LMFDB - Embedded newform 572.2.bh.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	572.73
Dual form			572.2.bh.a.525.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.501869 + 1.54459i) q^{3} +(1.48121 + 0.234601i) q^{5} +(-1.00750 + 1.97734i) q^{7} +(0.293155 + 0.212990i) q^{9} +O(q^{10})$	\(q+(-0.501869 + 1.54459i) q^{3} +(1.48121 + 0.234601i) q^{5} +(-1.00750 + 1.97734i) q^{7} +(0.293155 + 0.212990i) q^{9} +(-3.21215 + 0.825887i) q^{11} +(3.42752 - 1.11899i) q^{13} +(-1.10574 + 2.17013i) q^{15} +(-2.03747 + 1.48031i) q^{17} +(2.00766 + 3.94025i) q^{19} +(-2.54854 - 2.54854i) q^{21} +2.40322i q^{23} +(-2.61633 - 0.850097i) q^{25} +(-4.41784 + 3.20975i) q^{27} +(0.507451 - 0.164881i) q^{29} +(-0.920470 - 5.81162i) q^{31} +(0.336418 - 5.37595i) q^{33} +(-1.95621 + 2.69249i) q^{35} +(-1.91671 - 0.976610i) q^{37} +(0.00822078 + 5.85570i) q^{39} +(5.37463 + 10.5483i) q^{41} -1.84654 q^{43} +(0.384258 + 0.384258i) q^{45} +(-0.499326 - 0.979982i) q^{47} +(1.21970 + 1.67878i) q^{49} +(-1.26393 - 3.88998i) q^{51} +(-4.81917 - 3.50133i) q^{53} +(-4.95163 + 0.469741i) q^{55} +(-7.09367 + 1.12353i) q^{57} +(-0.860554 - 0.438474i) q^{59} +(4.22036 + 5.80883i) q^{61} +(-0.716507 + 0.365079i) q^{63} +(5.33939 - 0.853363i) q^{65} +(6.06836 + 6.06836i) q^{67} +(-3.71199 - 1.20610i) q^{69} +(0.590889 + 0.0935875i) q^{71} +(0.917834 - 1.80135i) q^{73} +(2.62611 - 3.61453i) q^{75} +(1.60319 - 7.18358i) q^{77} +(-2.48574 + 3.42133i) q^{79} +(-2.40465 - 7.40076i) q^{81} +(1.47752 - 9.32867i) q^{83} +(-3.36520 + 1.71466i) q^{85} +0.866554i q^{87} +(7.15305 - 7.15305i) q^{89} +(-1.24061 + 7.90473i) q^{91} +(9.43854 + 1.49492i) q^{93} +(2.04938 + 6.30735i) q^{95} +(-2.60263 - 16.4323i) q^{97} +(-1.11757 - 0.442042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.501869	+	1.54459i	−0.289754	+	0.891771i	0.695179	+	0.718836i	$0.255325\pi$
$3$	−0.501869	+	1.54459i	−0.289754	+	0.891771i	−0.984933	+	0.172935i	$0.944675\pi$
$4$		0			0
$5$	1.48121	+	0.234601i	0.662418	+	0.104917i	0.478586	−	0.878041i	$-0.341150\pi$
$5$	1.48121	+	0.234601i	0.662418	+	0.104917i	0.183832	+	0.982958i	$0.441150\pi$
$6$		0			0
$7$	−1.00750	+	1.97734i	−0.380800	+	0.747362i	−0.999260	−	0.0384537i	$-0.987757\pi$
$7$	−1.00750	+	1.97734i	−0.380800	+	0.747362i	0.618460	+	0.785816i	$0.287757\pi$
$8$		0			0
$9$	0.293155	+	0.212990i	0.0977185	+	0.0709966i
$10$		0			0
$11$	−3.21215	+	0.825887i	−0.968500	+	0.249014i
$11$	−3.21215	+	0.825887i	−0.968500	+	0.249014i
$12$		0			0
$13$	3.42752	−	1.11899i	0.950622	−	0.310352i
$13$	3.42752	−	1.11899i	0.950622	−	0.310352i
$14$		0			0
$15$	−1.10574	+	2.17013i	−0.285500	+	0.560325i
$16$		0			0
$17$	−2.03747	+	1.48031i	−0.494158	+	0.359027i	−0.806781	−	0.590850i	$-0.798792\pi$
$17$	−2.03747	+	1.48031i	−0.494158	+	0.359027i	0.312623	+	0.949877i	$0.398792\pi$
$18$		0			0
$19$	2.00766	+	3.94025i	0.460589	+	0.903956i	0.998154	+	0.0607342i	$0.0193442\pi$
$19$	2.00766	+	3.94025i	0.460589	+	0.903956i	−0.537565	+	0.843222i	$0.680656\pi$
$20$		0			0
$21$	−2.54854	−	2.54854i	−0.556138	−	0.556138i
$22$		0			0
$23$			2.40322i			0.501106i	0.968103	+	0.250553i	$0.0806124\pi$
$23$			2.40322i			0.501106i	−0.968103	+	0.250553i	$0.919388\pi$
$24$		0			0
$25$	−2.61633	−	0.850097i	−0.523266	−	0.170019i
$26$		0			0
$27$	−4.41784	+	3.20975i	−0.850213	+	0.617716i
$28$		0			0
$29$	0.507451	−	0.164881i	0.0942313	−	0.0306176i	−0.261522	−	0.965198i	$-0.584224\pi$
$29$	0.507451	−	0.164881i	0.0942313	−	0.0306176i	0.355753	+	0.934580i	$0.384224\pi$
$30$		0			0
$31$	−0.920470	−	5.81162i	−0.165321	−	1.04380i	−0.921201	−	0.389087i	$-0.872790\pi$
$31$	−0.920470	−	5.81162i	−0.165321	−	1.04380i	0.755880	−	0.654711i	$-0.227210\pi$
$32$		0			0
$33$	0.336418	−	5.37595i	0.0585628	−	0.935833i
$34$		0			0
$35$	−1.95621	+	2.69249i	−0.330660	+	0.455114i
$36$		0			0
$37$	−1.91671	−	0.976610i	−0.315104	−	0.160554i	0.289284	−	0.957243i	$-0.406583\pi$
$37$	−1.91671	−	0.976610i	−0.315104	−	0.160554i	−0.604389	+	0.796689i	$0.706583\pi$
$38$		0			0
$39$	0.00822078	+	5.85570i	0.00131638	+	0.937663i
$40$		0			0
$41$	5.37463	+	10.5483i	0.839376	+	1.64737i	0.759448	+	0.650568i	$0.225469\pi$
$41$	5.37463	+	10.5483i	0.839376	+	1.64737i	0.0799289	+	0.996801i	$0.474531\pi$
$42$		0			0
$43$	−1.84654			−0.281595			−0.140797	−	0.990038i	$-0.544967\pi$
$43$	−1.84654			−0.281595			−0.140797	+	0.990038i	$0.544967\pi$
$44$		0			0
$45$	0.384258	+	0.384258i	0.0572818	+	0.0572818i
$46$		0			0
$47$	−0.499326	−	0.979982i	−0.0728341	−	0.142945i	0.851718	−	0.524000i	$-0.175561\pi$
$47$	−0.499326	−	0.979982i	−0.0728341	−	0.142945i	−0.924552	+	0.381055i	$0.875561\pi$
$48$		0			0
$49$	1.21970	+	1.67878i	0.174243	+	0.239825i
$50$		0			0
$51$	−1.26393	−	3.88998i	−0.176986	−	0.544706i
$52$		0			0
$53$	−4.81917	−	3.50133i	−0.661964	−	0.480945i	0.205362	−	0.978686i	$-0.434163\pi$
$53$	−4.81917	−	3.50133i	−0.661964	−	0.480945i	−0.867326	+	0.497741i	$0.834163\pi$
$54$		0			0
$55$	−4.95163	+	0.469741i	−0.667678	+	0.0633398i
$56$		0			0
$57$	−7.09367	+	1.12353i	−0.939580	+	0.148815i
$58$		0			0
$59$	−0.860554	−	0.438474i	−0.112035	−	0.0570845i	0.397075	−	0.917786i	$-0.370025\pi$
$59$	−0.860554	−	0.438474i	−0.112035	−	0.0570845i	−0.509110	+	0.860702i	$0.670025\pi$
$60$		0			0
$61$	4.22036	+	5.80883i	0.540362	+	0.743744i	0.988665	−	0.150137i	$-0.0479715\pi$
$61$	4.22036	+	5.80883i	0.540362	+	0.743744i	−0.448303	+	0.893882i	$0.647972\pi$
$62$		0			0
$63$	−0.716507	+	0.365079i	−0.0902714	+	0.0459956i
$64$		0			0
$65$	5.33939	−	0.853363i	0.662270	−	0.105847i
$66$		0			0
$67$	6.06836	+	6.06836i	0.741368	+	0.741368i	0.972841	−	0.231473i	$-0.0743547\pi$
$67$	6.06836	+	6.06836i	0.741368	+	0.741368i	−0.231473	+	0.972841i	$0.574355\pi$
$68$		0			0
$69$	−3.71199	−	1.20610i	−0.446872	−	0.145197i
$70$		0			0
$71$	0.590889	+	0.0935875i	0.0701256	+	0.0111068i	0.191399	−	0.981512i	$-0.438698\pi$
$71$	0.590889	+	0.0935875i	0.0701256	+	0.0111068i	−0.121273	+	0.992619i	$0.538698\pi$
$72$		0			0
$73$	0.917834	−	1.80135i	0.107424	−	0.210832i	−0.831036	−	0.556218i	$-0.812252\pi$
$73$	0.917834	−	1.80135i	0.107424	−	0.210832i	0.938461	+	0.345386i	$0.112252\pi$
$74$		0			0
$75$	2.62611	−	3.61453i	0.303237	−	0.417370i
$76$		0			0
$77$	1.60319	−	7.18358i	0.182701	−	0.818645i
$78$		0			0
$79$	−2.48574	+	3.42133i	−0.279668	+	0.384930i	−0.925624	−	0.378445i	$-0.876459\pi$
$79$	−2.48574	+	3.42133i	−0.279668	+	0.384930i	0.645956	+	0.763375i	$0.276459\pi$
$80$		0			0
$81$	−2.40465	−	7.40076i	−0.267183	−	0.822306i
$82$		0			0
$83$	1.47752	−	9.32867i	0.162178	−	1.02395i	−0.763545	−	0.645754i	$-0.776543\pi$
$83$	1.47752	−	9.32867i	0.162178	−	1.02395i	0.925724	−	0.378200i	$-0.123457\pi$
$84$		0			0
$85$	−3.36520	+	1.71466i	−0.365008	+	0.185981i
$86$		0			0
$87$			0.866554i			0.0929043i
$88$		0			0
$89$	7.15305	−	7.15305i	0.758222	−	0.758222i	−0.217777	−	0.975999i	$-0.569880\pi$
$89$	7.15305	−	7.15305i	0.758222	−	0.758222i	0.975999	+	0.217777i	$0.0698805\pi$
$90$		0			0
$91$	−1.24061	+	7.90473i	−0.130052	+	0.828641i
$92$		0			0
$93$	9.43854	+	1.49492i	0.978731	+	0.155016i
$94$		0			0
$95$	2.04938	+	6.30735i	0.210262	+	0.647121i
$96$		0			0
$97$	−2.60263	−	16.4323i	−0.264257	−	1.66845i	−0.660896	−	0.750477i	$-0.729824\pi$
$97$	−2.60263	−	16.4323i	−0.264257	−	1.66845i	0.396639	−	0.917975i	$-0.370176\pi$
$98$		0			0
$99$	−1.11757	−	0.442042i	−0.112320	−	0.0444269i
$100$		0			0
$101$	7.16605	+	5.20644i	0.713049	+	0.518060i	0.884156	−	0.467192i	$-0.154734\pi$
$101$	7.16605	+	5.20644i	0.713049	+	0.518060i	−0.171107	+	0.985252i	$0.554734\pi$
$102$		0			0
$103$	18.3954	−	5.97702i	1.81255	−	0.588934i	0.812570	−	0.582864i	$-0.198068\pi$
$103$	18.3954	−	5.97702i	1.81255	−	0.588934i	0.999982	−	0.00606955i	$-0.00193201\pi$
$104$		0			0
$105$	−3.17704	−	4.37283i	−0.310048	−	0.426744i
$106$		0			0
$107$	11.5762	+	3.76133i	1.11911	+	0.363622i	0.809429	−	0.587218i	$-0.199777\pi$
$107$	11.5762	+	3.76133i	1.11911	+	0.363622i	0.309684	+	0.950840i	$0.399777\pi$
$108$		0			0
$109$	10.6779	−	10.6779i	1.02276	−	1.02276i	0.0230231	−	0.999735i	$-0.492671\pi$
$109$	10.6779	−	10.6779i	1.02276	−	1.02276i	0.999735	−	0.0230231i	$-0.00732912\pi$
$110$		0			0
$111$	2.47040	−	2.47040i	0.234480	−	0.234480i
$112$		0			0
$113$	−1.24612	+	3.83518i	−0.117226	+	0.360783i	−0.992405	−	0.123016i	$-0.960743\pi$
$113$	−1.24612	+	3.83518i	−0.117226	+	0.360783i	0.875179	+	0.483799i	$0.160743\pi$
$114$		0			0
$115$	−0.563797	+	3.55968i	−0.0525744	+	0.331942i
$116$		0			0
$117$	1.24313	+	0.401988i	0.114927	+	0.0371638i
$118$		0			0
$119$	−0.874309	−	5.52017i	−0.0801478	−	0.506033i
$120$		0			0
$121$	9.63582	−	5.30575i	0.875984	−	0.482341i
$122$		0			0
$123$	−18.9902	+	3.00775i	−1.71229	+	0.271200i
$124$		0			0
$125$	−10.3570	−	5.27716i	−0.926359	−	0.472004i
$126$		0			0
$127$	10.4335	−	7.58041i	0.925828	−	0.672653i	−0.0191402	−	0.999817i	$-0.506093\pi$
$127$	10.4335	−	7.58041i	0.925828	−	0.672653i	0.944968	+	0.327164i	$0.106093\pi$
$128$		0			0
$129$	0.926721	−	2.85215i	0.0815932	−	0.251118i
$130$		0			0
$131$			7.91729i			0.691737i	0.938283	+	0.345868i	$0.112416\pi$
$131$			7.91729i			0.691737i	−0.938283	+	0.345868i	$0.887584\pi$
$132$		0			0
$133$	−9.81393			−0.850975
$134$		0			0
$135$	−7.29676	+	3.71789i	−0.628005	+	0.319985i
$136$		0			0
$137$	1.55306	−	9.80561i	0.132686	−	0.837749i	−0.828124	−	0.560544i	$-0.810592\pi$
$137$	1.55306	−	9.80561i	0.132686	−	0.837749i	0.960811	−	0.277205i	$-0.0894081\pi$
$138$		0			0
$139$	16.8298	−	5.46832i	1.42748	−	0.463817i	0.509510	−	0.860465i	$-0.329827\pi$
$139$	16.8298	−	5.46832i	1.42748	−	0.463817i	0.917971	+	0.396648i	$0.129827\pi$
$140$		0			0
$141$	1.76427	−	0.279433i	0.148578	−	0.0235325i
$142$		0			0
$143$	−10.0855	+	6.42510i	−0.843395	+	0.537294i
$144$		0			0
$145$	0.790324	−	0.125175i	0.0656328	−	0.0103952i
$146$		0			0
$147$	−3.20516	+	1.04142i	−0.264357	+	0.0858948i
$148$		0			0
$149$	−0.460193	+	2.90555i	−0.0377005	+	0.238032i	−0.999342	−	0.0362788i	$-0.988450\pi$
$149$	−0.460193	+	2.90555i	−0.0377005	+	0.238032i	0.961641	+	0.274310i	$0.0884496\pi$
$150$		0			0
$151$	15.4679	−	7.88130i	1.25876	−	0.641371i	0.308027	−	0.951378i	$-0.400331\pi$
$151$	15.4679	−	7.88130i	1.25876	−	0.641371i	0.950734	+	0.310006i	$0.100331\pi$
$152$		0			0
$153$	−0.912585			−0.0737781
$154$		0			0
$155$		−	8.82419i		−	0.708776i
$156$		0			0
$157$	−4.59372	+	14.1380i	−0.366619	+	1.12834i	0.582342	+	0.812944i	$0.302136\pi$
$157$	−4.59372	+	14.1380i	−0.366619	+	1.12834i	−0.948961	+	0.315393i	$0.897864\pi$
$158$		0			0
$159$	7.82673	−	5.68645i	0.620700	−	0.450965i
$160$		0			0
$161$	−4.75197	−	2.42125i	−0.374508	−	0.190821i
$162$		0			0
$163$	−10.1440	+	1.60665i	−0.794540	+	0.125843i	−0.540492	−	0.841349i	$-0.681762\pi$
$163$	−10.1440	+	1.60665i	−0.794540	+	0.125843i	−0.254047	+	0.967192i	$0.581762\pi$
$164$		0			0
$165$	1.75951	−	7.88400i	0.136978	−	0.613769i
$166$		0			0
$167$	−0.478353	−	3.02020i	−0.0370161	−	0.233710i	0.962243	−	0.272191i	$-0.0877482\pi$
$167$	−0.478353	−	3.02020i	−0.0370161	−	0.233710i	−0.999259	+	0.0384805i	$0.987748\pi$
$168$		0			0
$169$	10.4957	−	7.67071i	0.807363	−	0.590054i
$170$		0			0
$171$	−0.250678	+	1.58272i	−0.0191698	+	0.121034i
$172$		0			0
$173$	−6.22847	+	19.1693i	−0.473542	+	1.45741i	0.374372	+	0.927279i	$0.377858\pi$
$173$	−6.22847	+	19.1693i	−0.473542	+	1.45741i	−0.847914	+	0.530134i	$0.822142\pi$
$174$		0			0
$175$	4.31689	−	4.31689i	0.326326	−	0.326326i
$176$		0			0
$177$	1.10915	−	1.10915i	0.0833687	−	0.0833687i
$178$		0			0
$179$	−23.2619	−	7.55826i	−1.73868	−	0.564931i	−0.744021	−	0.668156i	$-0.767084\pi$
$179$	−23.2619	−	7.55826i	−1.73868	−	0.564931i	−0.994658	+	0.103225i	$0.967084\pi$
$180$		0			0
$181$	−3.88102	−	5.34176i	−0.288474	−	0.397050i	0.640044	−	0.768338i	$-0.278916\pi$
$181$	−3.88102	−	5.34176i	−0.288474	−	0.397050i	−0.928518	+	0.371288i	$0.878916\pi$
$182$		0			0
$183$	−11.0903	+	3.60347i	−0.819822	+	0.266376i
$184$		0			0
$185$	−2.60993	−	1.89623i	−0.191886	−	0.139413i
$186$		0			0
$187$	5.32209	−	6.43769i	0.389189	−	0.470770i
$188$		0			0
$189$	−1.89576	−	11.9694i	−0.137896	−	0.870644i
$190$		0			0
$191$	3.48991	+	10.7408i	0.252521	+	0.777180i	0.994308	+	0.106545i	$0.0339787\pi$
$191$	3.48991	+	10.7408i	0.252521	+	0.777180i	−0.741787	+	0.670636i	$0.766021\pi$
$192$		0			0
$193$	−4.36213	−	0.690893i	−0.313993	−	0.0497316i	−0.00255085	−	0.999997i	$-0.500812\pi$
$193$	−4.36213	−	0.690893i	−0.313993	−	0.0497316i	−0.311442	+	0.950265i	$0.600812\pi$
$194$		0			0
$195$	−1.36158	+	8.67547i	−0.0975045	+	0.621263i
$196$		0			0
$197$	−11.2515	+	11.2515i	−0.801633	+	0.801633i	−0.983351	−	0.181717i	$-0.941834\pi$
$197$	−11.2515	+	11.2515i	−0.801633	+	0.801633i	0.181717	+	0.983351i	$0.441834\pi$
$198$		0			0
$199$			5.75738i			0.408130i	0.978957	+	0.204065i	$0.0654154\pi$
$199$			5.75738i			0.408130i	−0.978957	+	0.204065i	$0.934585\pi$
$200$		0			0
$201$	−12.4187	+	6.32762i	−0.875945	+	0.446316i
$202$		0			0
$203$	−0.185234	+	1.16952i	−0.0130008	+	0.0820841i
$204$		0			0
$205$	5.48633	+	16.8852i	0.383182	+	1.17931i
$206$		0			0
$207$	−0.511861	+	0.704517i	−0.0355768	+	0.0489673i
$208$		0			0
$209$	−9.70311	−	10.9986i	−0.671178	−	0.760788i
$210$		0			0
$211$	−1.87961	+	2.58705i	−0.129397	+	0.178100i	−0.868800	−	0.495164i	$-0.835108\pi$
$211$	−1.87961	+	2.58705i	−0.129397	+	0.178100i	0.739402	+	0.673264i	$0.235108\pi$
$212$		0			0
$213$	−0.441103	+	0.865714i	−0.0302239	+	0.0593177i
$214$		0			0
$215$	−2.73512	−	0.433200i	−0.186533	−	0.0295440i
$216$		0			0
$217$	12.4189	+	4.03514i	0.843050	+	0.273923i
$218$		0			0
$219$	2.32172	+	2.32172i	0.156887	+	0.156887i
$220$		0			0
$221$	−5.32700	+	7.35368i	−0.358333	+	0.494662i
$222$		0			0
$223$	10.0434	−	5.11738i	0.672557	−	0.342685i	−0.0841369	−	0.996454i	$-0.526813\pi$
$223$	10.0434	−	5.11738i	0.672557	−	0.342685i	0.756694	+	0.653769i	$0.226813\pi$
$224$		0			0
$225$	−0.585930	−	0.806463i	−0.0390620	−	0.0537642i
$226$		0			0
$227$	−9.29398	−	4.73552i	−0.616863	−	0.314307i	0.117491	−	0.993074i	$-0.462515\pi$
$227$	−9.29398	−	4.73552i	−0.616863	−	0.314307i	−0.734354	+	0.678767i	$0.762515\pi$
$228$		0			0
$229$	21.5972	−	3.42066i	1.42718	−	0.226043i	0.605434	−	0.795896i	$-0.293000\pi$
$229$	21.5972	−	3.42066i	1.42718	−	0.226043i	0.821747	+	0.569852i	$0.193000\pi$
$230$		0			0
$231$	10.2911	+	6.08150i	0.677106	+	0.400133i
$232$		0			0
$233$	−17.7318	−	12.8829i	−1.16165	−	0.843986i	−0.171662	−	0.985156i	$-0.554914\pi$
$233$	−17.7318	−	12.8829i	−1.16165	−	0.843986i	−0.989985	+	0.141170i	$0.954914\pi$
$234$		0			0
$235$	−0.509703	−	1.56870i	−0.0332493	−	0.102331i
$236$		0			0
$237$	−4.03705	−	5.55652i	−0.262235	−	0.360935i
$238$		0			0
$239$	6.31136	+	12.3867i	0.408248	+	0.801232i	0.999988	−	0.00489722i	$-0.00155884\pi$
$239$	6.31136	+	12.3867i	0.408248	+	0.801232i	−0.591740	+	0.806129i	$0.701559\pi$
$240$		0			0
$241$	0.494054	+	0.494054i	0.0318248	+	0.0318248i	0.722840	−	0.691015i	$-0.242836\pi$
$241$	0.494054	+	0.494054i	0.0318248	+	0.0318248i	−0.691015	+	0.722840i	$0.742836\pi$
$242$		0			0
$243$	−3.74426			−0.240195
$244$		0			0
$245$	1.41280	+	2.77277i	0.0902603	+	0.177146i
$246$		0			0
$247$	11.2904	+	11.2587i	0.718390	+	0.716376i
$248$		0			0
$249$	13.6675	+	6.96393i	0.866141	+	0.441321i
$250$		0			0
$251$	−8.21505	+	11.3070i	−0.518529	+	0.713694i	−0.985328	−	0.170669i	$-0.945407\pi$
$251$	−8.21505	+	11.3070i	−0.518529	+	0.713694i	0.466799	+	0.884363i	$0.345407\pi$
$252$		0			0
$253$	−1.98479	−	7.71950i	−0.124783	−	0.485321i
$254$		0			0
$255$	−0.959557	−	6.05840i	−0.0600898	−	0.379392i
$256$		0			0
$257$	4.20423	−	1.36604i	0.262252	−	0.0852110i	−0.174940	−	0.984579i	$-0.555973\pi$
$257$	4.20423	−	1.36604i	0.262252	−	0.0852110i	0.437192	+	0.899368i	$0.355973\pi$
$258$		0			0
$259$	3.86217	−	2.80603i	0.239984	−	0.174358i
$260$		0			0
$261$	0.183880	+	0.0597462i	0.0113819	+	0.00369820i
$262$		0			0
$263$			6.20303i			0.382496i	0.981542	+	0.191248i	$0.0612534\pi$
$263$			6.20303i			0.382496i	−0.981542	+	0.191248i	$0.938747\pi$
$264$		0			0
$265$	−6.31680	−	6.31680i	−0.388038	−	0.388038i
$266$		0			0
$267$	7.45866	+	14.6384i	0.456463	+	0.895858i
$268$		0			0
$269$	22.3524	−	16.2400i	1.36285	−	0.990167i	0.364590	−	0.931168i	$-0.381209\pi$
$269$	22.3524	−	16.2400i	1.36285	−	0.990167i	0.998258	−	0.0589992i	$-0.0187909\pi$
$270$		0			0
$271$	5.99578	−	11.7674i	0.364218	−	0.714818i	−0.634072	−	0.773274i	$-0.718618\pi$
$271$	5.99578	−	11.7674i	0.364218	−	0.714818i	0.998290	+	0.0584562i	$0.0186178\pi$
$272$		0			0
$273$	−11.5870	−	5.88338i	−0.701275	−	0.356078i
$274$		0			0
$275$	9.10613	+	0.569846i	0.549120	+	0.0343630i
$276$		0			0
$277$	8.68775	+	6.31202i	0.521996	+	0.379253i	0.817355	−	0.576134i	$-0.195439\pi$
$277$	8.68775	+	6.31202i	0.521996	+	0.379253i	−0.295359	+	0.955386i	$0.595439\pi$
$278$		0			0
$279$	0.967976	−	1.89976i	0.0579512	−	0.113736i
$280$		0			0
$281$	3.10902	+	0.492420i	0.185469	+	0.0293753i	0.248478	−	0.968638i	$-0.420070\pi$
$281$	3.10902	+	0.492420i	0.185469	+	0.0293753i	−0.0630092	+	0.998013i	$0.520070\pi$
$282$		0			0
$283$	−4.76366	+	14.6610i	−0.283170	+	0.871508i	0.703771	+	0.710427i	$0.251498\pi$
$283$	−4.76366	+	14.6610i	−0.283170	+	0.871508i	−0.986941	+	0.161081i	$0.948502\pi$
$284$		0			0
$285$	−10.7708			−0.638008
$286$		0			0
$287$	−26.2725			−1.55082
$288$		0			0
$289$	−3.29332	+	10.1358i	−0.193725	+	0.596224i
$290$		0			0
$291$	26.6875	+	4.22688i	1.56445	+	0.247784i
$292$		0			0
$293$	−9.30961	+	18.2711i	−0.543873	+	1.06741i	0.441542	+	0.897241i	$0.354432\pi$
$293$	−9.30961	+	18.2711i	−0.543873	+	1.06741i	−0.985415	+	0.170170i	$0.945568\pi$
$294$		0			0
$295$	−1.17180	−	0.851360i	−0.0682246	−	0.0495681i
$296$		0			0
$297$	11.5399	−	13.9588i	0.669611	−	0.809973i
$298$		0			0
$299$	2.68918	+	8.23707i	0.155519	+	0.476362i
$300$		0			0
$301$	1.86039	−	3.65123i	0.107231	−	0.210453i
$302$		0			0
$303$	−11.6382	+	8.45568i	−0.668600	+	0.485766i
$304$		0			0
$305$	4.88849	+	9.59421i	0.279914	+	0.549363i
$306$		0			0
$307$	−16.8680	−	16.8680i	−0.962710	−	0.962710i	0.0366197	−	0.999329i	$-0.488341\pi$
$307$	−16.8680	−	16.8680i	−0.962710	−	0.962710i	−0.999329	+	0.0366197i	$0.988341\pi$
$308$		0			0
$309$			31.4131i			1.78703i
$310$		0			0
$311$	−17.2725	−	5.61217i	−0.979433	−	0.318237i	−0.224815	−	0.974401i	$-0.572178\pi$
$311$	−17.2725	−	5.61217i	−0.979433	−	0.318237i	−0.754618	+	0.656164i	$0.772178\pi$
$312$		0			0
$313$	−10.0913	+	7.33175i	−0.570393	+	0.414415i	−0.835248	−	0.549873i	$-0.814676\pi$
$313$	−10.0913	+	7.33175i	−0.570393	+	0.414415i	0.264855	+	0.964288i	$0.414676\pi$
$314$		0			0
$315$	−1.14695	+	0.372666i	−0.0646232	+	0.0209973i
$316$		0			0
$317$	5.21643	+	32.9352i	0.292984	+	1.84983i	0.492994	+	0.870033i	$0.335903\pi$
$317$	5.21643	+	32.9352i	0.292984	+	1.84983i	−0.200010	+	0.979794i	$0.564097\pi$
$318$		0			0
$319$	−1.49384	+	0.948719i	−0.0836387	+	0.0531181i
$320$		0			0
$321$	−11.6195	+	15.9928i	−0.648535	+	0.892632i
$322$		0			0
$323$	−9.92333	−	5.05619i	−0.552149	−	0.281334i
$324$		0			0
$325$	−9.91877	+	0.0139249i	−0.550194	+	0.000772413i
$326$		0			0
$327$	11.1341	+	21.8519i	0.615718	+	1.20841i
$328$		0			0
$329$	2.44082			0.134567
$330$		0			0
$331$	−9.72074	−	9.72074i	−0.534300	−	0.534300i	0.387549	−	0.921849i	$-0.373322\pi$
$331$	−9.72074	−	9.72074i	−0.534300	−	0.534300i	−0.921849	+	0.387549i	$0.873322\pi$
$332$		0			0
$333$	−0.353885	−	0.694537i	−0.0193928	−	0.0380604i
$334$		0			0
$335$	7.56488	+	10.4122i	0.413314	+	0.568877i
$336$		0			0
$337$	−1.36740	−	4.20844i	−0.0744873	−	0.229248i	0.906880	−	0.421389i	$-0.138457\pi$
$337$	−1.36740	−	4.20844i	−0.0744873	−	0.229248i	−0.981367	+	0.192140i	$0.938457\pi$
$338$		0			0
$339$	−5.29840	−	3.84951i	−0.287769	−	0.209077i
$340$		0			0
$341$	7.75643	+	17.9076i	0.420034	+	0.969751i
$342$		0			0
$343$	−19.8916	+	3.15052i	−1.07405	+	0.170112i
$344$		0			0
$345$	−5.21530	−	2.65733i	−0.280782	−	0.143066i
$346$		0			0
$347$	−5.85127	−	8.05359i	−0.314113	−	0.432339i	0.622546	−	0.782584i	$-0.286099\pi$
$347$	−5.85127	−	8.05359i	−0.314113	−	0.432339i	−0.936658	+	0.350244i	$0.886099\pi$
$348$		0			0
$349$	4.13738	−	2.10810i	0.221469	−	0.112844i	−0.339736	−	0.940521i	$-0.610338\pi$
$349$	4.13738	−	2.10810i	0.221469	−	0.112844i	0.561205	+	0.827677i	$0.310338\pi$
$350$		0			0
$351$	−11.5505	+	15.9450i	−0.616522	+	0.851079i
$352$		0			0
$353$	−22.0621	−	22.0621i	−1.17425	−	1.17425i	−0.981187	−	0.193062i	$-0.938158\pi$
$353$	−22.0621	−	22.0621i	−1.17425	−	1.17425i	−0.193062	−	0.981187i	$-0.561842\pi$
$354$		0			0
$355$	0.853276	+	0.277246i	0.0452872	+	0.0147147i
$356$		0			0
$357$	8.96520	+	1.41995i	0.474489	+	0.0751517i
$358$		0			0
$359$	15.3124	−	30.0522i	0.808155	−	1.58609i	−0.00208594	−	0.999998i	$-0.500664\pi$
$359$	15.3124	−	30.0522i	0.808155	−	1.58609i	0.810241	−	0.586096i	$-0.199336\pi$
$360$		0			0
$361$	−0.326987	+	0.450059i	−0.0172099	+	0.0236873i
$362$		0			0
$363$	3.35931	+	17.5462i	0.176318	+	0.920937i
$364$		0			0
$365$	1.78211	−	2.45286i	0.0932797	−	0.128388i
$366$		0			0
$367$	−4.95912	−	15.2626i	−0.258864	−	0.796701i	−0.993044	−	0.117746i	$-0.962433\pi$
$367$	−4.95912	−	15.2626i	−0.258864	−	0.796701i	0.734180	−	0.678955i	$-0.237567\pi$
$368$		0			0
$369$	−0.671081	+	4.23704i	−0.0349351	+	0.220571i
$370$		0			0
$371$	11.7786	−	6.00151i	0.611516	−	0.311583i
$372$		0			0
$373$			22.8090i			1.18100i	0.807037	+	0.590502i	$0.201070\pi$
$373$			22.8090i			1.18100i	−0.807037	+	0.590502i	$0.798930\pi$
$374$		0			0
$375$	13.3489	−	13.3489i	0.689336	−	0.689336i
$376$		0			0
$377$	1.55480	−	1.13296i	0.0800761	−	0.0583506i
$378$		0			0
$379$	19.7078	+	3.12141i	1.01232	+	0.160336i	0.640491	−	0.767965i	$-0.278731\pi$
$379$	19.7078	+	3.12141i	1.01232	+	0.160336i	0.371829	+	0.928301i	$0.378731\pi$
$380$		0			0
$381$	6.47239	+	19.9200i	0.331590	+	1.02053i
$382$		0			0
$383$	−2.46820	−	15.5836i	−0.126119	−	0.796285i	−0.966946	−	0.254981i	$-0.917931\pi$
$383$	−2.46820	−	15.5836i	−0.126119	−	0.796285i	0.840827	−	0.541304i	$-0.182069\pi$
$384$		0			0
$385$	4.05994	−	10.2643i	0.206914	−	0.523117i
$386$		0			0
$387$	−0.541323	−	0.393294i	−0.0275170	−	0.0199923i
$388$		0			0
$389$	−9.36152	+	3.04174i	−0.474648	+	0.154222i	−0.536565	−	0.843859i	$-0.680278\pi$
$389$	−9.36152	+	3.04174i	−0.474648	+	0.154222i	0.0619175	+	0.998081i	$0.480278\pi$
$390$		0			0
$391$	−3.55750	−	4.89648i	−0.179911	−	0.247626i
$392$		0			0
$393$	−12.2290	−	3.97344i	−0.616871	−	0.200433i
$394$		0			0
$395$	−4.48456	+	4.48456i	−0.225643	+	0.225643i
$396$		0			0
$397$	6.74625	−	6.74625i	0.338585	−	0.338585i	−0.517250	−	0.855835i	$-0.673044\pi$
$397$	6.74625	−	6.74625i	0.338585	−	0.338585i	0.855835	+	0.517250i	$0.173044\pi$
$398$		0			0
$399$	4.92530	−	15.1585i	0.246574	−	0.758875i
$400$		0			0
$401$	1.69858	−	10.7244i	0.0848231	−	0.535552i	−0.908285	−	0.418352i	$-0.862608\pi$
$401$	1.69858	−	10.7244i	0.0848231	−	0.535552i	0.993108	−	0.117200i	$-0.0373920\pi$
$402$		0			0
$403$	−9.65807	−	18.8894i	−0.481103	−	0.940949i
$404$		0			0
$405$	−1.82557	−	11.5262i	−0.0907135	−	0.572743i
$406$		0			0
$407$	6.96332	+	1.55404i	0.345159	+	0.0770307i
$408$		0			0
$409$	−1.26953	+	0.201074i	−0.0627743	+	0.00994247i	−0.187743	−	0.982218i	$-0.560117\pi$
$409$	−1.26953	+	0.201074i	−0.0627743	+	0.00994247i	0.124968	+	0.992161i	$0.460117\pi$
$410$		0			0
$411$	14.3662	+	7.31996i	0.708634	+	0.361067i
$412$		0			0
$413$	1.73402	−	1.25984i	0.0853256	−	0.0619927i
$414$		0			0
$415$	4.37703	−	13.4711i	0.214860	−	0.661271i
$416$		0			0
$417$			28.7395i			1.40738i
$418$		0			0
$419$	−12.3048			−0.601129			−0.300564	−	0.953762i	$-0.597175\pi$
$419$	−12.3048			−0.601129			−0.300564	+	0.953762i	$0.597175\pi$
$420$		0			0
$421$	−20.6658	+	10.5297i	−1.00719	+	0.513189i	−0.878117	−	0.478447i	$-0.841200\pi$
$421$	−20.6658	+	10.5297i	−1.00719	+	0.513189i	−0.129073	+	0.991635i	$0.541200\pi$
$422$		0			0
$423$	0.0623462	−	0.393638i	0.00303138	−	0.0191394i
$424$		0			0
$425$	6.58909	−	2.14093i	0.319618	−	0.103850i
$426$		0			0
$427$	−15.7380	+	2.49266i	−0.761617	+	0.120628i
$428$		0			0
$429$	−4.86256	−	18.8026i	−0.234766	−	0.907798i
$430$		0			0
$431$	20.4004	−	3.23110i	0.982651	−	0.155637i	0.355619	−	0.934631i	$-0.384270\pi$
$431$	20.4004	−	3.23110i	0.982651	−	0.155637i	0.627031	+	0.778994i	$0.284270\pi$
$432$		0			0
$433$	20.9548	−	6.80862i	1.00702	−	0.327201i	0.241354	−	0.970437i	$-0.422408\pi$
$433$	20.9548	−	6.80862i	1.00702	−	0.327201i	0.765668	+	0.643236i	$0.222408\pi$
$434$		0			0
$435$	−0.203294	+	1.28355i	−0.00974722	+	0.0615415i
$436$		0			0
$437$	−9.46929	+	4.82485i	−0.452978	+	0.230804i
$438$		0			0
$439$	−25.8665			−1.23454			−0.617271	−	0.786751i	$-0.711762\pi$
$439$	−25.8665			−1.23454			−0.617271	+	0.786751i	$0.711762\pi$
$440$		0			0
$441$			0.751928i			0.0358061i
$442$		0			0
$443$	−4.75041	+	14.6202i	−0.225699	+	0.694629i	0.772521	+	0.634989i	$0.218995\pi$
$443$	−4.75041	+	14.6202i	−0.225699	+	0.694629i	−0.998220	+	0.0596400i	$0.981005\pi$
$444$		0			0
$445$	12.2733	−	8.91707i	0.581810	−	0.422710i
$446$		0			0
$447$	−4.25693	−	2.16901i	−0.201346	−	0.102591i
$448$		0			0
$449$	33.5732	−	5.31748i	1.58442	−	0.250947i	0.698785	−	0.715332i	$-0.253725\pi$
$449$	33.5732	−	5.31748i	1.58442	−	0.250947i	0.885634	+	0.464385i	$0.153725\pi$
$450$		0			0
$451$	−25.9758	−	29.4439i	−1.22315	−	1.38646i
$452$		0			0
$453$	4.41054	+	27.8470i	0.207225	+	1.30837i
$454$		0			0
$455$	−3.69207	+	11.4175i	−0.173087	+	0.535262i
$456$		0			0
$457$	−2.90407	+	18.3356i	−0.135847	+	0.857702i	0.821804	+	0.569770i	$0.192968\pi$
$457$	−2.90407	+	18.3356i	−0.135847	+	0.857702i	−0.957651	+	0.287932i	$0.907032\pi$
$458$		0			0
$459$	4.24979	−	13.0795i	0.198363	−	0.610499i
$460$		0			0
$461$	−9.52398	+	9.52398i	−0.443576	+	0.443576i	−0.893212	−	0.449636i	$-0.851554\pi$
$461$	−9.52398	+	9.52398i	−0.443576	+	0.443576i	0.449636	+	0.893212i	$0.351554\pi$
$462$		0			0
$463$	16.2698	−	16.2698i	0.756124	−	0.756124i	−0.219491	−	0.975615i	$-0.570440\pi$
$463$	16.2698	−	16.2698i	0.756124	−	0.756124i	0.975615	+	0.219491i	$0.0704396\pi$
$464$		0			0
$465$	13.6298	+	4.42858i	0.632066	+	0.205371i
$466$		0			0
$467$	2.10275	+	2.89419i	0.0973039	+	0.133927i	0.854893	−	0.518805i	$-0.173623\pi$
$467$	2.10275	+	2.89419i	0.0973039	+	0.133927i	−0.757589	+	0.652732i	$0.773623\pi$
$468$		0			0
$469$	−18.1131	+	5.88529i	−0.836383	+	0.271757i
$470$		0			0
$471$	−19.5320	−	14.1909i	−0.899989	−	0.653880i
$472$		0			0
$473$	5.93136	−	1.52503i	0.272724	−	0.0701211i
$474$		0			0
$475$	−1.90310	−	12.0157i	−0.0873203	−	0.551319i
$476$		0			0
$477$	−0.667018	−	2.05287i	−0.0305406	−	0.0939944i
$478$		0			0
$479$	−12.1260	−	1.92056i	−0.554049	−	0.0877527i	−0.126869	−	0.991919i	$-0.540493\pi$
$479$	−12.1260	−	1.92056i	−0.554049	−	0.0877527i	−0.427180	+	0.904167i	$0.640493\pi$
$480$		0			0
$481$	−7.66235	−	1.20257i	−0.349373	−	0.0548326i
$482$		0			0
$483$	6.12471	−	6.12471i	0.278684	−	0.278684i
$484$		0			0
$485$		−	24.9504i		−	1.13294i
$486$		0			0
$487$	17.5851	−	8.96006i	0.796857	−	0.406019i	−0.00764328	−	0.999971i	$-0.502433\pi$
$487$	17.5851	−	8.96006i	0.796857	−	0.406019i	0.804501	+	0.593952i	$0.202433\pi$
$488$		0			0
$489$	2.60933	−	16.4747i	0.117998	−	0.745011i
$490$		0			0
$491$	−4.18811	−	12.8897i	−0.189007	−	0.581702i	0.810988	−	0.585063i	$-0.198930\pi$
$491$	−4.18811	−	12.8897i	−0.189007	−	0.581702i	−0.999994	+	0.00336065i	$0.998930\pi$
$492$		0			0
$493$	−0.789841	+	1.08712i	−0.0355726	+	0.0489615i
$494$		0			0
$495$	−1.55165	−	0.916940i	−0.0697414	−	0.0412134i
$496$		0			0
$497$	−0.780376	+	1.07410i	−0.0350046	+	0.0481797i
$498$		0			0
$499$	14.0899	−	27.6531i	0.630752	−	1.23792i	−0.325546	−	0.945526i	$-0.605548\pi$
$499$	14.0899	−	27.6531i	0.630752	−	1.23792i	0.956298	−	0.292394i	$-0.0944520\pi$
$500$		0			0
$501$	4.90506	+	0.776885i	0.219142	+	0.0347086i
$502$		0			0
$503$	−36.2203	−	11.7687i	−1.61498	−	0.524740i	−0.644233	−	0.764830i	$-0.722823\pi$
$503$	−36.2203	−	11.7687i	−1.61498	−	0.524740i	−0.970751	+	0.240090i	$0.922823\pi$
$504$		0			0
$505$	9.39300	+	9.39300i	0.417983	+	0.417983i
$506$		0			0
$507$	6.58065	+	20.0613i	0.292257	+	0.890954i
$508$		0			0
$509$	10.0937	−	5.14299i	0.447395	−	0.227959i	−0.215752	−	0.976448i	$-0.569220\pi$
$509$	10.0937	−	5.14299i	0.447395	−	0.227959i	0.663147	+	0.748489i	$0.269220\pi$
$510$		0			0
$511$	2.63715	+	3.62973i	0.116661	+	0.160570i
$512$		0			0
$513$	−21.5167	−	10.9633i	−0.949987	−	0.484042i
$514$		0			0
$515$	28.6497	−	4.53766i	1.26246	−	0.199953i
$516$		0			0
$517$	2.41326	+	2.73546i	0.106135	+	0.120306i
$518$		0			0
$519$	−26.4828	−	19.2409i	−1.16247	−	0.844582i
$520$		0			0
$521$	−9.60000	−	29.5458i	−0.420584	−	1.29442i	−0.907160	−	0.420786i	$-0.861754\pi$
$521$	−9.60000	−	29.5458i	−0.420584	−	1.29442i	0.486576	−	0.873638i	$-0.338246\pi$
$522$		0			0
$523$	18.4181	+	25.3503i	0.805366	+	1.10849i	0.992022	+	0.126066i	$0.0402352\pi$
$523$	18.4181	+	25.3503i	0.805366	+	1.10849i	−0.186655	+	0.982425i	$0.559765\pi$
$524$		0			0
$525$	4.50132	+	8.83435i	0.196454	+	0.385562i
$526$		0			0
$527$	10.4784	+	10.4784i	0.456447	+	0.456447i
$528$		0			0
$529$	17.2245			0.748893
$530$		0			0
$531$	−0.158886	−	0.311830i	−0.00689504	−	0.0135323i
$532$		0			0
$533$	30.2251	+	30.1403i	1.30919	+	1.30552i
$534$		0			0
$535$	16.2644	+	8.28712i	0.703171	+	0.358283i
$536$		0			0
$537$	23.3489	−	32.1370i	1.00758	−	1.38681i
$538$		0			0
$539$	−5.30435	−	4.38515i	−0.228475	−	0.188882i
$540$		0			0
$541$	4.29065	+	27.0901i	0.184470	+	1.16470i	0.889981	+	0.455997i	$0.150717\pi$
$541$	4.29065	+	27.0901i	0.184470	+	1.16470i	−0.705512	+	0.708698i	$0.749283\pi$
$542$		0			0
$543$	10.1986	−	3.31373i	0.437664	−	0.142206i
$544$		0			0
$545$	18.3213	−	13.3112i	0.784798	−	0.570189i
$546$		0			0
$547$	13.1148	+	4.26125i	0.560747	+	0.182198i	0.575657	−	0.817691i	$-0.304746\pi$
$547$	13.1148	+	4.26125i	0.560747	+	0.182198i	−0.0149100	+	0.999889i	$0.504746\pi$
$548$		0			0
$549$			2.60178i			0.111041i
$550$		0			0
$551$	1.66846	+	1.66846i	0.0710788	+	0.0710788i
$552$		0			0
$553$	−4.26073	−	8.36215i	−0.181185	−	0.355595i
$554$		0			0
$555$	4.23874	−	3.07963i	0.179925	−	0.130723i
$556$		0			0
$557$	4.57235	−	8.97374i	0.193737	−	0.380230i	−0.773619	−	0.633650i	$-0.781556\pi$
$557$	4.57235	−	8.97374i	0.193737	−	0.380230i	0.967356	+	0.253421i	$0.0815557\pi$
$558$		0			0
$559$	−6.32904	+	2.06626i	−0.267690	+	0.0873934i
$560$		0			0
$561$	7.27262	+	11.4513i	0.307050	+	0.483476i
$562$		0			0
$563$	4.96997	+	3.61089i	0.209459	+	0.152181i	0.687569	−	0.726119i	$-0.258678\pi$
$563$	4.96997	+	3.61089i	0.209459	+	0.152181i	−0.478110	+	0.878300i	$0.658678\pi$
$564$		0			0
$565$	−2.74551	+	5.38837i	−0.115505	+	0.226690i
$566$		0			0
$567$	17.0565	+	2.70148i	0.716304	+	0.113451i
$568$		0			0
$569$	−0.513335	+	1.57988i	−0.0215201	+	0.0662322i	−0.961240	−	0.275714i	$-0.911086\pi$
$569$	−0.513335	+	1.57988i	−0.0215201	+	0.0662322i	0.939720	+	0.341946i	$0.111086\pi$
$570$		0			0
$571$	9.72307			0.406898			0.203449	−	0.979086i	$-0.434785\pi$
$571$	9.72307			0.406898			0.203449	+	0.979086i	$0.434785\pi$
$572$		0			0
$573$	−18.3417			−0.766236
$574$		0			0
$575$	2.04297	−	6.28762i	0.0851977	−	0.262212i
$576$		0			0
$577$	−28.5995	−	4.52972i	−1.19061	−	0.188575i	−0.470480	−	0.882411i	$-0.655919\pi$
$577$	−28.5995	−	4.52972i	−1.19061	−	0.188575i	−0.720133	+	0.693836i	$0.755919\pi$
$578$		0			0
$579$	3.25636	−	6.39097i	0.135330	−	0.265600i
$580$		0			0
$581$	16.9573	+	12.3202i	0.703508	+	0.511128i
$582$		0			0
$583$	18.3716	+	7.26671i	0.760874	+	0.300957i
$584$		0			0
$585$	1.74703	+	0.887069i	0.0722308	+	0.0366758i
$586$		0			0
$587$	13.2485	−	26.0016i	0.546823	−	1.07320i	−0.437893	−	0.899027i	$-0.644275\pi$
$587$	13.2485	−	26.0016i	0.546823	−	1.07320i	0.984715	−	0.174173i	$-0.0557250\pi$
$588$		0			0
$589$	21.0513	−	15.2946i	0.867403	−	0.630205i
$590$		0			0
$591$	−11.7322	−	23.0257i	−0.482597	−	0.947150i
$592$		0			0
$593$	−5.02389	−	5.02389i	−0.206306	−	0.206306i	0.596389	−	0.802695i	$-0.296602\pi$
$593$	−5.02389	−	5.02389i	−0.206306	−	0.206306i	−0.802695	+	0.596389i	$0.796602\pi$
$594$		0			0
$595$		−	8.38166i		−	0.343614i
$596$		0			0
$597$	−8.89281	−	2.88945i	−0.363958	−	0.118257i
$598$		0			0
$599$	−11.7148	+	8.51130i	−0.478654	+	0.347762i	−0.800804	−	0.598926i	$-0.795594\pi$
$599$	−11.7148	+	8.51130i	−0.478654	+	0.347762i	0.322151	+	0.946688i	$0.395594\pi$
$600$		0			0
$601$	−44.3638	+	14.4147i	−1.80964	+	0.587987i	−0.809639	+	0.586928i	$0.800337\pi$
$601$	−44.3638	+	14.4147i	−1.80964	+	0.587987i	−0.999999	+	0.00105874i	$0.999663\pi$
$602$		0			0
$603$	0.486473	+	3.07147i	0.0198107	+	0.125080i
$604$		0			0
$605$	15.5174	−	5.59837i	0.630873	−	0.227606i
$606$		0			0
$607$	13.4858	−	18.5616i	0.547371	−	0.753392i	−0.442281	−	0.896876i	$-0.645831\pi$
$607$	13.4858	−	18.5616i	0.547371	−	0.753392i	0.989653	+	0.143485i	$0.0458307\pi$
$608$		0			0
$609$	−1.71347	−	0.873055i	−0.0694332	−	0.0353780i
$610$		0			0
$611$	−2.80804	−	2.80016i	−0.113601	−	0.113282i
$612$		0			0
$613$	9.53607	+	18.7156i	0.385158	+	0.755916i	0.999450	−	0.0331632i	$-0.0105581\pi$
$613$	9.53607	+	18.7156i	0.385158	+	0.755916i	−0.614292	+	0.789079i	$0.710558\pi$
$614$		0			0
$615$	−28.8341			−1.16270
$616$		0			0
$617$	−15.7296	−	15.7296i	−0.633250	−	0.633250i	0.315632	−	0.948882i	$-0.397784\pi$
$617$	−15.7296	−	15.7296i	−0.633250	−	0.633250i	−0.948882	+	0.315632i	$0.897784\pi$
$618$		0			0
$619$	9.03389	+	17.7300i	0.363103	+	0.712629i	0.998211	−	0.0597940i	$-0.0190444\pi$
$619$	9.03389	+	17.7300i	0.363103	+	0.712629i	−0.635108	+	0.772423i	$0.719044\pi$
$620$		0			0
$621$	−7.71372	−	10.6170i	−0.309541	−	0.426047i
$622$		0			0
$623$	6.93726	+	21.3507i	0.277936	+	0.855398i
$624$		0			0
$625$	−2.97498	−	2.16145i	−0.118999	−	0.0864581i
$626$		0			0
$627$	21.8580	−	9.46751i	0.872926	−	0.378096i
$628$		0			0
$629$	5.35091	−	0.847501i	0.213355	−	0.0337921i
$630$		0			0
$631$	6.15774	+	3.13753i	0.245136	+	0.124903i	0.572242	−	0.820084i	$-0.306074\pi$
$631$	6.15774	+	3.13753i	0.245136	+	0.124903i	−0.327107	+	0.944987i	$0.606074\pi$
$632$		0			0
$633$	−3.05263	−	4.20159i	−0.121331	−	0.166998i
$634$		0			0
$635$	17.2327	−	8.78048i	0.683858	−	0.348443i
$636$		0			0
$637$	6.05909	+	4.38920i	0.240070	+	0.173907i
$638$		0			0
$639$	0.153289	+	0.153289i	0.00606402	+	0.00606402i
$640$		0			0
$641$	24.0087	+	7.80090i	0.948287	+	0.308117i	0.742019	−	0.670379i	$-0.233868\pi$
$641$	24.0087	+	7.80090i	0.948287	+	0.308117i	0.206267	+	0.978496i	$0.433868\pi$
$642$		0			0
$643$	4.17267	+	0.660886i	0.164554	+	0.0260628i	0.238168	−	0.971224i	$-0.423453\pi$
$643$	4.17267	+	0.660886i	0.164554	+	0.0260628i	−0.0736138	+	0.997287i	$0.523453\pi$
$644$		0			0
$645$	2.04179	−	4.00723i	0.0803953	−	0.157785i
$646$		0			0
$647$	−28.3464	+	39.0155i	−1.11441	+	1.53386i	−0.299661	+	0.954046i	$0.596873\pi$
$647$	−28.3464	+	39.0155i	−1.11441	+	1.53386i	−0.814751	+	0.579811i	$0.803127\pi$
$648$		0			0
$649$	3.12636	+	0.697724i	0.122720	+	0.0273881i
$650$		0			0
$651$	−12.4653	+	17.1570i	−0.488554	+	0.672437i
$652$		0			0
$653$	6.18068	+	19.0222i	0.241869	+	0.744395i	0.996136	+	0.0878274i	$0.0279924\pi$
$653$	6.18068	+	19.0222i	0.241869	+	0.744395i	−0.754267	+	0.656568i	$0.772008\pi$
$654$		0			0
$655$	−1.85740	+	11.7272i	−0.0725747	+	0.458219i
$656$		0			0
$657$	0.652738	−	0.332586i	0.0254657	−	0.0129754i
$658$		0			0
$659$		−	34.6431i		−	1.34950i	−0.738045	−	0.674751i	$-0.764251\pi$
$659$		−	34.6431i		−	1.34950i	0.738045	−	0.674751i	$-0.235749\pi$
$660$		0			0
$661$	−26.0628	+	26.0628i	−1.01372	+	1.01372i	−0.0138191	+	0.999905i	$0.504399\pi$
$661$	−26.0628	+	26.0628i	−1.01372	+	1.01372i	−0.999905	+	0.0138191i	$0.995601\pi$
$662$		0			0
$663$	−8.68499	−	11.9186i	−0.337297	−	0.462881i
$664$		0			0
$665$	−14.5365	−	2.30236i	−0.563702	−	0.0892816i
$666$		0			0
$667$	0.396245	+	1.21952i	0.0153427	+	0.0472198i
$668$		0			0
$669$	2.86379	+	18.0812i	0.110720	+	0.699061i
$670$		0			0
$671$	−18.3539	−	15.1733i	−0.708544	−	0.585758i
$672$		0			0
$673$	−1.78770	−	1.29884i	−0.0689108	−	0.0500666i	0.552797	−	0.833316i	$-0.313561\pi$
$673$	−1.78770	−	1.29884i	−0.0689108	−	0.0500666i	−0.621707	+	0.783250i	$0.713561\pi$
$674$		0			0
$675$	14.2871	−	4.64217i	0.549911	−	0.178677i
$676$		0			0
$677$	−16.5590	−	22.7915i	−0.636415	−	0.875950i	0.362003	−	0.932177i	$-0.382093\pi$
$677$	−16.5590	−	22.7915i	−0.636415	−	0.875950i	−0.998418	+	0.0562267i	$0.982093\pi$
$678$		0			0
$679$	35.1144	+	11.4094i	1.34757	+	0.437851i
$680$		0			0
$681$	11.9788	−	11.9788i	0.459029	−	0.459029i
$682$		0			0
$683$	22.2308	−	22.2308i	0.850637	−	0.850637i	−0.139574	−	0.990212i	$-0.544573\pi$
$683$	22.2308	−	22.2308i	0.850637	−	0.850637i	0.990212	+	0.139574i	$0.0445734\pi$
$684$		0			0
$685$	4.60081	−	14.1598i	0.175788	−	0.541019i
$686$		0			0
$687$	−5.55542	+	35.0756i	−0.211953	+	1.33822i
$688$		0			0
$689$	−20.4357	−	6.60827i	−0.778540	−	0.251755i
$690$		0			0
$691$	−2.59154	−	16.3624i	−0.0985870	−	0.622454i	−0.986665	−	0.162762i	$-0.947960\pi$
$691$	−2.59154	−	16.3624i	−0.0985870	−	0.622454i	0.888078	−	0.459692i	$-0.152040\pi$
$692$		0			0
$693$	2.00002	−	1.76444i	0.0759743	−	0.0670256i
$694$		0			0
$695$	26.2113	−	4.15146i	0.994252	−	0.157474i
$696$		0			0
$697$	−26.5654	−	13.5357i	−1.00624	−	0.512702i
$698$		0			0
$699$	28.7978	−	20.9229i	1.08923	−	0.791375i
$700$		0			0
$701$	−2.89023	+	8.89521i	−0.109162	+	0.335967i	−0.990685	−	0.136175i	$-0.956519\pi$
$701$	−2.89023	+	8.89521i	−0.109162	+	0.335967i	0.881522	+	0.472142i	$0.156519\pi$
$702$		0			0
$703$		−	9.51301i		−	0.358790i
$704$		0			0
$705$	2.67881			0.100890
$706$		0			0
$707$	−17.5147	+	8.92418i	−0.658708	+	0.335628i
$708$		0			0
$709$	0.0983942	−	0.621236i	0.00369527	−	0.0233310i	−0.985772	−	0.168089i	$-0.946240\pi$
$709$	0.0983942	−	0.621236i	0.00369527	−	0.0233310i	0.989467	+	0.144758i	$0.0462404\pi$
$710$		0			0
$711$	−1.45742	+	0.473544i	−0.0546575	+	0.0177593i
$712$		0			0
$713$	13.9666	−	2.21209i	0.523053	−	0.0828435i
$714$		0			0
$715$	−16.4462	+	7.15087i	−0.615051	+	0.267427i
$716$		0			0
$717$	−22.2999	+	3.53196i	−0.832807	+	0.131904i
$718$		0			0
$719$	−30.6448	+	9.95711i	−1.14286	+	0.371338i	−0.818449	−	0.574579i	$-0.805166\pi$
$719$	−30.6448	+	9.95711i	−1.14286	+	0.371338i	−0.324411	+	0.945916i	$0.605166\pi$
$720$		0			0
$721$	−6.71482	+	42.3957i	−0.250073	+	1.57890i
$722$		0			0
$723$	−1.01106	+	0.515162i	−0.0376018	+	0.0191591i
$724$		0			0
$725$	−1.46782			−0.0545136
$726$		0			0
$727$		−	16.3823i		−	0.607584i	−0.952738	−	0.303792i	$-0.901747\pi$
$727$		−	16.3823i		−	0.607584i	0.952738	−	0.303792i	$-0.0982529\pi$
$728$		0			0
$729$	9.09308	−	27.9856i	0.336781	−	1.03650i
$730$		0			0
$731$	3.76227	−	2.73345i	0.139152	−	0.101100i
$732$		0			0
$733$	−1.09733	−	0.559120i	−0.0405310	−	0.0206516i	0.433608	−	0.901102i	$-0.357240\pi$
$733$	−1.09733	−	0.559120i	−0.0405310	−	0.0206516i	−0.474139	+	0.880450i	$0.657240\pi$
$734$		0			0
$735$	−4.99184	+	0.790630i	−0.184127	+	0.0291628i
$736$		0			0
$737$	−24.5043	−	14.4807i	−0.902626	−	0.533403i
$738$		0			0
$739$	−5.84322	−	36.8926i	−0.214946	−	1.35712i	−0.825169	−	0.564887i	$-0.808920\pi$
$739$	−5.84322	−	36.8926i	−0.214946	−	1.35712i	0.610222	−	0.792230i	$-0.291080\pi$
$740$		0			0
$741$	−23.0565	+	11.7887i	−0.847000	+	0.433067i
$742$		0			0
$743$	−0.414351	+	2.61611i	−0.0152011	+	0.0959759i	−0.994122	−	0.108262i	$-0.965472\pi$
$743$	−0.414351	+	2.61611i	−0.0152011	+	0.0959759i	0.978921	+	0.204238i	$0.0654715\pi$
$744$		0			0
$745$	−1.36329	+	4.19577i	−0.0499470	+	0.153721i
$746$		0			0
$747$	2.42006	−	2.42006i	0.0885452	−	0.0885452i
$748$		0			0
$749$	−19.1005	+	19.1005i	−0.697916	+	0.697916i
$750$		0			0
$751$	−2.44633	−	0.794861i	−0.0892679	−	0.0290049i	0.264043	−	0.964511i	$-0.414944\pi$
$751$	−2.44633	−	0.794861i	−0.0892679	−	0.0290049i	−0.353310	+	0.935506i	$0.614944\pi$
$752$		0			0
$753$	−13.3419	−	18.3636i	−0.486206	−	0.669205i
$754$		0			0
$755$	24.7602	−	8.04509i	0.901117	−	0.292791i
$756$		0			0
$757$	−18.0641	−	13.1244i	−0.656552	−	0.477013i	0.208945	−	0.977927i	$-0.432997\pi$
$757$	−18.0641	−	13.1244i	−0.656552	−	0.477013i	−0.865497	+	0.500915i	$0.832997\pi$
$758$		0			0
$759$	12.9196	+	0.808486i	0.468951	+	0.0293462i
$760$		0			0
$761$	−2.51359	−	15.8702i	−0.0911177	−	0.575294i	−0.990433	−	0.137994i	$-0.955935\pi$
$761$	−2.51359	−	15.8702i	−0.0911177	−	0.575294i	0.899315	−	0.437301i	$-0.144065\pi$
$762$		0			0
$763$	10.3558	+	31.8718i	0.374904	+	1.15384i
$764$		0			0
$765$	−1.35173	−	0.214093i	−0.0488720	−	0.00774056i
$766$		0			0
$767$	−3.44021	−	0.539926i	−0.124219	−	0.0194956i
$768$		0			0
$769$	−10.6243	+	10.6243i	−0.383121	+	0.383121i	−0.872225	−	0.489105i	$-0.837324\pi$
$769$	−10.6243	+	10.6243i	−0.383121	+	0.383121i	0.489105	+	0.872225i	$0.337324\pi$
$770$		0			0
$771$			7.17939i			0.258559i
$772$		0			0
$773$	−36.7725	+	18.7365i	−1.32262	+	0.673907i	−0.965561	−	0.260176i	$-0.916219\pi$
$773$	−36.7725	+	18.7365i	−1.32262	+	0.673907i	−0.357055	+	0.934083i	$0.616219\pi$
$774$		0			0
$775$	−2.53219	+	15.9876i	−0.0909589	+	0.574292i
$776$		0			0
$777$	2.39587	+	7.37374i	0.0859515	+	0.264532i
$778$		0			0
$779$	−30.7726	+	42.3548i	−1.10254	+	1.51752i
$780$		0			0
$781$	−1.97532	+	0.187390i	−0.0706823	+	0.00670535i
$782$		0			0
$783$	−1.71261	+	2.35720i	−0.0612037	+	0.0842396i
$784$		0			0
$785$	−10.1211	+	19.8637i	−0.361236	+	0.708966i
$786$		0			0
$787$	−31.8761	−	5.04868i	−1.13626	−	0.179966i	−0.440166	−	0.897916i	$-0.645080\pi$
$787$	−31.8761	−	5.04868i	−1.13626	−	0.179966i	−0.696094	+	0.717951i	$0.745080\pi$
$788$		0			0
$789$	−9.58116	−	3.11311i	−0.341098	−	0.110830i
$790$		0			0
$791$	−6.32796	−	6.32796i	−0.224996	−	0.224996i
$792$		0			0
$793$	20.9654	+	15.1873i	0.744502	+	0.539317i
$794$		0			0
$795$	12.9271	−	6.58668i	0.458476	−	0.233605i
$796$		0			0
$797$	−12.0783	−	16.6244i	−0.427837	−	0.588867i	0.539618	−	0.841910i	$-0.318569\pi$
$797$	−12.0783	−	16.6244i	−0.427837	−	0.588867i	−0.967455	+	0.253043i	$0.918569\pi$
$798$		0			0
$799$	2.46803	+	1.25753i	0.0873128	+	0.0444881i
$800$		0			0
$801$	3.62048	−	0.573428i	0.127923	−	0.0202611i
$802$		0			0
$803$	−1.46051	+	6.54424i	−0.0515402	+	0.230941i
$804$		0			0
$805$	−6.47065	−	4.70120i	−0.228060	−	0.165696i
$806$		0			0
$807$	13.8662	+	42.6756i	0.488112	+	1.50225i
$808$		0			0
$809$	20.6583	+	28.4337i	0.726307	+	0.999675i	0.999291	+	0.0376568i	$0.0119894\pi$
$809$	20.6583	+	28.4337i	0.726307	+	0.999675i	−0.272984	+	0.962019i	$0.588011\pi$
$810$		0			0
$811$	−14.8399	−	29.1250i	−0.521101	−	1.02272i	−0.990211	−	0.139579i	$-0.955425\pi$
$811$	−14.8399	−	29.1250i	−0.521101	−	1.02272i	0.469110	−	0.883140i	$-0.344575\pi$
$812$		0			0
$813$	15.1667	+	15.1667i	0.531920	+	0.531920i
$814$		0			0
$815$	−15.4023			−0.539520
$816$		0			0
$817$	−3.70722	−	7.27584i	−0.129699	−	0.254549i
$818$		0			0
$819$	−2.04732	+	2.05308i	−0.0715392	+	0.0717403i
$820$		0			0
$821$	29.9048	+	15.2372i	1.04368	+	0.531783i	0.889821	−	0.456309i	$-0.150829\pi$
$821$	29.9048	+	15.2372i	1.04368	+	0.531783i	0.153862	+	0.988092i	$0.450829\pi$
$822$		0			0
$823$	−21.8364	+	30.0552i	−0.761168	+	1.04766i	0.235948	+	0.971766i	$0.424181\pi$
$823$	−21.8364	+	30.0552i	−0.761168	+	1.04766i	−0.997116	+	0.0758927i	$0.975819\pi$
$824$		0			0
$825$	−5.45026	+	13.7793i	−0.189754	+	0.479733i
$826$		0			0
$827$	6.87593	+	43.4129i	0.239100	+	1.50961i	0.756569	+	0.653913i	$0.226874\pi$
$827$	6.87593	+	43.4129i	0.239100	+	1.50961i	−0.517470	+	0.855701i	$0.673126\pi$
$828$		0			0
$829$	5.37987	−	1.74803i	0.186851	−	0.0607114i	−0.214097	−	0.976812i	$-0.568681\pi$
$829$	5.37987	−	1.74803i	0.186851	−	0.0607114i	0.400948	+	0.916101i	$0.368681\pi$
$830$		0			0
$831$	−14.1096	+	10.2512i	−0.489457	+	0.355611i
$832$		0			0
$833$	−4.97021	−	1.61492i	−0.172208	−	0.0559537i
$834$		0			0
$835$		−	4.58579i		−	0.158698i
$836$		0			0
$837$	22.7203	+	22.7203i	0.785329	+	0.785329i
$838$		0			0
$839$	12.8025	+	25.1263i	0.441991	+	0.867457i	0.999309	+	0.0371576i	$0.0118304\pi$
$839$	12.8025	+	25.1263i	0.441991	+	0.867457i	−0.557318	+	0.830299i	$0.688170\pi$
$840$		0			0
$841$	−23.2312	+	16.8784i	−0.801075	+	0.582015i
$842$		0			0
$843$	−2.32091	+	4.55504i	−0.0799363	+	0.156884i
$844$		0			0
$845$	17.3459	−	8.89964i	0.596719	−	0.306157i
$846$		0			0
$847$	0.783130	+	24.3988i	0.0269087	+	0.838353i
$848$		0			0
$849$	−20.2546	−	14.7158i	−0.695136	−	0.505046i
$850$		0			0
$851$	2.34701	−	4.60626i	0.0804544	−	0.157901i
$852$		0			0
$853$	−39.5996	−	6.27196i	−1.35586	−	0.214748i	−0.564166	−	0.825661i	$-0.690802\pi$
$853$	−39.5996	−	6.27196i	−1.35586	−	0.214748i	−0.791697	+	0.610913i	$0.790802\pi$
$854$		0			0
$855$	−0.742615	+	2.28553i	−0.0253969	+	0.0781636i
$856$		0			0
$857$	55.5673			1.89814			0.949071	−	0.315063i	$-0.102026\pi$
$857$	55.5673			1.89814			0.949071	+	0.315063i	$0.102026\pi$
$858$		0			0
$859$	56.2088			1.91782			0.958909	−	0.283714i	$-0.0915666\pi$
$859$	56.2088			1.91782			0.958909	+	0.283714i	$0.0915666\pi$
$860$		0			0
$861$	13.1853	−	40.5803i	0.449355	−	1.38297i
$862$		0			0
$863$	−12.0126	−	1.90261i	−0.408914	−	0.0647656i	−0.0514108	−	0.998678i	$-0.516372\pi$
$863$	−12.0126	−	1.90261i	−0.408914	−	0.0647656i	−0.357503	+	0.933912i	$0.616372\pi$
$864$		0			0
$865$	−13.7228	+	26.9325i	−0.466590	+	0.915734i
$866$		0			0
$867$	−14.0029	−	10.1737i	−0.475563	−	0.345517i
$868$		0			0
$869$	5.15895	−	13.0428i	0.175005	−	0.442446i
$870$		0			0
$871$	27.5898	+	14.0090i	0.934845	+	0.474675i
$872$		0			0
$873$	2.73695	−	5.37157i	0.0926317	−	0.181800i
$874$		0			0
$875$	20.8694	−	15.1625i	0.705516	−	0.512587i
$876$		0			0
$877$	−1.39191	−	2.73178i	−0.0470015	−	0.0922457i	0.866311	−	0.499505i	$-0.166485\pi$
$877$	−1.39191	−	2.73178i	−0.0470015	−	0.0922457i	−0.913313	+	0.407259i	$0.866485\pi$
$878$		0			0
$879$	−23.5493	−	23.5493i	−0.794297	−	0.794297i
$880$		0			0
$881$			35.0833i			1.18199i	0.806677	+	0.590993i	$0.201264\pi$
$881$			35.0833i			1.18199i	−0.806677	+	0.590993i	$0.798736\pi$
$882$		0			0
$883$	−15.5081	−	5.03887i	−0.521887	−	0.169572i	0.0362143	−	0.999344i	$-0.488470\pi$
$883$	−15.5081	−	5.03887i	−0.521887	−	0.169572i	−0.558102	+	0.829773i	$0.688470\pi$
$884$		0			0
$885$	1.90309	−	1.38268i	0.0639718	−	0.0464782i
$886$		0			0
$887$	3.85592	−	1.25286i	0.129469	−	0.0420670i	−0.243566	−	0.969884i	$-0.578317\pi$
$887$	3.85592	−	1.25286i	0.129469	−	0.0420670i	0.373035	+	0.927817i	$0.378317\pi$
$888$		0			0
$889$	4.47720	+	28.2679i	0.150160	+	0.948075i
$890$		0			0
$891$	13.8363	+	21.7864i	0.463533	+	0.729871i
$892$		0			0
$893$	2.85890	−	3.93494i	0.0956695	−	0.131678i
$894$		0			0
$895$	−32.6827	−	16.6527i	−1.09246	−	0.556637i
$896$		0			0
$897$	−14.0725	+	0.0197563i	−0.469868	+	0.000659644i
$898$		0			0
$899$	−1.42532	−	2.79734i	−0.0475370	−	0.0932967i
$900$		0			0
$901$	15.0020			0.499787
$902$		0			0
$903$	4.70599	+	4.70599i	0.156605	+	0.156605i
$904$		0			0
$905$	−4.49543	−	8.82277i	−0.149433	−	0.293279i
$906$		0			0
$907$	−29.2101	−	40.2042i	−0.969904	−	1.33496i	−0.942095	−	0.335345i	$-0.891147\pi$
$907$	−29.2101	−	40.2042i	−0.969904	−	1.33496i	−0.0278085	−	0.999613i	$-0.508853\pi$
$908$		0			0
$909$	0.991848	+	3.05259i	0.0328975	+	0.101248i
$910$		0			0
$911$	−14.3962	−	10.4594i	−0.476966	−	0.346536i	0.323184	−	0.946336i	$-0.395247\pi$
$911$	−14.3962	−	10.4594i	−0.476966	−	0.346536i	−0.800150	+	0.599800i	$0.795247\pi$
$912$		0			0
$913$	2.95843	+	31.1854i	0.0979097	+	1.03208i
$914$		0			0
$915$	−17.2725	+	2.73570i	−0.571012	+	0.0904395i
$916$		0			0
$917$	−15.6551	−	7.97669i	−0.516978	−	0.263413i
$918$		0			0
$919$	29.2294	+	40.2309i	0.964190	+	1.32709i	0.944927	+	0.327280i	$0.106132\pi$
$919$	29.2294	+	40.2309i	0.964190	+	1.32709i	0.0192630	+	0.999814i	$0.493868\pi$
$920$		0			0
$921$	34.5198	−	17.5887i	1.13747	−	0.579568i
$922$		0			0
$923$	2.13000	−	0.340425i	0.0701099	−	0.0112052i
$924$		0			0
$925$	4.18452	+	4.18452i	0.137586	+	0.137586i
$926$		0			0
$927$	6.66575	+	2.16583i	0.218932	+	0.0711353i
$928$		0			0
$929$	51.8881	+	8.21826i	1.70239	+	0.269632i	0.930545	−	0.366177i	$-0.119333\pi$
$929$	51.8881	+	8.21826i	1.70239	+	0.269632i	0.771846	+	0.635809i	$0.219333\pi$
$930$		0			0
$931$	−4.16606	+	8.17636i	−0.136537	+	0.267969i
$932$		0			0
$933$	17.3370	−	23.8624i	0.567589	−	0.781220i
$934$		0			0
$935$	9.39343	−	8.28701i	0.307198	−	0.271014i
$936$		0			0
$937$	5.65868	−	7.78851i	0.184861	−	0.254439i	−0.706521	−	0.707692i	$-0.749736\pi$
$937$	5.65868	−	7.78851i	0.184861	−	0.254439i	0.891382	+	0.453253i	$0.149736\pi$
$938$		0			0
$939$	−6.26007	−	19.2665i	−0.204290	−	0.628739i
$940$		0			0
$941$	4.02757	−	25.4291i	0.131295	−	0.828965i	−0.830864	−	0.556476i	$-0.812153\pi$
$941$	4.02757	−	25.4291i	0.131295	−	0.828965i	0.962159	−	0.272489i	$-0.0878469\pi$
$942$		0			0
$943$	−25.3499	+	12.9164i	−0.825506	+	0.420616i
$944$		0			0
$945$		−	18.1739i		−	0.591198i
$946$		0			0
$947$	−14.8669	+	14.8669i	−0.483110	+	0.483110i	−0.906124	−	0.423013i	$-0.860972\pi$
$947$	−14.8669	+	14.8669i	−0.483110	+	0.483110i	0.423013	+	0.906124i	$0.360972\pi$
$948$		0			0
$949$	1.13020	−	7.20120i	0.0366878	−	0.233761i
$950$		0			0
$951$	−53.4895	−	8.47190i	−1.73452	−	0.274720i
$952$		0			0
$953$	9.85712	+	30.3371i	0.319304	+	0.982715i	0.973947	+	0.226777i	$0.0728189\pi$
$953$	9.85712	+	30.3371i	0.319304	+	0.982715i	−0.654643	+	0.755938i	$0.727181\pi$
$954$		0			0
$955$	2.64949	+	16.7282i	0.0857354	+	0.541312i
$956$		0			0
$957$	−0.715676	−	2.78350i	−0.0231345	−	0.0899778i
$958$		0			0
$959$	17.8243	+	12.9501i	0.575575	+	0.418180i
$960$		0			0
$961$	−3.44492	+	1.11932i	−0.111126	+	0.0361071i
$962$		0			0
$963$	2.59250	+	3.56827i	0.0835421	+	0.114986i
$964$		0			0
$965$	−6.29915	−	2.04672i	−0.202777	−	0.0658862i
$966$		0			0
$967$	14.8764	−	14.8764i	0.478393	−	0.478393i	−0.426224	−	0.904617i	$-0.640157\pi$
$967$	14.8764	−	14.8764i	0.478393	−	0.478393i	0.904617	+	0.426224i	$0.140157\pi$
$968$		0			0
$969$	12.7900	−	12.7900i	0.410873	−	0.410873i
$970$		0			0
$971$	−17.0505	+	52.4760i	−0.547176	+	1.68404i	0.168582	+	0.985688i	$0.446081\pi$
$971$	−17.0505	+	52.4760i	−0.547176	+	1.68404i	−0.715758	+	0.698348i	$0.753919\pi$
$972$		0			0
$973$	−6.14332	+	38.7874i	−0.196946	+	1.24347i
$974$		0			0
$975$	4.95641	−	15.3274i	0.158732	−	0.490871i
$976$		0			0
$977$	−1.71869	−	10.8514i	−0.0549857	−	0.347166i	−0.999808	−	0.0195833i	$-0.993766\pi$
$977$	−1.71869	−	10.8514i	−0.0549857	−	0.347166i	0.944823	−	0.327583i	$-0.106234\pi$
$978$		0			0
$979$	−17.0691	+	28.8843i	−0.545530	+	0.923146i
$980$		0			0
$981$	5.40457	−	0.856000i	0.172555	−	0.0273300i
$982$		0			0
$983$	47.3333	+	24.1175i	1.50970	+	0.769229i	0.996052	−	0.0887734i	$-0.0282947\pi$
$983$	47.3333	+	24.1175i	1.50970	+	0.769229i	0.513645	+	0.858003i	$0.328295\pi$
$984$		0			0
$985$	−19.3054	+	14.0262i	−0.615121	+	0.446912i
$986$		0			0
$987$	−1.22497	+	3.77008i	−0.0389913	+	0.120003i
$988$		0			0
$989$		−	4.43764i		−	0.141109i
$990$		0			0
$991$	21.3011			0.676651			0.338325	−	0.941029i	$-0.390140\pi$
$991$	21.3011			0.676651			0.338325	+	0.941029i	$0.390140\pi$
$992$		0			0
$993$	19.8931	−	10.1361i	0.631289	−	0.321658i
$994$		0			0
$995$	−1.35069	+	8.52790i	−0.0428196	+	0.270353i
$996$		0			0
$997$	16.5374	−	5.37332i	0.523744	−	0.170175i	−0.0351996	−	0.999380i	$-0.511207\pi$
$997$	16.5374	−	5.37332i	0.523744	−	0.170175i	0.558944	+	0.829205i	$0.311207\pi$
$998$		0			0
$999$	11.6024	−	1.83763i	0.367082	−	0.0581401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.73.4	✓	112
11.8	odd	10	inner	572.2.bh.a.437.4	yes	112
13.5	odd	4	inner	572.2.bh.a.161.4	yes	112
143.96	even	20	inner	572.2.bh.a.525.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.73.4	✓	112	1.1	even	1	trivial
572.2.bh.a.161.4	yes	112	13.5	odd	4	inner
572.2.bh.a.437.4	yes	112	11.8	odd	10	inner
572.2.bh.a.525.4	yes	112	143.96	even	20	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.501869 + 1.54459i) q^{3} +(1.48121 + 0.234601i) q^{5} +(-1.00750 + 1.97734i) q^{7} +(0.293155 + 0.212990i) q^{9} +O(q^{10})\)	\(q+(-0.501869 + 1.54459i) q^{3} +(1.48121 + 0.234601i) q^{5} +(-1.00750 + 1.97734i) q^{7} +(0.293155 + 0.212990i) q^{9} +(-3.21215 + 0.825887i) q^{11} +(3.42752 - 1.11899i) q^{13} +(-1.10574 + 2.17013i) q^{15} +(-2.03747 + 1.48031i) q^{17} +(2.00766 + 3.94025i) q^{19} +(-2.54854 - 2.54854i) q^{21} +2.40322i q^{23} +(-2.61633 - 0.850097i) q^{25} +(-4.41784 + 3.20975i) q^{27} +(0.507451 - 0.164881i) q^{29} +(-0.920470 - 5.81162i) q^{31} +(0.336418 - 5.37595i) q^{33} +(-1.95621 + 2.69249i) q^{35} +(-1.91671 - 0.976610i) q^{37} +(0.00822078 + 5.85570i) q^{39} +(5.37463 + 10.5483i) q^{41} -1.84654 q^{43} +(0.384258 + 0.384258i) q^{45} +(-0.499326 - 0.979982i) q^{47} +(1.21970 + 1.67878i) q^{49} +(-1.26393 - 3.88998i) q^{51} +(-4.81917 - 3.50133i) q^{53} +(-4.95163 + 0.469741i) q^{55} +(-7.09367 + 1.12353i) q^{57} +(-0.860554 - 0.438474i) q^{59} +(4.22036 + 5.80883i) q^{61} +(-0.716507 + 0.365079i) q^{63} +(5.33939 - 0.853363i) q^{65} +(6.06836 + 6.06836i) q^{67} +(-3.71199 - 1.20610i) q^{69} +(0.590889 + 0.0935875i) q^{71} +(0.917834 - 1.80135i) q^{73} +(2.62611 - 3.61453i) q^{75} +(1.60319 - 7.18358i) q^{77} +(-2.48574 + 3.42133i) q^{79} +(-2.40465 - 7.40076i) q^{81} +(1.47752 - 9.32867i) q^{83} +(-3.36520 + 1.71466i) q^{85} +0.866554i q^{87} +(7.15305 - 7.15305i) q^{89} +(-1.24061 + 7.90473i) q^{91} +(9.43854 + 1.49492i) q^{93} +(2.04938 + 6.30735i) q^{95} +(-2.60263 - 16.4323i) q^{97} +(-1.11757 - 0.442042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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