LMFDB - Embedded newform 920.2.bv.a.433.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			433.12
Character	$\chi$	$=$	920.433
Dual form			920.2.bv.a.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21475 - 0.663302i) q^{3} +(0.933470 + 2.03190i) q^{5} +(-0.205002 + 0.273851i) q^{7} +(-0.586283 - 0.912274i) q^{9} +(0.437876 + 0.199971i) q^{11} +(-1.45611 + 1.09003i) q^{13} +(0.213837 - 3.08742i) q^{15} +(-0.429113 + 5.99978i) q^{17} +(2.24436 - 2.59013i) q^{19} +(0.430671 - 0.196681i) q^{21} +(4.77197 - 0.477794i) q^{23} +(-3.25727 + 3.79344i) q^{25} +(0.403282 + 5.63862i) q^{27} +(-7.06351 + 6.12056i) q^{29} +(-8.81071 - 2.58706i) q^{31} +(-0.399267 - 0.533358i) q^{33} +(-0.747802 - 0.160913i) q^{35} +(4.51781 + 0.982790i) q^{37} +(2.49182 - 0.358270i) q^{39} +(-5.19934 - 3.34142i) q^{41} +(2.67559 - 4.89997i) q^{43} +(1.30638 - 2.04285i) q^{45} +(-6.66836 + 6.66836i) q^{47} +(1.93916 + 6.60417i) q^{49} +(4.50093 - 7.00358i) q^{51} +(10.8030 + 8.08702i) q^{53} +(0.00242150 + 1.07639i) q^{55} +(-4.44437 + 1.65766i) q^{57} +(-5.21327 - 0.749555i) q^{59} +(-4.23334 + 14.4174i) q^{61} +(0.370016 + 0.0264641i) q^{63} +(-3.57407 - 1.94117i) q^{65} +(-2.35479 + 6.31343i) q^{67} +(-6.11366 - 2.58486i) q^{69} +(5.71261 + 12.5089i) q^{71} +(3.25371 - 0.232710i) q^{73} +(6.47295 - 2.44752i) q^{75} +(-0.144528 + 0.0789181i) q^{77} +(-1.00791 + 7.01019i) q^{79} +(1.89876 - 4.15771i) q^{81} +(1.64364 - 7.55568i) q^{83} +(-12.5915 + 4.72870i) q^{85} +(12.6402 - 2.74970i) q^{87} +(0.505952 - 0.148561i) q^{89} -0.622215i q^{91} +(8.98678 + 8.98678i) q^{93} +(7.35795 + 2.14252i) q^{95} +(-0.554245 - 2.54782i) q^{97} +(-0.0742905 - 0.516702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.21475	−	0.663302i	−0.701334	−	0.382957i	0.0886682	−	0.996061i	$-0.471739\pi$
$3$	−1.21475	−	0.663302i	−0.701334	−	0.382957i	−0.790002	+	0.613104i	$0.789921\pi$
$4$		0			0
$5$	0.933470	+	2.03190i	0.417460	+	0.908695i
$5$	0.933470	+	2.03190i	0.417460	+	0.908695i
$6$		0			0
$7$	−0.205002	+	0.273851i	−0.0774835	+	0.103506i	−0.837608	−	0.546271i	$-0.816047\pi$
$7$	−0.205002	+	0.273851i	−0.0774835	+	0.103506i	0.760125	+	0.649777i	$0.225138\pi$
$8$		0			0
$9$	−0.586283	−	0.912274i	−0.195428	−	0.304091i
$10$		0			0
$11$	0.437876	+	0.199971i	0.132024	+	0.0602935i	0.480332	−	0.877087i	$-0.340516\pi$
$11$	0.437876	+	0.199971i	0.132024	+	0.0602935i	−0.348307	+	0.937380i	$0.613243\pi$
$12$		0			0
$13$	−1.45611	+	1.09003i	−0.403852	+	0.302320i	−0.781826	−	0.623496i	$-0.785712\pi$
$13$	−1.45611	+	1.09003i	−0.403852	+	0.302320i	0.377974	+	0.925816i	$0.376621\pi$
$14$		0			0
$15$	0.213837	−	3.08742i	0.0552124	−	0.797169i
$16$		0			0
$17$	−0.429113	+	5.99978i	−0.104075	+	1.45516i	0.630266	+	0.776379i	$0.282946\pi$
$17$	−0.429113	+	5.99978i	−0.104075	+	1.45516i	−0.734341	+	0.678781i	$0.762509\pi$
$18$		0			0
$19$	2.24436	−	2.59013i	0.514892	−	0.594217i	−0.437452	−	0.899242i	$-0.644119\pi$
$19$	2.24436	−	2.59013i	0.514892	−	0.594217i	0.952345	+	0.305024i	$0.0986646\pi$
$20$		0			0
$21$	0.430671	−	0.196681i	0.0939802	−	0.0429193i
$22$		0			0
$23$	4.77197	−	0.477794i	0.995025	−	0.0996270i
$23$	4.77197	−	0.477794i	0.995025	−	0.0996270i
$24$		0			0
$25$	−3.25727	+	3.79344i	−0.651454	+	0.758688i
$26$		0			0
$27$	0.403282	+	5.63862i	0.0776116	+	1.08515i
$28$		0			0
$29$	−7.06351	+	6.12056i	−1.31166	+	1.13656i	−0.330407	+	0.943838i	$0.607186\pi$
$29$	−7.06351	+	6.12056i	−1.31166	+	1.13656i	−0.981253	+	0.192722i	$0.938268\pi$
$30$		0			0
$31$	−8.81071	−	2.58706i	−1.58245	−	0.464649i	−0.631856	−	0.775086i	$-0.717707\pi$
$31$	−8.81071	−	2.58706i	−1.58245	−	0.464649i	−0.950594	+	0.310436i	$0.899525\pi$
$32$		0			0
$33$	−0.399267	−	0.533358i	−0.0695034	−	0.0928457i
$34$		0			0
$35$	−0.747802	−	0.160913i	−0.126402	−	0.0271993i
$36$		0			0
$37$	4.51781	+	0.982790i	0.742724	+	0.161570i	0.567978	−	0.823044i	$-0.307726\pi$
$37$	4.51781	+	0.982790i	0.742724	+	0.161570i	0.174746	+	0.984614i	$0.444090\pi$
$38$		0			0
$39$	2.49182	−	0.358270i	0.399011	−	0.0573691i
$40$		0			0
$41$	−5.19934	−	3.34142i	−0.812001	−	0.521841i	0.0675106	−	0.997719i	$-0.478494\pi$
$41$	−5.19934	−	3.34142i	−0.812001	−	0.521841i	−0.879512	+	0.475877i	$0.842131\pi$
$42$		0			0
$43$	2.67559	−	4.89997i	0.408023	−	0.747239i	−0.590173	−	0.807277i	$-0.700940\pi$
$43$	2.67559	−	4.89997i	0.408023	−	0.747239i	0.998196	+	0.0600382i	$0.0191223\pi$
$44$		0			0
$45$	1.30638	−	2.04285i	0.194743	−	0.304530i
$46$		0			0
$47$	−6.66836	+	6.66836i	−0.972680	+	0.972680i	−0.999637	−	0.0269569i	$-0.991418\pi$
$47$	−6.66836	+	6.66836i	−0.972680	+	0.972680i	0.0269569	+	0.999637i	$0.491418\pi$
$48$		0			0
$49$	1.93916	+	6.60417i	0.277023	+	0.943453i
$50$		0			0
$51$	4.50093	−	7.00358i	0.630256	−	0.980697i
$52$		0			0
$53$	10.8030	+	8.08702i	1.48390	+	1.11084i	0.966994	+	0.254798i	$0.0820089\pi$
$53$	10.8030	+	8.08702i	1.48390	+	1.11084i	0.516911	+	0.856039i	$0.327082\pi$
$54$		0			0
$55$	0.00242150	+	1.07639i	0.000326515	+	0.145140i
$56$		0			0
$57$	−4.44437	+	1.65766i	−0.588671	+	0.219563i
$58$		0			0
$59$	−5.21327	−	0.749555i	−0.678710	−	0.0975838i	−0.205666	−	0.978622i	$-0.565936\pi$
$59$	−5.21327	−	0.749555i	−0.678710	−	0.0975838i	−0.473045	+	0.881039i	$0.656845\pi$
$60$		0			0
$61$	−4.23334	+	14.4174i	−0.542024	+	1.84596i	−0.00884702	+	0.999961i	$0.502816\pi$
$61$	−4.23334	+	14.4174i	−0.542024	+	1.84596i	−0.533177	+	0.846004i	$0.679002\pi$
$62$		0			0
$63$	0.370016	+	0.0264641i	0.0466177	+	0.00333416i
$64$		0			0
$65$	−3.57407	−	1.94117i	−0.443309	−	0.240772i
$66$		0			0
$67$	−2.35479	+	6.31343i	−0.287683	+	0.771308i	0.710059	+	0.704143i	$0.248668\pi$
$67$	−2.35479	+	6.31343i	−0.287683	+	0.771308i	−0.997742	+	0.0671659i	$0.978604\pi$
$68$		0			0
$69$	−6.11366	−	2.58486i	−0.735998	−	0.311180i
$70$		0			0
$71$	5.71261	+	12.5089i	0.677962	+	1.48453i	0.864789	+	0.502136i	$0.167452\pi$
$71$	5.71261	+	12.5089i	0.677962	+	1.48453i	−0.186827	+	0.982393i	$0.559820\pi$
$72$		0			0
$73$	3.25371	−	0.232710i	0.380818	−	0.0272367i	0.120382	−	0.992728i	$-0.461588\pi$
$73$	3.25371	−	0.232710i	0.380818	−	0.0272367i	0.260436	+	0.965491i	$0.416134\pi$
$74$		0			0
$75$	6.47295	−	2.44752i	0.747432	−	0.282615i
$76$		0			0
$77$	−0.144528	+	0.0789181i	−0.0164705	+	0.00899355i
$78$		0			0
$79$	−1.00791	+	7.01019i	−0.113399	+	0.788708i	0.851172	+	0.524886i	$0.175892\pi$
$79$	−1.00791	+	7.01019i	−0.113399	+	0.788708i	−0.964571	+	0.263822i	$0.915017\pi$
$80$		0			0
$81$	1.89876	−	4.15771i	0.210974	−	0.461968i
$82$		0			0
$83$	1.64364	−	7.55568i	0.180413	−	0.829344i	−0.794589	−	0.607147i	$-0.792314\pi$
$83$	1.64364	−	7.55568i	0.180413	−	0.829344i	0.975002	−	0.222196i	$-0.0713226\pi$
$84$		0			0
$85$	−12.5915	+	4.72870i	−1.36574	+	0.512899i
$86$		0			0
$87$	12.6402	−	2.74970i	1.35517	−	0.294798i
$88$		0			0
$89$	0.505952	−	0.148561i	0.0536308	−	0.0157474i	−0.254807	−	0.966992i	$-0.582012\pi$
$89$	0.505952	−	0.148561i	0.0536308	−	0.0157474i	0.308438	+	0.951244i	$0.400194\pi$
$90$		0			0
$91$		−	0.622215i		−	0.0652259i
$92$		0			0
$93$	8.98678	+	8.98678i	0.931885	+	0.931885i
$94$		0			0
$95$	7.35795	+	2.14252i	0.754909	+	0.219818i
$96$		0			0
$97$	−0.554245	−	2.54782i	−0.0562750	−	0.258692i	0.940411	−	0.340041i	$-0.110441\pi$
$97$	−0.554245	−	2.54782i	−0.0562750	−	0.258692i	−0.996686	+	0.0813487i	$0.974077\pi$
$98$		0			0
$99$	−0.0742905	−	0.516702i	−0.00746648	−	0.0519305i
$100$		0			0
$101$	13.8433	−	8.89658i	1.37746	−	0.885243i	0.378283	−	0.925690i	$-0.376515\pi$
$101$	13.8433	−	8.89658i	1.37746	−	0.885243i	0.999182	+	0.0404471i	$0.0128782\pi$
$102$		0			0
$103$	−4.44225	−	11.9101i	−0.437708	−	1.17354i	−0.949317	−	0.314321i	$-0.898223\pi$
$103$	−4.44225	−	11.9101i	−0.437708	−	1.17354i	0.511609	−	0.859218i	$-0.329050\pi$
$104$		0			0
$105$	0.801656	+	0.691487i	0.0782336	+	0.0674822i
$106$		0			0
$107$	6.07858	+	11.1321i	0.587638	+	1.07618i	0.987202	+	0.159474i	$0.0509798\pi$
$107$	6.07858	+	11.1321i	0.587638	+	1.07618i	−0.399564	+	0.916705i	$0.630838\pi$
$108$		0			0
$109$	−4.75520	−	5.48779i	−0.455465	−	0.525635i	0.480847	−	0.876805i	$-0.340329\pi$
$109$	−4.75520	−	5.48779i	−0.455465	−	0.525635i	−0.936312	+	0.351170i	$0.885784\pi$
$110$		0			0
$111$	−4.83611	−	4.19051i	−0.459023	−	0.397746i
$112$		0			0
$113$	−10.5184	−	3.92314i	−0.989483	−	0.369058i	−0.197969	−	0.980208i	$-0.563434\pi$
$113$	−10.5184	−	3.92314i	−0.989483	−	0.369058i	−0.791515	+	0.611150i	$0.790707\pi$
$114$		0			0
$115$	5.42532	+	9.25018i	0.505914	+	0.862584i
$116$		0			0
$117$	1.84810	+	0.689305i	0.170857	+	0.0637262i
$118$		0			0
$119$	−1.55508	−	1.34748i	−0.142554	−	0.123523i
$120$		0			0
$121$	−7.05172	−	8.13812i	−0.641066	−	0.739829i
$122$		0			0
$123$	4.09952	+	7.50771i	0.369641	+	0.676947i
$124$		0			0
$125$	−10.7485	−	3.07740i	−0.961373	−	0.275251i
$126$		0			0
$127$	3.79731	+	10.1810i	0.336957	+	0.903417i	0.989353	+	0.145538i	$0.0464914\pi$
$127$	3.79731	+	10.1810i	0.336957	+	0.903417i	−0.652396	+	0.757879i	$0.726236\pi$
$128$		0			0
$129$	−6.50032	+	4.17750i	−0.572321	+	0.367808i
$130$		0			0
$131$	−0.730718	−	5.08226i	−0.0638432	−	0.444039i	−0.996522	−	0.0833309i	$-0.973444\pi$
$131$	−0.730718	−	5.08226i	−0.0638432	−	0.444039i	0.932679	−	0.360708i	$-0.117465\pi$
$132$		0			0
$133$	0.249211	+	1.14560i	0.0216093	+	0.0993364i
$134$		0			0
$135$	−11.0807	+	6.08291i	−0.953673	+	0.523533i
$136$		0			0
$137$	5.18289	+	5.18289i	0.442804	+	0.442804i	0.892953	−	0.450149i	$-0.148629\pi$
$137$	5.18289	+	5.18289i	0.442804	+	0.442804i	−0.450149	+	0.892953i	$0.648629\pi$
$138$		0			0
$139$		−	20.3063i		−	1.72236i	−0.508302	−	0.861179i	$-0.669727\pi$
$139$		−	20.3063i		−	1.72236i	0.508302	−	0.861179i	$-0.330273\pi$
$140$		0			0
$141$	12.5235	−	3.67723i	1.05467	−	0.309679i
$142$		0			0
$143$	−0.855569	+	0.186118i	−0.0715463	+	0.0155639i
$144$		0			0
$145$	−19.0300	−	8.63901i	−1.58035	−	0.717431i
$146$		0			0
$147$	2.02497	−	9.30864i	0.167017	−	0.767764i
$148$		0			0
$149$	7.20474	−	15.7762i	0.590235	−	1.29243i	−0.345065	−	0.938579i	$-0.612143\pi$
$149$	7.20474	−	15.7762i	0.590235	−	1.29243i	0.935300	−	0.353856i	$-0.115130\pi$
$150$		0			0
$151$	1.43401	−	9.97378i	0.116698	−	0.811655i	−0.844452	−	0.535631i	$-0.820074\pi$
$151$	1.43401	−	9.97378i	0.116698	−	0.811655i	0.961151	−	0.276024i	$-0.0890170\pi$
$152$		0			0
$153$	5.72502	−	3.12610i	0.462841	−	0.252730i
$154$		0			0
$155$	−2.96788	−	20.3175i	−0.238386	−	1.63194i
$156$		0			0
$157$	13.7521	−	0.983567i	1.09753	−	0.0784972i	0.489195	−	0.872174i	$-0.337291\pi$
$157$	13.7521	−	0.983567i	1.09753	−	0.0784972i	0.608339	+	0.793677i	$0.291836\pi$
$158$		0			0
$159$	−7.75876	−	16.9893i	−0.615310	−	1.34734i
$160$		0			0
$161$	−0.847420	+	1.40476i	−0.0667861	+	0.110710i
$162$		0			0
$163$	−0.606290	+	1.62553i	−0.0474883	+	0.127321i	−0.958529	−	0.284996i	$-0.908008\pi$
$163$	−0.606290	+	1.62553i	−0.0474883	+	0.127321i	0.911040	+	0.412317i	$0.135280\pi$
$164$		0			0
$165$	0.711029	−	1.30914i	0.0553535	−	0.101917i
$166$		0			0
$167$	−9.50157	−	0.679565i	−0.735253	−	0.0525863i	−0.301310	−	0.953526i	$-0.597424\pi$
$167$	−9.50157	−	0.679565i	−0.735253	−	0.0525863i	−0.433944	+	0.900940i	$0.642878\pi$
$168$		0			0
$169$	−2.73043	+	9.29900i	−0.210033	+	0.715308i
$170$		0			0
$171$	−3.67874	−	0.528923i	−0.281320	−	0.0404478i
$172$		0			0
$173$	0.0778291	−	0.0290287i	0.00591723	−	0.00220701i	−0.346504	−	0.938049i	$-0.612631\pi$
$173$	0.0778291	−	0.0290287i	0.00591723	−	0.00220701i	0.352421	+	0.935842i	$0.385359\pi$
$174$		0			0
$175$	−0.371090	−	1.66967i	−0.0280518	−	0.126215i
$176$		0			0
$177$	5.83562	+	4.36849i	0.438632	+	0.328356i
$178$		0			0
$179$	4.07713	−	6.34413i	0.304739	−	0.474183i	−0.654783	−	0.755817i	$-0.727240\pi$
$179$	4.07713	−	6.34413i	0.304739	−	0.474183i	0.959522	+	0.281634i	$0.0908764\pi$
$180$		0			0
$181$	0.155884	+	0.530891i	0.0115867	+	0.0394608i	0.965083	−	0.261943i	$-0.0843631\pi$
$181$	0.155884	+	0.530891i	0.0115867	+	0.0394608i	−0.953497	+	0.301403i	$0.902545\pi$
$182$		0			0
$183$	14.7056	−	14.7056i	1.08707	−	1.08707i
$184$		0			0
$185$	2.22031	+	10.0972i	0.163240	+	0.742359i
$186$		0			0
$187$	−1.38768	+	2.54135i	−0.101477	+	0.185842i
$188$		0			0
$189$	−1.62681	−	1.04549i	−0.118333	−	0.0760482i
$190$		0			0
$191$	−6.89106	+	0.990785i	−0.498619	+	0.0716907i	−0.387036	−	0.922064i	$-0.626501\pi$
$191$	−6.89106	+	0.990785i	−0.498619	+	0.0716907i	−0.111583	+	0.993755i	$0.535592\pi$
$192$		0			0
$193$	−13.6814	−	2.97621i	−0.984808	−	0.214232i	−0.308801	−	0.951127i	$-0.599928\pi$
$193$	−13.6814	−	2.97621i	−0.984808	−	0.214232i	−0.676007	+	0.736895i	$0.736291\pi$
$194$		0			0
$195$	3.05401	+	4.72871i	0.218702	+	0.338630i
$196$		0			0
$197$	−5.28101	−	7.05460i	−0.376256	−	0.502619i	0.571944	−	0.820293i	$-0.306189\pi$
$197$	−5.28101	−	7.05460i	−0.376256	−	0.502619i	−0.948200	+	0.317673i	$0.897099\pi$
$198$		0			0
$199$	−16.6566	−	4.89080i	−1.18075	−	0.346700i	−0.368288	−	0.929712i	$-0.620056\pi$
$199$	−16.6566	−	4.89080i	−1.18075	−	0.346700i	−0.812464	+	0.583012i	$0.801874\pi$
$200$		0			0
$201$	7.04818	−	6.10728i	0.497140	−	0.430775i
$202$		0			0
$203$	−0.228087	−	3.18908i	−0.0160086	−	0.223829i
$204$		0			0
$205$	1.93601	−	13.6837i	0.135217	−	0.955710i
$206$		0			0
$207$	−3.23360	−	4.07322i	−0.224751	−	0.283109i
$208$		0			0
$209$	1.50070	−	0.685348i	0.103806	−	0.0474065i
$210$		0			0
$211$	−4.14939	+	4.78865i	−0.285656	+	0.329664i	−0.880383	−	0.474263i	$-0.842715\pi$
$211$	−4.14939	+	4.78865i	−0.285656	+	0.329664i	0.594727	+	0.803927i	$0.297260\pi$
$212$		0			0
$213$	1.35778	−	18.9843i	0.0930337	−	1.30078i
$214$		0			0
$215$	12.4539	+	0.862561i	0.849346	+	0.0588262i
$216$		0			0
$217$	2.51468	−	1.88247i	0.170708	−	0.127790i
$218$		0			0
$219$	−4.10679	−	1.87551i	−0.277511	−	0.126735i
$220$		0			0
$221$	−5.91510	−	9.20408i	−0.397893	−	0.619134i
$222$		0			0
$223$	−8.42173	+	11.2501i	−0.563961	+	0.753364i	−0.988364	−	0.152110i	$-0.951393\pi$
$223$	−8.42173	+	11.2501i	−0.563961	+	0.753364i	0.424403	+	0.905474i	$0.360484\pi$
$224$		0			0
$225$	5.37034	+	0.747492i	0.358023	+	0.0498328i
$226$		0			0
$227$	7.23215	+	3.94905i	0.480015	+	0.262108i	0.700989	−	0.713172i	$-0.252742\pi$
$227$	7.23215	+	3.94905i	0.480015	+	0.262108i	−0.220975	+	0.975280i	$0.570924\pi$
$228$		0			0
$229$	12.9303			0.854461			0.427230	−	0.904143i	$-0.359489\pi$
$229$	12.9303			0.854461			0.427230	+	0.904143i	$0.359489\pi$
$230$		0			0
$231$	0.227911			0.0149954
$232$		0			0
$233$	1.05078	+	0.573767i	0.0688386	+	0.0375887i	0.513300	−	0.858209i	$-0.328423\pi$
$233$	1.05078	+	0.573767i	0.0688386	+	0.0375887i	−0.444461	+	0.895798i	$0.646605\pi$
$234$		0			0
$235$	−19.7742	−	7.32475i	−1.28992	−	0.477814i
$236$		0			0
$237$	5.87423	−	7.84706i	0.381572	−	0.509721i
$238$		0			0
$239$	6.67177	+	10.3815i	0.431561	+	0.671522i	0.987125	−	0.159952i	$-0.0511338\pi$
$239$	6.67177	+	10.3815i	0.431561	+	0.671522i	−0.555564	+	0.831474i	$0.687497\pi$
$240$		0			0
$241$	11.5578	+	5.27826i	0.744502	+	0.340003i	0.751288	−	0.659974i	$-0.229433\pi$
$241$	11.5578	+	5.27826i	0.744502	+	0.340003i	−0.00678624	+	0.999977i	$0.502160\pi$
$242$		0			0
$243$	8.51209	−	6.37207i	0.546051	−	0.408769i
$244$		0			0
$245$	−11.6089	+	10.1050i	−0.741665	+	0.645583i
$246$		0			0
$247$	−0.444716	+	6.21794i	−0.0282966	+	0.395638i
$248$		0			0
$249$	−7.00830	+	8.08801i	−0.444133	+	0.512557i
$250$		0			0
$251$	22.1458	−	10.1136i	1.39783	−	0.638366i	0.433035	−	0.901377i	$-0.357443\pi$
$251$	22.1458	−	10.1136i	1.39783	−	0.638366i	0.964793	+	0.263011i	$0.0847155\pi$
$252$		0			0
$253$	2.18507	+	0.745042i	0.137374	+	0.0468404i
$254$		0			0
$255$	18.4321	+	2.60782i	1.15426	+	0.163308i
$256$		0			0
$257$	−0.0525736	−	0.735075i	−0.00327945	−	0.0458527i	0.995549	−	0.0942467i	$-0.0300442\pi$
$257$	−0.0525736	−	0.735075i	−0.00327945	−	0.0458527i	−0.998828	+	0.0483940i	$0.984590\pi$
$258$		0			0
$259$	−1.19530	+	1.03573i	−0.0742723	+	0.0643573i
$260$		0			0
$261$	9.72484	+	2.85547i	0.601953	+	0.176749i
$262$		0			0
$263$	10.9762	+	14.6624i	0.676820	+	0.904125i	0.999096	−	0.0425205i	$-0.0135388\pi$
$263$	10.9762	+	14.6624i	0.676820	+	0.904125i	−0.322276	+	0.946646i	$0.604448\pi$
$264$		0			0
$265$	−6.34778	+	29.4996i	−0.389941	+	1.81215i
$266$		0			0
$267$	−0.713144	−	0.155135i	−0.0436437	−	0.00949410i
$268$		0			0
$269$	16.0708	−	2.31063i	0.979855	−	0.140882i	0.366268	−	0.930509i	$-0.380635\pi$
$269$	16.0708	−	2.31063i	0.979855	−	0.140882i	0.613586	+	0.789628i	$0.289726\pi$
$270$		0			0
$271$	2.55320	+	1.64084i	0.155096	+	0.0996740i	0.615887	−	0.787835i	$-0.288798\pi$
$271$	2.55320	+	1.64084i	0.155096	+	0.0996740i	−0.460791	+	0.887509i	$0.652434\pi$
$272$		0			0
$273$	−0.412717	+	0.755834i	−0.0249787	+	0.0457451i
$274$		0			0
$275$	−2.18486	+	1.00970i	−0.131752	+	0.0608870i
$276$		0			0
$277$	11.0723	−	11.0723i	0.665268	−	0.665268i	−0.291349	−	0.956617i	$-0.594104\pi$
$277$	11.0723	−	11.0723i	0.665268	−	0.665268i	0.956617	+	0.291349i	$0.0941041\pi$
$278$		0			0
$279$	2.80546	+	9.55453i	0.167959	+	0.572015i
$280$		0			0
$281$	2.41198	−	3.75311i	0.143887	−	0.223892i	−0.761829	−	0.647779i	$-0.775698\pi$
$281$	2.41198	−	3.75311i	0.143887	−	0.223892i	0.905715	+	0.423887i	$0.139335\pi$
$282$		0			0
$283$	1.71562	+	1.28430i	0.101983	+	0.0763435i	0.649052	−	0.760744i	$-0.275166\pi$
$283$	1.71562	+	1.28430i	0.101983	+	0.0763435i	−0.547069	+	0.837087i	$0.684257\pi$
$284$		0			0
$285$	−7.51690	−	7.48316i	−0.445263	−	0.443264i
$286$		0			0
$287$	1.98093	−	0.738847i	0.116930	−	0.0436128i
$288$		0			0
$289$	−18.9863	−	2.72981i	−1.11684	−	0.160577i
$290$		0			0
$291$	−1.01671	+	3.46259i	−0.0596005	+	0.202981i
$292$		0			0
$293$	13.5945	+	0.972299i	0.794200	+	0.0568023i	0.462542	−	0.886597i	$-0.346937\pi$
$293$	13.5945	+	0.972299i	0.794200	+	0.0568023i	0.331658	+	0.943400i	$0.392392\pi$
$294$		0			0
$295$	−3.34341	−	11.2926i	−0.194661	−	0.657478i
$296$		0			0
$297$	−0.950973	+	2.54966i	−0.0551811	+	0.147946i
$298$		0			0
$299$	−6.42770	+	5.89731i	−0.371724	+	0.341050i
$300$		0			0
$301$	0.793360	+	1.73722i	0.0457285	+	0.100131i
$302$		0			0
$303$	−22.7173	+	1.62477i	−1.30507	+	0.0933407i
$304$		0			0
$305$	−33.2466	+	4.85650i	−1.90369	+	0.278082i
$306$		0			0
$307$	−28.6713	+	15.6557i	−1.63636	+	0.893519i	−0.644728	+	0.764412i	$0.723029\pi$
$307$	−28.6713	+	15.6557i	−1.63636	+	0.893519i	−0.991631	+	0.129108i	$0.958789\pi$
$308$		0			0
$309$	−2.50380	+	17.4143i	−0.142436	+	0.990667i
$310$		0			0
$311$	14.3216	−	31.3600i	0.812105	−	1.77826i	0.214020	−	0.976829i	$-0.431344\pi$
$311$	14.3216	−	31.3600i	0.812105	−	1.77826i	0.598085	−	0.801433i	$-0.295929\pi$
$312$		0			0
$313$	−0.401614	+	1.84619i	−0.0227005	+	0.104353i	−0.987103	−	0.160086i	$-0.948823\pi$
$313$	−0.401614	+	1.84619i	−0.0227005	+	0.104353i	0.964403	+	0.264438i	$0.0851866\pi$
$314$		0			0
$315$	0.291626	+	0.776541i	0.0164313	+	0.0437531i
$316$		0			0
$317$	29.6509	−	6.45016i	1.66536	−	0.362277i	0.721446	−	0.692470i	$-0.243478\pi$
$317$	29.6509	−	6.45016i	1.66536	−	0.362277i	0.943913	+	0.330193i	$0.107114\pi$
$318$		0			0
$319$	−4.31687	+	1.26755i	−0.241699	+	0.0709691i
$320$		0			0
$321$		−	17.5546i		−	0.979802i
$322$		0			0
$323$	14.5771	+	14.5771i	0.811094	+	0.811094i
$324$		0			0
$325$	0.607975	−	9.07419i	0.0337244	−	0.503345i
$326$		0			0
$327$	2.13630	+	9.82040i	0.118138	+	0.543069i
$328$		0			0
$329$	−0.459107	−	3.19316i	−0.0253114	−	0.176045i
$330$		0			0
$331$	−11.0838	+	7.12312i	−0.609220	+	0.391522i	−0.808565	−	0.588407i	$-0.799755\pi$
$331$	−11.0838	+	7.12312i	−0.609220	+	0.391522i	0.199344	+	0.979930i	$0.436119\pi$
$332$		0			0
$333$	−1.75214	−	4.69768i	−0.0960168	−	0.257431i
$334$		0			0
$335$	−15.0264	+	1.10869i	−0.820981	+	0.0605744i
$336$		0			0
$337$	13.9104	+	25.4751i	0.757750	+	1.38772i	0.916352	+	0.400373i	$0.131119\pi$
$337$	13.9104	+	25.4751i	0.757750	+	1.38772i	−0.158602	+	0.987343i	$0.550699\pi$
$338$		0			0
$339$	10.1749	+	11.7425i	0.552625	+	0.637763i
$340$		0			0
$341$	−3.34066	−	2.89470i	−0.180907	−	0.156757i
$342$		0			0
$343$	−4.44969	−	1.65965i	−0.240260	−	0.0896125i
$344$		0			0
$345$	−0.454729	−	14.8353i	−0.0244818	−	0.798703i
$346$		0			0
$347$	20.6424	+	7.69921i	1.10814	+	0.413315i	0.835882	−	0.548909i	$-0.184957\pi$
$347$	20.6424	+	7.69921i	1.10814	+	0.413315i	0.272258	+	0.962224i	$0.412229\pi$
$348$		0			0
$349$	9.46026	+	8.19736i	0.506396	+	0.438795i	0.870213	−	0.492676i	$-0.163981\pi$
$349$	9.46026	+	8.19736i	0.506396	+	0.438795i	−0.363817	+	0.931470i	$0.618527\pi$
$350$		0			0
$351$	−6.73348	−	7.77085i	−0.359407	−	0.414778i
$352$		0			0
$353$	−14.6828	−	26.8895i	−0.781485	−	1.43118i	−0.898924	−	0.438104i	$-0.855650\pi$
$353$	−14.6828	−	26.8895i	−0.781485	−	1.43118i	0.117439	−	0.993080i	$-0.462532\pi$
$354$		0			0
$355$	−20.0843	+	23.2841i	−1.06596	+	1.23579i
$356$		0			0
$357$	0.995236	+	2.66833i	0.0526735	+	0.141223i
$358$		0			0
$359$	27.5733	−	17.7203i	1.45526	−	0.935240i	0.456293	−	0.889830i	$-0.349177\pi$
$359$	27.5733	−	17.7203i	1.45526	−	0.935240i	0.998968	−	0.0454098i	$-0.0144593\pi$
$360$		0			0
$361$	1.03236	+	7.18021i	0.0543347	+	0.377906i
$362$		0			0
$363$	3.16802	+	14.5632i	0.166278	+	0.764368i
$364$		0			0
$365$	3.51009	+	6.39400i	0.183726	+	0.334677i
$366$		0			0
$367$	−16.9996	−	16.9996i	−0.887373	−	0.887373i	0.106897	−	0.994270i	$-0.465909\pi$
$367$	−16.9996	−	16.9996i	−0.887373	−	0.887373i	−0.994270	+	0.106897i	$0.965909\pi$
$368$		0			0
$369$			6.70224i			0.348905i
$370$		0			0
$371$	−4.42927	+	1.30055i	−0.229956	+	0.0675213i
$372$		0			0
$373$	3.74434	−	0.814532i	0.193875	−	0.0421749i	−0.114579	−	0.993414i	$-0.536552\pi$
$373$	3.74434	−	0.814532i	0.193875	−	0.0421749i	0.308454	+	0.951239i	$0.400188\pi$
$374$		0			0
$375$	11.0154	+	10.8677i	0.568834	+	0.561207i
$376$		0			0
$377$	3.61364	−	16.6116i	0.186112	−	0.855543i
$378$		0			0
$379$	3.26503	−	7.14942i	0.167713	−	0.367241i	−0.807050	−	0.590484i	$-0.798937\pi$
$379$	3.26503	−	7.14942i	0.167713	−	0.367241i	0.974763	+	0.223243i	$0.0716643\pi$
$380$		0			0
$381$	2.14030	−	14.8861i	0.109651	−	0.762637i
$382$		0			0
$383$	−20.1566	+	11.0063i	−1.02995	+	0.562398i	−0.903058	−	0.429519i	$-0.858683\pi$
$383$	−20.1566	+	11.0063i	−1.02995	+	0.562398i	−0.126896	+	0.991916i	$0.540501\pi$
$384$		0			0
$385$	−0.295266	−	0.219999i	−0.0150482	−	0.0112122i
$386$		0			0
$387$	−6.03877	+	0.431901i	−0.306968	+	0.0219548i
$388$		0			0
$389$	9.91792	+	21.7172i	0.502859	+	1.10111i	0.975530	+	0.219868i	$0.0705626\pi$
$389$	9.91792	+	21.7172i	0.502859	+	1.10111i	−0.472671	+	0.881239i	$0.656710\pi$
$390$		0			0
$391$	0.818945	+	28.8358i	0.0414159	+	1.45829i
$392$		0			0
$393$	−2.48343	+	6.65834i	−0.125273	+	0.335869i
$394$		0			0
$395$	−15.1849	+	4.49582i	−0.764035	+	0.226209i
$396$		0			0
$397$	−29.9011	−	2.13857i	−1.50069	−	0.107332i	−0.703343	−	0.710851i	$-0.748310\pi$
$397$	−29.9011	−	2.13857i	−1.50069	−	0.107332i	−0.797348	+	0.603519i	$0.793765\pi$
$398$		0			0
$399$	0.457153	−	1.55692i	0.0228863	−	0.0779435i
$400$		0			0
$401$	−18.2622	−	2.62571i	−0.911971	−	0.131122i	−0.329671	−	0.944096i	$-0.606938\pi$
$401$	−18.2622	−	2.62571i	−0.911971	−	0.131122i	−0.582300	+	0.812974i	$0.697847\pi$
$402$		0			0
$403$	15.6493	−	5.83690i	0.779549	−	0.290757i
$404$		0			0
$405$	10.2205	−	0.0229926i	0.507861	−	0.00114251i
$406$		0			0
$407$	1.78171	+	1.33377i	0.0883161	+	0.0661126i
$408$		0			0
$409$	3.32710	−	5.17708i	0.164515	−	0.255990i	−0.749202	−	0.662341i	$-0.769563\pi$
$409$	3.32710	−	5.17708i	0.164515	−	0.255990i	0.913717	+	0.406352i	$0.133199\pi$
$410$		0			0
$411$	−2.85807	−	9.73371i	−0.140978	−	0.480128i
$412$		0			0
$413$	1.27400	−	1.27400i	0.0626894	−	0.0626894i
$414$		0			0
$415$	16.8867	−	3.71328i	0.828936	−	0.182278i
$416$		0			0
$417$	−13.4692	+	24.6670i	−0.659590	+	1.20795i
$418$		0			0
$419$	−16.3546	−	10.5104i	−0.798973	−	0.513469i	0.0763072	−	0.997084i	$-0.475687\pi$
$419$	−16.3546	−	10.5104i	−0.798973	−	0.513469i	−0.875281	+	0.483615i	$0.839323\pi$
$420$		0			0
$421$	22.8972	−	3.29212i	1.11594	−	0.160448i	0.440423	−	0.897790i	$-0.354829\pi$
$421$	22.8972	−	3.29212i	1.11594	−	0.160448i	0.675520	+	0.737342i	$0.263919\pi$
$422$		0			0
$423$	9.99291	+	2.17382i	0.485872	+	0.105695i
$424$		0			0
$425$	−21.3621	−	21.1707i	−1.03621	−	1.02693i
$426$		0			0
$427$	−3.08038	−	4.11491i	−0.149070	−	0.199135i
$428$		0			0
$429$	1.16275	+	0.341415i	0.0561382	+	0.0164837i
$430$		0			0
$431$	−5.28791	+	4.58200i	−0.254710	+	0.220707i	−0.772851	−	0.634588i	$-0.781170\pi$
$431$	−5.28791	+	4.58200i	−0.254710	+	0.220707i	0.518141	+	0.855295i	$0.326624\pi$
$432$		0			0
$433$	−0.355679	−	4.97304i	−0.0170928	−	0.238989i	−0.998815	−	0.0486692i	$-0.984502\pi$
$433$	−0.355679	−	4.97304i	−0.0170928	−	0.238989i	0.981722	−	0.190320i	$-0.0609525\pi$
$434$		0			0
$435$	17.3863	+	23.1168i	0.833610	+	1.10837i
$436$		0			0
$437$	9.47249	−	13.4324i	0.453130	−	0.642558i
$438$		0			0
$439$	−2.42656	+	1.10817i	−0.115813	+	0.0528901i	−0.472479	−	0.881342i	$-0.656641\pi$
$439$	−2.42656	+	1.10817i	−0.115813	+	0.0528901i	0.356666	+	0.934232i	$0.383913\pi$
$440$		0			0
$441$	4.88792	−	5.64096i	0.232758	−	0.268617i
$442$		0			0
$443$	1.09727	−	15.3419i	0.0521331	−	0.728916i	−0.902417	−	0.430864i	$-0.858209\pi$
$443$	1.09727	−	15.3419i	0.0521331	−	0.728916i	0.954550	−	0.298052i	$-0.0963368\pi$
$444$		0			0
$445$	0.774152	+	0.889368i	0.0366983	+	0.0421601i
$446$		0			0
$447$	−19.2163	+	14.3851i	−0.908900	+	0.680394i
$448$		0			0
$449$	11.7182	+	5.35152i	0.553016	+	0.252554i	0.672265	−	0.740311i	$-0.265322\pi$
$449$	11.7182	+	5.35152i	0.553016	+	0.252554i	−0.119249	+	0.992864i	$0.538049\pi$
$450$		0			0
$451$	−1.60848	−	2.50284i	−0.0757403	−	0.117854i
$452$		0			0
$453$	−8.35759	+	11.1644i	−0.392674	+	0.524551i
$454$		0			0
$455$	1.26428	−	0.580819i	0.0592705	−	0.0272292i
$456$		0			0
$457$	−6.54577	−	3.57426i	−0.306198	−	0.167197i	0.318802	−	0.947821i	$-0.396719\pi$
$457$	−6.54577	−	3.57426i	−0.306198	−	0.167197i	−0.625000	+	0.780624i	$0.714901\pi$
$458$		0			0
$459$	−34.0035			−1.58715
$460$		0			0
$461$	1.78272			0.0830295			0.0415147	−	0.999138i	$-0.486782\pi$
$461$	1.78272			0.0830295			0.0415147	+	0.999138i	$0.486782\pi$
$462$		0			0
$463$	15.4286	+	8.42465i	0.717028	+	0.391527i	0.795957	−	0.605354i	$-0.206968\pi$
$463$	15.4286	+	8.42465i	0.717028	+	0.391527i	−0.0789291	+	0.996880i	$0.525150\pi$
$464$		0			0
$465$	−9.87139	+	26.6492i	−0.457775	+	1.23583i
$466$		0			0
$467$	−23.4916	+	31.3812i	−1.08706	+	1.45215i	−0.206362	+	0.978476i	$0.566162\pi$
$467$	−23.4916	+	31.3812i	−1.08706	+	1.45215i	−0.880702	+	0.473671i	$0.842929\pi$
$468$		0			0
$469$	−1.24620	−	1.93913i	−0.0575443	−	0.0895406i
$470$		0			0
$471$	−17.3577	−	7.92699i	−0.799800	−	0.365256i
$472$		0			0
$473$	2.15143	−	1.61054i	0.0989227	−	0.0740526i
$474$		0			0
$475$	2.51502	+	16.9506i	0.115397	+	0.777748i
$476$		0			0
$477$	1.04397	−	14.5966i	0.0478000	−	0.668331i
$478$		0			0
$479$	2.50775	−	2.89410i	0.114582	−	0.132235i	−0.695561	−	0.718467i	$-0.744844\pi$
$479$	2.50775	−	2.89410i	0.114582	−	0.132235i	0.810143	+	0.586232i	$0.199389\pi$
$480$		0			0
$481$	−7.64970	+	3.49350i	−0.348796	+	0.159290i
$482$		0			0
$483$	1.96118	−	1.14433i	0.0892367	−	0.0520688i
$484$		0			0
$485$	4.65956	−	3.50449i	0.211580	−	0.159131i
$486$		0			0
$487$	2.72669	+	38.1241i	0.123558	+	1.72757i	0.560564	+	0.828111i	$0.310584\pi$
$487$	2.72669	+	38.1241i	0.123558	+	1.72757i	−0.437006	+	0.899458i	$0.643961\pi$
$488$		0			0
$489$	1.81470	−	1.57245i	0.0820638	−	0.0711087i
$490$		0			0
$491$	−14.5271	−	4.26553i	−0.655598	−	0.192501i	−0.0630177	−	0.998012i	$-0.520072\pi$
$491$	−14.5271	−	4.26553i	−0.655598	−	0.192501i	−0.592580	+	0.805512i	$0.701891\pi$
$492$		0			0
$493$	−33.6910	−	45.0059i	−1.51737	−	2.02696i
$494$		0			0
$495$	0.980541	−	0.633277i	0.0440720	−	0.0284637i
$496$		0			0
$497$	−4.59666	−	0.999942i	−0.206188	−	0.0448535i
$498$		0			0
$499$	−21.1033	+	3.03420i	−0.944714	+	0.135829i	−0.597422	−	0.801927i	$-0.703808\pi$
$499$	−21.1033	+	3.03420i	−0.944714	+	0.135829i	−0.347293	+	0.937757i	$0.612899\pi$
$500$		0			0
$501$	11.0912	+	7.12790i	0.495520	+	0.318451i
$502$		0			0
$503$	0.730270	−	1.33739i	0.0325611	−	0.0596312i	−0.860892	−	0.508788i	$-0.830094\pi$
$503$	0.730270	−	1.33739i	0.0325611	−	0.0596312i	0.893453	+	0.449157i	$0.148276\pi$
$504$		0			0
$505$	30.9993	+	19.8237i	1.37945	+	0.882142i
$506$		0			0
$507$	9.48483	−	9.48483i	0.421236	−	0.421236i
$508$		0			0
$509$	3.13431	+	10.6745i	0.138926	+	0.473138i	0.999335	−	0.0364663i	$-0.0116102\pi$
$509$	3.13431	+	10.6745i	0.138926	+	0.473138i	−0.860409	+	0.509604i	$0.829792\pi$
$510$		0			0
$511$	−0.603290	+	0.938738i	−0.0266880	+	0.0415273i
$512$		0			0
$513$	15.5099	+	11.6105i	0.684778	+	0.512618i
$514$		0			0
$515$	20.0535	−	20.1440i	0.883664	−	0.887649i
$516$		0			0
$517$	−4.25339	+	1.58643i	−0.187064	+	0.0697712i
$518$		0			0
$519$	−0.113797	−	0.0163616i	−0.00499515	−	0.000718194i
$520$		0			0
$521$	1.21793	−	4.14789i	0.0533586	−	0.181723i	−0.928502	−	0.371328i	$-0.878903\pi$
$521$	1.21793	−	4.14789i	0.0533586	−	0.181723i	0.981860	+	0.189605i	$0.0607208\pi$
$522$		0			0
$523$	−14.0370	−	1.00394i	−0.613793	−	0.0438994i	−0.239018	−	0.971015i	$-0.576826\pi$
$523$	−14.0370	−	1.00394i	−0.613793	−	0.0438994i	−0.374775	+	0.927116i	$0.622280\pi$
$524$		0			0
$525$	−0.656715	+	2.27437i	−0.0286614	+	0.0992616i
$526$		0			0
$527$	19.3026	−	51.7522i	0.840833	−	2.25436i
$528$		0			0
$529$	22.5434	−	4.56004i	0.980149	−	0.198263i
$530$		0			0
$531$	2.37265	+	5.19538i	0.102964	+	0.225460i
$532$		0			0
$533$	11.2131	−	0.801974i	0.485691	−	0.0347373i
$534$		0			0
$535$	−16.9452	+	22.7426i	−0.732603	+	0.983246i
$536$		0			0
$537$	−9.16075	+	5.00215i	−0.395315	+	0.215859i
$538$		0			0
$539$	−0.471533	+	3.27958i	−0.0203103	+	0.141262i
$540$		0			0
$541$	−15.8761	+	34.7639i	−0.682568	+	1.49462i	0.177330	+	0.984151i	$0.443254\pi$
$541$	−15.8761	+	34.7639i	−0.682568	+	1.49462i	−0.859899	+	0.510465i	$0.829473\pi$
$542$		0			0
$543$	0.162782	−	0.748296i	0.00698564	−	0.0321125i
$544$		0			0
$545$	6.71183	−	14.7848i	0.287503	−	0.633311i
$546$		0			0
$547$	11.9966	−	2.60970i	0.512937	−	0.111583i	0.0513554	−	0.998680i	$-0.483646\pi$
$547$	11.9966	−	2.60970i	0.512937	−	0.111583i	0.461581	+	0.887098i	$0.347282\pi$
$548$		0			0
$549$	15.6346	−	4.59073i	0.667268	−	0.195928i
$550$		0			0
$551$			32.0322i			1.36462i
$552$		0			0
$553$	−1.71312	−	1.71312i	−0.0728494	−	0.0728494i
$554$		0			0
$555$	4.00036	−	13.7382i	0.169806	−	0.583155i
$556$		0			0
$557$	3.43979	+	15.8125i	0.145749	+	0.669995i	0.990803	+	0.135315i	$0.0432045\pi$
$557$	3.43979	+	15.8125i	0.145749	+	0.669995i	−0.845054	+	0.534681i	$0.820432\pi$
$558$		0			0
$559$	1.44517	+	10.0514i	0.0611241	+	0.425127i
$560$		0			0
$561$	3.37136	−	2.16664i	0.142339	−	0.0914757i
$562$		0			0
$563$	15.8213	+	42.4186i	0.666789	+	1.78773i	0.614248	+	0.789113i	$0.289459\pi$
$563$	15.8213	+	42.4186i	0.666789	+	1.78773i	0.0525413	+	0.998619i	$0.483268\pi$
$564$		0			0
$565$	−1.84711	−	25.0344i	−0.0777086	−	1.05321i
$566$		0			0
$567$	0.749342	+	1.37232i	0.0314694	+	0.0576320i
$568$		0			0
$569$	14.6434	+	16.8994i	0.613883	+	0.708459i	0.974533	−	0.224242i	$-0.0719906\pi$
$569$	14.6434	+	16.8994i	0.613883	+	0.708459i	−0.360650	+	0.932701i	$0.617445\pi$
$570$		0			0
$571$	−3.23046	−	2.79921i	−0.135190	−	0.117143i	0.584641	−	0.811292i	$-0.301235\pi$
$571$	−3.23046	−	2.79921i	−0.135190	−	0.117143i	−0.719831	+	0.694149i	$0.755781\pi$
$572$		0			0
$573$	9.02808	+	3.36730i	0.377153	+	0.140671i
$574$		0			0
$575$	−13.7311	+	19.6585i	−0.572627	+	0.819816i
$576$		0			0
$577$	6.97385	+	2.60111i	0.290325	+	0.108286i	0.490407	−	0.871493i	$-0.336848\pi$
$577$	6.97385	+	2.60111i	0.290325	+	0.108286i	−0.200082	+	0.979779i	$0.564121\pi$
$578$		0			0
$579$	14.6453	+	12.6902i	0.608638	+	0.527388i
$580$		0			0
$581$	1.73218	+	1.99904i	0.0718629	+	0.0829343i
$582$		0			0
$583$	3.11320	+	5.70139i	0.128935	+	0.236128i
$584$		0			0
$585$	0.324542	+	4.39860i	0.0134182	+	0.181860i
$586$		0			0
$587$	2.72897	+	7.31666i	0.112637	+	0.301991i	0.981021	−	0.193901i	$-0.0621140\pi$
$587$	2.72897	+	7.31666i	0.112637	+	0.301991i	−0.868384	+	0.495892i	$0.834841\pi$
$588$		0			0
$589$	−26.4753	+	17.0146i	−1.09089	+	0.701075i
$590$		0			0
$591$	1.73576	+	12.0725i	0.0713995	+	0.496594i
$592$		0			0
$593$	0.731036	+	3.36052i	0.0300201	+	0.138000i	0.989718	−	0.143035i	$-0.0456860\pi$
$593$	0.731036	+	3.36052i	0.0300201	+	0.138000i	−0.959698	+	0.281035i	$0.909322\pi$
$594$		0			0
$595$	1.28634	−	4.41760i	0.0527346	−	0.181104i
$596$		0			0
$597$	16.9894	+	16.9894i	0.695330	+	0.695330i
$598$		0			0
$599$		−	9.17302i		−	0.374799i	−0.982284	−	0.187400i	$-0.939994\pi$
$599$		−	9.17302i		−	0.374799i	0.982284	−	0.187400i	$-0.0600060\pi$
$600$		0			0
$601$	−1.24243	+	0.364811i	−0.0506799	+	0.0148810i	−0.306974	−	0.951718i	$-0.599317\pi$
$601$	−1.24243	+	0.364811i	−0.0506799	+	0.0148810i	0.256294	+	0.966599i	$0.417498\pi$
$602$		0			0
$603$	7.14015	−	1.55324i	0.290769	−	0.0632530i
$604$		0			0
$605$	9.95331	−	21.9251i	0.404660	−	0.891382i
$606$		0			0
$607$	4.38250	−	20.1460i	0.177880	−	0.817702i	−0.798560	−	0.601915i	$-0.794405\pi$
$607$	4.38250	−	20.1460i	0.177880	−	0.817702i	0.976440	−	0.215787i	$-0.0692318\pi$
$608$		0			0
$609$	−1.83825	+	4.02521i	−0.0744897	+	0.163110i
$610$		0			0
$611$	2.44115	−	16.9786i	0.0987583	−	0.686879i
$612$		0			0
$613$	15.7353	−	8.59214i	0.635544	−	0.347033i	−0.128962	−	0.991649i	$-0.541165\pi$
$613$	15.7353	−	8.59214i	0.635544	−	0.347033i	0.764506	+	0.644616i	$0.222983\pi$
$614$		0			0
$615$	−11.4282	+	15.3380i	−0.460828	+	0.618490i
$616$		0			0
$617$	−26.7290	+	1.91170i	−1.07607	+	0.0769620i	−0.598106	−	0.801417i	$-0.704080\pi$
$617$	−26.7290	+	1.91170i	−1.07607	+	0.0769620i	−0.477964	+	0.878379i	$0.658625\pi$
$618$		0			0
$619$	−7.48869	−	16.3979i	−0.300996	−	0.659089i	0.697341	−	0.716740i	$-0.254366\pi$
$619$	−7.48869	−	16.3979i	−0.300996	−	0.659089i	−0.998337	+	0.0576506i	$0.981639\pi$
$620$		0			0
$621$	4.61855	+	26.7146i	0.185336	+	1.07202i
$622$		0			0
$623$	−0.0630377	+	0.169011i	−0.00252555	+	0.00677127i
$624$		0			0
$625$	−3.78040	−	24.7125i	−0.151216	−	0.988501i
$626$		0			0
$627$	−2.27757	−	0.162895i	−0.0909573	−	0.00650539i
$628$		0			0
$629$	−7.83518	+	26.6842i	−0.312409	+	1.06397i
$630$		0			0
$631$	−19.3844	−	2.78705i	−0.771680	−	0.110951i	−0.254783	−	0.966998i	$-0.582004\pi$
$631$	−19.3844	−	2.78705i	−0.771680	−	0.110951i	−0.516897	+	0.856048i	$0.672913\pi$
$632$		0			0
$633$	8.21678	−	3.06470i	0.326588	−	0.121811i
$634$		0			0
$635$	−17.1421	+	17.2194i	−0.680264	+	0.683332i
$636$		0			0
$637$	−10.0224	−	7.50265i	−0.397101	−	0.297266i
$638$		0			0
$639$	8.06230	−	12.5452i	0.318940	−	0.496280i
$640$		0			0
$641$	−6.91160	−	23.5387i	−0.272992	−	0.929724i	−0.975859	−	0.218403i	$-0.929915\pi$
$641$	−6.91160	−	23.5387i	−0.272992	−	0.929724i	0.702867	−	0.711321i	$-0.251903\pi$
$642$		0			0
$643$	−22.6055	+	22.6055i	−0.891474	+	0.891474i	−0.994662	−	0.103188i	$-0.967096\pi$
$643$	−22.6055	+	22.6055i	−0.891474	+	0.891474i	0.103188	+	0.994662i	$0.467096\pi$
$644$		0			0
$645$	−14.5561	−	9.30845i	−0.573147	−	0.366520i
$646$		0			0
$647$	17.2300	−	31.5544i	0.677381	−	1.24053i	−0.282270	−	0.959335i	$-0.591087\pi$
$647$	17.2300	−	31.5544i	0.677381	−	1.24053i	0.959651	−	0.281195i	$-0.0907309\pi$
$648$		0			0
$649$	−2.13288	−	1.37072i	−0.0837227	−	0.0538053i
$650$		0			0
$651$	−4.30335	+	0.618728i	−0.168661	+	0.0242499i
$652$		0			0
$653$	6.38617	+	1.38923i	0.249910	+	0.0543646i	0.335775	−	0.941942i	$-0.391002\pi$
$653$	6.38617	+	1.38923i	0.249910	+	0.0543646i	−0.0858650	+	0.996307i	$0.527365\pi$
$654$		0			0
$655$	9.64456	−	6.22888i	0.376844	−	0.243383i
$656$		0			0
$657$	−2.11989	−	2.83184i	−0.0827048	−	0.110481i
$658$		0			0
$659$	42.0499	+	12.3470i	1.63803	+	0.480970i	0.965782	−	0.259355i	$-0.0835099\pi$
$659$	42.0499	+	12.3470i	1.63803	+	0.480970i	0.672250	+	0.740324i	$0.265328\pi$
$660$		0			0
$661$	3.70631	−	3.21154i	0.144159	−	0.124914i	−0.579796	−	0.814762i	$-0.696868\pi$
$661$	3.70631	−	3.21154i	0.144159	−	0.124914i	0.723955	+	0.689847i	$0.242322\pi$
$662$		0			0
$663$	1.08027	+	15.1041i	0.0419541	+	0.586596i
$664$		0			0
$665$	−2.09513	+	1.57576i	−0.0812455	+	0.0611053i
$666$		0			0
$667$	−30.7825	+	32.5821i	−1.19190	+	1.26158i
$668$		0			0
$669$	17.6925	−	8.07989i	0.684031	−	0.312387i
$670$		0			0
$671$	−4.73675	+	5.46650i	−0.182860	+	0.211032i
$672$		0			0
$673$	−1.74162	+	24.3510i	−0.0671344	+	0.938661i	0.846569	+	0.532279i	$0.178664\pi$
$673$	−1.74162	+	24.3510i	−0.0671344	+	0.938661i	−0.913703	+	0.406382i	$0.866790\pi$
$674$		0			0
$675$	−22.7034	−	16.8367i	−0.873853	−	0.648044i
$676$		0			0
$677$	−16.3048	+	12.2056i	−0.626646	+	0.469101i	−0.864793	−	0.502128i	$-0.832551\pi$
$677$	−16.3048	+	12.2056i	−0.626646	+	0.469101i	0.238148	+	0.971229i	$0.423460\pi$
$678$		0			0
$679$	0.811345	+	0.370529i	0.0311366	+	0.0142196i
$680$		0			0
$681$	−6.16581	−	9.59419i	−0.236275	−	0.367650i
$682$		0			0
$683$	3.17237	−	4.23779i	0.121387	−	0.162155i	−0.735731	−	0.677274i	$-0.763161\pi$
$683$	3.17237	−	4.23779i	0.121387	−	0.162155i	0.857119	+	0.515119i	$0.172252\pi$
$684$		0			0
$685$	−5.69306	+	15.3692i	−0.217521	+	0.587227i
$686$		0			0
$687$	−15.7071	−	8.57672i	−0.599263	−	0.327222i
$688$		0			0
$689$	−24.5454			−0.935106
$690$		0			0
$691$	−19.3261			−0.735198			−0.367599	−	0.929984i	$-0.619820\pi$
$691$	−19.3261			−0.735198			−0.367599	+	0.929984i	$0.619820\pi$
$692$		0			0
$693$	0.156729	+	0.0855805i	0.00595364	+	0.00325094i
$694$		0			0
$695$	41.2605	−	18.9553i	1.56510	−	0.719016i
$696$		0			0
$697$	22.2789	−	29.7611i	0.843872	−	1.12728i
$698$		0			0
$699$	−0.895845	−	1.39396i	−0.0338840	−	0.0527245i
$700$		0			0
$701$	−9.11833	−	4.16420i	−0.344395	−	0.157280i	0.235706	−	0.971824i	$-0.424260\pi$
$701$	−9.11833	−	4.16420i	−0.344395	−	0.157280i	−0.580101	+	0.814545i	$0.696987\pi$
$702$		0			0
$703$	12.6852	−	9.49600i	0.478430	−	0.358148i
$704$		0			0
$705$	19.1621	+	22.0140i	0.721686	+	0.829094i
$706$		0			0
$707$	−0.401581	+	5.61483i	−0.0151030	+	0.211167i
$708$		0			0
$709$	−9.38474	+	10.8306i	−0.352451	+	0.406750i	−0.904096	−	0.427328i	$-0.859455\pi$
$709$	−9.38474	+	10.8306i	−0.352451	+	0.406750i	0.551645	+	0.834079i	$0.314000\pi$
$710$		0			0
$711$	6.98614	−	3.19046i	0.262001	−	0.119652i
$712$		0			0
$713$	−43.2805	−	8.13566i	−1.62087	−	0.304683i
$714$		0			0
$715$	−1.17682	−	1.56470i	−0.0440106	−	0.0585164i
$716$		0			0
$717$	−1.21846	−	17.0363i	−0.0455041	−	0.636231i
$718$		0			0
$719$	16.3929	−	14.2045i	0.611352	−	0.529739i	−0.293229	−	0.956042i	$-0.594730\pi$
$719$	16.3929	−	14.2045i	0.611352	−	0.529739i	0.904580	+	0.426303i	$0.140184\pi$
$720$		0			0
$721$	4.17227	+	1.22509i	0.155383	+	0.0456247i
$722$		0			0
$723$	−10.5387	−	14.0780i	−0.391938	−	0.523568i
$724$		0			0
$725$	−0.210259	−	46.7313i	−0.00780884	−	1.73556i
$726$		0			0
$727$	12.1405	+	2.64100i	0.450266	+	0.0979494i	0.431980	−	0.901883i	$-0.357815\pi$
$727$	12.1405	+	2.64100i	0.450266	+	0.0979494i	0.0182865	+	0.999833i	$0.494179\pi$
$728$		0			0
$729$	−28.1394	+	4.04583i	−1.04220	+	0.149846i
$730$		0			0
$731$	28.2506	+	18.1556i	1.04489	+	0.671508i
$732$		0			0
$733$	6.90727	−	12.6497i	0.255126	−	0.467228i	−0.718454	−	0.695574i	$-0.755150\pi$
$733$	6.90727	−	12.6497i	0.255126	−	0.467228i	0.973580	+	0.228346i	$0.0733318\pi$
$734$		0			0
$735$	20.8045	−	4.57479i	0.767386	−	0.168744i
$736$		0			0
$737$	−2.29361	+	2.29361i	−0.0844861	+	0.0844861i
$738$		0			0
$739$	−9.19622	−	31.3194i	−0.338288	−	1.15210i	−0.936471	−	0.350745i	$-0.885929\pi$
$739$	−9.19622	−	31.3194i	−0.338288	−	1.15210i	0.598183	−	0.801360i	$-0.295890\pi$
$740$		0			0
$741$	4.66459	−	7.25824i	0.171358	−	0.266638i
$742$		0			0
$743$	25.8905	+	19.3814i	0.949832	+	0.711035i	0.957348	−	0.288936i	$-0.0933016\pi$
$743$	25.8905	+	19.3814i	0.949832	+	0.711035i	−0.00751631	+	0.999972i	$0.502393\pi$
$744$		0			0
$745$	38.7811	−	0.0872439i	1.42083	−	0.00319637i
$746$		0			0
$747$	−7.85649	+	2.93032i	−0.287454	+	0.107215i
$748$		0			0
$749$	−4.29465	−	0.617478i	−0.156923	−	0.0225622i
$750$		0			0
$751$	−7.87817	+	26.8306i	−0.287479	+	0.979062i	0.681480	+	0.731837i	$0.261337\pi$
$751$	−7.87817	+	26.8306i	−0.287479	+	0.979062i	−0.968958	+	0.247225i	$0.920481\pi$
$752$		0			0
$753$	−33.6099	−	2.40382i	−1.22481	−	0.0876002i
$754$		0			0
$755$	21.6044	−	6.39645i	0.786264	−	0.232790i
$756$		0			0
$757$	8.74260	−	23.4398i	0.317755	−	0.851935i	−0.675644	−	0.737228i	$-0.736134\pi$
$757$	8.74260	−	23.4398i	0.317755	−	0.851935i	0.993399	−	0.114707i	$-0.0365929\pi$
$758$		0			0
$759$	−2.16012	−	2.35440i	−0.0784075	−	0.0854593i
$760$		0			0
$761$	14.0409	+	30.7452i	0.508981	+	1.11451i	0.973445	+	0.228921i	$0.0735198\pi$
$761$	14.0409	+	30.7452i	0.508981	+	1.11451i	−0.464464	+	0.885592i	$0.653753\pi$
$762$		0			0
$763$	2.47766	−	0.177206i	0.0896974	−	0.00641528i
$764$		0			0
$765$	11.6961	+	8.71458i	0.422872	+	0.315076i
$766$		0			0
$767$	8.40813	−	4.59119i	0.303600	−	0.165778i
$768$		0			0
$769$	3.25665	−	22.6505i	0.117438	−	0.816798i	−0.842922	−	0.538035i	$-0.819167\pi$
$769$	3.25665	−	22.6505i	0.117438	−	0.816798i	0.960360	−	0.278762i	$-0.0899242\pi$
$770$		0			0
$771$	−0.423713	+	0.927802i	−0.0152597	+	0.0334140i
$772$		0			0
$773$	−3.13807	+	14.4255i	−0.112868	+	0.518848i	0.885646	+	0.464361i	$0.153716\pi$
$773$	−3.13807	+	14.4255i	−0.112868	+	0.518848i	−0.998514	+	0.0544868i	$0.982648\pi$
$774$		0			0
$775$	38.5127	−	24.9962i	1.38342	−	0.897889i
$776$		0			0
$777$	2.13899	−	0.465309i	0.0767358	−	0.0166929i
$778$		0			0
$779$	−20.3239	+	5.96764i	−0.728180	+	0.213813i
$780$		0			0
$781$			6.61968i			0.236871i
$782$		0			0
$783$	−37.3601	−	37.3601i	−1.33514	−	1.33514i
$784$		0			0
$785$	14.8357	+	27.0248i	0.529507	+	0.964555i
$786$		0			0
$787$	0.460569	+	2.11720i	0.0164175	+	0.0754702i	0.984627	−	0.174672i	$-0.0558864\pi$
$787$	0.460569	+	2.11720i	0.0164175	+	0.0754702i	−0.968209	+	0.250142i	$0.919523\pi$
$788$		0			0
$789$	−3.60764	−	25.0917i	−0.128435	−	0.893287i
$790$		0			0
$791$	3.23064	−	2.07621i	0.114868	−	0.0738214i
$792$		0			0
$793$	−9.55123	−	25.6078i	−0.339174	−	0.909361i
$794$		0			0
$795$	27.2781	−	31.6241i	0.967454	−	1.12159i
$796$		0			0
$797$	17.0460	+	31.2174i	0.603800	+	1.10578i	0.983541	+	0.180684i	$0.0578311\pi$
$797$	17.0460	+	31.2174i	0.603800	+	1.10578i	−0.379741	+	0.925093i	$0.623987\pi$
$798$		0			0
$799$	−37.1472	−	42.8701i	−1.31417	−	1.51664i
$800$		0			0
$801$	−0.432159	−	0.374468i	−0.0152696	−	0.0132312i
$802$		0			0
$803$	1.47126	+	0.548750i	0.0519195	+	0.0193650i
$804$		0			0
$805$	−3.64537	−	0.410578i	−0.128483	−	0.0144710i
$806$		0			0
$807$	−21.0546	−	7.85296i	−0.741157	−	0.276437i
$808$		0			0
$809$	8.63341	+	7.48089i	0.303535	+	0.263014i	0.793288	−	0.608847i	$-0.208368\pi$
$809$	8.63341	+	7.48089i	0.303535	+	0.263014i	−0.489753	+	0.871861i	$0.662913\pi$
$810$		0			0
$811$	5.12440	+	5.91387i	0.179942	+	0.207664i	0.838554	−	0.544819i	$-0.183402\pi$
$811$	5.12440	+	5.91387i	0.179942	+	0.207664i	−0.658612	+	0.752483i	$0.728856\pi$
$812$		0			0
$813$	−2.01312	−	3.68675i	−0.0706031	−	0.129300i
$814$		0			0
$815$	−3.86887	+	0.285457i	−0.135521	+	0.00999911i
$816$		0			0
$817$	−6.68659	−	17.9274i	−0.233934	−	0.627202i
$818$		0			0
$819$	−0.567631	+	0.364794i	−0.0198346	+	0.0127469i
$820$		0			0
$821$	5.49638	+	38.2282i	0.191825	+	1.33417i	0.827174	+	0.561946i	$0.189947\pi$
$821$	5.49638	+	38.2282i	0.191825	+	1.33417i	−0.635349	+	0.772225i	$0.719144\pi$
$822$		0			0
$823$	−3.81542	−	17.5392i	−0.132997	−	0.611377i	−0.994599	−	0.103793i	$-0.966902\pi$
$823$	−3.81542	−	17.5392i	−0.132997	−	0.611377i	0.861602	−	0.507585i	$-0.169462\pi$
$824$		0			0
$825$	3.32378	+	0.222695i	0.115719	+	0.00775325i
$826$		0			0
$827$	−21.8354	−	21.8354i	−0.759291	−	0.759291i	0.216902	−	0.976193i	$-0.430405\pi$
$827$	−21.8354	−	21.8354i	−0.759291	−	0.759291i	−0.976193	+	0.216902i	$0.930405\pi$
$828$		0			0
$829$			37.2747i			1.29460i	0.762234	+	0.647302i	$0.224103\pi$
$829$			37.2747i			1.29460i	−0.762234	+	0.647302i	$0.775897\pi$
$830$		0			0
$831$	−20.7942	+	6.10574i	−0.721344	+	0.211806i
$832$		0			0
$833$	−40.4557	+	8.80060i	−1.40171	+	0.304923i
$834$		0			0
$835$	−7.48861	−	19.9406i	−0.259154	−	0.690074i
$836$		0			0
$837$	11.0342	−	50.7235i	0.381399	−	1.75326i
$838$		0			0
$839$	3.22273	−	7.05680i	0.111261	−	0.243628i	−0.845808	−	0.533487i	$-0.820881\pi$
$839$	3.22273	−	7.05680i	0.111261	−	0.243628i	0.957069	+	0.289859i	$0.0936085\pi$
$840$		0			0
$841$	8.30471	−	57.7605i	0.286369	−	1.99174i
$842$		0			0
$843$	−5.41939	+	2.95921i	−0.186654	+	0.101921i
$844$		0			0
$845$	−21.4435	+	3.13236i	−0.737677	+	0.107756i
$846$		0			0
$847$	3.67425	−	0.262788i	0.126249	−	0.00902949i
$848$		0			0
$849$	−1.23217	−	2.69807i	−0.0422878	−	0.0925974i
$850$		0			0
$851$	22.0284	+	2.53126i	0.755126	+	0.0867706i
$852$		0			0
$853$	−3.59897	+	9.64922i	−0.123226	+	0.330383i	−0.983886	−	0.178798i	$-0.942779\pi$
$853$	−3.59897	+	9.64922i	−0.123226	+	0.330383i	0.860659	+	0.509181i	$0.170052\pi$
$854$		0			0
$855$	−2.35927	−	7.96858i	−0.0806854	−	0.272520i
$856$		0			0
$857$	−34.4775	−	2.46588i	−1.17773	−	0.0842329i	−0.531284	−	0.847193i	$-0.678290\pi$
$857$	−34.4775	−	2.46588i	−1.17773	−	0.0842329i	−0.646445	+	0.762961i	$0.723745\pi$
$858$		0			0
$859$	5.50305	−	18.7417i	0.187762	−	0.639458i	−0.810774	−	0.585360i	$-0.800953\pi$
$859$	5.50305	−	18.7417i	0.187762	−	0.639458i	0.998536	−	0.0540983i	$-0.0172284\pi$
$860$		0			0
$861$	−2.89640	−	0.416440i	−0.0987091	−	0.0141922i
$862$		0			0
$863$	−0.968710	+	0.361310i	−0.0329753	+	0.0122991i	−0.365898	−	0.930655i	$-0.619238\pi$
$863$	−0.968710	+	0.361310i	−0.0329753	+	0.0122991i	0.332922	+	0.942954i	$0.391965\pi$
$864$		0			0
$865$	0.131635	+	0.131044i	0.00447571	+	0.00445562i
$866$		0			0
$867$	21.2528	+	15.9096i	0.721783	+	0.540320i
$868$		0			0
$869$	−1.84318	+	2.86804i	−0.0625255	+	0.0972916i
$870$		0			0
$871$	−3.45300	−	11.7598i	−0.117000	−	0.398467i
$872$		0			0
$873$	−1.99937	+	1.99937i	−0.0676683	+	0.0676683i
$874$		0			0
$875$	3.04621	−	2.31261i	0.102981	−	0.0781803i
$876$		0			0
$877$	15.6553	−	28.6705i	0.528641	−	0.968134i	−0.467799	−	0.883835i	$-0.654953\pi$
$877$	15.6553	−	28.6705i	0.528641	−	0.968134i	0.996440	−	0.0842994i	$-0.0268652\pi$
$878$		0			0
$879$	−15.8690	−	10.1984i	−0.535247	−	0.343982i
$880$		0			0
$881$	16.4824	−	2.36981i	0.555306	−	0.0798410i	0.141052	−	0.990002i	$-0.454952\pi$
$881$	16.4824	−	2.36981i	0.555306	−	0.0798410i	0.414254	+	0.910161i	$0.364042\pi$
$882$		0			0
$883$	25.8688	+	5.62741i	0.870554	+	0.189377i	0.625587	−	0.780154i	$-0.284859\pi$
$883$	25.8688	+	5.62741i	0.870554	+	0.189377i	0.244967	+	0.969532i	$0.421223\pi$
$884$		0			0
$885$	−3.42898	+	15.9353i	−0.115264	+	0.535659i
$886$		0			0
$887$	1.42395	+	1.90218i	0.0478116	+	0.0638688i	0.823810	−	0.566866i	$-0.191844\pi$
$887$	1.42395	+	1.90218i	0.0478116	+	0.0638688i	−0.775998	+	0.630735i	$0.782753\pi$
$888$		0			0
$889$	−3.56653	−	1.04723i	−0.119618	−	0.0351229i
$890$		0			0
$891$	1.66284	−	1.44086i	0.0557074	−	0.0482707i
$892$		0			0
$893$	2.30572	+	32.2381i	0.0771579	+	1.07881i
$894$		0			0
$895$	16.6965	+	2.36227i	0.558104	+	0.0789621i
$896$		0			0
$897$	11.7197	−	2.90023i	0.391310	−	0.0968359i
$898$		0			0
$899$	78.0688	−	35.6528i	2.60374	−	1.18909i
$900$		0			0
$901$	−53.1560	+	61.3453i	−1.77088	+	2.04371i
$902$		0			0
$903$	0.188567	−	2.63651i	0.00627513	−	0.0877377i
$904$		0			0
$905$	−0.933207	+	0.812312i	−0.0310209	+	0.0270022i
$906$		0			0
$907$	11.1744	−	8.36505i	0.371040	−	0.277757i	−0.397444	−	0.917627i	$-0.630103\pi$
$907$	11.1744	−	8.36505i	0.371040	−	0.277757i	0.768483	+	0.639870i	$0.221012\pi$
$908$		0			0
$909$	−16.2322	−	7.41301i	−0.538389	−	0.245874i
$910$		0			0
$911$	−4.12898	−	6.42481i	−0.136799	−	0.212864i	0.766094	−	0.642728i	$-0.222198\pi$
$911$	−4.12898	−	6.42481i	−0.136799	−	0.212864i	−0.902893	+	0.429865i	$0.858561\pi$
$912$		0			0
$913$	2.23063	−	2.97977i	0.0738230	−	0.0986159i
$914$		0			0
$915$	43.6075	+	16.1531i	1.44162	+	0.534005i
$916$		0			0
$917$	1.54158	+	0.841766i	0.0509074	+	0.0277976i
$918$		0			0
$919$	19.5874			0.646130			0.323065	−	0.946377i	$-0.395287\pi$
$919$	19.5874			0.646130			0.323065	+	0.946377i	$0.395287\pi$
$920$		0			0
$921$	45.2129			1.48981
$922$		0			0
$923$	−21.9532	−	11.9874i	−0.722599	−	0.394569i
$924$		0			0
$925$	−18.4439	+	13.9368i	−0.606431	+	0.458241i
$926$		0			0
$927$	−8.26088	+	11.0352i	−0.271323	+	0.362445i
$928$		0			0
$929$	−17.0422	−	26.5181i	−0.559135	−	0.870031i	0.440480	−	0.897762i	$-0.354808\pi$
$929$	−17.0422	−	26.5181i	−0.559135	−	0.870031i	−0.999615	+	0.0277309i	$0.991172\pi$
$930$		0			0
$931$	21.4579	+	9.79947i	0.703253	+	0.321165i
$932$		0			0
$933$	−38.1983	+	28.5949i	−1.25056	+	0.936154i
$934$		0			0
$935$	−6.45913	−	0.447363i	−0.211236	−	0.0146303i
$936$		0			0
$937$	−1.28410	+	17.9541i	−0.0419498	+	0.586535i	0.932390	+	0.361453i	$0.117719\pi$
$937$	−1.28410	+	17.9541i	−0.0419498	+	0.586535i	−0.974340	+	0.225081i	$0.927735\pi$
$938$		0			0
$939$	1.71244	−	1.97626i	0.0558833	−	0.0644928i
$940$		0			0
$941$	45.7808	−	20.9074i	1.49241	−	0.681562i	0.508639	−	0.860980i	$-0.330149\pi$
$941$	45.7808	−	20.9074i	1.49241	−	0.681562i	0.983773	+	0.179418i	$0.0574214\pi$
$942$		0			0
$943$	−26.4076	−	13.4609i	−0.859951	−	0.438348i
$944$		0			0
$945$	0.605754	−	4.28146i	0.0197052	−	0.139276i
$946$		0			0
$947$	−3.01599	−	42.1691i	−0.0980065	−	1.37031i	−0.773898	−	0.633310i	$-0.781696\pi$
$947$	−3.01599	−	42.1691i	−0.0980065	−	1.37031i	0.675892	−	0.737001i	$-0.263759\pi$
$948$		0			0
$949$	−4.48410	+	3.88549i	−0.145560	+	0.126128i
$950$		0			0
$951$	−40.2967	−	11.8322i	−1.30671	−	0.383685i
$952$		0			0
$953$	−5.45650	−	7.28903i	−0.176753	−	0.236115i	0.703412	−	0.710783i	$-0.251659\pi$
$953$	−5.45650	−	7.28903i	−0.176753	−	0.236115i	−0.880165	+	0.474668i	$0.842568\pi$
$954$		0			0
$955$	−8.44577	−	13.0771i	−0.273299	−	0.423165i
$956$		0			0
$957$	6.08467	+	1.32364i	0.196690	+	0.0427872i
$958$		0			0
$959$	−2.48184	+	0.356835i	−0.0801428	+	0.0115228i
$960$		0			0
$961$	44.8569	+	28.8278i	1.44700	+	0.929928i
$962$		0			0
$963$	6.59174	−	12.0719i	0.212416	−	0.389011i
$964$		0			0
$965$	−6.72380	−	30.5775i	−0.216447	−	0.984324i
$966$		0			0
$967$	38.9774	−	38.9774i	1.25343	−	1.25343i	0.299254	−	0.954174i	$-0.403262\pi$
$967$	38.9774	−	38.9774i	1.25343	−	1.25343i	0.954174	−	0.299254i	$-0.0967376\pi$
$968$		0			0
$969$	−8.03849	−	27.3766i	−0.258233	−	0.879462i
$970$		0			0
$971$	−26.1330	+	40.6638i	−0.838649	+	1.30496i	0.111689	+	0.993743i	$0.464374\pi$
$971$	−26.1330	+	40.6638i	−0.838649	+	1.30496i	−0.950338	+	0.311219i	$0.899263\pi$
$972$		0			0
$973$	5.56090	+	4.16284i	0.178274	+	0.133454i
$974$		0			0
$975$	−6.75746	+	10.6196i	−0.216412	+	0.340098i
$976$		0			0
$977$	−8.30510	+	3.09764i	−0.265704	+	0.0991023i	−0.478785	−	0.877932i	$-0.658923\pi$
$977$	−8.30510	+	3.09764i	−0.265704	+	0.0991023i	0.213082	+	0.977034i	$0.431650\pi$
$978$		0			0
$979$	0.251252	+	0.0361245i	0.00803004	+	0.00115455i
$980$		0			0
$981$	−2.21848	+	7.55544i	−0.0708305	+	0.241227i
$982$		0			0
$983$	39.1545	+	2.80039i	1.24883	+	0.0893184i	0.680049	−	0.733167i	$-0.261959\pi$
$983$	39.1545	+	2.80039i	1.24883	+	0.0893184i	0.568786	+	0.822486i	$0.307413\pi$
$984$		0			0
$985$	9.40461	−	17.3158i	0.299656	−	0.551726i
$986$		0			0
$987$	−1.56033	+	4.18341i	−0.0496659	+	0.133159i
$988$		0			0
$989$	10.4266	−	24.6609i	0.331548	−	0.784171i
$990$		0			0
$991$	16.1771	+	35.4229i	0.513883	+	1.12525i	0.971704	+	0.236202i	$0.0759028\pi$
$991$	16.1771	+	35.4229i	0.513883	+	1.12525i	−0.457821	+	0.889044i	$0.651370\pi$
$992$		0			0
$993$	18.1888	−	1.30089i	0.577203	−	0.0412824i
$994$		0			0
$995$	−5.61074	−	38.4099i	−0.177872	−	1.21768i
$996$		0			0
$997$	29.1410	−	15.9122i	0.922905	−	0.503944i	0.0537891	−	0.998552i	$-0.482870\pi$
$997$	29.1410	−	15.9122i	0.922905	−	0.503944i	0.869116	+	0.494608i	$0.164688\pi$
$998$		0			0
$999$	−3.71963	+	25.8706i	−0.117684	+	0.818508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.433.12	yes	720
5.2	odd	4	inner	920.2.bv.a.617.12	yes	720
23.17	odd	22	inner	920.2.bv.a.753.12	yes	720
115.17	even	44	inner	920.2.bv.a.17.12	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.12	✓	720	115.17	even	44	inner
920.2.bv.a.433.12	yes	720	1.1	even	1	trivial
920.2.bv.a.617.12	yes	720	5.2	odd	4	inner
920.2.bv.a.753.12	yes	720	23.17	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21475 - 0.663302i) q^{3} +(0.933470 + 2.03190i) q^{5} +(-0.205002 + 0.273851i) q^{7} +(-0.586283 - 0.912274i) q^{9} +(0.437876 + 0.199971i) q^{11} +(-1.45611 + 1.09003i) q^{13} +(0.213837 - 3.08742i) q^{15} +(-0.429113 + 5.99978i) q^{17} +(2.24436 - 2.59013i) q^{19} +(0.430671 - 0.196681i) q^{21} +(4.77197 - 0.477794i) q^{23} +(-3.25727 + 3.79344i) q^{25} +(0.403282 + 5.63862i) q^{27} +(-7.06351 + 6.12056i) q^{29} +(-8.81071 - 2.58706i) q^{31} +(-0.399267 - 0.533358i) q^{33} +(-0.747802 - 0.160913i) q^{35} +(4.51781 + 0.982790i) q^{37} +(2.49182 - 0.358270i) q^{39} +(-5.19934 - 3.34142i) q^{41} +(2.67559 - 4.89997i) q^{43} +(1.30638 - 2.04285i) q^{45} +(-6.66836 + 6.66836i) q^{47} +(1.93916 + 6.60417i) q^{49} +(4.50093 - 7.00358i) q^{51} +(10.8030 + 8.08702i) q^{53} +(0.00242150 + 1.07639i) q^{55} +(-4.44437 + 1.65766i) q^{57} +(-5.21327 - 0.749555i) q^{59} +(-4.23334 + 14.4174i) q^{61} +(0.370016 + 0.0264641i) q^{63} +(-3.57407 - 1.94117i) q^{65} +(-2.35479 + 6.31343i) q^{67} +(-6.11366 - 2.58486i) q^{69} +(5.71261 + 12.5089i) q^{71} +(3.25371 - 0.232710i) q^{73} +(6.47295 - 2.44752i) q^{75} +(-0.144528 + 0.0789181i) q^{77} +(-1.00791 + 7.01019i) q^{79} +(1.89876 - 4.15771i) q^{81} +(1.64364 - 7.55568i) q^{83} +(-12.5915 + 4.72870i) q^{85} +(12.6402 - 2.74970i) q^{87} +(0.505952 - 0.148561i) q^{89} -0.622215i q^{91} +(8.98678 + 8.98678i) q^{93} +(7.35795 + 2.14252i) q^{95} +(-0.554245 - 2.54782i) q^{97} +(-0.0742905 - 0.516702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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