LMFDB - Embedded newform 460.2.x.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([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("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	460.17
Dual form			460.2.x.a.433.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.302476 - 0.165164i) q^{3} +(0.209636 + 2.22622i) q^{5} +(1.78504 + 2.38454i) q^{7} +(-1.55771 + 2.42384i) q^{9} +O(q^{10})$	\(q+(0.302476 - 0.165164i) q^{3} +(0.209636 + 2.22622i) q^{5} +(1.78504 + 2.38454i) q^{7} +(-1.55771 + 2.42384i) q^{9} +(-4.07006 + 1.85874i) q^{11} +(-3.33665 - 2.49778i) q^{13} +(0.431102 + 0.638753i) q^{15} +(-0.0454815 - 0.635915i) q^{17} +(-2.20487 - 2.54456i) q^{19} +(0.933773 + 0.426440i) q^{21} +(3.91542 + 2.76939i) q^{23} +(-4.91211 + 0.933392i) q^{25} +(-0.144594 + 2.02169i) q^{27} +(5.92400 + 5.13317i) q^{29} +(9.56653 - 2.80899i) q^{31} +(-0.924099 + 1.23445i) q^{33} +(-4.93430 + 4.47378i) q^{35} +(-7.13797 + 1.55277i) q^{37} +(-1.42180 - 0.204424i) q^{39} +(5.64206 - 3.62593i) q^{41} +(5.37162 + 9.83738i) q^{43} +(-5.72256 - 2.95968i) q^{45} +(2.02897 + 2.02897i) q^{47} +(-0.527516 + 1.79655i) q^{49} +(-0.118787 - 0.184837i) q^{51} +(2.88890 - 2.16261i) q^{53} +(-4.99119 - 8.67120i) q^{55} +(-1.08719 - 0.405501i) q^{57} +(11.8196 - 1.69940i) q^{59} +(-4.15281 - 14.1432i) q^{61} +(-8.56033 + 0.612247i) q^{63} +(4.86113 - 7.95174i) q^{65} +(-0.766670 - 2.05552i) q^{67} +(1.64172 + 0.190986i) q^{69} +(-3.91521 + 8.57311i) q^{71} +(10.7389 + 0.768059i) q^{73} +(-1.33163 + 1.09363i) q^{75} +(-11.6975 - 6.38730i) q^{77} +(0.325925 + 2.26686i) q^{79} +(-3.30054 - 7.22718i) q^{81} +(2.33042 + 10.7128i) q^{83} +(1.40615 - 0.234562i) q^{85} +(2.63968 + 0.574228i) q^{87} +(-2.32594 - 0.682958i) q^{89} -12.4150i q^{91} +(2.42970 - 2.42970i) q^{93} +(5.20252 - 5.44196i) q^{95} +(-1.80046 + 8.27658i) q^{97} +(1.83469 - 12.7606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.302476	−	0.165164i	0.174635	−	0.0953577i	−0.389554	−	0.921004i	$-0.627371\pi$
$3$	0.302476	−	0.165164i	0.174635	−	0.0953577i	0.564189	+	0.825646i	$0.309189\pi$
$4$		0			0
$5$	0.209636	+	2.22622i	0.0937521	+	0.995596i
$5$	0.209636	+	2.22622i	0.0937521	+	0.995596i
$6$		0			0
$7$	1.78504	+	2.38454i	0.674683	+	0.901271i	0.999001	−	0.0446772i	$-0.0142259\pi$
$7$	1.78504	+	2.38454i	0.674683	+	0.901271i	−0.324319	+	0.945948i	$0.605135\pi$
$8$		0			0
$9$	−1.55771	+	2.42384i	−0.519237	+	0.807948i
$10$		0			0
$11$	−4.07006	+	1.85874i	−1.22717	+	0.560430i	−0.920260	−	0.391308i	$-0.872023\pi$
$11$	−4.07006	+	1.85874i	−1.22717	+	0.560430i	−0.306911	+	0.951738i	$0.599295\pi$
$12$		0			0
$13$	−3.33665	−	2.49778i	−0.925420	−	0.692761i	0.0263243	−	0.999653i	$-0.491620\pi$
$13$	−3.33665	−	2.49778i	−0.925420	−	0.692761i	−0.951744	+	0.306893i	$0.900711\pi$
$14$		0			0
$15$	0.431102	+	0.638753i	0.111310	+	0.164925i
$16$		0			0
$17$	−0.0454815	−	0.635915i	−0.0110309	−	0.154232i	−0.999982	−	0.00599033i	$-0.998093\pi$
$17$	−0.0454815	−	0.635915i	−0.0110309	−	0.154232i	0.988951	−	0.148242i	$-0.0473613\pi$
$18$		0			0
$19$	−2.20487	−	2.54456i	−0.505832	−	0.583761i	0.444195	−	0.895930i	$-0.353490\pi$
$19$	−2.20487	−	2.54456i	−0.505832	−	0.583761i	−0.950027	+	0.312169i	$0.898944\pi$
$20$		0			0
$21$	0.933773	+	0.426440i	0.203766	+	0.0930568i
$22$		0			0
$23$	3.91542	+	2.76939i	0.816421	+	0.577457i
$23$	3.91542	+	2.76939i	0.816421	+	0.577457i
$24$		0			0
$25$	−4.91211	+	0.933392i	−0.982421	+	0.186678i
$26$		0			0
$27$	−0.144594	+	2.02169i	−0.0278272	+	0.389075i
$28$		0			0
$29$	5.92400	+	5.13317i	1.10006	+	0.953207i	0.999131	−	0.0416872i	$-0.0132733\pi$
$29$	5.92400	+	5.13317i	1.10006	+	0.953207i	0.100928	+	0.994894i	$0.467819\pi$
$30$		0			0
$31$	9.56653	−	2.80899i	1.71820	−	0.504509i	0.733637	−	0.679541i	$-0.237821\pi$
$31$	9.56653	−	2.80899i	1.71820	−	0.504509i	0.984563	+	0.175032i	$0.0560030\pi$
$32$		0			0
$33$	−0.924099	+	1.23445i	−0.160865	+	0.214891i
$34$		0			0
$35$	−4.93430	+	4.47378i	−0.834048	+	0.756207i
$36$		0			0
$37$	−7.13797	+	1.55277i	−1.17347	+	0.255274i	−0.756716	−	0.653744i	$-0.773197\pi$
$37$	−7.13797	+	1.55277i	−1.17347	+	0.255274i	−0.416758	+	0.909017i	$0.636834\pi$
$38$		0			0
$39$	−1.42180	−	0.204424i	−0.227670	−	0.0327340i
$40$		0			0
$41$	5.64206	−	3.62593i	0.881141	−	0.566275i	−0.0200003	−	0.999800i	$-0.506367\pi$
$41$	5.64206	−	3.62593i	0.881141	−	0.566275i	0.901142	+	0.433525i	$0.142730\pi$
$42$		0			0
$43$	5.37162	+	9.83738i	0.819164	+	1.50019i	0.865301	+	0.501252i	$0.167127\pi$
$43$	5.37162	+	9.83738i	0.819164	+	1.50019i	−0.0461372	+	0.998935i	$0.514691\pi$
$44$		0			0
$45$	−5.72256	−	2.95968i	−0.853069	−	0.441203i
$46$		0			0
$47$	2.02897	+	2.02897i	0.295956	+	0.295956i	0.839428	−	0.543472i	$-0.182890\pi$
$47$	2.02897	+	2.02897i	0.295956	+	0.295956i	−0.543472	+	0.839428i	$0.682890\pi$
$48$		0			0
$49$	−0.527516	+	1.79655i	−0.0753594	+	0.256650i
$50$		0			0
$51$	−0.118787	−	0.184837i	−0.0166336	−	0.0258823i
$52$		0			0
$53$	2.88890	−	2.16261i	0.396821	−	0.297057i	−0.382169	−	0.924092i	$-0.624823\pi$
$53$	2.88890	−	2.16261i	0.396821	−	0.297057i	0.778991	+	0.627036i	$0.215732\pi$
$54$		0			0
$55$	−4.99119	−	8.67120i	−0.673012	−	1.16922i
$56$		0			0
$57$	−1.08719	−	0.405501i	−0.144002	−	0.0537099i
$58$		0			0
$59$	11.8196	−	1.69940i	1.53878	−	0.221243i	0.679854	−	0.733347i	$-0.262043\pi$
$59$	11.8196	−	1.69940i	1.53878	−	0.221243i	0.858923	+	0.512104i	$0.171134\pi$
$60$		0			0
$61$	−4.15281	−	14.1432i	−0.531713	−	1.81085i	−0.583401	−	0.812184i	$-0.698278\pi$
$61$	−4.15281	−	14.1432i	−0.531713	−	1.81085i	0.0516880	−	0.998663i	$-0.483540\pi$
$62$		0			0
$63$	−8.56033	+	0.612247i	−1.07850	+	0.0771358i
$64$		0			0
$65$	4.86113	−	7.95174i	0.602949	−	0.986292i
$66$		0			0
$67$	−0.766670	−	2.05552i	−0.0936637	−	0.251122i	0.881667	−	0.471873i	$-0.156422\pi$
$67$	−0.766670	−	2.05552i	−0.0936637	−	0.251122i	−0.975330	+	0.220751i	$0.929149\pi$
$68$		0			0
$69$	1.64172	+	0.190986i	0.197640	+	0.0229920i
$70$		0			0
$71$	−3.91521	+	8.57311i	−0.464650	+	1.01744i	0.521753	+	0.853096i	$0.325278\pi$
$71$	−3.91521	+	8.57311i	−0.464650	+	1.01744i	−0.986403	+	0.164344i	$0.947449\pi$
$72$		0			0
$73$	10.7389	+	0.768059i	1.25689	+	0.0898945i	0.683843	−	0.729629i	$-0.260307\pi$
$73$	10.7389	+	0.768059i	1.25689	+	0.0898945i	0.573046	+	0.819523i	$0.305762\pi$
$74$		0			0
$75$	−1.33163	+	1.09363i	−0.153763	+	0.126282i
$76$		0			0
$77$	−11.6975	−	6.38730i	−1.33305	−	0.727900i
$78$		0			0
$79$	0.325925	+	2.26686i	0.0366695	+	0.255042i	0.999907	−	0.0136080i	$-0.00433170\pi$
$79$	0.325925	+	2.26686i	0.0366695	+	0.255042i	−0.963238	+	0.268650i	$0.913423\pi$
$80$		0			0
$81$	−3.30054	−	7.22718i	−0.366727	−	0.803020i
$82$		0			0
$83$	2.33042	+	10.7128i	0.255797	+	1.17588i	0.908375	+	0.418157i	$0.137324\pi$
$83$	2.33042	+	10.7128i	0.255797	+	1.17588i	−0.652578	+	0.757722i	$0.726313\pi$
$84$		0			0
$85$	1.40615	−	0.234562i	0.152518	−	0.0254419i
$86$		0			0
$87$	2.63968	+	0.574228i	0.283004	+	0.0615637i
$88$		0			0
$89$	−2.32594	−	0.682958i	−0.246549	−	0.0723934i	0.156123	−	0.987738i	$-0.450100\pi$
$89$	−2.32594	−	0.682958i	−0.246549	−	0.0723934i	−0.402672	+	0.915344i	$0.631919\pi$
$90$		0			0
$91$		−	12.4150i		−	1.30145i
$92$		0			0
$93$	2.42970	−	2.42970i	0.251948	−	0.251948i
$94$		0			0
$95$	5.20252	−	5.44196i	0.533767	−	0.558333i
$96$		0			0
$97$	−1.80046	+	8.27658i	−0.182809	+	0.840359i	0.790789	+	0.612089i	$0.209671\pi$
$97$	−1.80046	+	8.27658i	−0.182809	+	0.840359i	−0.973598	+	0.228270i	$0.926693\pi$
$98$		0			0
$99$	1.83469	−	12.7606i	0.184394	−	1.28249i
$100$		0			0
$101$	−5.40762	−	3.47527i	−0.538078	−	0.345802i	0.243208	−	0.969974i	$-0.421800\pi$
$101$	−5.40762	−	3.47527i	−0.538078	−	0.345802i	−0.781287	+	0.624172i	$0.785436\pi$
$102$		0			0
$103$	−2.59526	+	6.95817i	−0.255719	+	0.685608i	0.744127	+	0.668038i	$0.232866\pi$
$103$	−2.59526	+	6.95817i	−0.255719	+	0.685608i	−0.999846	+	0.0175702i	$0.994407\pi$
$104$		0			0
$105$	−0.753596	+	2.16818i	−0.0735434	+	0.211593i
$106$		0			0
$107$	−1.86154	+	3.40916i	−0.179962	+	0.329576i	−0.952051	−	0.305938i	$-0.901030\pi$
$107$	−1.86154	+	3.40916i	−0.179962	+	0.329576i	0.772089	+	0.635514i	$0.219212\pi$
$108$		0			0
$109$	5.64043	−	6.50940i	0.540255	−	0.623488i	−0.418330	−	0.908295i	$-0.637384\pi$
$109$	5.64043	−	6.50940i	0.540255	−	0.623488i	0.958585	+	0.284808i	$0.0919297\pi$
$110$		0			0
$111$	−1.90260	+	1.64861i	−0.180587	+	0.156479i
$112$		0			0
$113$	−10.7153	+	3.99661i	−1.00801	+	0.375970i	−0.798603	−	0.601858i	$-0.794427\pi$
$113$	−10.7153	+	3.99661i	−1.00801	+	0.375970i	−0.209411	+	0.977828i	$0.567155\pi$
$114$		0			0
$115$	−5.34445	+	9.29714i	−0.498373	+	0.866963i
$116$		0			0
$117$	11.2518	−	4.19669i	1.04023	−	0.387984i
$118$		0			0
$119$	1.43518	−	1.24359i	0.131562	−	0.113999i
$120$		0			0
$121$	5.90706	−	6.81711i	0.537005	−	0.619737i
$122$		0			0
$123$	1.10771	−	2.02862i	0.0998790	−	0.182915i
$124$		0			0
$125$	−3.10769	−	10.7398i	−0.277960	−	0.960593i
$126$		0			0
$127$	4.35413	−	11.6739i	0.386367	−	1.03589i	−0.587591	−	0.809158i	$-0.699923\pi$
$127$	4.35413	−	11.6739i	0.386367	−	1.03589i	0.973957	−	0.226731i	$-0.0728038\pi$
$128$		0			0
$129$	3.24957	+	2.08837i	0.286109	+	0.183871i
$130$		0			0
$131$	1.90128	−	13.2237i	0.166116	−	1.15536i	−0.720703	−	0.693244i	$-0.756181\pi$
$131$	1.90128	−	13.2237i	0.166116	−	1.15536i	0.886819	−	0.462118i	$-0.152910\pi$
$132$		0			0
$133$	2.13180	−	9.79974i	0.184851	−	0.849745i
$134$		0			0
$135$	−4.53104	+	0.101921i	−0.389970	+	0.00877196i
$136$		0			0
$137$	11.7160	−	11.7160i	1.00097	−	1.00097i	0.000966797	−	1.00000i	$-0.499692\pi$
$137$	11.7160	−	11.7160i	1.00097	−	1.00097i	1.00000		0.000966797i	$-0.000307741\pi$
$138$		0			0
$139$			7.58540i			0.643385i	0.946844	+	0.321693i	$0.104252\pi$
$139$			7.58540i			0.643385i	−0.946844	+	0.321693i	$0.895748\pi$
$140$		0			0
$141$	0.948829	+	0.278601i	0.0799058	+	0.0234625i
$142$		0			0
$143$	18.2231	+	3.96419i	1.52389	+	0.331502i
$144$		0			0
$145$	−10.1857	+	14.2642i	−0.845875	+	1.18458i
$146$		0			0
$147$	0.137166	+	0.630541i	0.0113132	+	0.0520061i
$148$		0			0
$149$	3.13411	+	6.86275i	0.256756	+	0.562218i	0.993484	−	0.113971i	$-0.0363573\pi$
$149$	3.13411	+	6.86275i	0.256756	+	0.562218i	−0.736728	+	0.676190i	$0.763630\pi$
$150$		0			0
$151$	−0.0913361	−	0.635256i	−0.00743282	−	0.0516964i	0.985767	−	0.168115i	$-0.0537678\pi$
$151$	−0.0913361	−	0.635256i	−0.00743282	−	0.0516964i	−0.993200	+	0.116418i	$0.962859\pi$
$152$		0			0
$153$	1.61221	+	0.880331i	0.130339	+	0.0711705i
$154$		0			0
$155$	8.25891	+	20.7083i	0.663372	+	1.66333i
$156$		0			0
$157$	−21.3879	−	1.52969i	−1.70694	−	0.122083i	−0.816546	−	0.577280i	$-0.804114\pi$
$157$	−21.3879	−	1.52969i	−1.70694	−	0.122083i	−0.890390	+	0.455198i	$0.849569\pi$
$158$		0			0
$159$	0.516638	−	1.13128i	0.0409721	−	0.0897163i
$160$		0			0
$161$	0.385476	+	14.2799i	0.0303798	+	1.12542i
$162$		0			0
$163$	−5.79862	−	15.5467i	−0.454183	−	1.21771i	−0.939249	−	0.343235i	$-0.888477\pi$
$163$	−5.79862	−	15.5467i	−0.454183	−	1.21771i	0.485066	−	0.874477i	$-0.338796\pi$
$164$		0			0
$165$	−2.94189	−	1.79846i	−0.229026	−	0.140010i
$166$		0			0
$167$	−11.6385	+	0.832401i	−0.900613	+	0.0644131i	−0.513962	−	0.857813i	$-0.671823\pi$
$167$	−11.6385	+	0.832401i	−0.900613	+	0.0644131i	−0.386651	+	0.922226i	$0.626368\pi$
$168$		0			0
$169$	1.23178	+	4.19504i	0.0947520	+	0.322696i
$170$		0			0
$171$	9.60216	−	1.38058i	0.734295	−	0.105576i
$172$		0			0
$173$	9.10206	+	3.39489i	0.692017	+	0.258109i	0.670770	−	0.741665i	$-0.265964\pi$
$173$	9.10206	+	3.39489i	0.692017	+	0.258109i	0.0212469	+	0.999774i	$0.493236\pi$
$174$		0			0
$175$	−10.9940	−	10.0470i	−0.831070	−	0.759479i
$176$		0			0
$177$	3.29446	−	2.46620i	0.247626	−	0.185371i
$178$		0			0
$179$	6.14156	+	9.55645i	0.459041	+	0.714282i	0.991202	−	0.132361i	$-0.0422559\pi$
$179$	6.14156	+	9.55645i	0.459041	+	0.714282i	−0.532160	+	0.846644i	$0.678620\pi$
$180$		0			0
$181$	1.88899	−	6.43331i	0.140408	−	0.478184i	−0.859023	−	0.511938i	$-0.828928\pi$
$181$	1.88899	−	6.43331i	0.140408	−	0.478184i	0.999430	+	0.0337534i	$0.0107461\pi$
$182$		0			0
$183$	−3.59207	−	3.59207i	−0.265534	−	0.265534i
$184$		0			0
$185$	−4.95318	−	15.5652i	−0.364165	−	1.14437i
$186$		0			0
$187$	1.36711	+	2.50368i	0.0999730	+	0.183087i
$188$		0			0
$189$	−5.07891	+	3.26402i	−0.369436	+	0.237422i
$190$		0			0
$191$	4.51343	+	0.648934i	0.326581	+	0.0469552i	0.303655	−	0.952782i	$-0.401793\pi$
$191$	4.51343	+	0.648934i	0.326581	+	0.0469552i	0.0229253	+	0.999737i	$0.492702\pi$
$192$		0			0
$193$	−20.9166	+	4.55014i	−1.50561	+	0.327526i	−0.888327	−	0.459212i	$-0.848132\pi$
$193$	−20.9166	+	4.55014i	−1.50561	+	0.327526i	−0.617287	+	0.786738i	$0.711768\pi$
$194$		0			0
$195$	0.157032	−	3.20809i	0.0112453	−	0.229736i
$196$		0			0
$197$	−12.9606	+	17.3134i	−0.923407	+	1.23353i	0.0486574	+	0.998816i	$0.484506\pi$
$197$	−12.9606	+	17.3134i	−0.923407	+	1.23353i	−0.972065	+	0.234712i	$0.924585\pi$
$198$		0			0
$199$	5.05694	−	1.48485i	0.358477	−	0.105258i	−0.0975346	−	0.995232i	$-0.531096\pi$
$199$	5.05694	−	1.48485i	0.358477	−	0.105258i	0.456012	+	0.889974i	$0.349277\pi$
$200$		0			0
$201$	−0.571398	−	0.495119i	−0.0403033	−	0.0349230i
$202$		0			0
$203$	−1.66566	+	23.2889i	−0.116906	+	1.63456i
$204$		0			0
$205$	9.25489	+	11.8003i	0.646390	+	0.824171i
$206$		0			0
$207$	−12.8116	+	5.17646i	−0.890471	+	0.359789i
$208$		0			0
$209$	13.7036	+	6.25824i	0.947900	+	0.432891i
$210$		0			0
$211$	−0.484315	−	0.558929i	−0.0333416	−	0.0384783i	0.738834	−	0.673888i	$-0.235377\pi$
$211$	−0.484315	−	0.558929i	−0.0333416	−	0.0384783i	−0.772175	+	0.635409i	$0.780831\pi$
$212$		0			0
$213$	0.231716	+	3.23981i	0.0158769	+	0.221988i
$214$		0			0
$215$	−20.7741	+	14.0207i	−1.41678	+	0.956202i
$216$		0			0
$217$	23.7748	+	17.7976i	1.61394	+	1.20818i
$218$		0			0
$219$	3.37510	−	1.54136i	0.228068	−	0.104155i
$220$		0			0
$221$	−1.43662	+	2.23543i	−0.0966376	+	0.150371i
$222$		0			0
$223$	2.11949	+	2.83131i	0.141931	+	0.189598i	0.865874	−	0.500262i	$-0.166763\pi$
$223$	2.11949	+	2.83131i	0.141931	+	0.189598i	−0.723943	+	0.689860i	$0.757672\pi$
$224$		0			0
$225$	5.38924	−	13.3601i	0.359283	−	0.890675i
$226$		0			0
$227$	4.49324	−	2.45350i	0.298227	−	0.162844i	−0.323168	−	0.946342i	$-0.604748\pi$
$227$	4.49324	−	2.45350i	0.298227	−	0.162844i	0.621395	+	0.783497i	$0.286566\pi$
$228$		0			0
$229$	−21.1248			−1.39596			−0.697982	−	0.716116i	$-0.745918\pi$
$229$	−21.1248			−1.39596			−0.697982	+	0.716116i	$0.745918\pi$
$230$		0			0
$231$	−4.59316			−0.302207
$232$		0			0
$233$	14.0757	−	7.68589i	0.922127	−	0.503519i	0.0532685	−	0.998580i	$-0.483036\pi$
$233$	14.0757	−	7.68589i	0.922127	−	0.503519i	0.868858	+	0.495061i	$0.164854\pi$
$234$		0			0
$235$	−4.09159	+	4.94228i	−0.266906	+	0.322399i
$236$		0			0
$237$	0.472989	+	0.631839i	0.0307239	+	0.0410424i
$238$		0			0
$239$	4.62185	−	7.19174i	0.298963	−	0.465195i	−0.658978	−	0.752163i	$-0.729011\pi$
$239$	4.62185	−	7.19174i	0.298963	−	0.465195i	0.957940	+	0.286967i	$0.0926471\pi$
$240$		0			0
$241$	4.67760	−	2.13619i	0.301311	−	0.137604i	−0.259022	−	0.965871i	$-0.583400\pi$
$241$	4.67760	−	2.13619i	0.301311	−	0.137604i	0.560333	+	0.828267i	$0.310673\pi$
$242$		0			0
$243$	−7.05975	−	5.28487i	−0.452883	−	0.339024i
$244$		0			0
$245$	−4.11011	−	0.797743i	−0.262585	−	0.0509659i
$246$		0			0
$247$	1.00113	+	13.9976i	0.0637002	+	0.890645i
$248$		0			0
$249$	2.47426	+	2.85545i	0.156800	+	0.180957i
$250$		0			0
$251$	19.5987	+	8.95043i	1.23706	+	0.564946i	0.923126	−	0.384499i	$-0.125626\pi$
$251$	19.5987	+	8.95043i	1.23706	+	0.564946i	0.313934	+	0.949445i	$0.398353\pi$
$252$		0			0
$253$	−21.0836	−	3.99386i	−1.32551	−	0.251092i
$254$		0			0
$255$	0.386585	−	0.303195i	0.0242089	−	0.0189868i
$256$		0			0
$257$	−1.77761	+	24.8543i	−0.110885	+	1.55037i	0.572252	+	0.820078i	$0.306070\pi$
$257$	−1.77761	+	24.8543i	−0.110885	+	1.55037i	−0.683137	+	0.730290i	$0.739385\pi$
$258$		0			0
$259$	−16.4442	−	14.2490i	−1.02179	−	0.885389i
$260$		0			0
$261$	−21.6699	+	6.36285i	−1.34133	+	0.393851i
$262$		0			0
$263$	7.03724	−	9.40065i	0.433935	−	0.579669i	−0.529265	−	0.848457i	$-0.677532\pi$
$263$	7.03724	−	9.40065i	0.433935	−	0.579669i	0.963199	+	0.268788i	$0.0866231\pi$
$264$		0			0
$265$	5.42005	+	5.97797i	0.332951	+	0.367224i
$266$		0			0
$267$	−0.816342	+	0.177584i	−0.0499593	+	0.0108680i
$268$		0			0
$269$	−10.2105	−	1.46805i	−0.622545	−	0.0895084i	−0.176178	−	0.984358i	$-0.556373\pi$
$269$	−10.2105	−	1.46805i	−0.622545	−	0.0895084i	−0.446367	+	0.894850i	$0.647282\pi$
$270$		0			0
$271$	15.1139	−	9.71310i	0.918103	−	0.590029i	0.00599611	−	0.999982i	$-0.498091\pi$
$271$	15.1139	−	9.71310i	0.918103	−	0.590029i	0.912107	+	0.409953i	$0.134455\pi$
$272$		0			0
$273$	−2.05052	−	3.75524i	−0.124103	−	0.227278i
$274$		0			0
$275$	18.2577	−	12.9293i	1.10098	−	0.779665i
$276$		0			0
$277$	−12.1226	−	12.1226i	−0.728375	−	0.728375i	0.241921	−	0.970296i	$-0.422223\pi$
$277$	−12.1226	−	12.1226i	−0.728375	−	0.728375i	−0.970296	+	0.241921i	$0.922223\pi$
$278$		0			0
$279$	−8.09334	+	27.5634i	−0.484535	+	1.65018i
$280$		0			0
$281$	10.7021	+	16.6528i	0.638433	+	0.993420i	0.998176	+	0.0603692i	$0.0192278\pi$
$281$	10.7021	+	16.6528i	0.638433	+	0.993420i	−0.359744	+	0.933051i	$0.617136\pi$
$282$		0			0
$283$	−5.35702	+	4.01021i	−0.318442	+	0.238382i	−0.746526	−	0.665356i	$-0.768280\pi$
$283$	−5.35702	+	4.01021i	−0.318442	+	0.238382i	0.428084	+	0.903739i	$0.359189\pi$
$284$		0			0
$285$	0.674820	−	2.50533i	0.0399729	−	0.148403i
$286$		0			0
$287$	18.7175	+	6.98126i	1.10486	+	0.412091i
$288$		0			0
$289$	16.4246	−	2.36151i	0.966156	−	0.138912i
$290$		0			0
$291$	0.822400	+	2.80084i	0.0482099	+	0.164188i
$292$		0			0
$293$	11.4646	−	0.819967i	0.669771	−	0.0479030i	0.267687	−	0.963506i	$-0.413741\pi$
$293$	11.4646	−	0.819967i	0.669771	−	0.0479030i	0.402084	+	0.915603i	$0.368286\pi$
$294$		0			0
$295$	6.26104	+	25.9567i	0.364532	+	1.51126i
$296$		0			0
$297$	−3.16929	−	8.49718i	−0.183901	−	0.493057i
$298$		0			0
$299$	−6.14704	−	19.0203i	−0.355492	−	1.09997i
$300$		0			0
$301$	−13.8690	+	30.3690i	−0.799399	+	1.75044i
$302$		0			0
$303$	−2.20967	−	0.158038i	−0.126942	−	0.00907907i
$304$		0			0
$305$	30.6152	−	12.2100i	1.75302	−	0.699142i
$306$		0			0
$307$	8.69945	+	4.75026i	0.496504	+	0.271112i	0.707930	−	0.706282i	$-0.249629\pi$
$307$	8.69945	+	4.75026i	0.496504	+	0.271112i	−0.211426	+	0.977394i	$0.567811\pi$
$308$		0			0
$309$	0.364237	+	2.53332i	0.0207207	+	0.144116i
$310$		0			0
$311$	−7.27275	−	15.9251i	−0.412400	−	0.903030i	−0.995861	−	0.0908890i	$-0.971029\pi$
$311$	−7.27275	−	15.9251i	−0.412400	−	0.903030i	0.583461	−	0.812141i	$-0.301698\pi$
$312$		0			0
$313$	4.19015	+	19.2618i	0.236842	+	1.08874i	0.929886	+	0.367848i	$0.119905\pi$
$313$	4.19015	+	19.2618i	0.236842	+	1.08874i	−0.693044	+	0.720895i	$0.743731\pi$
$314$		0			0
$315$	−3.15755	−	18.9288i	−0.177908	−	1.06652i
$316$		0			0
$317$	−11.7614	−	2.55854i	−0.660587	−	0.143702i	−0.130240	−	0.991482i	$-0.541575\pi$
$317$	−11.7614	−	2.55854i	−0.660587	−	0.143702i	−0.530347	+	0.847781i	$0.677938\pi$
$318$		0			0
$319$	−33.6523	−	9.88120i	−1.88417	−	0.553241i
$320$		0			0
$321$			1.33865i			0.0747161i
$322$		0			0
$323$	−1.51784	+	1.51784i	−0.0844549	+	0.0844549i
$324$		0			0
$325$	18.7214	+	9.15498i	1.03848	+	0.507827i
$326$		0			0
$327$	0.630973	−	2.90053i	0.0348929	−	0.160400i
$328$		0			0
$329$	−1.21636	+	8.45996i	−0.0670600	+	0.466413i
$330$		0			0
$331$	−11.7823	−	7.57205i	−0.647616	−	0.416198i	0.175178	−	0.984537i	$-0.443950\pi$
$331$	−11.7823	−	7.57205i	−0.647616	−	0.416198i	−0.822794	+	0.568339i	$0.807586\pi$
$332$		0			0
$333$	7.35521	−	19.7201i	0.403063	−	1.08065i
$334$		0			0
$335$	4.41532	−	2.13769i	0.241235	−	0.116794i
$336$		0			0
$337$	12.5892	−	23.0554i	0.685777	−	1.25591i	−0.270295	−	0.962777i	$-0.587121\pi$
$337$	12.5892	−	23.0554i	0.685777	−	1.25591i	0.956073	−	0.293130i	$-0.0946968\pi$
$338$		0			0
$339$	−2.58103	+	2.97867i	−0.140182	+	0.161779i
$340$		0			0
$341$	−33.7152	+	29.2144i	−1.82578	+	1.58205i
$342$		0			0
$343$	14.3104	−	5.33749i	0.772688	−	0.288198i
$344$		0			0
$345$	−0.0810121	+	3.69487i	−0.00436154	+	0.198925i
$346$		0			0
$347$	3.53267	−	1.31762i	0.189644	−	0.0707334i	−0.252848	−	0.967506i	$-0.581367\pi$
$347$	3.53267	−	1.31762i	0.189644	−	0.0707334i	0.442492	+	0.896773i	$0.354095\pi$
$348$		0			0
$349$	10.1672	−	8.80991i	0.544237	−	0.471584i	−0.338819	−	0.940851i	$-0.610028\pi$
$349$	10.1672	−	8.80991i	0.544237	−	0.471584i	0.883056	+	0.469268i	$0.155482\pi$
$350$		0			0
$351$	5.53221	−	6.38451i	0.295288	−	0.340780i
$352$		0			0
$353$	−0.377814	+	0.691914i	−0.0201090	+	0.0368269i	−0.887540	−	0.460730i	$-0.847588\pi$
$353$	−0.377814	+	0.691914i	−0.0201090	+	0.0368269i	0.867431	+	0.497557i	$0.165769\pi$
$354$		0			0
$355$	−19.9064	−	6.91888i	−1.05652	−	0.367216i
$356$		0			0
$357$	0.228710	−	0.613195i	0.0121046	−	0.0324537i
$358$		0			0
$359$	−4.30233	−	2.76494i	−0.227068	−	0.145928i	0.422161	−	0.906521i	$-0.361272\pi$
$359$	−4.30233	−	2.76494i	−0.227068	−	0.145928i	−0.649229	+	0.760593i	$0.724908\pi$
$360$		0			0
$361$	1.09067	−	7.58577i	0.0574037	−	0.399251i
$362$		0			0
$363$	0.660800	−	3.03765i	0.0346830	−	0.159435i
$364$		0			0
$365$	0.541385	+	24.0681i	0.0283374	+	1.25978i
$366$		0			0
$367$	−6.04140	+	6.04140i	−0.315359	+	0.315359i	−0.846981	−	0.531623i	$-0.821582\pi$
$367$	−6.04140	+	6.04140i	−0.315359	+	0.315359i	0.531623	+	0.846981i	$0.321582\pi$
$368$		0			0
$369$			19.3236i			1.00595i
$370$		0			0
$371$	10.3136	+	3.02836i	0.535457	+	0.157224i
$372$		0			0
$373$	24.9275	+	5.42265i	1.29070	+	0.280774i	0.804959	−	0.593330i	$-0.202187\pi$
$373$	24.9275	+	5.42265i	1.29070	+	0.280774i	0.485739	+	0.874104i	$0.338551\pi$
$374$		0			0
$375$	−2.71382	−	2.73524i	−0.140141	−	0.141247i
$376$		0			0
$377$	−6.94474	−	31.9245i	−0.357672	−	1.64419i
$378$		0			0
$379$	−13.4024	−	29.3471i	−0.688434	−	1.50746i	−0.853453	−	0.521170i	$-0.825496\pi$
$379$	−13.4024	−	29.3471i	−0.688434	−	1.50746i	0.165019	−	0.986290i	$-0.447231\pi$
$380$		0			0
$381$	−0.611089	−	4.25021i	−0.0313070	−	0.217745i
$382$		0			0
$383$	−23.7735	−	12.9813i	−1.21477	−	0.663313i	−0.261431	−	0.965222i	$-0.584194\pi$
$383$	−23.7735	−	12.9813i	−1.21477	−	0.663313i	−0.953337	+	0.301909i	$0.902376\pi$
$384$		0			0
$385$	11.7673	−	27.3801i	0.599718	−	1.39542i
$386$		0			0
$387$	−32.2117	−	2.30383i	−1.63741	−	0.117110i
$388$		0			0
$389$	0.638490	−	1.39810i	0.0323727	−	0.0708864i	−0.892755	−	0.450543i	$-0.851230\pi$
$389$	0.638490	−	1.39810i	0.0323727	−	0.0708864i	0.925128	+	0.379656i	$0.123958\pi$
$390$		0			0
$391$	1.58302	−	2.61583i	0.0800565	−	0.132288i
$392$		0			0
$393$	−1.60899	−	4.31388i	−0.0811630	−	0.217607i
$394$		0			0
$395$	−4.97820	+	1.20080i	−0.250481	+	0.0604186i
$396$		0			0
$397$	15.3843	−	1.10031i	0.772117	−	0.0552229i	0.320279	−	0.947323i	$-0.396223\pi$
$397$	15.3843	−	1.10031i	0.772117	−	0.0552229i	0.451837	+	0.892100i	$0.350769\pi$
$398$		0			0
$399$	−0.973748	−	3.31628i	−0.0487484	−	0.166022i
$400$		0			0
$401$	0.707190	−	0.101679i	0.0353154	−	0.00507758i	−0.124635	−	0.992203i	$-0.539776\pi$
$401$	0.707190	−	0.101679i	0.0353154	−	0.00507758i	0.159950	+	0.987125i	$0.448867\pi$
$402$		0			0
$403$	−38.9364	−	14.5225i	−1.93956	−	0.723419i
$404$		0			0
$405$	15.3974	−	8.86281i	0.765102	−	0.440396i
$406$		0			0
$407$	26.1658	−	19.5875i	1.29699	−	0.970915i
$408$		0			0
$409$	7.32402	+	11.3964i	0.362150	+	0.563516i	0.973741	−	0.227658i	$-0.0731068\pi$
$409$	7.32402	+	11.3964i	0.362150	+	0.563516i	−0.611592	+	0.791174i	$0.709470\pi$
$410$		0			0
$411$	1.60874	−	5.47888i	0.0793535	−	0.270253i
$412$		0			0
$413$	25.1507	+	25.1507i	1.23759	+	1.23759i
$414$		0			0
$415$	−23.3604	+	7.43380i	−1.14672	+	0.364911i
$416$		0			0
$417$	1.25284	+	2.29440i	0.0613517	+	0.112357i
$418$		0			0
$419$	5.04022	−	3.23915i	0.246231	−	0.158243i	−0.411704	−	0.911317i	$-0.635066\pi$
$419$	5.04022	−	3.23915i	0.246231	−	0.158243i	0.657935	+	0.753074i	$0.271430\pi$
$420$		0			0
$421$	16.9557	+	2.43787i	0.826372	+	0.118814i	0.542509	−	0.840050i	$-0.317475\pi$
$421$	16.9557	+	2.43787i	0.826372	+	0.118814i	0.283864	+	0.958865i	$0.408384\pi$
$422$		0			0
$423$	−8.07846	+	1.75736i	−0.392788	+	0.0854458i
$424$		0			0
$425$	0.816967	+	3.08123i	0.0396287	+	0.149462i
$426$		0			0
$427$	26.3120	−	35.1487i	1.27333	−	1.70096i
$428$		0			0
$429$	6.16679	−	1.81073i	0.297735	−	0.0874230i
$430$		0			0
$431$	−1.98165	−	1.71711i	−0.0954528	−	0.0827103i	0.605827	−	0.795596i	$-0.292842\pi$
$431$	−1.98165	−	1.71711i	−0.0954528	−	0.0827103i	−0.701280	+	0.712886i	$0.747388\pi$
$432$		0			0
$433$	−0.251387	+	3.51485i	−0.0120809	+	0.168913i	0.987830	+	0.155540i	$0.0497116\pi$
$433$	−0.251387	+	3.51485i	−0.0120809	+	0.168913i	−0.999911	+	0.0133735i	$0.995743\pi$
$434$		0			0
$435$	−0.724985	+	5.99689i	−0.0347604	+	0.287529i
$436$		0			0
$437$	−1.58612	−	16.0691i	−0.0758746	−	0.768691i
$438$		0			0
$439$	−3.55101	−	1.62169i	−0.169480	−	0.0773991i	0.328868	−	0.944376i	$-0.393333\pi$
$439$	−3.55101	−	1.62169i	−0.169480	−	0.0773991i	−0.498349	+	0.866977i	$0.666060\pi$
$440$		0			0
$441$	−3.53285	−	4.07712i	−0.168231	−	0.194149i
$442$		0			0
$443$	−0.265293	−	3.70928i	−0.0126044	−	0.176233i	−0.999855	−	0.0170563i	$-0.994571\pi$
$443$	−0.265293	−	3.70928i	−0.0126044	−	0.176233i	0.987250	−	0.159177i	$-0.0508840\pi$
$444$		0			0
$445$	1.03281	−	5.32123i	0.0489601	−	0.252251i
$446$		0			0
$447$	2.08147	+	1.55817i	0.0984504	+	0.0736990i
$448$		0			0
$449$	−0.202675	+	0.0925584i	−0.00956480	+	0.00436810i	−0.420192	−	0.907435i	$-0.638037\pi$
$449$	−0.202675	+	0.0925584i	−0.00956480	+	0.00436810i	0.410627	+	0.911803i	$0.365310\pi$
$450$		0			0
$451$	−16.2239	+	25.2449i	−0.763953	+	1.18873i
$452$		0			0
$453$	−0.132549	−	0.177064i	−0.00622768	−	0.00831920i
$454$		0			0
$455$	27.6385	−	2.60263i	1.29572	−	0.122013i
$456$		0			0
$457$	20.6685	−	11.2859i	0.966832	−	0.527930i	0.0834137	−	0.996515i	$-0.473418\pi$
$457$	20.6685	−	11.2859i	0.966832	−	0.527930i	0.883419	+	0.468585i	$0.155236\pi$
$458$		0			0
$459$	1.29220			0.0603148
$460$		0			0
$461$	−42.6375			−1.98583			−0.992913	−	0.118844i	$-0.962081\pi$
$461$	−42.6375			−1.98583			−0.992913	+	0.118844i	$0.962081\pi$
$462$		0			0
$463$	18.1935	−	9.93439i	0.845523	−	0.461690i	0.00277302	−	0.999996i	$-0.499117\pi$
$463$	18.1935	−	9.93439i	0.845523	−	0.461690i	0.842750	+	0.538306i	$0.180936\pi$
$464$		0			0
$465$	5.91840	+	4.89969i	0.274459	+	0.227218i
$466$		0			0
$467$	14.5002	+	19.3700i	0.670988	+	0.896335i	0.998828	−	0.0483980i	$-0.0154116\pi$
$467$	14.5002	+	19.3700i	0.670988	+	0.896335i	−0.327840	+	0.944733i	$0.606321\pi$
$468$		0			0
$469$	3.53293	−	5.49735i	0.163136	−	0.253844i
$470$		0			0
$471$	−6.72196	+	3.06982i	−0.309732	+	0.141450i
$472$		0			0
$473$	−40.1479	−	30.0544i	−1.84600	−	1.38190i
$474$		0			0
$475$	13.2056	+	10.4411i	0.605916	+	0.479072i
$476$		0			0
$477$	0.741746	+	10.3710i	0.0339622	+	0.474854i
$478$		0			0
$479$	2.51217	+	2.89920i	0.114784	+	0.132468i	0.810234	−	0.586107i	$-0.199340\pi$
$479$	2.51217	+	2.89920i	0.114784	+	0.132468i	−0.695450	+	0.718575i	$0.744795\pi$
$480$		0			0
$481$	27.6954	+	12.6480i	1.26280	+	0.576701i
$482$		0			0
$483$	2.47513	+	4.25567i	0.112622	+	0.193640i
$484$		0			0
$485$	−18.8029	−	2.27315i	−0.853797	−	0.103218i
$486$		0			0
$487$	−0.231814	+	3.24118i	−0.0105045	+	0.146872i	0.989493	+	0.144581i	$0.0461836\pi$
$487$	−0.231814	+	3.24118i	−0.0105045	+	0.146872i	−0.999997	+	0.00229033i	$0.999271\pi$
$488$		0			0
$489$	−4.32171	−	3.74478i	−0.195434	−	0.169345i
$490$		0			0
$491$	14.6414	−	4.29911i	0.660758	−	0.194016i	0.0658744	−	0.997828i	$-0.479016\pi$
$491$	14.6414	−	4.29911i	0.660758	−	0.194016i	0.594884	+	0.803812i	$0.297198\pi$
$492$		0			0
$493$	2.99483	−	4.00062i	0.134880	−	0.180179i
$494$		0			0
$495$	28.7925	+	1.40935i	1.29412	+	0.0633458i
$496$		0			0
$497$	−27.4317	+	5.96740i	−1.23048	+	0.267675i
$498$		0			0
$499$	−8.98095	−	1.29126i	−0.402042	−	0.0578050i	−0.0616721	−	0.998096i	$-0.519643\pi$
$499$	−8.98095	−	1.29126i	−0.402042	−	0.0578050i	−0.340370	+	0.940292i	$0.610552\pi$
$500$		0			0
$501$	−3.38288	+	2.17404i	−0.151136	+	0.0971291i
$502$		0			0
$503$	−12.2062	−	22.3539i	−0.544247	−	0.996713i	−0.994592	−	0.103859i	$-0.966881\pi$
$503$	−12.2062	−	22.3539i	−0.544247	−	0.996713i	0.450345	−	0.892854i	$-0.351301\pi$
$504$		0			0
$505$	6.60308	−	12.7671i	0.293833	−	0.568128i
$506$		0			0
$507$	1.06545	+	1.06545i	0.0473185	+	0.0473185i
$508$		0			0
$509$	4.90553	−	16.7067i	0.217434	−	0.740512i	−0.776460	−	0.630167i	$-0.782986\pi$
$509$	4.90553	−	16.7067i	0.217434	−	0.740512i	0.993893	−	0.110345i	$-0.0351955\pi$
$510$		0			0
$511$	17.3379	+	26.9782i	0.766982	+	1.19345i
$512$		0			0
$513$	5.46312	−	4.08964i	0.241203	−	0.180562i
$514$		0			0
$515$	−16.0345	−	4.31894i	−0.706563	−	0.190315i
$516$		0			0
$517$	−12.0294	−	4.48672i	−0.529051	−	0.197326i
$518$		0			0
$519$	3.31387	−	0.476463i	0.145463	−	0.0209144i
$520$		0			0
$521$	3.26119	+	11.1066i	0.142876	+	0.486589i	0.999573	−	0.0292303i	$-0.00930563\pi$
$521$	3.26119	+	11.1066i	0.142876	+	0.486589i	−0.856697	+	0.515820i	$0.827487\pi$
$522$		0			0
$523$	10.8534	−	0.776254i	0.474588	−	0.0339432i	0.168003	−	0.985786i	$-0.446268\pi$
$523$	10.8534	−	0.776254i	0.474588	−	0.0339432i	0.306585	+	0.951843i	$0.400814\pi$
$524$		0			0
$525$	−4.98483	−	1.22314i	−0.217556	−	0.0533823i
$526$		0			0
$527$	−2.22138	−	5.95574i	−0.0967647	−	0.259436i
$528$		0			0
$529$	7.66098	+	21.6866i	0.333086	+	0.942896i
$530$		0			0
$531$	−14.2924	+	31.2960i	−0.620237	+	1.35813i
$532$		0			0
$533$	−27.8824	−	1.99419i	−1.20772	−	0.0863777i
$534$		0			0
$535$	−7.97978	−	3.42952i	−0.344996	−	0.148271i
$536$		0			0
$537$	3.43606	+	1.87623i	0.148277	+	0.0809653i
$538$		0			0
$539$	−1.19230	−	8.29260i	−0.0513558	−	0.357188i
$540$		0			0
$541$	−10.6896	−	23.4069i	−0.459581	−	1.00634i	−0.987583	−	0.157098i	$-0.949786\pi$
$541$	−10.6896	−	23.4069i	−0.459581	−	1.00634i	0.528002	−	0.849243i	$-0.322941\pi$
$542$		0			0
$543$	−0.491179	−	2.25791i	−0.0210785	−	0.0968964i
$544$		0			0
$545$	15.6738	+	11.1922i	0.671392	+	0.479422i
$546$		0			0
$547$	28.6765	+	6.23818i	1.22612	+	0.266725i	0.778583	−	0.627541i	$-0.215939\pi$
$547$	28.6765	+	6.23818i	1.22612	+	0.266725i	0.447534	+	0.894267i	$0.352302\pi$
$548$		0			0
$549$	40.7497	+	11.9652i	1.73916	+	0.510662i
$550$		0			0
$551$		−	26.3919i		−	1.12433i
$552$		0			0
$553$	−4.82362	+	4.82362i	−0.205121	+	0.205121i
$554$		0			0
$555$	−4.06903	−	3.89000i	−0.172721	−	0.165121i
$556$		0			0
$557$	−3.41562	+	15.7014i	−0.144725	+	0.665288i	0.846422	+	0.532513i	$0.178752\pi$
$557$	−3.41562	+	15.7014i	−0.144725	+	0.665288i	−0.991146	+	0.132775i	$0.957611\pi$
$558$		0			0
$559$	6.64846	−	46.2410i	0.281200	−	1.95579i
$560$		0			0
$561$	0.827036	+	0.531504i	0.0349175	+	0.0224401i
$562$		0			0
$563$	−2.23792	+	6.00011i	−0.0943173	+	0.252874i	−0.975538	−	0.219830i	$-0.929450\pi$
$563$	−2.23792	+	6.00011i	−0.0943173	+	0.252874i	0.881221	+	0.472705i	$0.156722\pi$
$564$		0			0
$565$	−11.1437	−	23.0168i	−0.468817	−	0.968326i
$566$		0			0
$567$	11.3419	−	20.7711i	0.476314	−	0.872304i
$568$		0			0
$569$	−21.2256	+	24.4956i	−0.889823	+	1.02691i	0.109635	+	0.993972i	$0.465032\pi$
$569$	−21.2256	+	24.4956i	−0.889823	+	1.02691i	−0.999457	+	0.0329383i	$0.989514\pi$
$570$		0			0
$571$	−15.0953	+	13.0802i	−0.631719	+	0.547387i	−0.910783	−	0.412885i	$-0.864521\pi$
$571$	−15.0953	+	13.0802i	−0.631719	+	0.547387i	0.279064	+	0.960272i	$0.409976\pi$
$572$		0			0
$573$	1.47239	−	0.549171i	0.0615098	−	0.0229420i
$574$		0			0
$575$	−21.8179	−	9.94891i	−0.909868	−	0.414898i
$576$		0			0
$577$	−12.4315	+	4.63669i	−0.517528	+	0.193028i	−0.594636	−	0.803995i	$-0.702704\pi$
$577$	−12.4315	+	4.63669i	−0.517528	+	0.193028i	0.0771083	+	0.997023i	$0.475431\pi$
$578$		0			0
$579$	−5.57526	+	4.83099i	−0.231700	+	0.200769i
$580$		0			0
$581$	−21.3851	+	24.6797i	−0.887203	+	1.02389i
$582$		0			0
$583$	−7.73831	+	14.1717i	−0.320488	+	0.586930i
$584$		0			0
$585$	11.7015	+	24.1691i	0.483799	+	0.999270i
$586$		0			0
$587$	−0.502079	+	1.34613i	−0.0207230	+	0.0555606i	−0.946899	−	0.321530i	$-0.895803\pi$
$587$	−0.502079	+	1.34613i	−0.0207230	+	0.0555606i	0.926176	+	0.377091i	$0.123076\pi$
$588$		0			0
$589$	−28.2406	−	18.1491i	−1.16363	−	0.747822i
$590$		0			0
$591$	−1.06073	+	7.37752i	−0.0436325	+	0.303471i
$592$		0			0
$593$	7.33463	−	33.7168i	0.301197	−	1.38458i	−0.539003	−	0.842304i	$-0.681199\pi$
$593$	7.33463	−	33.7168i	0.301197	−	1.38458i	0.840200	−	0.542277i	$-0.182438\pi$
$594$		0			0
$595$	3.06936	+	2.93432i	0.125832	+	0.120295i
$596$		0			0
$597$	1.28436	−	1.28436i	0.0525653	−	0.0525653i
$598$		0			0
$599$			3.52377i			0.143977i	0.997405	+	0.0719887i	$0.0229346\pi$
$599$			3.52377i			0.143977i	−0.997405	+	0.0719887i	$0.977065\pi$
$600$		0			0
$601$	6.63203	+	1.94734i	0.270526	+	0.0794336i	0.414182	−	0.910194i	$-0.364068\pi$
$601$	6.63203	+	1.94734i	0.270526	+	0.0794336i	−0.143656	+	0.989628i	$0.545886\pi$
$602$		0			0
$603$	6.17652	+	1.34362i	0.251527	+	0.0547164i
$604$		0			0
$605$	16.4147	+	11.7213i	0.667353	+	0.476539i
$606$		0			0
$607$	0.974312	+	4.47884i	0.0395461	+	0.181790i	0.992683	−	0.120748i	$-0.0385294\pi$
$607$	0.974312	+	4.47884i	0.0395461	+	0.181790i	−0.953137	+	0.302539i	$0.902166\pi$
$608$		0			0
$609$	3.34268	+	7.31945i	0.135452	+	0.296599i
$610$		0			0
$611$	−1.70203	−	11.8379i	−0.0688569	−	0.478910i
$612$		0			0
$613$	−19.0549	−	10.4047i	−0.769618	−	0.420243i	0.0459209	−	0.998945i	$-0.485378\pi$
$613$	−19.0549	−	10.4047i	−0.769618	−	0.420243i	−0.815539	+	0.578702i	$0.803560\pi$
$614$		0			0
$615$	4.74838	+	2.04074i	0.191473	+	0.0822905i
$616$		0			0
$617$	−19.4296	−	1.38964i	−0.782208	−	0.0559446i	−0.325478	−	0.945550i	$-0.605525\pi$
$617$	−19.4296	−	1.38964i	−0.782208	−	0.0559446i	−0.456730	+	0.889605i	$0.650980\pi$
$618$		0			0
$619$	6.75360	−	14.7883i	0.271450	−	0.594393i	−0.723987	−	0.689814i	$-0.757692\pi$
$619$	6.75360	−	14.7883i	0.271450	−	0.594393i	0.995437	+	0.0954206i	$0.0304196\pi$
$620$		0			0
$621$	−6.16500	+	7.51533i	−0.247393	+	0.301580i
$622$		0			0
$623$	−2.52337	−	6.76541i	−0.101097	−	0.271050i
$624$		0			0
$625$	23.2576	−	9.16984i	0.930302	−	0.366793i
$626$		0			0
$627$	5.17865	−	0.370385i	0.206815	−	0.0147917i
$628$		0			0
$629$	1.31207	+	4.46852i	0.0523158	+	0.178171i
$630$		0			0
$631$	−29.1264	+	4.18774i	−1.15950	+	0.166711i	−0.695100	−	0.718913i	$-0.744640\pi$
$631$	−29.1264	+	4.18774i	−1.15950	+	0.166711i	−0.464402	+	0.885624i	$0.653731\pi$
$632$		0			0
$633$	−0.238809	−	0.0890710i	−0.00949179	−	0.00354026i
$634$		0			0
$635$	26.9014	+	7.24599i	1.06755	+	0.287548i
$636$		0			0
$637$	6.24754	−	4.67685i	0.247536	−	0.185303i
$638$		0			0
$639$	−14.6811	−	22.8443i	−0.580776	−	0.903705i
$640$		0			0
$641$	−7.88391	+	26.8501i	−0.311396	+	1.06052i	0.643960	+	0.765059i	$0.277290\pi$
$641$	−7.88391	+	26.8501i	−0.311396	+	1.06052i	−0.955356	+	0.295458i	$0.904528\pi$
$642$		0			0
$643$	1.37131	+	1.37131i	0.0540791	+	0.0540791i	0.733629	−	0.679550i	$-0.237825\pi$
$643$	1.37131	+	1.37131i	0.0540791	+	0.0540791i	−0.679550	+	0.733629i	$0.737825\pi$
$644$		0			0
$645$	−3.96795	+	7.67205i	−0.156238	+	0.302087i
$646$		0			0
$647$	22.4179	+	41.0553i	0.881338	+	1.61405i	0.785678	+	0.618636i	$0.212314\pi$
$647$	22.4179	+	41.0553i	0.881338	+	1.61405i	0.0956599	+	0.995414i	$0.469504\pi$
$648$		0			0
$649$	−44.9477	+	28.8861i	−1.76435	+	1.13388i
$650$		0			0
$651$	10.1308	+	1.45659i	0.397059	+	0.0570884i
$652$		0			0
$653$	−12.0153	+	2.61377i	−0.470195	+	0.102285i	−0.441419	−	0.897301i	$-0.645525\pi$
$653$	−12.0153	+	2.61377i	−0.470195	+	0.102285i	−0.0287764	+	0.999586i	$0.509161\pi$
$654$		0			0
$655$	29.8375	+	1.46051i	1.16585	+	0.0570668i
$656$		0			0
$657$	−18.5897	+	24.8329i	−0.725253	+	0.968825i
$658$		0			0
$659$	−34.2669	+	10.0617i	−1.33485	+	0.391947i	−0.869829	−	0.493354i	$-0.835771\pi$
$659$	−34.2669	+	10.0617i	−1.33485	+	0.391947i	−0.465019	+	0.885301i	$0.653953\pi$
$660$		0			0
$661$	17.8475	+	15.4650i	0.694189	+	0.601518i	0.928805	−	0.370570i	$-0.120838\pi$
$661$	17.8475	+	15.4650i	0.694189	+	0.601518i	−0.234615	+	0.972088i	$0.575383\pi$
$662$		0			0
$663$	−0.0653306	+	0.913441i	−0.00253723	+	0.0354751i
$664$		0			0
$665$	22.2633	+	2.69148i	0.863333	+	0.104371i
$666$		0			0
$667$	8.97917	+	36.5044i	0.347675	+	1.41345i
$668$		0			0
$669$	1.10872	+	0.506338i	0.0428658	+	0.0195761i
$670$		0			0
$671$	43.1906	+	49.8447i	1.66736	+	1.92423i
$672$		0			0
$673$	0.751266	+	10.5041i	0.0289592	+	0.404902i	0.991170	+	0.132597i	$0.0423315\pi$
$673$	0.751266	+	10.5041i	0.0289592	+	0.404902i	−0.962211	+	0.272305i	$0.912214\pi$
$674$		0			0
$675$	−1.17677	−	10.0657i	−0.0452938	−	0.387430i
$676$		0			0
$677$	−3.95319	−	2.95932i	−0.151933	−	0.113736i	0.520607	−	0.853797i	$-0.325706\pi$
$677$	−3.95319	−	2.95932i	−0.151933	−	0.113736i	−0.672540	+	0.740061i	$0.734797\pi$
$678$		0			0
$679$	−22.9497	+	10.4808i	−0.880729	+	0.402216i
$680$		0			0
$681$	0.953868	−	1.48425i	0.0365523	−	0.0568765i
$682$		0			0
$683$	−19.3336	−	25.8266i	−0.739778	−	0.988228i	−0.999744	−	0.0226103i	$-0.992802\pi$
$683$	−19.3336	−	25.8266i	−0.739778	−	0.988228i	0.259966	−	0.965618i	$-0.416289\pi$
$684$		0			0
$685$	28.5385	+	23.6263i	1.09040	+	0.902715i
$686$		0			0
$687$	−6.38973	+	3.48906i	−0.243783	+	0.133116i
$688$		0			0
$689$	−15.0410			−0.573016
$690$		0			0
$691$	9.98937			0.380014			0.190007	−	0.981783i	$-0.439149\pi$
$691$	9.98937			0.380014			0.190007	+	0.981783i	$0.439149\pi$
$692$		0			0
$693$	33.7031	−	18.4033i	1.28027	−	0.699083i
$694$		0			0
$695$	−16.8868	+	1.59017i	−0.640551	+	0.0603187i
$696$		0			0
$697$	−2.56239	−	3.42295i	−0.0970575	−	0.129654i
$698$		0			0
$699$	2.98811	−	4.64959i	0.113021	−	0.175864i
$700$		0			0
$701$	46.0955	−	21.0511i	1.74100	−	0.795090i	0.749971	−	0.661471i	$-0.230067\pi$
$701$	46.0955	−	21.0511i	1.74100	−	0.795090i	0.991033	−	0.133619i	$-0.0426599\pi$
$702$		0			0
$703$	19.6894	+	14.7393i	0.742600	+	0.555903i
$704$		0			0
$705$	−0.421319	+	2.17071i	−0.0158678	+	0.0817535i
$706$		0			0
$707$	−1.36593	−	19.0982i	−0.0513710	−	0.718261i
$708$		0			0
$709$	−4.82672	−	5.57033i	−0.181271	−	0.209198i	0.657840	−	0.753157i	$-0.271470\pi$
$709$	−4.82672	−	5.57033i	−0.181271	−	0.209198i	−0.839112	+	0.543959i	$0.816925\pi$
$710$		0			0
$711$	−6.00221	−	2.74112i	−0.225101	−	0.102800i
$712$		0			0
$713$	45.2361	+	15.4951i	1.69411	+	0.580295i
$714$		0			0
$715$	−5.00494	+	41.3996i	−0.187174	+	1.54826i
$716$		0			0
$717$	0.210180	−	2.93869i	0.00784930	−	0.109748i
$718$		0			0
$719$	25.1615	+	21.8026i	0.938366	+	0.813099i	0.982564	−	0.185924i	$-0.0595278\pi$
$719$	25.1615	+	21.8026i	0.938366	+	0.813099i	−0.0441982	+	0.999023i	$0.514073\pi$
$720$		0			0
$721$	−21.2247	+	6.23212i	−0.790448	+	0.232096i
$722$		0			0
$723$	1.06204	−	1.41872i	0.0394977	−	0.0527627i
$724$		0			0
$725$	−33.8906	−	19.6853i	−1.25866	−	0.731093i
$726$		0			0
$727$	24.8329	−	5.40207i	0.921002	−	0.200352i	0.273021	−	0.962008i	$-0.411977\pi$
$727$	24.8329	−	5.40207i	0.921002	−	0.200352i	0.647981	+	0.761657i	$0.275614\pi$
$728$		0			0
$729$	20.5846	+	2.95962i	0.762393	+	0.109616i
$730$		0			0
$731$	6.01143	−	3.86331i	0.222341	−	0.142890i
$732$		0			0
$733$	6.36324	+	11.6534i	0.235031	+	0.430428i	0.968400	−	0.249404i	$-0.0802346\pi$
$733$	6.36324	+	11.6534i	0.235031	+	0.430428i	−0.733368	+	0.679832i	$0.762053\pi$
$734$		0			0
$735$	−1.37497	+	0.437545i	−0.0507164	+	0.0161391i
$736$		0			0
$737$	6.94107	+	6.94107i	0.255678	+	0.255678i
$738$		0			0
$739$	−12.3137	+	41.9367i	−0.452967	+	1.54266i	0.344194	+	0.938899i	$0.388152\pi$
$739$	−12.3137	+	41.9367i	−0.452967	+	1.54266i	−0.797161	+	0.603766i	$0.793666\pi$
$740$		0			0
$741$	2.61472	+	4.06858i	0.0960540	+	0.149463i
$742$		0			0
$743$	−2.15126	+	1.61042i	−0.0789222	+	0.0590804i	−0.638010	−	0.770028i	$-0.720242\pi$
$743$	−2.15126	+	1.61042i	−0.0789222	+	0.0590804i	0.559088	+	0.829108i	$0.311151\pi$
$744$		0			0
$745$	−14.6210	+	8.41590i	−0.535671	+	0.308335i
$746$		0			0
$747$	−29.5962	−	11.0388i	−1.08287	−	0.403889i
$748$		0			0
$749$	−11.4522	+	1.64658i	−0.418454	+	0.0601647i
$750$		0			0
$751$	−5.89641	−	20.0813i	−0.215163	−	0.732779i	−0.994365	−	0.106006i	$-0.966194\pi$
$751$	−5.89641	−	20.0813i	−0.215163	−	0.732779i	0.779202	−	0.626773i	$-0.215624\pi$
$752$		0			0
$753$	7.40643	−	0.529718i	0.269905	−	0.0193040i
$754$		0			0
$755$	1.39507	−	0.336507i	0.0507719	−	0.0122467i
$756$		0			0
$757$	1.93674	+	5.19260i	0.0703920	+	0.188728i	0.967382	−	0.253323i	$-0.0815236\pi$
$757$	1.93674	+	5.19260i	0.0703920	+	0.188728i	−0.896990	+	0.442051i	$0.854251\pi$
$758$		0			0
$759$	−7.03691	+	2.27421i	−0.255424	+	0.0825484i
$760$		0			0
$761$	20.9702	−	45.9184i	0.760171	−	1.66454i	0.0129951	−	0.999916i	$-0.495863\pi$
$761$	20.9702	−	45.9184i	0.760171	−	1.66454i	0.747176	−	0.664627i	$-0.231409\pi$
$762$		0			0
$763$	25.5903	+	1.83026i	0.926432	+	0.0662597i
$764$		0			0
$765$	−1.62183	+	3.77367i	−0.0586375	+	0.136437i
$766$		0			0
$767$	−43.6825	−	23.8524i	−1.57728	−	0.861262i
$768$		0			0
$769$	−0.579262	−	4.02886i	−0.0208887	−	0.145284i	0.976708	−	0.214573i	$-0.0688361\pi$
$769$	−0.579262	−	4.02886i	−0.0208887	−	0.145284i	−0.997597	+	0.0692889i	$0.977927\pi$
$770$		0			0
$771$	3.56736	+	7.81142i	0.128475	+	0.281321i
$772$		0			0
$773$	−5.14247	−	23.6395i	−0.184962	−	0.850255i	−0.972300	−	0.233735i	$-0.924905\pi$
$773$	−5.14247	−	23.6395i	−0.184962	−	0.850255i	0.787339	−	0.616521i	$-0.211458\pi$
$774$		0			0
$775$	−44.3699	+	22.7274i	−1.59382	+	0.816391i
$776$		0			0
$777$	−7.32740	−	1.59398i	−0.262869	−	0.0571837i
$778$		0			0
$779$	−21.6664	−	6.36183i	−0.776279	−	0.227936i
$780$		0			0
$781$		−	42.1704i		−	1.50898i
$782$		0			0
$783$	−11.2343	+	11.2343i	−0.401480	+	0.401480i
$784$		0			0
$785$	−1.07824	−	47.9347i	−0.0384840	−	1.71086i
$786$		0			0
$787$	−8.15271	+	37.4774i	−0.290613	+	1.33592i	0.567885	+	0.823108i	$0.307762\pi$
$787$	−8.15271	+	37.4774i	−0.290613	+	1.33592i	−0.858498	+	0.512817i	$0.828602\pi$
$788$		0			0
$789$	0.575943	−	4.00577i	0.0205041	−	0.142609i
$790$		0			0
$791$	−28.6574	−	18.4170i	−1.01894	−	0.654833i
$792$		0			0
$793$	−21.4701	+	57.5636i	−0.762426	+	2.04414i
$794$		0			0
$795$	2.62678	+	0.912993i	0.0931624	+	0.0323805i
$796$		0			0
$797$	−0.466800	+	0.854880i	−0.0165349	+	0.0302814i	−0.885816	−	0.464037i	$-0.846400\pi$
$797$	−0.466800	+	0.854880i	−0.0165349	+	0.0302814i	0.869281	+	0.494318i	$0.164582\pi$
$798$		0			0
$799$	1.19797	−	1.38253i	0.0423812	−	0.0489105i
$800$		0			0
$801$	5.27853	−	4.57387i	0.186508	−	0.161610i
$802$		0			0
$803$	−45.1355	+	16.8347i	−1.59280	+	0.594083i
$804$		0			0
$805$	−31.7095	+	3.85174i	−1.11761	+	0.135756i
$806$		0			0
$807$	−3.33090	+	1.24236i	−0.117253	+	0.0437331i
$808$		0			0
$809$	−7.17793	+	6.21972i	−0.252363	+	0.218674i	−0.771850	−	0.635805i	$-0.780668\pi$
$809$	−7.17793	+	6.21972i	−0.252363	+	0.218674i	0.519487	+	0.854478i	$0.326123\pi$
$810$		0			0
$811$	2.68615	−	3.09999i	0.0943236	−	0.108855i	−0.706625	−	0.707588i	$-0.749783\pi$
$811$	2.68615	−	3.09999i	0.0943236	−	0.108855i	0.800949	+	0.598733i	$0.204329\pi$
$812$		0			0
$813$	2.96733	−	5.43425i	0.104069	−	0.190587i
$814$		0			0
$815$	33.3948	−	16.1682i	1.16977	−	0.566346i
$816$		0			0
$817$	13.1881	−	35.3585i	0.461392	−	1.23704i
$818$		0			0
$819$	30.0921	+	19.3390i	1.05150	+	0.675759i
$820$		0			0
$821$	3.39889	−	23.6398i	0.118622	−	0.825035i	−0.840453	−	0.541884i	$-0.817711\pi$
$821$	3.39889	−	23.6398i	0.118622	−	0.825035i	0.959075	−	0.283151i	$-0.0913797\pi$
$822$		0			0
$823$	−11.5782	+	53.2240i	−0.403589	+	1.85527i	0.105303	+	0.994440i	$0.466419\pi$
$823$	−11.5782	+	53.2240i	−0.403589	+	1.85527i	−0.508892	+	0.860830i	$0.669945\pi$
$824$		0			0
$825$	3.38705	−	6.92631i	0.117922	−	0.241143i
$826$		0			0
$827$	−2.73117	+	2.73117i	−0.0949721	+	0.0949721i	−0.752997	−	0.658024i	$-0.771392\pi$
$827$	−2.73117	+	2.73117i	−0.0949721	+	0.0949721i	0.658024	+	0.752997i	$0.271392\pi$
$828$		0			0
$829$		−	38.4472i		−	1.33533i	−0.744463	−	0.667664i	$-0.767294\pi$
$829$		−	38.4472i		−	1.33533i	0.744463	−	0.667664i	$-0.232706\pi$
$830$		0			0
$831$	−5.66901	−	1.66457i	−0.196656	−	0.0577433i
$832$		0			0
$833$	1.16645	+	0.253745i	0.0404150	+	0.00879174i
$834$		0			0
$835$	−4.29295	−	25.7353i	−0.148564	−	0.890607i
$836$		0			0
$837$	4.29564	+	19.7468i	0.148479	+	0.682548i
$838$		0			0
$839$	0.911476	+	1.99586i	0.0314677	+	0.0689046i	0.924713	−	0.380665i	$-0.124305\pi$
$839$	0.911476	+	1.99586i	0.0314677	+	0.0689046i	−0.893245	+	0.449569i	$0.851578\pi$
$840$		0			0
$841$	4.61715	+	32.1130i	0.159212	+	1.10735i
$842$		0			0
$843$	5.98756	+	3.26946i	0.206223	+	0.112606i
$844$		0			0
$845$	−9.08086	+	3.62164i	−0.312391	+	0.124588i
$846$		0			0
$847$	26.8000	+	1.91677i	0.920859	+	0.0658612i
$848$		0			0
$849$	−0.958024	+	2.09778i	−0.0328793	+	0.0719956i
$850$		0			0
$851$	−32.2483	−	13.6881i	−1.10546	−	0.469221i
$852$		0			0
$853$	−2.99281	−	8.02403i	−0.102472	−	0.274738i	0.875589	−	0.483057i	$-0.160474\pi$
$853$	−2.99281	−	8.02403i	−0.102472	−	0.274738i	−0.978061	+	0.208319i	$0.933201\pi$
$854$		0			0
$855$	5.08644	+	21.0871i	0.173952	+	0.721163i
$856$		0			0
$857$	−26.3916	+	1.88756i	−0.901519	+	0.0644779i	−0.514399	−	0.857551i	$-0.671985\pi$
$857$	−26.3916	+	1.88756i	−0.901519	+	0.0644779i	−0.387121	+	0.922029i	$0.626530\pi$
$858$		0			0
$859$	−8.55931	−	29.1503i	−0.292040	−	0.994597i	−0.966581	−	0.256360i	$-0.917477\pi$
$859$	−8.55931	−	29.1503i	−0.292040	−	0.994597i	0.674541	−	0.738237i	$-0.264341\pi$
$860$		0			0
$861$	6.81464	−	0.979798i	0.232242	−	0.0333914i
$862$		0			0
$863$	−14.1382	−	5.27326i	−0.481269	−	0.179504i	0.0971079	−	0.995274i	$-0.469041\pi$
$863$	−14.1382	−	5.27326i	−0.481269	−	0.179504i	−0.578377	+	0.815770i	$0.696314\pi$
$864$		0			0
$865$	−5.64966	+	20.9749i	−0.192094	+	0.713167i
$866$		0			0
$867$	4.57802	−	3.42706i	0.155478	−	0.116389i
$868$		0			0
$869$	−5.54003	−	8.62046i	−0.187933	−	0.292429i
$870$		0			0
$871$	−2.57614	+	8.77353i	−0.0872892	+	0.297280i
$872$		0			0
$873$	−17.2565	−	17.2565i	−0.584046	−	0.584046i
$874$		0			0
$875$	20.0620	−	26.5813i	0.678219	−	0.898613i
$876$		0			0
$877$	16.7385	+	30.6542i	0.565218	+	1.03512i	0.991448	+	0.130504i	$0.0416597\pi$
$877$	16.7385	+	30.6542i	0.565218	+	1.03512i	−0.426230	+	0.904615i	$0.640159\pi$
$878$		0			0
$879$	3.33235	−	2.14157i	0.112397	−	0.0722334i
$880$		0			0
$881$	−21.9413	−	3.15468i	−0.739220	−	0.106284i	−0.237589	−	0.971366i	$-0.576357\pi$
$881$	−21.9413	−	3.15468i	−0.739220	−	0.106284i	−0.501631	+	0.865082i	$0.667266\pi$
$882$		0			0
$883$	30.2164	−	6.57318i	1.01686	−	0.221205i	0.326907	−	0.945056i	$-0.393993\pi$
$883$	30.2164	−	6.57318i	1.01686	−	0.221205i	0.689956	+	0.723851i	$0.257630\pi$
$884$		0			0
$885$	6.18094	+	6.81718i	0.207770	+	0.229157i
$886$		0			0
$887$	−3.85118	+	5.14458i	−0.129310	+	0.172738i	−0.860524	−	0.509411i	$-0.829863\pi$
$887$	−3.85118	+	5.14458i	−0.129310	+	0.172738i	0.731213	+	0.682149i	$0.238954\pi$
$888$		0			0
$889$	35.6091	−	10.4558i	1.19429	−	0.350676i
$890$		0			0
$891$	26.8668	+	23.2803i	0.900073	+	0.779918i
$892$		0			0
$893$	0.689213	−	9.63645i	0.0230636	−	0.322472i
$894$		0			0
$895$	−19.9873	+	15.6758i	−0.668100	+	0.523985i
$896$		0			0
$897$	−5.00081	−	4.73792i	−0.166972	−	0.158195i
$898$		0			0
$899$	71.0912	+	32.4662i	2.37102	+	1.08281i
$900$		0			0
$901$	−1.50662	−	1.73874i	−0.0501930	−	0.0579258i
$902$		0			0
$903$	0.820819	+	11.4766i	0.0273152	+	0.381916i
$904$		0			0
$905$	14.7180	+	2.85665i	0.489241	+	0.0949584i
$906$		0			0
$907$	12.8079	+	9.58785i	0.425278	+	0.318359i	0.790390	−	0.612605i	$-0.209878\pi$
$907$	12.8079	+	9.58785i	0.425278	+	0.318359i	−0.365111	+	0.930964i	$0.618969\pi$
$908$		0			0
$909$	16.8470	−	7.69377i	0.558780	−	0.255186i
$910$		0			0
$911$	−7.59910	+	11.8244i	−0.251769	+	0.391761i	−0.944016	−	0.329901i	$-0.892985\pi$
$911$	−7.59910	+	11.8244i	−0.251769	+	0.391761i	0.692246	+	0.721661i	$0.256621\pi$
$912$		0			0
$913$	−29.3972	−	39.2700i	−0.972904	−	1.29965i
$914$		0			0
$915$	7.24371	−	8.74977i	0.239470	−	0.289258i
$916$		0			0
$917$	34.9263	−	19.0712i	1.15337	−	0.629787i
$918$		0			0
$919$	14.3036			0.471833			0.235916	−	0.971773i	$-0.424191\pi$
$919$	14.3036			0.471833			0.235916	+	0.971773i	$0.424191\pi$
$920$		0			0
$921$	3.41595			0.112559
$922$		0			0
$923$	34.4774	−	18.8261i	1.13484	−	0.619669i
$924$		0			0
$925$	33.6131	−	14.2899i	1.10519	−	0.469849i
$926$		0			0
$927$	−12.8228	−	17.1293i	−0.421157	−	0.562601i
$928$		0			0
$929$	13.4879	−	20.9875i	0.442522	−	0.688578i	−0.546314	−	0.837580i	$-0.683970\pi$
$929$	13.4879	−	20.9875i	0.442522	−	0.688578i	0.988837	+	0.149002i	$0.0476060\pi$
$930$		0			0
$931$	5.73453	−	2.61887i	0.187942	−	0.0858301i
$932$		0			0
$933$	−4.83009	−	3.61576i	−0.158130	−	0.118375i
$934$		0			0
$935$	−5.28714	+	3.56835i	−0.172908	+	0.116697i
$936$		0			0
$937$	0.599661	+	8.38436i	0.0195901	+	0.273905i	0.997800	+	0.0662890i	$0.0211159\pi$
$937$	0.599661	+	8.38436i	0.0195901	+	0.273905i	−0.978210	+	0.207616i	$0.933430\pi$
$938$		0			0
$939$	4.44879	+	5.13417i	0.145181	+	0.167547i
$940$		0			0
$941$	−44.3803	−	20.2678i	−1.44676	−	0.660712i	−0.471517	−	0.881857i	$-0.656293\pi$
$941$	−44.3803	−	20.2678i	−1.44676	−	0.660712i	−0.975241	+	0.221145i	$0.929021\pi$
$942$		0			0
$943$	32.1326	+	1.42802i	1.04638	+	0.0465027i
$944$		0			0
$945$	−8.33114	−	10.6225i	−0.271012	−	0.345550i
$946$		0			0
$947$	2.97980	−	41.6631i	0.0968306	−	1.35387i	−0.684163	−	0.729329i	$-0.739832\pi$
$947$	2.97980	−	41.6631i	0.0968306	−	1.35387i	0.780994	−	0.624539i	$-0.214713\pi$
$948$		0			0
$949$	−33.9134	−	29.3861i	−1.10087	−	0.953913i
$950$		0			0
$951$	−3.98013	+	1.16867i	−0.129064	+	0.0378967i
$952$		0			0
$953$	4.63874	−	6.19663i	0.150263	−	0.200729i	−0.719093	−	0.694914i	$-0.755443\pi$
$953$	4.63874	−	6.19663i	0.150263	−	0.200729i	0.869357	+	0.494185i	$0.164533\pi$
$954$		0			0
$955$	−0.498491	+	10.1839i	−0.0161308	+	0.329544i
$956$		0			0
$957$	−11.8110	+	2.56933i	−0.381796	+	0.0830547i
$958$		0			0
$959$	48.8509	+	7.02369i	1.57748	+	0.226807i
$960$		0			0
$961$	57.5493	−	36.9847i	1.85643	−	1.19305i
$962$		0			0
$963$	−5.36353	−	9.82257i	−0.172837	−	0.316528i
$964$		0			0
$965$	−14.5145	−	45.6112i	−0.467238	−	1.46828i
$966$		0			0
$967$	−17.7339	−	17.7339i	−0.570283	−	0.570283i	0.361924	−	0.932207i	$-0.382120\pi$
$967$	−17.7339	−	17.7339i	−0.570283	−	0.570283i	−0.932207	+	0.361924i	$0.882120\pi$
$968$		0			0
$969$	−0.208417	+	0.709803i	−0.00669532	+	0.0228022i
$970$		0			0
$971$	−27.2739	−	42.4390i	−0.875260	−	1.36193i	−0.931587	−	0.363519i	$-0.881575\pi$
$971$	−27.2739	−	42.4390i	−0.875260	−	1.36193i	0.0563266	−	0.998412i	$-0.482061\pi$
$972$		0			0
$973$	−18.0877	+	13.5403i	−0.579864	+	0.434081i
$974$		0			0
$975$	7.17484	−	0.322944i	0.229779	−	0.0103425i
$976$		0			0
$977$	−37.6583	−	14.0458i	−1.20479	−	0.449365i	−0.334736	−	0.942312i	$-0.608647\pi$
$977$	−37.6583	−	14.0458i	−1.20479	−	0.449365i	−0.870059	+	0.492947i	$0.835920\pi$
$978$		0			0
$979$	10.7362	−	1.54363i	0.343130	−	0.0493346i
$980$		0			0
$981$	6.99162	+	23.8113i	0.223225	+	0.760236i
$982$		0			0
$983$	30.7487	−	2.19919i	0.980731	−	0.0701433i	0.428243	−	0.903664i	$-0.359133\pi$
$983$	30.7487	−	2.19919i	0.980731	−	0.0701433i	0.552489	+	0.833521i	$0.313678\pi$
$984$		0			0
$985$	−41.2604	−	25.2237i	−1.31467	−	0.803695i
$986$		0			0
$987$	1.02936	+	2.75983i	0.0327650	+	0.0878465i
$988$		0			0
$989$	−6.21141	+	53.3936i	−0.197511	+	1.69782i
$990$		0			0
$991$	7.28457	−	15.9510i	0.231402	−	0.506700i	−0.757938	−	0.652327i	$-0.773793\pi$
$991$	7.28457	−	15.9510i	0.231402	−	0.506700i	0.989339	+	0.145628i	$0.0465201\pi$
$992$		0			0
$993$	−4.81451	−	0.344340i	−0.152784	−	0.0109273i
$994$		0			0
$995$	4.36572	+	10.9466i	0.138403	+	0.347030i
$996$		0			0
$997$	36.6477	+	20.0111i	1.16064	+	0.633759i	0.939859	−	0.341564i	$-0.110956\pi$
$997$	36.6477	+	20.0111i	1.16064	+	0.633759i	0.220784	+	0.975323i	$0.429138\pi$
$998$		0			0
$999$	−2.10711	−	14.6553i	−0.0666661	−	0.463673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.17.6	✓	240
5.3	odd	4	inner	460.2.x.a.293.6	yes	240
23.19	odd	22	inner	460.2.x.a.157.6	yes	240
115.88	even	44	inner	460.2.x.a.433.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.17.6	✓	240	1.1	even	1	trivial
460.2.x.a.157.6	yes	240	23.19	odd	22	inner
460.2.x.a.293.6	yes	240	5.3	odd	4	inner
460.2.x.a.433.6	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.302476 - 0.165164i) q^{3} +(0.209636 + 2.22622i) q^{5} +(1.78504 + 2.38454i) q^{7} +(-1.55771 + 2.42384i) q^{9} +O(q^{10})\)	\(q+(0.302476 - 0.165164i) q^{3} +(0.209636 + 2.22622i) q^{5} +(1.78504 + 2.38454i) q^{7} +(-1.55771 + 2.42384i) q^{9} +(-4.07006 + 1.85874i) q^{11} +(-3.33665 - 2.49778i) q^{13} +(0.431102 + 0.638753i) q^{15} +(-0.0454815 - 0.635915i) q^{17} +(-2.20487 - 2.54456i) q^{19} +(0.933773 + 0.426440i) q^{21} +(3.91542 + 2.76939i) q^{23} +(-4.91211 + 0.933392i) q^{25} +(-0.144594 + 2.02169i) q^{27} +(5.92400 + 5.13317i) q^{29} +(9.56653 - 2.80899i) q^{31} +(-0.924099 + 1.23445i) q^{33} +(-4.93430 + 4.47378i) q^{35} +(-7.13797 + 1.55277i) q^{37} +(-1.42180 - 0.204424i) q^{39} +(5.64206 - 3.62593i) q^{41} +(5.37162 + 9.83738i) q^{43} +(-5.72256 - 2.95968i) q^{45} +(2.02897 + 2.02897i) q^{47} +(-0.527516 + 1.79655i) q^{49} +(-0.118787 - 0.184837i) q^{51} +(2.88890 - 2.16261i) q^{53} +(-4.99119 - 8.67120i) q^{55} +(-1.08719 - 0.405501i) q^{57} +(11.8196 - 1.69940i) q^{59} +(-4.15281 - 14.1432i) q^{61} +(-8.56033 + 0.612247i) q^{63} +(4.86113 - 7.95174i) q^{65} +(-0.766670 - 2.05552i) q^{67} +(1.64172 + 0.190986i) q^{69} +(-3.91521 + 8.57311i) q^{71} +(10.7389 + 0.768059i) q^{73} +(-1.33163 + 1.09363i) q^{75} +(-11.6975 - 6.38730i) q^{77} +(0.325925 + 2.26686i) q^{79} +(-3.30054 - 7.22718i) q^{81} +(2.33042 + 10.7128i) q^{83} +(1.40615 - 0.234562i) q^{85} +(2.63968 + 0.574228i) q^{87} +(-2.32594 - 0.682958i) q^{89} -12.4150i q^{91} +(2.42970 - 2.42970i) q^{93} +(5.20252 - 5.44196i) q^{95} +(-1.80046 + 8.27658i) q^{97} +(1.83469 - 12.7606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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