LMFDB - Embedded newform 920.2.bv.a.17.1

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			17.1
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.89859 + 1.58275i) q^{3} +(-2.21695 + 0.291804i) q^{5} +(0.277250 + 0.370363i) q^{7} +(4.27482 - 6.65174i) q^{9} +(1.52773 - 0.697690i) q^{11} +(5.64247 + 4.22390i) q^{13} +(5.96417 - 4.35469i) q^{15} +(-0.394803 - 5.52007i) q^{17} +(0.267286 + 0.308464i) q^{19} +(-1.38983 - 0.634712i) q^{21} +(-0.247460 + 4.78944i) q^{23} +(4.82970 - 1.29383i) q^{25} +(-1.15609 + 16.1642i) q^{27} +(-2.52681 - 2.18949i) q^{29} +(-5.05084 + 1.48306i) q^{31} +(-3.32399 + 4.44033i) q^{33} +(-0.722721 - 0.740171i) q^{35} +(3.55355 - 0.773028i) q^{37} +(-23.0406 - 3.31274i) q^{39} +(-1.01912 + 0.654949i) q^{41} +(2.68125 + 4.91033i) q^{43} +(-7.53603 + 15.9940i) q^{45} +(3.98168 + 3.98168i) q^{47} +(1.91183 - 6.51108i) q^{49} +(9.88127 + 15.3756i) q^{51} +(-9.74431 + 7.29450i) q^{53} +(-3.18330 + 1.99254i) q^{55} +(-1.26297 - 0.471065i) q^{57} +(-4.26171 + 0.612742i) q^{59} +(2.08404 + 7.09759i) q^{61} +(3.64875 - 0.260964i) q^{63} +(-13.7416 - 7.71767i) q^{65} +(-1.39754 - 3.74696i) q^{67} +(-6.86321 - 14.2743i) q^{69} +(4.57599 - 10.0200i) q^{71} +(-3.29574 - 0.235716i) q^{73} +(-11.9515 + 11.3945i) q^{75} +(0.681961 + 0.372379i) q^{77} +(1.81922 + 12.6530i) q^{79} +(-12.3789 - 27.1060i) q^{81} +(0.865786 + 3.97995i) q^{83} +(2.48603 + 12.1225i) q^{85} +(10.7896 + 2.34714i) q^{87} +(11.9121 + 3.49772i) q^{89} +3.26084i q^{91} +(12.2930 - 12.2930i) q^{93} +(-0.682569 - 0.605854i) q^{95} +(-3.69805 + 16.9997i) q^{97} +(1.88990 - 13.1445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.89859	+	1.58275i	−1.67350	+	0.913802i	−0.692111	+	0.721792i	$0.743319\pi$
$3$	−2.89859	+	1.58275i	−1.67350	+	0.913802i	−0.981393	+	0.192010i	$0.938499\pi$
$4$		0			0
$5$	−2.21695	+	0.291804i	−0.991448	+	0.130499i
$5$	−2.21695	+	0.291804i	−0.991448	+	0.130499i
$6$		0			0
$7$	0.277250	+	0.370363i	0.104791	+	0.139984i	0.849871	−	0.526991i	$-0.176680\pi$
$7$	0.277250	+	0.370363i	0.104791	+	0.139984i	−0.745080	+	0.666975i	$0.767589\pi$
$8$		0			0
$9$	4.27482	−	6.65174i	1.42494	−	2.21725i
$10$		0			0
$11$	1.52773	−	0.697690i	0.460627	−	0.210361i	−0.171565	−	0.985173i	$-0.554882\pi$
$11$	1.52773	−	0.697690i	0.460627	−	0.210361i	0.632193	+	0.774811i	$0.282155\pi$
$12$		0			0
$13$	5.64247	+	4.22390i	1.56494	+	1.17150i	0.909084	+	0.416613i	$0.136783\pi$
$13$	5.64247	+	4.22390i	1.56494	+	1.17150i	0.655856	+	0.754886i	$0.272308\pi$
$14$		0			0
$15$	5.96417	−	4.35469i	1.53994	−	1.12438i
$16$		0			0
$17$	−0.394803	−	5.52007i	−0.0957538	−	1.33881i	−0.787340	−	0.616519i	$-0.788542\pi$
$17$	−0.394803	−	5.52007i	−0.0957538	−	1.33881i	0.691586	−	0.722294i	$-0.256912\pi$
$18$		0			0
$19$	0.267286	+	0.308464i	0.0613196	+	0.0707665i	0.785581	−	0.618759i	$-0.212364\pi$
$19$	0.267286	+	0.308464i	0.0613196	+	0.0707665i	−0.724261	+	0.689526i	$0.757819\pi$
$20$		0			0
$21$	−1.38983	−	0.634712i	−0.303285	−	0.138506i
$22$		0			0
$23$	−0.247460	+	4.78944i	−0.0515990	+	0.998668i
$23$	−0.247460	+	4.78944i	−0.0515990	+	0.998668i
$24$		0			0
$25$	4.82970	−	1.29383i	0.965940	−	0.258765i
$26$		0			0
$27$	−1.15609	+	16.1642i	−0.222489	+	3.11080i
$28$		0			0
$29$	−2.52681	−	2.18949i	−0.469216	−	0.406578i	0.387900	−	0.921702i	$-0.373201\pi$
$29$	−2.52681	−	2.18949i	−0.469216	−	0.406578i	−0.857116	+	0.515123i	$0.827746\pi$
$30$		0			0
$31$	−5.05084	+	1.48306i	−0.907157	+	0.266365i	−0.701844	−	0.712331i	$-0.747640\pi$
$31$	−5.05084	+	1.48306i	−0.907157	+	0.266365i	−0.205313	+	0.978696i	$0.565821\pi$
$32$		0			0
$33$	−3.32399	+	4.44033i	−0.578633	+	0.772963i
$34$		0			0
$35$	−0.722721	−	0.740171i	−0.122162	−	0.125112i
$36$		0			0
$37$	3.55355	−	0.773028i	0.584200	−	0.127085i	0.0892545	−	0.996009i	$-0.471552\pi$
$37$	3.55355	−	0.773028i	0.584200	−	0.127085i	0.494946	+	0.868924i	$0.335188\pi$
$38$		0			0
$39$	−23.0406	−	3.31274i	−3.68945	−	0.530463i
$40$		0			0
$41$	−1.01912	+	0.654949i	−0.159160	+	0.102286i	−0.617796	−	0.786338i	$-0.711974\pi$
$41$	−1.01912	+	0.654949i	−0.159160	+	0.102286i	0.458636	+	0.888624i	$0.348338\pi$
$42$		0			0
$43$	2.68125	+	4.91033i	0.408886	+	0.748819i	0.998255	−	0.0590448i	$-0.0188055\pi$
$43$	2.68125	+	4.91033i	0.408886	+	0.748819i	−0.589369	+	0.807864i	$0.700624\pi$
$44$		0			0
$45$	−7.53603	+	15.9940i	−1.12341	+	2.38424i
$46$		0			0
$47$	3.98168	+	3.98168i	0.580787	+	0.580787i	0.935120	−	0.354332i	$-0.115292\pi$
$47$	3.98168	+	3.98168i	0.580787	+	0.580787i	−0.354332	+	0.935120i	$0.615292\pi$
$48$		0			0
$49$	1.91183	−	6.51108i	0.273118	−	0.930155i
$50$		0			0
$51$	9.88127	+	15.3756i	1.38365	+	2.15301i
$52$		0			0
$53$	−9.74431	+	7.29450i	−1.33848	+	1.00198i	−0.340388	+	0.940285i	$0.610559\pi$
$53$	−9.74431	+	7.29450i	−1.33848	+	1.00198i	−0.998095	+	0.0616914i	$0.980351\pi$
$54$		0			0
$55$	−3.18330	+	1.99254i	−0.429236	+	0.268674i
$56$		0			0
$57$	−1.26297	−	0.471065i	−0.167285	−	0.0623941i
$58$		0			0
$59$	−4.26171	+	0.612742i	−0.554828	+	0.0797722i	−0.414025	−	0.910265i	$-0.635877\pi$
$59$	−4.26171	+	0.612742i	−0.554828	+	0.0797722i	−0.140803	+	0.990038i	$0.544968\pi$
$60$		0			0
$61$	2.08404	+	7.09759i	0.266834	+	0.908753i	0.978502	+	0.206237i	$0.0661218\pi$
$61$	2.08404	+	7.09759i	0.266834	+	0.908753i	−0.711668	+	0.702516i	$0.752060\pi$
$62$		0			0
$63$	3.64875	−	0.260964i	0.459699	−	0.0328783i
$64$		0			0
$65$	−13.7416	−	7.71767i	−1.70444	−	0.957259i
$66$		0			0
$67$	−1.39754	−	3.74696i	−0.170737	−	0.457764i	0.823195	−	0.567759i	$-0.192189\pi$
$67$	−1.39754	−	3.74696i	−0.170737	−	0.457764i	−0.993932	+	0.109995i	$0.964917\pi$
$68$		0			0
$69$	−6.86321	−	14.2743i	−0.826234	−	1.71843i
$70$		0			0
$71$	4.57599	−	10.0200i	0.543070	−	1.18916i	−0.416874	−	0.908964i	$-0.636874\pi$
$71$	4.57599	−	10.0200i	0.543070	−	1.18916i	0.959944	−	0.280192i	$-0.0903983\pi$
$72$		0			0
$73$	−3.29574	−	0.235716i	−0.385737	−	0.0275884i	−0.122875	−	0.992422i	$-0.539212\pi$
$73$	−3.29574	−	0.235716i	−0.385737	−	0.0275884i	−0.262861	+	0.964834i	$0.584666\pi$
$74$		0			0
$75$	−11.9515	+	11.3945i	−1.38004	+	1.31572i
$76$		0			0
$77$	0.681961	+	0.372379i	0.0777166	+	0.0424365i
$78$		0			0
$79$	1.81922	+	12.6530i	0.204678	+	1.42357i	0.790169	+	0.612889i	$0.209993\pi$
$79$	1.81922	+	12.6530i	0.204678	+	1.42357i	−0.585490	+	0.810679i	$0.699098\pi$
$80$		0			0
$81$	−12.3789	−	27.1060i	−1.37544	−	3.01178i
$82$		0			0
$83$	0.865786	+	3.97995i	0.0950323	+	0.436857i	0.999937	+	0.0112419i	$0.00357848\pi$
$83$	0.865786	+	3.97995i	0.0950323	+	0.436857i	−0.904904	+	0.425615i	$0.860058\pi$
$84$		0			0
$85$	2.48603	+	12.1225i	0.269648	+	1.31487i
$86$		0			0
$87$	10.7896	+	2.34714i	1.15677	+	0.251639i
$88$		0			0
$89$	11.9121	+	3.49772i	1.26268	+	0.370757i	0.843493	−	0.537141i	$-0.180496\pi$
$89$	11.9121	+	3.49772i	1.26268	+	0.370757i	0.419191	+	0.907898i	$0.362314\pi$
$90$		0			0
$91$			3.26084i			0.341828i
$92$		0			0
$93$	12.2930	−	12.2930i	1.27473	−	1.27473i
$94$		0			0
$95$	−0.682569	−	0.605854i	−0.0700301	−	0.0621593i
$96$		0			0
$97$	−3.69805	+	16.9997i	−0.375480	+	1.72605i	0.270518	+	0.962715i	$0.412805\pi$
$97$	−3.69805	+	16.9997i	−0.375480	+	1.72605i	−0.645998	+	0.763339i	$0.723558\pi$
$98$		0			0
$99$	1.88990	−	13.1445i	0.189942	−	1.32108i
$100$		0			0
$101$	11.6452	+	7.48394i	1.15874	+	0.744680i	0.971361	−	0.237607i	$-0.0763630\pi$
$101$	11.6452	+	7.48394i	1.15874	+	0.744680i	0.187383	+	0.982287i	$0.439999\pi$
$102$		0			0
$103$	−3.58274	+	9.60570i	−0.353018	+	0.946478i	0.632144	+	0.774851i	$0.282175\pi$
$103$	−3.58274	+	9.60570i	−0.353018	+	0.946478i	−0.985162	+	0.171627i	$0.945098\pi$
$104$		0			0
$105$	3.26638	+	1.00157i	0.318766	+	0.0977429i
$106$		0			0
$107$	−0.259542	+	0.475316i	−0.0250909	+	0.0459505i	−0.889924	−	0.456110i	$-0.849243\pi$
$107$	−0.259542	+	0.475316i	−0.0250909	+	0.0459505i	0.864833	+	0.502060i	$0.167424\pi$
$108$		0			0
$109$	1.20330	−	1.38868i	0.115255	−	0.133012i	−0.695190	−	0.718826i	$-0.744680\pi$
$109$	1.20330	−	1.38868i	0.115255	−	0.133012i	0.810445	+	0.585814i	$0.199225\pi$
$110$		0			0
$111$	−9.07679	+	7.86508i	−0.861531	+	0.746521i
$112$		0			0
$113$	2.48103	−	0.925377i	0.233396	−	0.0870521i	−0.230045	−	0.973180i	$-0.573887\pi$
$113$	2.48103	−	0.925377i	0.233396	−	0.0870521i	0.463441	+	0.886128i	$0.346615\pi$
$114$		0			0
$115$	−0.848971	−	10.6901i	−0.0791670	−	0.996861i
$116$		0			0
$117$	52.2168	−	19.4759i	4.82745	−	1.80054i
$118$		0			0
$119$	1.93497	−	1.67666i	0.177378	−	0.153699i
$120$		0			0
$121$	−5.35629	+	6.18149i	−0.486935	+	0.561953i
$122$		0			0
$123$	1.91739	−	3.51145i	0.172886	−	0.316616i
$124$		0			0
$125$	−10.3296	+	4.27767i	−0.923912	+	0.382606i
$126$		0			0
$127$	3.40426	−	9.12718i	0.302079	−	0.809906i	−0.693879	−	0.720092i	$-0.744100\pi$
$127$	3.40426	−	9.12718i	0.302079	−	0.809906i	0.995958	−	0.0898147i	$-0.0286275\pi$
$128$		0			0
$129$	−15.5437	−	9.98931i	−1.36854	−	0.879510i
$130$		0			0
$131$	−0.0463141	+	0.322122i	−0.00404648	+	0.0281439i	−0.991745	−	0.128229i	$-0.959071\pi$
$131$	−0.0463141	+	0.322122i	−0.00404648	+	0.0281439i	0.987698	+	0.156372i	$0.0499800\pi$
$132$		0			0
$133$	−0.0401386	+	0.184514i	−0.00348046	+	0.0159994i
$134$		0			0
$135$	−2.15379	−	36.1725i	−0.185369	−	3.11324i
$136$		0			0
$137$	0.300700	−	0.300700i	0.0256905	−	0.0256905i	−0.694145	−	0.719835i	$-0.744217\pi$
$137$	0.300700	−	0.300700i	0.0256905	−	0.0256905i	0.719835	+	0.694145i	$0.244217\pi$
$138$		0			0
$139$			13.5410i			1.14853i	0.818669	+	0.574265i	$0.194712\pi$
$139$			13.5410i			1.14853i	−0.818669	+	0.574265i	$0.805288\pi$
$140$		0			0
$141$	−17.8433	−	5.23926i	−1.50267	−	0.441225i
$142$		0			0
$143$	11.5671	+	2.51628i	0.967292	+	0.210422i
$144$		0			0
$145$	6.24070	+	4.11665i	0.518262	+	0.341869i
$146$		0			0
$147$	4.76382	+	21.8989i	0.392913	+	1.80619i
$148$		0			0
$149$	0.0819658	+	0.179480i	0.00671490	+	0.0147036i	0.912960	−	0.408050i	$-0.133791\pi$
$149$	0.0819658	+	0.179480i	0.00671490	+	0.0147036i	−0.906245	+	0.422753i	$0.861064\pi$
$150$		0			0
$151$	−2.03922	−	14.1831i	−0.165949	−	1.15420i	−0.887152	−	0.461477i	$-0.847320\pi$
$151$	−2.03922	−	14.1831i	−0.165949	−	1.15420i	0.721203	−	0.692724i	$-0.243589\pi$
$152$		0			0
$153$	−38.4058	−	20.9711i	−3.10492	−	1.69542i
$154$		0			0
$155$	10.7647	−	4.76172i	0.864639	−	0.382470i
$156$		0			0
$157$	14.7872	+	1.05760i	1.18015	+	0.0844057i	0.647590	−	0.761989i	$-0.275777\pi$
$157$	14.7872	+	1.05760i	1.18015	+	0.0844057i	0.532556	+	0.846395i	$0.321232\pi$
$158$		0			0
$159$	16.6994	−	36.5666i	1.32435	−	2.89992i
$160$		0			0
$161$	−1.84244	+	1.23622i	−0.145204	+	0.0974280i
$162$		0			0
$163$	−5.05059	−	13.5411i	−0.395593	−	1.06062i	−0.970223	−	0.242212i	$-0.922127\pi$
$163$	−5.05059	−	13.5411i	−0.395593	−	1.06062i	0.574631	−	0.818413i	$-0.305146\pi$
$164$		0			0
$165$	6.07340	−	10.8139i	0.472814	−	0.841863i
$166$		0			0
$167$	−9.53339	+	0.681842i	−0.737716	+	0.0527625i	−0.435140	−	0.900363i	$-0.643301\pi$
$167$	−9.53339	+	0.681842i	−0.737716	+	0.0527625i	−0.302576	+	0.953125i	$0.597847\pi$
$168$		0			0
$169$	10.3336	+	35.1931i	0.794893	+	2.70716i
$170$		0			0
$171$	3.19442	−	0.459289i	0.244284	−	0.0351227i
$172$		0			0
$173$	−3.82272	−	1.42580i	−0.290636	−	0.108402i	0.199917	−	0.979813i	$-0.435933\pi$
$173$	−3.82272	−	1.42580i	−0.290636	−	0.108402i	−0.490554	+	0.871411i	$0.663205\pi$
$174$		0			0
$175$	1.81822	+	1.43003i	0.137444	+	0.108100i
$176$		0			0
$177$	11.3832	−	8.52133i	0.855611	−	0.640502i
$178$		0			0
$179$	1.33214	+	2.07285i	0.0995686	+	0.154932i	0.887464	−	0.460878i	$-0.152465\pi$
$179$	1.33214	+	2.07285i	0.0995686	+	0.154932i	−0.787895	+	0.615810i	$0.788829\pi$
$180$		0			0
$181$	−6.01702	+	20.4921i	−0.447242	+	1.52316i	0.360005	+	0.932950i	$0.382775\pi$
$181$	−6.01702	+	20.4921i	−0.447242	+	1.52316i	−0.807247	+	0.590214i	$0.799043\pi$
$182$		0			0
$183$	−17.2745	−	17.2745i	−1.27697	−	1.27697i
$184$		0			0
$185$	−7.65246	+	2.75070i	−0.562620	+	0.202236i
$186$		0			0
$187$	−4.45445	−	8.15771i	−0.325741	−	0.596551i
$188$		0			0
$189$	−6.30714	+	4.05336i	−0.458777	+	0.294838i
$190$		0			0
$191$	−10.4741	−	1.50595i	−0.757879	−	0.108967i	−0.247467	−	0.968896i	$-0.579598\pi$
$191$	−10.4741	−	1.50595i	−0.757879	−	0.108967i	−0.510412	+	0.859930i	$0.670507\pi$
$192$		0			0
$193$	−17.1874	+	3.73889i	−1.23718	+	0.269131i	−0.783136	−	0.621851i	$-0.786381\pi$
$193$	−17.1874	+	3.73889i	−1.23718	+	0.269131i	−0.454039	+	0.890982i	$0.650017\pi$
$194$		0			0
$195$	52.0465	+	0.620831i	3.72712	+	0.0444586i
$196$		0			0
$197$	2.16977	−	2.89848i	0.154590	−	0.206508i	−0.716559	−	0.697526i	$-0.754284\pi$
$197$	2.16977	−	2.89848i	0.154590	−	0.206508i	0.871149	+	0.491018i	$0.163375\pi$
$198$		0			0
$199$	13.8175	−	4.05719i	0.979498	−	0.287607i	0.247481	−	0.968893i	$-0.420397\pi$
$199$	13.8175	−	4.05719i	0.979498	−	0.287607i	0.732017	+	0.681286i	$0.238579\pi$
$200$		0			0
$201$	9.98142	+	8.64895i	0.704035	+	0.610050i
$202$		0			0
$203$	0.110348	−	1.54287i	0.00774493	−	0.108288i
$204$		0			0
$205$	2.06822	−	1.74937i	0.144451	−	0.122181i
$206$		0			0
$207$	30.8003	+	22.1200i	2.14077	+	1.53745i
$208$		0			0
$209$	0.623552	+	0.284767i	0.0431320	+	0.0196977i
$210$		0			0
$211$	−7.64202	−	8.81936i	−0.526098	−	0.607150i	0.429049	−	0.903281i	$-0.358849\pi$
$211$	−7.64202	−	8.81936i	−0.526098	−	0.607150i	−0.955147	+	0.296131i	$0.904303\pi$
$212$		0			0
$213$	2.59527	+	36.2866i	0.177825	+	2.48632i
$214$		0			0
$215$	−7.37703	−	10.1035i	−0.503109	−	0.689056i
$216$		0			0
$217$	−1.94961	−	1.45946i	−0.132348	−	0.0990748i
$218$		0			0
$219$	9.92608	−	4.53309i	0.670742	−	0.306318i
$220$		0			0
$221$	21.0885	−	32.8144i	1.41857	−	2.20734i
$222$		0			0
$223$	15.7028	+	20.9765i	1.05154	+	1.40469i	0.909926	+	0.414770i	$0.136138\pi$
$223$	15.7028	+	20.9765i	1.05154	+	1.40469i	0.141613	+	0.989922i	$0.454771\pi$
$224$		0			0
$225$	12.0399	−	37.6568i	0.802659	−	2.51045i
$226$		0			0
$227$	−17.6816	+	9.65490i	−1.17357	+	0.640818i	−0.943181	−	0.332280i	$-0.892182\pi$
$227$	−17.6816	+	9.65490i	−1.17357	+	0.640818i	−0.230391	+	0.973098i	$0.574000\pi$
$228$		0			0
$229$	3.00254			0.198414			0.0992068	−	0.995067i	$-0.468369\pi$
$229$	3.00254			0.198414			0.0992068	+	0.995067i	$0.468369\pi$
$230$		0			0
$231$	−2.56611			−0.168838
$232$		0			0
$233$	18.1642	−	9.91842i	1.18998	−	0.649777i	0.242672	−	0.970108i	$-0.421976\pi$
$233$	18.1642	−	9.91842i	1.18998	−	0.649777i	0.947306	+	0.320331i	$0.103794\pi$
$234$		0			0
$235$	−9.98903	−	7.66530i	−0.651613	−	0.500029i
$236$		0			0
$237$	−25.2997	−	33.7964i	−1.64339	−	2.19531i
$238$		0			0
$239$	9.33935	−	14.5323i	0.604112	−	0.940017i	−0.395654	−	0.918400i	$-0.629482\pi$
$239$	9.33935	−	14.5323i	0.604112	−	0.940017i	0.999766	−	0.0216176i	$-0.00688162\pi$
$240$		0			0
$241$	7.76277	−	3.54514i	0.500044	−	0.228362i	−0.149393	−	0.988778i	$-0.547732\pi$
$241$	7.76277	−	3.54514i	0.500044	−	0.228362i	0.649437	+	0.760415i	$0.275005\pi$
$242$		0			0
$243$	39.8641	+	29.8419i	2.55728	+	1.91436i
$244$		0			0
$245$	−2.33846	+	14.9926i	−0.149399	+	0.957842i
$246$		0			0
$247$	0.205230	+	2.86949i	0.0130585	+	0.182581i
$248$		0			0
$249$	−8.80884	−	10.1659i	−0.558237	−	0.644240i
$250$		0			0
$251$	−14.5282	−	6.63480i	−0.917011	−	0.418785i	−0.0997235	−	0.995015i	$-0.531796\pi$
$251$	−14.5282	−	6.63480i	−0.917011	−	0.418785i	−0.817287	+	0.576230i	$0.804523\pi$
$252$		0			0
$253$	2.96349	+	7.48961i	0.186313	+	0.470868i
$254$		0			0
$255$	−26.3929	−	31.2034i	−1.65279	−	1.95403i
$256$		0			0
$257$	−1.12394	+	15.7147i	−0.0701093	+	0.980256i	0.833671	+	0.552261i	$0.186235\pi$
$257$	−1.12394	+	15.7147i	−0.0701093	+	0.980256i	−0.903781	+	0.427996i	$0.859220\pi$
$258$		0			0
$259$	1.27152	+	1.10178i	0.0790086	+	0.0684613i
$260$		0			0
$261$	−25.3656	+	7.44801i	−1.57009	+	0.461020i
$262$		0			0
$263$	−6.22865	+	8.32050i	−0.384075	+	0.513064i	−0.950363	−	0.311144i	$-0.899288\pi$
$263$	−6.22865	+	8.32050i	−0.384075	+	0.513064i	0.566288	+	0.824207i	$0.308379\pi$
$264$		0			0
$265$	19.4740	−	19.0149i	1.19628	−	1.16808i
$266$		0			0
$267$	−40.0644	+	8.71548i	−2.45190	+	0.533379i
$268$		0			0
$269$	−14.1387	−	2.03284i	−0.862055	−	0.123945i	−0.302914	−	0.953018i	$-0.597960\pi$
$269$	−14.1387	−	2.03284i	−0.862055	−	0.123945i	−0.559140	+	0.829073i	$0.688869\pi$
$270$		0			0
$271$	3.35136	−	2.15379i	0.203581	−	0.130833i	−0.434878	−	0.900489i	$-0.643209\pi$
$271$	3.35136	−	2.15379i	0.203581	−	0.130833i	0.638459	+	0.769656i	$0.279572\pi$
$272$		0			0
$273$	−5.16109	−	9.45183i	−0.312364	−	0.572051i
$274$		0			0
$275$	6.47578	−	5.34625i	0.390504	−	0.322391i
$276$		0			0
$277$	7.14537	+	7.14537i	0.429324	+	0.429324i	0.888398	−	0.459074i	$-0.151819\pi$
$277$	7.14537	+	7.14537i	0.429324	+	0.429324i	−0.459074	+	0.888398i	$0.651819\pi$
$278$		0			0
$279$	−11.7265	+	39.9367i	−0.702045	+	2.39095i
$280$		0			0
$281$	14.5611	+	22.6575i	0.868643	+	1.35163i	0.935299	+	0.353858i	$0.115131\pi$
$281$	14.5611	+	22.6575i	0.868643	+	1.35163i	−0.0666563	+	0.997776i	$0.521233\pi$
$282$		0			0
$283$	−11.6045	+	8.68704i	−0.689817	+	0.516391i	−0.885713	−	0.464234i	$-0.846330\pi$
$283$	−11.6045	+	8.68704i	−0.689817	+	0.516391i	0.195895	+	0.980625i	$0.437239\pi$
$284$		0			0
$285$	2.93741	+	0.675786i	0.173997	+	0.0400301i
$286$		0			0
$287$	−0.525120	−	0.195860i	−0.0309968	−	0.0115612i
$288$		0			0
$289$	−13.4883	+	1.93933i	−0.793430	+	0.114078i
$290$		0			0
$291$	−16.1871	−	55.1282i	−0.948905	−	3.23167i
$292$		0			0
$293$	−7.61826	+	0.544869i	−0.445064	+	0.0318316i	−0.292073	−	0.956396i	$-0.594345\pi$
$293$	−7.61826	+	0.544869i	−0.445064	+	0.0318316i	−0.152991	+	0.988228i	$0.548890\pi$
$294$		0			0
$295$	9.26919	−	2.60200i	0.539673	−	0.151494i
$296$		0			0
$297$	9.51142	+	25.5011i	0.551909	+	1.47972i
$298$		0			0
$299$	−21.6264	+	25.9790i	−1.25069	+	1.50241i
$300$		0			0
$301$	−1.07523	+	2.35442i	−0.0619751	+	0.135707i
$302$		0			0
$303$	−45.6000	−	3.26138i	−2.61965	−	0.187361i
$304$		0			0
$305$	−6.69131	−	15.1268i	−0.383143	−	0.866160i
$306$		0			0
$307$	−26.7632	−	14.6138i	−1.52745	−	0.834053i	−0.527574	−	0.849509i	$-0.676898\pi$
$307$	−26.7632	−	14.6138i	−1.52745	−	0.834053i	−0.999881	+	0.0154562i	$0.995080\pi$
$308$		0			0
$309$	−4.81853	−	33.5136i	−0.274117	−	1.90652i
$310$		0			0
$311$	1.99242	+	4.36280i	0.112980	+	0.247392i	0.957672	−	0.287860i	$-0.0929439\pi$
$311$	1.99242	+	4.36280i	0.112980	+	0.247392i	−0.844692	+	0.535252i	$0.820217\pi$
$312$		0			0
$313$	3.44103	+	15.8182i	0.194498	+	0.894095i	0.966136	+	0.258033i	$0.0830742\pi$
$313$	3.44103	+	15.8182i	0.194498	+	0.894095i	−0.771638	+	0.636062i	$0.780562\pi$
$314$		0			0
$315$	−8.01293	+	1.64326i	−0.451477	+	0.0925873i
$316$		0			0
$317$	−10.5697	−	2.29930i	−0.593655	−	0.129142i	−0.0943069	−	0.995543i	$-0.530063\pi$
$317$	−10.5697	−	2.29930i	−0.593655	−	0.129142i	−0.499348	+	0.866401i	$0.666427\pi$
$318$		0			0
$319$	−5.38786	−	1.58202i	−0.301662	−	0.0885760i
$320$		0			0
$321$		−	1.78854i		−	0.0998264i
$322$		0			0
$323$	1.59722	−	1.59722i	0.0888716	−	0.0888716i
$324$		0			0
$325$	32.7164	+	13.0998i	1.81478	+	0.726646i
$326$		0			0
$327$	−1.28994	+	5.92975i	−0.0713337	+	0.327916i
$328$		0			0
$329$	−0.370744	+	2.57858i	−0.0204398	+	0.142162i
$330$		0			0
$331$	28.8726	+	18.5553i	1.58698	+	1.01989i	0.973069	+	0.230514i	$0.0740406\pi$
$331$	28.8726	+	18.5553i	1.58698	+	1.01989i	0.613910	+	0.789376i	$0.289596\pi$
$332$		0			0
$333$	10.0488	−	26.9419i	0.550671	−	1.47641i
$334$		0			0
$335$	4.19166	+	7.89901i	0.229015	+	0.431569i
$336$		0			0
$337$	−3.03384	+	5.55606i	−0.165264	+	0.302658i	−0.947166	−	0.320743i	$-0.896068\pi$
$337$	−3.03384	+	5.55606i	−0.165264	+	0.302658i	0.781903	+	0.623400i	$0.214249\pi$
$338$		0			0
$339$	−5.72686	+	6.60915i	−0.311040	+	0.358960i
$340$		0			0
$341$	−6.68159	+	5.78963i	−0.361828	+	0.313526i
$342$		0			0
$343$	5.97581	−	2.22886i	0.322663	−	0.120347i
$344$		0			0
$345$	19.3807	+	29.6427i	1.04342	+	1.59591i
$346$		0			0
$347$	−4.04574	+	1.50898i	−0.217187	+	0.0810064i	−0.455702	−	0.890132i	$-0.650612\pi$
$347$	−4.04574	+	1.50898i	−0.217187	+	0.0810064i	0.238516	+	0.971139i	$0.423339\pi$
$348$		0			0
$349$	20.6251	−	17.8717i	1.10403	−	0.956651i	0.104751	−	0.994498i	$-0.466595\pi$
$349$	20.6251	−	17.8717i	1.10403	−	0.956651i	0.999284	+	0.0378470i	$0.0120499\pi$
$350$		0			0
$351$	−74.7992	+	86.3229i	−3.99249	+	4.60758i
$352$		0			0
$353$	2.23763	−	4.09791i	0.119097	−	0.218110i	−0.811329	−	0.584590i	$-0.801255\pi$
$353$	2.23763	−	4.09791i	0.119097	−	0.218110i	0.930426	+	0.366480i	$0.119437\pi$
$354$		0			0
$355$	−7.22084	+	23.5491i	−0.383242	+	1.24986i
$356$		0			0
$357$	−2.95495	+	7.92252i	−0.156392	+	0.419304i
$358$		0			0
$359$	25.5307	+	16.4076i	1.34746	+	0.865960i	0.997491	−	0.0708003i	$-0.0225553\pi$
$359$	25.5307	+	16.4076i	1.34746	+	0.865960i	0.349970	+	0.936761i	$0.386192\pi$
$360$		0			0
$361$	2.68027	−	18.6417i	0.141067	−	0.981143i
$362$		0			0
$363$	5.74194	−	26.3953i	0.301374	−	1.38539i
$364$		0			0
$365$	7.37525	−	0.439139i	0.386038	−	0.0229856i
$366$		0			0
$367$	21.2601	−	21.2601i	1.10977	−	1.10977i	0.116587	−	0.993180i	$-0.462805\pi$
$367$	21.2601	−	21.2601i	1.10977	−	1.10977i	0.993180	−	0.116587i	$-0.0371954\pi$
$368$		0			0
$369$			9.57872i			0.498648i
$370$		0			0
$371$	−5.40322	−	1.58653i	−0.280521	−	0.0823684i
$372$		0			0
$373$	14.5843	+	3.17261i	0.755145	+	0.164272i	0.573628	−	0.819116i	$-0.305536\pi$
$373$	14.5843	+	3.17261i	0.755145	+	0.164272i	0.181517	+	0.983388i	$0.441899\pi$
$374$		0			0
$375$	23.1710	−	28.7485i	1.19654	−	1.48456i
$376$		0			0
$377$	−5.00924	−	23.0271i	−0.257989	−	1.18596i
$378$		0			0
$379$	5.71756	+	12.5197i	0.293691	+	0.643094i	0.997750	−	0.0670480i	$-0.0213581\pi$
$379$	5.71756	+	12.5197i	0.293691	+	0.643094i	−0.704059	+	0.710142i	$0.748631\pi$
$380$		0			0
$381$	4.57849	+	31.8441i	0.234563	+	1.63142i
$382$		0			0
$383$	6.89706	+	3.76608i	0.352423	+	0.192438i	0.645702	−	0.763589i	$-0.276565\pi$
$383$	6.89706	+	3.76608i	0.352423	+	0.192438i	−0.293279	+	0.956027i	$0.594746\pi$
$384$		0			0
$385$	−1.62053	−	0.626545i	−0.0825899	−	0.0319317i
$386$		0			0
$387$	44.1241	+	3.15582i	2.24295	+	0.160419i
$388$		0			0
$389$	−15.0698	+	32.9982i	−0.764068	+	1.67307i	−0.0247723	+	0.999693i	$0.507886\pi$
$389$	−15.0698	+	32.9982i	−0.764068	+	1.67307i	−0.739295	+	0.673381i	$0.764841\pi$
$390$		0			0
$391$	26.5357	−	0.524889i	1.34197	−	0.0265448i
$392$		0			0
$393$	−0.375593	−	1.00700i	−0.0189462	−	0.0507966i
$394$		0			0
$395$	−7.72529	−	27.5201i	−0.388702	−	1.38468i
$396$		0			0
$397$	−8.90774	+	0.637094i	−0.447067	+	0.0319748i	−0.293058	−	0.956095i	$-0.594673\pi$
$397$	−8.90774	+	0.637094i	−0.447067	+	0.0319748i	−0.154009	+	0.988069i	$0.549218\pi$
$398$		0			0
$399$	−0.175695	−	0.598361i	−0.00879574	−	0.0299555i
$400$		0			0
$401$	−19.8982	+	2.86092i	−0.993666	+	0.142868i	−0.619921	−	0.784664i	$-0.712836\pi$
$401$	−19.8982	+	2.86092i	−0.993666	+	0.142868i	−0.373745	+	0.927532i	$0.621926\pi$
$402$		0			0
$403$	−34.7635	−	12.9661i	−1.73169	−	0.645888i
$404$		0			0
$405$	35.3530	+	56.4804i	1.75671	+	2.80654i
$406$		0			0
$407$	4.88953	−	3.66025i	0.242365	−	0.181432i
$408$		0			0
$409$	0.0605970	+	0.0942907i	0.00299633	+	0.00466238i	0.842748	−	0.538308i	$-0.180936\pi$
$409$	0.0605970	+	0.0942907i	0.00299633	+	0.00466238i	−0.839752	+	0.542970i	$0.817300\pi$
$410$		0			0
$411$	−0.395673	+	1.34754i	−0.0195171	+	0.0664692i
$412$		0			0
$413$	−1.40850	−	1.40850i	−0.0693076	−	0.0693076i
$414$		0			0
$415$	−3.08077	−	8.57070i	−0.151229	−	0.420719i
$416$		0			0
$417$	−21.4320	−	39.2498i	−1.04953	−	1.92207i
$418$		0			0
$419$	21.8072	−	14.0146i	1.06535	−	0.684659i	0.114223	−	0.993455i	$-0.463562\pi$
$419$	21.8072	−	14.0146i	1.06535	−	0.684659i	0.951128	+	0.308796i	$0.0999259\pi$
$420$		0			0
$421$	−17.7205	−	2.54783i	−0.863645	−	0.124173i	−0.303765	−	0.952747i	$-0.598244\pi$
$421$	−17.7205	−	2.54783i	−0.863645	−	0.124173i	−0.559880	+	0.828574i	$0.689153\pi$
$422$		0			0
$423$	43.5060	−	9.46416i	2.11534	−	0.460163i
$424$		0			0
$425$	−9.04879	−	26.1495i	−0.438931	−	1.26844i
$426$		0			0
$427$	−2.05088	+	2.73966i	−0.0992491	+	0.132581i
$428$		0			0
$429$	−37.5110	+	11.0142i	−1.81105	+	0.531772i
$430$		0			0
$431$	19.8060	+	17.1620i	0.954021	+	0.826664i	0.984947	−	0.172858i	$-0.0553001\pi$
$431$	19.8060	+	17.1620i	0.954021	+	0.826664i	−0.0309257	+	0.999522i	$0.509846\pi$
$432$		0			0
$433$	−0.0959101	+	1.34100i	−0.00460914	+	0.0644443i	−0.999236	−	0.0390798i	$-0.987557\pi$
$433$	−0.0959101	+	1.34100i	−0.00460914	+	0.0644443i	0.994627	+	0.103524i	$0.0330119\pi$
$434$		0			0
$435$	−24.6049	−	2.05503i	−1.17971	−	0.0985310i
$436$		0			0
$437$	−1.54351	+	1.20382i	−0.0738363	+	0.0575864i
$438$		0			0
$439$	4.37253	+	1.99687i	0.208689	+	0.0953052i	0.517017	−	0.855975i	$-0.327042\pi$
$439$	4.37253	+	1.99687i	0.208689	+	0.0953052i	−0.308328	+	0.951280i	$0.599769\pi$
$440$		0			0
$441$	−35.1374	−	40.5507i	−1.67321	−	1.93098i
$442$		0			0
$443$	−2.60677	−	36.4474i	−0.123851	−	1.73167i	−0.557145	−	0.830415i	$-0.688103\pi$
$443$	−2.60677	−	36.4474i	−0.123851	−	1.73167i	0.433294	−	0.901253i	$-0.357351\pi$
$444$		0			0
$445$	−27.4292	−	4.27825i	−1.30027	−	0.202808i
$446$		0			0
$447$	−0.521658	−	0.390508i	−0.0246736	−	0.0184704i
$448$		0			0
$449$	−6.57829	+	3.00421i	−0.310449	+	0.141777i	−0.564546	−	0.825401i	$-0.690949\pi$
$449$	−6.57829	+	3.00421i	−0.310449	+	0.141777i	0.254097	+	0.967179i	$0.418222\pi$
$450$		0			0
$451$	−1.09999	+	1.71161i	−0.0517964	+	0.0805968i
$452$		0			0
$453$	28.3591	+	37.8833i	1.33243	+	1.77991i
$454$		0			0
$455$	−0.951524	−	7.22910i	−0.0446081	−	0.338905i
$456$		0			0
$457$	24.1152	−	13.1679i	1.12806	−	0.615968i	0.196845	−	0.980435i	$-0.436931\pi$
$457$	24.1152	−	13.1679i	1.12806	−	0.615968i	0.931216	+	0.364467i	$0.118749\pi$
$458$		0			0
$459$	89.6840			4.18609
$460$		0			0
$461$	3.96880			0.184845			0.0924227	−	0.995720i	$-0.470539\pi$
$461$	3.96880			0.184845			0.0924227	+	0.995720i	$0.470539\pi$
$462$		0			0
$463$	−7.99762	+	4.36703i	−0.371681	+	0.202953i	−0.654223	−	0.756302i	$-0.727004\pi$
$463$	−7.99762	+	4.36703i	−0.371681	+	0.202953i	0.282542	+	0.959255i	$0.408822\pi$
$464$		0			0
$465$	−23.6658	+	30.8401i	−1.09747	+	1.43017i
$466$		0			0
$467$	5.85317	+	7.81892i	0.270853	+	0.361817i	0.915259	−	0.402867i	$-0.131986\pi$
$467$	5.85317	+	7.81892i	0.270853	+	0.361817i	−0.644406	+	0.764684i	$0.722895\pi$
$468$		0			0
$469$	1.00027	−	1.55644i	0.0461880	−	0.0718699i
$470$		0			0
$471$	−44.5359	+	20.3389i	−2.05211	+	0.937166i
$472$		0			0
$473$	7.52210	+	5.63098i	0.345867	+	0.258913i
$474$		0			0
$475$	1.69001	+	1.14397i	0.0775429	+	0.0524889i
$476$		0			0
$477$	6.86600	+	95.9993i	0.314373	+	4.39551i
$478$		0			0
$479$	−12.9637	−	14.9609i	−0.592326	−	0.683581i	0.377882	−	0.925854i	$-0.376653\pi$
$479$	−12.9637	−	14.9609i	−0.592326	−	0.683581i	−0.970208	+	0.242273i	$0.922107\pi$
$480$		0			0
$481$	23.3160	+	10.6481i	1.06312	+	0.485510i
$482$		0			0
$483$	3.38385	−	6.49943i	0.153970	−	0.295734i
$484$		0			0
$485$	3.23781	−	38.7664i	0.147022	−	1.76029i
$486$		0			0
$487$	−0.144496	+	2.02032i	−0.00654773	+	0.0915493i	−0.999675	−	0.0254894i	$-0.991886\pi$
$487$	−0.144496	+	2.02032i	−0.00654773	+	0.0915493i	0.993127	+	0.117039i	$0.0373401\pi$
$488$		0			0
$489$	36.0719	+	31.2565i	1.63123	+	1.41347i
$490$		0			0
$491$	12.6632	−	3.71824i	0.571481	−	0.167802i	0.0167910	−	0.999859i	$-0.494655\pi$
$491$	12.6632	−	3.71824i	0.571481	−	0.167802i	0.554690	+	0.832057i	$0.312837\pi$
$492$		0			0
$493$	−11.0885	+	14.8126i	−0.499403	+	0.667125i
$494$		0			0
$495$	−0.354181	+	29.6922i	−0.0159192	+	1.33457i
$496$		0			0
$497$	4.97973	−	1.08327i	0.223371	−	0.0485915i
$498$		0			0
$499$	−7.75124	−	1.11446i	−0.346993	−	0.0498901i	−0.0333849	−	0.999443i	$-0.510629\pi$
$499$	−7.75124	−	1.11446i	−0.346993	−	0.0498901i	−0.313608	+	0.949552i	$0.601538\pi$
$500$		0			0
$501$	26.5542	−	17.0654i	1.18636	−	0.762425i
$502$		0			0
$503$	9.96367	+	18.2471i	0.444258	+	0.813598i	0.999840	−	0.0178636i	$-0.00568646\pi$
$503$	9.96367	+	18.2471i	0.444258	+	0.813598i	−0.555582	+	0.831462i	$0.687505\pi$
$504$		0			0
$505$	−28.0007	−	13.1934i	−1.24602	−	0.587097i
$506$		0			0
$507$	−85.6548	−	85.6548i	−3.80406	−	3.80406i
$508$		0			0
$509$	−4.38366	+	14.9294i	−0.194303	+	0.661734i	0.803490	+	0.595319i	$0.202974\pi$
$509$	−4.38366	+	14.9294i	−0.194303	+	0.661734i	−0.997792	+	0.0664148i	$0.978844\pi$
$510$		0			0
$511$	−0.826442	−	1.28597i	−0.0365596	−	0.0568879i
$512$		0			0
$513$	−5.29509	+	3.96385i	−0.233784	+	0.175008i
$514$		0			0
$515$	5.13977	−	22.3408i	0.226485	−	0.984452i
$516$		0			0
$517$	8.86090	+	3.30494i	0.389702	+	0.145351i
$518$		0			0
$519$	13.3372	−	1.91760i	0.585439	−	0.0841734i
$520$		0			0
$521$	−6.24355	−	21.2636i	−0.273535	−	0.931575i	−0.975617	−	0.219479i	$-0.929564\pi$
$521$	−6.24355	−	21.2636i	−0.273535	−	0.931575i	0.702082	−	0.712096i	$-0.252254\pi$
$522$		0			0
$523$	−32.9241	+	2.35478i	−1.43967	+	0.102967i	−0.769218	−	0.638986i	$-0.779354\pi$
$523$	−32.9241	+	2.35478i	−1.43967	+	0.102967i	−0.670452	+	0.741953i	$0.733900\pi$
$524$		0			0
$525$	−7.53365	−	1.26728i	−0.328796	−	0.0553085i
$526$		0			0
$527$	10.1807	+	27.2954i	0.443477	+	1.18901i
$528$		0			0
$529$	−22.8775	−	2.37039i	−0.994675	−	0.103061i
$530$		0			0
$531$	−14.1422	+	30.9672i	−0.613721	+	1.34386i
$532$		0			0
$533$	−8.51680	−	0.609134i	−0.368904	−	0.0263845i
$534$		0			0
$535$	0.436692	−	1.12948i	0.0188798	−	0.0488319i
$536$		0			0
$537$	−7.14213	−	3.89990i	−0.308205	−	0.168293i
$538$		0			0
$539$	−1.62197	−	11.2810i	−0.0698631	−	0.485908i
$540$		0			0
$541$	4.43053	+	9.70151i	0.190483	+	0.417100i	0.980644	−	0.195800i	$-0.0627302\pi$
$541$	4.43053	+	9.70151i	0.190483	+	0.417100i	−0.790161	+	0.612900i	$0.790003\pi$
$542$		0			0
$543$	−14.9930	−	68.9217i	−0.643411	−	2.95771i
$544$		0			0
$545$	−2.26243	+	3.42976i	−0.0969118	+	0.146915i
$546$		0			0
$547$	16.9673	+	3.69102i	0.725471	+	0.157817i	0.560112	−	0.828417i	$-0.310758\pi$
$547$	16.9673	+	3.69102i	0.725471	+	0.157817i	0.165359	+	0.986233i	$0.447122\pi$
$548$		0			0
$549$	56.1202	+	16.4784i	2.39515	+	0.703280i
$550$		0			0
$551$		−	1.36465i		−	0.0581360i
$552$		0			0
$553$	−4.18180	+	4.18180i	−0.177828	+	0.177828i
$554$		0			0
$555$	17.8277	−	20.0851i	0.756744	−	0.852565i
$556$		0			0
$557$	−4.08098	+	18.7600i	−0.172917	+	0.794885i	0.806209	+	0.591630i	$0.201516\pi$
$557$	−4.08098	+	18.7600i	−0.172917	+	0.794885i	−0.979126	+	0.203255i	$0.934848\pi$
$558$		0			0
$559$	−5.61192	+	39.0317i	−0.237359	+	1.65087i
$560$		0			0
$561$	25.8233	+	16.5956i	1.09026	+	0.700667i
$562$		0			0
$563$	12.0415	−	32.2846i	0.507489	−	1.36063i	−0.390495	−	0.920605i	$-0.627696\pi$
$563$	12.0415	−	32.2846i	0.507489	−	1.36063i	0.897985	−	0.440027i	$-0.145031\pi$
$564$		0			0
$565$	−5.23028	+	2.77548i	−0.220040	+	0.116766i
$566$		0			0
$567$	6.60701	−	12.0998i	0.277468	−	0.508145i
$568$		0			0
$569$	6.01483	−	6.94148i	0.252155	−	0.291002i	−0.615534	−	0.788111i	$-0.711059\pi$
$569$	6.01483	−	6.94148i	0.252155	−	0.291002i	0.867688	+	0.497109i	$0.165605\pi$
$570$		0			0
$571$	22.6676	−	19.6416i	0.948608	−	0.821974i	−0.0355314	−	0.999369i	$-0.511312\pi$
$571$	22.6676	−	19.6416i	0.948608	−	0.821974i	0.984140	+	0.177395i	$0.0567669\pi$
$572$		0			0
$573$	32.7437	−	12.2128i	1.36789	−	0.510196i
$574$		0			0
$575$	5.00155	+	23.4517i	0.208579	+	0.978006i
$576$		0			0
$577$	−15.0896	+	5.62813i	−0.628188	+	0.234302i	−0.643337	−	0.765583i	$-0.722451\pi$
$577$	−15.0896	+	5.62813i	−0.628188	+	0.234302i	0.0151488	+	0.999885i	$0.495178\pi$
$578$		0			0
$579$	43.9015	−	38.0409i	1.82448	−	1.58092i
$580$		0			0
$581$	−1.23399	+	1.42410i	−0.0511944	+	0.0590815i
$582$		0			0
$583$	−9.79735	+	17.9425i	−0.405765	+	0.743103i
$584$		0			0
$585$	−110.079	+	58.4140i	−4.55120	+	2.41512i
$586$		0			0
$587$	1.05036	−	2.81612i	0.0433529	−	0.116234i	−0.913469	−	0.406908i	$-0.866607\pi$
$587$	1.05036	−	2.81612i	0.0433529	−	0.116234i	0.956822	+	0.290674i	$0.0938797\pi$
$588$		0			0
$589$	−1.80749	−	1.16160i	−0.0744762	−	0.0478630i
$590$		0			0
$591$	−1.70172	+	11.8357i	−0.0699994	+	0.486856i
$592$		0			0
$593$	−2.42121	+	11.1301i	−0.0994274	+	0.457060i	0.900334	+	0.435200i	$0.143322\pi$
$593$	−2.42121	+	11.1301i	−0.0994274	+	0.457060i	−0.999761	+	0.0218599i	$0.993041\pi$
$594$		0			0
$595$	−3.80046	+	4.28169i	−0.155804	+	0.175532i
$596$		0			0
$597$	−33.6299	+	33.6299i	−1.37638	+	1.37638i
$598$		0			0
$599$		−	16.2052i		−	0.662128i	−0.943608	−	0.331064i	$-0.892592\pi$
$599$		−	16.2052i		−	0.662128i	0.943608	−	0.331064i	$-0.107408\pi$
$600$		0			0
$601$	15.8031	+	4.64021i	0.644623	+	0.189278i	0.587673	−	0.809099i	$-0.300044\pi$
$601$	15.8031	+	4.64021i	0.644623	+	0.189278i	0.0569499	+	0.998377i	$0.481862\pi$
$602$		0			0
$603$	−30.8981	−	6.72147i	−1.25827	−	0.273719i
$604$		0			0
$605$	10.0708	−	15.2670i	0.409437	−	0.620692i
$606$		0			0
$607$	2.12376	+	9.76277i	0.0862008	+	0.396259i	0.999950	−	0.0100205i	$-0.00318966\pi$
$607$	2.12376	+	9.76277i	0.0862008	+	0.396259i	−0.913749	+	0.406279i	$0.866826\pi$
$608$		0			0
$609$	2.12213	+	4.64681i	0.0859929	+	0.188298i
$610$		0			0
$611$	5.64829	+	39.2847i	0.228505	+	1.58929i
$612$		0			0
$613$	8.32878	+	4.54786i	0.336396	+	0.183686i	0.638564	−	0.769568i	$-0.279529\pi$
$613$	8.32878	+	4.54786i	0.336396	+	0.183686i	−0.302168	+	0.953255i	$0.597710\pi$
$614$		0			0
$615$	−3.22611	+	8.34419i	−0.130089	+	0.336470i
$616$		0			0
$617$	32.6728	+	2.33681i	1.31536	+	0.0940763i	0.711314	−	0.702874i	$-0.248100\pi$
$617$	32.6728	+	2.33681i	1.31536	+	0.0940763i	0.604045	+	0.796950i	$0.293555\pi$
$618$		0			0
$619$	13.9654	−	30.5800i	0.561318	−	1.22912i	−0.389974	−	0.920826i	$-0.627516\pi$
$619$	13.9654	−	30.5800i	0.561318	−	1.22912i	0.951292	−	0.308290i	$-0.0997567\pi$
$620$		0			0
$621$	−77.1315	−	9.53701i	−3.09518	−	0.382707i
$622$		0			0
$623$	2.00721	+	5.38155i	0.0804173	+	0.215607i
$624$		0			0
$625$	21.6520	−	12.4976i	0.866081	−	0.499903i
$626$		0			0
$627$	−2.25814	+	0.161505i	−0.0901814	+	0.00644990i
$628$		0			0
$629$	−5.67012	−	19.3107i	−0.226082	−	0.769966i
$630$		0			0
$631$	20.8438	−	2.99689i	0.829780	−	0.119304i	0.285680	−	0.958325i	$-0.407780\pi$
$631$	20.8438	−	2.99689i	0.829780	−	0.119304i	0.544100	+	0.839021i	$0.316871\pi$
$632$		0			0
$633$	36.1100	+	13.4683i	1.43524	+	0.535318i
$634$		0			0
$635$	−4.88372	+	21.2278i	−0.193805	+	0.842401i
$636$		0			0
$637$	38.2896	−	28.6632i	1.51709	−	1.13568i
$638$		0			0
$639$	−47.0890	−	73.2720i	−1.86281	−	2.89860i
$640$		0			0
$641$	0.357796	−	1.21854i	0.0141321	−	0.0481295i	−0.952125	−	0.305709i	$-0.901107\pi$
$641$	0.357796	−	1.21854i	0.0141321	−	0.0481295i	0.966257	+	0.257579i	$0.0829248\pi$
$642$		0			0
$643$	−12.8113	−	12.8113i	−0.505229	−	0.505229i	0.407830	−	0.913058i	$-0.366286\pi$
$643$	−12.8113	−	12.8113i	−0.505229	−	0.505229i	−0.913058	+	0.407830i	$0.866286\pi$
$644$		0			0
$645$	37.3744	+	17.6101i	1.47162	+	0.693396i
$646$		0			0
$647$	−9.51355	−	17.4228i	−0.374016	−	0.684960i	0.621093	−	0.783737i	$-0.286689\pi$
$647$	−9.51355	−	17.4228i	−0.374016	−	0.684960i	−0.995110	+	0.0987769i	$0.968507\pi$
$648$		0			0
$649$	−6.08324	+	3.90946i	−0.238788	+	0.153460i
$650$		0			0
$651$	7.96110	+	1.14463i	0.312020	+	0.0448617i
$652$		0			0
$653$	16.1892	−	3.52174i	0.633532	−	0.137817i	0.115680	−	0.993287i	$-0.463095\pi$
$653$	16.1892	−	3.52174i	0.633532	−	0.137817i	0.517852	+	0.855470i	$0.326732\pi$
$654$		0			0
$655$	0.00867959	−	0.727641i	0.000339140	−	0.0284313i
$656$		0			0
$657$	−15.6566	+	20.9147i	−0.610822	+	0.815962i
$658$		0			0
$659$	−19.8916	+	5.84070i	−0.774866	+	0.227521i	−0.645177	−	0.764033i	$-0.723216\pi$
$659$	−19.8916	+	5.84070i	−0.774866	+	0.227521i	−0.129690	+	0.991555i	$0.541398\pi$
$660$		0			0
$661$	−7.02406	−	6.08639i	−0.273204	−	0.236733i	0.507472	−	0.861668i	$-0.330580\pi$
$661$	−7.02406	−	6.08639i	−0.273204	−	0.236733i	−0.780677	+	0.624935i	$0.785125\pi$
$662$		0			0
$663$	−9.19004	+	128.494i	−0.356912	+	4.99028i
$664$		0			0
$665$	0.0351432	−	0.420771i	0.00136280	−	0.0163168i
$666$		0			0
$667$	11.1117	−	11.5602i	0.430248	−	0.447612i
$668$		0			0
$669$	−78.7168	−	35.9487i	−3.04337	−	1.38986i
$670$		0			0
$671$	8.13576	+	9.38917i	0.314077	+	0.362465i
$672$		0			0
$673$	1.35894	+	19.0005i	0.0523834	+	0.732416i	0.953986	+	0.299851i	$0.0969370\pi$
$673$	1.35894	+	19.0005i	0.0523834	+	0.732416i	−0.901603	+	0.432565i	$0.857608\pi$
$674$		0			0
$675$	15.3301	+	79.5641i	0.590057	+	3.06242i
$676$		0			0
$677$	−12.5147	−	9.36836i	−0.480977	−	0.360055i	0.331109	−	0.943593i	$-0.392577\pi$
$677$	−12.5147	−	9.36836i	−0.480977	−	0.360055i	−0.812086	+	0.583537i	$0.801668\pi$
$678$		0			0
$679$	−7.32132	+	3.34354i	−0.280967	+	0.128313i
$680$		0			0
$681$	35.9706	−	55.9713i	1.37839	−	2.14482i
$682$		0			0
$683$	−19.8992	−	26.5822i	−0.761420	−	1.01714i	−0.998953	−	0.0457589i	$-0.985429\pi$
$683$	−19.8992	−	26.5822i	−0.761420	−	1.01714i	0.237532	−	0.971380i	$-0.423662\pi$
$684$		0			0
$685$	−0.578890	+	0.754381i	−0.0221183	+	0.0288234i
$686$		0			0
$687$	−8.70315	+	4.75228i	−0.332046	+	0.181311i
$688$		0			0
$689$	−85.7932			−3.26846
$690$		0			0
$691$	8.81520			0.335346			0.167673	−	0.985843i	$-0.446375\pi$
$691$	8.81520			0.335346			0.167673	+	0.985843i	$0.446375\pi$
$692$		0			0
$693$	5.39222	−	2.94438i	0.204834	−	0.111848i
$694$		0			0
$695$	−3.95131	−	30.0196i	−0.149882	−	1.13871i
$696$		0			0
$697$	4.01772	+	5.36704i	0.152182	+	0.203291i
$698$		0			0
$699$	−36.9523	+	57.4989i	−1.39766	+	2.17481i
$700$		0			0
$701$	−6.58573	+	3.00760i	−0.248739	+	0.113596i	−0.535884	−	0.844292i	$-0.680021\pi$
$701$	−6.58573	+	3.00760i	−0.248739	+	0.113596i	0.287144	+	0.957887i	$0.407294\pi$
$702$		0			0
$703$	1.18827	+	0.889524i	0.0448163	+	0.0335490i
$704$		0			0
$705$	41.0864	+	6.40842i	1.54740	+	0.241355i
$706$		0			0
$707$	0.456870	+	6.38788i	0.0171824	+	0.240241i
$708$		0			0
$709$	25.8366	+	29.8170i	0.970313	+	1.11980i	0.992767	+	0.120053i	$0.0383066\pi$
$709$	25.8366	+	29.8170i	0.970313	+	1.11980i	−0.0224540	+	0.999748i	$0.507148\pi$
$710$		0			0
$711$	91.9410	+	41.9881i	3.44806	+	1.57468i
$712$		0			0
$713$	−5.85315	−	24.5577i	−0.219202	−	0.919693i
$714$		0			0
$715$	−26.3780	−	2.20312i	−0.986480	−	0.0823919i
$716$		0			0
$717$	−4.06994	+	56.9051i	−0.151995	+	2.12516i
$718$		0			0
$719$	1.54995	+	1.34304i	0.0578032	+	0.0500868i	0.683283	−	0.730153i	$-0.260551\pi$
$719$	1.54995	+	1.34304i	0.0578032	+	0.0500868i	−0.625480	+	0.780240i	$0.715097\pi$
$720$		0			0
$721$	−4.55091	+	1.33627i	−0.169485	+	0.0497652i
$722$		0			0
$723$	−16.8900	+	22.5624i	−0.628147	+	0.839107i
$724$		0			0
$725$	−15.0365	−	7.30534i	−0.558443	−	0.271314i
$726$		0			0
$727$	−35.2315	+	7.66413i	−1.30666	+	0.284247i	−0.811397	−	0.584495i	$-0.801293\pi$
$727$	−35.2315	+	7.66413i	−1.30666	+	0.284247i	−0.495265	+	0.868742i	$0.664929\pi$
$728$		0			0
$729$	−74.2951	−	10.6820i	−2.75167	−	0.395631i
$730$		0			0
$731$	26.0468	−	16.7393i	0.963376	−	0.619124i
$732$		0			0
$733$	−12.3672	−	22.6488i	−0.456792	−	0.836553i	0.543203	−	0.839601i	$-0.317211\pi$
$733$	−12.3672	−	22.6488i	−0.456792	−	0.836553i	−0.999995	+	0.00304868i	$0.999030\pi$
$734$		0			0
$735$	−16.9513	−	47.1587i	−0.625259	−	1.73947i
$736$		0			0
$737$	−4.74929	−	4.74929i	−0.174942	−	0.174942i
$738$		0			0
$739$	−6.61217	+	22.5190i	−0.243233	+	0.828375i	0.743875	+	0.668319i	$0.232986\pi$
$739$	−6.61217	+	22.5190i	−0.243233	+	0.828375i	−0.987108	+	0.160056i	$0.948832\pi$
$740$		0			0
$741$	−5.13656	−	7.99265i	−0.188696	−	0.293617i
$742$		0			0
$743$	24.5162	−	18.3526i	0.899412	−	0.673292i	−0.0460795	−	0.998938i	$-0.514673\pi$
$743$	24.5162	−	18.3526i	0.899412	−	0.673292i	0.945492	+	0.325646i	$0.105582\pi$
$744$		0			0
$745$	−0.234087	−	0.373980i	−0.00857627	−	0.0137016i
$746$		0			0
$747$	30.1747	+	11.2546i	1.10403	+	0.411784i
$748$		0			0
$749$	−0.247997	+	0.0356566i	−0.00906162	+	0.00130286i
$750$		0			0
$751$	−10.1918	−	34.7101i	−0.371905	−	1.26659i	−0.906760	−	0.421647i	$-0.861452\pi$
$751$	−10.1918	−	34.7101i	−0.371905	−	1.26659i	0.534855	−	0.844944i	$-0.320366\pi$
$752$		0			0
$753$	52.6125	−	3.76292i	1.91731	−	0.137129i
$754$		0			0
$755$	8.65950	+	30.8480i	0.315151	+	1.12267i
$756$		0			0
$757$	−11.1414	−	29.8711i	−0.404940	−	1.08569i	−0.966143	−	0.258007i	$-0.916934\pi$
$757$	−11.1414	−	29.8711i	−0.404940	−	1.08569i	0.561203	−	0.827678i	$-0.310339\pi$
$758$		0			0
$759$	−20.4442	−	17.0189i	−0.742076	−	0.617746i
$760$		0			0
$761$	0.0561323	−	0.122913i	0.00203479	−	0.00445558i	−0.908612	−	0.417642i	$-0.862857\pi$
$761$	0.0561323	−	0.122913i	0.00203479	−	0.00445558i	0.910647	+	0.413186i	$0.135584\pi$
$762$		0			0
$763$	0.847930	+	0.0606452i	0.0306971	+	0.00219550i
$764$		0			0
$765$	91.2630	+	35.2850i	3.29962	+	1.27573i
$766$		0			0
$767$	−26.6348	−	14.5437i	−0.961726	−	0.525142i
$768$		0			0
$769$	−6.30778	−	43.8716i	−0.227464	−	1.58205i	−0.708733	−	0.705476i	$-0.750733\pi$
$769$	−6.30778	−	43.8716i	−0.227464	−	1.58205i	0.481269	−	0.876573i	$-0.340176\pi$
$770$		0			0
$771$	−21.6146	−	47.3295i	−0.778432	−	1.70453i
$772$		0			0
$773$	−2.06653	−	9.49970i	−0.0743281	−	0.341681i	0.924932	−	0.380132i	$-0.124121\pi$
$773$	−2.06653	−	9.49970i	−0.0743281	−	0.341681i	−0.999260	+	0.0384510i	$0.987758\pi$
$774$		0			0
$775$	−22.4752	+	13.6976i	−0.807333	+	0.492034i
$776$		0			0
$777$	−5.42947	−	1.18111i	−0.194781	−	0.0423721i
$778$		0			0
$779$	−0.474425	−	0.139304i	−0.0169980	−	0.00499107i
$780$		0			0
$781$		−	18.5005i		−	0.661999i
$782$		0			0
$783$	38.3126	−	38.3126i	1.36918	−	1.36918i
$784$		0			0
$785$	−33.0910	+	1.97031i	−1.18107	+	0.0703234i
$786$		0			0
$787$	−3.98499	+	18.3187i	−0.142050	+	0.652991i	0.849962	+	0.526844i	$0.176625\pi$
$787$	−3.98499	+	18.3187i	−0.142050	+	0.652991i	−0.992012	+	0.126147i	$0.959739\pi$
$788$		0			0
$789$	4.88503	−	33.9761i	0.173912	−	1.20958i
$790$		0			0
$791$	1.03059	+	0.662320i	0.0366436	+	0.0235494i
$792$		0			0
$793$	−18.2204	+	48.8507i	−0.647024	+	1.73474i
$794$		0			0
$795$	−26.3514	+	85.9391i	−0.934588	+	3.04795i
$796$		0			0
$797$	11.8989	−	21.7912i	0.421481	−	0.771884i	−0.577529	−	0.816370i	$-0.695983\pi$
$797$	11.8989	−	21.7912i	0.421481	−	0.771884i	0.999010	+	0.0444856i	$0.0141649\pi$
$798$		0			0
$799$	20.4072	−	23.5511i	0.721953	−	0.833178i
$800$		0			0
$801$	74.1881	−	64.2843i	2.62131	−	2.27138i
$802$		0			0
$803$	−5.19944	+	1.93929i	−0.183484	+	0.0684361i
$804$		0			0
$805$	3.72385	−	3.27827i	0.131249	−	0.115544i
$806$		0			0
$807$	44.2000	−	16.4857i	1.55591	−	0.580325i
$808$		0			0
$809$	−32.0821	+	27.7993i	−1.12795	+	0.977373i	−0.999896	−	0.0143950i	$-0.995418\pi$
$809$	−32.0821	+	27.7993i	−1.12795	+	0.977373i	−0.128052	+	0.991768i	$0.540872\pi$
$810$		0			0
$811$	25.3838	−	29.2945i	0.891347	−	1.02867i	−0.108056	−	0.994145i	$-0.534463\pi$
$811$	25.3838	−	29.2945i	0.891347	−	1.02867i	0.999404	−	0.0345250i	$-0.0109918\pi$
$812$		0			0
$813$	−6.30532	+	11.5473i	−0.221137	+	0.404982i
$814$		0			0
$815$	15.1482	+	28.5462i	0.530620	+	0.999930i
$816$		0			0
$817$	−0.798004	+	2.13953i	−0.0279186	+	0.0748527i
$818$		0			0
$819$	21.6902	+	13.9395i	0.757918	+	0.487085i
$820$		0			0
$821$	4.10869	−	28.5766i	0.143394	−	0.997329i	−0.783335	−	0.621599i	$-0.786483\pi$
$821$	4.10869	−	28.5766i	0.143394	−	0.997329i	0.926730	−	0.375729i	$-0.122608\pi$
$822$		0			0
$823$	−9.23296	+	42.4433i	−0.321841	+	1.47948i	0.477516	+	0.878623i	$0.341537\pi$
$823$	−9.23296	+	42.4433i	−0.321841	+	1.47948i	−0.799357	+	0.600856i	$0.794827\pi$
$824$		0			0
$825$	−10.3089	+	25.7461i	−0.358909	+	0.896366i
$826$		0			0
$827$	−17.4874	+	17.4874i	−0.608095	+	0.608095i	−0.942448	−	0.334353i	$-0.891482\pi$
$827$	−17.4874	+	17.4874i	−0.608095	+	0.608095i	0.334353	+	0.942448i	$0.391482\pi$
$828$		0			0
$829$		−	5.11731i		−	0.177731i	−0.996044	−	0.0888657i	$-0.971676\pi$
$829$		−	5.11731i		−	0.177731i	0.996044	−	0.0888657i	$-0.0283242\pi$
$830$		0			0
$831$	−32.0209	−	9.40218i	−1.11079	−	0.326158i
$832$		0			0
$833$	−36.6964	−	7.98282i	−1.27146	−	0.276588i
$834$		0			0
$835$	20.9361	−	4.29348i	0.724522	−	0.148582i
$836$		0			0
$837$	−18.1333	−	83.3573i	−0.626778	−	2.88125i
$838$		0			0
$839$	18.2019	+	39.8567i	0.628401	+	1.37601i	0.909248	+	0.416254i	$0.136657\pi$
$839$	18.2019	+	39.8567i	0.628401	+	1.37601i	−0.280847	+	0.959752i	$0.590615\pi$
$840$		0			0
$841$	−2.53625	−	17.6400i	−0.0874567	−	0.608275i
$842$		0			0
$843$	−78.0679	−	42.6283i	−2.68880	−	1.46820i
$844$		0			0
$845$	−33.1785	−	75.0057i	−1.14138	−	2.58028i
$846$		0			0
$847$	−3.77442	−	0.269952i	−0.129691	−	0.00927566i
$848$		0			0
$849$	19.8874	−	43.5473i	0.682533	−	1.49454i
$850$		0			0
$851$	2.82301	+	17.2108i	0.0967716	+	0.589980i
$852$		0			0
$853$	−6.89012	−	18.4731i	−0.235913	−	0.632508i	0.764006	−	0.645209i	$-0.223230\pi$
$853$	−6.89012	−	18.4731i	−0.235913	−	0.632508i	−0.999919	+	0.0127012i	$0.995957\pi$
$854$		0			0
$855$	−6.94784	+	1.95036i	−0.237611	+	0.0667010i
$856$		0			0
$857$	31.1811	−	2.23011i	1.06512	−	0.0761792i	0.472243	−	0.881469i	$-0.343445\pi$
$857$	31.1811	−	2.23011i	1.06512	−	0.0761792i	0.592882	+	0.805289i	$0.297990\pi$
$858$		0			0
$859$	1.38318	+	4.71066i	0.0471933	+	0.160726i	0.979718	−	0.200380i	$-0.0642176\pi$
$859$	1.38318	+	4.71066i	0.0471933	+	0.160726i	−0.932525	+	0.361106i	$0.882399\pi$
$860$		0			0
$861$	1.83211	−	0.263417i	0.0624380	−	0.00897723i
$862$		0			0
$863$	−42.2704	−	15.7660i	−1.43890	−	0.536682i	−0.495579	−	0.868563i	$-0.665044\pi$
$863$	−42.2704	−	15.7660i	−1.43890	−	0.536682i	−0.943321	+	0.331881i	$0.892317\pi$
$864$		0			0
$865$	8.89083	+	2.04544i	0.302297	+	0.0695471i
$866$		0			0
$867$	36.0276	−	26.9700i	1.22356	−	0.915948i
$868$		0			0
$869$	11.6071	+	18.0610i	0.393744	+	0.612678i
$870$		0			0
$871$	7.94119	−	27.0452i	0.269077	−	0.916392i
$872$		0			0
$873$	97.2689	+	97.2689i	3.29205	+	3.29205i
$874$		0			0
$875$	−4.44818	−	2.63973i	−0.150376	−	0.0892392i
$876$		0			0
$877$	−9.42341	−	17.2577i	−0.318206	−	0.582751i	0.668798	−	0.743444i	$-0.266809\pi$
$877$	−9.42341	−	17.2577i	−0.318206	−	0.582751i	−0.987004	+	0.160693i	$0.948627\pi$
$878$		0			0
$879$	21.2199	−	13.6372i	0.715728	−	0.459970i
$880$		0			0
$881$	−12.4402	−	1.78863i	−0.419121	−	0.0602604i	−0.0704715	−	0.997514i	$-0.522450\pi$
$881$	−12.4402	−	1.78863i	−0.419121	−	0.0602604i	−0.348649	+	0.937253i	$0.613359\pi$
$882$		0			0
$883$	54.6432	−	11.8869i	1.83889	−	0.400026i	0.847481	−	0.530826i	$-0.178118\pi$
$883$	54.6432	−	11.8869i	1.83889	−	0.400026i	0.991409	+	0.130800i	$0.0417545\pi$
$884$		0			0
$885$	−22.7493	+	22.2130i	−0.764709	+	0.746681i
$886$		0			0
$887$	33.3122	−	44.4999i	1.11852	−	1.49416i	0.271618	−	0.962405i	$-0.412441\pi$
$887$	33.3122	−	44.4999i	1.11852	−	1.49416i	0.846897	−	0.531757i	$-0.178468\pi$
$888$		0			0
$889$	4.32420	−	1.26970i	0.145029	−	0.0425843i
$890$		0			0
$891$	−37.8232	−	32.7740i	−1.26713	−	1.09797i
$892$		0			0
$893$	−0.163959	+	2.29245i	−0.00548669	+	0.0767139i
$894$		0			0
$895$	−3.55814	−	4.20667i	−0.118936	−	0.140613i
$896$		0			0
$897$	21.5678	−	109.532i	0.720128	−	3.65716i
$898$		0			0
$899$	16.0096	+	7.31136i	0.533951	+	0.243847i
$900$		0			0
$901$	44.1132	+	50.9093i	1.46962	+	1.69604i
$902$		0			0
$903$	−0.609815	−	8.52633i	−0.0202934	−	0.283739i
$904$		0			0
$905$	7.35974	−	47.1856i	0.244646	−	1.56850i
$906$		0			0
$907$	−13.9616	−	10.4515i	−0.463587	−	0.347037i	0.341813	−	0.939768i	$-0.388959\pi$
$907$	−13.9616	−	10.4515i	−0.463587	−	0.347037i	−0.805401	+	0.592731i	$0.798050\pi$
$908$		0			0
$909$	99.5625	−	45.4687i	3.30228	−	1.50810i
$910$		0			0
$911$	8.95227	−	13.9300i	0.296602	−	0.461522i	−0.660684	−	0.750664i	$-0.729734\pi$
$911$	8.95227	−	13.9300i	0.296602	−	0.461522i	0.957286	+	0.289142i	$0.0933701\pi$
$912$		0			0
$913$	4.09946	+	5.47624i	0.135672	+	0.181237i
$914$		0			0
$915$	43.3374	+	33.2559i	1.43269	+	1.09941i
$916$		0			0
$917$	−0.132142	+	0.0721552i	−0.00436373	+	0.00238277i
$918$		0			0
$919$	22.4074			0.739151			0.369576	−	0.929201i	$-0.379503\pi$
$919$	22.4074			0.739151			0.369576	+	0.929201i	$0.379503\pi$
$920$		0			0
$921$	100.706			3.31836
$922$		0			0
$923$	68.1434	−	37.2091i	2.24297	−	1.22475i
$924$		0			0
$925$	16.1624	−	8.33117i	0.531417	−	0.273927i
$926$		0			0
$927$	48.5791	+	64.8941i	1.59555	+	2.13140i
$928$		0			0
$929$	14.4349	−	22.4612i	0.473595	−	0.736929i	−0.519471	−	0.854488i	$-0.673871\pi$
$929$	14.4349	−	22.4612i	0.473595	−	0.736929i	0.993066	+	0.117560i	$0.0375072\pi$
$930$		0			0
$931$	2.51944	−	1.15059i	0.0825713	−	0.0377091i
$932$		0			0
$933$	−12.6805	−	9.49247i	−0.415139	−	0.310769i
$934$		0			0
$935$	12.2557	+	16.7854i	0.400805	+	0.548941i
$936$		0			0
$937$	−0.630782	−	8.81948i	−0.0206067	−	0.288120i	−0.997298	−	0.0734687i	$-0.976593\pi$
$937$	−0.630782	−	8.81948i	−0.0206067	−	0.288120i	0.976691	−	0.214651i	$-0.0688615\pi$
$938$		0			0
$939$	−35.0103	−	40.4041i	−1.14252	−	1.31854i
$940$		0			0
$941$	−11.1980	−	5.11397i	−0.365046	−	0.166711i	0.224443	−	0.974487i	$-0.427944\pi$
$941$	−11.1980	−	5.11397i	−0.365046	−	0.166711i	−0.589489	+	0.807776i	$0.700671\pi$
$942$		0			0
$943$	−2.88465	−	5.04310i	−0.0939371	−	0.164226i
$944$		0			0
$945$	12.7998	−	10.8265i	0.416378	−	0.352187i
$946$		0			0
$947$	−0.124143	+	1.73575i	−0.00403411	+	0.0564043i	−0.999070	−	0.0431085i	$-0.986274\pi$
$947$	−0.124143	+	1.73575i	−0.00403411	+	0.0564043i	0.995036	+	0.0995128i	$0.0317284\pi$
$948$		0			0
$949$	−17.6005	−	15.2509i	−0.571335	−	0.495064i
$950$		0			0
$951$	34.2766	−	10.0645i	1.11149	−	0.326364i
$952$		0			0
$953$	−6.68032	+	8.92387i	−0.216397	+	0.289072i	−0.895584	−	0.444893i	$-0.853242\pi$
$953$	−6.68032	+	8.92387i	−0.216397	+	0.289072i	0.679187	+	0.733965i	$0.262333\pi$
$954$		0			0
$955$	23.6600	+	0.282225i	0.765618	+	0.00913260i
$956$		0			0
$957$	18.1212	−	3.94202i	0.585774	−	0.127427i
$958$		0			0
$959$	0.194737	+	0.0279990i	0.00628839	+	0.000904133i
$960$		0			0
$961$	−2.76738	+	1.77849i	−0.0892703	+	0.0573705i
$962$		0			0
$963$	2.05218	+	3.75829i	0.0661307	+	0.121109i
$964$		0			0
$965$	37.0125	−	13.3043i	1.19147	−	0.428279i
$966$		0			0
$967$	16.3626	+	16.3626i	0.526185	+	0.526185i	0.919433	−	0.393248i	$-0.128649\pi$
$967$	16.3626	+	16.3626i	0.526185	+	0.526185i	−0.393248	+	0.919433i	$0.628649\pi$
$968$		0			0
$969$	−2.10169	+	7.15768i	−0.0675159	+	0.229938i
$970$		0			0
$971$	−11.3645	−	17.6835i	−0.364704	−	0.567491i	0.609605	−	0.792705i	$-0.291328\pi$
$971$	−11.3645	−	17.6835i	−0.364704	−	0.567491i	−0.974309	+	0.225214i	$0.927692\pi$
$972$		0			0
$973$	−5.01507	+	3.75423i	−0.160776	+	0.120355i
$974$		0			0
$975$	−115.565	+	13.8110i	−3.70105	+	0.442306i
$976$		0			0
$977$	1.80691	+	0.673941i	0.0578081	+	0.0215613i	0.378202	−	0.925723i	$-0.376543\pi$
$977$	1.80691	+	0.673941i	0.0578081	+	0.0215613i	−0.320394	+	0.947284i	$0.603815\pi$
$978$		0			0
$979$	20.6388	−	2.96741i	0.659619	−	0.0948389i
$980$		0			0
$981$	−4.09327	−	13.9404i	−0.130688	−	0.445083i
$982$		0			0
$983$	−26.8295	+	1.91888i	−0.855728	+	0.0612029i	−0.492306	−	0.870422i	$-0.663846\pi$
$983$	−26.8295	+	1.91888i	−0.855728	+	0.0612029i	−0.363421	+	0.931625i	$0.618392\pi$
$984$		0			0
$985$	−3.96448	+	7.05892i	−0.126319	+	0.224916i
$986$		0			0
$987$	−3.00662	−	8.06106i	−0.0957018	−	0.256586i
$988$		0			0
$989$	−24.1813	+	11.6266i	−0.768920	+	0.369703i
$990$		0			0
$991$	−5.82973	+	12.7653i	−0.185187	+	0.405504i	−0.979342	−	0.202212i	$-0.935187\pi$
$991$	−5.82973	+	12.7653i	−0.185187	+	0.405504i	0.794154	+	0.607716i	$0.207914\pi$
$992$		0			0
$993$	−113.058	−	8.08608i	−3.58779	−	0.256604i
$994$		0			0
$995$	−29.4488	+	13.0266i	−0.933590	+	0.412970i
$996$		0			0
$997$	−19.7974	−	10.8102i	−0.626990	−	0.342362i	0.134140	−	0.990962i	$-0.457173\pi$
$997$	−19.7974	−	10.8102i	−0.626990	−	0.342362i	−0.761129	+	0.648600i	$0.775355\pi$
$998$		0			0
$999$	8.38717	+	58.3341i	0.265358	+	1.84561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.1	✓	720
5.3	odd	4	inner	920.2.bv.a.753.1	yes	720
23.19	odd	22	inner	920.2.bv.a.617.1	yes	720
115.88	even	44	inner	920.2.bv.a.433.1	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.1	✓	720	1.1	even	1	trivial
920.2.bv.a.433.1	yes	720	115.88	even	44	inner
920.2.bv.a.617.1	yes	720	23.19	odd	22	inner
920.2.bv.a.753.1	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.89859 + 1.58275i) q^{3} +(-2.21695 + 0.291804i) q^{5} +(0.277250 + 0.370363i) q^{7} +(4.27482 - 6.65174i) q^{9} +(1.52773 - 0.697690i) q^{11} +(5.64247 + 4.22390i) q^{13} +(5.96417 - 4.35469i) q^{15} +(-0.394803 - 5.52007i) q^{17} +(0.267286 + 0.308464i) q^{19} +(-1.38983 - 0.634712i) q^{21} +(-0.247460 + 4.78944i) q^{23} +(4.82970 - 1.29383i) q^{25} +(-1.15609 + 16.1642i) q^{27} +(-2.52681 - 2.18949i) q^{29} +(-5.05084 + 1.48306i) q^{31} +(-3.32399 + 4.44033i) q^{33} +(-0.722721 - 0.740171i) q^{35} +(3.55355 - 0.773028i) q^{37} +(-23.0406 - 3.31274i) q^{39} +(-1.01912 + 0.654949i) q^{41} +(2.68125 + 4.91033i) q^{43} +(-7.53603 + 15.9940i) q^{45} +(3.98168 + 3.98168i) q^{47} +(1.91183 - 6.51108i) q^{49} +(9.88127 + 15.3756i) q^{51} +(-9.74431 + 7.29450i) q^{53} +(-3.18330 + 1.99254i) q^{55} +(-1.26297 - 0.471065i) q^{57} +(-4.26171 + 0.612742i) q^{59} +(2.08404 + 7.09759i) q^{61} +(3.64875 - 0.260964i) q^{63} +(-13.7416 - 7.71767i) q^{65} +(-1.39754 - 3.74696i) q^{67} +(-6.86321 - 14.2743i) q^{69} +(4.57599 - 10.0200i) q^{71} +(-3.29574 - 0.235716i) q^{73} +(-11.9515 + 11.3945i) q^{75} +(0.681961 + 0.372379i) q^{77} +(1.81922 + 12.6530i) q^{79} +(-12.3789 - 27.1060i) q^{81} +(0.865786 + 3.97995i) q^{83} +(2.48603 + 12.1225i) q^{85} +(10.7896 + 2.34714i) q^{87} +(11.9121 + 3.49772i) q^{89} +3.26084i q^{91} +(12.2930 - 12.2930i) q^{93} +(-0.682569 - 0.605854i) q^{95} +(-3.69805 + 16.9997i) q^{97} +(1.88990 - 13.1445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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