LMFDB - Embedded newform 920.2.bv.a.17.12

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			17.12
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.12

$q$-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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	−0.790002	−	0.613104i	$-0.789921\pi$
$3$	−1.21475	+	0.663302i	−0.701334	+	0.382957i	0.0886682	+	0.996061i	$0.471739\pi$
$4$		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	0.760125	−	0.649777i	$-0.225138\pi$
$7$	−0.205002	−	0.273851i	−0.0774835	−	0.103506i	−0.837608	+	0.546271i	$0.816047\pi$
$8$		0			0
$9$	−0.586283	+	0.912274i	−0.195428	+	0.304091i
$10$		0			0
$11$	0.437876	−	0.199971i	0.132024	−	0.0602935i	−0.348307	−	0.937380i	$-0.613243\pi$
$11$	0.437876	−	0.199971i	0.132024	−	0.0602935i	0.480332	+	0.877087i	$0.340516\pi$
$12$		0			0
$13$	−1.45611	−	1.09003i	−0.403852	−	0.302320i	0.377974	−	0.925816i	$-0.376621\pi$
$13$	−1.45611	−	1.09003i	−0.403852	−	0.302320i	−0.781826	+	0.623496i	$0.785712\pi$
$14$		0			0
$15$	0.213837	+	3.08742i	0.0552124	+	0.797169i
$16$		0			0
$17$	−0.429113	−	5.99978i	−0.104075	−	1.45516i	−0.734341	−	0.678781i	$-0.762509\pi$
$17$	−0.429113	−	5.99978i	−0.104075	−	1.45516i	0.630266	−	0.776379i	$-0.282946\pi$
$18$		0			0
$19$	2.24436	+	2.59013i	0.514892	+	0.594217i	0.952345	−	0.305024i	$-0.0986646\pi$
$19$	2.24436	+	2.59013i	0.514892	+	0.594217i	−0.437452	+	0.899242i	$0.644119\pi$
$20$		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	−0.981253	−	0.192722i	$-0.938268\pi$
$29$	−7.06351	−	6.12056i	−1.31166	−	1.13656i	−0.330407	−	0.943838i	$-0.607186\pi$
$30$		0			0
$31$	−8.81071	+	2.58706i	−1.58245	+	0.464649i	−0.950594	−	0.310436i	$-0.899525\pi$
$31$	−8.81071	+	2.58706i	−1.58245	+	0.464649i	−0.631856	+	0.775086i	$0.717707\pi$
$32$		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	0.174746	−	0.984614i	$-0.444090\pi$
$37$	4.51781	−	0.982790i	0.742724	−	0.161570i	0.567978	+	0.823044i	$0.307726\pi$
$38$		0			0
$39$	2.49182	+	0.358270i	0.399011	+	0.0573691i
$40$		0			0
$41$	−5.19934	+	3.34142i	−0.812001	+	0.521841i	−0.879512	−	0.475877i	$-0.842131\pi$
$41$	−5.19934	+	3.34142i	−0.812001	+	0.521841i	0.0675106	+	0.997719i	$0.478494\pi$
$42$		0			0
$43$	2.67559	+	4.89997i	0.408023	+	0.747239i	0.998196	−	0.0600382i	$-0.0191223\pi$
$43$	2.67559	+	4.89997i	0.408023	+	0.747239i	−0.590173	+	0.807277i	$0.700940\pi$
$44$		0			0
$45$	1.30638	+	2.04285i	0.194743	+	0.304530i
$46$		0			0
$47$	−6.66836	−	6.66836i	−0.972680	−	0.972680i	0.0269569	−	0.999637i	$-0.491418\pi$
$47$	−6.66836	−	6.66836i	−0.972680	−	0.972680i	−0.999637	+	0.0269569i	$0.991418\pi$
$48$		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	0.516911	−	0.856039i	$-0.327082\pi$
$53$	10.8030	−	8.08702i	1.48390	−	1.11084i	0.966994	−	0.254798i	$-0.0820089\pi$
$54$		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	−0.473045	−	0.881039i	$-0.656845\pi$
$59$	−5.21327	+	0.749555i	−0.678710	+	0.0975838i	−0.205666	+	0.978622i	$0.565936\pi$
$60$		0			0
$61$	−4.23334	−	14.4174i	−0.542024	−	1.84596i	−0.533177	−	0.846004i	$-0.679002\pi$
$61$	−4.23334	−	14.4174i	−0.542024	−	1.84596i	−0.00884702	−	0.999961i	$-0.502816\pi$
$62$		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	−0.997742	−	0.0671659i	$-0.978604\pi$
$67$	−2.35479	−	6.31343i	−0.287683	−	0.771308i	0.710059	−	0.704143i	$-0.248668\pi$
$68$		0			0
$69$	−6.11366	+	2.58486i	−0.735998	+	0.311180i
$70$		0			0
$71$	5.71261	−	12.5089i	0.677962	−	1.48453i	−0.186827	−	0.982393i	$-0.559820\pi$
$71$	5.71261	−	12.5089i	0.677962	−	1.48453i	0.864789	−	0.502136i	$-0.167452\pi$
$72$		0			0
$73$	3.25371	+	0.232710i	0.380818	+	0.0272367i	0.260436	−	0.965491i	$-0.416134\pi$
$73$	3.25371	+	0.232710i	0.380818	+	0.0272367i	0.120382	+	0.992728i	$0.461588\pi$
$74$		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	−0.964571	−	0.263822i	$-0.915017\pi$
$79$	−1.00791	−	7.01019i	−0.113399	−	0.788708i	0.851172	−	0.524886i	$-0.175892\pi$
$80$		0			0
$81$	1.89876	+	4.15771i	0.210974	+	0.461968i
$82$		0			0
$83$	1.64364	+	7.55568i	0.180413	+	0.829344i	0.975002	+	0.222196i	$0.0713226\pi$
$83$	1.64364	+	7.55568i	0.180413	+	0.829344i	−0.794589	+	0.607147i	$0.792314\pi$
$84$		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	0.308438	−	0.951244i	$-0.400194\pi$
$89$	0.505952	+	0.148561i	0.0536308	+	0.0157474i	−0.254807	+	0.966992i	$0.582012\pi$
$90$		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	−0.996686	−	0.0813487i	$-0.974077\pi$
$97$	−0.554245	+	2.54782i	−0.0562750	+	0.258692i	0.940411	+	0.340041i	$0.110441\pi$
$98$		0			0
$99$	−0.0742905	+	0.516702i	−0.00746648	+	0.0519305i
$100$		0			0
$101$	13.8433	+	8.89658i	1.37746	+	0.885243i	0.999182	−	0.0404471i	$-0.0128782\pi$
$101$	13.8433	+	8.89658i	1.37746	+	0.885243i	0.378283	+	0.925690i	$0.376515\pi$
$102$		0			0
$103$	−4.44225	+	11.9101i	−0.437708	+	1.17354i	0.511609	+	0.859218i	$0.329050\pi$
$103$	−4.44225	+	11.9101i	−0.437708	+	1.17354i	−0.949317	+	0.314321i	$0.898223\pi$
$104$		0			0
$105$	0.801656	−	0.691487i	0.0782336	−	0.0674822i
$106$		0			0
$107$	6.07858	−	11.1321i	0.587638	−	1.07618i	−0.399564	−	0.916705i	$-0.630838\pi$
$107$	6.07858	−	11.1321i	0.587638	−	1.07618i	0.987202	−	0.159474i	$-0.0509798\pi$
$108$		0			0
$109$	−4.75520	+	5.48779i	−0.455465	+	0.525635i	−0.936312	−	0.351170i	$-0.885784\pi$
$109$	−4.75520	+	5.48779i	−0.455465	+	0.525635i	0.480847	+	0.876805i	$0.340329\pi$
$110$		0			0
$111$	−4.83611	+	4.19051i	−0.459023	+	0.397746i
$112$		0			0
$113$	−10.5184	+	3.92314i	−0.989483	+	0.369058i	−0.791515	−	0.611150i	$-0.790707\pi$
$113$	−10.5184	+	3.92314i	−0.989483	+	0.369058i	−0.197969	+	0.980208i	$0.563434\pi$
$114$		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	−0.652396	−	0.757879i	$-0.726236\pi$
$127$	3.79731	−	10.1810i	0.336957	−	0.903417i	0.989353	−	0.145538i	$-0.0464914\pi$
$128$		0			0
$129$	−6.50032	−	4.17750i	−0.572321	−	0.367808i
$130$		0			0
$131$	−0.730718	+	5.08226i	−0.0638432	+	0.444039i	0.932679	+	0.360708i	$0.117465\pi$
$131$	−0.730718	+	5.08226i	−0.0638432	+	0.444039i	−0.996522	+	0.0833309i	$0.973444\pi$
$132$		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	−0.450149	−	0.892953i	$-0.648629\pi$
$137$	5.18289	−	5.18289i	0.442804	−	0.442804i	0.892953	+	0.450149i	$0.148629\pi$
$138$		0			0
$139$			20.3063i			1.72236i	0.508302	+	0.861179i	$0.330273\pi$
$139$			20.3063i			1.72236i	−0.508302	+	0.861179i	$0.669727\pi$
$140$		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	0.935300	+	0.353856i	$0.115130\pi$
$149$	7.20474	+	15.7762i	0.590235	+	1.29243i	−0.345065	+	0.938579i	$0.612143\pi$
$150$		0			0
$151$	1.43401	+	9.97378i	0.116698	+	0.811655i	0.961151	+	0.276024i	$0.0890170\pi$
$151$	1.43401	+	9.97378i	0.116698	+	0.811655i	−0.844452	+	0.535631i	$0.820074\pi$
$152$		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	0.608339	−	0.793677i	$-0.291836\pi$
$157$	13.7521	+	0.983567i	1.09753	+	0.0784972i	0.489195	+	0.872174i	$0.337291\pi$
$158$		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	0.911040	−	0.412317i	$-0.135280\pi$
$163$	−0.606290	−	1.62553i	−0.0474883	−	0.127321i	−0.958529	+	0.284996i	$0.908008\pi$
$164$		0			0
$165$	0.711029	+	1.30914i	0.0553535	+	0.101917i
$166$		0			0
$167$	−9.50157	+	0.679565i	−0.735253	+	0.0525863i	−0.433944	−	0.900940i	$-0.642878\pi$
$167$	−9.50157	+	0.679565i	−0.735253	+	0.0525863i	−0.301310	+	0.953526i	$0.597424\pi$
$168$		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	0.352421	−	0.935842i	$-0.385359\pi$
$173$	0.0778291	+	0.0290287i	0.00591723	+	0.00220701i	−0.346504	+	0.938049i	$0.612631\pi$
$174$		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	0.959522	−	0.281634i	$-0.0908764\pi$
$179$	4.07713	+	6.34413i	0.304739	+	0.474183i	−0.654783	+	0.755817i	$0.727240\pi$
$180$		0			0
$181$	0.155884	−	0.530891i	0.0115867	−	0.0394608i	−0.953497	−	0.301403i	$-0.902545\pi$
$181$	0.155884	−	0.530891i	0.0115867	−	0.0394608i	0.965083	+	0.261943i	$0.0843631\pi$
$182$		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	−0.111583	−	0.993755i	$-0.535592\pi$
$191$	−6.89106	−	0.990785i	−0.498619	−	0.0716907i	−0.387036	+	0.922064i	$0.626501\pi$
$192$		0			0
$193$	−13.6814	+	2.97621i	−0.984808	+	0.214232i	−0.676007	−	0.736895i	$-0.736291\pi$
$193$	−13.6814	+	2.97621i	−0.984808	+	0.214232i	−0.308801	+	0.951127i	$0.599928\pi$
$194$		0			0
$195$	3.05401	−	4.72871i	0.218702	−	0.338630i
$196$		0			0
$197$	−5.28101	+	7.05460i	−0.376256	+	0.502619i	−0.948200	−	0.317673i	$-0.897099\pi$
$197$	−5.28101	+	7.05460i	−0.376256	+	0.502619i	0.571944	+	0.820293i	$0.306189\pi$
$198$		0			0
$199$	−16.6566	+	4.89080i	−1.18075	+	0.346700i	−0.812464	−	0.583012i	$-0.801874\pi$
$199$	−16.6566	+	4.89080i	−1.18075	+	0.346700i	−0.368288	+	0.929712i	$0.620056\pi$
$200$		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	0.594727	−	0.803927i	$-0.297260\pi$
$211$	−4.14939	−	4.78865i	−0.285656	−	0.329664i	−0.880383	+	0.474263i	$0.842715\pi$
$212$		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	0.424403	−	0.905474i	$-0.360484\pi$
$223$	−8.42173	−	11.2501i	−0.563961	−	0.753364i	−0.988364	+	0.152110i	$0.951393\pi$
$224$		0			0
$225$	5.37034	−	0.747492i	0.358023	−	0.0498328i
$226$		0			0
$227$	7.23215	−	3.94905i	0.480015	−	0.262108i	−0.220975	−	0.975280i	$-0.570924\pi$
$227$	7.23215	−	3.94905i	0.480015	−	0.262108i	0.700989	+	0.713172i	$0.252742\pi$
$228$		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	−0.444461	−	0.895798i	$-0.646605\pi$
$233$	1.05078	−	0.573767i	0.0688386	−	0.0375887i	0.513300	+	0.858209i	$0.328423\pi$
$234$		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	−0.555564	−	0.831474i	$-0.687497\pi$
$239$	6.67177	−	10.3815i	0.431561	−	0.671522i	0.987125	+	0.159952i	$0.0511338\pi$
$240$		0			0
$241$	11.5578	−	5.27826i	0.744502	−	0.340003i	−0.00678624	−	0.999977i	$-0.502160\pi$
$241$	11.5578	−	5.27826i	0.744502	−	0.340003i	0.751288	+	0.659974i	$0.229433\pi$
$242$		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	0.964793	−	0.263011i	$-0.0847155\pi$
$251$	22.1458	+	10.1136i	1.39783	+	0.638366i	0.433035	+	0.901377i	$0.357443\pi$
$252$		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	−0.998828	−	0.0483940i	$-0.984590\pi$
$257$	−0.0525736	+	0.735075i	−0.00327945	+	0.0458527i	0.995549	+	0.0942467i	$0.0300442\pi$
$258$		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	−0.322276	−	0.946646i	$-0.604448\pi$
$263$	10.9762	−	14.6624i	0.676820	−	0.904125i	0.999096	+	0.0425205i	$0.0135388\pi$
$264$		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	0.613586	−	0.789628i	$-0.289726\pi$
$269$	16.0708	+	2.31063i	0.979855	+	0.140882i	0.366268	+	0.930509i	$0.380635\pi$
$270$		0			0
$271$	2.55320	−	1.64084i	0.155096	−	0.0996740i	−0.460791	−	0.887509i	$-0.652434\pi$
$271$	2.55320	−	1.64084i	0.155096	−	0.0996740i	0.615887	+	0.787835i	$0.288798\pi$
$272$		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	0.956617	−	0.291349i	$-0.0941041\pi$
$277$	11.0723	+	11.0723i	0.665268	+	0.665268i	−0.291349	+	0.956617i	$0.594104\pi$
$278$		0			0
$279$	2.80546	−	9.55453i	0.167959	−	0.572015i
$280$		0			0
$281$	2.41198	+	3.75311i	0.143887	+	0.223892i	0.905715	−	0.423887i	$-0.139335\pi$
$281$	2.41198	+	3.75311i	0.143887	+	0.223892i	−0.761829	+	0.647779i	$0.775698\pi$
$282$		0			0
$283$	1.71562	−	1.28430i	0.101983	−	0.0763435i	−0.547069	−	0.837087i	$-0.684257\pi$
$283$	1.71562	−	1.28430i	0.101983	−	0.0763435i	0.649052	+	0.760744i	$0.275166\pi$
$284$		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	0.331658	−	0.943400i	$-0.392392\pi$
$293$	13.5945	−	0.972299i	0.794200	−	0.0568023i	0.462542	+	0.886597i	$0.346937\pi$
$294$		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	−0.991631	−	0.129108i	$-0.958789\pi$
$307$	−28.6713	−	15.6557i	−1.63636	−	0.893519i	−0.644728	−	0.764412i	$-0.723029\pi$
$308$		0			0
$309$	−2.50380	−	17.4143i	−0.142436	−	0.990667i
$310$		0			0
$311$	14.3216	+	31.3600i	0.812105	+	1.77826i	0.598085	+	0.801433i	$0.295929\pi$
$311$	14.3216	+	31.3600i	0.812105	+	1.77826i	0.214020	+	0.976829i	$0.431344\pi$
$312$		0			0
$313$	−0.401614	−	1.84619i	−0.0227005	−	0.104353i	0.964403	−	0.264438i	$-0.0851866\pi$
$313$	−0.401614	−	1.84619i	−0.0227005	−	0.104353i	−0.987103	+	0.160086i	$0.948823\pi$
$314$		0			0
$315$	0.291626	−	0.776541i	0.0164313	−	0.0437531i
$316$		0			0
$317$	29.6509	+	6.45016i	1.66536	+	0.362277i	0.943913	−	0.330193i	$-0.107114\pi$
$317$	29.6509	+	6.45016i	1.66536	+	0.362277i	0.721446	+	0.692470i	$0.243478\pi$
$318$		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	0.199344	−	0.979930i	$-0.436119\pi$
$331$	−11.0838	−	7.12312i	−0.609220	−	0.391522i	−0.808565	+	0.588407i	$0.799755\pi$
$332$		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	−0.158602	−	0.987343i	$-0.550699\pi$
$337$	13.9104	−	25.4751i	0.757750	−	1.38772i	0.916352	−	0.400373i	$-0.131119\pi$
$338$		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	0.272258	−	0.962224i	$-0.412229\pi$
$347$	20.6424	−	7.69921i	1.10814	−	0.413315i	0.835882	+	0.548909i	$0.184957\pi$
$348$		0			0
$349$	9.46026	−	8.19736i	0.506396	−	0.438795i	−0.363817	−	0.931470i	$-0.618527\pi$
$349$	9.46026	−	8.19736i	0.506396	−	0.438795i	0.870213	+	0.492676i	$0.163981\pi$
$350$		0			0
$351$	−6.73348	+	7.77085i	−0.359407	+	0.414778i
$352$		0			0
$353$	−14.6828	+	26.8895i	−0.781485	+	1.43118i	0.117439	+	0.993080i	$0.462532\pi$
$353$	−14.6828	+	26.8895i	−0.781485	+	1.43118i	−0.898924	+	0.438104i	$0.855650\pi$
$354$		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	0.998968	+	0.0454098i	$0.0144593\pi$
$359$	27.5733	+	17.7203i	1.45526	+	0.935240i	0.456293	+	0.889830i	$0.349177\pi$
$360$		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	−0.994270	−	0.106897i	$-0.965909\pi$
$367$	−16.9996	+	16.9996i	−0.887373	+	0.887373i	0.106897	+	0.994270i	$0.465909\pi$
$368$		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	0.308454	−	0.951239i	$-0.400188\pi$
$373$	3.74434	+	0.814532i	0.193875	+	0.0421749i	−0.114579	+	0.993414i	$0.536552\pi$
$374$		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	0.974763	−	0.223243i	$-0.0716643\pi$
$379$	3.26503	+	7.14942i	0.167713	+	0.367241i	−0.807050	+	0.590484i	$0.798937\pi$
$380$		0			0
$381$	2.14030	+	14.8861i	0.109651	+	0.762637i
$382$		0			0
$383$	−20.1566	−	11.0063i	−1.02995	−	0.562398i	−0.126896	−	0.991916i	$-0.540501\pi$
$383$	−20.1566	−	11.0063i	−1.02995	−	0.562398i	−0.903058	+	0.429519i	$0.858683\pi$
$384$		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	−0.472671	−	0.881239i	$-0.656710\pi$
$389$	9.91792	−	21.7172i	0.502859	−	1.10111i	0.975530	−	0.219868i	$-0.0705626\pi$
$390$		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	−0.797348	−	0.603519i	$-0.793765\pi$
$397$	−29.9011	+	2.13857i	−1.50069	+	0.107332i	−0.703343	+	0.710851i	$0.748310\pi$
$398$		0			0
$399$	0.457153	+	1.55692i	0.0228863	+	0.0779435i
$400$		0			0
$401$	−18.2622	+	2.62571i	−0.911971	+	0.131122i	−0.582300	−	0.812974i	$-0.697847\pi$
$401$	−18.2622	+	2.62571i	−0.911971	+	0.131122i	−0.329671	+	0.944096i	$0.606938\pi$
$402$		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	0.913717	−	0.406352i	$-0.133199\pi$
$409$	3.32710	+	5.17708i	0.164515	+	0.255990i	−0.749202	+	0.662341i	$0.769563\pi$
$410$		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	−0.875281	−	0.483615i	$-0.839323\pi$
$419$	−16.3546	+	10.5104i	−0.798973	+	0.513469i	0.0763072	+	0.997084i	$0.475687\pi$
$420$		0			0
$421$	22.8972	+	3.29212i	1.11594	+	0.160448i	0.675520	−	0.737342i	$-0.263919\pi$
$421$	22.8972	+	3.29212i	1.11594	+	0.160448i	0.440423	+	0.897790i	$0.354829\pi$
$422$		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	0.518141	−	0.855295i	$-0.326624\pi$
$431$	−5.28791	−	4.58200i	−0.254710	−	0.220707i	−0.772851	+	0.634588i	$0.781170\pi$
$432$		0			0
$433$	−0.355679	+	4.97304i	−0.0170928	+	0.238989i	0.981722	+	0.190320i	$0.0609525\pi$
$433$	−0.355679	+	4.97304i	−0.0170928	+	0.238989i	−0.998815	+	0.0486692i	$0.984502\pi$
$434$		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	0.356666	−	0.934232i	$-0.383913\pi$
$439$	−2.42656	−	1.10817i	−0.115813	−	0.0528901i	−0.472479	+	0.881342i	$0.656641\pi$
$440$		0			0
$441$	4.88792	+	5.64096i	0.232758	+	0.268617i
$442$		0			0
$443$	1.09727	+	15.3419i	0.0521331	+	0.728916i	0.954550	+	0.298052i	$0.0963368\pi$
$443$	1.09727	+	15.3419i	0.0521331	+	0.728916i	−0.902417	+	0.430864i	$0.858209\pi$
$444$		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	−0.119249	−	0.992864i	$-0.538049\pi$
$449$	11.7182	−	5.35152i	0.553016	−	0.252554i	0.672265	+	0.740311i	$0.265322\pi$
$450$		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	−0.625000	−	0.780624i	$-0.714901\pi$
$457$	−6.54577	+	3.57426i	−0.306198	+	0.167197i	0.318802	+	0.947821i	$0.396719\pi$
$458$		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	−0.0789291	−	0.996880i	$-0.525150\pi$
$463$	15.4286	−	8.42465i	0.717028	−	0.391527i	0.795957	+	0.605354i	$0.206968\pi$
$464$		0			0
$465$	−9.87139	−	26.6492i	−0.457775	−	1.23583i
$466$		0			0
$467$	−23.4916	−	31.3812i	−1.08706	−	1.45215i	−0.880702	−	0.473671i	$-0.842929\pi$
$467$	−23.4916	−	31.3812i	−1.08706	−	1.45215i	−0.206362	−	0.978476i	$-0.566162\pi$
$468$		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	0.810143	−	0.586232i	$-0.199389\pi$
$479$	2.50775	+	2.89410i	0.114582	+	0.132235i	−0.695561	+	0.718467i	$0.744844\pi$
$480$		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	−0.437006	−	0.899458i	$-0.643961\pi$
$487$	2.72669	−	38.1241i	0.123558	−	1.72757i	0.560564	−	0.828111i	$-0.310584\pi$
$488$		0			0
$489$	1.81470	+	1.57245i	0.0820638	+	0.0711087i
$490$		0			0
$491$	−14.5271	+	4.26553i	−0.655598	+	0.192501i	−0.592580	−	0.805512i	$-0.701891\pi$
$491$	−14.5271	+	4.26553i	−0.655598	+	0.192501i	−0.0630177	+	0.998012i	$0.520072\pi$
$492$		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	−0.347293	−	0.937757i	$-0.612899\pi$
$499$	−21.1033	−	3.03420i	−0.944714	−	0.135829i	−0.597422	+	0.801927i	$0.703808\pi$
$500$		0			0
$501$	11.0912	−	7.12790i	0.495520	−	0.318451i
$502$		0			0
$503$	0.730270	+	1.33739i	0.0325611	+	0.0596312i	0.893453	−	0.449157i	$-0.148276\pi$
$503$	0.730270	+	1.33739i	0.0325611	+	0.0596312i	−0.860892	+	0.508788i	$0.830094\pi$
$504$		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	−0.860409	−	0.509604i	$-0.829792\pi$
$509$	3.13431	−	10.6745i	0.138926	−	0.473138i	0.999335	+	0.0364663i	$0.0116102\pi$
$510$		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	0.981860	−	0.189605i	$-0.0607208\pi$
$521$	1.21793	+	4.14789i	0.0533586	+	0.181723i	−0.928502	+	0.371328i	$0.878903\pi$
$522$		0			0
$523$	−14.0370	+	1.00394i	−0.613793	+	0.0438994i	−0.374775	−	0.927116i	$-0.622280\pi$
$523$	−14.0370	+	1.00394i	−0.613793	+	0.0438994i	−0.239018	+	0.971015i	$0.576826\pi$
$524$		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	−0.859899	−	0.510465i	$-0.829473\pi$
$541$	−15.8761	−	34.7639i	−0.682568	−	1.49462i	0.177330	−	0.984151i	$-0.443254\pi$
$542$		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	0.461581	−	0.887098i	$-0.347282\pi$
$547$	11.9966	+	2.60970i	0.512937	+	0.111583i	0.0513554	+	0.998680i	$0.483646\pi$
$548$		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	−0.845054	−	0.534681i	$-0.820432\pi$
$557$	3.43979	−	15.8125i	0.145749	−	0.669995i	0.990803	−	0.135315i	$-0.0432045\pi$
$558$		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	0.0525413	−	0.998619i	$-0.483268\pi$
$563$	15.8213	−	42.4186i	0.666789	−	1.78773i	0.614248	−	0.789113i	$-0.289459\pi$
$564$		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	−0.360650	−	0.932701i	$-0.617445\pi$
$569$	14.6434	−	16.8994i	0.613883	−	0.708459i	0.974533	+	0.224242i	$0.0719906\pi$
$570$		0			0
$571$	−3.23046	+	2.79921i	−0.135190	+	0.117143i	−0.719831	−	0.694149i	$-0.755781\pi$
$571$	−3.23046	+	2.79921i	−0.135190	+	0.117143i	0.584641	+	0.811292i	$0.301235\pi$
$572$		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	−0.200082	−	0.979779i	$-0.564121\pi$
$577$	6.97385	−	2.60111i	0.290325	−	0.108286i	0.490407	+	0.871493i	$0.336848\pi$
$578$		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	−0.868384	−	0.495892i	$-0.834841\pi$
$587$	2.72897	−	7.31666i	0.112637	−	0.301991i	0.981021	+	0.193901i	$0.0621140\pi$
$588$		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	−0.959698	−	0.281035i	$-0.909322\pi$
$593$	0.731036	−	3.36052i	0.0300201	−	0.138000i	0.989718	+	0.143035i	$0.0456860\pi$
$594$		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	$0.0600060\pi$
$599$			9.17302i			0.374799i	−0.982284	+	0.187400i	$0.939994\pi$
$600$		0			0
$601$	−1.24243	−	0.364811i	−0.0506799	−	0.0148810i	0.256294	−	0.966599i	$-0.417498\pi$
$601$	−1.24243	−	0.364811i	−0.0506799	−	0.0148810i	−0.306974	+	0.951718i	$0.599317\pi$
$602$		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	0.976440	+	0.215787i	$0.0692318\pi$
$607$	4.38250	+	20.1460i	0.177880	+	0.817702i	−0.798560	+	0.601915i	$0.794405\pi$
$608$		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	0.764506	−	0.644616i	$-0.222983\pi$
$613$	15.7353	+	8.59214i	0.635544	+	0.347033i	−0.128962	+	0.991649i	$0.541165\pi$
$614$		0			0
$615$	−11.4282	−	15.3380i	−0.460828	−	0.618490i
$616$		0			0
$617$	−26.7290	−	1.91170i	−1.07607	−	0.0769620i	−0.477964	−	0.878379i	$-0.658625\pi$
$617$	−26.7290	−	1.91170i	−1.07607	−	0.0769620i	−0.598106	+	0.801417i	$0.704080\pi$
$618$		0			0
$619$	−7.48869	+	16.3979i	−0.300996	+	0.659089i	−0.998337	−	0.0576506i	$-0.981639\pi$
$619$	−7.48869	+	16.3979i	−0.300996	+	0.659089i	0.697341	+	0.716740i	$0.254366\pi$
$620$		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	−0.516897	−	0.856048i	$-0.672913\pi$
$631$	−19.3844	+	2.78705i	−0.771680	+	0.110951i	−0.254783	+	0.966998i	$0.582004\pi$
$632$		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	0.702867	+	0.711321i	$0.251903\pi$
$641$	−6.91160	+	23.5387i	−0.272992	+	0.929724i	−0.975859	+	0.218403i	$0.929915\pi$
$642$		0			0
$643$	−22.6055	−	22.6055i	−0.891474	−	0.891474i	0.103188	−	0.994662i	$-0.467096\pi$
$643$	−22.6055	−	22.6055i	−0.891474	−	0.891474i	−0.994662	+	0.103188i	$0.967096\pi$
$644$		0			0
$645$	−14.5561	+	9.30845i	−0.573147	+	0.366520i
$646$		0			0
$647$	17.2300	+	31.5544i	0.677381	+	1.24053i	0.959651	+	0.281195i	$0.0907309\pi$
$647$	17.2300	+	31.5544i	0.677381	+	1.24053i	−0.282270	+	0.959335i	$0.591087\pi$
$648$		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	−0.0858650	−	0.996307i	$-0.527365\pi$
$653$	6.38617	−	1.38923i	0.249910	−	0.0543646i	0.335775	+	0.941942i	$0.391002\pi$
$654$		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	0.672250	−	0.740324i	$-0.265328\pi$
$659$	42.0499	−	12.3470i	1.63803	−	0.480970i	0.965782	+	0.259355i	$0.0835099\pi$
$660$		0			0
$661$	3.70631	+	3.21154i	0.144159	+	0.124914i	0.723955	−	0.689847i	$-0.242322\pi$
$661$	3.70631	+	3.21154i	0.144159	+	0.124914i	−0.579796	+	0.814762i	$0.696868\pi$
$662$		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	−0.913703	−	0.406382i	$-0.866790\pi$
$673$	−1.74162	−	24.3510i	−0.0671344	−	0.938661i	0.846569	−	0.532279i	$-0.178664\pi$
$674$		0			0
$675$	−22.7034	+	16.8367i	−0.873853	+	0.648044i
$676$		0			0
$677$	−16.3048	−	12.2056i	−0.626646	−	0.469101i	0.238148	−	0.971229i	$-0.423460\pi$
$677$	−16.3048	−	12.2056i	−0.626646	−	0.469101i	−0.864793	+	0.502128i	$0.832551\pi$
$678$		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	0.857119	−	0.515119i	$-0.172252\pi$
$683$	3.17237	+	4.23779i	0.121387	+	0.162155i	−0.735731	+	0.677274i	$0.763161\pi$
$684$		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	−0.580101	−	0.814545i	$-0.696987\pi$
$701$	−9.11833	+	4.16420i	−0.344395	+	0.157280i	0.235706	+	0.971824i	$0.424260\pi$
$702$		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	0.551645	−	0.834079i	$-0.314000\pi$
$709$	−9.38474	−	10.8306i	−0.352451	−	0.406750i	−0.904096	+	0.427328i	$0.859455\pi$
$710$		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	0.904580	−	0.426303i	$-0.140184\pi$
$719$	16.3929	+	14.2045i	0.611352	+	0.529739i	−0.293229	+	0.956042i	$0.594730\pi$
$720$		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	0.0182865	−	0.999833i	$-0.494179\pi$
$727$	12.1405	−	2.64100i	0.450266	−	0.0979494i	0.431980	+	0.901883i	$0.357815\pi$
$728$		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	0.973580	−	0.228346i	$-0.0733318\pi$
$733$	6.90727	+	12.6497i	0.255126	+	0.467228i	−0.718454	+	0.695574i	$0.755150\pi$
$734$		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	0.598183	+	0.801360i	$0.295890\pi$
$739$	−9.19622	+	31.3194i	−0.338288	+	1.15210i	−0.936471	+	0.350745i	$0.885929\pi$
$740$		0			0
$741$	4.66459	+	7.25824i	0.171358	+	0.266638i
$742$		0			0
$743$	25.8905	−	19.3814i	0.949832	−	0.711035i	−0.00751631	−	0.999972i	$-0.502393\pi$
$743$	25.8905	−	19.3814i	0.949832	−	0.711035i	0.957348	+	0.288936i	$0.0933016\pi$
$744$		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	−0.968958	−	0.247225i	$-0.920481\pi$
$751$	−7.87817	−	26.8306i	−0.287479	−	0.979062i	0.681480	−	0.731837i	$-0.261337\pi$
$752$		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	0.993399	+	0.114707i	$0.0365929\pi$
$757$	8.74260	+	23.4398i	0.317755	+	0.851935i	−0.675644	+	0.737228i	$0.736134\pi$
$758$		0			0
$759$	−2.16012	+	2.35440i	−0.0784075	+	0.0854593i
$760$		0			0
$761$	14.0409	−	30.7452i	0.508981	−	1.11451i	−0.464464	−	0.885592i	$-0.653753\pi$
$761$	14.0409	−	30.7452i	0.508981	−	1.11451i	0.973445	−	0.228921i	$-0.0735198\pi$
$762$		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	0.960360	+	0.278762i	$0.0899242\pi$
$769$	3.25665	+	22.6505i	0.117438	+	0.816798i	−0.842922	+	0.538035i	$0.819167\pi$
$770$		0			0
$771$	−0.423713	−	0.927802i	−0.0152597	−	0.0334140i
$772$		0			0
$773$	−3.13807	−	14.4255i	−0.112868	−	0.518848i	−0.998514	−	0.0544868i	$-0.982648\pi$
$773$	−3.13807	−	14.4255i	−0.112868	−	0.518848i	0.885646	−	0.464361i	$-0.153716\pi$
$774$		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	−0.968209	−	0.250142i	$-0.919523\pi$
$787$	0.460569	−	2.11720i	0.0164175	−	0.0754702i	0.984627	+	0.174672i	$0.0558864\pi$
$788$		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	−0.379741	−	0.925093i	$-0.623987\pi$
$797$	17.0460	−	31.2174i	0.603800	−	1.10578i	0.983541	−	0.180684i	$-0.0578311\pi$
$798$		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	−0.489753	−	0.871861i	$-0.662913\pi$
$809$	8.63341	−	7.48089i	0.303535	−	0.263014i	0.793288	+	0.608847i	$0.208368\pi$
$810$		0			0
$811$	5.12440	−	5.91387i	0.179942	−	0.207664i	−0.658612	−	0.752483i	$-0.728856\pi$
$811$	5.12440	−	5.91387i	0.179942	−	0.207664i	0.838554	+	0.544819i	$0.183402\pi$
$812$		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	−0.635349	−	0.772225i	$-0.719144\pi$
$821$	5.49638	−	38.2282i	0.191825	−	1.33417i	0.827174	−	0.561946i	$-0.189947\pi$
$822$		0			0
$823$	−3.81542	+	17.5392i	−0.132997	+	0.611377i	0.861602	+	0.507585i	$0.169462\pi$
$823$	−3.81542	+	17.5392i	−0.132997	+	0.611377i	−0.994599	+	0.103793i	$0.966902\pi$
$824$		0			0
$825$	3.32378	−	0.222695i	0.115719	−	0.00775325i
$826$		0			0
$827$	−21.8354	+	21.8354i	−0.759291	+	0.759291i	−0.976193	−	0.216902i	$-0.930405\pi$
$827$	−21.8354	+	21.8354i	−0.759291	+	0.759291i	0.216902	+	0.976193i	$0.430405\pi$
$828$		0			0
$829$		−	37.2747i		−	1.29460i	−0.762234	−	0.647302i	$-0.775897\pi$
$829$		−	37.2747i		−	1.29460i	0.762234	−	0.647302i	$-0.224103\pi$
$830$		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	0.957069	−	0.289859i	$-0.0936085\pi$
$839$	3.22273	+	7.05680i	0.111261	+	0.243628i	−0.845808	+	0.533487i	$0.820881\pi$
$840$		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	0.860659	−	0.509181i	$-0.170052\pi$
$853$	−3.59897	−	9.64922i	−0.123226	−	0.330383i	−0.983886	+	0.178798i	$0.942779\pi$
$854$		0			0
$855$	−2.35927	+	7.96858i	−0.0806854	+	0.272520i
$856$		0			0
$857$	−34.4775	+	2.46588i	−1.17773	+	0.0842329i	−0.646445	−	0.762961i	$-0.723745\pi$
$857$	−34.4775	+	2.46588i	−1.17773	+	0.0842329i	−0.531284	+	0.847193i	$0.678290\pi$
$858$		0			0
$859$	5.50305	+	18.7417i	0.187762	+	0.639458i	0.998536	+	0.0540983i	$0.0172284\pi$
$859$	5.50305	+	18.7417i	0.187762	+	0.639458i	−0.810774	+	0.585360i	$0.800953\pi$
$860$		0			0
$861$	−2.89640	+	0.416440i	−0.0987091	+	0.0141922i
$862$		0			0
$863$	−0.968710	−	0.361310i	−0.0329753	−	0.0122991i	0.332922	−	0.942954i	$-0.391965\pi$
$863$	−0.968710	−	0.361310i	−0.0329753	−	0.0122991i	−0.365898	+	0.930655i	$0.619238\pi$
$864$		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	0.996440	+	0.0842994i	$0.0268652\pi$
$877$	15.6553	+	28.6705i	0.528641	+	0.968134i	−0.467799	+	0.883835i	$0.654953\pi$
$878$		0			0
$879$	−15.8690	+	10.1984i	−0.535247	+	0.343982i
$880$		0			0
$881$	16.4824	+	2.36981i	0.555306	+	0.0798410i	0.414254	−	0.910161i	$-0.364042\pi$
$881$	16.4824	+	2.36981i	0.555306	+	0.0798410i	0.141052	+	0.990002i	$0.454952\pi$
$882$		0			0
$883$	25.8688	−	5.62741i	0.870554	−	0.189377i	0.244967	−	0.969532i	$-0.421223\pi$
$883$	25.8688	−	5.62741i	0.870554	−	0.189377i	0.625587	+	0.780154i	$0.284859\pi$
$884$		0			0
$885$	−3.42898	−	15.9353i	−0.115264	−	0.535659i
$886$		0			0
$887$	1.42395	−	1.90218i	0.0478116	−	0.0638688i	−0.775998	−	0.630735i	$-0.782753\pi$
$887$	1.42395	−	1.90218i	0.0478116	−	0.0638688i	0.823810	+	0.566866i	$0.191844\pi$
$888$		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	0.768483	−	0.639870i	$-0.221012\pi$
$907$	11.1744	+	8.36505i	0.371040	+	0.277757i	−0.397444	+	0.917627i	$0.630103\pi$
$908$		0			0
$909$	−16.2322	+	7.41301i	−0.538389	+	0.245874i
$910$		0			0
$911$	−4.12898	+	6.42481i	−0.136799	+	0.212864i	−0.902893	−	0.429865i	$-0.858561\pi$
$911$	−4.12898	+	6.42481i	−0.136799	+	0.212864i	0.766094	+	0.642728i	$0.222198\pi$
$912$		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	−0.999615	−	0.0277309i	$-0.991172\pi$
$929$	−17.0422	+	26.5181i	−0.559135	+	0.870031i	0.440480	+	0.897762i	$0.354808\pi$
$930$		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	−0.974340	−	0.225081i	$-0.927735\pi$
$937$	−1.28410	−	17.9541i	−0.0419498	−	0.586535i	0.932390	−	0.361453i	$-0.117719\pi$
$938$		0			0
$939$	1.71244	+	1.97626i	0.0558833	+	0.0644928i
$940$		0			0
$941$	45.7808	+	20.9074i	1.49241	+	0.681562i	0.983773	−	0.179418i	$-0.0574214\pi$
$941$	45.7808	+	20.9074i	1.49241	+	0.681562i	0.508639	+	0.860980i	$0.330149\pi$
$942$		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	0.675892	+	0.737001i	$0.263759\pi$
$947$	−3.01599	+	42.1691i	−0.0980065	+	1.37031i	−0.773898	+	0.633310i	$0.781696\pi$
$948$		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	−0.880165	−	0.474668i	$-0.842568\pi$
$953$	−5.45650	+	7.28903i	−0.176753	+	0.236115i	0.703412	+	0.710783i	$0.251659\pi$
$954$		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	0.954174	+	0.299254i	$0.0967376\pi$
$967$	38.9774	+	38.9774i	1.25343	+	1.25343i	0.299254	+	0.954174i	$0.403262\pi$
$968$		0			0
$969$	−8.03849	+	27.3766i	−0.258233	+	0.879462i
$970$		0			0
$971$	−26.1330	−	40.6638i	−0.838649	−	1.30496i	−0.950338	−	0.311219i	$-0.899263\pi$
$971$	−26.1330	−	40.6638i	−0.838649	−	1.30496i	0.111689	−	0.993743i	$-0.464374\pi$
$972$		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	0.213082	−	0.977034i	$-0.431650\pi$
$977$	−8.30510	−	3.09764i	−0.265704	−	0.0991023i	−0.478785	+	0.877932i	$0.658923\pi$
$978$		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	0.568786	−	0.822486i	$-0.307413\pi$
$983$	39.1545	−	2.80039i	1.24883	−	0.0893184i	0.680049	+	0.733167i	$0.261959\pi$
$984$		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	−0.457821	−	0.889044i	$-0.651370\pi$
$991$	16.1771	−	35.4229i	0.513883	−	1.12525i	0.971704	−	0.236202i	$-0.0759028\pi$
$992$		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	0.869116	−	0.494608i	$-0.164688\pi$
$997$	29.1410	+	15.9122i	0.922905	+	0.503944i	0.0537891	+	0.998552i	$0.482870\pi$
$998$		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.17.12	✓	720
5.3	odd	4	inner	920.2.bv.a.753.12	yes	720
23.19	odd	22	inner	920.2.bv.a.617.12	yes	720
115.88	even	44	inner	920.2.bv.a.433.12	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.12	✓	720	1.1	even	1	trivial
920.2.bv.a.433.12	yes	720	115.88	even	44	inner
920.2.bv.a.617.12	yes	720	23.19	odd	22	inner
920.2.bv.a.753.12	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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