LMFDB - Embedded newform 460.2.x.a.33.5

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			33.5
Character	$\chi$	$=$	460.33
Dual form			460.2.x.a.237.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0813911 - 0.374149i) q^{3} +(-2.18808 - 0.460771i) q^{5} +(0.364123 + 0.666841i) q^{7} +(2.59553 - 1.18534i) q^{9} +O(q^{10})$	\(q+(-0.0813911 - 0.374149i) q^{3} +(-2.18808 - 0.460771i) q^{5} +(0.364123 + 0.666841i) q^{7} +(2.59553 - 1.18534i) q^{9} +(3.87303 + 3.35600i) q^{11} +(-1.73219 - 0.945848i) q^{13} +(0.00569308 + 0.856170i) q^{15} +(3.67454 - 4.90861i) q^{17} +(0.852683 - 5.93054i) q^{19} +(0.219862 - 0.190511i) q^{21} +(0.970011 - 4.69671i) q^{23} +(4.57538 + 2.01641i) q^{25} +(-1.34314 - 1.79422i) q^{27} +(0.236919 - 0.0340638i) q^{29} +(4.27471 - 2.74719i) q^{31} +(0.940413 - 1.72224i) q^{33} +(-0.489468 - 1.62688i) q^{35} +(-2.11094 + 5.65965i) q^{37} +(-0.212903 + 0.725081i) q^{39} +(-5.12993 + 11.2330i) q^{41} +(8.10392 - 1.76290i) q^{43} +(-6.22540 + 1.39767i) q^{45} +(-2.45395 + 2.45395i) q^{47} +(3.47239 - 5.40315i) q^{49} +(-2.13563 - 0.975309i) q^{51} +(-8.77193 + 4.78984i) q^{53} +(-6.92814 - 9.12777i) q^{55} +(-2.28831 + 0.163663i) q^{57} +(2.08663 + 7.10642i) q^{59} +(-2.01449 - 3.13461i) q^{61} +(1.73553 + 1.29920i) q^{63} +(3.35435 + 2.86773i) q^{65} +(0.204097 - 2.85366i) q^{67} +(-1.83622 + 0.0193419i) q^{69} +(9.10398 + 10.5066i) q^{71} +(3.41907 - 2.55948i) q^{73} +(0.382042 - 1.87599i) q^{75} +(-0.827659 + 3.80469i) q^{77} +(2.79542 - 0.820810i) q^{79} +(5.04373 - 5.82077i) q^{81} +(0.157046 + 0.0585753i) q^{83} +(-10.3019 + 9.04731i) q^{85} +(-0.0320281 - 0.0858705i) q^{87} +(-10.6832 - 6.86564i) q^{89} -1.49950i q^{91} +(-1.37578 - 1.37578i) q^{93} +(-4.59836 + 12.5836i) q^{95} +(-13.3962 + 4.99652i) q^{97} +(14.0306 + 4.11975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

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
$3$	−0.0813911	−	0.374149i	−0.0469912	−	0.216015i	0.947664	−	0.319270i	$-0.103438\pi$
$3$	−0.0813911	−	0.374149i	−0.0469912	−	0.216015i	−0.994655	+	0.103255i	$0.967074\pi$
$4$		0			0
$5$	−2.18808	−	0.460771i	−0.978539	−	0.206063i
$5$	−2.18808	−	0.460771i	−0.978539	−	0.206063i
$6$		0			0
$7$	0.364123	+	0.666841i	0.137625	+	0.252042i	0.937397	−	0.348262i	$-0.113228\pi$
$7$	0.364123	+	0.666841i	0.137625	+	0.252042i	−0.799772	+	0.600304i	$0.795046\pi$
$8$		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
$13$	−1.73219	−	0.945848i	−0.480423	−	0.262331i	0.220739	−	0.975333i	$-0.429153\pi$
$13$	−1.73219	−	0.945848i	−0.480423	−	0.262331i	−0.701162	+	0.713002i	$0.747335\pi$
$14$		0			0
$15$	0.00569308	+	0.856170i	0.00146995	+	0.221062i
$16$		0			0
$17$	3.67454	−	4.90861i	0.891207	−	1.19051i	−0.0896866	−	0.995970i	$-0.528587\pi$
$17$	3.67454	−	4.90861i	0.891207	−	1.19051i	0.980894	−	0.194544i	$-0.0623226\pi$
$18$		0			0
$19$	0.852683	−	5.93054i	0.195619	−	1.36056i	−0.621194	−	0.783657i	$-0.713352\pi$
$19$	0.852683	−	5.93054i	0.195619	−	1.36056i	0.816813	−	0.576903i	$-0.195739\pi$
$20$		0			0
$21$	0.219862	−	0.190511i	0.0479777	−	0.0415729i
$22$		0			0
$23$	0.970011	−	4.69671i	0.202261	−	0.979332i
$23$	0.970011	−	4.69671i	0.202261	−	0.979332i
$24$		0			0
$25$	4.57538	+	2.01641i	0.915076	+	0.403282i
$26$		0			0
$27$	−1.34314	−	1.79422i	−0.258487	−	0.345298i
$28$		0			0
$29$	0.236919	−	0.0340638i	0.0439948	−	0.00632549i	−0.120282	−	0.992740i	$-0.538380\pi$
$29$	0.236919	−	0.0340638i	0.0439948	−	0.00632549i	0.164277	+	0.986414i	$0.447471\pi$
$30$		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
$33$	0.940413	−	1.72224i	0.163705	−	0.299803i
$34$		0			0
$35$	−0.489468	−	1.62688i	−0.0827352	−	0.274993i
$36$		0			0
$37$	−2.11094	+	5.65965i	−0.347036	+	0.930441i	0.639774	+	0.768563i	$0.279028\pi$
$37$	−2.11094	+	5.65965i	−0.347036	+	0.930441i	−0.986811	+	0.161878i	$0.948245\pi$
$38$		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
$43$	8.10392	−	1.76290i	1.23584	−	0.268840i	0.453251	−	0.891383i	$-0.350264\pi$
$43$	8.10392	−	1.76290i	1.23584	−	0.268840i	0.782586	+	0.622543i	$0.213900\pi$
$44$		0			0
$45$	−6.22540	+	1.39767i	−0.928028	+	0.208352i
$46$		0			0
$47$	−2.45395	+	2.45395i	−0.357946	+	0.357946i	−0.863055	−	0.505110i	$-0.831452\pi$
$47$	−2.45395	+	2.45395i	−0.357946	+	0.357946i	0.505110	+	0.863055i	$0.331452\pi$
$48$		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
$53$	−8.77193	+	4.78984i	−1.20492	+	0.657935i	−0.950970	−	0.309283i	$-0.899911\pi$
$53$	−8.77193	+	4.78984i	−1.20492	+	0.657935i	−0.253947	+	0.967218i	$0.581729\pi$
$54$		0			0
$55$	−6.92814	−	9.12777i	−0.934191	−	1.23079i
$56$		0			0
$57$	−2.28831	+	0.163663i	−0.303094	+	0.0216777i
$58$		0			0
$59$	2.08663	+	7.10642i	0.271656	+	0.925177i	0.976446	+	0.215761i	$0.0692231\pi$
$59$	2.08663	+	7.10642i	0.271656	+	0.925177i	−0.704790	+	0.709416i	$0.748959\pi$
$60$		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
$63$	1.73553	+	1.29920i	0.218656	+	0.163684i
$64$		0			0
$65$	3.35435	+	2.86773i	0.416056	+	0.355699i
$66$		0			0
$67$	0.204097	−	2.85366i	0.0249345	−	0.348630i	−0.969635	−	0.244556i	$-0.921358\pi$
$67$	0.204097	−	2.85366i	0.0249345	−	0.348630i	0.994570	−	0.104073i	$-0.0331877\pi$
$68$		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
$73$	3.41907	−	2.55948i	0.400172	−	0.299565i	−0.380172	−	0.924916i	$-0.624135\pi$
$73$	3.41907	−	2.55948i	0.400172	−	0.299565i	0.780343	+	0.625351i	$0.215044\pi$
$74$		0			0
$75$	0.382042	−	1.87599i	0.0441144	−	0.216621i
$76$		0			0
$77$	−0.827659	+	3.80469i	−0.0943205	+	0.433584i
$78$		0			0
$79$	2.79542	−	0.820810i	0.314510	−	0.0923484i	−0.120668	−	0.992693i	$-0.538504\pi$
$79$	2.79542	−	0.820810i	0.314510	−	0.0923484i	0.435178	+	0.900345i	$0.356686\pi$
$80$		0			0
$81$	5.04373	−	5.82077i	0.560414	−	0.646753i
$82$		0			0
$83$	0.157046	+	0.0585753i	0.0172381	+	0.00642947i	0.358068	−	0.933695i	$-0.383435\pi$
$83$	0.157046	+	0.0585753i	0.0172381	+	0.00642947i	−0.340830	+	0.940125i	$0.610708\pi$
$84$		0			0
$85$	−10.3019	+	9.04731i	−1.11740	+	0.981319i
$86$		0			0
$87$	−0.0320281	−	0.0858705i	−0.00343377	−	0.00920629i
$88$		0			0
$89$	−10.6832	−	6.86564i	−1.13241	−	0.727757i	−0.166350	−	0.986067i	$-0.553198\pi$
$89$	−10.6832	−	6.86564i	−1.13241	−	0.727757i	−0.966062	+	0.258310i	$0.916834\pi$
$90$		0			0
$91$		−	1.49950i		−	0.157190i
$92$		0			0
$93$	−1.37578	−	1.37578i	−0.142662	−	0.142662i
$94$		0			0
$95$	−4.59836	+	12.5836i	−0.471782	+	1.29105i
$96$		0			0
$97$	−13.3962	+	4.99652i	−1.36018	+	0.507320i	−0.920467	−	0.390820i	$-0.872191\pi$
$97$	−13.3962	+	4.99652i	−1.36018	+	0.507320i	−0.439710	+	0.898140i	$0.644919\pi$
$98$		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
$103$	−0.957103	−	13.3820i	−0.0943061	−	1.31857i	−0.795653	−	0.605752i	$-0.792872\pi$
$103$	−0.957103	−	13.3820i	−0.0943061	−	1.31857i	0.701347	−	0.712820i	$-0.252582\pi$
$104$		0			0
$105$	−0.568856	+	0.315547i	−0.0555147	+	0.0307943i
$106$		0			0
$107$	−16.7660	−	3.64722i	−1.62083	−	0.352590i	−0.691655	−	0.722228i	$-0.743118\pi$
$107$	−16.7660	−	3.64722i	−1.62083	−	0.352590i	−0.929176	+	0.369637i	$0.879482\pi$
$108$		0			0
$109$	0.432294	+	3.00667i	0.0414063	+	0.287987i	0.999995	+	0.00319259i	$0.00101623\pi$
$109$	0.432294	+	3.00667i	0.0414063	+	0.287987i	−0.958589	+	0.284794i	$0.908075\pi$
$110$		0			0
$111$	2.28936	+	0.329161i	0.217297	+	0.0312426i
$112$		0			0
$113$	−9.78733	−	0.700004i	−0.920714	−	0.0658508i	−0.397071	−	0.917788i	$-0.629973\pi$
$113$	−9.78733	−	0.700004i	−0.920714	−	0.0658508i	−0.523644	+	0.851937i	$0.675428\pi$
$114$		0			0
$115$	−4.28657	+	9.82982i	−0.399725	+	0.916635i
$116$		0			0
$117$	−5.61711	−	0.401744i	−0.519302	−	0.0371412i
$118$		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
$123$	4.62034	+	1.00509i	0.416602	+	0.0906262i
$124$		0			0
$125$	−9.08219	−	6.52026i	−0.812336	−	0.583190i
$126$		0			0
$127$	−1.27294	−	17.7981i	−0.112955	−	1.57932i	−0.665858	−	0.746078i	$-0.731934\pi$
$127$	−1.27294	−	17.7981i	−0.112955	−	1.57932i	0.552903	−	0.833246i	$-0.313520\pi$
$128$		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
$133$	4.26521	−	1.59084i	0.369840	−	0.137943i
$134$		0			0
$135$	2.11216	+	4.54478i	0.181786	+	0.391152i
$136$		0			0
$137$	13.1433	+	13.1433i	1.12291	+	1.12291i	0.991302	+	0.131605i	$0.0420130\pi$
$137$	13.1433	+	13.1433i	1.12291	+	1.12291i	0.131605	+	0.991302i	$0.457987\pi$
$138$		0			0
$139$			9.06223i			0.768648i	0.923198	+	0.384324i	$0.125565\pi$
$139$			9.06223i			0.768648i	−0.923198	+	0.384324i	$0.874435\pi$
$140$		0			0
$141$	1.11787	+	0.718414i	0.0941419	+	0.0605014i
$142$		0			0
$143$	−3.53456	−	9.47653i	−0.295575	−	0.792467i
$144$		0			0
$145$	−0.534093	−	0.0346312i	−0.0443540	−	0.00287596i
$146$		0			0
$147$	−2.30421	−	0.859424i	−0.190048	−	0.0708841i
$148$		0			0
$149$	−4.20800	+	4.85629i	−0.344733	+	0.397843i	−0.901467	−	0.432848i	$-0.857509\pi$
$149$	−4.20800	+	4.85629i	−0.344733	+	0.397843i	0.556734	+	0.830691i	$0.312054\pi$
$150$		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
$153$	3.71902	−	17.0961i	0.300665	−	1.38213i
$154$		0			0
$155$	−10.6192	+	4.04141i	−0.852957	+	0.324613i
$156$		0			0
$157$	−12.3582	+	9.25126i	−0.986295	+	0.738331i	−0.965218	−	0.261447i	$-0.915800\pi$
$157$	−12.3582	+	9.25126i	−0.986295	+	0.738331i	−0.0210771	+	0.999778i	$0.506710\pi$
$158$		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
$163$	−1.16387	+	16.2730i	−0.0911614	+	1.27460i	0.721725	+	0.692180i	$0.243350\pi$
$163$	−1.16387	+	16.2730i	−0.0911614	+	1.27460i	−0.812886	+	0.582422i	$0.802105\pi$
$164$		0			0
$165$	−2.85126	+	3.33508i	−0.221970	+	0.259635i
$166$		0			0
$167$	7.34896	+	5.50136i	0.568679	+	0.425708i	0.844542	−	0.535489i	$-0.179873\pi$
$167$	7.34896	+	5.50136i	0.568679	+	0.425708i	−0.275863	+	0.961197i	$0.588964\pi$
$168$		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
$173$	8.29460	−	0.593241i	0.630627	−	0.0451033i	0.247632	−	0.968854i	$-0.420347\pi$
$173$	8.29460	−	0.593241i	0.630627	−	0.0451033i	0.382994	+	0.923751i	$0.374893\pi$
$174$		0			0
$175$	0.321376	+	3.78527i	0.0242937	+	0.286140i
$176$		0			0
$177$	2.48903	−	1.35911i	0.187087	−	0.102157i
$178$		0			0
$179$	−8.25754	−	3.77109i	−0.617197	−	0.281865i	0.0821797	−	0.996618i	$-0.473812\pi$
$179$	−8.25754	−	3.77109i	−0.617197	−	0.281865i	−0.699377	+	0.714753i	$0.746539\pi$
$180$		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
$187$	30.7049	−	6.67944i	2.24536	−	0.488449i
$188$		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
$193$	−1.66016	+	4.45105i	−0.119501	+	0.320394i	−0.982904	−	0.184121i	$-0.941056\pi$
$193$	−1.66016	+	4.45105i	−0.119501	+	0.320394i	0.863403	+	0.504515i	$0.168329\pi$
$194$		0			0
$195$	0.799946	−	1.48844i	0.0572853	−	0.106589i
$196$		0			0
$197$	11.6023	−	21.2481i	0.826632	−	1.51386i	−0.0309518	−	0.999521i	$-0.509854\pi$
$197$	11.6023	−	21.2481i	0.826632	−	1.51386i	0.857584	−	0.514343i	$-0.171964\pi$
$198$		0			0
$199$	3.69177	−	2.37256i	0.261703	−	0.168186i	−0.403209	−	0.915108i	$-0.632105\pi$
$199$	3.69177	−	2.37256i	0.261703	−	0.168186i	0.664912	+	0.746922i	$0.268469\pi$
$200$		0			0
$201$	−1.08430	+	0.155899i	−0.0764809	+	0.0109963i
$202$		0			0
$203$	0.108983	+	0.145584i	0.00764909	+	0.0102180i
$204$		0			0
$205$	16.4005	−	22.2149i	1.14546	−	1.55156i
$206$		0			0
$207$	−3.04950	−	13.3403i	−0.211955	−	0.927212i
$208$		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
$213$	3.19003	−	4.26139i	0.218578	−	0.291985i
$214$		0			0
$215$	−18.5443	+	0.123310i	−1.26471	+	0.00840966i
$216$		0			0
$217$	3.38846	+	1.85024i	0.230024	+	0.125602i
$218$		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
$223$	−6.53314	−	11.9646i	−0.437491	−	0.801206i	0.562175	−	0.827018i	$-0.309965\pi$
$223$	−6.53314	−	11.9646i	−0.437491	−	0.801206i	−0.999667	+	0.0258123i	$0.991783\pi$
$224$		0			0
$225$	14.2657	−	0.189727i	0.951045	−	0.0126484i
$226$		0			0
$227$	0.465894	+	2.14168i	0.0309224	+	0.142148i	0.990020	−	0.140928i	$-0.0450087\pi$
$227$	0.465894	+	2.14168i	0.0309224	+	0.142148i	−0.959097	+	0.283076i	$0.908645\pi$
$228$		0			0
$229$	3.36018			0.222047			0.111024	−	0.993818i	$-0.464587\pi$
$229$	3.36018			0.222047			0.111024	+	0.993818i	$0.464587\pi$
$230$		0			0
$231$	1.49088			0.0980930
$232$		0			0
$233$	4.69639	+	21.5890i	0.307671	+	1.41434i	0.828170	+	0.560477i	$0.189382\pi$
$233$	4.69639	+	21.5890i	0.307671	+	1.41434i	−0.520499	+	0.853862i	$0.674254\pi$
$234$		0			0
$235$	6.50015	−	4.23873i	0.424023	−	0.276504i
$236$		0			0
$237$	−0.534628	−	0.979098i	−0.0347278	−	0.0635993i
$238$		0			0
$239$	1.77417	−	0.810235i	0.114761	−	0.0524097i	−0.357207	−	0.934025i	$-0.616271\pi$
$239$	1.77417	−	0.810235i	0.114761	−	0.0524097i	0.471968	+	0.881616i	$0.343544\pi$
$240$		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
$243$	−8.48967	−	4.63571i	−0.544613	−	0.297381i
$244$		0			0
$245$	−10.0875	+	10.2225i	−0.644466	+	0.653094i
$246$		0			0
$247$	−7.08640	+	9.46632i	−0.450897	+	0.602328i
$248$		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
$253$	19.5190	−	14.9351i	1.22715	−	0.938964i
$254$		0			0
$255$	4.22353	+	3.11809i	0.264488	+	0.195262i
$256$		0			0
$257$	12.1496	+	16.2299i	0.757870	+	1.01240i	0.999120	+	0.0419324i	$0.0133514\pi$
$257$	12.1496	+	16.2299i	0.757870	+	1.01240i	−0.241251	+	0.970463i	$0.577558\pi$
$258$		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
$263$	−13.7075	+	25.1033i	−0.845238	+	1.54794i	−0.00874389	+	0.999962i	$0.502783\pi$
$263$	−13.7075	+	25.1033i	−0.845238	+	1.54794i	−0.836494	+	0.547976i	$0.815399\pi$
$264$		0			0
$265$	21.4007	−	6.43869i	1.31463	−	0.395525i
$266$		0			0
$267$	−1.69926	+	4.55589i	−0.103993	+	0.278816i
$268$		0			0
$269$	−0.495938	+	1.68901i	−0.0302379	+	0.102981i	−0.973229	−	0.229836i	$-0.926181\pi$
$269$	−0.495938	+	1.68901i	−0.0302379	+	0.102981i	0.942991	+	0.332817i	$0.107999\pi$
$270$		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
$273$	−0.561037	+	0.122046i	−0.0339555	+	0.00738656i
$274$		0			0
$275$	10.9535	+	23.1646i	0.660521	+	1.39688i
$276$		0			0
$277$	−14.9575	+	14.9575i	−0.898710	+	0.898710i	−0.995322	−	0.0966123i	$-0.969199\pi$
$277$	−14.9575	+	14.9575i	−0.898710	+	0.898710i	0.0966123	+	0.995322i	$0.469199\pi$
$278$		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
$283$	7.07246	−	3.86185i	0.420414	−	0.229563i	−0.255094	−	0.966916i	$-0.582106\pi$
$283$	7.07246	−	3.86185i	0.420414	−	0.229563i	0.675508	+	0.737353i	$0.263925\pi$
$284$		0			0
$285$	5.08241	+	0.696279i	0.301056	+	0.0412440i
$286$		0			0
$287$	−9.35853	+	0.669335i	−0.552416	+	0.0395096i
$288$		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
$293$	−7.08639	−	5.30481i	−0.413991	−	0.309910i	0.371902	−	0.928272i	$-0.378706\pi$
$293$	−7.08639	−	5.30481i	−0.413991	−	0.309910i	−0.785894	+	0.618362i	$0.787797\pi$
$294$		0			0
$295$	−1.29128	−	16.5109i	−0.0751814	−	0.961300i
$296$		0			0
$297$	0.819394	−	11.4566i	0.0475461	−	0.664781i
$298$		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
$303$	2.55905	−	1.91568i	0.147013	−	0.110053i
$304$		0			0
$305$	2.96353	+	7.78700i	0.169691	+	0.445882i
$306$		0			0
$307$	0.999657	−	4.59535i	0.0570534	−	0.262270i	−0.939781	−	0.341778i	$-0.888971\pi$
$307$	0.999657	−	4.59535i	0.0570534	−	0.262270i	0.996834	+	0.0795072i	$0.0253347\pi$
$308$		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
$313$	−10.4393	−	3.89366i	−0.590064	−	0.220083i	0.0366546	−	0.999328i	$-0.488330\pi$
$313$	−10.4393	−	3.89366i	−0.590064	−	0.220083i	−0.626719	+	0.779245i	$0.715603\pi$
$314$		0			0
$315$	−3.19883	−	3.64243i	−0.180234	−	0.205228i
$316$		0			0
$317$	−5.87110	−	15.7410i	−0.329754	−	0.884104i	−0.990991	−	0.133927i	$-0.957241\pi$
$317$	−5.87110	−	15.7410i	−0.329754	−	0.884104i	0.661237	−	0.750177i	$-0.270032\pi$
$318$		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
$325$	−6.01822	−	7.82042i	−0.333831	−	0.433799i
$326$		0			0
$327$	1.08976	−	0.406459i	0.0602638	−	0.0224772i
$328$		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
$333$	1.22960	+	17.1920i	0.0673814	+	0.942115i
$334$		0			0
$335$	−1.76146	+	6.14998i	−0.0962391	+	0.336009i
$336$		0			0
$337$	2.90004	+	0.630864i	0.157975	+	0.0343654i	0.290857	−	0.956766i	$-0.406060\pi$
$337$	2.90004	+	0.630864i	0.157975	+	0.0343654i	−0.132882	+	0.991132i	$0.542423\pi$
$338$		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
$343$	10.1723	+	0.727538i	0.549253	+	0.0392834i
$344$		0			0
$345$	4.02671	+	0.803756i	0.216791	+	0.0432728i
$346$		0			0
$347$	10.2838	+	0.735510i	0.552062	+	0.0394842i	0.344584	−	0.938756i	$-0.388020\pi$
$347$	10.2838	+	0.735510i	0.552062	+	0.0394842i	0.207478	+	0.978240i	$0.433475\pi$
$348$		0			0
$349$	−23.5070	−	3.37980i	−1.25830	−	0.180917i	−0.519285	−	0.854601i	$-0.673802\pi$
$349$	−23.5070	−	3.37980i	−1.25830	−	0.180917i	−0.739019	+	0.673685i	$0.764711\pi$
$350$		0			0
$351$	0.629510	+	4.37834i	0.0336007	+	0.233698i
$352$		0			0
$353$	15.3102	+	3.33053i	0.814879	+	0.177266i	0.600645	−	0.799516i	$-0.294911\pi$
$353$	15.3102	+	3.33053i	0.814879	+	0.177266i	0.214235	+	0.976782i	$0.431274\pi$
$354$		0			0
$355$	−15.0791	−	27.1840i	−0.800316	−	1.44278i
$356$		0			0
$357$	−0.127255	−	1.77926i	−0.00673504	−	0.0941682i
$358$		0			0
$359$	11.2250	+	24.5792i	0.592431	+	1.29724i	0.933962	+	0.357372i	$0.116327\pi$
$359$	11.2250	+	24.5792i	0.592431	+	1.29724i	−0.341531	+	0.939870i	$0.610946\pi$
$360$		0			0
$361$	−16.2139	−	4.76082i	−0.853362	−	0.250570i
$362$		0			0
$363$	5.47574	−	2.04235i	0.287402	−	0.107195i
$364$		0			0
$365$	−8.66053	+	4.02494i	−0.453313	+	0.210675i
$366$		0			0
$367$	14.1134	+	14.1134i	0.736712	+	0.736712i	0.971940	−	0.235228i	$-0.0755838\pi$
$367$	14.1134	+	14.1134i	0.736712	+	0.736712i	−0.235228	+	0.971940i	$0.575584\pi$
$368$		0			0
$369$			35.2363i			1.83433i
$370$		0			0
$371$	−6.38812	−	4.10539i	−0.331655	−	0.213141i
$372$		0			0
$373$	3.77321	+	10.1164i	0.195370	+	0.523806i	0.997286	−	0.0736307i	$-0.0234586\pi$
$373$	3.77321	+	10.1164i	0.195370	+	0.523806i	−0.801916	+	0.597437i	$0.796186\pi$
$374$		0			0
$375$	−1.70034	+	3.92878i	−0.0878052	+	0.202882i
$376$		0			0
$377$	−0.442608	−	0.165084i	−0.0227955	−	0.00850228i
$378$		0			0
$379$	−2.79375	+	3.22416i	−0.143506	+	0.165614i	−0.822952	−	0.568111i	$-0.807674\pi$
$379$	−2.79375	+	3.22416i	−0.143506	+	0.165614i	0.679447	+	0.733725i	$0.262220\pi$
$380$		0			0
$381$	−6.55553	+	1.92488i	−0.335850	+	0.0986144i
$382$		0			0
$383$	−6.39333	+	29.3897i	−0.326684	+	1.50174i	0.461965	+	0.886898i	$0.347145\pi$
$383$	−6.39333	+	29.3897i	−0.326684	+	1.50174i	−0.788649	+	0.614844i	$0.789219\pi$
$384$		0			0
$385$	3.56407	−	7.94360i	0.181642	−	0.404843i
$386$		0			0
$387$	18.9444	−	14.1816i	0.962996	−	0.720890i
$388$		0			0
$389$	0.519368	+	0.599383i	0.0263330	+	0.0303899i	0.768763	−	0.639533i	$-0.220872\pi$
$389$	0.519368	+	0.599383i	0.0263330	+	0.0303899i	−0.742430	+	0.669923i	$0.766327\pi$
$390$		0			0
$391$	−19.4900	−	22.0197i	−0.985651	−	1.11358i
$392$		0			0
$393$	−0.124970	+	1.74731i	−0.00630389	+	0.0881399i
$394$		0			0
$395$	−6.49481	+	0.507947i	−0.326789	+	0.0255576i
$396$		0			0
$397$	14.9801	+	11.2140i	0.751831	+	0.562813i	0.905013	−	0.425385i	$-0.139861\pi$
$397$	14.9801	+	11.2140i	0.751831	+	0.562813i	−0.153182	+	0.988198i	$0.548952\pi$
$398$		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
$403$	−10.0030	+	0.715432i	−0.498287	+	0.0356382i
$404$		0			0
$405$	−13.7181	+	10.4123i	−0.681659	+	0.517392i
$406$		0			0
$407$	−27.1695	+	14.8357i	−1.34674	+	0.735377i
$408$		0			0
$409$	4.14266	+	1.89189i	0.204841	+	0.0935480i	0.515194	−	0.857074i	$-0.327720\pi$
$409$	4.14266	+	1.89189i	0.204841	+	0.0935480i	−0.310353	+	0.950622i	$0.600447\pi$
$410$		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
$417$	3.39062	−	0.737585i	0.166040	−	0.0361197i
$418$		0			0
$419$	−6.28729	+	13.7673i	−0.307154	+	0.672574i	−0.998764	−	0.0496968i	$-0.984174\pi$
$419$	−6.28729	+	13.7673i	−0.307154	+	0.672574i	0.691610	+	0.722271i	$0.256902\pi$
$420$		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
$423$	−3.46054	+	9.27808i	−0.168257	+	0.451116i
$424$		0			0
$425$	26.7102	−	15.0494i	1.29563	−	0.730003i
$426$		0			0
$427$	1.35677	−	2.48473i	0.0656585	−	0.120245i
$428$		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
$433$	11.8714	+	15.8584i	0.570504	+	0.762105i	0.989287	−	0.145982i	$-0.0466341\pi$
$433$	11.8714	+	15.8584i	0.570504	+	0.762105i	−0.418783	+	0.908086i	$0.637543\pi$
$434$		0			0
$435$	0.0305132	+	0.202649i	0.00146300	+	0.00971628i
$436$		0			0
$437$	−27.0269	−	9.75749i	−1.29287	−	0.466764i
$438$		0			0
$439$	−24.8939	+	21.5707i	−1.18812	+	1.02951i	−0.189253	+	0.981928i	$0.560607\pi$
$439$	−24.8939	+	21.5707i	−1.18812	+	1.02951i	−0.998867	+	0.0475836i	$0.984848\pi$
$440$		0			0
$441$	2.60814	−	18.1400i	0.124197	−	0.863811i
$442$		0			0
$443$	−19.3197	+	25.8081i	−0.917907	+	1.22618i	0.0558158	+	0.998441i	$0.482224\pi$
$443$	−19.3197	+	25.8081i	−0.917907	+	1.22618i	−0.973722	+	0.227738i	$0.926867\pi$
$444$		0			0
$445$	20.2121	+	19.9451i	0.958145	+	0.945487i
$446$		0			0
$447$	2.15947	+	1.17916i	0.102140	+	0.0557724i
$448$		0			0
$449$	0.901396	+	0.781064i	0.0425395	+	0.0368607i	0.675871	−	0.737020i	$-0.263768\pi$
$449$	0.901396	+	0.781064i	0.0425395	+	0.0368607i	−0.633332	+	0.773881i	$0.718313\pi$
$450$		0			0
$451$	−57.5662	+	26.2896i	−2.71068	+	1.23793i
$452$		0			0
$453$	−2.42080	−	4.43337i	−0.113739	−	0.208298i
$454$		0			0
$455$	−0.690927	+	3.28103i	−0.0323912	+	0.153817i
$456$		0			0
$457$	1.29238	+	5.94097i	0.0604550	+	0.277907i	0.997444	−	0.0714515i	$-0.0227631\pi$
$457$	1.29238	+	5.94097i	0.0604550	+	0.277907i	−0.936989	+	0.349359i	$0.886399\pi$
$458$		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
$463$	1.25990	+	5.79168i	0.0585526	+	0.269162i	0.997111	−	0.0759585i	$-0.0242016\pi$
$463$	1.25990	+	5.79168i	0.0585526	+	0.269162i	−0.938558	+	0.345121i	$0.887838\pi$
$464$		0			0
$465$	2.37640	+	3.64424i	0.110203	+	0.168998i
$466$		0			0
$467$	−3.63267	−	6.65274i	−0.168100	−	0.307852i	0.780026	−	0.625747i	$-0.215206\pi$
$467$	−3.63267	−	6.65274i	−0.168100	−	0.307852i	−0.948126	+	0.317895i	$0.897024\pi$
$468$		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
$473$	37.3030	+	20.3690i	1.71519	+	0.936567i
$474$		0			0
$475$	15.8597	−	25.4151i	0.727695	−	1.16613i
$476$		0			0
$477$	−17.0902	+	22.8299i	−0.782509	+	1.04531i
$478$		0			0
$479$	−1.50152	+	10.4433i	−0.0686063	+	0.477168i	0.926334	+	0.376703i	$0.122942\pi$
$479$	−1.50152	+	10.4433i	−0.0686063	+	0.477168i	−0.994941	+	0.100465i	$0.967967\pi$
$480$		0			0
$481$	9.00972	−	7.80697i	0.410808	−	0.355967i
$482$		0			0
$483$	−0.681507	−	1.21742i	−0.0310096	−	0.0553947i
$484$		0			0
$485$	31.6142	−	4.76020i	1.43553	−	0.216150i
$486$		0			0
$487$	−5.80644	−	7.75649i	−0.263115	−	0.351480i	0.649456	−	0.760399i	$-0.274997\pi$
$487$	−5.80644	−	7.75649i	−0.263115	−	0.351480i	−0.912571	+	0.408919i	$0.865906\pi$
$488$		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
$493$	0.703363	−	1.28811i	0.0316779	−	0.0580137i
$494$		0			0
$495$	−28.8017	−	15.4792i	−1.29454	−	0.695739i
$496$		0			0
$497$	−3.69123	+	9.89658i	−0.165574	+	0.443922i
$498$		0			0
$499$	−6.87292	+	23.4070i	−0.307674	+	1.04784i	0.649988	+	0.759945i	$0.274774\pi$
$499$	−6.87292	+	23.4070i	−0.307674	+	1.04784i	−0.957662	+	0.287896i	$0.907044\pi$
$500$		0			0
$501$	1.46019	−	3.19737i	0.0652364	−	0.142848i
$502$		0			0
$503$	12.8138	−	2.78748i	0.571341	−	0.124288i	0.0823921	−	0.996600i	$-0.473744\pi$
$503$	12.8138	−	2.78748i	0.571341	−	0.124288i	0.488949	+	0.872312i	$0.337380\pi$
$504$		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	−0.952944	−	0.303146i	$-0.901963\pi$
$509$	−6.34699	+	9.87611i	−0.281325	+	0.437751i	0.671619	+	0.740897i	$0.265599\pi$
$510$		0			0
$511$	2.95173	+	1.34801i	0.130577	+	0.0596324i
$512$		0			0
$513$	−11.7860	+	6.43563i	−0.520363	+	0.284140i
$514$		0			0
$515$	−4.07185	+	29.7220i	−0.179427	+	1.30971i
$516$		0			0
$517$	−17.7397	+	1.26877i	−0.780190	+	0.0558003i
$518$		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
$523$	19.3559	+	14.4896i	0.846373	+	0.633587i	0.931887	−	0.362750i	$-0.118162\pi$
$523$	19.3559	+	14.4896i	0.846373	+	0.633587i	−0.0855132	+	0.996337i	$0.527253\pi$
$524$		0			0
$525$	1.39010	−	0.428330i	0.0606689	−	0.0186939i
$526$		0			0
$527$	2.22271	−	31.0776i	0.0968229	−	1.35376i
$528$		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
$533$	19.5107	−	14.6055i	0.845102	−	0.632636i
$534$		0			0
$535$	35.0048	+	15.7057i	1.51339	+	0.679017i
$536$		0			0
$537$	−0.738860	+	3.39648i	−0.0318841	+	0.146569i
$538$		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
$543$	3.86601	+	1.44195i	0.165906	+	0.0618799i
$544$		0			0
$545$	0.439495	−	6.77803i	0.0188259	−	0.290339i
$546$		0			0
$547$	6.96027	+	18.6612i	0.297600	+	0.797895i	0.996571	+	0.0827455i	$0.0263689\pi$
$547$	6.96027	+	18.6612i	0.297600	+	0.797895i	−0.698971	+	0.715150i	$0.746358\pi$
$548$		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
$555$	−4.85764	−	1.77510i	−0.206195	−	0.0753490i
$556$		0			0
$557$	7.29701	−	2.72165i	0.309184	−	0.115320i	−0.190082	−	0.981768i	$-0.560875\pi$
$557$	7.29701	−	2.72165i	0.309184	−	0.115320i	0.499267	+	0.866448i	$0.333603\pi$
$558$		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
$563$	−1.66268	−	23.2472i	−0.0700734	−	0.979754i	−0.903904	−	0.427735i	$-0.859312\pi$
$563$	−1.66268	−	23.2472i	−0.0700734	−	0.979754i	0.833831	−	0.552020i	$-0.186143\pi$
$564$		0			0
$565$	21.0929	+	6.04138i	0.887385	+	0.254163i
$566$		0			0
$567$	5.71806	+	1.24389i	0.240136	+	0.0522384i
$568$		0			0
$569$	−5.09259	−	35.4197i	−0.213492	−	1.48487i	−0.761372	−	0.648315i	$-0.775474\pi$
$569$	−5.09259	−	35.4197i	−0.213492	−	1.48487i	0.547880	−	0.836557i	$-0.315435\pi$
$570$		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
$573$	3.81839	+	0.273097i	0.159516	+	0.0114088i
$574$		0			0
$575$	13.9087	−	19.5333i	0.580031	−	0.814594i
$576$		0			0
$577$	40.9574	+	2.92933i	1.70508	+	0.121950i	0.889572	−	0.456795i	$-0.151003\pi$
$577$	40.9574	+	2.92933i	1.70508	+	0.121950i	0.815508	+	0.578745i	$0.196457\pi$
$578$		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
$583$	−50.0486	−	10.8874i	−2.07280	−	0.450910i
$584$		0			0
$585$	12.1056	+	3.46725i	0.500504	+	0.143353i
$586$		0			0
$587$	−0.719022	−	10.0532i	−0.0296772	−	0.414942i	−0.990475	−	0.137692i	$-0.956032\pi$
$587$	−0.719022	−	10.0532i	−0.0296772	−	0.414942i	0.960798	−	0.277250i	$-0.0894230\pi$
$588$		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
$593$	−40.7993	+	15.2174i	−1.67543	+	0.624902i	−0.994237	−	0.107205i	$-0.965810\pi$
$593$	−40.7993	+	15.2174i	−1.67543	+	0.624902i	−0.681190	+	0.732107i	$0.738537\pi$
$594$		0			0
$595$	−9.78428	−	3.57542i	−0.401117	−	0.146578i
$596$		0			0
$597$	−1.18817	−	1.18817i	−0.0486285	−	0.0486285i
$598$		0			0
$599$		−	17.7605i		−	0.725676i	−0.931852	−	0.362838i	$-0.881808\pi$
$599$		−	17.7605i		−	0.725676i	0.931852	−	0.362838i	$-0.118192\pi$
$600$		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
$603$	−2.85281	−	7.64868i	−0.116175	−	0.311478i
$604$		0			0
$605$	2.20834	−	34.0577i	0.0897818	−	1.38464i
$606$		0			0
$607$	36.5837	+	13.6450i	1.48489	+	0.553834i	0.955615	−	0.294620i	$-0.0951929\pi$
$607$	36.5837	+	13.6450i	1.48489	+	0.553834i	0.529271	+	0.848453i	$0.322466\pi$
$608$		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
$613$	−2.26993	+	10.4347i	−0.0916817	+	0.421454i	0.908313	+	0.418290i	$0.137371\pi$
$613$	−2.26993	+	10.4347i	−0.0916817	+	0.421454i	−0.999995	+	0.00316336i	$0.998993\pi$
$614$		0			0
$615$	−9.64654	−	4.32814i	−0.388986	−	0.174527i
$616$		0			0
$617$	26.0215	−	19.4794i	1.04758	−	0.784212i	0.0705961	−	0.997505i	$-0.477510\pi$
$617$	26.0215	−	19.4794i	1.04758	−	0.784212i	0.976988	+	0.213293i	$0.0684190\pi$
$618$		0			0
$619$	−15.1108	−	17.4388i	−0.607356	−	0.700926i	0.365899	−	0.930655i	$-0.380762\pi$
$619$	−15.1108	−	17.4388i	−0.607356	−	0.700926i	−0.973255	+	0.229729i	$0.926216\pi$
$620$		0			0
$621$	−9.72979	+	4.56791i	−0.390443	+	0.183304i
$622$		0			0
$623$	0.688315	−	9.62390i	0.0275767	−	0.385573i
$624$		0			0
$625$	16.8682	+	18.4517i	0.674728	+	0.738067i
$626$		0			0
$627$	−9.41193	−	7.04568i	−0.375876	−	0.281377i
$628$		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
$633$	4.72708	−	0.338087i	0.187884	−	0.0134378i
$634$		0			0
$635$	−5.41554	+	39.5301i	−0.214909	+	1.56871i
$636$		0			0
$637$	−11.1254	+	6.07493i	−0.440805	+	0.240698i
$638$		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	$-0.799645\pi$
$643$	−5.57032	+	5.57032i	−0.219672	+	0.219672i	0.588688	+	0.808360i	$0.299645\pi$
$644$		0			0
$645$	1.55548	+	6.92830i	0.0612470	+	0.272802i
$646$		0			0
$647$	10.9501	−	2.38204i	0.430492	−	0.0936477i	0.00790189	−	0.999969i	$-0.497485\pi$
$647$	10.9501	−	2.38204i	0.430492	−	0.0936477i	0.422590	+	0.906321i	$0.361121\pi$
$648$		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
$653$	3.71986	−	9.97334i	0.145570	−	0.390287i	−0.843618	−	0.536944i	$-0.819579\pi$
$653$	3.71986	−	9.97334i	0.145570	−	0.390287i	0.989187	+	0.146657i	$0.0468514\pi$
$654$		0			0
$655$	9.01109	+	4.84292i	0.352092	+	0.189229i
$656$		0			0
$657$	5.84045	−	10.6960i	0.227858	−	0.417290i
$658$		0			0
$659$	0.303280	−	0.194906i	0.0118141	−	0.00759247i	−0.534720	−	0.845029i	$-0.679583\pi$
$659$	0.303280	−	0.194906i	0.0118141	−	0.00759247i	0.546535	+	0.837437i	$0.315947\pi$
$660$		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
$663$	2.77682	+	3.70940i	0.107843	+	0.144061i
$664$		0			0
$665$	−10.0656	+	1.51560i	−0.390328	+	0.0587724i
$666$		0			0
$667$	0.0698262	−	1.14578i	0.00270368	−	0.0443649i
$668$		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
$673$	3.19790	−	4.27189i	0.123270	−	0.164669i	−0.734661	−	0.678434i	$-0.762659\pi$
$673$	3.19790	−	4.27189i	0.123270	−	0.164669i	0.857931	+	0.513765i	$0.171750\pi$
$674$		0			0
$675$	−2.52748	−	10.9176i	−0.0972827	−	0.420217i
$676$		0			0
$677$	−13.5310	−	7.38850i	−0.520039	−	0.283963i	0.197715	−	0.980260i	$-0.436648\pi$
$677$	−13.5310	−	7.38850i	−0.520039	−	0.283963i	−0.717754	+	0.696297i	$0.754830\pi$
$678$		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
$683$	−2.06288	−	3.77788i	−0.0789338	−	0.144556i	0.835231	−	0.549899i	$-0.185334\pi$
$683$	−2.06288	−	3.77788i	−0.0789338	−	0.144556i	−0.914165	+	0.405343i	$0.867152\pi$
$684$		0			0
$685$	−22.7025	−	34.8146i	−0.867418	−	1.33020i
$686$		0			0
$687$	−0.273489	−	1.25721i	−0.0104343	−	0.0479655i
$688$		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
$693$	2.36163	+	10.8562i	0.0897110	+	0.412395i
$694$		0			0
$695$	4.17561	−	19.8289i	0.158390	−	0.752152i
$696$		0			0
$697$	36.2882	+	66.4568i	1.37451	+	2.51723i
$698$		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
$703$	31.7648	+	17.3449i	1.19803	+	0.654175i
$704$		0			0
$705$	−2.11497	−	2.08703i	−0.0796544	−	0.0786021i
$706$		0			0
$707$	−3.80123	+	5.07785i	−0.142960	+	0.190972i
$708$		0			0
$709$	5.35970	−	37.2775i	0.201288	−	1.39999i	−0.599182	−	0.800613i	$-0.704507\pi$
$709$	5.35970	−	37.2775i	0.201288	−	1.39999i	0.800469	−	0.599374i	$-0.204584\pi$
$710$		0			0
$711$	6.28267	−	5.44397i	0.235619	−	0.204165i
$712$		0			0
$713$	−8.75624	−	22.7419i	−0.327924	−	0.851690i
$714$		0			0
$715$	3.36739	+	22.3640i	0.125933	+	0.836367i
$716$		0			0
$717$	−0.447550	−	0.597857i	−0.0167141	−	0.0223274i
$718$		0			0
$719$	18.3753	−	2.64196i	0.685281	−	0.0985286i	0.209125	−	0.977889i	$-0.432939\pi$
$719$	18.3753	−	2.64196i	0.685281	−	0.0985286i	0.476157	+	0.879360i	$0.342029\pi$
$720$		0			0
$721$	8.57519	−	5.51094i	0.319357	−	0.205238i
$722$		0			0
$723$	−0.583171	+	1.06800i	−0.0216884	+	0.0397193i
$724$		0			0
$725$	1.15268	+	0.321871i	0.0428095	+	0.0119540i
$726$		0			0
$727$	13.0609	−	35.0175i	0.484400	−	1.29873i	−0.433227	−	0.901285i	$-0.642625\pi$
$727$	13.0609	−	35.0175i	0.484400	−	1.29873i	0.917627	−	0.397442i	$-0.130102\pi$
$728$		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
$733$	−5.07831	+	1.10472i	−0.187572	+	0.0408037i	−0.305370	−	0.952234i	$-0.598780\pi$
$733$	−5.07831	+	1.10472i	−0.187572	+	0.0408037i	0.117798	+	0.993038i	$0.462416\pi$
$734$		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	−0.673081	−	0.739569i	$-0.735030\pi$
$739$	7.59162	−	11.8128i	0.279262	−	0.434541i	0.952343	+	0.305028i	$0.0986659\pi$
$740$		0			0
$741$	4.11859	+	1.88090i	0.151300	+	0.0690964i
$742$		0			0
$743$	−20.2350	+	11.0492i	−0.742352	+	0.405355i	−0.805459	−	0.592652i	$-0.798081\pi$
$743$	−20.2350	+	11.0492i	−0.742352	+	0.405355i	0.0631068	+	0.998007i	$0.479899\pi$
$744$		0			0
$745$	11.4451	−	8.68703i	0.419315	−	0.318268i
$746$		0			0
$747$	0.477051	−	0.0341193i	0.0174544	−	0.00124836i
$748$		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
$753$	−8.25807	−	6.18192i	−0.300941	−	0.225282i
$754$		0			0
$755$	−29.4086	+	2.29999i	−1.07029	+	0.0837051i
$756$		0			0
$757$	0.633661	−	8.85974i	0.0230308	−	0.322013i	−0.972856	−	0.231410i	$-0.925666\pi$
$757$	0.633661	−	8.85974i	0.0230308	−	0.322013i	0.995887	−	0.0906028i	$-0.0288794\pi$
$758$		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
$763$	−1.84756	+	1.38307i	−0.0668863	+	0.0500705i
$764$		0			0
$765$	−16.0149	+	35.6939i	−0.579019	+	1.29052i
$766$		0			0
$767$	3.10715	−	14.2833i	0.112193	−	0.515741i
$768$		0			0
$769$	−44.0848	+	12.9445i	−1.58974	+	0.466789i	−0.952667	−	0.304017i	$-0.901672\pi$
$769$	−44.0848	+	12.9445i	−1.58974	+	0.466789i	−0.637070	+	0.770806i	$0.719854\pi$
$770$		0			0
$771$	5.08355	−	5.86672i	0.183079	−	0.211285i
$772$		0			0
$773$	18.5447	+	6.91682i	0.667007	+	0.248781i	0.660080	−	0.751195i	$-0.270522\pi$
$773$	18.5447	+	6.91682i	0.667007	+	0.248781i	0.00692673	+	0.999976i	$0.497795\pi$
$774$		0			0
$775$	25.0979	−	3.94987i	0.901543	−	0.141884i
$776$		0			0
$777$	0.614112	+	1.64650i	0.0220311	+	0.0590677i
$778$		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
$785$	31.3035	−	14.5482i	1.11727	−	0.519246i
$786$		0			0
$787$	−18.9581	+	7.07101i	−0.675783	+	0.252054i	−0.663840	−	0.747874i	$-0.731074\pi$
$787$	−18.9581	+	7.07101i	−0.675783	+	0.252054i	−0.0119433	+	0.999929i	$0.503802\pi$
$788$		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
$793$	0.524621	+	7.33516i	0.0186298	+	0.260479i
$794$		0			0
$795$	−4.15086	−	7.48300i	−0.147216	−	0.265395i
$796$		0			0
$797$	29.1113	+	6.33277i	1.03117	+	0.224318i	0.696154	−	0.717893i	$-0.254893\pi$
$797$	29.1113	+	6.33277i	1.03117	+	0.224318i	0.335020	+	0.942211i	$0.391257\pi$
$798$		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
$803$	21.8318	+	1.56144i	0.770426	+	0.0551020i
$804$		0			0
$805$	−8.11576	+	0.720799i	−0.286043	+	0.0254048i
$806$		0			0
$807$	0.672307	+	0.0480843i	0.0236663	+	0.00169265i
$808$		0			0
$809$	−30.6605	−	4.40831i	−1.07797	−	0.154988i	−0.419617	−	0.907701i	$-0.637836\pi$
$809$	−30.6605	−	4.40831i	−1.07797	−	0.154988i	−0.658348	+	0.752713i	$0.728745\pi$
$810$		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
$813$	0.386028	+	0.0839752i	0.0135386	+	0.00294514i
$814$		0			0
$815$	10.0448	−	35.0704i	0.351854	−	1.22846i
$816$		0			0
$817$	−3.54488	−	49.5638i	−0.124020	−	1.73402i
$818$		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
$823$	−30.7790	+	11.4800i	−1.07289	+	0.400166i	−0.822961	−	0.568098i	$-0.807679\pi$
$823$	−30.7790	+	11.4800i	−1.07289	+	0.400166i	−0.249927	+	0.968265i	$0.580407\pi$
$824$		0			0
$825$	7.77548	−	5.98364i	0.270708	−	0.208323i
$826$		0			0
$827$	0.734605	+	0.734605i	0.0255447	+	0.0255447i	0.719764	−	0.694219i	$-0.244250\pi$
$827$	0.734605	+	0.734605i	0.0255447	+	0.0255447i	−0.694219	+	0.719764i	$0.744250\pi$
$828$		0			0
$829$			7.04306i			0.244616i	0.992492	+	0.122308i	$0.0390295\pi$
$829$			7.04306i			0.244616i	−0.992492	+	0.122308i	$0.960971\pi$
$830$		0			0
$831$	6.81375	+	4.37893i	0.236366	+	0.151903i
$832$		0			0
$833$	−13.7625	−	36.8987i	−0.476843	−	1.27847i
$834$		0			0
$835$	−13.5452	−	15.4236i	−0.468752	−	0.533756i
$836$		0			0
$837$	−10.6706	−	3.97992i	−0.368830	−	0.137566i
$838$		0			0
$839$	−33.7094	+	38.9027i	−1.16378	+	1.34307i	−0.235193	+	0.971949i	$0.575572\pi$
$839$	−33.7094	+	38.9027i	−1.16378	+	1.34307i	−0.928584	+	0.371122i	$0.878973\pi$
$840$		0			0
$841$	−27.7703	+	8.15410i	−0.957597	+	0.281176i
$842$		0			0
$843$	−1.21925	+	5.60478i	−0.0419931	+	0.193039i
$844$		0			0
$845$	7.24147	+	19.0278i	0.249114	+	0.654575i
$846$		0			0
$847$	−9.28350	+	6.94954i	−0.318985	+	0.238789i
$848$		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
$853$	3.47860	−	48.6372i	0.119105	−	1.66531i	−0.489628	−	0.871931i	$-0.662868\pi$
$853$	3.47860	−	48.6372i	0.119105	−	1.66531i	0.608733	−	0.793375i	$-0.291678\pi$
$854$		0			0
$855$	2.98065	+	38.1118i	0.101936	+	1.30340i
$856$		0			0
$857$	0.536976	+	0.401975i	0.0183427	+	0.0137312i	0.608410	−	0.793623i	$-0.291808\pi$
$857$	0.536976	+	0.401975i	0.0183427	+	0.0137312i	−0.590067	+	0.807354i	$0.700899\pi$
$858$		0			0
$859$	−11.4824	−	17.8670i	−0.391775	−	0.609614i	0.588204	−	0.808712i	$-0.299835\pi$
$859$	−11.4824	−	17.8670i	−0.391775	−	0.609614i	−0.979980	+	0.199098i	$0.936199\pi$
$860$		0			0
$861$	1.01213	+	3.44701i	0.0344934	+	0.117474i
$862$		0			0
$863$	50.7792	−	3.63180i	1.72854	−	0.123628i	0.828658	−	0.559755i	$-0.189105\pi$
$863$	50.7792	−	3.63180i	1.72854	−	0.123628i	0.899885	+	0.436127i	$0.143650\pi$
$864$		0			0
$865$	−18.4226	−	2.52385i	−0.626387	−	0.0858136i
$866$		0			0
$867$	−6.92180	+	3.77959i	−0.235077	+	0.128362i
$868$		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
$877$	−32.6912	+	7.11153i	−1.10390	+	0.240139i	−0.727357	−	0.686259i	$-0.759252\pi$
$877$	−32.6912	+	7.11153i	−1.10390	+	0.240139i	−0.376545	+	0.926398i	$0.622888\pi$
$878$		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
$883$	12.3790	−	33.1893i	0.416586	−	1.11691i	−0.544039	−	0.839060i	$-0.683106\pi$
$883$	12.3790	−	33.1893i	0.416586	−	1.11691i	0.960625	−	0.277849i	$-0.0896216\pi$
$884$		0			0
$885$	−6.07243	+	1.82697i	−0.204122	+	0.0614130i
$886$		0			0
$887$	−0.828473	+	1.51723i	−0.0278174	+	0.0509438i	−0.891218	−	0.453575i	$-0.850148\pi$
$887$	−0.828473	+	1.51723i	−0.0278174	+	0.0509438i	0.863401	+	0.504519i	$0.168330\pi$
$888$		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
$893$	12.4608	+	16.6457i	0.416985	+	0.557027i
$894$		0			0
$895$	16.3305	+	12.0563i	0.545869	+	0.402997i
$896$		0			0
$897$	3.19898	+	1.70328i	0.106811	+	0.0568709i
$898$		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
$903$	1.44589	−	1.93148i	0.0481162	−	0.0642757i
$904$		0			0
$905$	16.9249	−	17.1514i	0.562601	−	0.570133i
$906$		0			0
$907$	8.34561	+	4.55705i	0.277111	+	0.151314i	0.611795	−	0.791016i	$-0.290448\pi$
$907$	8.34561	+	4.55705i	0.277111	+	0.151314i	−0.334684	+	0.942330i	$0.608630\pi$
$908$		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
$913$	0.411666	+	0.753911i	0.0136242	+	0.0249508i
$914$		0			0
$915$	2.67229	−	1.74260i	0.0883433	−	0.0576084i
$916$		0			0
$917$	−0.738875	−	3.39655i	−0.0243998	−	0.112164i
$918$		0			0
$919$	9.29283			0.306542			0.153271	−	0.988184i	$-0.451019\pi$
$919$	9.29283			0.306542			0.153271	+	0.988184i	$0.451019\pi$
$920$		0			0
$921$	−1.80071			−0.0593354
$922$		0			0
$923$	−5.83223	−	26.8103i	−0.191970	−	0.882473i
$924$		0			0
$925$	−21.0705	+	21.6385i	−0.692794	+	0.711470i
$926$		0			0
$927$	−18.3465	−	33.5990i	−0.602577	−	1.10354i
$928$		0			0
$929$	−22.4618	+	10.2579i	−0.736946	+	0.336552i	−0.748279	−	0.663384i	$-0.769120\pi$
$929$	−22.4618	+	10.2579i	−0.736946	+	0.336552i	0.0113332	+	0.999936i	$0.496392\pi$
$930$		0			0
$931$	−29.0828	−	25.2004i	−0.953149	−	0.825908i
$932$		0			0
$933$	−4.92563	−	2.68960i	−0.161258	−	0.0880534i
$934$		0			0
$935$	−70.2624	+	0.467208i	−2.29783	+	0.0152793i
$936$		0			0
$937$	−16.1245	+	21.5398i	−0.526764	+	0.703674i	−0.982463	−	0.186460i	$-0.940298\pi$
$937$	−16.1245	+	21.5398i	−0.526764	+	0.703674i	0.455699	+	0.890134i	$0.349389\pi$
$938$		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
$943$	47.7819	+	34.9899i	1.55599	+	1.13943i
$944$		0			0
$945$	−2.26156	+	3.06333i	−0.0735684	+	0.0996502i
$946$		0			0
$947$	−1.87305	−	2.50210i	−0.0608659	−	0.0813074i	0.769075	−	0.639158i	$-0.220717\pi$
$947$	−1.87305	−	2.50210i	−0.0608659	−	0.0813074i	−0.829941	+	0.557851i	$0.811626\pi$
$948$		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
$953$	−5.81703	+	10.6531i	−0.188432	+	0.345088i	−0.954768	−	0.297353i	$-0.903896\pi$
$953$	−5.81703	+	10.6531i	−0.188432	+	0.345088i	0.766335	+	0.642441i	$0.222078\pi$
$954$		0			0
$955$	10.5833	−	19.6920i	0.342466	−	0.637217i
$956$		0			0
$957$	0.164136	−	0.440065i	0.00530576	−	0.0142253i
$958$		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
$963$	−47.8399	+	10.4069i	−1.54162	+	0.335359i
$964$		0			0
$965$	5.68347	−	8.97431i	0.182957	−	0.288893i
$966$		0			0
$967$	−29.6179	+	29.6179i	−0.952448	+	0.952448i	−0.998920	−	0.0464715i	$-0.985202\pi$
$967$	−29.6179	+	29.6179i	−0.952448	+	0.952448i	0.0464715	+	0.998920i	$0.485202\pi$
$968$		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
$973$	−6.04306	+	3.29976i	−0.193732	+	0.105786i
$974$		0			0
$975$	−2.43617	+	2.88822i	−0.0780200	+	0.0924972i
$976$		0			0
$977$	−35.0367	+	2.50587i	−1.12092	+	0.0801700i	−0.619474	−	0.785017i	$-0.712654\pi$
$977$	−35.0367	+	2.50587i	−1.12092	+	0.0801700i	−0.501449	+	0.865187i	$0.667200\pi$
$978$		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
$983$	−20.2122	−	15.1307i	−0.644670	−	0.482594i	0.226217	−	0.974077i	$-0.427364\pi$
$983$	−20.2122	−	15.1307i	−0.644670	−	0.482594i	−0.870887	+	0.491483i	$0.836455\pi$
$984$		0			0
$985$	−35.1774	+	41.1465i	−1.12084	+	1.31104i
$986$		0			0
$987$	−0.0720245	+	1.00703i	−0.00229257	+	0.0320543i
$988$		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
$993$	−0.615981	+	0.461117i	−0.0195476	+	0.0146331i
$994$		0			0
$995$	−9.17109	+	3.49028i	−0.290743	+	0.110649i
$996$		0			0
$997$	−7.28788	+	33.5019i	−0.230810	+	1.06101i	0.705191	+	0.709017i	$0.250861\pi$
$997$	−7.28788	+	33.5019i	−0.230810	+	1.06101i	−0.936001	+	0.351998i	$0.885503\pi$
$998$		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.33.5	✓	240
5.2	odd	4	inner	460.2.x.a.217.5	yes	240
23.7	odd	22	inner	460.2.x.a.53.5	yes	240
115.7	even	44	inner	460.2.x.a.237.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.5	✓	240	1.1	even	1	trivial
460.2.x.a.53.5	yes	240	23.7	odd	22	inner
460.2.x.a.217.5	yes	240	5.2	odd	4	inner
460.2.x.a.237.5	yes	240	115.7	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)

\(f(q)\)	\(=\)	\(q+(-0.0813911 - 0.374149i) q^{3} +(-2.18808 - 0.460771i) q^{5} +(0.364123 + 0.666841i) q^{7} +(2.59553 - 1.18534i) q^{9} +O(q^{10})\)	\(q+(-0.0813911 - 0.374149i) q^{3} +(-2.18808 - 0.460771i) q^{5} +(0.364123 + 0.666841i) q^{7} +(2.59553 - 1.18534i) q^{9} +(3.87303 + 3.35600i) q^{11} +(-1.73219 - 0.945848i) q^{13} +(0.00569308 + 0.856170i) q^{15} +(3.67454 - 4.90861i) q^{17} +(0.852683 - 5.93054i) q^{19} +(0.219862 - 0.190511i) q^{21} +(0.970011 - 4.69671i) q^{23} +(4.57538 + 2.01641i) q^{25} +(-1.34314 - 1.79422i) q^{27} +(0.236919 - 0.0340638i) q^{29} +(4.27471 - 2.74719i) q^{31} +(0.940413 - 1.72224i) q^{33} +(-0.489468 - 1.62688i) q^{35} +(-2.11094 + 5.65965i) q^{37} +(-0.212903 + 0.725081i) q^{39} +(-5.12993 + 11.2330i) q^{41} +(8.10392 - 1.76290i) q^{43} +(-6.22540 + 1.39767i) q^{45} +(-2.45395 + 2.45395i) q^{47} +(3.47239 - 5.40315i) q^{49} +(-2.13563 - 0.975309i) q^{51} +(-8.77193 + 4.78984i) q^{53} +(-6.92814 - 9.12777i) q^{55} +(-2.28831 + 0.163663i) q^{57} +(2.08663 + 7.10642i) q^{59} +(-2.01449 - 3.13461i) q^{61} +(1.73553 + 1.29920i) q^{63} +(3.35435 + 2.86773i) q^{65} +(0.204097 - 2.85366i) q^{67} +(-1.83622 + 0.0193419i) q^{69} +(9.10398 + 10.5066i) q^{71} +(3.41907 - 2.55948i) q^{73} +(0.382042 - 1.87599i) q^{75} +(-0.827659 + 3.80469i) q^{77} +(2.79542 - 0.820810i) q^{79} +(5.04373 - 5.82077i) q^{81} +(0.157046 + 0.0585753i) q^{83} +(-10.3019 + 9.04731i) q^{85} +(-0.0320281 - 0.0858705i) q^{87} +(-10.6832 - 6.86564i) q^{89} -1.49950i q^{91} +(-1.37578 - 1.37578i) q^{93} +(-4.59836 + 12.5836i) q^{95} +(-13.3962 + 4.99652i) q^{97} +(14.0306 + 4.11975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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

Related objects

Downloads

Learn more