LMFDB - Embedded newform 920.2.bv.a.17.7

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			17.7
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99325 + 1.08840i) q^{3} +(2.23196 + 0.135499i) q^{5} +(2.37528 + 3.17300i) q^{7} +(1.16653 - 1.81515i) q^{9} +(-4.87592 + 2.22676i) q^{11} +(2.78911 + 2.08790i) q^{13} +(-4.59634 + 2.15918i) q^{15} +(-0.208644 - 2.91722i) q^{17} +(3.34444 + 3.85969i) q^{19} +(-8.18803 - 3.73935i) q^{21} +(-1.73442 - 4.47122i) q^{23} +(4.96328 + 0.604856i) q^{25} +(0.136469 - 1.90809i) q^{27} +(2.80201 + 2.42796i) q^{29} +(2.59751 - 0.762699i) q^{31} +(7.29535 - 9.74544i) q^{33} +(4.87159 + 7.40386i) q^{35} +(-6.77945 + 1.47478i) q^{37} +(-7.83188 - 1.12605i) q^{39} +(-8.94334 + 5.74753i) q^{41} +(4.99899 + 9.15497i) q^{43} +(2.84959 - 3.89328i) q^{45} +(-6.44848 - 6.44848i) q^{47} +(-2.45386 + 8.35707i) q^{49} +(3.59098 + 5.58768i) q^{51} +(1.02005 - 0.763601i) q^{53} +(-11.1846 + 4.30935i) q^{55} +(-10.8672 - 4.05325i) q^{57} +(-6.16760 + 0.886766i) q^{59} +(-2.17763 - 7.41633i) q^{61} +(8.53030 - 0.610099i) q^{63} +(5.94227 + 5.03803i) q^{65} +(2.34825 + 6.29590i) q^{67} +(8.32360 + 7.02454i) q^{69} +(-5.70971 + 12.5025i) q^{71} +(-3.20239 - 0.229039i) q^{73} +(-10.5514 + 4.19640i) q^{75} +(-18.6472 - 10.1821i) q^{77} +(-0.287493 - 1.99956i) q^{79} +(4.49374 + 9.83991i) q^{81} +(-0.0821702 - 0.377730i) q^{83} +(-0.0704040 - 6.53939i) q^{85} +(-8.22770 - 1.78983i) q^{87} +(9.49169 + 2.78701i) q^{89} +13.8092i q^{91} +(-4.34738 + 4.34738i) q^{93} +(6.94166 + 9.06783i) q^{95} +(0.806253 - 3.70628i) q^{97} +(-1.64599 + 11.4481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.99325	+	1.08840i	−1.15081	+	0.628387i	−0.937289	−	0.348552i	$-0.886673\pi$
$3$	−1.99325	+	1.08840i	−1.15081	+	0.628387i	−0.213516	+	0.976940i	$0.568492\pi$
$4$		0			0
$5$	2.23196	+	0.135499i	0.998162	+	0.0605970i
$5$	2.23196	+	0.135499i	0.998162	+	0.0605970i
$6$		0			0
$7$	2.37528	+	3.17300i	0.897771	+	1.19928i	0.979260	+	0.202607i	$0.0649415\pi$
$7$	2.37528	+	3.17300i	0.897771	+	1.19928i	−0.0814891	+	0.996674i	$0.525968\pi$
$8$		0			0
$9$	1.16653	−	1.81515i	0.388842	−	0.605050i
$10$		0			0
$11$	−4.87592	+	2.22676i	−1.47015	+	0.671393i	−0.979772	−	0.200119i	$-0.935867\pi$
$11$	−4.87592	+	2.22676i	−1.47015	+	0.671393i	−0.490374	+	0.871512i	$0.663140\pi$
$12$		0			0
$13$	2.78911	+	2.08790i	0.773560	+	0.579080i	0.911471	−	0.411365i	$-0.134948\pi$
$13$	2.78911	+	2.08790i	0.773560	+	0.579080i	−0.137911	+	0.990445i	$0.544039\pi$
$14$		0			0
$15$	−4.59634	+	2.15918i	−1.18677	+	0.557497i
$16$		0			0
$17$	−0.208644	−	2.91722i	−0.0506036	−	0.707530i	−0.957912	−	0.287064i	$-0.907321\pi$
$17$	−0.208644	−	2.91722i	−0.0506036	−	0.707530i	0.907308	−	0.420467i	$-0.138134\pi$
$18$		0			0
$19$	3.34444	+	3.85969i	0.767267	+	0.885473i	0.996122	−	0.0879875i	$-0.0280436\pi$
$19$	3.34444	+	3.85969i	0.767267	+	0.885473i	−0.228855	+	0.973461i	$0.573498\pi$
$20$		0			0
$21$	−8.18803	−	3.73935i	−1.78677	−	0.815992i
$22$		0			0
$23$	−1.73442	−	4.47122i	−0.361651	−	0.932314i
$23$	−1.73442	−	4.47122i	−0.361651	−	0.932314i
$24$		0			0
$25$	4.96328	+	0.604856i	0.992656	+	0.120971i
$26$		0			0
$27$	0.136469	−	1.90809i	0.0262635	−	0.367212i
$28$		0			0
$29$	2.80201	+	2.42796i	0.520320	+	0.450860i	0.874997	−	0.484129i	$-0.160863\pi$
$29$	2.80201	+	2.42796i	0.520320	+	0.450860i	−0.354676	+	0.934989i	$0.615409\pi$
$30$		0			0
$31$	2.59751	−	0.762699i	0.466527	−	0.136985i	−0.0400165	−	0.999199i	$-0.512741\pi$
$31$	2.59751	−	0.762699i	0.466527	−	0.136985i	0.506544	+	0.862214i	$0.330923\pi$
$32$		0			0
$33$	7.29535	−	9.74544i	1.26996	−	1.69646i
$34$		0			0
$35$	4.87159	+	7.40386i	0.823448	+	1.25148i
$36$		0			0
$37$	−6.77945	+	1.47478i	−1.11453	+	0.242452i	−0.731876	−	0.681438i	$-0.761355\pi$
$37$	−6.77945	+	1.47478i	−1.11453	+	0.242452i	−0.382658	+	0.923890i	$0.624991\pi$
$38$		0			0
$39$	−7.83188	−	1.12605i	−1.25410	−	0.180313i
$40$		0			0
$41$	−8.94334	+	5.74753i	−1.39671	+	0.897614i	−0.999795	−	0.0202394i	$-0.993557\pi$
$41$	−8.94334	+	5.74753i	−1.39671	+	0.897614i	−0.396919	+	0.917853i	$0.629921\pi$
$42$		0			0
$43$	4.99899	+	9.15497i	0.762339	+	1.39612i	0.913178	+	0.407561i	$0.133621\pi$
$43$	4.99899	+	9.15497i	0.762339	+	1.39612i	−0.150839	+	0.988558i	$0.548198\pi$
$44$		0			0
$45$	2.84959	−	3.89328i	0.424792	−	0.580376i
$46$		0			0
$47$	−6.44848	−	6.44848i	−0.940608	−	0.940608i	0.0577249	−	0.998333i	$-0.481615\pi$
$47$	−6.44848	−	6.44848i	−0.940608	−	0.940608i	−0.998333	+	0.0577249i	$0.981615\pi$
$48$		0			0
$49$	−2.45386	+	8.35707i	−0.350551	+	1.19387i
$50$		0			0
$51$	3.59098	+	5.58768i	0.502838	+	0.782431i
$52$		0			0
$53$	1.02005	−	0.763601i	0.140115	−	0.104889i	−0.526921	−	0.849914i	$-0.676654\pi$
$53$	1.02005	−	0.763601i	0.140115	−	0.104889i	0.667036	+	0.745026i	$0.267563\pi$
$54$		0			0
$55$	−11.1846	+	4.30935i	−1.50813	+	0.581073i
$56$		0			0
$57$	−10.8672	−	4.05325i	−1.43940	−	0.536867i
$58$		0			0
$59$	−6.16760	+	0.886766i	−0.802952	+	0.115447i	−0.531559	−	0.847021i	$-0.678394\pi$
$59$	−6.16760	+	0.886766i	−0.802952	+	0.115447i	−0.271394	+	0.962468i	$0.587484\pi$
$60$		0			0
$61$	−2.17763	−	7.41633i	−0.278817	−	0.949564i	−0.973200	−	0.229959i	$-0.926141\pi$
$61$	−2.17763	−	7.41633i	−0.278817	−	0.949564i	0.694383	−	0.719605i	$-0.255677\pi$
$62$		0			0
$63$	8.53030	−	0.610099i	1.07472	−	0.0768653i
$64$		0			0
$65$	5.94227	+	5.03803i	0.737048	+	0.624891i
$66$		0			0
$67$	2.34825	+	6.29590i	0.286885	+	0.769167i	0.997825	+	0.0659152i	$0.0209967\pi$
$67$	2.34825	+	6.29590i	0.286885	+	0.769167i	−0.710941	+	0.703252i	$0.751731\pi$
$68$		0			0
$69$	8.32360	+	7.02454i	1.00204	+	0.845655i
$70$		0			0
$71$	−5.70971	+	12.5025i	−0.677618	+	1.48378i	0.187529	+	0.982259i	$0.439952\pi$
$71$	−5.70971	+	12.5025i	−0.677618	+	1.48378i	−0.865147	+	0.501518i	$0.832775\pi$
$72$		0			0
$73$	−3.20239	−	0.229039i	−0.374811	−	0.0268070i	−0.117337	−	0.993092i	$-0.537436\pi$
$73$	−3.20239	−	0.229039i	−0.374811	−	0.0268070i	−0.257474	+	0.966285i	$0.582890\pi$
$74$		0			0
$75$	−10.5514	+	4.19640i	−1.21837	+	0.484558i
$76$		0			0
$77$	−18.6472	−	10.1821i	−2.12504	−	1.16036i
$78$		0			0
$79$	−0.287493	−	1.99956i	−0.0323455	−	0.224968i	0.967237	−	0.253877i	$-0.0817058\pi$
$79$	−0.287493	−	1.99956i	−0.0323455	−	0.224968i	−0.999582	+	0.0289090i	$0.990797\pi$
$80$		0			0
$81$	4.49374	+	9.83991i	0.499304	+	1.09332i
$82$		0			0
$83$	−0.0821702	−	0.377730i	−0.00901935	−	0.0414613i	0.972417	−	0.233248i	$-0.0749354\pi$
$83$	−0.0821702	−	0.377730i	−0.00901935	−	0.0414613i	−0.981437	+	0.191787i	$0.938572\pi$
$84$		0			0
$85$	−0.0704040	−	6.53939i	−0.00763638	−	0.709296i
$86$		0			0
$87$	−8.22770	−	1.78983i	−0.882102	−	0.191890i
$88$		0			0
$89$	9.49169	+	2.78701i	1.00612	+	0.295423i	0.742964	−	0.669331i	$-0.233419\pi$
$89$	9.49169	+	2.78701i	1.00612	+	0.295423i	0.263153	+	0.964754i	$0.415238\pi$
$90$		0			0
$91$			13.8092i			1.44760i
$92$		0			0
$93$	−4.34738	+	4.34738i	−0.450803	+	0.450803i
$94$		0			0
$95$	6.94166	+	9.06783i	0.712200	+	0.930340i
$96$		0			0
$97$	0.806253	−	3.70628i	0.0818626	−	0.376316i	−0.917929	−	0.396745i	$-0.870140\pi$
$97$	0.806253	−	3.70628i	0.0818626	−	0.376316i	0.999791	+	0.0204292i	$0.00650326\pi$
$98$		0			0
$99$	−1.64599	+	11.4481i	−0.165428	+	1.15058i
$100$		0			0
$101$	8.65562	+	5.56263i	0.861266	+	0.553502i	0.895070	−	0.445926i	$-0.147126\pi$
$101$	8.65562	+	5.56263i	0.861266	+	0.553502i	−0.0338036	+	0.999428i	$0.510762\pi$
$102$		0			0
$103$	1.10515	−	2.96303i	0.108894	−	0.291956i	−0.871061	−	0.491175i	$-0.836568\pi$
$103$	1.10515	−	2.96303i	0.108894	−	0.291956i	0.979955	+	0.199219i	$0.0638404\pi$
$104$		0			0
$105$	−17.7687	−	9.45553i	−1.73404	−	0.922766i
$106$		0			0
$107$	1.70015	−	3.11360i	0.164360	−	0.301003i	−0.782499	−	0.622652i	$-0.786055\pi$
$107$	1.70015	−	3.11360i	0.164360	−	0.301003i	0.946859	+	0.321649i	$0.104237\pi$
$108$		0			0
$109$	−3.67699	+	4.24347i	−0.352192	+	0.406451i	−0.904008	−	0.427515i	$-0.859389\pi$
$109$	−3.67699	+	4.24347i	−0.352192	+	0.406451i	0.551817	+	0.833965i	$0.313935\pi$
$110$		0			0
$111$	11.9080	−	10.3184i	1.13026	−	0.979375i
$112$		0			0
$113$	2.48942	−	0.928507i	0.234185	−	0.0873466i	−0.229632	−	0.973278i	$-0.573752\pi$
$113$	2.48942	−	0.928507i	0.234185	−	0.0873466i	0.463817	+	0.885931i	$0.346479\pi$
$114$		0			0
$115$	−3.26530	−	10.2146i	−0.304491	−	0.952515i
$116$		0			0
$117$	7.04343	−	2.62706i	0.651165	−	0.242872i
$118$		0			0
$119$	8.76076	−	7.59124i	0.803098	−	0.695888i
$120$		0			0
$121$	11.6127	−	13.4018i	1.05570	−	1.21834i
$122$		0			0
$123$	11.5707	−	21.1902i	1.04330	−	1.91066i
$124$		0			0
$125$	10.9959	+	2.02253i	0.983501	+	0.180901i
$126$		0			0
$127$	5.78190	−	15.5019i	0.513061	−	1.37557i	−0.379730	−	0.925097i	$-0.623983\pi$
$127$	5.78190	−	15.5019i	0.513061	−	1.37557i	0.892791	−	0.450472i	$-0.148744\pi$
$128$		0			0
$129$	−19.9285	−	12.8073i	−1.75461	−	1.12762i
$130$		0			0
$131$	1.15641	−	8.04299i	0.101036	−	0.702719i	−0.874843	−	0.484406i	$-0.839036\pi$
$131$	1.15641	−	8.04299i	0.101036	−	0.702719i	0.975879	−	0.218313i	$-0.0700552\pi$
$132$		0			0
$133$	−4.30282	+	19.7797i	−0.373102	+	1.71512i
$134$		0			0
$135$	0.563138	−	4.24029i	0.0484672	−	0.364946i
$136$		0			0
$137$	−2.16259	+	2.16259i	−0.184763	+	0.184763i	−0.793427	−	0.608665i	$-0.791705\pi$
$137$	−2.16259	+	2.16259i	−0.184763	+	0.184763i	0.608665	+	0.793427i	$0.291705\pi$
$138$		0			0
$139$			21.1129i			1.79078i	0.445287	+	0.895388i	$0.353102\pi$
$139$			21.1129i			1.79078i	−0.445287	+	0.895388i	$0.646898\pi$
$140$		0			0
$141$	19.8720	+	5.83494i	1.67352	+	0.491391i
$142$		0			0
$143$	−18.2487	−	3.96977i	−1.52604	−	0.331969i
$144$		0			0
$145$	5.92499	+	5.79877i	0.492043	+	0.481561i
$146$		0			0
$147$	−4.20467	−	19.3285i	−0.346795	−	1.59419i
$148$		0			0
$149$	9.03540	+	19.7848i	0.740209	+	1.62083i	0.783211	+	0.621756i	$0.213581\pi$
$149$	9.03540	+	19.7848i	0.740209	+	1.62083i	−0.0430021	+	0.999075i	$0.513692\pi$
$150$		0			0
$151$	−3.32873	−	23.1518i	−0.270888	−	1.88407i	−0.439283	−	0.898349i	$-0.644768\pi$
$151$	−3.32873	−	23.1518i	−0.270888	−	1.88407i	0.168395	−	0.985720i	$-0.446142\pi$
$152$		0			0
$153$	−5.53859	−	3.02430i	−0.447768	−	0.244500i
$154$		0			0
$155$	5.90089	−	1.35035i	0.473971	−	0.108463i
$156$		0			0
$157$	−16.6965	−	1.19416i	−1.33253	−	0.0953041i	−0.613173	−	0.789949i	$-0.710107\pi$
$157$	−16.6965	−	1.19416i	−1.33253	−	0.0953041i	−0.719353	+	0.694645i	$0.755562\pi$
$158$		0			0
$159$	−1.20212	+	2.63227i	−0.0953343	+	0.208753i
$160$		0			0
$161$	10.0675	−	16.1237i	0.793427	−	1.27073i
$162$		0			0
$163$	−3.86782	−	10.3700i	−0.302951	−	0.812243i	−0.995833	−	0.0911921i	$-0.970932\pi$
$163$	−3.86782	−	10.3700i	−0.302951	−	0.812243i	0.692882	−	0.721051i	$-0.256340\pi$
$164$		0			0
$165$	17.6034	−	20.7629i	1.37042	−	1.61639i
$166$		0			0
$167$	18.2085	−	1.30229i	1.40901	−	0.100775i	0.654005	−	0.756490i	$-0.273088\pi$
$167$	18.2085	−	1.30229i	1.40901	−	0.100775i	0.755008	+	0.655716i	$0.227633\pi$
$168$		0			0
$169$	−0.242721	−	0.826631i	−0.0186708	−	0.0635870i
$170$		0			0
$171$	10.9073	−	1.56823i	0.834101	−	0.119926i
$172$		0			0
$173$	7.89669	+	2.94531i	0.600375	+	0.223928i	0.631230	−	0.775596i	$-0.282550\pi$
$173$	7.89669	+	2.94531i	0.600375	+	0.223928i	−0.0308554	+	0.999524i	$0.509823\pi$
$174$		0			0
$175$	9.86996	+	17.1852i	0.746099	+	1.29908i
$176$		0			0
$177$	11.3284	−	8.48036i	0.851497	−	0.637423i
$178$		0			0
$179$	−3.27201	−	5.09135i	−0.244562	−	0.380545i	0.697173	−	0.716903i	$-0.254441\pi$
$179$	−3.27201	−	5.09135i	−0.244562	−	0.380545i	−0.941734	+	0.336358i	$0.890805\pi$
$180$		0			0
$181$	0.474302	−	1.61532i	0.0352546	−	0.120066i	−0.939986	−	0.341214i	$-0.889162\pi$
$181$	0.474302	−	1.61532i	0.0352546	−	0.120066i	0.975240	+	0.221148i	$0.0709802\pi$
$182$		0			0
$183$	12.4125	+	12.4125i	0.917559	+	0.917559i
$184$		0			0
$185$	−15.3313	+	2.37304i	−1.12718	+	0.174469i
$186$		0			0
$187$	7.51328	+	13.7595i	0.549425	+	1.00620i
$188$		0			0
$189$	6.37853	−	4.09923i	0.463970	−	0.298175i
$190$		0			0
$191$	−7.29360	−	1.04866i	−0.527746	−	0.0758785i	−0.126709	−	0.991940i	$-0.540441\pi$
$191$	−7.29360	−	1.04866i	−0.527746	−	0.0758785i	−0.401038	+	0.916062i	$0.631350\pi$
$192$		0			0
$193$	16.0249	−	3.48601i	1.15350	−	0.250929i	0.405161	−	0.914245i	$-0.367215\pi$
$193$	16.0249	−	3.48601i	1.15350	−	0.250929i	0.748339	+	0.663316i	$0.230852\pi$
$194$		0			0
$195$	−17.3278	−	3.57452i	−1.24087	−	0.255976i
$196$		0			0
$197$	5.50148	−	7.34912i	0.391964	−	0.523603i	−0.560540	−	0.828127i	$-0.689406\pi$
$197$	5.50148	−	7.34912i	0.391964	−	0.523603i	0.952505	+	0.304524i	$0.0984974\pi$
$198$		0			0
$199$	15.4804	−	4.54545i	1.09737	−	0.322218i	0.317566	−	0.948236i	$-0.397135\pi$
$199$	15.4804	−	4.54545i	1.09737	−	0.322218i	0.779808	+	0.626018i	$0.215316\pi$
$200$		0			0
$201$	−11.5331	−	9.99350i	−0.813483	−	0.704887i
$202$		0			0
$203$	−1.04835	+	14.6579i	−0.0735798	+	1.02878i
$204$		0			0
$205$	−20.7399	+	11.6164i	−1.44854	+	0.811328i
$206$		0			0
$207$	−10.1392	−	2.06757i	−0.704722	−	0.143706i
$208$		0			0
$209$	−24.9018	−	11.3723i	−1.72249	−	0.786637i
$210$		0			0
$211$	16.2416	+	18.7438i	1.11812	+	1.29038i	0.952618	+	0.304170i	$0.0983791\pi$
$211$	16.2416	+	18.7438i	1.11812	+	1.29038i	0.165502	+	0.986209i	$0.447075\pi$
$212$		0			0
$213$	−2.22683	−	31.1352i	−0.152580	−	2.13335i
$214$		0			0
$215$	9.91705	+	21.1109i	0.676337	+	1.43975i
$216$		0			0
$217$	8.58986	+	6.43029i	0.583118	+	0.436517i
$218$		0			0
$219$	6.63246	−	3.02894i	0.448180	−	0.204677i
$220$		0			0
$221$	5.50894	−	8.57208i	0.370572	−	0.576621i
$222$		0			0
$223$	−5.30883	−	7.09177i	−0.355506	−	0.474900i	0.586763	−	0.809759i	$-0.300402\pi$
$223$	−5.30883	−	7.09177i	−0.355506	−	0.474900i	−0.942268	+	0.334859i	$0.891311\pi$
$224$		0			0
$225$	6.88770	−	8.30352i	0.459180	−	0.553568i
$226$		0			0
$227$	10.4959	−	5.73121i	0.696639	−	0.380394i	−0.0915720	−	0.995798i	$-0.529189\pi$
$227$	10.4959	−	5.73121i	0.696639	−	0.380394i	0.788211	+	0.615405i	$0.211007\pi$
$228$		0			0
$229$	17.0601			1.12736			0.563681	−	0.825993i	$-0.309385\pi$
$229$	17.0601			1.12736			0.563681	+	0.825993i	$0.309385\pi$
$230$		0			0
$231$	48.2508			3.17467
$232$		0			0
$233$	0.0637924	−	0.0348333i	0.00417918	−	0.00228200i	−0.477158	−	0.878818i	$-0.658333\pi$
$233$	0.0637924	−	0.0348333i	0.00417918	−	0.00228200i	0.481337	+	0.876536i	$0.340151\pi$
$234$		0			0
$235$	−13.5190	−	15.2665i	−0.881881	−	0.995877i
$236$		0			0
$237$	2.74936	+	3.67272i	0.178590	+	0.238569i
$238$		0			0
$239$	−11.7537	+	18.2891i	−0.760281	+	1.18302i	0.218042	+	0.975939i	$0.430033\pi$
$239$	−11.7537	+	18.2891i	−0.760281	+	1.18302i	−0.978324	+	0.207081i	$0.933603\pi$
$240$		0			0
$241$	−13.6272	+	6.22332i	−0.877802	+	0.400879i	−0.802761	−	0.596301i	$-0.796636\pi$
$241$	−13.6272	+	6.22332i	−0.877802	+	0.400879i	−0.0750419	+	0.997180i	$0.523909\pi$
$242$		0			0
$243$	−15.0727	−	11.2833i	−0.966913	−	0.723822i
$244$		0			0
$245$	−6.60928	+	18.3201i	−0.422252	+	1.17043i
$246$		0			0
$247$	1.26936	+	17.7480i	0.0807674	+	1.12928i
$248$		0			0
$249$	0.574907	+	0.663478i	0.0364333	+	0.0420462i
$250$		0			0
$251$	−14.4791	−	6.61237i	−0.913910	−	0.417369i	−0.0977611	−	0.995210i	$-0.531168\pi$
$251$	−14.4791	−	6.61237i	−0.913910	−	0.417369i	−0.816149	+	0.577841i	$0.803895\pi$
$252$		0			0
$253$	18.4132	+	17.9392i	1.15763	+	1.12783i
$254$		0			0
$255$	7.25780	+	12.9580i	0.454501	+	0.811464i
$256$		0			0
$257$	−0.429263	+	6.00188i	−0.0267767	+	0.374387i	0.966341	+	0.257265i	$0.0828214\pi$
$257$	−0.429263	+	6.00188i	−0.0267767	+	0.374387i	−0.993118	+	0.117122i	$0.962633\pi$
$258$		0			0
$259$	−20.7826	−	18.0082i	−1.29137	−	1.11897i
$260$		0			0
$261$	7.67573	−	2.25380i	0.475116	−	0.139507i
$262$		0			0
$263$	16.9052	−	22.5827i	1.04242	−	1.39251i	0.126122	−	0.992015i	$-0.459747\pi$
$263$	16.9052	−	22.5827i	1.04242	−	1.39251i	0.916298	−	0.400496i	$-0.131162\pi$
$264$		0			0
$265$	2.38018	−	1.56611i	0.146213	−	0.0962054i
$266$		0			0
$267$	−21.9527	+	4.77552i	−1.34349	+	0.292257i
$268$		0			0
$269$	−11.2892	−	1.62315i	−0.688316	−	0.0989649i	−0.210723	−	0.977546i	$-0.567582\pi$
$269$	−11.2892	−	1.62315i	−0.688316	−	0.0989649i	−0.477593	+	0.878581i	$0.658491\pi$
$270$		0			0
$271$	2.28151	−	1.46624i	0.138592	−	0.0890677i	−0.469507	−	0.882928i	$-0.655569\pi$
$271$	2.28151	−	1.46624i	0.138592	−	0.0890677i	0.608100	+	0.793861i	$0.291932\pi$
$272$		0			0
$273$	−15.0299	−	27.5252i	−0.909652	−	1.66590i
$274$		0			0
$275$	−25.5474	+	8.10280i	−1.54057	+	0.488617i
$276$		0			0
$277$	2.52597	+	2.52597i	0.151771	+	0.151771i	0.778908	−	0.627138i	$-0.215774\pi$
$277$	2.52597	+	2.52597i	0.151771	+	0.151771i	−0.627138	+	0.778908i	$0.715774\pi$
$278$		0			0
$279$	1.64566	−	5.60459i	0.0985228	−	0.335538i
$280$		0			0
$281$	−0.829869	−	1.29130i	−0.0495058	−	0.0770326i	0.815618	−	0.578590i	$-0.196397\pi$
$281$	−0.829869	−	1.29130i	−0.0495058	−	0.0770326i	−0.865124	+	0.501558i	$0.832761\pi$
$282$		0			0
$283$	3.63680	−	2.72247i	0.216185	−	0.161834i	−0.485697	−	0.874127i	$-0.661434\pi$
$283$	3.63680	−	2.72247i	0.216185	−	0.161834i	0.701882	+	0.712293i	$0.252343\pi$
$284$		0			0
$285$	−23.7059	−	10.5192i	−1.40422	−	0.623103i
$286$		0			0
$287$	−39.4798	−	14.7252i	−2.33042	−	0.869202i
$288$		0			0
$289$	8.36031	−	1.20203i	0.491783	−	0.0707077i
$290$		0			0
$291$	2.42685	+	8.26509i	0.142264	+	0.484508i
$292$		0			0
$293$	9.68589	−	0.692748i	0.565856	−	0.0404708i	0.214519	−	0.976720i	$-0.431182\pi$
$293$	9.68589	−	0.692748i	0.565856	−	0.0404708i	0.351337	+	0.936249i	$0.385727\pi$
$294$		0			0
$295$	−13.8860	+	1.14352i	−0.808473	+	0.0665785i
$296$		0			0
$297$	3.58345	+	9.60759i	0.207933	+	0.557489i
$298$		0			0
$299$	4.49799	−	16.0920i	0.260125	−	0.930625i
$300$		0			0
$301$	−17.1747	+	37.6074i	−0.989934	+	2.16765i
$302$		0			0
$303$	−23.3072	−	1.66696i	−1.33896	−	0.0957646i
$304$		0			0
$305$	−3.85548	−	16.8480i	−0.220764	−	0.964715i
$306$		0			0
$307$	28.8262	+	15.7403i	1.64520	+	0.898345i	0.989702	+	0.143145i	$0.0457214\pi$
$307$	28.8262	+	15.7403i	1.64520	+	0.898345i	0.655494	+	0.755200i	$0.272460\pi$
$308$		0			0
$309$	1.02211	+	7.10892i	0.0581457	+	0.404412i
$310$		0			0
$311$	−6.34921	−	13.9028i	−0.360031	−	0.788357i	−0.999804	−	0.0197935i	$-0.993699\pi$
$311$	−6.34921	−	13.9028i	−0.360031	−	0.788357i	0.639774	−	0.768563i	$-0.279028\pi$
$312$		0			0
$313$	4.50699	+	20.7183i	0.254750	+	1.17107i	0.909658	+	0.415359i	$0.136344\pi$
$313$	4.50699	+	20.7183i	0.254750	+	1.17107i	−0.654908	+	0.755709i	$0.727292\pi$
$314$		0			0
$315$	19.1219	−	0.205870i	1.07740	−	0.0115994i
$316$		0			0
$317$	−13.5407	−	2.94559i	−0.760520	−	0.165441i	−0.184450	−	0.982842i	$-0.559051\pi$
$317$	−13.5407	−	2.94559i	−0.760520	−	0.165441i	−0.576069	+	0.817401i	$0.695414\pi$
$318$		0			0
$319$	−19.0689	−	5.59912i	−1.06765	−	0.313491i
$320$		0			0
$321$			8.05664i			0.449678i
$322$		0			0
$323$	10.5618	−	10.5618i	0.587673	−	0.587673i
$324$		0			0
$325$	12.5803	+	12.0499i	0.697827	+	0.668406i
$326$		0			0
$327$	2.71058	−	12.4603i	0.149896	−	0.689059i
$328$		0			0
$329$	5.14410	−	35.7780i	0.283603	−	1.97250i
$330$		0			0
$331$	−24.9493	−	16.0340i	−1.37134	−	0.881306i	−0.372433	−	0.928059i	$-0.621476\pi$
$331$	−24.9493	−	16.0340i	−1.37134	−	0.881306i	−0.998906	+	0.0467531i	$0.985113\pi$
$332$		0			0
$333$	−5.23146	+	14.0261i	−0.286682	+	0.768625i
$334$		0			0
$335$	4.38811	+	14.3704i	0.239748	+	0.785138i
$336$		0			0
$337$	−1.36294	+	2.49603i	−0.0742439	+	0.135968i	−0.912164	−	0.409825i	$-0.865590\pi$
$337$	−1.36294	+	2.49603i	−0.0742439	+	0.135968i	0.837920	+	0.545793i	$0.183771\pi$
$338$		0			0
$339$	−3.95147	+	4.56024i	−0.214614	+	0.247678i
$340$		0			0
$341$	−10.9669	+	9.50290i	−0.593892	+	0.514611i
$342$		0			0
$343$	−6.34994	+	2.36840i	−0.342864	+	0.127882i
$344$		0			0
$345$	17.6261	+	16.8063i	0.948959	+	0.904822i
$346$		0			0
$347$	22.5678	−	8.41735i	1.21150	−	0.451867i	0.339145	−	0.940734i	$-0.389862\pi$
$347$	22.5678	−	8.41735i	1.21150	−	0.451867i	0.872358	+	0.488867i	$0.162590\pi$
$348$		0			0
$349$	7.08349	−	6.13788i	0.379171	−	0.328553i	−0.444336	−	0.895860i	$-0.646560\pi$
$349$	7.08349	−	6.13788i	0.379171	−	0.328553i	0.823506	+	0.567307i	$0.192015\pi$
$350$		0			0
$351$	4.36454	−	5.03694i	0.232962	−	0.268852i
$352$		0			0
$353$	13.0434	−	23.8873i	0.694232	−	1.27139i	−0.258039	−	0.966135i	$-0.583076\pi$
$353$	13.0434	−	23.8873i	0.694232	−	1.27139i	0.952270	−	0.305256i	$-0.0987419\pi$
$354$		0			0
$355$	−14.4379	+	27.1315i	−0.766285	+	1.43999i
$356$		0			0
$357$	−9.20012	+	24.6665i	−0.486922	+	1.30549i
$358$		0			0
$359$	6.59810	+	4.24034i	0.348234	+	0.223797i	0.703051	−	0.711139i	$-0.251820\pi$
$359$	6.59810	+	4.24034i	0.348234	+	0.223797i	−0.354817	+	0.934936i	$0.615457\pi$
$360$		0			0
$361$	−1.00794	+	7.01037i	−0.0530494	+	0.368967i
$362$		0			0
$363$	−8.56058	+	39.3523i	−0.449314	+	2.06546i
$364$		0			0
$365$	−7.11657	−	0.945127i	−0.372498	−	0.0494702i
$366$		0			0
$367$	0.653928	−	0.653928i	0.0341348	−	0.0341348i	−0.689833	−	0.723968i	$-0.742316\pi$
$367$	0.653928	−	0.653928i	0.0341348	−	0.0341348i	0.723968	+	0.689833i	$0.242316\pi$
$368$		0			0
$369$			22.9382i			1.19411i
$370$		0			0
$371$	4.84582	+	1.42286i	0.251582	+	0.0738712i
$372$		0			0
$373$	0.534834	+	0.116346i	0.0276926	+	0.00602416i	0.226390	−	0.974037i	$-0.427308\pi$
$373$	0.534834	+	0.116346i	0.0276926	+	0.00602416i	−0.198698	+	0.980061i	$0.563671\pi$
$374$		0			0
$375$	−24.1189	+	7.93648i	−1.24549	+	0.409838i
$376$		0			0
$377$	2.74578	+	12.6222i	0.141415	+	0.650074i
$378$		0			0
$379$	−2.08835	−	4.57284i	−0.107271	−	0.234891i	0.848383	−	0.529384i	$-0.177577\pi$
$379$	−2.08835	−	4.57284i	−0.107271	−	0.234891i	−0.955654	+	0.294492i	$0.904849\pi$
$380$		0			0
$381$	5.34743	+	37.1922i	0.273957	+	1.90541i
$382$		0			0
$383$	31.2782	+	17.0792i	1.59824	+	0.872706i	0.997302	+	0.0734107i	$0.0233884\pi$
$383$	31.2782	+	17.0792i	1.59824	+	0.872706i	0.600939	+	0.799295i	$0.294793\pi$
$384$		0			0
$385$	−40.2401	−	25.2528i	−2.05082	−	1.28700i
$386$		0			0
$387$	22.4491	+	1.60559i	1.14115	+	0.0816168i
$388$		0			0
$389$	−3.31320	+	7.25490i	−0.167986	+	0.367838i	−0.974838	−	0.222916i	$-0.928442\pi$
$389$	−3.31320	+	7.25490i	−0.167986	+	0.367838i	0.806852	+	0.590754i	$0.201170\pi$
$390$		0			0
$391$	−12.6817	+	5.99257i	−0.641339	+	0.303057i
$392$		0			0
$393$	6.44897	+	17.2903i	0.325307	+	0.872183i
$394$		0			0
$395$	−0.370734	−	4.50188i	−0.0186537	−	0.226514i
$396$		0			0
$397$	−15.8118	+	1.13088i	−0.793572	+	0.0567574i	−0.462237	−	0.886756i	$-0.652953\pi$
$397$	−15.8118	+	1.13088i	−0.793572	+	0.0567574i	−0.331334	+	0.943514i	$0.607499\pi$
$398$		0			0
$399$	−12.9516	−	44.1092i	−0.648393	−	2.20822i
$400$		0			0
$401$	24.5180	−	3.52515i	1.22437	−	0.176038i	0.500354	−	0.865821i	$-0.333203\pi$
$401$	24.5180	−	3.52515i	1.22437	−	0.176038i	0.724016	+	0.689783i	$0.242294\pi$
$402$		0			0
$403$	8.83719	+	3.29610i	0.440212	+	0.164191i
$404$		0			0
$405$	8.69654	+	22.5712i	0.432134	+	1.12157i
$406$		0			0
$407$	29.7721	−	22.2871i	1.47575	−	1.10473i
$408$		0			0
$409$	14.0692	+	21.8921i	0.695676	+	1.08249i	0.991856	+	0.127361i	$0.0406507\pi$
$409$	14.0692	+	21.8921i	0.695676	+	1.08249i	−0.296180	+	0.955132i	$0.595713\pi$
$410$		0			0
$411$	1.95683	−	6.66435i	0.0965233	−	0.328728i
$412$		0			0
$413$	−17.4635	−	17.4635i	−0.859321	−	0.859321i
$414$		0			0
$415$	−0.132218	−	0.854212i	−0.00649034	−	0.0419316i
$416$		0			0
$417$	−22.9793	−	42.0835i	−1.12530	−	2.06084i
$418$		0			0
$419$	18.6995	−	12.0175i	0.913532	−	0.587091i	0.00275771	−	0.999996i	$-0.499122\pi$
$419$	18.6995	−	12.0175i	0.913532	−	0.587091i	0.910774	+	0.412905i	$0.135486\pi$
$420$		0			0
$421$	25.6379	+	3.68617i	1.24952	+	0.179653i	0.735142	−	0.677913i	$-0.237115\pi$
$421$	25.6379	+	3.68617i	1.24952	+	0.179653i	0.514373	+	0.857566i	$0.328025\pi$
$422$		0			0
$423$	−19.2273	+	4.18264i	−0.934863	+	0.203367i
$424$		0			0
$425$	0.728942	−	14.6052i	0.0353589	−	0.708456i
$426$		0			0
$427$	18.3595	−	24.5255i	0.888481	−	1.18687i
$428$		0			0
$429$	40.6951	−	11.9491i	1.96478	−	0.576910i
$430$		0			0
$431$	0.631605	+	0.547288i	0.0304233	+	0.0263620i	0.669940	−	0.742415i	$-0.266320\pi$
$431$	0.631605	+	0.547288i	0.0304233	+	0.0263620i	−0.639516	+	0.768777i	$0.720865\pi$
$432$		0			0
$433$	−0.102678	+	1.43562i	−0.00493437	+	0.0689915i	−0.999323	−	0.0368007i	$-0.988283\pi$
$433$	−0.102678	+	1.43562i	−0.00493437	+	0.0689915i	0.994388	+	0.105792i	$0.0337379\pi$
$434$		0			0
$435$	−18.1214	−	5.10967i	−0.868854	−	0.244990i
$436$		0			0
$437$	11.4569	−	21.6480i	0.548056	−	1.03557i
$438$		0			0
$439$	18.1653	+	8.29582i	0.866984	+	0.395938i	0.798701	−	0.601728i	$-0.205521\pi$
$439$	18.1653	+	8.29582i	0.866984	+	0.395938i	0.0682824	+	0.997666i	$0.478248\pi$
$440$		0			0
$441$	12.3069	+	14.2029i	0.586041	+	0.676327i
$442$		0			0
$443$	−1.86383	−	26.0598i	−0.0885533	−	1.23814i	−0.826367	−	0.563132i	$-0.809596\pi$
$443$	−1.86383	−	26.0598i	−0.0885533	−	1.23814i	0.737814	−	0.675004i	$-0.235858\pi$
$444$		0			0
$445$	20.8074	+	7.50661i	0.986366	+	0.355847i
$446$		0			0
$447$	−39.5436	−	29.6019i	−1.87035	−	1.40012i
$448$		0			0
$449$	−13.2972	+	6.07261i	−0.627532	+	0.286584i	−0.703685	−	0.710512i	$-0.748463\pi$
$449$	−13.2972	+	6.07261i	−0.627532	+	0.286584i	0.0761531	+	0.997096i	$0.475736\pi$
$450$		0			0
$451$	30.8086	−	47.9392i	1.45072	−	2.25737i
$452$		0			0
$453$	31.8334	+	42.5245i	1.49566	+	1.99797i
$454$		0			0
$455$	−1.87113	+	30.8216i	−0.0877200	+	1.44494i
$456$		0			0
$457$	−20.3587	+	11.1167i	−0.952340	+	0.520017i	−0.878756	−	0.477272i	$-0.841626\pi$
$457$	−20.3587	+	11.1167i	−0.952340	+	0.520017i	−0.0735844	+	0.997289i	$0.523444\pi$
$458$		0			0
$459$	−5.59480			−0.261143
$460$		0			0
$461$	1.56783			0.0730213			0.0365106	−	0.999333i	$-0.488376\pi$
$461$	1.56783			0.0730213			0.0365106	+	0.999333i	$0.488376\pi$
$462$		0			0
$463$	18.4273	−	10.0621i	0.856389	−	0.467624i	0.00985076	−	0.999951i	$-0.496864\pi$
$463$	18.4273	−	10.0621i	0.856389	−	0.467624i	0.846538	+	0.532328i	$0.178683\pi$
$464$		0			0
$465$	−10.2922	+	9.11412i	−0.477292	+	0.422657i
$466$		0			0
$467$	4.09069	+	5.46452i	0.189295	+	0.252868i	0.885141	−	0.465322i	$-0.154062\pi$
$467$	4.09069	+	5.46452i	0.189295	+	0.252868i	−0.695847	+	0.718190i	$0.744971\pi$
$468$		0			0
$469$	−14.3992	+	22.4055i	−0.664891	+	1.03459i
$470$		0			0
$471$	34.5801	−	15.7922i	1.59337	−	0.727666i
$472$		0			0
$473$	−44.7606	−	33.5073i	−2.05809	−	1.54067i
$474$		0			0
$475$	14.2648	+	21.1796i	0.654515	+	0.971787i
$476$		0			0
$477$	−0.196134	−	2.74231i	−0.00898035	−	0.125562i
$478$		0			0
$479$	−17.0300	−	19.6536i	−0.778120	−	0.897998i	0.218852	−	0.975758i	$-0.429769\pi$
$479$	−17.0300	−	19.6536i	−0.778120	−	0.897998i	−0.996972	+	0.0777600i	$0.975223\pi$
$480$		0			0
$481$	−21.9878	−	10.0415i	−1.00256	−	0.457853i
$482$		0			0
$483$	−2.51798	+	43.0960i	−0.114572	+	1.96094i
$484$		0			0
$485$	2.30172	−	8.16303i	0.104516	−	0.370664i
$486$		0			0
$487$	−2.39737	+	33.5196i	−0.108635	+	1.51892i	0.592314	+	0.805707i	$0.298214\pi$
$487$	−2.39737	+	33.5196i	−0.108635	+	1.51892i	−0.700949	+	0.713211i	$0.747240\pi$
$488$		0			0
$489$	18.9963	+	16.4604i	0.859041	+	0.744363i
$490$		0			0
$491$	−21.8275	+	6.40913i	−0.985060	+	0.289240i	−0.734312	−	0.678812i	$-0.762495\pi$
$491$	−21.8275	+	6.40913i	−0.985060	+	0.289240i	−0.250749	+	0.968052i	$0.580677\pi$
$492$		0			0
$493$	6.49826	−	8.68067i	0.292667	−	0.390958i
$494$		0			0
$495$	−5.22499	+	25.3287i	−0.234846	+	1.13844i
$496$		0			0
$497$	−53.2327	+	11.5801i	−2.38781	+	0.519437i
$498$		0			0
$499$	−15.0357	−	2.16181i	−0.673092	−	0.0967760i	−0.202710	−	0.979239i	$-0.564975\pi$
$499$	−15.0357	−	2.16181i	−0.673092	−	0.0967760i	−0.470382	+	0.882463i	$0.655884\pi$
$500$		0			0
$501$	−34.8767	+	22.4139i	−1.55817	+	1.00138i
$502$		0			0
$503$	18.9326	+	34.6726i	0.844165	+	1.54597i	0.837790	+	0.545993i	$0.183848\pi$
$503$	18.9326	+	34.6726i	0.844165	+	1.54597i	0.00637548	+	0.999980i	$0.497971\pi$
$504$		0			0
$505$	18.5652	+	13.5884i	0.826143	+	0.604675i
$506$		0			0
$507$	1.38351	+	1.38351i	0.0614438	+	0.0614438i
$508$		0			0
$509$	−3.33427	+	11.3555i	−0.147789	+	0.503322i	−0.999796	−	0.0202081i	$-0.993567\pi$
$509$	−3.33427	+	11.3555i	−0.147789	+	0.503322i	0.852007	+	0.523530i	$0.175385\pi$
$510$		0			0
$511$	−6.87982	−	10.7052i	−0.304346	−	0.473571i
$512$		0			0
$513$	7.82105	−	5.85477i	0.345308	−	0.258494i
$514$		0			0
$515$	2.86814	−	6.46362i	0.126386	−	0.284821i
$516$		0			0
$517$	45.8015	+	17.0831i	2.01435	+	0.751313i
$518$		0			0
$519$	−18.9458	+	2.72399i	−0.831628	+	0.119570i
$520$		0			0
$521$	−4.63767	−	15.7944i	−0.203180	−	0.691967i	−0.996532	−	0.0832049i	$-0.973484\pi$
$521$	−4.63767	−	15.7944i	−0.203180	−	0.691967i	0.793352	−	0.608763i	$-0.208334\pi$
$522$		0			0
$523$	−13.0794	+	0.935457i	−0.571922	+	0.0409047i	−0.354306	−	0.935130i	$-0.615283\pi$
$523$	−13.0794	+	0.935457i	−0.571922	+	0.0409047i	−0.217617	+	0.976034i	$0.569828\pi$
$524$		0			0
$525$	−38.3777	−	23.5120i	−1.67494	−	1.02615i
$526$		0			0
$527$	−2.76692	−	7.41839i	−0.120529	−	0.323150i
$528$		0			0
$529$	−16.9836	+	15.5099i	−0.738417	+	0.674344i
$530$		0			0
$531$	−5.58505	+	12.2296i	−0.242371	+	0.530717i
$532$		0			0
$533$	−36.9442	−	2.64230i	−1.60023	−	0.114451i
$534$		0			0
$535$	4.21656	−	6.71905i	0.182298	−	0.290490i
$536$		0			0
$537$	12.0634	+	6.58710i	0.520573	+	0.284254i
$538$		0			0
$539$	−6.64437	−	46.2126i	−0.286193	−	1.99052i
$540$		0			0
$541$	3.85214	+	8.43500i	0.165616	+	0.362649i	0.974184	−	0.225753i	$-0.0724844\pi$
$541$	3.85214	+	8.43500i	0.165616	+	0.362649i	−0.808568	+	0.588402i	$0.799757\pi$
$542$		0			0
$543$	0.812713	+	3.73598i	0.0348768	+	0.160326i
$544$		0			0
$545$	−8.78187	+	8.97302i	−0.376174	+	0.384362i
$546$		0			0
$547$	−16.0775	−	3.49744i	−0.687423	−	0.149540i	−0.144730	−	0.989471i	$-0.546231\pi$
$547$	−16.0775	−	3.49744i	−0.687423	−	0.149540i	−0.542692	+	0.839932i	$0.682595\pi$
$548$		0			0
$549$	−16.0020	−	4.69862i	−0.682950	−	0.200532i
$550$		0			0
$551$			18.9350i			0.806660i
$552$		0			0
$553$	5.66172	−	5.66172i	0.240761	−	0.240761i
$554$		0			0
$555$	27.9763	−	21.4166i	1.18753	−	0.909085i
$556$		0			0
$557$	0.755616	−	3.47351i	0.0320165	−	0.147177i	−0.958364	−	0.285550i	$-0.907824\pi$
$557$	0.755616	−	3.47351i	0.0320165	−	0.147177i	0.990380	+	0.138373i	$0.0441872\pi$
$558$		0			0
$559$	−5.17194	+	35.9716i	−0.218750	+	1.52144i
$560$		0			0
$561$	−29.9518	−	19.2488i	−1.26456	−	0.812686i
$562$		0			0
$563$	−7.63159	+	20.4611i	−0.321633	+	0.862332i	0.671031	+	0.741429i	$0.265852\pi$
$563$	−7.63159	+	20.4611i	−0.321633	+	0.862332i	−0.992664	+	0.120903i	$0.961421\pi$
$564$		0			0
$565$	5.68210	−	1.73508i	0.239048	−	0.0729952i
$566$		0			0
$567$	−20.5482	+	37.6312i	−0.862942	+	1.58036i
$568$		0			0
$569$	1.87113	−	2.15940i	0.0784420	−	0.0905268i	−0.715172	−	0.698949i	$-0.753652\pi$
$569$	1.87113	−	2.15940i	0.0784420	−	0.0905268i	0.793614	+	0.608422i	$0.208197\pi$
$570$		0			0
$571$	−9.12423	+	7.90619i	−0.381837	+	0.330864i	−0.824539	−	0.565805i	$-0.808565\pi$
$571$	−9.12423	+	7.90619i	−0.381837	+	0.330864i	0.442702	+	0.896669i	$0.354020\pi$
$572$		0			0
$573$	15.6794	−	5.84810i	0.655015	−	0.244308i
$574$		0			0
$575$	−5.90395	−	23.2410i	−0.246212	−	0.969216i
$576$		0			0
$577$	26.2294	−	9.78305i	1.09194	−	0.407274i	0.261969	−	0.965076i	$-0.415628\pi$
$577$	26.2294	−	9.78305i	1.09194	−	0.407274i	0.829974	+	0.557802i	$0.188355\pi$
$578$		0			0
$579$	−28.1476	+	24.3900i	−1.16977	+	1.01362i
$580$		0			0
$581$	1.00336	−	1.15794i	0.0416264	−	0.0480395i
$582$		0			0
$583$	−3.27334	+	5.99467i	−0.135568	+	0.248274i
$584$		0			0
$585$	16.0766	−	4.90912i	0.664686	−	0.202967i
$586$		0			0
$587$	−7.36035	+	19.7339i	−0.303794	+	0.814504i	0.691916	+	0.721978i	$0.256767\pi$
$587$	−7.36035	+	19.7339i	−0.303794	+	0.814504i	−0.995710	+	0.0925260i	$0.970506\pi$
$588$		0			0
$589$	11.6310	+	7.47479i	0.479247	+	0.307993i
$590$		0			0
$591$	−2.96708	+	20.6365i	−0.122049	+	0.848871i
$592$		0			0
$593$	−0.152375	+	0.700456i	−0.00625728	+	0.0287643i	−0.980170	−	0.198160i	$-0.936503\pi$
$593$	−0.152375	+	0.700456i	−0.00625728	+	0.0287643i	0.973912	+	0.226924i	$0.0728670\pi$
$594$		0			0
$595$	20.5823	−	15.7563i	0.843790	−	0.645944i
$596$		0			0
$597$	−25.9090	+	25.9090i	−1.06039	+	1.06039i
$598$		0			0
$599$			1.85961i			0.0759815i	0.999278	+	0.0379907i	$0.0120957\pi$
$599$			1.85961i			0.0759815i	−0.999278	+	0.0379907i	$0.987904\pi$
$600$		0			0
$601$	25.5142	+	7.49165i	1.04075	+	0.305591i	0.757073	−	0.653330i	$-0.226629\pi$
$601$	25.5142	+	7.49165i	1.04075	+	0.305591i	0.283673	+	0.958921i	$0.408447\pi$
$602$		0			0
$603$	14.1673	+	3.08191i	0.576938	+	0.125505i
$604$		0			0
$605$	27.7350	−	28.3387i	1.12759	−	1.15213i
$606$		0			0
$607$	1.31510	+	6.04540i	0.0533781	+	0.245375i	0.996103	−	0.0881954i	$-0.0281100\pi$
$607$	1.31510	+	6.04540i	0.0533781	+	0.245375i	−0.942725	+	0.333571i	$0.891746\pi$
$608$		0			0
$609$	−13.8640	−	30.3579i	−0.561796	−	1.23016i
$610$		0			0
$611$	−4.52173	−	31.4493i	−0.182930	−	1.27230i
$612$		0			0
$613$	7.98737	+	4.36144i	0.322607	+	0.176157i	0.632389	−	0.774651i	$-0.282074\pi$
$613$	7.98737	+	4.36144i	0.322607	+	0.176157i	−0.309782	+	0.950808i	$0.600256\pi$
$614$		0			0
$615$	28.6966	−	45.7279i	1.15716	−	1.84393i
$616$		0			0
$617$	−12.2932	−	0.879229i	−0.494907	−	0.0353964i	−0.178344	−	0.983968i	$-0.557074\pi$
$617$	−12.2932	−	0.879229i	−0.494907	−	0.0353964i	−0.316562	+	0.948572i	$0.602529\pi$
$618$		0			0
$619$	6.64250	−	14.5450i	0.266984	−	0.584614i	−0.727894	−	0.685689i	$-0.759501\pi$
$619$	6.64250	−	14.5450i	0.266984	−	0.584614i	0.994879	+	0.101075i	$0.0322282\pi$
$620$		0			0
$621$	−8.76819	+	2.69924i	−0.351855	+	0.108317i
$622$		0			0
$623$	13.7022	+	36.7371i	0.548968	+	1.47184i
$624$		0			0
$625$	24.2683	+	6.00414i	0.970732	+	0.240166i
$626$		0			0
$627$	62.0132	−	4.43527i	2.47657	−	0.177128i
$628$		0			0
$629$	5.71675	+	19.4695i	0.227942	+	0.776298i
$630$		0			0
$631$	−10.8402	+	1.55859i	−0.431543	+	0.0620465i	−0.354664	−	0.934994i	$-0.615405\pi$
$631$	−10.8402	+	1.55859i	−0.431543	+	0.0620465i	−0.0768792	+	0.997040i	$0.524496\pi$
$632$		0			0
$633$	−52.7745	−	19.6839i	−2.09760	−	0.782363i
$634$		0			0
$635$	15.0055	−	33.8161i	0.595473	−	1.34195i
$636$		0			0
$637$	−24.2928	+	18.1854i	−0.962517	+	0.720531i
$638$		0			0
$639$	16.0334	+	24.9485i	0.634273	+	0.986948i
$640$		0			0
$641$	−7.17857	+	24.4480i	−0.283537	+	0.965637i	0.687396	+	0.726283i	$0.258754\pi$
$641$	−7.17857	+	24.4480i	−0.283537	+	0.965637i	−0.970932	+	0.239354i	$0.923064\pi$
$642$		0			0
$643$	−9.17426	−	9.17426i	−0.361797	−	0.361797i	0.502677	−	0.864474i	$-0.332349\pi$
$643$	−9.17426	−	9.17426i	−0.361797	−	0.361797i	−0.864474	+	0.502677i	$0.832349\pi$
$644$		0			0
$645$	−42.7442	−	31.2856i	−1.68305	−	1.23187i
$646$		0			0
$647$	−16.6546	−	30.5006i	−0.654759	−	1.19910i	−0.968363	−	0.249547i	$-0.919718\pi$
$647$	−16.6546	−	30.5006i	−0.654759	−	1.19910i	0.313604	−	0.949554i	$-0.398464\pi$
$648$		0			0
$649$	28.0981	−	18.0575i	1.10295	−	0.708821i
$650$		0			0
$651$	−24.1205	−	3.46800i	−0.945357	−	0.135922i
$652$		0			0
$653$	−21.5314	+	4.68388i	−0.842591	+	0.183294i	−0.613089	−	0.790014i	$-0.710073\pi$
$653$	−21.5314	+	4.68388i	−0.842591	+	0.183294i	−0.229502	+	0.973308i	$0.573710\pi$
$654$		0			0
$655$	3.67087	−	17.7949i	0.143433	−	0.695305i
$656$		0			0
$657$	−4.15141	+	5.54564i	−0.161962	+	0.216356i
$658$		0			0
$659$	40.8529	−	11.9955i	1.59140	−	0.467278i	0.638264	−	0.769817i	$-0.279653\pi$
$659$	40.8529	−	11.9955i	1.59140	−	0.467278i	0.953137	+	0.302540i	$0.0978345\pi$
$660$		0			0
$661$	9.26694	+	8.02985i	0.360442	+	0.312325i	0.816190	−	0.577784i	$-0.196082\pi$
$661$	9.26694	+	8.02985i	0.360442	+	0.312325i	−0.455747	+	0.890109i	$0.650628\pi$
$662$		0			0
$663$	−1.65088	+	23.0823i	−0.0641147	+	0.896441i
$664$		0			0
$665$	−12.2838	+	43.5645i	−0.476347	+	1.68936i
$666$		0			0
$667$	5.99607	−	16.7395i	0.232169	−	0.648156i
$668$		0			0
$669$	18.3005	+	8.35757i	0.707539	+	0.323122i
$670$		0			0
$671$	27.1323	+	31.3124i	1.04743	+	1.20880i
$672$		0			0
$673$	−1.23559	−	17.2758i	−0.0476285	−	0.665933i	−0.964050	−	0.265720i	$-0.914390\pi$
$673$	−1.23559	−	17.2758i	−0.0476285	−	0.665933i	0.916422	−	0.400214i	$-0.131064\pi$
$674$		0			0
$675$	1.83146	−	9.38785i	0.0704928	−	0.361338i
$676$		0			0
$677$	34.4064	+	25.7563i	1.32235	+	0.989896i	0.999049	+	0.0435979i	$0.0138820\pi$
$677$	34.4064	+	25.7563i	1.32235	+	0.989896i	0.323297	+	0.946298i	$0.395209\pi$
$678$		0			0
$679$	13.6751	−	6.24522i	0.524803	−	0.239669i
$680$		0			0
$681$	−14.6832	+	22.8475i	−0.562662	+	0.875519i
$682$		0			0
$683$	19.6794	+	26.2886i	0.753012	+	1.00591i	0.999326	+	0.0367160i	$0.0116897\pi$
$683$	19.6794	+	26.2886i	0.753012	+	1.00591i	−0.246314	+	0.969190i	$0.579219\pi$
$684$		0			0
$685$	−5.11984	+	4.53378i	−0.195619	+	0.173227i
$686$		0			0
$687$	−34.0051	+	18.5682i	−1.29737	+	0.708420i
$688$		0			0
$689$	4.43936			0.169126
$690$		0			0
$691$	−38.8556			−1.47814			−0.739069	−	0.673630i	$-0.764734\pi$
$691$	−38.8556			−1.47814			−0.739069	+	0.673630i	$0.764734\pi$
$692$		0			0
$693$	−40.2345	+	21.9697i	−1.52838	+	0.834561i
$694$		0			0
$695$	−2.86078	+	47.1232i	−0.108516	+	1.78749i
$696$		0			0
$697$	18.6328	+	24.8905i	0.705768	+	0.942795i
$698$		0			0
$699$	−0.0892419	+	0.138863i	−0.00337544	+	0.00525228i
$700$		0			0
$701$	−12.1821	+	5.56340i	−0.460113	+	0.210127i	−0.631966	−	0.774996i	$-0.717752\pi$
$701$	−12.1821	+	5.56340i	−0.460113	+	0.210127i	0.171853	+	0.985123i	$0.445025\pi$
$702$		0			0
$703$	−28.3656	−	21.2342i	−1.06983	−	0.800865i
$704$		0			0
$705$	43.5628	+	15.7160i	1.64067	+	0.591898i
$706$		0			0
$707$	2.90928	+	40.6771i	0.109415	+	1.52982i
$708$		0			0
$709$	−4.77476	−	5.51037i	−0.179320	−	0.206946i	0.658973	−	0.752167i	$-0.270991\pi$
$709$	−4.77476	−	5.51037i	−0.179320	−	0.206946i	−0.838293	+	0.545221i	$0.816446\pi$
$710$		0			0
$711$	−3.96487	−	1.81069i	−0.148694	−	0.0679063i
$712$		0			0
$713$	−7.91537	−	10.2912i	−0.296433	−	0.385409i
$714$		0			0
$715$	−40.1925	−	11.3330i	−1.50312	−	0.423832i
$716$		0			0
$717$	3.52224	−	49.2474i	0.131541	−	1.83918i
$718$		0			0
$719$	14.4960	+	12.5609i	0.540610	+	0.468441i	0.881847	−	0.471536i	$-0.156300\pi$
$719$	14.4960	+	12.5609i	0.540610	+	0.468441i	−0.341237	+	0.939977i	$0.610846\pi$
$720$		0			0
$721$	12.0267	−	3.53137i	0.447899	−	0.131515i
$722$		0			0
$723$	20.3889	−	27.2364i	0.758273	−	1.01293i
$724$		0			0
$725$	12.4386	+	13.7454i	0.461958	+	0.510493i
$726$		0			0
$727$	−2.37463	+	0.516568i	−0.0880700	+	0.0191585i	−0.256384	−	0.966575i	$-0.582531\pi$
$727$	−2.37463	+	0.516568i	−0.0880700	+	0.0191585i	0.168314	+	0.985733i	$0.446168\pi$
$728$		0			0
$729$	10.2023	+	1.46687i	0.377864	+	0.0543286i
$730$		0			0
$731$	25.6641	−	16.4933i	0.949219	−	0.610026i
$732$		0			0
$733$	−20.3552	−	37.2777i	−0.751836	−	1.37688i	−0.920314	−	0.391180i	$-0.872067\pi$
$733$	−20.3552	−	37.2777i	−0.751836	−	1.37688i	0.168478	−	0.985705i	$-0.446115\pi$
$734$		0			0
$735$	−6.76565	−	43.7102i	−0.249555	−	1.61228i
$736$		0			0
$737$	−25.4693	−	25.4693i	−0.938175	−	0.938175i
$738$		0			0
$739$	−3.22051	+	10.9680i	−0.118468	+	0.403466i	−0.997280	−	0.0737024i	$-0.976519\pi$
$739$	−3.22051	+	10.9680i	−0.118468	+	0.403466i	0.878812	+	0.477168i	$0.158337\pi$
$740$		0			0
$741$	−21.8470	−	33.9946i	−0.802570	−	1.24882i
$742$		0			0
$743$	−7.93373	+	5.93912i	−0.291060	+	0.217885i	−0.734822	−	0.678260i	$-0.762734\pi$
$743$	−7.93373	+	5.93912i	−0.291060	+	0.217885i	0.443762	+	0.896145i	$0.353644\pi$
$744$		0			0
$745$	17.4858	+	45.3831i	0.640631	+	1.66271i
$746$		0			0
$747$	−0.781491	−	0.291481i	−0.0285933	−	0.0106647i
$748$		0			0
$749$	13.9178	−	2.00108i	0.508545	−	0.0731177i
$750$		0			0
$751$	−3.01659	−	10.2736i	−0.110077	−	0.374888i	0.885967	−	0.463748i	$-0.153496\pi$
$751$	−3.01659	−	10.2736i	−0.110077	−	0.374888i	−0.996044	+	0.0888604i	$0.971678\pi$
$752$		0			0
$753$	36.0573	−	2.57887i	1.31400	−	0.0939793i
$754$		0			0
$755$	−4.29254	−	52.1249i	−0.156221	−	1.89702i
$756$		0			0
$757$	−16.8754	−	45.2446i	−0.613345	−	1.64444i	−0.755925	−	0.654659i	$-0.772812\pi$
$757$	−16.8754	−	45.2446i	−0.613345	−	1.64444i	0.142580	−	0.989783i	$-0.454460\pi$
$758$		0			0
$759$	−56.2272	−	15.7164i	−2.04092	−	0.570470i
$760$		0			0
$761$	−19.7963	+	43.3479i	−0.717617	+	1.57136i	0.0995982	+	0.995028i	$0.468244\pi$
$761$	−19.7963	+	43.3479i	−0.717617	+	1.57136i	−0.817215	+	0.576333i	$0.804483\pi$
$762$		0			0
$763$	−22.1984	−	1.58766i	−0.803636	−	0.0574772i
$764$		0			0
$765$	−11.9521	−	7.50058i	−0.432129	−	0.271184i
$766$		0			0
$767$	−19.0536	−	10.4040i	−0.687985	−	0.375668i
$768$		0			0
$769$	−2.07172	−	14.4092i	−0.0747083	−	0.519607i	−0.992471	−	0.122479i	$-0.960916\pi$
$769$	−2.07172	−	14.4092i	−0.0747083	−	0.519607i	0.917763	−	0.397129i	$-0.129993\pi$
$770$		0			0
$771$	−5.67681	−	12.4305i	−0.204445	−	0.447673i
$772$		0			0
$773$	−2.41399	−	11.0969i	−0.0868252	−	0.399129i	0.913138	−	0.407650i	$-0.133651\pi$
$773$	−2.41399	−	11.0969i	−0.0868252	−	0.399129i	−0.999964	+	0.00852039i	$0.997288\pi$
$774$		0			0
$775$	13.3535	−	2.21437i	0.479672	−	0.0795424i
$776$		0			0
$777$	61.0250	+	13.2752i	2.18926	+	0.476244i
$778$		0			0
$779$	−52.0941	−	15.2962i	−1.86647	−	0.548044i
$780$		0			0
$781$		−	73.6755i		−	2.63632i
$782$		0			0
$783$	5.01515	−	5.01515i	0.179227	−	0.179227i
$784$		0			0
$785$	−37.1041	−	4.92767i	−1.32430	−	0.175876i
$786$		0			0
$787$	0.515542	−	2.36991i	0.0183771	−	0.0844782i	−0.967045	−	0.254606i	$-0.918054\pi$
$787$	0.515542	−	2.36991i	0.0183771	−	0.0844782i	0.985422	+	0.170128i	$0.0544180\pi$
$788$		0			0
$789$	−9.11738	+	63.4127i	−0.324587	+	2.25755i
$790$		0			0
$791$	8.85923	+	5.69348i	0.314998	+	0.202437i
$792$		0			0
$793$	9.41092	−	25.2317i	0.334192	−	0.896002i
$794$		0			0
$795$	−3.03975	+	5.71224i	−0.107809	+	0.202592i
$796$		0			0
$797$	11.2615	−	20.6239i	0.398903	−	0.730536i	−0.598609	−	0.801042i	$-0.704280\pi$
$797$	11.2615	−	20.6239i	0.398903	−	0.730536i	0.997511	+	0.0705058i	$0.0224613\pi$
$798$		0			0
$799$	−17.4662	+	20.1571i	−0.617910	+	0.713106i
$800$		0			0
$801$	16.1312	−	13.9777i	0.569966	−	0.493879i
$802$		0			0
$803$	16.1246	−	6.01417i	0.569025	−	0.212235i
$804$		0			0
$805$	24.6549	−	34.6233i	0.868971	−	1.22031i
$806$		0			0
$807$	24.2689	−	9.05184i	0.854306	−	0.318640i
$808$		0			0
$809$	20.5641	−	17.8189i	0.722994	−	0.626478i	−0.213589	−	0.976924i	$-0.568515\pi$
$809$	20.5641	−	17.8189i	0.722994	−	0.626478i	0.936583	+	0.350446i	$0.113970\pi$
$810$		0			0
$811$	−9.60647	+	11.0865i	−0.337329	+	0.389298i	−0.898917	−	0.438118i	$-0.855645\pi$
$811$	−9.60647	+	11.0865i	−0.337329	+	0.389298i	0.561588	+	0.827417i	$0.310190\pi$
$812$		0			0
$813$	−2.95178	+	5.40579i	−0.103524	+	0.189589i
$814$		0			0
$815$	−7.22768	−	23.6695i	−0.253175	−	0.829108i
$816$		0			0
$817$	−18.6165	+	49.9128i	−0.651309	+	1.74623i
$818$		0			0
$819$	25.0658	+	16.1088i	0.875869	+	0.562887i
$820$		0			0
$821$	6.82727	−	47.4847i	0.238273	−	1.65723i	−0.422292	−	0.906460i	$-0.638774\pi$
$821$	6.82727	−	47.4847i	0.238273	−	1.65723i	0.660566	−	0.750768i	$-0.270316\pi$
$822$		0			0
$823$	6.92018	−	31.8115i	0.241222	−	1.10888i	−0.684008	−	0.729475i	$-0.739765\pi$
$823$	6.92018	−	31.8115i	0.241222	−	1.10888i	0.925230	−	0.379406i	$-0.123872\pi$
$824$		0			0
$825$	42.1034	−	43.9567i	1.46585	−	1.53038i
$826$		0			0
$827$	3.20948	−	3.20948i	0.111605	−	0.111605i	−0.649099	−	0.760704i	$-0.724854\pi$
$827$	3.20948	−	3.20948i	0.111605	−	0.111605i	0.760704	+	0.649099i	$0.224854\pi$
$828$		0			0
$829$		−	2.07144i		−	0.0719442i	−0.999353	−	0.0359721i	$-0.988547\pi$
$829$		−	2.07144i		−	0.0719442i	0.999353	−	0.0359721i	$-0.0114527\pi$
$830$		0			0
$831$	−7.78416	−	2.28564i	−0.270030	−	0.0792879i
$832$		0			0
$833$	24.8914	+	5.41480i	0.862437	+	0.187612i
$834$		0			0
$835$	40.8170	−	0.439441i	1.41253	−	0.0152075i
$836$		0			0
$837$	−1.10082	−	5.06038i	−0.0380498	−	0.174912i
$838$		0			0
$839$	21.5980	+	47.2930i	0.745645	+	1.63273i	0.774040	+	0.633137i	$0.218233\pi$
$839$	21.5980	+	47.2930i	0.745645	+	1.63273i	−0.0283949	+	0.999597i	$0.509040\pi$
$840$		0			0
$841$	−2.17084	−	15.0985i	−0.0748565	−	0.520638i
$842$		0			0
$843$	3.05959	+	1.67066i	0.105378	+	0.0575407i
$844$		0			0
$845$	−0.429735	−	1.87790i	−0.0147833	−	0.0646016i
$846$		0			0
$847$	70.1072	+	5.01416i	2.40891	+	0.172289i
$848$		0			0
$849$	−4.28593	+	9.38487i	−0.147093	+	0.322088i
$850$		0			0
$851$	18.3525	+	27.7545i	0.629114	+	0.951413i
$852$		0			0
$853$	7.07203	+	18.9608i	0.242142	+	0.649207i	0.999995	−	0.00321843i	$-0.00102446\pi$
$853$	7.07203	+	18.9608i	0.242142	+	0.649207i	−0.757853	+	0.652425i	$0.773752\pi$
$854$		0			0
$855$	24.5571	−	2.02230i	0.839836	−	0.0691613i
$856$		0			0
$857$	−10.7245	+	0.767030i	−0.366341	+	0.0262013i	−0.253297	−	0.967389i	$-0.581515\pi$
$857$	−10.7245	+	0.767030i	−0.366341	+	0.0262013i	−0.113045	+	0.993590i	$0.536060\pi$
$858$		0			0
$859$	7.25059	+	24.6933i	0.247387	+	0.842523i	0.985764	+	0.168135i	$0.0537744\pi$
$859$	7.25059	+	24.6933i	0.247387	+	0.842523i	−0.738377	+	0.674388i	$0.764407\pi$
$860$		0			0
$861$	94.7203	−	13.6187i	3.22806	−	0.464125i
$862$		0			0
$863$	0.250868	+	0.0935691i	0.00853966	+	0.00318513i	0.353730	−	0.935347i	$-0.384913\pi$
$863$	0.250868	+	0.0935691i	0.00853966	+	0.00318513i	−0.345191	+	0.938533i	$0.612186\pi$
$864$		0			0
$865$	17.2260	+	7.64381i	0.585702	+	0.259897i
$866$		0			0
$867$	−15.3559	+	11.4953i	−0.521515	+	0.390401i
$868$		0			0
$869$	5.85432	+	9.10951i	0.198594	+	0.309019i
$870$		0			0
$871$	−6.59570	+	22.4629i	−0.223487	+	0.761126i
$872$		0			0
$873$	−5.78695	−	5.78695i	−0.195859	−	0.195859i
$874$		0			0
$875$	19.7008	+	39.6940i	0.666008	+	1.34190i
$876$		0			0
$877$	−20.9719	−	38.4071i	−0.708170	−	1.29692i	−0.945543	−	0.325498i	$-0.894468\pi$
$877$	−20.9719	−	38.4071i	−0.708170	−	1.29692i	0.237373	−	0.971419i	$-0.423714\pi$
$878$		0			0
$879$	−18.5524	+	11.9229i	−0.625758	+	0.402151i
$880$		0			0
$881$	−51.8686	−	7.45758i	−1.74750	−	0.251252i	−0.806878	−	0.590718i	$-0.798845\pi$
$881$	−51.8686	−	7.45758i	−1.74750	−	0.251252i	−0.940618	+	0.339466i	$0.889754\pi$
$882$		0			0
$883$	36.1409	−	7.86196i	1.21624	−	0.264576i	0.441734	−	0.897146i	$-0.354364\pi$
$883$	36.1409	−	7.86196i	1.21624	−	0.264576i	0.774503	+	0.632570i	$0.218000\pi$
$884$		0			0
$885$	26.4337	−	17.3928i	0.888558	−	0.584653i
$886$		0			0
$887$	−5.48215	+	7.32330i	−0.184073	+	0.245892i	−0.883080	−	0.469222i	$-0.844534\pi$
$887$	−5.48215	+	7.32330i	−0.184073	+	0.245892i	0.699008	+	0.715114i	$0.253625\pi$
$888$		0			0
$889$	62.9211	−	18.4753i	2.11031	−	0.619642i
$890$		0			0
$891$	−43.8222	−	37.9722i	−1.46810	−	1.27212i
$892$		0			0
$893$	3.32258	−	46.4557i	0.111186	−	1.55458i
$894$		0			0
$895$	−6.61312	−	11.8070i	−0.221052	−	0.394666i
$896$		0			0
$897$	8.54891	+	36.9711i	0.285440	+	1.23443i
$898$		0			0
$899$	9.13006	+	4.16956i	0.304505	+	0.139063i
$900$		0			0
$901$	−2.44042	−	2.81640i	−0.0813022	−	0.0938278i
$902$		0			0
$903$	−6.69827	−	93.6540i	−0.222904	−	3.11661i
$904$		0			0
$905$	1.27750	−	3.54107i	0.0424654	−	0.117709i
$906$		0			0
$907$	−34.7268	−	25.9961i	−1.15308	−	0.863187i	−0.160776	−	0.986991i	$-0.551400\pi$
$907$	−34.7268	−	25.9961i	−1.15308	−	0.863187i	−0.992307	+	0.123804i	$0.960491\pi$
$908$		0			0
$909$	20.1940	−	9.22230i	0.669793	−	0.305884i
$910$		0			0
$911$	16.4956	−	25.6677i	0.546524	−	0.850409i	−0.452623	−	0.891702i	$-0.649512\pi$
$911$	16.4956	−	25.6677i	0.546524	−	0.850409i	0.999147	+	0.0412936i	$0.0131479\pi$
$912$		0			0
$913$	1.24177	+	1.65881i	0.0410966	+	0.0548986i
$914$		0			0
$915$	26.0223	+	29.3861i	0.860271	+	0.971474i
$916$		0			0
$917$	28.2672	−	15.4351i	0.933465	−	0.509710i
$918$		0			0
$919$	−8.67897			−0.286293			−0.143146	−	0.989702i	$-0.545722\pi$
$919$	−8.67897			−0.286293			−0.143146	+	0.989702i	$0.545722\pi$
$920$		0			0
$921$	−74.5896			−2.45781
$922$		0			0
$923$	−42.0291	+	22.9496i	−1.38340	+	0.755395i
$924$		0			0
$925$	−34.5403	+	3.21915i	−1.13568	+	0.105845i
$926$		0			0
$927$	−4.08916	−	5.46247i	−0.134306	−	0.179411i
$928$		0			0
$929$	3.52606	−	5.48666i	0.115686	−	0.180011i	−0.778582	−	0.627543i	$-0.784061\pi$
$929$	3.52606	−	5.48666i	0.115686	−	0.180011i	0.894268	+	0.447532i	$0.147697\pi$
$930$		0			0
$931$	−40.4625	+	18.4786i	−1.32610	+	0.605611i
$932$		0			0
$933$	27.7874	+	20.8014i	0.909719	+	0.681007i
$934$		0			0
$935$	14.9049	+	31.7288i	0.487443	+	1.03764i
$936$		0			0
$937$	0.473246	+	6.61684i	0.0154603	+	0.216163i	0.999309	+	0.0371622i	$0.0118318\pi$
$937$	0.473246	+	6.61684i	0.0154603	+	0.216163i	−0.983849	+	0.179001i	$0.942714\pi$
$938$		0			0
$939$	−31.5334	−	36.3914i	−1.02905	−	1.18759i
$940$		0			0
$941$	22.1158	+	10.1000i	0.720955	+	0.329249i	0.741881	−	0.670532i	$-0.233934\pi$
$941$	22.1158	+	10.1000i	0.720955	+	0.329249i	−0.0209258	+	0.999781i	$0.506661\pi$
$942$		0			0
$943$	41.2100	+	30.0190i	1.34198	+	0.977553i
$944$		0			0
$945$	14.7921	−	8.28503i	0.481186	−	0.269512i
$946$		0			0
$947$	−1.66347	+	23.2584i	−0.0540555	+	0.755795i	0.896067	+	0.443919i	$0.146412\pi$
$947$	−1.66347	+	23.2584i	−0.0540555	+	0.755795i	−0.950123	+	0.311877i	$0.899042\pi$
$948$		0			0
$949$	−8.45360	−	7.32509i	−0.274416	−	0.237782i
$950$		0			0
$951$	30.1960	−	8.86634i	0.979171	−	0.287511i
$952$		0			0
$953$	34.4398	−	46.0062i	1.11561	−	1.49029i	0.265185	−	0.964198i	$-0.414567\pi$
$953$	34.4398	−	46.0062i	1.11561	−	1.49029i	0.850430	−	0.526089i	$-0.176342\pi$
$954$		0			0
$955$	−16.1369	−	3.32884i	−0.522178	−	0.107719i
$956$		0			0
$957$	44.1032	−	9.59405i	1.42565	−	0.310132i
$958$		0			0
$959$	−11.9987	−	1.72515i	−0.387457	−	0.0557079i
$960$		0			0
$961$	−19.9135	+	12.7976i	−0.642371	+	0.412827i
$962$		0			0
$963$	−3.66838	−	6.71813i	−0.118212	−	0.216489i
$964$		0			0
$965$	36.2394	−	5.60927i	1.16659	−	0.180569i
$966$		0			0
$967$	20.5203	+	20.5203i	0.659889	+	0.659889i	0.955354	−	0.295465i	$-0.0954745\pi$
$967$	20.5203	+	20.5203i	0.659889	+	0.659889i	−0.295465	+	0.955354i	$0.595475\pi$
$968$		0			0
$969$	−9.55687	+	32.5477i	−0.307011	+	1.04558i
$970$		0			0
$971$	28.9995	+	45.1242i	0.930639	+	1.44810i	0.893638	+	0.448788i	$0.148144\pi$
$971$	28.9995	+	45.1242i	0.930639	+	1.44810i	0.0370009	+	0.999315i	$0.488220\pi$
$972$		0			0
$973$	−66.9914	+	50.1491i	−2.14764	+	1.60771i
$974$		0			0
$975$	−38.1907	−	10.3261i	−1.22308	−	0.330699i
$976$		0			0
$977$	41.1218	+	15.3376i	1.31560	+	0.490694i	0.906659	−	0.421865i	$-0.138624\pi$
$977$	41.1218	+	15.3376i	1.31560	+	0.490694i	0.408944	+	0.912560i	$0.365897\pi$
$978$		0			0
$979$	−52.4867	+	7.54645i	−1.67748	+	0.241186i
$980$		0			0
$981$	3.41323	+	11.6244i	0.108976	+	0.371139i
$982$		0			0
$983$	−49.0502	+	3.50814i	−1.56446	+	0.111892i	−0.826493	−	0.562947i	$-0.809667\pi$
$983$	−49.0502	+	3.50814i	−1.56446	+	0.111892i	−0.737964	+	0.674840i	$0.764213\pi$
$984$		0			0
$985$	13.2749	−	15.6575i	0.422973	−	0.498889i
$986$		0			0
$987$	28.6872	+	76.9134i	0.913124	+	2.44818i
$988$		0			0
$989$	32.2635	−	38.2301i	1.02592	−	1.21565i
$990$		0			0
$991$	0.114747	−	0.251262i	0.00364507	−	0.00798159i	−0.907801	−	0.419402i	$-0.862240\pi$
$991$	0.114747	−	0.251262i	0.00364507	−	0.00798159i	0.911446	+	0.411420i	$0.134967\pi$
$992$		0			0
$993$	67.1817	+	4.80493i	2.13195	+	0.152480i
$994$		0			0
$995$	35.1674	−	8.04767i	1.11488	−	0.255128i
$996$		0			0
$997$	−16.4442	−	8.97919i	−0.520792	−	0.284374i	0.197275	−	0.980348i	$-0.436791\pi$
$997$	−16.4442	−	8.97919i	−0.520792	−	0.284374i	−0.718067	+	0.695974i	$0.754973\pi$
$998$		0			0
$999$	1.88883	+	13.1371i	0.0597598	+	0.415639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.7	✓	720
5.3	odd	4	inner	920.2.bv.a.753.7	yes	720
23.19	odd	22	inner	920.2.bv.a.617.7	yes	720
115.88	even	44	inner	920.2.bv.a.433.7	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.7	✓	720	1.1	even	1	trivial
920.2.bv.a.433.7	yes	720	115.88	even	44	inner
920.2.bv.a.617.7	yes	720	23.19	odd	22	inner
920.2.bv.a.753.7	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)

\(f(q)\)	\(=\)	\(q+(-1.99325 + 1.08840i) q^{3} +(2.23196 + 0.135499i) q^{5} +(2.37528 + 3.17300i) q^{7} +(1.16653 - 1.81515i) q^{9} +(-4.87592 + 2.22676i) q^{11} +(2.78911 + 2.08790i) q^{13} +(-4.59634 + 2.15918i) q^{15} +(-0.208644 - 2.91722i) q^{17} +(3.34444 + 3.85969i) q^{19} +(-8.18803 - 3.73935i) q^{21} +(-1.73442 - 4.47122i) q^{23} +(4.96328 + 0.604856i) q^{25} +(0.136469 - 1.90809i) q^{27} +(2.80201 + 2.42796i) q^{29} +(2.59751 - 0.762699i) q^{31} +(7.29535 - 9.74544i) q^{33} +(4.87159 + 7.40386i) q^{35} +(-6.77945 + 1.47478i) q^{37} +(-7.83188 - 1.12605i) q^{39} +(-8.94334 + 5.74753i) q^{41} +(4.99899 + 9.15497i) q^{43} +(2.84959 - 3.89328i) q^{45} +(-6.44848 - 6.44848i) q^{47} +(-2.45386 + 8.35707i) q^{49} +(3.59098 + 5.58768i) q^{51} +(1.02005 - 0.763601i) q^{53} +(-11.1846 + 4.30935i) q^{55} +(-10.8672 - 4.05325i) q^{57} +(-6.16760 + 0.886766i) q^{59} +(-2.17763 - 7.41633i) q^{61} +(8.53030 - 0.610099i) q^{63} +(5.94227 + 5.03803i) q^{65} +(2.34825 + 6.29590i) q^{67} +(8.32360 + 7.02454i) q^{69} +(-5.70971 + 12.5025i) q^{71} +(-3.20239 - 0.229039i) q^{73} +(-10.5514 + 4.19640i) q^{75} +(-18.6472 - 10.1821i) q^{77} +(-0.287493 - 1.99956i) q^{79} +(4.49374 + 9.83991i) q^{81} +(-0.0821702 - 0.377730i) q^{83} +(-0.0704040 - 6.53939i) q^{85} +(-8.22770 - 1.78983i) q^{87} +(9.49169 + 2.78701i) q^{89} +13.8092i q^{91} +(-4.34738 + 4.34738i) q^{93} +(6.94166 + 9.06783i) q^{95} +(0.806253 - 3.70628i) q^{97} +(-1.64599 + 11.4481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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