LMFDB - Embedded newform 460.2.x.a.217.5

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			217.5
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374149 + 0.0813911i) q^{3} +(-1.78111 - 1.35190i) q^{5} +(-0.666841 + 0.364123i) q^{7} +(-2.59553 + 1.18534i) q^{9} +O(q^{10})$	\(q+(-0.374149 + 0.0813911i) q^{3} +(-1.78111 - 1.35190i) q^{5} +(-0.666841 + 0.364123i) q^{7} +(-2.59553 + 1.18534i) q^{9} +(3.87303 + 3.35600i) q^{11} +(-0.945848 + 1.73219i) q^{13} +(0.776435 + 0.360845i) q^{15} +(4.90861 + 3.67454i) q^{17} +(-0.852683 + 5.93054i) q^{19} +(0.219862 - 0.190511i) q^{21} +(-4.69671 - 0.970011i) q^{23} +(1.34474 + 4.81577i) q^{25} +(1.79422 - 1.34314i) q^{27} +(-0.236919 + 0.0340638i) q^{29} +(4.27471 - 2.74719i) q^{31} +(-1.72224 - 0.940413i) q^{33} +(1.67998 + 0.252957i) q^{35} +(-5.65965 - 2.11094i) q^{37} +(0.212903 - 0.725081i) q^{39} +(-5.12993 + 11.2330i) q^{41} +(-1.76290 - 8.10392i) q^{43} +(6.22540 + 1.39767i) q^{45} +(-2.45395 - 2.45395i) q^{47} +(-3.47239 + 5.40315i) q^{49} +(-2.13563 - 0.975309i) q^{51} +(4.78984 + 8.77193i) q^{53} +(-2.36134 - 11.2134i) q^{55} +(-0.163663 - 2.28831i) q^{57} +(-2.08663 - 7.10642i) q^{59} +(-2.01449 - 3.13461i) q^{61} +(1.29920 - 1.73553i) q^{63} +(4.02641 - 1.80654i) q^{65} +(2.85366 + 0.204097i) q^{67} +(1.83622 - 0.0193419i) q^{69} +(9.10398 + 10.5066i) q^{71} +(-2.55948 - 3.41907i) q^{73} +(-0.895095 - 1.69237i) q^{75} +(-3.80469 - 0.827659i) q^{77} +(-2.79542 + 0.820810i) q^{79} +(5.04373 - 5.82077i) q^{81} +(0.0585753 - 0.157046i) q^{83} +(-3.77520 - 13.1807i) q^{85} +(0.0858705 - 0.0320281i) q^{87} +(10.6832 + 6.86564i) q^{89} -1.49950i q^{91} +(-1.37578 + 1.37578i) q^{93} +(9.53622 - 9.41023i) q^{95} +(-4.99652 - 13.3962i) q^{97} +(-14.0306 - 4.11975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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
$3$	−0.374149	+	0.0813911i	−0.216015	+	0.0469912i	−0.319270	−	0.947664i	$-0.603438\pi$
$3$	−0.374149	+	0.0813911i	−0.216015	+	0.0469912i	0.103255	+	0.994655i	$0.467074\pi$
$4$		0			0
$5$	−1.78111	−	1.35190i	−0.796539	−	0.604587i
$5$	−1.78111	−	1.35190i	−0.796539	−	0.604587i
$6$		0			0
$7$	−0.666841	+	0.364123i	−0.252042	+	0.137625i	−0.600304	−	0.799772i	$-0.704954\pi$
$7$	−0.666841	+	0.364123i	−0.252042	+	0.137625i	0.348262	+	0.937397i	$0.386772\pi$
$8$		0			0
$9$	−2.59553	+	1.18534i	−0.865178	+	0.395113i
$10$		0			0
$11$	3.87303	+	3.35600i	1.16776	+	1.01187i	0.999659	+	0.0261018i	$0.00830939\pi$
$11$	3.87303	+	3.35600i	1.16776	+	1.01187i	0.168102	+	0.985770i	$0.446236\pi$
$12$		0			0
$13$	−0.945848	+	1.73219i	−0.262331	+	0.480423i	−0.975333	−	0.220739i	$-0.929153\pi$
$13$	−0.945848	+	1.73219i	−0.262331	+	0.480423i	0.713002	+	0.701162i	$0.247335\pi$
$14$		0			0
$15$	0.776435	+	0.360845i	0.200475	+	0.0931697i
$16$		0			0
$17$	4.90861	+	3.67454i	1.19051	+	0.891207i	0.995970	−	0.0896866i	$-0.0285865\pi$
$17$	4.90861	+	3.67454i	1.19051	+	0.891207i	0.194544	+	0.980894i	$0.437677\pi$
$18$		0			0
$19$	−0.852683	+	5.93054i	−0.195619	+	1.36056i	0.621194	+	0.783657i	$0.286648\pi$
$19$	−0.852683	+	5.93054i	−0.195619	+	1.36056i	−0.816813	+	0.576903i	$0.804261\pi$
$20$		0			0
$21$	0.219862	−	0.190511i	0.0479777	−	0.0415729i
$22$		0			0
$23$	−4.69671	−	0.970011i	−0.979332	−	0.202261i
$23$	−4.69671	−	0.970011i	−0.979332	−	0.202261i
$24$		0			0
$25$	1.34474	+	4.81577i	0.268948	+	0.963155i
$26$		0			0
$27$	1.79422	−	1.34314i	0.345298	−	0.258487i
$28$		0			0
$29$	−0.236919	+	0.0340638i	−0.0439948	+	0.00632549i	−0.164277	−	0.986414i	$-0.552529\pi$
$29$	−0.236919	+	0.0340638i	−0.0439948	+	0.00632549i	0.120282	+	0.992740i	$0.461620\pi$
$30$		0			0
$31$	4.27471	−	2.74719i	0.767761	−	0.493410i	−0.0971903	−	0.995266i	$-0.530986\pi$
$31$	4.27471	−	2.74719i	0.767761	−	0.493410i	0.864951	+	0.501856i	$0.167349\pi$
$32$		0			0
$33$	−1.72224	−	0.940413i	−0.299803	−	0.163705i
$34$		0			0
$35$	1.67998	+	0.252957i	0.283968	+	0.0427575i
$36$		0			0
$37$	−5.65965	−	2.11094i	−0.930441	−	0.347036i	−0.161878	−	0.986811i	$-0.551755\pi$
$37$	−5.65965	−	2.11094i	−0.930441	−	0.347036i	−0.768563	+	0.639774i	$0.779028\pi$
$38$		0			0
$39$	0.212903	−	0.725081i	0.0340918	−	0.116106i
$40$		0			0
$41$	−5.12993	+	11.2330i	−0.801160	+	1.75430i	−0.159660	+	0.987172i	$0.551040\pi$
$41$	−5.12993	+	11.2330i	−0.801160	+	1.75430i	−0.641500	+	0.767123i	$0.721687\pi$
$42$		0			0
$43$	−1.76290	−	8.10392i	−0.268840	−	1.23584i	−0.891383	−	0.453251i	$-0.850264\pi$
$43$	−1.76290	−	8.10392i	−0.268840	−	1.23584i	0.622543	−	0.782586i	$-0.286100\pi$
$44$		0			0
$45$	6.22540	+	1.39767i	0.928028	+	0.208352i
$46$		0			0
$47$	−2.45395	−	2.45395i	−0.357946	−	0.357946i	0.505110	−	0.863055i	$-0.331452\pi$
$47$	−2.45395	−	2.45395i	−0.357946	−	0.357946i	−0.863055	+	0.505110i	$0.831452\pi$
$48$		0			0
$49$	−3.47239	+	5.40315i	−0.496056	+	0.771879i
$50$		0			0
$51$	−2.13563	−	0.975309i	−0.299048	−	0.136571i
$52$		0			0
$53$	4.78984	+	8.77193i	0.657935	+	1.20492i	0.967218	+	0.253947i	$0.0817290\pi$
$53$	4.78984	+	8.77193i	0.657935	+	1.20492i	−0.309283	+	0.950970i	$0.600089\pi$
$54$		0			0
$55$	−2.36134	−	11.2134i	−0.318403	−	1.51201i
$56$		0			0
$57$	−0.163663	−	2.28831i	−0.0216777	−	0.303094i
$58$		0			0
$59$	−2.08663	−	7.10642i	−0.271656	−	0.925177i	−0.976446	−	0.215761i	$-0.930777\pi$
$59$	−2.08663	−	7.10642i	−0.271656	−	0.925177i	0.704790	−	0.709416i	$-0.251041\pi$
$60$		0			0
$61$	−2.01449	−	3.13461i	−0.257929	−	0.401346i	0.688004	−	0.725707i	$-0.258487\pi$
$61$	−2.01449	−	3.13461i	−0.257929	−	0.401346i	−0.945933	+	0.324361i	$0.894851\pi$
$62$		0			0
$63$	1.29920	−	1.73553i	0.163684	−	0.218656i
$64$		0			0
$65$	4.02641	−	1.80654i	0.499415	−	0.224074i
$66$		0			0
$67$	2.85366	+	0.204097i	0.348630	+	0.0249345i	0.244556	−	0.969635i	$-0.421358\pi$
$67$	2.85366	+	0.204097i	0.348630	+	0.0249345i	0.104073	+	0.994570i	$0.466812\pi$
$68$		0			0
$69$	1.83622	−	0.0193419i	0.221055	−	0.00232849i
$70$		0			0
$71$	9.10398	+	10.5066i	1.08044	+	1.24690i	0.967385	+	0.253310i	$0.0815194\pi$
$71$	9.10398	+	10.5066i	1.08044	+	1.24690i	0.113059	+	0.993588i	$0.463935\pi$
$72$		0			0
$73$	−2.55948	−	3.41907i	−0.299565	−	0.400172i	0.625351	−	0.780343i	$-0.284956\pi$
$73$	−2.55948	−	3.41907i	−0.299565	−	0.400172i	−0.924916	+	0.380172i	$0.875865\pi$
$74$		0			0
$75$	−0.895095	−	1.69237i	−0.103357	−	0.195418i
$76$		0			0
$77$	−3.80469	−	0.827659i	−0.433584	−	0.0943205i
$78$		0			0
$79$	−2.79542	+	0.820810i	−0.314510	+	0.0923484i	−0.435178	−	0.900345i	$-0.643314\pi$
$79$	−2.79542	+	0.820810i	−0.314510	+	0.0923484i	0.120668	+	0.992693i	$0.461496\pi$
$80$		0			0
$81$	5.04373	−	5.82077i	0.560414	−	0.646753i
$82$		0			0
$83$	0.0585753	−	0.157046i	0.00642947	−	0.0172381i	−0.933695	−	0.358068i	$-0.883435\pi$
$83$	0.0585753	−	0.157046i	0.00642947	−	0.0172381i	0.940125	+	0.340830i	$0.110708\pi$
$84$		0			0
$85$	−3.77520	−	13.1807i	−0.409477	−	1.42965i
$86$		0			0
$87$	0.0858705	−	0.0320281i	0.00920629	−	0.00343377i
$88$		0			0
$89$	10.6832	+	6.86564i	1.13241	+	0.727757i	0.966062	−	0.258310i	$-0.0831656\pi$
$89$	10.6832	+	6.86564i	1.13241	+	0.727757i	0.166350	+	0.986067i	$0.446802\pi$
$90$		0			0
$91$		−	1.49950i		−	0.157190i
$92$		0			0
$93$	−1.37578	+	1.37578i	−0.142662	+	0.142662i
$94$		0			0
$95$	9.53622	−	9.41023i	0.978395	−	0.965469i
$96$		0			0
$97$	−4.99652	−	13.3962i	−0.507320	−	1.36018i	−0.898140	−	0.439710i	$-0.855081\pi$
$97$	−4.99652	−	13.3962i	−0.507320	−	1.36018i	0.390820	−	0.920467i	$-0.372191\pi$
$98$		0			0
$99$	−14.0306	−	4.11975i	−1.41013	−	0.414050i
$100$		0			0
$101$	3.46810	+	7.59408i	0.345089	+	0.755639i	1.00000		6.66447e-5i	$-2.12137e-5\pi$
$101$	3.46810	+	7.59408i	0.345089	+	0.755639i	−0.654911	+	0.755706i	$0.727294\pi$
$102$		0			0
$103$	−13.3820	+	0.957103i	−1.31857	+	0.0943061i	−0.712820	−	0.701347i	$-0.752582\pi$
$103$	−13.3820	+	0.957103i	−1.31857	+	0.0943061i	−0.605752	+	0.795653i	$0.707128\pi$
$104$		0			0
$105$	−0.649150	+	0.0420916i	−0.0633506	+	0.00410772i
$106$		0			0
$107$	3.64722	−	16.7660i	0.352590	−	1.62083i	−0.369637	−	0.929176i	$-0.620518\pi$
$107$	3.64722	−	16.7660i	0.352590	−	1.62083i	0.722228	−	0.691655i	$-0.243118\pi$
$108$		0			0
$109$	−0.432294	−	3.00667i	−0.0414063	−	0.287987i	−0.999995	−	0.00319259i	$-0.998984\pi$
$109$	−0.432294	−	3.00667i	−0.0414063	−	0.287987i	0.958589	−	0.284794i	$-0.0919253\pi$
$110$		0			0
$111$	2.28936	+	0.329161i	0.217297	+	0.0312426i
$112$		0			0
$113$	−0.700004	+	9.78733i	−0.0658508	+	0.920714i	0.851937	+	0.523644i	$0.175428\pi$
$113$	−0.700004	+	9.78733i	−0.0658508	+	0.920714i	−0.917788	+	0.397071i	$0.870027\pi$
$114$		0			0
$115$	7.05402	+	8.07718i	0.657791	+	0.753201i
$116$		0			0
$117$	0.401744	−	5.61711i	0.0371412	−	0.519302i
$118$		0			0
$119$	−4.61125	−	0.662997i	−0.422712	−	0.0607769i
$120$		0			0
$121$	2.17216	+	15.1077i	0.197469	+	1.37343i
$122$		0			0
$123$	1.00509	−	4.62034i	0.0906262	−	0.416602i
$124$		0			0
$125$	4.11530	−	10.3954i	0.368084	−	0.929793i
$126$		0			0
$127$	17.7981	−	1.27294i	1.57932	−	0.112955i	0.746078	−	0.665858i	$-0.231934\pi$
$127$	17.7981	−	1.27294i	1.57932	−	0.112955i	0.833246	+	0.552903i	$0.186480\pi$
$128$		0			0
$129$	1.31918	+	2.88859i	0.116147	+	0.254326i
$130$		0			0
$131$	−4.38969	−	1.28893i	−0.383529	−	0.112614i	0.0842840	−	0.996442i	$-0.473140\pi$
$131$	−4.38969	−	1.28893i	−0.383529	−	0.112614i	−0.467813	+	0.883828i	$0.654958\pi$
$132$		0			0
$133$	−1.59084	−	4.26521i	−0.137943	−	0.369840i
$134$		0			0
$135$	−5.01150	−	0.0333238i	−0.431321	−	0.00286805i
$136$		0			0
$137$	−13.1433	+	13.1433i	−1.12291	+	1.12291i	−0.131605	+	0.991302i	$0.542013\pi$
$137$	−13.1433	+	13.1433i	−1.12291	+	1.12291i	−0.991302	+	0.131605i	$0.957987\pi$
$138$		0			0
$139$		−	9.06223i		−	0.768648i	−0.923198	−	0.384324i	$-0.874435\pi$
$139$		−	9.06223i		−	0.768648i	0.923198	−	0.384324i	$-0.125565\pi$
$140$		0			0
$141$	1.11787	+	0.718414i	0.0941419	+	0.0605014i
$142$		0			0
$143$	−9.47653	+	3.53456i	−0.792467	+	0.295575i
$144$		0			0
$145$	0.468031	+	0.259619i	0.0388678	+	0.0215602i
$146$		0			0
$147$	0.859424	−	2.30421i	0.0708841	−	0.190048i
$148$		0			0
$149$	4.20800	−	4.85629i	0.344733	−	0.397843i	−0.556734	−	0.830691i	$-0.687946\pi$
$149$	4.20800	−	4.85629i	0.344733	−	0.397843i	0.901467	+	0.432848i	$0.142491\pi$
$150$		0			0
$151$	12.6577	−	3.71664i	1.03007	−	0.302456i	0.277330	−	0.960775i	$-0.410550\pi$
$151$	12.6577	−	3.71664i	1.03007	−	0.302456i	0.752739	+	0.658319i	$0.228732\pi$
$152$		0			0
$153$	−17.0961	−	3.71902i	−1.38213	−	0.300665i
$154$		0			0
$155$	−11.3277	−	0.885916i	−0.909861	−	0.0711585i
$156$		0			0
$157$	−9.25126	−	12.3582i	−0.738331	−	0.986295i	−0.999778	−	0.0210771i	$-0.993290\pi$
$157$	−9.25126	−	12.3582i	−0.738331	−	0.986295i	0.261447	−	0.965218i	$-0.415800\pi$
$158$		0			0
$159$	−2.50607	−	2.89216i	−0.198744	−	0.229363i
$160$		0			0
$161$	3.48516	−	1.06334i	0.274669	−	0.0838026i
$162$		0			0
$163$	16.2730	+	1.16387i	1.27460	+	0.0911614i	0.692180	−	0.721725i	$-0.256650\pi$
$163$	16.2730	+	1.16387i	1.27460	+	0.0911614i	0.582422	+	0.812886i	$0.302105\pi$
$164$		0			0
$165$	1.79616	+	4.00328i	0.139831	+	0.311655i
$166$		0			0
$167$	−5.50136	+	7.34896i	−0.425708	+	0.568679i	−0.961197	−	0.275863i	$-0.911036\pi$
$167$	−5.50136	+	7.34896i	−0.425708	+	0.568679i	0.535489	+	0.844542i	$0.320127\pi$
$168$		0			0
$169$	4.92247	+	7.65952i	0.378652	+	0.589194i
$170$		0			0
$171$	−4.81654	−	16.4036i	−0.368330	−	1.25442i
$172$		0			0
$173$	−0.593241	−	8.29460i	−0.0451033	−	0.630627i	−0.968854	−	0.247632i	$-0.920347\pi$
$173$	−0.593241	−	8.29460i	−0.0451033	−	0.630627i	0.923751	−	0.382994i	$-0.125107\pi$
$174$		0			0
$175$	−2.65026	−	2.72170i	−0.200341	−	0.205741i
$176$		0			0
$177$	1.35911	+	2.48903i	0.102157	+	0.187087i
$178$		0			0
$179$	8.25754	+	3.77109i	0.617197	+	0.281865i	0.699377	−	0.714753i	$-0.253461\pi$
$179$	8.25754	+	3.77109i	0.617197	+	0.281865i	−0.0821797	+	0.996618i	$0.526188\pi$
$180$		0			0
$181$	−5.82600	+	9.06544i	−0.433043	+	0.673829i	−0.987363	−	0.158475i	$-0.949342\pi$
$181$	−5.82600	+	9.06544i	−0.433043	+	0.673829i	0.554320	+	0.832304i	$0.312979\pi$
$182$		0			0
$183$	1.00885	+	1.00885i	0.0745764	+	0.0745764i
$184$		0			0
$185$	7.22671	+	11.4111i	0.531318	+	0.838961i
$186$		0			0
$187$	6.67944	+	30.7049i	0.488449	+	2.24536i
$188$		0			0
$189$	−0.707393	+	1.54897i	−0.0514553	+	0.112671i
$190$		0			0
$191$	−2.81670	+	9.59280i	−0.203809	+	0.694111i	0.792623	+	0.609712i	$0.208715\pi$
$191$	−2.81670	+	9.59280i	−0.203809	+	0.694111i	−0.996432	+	0.0843986i	$0.973103\pi$
$192$		0			0
$193$	4.45105	+	1.66016i	0.320394	+	0.119501i	0.504515	−	0.863403i	$-0.331671\pi$
$193$	4.45105	+	1.66016i	0.320394	+	0.119501i	−0.184121	+	0.982904i	$0.558944\pi$
$194$		0			0
$195$	−1.35944	+	1.00363i	−0.0973516	+	0.0718714i
$196$		0			0
$197$	21.2481	+	11.6023i	1.51386	+	0.826632i	0.999521	−	0.0309518i	$-0.00985384\pi$
$197$	21.2481	+	11.6023i	1.51386	+	0.826632i	0.514343	+	0.857584i	$0.328036\pi$
$198$		0			0
$199$	−3.69177	+	2.37256i	−0.261703	+	0.168186i	−0.664912	−	0.746922i	$-0.731531\pi$
$199$	−3.69177	+	2.37256i	−0.261703	+	0.168186i	0.403209	+	0.915108i	$0.367895\pi$
$200$		0			0
$201$	−1.08430	+	0.155899i	−0.0764809	+	0.0109963i
$202$		0			0
$203$	0.145584	−	0.108983i	0.0102180	−	0.00764909i
$204$		0			0
$205$	24.3228	−	13.0721i	1.69878	−	0.912993i
$206$		0			0
$207$	13.3403	−	3.04950i	0.927212	−	0.211955i
$208$		0			0
$209$	−23.2053	+	20.1075i	−1.60515	+	1.39087i
$210$		0			0
$211$	−1.76143	+	12.2510i	−0.121262	+	0.843396i	0.834867	+	0.550451i	$0.185544\pi$
$211$	−1.76143	+	12.2510i	−0.121262	+	0.843396i	−0.956129	+	0.292945i	$0.905365\pi$
$212$		0			0
$213$	−4.26139	−	3.19003i	−0.291985	−	0.218578i
$214$		0			0
$215$	−7.81576	+	16.8173i	−0.533030	+	1.14693i
$216$		0			0
$217$	−1.85024	+	3.38846i	−0.125602	+	0.230024i
$218$		0			0
$219$	1.23591	+	1.07092i	0.0835150	+	0.0723662i
$220$		0			0
$221$	−11.0078	+	5.02710i	−0.740466	+	0.338159i
$222$		0			0
$223$	−11.9646	+	6.53314i	−0.801206	+	0.437491i	−0.827018	−	0.562175i	$-0.809965\pi$
$223$	−11.9646	+	6.53314i	−0.801206	+	0.437491i	0.0258123	+	0.999667i	$0.491783\pi$
$224$		0			0
$225$	−9.19865	−	10.9055i	−0.613243	−	0.727035i
$226$		0			0
$227$	−2.14168	+	0.465894i	−0.142148	+	0.0309224i	−0.283076	−	0.959097i	$-0.591355\pi$
$227$	−2.14168	+	0.465894i	−0.142148	+	0.0309224i	0.140928	+	0.990020i	$0.454991\pi$
$228$		0			0
$229$	−3.36018			−0.222047			−0.111024	−	0.993818i	$-0.535413\pi$
$229$	−3.36018			−0.222047			−0.111024	+	0.993818i	$0.535413\pi$
$230$		0			0
$231$	1.49088			0.0980930
$232$		0			0
$233$	21.5890	−	4.69639i	1.41434	−	0.307671i	0.560477	−	0.828170i	$-0.310618\pi$
$233$	21.5890	−	4.69639i	1.41434	−	0.307671i	0.853862	+	0.520499i	$0.174254\pi$
$234$		0			0
$235$	1.05328	+	7.68826i	0.0687081	+	0.501527i
$236$		0			0
$237$	0.979098	−	0.534628i	0.0635993	−	0.0347278i
$238$		0			0
$239$	−1.77417	+	0.810235i	−0.114761	+	0.0524097i	−0.471968	−	0.881616i	$-0.656456\pi$
$239$	−1.77417	+	0.810235i	−0.114761	+	0.0524097i	0.357207	+	0.934025i	$0.383729\pi$
$240$		0			0
$241$	−2.40175	−	2.08113i	−0.154710	−	0.134057i	0.574066	−	0.818809i	$-0.305365\pi$
$241$	−2.40175	−	2.08113i	−0.154710	−	0.134057i	−0.728776	+	0.684752i	$0.759911\pi$
$242$		0			0
$243$	−4.63571	+	8.48967i	−0.297381	+	0.544613i
$244$		0			0
$245$	13.4892	−	4.92931i	0.861796	−	0.314922i
$246$		0			0
$247$	−9.46632	−	7.08640i	−0.602328	−	0.450897i
$248$		0			0
$249$	−0.00913370	+	0.0635263i	−0.000578825	+	0.00402581i
$250$		0			0
$251$	20.3605	−	17.6425i	1.28514	−	1.11358i	0.297859	−	0.954610i	$-0.403727\pi$
$251$	20.3605	−	17.6425i	1.28514	−	1.11358i	0.987283	−	0.158972i	$-0.0508180\pi$
$252$		0			0
$253$	−14.9351	−	19.5190i	−0.938964	−	1.22715i
$254$		0			0
$255$	2.48528	+	4.62429i	0.155634	+	0.289584i
$256$		0			0
$257$	−16.2299	+	12.1496i	−1.01240	+	0.757870i	−0.970463	−	0.241251i	$-0.922442\pi$
$257$	−16.2299	+	12.1496i	−1.01240	+	0.757870i	−0.0419324	+	0.999120i	$0.513351\pi$
$258$		0			0
$259$	4.54273	−	0.653146i	0.282271	−	0.0405845i
$260$		0			0
$261$	0.574554	−	0.369243i	0.0355640	−	0.0228556i
$262$		0			0
$263$	25.1033	+	13.7075i	1.54794	+	0.845238i	0.999962	+	0.00874389i	$0.00278330\pi$
$263$	25.1033	+	13.7075i	1.54794	+	0.845238i	0.547976	+	0.836494i	$0.315399\pi$
$264$		0			0
$265$	3.32751	−	22.0992i	0.204407	−	1.35754i
$266$		0			0
$267$	−4.55589	−	1.69926i	−0.278816	−	0.103993i
$268$		0			0
$269$	0.495938	−	1.68901i	0.0302379	−	0.102981i	−0.942991	−	0.332817i	$-0.892001\pi$
$269$	0.495938	−	1.68901i	0.0302379	−	0.102981i	0.973229	+	0.229836i	$0.0738190\pi$
$270$		0			0
$271$	−0.428604	+	0.938512i	−0.0260358	+	0.0570105i	−0.922203	−	0.386706i	$-0.873613\pi$
$271$	−0.428604	+	0.938512i	−0.0260358	+	0.0570105i	0.896167	+	0.443716i	$0.146340\pi$
$272$		0			0
$273$	0.122046	+	0.561037i	0.00738656	+	0.0339555i
$274$		0			0
$275$	−10.9535	+	23.1646i	−0.660521	+	1.39688i
$276$		0			0
$277$	−14.9575	−	14.9575i	−0.898710	−	0.898710i	0.0966123	−	0.995322i	$-0.469199\pi$
$277$	−14.9575	−	14.9575i	−0.898710	−	0.898710i	−0.995322	+	0.0966123i	$0.969199\pi$
$278$		0			0
$279$	−7.83880	+	12.1974i	−0.469297	+	0.730240i
$280$		0			0
$281$	−13.6264	−	6.22295i	−0.812881	−	0.371230i	−0.0347999	−	0.999394i	$-0.511079\pi$
$281$	−13.6264	−	6.22295i	−0.812881	−	0.371230i	−0.778081	+	0.628164i	$0.783807\pi$
$282$		0			0
$283$	−3.86185	−	7.07246i	−0.229563	−	0.420414i	0.737353	−	0.675508i	$-0.236075\pi$
$283$	−3.86185	−	7.07246i	−0.229563	−	0.420414i	−0.966916	+	0.255094i	$0.917894\pi$
$284$		0			0
$285$	−2.80206	+	4.29699i	−0.165980	+	0.254532i
$286$		0			0
$287$	−0.669335	−	9.35853i	−0.0395096	−	0.552416i
$288$		0			0
$289$	5.80277	+	19.7624i	0.341340	+	1.16250i
$290$		0			0
$291$	2.95977	+	4.60550i	0.173505	+	0.269979i
$292$		0			0
$293$	−5.30481	+	7.08639i	−0.309910	+	0.413991i	−0.928272	−	0.371902i	$-0.878706\pi$
$293$	−5.30481	+	7.08639i	−0.309910	+	0.413991i	0.618362	+	0.785894i	$0.287797\pi$
$294$		0			0
$295$	−5.89063	+	15.4783i	−0.342965	+	0.901179i
$296$		0			0
$297$	11.4566	+	0.819394i	0.664781	+	0.0475461i
$298$		0			0
$299$	6.12262	−	7.21812i	0.354080	−	0.417434i
$300$		0			0
$301$	4.12640	+	4.76212i	0.237842	+	0.274484i
$302$		0			0
$303$	−1.91568	−	2.55905i	−0.110053	−	0.147013i
$304$		0			0
$305$	−0.649635	+	8.30650i	−0.0371980	+	0.475629i
$306$		0			0
$307$	4.59535	+	0.999657i	0.262270	+	0.0570534i	0.341778	−	0.939781i	$-0.388971\pi$
$307$	4.59535	+	0.999657i	0.262270	+	0.0570534i	−0.0795072	+	0.996834i	$0.525335\pi$
$308$		0			0
$309$	4.92898	−	1.44728i	0.280400	−	0.0823328i
$310$		0			0
$311$	9.59820	−	11.0769i	0.544264	−	0.628114i	−0.415273	−	0.909697i	$-0.636314\pi$
$311$	9.59820	−	11.0769i	0.544264	−	0.628114i	0.959537	+	0.281583i	$0.0908593\pi$
$312$		0			0
$313$	−3.89366	+	10.4393i	−0.220083	+	0.590064i	−0.999328	−	0.0366546i	$-0.988330\pi$
$313$	−3.89366	+	10.4393i	−0.220083	+	0.590064i	0.779245	+	0.626719i	$0.215603\pi$
$314$		0			0
$315$	−4.66028	+	1.33479i	−0.262577	+	0.0752067i
$316$		0			0
$317$	15.7410	−	5.87110i	0.884104	−	0.329754i	0.133927	−	0.990991i	$-0.457241\pi$
$317$	15.7410	−	5.87110i	0.884104	−	0.329754i	0.750177	+	0.661237i	$0.229968\pi$
$318$		0			0
$319$	−1.03191	−	0.663169i	−0.0577760	−	0.0371304i
$320$		0			0
$321$			6.56984i			0.366693i
$322$		0			0
$323$	−25.9775	+	25.9775i	−1.44543	+	1.44543i
$324$		0			0
$325$	−9.61376	−	2.22564i	−0.533276	−	0.123456i
$326$		0			0
$327$	0.406459	+	1.08976i	0.0224772	+	0.0602638i
$328$		0			0
$329$	2.52993	+	0.742856i	0.139480	+	0.0409550i
$330$		0			0
$331$	−0.834797	−	1.82795i	−0.0458846	−	0.100473i	0.885301	−	0.465018i	$-0.153952\pi$
$331$	−0.834797	−	1.82795i	−0.0458846	−	0.100473i	−0.931186	+	0.364544i	$0.881225\pi$
$332$		0			0
$333$	17.1920	−	1.22960i	0.942115	−	0.0673814i
$334$		0			0
$335$	−4.80677	−	4.22137i	−0.262622	−	0.230638i
$336$		0			0
$337$	−0.630864	+	2.90004i	−0.0343654	+	0.157975i	−0.991132	−	0.132882i	$-0.957577\pi$
$337$	−0.630864	+	2.90004i	−0.0343654	+	0.157975i	0.956766	+	0.290857i	$0.0939405\pi$
$338$		0			0
$339$	−0.534696	−	3.71889i	−0.0290407	−	0.201983i
$340$		0			0
$341$	25.7756	+	3.70598i	1.39583	+	0.200690i
$342$		0			0
$343$	0.727538	−	10.1723i	0.0392834	−	0.549253i
$344$		0			0
$345$	−3.29667	−	2.44793i	−0.177487	−	0.131792i
$346$		0			0
$347$	−0.735510	+	10.2838i	−0.0394842	+	0.552062i	0.938756	+	0.344584i	$0.111980\pi$
$347$	−0.735510	+	10.2838i	−0.0394842	+	0.552062i	−0.978240	+	0.207478i	$0.933475\pi$
$348$		0			0
$349$	23.5070	+	3.37980i	1.25830	+	0.180917i	0.739019	−	0.673685i	$-0.235289\pi$
$349$	23.5070	+	3.37980i	1.25830	+	0.180917i	0.519285	+	0.854601i	$0.326198\pi$
$350$		0			0
$351$	0.629510	+	4.37834i	0.0336007	+	0.233698i
$352$		0			0
$353$	3.33053	−	15.3102i	0.177266	−	0.814879i	−0.799516	−	0.600645i	$-0.794911\pi$
$353$	3.33053	−	15.3102i	0.177266	−	0.814879i	0.976782	−	0.214235i	$-0.0687257\pi$
$354$		0			0
$355$	−2.01144	−	31.0210i	−0.106756	−	1.64643i
$356$		0			0
$357$	1.77926	−	0.127255i	0.0941682	−	0.00673504i
$358$		0			0
$359$	−11.2250	−	24.5792i	−0.592431	−	1.29724i	−0.933962	−	0.357372i	$-0.883673\pi$
$359$	−11.2250	−	24.5792i	−0.592431	−	1.29724i	0.341531	−	0.939870i	$-0.389054\pi$
$360$		0			0
$361$	−16.2139	−	4.76082i	−0.853362	−	0.250570i
$362$		0			0
$363$	−2.04235	−	5.47574i	−0.107195	−	0.287402i
$364$		0			0
$365$	−0.0635018	+	9.54991i	−0.00332384	+	0.499865i
$366$		0			0
$367$	−14.1134	+	14.1134i	−0.736712	+	0.736712i	−0.971940	−	0.235228i	$-0.924416\pi$
$367$	−14.1134	+	14.1134i	−0.736712	+	0.736712i	0.235228	+	0.971940i	$0.424416\pi$
$368$		0			0
$369$		−	35.2363i		−	1.83433i
$370$		0			0
$371$	−6.38812	−	4.10539i	−0.331655	−	0.213141i
$372$		0			0
$373$	10.1164	−	3.77321i	0.523806	−	0.195370i	−0.0736307	−	0.997286i	$-0.523459\pi$
$373$	10.1164	−	3.77321i	0.523806	−	0.195370i	0.597437	+	0.801916i	$0.296186\pi$
$374$		0			0
$375$	−0.693643	+	4.22438i	−0.0358196	+	0.218146i
$376$		0			0
$377$	0.165084	−	0.442608i	0.00850228	−	0.0227955i
$378$		0			0
$379$	2.79375	−	3.22416i	0.143506	−	0.165614i	−0.679447	−	0.733725i	$-0.737780\pi$
$379$	2.79375	−	3.22416i	0.143506	−	0.165614i	0.822952	+	0.568111i	$0.192326\pi$
$380$		0			0
$381$	−6.55553	+	1.92488i	−0.335850	+	0.0986144i
$382$		0			0
$383$	29.3897	+	6.39333i	1.50174	+	0.326684i	0.886898	−	0.461965i	$-0.152855\pi$
$383$	29.3897	+	6.39333i	1.50174	+	0.326684i	0.614844	+	0.788649i	$0.289219\pi$
$384$		0			0
$385$	5.65767	+	6.61771i	0.288342	+	0.337270i
$386$		0			0
$387$	14.1816	+	18.9444i	0.720890	+	0.962996i
$388$		0			0
$389$	−0.519368	−	0.599383i	−0.0263330	−	0.0303899i	0.742430	−	0.669923i	$-0.233673\pi$
$389$	−0.519368	−	0.599383i	−0.0263330	−	0.0303899i	−0.768763	+	0.639533i	$0.779128\pi$
$390$		0			0
$391$	−19.4900	−	22.0197i	−0.985651	−	1.11358i
$392$		0			0
$393$	1.74731	+	0.124970i	0.0881399	+	0.00630389i
$394$		0			0
$395$	6.08862	+	2.31717i	0.306352	+	0.116590i
$396$		0			0
$397$	−11.2140	+	14.9801i	−0.562813	+	0.751831i	−0.988198	−	0.153182i	$-0.951048\pi$
$397$	−11.2140	+	14.9801i	−0.562813	+	0.751831i	0.425385	+	0.905013i	$0.360139\pi$
$398$		0			0
$399$	0.942362	+	1.46634i	0.0471771	+	0.0734090i
$400$		0			0
$401$	−7.11592	−	24.2346i	−0.355352	−	1.21022i	−0.922304	−	0.386466i	$-0.873696\pi$
$401$	−7.11592	−	24.2346i	−0.355352	−	1.21022i	0.566952	−	0.823751i	$-0.308123\pi$
$402$		0			0
$403$	0.715432	+	10.0030i	0.0356382	+	0.498287i
$404$		0			0
$405$	−16.8526	+	3.54886i	−0.837410	+	0.176344i
$406$		0			0
$407$	−14.8357	−	27.1695i	−0.735377	−	1.34674i
$408$		0			0
$409$	−4.14266	−	1.89189i	−0.204841	−	0.0935480i	0.310353	−	0.950622i	$-0.399553\pi$
$409$	−4.14266	−	1.89189i	−0.204841	−	0.0935480i	−0.515194	+	0.857074i	$0.672280\pi$
$410$		0			0
$411$	3.84780	−	5.98730i	0.189798	−	0.295332i
$412$		0			0
$413$	3.97906	+	3.97906i	0.195797	+	0.195797i
$414$		0			0
$415$	−0.316640	+	0.200530i	−0.0155432	+	0.00984362i
$416$		0			0
$417$	0.737585	+	3.39062i	0.0361197	+	0.166040i
$418$		0			0
$419$	6.28729	−	13.7673i	0.307154	−	0.672574i	−0.691610	−	0.722271i	$-0.743098\pi$
$419$	6.28729	−	13.7673i	0.307154	−	0.672574i	0.998764	+	0.0496968i	$0.0158255\pi$
$420$		0			0
$421$	8.98996	−	30.6170i	0.438144	−	1.49218i	−0.384232	−	0.923236i	$-0.625534\pi$
$421$	8.98996	−	30.6170i	0.438144	−	1.49218i	0.822376	−	0.568944i	$-0.192648\pi$
$422$		0			0
$423$	9.27808	+	3.46054i	0.451116	+	0.168257i
$424$		0			0
$425$	−11.0950	+	28.5801i	−0.538184	+	1.38634i
$426$		0			0
$427$	2.48473	+	1.35677i	0.120245	+	0.0656585i
$428$		0			0
$429$	3.25795	−	2.09376i	0.157295	−	0.101088i
$430$		0			0
$431$	−14.5232	+	2.08812i	−0.699558	+	0.100581i	−0.482912	−	0.875669i	$-0.660421\pi$
$431$	−14.5232	+	2.08812i	−0.699558	+	0.100581i	−0.216646	+	0.976250i	$0.569512\pi$
$432$		0			0
$433$	15.8584	−	11.8714i	0.762105	−	0.570504i	−0.145982	−	0.989287i	$-0.546634\pi$
$433$	15.8584	−	11.8714i	0.762105	−	0.570504i	0.908086	+	0.418783i	$0.137543\pi$
$434$		0			0
$435$	−0.196244	−	0.0590426i	−0.00940918	−	0.00283088i
$436$		0			0
$437$	9.75749	−	27.0269i	0.466764	−	1.29287i
$438$		0			0
$439$	24.8939	−	21.5707i	1.18812	−	1.02951i	0.189253	−	0.981928i	$-0.439393\pi$
$439$	24.8939	−	21.5707i	1.18812	−	1.02951i	0.998867	−	0.0475836i	$-0.0151520\pi$
$440$		0			0
$441$	2.60814	−	18.1400i	0.124197	−	0.863811i
$442$		0			0
$443$	25.8081	+	19.3197i	1.22618	+	0.917907i	0.998441	−	0.0558158i	$-0.0177760\pi$
$443$	25.8081	+	19.3197i	1.22618	+	0.917907i	0.227738	+	0.973722i	$0.426867\pi$
$444$		0			0
$445$	−9.74626	−	26.6710i	−0.462017	−	1.26433i
$446$		0			0
$447$	−1.17916	+	2.15947i	−0.0557724	+	0.102140i
$448$		0			0
$449$	−0.901396	−	0.781064i	−0.0425395	−	0.0368607i	0.633332	−	0.773881i	$-0.281687\pi$
$449$	−0.901396	−	0.781064i	−0.0425395	−	0.0368607i	−0.675871	+	0.737020i	$0.736232\pi$
$450$		0			0
$451$	−57.5662	+	26.2896i	−2.71068	+	1.23793i
$452$		0			0
$453$	−4.43337	+	2.42080i	−0.208298	+	0.113739i
$454$		0			0
$455$	−2.02717	+	2.67078i	−0.0950353	+	0.125208i
$456$		0			0
$457$	−5.94097	+	1.29238i	−0.277907	+	0.0604550i	−0.349359	−	0.936989i	$-0.613601\pi$
$457$	−5.94097	+	1.29238i	−0.277907	+	0.0604550i	0.0714515	+	0.997444i	$0.477237\pi$
$458$		0			0
$459$	13.7425			0.641447
$460$		0			0
$461$	−27.7712			−1.29343			−0.646717	−	0.762730i	$-0.723859\pi$
$461$	−27.7712			−1.29343			−0.646717	+	0.762730i	$0.723859\pi$
$462$		0			0
$463$	5.79168	−	1.25990i	0.269162	−	0.0585526i	−0.0759585	−	0.997111i	$-0.524202\pi$
$463$	5.79168	−	1.25990i	0.269162	−	0.0585526i	0.345121	+	0.938558i	$0.387838\pi$
$464$		0			0
$465$	4.31035	−	0.590508i	0.199887	−	0.0273842i
$466$		0			0
$467$	6.65274	−	3.63267i	0.307852	−	0.168100i	−0.317895	−	0.948126i	$-0.602976\pi$
$467$	6.65274	−	3.63267i	0.307852	−	0.168100i	0.625747	+	0.780026i	$0.284794\pi$
$468$		0			0
$469$	−1.97725	+	0.902980i	−0.0913009	+	0.0416957i
$470$		0			0
$471$	4.46720	+	3.87085i	0.205838	+	0.178360i
$472$		0			0
$473$	20.3690	−	37.3030i	0.936567	−	1.71519i
$474$		0			0
$475$	−29.7068	+	3.86871i	−1.36304	+	0.177508i
$476$		0			0
$477$	−22.8299	−	17.0902i	−1.04531	−	0.782509i
$478$		0			0
$479$	1.50152	−	10.4433i	0.0686063	−	0.477168i	−0.926334	−	0.376703i	$-0.877058\pi$
$479$	1.50152	−	10.4433i	0.0686063	−	0.477168i	0.994941	−	0.100465i	$-0.0320330\pi$
$480$		0			0
$481$	9.00972	−	7.80697i	0.410808	−	0.355967i
$482$		0			0
$483$	−1.21742	+	0.681507i	−0.0553947	+	0.0310096i
$484$		0			0
$485$	−9.21092	+	30.6149i	−0.418246	+	1.39015i
$486$		0			0
$487$	7.75649	−	5.80644i	0.351480	−	0.263115i	−0.408919	−	0.912571i	$-0.634094\pi$
$487$	7.75649	−	5.80644i	0.351480	−	0.263115i	0.760399	+	0.649456i	$0.225003\pi$
$488$		0			0
$489$	−6.18327	+	0.889020i	−0.279617	+	0.0402029i
$490$		0			0
$491$	−6.44176	+	4.13987i	−0.290713	+	0.186830i	−0.677866	−	0.735186i	$-0.737095\pi$
$491$	−6.44176	+	4.13987i	−0.290713	+	0.186830i	0.387153	+	0.922015i	$0.373459\pi$
$492$		0			0
$493$	−1.28811	−	0.703363i	−0.0580137	−	0.0316779i
$494$		0			0
$495$	19.4206	+	26.3056i	0.872890	+	1.18235i
$496$		0			0
$497$	−9.89658	−	3.69123i	−0.443922	−	0.165574i
$498$		0			0
$499$	6.87292	−	23.4070i	0.307674	−	1.04784i	−0.649988	−	0.759945i	$-0.725226\pi$
$499$	6.87292	−	23.4070i	0.307674	−	1.04784i	0.957662	−	0.287896i	$-0.0929559\pi$
$500$		0			0
$501$	1.46019	−	3.19737i	0.0652364	−	0.142848i
$502$		0			0
$503$	−2.78748	−	12.8138i	−0.124288	−	0.571341i	−0.996600	−	0.0823921i	$-0.973744\pi$
$503$	−2.78748	−	12.8138i	−0.124288	−	0.571341i	0.872312	−	0.488949i	$-0.162620\pi$
$504$		0			0
$505$	4.08934	−	18.2145i	0.181973	−	0.810532i
$506$		0			0
$507$	−2.46516	−	2.46516i	−0.109481	−	0.109481i
$508$		0			0
$509$	6.34699	−	9.87611i	0.281325	−	0.437751i	−0.671619	−	0.740897i	$-0.734401\pi$
$509$	6.34699	−	9.87611i	0.281325	−	0.437751i	0.952944	+	0.303146i	$0.0980370\pi$
$510$		0			0
$511$	2.95173	+	1.34801i	0.130577	+	0.0596324i
$512$		0			0
$513$	6.43563	+	11.7860i	0.284140	+	0.520363i
$514$		0			0
$515$	25.1289	+	16.3865i	1.10731	+	0.722074i
$516$		0			0
$517$	−1.26877	−	17.7397i	−0.0558003	−	0.780190i
$518$		0			0
$519$	0.897068	+	3.05513i	0.0393769	+	0.134105i
$520$		0			0
$521$	−17.6525	−	27.4677i	−0.773368	−	1.20338i	−0.974625	−	0.223845i	$-0.928139\pi$
$521$	−17.6525	−	27.4677i	−0.773368	−	1.20338i	0.201257	−	0.979539i	$-0.435497\pi$
$522$		0			0
$523$	14.4896	−	19.3559i	0.633587	−	0.846373i	−0.362750	−	0.931887i	$-0.618162\pi$
$523$	14.4896	−	19.3559i	0.633587	−	0.846373i	0.996337	+	0.0855132i	$0.0272530\pi$
$524$		0			0
$525$	1.21311	+	0.802615i	0.0529447	+	0.0350290i
$526$		0			0
$527$	31.0776	+	2.22271i	1.35376	+	0.0968229i
$528$		0			0
$529$	21.1182	+	9.11172i	0.918181	+	0.396162i
$530$		0			0
$531$	13.8394	+	15.9716i	0.600581	+	0.693107i
$532$		0			0
$533$	−14.6055	−	19.5107i	−0.632636	−	0.845102i
$534$		0			0
$535$	−29.1621	+	24.9315i	−1.26079	+	1.07788i
$536$		0			0
$537$	−3.39648	−	0.738860i	−0.146569	−	0.0318841i
$538$		0			0
$539$	−31.5816	+	9.27321i	−1.36032	+	0.399425i
$540$		0			0
$541$	1.07664	−	1.24251i	0.0462882	−	0.0534195i	−0.732133	−	0.681161i	$-0.761475\pi$
$541$	1.07664	−	1.24251i	0.0462882	−	0.0534195i	0.778422	+	0.627742i	$0.216021\pi$
$542$		0			0
$543$	1.44195	−	3.86601i	0.0618799	−	0.165906i
$544$		0			0
$545$	−3.29475	+	5.93965i	−0.141132	+	0.254427i
$546$		0			0
$547$	−18.6612	+	6.96027i	−0.797895	+	0.297600i	−0.715150	−	0.698971i	$-0.753642\pi$
$547$	−18.6612	+	6.96027i	−0.797895	+	0.297600i	−0.0827455	+	0.996571i	$0.526369\pi$
$548$		0			0
$549$	8.94427	+	5.74813i	0.381732	+	0.245324i
$550$		0			0
$551$		−	1.43410i		−	0.0610949i
$552$		0			0
$553$	1.56523	−	1.56523i	0.0665602	−	0.0665602i
$554$		0			0
$555$	−3.63263	−	3.68126i	−0.154197	−	0.156261i
$556$		0			0
$557$	2.72165	+	7.29701i	0.115320	+	0.309184i	0.981768	−	0.190082i	$-0.0608755\pi$
$557$	2.72165	+	7.29701i	0.115320	+	0.309184i	−0.866448	+	0.499267i	$0.833603\pi$
$558$		0			0
$559$	15.7050	+	4.61140i	0.664250	+	0.195041i
$560$		0			0
$561$	−4.99821	−	10.9446i	−0.211025	−	0.462080i
$562$		0			0
$563$	−23.2472	+	1.66268i	−0.979754	+	0.0700734i	−0.552020	−	0.833831i	$-0.686143\pi$
$563$	−23.2472	+	1.66268i	−0.979754	+	0.0700734i	−0.427735	+	0.903904i	$0.640688\pi$
$564$		0			0
$565$	14.4783	−	16.4860i	0.609105	−	0.693572i
$566$		0			0
$567$	−1.24389	+	5.71806i	−0.0522384	+	0.240136i
$568$		0			0
$569$	5.09259	+	35.4197i	0.213492	+	1.48487i	0.761372	+	0.648315i	$0.224526\pi$
$569$	5.09259	+	35.4197i	0.213492	+	1.48487i	−0.547880	+	0.836557i	$0.684565\pi$
$570$		0			0
$571$	28.8502	+	4.14803i	1.20734	+	0.173590i	0.716455	−	0.697634i	$-0.245764\pi$
$571$	28.8502	+	4.14803i	1.20734	+	0.173590i	0.490887	+	0.871223i	$0.336673\pi$
$572$		0			0
$573$	0.273097	−	3.81839i	0.0114088	−	0.159516i
$574$		0			0
$575$	−1.64450	−	23.9227i	−0.0685804	−	0.997646i
$576$		0			0
$577$	−2.92933	+	40.9574i	−0.121950	+	1.70508i	0.456795	+	0.889572i	$0.348997\pi$
$577$	−2.92933	+	40.9574i	−0.121950	+	1.70508i	−0.578745	+	0.815508i	$0.696457\pi$
$578$		0			0
$579$	−1.80048	−	0.258870i	−0.0748254	−	0.0107583i
$580$		0			0
$581$	0.0181238	+	0.126054i	0.000751900	+	0.00522958i
$582$		0			0
$583$	−10.8874	+	50.0486i	−0.450910	+	2.07280i
$584$		0			0
$585$	−8.30932	+	9.46160i	−0.343548	+	0.391189i
$586$		0			0
$587$	10.0532	−	0.719022i	0.414942	−	0.0296772i	0.137692	−	0.990475i	$-0.456032\pi$
$587$	10.0532	−	0.719022i	0.414942	−	0.0296772i	0.277250	+	0.960798i	$0.410577\pi$
$588$		0			0
$589$	12.6474	+	27.6938i	0.521125	+	1.14110i
$590$		0			0
$591$	−8.89428	−	2.61160i	−0.365862	−	0.107427i
$592$		0			0
$593$	15.2174	+	40.7993i	0.624902	+	1.67543i	0.732107	+	0.681190i	$0.238537\pi$
$593$	15.2174	+	40.7993i	0.624902	+	1.67543i	−0.107205	+	0.994237i	$0.534190\pi$
$594$		0			0
$595$	7.31686	+	7.41481i	0.299962	+	0.303978i
$596$		0			0
$597$	1.18817	−	1.18817i	0.0486285	−	0.0486285i
$598$		0			0
$599$			17.7605i			0.725676i	0.931852	+	0.362838i	$0.118192\pi$
$599$			17.7605i			0.725676i	−0.931852	+	0.362838i	$0.881808\pi$
$600$		0			0
$601$	18.5709	+	11.9348i	0.757523	+	0.486830i	0.861505	−	0.507749i	$-0.169522\pi$
$601$	18.5709	+	11.9348i	0.757523	+	0.486830i	−0.103982	+	0.994579i	$0.533159\pi$
$602$		0			0
$603$	−7.64868	+	2.85281i	−0.311478	+	0.116175i
$604$		0			0
$605$	16.5552	−	29.8451i	0.673065	−	1.21338i
$606$		0			0
$607$	−13.6450	+	36.5837i	−0.553834	+	1.48489i	0.294620	+	0.955615i	$0.404807\pi$
$607$	−13.6450	+	36.5837i	−0.553834	+	1.48489i	−0.848453	+	0.529271i	$0.822466\pi$
$608$		0			0
$609$	−0.0455998	+	0.0526250i	−0.00184780	+	0.00213247i
$610$		0			0
$611$	6.57178	−	1.92965i	0.265866	−	0.0780652i
$612$		0			0
$613$	10.4347	+	2.26993i	0.421454	+	0.0916817i	0.418290	−	0.908313i	$-0.362629\pi$
$613$	10.4347	+	2.26993i	0.421454	+	0.0916817i	0.00316336	+	0.999995i	$0.498993\pi$
$614$		0			0
$615$	−8.03641	+	6.87057i	−0.324059	+	0.277048i
$616$		0			0
$617$	19.4794	+	26.0215i	0.784212	+	1.04758i	0.997505	+	0.0705961i	$0.0224901\pi$
$617$	19.4794	+	26.0215i	0.784212	+	1.04758i	−0.213293	+	0.976988i	$0.568419\pi$
$618$		0			0
$619$	15.1108	+	17.4388i	0.607356	+	0.700926i	0.973255	−	0.229729i	$-0.0737839\pi$
$619$	15.1108	+	17.4388i	0.607356	+	0.700926i	−0.365899	+	0.930655i	$0.619238\pi$
$620$		0			0
$621$	−9.72979	+	4.56791i	−0.390443	+	0.183304i
$622$		0			0
$623$	−9.62390	−	0.688315i	−0.385573	−	0.0275767i
$624$		0			0
$625$	−21.3833	+	12.9519i	−0.855334	+	0.518077i
$626$		0			0
$627$	7.04568	−	9.41193i	0.281377	−	0.375876i
$628$		0			0
$629$	−20.0243	−	31.1584i	−0.798421	−	1.24237i
$630$		0			0
$631$	−2.25012	−	7.66319i	−0.0895757	−	0.305067i	0.902503	−	0.430683i	$-0.141727\pi$
$631$	−2.25012	−	7.66319i	−0.0895757	−	0.305067i	−0.992079	+	0.125616i	$0.959909\pi$
$632$		0			0
$633$	−0.338087	−	4.72708i	−0.0134378	−	0.187884i
$634$		0			0
$635$	−33.4213	−	21.7939i	−1.32628	−	0.864866i
$636$		0			0
$637$	−6.07493	−	11.1254i	−0.240698	−	0.440805i
$638$		0			0
$639$	−36.0835	−	16.4788i	−1.42744	−	0.651891i
$640$		0			0
$641$	−1.55894	+	2.42577i	−0.0615746	+	0.0958120i	−0.870676	−	0.491858i	$-0.836318\pi$
$641$	−1.55894	+	2.42577i	−0.0615746	+	0.0958120i	0.809101	+	0.587669i	$0.199954\pi$
$642$		0			0
$643$	5.57032	+	5.57032i	0.219672	+	0.219672i	0.808360	−	0.588688i	$-0.200355\pi$
$643$	5.57032	+	5.57032i	0.219672	+	0.219672i	−0.588688	+	0.808360i	$0.700355\pi$
$644$		0			0
$645$	1.55548	−	6.92830i	0.0612470	−	0.272802i
$646$		0			0
$647$	2.38204	+	10.9501i	0.0936477	+	0.430492i	0.999969	+	0.00790189i	$0.00251528\pi$
$647$	2.38204	+	10.9501i	0.0936477	+	0.430492i	−0.906321	+	0.422590i	$0.861121\pi$
$648$		0			0
$649$	15.7675	−	34.5261i	0.618930	−	1.35527i
$650$		0			0
$651$	0.416474	−	1.41838i	0.0163229	−	0.0555908i
$652$		0			0
$653$	−9.97334	−	3.71986i	−0.390287	−	0.145570i	0.146657	−	0.989187i	$-0.453149\pi$
$653$	−9.97334	−	3.71986i	−0.390287	−	0.145570i	−0.536944	+	0.843618i	$0.680421\pi$
$654$		0			0
$655$	6.07604	+	8.23015i	0.237411	+	0.321578i
$656$		0			0
$657$	10.6960	+	5.84045i	0.417290	+	0.227858i
$658$		0			0
$659$	−0.303280	+	0.194906i	−0.0118141	+	0.00759247i	−0.546535	−	0.837437i	$-0.684053\pi$
$659$	−0.303280	+	0.194906i	−0.0118141	+	0.00759247i	0.534720	+	0.845029i	$0.320417\pi$
$660$		0			0
$661$	−32.5363	+	4.67801i	−1.26552	+	0.181954i	−0.742196	−	0.670183i	$-0.766216\pi$
$661$	−32.5363	+	4.67801i	−1.26552	+	0.181954i	−0.523320	+	0.852136i	$0.675307\pi$
$662$		0			0
$663$	3.70940	−	2.77682i	0.144061	−	0.107843i
$664$		0			0
$665$	−2.93266	+	9.74748i	−0.113724	+	0.377991i
$666$		0			0
$667$	1.14578	+	0.0698262i	0.0443649	+	0.00270368i
$668$		0			0
$669$	3.94479	−	3.41818i	0.152514	−	0.132154i
$670$		0			0
$671$	2.71756	−	18.9011i	0.104910	−	0.729668i
$672$		0			0
$673$	−4.27189	−	3.19790i	−0.164669	−	0.123270i	0.513765	−	0.857931i	$-0.328250\pi$
$673$	−4.27189	−	3.19790i	−0.164669	−	0.123270i	−0.678434	+	0.734661i	$0.737341\pi$
$674$		0			0
$675$	8.88100	+	6.83439i	0.341830	+	0.263056i
$676$		0			0
$677$	7.38850	−	13.5310i	0.283963	−	0.520039i	−0.696297	−	0.717754i	$-0.745170\pi$
$677$	7.38850	−	13.5310i	0.283963	−	0.520039i	0.980260	+	0.197715i	$0.0633520\pi$
$678$		0			0
$679$	8.20974	+	7.11378i	0.315061	+	0.273002i
$680$		0			0
$681$	0.763387	−	0.348627i	0.0292531	−	0.0133594i
$682$		0			0
$683$	−3.77788	+	2.06288i	−0.144556	+	0.0789338i	−0.549899	−	0.835231i	$-0.685334\pi$
$683$	−3.77788	+	2.06288i	−0.144556	+	0.0789338i	0.405343	+	0.914165i	$0.367152\pi$
$684$		0			0
$685$	41.1781	−	5.64131i	1.57333	−	0.215543i
$686$		0			0
$687$	1.25721	−	0.273489i	0.0479655	−	0.0104343i
$688$		0			0
$689$	−19.7251			−0.751467
$690$		0			0
$691$	7.87274			0.299493			0.149747	−	0.988724i	$-0.452154\pi$
$691$	7.87274			0.299493			0.149747	+	0.988724i	$0.452154\pi$
$692$		0			0
$693$	10.8562	−	2.36163i	0.412395	−	0.0897110i
$694$		0			0
$695$	−12.2512	+	16.1409i	−0.464715	+	0.612258i
$696$		0			0
$697$	−66.4568	+	36.2882i	−2.51723	+	1.37451i
$698$		0			0
$699$	−7.69525	+	3.51430i	−0.291061	+	0.132923i
$700$		0			0
$701$	3.38990	+	2.93736i	0.128035	+	0.110943i	0.716524	−	0.697562i	$-0.245732\pi$
$701$	3.38990	+	2.93736i	0.128035	+	0.110943i	−0.588490	+	0.808505i	$0.700277\pi$
$702$		0			0
$703$	17.3449	−	31.7648i	0.654175	−	1.19803i
$704$		0			0
$705$	−1.01984	−	2.79083i	−0.0384093	−	0.105109i
$706$		0			0
$707$	−5.07785	−	3.80123i	−0.190972	−	0.142960i
$708$		0			0
$709$	−5.35970	+	37.2775i	−0.201288	+	1.39999i	0.599182	+	0.800613i	$0.295493\pi$
$709$	−5.35970	+	37.2775i	−0.201288	+	1.39999i	−0.800469	+	0.599374i	$0.795416\pi$
$710$		0			0
$711$	6.28267	−	5.44397i	0.235619	−	0.204165i
$712$		0			0
$713$	−22.7419	+	8.75624i	−0.851690	+	0.327924i
$714$		0			0
$715$	21.6571	+	6.51584i	0.809931	+	0.243679i
$716$		0			0
$717$	0.597857	−	0.447550i	0.0223274	−	0.0167141i
$718$		0			0
$719$	−18.3753	+	2.64196i	−0.685281	+	0.0985286i	−0.476157	−	0.879360i	$-0.657971\pi$
$719$	−18.3753	+	2.64196i	−0.685281	+	0.0985286i	−0.209125	+	0.977889i	$0.567061\pi$
$720$		0			0
$721$	8.57519	−	5.51094i	0.319357	−	0.205238i
$722$		0			0
$723$	1.06800	+	0.583171i	0.0397193	+	0.0216884i
$724$		0			0
$725$	−0.482638	−	1.09514i	−0.0179247	−	0.0406725i
$726$		0			0
$727$	35.0175	+	13.0609i	1.29873	+	0.484400i	0.901285	−	0.433227i	$-0.142625\pi$
$727$	35.0175	+	13.0609i	1.29873	+	0.484400i	0.397442	+	0.917627i	$0.369898\pi$
$728$		0			0
$729$	−5.46624	+	18.6163i	−0.202453	+	0.689493i
$730$		0			0
$731$	21.1248	−	46.2569i	0.781329	−	1.71087i
$732$		0			0
$733$	1.10472	+	5.07831i	0.0408037	+	0.187572i	0.993038	−	0.117798i	$-0.0375835\pi$
$733$	1.10472	+	5.07831i	0.0408037	+	0.187572i	−0.952234	+	0.305370i	$0.901220\pi$
$734$		0			0
$735$	−4.64579	+	2.94220i	−0.171362	+	0.108525i
$736$		0			0
$737$	10.3673	+	10.3673i	0.381886	+	0.381886i
$738$		0			0
$739$	−7.59162	+	11.8128i	−0.279262	+	0.434541i	−0.952343	−	0.305028i	$-0.901334\pi$
$739$	−7.59162	+	11.8128i	−0.279262	+	0.434541i	0.673081	+	0.739569i	$0.264970\pi$
$740$		0			0
$741$	4.11859	+	1.88090i	0.151300	+	0.0690964i
$742$		0			0
$743$	11.0492	+	20.2350i	0.405355	+	0.742352i	0.998007	−	0.0631068i	$-0.0201009\pi$
$743$	11.0492	+	20.2350i	0.405355	+	0.742352i	−0.592652	+	0.805459i	$0.701919\pi$
$744$		0			0
$745$	−14.0602	+	2.96082i	−0.515124	+	0.108476i
$746$		0			0
$747$	0.0341193	+	0.477051i	0.00124836	+	0.0174544i
$748$		0			0
$749$	3.67277	+	12.5083i	0.134200	+	0.457043i
$750$		0			0
$751$	−9.54778	−	14.8566i	−0.348404	−	0.542127i	0.622185	−	0.782870i	$-0.286245\pi$
$751$	−9.54778	−	14.8566i	−0.348404	−	0.542127i	−0.970589	+	0.240744i	$0.922609\pi$
$752$		0			0
$753$	−6.18192	+	8.25807i	−0.225282	+	0.300941i
$754$		0			0
$755$	−27.5693	−	10.4922i	−1.00335	−	0.381849i
$756$		0			0
$757$	8.85974	+	0.633661i	0.322013	+	0.0230308i	0.231410	−	0.972856i	$-0.425666\pi$
$757$	8.85974	+	0.633661i	0.322013	+	0.0230308i	0.0906028	+	0.995887i	$0.471121\pi$
$758$		0			0
$759$	7.17664	+	6.08744i	0.260496	+	0.220960i
$760$		0			0
$761$	15.7574	+	18.1850i	0.571206	+	0.659207i	0.965690	−	0.259696i	$-0.0836223\pi$
$761$	15.7574	+	18.1850i	0.571206	+	0.659207i	−0.394484	+	0.918903i	$0.629077\pi$
$762$		0			0
$763$	1.38307	+	1.84756i	0.0500705	+	0.0668863i
$764$		0			0
$765$	25.4223	+	29.7361i	0.919145	+	1.07511i
$766$		0			0
$767$	14.2833	+	3.10715i	0.515741	+	0.112193i
$768$		0			0
$769$	44.0848	−	12.9445i	1.58974	−	0.466789i	0.637070	−	0.770806i	$-0.280146\pi$
$769$	44.0848	−	12.9445i	1.58974	−	0.466789i	0.952667	+	0.304017i	$0.0983278\pi$
$770$		0			0
$771$	5.08355	−	5.86672i	0.183079	−	0.211285i
$772$		0			0
$773$	6.91682	−	18.5447i	0.248781	−	0.667007i	−0.751195	−	0.660080i	$-0.770522\pi$
$773$	6.91682	−	18.5447i	0.248781	−	0.667007i	0.999976	−	0.00692673i	$-0.00220486\pi$
$774$		0			0
$775$	18.9782	+	16.8918i	0.681718	+	0.606771i
$776$		0			0
$777$	−1.64650	+	0.614112i	−0.0590677	+	0.0220311i
$778$		0			0
$779$	−62.2434	−	40.0014i	−2.23010	−	1.43320i
$780$		0			0
$781$			71.2451i			2.54935i
$782$		0			0
$783$	−0.379333	+	0.379333i	−0.0135562	+	0.0135562i
$784$		0			0
$785$	−0.229528	+	34.5182i	−0.00819219	+	1.23201i
$786$		0			0
$787$	−7.07101	−	18.9581i	−0.252054	−	0.675783i	−0.999929	−	0.0119433i	$-0.996198\pi$
$787$	−7.07101	−	18.9581i	−0.252054	−	0.675783i	0.747874	−	0.663840i	$-0.231074\pi$
$788$		0			0
$789$	−10.5081	−	3.08544i	−0.374097	−	0.109845i
$790$		0			0
$791$	−3.09700	−	6.78148i	−0.110117	−	0.241122i
$792$		0			0
$793$	7.33516	−	0.524621i	0.260479	−	0.0186298i
$794$		0			0
$795$	0.553693	+	8.53922i	0.0196375	+	0.302855i
$796$		0			0
$797$	−6.33277	+	29.1113i	−0.224318	+	1.03117i	0.717893	+	0.696154i	$0.245107\pi$
$797$	−6.33277	+	29.1113i	−0.224318	+	1.03117i	−0.942211	+	0.335020i	$0.891257\pi$
$798$		0			0
$799$	−3.02835	−	21.0626i	−0.107135	−	0.745143i
$800$		0			0
$801$	−35.8666	−	5.15684i	−1.26728	−	0.182208i
$802$		0			0
$803$	1.56144	−	21.8318i	0.0551020	−	0.770426i
$804$		0			0
$805$	−7.64499	−	2.81766i	−0.269451	−	0.0993095i
$806$		0			0
$807$	−0.0480843	+	0.672307i	−0.00169265	+	0.0236663i
$808$		0			0
$809$	30.6605	+	4.40831i	1.07797	+	0.154988i	0.658348	−	0.752713i	$-0.271255\pi$
$809$	30.6605	+	4.40831i	1.07797	+	0.154988i	0.419617	+	0.907701i	$0.362164\pi$
$810$		0			0
$811$	−0.648322	−	4.50918i	−0.0227657	−	0.158339i	0.975267	−	0.221028i	$-0.0709413\pi$
$811$	−0.648322	−	4.50918i	−0.0227657	−	0.158339i	−0.998033	+	0.0626896i	$0.980032\pi$
$812$		0			0
$813$	0.0839752	−	0.386028i	0.00294514	−	0.0135386i
$814$		0			0
$815$	−27.4107	−	24.0725i	−0.960155	−	0.843222i
$816$		0			0
$817$	49.5638	−	3.54488i	1.73402	−	0.124020i
$818$		0			0
$819$	1.77742	+	3.89200i	0.0621080	+	0.135998i
$820$		0			0
$821$	−16.8052	−	4.93444i	−0.586504	−	0.172213i	−0.0250004	−	0.999687i	$-0.507959\pi$
$821$	−16.8052	−	4.93444i	−0.586504	−	0.172213i	−0.561504	+	0.827474i	$0.689777\pi$
$822$		0			0
$823$	11.4800	+	30.7790i	0.400166	+	1.07289i	0.968265	+	0.249927i	$0.0804066\pi$
$823$	11.4800	+	30.7790i	0.400166	+	1.07289i	−0.568098	+	0.822961i	$0.692321\pi$
$824$		0			0
$825$	2.21285	−	9.55852i	0.0770417	−	0.332785i
$826$		0			0
$827$	−0.734605	+	0.734605i	−0.0255447	+	0.0255447i	−0.719764	−	0.694219i	$-0.755750\pi$
$827$	−0.734605	+	0.734605i	−0.0255447	+	0.0255447i	0.694219	+	0.719764i	$0.255750\pi$
$828$		0			0
$829$		−	7.04306i		−	0.244616i	−0.992492	−	0.122308i	$-0.960971\pi$
$829$		−	7.04306i		−	0.244616i	0.992492	−	0.122308i	$-0.0390295\pi$
$830$		0			0
$831$	6.81375	+	4.37893i	0.236366	+	0.151903i
$832$		0			0
$833$	−36.8987	+	13.7625i	−1.27847	+	0.476843i
$834$		0			0
$835$	19.7336	−	5.65206i	0.682909	−	0.195597i
$836$		0			0
$837$	3.97992	−	10.6706i	0.137566	−	0.368830i
$838$		0			0
$839$	33.7094	−	38.9027i	1.16378	−	1.34307i	0.235193	−	0.971949i	$-0.424428\pi$
$839$	33.7094	−	38.9027i	1.16378	−	1.34307i	0.928584	−	0.371122i	$-0.121027\pi$
$840$		0			0
$841$	−27.7703	+	8.15410i	−0.957597	+	0.281176i
$842$		0			0
$843$	5.60478	+	1.21925i	0.193039	+	0.0419931i
$844$		0			0
$845$	1.58740	−	20.2972i	0.0546083	−	0.698244i
$846$		0			0
$847$	−6.94954	−	9.28350i	−0.238789	−	0.318985i
$848$		0			0
$849$	2.02054	+	2.33183i	0.0693449	+	0.0800283i
$850$		0			0
$851$	24.5341	+	15.4044i	0.841018	+	0.528056i
$852$		0			0
$853$	−48.6372	−	3.47860i	−1.66531	−	0.119105i	−0.793375	−	0.608733i	$-0.791678\pi$
$853$	−48.6372	−	3.47860i	−1.66531	−	0.119105i	−0.871931	+	0.489628i	$0.837132\pi$
$854$		0			0
$855$	−13.5972	+	35.7282i	−0.465016	+	1.22188i
$856$		0			0
$857$	−0.401975	+	0.536976i	−0.0137312	+	0.0183427i	−0.807354	−	0.590067i	$-0.799101\pi$
$857$	−0.401975	+	0.536976i	−0.0137312	+	0.0183427i	0.793623	+	0.608410i	$0.208192\pi$
$858$		0			0
$859$	11.4824	+	17.8670i	0.391775	+	0.609614i	0.979980	−	0.199098i	$-0.0638013\pi$
$859$	11.4824	+	17.8670i	0.391775	+	0.609614i	−0.588204	+	0.808712i	$0.700165\pi$
$860$		0			0
$861$	1.01213	+	3.44701i	0.0344934	+	0.117474i
$862$		0			0
$863$	−3.63180	−	50.7792i	−0.123628	−	1.72854i	−0.559755	−	0.828658i	$-0.689105\pi$
$863$	−3.63180	−	50.7792i	−0.123628	−	1.72854i	0.436127	−	0.899885i	$-0.356350\pi$
$864$		0			0
$865$	−10.1568	+	15.5756i	−0.345342	+	0.529588i
$866$		0			0
$867$	−3.77959	−	6.92180i	−0.128362	−	0.235077i
$868$		0			0
$869$	−13.5814	−	6.20241i	−0.460717	−	0.210402i
$870$		0			0
$871$	−3.05266	+	4.75003i	−0.103435	+	0.160949i
$872$		0			0
$873$	28.8477	+	28.8477i	0.976346	+	0.976346i
$874$		0			0
$875$	1.04095	+	8.43055i	0.0351905	+	0.285005i
$876$		0			0
$877$	−7.11153	−	32.6912i	−0.240139	−	1.10390i	−0.926398	−	0.376545i	$-0.877112\pi$
$877$	−7.11153	−	32.6912i	−0.240139	−	1.10390i	0.686259	−	0.727357i	$-0.259252\pi$
$878$		0			0
$879$	1.40802	−	3.08313i	0.0474913	−	0.103991i
$880$		0			0
$881$	3.12962	−	10.6585i	0.105440	−	0.359095i	−0.889824	−	0.456303i	$-0.849173\pi$
$881$	3.12962	−	10.6585i	0.105440	−	0.359095i	0.995264	+	0.0972085i	$0.0309914\pi$
$882$		0			0
$883$	−33.1893	−	12.3790i	−1.11691	−	0.416586i	−0.277849	−	0.960625i	$-0.589622\pi$
$883$	−33.1893	−	12.3790i	−1.11691	−	0.416586i	−0.839060	+	0.544039i	$0.816894\pi$
$884$		0			0
$885$	0.944178	−	6.27062i	0.0317382	−	0.210785i
$886$		0			0
$887$	−1.51723	−	0.828473i	−0.0509438	−	0.0278174i	0.453575	−	0.891218i	$-0.350148\pi$
$887$	−1.51723	−	0.828473i	−0.0509438	−	0.0278174i	−0.504519	+	0.863401i	$0.668330\pi$
$888$		0			0
$889$	−11.4050	+	7.32953i	−0.382511	+	0.245825i
$890$		0			0
$891$	39.0690	−	5.61727i	1.30886	−	0.188186i
$892$		0			0
$893$	16.6457	−	12.4608i	0.557027	−	0.416985i
$894$		0			0
$895$	−9.60949	−	17.8801i	−0.321210	−	0.597666i
$896$		0			0
$897$	−1.70328	+	3.19898i	−0.0568709	+	0.106811i
$898$		0			0
$899$	−0.919181	+	0.796475i	−0.0306564	+	0.0265639i
$900$		0			0
$901$	−8.72137	+	60.6585i	−0.290551	+	2.02083i
$902$		0			0
$903$	−1.93148	−	1.44589i	−0.0642757	−	0.0481162i
$904$		0			0
$905$	22.6323	−	8.27042i	0.752324	−	0.274918i
$906$		0			0
$907$	−4.55705	+	8.34561i	−0.151314	+	0.277111i	−0.942330	−	0.334684i	$-0.891370\pi$
$907$	−4.55705	+	8.34561i	−0.151314	+	0.277111i	0.791016	+	0.611795i	$0.209552\pi$
$908$		0			0
$909$	−18.0031	−	15.5998i	−0.597126	−	0.517413i
$910$		0			0
$911$	11.9969	−	5.47880i	0.397475	−	0.181521i	−0.206642	−	0.978417i	$-0.566253\pi$
$911$	11.9969	−	5.47880i	0.397475	−	0.181521i	0.604117	+	0.796896i	$0.293526\pi$
$912$		0			0
$913$	0.753911	−	0.411666i	0.0249508	−	0.0136242i
$914$		0			0
$915$	−0.433015	−	3.16074i	−0.0143150	−	0.104491i
$916$		0			0
$917$	3.39655	−	0.738875i	0.112164	−	0.0243998i
$918$		0			0
$919$	−9.29283			−0.306542			−0.153271	−	0.988184i	$-0.548981\pi$
$919$	−9.29283			−0.306542			−0.153271	+	0.988184i	$0.548981\pi$
$920$		0			0
$921$	−1.80071			−0.0593354
$922$		0			0
$923$	−26.8103	+	5.83223i	−0.882473	+	0.191970i
$924$		0			0
$925$	2.55505	−	30.0943i	0.0840096	−	0.989493i
$926$		0			0
$927$	33.5990	−	18.3465i	1.10354	−	0.602577i
$928$		0			0
$929$	22.4618	−	10.2579i	0.736946	−	0.336552i	−0.0113332	−	0.999936i	$-0.503608\pi$
$929$	22.4618	−	10.2579i	0.736946	−	0.336552i	0.748279	+	0.663384i	$0.230880\pi$
$930$		0			0
$931$	−29.0828	−	25.2004i	−0.953149	−	0.825908i
$932$		0			0
$933$	−2.68960	+	4.92563i	−0.0880534	+	0.161258i
$934$		0			0
$935$	29.6131	−	63.7189i	0.968450	−	2.08383i
$936$		0			0
$937$	−21.5398	−	16.1245i	−0.703674	−	0.526764i	0.186460	−	0.982463i	$-0.440298\pi$
$937$	−21.5398	−	16.1245i	−0.703674	−	0.526764i	−0.890134	+	0.455699i	$0.849389\pi$
$938$		0			0
$939$	0.607142	−	4.22277i	0.0198133	−	0.137805i
$940$		0			0
$941$	15.9497	−	13.8205i	0.519944	−	0.450534i	−0.354924	−	0.934895i	$-0.615493\pi$
$941$	15.9497	−	13.8205i	0.519944	−	0.450534i	0.874868	+	0.484361i	$0.160948\pi$
$942$		0			0
$943$	34.9899	−	47.7819i	1.13943	−	1.55599i
$944$		0			0
$945$	3.35401	−	1.80258i	0.109106	−	0.0586379i
$946$		0			0
$947$	2.50210	−	1.87305i	0.0813074	−	0.0608659i	−0.557851	−	0.829941i	$-0.688374\pi$
$947$	2.50210	−	1.87305i	0.0813074	−	0.0608659i	0.639158	+	0.769075i	$0.279283\pi$
$948$		0			0
$949$	8.34336	−	1.19959i	0.270837	−	0.0389405i
$950$		0			0
$951$	−5.41164	+	3.47785i	−0.175484	+	0.112777i
$952$		0			0
$953$	10.6531	+	5.81703i	0.345088	+	0.188432i	0.642441	−	0.766335i	$-0.277922\pi$
$953$	10.6531	+	5.81703i	0.345088	+	0.188432i	−0.297353	+	0.954768i	$0.596104\pi$
$954$		0			0
$955$	17.9854	−	13.2780i	0.581993	−	0.429666i
$956$		0			0
$957$	0.440065	+	0.164136i	0.0142253	+	0.00530576i
$958$		0			0
$959$	3.97871	−	13.5503i	0.128479	−	0.437560i
$960$		0			0
$961$	−2.15176	+	4.71169i	−0.0694115	+	0.151990i
$962$		0			0
$963$	10.4069	+	47.8399i	0.335359	+	1.54162i
$964$		0			0
$965$	−5.68347	−	8.97431i	−0.182957	−	0.288893i
$966$		0			0
$967$	−29.6179	−	29.6179i	−0.952448	−	0.952448i	0.0464715	−	0.998920i	$-0.485202\pi$
$967$	−29.6179	−	29.6179i	−0.952448	−	0.952448i	−0.998920	+	0.0464715i	$0.985202\pi$
$968$		0			0
$969$	7.60512	−	11.8338i	0.244312	−	0.380156i
$970$		0			0
$971$	−23.9367	−	10.9315i	−0.768164	−	0.350809i	−0.00751499	−	0.999972i	$-0.502392\pi$
$971$	−23.9367	−	10.9315i	−0.768164	−	0.350809i	−0.760650	+	0.649163i	$0.775119\pi$
$972$		0			0
$973$	3.29976	+	6.04306i	0.105786	+	0.193732i
$974$		0			0
$975$	3.77813	+	0.0502473i	0.120997	+	0.00160920i
$976$		0			0
$977$	−2.50587	−	35.0367i	−0.0801700	−	1.12092i	−0.865187	−	0.501449i	$-0.832800\pi$
$977$	−2.50587	−	35.0367i	−0.0801700	−	1.12092i	0.785017	−	0.619474i	$-0.212654\pi$
$978$		0			0
$979$	18.3351	+	62.4435i	0.585991	+	1.99570i
$980$		0			0
$981$	4.68596	+	7.29150i	0.149611	+	0.232800i
$982$		0			0
$983$	−15.1307	+	20.2122i	−0.482594	+	0.644670i	−0.974077	−	0.226217i	$-0.927364\pi$
$983$	−15.1307	+	20.2122i	−0.482594	+	0.644670i	0.491483	+	0.870887i	$0.336455\pi$
$984$		0			0
$985$	−22.1601	−	49.3904i	−0.706080	−	1.57371i
$986$		0			0
$987$	−1.00703	−	0.0720245i	−0.0320543	−	0.00229257i
$988$		0			0
$989$	0.418938	+	39.7718i	0.0133214	+	1.26467i
$990$		0			0
$991$	18.1305	+	20.9237i	0.575934	+	0.664664i	0.966726	−	0.255816i	$-0.0823440\pi$
$991$	18.1305	+	20.9237i	0.575934	+	0.664664i	−0.390791	+	0.920479i	$0.627799\pi$
$992$		0			0
$993$	0.461117	+	0.615981i	0.0146331	+	0.0195476i
$994$		0			0
$995$	9.78292	+	0.765104i	0.310140	+	0.0242554i
$996$		0			0
$997$	−33.5019	−	7.28788i	−1.06101	−	0.230810i	−0.351998	−	0.936001i	$-0.614497\pi$
$997$	−33.5019	−	7.28788i	−1.06101	−	0.230810i	−0.709017	+	0.705191i	$0.750861\pi$
$998$		0			0
$999$	−12.9899	+	3.81419i	−0.410984	+	0.120676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.5	yes	240
5.3	odd	4	inner	460.2.x.a.33.5	✓	240
23.7	odd	22	inner	460.2.x.a.237.5	yes	240
115.53	even	44	inner	460.2.x.a.53.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.5	✓	240	5.3	odd	4	inner
460.2.x.a.53.5	yes	240	115.53	even	44	inner
460.2.x.a.217.5	yes	240	1.1	even	1	trivial
460.2.x.a.237.5	yes	240	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374149 + 0.0813911i) q^{3} +(-1.78111 - 1.35190i) q^{5} +(-0.666841 + 0.364123i) q^{7} +(-2.59553 + 1.18534i) q^{9} +O(q^{10})\)	\(q+(-0.374149 + 0.0813911i) q^{3} +(-1.78111 - 1.35190i) q^{5} +(-0.666841 + 0.364123i) q^{7} +(-2.59553 + 1.18534i) q^{9} +(3.87303 + 3.35600i) q^{11} +(-0.945848 + 1.73219i) q^{13} +(0.776435 + 0.360845i) q^{15} +(4.90861 + 3.67454i) q^{17} +(-0.852683 + 5.93054i) q^{19} +(0.219862 - 0.190511i) q^{21} +(-4.69671 - 0.970011i) q^{23} +(1.34474 + 4.81577i) q^{25} +(1.79422 - 1.34314i) q^{27} +(-0.236919 + 0.0340638i) q^{29} +(4.27471 - 2.74719i) q^{31} +(-1.72224 - 0.940413i) q^{33} +(1.67998 + 0.252957i) q^{35} +(-5.65965 - 2.11094i) q^{37} +(0.212903 - 0.725081i) q^{39} +(-5.12993 + 11.2330i) q^{41} +(-1.76290 - 8.10392i) q^{43} +(6.22540 + 1.39767i) q^{45} +(-2.45395 - 2.45395i) q^{47} +(-3.47239 + 5.40315i) q^{49} +(-2.13563 - 0.975309i) q^{51} +(4.78984 + 8.77193i) q^{53} +(-2.36134 - 11.2134i) q^{55} +(-0.163663 - 2.28831i) q^{57} +(-2.08663 - 7.10642i) q^{59} +(-2.01449 - 3.13461i) q^{61} +(1.29920 - 1.73553i) q^{63} +(4.02641 - 1.80654i) q^{65} +(2.85366 + 0.204097i) q^{67} +(1.83622 - 0.0193419i) q^{69} +(9.10398 + 10.5066i) q^{71} +(-2.55948 - 3.41907i) q^{73} +(-0.895095 - 1.69237i) q^{75} +(-3.80469 - 0.827659i) q^{77} +(-2.79542 + 0.820810i) q^{79} +(5.04373 - 5.82077i) q^{81} +(0.0585753 - 0.157046i) q^{83} +(-3.77520 - 13.1807i) q^{85} +(0.0858705 - 0.0320281i) q^{87} +(10.6832 + 6.86564i) q^{89} -1.49950i q^{91} +(-1.37578 + 1.37578i) q^{93} +(9.53622 - 9.41023i) q^{95} +(-4.99652 - 13.3962i) q^{97} +(-14.0306 - 4.11975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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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