252\pi$
$18$		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
$23$	−0.813079	−	3.03445i	−0.169539	−	0.632727i	−0.997418	−	0.0718201i	$-0.977119\pi$
$23$	−0.813079	−	3.03445i	−0.169539	−	0.632727i	0.827879	−	0.560907i	$-0.189547\pi$
$24$		0			0
$25$	4.99070	−	0.304738i	0.998141	−	0.0609476i
$26$		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	$-0.482504\pi$
$29$	4.80457	−	8.32175i	0.892186	−	1.54531i	0.837249	−	0.546821i	$-0.184162\pi$
$30$		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
$33$	−4.51074	+	16.8343i	−0.785220	+	2.93048i
$34$		0			0
$35$	−0.316054	−	0.297344i	−0.0534229	−	0.0502603i
$36$		0			0
$37$	−4.78673	+	4.78673i	−0.786933	+	0.786933i	−0.980990	−	0.194057i	$-0.937835\pi$
$37$	−4.78673	+	4.78673i	−0.786933	+	0.786933i	0.194057	+	0.980990i	$0.437835\pi$
$38$		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
$43$	−2.98045	−	0.798608i	−0.454514	−	0.121787i	0.0242968	−	0.999705i	$-0.492265\pi$
$43$	−2.98045	−	0.798608i	−0.454514	−	0.121787i	−0.478811	+	0.877918i	$0.658932\pi$
$44$		0			0
$45$	14.3177	+	7.69409i	2.13435	+	1.14697i
$46$		0			0
$47$	4.83587	−	1.29577i	0.705384	−	0.189007i	0.111743	−	0.993737i	$-0.464357\pi$
$47$	4.83587	−	1.29577i	0.705384	−	0.189007i	0.593641	+	0.804730i	$0.297690\pi$
$48$		0			0
$49$		−	6.96234i		−	0.994620i
$50$		0			0
$51$	−13.4854	−	7.78582i	−1.88834	−	1.09023i
$52$		0			0
$53$	4.44051	−	1.18983i	0.609950	−	0.163436i	0.0593952	−	0.998235i	$-0.481083\pi$
$53$	4.44051	−	1.18983i	0.609950	−	0.163436i	0.550555	+	0.834799i	$0.314416\pi$
$54$		0			0
$55$	12.1554	−	0.370767i	1.63904	−	0.0499942i
$56$		0			0
$57$	13.9670	+	0.184873i	1.84998	+	0.0244870i
$58$		0			0
$59$	−1.38677	−	2.40196i	−0.180543	−	0.312709i	0.761523	−	0.648138i	$-0.224452\pi$
$59$	−1.38677	−	2.40196i	−0.180543	−	0.312709i	−0.942065	+	0.335429i	$0.891119\pi$
$60$		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
$63$	−0.365105	−	1.36259i	−0.0459989	−	0.171670i
$64$		0			0
$65$	−5.75014	+	1.73028i	−0.713217	+	0.214615i
$66$		0			0
$67$	−0.793949	−	2.96306i	−0.0969963	−	0.361995i	0.900318	−	0.435232i	$-0.143334\pi$
$67$	−0.793949	−	2.96306i	−0.0969963	−	0.361995i	−0.997315	+	0.0732371i	$0.976667\pi$
$68$		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
$73$	1.86752	+	0.500400i	0.218576	+	0.0585673i	0.366445	−	0.930440i	$-0.380575\pi$
$73$	1.86752	+	0.500400i	0.218576	+	0.0585673i	−0.147869	+	0.989007i	$0.547241\pi$
$74$		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	0.952428	−	0.304763i	$-0.0985774\pi$
$79$	1.88680	+	3.26803i	0.212281	+	0.367682i	−0.740147	+	0.672445i	$0.765244\pi$
$80$		0			0
$81$	11.0159	+	19.0801i	1.22399	+	2.12001i
$82$		0			0
$83$	−10.6496	+	10.6496i	−1.16894	+	1.16894i	−0.186485	+	0.982458i	$0.559710\pi$
$83$	−10.6496	+	10.6496i	−1.16894	+	1.16894i	−0.982458	+	0.186485i	$0.940290\pi$
$84$		0			0
$85$	−2.49094	+	10.5762i	−0.270180	+	1.14715i
$86$		0			0
$87$	−21.7738	−	21.7738i	−2.33440	−	2.33440i
$88$		0			0
$89$	−2.07573	+	3.59527i	−0.220027	+	0.381098i	−0.954816	−	0.297198i	$-0.903948\pi$
$89$	−2.07573	+	3.59527i	−0.220027	+	0.381098i	0.734789	+	0.678296i	$0.237281\pi$
$90$		0			0
$91$	0.451326	+	0.260573i	0.0473118	+	0.0273155i
$92$		0			0
$93$	−1.38677	−	0.371583i	−0.143801	−	0.0385314i
$94$		0			0
$95$	−2.68474	−	9.36975i	−0.275449	−	0.961316i
$96$		0			0
$97$	7.49651	+	2.00868i	0.761155	+	0.203951i	0.618460	−	0.785816i	$-0.287757\pi$
$97$	7.49651	+	2.00868i	0.761155	+	0.203951i	0.142695	+	0.989767i	$0.454423\pi$
$98$		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	$-0.166529\pi$
$103$	3.72076	+	3.72076i	0.366617	+	0.366617i	−0.499625	+	0.866242i	$0.666529\pi$
$104$		0			0
$105$	−1.18252	+	0.731680i	−0.115402	+	0.0714047i
$106$		0			0
$107$	6.65809	−	6.65809i	0.643662	−	0.643662i	−0.307792	−	0.951454i	$-0.599590\pi$
$107$	6.65809	−	6.65809i	0.643662	−	0.643662i	0.951454	+	0.307792i	$0.0995900\pi$
$108$		0			0
$109$	−4.65411	−	8.06116i	−0.445783	−	0.772119i	0.552323	−	0.833630i	$-0.313741\pi$
$109$	−4.65411	−	8.06116i	−0.445783	−	0.772119i	−0.998106	+	0.0615111i	$0.980408\pi$
$110$		0			0
$111$	10.8465	+	18.7866i	1.02950	+	1.78315i
$112$		0			0
$113$	13.3083	+	13.3083i	1.25194	+	1.25194i	0.954849	+	0.297091i	$0.0960164\pi$
$113$	13.3083	+	13.3083i	1.25194	+	1.25194i	0.297091	+	0.954849i	$0.403984\pi$
$114$		0			0
$115$	2.02412	+	6.72666i	0.188750	+	0.627264i
$116$		0			0
$117$	−18.8554	−	5.05230i	−1.74319	−	0.467085i
$118$		0			0
$119$	0.816666	−	0.471503i	0.0748637	−	0.0432226i
$120$		0			0
$121$	18.5783			1.68894
$122$		0			0
$123$	2.46638	+	9.20466i	0.222386	+	0.829956i
$124$		0			0
$125$	−11.1336	+	1.02133i	−0.995819	+	0.0913506i
$126$		0			0
$127$	2.28608	+	8.53177i	0.202857	+	0.757072i	0.990092	+	0.140419i	$0.0448451\pi$
$127$	2.28608	+	8.53177i	0.202857	+	0.757072i	−0.787235	+	0.616653i	$0.788488\pi$
$128$		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
$133$	−0.432611	+	0.726913i	−0.0375121	+	0.0630313i
$134$		0			0
$135$	20.9609	−	22.2798i	1.80403	−	1.91754i
$136$		0			0
$137$	13.4998	−	3.61726i	1.15337	−	0.309043i	0.369053	−	0.929408i	$-0.379682\pi$
$137$	13.4998	−	3.61726i	1.15337	−	0.309043i	0.784313	+	0.620365i	$0.213016\pi$
$138$		0			0
$139$	−10.8105	−	6.24144i	−0.916933	−	0.529392i	−0.0342778	−	0.999412i	$-0.510913\pi$
$139$	−10.8105	−	6.24144i	−0.916933	−	0.529392i	−0.882655	+	0.470021i	$0.844246\pi$
$140$		0			0
$141$		−	16.0434i		−	1.35109i
$142$		0			0
$143$	−14.1074	+	3.78006i	−1.17972	+	0.316104i
$144$		0			0
$145$	−10.1710	+	18.9269i	−0.844658	+	1.57179i
$146$		0			0
$147$	−21.5508	−	5.77453i	−1.77748	−	0.476275i
$148$		0			0
$149$	−14.2418	+	8.22251i	−1.16673	+	0.673614i	−0.952909	−	0.303258i	$-0.901926\pi$
$149$	−14.2418	+	8.22251i	−1.16673	+	0.673614i	−0.213825	+	0.976872i	$0.568592\pi$
$150$		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
$155$	0.0305428	+	1.00133i	0.00245326	+	0.0804289i
$156$		0			0
$157$	1.29219	−	4.82253i	0.103128	−	0.384880i	−0.894998	−	0.446071i	$-0.852823\pi$
$157$	1.29219	−	4.82253i	0.103128	−	0.384880i	0.998126	+	0.0611904i	$0.0194897\pi$
$158$		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	−0.856586	−	0.516004i	$-0.827419\pi$
$163$	−4.34827	+	4.34827i	−0.340583	+	0.340583i	0.516004	+	0.856586i	$0.327419\pi$
$164$		0			0
$165$	8.93399	−	37.9327i	0.695510	−	2.95306i
$166$		0			0
$167$	−3.89791	−	14.5472i	−0.301630	−	1.12570i	−0.935808	−	0.352510i	$-0.885328\pi$
$167$	−3.89791	−	14.5472i	−0.301630	−	1.12570i	0.634178	−	0.773187i	$-0.281339\pi$
$168$		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
$173$	−1.05131	+	3.92353i	−0.0799295	+	0.298301i	−0.994306	−	0.106565i	$-0.966015\pi$
$173$	−1.05131	+	3.92353i	−0.0799295	+	0.298301i	0.914376	+	0.404865i	$0.132682\pi$
$174$		0			0
$175$	0.726661	+	0.643026i	0.0549304	+	0.0486082i
$176$		0			0
$177$	−8.58508	+	2.30037i	−0.645294	+	0.172906i
$178$		0			0
$179$	−25.6525			−1.91736			−0.958679	−	0.284491i	$-0.908176\pi$
$179$	−25.6525			−1.91736			−0.958679	+	0.284491i	$0.908176\pi$
$180$		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
$185$	10.3721	−	11.0248i	0.762575	−	0.810559i
$186$		0			0
$187$	−6.83995	+	25.5270i	−0.500186	+	1.86672i
$188$		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
$193$	5.97497	−	22.2989i	0.430087	−	1.60511i	−0.322469	−	0.946580i	$-0.604513\pi$
$193$	5.97497	−	22.2989i	0.430087	−	1.60511i	0.752556	−	0.658528i	$-0.228821\pi$
$194$		0			0
$195$	0.586671	+	19.2337i	0.0420124	+	1.37736i
$196$		0			0
$197$	12.1359	+	12.1359i	0.864645	+	0.864645i	0.991873	−	0.127228i	$-0.0406081\pi$
$197$	12.1359	+	12.1359i	0.864645	+	0.864645i	−0.127228	+	0.991873i	$0.540608\pi$
$198$		0			0
$199$	14.7454	+	8.51325i	1.04527	+	0.603488i	0.921322	−	0.388800i	$-0.127110\pi$
$199$	14.7454	+	8.51325i	1.04527	+	0.603488i	0.123950	+	0.992288i	$0.460444\pi$
$200$		0			0
$201$	−9.83017			−0.693367
$202$		0			0
$203$	1.80124	−	0.482642i	0.126423	−	0.0338748i
$204$		0			0
$205$	5.65453	−	3.49873i	0.394929	−	0.244362i
$206$		0			0
$207$	−5.91030	+	22.0576i	−0.410795	+	1.53311i
$208$		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
$213$	−9.78967	−	36.5355i	−0.670777	−	2.50337i
$214$		0			0
$215$	6.71583	+	1.58173i	0.458016	+	0.107873i
$216$		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
$223$	−0.375005	+	1.39954i	−0.0251122	+	0.0937199i	−0.977345	−	0.211654i	$-0.932115\pi$
$223$	−0.375005	+	1.39954i	−0.0251122	+	0.0937199i	0.952232	+	0.305374i	$0.0987816\pi$
$224$		0			0
$225$	−32.5249	−	16.2204i	−2.16833	−	1.08136i
$226$		0			0
$227$	−4.20077	+	4.20077i	−0.278815	+	0.278815i	−0.832636	−	0.553821i	$-0.813169\pi$
$227$	−4.20077	+	4.20077i	−0.278815	+	0.278815i	0.553821	+	0.832636i	$0.313169\pi$
$228$		0			0
$229$		−	24.6251i		−	1.62727i	−0.581376	−	0.813635i	$-0.697486\pi$
$229$		−	24.6251i		−	1.62727i	0.581376	−	0.813635i	$-0.302514\pi$
$230$		0			0
$231$	−2.92905	+	1.69109i	−0.192717	+	0.111265i
$232$		0			0
$233$	15.3261	+	4.10662i	1.00405	+	0.269034i	0.723140	−	0.690701i	$-0.242698\pi$
$233$	15.3261	+	4.10662i	1.00405	+	0.269034i	0.280907	+	0.959735i	$0.409365\pi$
$234$		0			0
$235$	−10.7200	+	3.22575i	−0.699293	+	0.210425i
$236$		0			0
$237$	11.6806	−	3.12980i	0.758734	−	0.203302i
$238$		0			0
$239$			4.41162i			0.285364i	0.989769	+	0.142682i	$0.0455726\pi$
$239$			4.41162i			0.285364i	−0.989769	+	0.142682i	$0.954427\pi$
$240$		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
$243$	28.5536	−	7.65093i	1.83172	−	0.490807i
$244$		0			0
$245$	0.474645	+	15.5610i	0.0303240	+	0.994158i
$246$		0			0
$247$	5.71810	+	10.2139i	0.363834	+	0.649894i
$248$		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
$253$	4.42201	+	16.5032i	0.278009	+	1.03754i
$254$		0			0
$255$	30.6711	+	16.4822i	1.92070	+	1.03215i
$256$		0			0
$257$	−2.88174	−	10.7548i	−0.179758	−	0.670866i	−0.995692	−	0.0927211i	$-0.970443\pi$
$257$	−2.88174	−	10.7548i	−0.179758	−	0.670866i	0.815934	−	0.578145i	$-0.196223\pi$
$258$		0			0
$259$	−1.31371			−0.0816297
$260$		0			0
$261$	−60.4912	+	34.9246i	−3.74431	+	2.16178i
$262$		0			0
$263$	−6.48694	−	1.73817i	−0.400002	−	0.107180i	0.0532094	−	0.998583i	$-0.483055\pi$
$263$	−6.48694	−	1.73817i	−0.400002	−	0.107180i	−0.453211	+	0.891403i	$0.649722\pi$
$264$		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	$0.0113782\pi$
$269$	8.70299	+	15.0740i	0.530631	+	0.919079i	−0.468730	+	0.883341i	$0.655288\pi$
$270$		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
$275$	−27.1424	+	1.65735i	−1.63675	+	0.0999419i
$276$		0			0
$277$	−3.11564	−	3.11564i	−0.187201	−	0.187201i	0.607284	−	0.794485i	$-0.292259\pi$
$277$	−3.11564	−	3.11564i	−0.187201	−	0.187201i	−0.794485	+	0.607284i	$0.792259\pi$
$278$		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
$283$	21.5026	+	5.76161i	1.27820	+	0.342492i	0.833166	−	0.553023i	$-0.186526\pi$
$283$	21.5026	+	5.76161i	1.27820	+	0.342492i	0.445032	+	0.895515i	$0.353192\pi$
$284$		0			0
$285$	−31.2293	+	0.538981i	−1.84986	+	0.0319265i
$286$		0			0
$287$	−0.557426	−	0.149362i	−0.0329038	−	0.00881655i
$288$		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	$-0.313094\pi$
$293$	−4.76693	−	4.76693i	−0.278487	−	0.278487i	−0.832505	+	0.554018i	$0.813094\pi$
$294$		0			0
$295$	3.26323	+	5.27392i	0.189993	+	0.307059i
$296$		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
$307$	3.17160	+	0.849827i	0.181013	+	0.0485022i	0.348187	−	0.937425i	$-0.386798\pi$
$307$	3.17160	+	0.849827i	0.181013	+	0.0485022i	−0.167174	+	0.985927i	$0.553464\pi$
$308$		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
$313$	−3.36656	−	12.5642i	−0.190289	−	0.710169i	−0.993436	−	0.114388i	$-0.963509\pi$
$313$	−3.36656	−	12.5642i	−0.190289	−	0.710169i	0.803147	−	0.595781i	$-0.203157\pi$
$314$		0			0
$315$	0.908912	+	3.02054i	0.0512114	+	0.170188i
$316$		0			0
$317$	3.68876	+	13.7666i	0.207181	+	0.773211i	0.988774	+	0.149421i	$0.0477411\pi$
$317$	3.68876	+	13.7666i	0.207181	+	0.773211i	−0.781592	+	0.623790i	$0.785592\pi$
$318$		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
$323$	21.1791	+	0.280335i	1.17844	+	0.0155983i
$324$		0			0
$325$	12.7338	−	4.25923i	0.706342	−	0.236259i
$326$		0			0
$327$	−28.8121	+	7.72019i	−1.59331	+	0.426927i
$328$		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
$333$	47.5307	−	12.7358i	2.60467	−	0.697919i
$334$		0			0
$335$	1.97650	+	6.56839i	0.107988	+	0.358869i
$336$		0			0
$337$	9.99167	+	2.67726i	0.544281	+	0.145840i	0.520475	−	0.853877i	$-0.325755\pi$
$337$	9.99167	+	2.67726i	0.544281	+	0.145840i	0.0238059	+	0.999717i	$0.492422\pi$
$338$		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
$345$	22.5001	−	0.686302i	1.21136	−	0.0369493i
$346$		0			0
$347$	−3.12967	+	11.6801i	−0.168010	+	0.627020i	0.829628	+	0.558317i	$0.188553\pi$
$347$	−3.12967	+	11.6801i	−0.168010	+	0.627020i	−0.997637	+	0.0687031i	$0.978114\pi$
$348$		0			0
$349$		−	26.3286i		−	1.40934i	−0.709536	−	0.704670i	$-0.751095\pi$
$349$		−	26.3286i		−	1.40934i	0.709536	−	0.704670i	$-0.248905\pi$
$350$		0			0
$351$	−18.3688	+	31.8157i	−0.980454	+	1.69820i
$352$		0			0
$353$	−19.1514	+	19.1514i	−1.01933	+	1.01933i	−0.0195178	+	0.999810i	$0.506213\pi$
$353$	−19.1514	+	19.1514i	−1.01933	+	1.01933i	−0.999810	+	0.0195178i	$0.993787\pi$
$354$		0			0
$355$	−22.4442	+	13.8873i	−1.19122	+	0.737063i
$356$		0			0
$357$	−0.782123	−	2.91892i	−0.0413944	−	0.154486i
$358$		0			0
$359$	−2.59548	+	1.49850i	−0.136984	+	0.0790878i	−0.566926	−	0.823769i	$-0.691867\pi$
$359$	−2.59548	+	1.49850i	−0.136984	+	0.0790878i	0.429942	+	0.902857i	$0.358534\pi$
$360$		0			0
$361$	−16.7002	+	9.06115i	−0.878956	+	0.476903i
$362$		0			0
$363$	15.4088	−	57.5063i	0.808751	−	3.01830i
$364$		0			0
$365$	−4.20807	−	0.991093i	−0.220260	−	0.0518762i
$366$		0			0
$367$	12.3670	−	3.31372i	0.645551	−	0.172975i	0.0788343	−	0.996888i	$-0.474880\pi$
$367$	12.3670	−	3.31372i	0.645551	−	0.172975i	0.566716	+	0.823913i	$0.308214\pi$
$368$		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	0.992050	+	0.125848i	$0.0401652\pi$
$373$	21.5902	+	21.5902i	1.11790	+	1.11790i	0.125848	+	0.992050i	$0.459835\pi$
$374$		0			0
$375$	−6.07277	+	35.3094i	−0.313597	+	1.82337i
$376$		0			0
$377$	6.67876	−	24.9255i	0.343974	−	1.28373i
$378$		0			0
$379$	1.40439			0.0721386			0.0360693	−	0.999349i	$-0.488516\pi$
$379$	1.40439			0.0721386			0.0360693	+	0.999349i	$0.488516\pi$
$380$		0			0
$381$	28.3048			1.45010
$382$		0			0
$383$	7.24237	−	27.0289i	0.370068	−	1.38111i	−0.490352	−	0.871525i	$-0.663132\pi$
$383$	7.24237	−	27.0289i	0.370068	−	1.38111i	0.860419	−	0.509587i	$-0.170202\pi$
$384$		0			0
$385$	1.71889	+	1.61713i	0.0876028	+	0.0824168i
$386$		0			0
$387$	15.8599	+	15.8599i	0.806203	+	0.806203i
$388$		0			0
$389$	−15.8300	−	9.13946i	−0.802613	−	0.463389i	0.0417711	−	0.999127i	$-0.486700\pi$
$389$	−15.8300	−	9.13946i	−0.802613	−	0.463389i	−0.844384	+	0.535738i	$0.820033\pi$
$390$		0			0
$391$	−15.2653			−0.772001
$392$		0			0
$393$	−4.46086	+	1.19528i	−0.225021	+	0.0602941i
$394$		0			0
$395$	−4.43983	−	7.17550i	−0.223392	−	0.361039i
$396$		0			0
$397$	−3.34165	+	12.4712i	−0.167712	+	0.625911i	0.829966	+	0.557814i	$0.188360\pi$
$397$	−3.34165	+	12.4712i	−0.167712	+	0.625911i	−0.997679	+	0.0680976i	$0.978307\pi$
$398$		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
$403$	−0.311392	−	1.16213i	−0.0155115	−	0.0578898i
$404$		0			0
$405$	−25.9216	−	41.8936i	−1.28806	−	2.08171i
$406$		0			0
$407$	26.0331	−	26.0331i	1.29041	−	1.29041i
$408$		0			0
$409$	−3.17563	+	5.50035i	−0.157025	+	0.271975i	−0.933794	−	0.357810i	$-0.883524\pi$
$409$	−3.17563	+	5.50035i	−0.157025	+	0.271975i	0.776770	+	0.629785i	$0.216857\pi$
$410$		0			0
$411$		−	44.7866i		−	2.20916i
$412$		0			0
$413$	0.139308	−	0.519905i	0.00685490	−	0.0255829i
$414$		0			0
$415$	23.0761	−	24.5281i	1.13276	−	1.20404i
$416$		0			0
$417$	−28.2855	+	28.2855i	−1.38515	+	1.38515i
$418$		0			0
$419$		−	32.1321i		−	1.56975i	−0.619651	−	0.784877i	$-0.712726\pi$
$419$		−	32.1321i		−	1.56975i	0.619651	−	0.784877i	$-0.287274\pi$
$420$		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
$423$	−35.1521	−	9.41898i	−1.70915	−	0.457966i
$424$		0			0
$425$	4.84630	−	23.8080i	0.235080	−	1.15486i
$426$		0			0
$427$	2.09462	−	0.561250i	0.101366	−	0.0271608i
$428$		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
$433$	−18.2612	+	4.89308i	−0.877579	+	0.235147i	−0.669362	−	0.742936i	$-0.733433\pi$
$433$	−18.2612	+	4.89308i	−0.877579	+	0.235147i	−0.208217	+	0.978083i	$0.566766\pi$
$434$		0			0
$435$	50.1495	+	47.1807i	2.40448	+	2.26214i
$436$		0			0
$437$	11.9485	−	6.68918i	0.571573	−	0.319987i
$438$		0			0
$439$	−3.60234	−	6.23944i	−0.171930	−	0.297792i	0.767164	−	0.641451i	$-0.221667\pi$
$439$	−3.60234	−	6.23944i	−0.171930	−	0.297792i	−0.939095	+	0.343658i	$0.888334\pi$
$440$		0			0
$441$	−25.3048	+	43.8291i	−1.20499	+	2.08710i
$442$		0			0
$443$	−1.64721	−	6.14747i	−0.0782612	−	0.292075i	0.915692	−	0.401881i	$-0.131644\pi$
$443$	−1.64721	−	6.14747i	−0.0782612	−	0.292075i	−0.993953	+	0.109806i	$0.964977\pi$
$444$		0			0
$445$	4.39421	−	8.17703i	0.208306	−	0.387629i
$446$		0			0
$447$	13.6394	+	50.9030i	0.645122	+	2.40763i
$448$		0			0
$449$	−11.8083			−0.557268			−0.278634	−	0.960397i	$-0.589882\pi$
$449$	−11.8083			−0.557268			−0.278634	+	0.960397i	$0.589882\pi$
$450$		0			0
$451$	14.0061	−	8.08641i	0.659520	−	0.380774i
$452$		0			0
$453$	26.8582	+	7.19663i	1.26191	+	0.338127i
$454$		0			0
$455$	−1.02649	−	0.551620i	−0.0481227	−	0.0258604i
$456$		0			0
$457$	1.13144	+	1.13144i	0.0529263	+	0.0529263i	0.733075	−	0.680148i	$-0.238085\pi$
$457$	1.13144	+	1.13144i	0.0529263	+	0.0529263i	−0.680148	+	0.733075i	$0.738085\pi$
$458$		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	−0.853949	−	0.520357i	$-0.825799\pi$
$463$	−7.17804	+	7.17804i	−0.333592	+	0.333592i	0.520357	+	0.853949i	$0.325799\pi$
$464$		0			0
$465$	3.12480	+	0.735959i	0.144909	+	0.0341293i
$466$		0			0
$467$	13.3434	+	13.3434i	0.617457	+	0.617457i	0.944878	−	0.327421i	$-0.106180\pi$
$467$	13.3434	+	13.3434i	0.617457	+	0.617457i	−0.327421	+	0.944878i	$0.606180\pi$
$468$		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
$473$	16.2095	+	4.34331i	0.745311	+	0.199706i
$474$		0			0
$475$	6.63924	+	20.7586i	0.304629	+	0.952471i
$476$		0			0
$477$	−32.2782	−	8.64892i	−1.47792	−	0.396007i
$478$		0			0
$479$	−15.3649	−	8.87094i	−0.702041	−	0.405324i	0.106066	−	0.994359i	$-0.466175\pi$
$479$	−15.3649	−	8.87094i	−0.702041	−	0.405324i	−0.808107	+	0.589035i	$0.799508\pi$
$480$		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
$485$	−16.8918	−	3.97840i	−0.767019	−	0.180650i
$486$		0			0
$487$	24.7545	−	24.7545i	1.12174	−	1.12174i	0.130255	−	0.991481i	$-0.458420\pi$
$487$	24.7545	−	24.7545i	1.12174	−	1.12174i	0.991481	−	0.130255i	$-0.0415796\pi$
$488$		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
$497$	2.21256	+	0.592854i	0.0992469	+	0.0265931i
$498$		0			0
$499$	22.8568	−	13.1964i	1.02321	−	0.590750i	0.108178	−	0.994132i	$-0.465498\pi$
$499$	22.8568	−	13.1964i	1.02321	−	0.590750i	0.915032	+	0.403381i	$0.132165\pi$
$500$		0			0
$501$	−48.2615			−2.15617
$502$		0			0
$503$	11.3798	+	42.4701i	0.507401	+	1.89365i	0.444849	+	0.895606i	$0.353257\pi$
$503$	11.3798	+	42.4701i	0.507401	+	1.89365i	0.0625524	+	0.998042i	$0.480076\pi$
$504$		0			0
$505$	1.15980	−	2.15824i	0.0516105	−	0.0960402i
$506$		0			0
$507$	4.80087	+	17.9171i	0.213214	+	0.795727i
$508$		0			0
$509$	9.13718	−	15.8261i	0.404998	−	0.701478i	−0.589323	−	0.807898i	$-0.700605\pi$
$509$	9.13718	−	15.8261i	0.404998	−	0.701478i	0.994321	+	0.106420i	$0.0339388\pi$
$510$		0			0
$511$	0.187601	+	0.324934i	0.00829898	+	0.0143743i
$512$		0			0
$513$	−51.2428	−	30.4964i	−2.26243	−	1.34645i
$514$		0			0
$515$	−8.56966	−	8.06235i	−0.377624	−	0.355270i
$516$		0			0
$517$	−26.3003	+	7.04715i	−1.15669	+	0.309933i
$518$		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
$523$	−8.25991	+	2.21323i	−0.361180	+	0.0967780i	−0.434846	−	0.900505i	$-0.643197\pi$
$523$	−8.25991	+	2.21323i	−0.361180	+	0.0967780i	0.0736652	+	0.997283i	$0.476530\pi$
$524$		0			0
$525$	2.59307	−	1.71594i	0.113171	−	0.0748898i
$526$		0			0
$527$	−2.10285	−	0.563457i	−0.0916016	−	0.0245446i
$528$		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
$535$	−14.4271	+	15.3349i	−0.623739	+	0.662987i
$536$		0			0
$537$	−21.2760	+	79.4033i	−0.918129	+	3.42650i
$538$		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
$545$	10.9516	+	17.6996i	0.469116	+	0.758169i
$546$		0			0
$547$	−8.09830	−	30.2233i	−0.346258	−	1.29225i	−0.891135	−	0.453737i	$-0.850090\pi$
$547$	−8.09830	−	30.2233i	−0.346258	−	1.29225i	0.544877	−	0.838516i	$-0.316576\pi$
$548$		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
$553$	−0.189538	+	0.707364i	−0.00805996	+	0.0300802i
$554$		0			0
$555$	−25.5229	−	41.2492i	−1.08339	−	1.75093i
$556$		0			0
$557$	24.5196	−	6.57002i	1.03893	−	0.278381i	0.301260	−	0.953542i	$-0.402593\pi$
$557$	24.5196	−	6.57002i	1.03893	−	0.278381i	0.737670	+	0.675161i	$0.235926\pi$
$558$		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	$-0.152039\pi$
$563$	10.1647	+	10.1647i	0.428392	+	0.428392i	−0.459689	+	0.888080i	$0.652039\pi$
$564$		0			0
$565$	−30.6517	−	28.8372i	−1.28953	−	1.21319i
$566$		0			0
$567$	−1.10660	+	4.12989i	−0.0464729	+	0.173439i
$568$		0			0
$569$	17.6738			0.740926			0.370463	−	0.928847i	$-0.379199\pi$
$569$	17.6738			0.740926			0.370463	+	0.928847i	$0.379199\pi$
$570$		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
$573$	−0.00785641	+	0.0293205i	−0.000328206	+	0.00122488i
$574$		0			0
$575$	−4.98255	−	14.8963i	−0.207787	−	0.621218i
$576$		0			0
$577$	−33.4182	−	33.4182i	−1.39122	−	1.39122i	−0.822605	−	0.568614i	$-0.807480\pi$
$577$	−33.4182	−	33.4182i	−1.39122	−	1.39122i	−0.568614	−	0.822605i	$-0.692520\pi$
$578$		0			0
$579$	−64.0671	−	36.9891i	−2.66254	−	1.53722i
$580$		0			0
$581$	−2.92275			−0.121256
$582$		0			0
$583$	−24.1501	+	6.47100i	−1.00020	+	0.268002i
$584$		0			0
$585$	42.4869	+	10.0066i	1.75662	+	0.413722i
$586$		0			0
$587$	9.64470	−	35.9945i	0.398079	−	1.48565i	−0.418393	−	0.908266i	$-0.637406\pi$
$587$	9.64470	−	35.9945i	0.398079	−	1.48565i	0.816472	−	0.577385i	$-0.195927\pi$
$588$		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
$593$	−2.78425	−	10.3910i	−0.114335	−	0.426705i	0.884901	−	0.465779i	$-0.154226\pi$
$593$	−2.78425	−	10.3910i	−0.114335	−	0.426705i	−0.999236	+	0.0390739i	$0.987559\pi$
$594$		0			0
$595$	−1.79313	+	1.10950i	−0.0735111	+	0.0454849i
$596$		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	$0.408731\pi$
$599$	−16.8693	+	29.2185i	−0.689261	+	1.19384i	−0.972077	+	0.234661i	$0.924602\pi$
$600$		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
$603$	−5.77124	+	21.5386i	−0.235023	+	0.877119i
$604$		0			0
$605$	−41.5231	+	1.26655i	−1.68815	+	0.0514924i
$606$		0			0
$607$	26.7620	−	26.7620i	1.08624	−	1.08624i	0.0903240	−	0.995912i	$-0.471210\pi$
$607$	26.7620	−	26.7620i	1.08624	−	1.08624i	0.995912	−	0.0903240i	$-0.0287903\pi$
$608$		0			0
$609$		−	5.97577i		−	0.242150i
$610$		0			0
$611$	11.6433	−	6.72227i	0.471038	−	0.271954i
$612$		0			0
$613$	35.4747	+	9.50543i	1.43281	+	0.383921i	0.890010	−	0.455941i	$-0.150697\pi$
$613$	35.4747	+	9.50543i	1.43281	+	0.383921i	0.542801	+	0.839861i	$0.317364\pi$
$614$		0			0
$615$	−6.13994	−	20.4045i	−0.247586	−	0.822790i
$616$		0			0
$617$	−7.90202	+	2.11734i	−0.318123	+	0.0852409i	−0.414347	−	0.910119i	$-0.635990\pi$
$617$	−7.90202	+	2.11734i	−0.318123	+	0.0852409i	0.0962240	+	0.995360i	$0.469323\pi$
$618$		0			0
$619$			2.04139i			0.0820503i	0.999158	+	0.0410251i	$0.0130624\pi$
$619$			2.04139i			0.0820503i	−0.999158	+	0.0410251i	$0.986938\pi$
$620$		0			0
$621$	37.2188	+	21.4883i	1.49354	+	0.862295i
$622$		0			0
$623$	−0.778196	+	0.208517i	−0.0311777	+	0.00835405i
$624$		0			0
$625$	24.8143	−	3.04172i	0.992571	−	0.121669i
$626$		0			0
$627$	−75.9610	−	1.00545i	−3.03359	−	0.0401537i
$628$		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
$633$	0.637395	+	2.37879i	0.0253342	+	0.0945485i
$634$		0			0
$635$	−5.69110	−	18.9129i	−0.225844	−	0.750536i
$636$		0			0
$637$	−4.83913	−	18.0599i	−0.191733	−	0.715558i
$638$		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
$643$	−40.5068	−	10.8538i	−1.59743	−	0.428030i	−0.653166	−	0.757215i	$-0.726559\pi$
$643$	−40.5068	−	10.8538i	−1.59743	−	0.428030i	−0.944266	+	0.329185i	$0.893226\pi$
$644$		0			0
$645$	10.4661	−	19.4759i	0.412101	−	0.766863i
$646$		0			0
$647$	21.3988	+	21.3988i	0.841272	+	0.841272i	0.989024	−	0.147752i	$-0.0472039\pi$
$647$	21.3988	+	21.3988i	0.841272	+	0.841272i	−0.147752	+	0.989024i	$0.547204\pi$
$648$		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	−0.170468	−	0.985363i	$-0.554528\pi$
$653$	20.8237	−	20.8237i	0.814895	−	0.814895i	0.985363	+	0.170468i	$0.0545279\pi$
$654$		0			0
$655$	1.69559	+	2.74036i	0.0662524	+	0.107075i
$656$		0			0
$657$	−9.93763	−	9.93763i	−0.387704	−	0.387704i
$658$		0			0
$659$	12.3111	−	21.3235i	0.479573	−	0.830645i	−0.520153	−	0.854073i	$-0.674125\pi$
$659$	12.3111	−	21.3235i	0.479573	−	0.830645i	0.999726	+	0.0234286i	$0.00745825\pi$
$660$		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
$663$	−40.3919	−	10.8230i	−1.56869	−	0.420329i
$664$		0			0
$665$	0.917342	−	1.65416i	0.0355730	−	0.0641457i
$666$		0			0
$667$	−29.1585	−	7.81298i	−1.12902	−	0.302520i
$668$		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	$-0.375458\pi$
$673$	−14.0886	−	14.0886i	−0.543077	−	0.543077i	−0.924430	+	0.381353i	$0.875458\pi$
$674$		0			0
$675$	−45.3293	+	51.2251i	−1.74473	+	1.97165i
$676$		0			0
$677$	6.44919	−	6.44919i	0.247862	−	0.247862i	−0.572230	−	0.820093i	$-0.693922\pi$
$677$	6.44919	−	6.44919i	0.247862	−	0.247862i	0.820093	+	0.572230i	$0.193922\pi$
$678$		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	0.996132	+	0.0878690i	$0.0280057\pi$
$683$	28.3296	+	28.3296i	1.08400	+	1.08400i	0.0878690	+	0.996132i	$0.471994\pi$
$684$		0			0
$685$	−29.9258	+	9.00501i	−1.14341	+	0.344064i
$686$		0			0
$687$	−76.2230	−	20.4239i	−2.90809	−	0.779220i
$688$		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
$693$	1.98566	+	7.41058i	0.0754289	+	0.281505i
$694$		0			0
$695$	24.5872	+	13.2128i	0.932647	+	0.501190i
$696$		0			0
$697$	3.73994	+	13.9576i	0.141660	+	0.528684i
$698$		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
$703$	−25.3566	−	15.0906i	−0.956343	−	0.569153i
$704$		0			0
$705$	1.09373	+	35.8574i	0.0411922	+	1.35047i
$706$		0			0
$707$	−0.205396	+	0.0550357i	−0.00772471	+	0.00206983i
$708$		0			0
$709$	20.3338	+	11.7398i	0.763654	+	0.440896i	0.830606	−	0.556861i	$-0.187994\pi$
$709$	20.3338	+	11.7398i	0.763654	+	0.440896i	−0.0669523	+	0.997756i	$0.521328\pi$
$710$		0			0
$711$		−	27.4304i		−	1.02872i
$712$		0			0
$713$	−1.35949	+	0.364274i	−0.0509132	+	0.0136422i
$714$		0			0
$715$	31.2727	−	9.41029i	1.16953	−	0.351925i
$716$		0			0
$717$	13.6555	+	3.65897i	0.509973	+	0.136647i
$718$		0			0
$719$	8.64356	−	4.99036i	0.322350	−	0.186109i	−0.330089	−	0.943950i	$-0.607079\pi$
$719$	8.64356	−	4.99036i	0.322350	−	0.186109i	0.652440	+	0.757841i	$0.273746\pi$
$720$		0			0
$721$			1.02115i			0.0380298i
$722$		0			0
$723$	−26.8064	+	26.8064i	−0.996941	+	0.996941i
$724$		0			0
$725$	21.4422	−	42.9956i	0.796344	−	1.59681i
$726$		0			0
$727$	−8.53725	+	31.8614i	−0.316629	+	1.18168i	0.605834	+	0.795591i	$0.292839\pi$
$727$	−8.53725	+	31.8614i	−0.316629	+	1.18168i	−0.922463	+	0.386085i	$0.873827\pi$
$728$		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	−0.999538	−	0.0303850i	$-0.990327\pi$
$733$	−26.2388	+	26.2388i	−0.969153	+	0.969153i	0.0303850	+	0.999538i	$0.490327\pi$
$734$		0			0
$735$	48.5604	+	11.4370i	1.79118	+	0.421862i
$736$		0			0
$737$	4.31797	+	16.1149i	0.159054	+	0.593599i
$738$		0			0
$739$	−2.68922	+	1.55262i	−0.0989246	+	0.0571141i	−0.548646	−	0.836055i	$-0.684857\pi$
$739$	−2.68922	+	1.55262i	−0.0989246	+	0.0571141i	0.449722	+	0.893169i	$0.351523\pi$
$740$		0			0
$741$	36.3581	−	9.22813i	1.33565	−	0.339004i
$742$		0			0
$743$	1.03330	−	3.85631i	0.0379079	−	0.141474i	−0.944378	−	0.328861i	$-0.893335\pi$
$743$	1.03330	−	3.85631i	0.0379079	−	0.141474i	0.982286	+	0.187387i	$0.0600018\pi$
$744$		0			0
$745$	31.2703	−	19.3484i	1.14565	−	0.708872i
$746$		0			0
$747$	105.747	−	28.3348i	3.86908	−	1.03672i
$748$		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
$755$	−0.591537	−	19.3933i	−0.0215282	−	0.705793i
$756$		0			0
$757$	−8.52402	+	31.8121i	−0.309811	+	1.15623i	0.618914	+	0.785459i	$0.287573\pi$
$757$	−8.52402	+	31.8121i	−0.309811	+	1.15623i	−0.928724	+	0.370771i	$0.879094\pi$
$758$		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
$763$	0.467528	−	1.74484i	0.0169256	−	0.0631674i
$764$		0			0
$765$	54.1205	−	57.5259i	1.95673	−	2.07985i
$766$		0			0
$767$	−5.26667	−	5.26667i	−0.190169	−	0.190169i
$768$		0			0
$769$	30.9201	+	17.8517i	1.11501	+	0.643749i	0.940121	−	0.340840i	$-0.110711\pi$
$769$	30.9201	+	17.8517i	1.11501	+	0.643749i	0.174885	+	0.984589i	$0.444045\pi$
$770$		0			0
$771$	−35.6799			−1.28498
$772$		0			0
$773$	−9.79800	+	2.62537i	−0.352410	+	0.0944279i	−0.430681	−	0.902504i	$-0.641727\pi$
$773$	−9.79800	+	2.62537i	−0.352410	+	0.0944279i	0.0782714	+	0.996932i	$0.475060\pi$
$774$		0			0
$775$	−0.136528	−	2.23592i	−0.00490423	−	0.0803168i
$776$		0			0
$777$	−1.08958	+	4.06637i	−0.0390885	+	0.145880i
$778$		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
$783$	34.0232	+	126.976i	1.21589	+	4.53777i
$784$		0			0
$785$	−2.55932	+	10.8666i	−0.0913462	+	0.387845i
$786$		0			0
$787$	−27.0647	+	27.0647i	−0.964752	+	0.964752i	−0.999400	−	0.0346473i	$-0.988969\pi$
$787$	−27.0647	+	27.0647i	−0.964752	+	0.964752i	0.0346473	+	0.999400i	$0.488969\pi$
$788$		0			0
$789$	−10.7605	+	18.6377i	−0.383082	+	0.663518i
$790$		0			0
$791$			3.65243i			0.129866i
$792$		0			0
$793$	7.76655	−	28.9851i	0.275798	−	1.02929i
$794$		0			0
$795$	1.00431	+	32.9258i	0.0356192	+	1.16776i
$796$		0			0
$797$	13.4978	−	13.4978i	0.478116	−	0.478116i	−0.426413	−	0.904529i	$-0.640223\pi$
$797$	13.4978	−	13.4978i	0.478116	−	0.478116i	0.904529	+	0.426413i	$0.140223\pi$
$798$		0			0
$799$		−	24.3276i		−	0.860650i
$800$		0			0
$801$	26.1341	−	15.0886i	0.923405	−	0.533128i
$802$		0			0
$803$	−10.1567	−	2.72147i	−0.358421	−	0.0960387i
$804$		0			0
$805$	−0.645299	+	1.20082i	−0.0227438	+	0.0423232i
$806$		0			0
$807$	53.8775	−	14.4364i	1.89658	−	0.508186i
$808$		0			0
$809$			30.1477i			1.05994i	0.848018	+	0.529968i	$0.177796\pi$
$809$			30.1477i			1.05994i	−0.848018	+	0.529968i	$0.822204\pi$
$810$		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
$813$	12.8358	−	3.43935i	0.450172	−	0.120623i
$814$		0			0
$815$	9.42208	−	10.0149i	0.330041	−	0.350808i
$816$		0			0
$817$	0.178011	−	13.4486i	0.00622780	−	0.470506i
$818$		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
$823$	−5.52303	−	20.6122i	−0.192521	−	0.718496i	−0.992895	−	0.118996i	$-0.962033\pi$
$823$	−5.52303	−	20.6122i	−0.192521	−	0.718496i	0.800374	−	0.599501i	$-0.204634\pi$
$824$		0			0
$825$	−17.3817	+	85.3897i	−0.605154	+	2.97289i
$826$		0			0
$827$	10.8733	+	40.5797i	0.378101	+	1.41109i	0.848760	+	0.528778i	$0.177350\pi$
$827$	10.8733	+	40.5797i	0.378101	+	1.41109i	−0.470658	+	0.882315i	$0.655984\pi$
$828$		0			0
$829$	−8.24412			−0.286330			−0.143165	−	0.989699i	$-0.545728\pi$
$829$	−8.24412			−0.286330			−0.143165	+	0.989699i	$0.545728\pi$
$830$		0			0
$831$	−12.2281	+	7.05987i	−0.424187	+	0.244904i
$832$		0			0
$833$	−32.6790	−	8.75631i	−1.13226	−	0.303388i
$834$		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	0.572393	−	0.819979i	$-0.306015\pi$
$839$	−12.2792	−	21.2683i	−0.423927	−	0.734262i	−0.996320	+	0.0857171i	$0.972682\pi$
$840$		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
$845$	11.0067	−	6.81037i	0.378642	−	0.234284i
$846$		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
$853$	19.4994	+	5.22484i	0.667646	+	0.178895i	0.576694	−	0.816960i	$-0.304342\pi$
$853$	19.4994	+	5.22484i	0.667646	+	0.178895i	0.0909519	+	0.995855i	$0.471009\pi$
$854$		0			0
$855$	−17.1536	+	68.7419i	−0.586641	+	2.35092i
$856$		0			0
$857$	−4.37606	−	1.17256i	−0.149483	−	0.0400539i	0.183301	−	0.983057i	$-0.441322\pi$
$857$	−4.37606	−	1.17256i	−0.149483	−	0.0400539i	−0.332785	+	0.943003i	$0.607988\pi$
$858$		0			0
$859$	27.2399	+	15.7270i	0.929413	+	0.536597i	0.886626	−	0.462487i	$-0.153043\pi$
$859$	27.2399	+	15.7270i	0.929413	+	0.536597i	0.0427871	+	0.999084i	$0.486376\pi$
$860$		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	$-0.0726182\pi$
$863$	21.9717	+	21.9717i	0.747926	+	0.747926i	−0.226163	+	0.974089i	$0.572618\pi$
$864$		0			0
$865$	2.08222	−	8.84088i	0.0707977	−	0.300599i
$866$		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
$877$	−10.1632	−	2.72321i	−0.343186	−	0.0919564i	0.0831094	−	0.996540i	$-0.473515\pi$
$877$	−10.1632	−	2.72321i	−0.343186	−	0.0919564i	−0.426295	+	0.904584i	$0.640182\pi$
$878$		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
$883$	5.28376	+	19.7192i	0.177813	+	0.663605i	0.996055	+	0.0887328i	$0.0282817\pi$
$883$	5.28376	+	19.7192i	0.177813	+	0.663605i	−0.818243	+	0.574873i	$0.805052\pi$
$884$		0			0
$885$	19.0311	−	5.72666i	0.639723	−	0.192499i
$886$		0			0
$887$	−11.9957	−	44.7684i	−0.402775	−	1.50318i	−0.808123	−	0.589014i	$-0.799516\pi$
$887$	−11.9957	−	44.7684i	−0.402775	−	1.50318i	0.405348	−	0.914163i	$-0.367150\pi$
$888$		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
$893$	10.6602	+	19.0417i	0.356731	+	0.637207i
$894$		0			0
$895$	57.3341	−	1.74881i	1.91647	−	0.0584564i
$896$		0			0
$897$	−26.1132	+	6.99702i	−0.871896	+	0.233624i
$898$		0			0
$899$	−3.72829	−	2.15253i	−0.124346	−	0.0717909i
$900$		0			0
$901$		−	22.3387i		−	0.744211i
$902$		0			0
$903$	−1.85349	+	0.496642i	−0.0616804	+	0.0165272i
$904$		0			0
$905$	−37.8463	−	20.3380i	−1.25805	−	0.676058i
$906$		0			0
$907$	−32.3725	−	8.67420i	−1.07491	−	0.288022i	−0.322403	−	0.946603i	$-0.604490\pi$
$907$	−32.3725	−	8.67420i	−1.07491	−	0.288022i	−0.752510	+	0.658581i	$0.771157\pi$
$908$		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
$915$	58.3174	+	54.8651i	1.92791	+	1.81378i
$916$		0			0
$917$	0.0723854	−	0.270146i	0.00239038	−	0.00892100i
$918$		0			0
$919$		−	20.8285i		−	0.687070i	−0.939140	−	0.343535i	$-0.888376\pi$
$919$		−	20.8285i		−	0.687070i	0.939140	−	0.343535i	$-0.111624\pi$
$920$		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
$925$	−22.4304	+	25.3478i	−0.737508	+	0.833432i
$926$		0			0
$927$	−9.89965	−	36.9460i	−0.325147	−	1.21347i
$928$		0			0
$929$	18.6425	−	10.7633i	0.611641	−	0.353131i	−0.161966	−	0.986796i	$-0.551784\pi$
$929$	18.6425	−	10.7633i	0.611641	−	0.353131i	0.773608	+	0.633665i	$0.218450\pi$
$930$		0			0
$931$	29.4154	−	7.46601i	0.964052	−	0.244689i
$932$		0			0
$933$	11.3715	−	42.4391i	0.372287	−	1.38939i
$934$		0			0
$935$	13.5472	−	57.5199i	0.443041	−	1.88110i
$936$		0			0
$937$	−12.6073	+	3.37812i	−0.411863	+	0.110358i	−0.458800	−	0.888540i	$-0.651721\pi$
$937$	−12.6073	+	3.37812i	−0.411863	+	0.110358i	0.0469373	+	0.998898i	$0.485054\pi$
$938$		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
$945$	5.93366	−	0.180990i	0.193022	−	0.00588759i
$946$		0			0
$947$	6.33703	−	23.6501i	0.205926	−	0.768526i	−0.783240	−	0.621720i	$-0.786434\pi$
$947$	6.33703	−	23.6501i	0.205926	−	0.768526i	0.989165	−	0.146806i	$-0.0468992\pi$
$948$		0			0
$949$	5.19202			0.168540
$950$		0			0
$951$	45.6719			1.48101
$952$		0			0
$953$	−10.5752	+	39.4672i	−0.342565	+	1.27847i	0.552867	+	0.833270i	$0.313534\pi$
$953$	−10.5752	+	39.4672i	−0.342565	+	1.27847i	−0.895432	+	0.445199i	$0.853133\pi$
$954$		0			0
$955$	0.0211712		0.000645769i	0.000685085		2.08966e-5i
$956$		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
$963$	−66.1128	+	17.7149i	−2.13046	+	0.570854i
$964$		0			0
$965$	−11.8340	+	50.2460i	−0.380951	+	1.61747i
$966$		0			0
$967$	−8.32700	+	31.0768i	−0.267778	+	0.999362i	0.692750	+	0.721178i	$0.256399\pi$
$967$	−8.32700	+	31.0768i	−0.267778	+	0.999362i	−0.960528	+	0.278184i	$0.910268\pi$
$968$		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
$973$	−0.626982	−	2.33993i	−0.0201001	−	0.0750147i
$974$		0			0
$975$	−2.62245	−	42.9479i	−0.0839857	−	1.37544i
$976$		0			0
$977$	−10.2263	+	10.2263i	−0.327168	+	0.327168i	−0.851509	−	0.524341i	$-0.824312\pi$
$977$	−10.2263	+	10.2263i	−0.327168	+	0.327168i	0.524341	+	0.851509i	$0.324312\pi$
$978$		0			0
$979$	11.2891	−	19.5532i	0.360800	−	0.624923i
$980$		0			0
$981$			67.6619i			2.16028i
$982$		0			0
$983$	11.8576	−	44.2533i	0.378200	−	1.41146i	−0.470413	−	0.882446i	$-0.655895\pi$
$983$	11.8576	−	44.2533i	0.378200	−	1.41146i	0.848613	−	0.529014i	$-0.177438\pi$
$984$		0			0
$985$	−27.9514	−	26.2967i	−0.890605	−	0.837882i
$986$		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
$993$	−37.7285	−	10.1093i	−1.19728	−	0.320809i
$994$		0			0
$995$	−33.5367	−	18.0221i	−1.06319	−	0.571339i
$996$		0			0
$997$	−33.2600	+	8.91198i	−1.05335	+	0.282245i	−0.743637	−	0.668584i	$-0.766901\pi$
$997$	−33.2600	+	8.91198i	−1.05335	+	0.282245i	−0.309717	+	0.950829i	$0.600234\pi$
$998$		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.297.9	yes	36
5.3	odd	4	inner	380.2.y.b.373.9	yes	36
19.8	odd	6	inner	380.2.y.b.217.9	✓	36
95.8	even	12	inner	380.2.y.b.293.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.y.b.217.9	✓	36	19.8	odd	6	inner
380.2.y.b.293.9	yes	36	95.8	even	12	inner
380.2.y.b.297.9	yes	36	1.1	even	1	trivial
380.2.y.b.373.9	yes	36	5.3	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.829395 - 3.09534i) q^{3} +(-2.23503 + 0.0681732i) q^{5} +(0.137224 + 0.137224i) q^{7} +(-6.29517 - 3.63452i) q^{9} +O(q^{10})\)	\(q+(0.829395 - 3.09534i) q^{3} +(-2.23503 + 0.0681732i) q^{5} +(0.137224 + 0.137224i) q^{7} +(-6.29517 - 3.63452i) q^{9} -5.43860 q^{11} +(2.59394 - 0.695043i) q^{13} +(-1.64270 + 6.97472i) q^{15} +(1.25767 - 4.69368i) q^{17} +(1.07234 + 4.22494i) q^{19} +(0.538567 - 0.310942i) q^{21} +(-0.813079 - 3.03445i) q^{23} +(4.99070 - 0.304738i) q^{25} +(-9.67343 + 9.67343i) q^{27} +(4.80457 - 8.32175i) q^{29} -0.448018i q^{31} +(-4.51074 + 16.8343i) q^{33} +(-0.316054 - 0.297344i) q^{35} +(-4.78673 + 4.78673i) q^{37} -8.60559i q^{39} +(-2.57531 + 1.48686i) q^{41} +(-2.98045 - 0.798608i) q^{43} +(14.3177 + 7.69409i) q^{45} +(4.83587 - 1.29577i) q^{47} -6.96234i q^{49} +(-13.4854 - 7.78582i) q^{51} +(4.44051 - 1.18983i) q^{53} +(12.1554 - 0.370767i) q^{55} +(13.9670 + 0.184873i) q^{57} +(-1.38677 - 2.40196i) q^{59} +(5.58710 - 9.67713i) q^{61} +(-0.365105 - 1.36259i) q^{63} +(-5.75014 + 1.73028i) q^{65} +(-0.793949 - 2.96306i) q^{67} -10.0670 q^{69} +(10.2220 - 5.90170i) q^{71} +(1.86752 + 0.500400i) q^{73} +(3.19599 - 15.7007i) q^{75} +(-0.746305 - 0.746305i) q^{77} +(1.88680 + 3.26803i) q^{79} +(11.0159 + 19.0801i) q^{81} +(-10.6496 + 10.6496i) q^{83} +(-2.49094 + 10.5762i) q^{85} +(-21.7738 - 21.7738i) q^{87} +(-2.07573 + 3.59527i) q^{89} +(0.451326 + 0.260573i) q^{91} +(-1.38677 - 0.371583i) q^{93} +(-2.68474 - 9.36975i) q^{95} +(7.49651 + 2.00868i) q^{97} +(34.2369 + 19.7667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{3} - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 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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