LMFDB - Embedded newform 380.2.y.b.293.9

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			293.9
Character	$\chi$	$=$	380.293
Dual form			380.2.y.b.297.9

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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
$3$	0.829395	+	3.09534i	0.478851	+	1.78710i	0.606282	+	0.795249i	$0.292660\pi$
$3$	0.829395	+	3.09534i	0.478851	+	1.78710i	−0.127431	+	0.991847i	$0.540673\pi$
$4$		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	−0.680698	−	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
$13$	2.59394	+	0.695043i	0.719429	+	0.192770i	0.599917	−	0.800062i	$-0.295200\pi$
$13$	2.59394	+	0.695043i	0.719429	+	0.192770i	0.119512	+	0.992833i	$0.461867\pi$
$14$		0			0
$15$	−1.64270	−	6.97472i	−0.424144	−	1.80087i
$16$		0			0
$17$	1.25767	+	4.69368i	0.305029	+	1.13838i	0.932920	+	0.360083i	$0.117252\pi$
$17$	1.25767	+	4.69368i	0.305029	+	1.13838i	−0.627891	+	0.778301i	$0.716082\pi$
$18$		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	0.827879	+	0.560907i	$0.189547\pi$
$23$	−0.813079	+	3.03445i	−0.169539	+	0.632727i	−0.997418	+	0.0718201i	$0.977119\pi$
$24$		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	0.837249	+	0.546821i	$0.184162\pi$
$29$	4.80457	+	8.32175i	0.892186	+	1.54531i	0.0549362	+	0.998490i	$0.482504\pi$
$30$		0			0
$31$			0.448018i			0.0804664i	0.999190	+	0.0402332i	$0.0128101\pi$
$31$			0.448018i			0.0804664i	−0.999190	+	0.0402332i	$0.987190\pi$
$32$		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	0.194057	−	0.980990i	$-0.437835\pi$
$37$	−4.78673	−	4.78673i	−0.786933	−	0.786933i	−0.980990	+	0.194057i	$0.937835\pi$
$38$		0			0
$39$			8.60559i			1.37800i
$40$		0			0
$41$	−2.57531	−	1.48686i	−0.402196	−	0.232208i	0.285235	−	0.958458i	$-0.407928\pi$
$41$	−2.57531	−	1.48686i	−0.402196	−	0.232208i	−0.687431	+	0.726250i	$0.741262\pi$
$42$		0			0
$43$	−2.98045	+	0.798608i	−0.454514	+	0.121787i	−0.478811	−	0.877918i	$-0.658932\pi$
$43$	−2.98045	+	0.798608i	−0.454514	+	0.121787i	0.0242968	+	0.999705i	$0.492265\pi$
$44$		0			0
$45$	14.3177	−	7.69409i	2.13435	−	1.14697i
$46$		0			0
$47$	4.83587	+	1.29577i	0.705384	+	0.189007i	0.593641	−	0.804730i	$-0.297690\pi$
$47$	4.83587	+	1.29577i	0.705384	+	0.189007i	0.111743	+	0.993737i	$0.464357\pi$
$48$		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	0.550555	−	0.834799i	$-0.314416\pi$
$53$	4.44051	+	1.18983i	0.609950	+	0.163436i	0.0593952	+	0.998235i	$0.481083\pi$
$54$		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	−0.942065	−	0.335429i	$-0.891119\pi$
$59$	−1.38677	+	2.40196i	−0.180543	+	0.312709i	0.761523	+	0.648138i	$0.224452\pi$
$60$		0			0
$61$	5.58710	+	9.67713i	0.715354	+	1.23903i	0.962823	+	0.270134i	$0.0870680\pi$
$61$	5.58710	+	9.67713i	0.715354	+	1.23903i	−0.247468	+	0.968896i	$0.579599\pi$
$62$		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	−0.997315	−	0.0732371i	$-0.976667\pi$
$67$	−0.793949	+	2.96306i	−0.0969963	+	0.361995i	0.900318	+	0.435232i	$0.143334\pi$
$68$		0			0
$69$	−10.0670			−1.21193
$70$		0			0
$71$	10.2220	+	5.90170i	1.21313	+	0.700403i	0.963440	−	0.267923i	$-0.0863372\pi$
$71$	10.2220	+	5.90170i	1.21313	+	0.700403i	0.249692	+	0.968325i	$0.419670\pi$
$72$		0			0
$73$	1.86752	−	0.500400i	0.218576	−	0.0585673i	−0.147869	−	0.989007i	$-0.547241\pi$
$73$	1.86752	−	0.500400i	0.218576	−	0.0585673i	0.366445	+	0.930440i	$0.380575\pi$
$74$		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	$-0.765244\pi$
$79$	1.88680	−	3.26803i	0.212281	−	0.367682i	0.952428	+	0.304763i	$0.0985774\pi$
$80$		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
$85$	−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	0.734789	−	0.678296i	$-0.237281\pi$
$89$	−2.07573	−	3.59527i	−0.220027	−	0.381098i	−0.954816	+	0.297198i	$0.903948\pi$
$90$		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	0.142695	−	0.989767i	$-0.454423\pi$
$97$	7.49651	−	2.00868i	0.761155	−	0.203951i	0.618460	+	0.785816i	$0.287757\pi$
$98$		0			0
$99$	34.2369	−	19.7667i	3.44094	−	1.98663i
$100$		0			0
$101$	−0.547865	−	0.948930i	−0.0545146	−	0.0944221i	0.837480	−	0.546468i	$-0.184028\pi$
$101$	−0.547865	−	0.948930i	−0.0545146	−	0.0944221i	−0.891995	+	0.452045i	$0.850694\pi$
$102$		0			0
$103$	3.72076	−	3.72076i	0.366617	−	0.366617i	−0.499625	−	0.866242i	$-0.666529\pi$
$103$	3.72076	−	3.72076i	0.366617	−	0.366617i	0.866242	+	0.499625i	$0.166529\pi$
$104$		0			0
$105$	−1.18252	−	0.731680i	−0.115402	−	0.0714047i
$106$		0			0
$107$	6.65809	+	6.65809i	0.643662	+	0.643662i	0.951454	−	0.307792i	$-0.0995900\pi$
$107$	6.65809	+	6.65809i	0.643662	+	0.643662i	−0.307792	+	0.951454i	$0.599590\pi$
$108$		0			0
$109$	−4.65411	+	8.06116i	−0.445783	+	0.772119i	−0.998106	−	0.0615111i	$-0.980408\pi$
$109$	−4.65411	+	8.06116i	−0.445783	+	0.772119i	0.552323	+	0.833630i	$0.313741\pi$
$110$		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	$-0.403984\pi$
$113$	13.3083	−	13.3083i	1.25194	−	1.25194i	0.954849	−	0.297091i	$-0.0960164\pi$
$114$		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	−0.787235	−	0.616653i	$-0.788488\pi$
$127$	2.28608	−	8.53177i	0.202857	−	0.757072i	0.990092	−	0.140419i	$-0.0448451\pi$
$128$		0			0
$129$	−4.94393	−	8.56314i	−0.435289	−	0.753943i
$130$		0			0
$131$	−0.720576	+	1.24808i	−0.0629571	+	0.109045i	−0.895786	−	0.444486i	$-0.853386\pi$
$131$	−0.720576	+	1.24808i	−0.0629571	+	0.109045i	0.832829	+	0.553531i	$0.186720\pi$
$132$		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	0.784313	−	0.620365i	$-0.213016\pi$
$137$	13.4998	+	3.61726i	1.15337	+	0.309043i	0.369053	+	0.929408i	$0.379682\pi$
$138$		0			0
$139$	−10.8105	+	6.24144i	−0.916933	+	0.529392i	−0.882655	−	0.470021i	$-0.844246\pi$
$139$	−10.8105	+	6.24144i	−0.916933	+	0.529392i	−0.0342778	+	0.999412i	$0.510913\pi$
$140$		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	−0.213825	−	0.976872i	$-0.568592\pi$
$149$	−14.2418	−	8.22251i	−1.16673	−	0.673614i	−0.952909	+	0.303258i	$0.901926\pi$
$150$		0			0
$151$		−	8.67696i		−	0.706121i	−0.935600	−	0.353061i	$-0.885141\pi$
$151$		−	8.67696i		−	0.706121i	0.935600	−	0.353061i	$-0.114859\pi$
$152$		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	0.998126	−	0.0611904i	$-0.0194897\pi$
$157$	1.29219	+	4.82253i	0.103128	+	0.384880i	−0.894998	+	0.446071i	$0.852823\pi$
$158$		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
$165$	8.93399	+	37.9327i	0.695510	+	2.95306i
$166$		0			0
$167$	−3.89791	+	14.5472i	−0.301630	+	1.12570i	0.634178	+	0.773187i	$0.281339\pi$
$167$	−3.89791	+	14.5472i	−0.301630	+	1.12570i	−0.935808	+	0.352510i	$0.885328\pi$
$168$		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	0.914376	−	0.404865i	$-0.132682\pi$
$173$	−1.05131	−	3.92353i	−0.0799295	−	0.298301i	−0.994306	+	0.106565i	$0.966015\pi$
$174$		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	0.268406	−	0.963306i	$-0.413503\pi$
$181$	16.6402	−	9.60723i	1.23686	−	0.714099i	0.968450	+	0.249206i	$0.0801698\pi$
$182$		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	0.752556	+	0.658528i	$0.228821\pi$
$193$	5.97497	+	22.2989i	0.430087	+	1.60511i	−0.322469	+	0.946580i	$0.604513\pi$
$194$		0			0
$195$	0.586671	−	19.2337i	0.0420124	−	1.37736i
$196$		0			0
$197$	12.1359	−	12.1359i	0.864645	−	0.864645i	−0.127228	−	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	$-0.460444\pi$
$199$	14.7454	−	8.51325i	1.04527	−	0.603488i	0.921322	+	0.388800i	$0.127110\pi$
$200$		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	0.476916	−	0.878949i	$-0.341755\pi$
$211$	−0.665546	−	0.384253i	−0.0458181	−	0.0264531i	−0.522734	+	0.852496i	$0.675088\pi$
$212$		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	0.952232	−	0.305374i	$-0.0987816\pi$
$223$	−0.375005	−	1.39954i	−0.0251122	−	0.0937199i	−0.977345	+	0.211654i	$0.932115\pi$
$224$		0			0
$225$	−32.5249	+	16.2204i	−2.16833	+	1.08136i
$226$		0			0
$227$	−4.20077	−	4.20077i	−0.278815	−	0.278815i	0.553821	−	0.832636i	$-0.313169\pi$
$227$	−4.20077	−	4.20077i	−0.278815	−	0.278815i	−0.832636	+	0.553821i	$0.813169\pi$
$228$		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
$233$	15.3261	−	4.10662i	1.00405	−	0.269034i	0.280907	−	0.959735i	$-0.409365\pi$
$233$	15.3261	−	4.10662i	1.00405	−	0.269034i	0.723140	+	0.690701i	$0.242698\pi$
$234$		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	$-0.954427\pi$
$239$		−	4.41162i		−	0.285364i	0.989769	−	0.142682i	$-0.0455726\pi$
$240$		0			0
$241$	−10.2452	+	5.91506i	−0.659950	+	0.381022i	−0.792258	−	0.610186i	$-0.791095\pi$
$241$	−10.2452	+	5.91506i	−0.659950	+	0.381022i	0.132308	+	0.991209i	$0.457761\pi$
$242$		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	−0.904412	−	0.426659i	$-0.859690\pi$
$251$	−13.0182	−	22.5483i	−0.821704	−	1.42323i	0.0827086	−	0.996574i	$-0.473643\pi$
$252$		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	0.815934	+	0.578145i	$0.196223\pi$
$257$	−2.88174	+	10.7548i	−0.179758	+	0.670866i	−0.995692	+	0.0927211i	$0.970443\pi$
$258$		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	−0.453211	−	0.891403i	$-0.649722\pi$
$263$	−6.48694	+	1.73817i	−0.400002	+	0.107180i	0.0532094	+	0.998583i	$0.483055\pi$
$264$		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	−0.468730	−	0.883341i	$-0.655288\pi$
$269$	8.70299	−	15.0740i	0.530631	−	0.919079i	0.999361	−	0.0357382i	$-0.0113782\pi$
$270$		0			0
$271$	2.07341	−	3.59125i	0.125951	−	0.218153i	−0.796154	−	0.605095i	$-0.793135\pi$
$271$	2.07341	−	3.59125i	0.125951	−	0.218153i	0.922104	+	0.386942i	$0.126469\pi$
$272$		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	−0.794485	−	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	−0.375581	−	0.926790i	$-0.622557\pi$
$281$	4.01060	−	2.31552i	0.239252	−	0.138132i	0.614833	+	0.788657i	$0.289223\pi$
$282$		0			0
$283$	21.5026	−	5.76161i	1.27820	−	0.342492i	0.445032	−	0.895515i	$-0.353192\pi$
$283$	21.5026	−	5.76161i	1.27820	−	0.342492i	0.833166	+	0.553023i	$0.186526\pi$
$284$		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	−0.832505	−	0.554018i	$-0.813094\pi$
$293$	−4.76693	+	4.76693i	−0.278487	+	0.278487i	0.554018	+	0.832505i	$0.313094\pi$
$294$		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	−0.167174	−	0.985927i	$-0.553464\pi$
$307$	3.17160	−	0.849827i	0.181013	−	0.0485022i	0.348187	+	0.937425i	$0.386798\pi$
$308$		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	0.803147	+	0.595781i	$0.203157\pi$
$313$	−3.36656	+	12.5642i	−0.190289	+	0.710169i	−0.993436	+	0.114388i	$0.963509\pi$
$314$		0			0
$315$	0.908912	−	3.02054i	0.0512114	−	0.170188i
$316$		0			0
$317$	3.68876	−	13.7666i	0.207181	−	0.773211i	−0.781592	−	0.623790i	$-0.785592\pi$
$317$	3.68876	−	13.7666i	0.207181	−	0.773211i	0.988774	−	0.149421i	$-0.0477411\pi$
$318$		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	$0.108729\pi$
$331$			12.1888i			0.669956i	−0.942226	+	0.334978i	$0.891271\pi$
$332$		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	0.0238059	−	0.999717i	$-0.492422\pi$
$337$	9.99167	−	2.67726i	0.544281	−	0.145840i	0.520475	+	0.853877i	$0.325755\pi$
$338$		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	−0.997637	−	0.0687031i	$-0.978114\pi$
$347$	−3.12967	−	11.6801i	−0.168010	−	0.627020i	0.829628	−	0.558317i	$-0.188553\pi$
$348$		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
$355$	−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	0.429942	−	0.902857i	$-0.358534\pi$
$359$	−2.59548	−	1.49850i	−0.136984	−	0.0790878i	−0.566926	+	0.823769i	$0.691867\pi$
$360$		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	0.566716	−	0.823913i	$-0.308214\pi$
$367$	12.3670	+	3.31372i	0.645551	+	0.172975i	0.0788343	+	0.996888i	$0.474880\pi$
$368$		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	$-0.459835\pi$
$373$	21.5902	−	21.5902i	1.11790	−	1.11790i	0.992050	−	0.125848i	$-0.0401652\pi$
$374$		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	0.860419	+	0.509587i	$0.170202\pi$
$383$	7.24237	+	27.0289i	0.370068	+	1.38111i	−0.490352	+	0.871525i	$0.663132\pi$
$384$		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	−0.844384	−	0.535738i	$-0.820033\pi$
$389$	−15.8300	+	9.13946i	−0.802613	+	0.463389i	0.0417711	+	0.999127i	$0.486700\pi$
$390$		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	−0.997679	−	0.0680976i	$-0.978307\pi$
$397$	−3.34165	−	12.4712i	−0.167712	−	0.625911i	0.829966	−	0.557814i	$-0.188360\pi$
$398$		0			0
$399$	1.89124	−	1.94198i	0.0946803	−	0.0972204i
$400$		0			0
$401$	−12.9309	−	7.46568i	−0.645740	−	0.372818i	0.141082	−	0.989998i	$-0.454942\pi$
$401$	−12.9309	−	7.46568i	−0.645740	−	0.372818i	−0.786822	+	0.617180i	$0.788275\pi$
$402$		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	0.776770	−	0.629785i	$-0.216857\pi$
$409$	−3.17563	−	5.50035i	−0.157025	−	0.271975i	−0.933794	+	0.357810i	$0.883524\pi$
$410$		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	$0.287274\pi$
$419$			32.1321i			1.56975i	−0.619651	+	0.784877i	$0.712726\pi$
$420$		0			0
$421$	18.2090	+	10.5130i	0.887451	+	0.512370i	0.873108	−	0.487527i	$-0.162101\pi$
$421$	18.2090	+	10.5130i	0.887451	+	0.512370i	0.0143432	+	0.999897i	$0.495434\pi$
$422$		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	−0.924711	−	0.380670i	$-0.875693\pi$
$431$	−21.9521	+	12.6741i	−1.05740	+	0.610488i	−0.132686	+	0.991158i	$0.542360\pi$
$432$		0			0
$433$	−18.2612	−	4.89308i	−0.877579	−	0.235147i	−0.208217	−	0.978083i	$-0.566766\pi$
$433$	−18.2612	−	4.89308i	−0.877579	−	0.235147i	−0.669362	+	0.742936i	$0.733433\pi$
$434$		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	−0.939095	−	0.343658i	$-0.888334\pi$
$439$	−3.60234	+	6.23944i	−0.171930	+	0.297792i	0.767164	+	0.641451i	$0.221667\pi$
$440$		0			0
$441$	−25.3048	−	43.8291i	−1.20499	−	2.08710i
$442$		0			0
$443$	−1.64721	+	6.14747i	−0.0782612	+	0.292075i	−0.993953	−	0.109806i	$-0.964977\pi$
$443$	−1.64721	+	6.14747i	−0.0782612	+	0.292075i	0.915692	+	0.401881i	$0.131644\pi$
$444$		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	−0.680148	−	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	−0.757856	−	0.652422i	$-0.773753\pi$
$461$	3.99545	−	6.92032i	0.186087	−	0.322311i	0.943942	+	0.330111i	$0.107086\pi$
$462$		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
$465$	3.12480	−	0.735959i	0.144909	−	0.0341293i
$466$		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
$473$	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	−0.808107	−	0.589035i	$-0.799508\pi$
$479$	−15.3649	+	8.87094i	−0.702041	+	0.405324i	0.106066	+	0.994359i	$0.466175\pi$
$480$		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	0.991481	+	0.130255i	$0.0415796\pi$
$487$	24.7545	+	24.7545i	1.12174	+	1.12174i	0.130255	+	0.991481i	$0.458420\pi$
$488$		0			0
$489$	9.85296	−	17.0658i	0.445566	−	0.771743i
$490$		0			0
$491$	0.433880	−	0.751503i	0.0195808	−	0.0339149i	−0.856069	−	0.516862i	$-0.827100\pi$
$491$	0.433880	−	0.751503i	0.0195808	−	0.0339149i	0.875650	+	0.482947i	$0.160434\pi$
$492$		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	0.915032	−	0.403381i	$-0.132165\pi$
$499$	22.8568	+	13.1964i	1.02321	+	0.590750i	0.108178	+	0.994132i	$0.465498\pi$
$500$		0			0
$501$	−48.2615			−2.15617
$502$		0			0
$503$	11.3798	−	42.4701i	0.507401	−	1.89365i	0.0625524	−	0.998042i	$-0.480076\pi$
$503$	11.3798	−	42.4701i	0.507401	−	1.89365i	0.444849	−	0.895606i	$-0.353257\pi$
$504$		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	0.994321	−	0.106420i	$-0.0339388\pi$
$509$	9.13718	+	15.8261i	0.404998	+	0.701478i	−0.589323	+	0.807898i	$0.700605\pi$
$510$		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	$0.00315796\pi$
$521$			0.452896i			0.0198417i	−0.999951	+	0.00992087i	$0.996842\pi$
$522$		0			0
$523$	−8.25991	−	2.21323i	−0.361180	−	0.0967780i	0.0736652	−	0.997283i	$-0.476530\pi$
$523$	−8.25991	−	2.21323i	−0.361180	−	0.0967780i	−0.434846	+	0.900505i	$0.643197\pi$
$524$		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	0.985075	−	0.172124i	$-0.0550631\pi$
$541$	7.98899	+	13.8373i	0.343474	+	0.594914i	−0.641602	+	0.767038i	$0.721730\pi$
$542$		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	0.544877	+	0.838516i	$0.316576\pi$
$547$	−8.09830	+	30.2233i	−0.346258	+	1.29225i	−0.891135	+	0.453737i	$0.850090\pi$
$548$		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	0.737670	−	0.675161i	$-0.235926\pi$
$557$	24.5196	+	6.57002i	1.03893	+	0.278381i	0.301260	+	0.953542i	$0.402593\pi$
$558$		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	−0.459689	−	0.888080i	$-0.652039\pi$
$563$	10.1647	−	10.1647i	0.428392	−	0.428392i	0.888080	+	0.459689i	$0.152039\pi$
$564$		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	−0.568614	+	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
$583$	−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	0.816472	+	0.577385i	$0.195927\pi$
$587$	9.64470	+	35.9945i	0.398079	+	1.48565i	−0.418393	+	0.908266i	$0.637406\pi$
$588$		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	−0.999236	−	0.0390739i	$-0.987559\pi$
$593$	−2.78425	+	10.3910i	−0.114335	+	0.426705i	0.884901	+	0.465779i	$0.154226\pi$
$594$		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	−0.972077	−	0.234661i	$-0.924602\pi$
$599$	−16.8693	−	29.2185i	−0.689261	−	1.19384i	0.282816	−	0.959174i	$-0.408731\pi$
$600$		0			0
$601$			43.0890i			1.75764i	0.477157	+	0.878818i	$0.341667\pi$
$601$			43.0890i			1.75764i	−0.477157	+	0.878818i	$0.658333\pi$
$602$		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	0.995912	+	0.0903240i	$0.0287903\pi$
$607$	26.7620	+	26.7620i	1.08624	+	1.08624i	0.0903240	+	0.995912i	$0.471210\pi$
$608$		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	0.542801	−	0.839861i	$-0.317364\pi$
$613$	35.4747	−	9.50543i	1.43281	−	0.383921i	0.890010	+	0.455941i	$0.150697\pi$
$614$		0			0
$615$	−6.13994	+	20.4045i	−0.247586	+	0.822790i
$616$		0			0
$617$	−7.90202	−	2.11734i	−0.318123	−	0.0852409i	0.0962240	−	0.995360i	$-0.469323\pi$
$617$	−7.90202	−	2.11734i	−0.318123	−	0.0852409i	−0.414347	+	0.910119i	$0.635990\pi$
$618$		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
$623$	−0.778196	−	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	0.996987	+	0.0775707i	$0.0247163\pi$
$631$	14.2095	+	24.6116i	0.565672	+	0.979772i	−0.431315	+	0.902201i	$0.641950\pi$
$632$		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	0.785717	−	0.618586i	$-0.212294\pi$
$641$	16.2760	+	9.39696i	0.642864	+	0.371158i	−0.142853	+	0.989744i	$0.545628\pi$
$642$		0			0
$643$	−40.5068	+	10.8538i	−1.59743	+	0.428030i	−0.944266	−	0.329185i	$-0.893226\pi$
$643$	−40.5068	+	10.8538i	−1.59743	+	0.428030i	−0.653166	+	0.757215i	$0.726559\pi$
$644$		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
$655$	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	0.999726	−	0.0234286i	$-0.00745825\pi$
$659$	12.3111	+	21.3235i	0.479573	+	0.830645i	−0.520153	+	0.854073i	$0.674125\pi$
$660$		0			0
$661$	−40.5364	+	23.4037i	−1.57668	+	0.910298i	−0.581365	+	0.813643i	$0.697481\pi$
$661$	−40.5364	+	23.4037i	−1.57668	+	0.910298i	−0.995318	+	0.0966557i	$0.969185\pi$
$662$		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	−0.924430	−	0.381353i	$-0.875458\pi$
$673$	−14.0886	+	14.0886i	−0.543077	+	0.543077i	0.381353	+	0.924430i	$0.375458\pi$
$674$		0			0
$675$	−45.3293	−	51.2251i	−1.74473	−	1.97165i
$676$		0			0
$677$	6.44919	+	6.44919i	0.247862	+	0.247862i	0.820093	−	0.572230i	$-0.193922\pi$
$677$	6.44919	+	6.44919i	0.247862	+	0.247862i	−0.572230	+	0.820093i	$0.693922\pi$
$678$		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	$-0.471994\pi$
$683$	28.3296	−	28.3296i	1.08400	−	1.08400i	0.996132	−	0.0878690i	$-0.0280057\pi$
$684$		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	−0.0681632	−	0.997674i	$-0.521714\pi$
$701$	21.9736	−	38.0593i	0.829930	−	1.43748i	0.898093	−	0.439806i	$-0.144953\pi$
$702$		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	−0.0669523	−	0.997756i	$-0.521328\pi$
$709$	20.3338	−	11.7398i	0.763654	−	0.440896i	0.830606	+	0.556861i	$0.187994\pi$
$710$		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	0.652440	−	0.757841i	$-0.273746\pi$
$719$	8.64356	+	4.99036i	0.322350	+	0.186109i	−0.330089	+	0.943950i	$0.607079\pi$
$720$		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	−0.922463	−	0.386085i	$-0.873827\pi$
$727$	−8.53725	−	31.8614i	−0.316629	−	1.18168i	0.605834	−	0.795591i	$-0.292839\pi$
$728$		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
$735$	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	0.449722	−	0.893169i	$-0.351523\pi$
$739$	−2.68922	−	1.55262i	−0.0989246	−	0.0571141i	−0.548646	+	0.836055i	$0.684857\pi$
$740$		0			0
$741$	36.3581	+	9.22813i	1.33565	+	0.339004i
$742$		0			0
$743$	1.03330	+	3.85631i	0.0379079	+	0.141474i	0.982286	−	0.187387i	$-0.0600018\pi$
$743$	1.03330	+	3.85631i	0.0379079	+	0.141474i	−0.944378	+	0.328861i	$0.893335\pi$
$744$		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	−0.547084	−	0.837077i	$-0.684262\pi$
$751$	−2.62250	+	1.51410i	−0.0956963	+	0.0552503i	0.451388	+	0.892328i	$0.350929\pi$
$752$		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	−0.928724	−	0.370771i	$-0.879094\pi$
$757$	−8.52402	−	31.8121i	−0.309811	−	1.15623i	0.618914	−	0.785459i	$-0.287573\pi$
$758$		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	0.174885	−	0.984589i	$-0.444045\pi$
$769$	30.9201	−	17.8517i	1.11501	−	0.643749i	0.940121	+	0.340840i	$0.110711\pi$
$770$		0			0
$771$	−35.6799			−1.28498
$772$		0			0
$773$	−9.79800	−	2.62537i	−0.352410	−	0.0944279i	0.0782714	−	0.996932i	$-0.475060\pi$
$773$	−9.79800	−	2.62537i	−0.352410	−	0.0944279i	−0.430681	+	0.902504i	$0.641727\pi$
$774$		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	0.0346473	−	0.999400i	$-0.488969\pi$
$787$	−27.0647	−	27.0647i	−0.964752	−	0.964752i	−0.999400	+	0.0346473i	$0.988969\pi$
$788$		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	0.904529	−	0.426413i	$-0.140223\pi$
$797$	13.4978	+	13.4978i	0.478116	+	0.478116i	−0.426413	+	0.904529i	$0.640223\pi$
$798$		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	$-0.822204\pi$
$809$		−	30.1477i		−	1.05994i	0.848018	−	0.529968i	$-0.177796\pi$
$810$		0			0
$811$	−14.5538	+	8.40263i	−0.511052	+	0.295056i	−0.733266	−	0.679942i	$-0.762005\pi$
$811$	−14.5538	+	8.40263i	−0.511052	+	0.295056i	0.222214	+	0.974998i	$0.428672\pi$
$812$		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	0.705591	−	0.708619i	$-0.250682\pi$
$821$	−7.47522	−	12.9475i	−0.260887	−	0.451869i	−0.966478	+	0.256750i	$0.917348\pi$
$822$		0			0
$823$	−5.52303	+	20.6122i	−0.192521	+	0.718496i	0.800374	+	0.599501i	$0.204634\pi$
$823$	−5.52303	+	20.6122i	−0.192521	+	0.718496i	−0.992895	+	0.118996i	$0.962033\pi$
$824$		0			0
$825$	−17.3817	−	85.3897i	−0.605154	−	2.97289i
$826$		0			0
$827$	10.8733	−	40.5797i	0.378101	−	1.41109i	−0.470658	−	0.882315i	$-0.655984\pi$
$827$	10.8733	−	40.5797i	0.378101	−	1.41109i	0.848760	−	0.528778i	$-0.177350\pi$
$828$		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	−0.996320	−	0.0857171i	$-0.972682\pi$
$839$	−12.2792	+	21.2683i	−0.423927	+	0.734262i	0.572393	+	0.819979i	$0.306015\pi$
$840$		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	0.0909519	−	0.995855i	$-0.471009\pi$
$853$	19.4994	−	5.22484i	0.667646	−	0.178895i	0.576694	+	0.816960i	$0.304342\pi$
$854$		0			0
$855$	−17.1536	−	68.7419i	−0.586641	−	2.35092i
$856$		0			0
$857$	−4.37606	+	1.17256i	−0.149483	+	0.0400539i	−0.332785	−	0.943003i	$-0.607988\pi$
$857$	−4.37606	+	1.17256i	−0.149483	+	0.0400539i	0.183301	+	0.983057i	$0.441322\pi$
$858$		0			0
$859$	27.2399	−	15.7270i	0.929413	−	0.536597i	0.0427871	−	0.999084i	$-0.486376\pi$
$859$	27.2399	−	15.7270i	0.929413	−	0.536597i	0.886626	+	0.462487i	$0.153043\pi$
$860$		0			0
$861$	−0.924652	−	1.60154i	−0.0315120	−	0.0545805i
$862$		0			0
$863$	21.9717	−	21.9717i	0.747926	−	0.747926i	−0.226163	−	0.974089i	$-0.572618\pi$
$863$	21.9717	−	21.9717i	0.747926	−	0.747926i	0.974089	+	0.226163i	$0.0726182\pi$
$864$		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	−0.426295	−	0.904584i	$-0.640182\pi$
$877$	−10.1632	+	2.72321i	−0.343186	+	0.0919564i	0.0831094	+	0.996540i	$0.473515\pi$
$878$		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	−0.818243	−	0.574873i	$-0.805052\pi$
$883$	5.28376	−	19.7192i	0.177813	−	0.663605i	0.996055	−	0.0887328i	$-0.0282817\pi$
$884$		0			0
$885$	19.0311	+	5.72666i	0.639723	+	0.192499i
$886$		0			0
$887$	−11.9957	+	44.7684i	−0.402775	+	1.50318i	0.405348	+	0.914163i	$0.367150\pi$
$887$	−11.9957	+	44.7684i	−0.402775	+	1.50318i	−0.808123	+	0.589014i	$0.799516\pi$
$888$		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	−0.752510	−	0.658581i	$-0.771157\pi$
$907$	−32.3725	+	8.67420i	−1.07491	+	0.288022i	−0.322403	+	0.946603i	$0.604490\pi$
$908$		0			0
$909$	6.89781	+	3.98245i	0.228786	+	0.132090i
$910$		0			0
$911$		−	15.8550i		−	0.525301i	−0.964891	−	0.262651i	$-0.915403\pi$
$911$		−	15.8550i		−	0.525301i	0.964891	−	0.262651i	$-0.0845966\pi$
$912$		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	$0.111624\pi$
$919$			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
$925$	−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	0.773608	−	0.633665i	$-0.218450\pi$
$929$	18.6425	+	10.7633i	0.611641	+	0.353131i	−0.161966	+	0.986796i	$0.551784\pi$
$930$		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	0.0469373	−	0.998898i	$-0.485054\pi$
$937$	−12.6073	−	3.37812i	−0.411863	−	0.110358i	−0.458800	+	0.888540i	$0.651721\pi$
$938$		0			0
$939$	−41.6826			−1.36026
$940$		0			0
$941$	−7.26556	+	4.19477i	−0.236850	+	0.136746i	−0.613728	−	0.789517i	$-0.710331\pi$
$941$	−7.26556	+	4.19477i	−0.236850	+	0.136746i	0.376878	+	0.926263i	$0.376998\pi$
$942$		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	0.989165	+	0.146806i	$0.0468992\pi$
$947$	6.33703	+	23.6501i	0.205926	+	0.768526i	−0.783240	+	0.621720i	$0.786434\pi$
$948$		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	−0.895432	−	0.445199i	$-0.853133\pi$
$953$	−10.5752	−	39.4672i	−0.342565	−	1.27847i	0.552867	−	0.833270i	$-0.313534\pi$
$954$		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	−0.960528	−	0.278184i	$-0.910268\pi$
$967$	−8.32700	−	31.0768i	−0.267778	−	0.999362i	0.692750	−	0.721178i	$-0.256399\pi$
$968$		0			0
$969$	18.4336	+	65.3242i	0.592173	+	2.09852i
$970$		0			0
$971$	−9.21708	−	5.32148i	−0.295790	−	0.170775i	0.344760	−	0.938691i	$-0.387960\pi$
$971$	−9.21708	−	5.32148i	−0.295790	−	0.170775i	−0.640550	+	0.767916i	$0.721294\pi$
$972$		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	0.524341	−	0.851509i	$-0.324312\pi$
$977$	−10.2263	−	10.2263i	−0.327168	−	0.327168i	−0.851509	+	0.524341i	$0.824312\pi$
$978$		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	0.848613	+	0.529014i	$0.177438\pi$
$983$	11.8576	+	44.2533i	0.378200	+	1.41146i	−0.470413	+	0.882446i	$0.655895\pi$
$984$		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	−0.144280	−	0.989537i	$-0.546086\pi$
$991$	−33.7903	−	19.5088i	−1.07338	−	0.619718i	−0.929104	+	0.369819i	$0.879420\pi$
$992$		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	−0.309717	−	0.950829i	$-0.600234\pi$
$997$	−33.2600	−	8.91198i	−1.05335	−	0.282245i	−0.743637	+	0.668584i	$0.766901\pi$
$998$		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.293.9	yes	36
5.2	odd	4	inner	380.2.y.b.217.9	✓	36
19.12	odd	6	inner	380.2.y.b.373.9	yes	36
95.12	even	12	inner	380.2.y.b.297.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.y.b.217.9	✓	36	5.2	odd	4	inner
380.2.y.b.293.9	yes	36	1.1	even	1	trivial
380.2.y.b.297.9	yes	36	95.12	even	12	inner
380.2.y.b.373.9	yes	36	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
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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