LMFDB - Embedded newform 460.2.m.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	460.121
Dual form			460.2.m.b.441.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08763 - 0.319356i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0860775 - 0.598682i) q^{7} +(-1.44281 - 0.927240i) q^{9} +O(q^{10})$	\(q+(-1.08763 - 0.319356i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0860775 - 0.598682i) q^{7} +(-1.44281 - 0.927240i) q^{9} +(0.638317 + 1.39772i) q^{11} +(0.955890 + 6.64836i) q^{13} +(1.08763 - 0.319356i) q^{15} +(-1.77424 + 2.04759i) q^{17} +(-0.883646 - 1.01978i) q^{19} +(-0.284813 + 0.623654i) q^{21} +(2.16812 + 4.27776i) q^{23} +(0.415415 - 0.909632i) q^{25} +(3.50007 + 4.03929i) q^{27} +(-4.67992 + 5.40091i) q^{29} +(-5.55035 + 1.62973i) q^{31} +(-0.247881 - 1.72405i) q^{33} +(0.251259 + 0.550180i) q^{35} +(-6.24558 - 4.01379i) q^{37} +(1.08354 - 7.53621i) q^{39} +(-6.41523 + 4.12282i) q^{41} +(12.2303 + 3.59114i) q^{43} +1.71508 q^{45} +1.94960 q^{47} +(6.36544 + 1.86906i) q^{49} +(2.58363 - 1.66040i) q^{51} +(-1.59658 + 11.1045i) q^{53} +(-1.29265 - 0.830737i) q^{55} +(0.635405 + 1.39134i) q^{57} +(-1.88194 - 13.0892i) q^{59} +(5.45871 - 1.60282i) q^{61} +(-0.679316 + 0.783972i) q^{63} +(-4.39852 - 5.07616i) q^{65} +(-0.362734 + 0.794276i) q^{67} +(-0.991980 - 5.34502i) q^{69} +(3.21463 - 7.03905i) q^{71} +(-5.25949 - 6.06978i) q^{73} +(-0.742314 + 0.856676i) q^{75} +(0.891735 - 0.261837i) q^{77} +(-1.07587 - 7.48285i) q^{79} +(-0.379392 - 0.830752i) q^{81} +(-4.24387 - 2.72737i) q^{83} +(0.385580 - 2.68177i) q^{85} +(6.81483 - 4.37962i) q^{87} +(-14.1050 - 4.14160i) q^{89} +4.06253 q^{91} +6.55719 q^{93} +(1.29471 + 0.380160i) q^{95} +(-6.87619 + 4.41906i) q^{97} +(0.375049 - 2.60852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.08763	−	0.319356i	−0.627942	−	0.184381i	−0.0477492	−	0.998859i	$-0.515205\pi$
$3$	−1.08763	−	0.319356i	−0.627942	−	0.184381i	−0.580193	+	0.814479i	$0.697023\pi$
$4$		0			0
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$		0			0
$7$	0.0860775	−	0.598682i	0.0325342	−	0.226281i	−0.967067	−	0.254522i	$-0.918082\pi$
$7$	0.0860775	−	0.598682i	0.0325342	−	0.226281i	0.999601	+	0.0282418i	$0.00899085\pi$
$8$		0			0
$9$	−1.44281	−	0.927240i	−0.480938	−	0.309080i
$10$		0			0
$11$	0.638317	+	1.39772i	0.192460	+	0.421428i	0.981120	−	0.193401i	$-0.0619520\pi$
$11$	0.638317	+	1.39772i	0.192460	+	0.421428i	−0.788660	+	0.614830i	$0.789225\pi$
$12$		0			0
$13$	0.955890	+	6.64836i	0.265116	+	1.84392i	0.492743	+	0.870175i	$0.335994\pi$
$13$	0.955890	+	6.64836i	0.265116	+	1.84392i	−0.227627	+	0.973748i	$0.573097\pi$
$14$		0			0
$15$	1.08763	−	0.319356i	0.280824	−	0.0824575i
$16$		0			0
$17$	−1.77424	+	2.04759i	−0.430317	+	0.496613i	−0.928952	−	0.370199i	$-0.879289\pi$
$17$	−1.77424	+	2.04759i	−0.430317	+	0.496613i	0.498635	+	0.866812i	$0.333835\pi$
$18$		0			0
$19$	−0.883646	−	1.01978i	−0.202722	−	0.233954i	0.645280	−	0.763946i	$-0.276741\pi$
$19$	−0.883646	−	1.01978i	−0.202722	−	0.233954i	−0.848003	+	0.529992i	$0.822195\pi$
$20$		0			0
$21$	−0.284813	+	0.623654i	−0.0621513	+	0.136092i
$22$		0			0
$23$	2.16812	+	4.27776i	0.452085	+	0.891975i
$23$	2.16812	+	4.27776i	0.452085	+	0.891975i
$24$		0			0
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$		0			0
$27$	3.50007	+	4.03929i	0.673588	+	0.777362i
$28$		0			0
$29$	−4.67992	+	5.40091i	−0.869039	+	1.00292i	0.130895	+	0.991396i	$0.458215\pi$
$29$	−4.67992	+	5.40091i	−0.869039	+	1.00292i	−0.999934	+	0.0115282i	$0.996330\pi$
$30$		0			0
$31$	−5.55035	+	1.62973i	−0.996873	+	0.292708i	−0.739172	−	0.673517i	$-0.764783\pi$
$31$	−5.55035	+	1.62973i	−0.996873	+	0.292708i	−0.257701	+	0.966225i	$0.582965\pi$
$32$		0			0
$33$	−0.247881	−	1.72405i	−0.0431506	−	0.300119i
$34$		0			0
$35$	0.251259	+	0.550180i	0.0424705	+	0.0929974i
$36$		0			0
$37$	−6.24558	−	4.01379i	−1.02677	−	0.659863i	−0.0850871	−	0.996374i	$-0.527117\pi$
$37$	−6.24558	−	4.01379i	−1.02677	−	0.659863i	−0.941680	+	0.336511i	$0.890753\pi$
$38$		0			0
$39$	1.08354	−	7.53621i	0.173506	−	1.20676i
$40$		0			0
$41$	−6.41523	+	4.12282i	−1.00189	+	0.643876i	−0.935282	−	0.353903i	$-0.884854\pi$
$41$	−6.41523	+	4.12282i	−1.00189	+	0.643876i	−0.0666087	+	0.997779i	$0.521218\pi$
$42$		0			0
$43$	12.2303	+	3.59114i	1.86511	+	0.547644i	0.998845	+	0.0480524i	$0.0153014\pi$
$43$	12.2303	+	3.59114i	1.86511	+	0.547644i	0.866261	+	0.499592i	$0.166517\pi$
$44$		0			0
$45$	1.71508			0.255668
$46$		0			0
$47$	1.94960			0.284378			0.142189	−	0.989840i	$-0.454586\pi$
$47$	1.94960			0.284378			0.142189	+	0.989840i	$0.454586\pi$
$48$		0			0
$49$	6.36544	+	1.86906i	0.909349	+	0.267009i
$50$		0			0
$51$	2.58363	−	1.66040i	0.361780	−	0.232502i
$52$		0			0
$53$	−1.59658	+	11.1045i	−0.219308	+	1.52532i	0.521296	+	0.853376i	$0.325449\pi$
$53$	−1.59658	+	11.1045i	−0.219308	+	1.52532i	−0.740603	+	0.671942i	$0.765460\pi$
$54$		0			0
$55$	−1.29265	−	0.830737i	−0.174301	−	0.112016i
$56$		0			0
$57$	0.635405	+	1.39134i	0.0841614	+	0.184288i
$58$		0			0
$59$	−1.88194	−	13.0892i	−0.245008	−	1.70406i	−0.626277	−	0.779601i	$-0.715422\pi$
$59$	−1.88194	−	13.0892i	−0.245008	−	1.70406i	0.381269	−	0.924464i	$-0.375487\pi$
$60$		0			0
$61$	5.45871	−	1.60282i	0.698916	−	0.205220i	0.0870758	−	0.996202i	$-0.472248\pi$
$61$	5.45871	−	1.60282i	0.698916	−	0.205220i	0.611840	+	0.790981i	$0.290430\pi$
$62$		0			0
$63$	−0.679316	+	0.783972i	−0.0855857	+	0.0987712i
$64$		0			0
$65$	−4.39852	−	5.07616i	−0.545569	−	0.629621i
$66$		0			0
$67$	−0.362734	+	0.794276i	−0.0443150	+	0.0970363i	−0.930495	−	0.366306i	$-0.880623\pi$
$67$	−0.362734	+	0.794276i	−0.0443150	+	0.0970363i	0.886180	+	0.463342i	$0.153350\pi$
$68$		0			0
$69$	−0.991980	−	5.34502i	−0.119420	−	0.643465i
$70$		0			0
$71$	3.21463	−	7.03905i	0.381506	−	0.835382i	−0.617309	−	0.786721i	$-0.711777\pi$
$71$	3.21463	−	7.03905i	0.381506	−	0.835382i	0.998815	−	0.0486613i	$-0.0154955\pi$
$72$		0			0
$73$	−5.25949	−	6.06978i	−0.615577	−	0.710414i	0.359284	−	0.933228i	$-0.383021\pi$
$73$	−5.25949	−	6.06978i	−0.615577	−	0.710414i	−0.974861	+	0.222815i	$0.928476\pi$
$74$		0			0
$75$	−0.742314	+	0.856676i	−0.0857150	+	0.0989204i
$76$		0			0
$77$	0.891735	−	0.261837i	0.101623	−	0.0298391i
$78$		0			0
$79$	−1.07587	−	7.48285i	−0.121045	−	0.841887i	−0.956376	−	0.292139i	$-0.905633\pi$
$79$	−1.07587	−	7.48285i	−0.121045	−	0.841887i	0.835331	−	0.549748i	$-0.185276\pi$
$80$		0			0
$81$	−0.379392	−	0.830752i	−0.0421547	−	0.0923058i
$82$		0			0
$83$	−4.24387	−	2.72737i	−0.465825	−	0.299367i	0.286594	−	0.958052i	$-0.407477\pi$
$83$	−4.24387	−	2.72737i	−0.465825	−	0.299367i	−0.752419	+	0.658685i	$0.771113\pi$
$84$		0			0
$85$	0.385580	−	2.68177i	0.0418220	−	0.290879i
$86$		0			0
$87$	6.81483	−	4.37962i	0.730626	−	0.469545i
$88$		0			0
$89$	−14.1050	−	4.14160i	−1.49513	−	0.439009i	−0.570953	−	0.820983i	$-0.693426\pi$
$89$	−14.1050	−	4.14160i	−1.49513	−	0.439009i	−0.924173	+	0.381974i	$0.875244\pi$
$90$		0			0
$91$	4.06253			0.425869
$92$		0			0
$93$	6.55719			0.679948
$94$		0			0
$95$	1.29471	+	0.380160i	0.132834	+	0.0390036i
$96$		0			0
$97$	−6.87619	+	4.41906i	−0.698171	+	0.448687i	−0.840982	−	0.541063i	$-0.818022\pi$
$97$	−6.87619	+	4.41906i	−0.698171	+	0.448687i	0.142811	+	0.989750i	$0.454386\pi$
$98$		0			0
$99$	0.375049	−	2.60852i	0.0376939	−	0.262167i
$100$		0			0
$101$	0.932796	+	0.599471i	0.0928166	+	0.0596496i	0.586226	−	0.810148i	$-0.300613\pi$
$101$	0.932796	+	0.599471i	0.0928166	+	0.0596496i	−0.493409	+	0.869797i	$0.664249\pi$
$102$		0			0
$103$	1.91485	+	4.19294i	0.188676	+	0.413143i	0.980204	−	0.197990i	$-0.0634414\pi$
$103$	1.91485	+	4.19294i	0.188676	+	0.413143i	−0.791528	+	0.611133i	$0.790714\pi$
$104$		0			0
$105$	−0.0975727	−	0.678633i	−0.00952212	−	0.0662278i
$106$		0			0
$107$	4.45922	−	1.30935i	0.431089	−	0.126579i	−0.0589872	−	0.998259i	$-0.518787\pi$
$107$	4.45922	−	1.30935i	0.431089	−	0.126579i	0.490076	+	0.871680i	$0.336969\pi$
$108$		0			0
$109$	9.65719	−	11.1450i	0.924991	−	1.06750i	−0.0725464	−	0.997365i	$-0.523113\pi$
$109$	9.65719	−	11.1450i	0.924991	−	1.06750i	0.997538	−	0.0701319i	$-0.0223420\pi$
$110$		0			0
$111$	5.51104	+	6.36008i	0.523085	+	0.603672i
$112$		0			0
$113$	−3.22312	+	7.05765i	−0.303206	+	0.663928i	−0.998497	−	0.0547998i	$-0.982548\pi$
$113$	−3.22312	+	7.05765i	−0.303206	+	0.663928i	0.695292	+	0.718728i	$0.255275\pi$
$114$		0			0
$115$	−4.13667	−	2.42651i	−0.385747	−	0.226273i
$116$		0			0
$117$	4.78546	−	10.4787i	0.442416	−	0.968755i
$118$		0			0
$119$	1.07313	+	1.23846i	0.0983737	+	0.113529i
$120$		0			0
$121$	5.65730	−	6.52887i	0.514300	−	0.593533i
$122$		0			0
$123$	8.29403	−	2.43535i	0.747848	−	0.219588i
$124$		0			0
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$		0			0
$127$	−3.24045	−	7.09559i	−0.287543	−	0.629631i	0.709646	−	0.704558i	$-0.248855\pi$
$127$	−3.24045	−	7.09559i	−0.287543	−	0.629631i	−0.997189	+	0.0749270i	$0.976128\pi$
$128$		0			0
$129$	−12.1552	−	7.81166i	−1.07020	−	0.687778i
$130$		0			0
$131$	−2.89443	+	20.1312i	−0.252887	+	1.75887i	0.327803	+	0.944746i	$0.393692\pi$
$131$	−2.89443	+	20.1312i	−0.252887	+	1.75887i	−0.580690	+	0.814125i	$0.697217\pi$
$132$		0			0
$133$	−0.686587	+	0.441243i	−0.0595347	+	0.0382606i
$134$		0			0
$135$	−5.12825	−	1.50579i	−0.441369	−	0.129598i
$136$		0			0
$137$	1.11714			0.0954435			0.0477218	−	0.998861i	$-0.484804\pi$
$137$	1.11714			0.0954435			0.0477218	+	0.998861i	$0.484804\pi$
$138$		0			0
$139$	5.39501			0.457599			0.228799	−	0.973474i	$-0.426520\pi$
$139$	5.39501			0.457599			0.228799	+	0.973474i	$0.426520\pi$
$140$		0			0
$141$	−2.12044	−	0.622617i	−0.178573	−	0.0524338i
$142$		0			0
$143$	−8.68239	+	5.57983i	−0.726058	+	0.466609i
$144$		0			0
$145$	1.01704	−	7.07369i	0.0844609	−	0.587438i
$146$		0			0
$147$	−6.32634	−	4.06569i	−0.521787	−	0.335332i
$148$		0			0
$149$	4.17744	+	9.14732i	0.342229	+	0.749378i	0.999993	−	0.00384695i	$-0.00122453\pi$
$149$	4.17744	+	9.14732i	0.342229	+	0.749378i	−0.657763	+	0.753225i	$0.728497\pi$
$150$		0			0
$151$	0.346570	+	2.41045i	0.0282035	+	0.196159i	0.999052	−	0.0435348i	$-0.0138619\pi$
$151$	0.346570	+	2.41045i	0.0282035	+	0.196159i	−0.970848	+	0.239694i	$0.922953\pi$
$152$		0			0
$153$	4.45851	−	1.30914i	0.360449	−	0.105837i
$154$		0			0
$155$	3.78815	−	4.37176i	0.304272	−	0.351149i
$156$		0			0
$157$	12.2407	+	14.1266i	0.976917	+	1.12742i	0.991834	+	0.127533i	$0.0407060\pi$
$157$	12.2407	+	14.1266i	0.976917	+	1.12742i	−0.0149174	+	0.999889i	$0.504749\pi$
$158$		0			0
$159$	5.28278	−	11.5677i	0.418952	−	0.917376i
$160$		0			0
$161$	2.74765	−	0.929796i	0.216545	−	0.0732782i
$162$		0			0
$163$	5.88160	−	12.8789i	0.460682	−	1.00875i	−0.526649	−	0.850083i	$-0.676552\pi$
$163$	5.88160	−	12.8789i	0.460682	−	1.00875i	0.987332	−	0.158671i	$-0.0507208\pi$
$164$		0			0
$165$	1.14062	+	1.31635i	0.0887974	+	0.102478i
$166$		0			0
$167$	−7.33425	+	8.46417i	−0.567541	+	0.654977i	−0.964879	−	0.262695i	$-0.915389\pi$
$167$	−7.33425	+	8.46417i	−0.567541	+	0.654977i	0.397338	+	0.917672i	$0.369934\pi$
$168$		0			0
$169$	−30.8136	+	9.04768i	−2.37027	+	0.695975i
$170$		0			0
$171$	0.329354	+	2.29071i	0.0251863	+	0.175175i
$172$		0			0
$173$	1.75063	+	3.83334i	0.133098	+	0.291443i	0.964433	−	0.264328i	$-0.0851502\pi$
$173$	1.75063	+	3.83334i	0.133098	+	0.291443i	−0.831335	+	0.555772i	$0.812423\pi$
$174$		0			0
$175$	−0.508822	−	0.327000i	−0.0384634	−	0.0247189i
$176$		0			0
$177$	−2.13326	+	14.8372i	−0.160346	+	1.11523i
$178$		0			0
$179$	9.97922	−	6.41326i	0.745882	−	0.479349i	−0.111671	−	0.993745i	$-0.535620\pi$
$179$	9.97922	−	6.41326i	0.745882	−	0.479349i	0.857553	+	0.514396i	$0.171984\pi$
$180$		0			0
$181$	7.32964	+	2.15218i	0.544808	+	0.159970i	0.542544	−	0.840027i	$-0.317461\pi$
$181$	7.32964	+	2.15218i	0.544808	+	0.159970i	0.00226376	+	0.999997i	$0.499279\pi$
$182$		0			0
$183$	−6.44892			−0.476718
$184$		0			0
$185$	7.42413			0.545833
$186$		0			0
$187$	−3.99448	−	1.17289i	−0.292106	−	0.0857699i
$188$		0			0
$189$	2.71953	−	1.74773i	0.197817	−	0.127129i
$190$		0			0
$191$	−3.33696	+	23.2090i	−0.241454	+	1.67935i	0.403386	+	0.915030i	$0.367833\pi$
$191$	−3.33696	+	23.2090i	−0.241454	+	1.67935i	−0.644840	+	0.764317i	$0.723076\pi$
$192$		0			0
$193$	3.65435	+	2.34851i	0.263046	+	0.169049i	0.665515	−	0.746384i	$-0.268212\pi$
$193$	3.65435	+	2.34851i	0.263046	+	0.169049i	−0.402470	+	0.915433i	$0.631848\pi$
$194$		0			0
$195$	3.16285	+	6.92567i	0.226496	+	0.495958i
$196$		0			0
$197$	0.648959	+	4.51361i	0.0462364	+	0.321581i	0.999793	+	0.0203662i	$0.00648320\pi$
$197$	0.648959	+	4.51361i	0.0462364	+	0.321581i	−0.953556	+	0.301215i	$0.902608\pi$
$198$		0			0
$199$	−11.9285	+	3.50254i	−0.845592	+	0.248288i	−0.675702	−	0.737175i	$-0.736159\pi$
$199$	−11.9285	+	3.50254i	−0.845592	+	0.248288i	−0.169890	+	0.985463i	$0.554341\pi$
$200$		0			0
$201$	0.648177	−	0.748036i	0.0457189	−	0.0527624i
$202$		0			0
$203$	2.83059	+	3.26668i	0.198669	+	0.229276i
$204$		0			0
$205$	3.16787	−	6.93667i	0.221254	−	0.484478i
$206$		0			0
$207$	0.838317	−	8.18238i	0.0582670	−	0.568715i
$208$		0			0
$209$	0.861323	−	1.88603i	0.0595790	−	0.130460i
$210$		0			0
$211$	−13.6904	−	15.7996i	−0.942489	−	1.08769i	−0.996021	−	0.0891238i	$-0.971593\pi$
$211$	−13.6904	−	15.7996i	−0.942489	−	1.08769i	0.0535318	−	0.998566i	$-0.482952\pi$
$212$		0			0
$213$	−5.74429	+	6.62926i	−0.393592	+	0.454229i
$214$		0			0
$215$	−12.2303	+	3.59114i	−0.834101	+	0.244914i
$216$		0			0
$217$	0.497930	+	3.46318i	0.0338017	+	0.235096i
$218$		0			0
$219$	3.78195	+	8.28131i	0.255560	+	0.559599i
$220$		0			0
$221$	−15.3091	−	9.83854i	−1.02980	−	0.661812i
$222$		0			0
$223$	−2.22625	+	15.4839i	−0.149081	+	1.03688i	0.768648	+	0.639672i	$0.220930\pi$
$223$	−2.22625	+	15.4839i	−0.149081	+	1.03688i	−0.917729	+	0.397208i	$0.869979\pi$
$224$		0			0
$225$	−1.44281	+	0.927240i	−0.0961876	+	0.0618160i
$226$		0			0
$227$	4.91126	+	1.44207i	0.325972	+	0.0957139i	0.440624	−	0.897692i	$-0.354757\pi$
$227$	4.91126	+	1.44207i	0.325972	+	0.0957139i	−0.114652	+	0.993406i	$0.536575\pi$
$228$		0			0
$229$	20.9326			1.38326			0.691632	−	0.722250i	$-0.256892\pi$
$229$	20.9326			1.38326			0.691632	+	0.722250i	$0.256892\pi$
$230$		0			0
$231$	−1.05349			−0.0693149
$232$		0			0
$233$	−5.23987	−	1.53857i	−0.343276	−	0.100795i	0.105550	−	0.994414i	$-0.466340\pi$
$233$	−5.23987	−	1.53857i	−0.343276	−	0.100795i	−0.448826	+	0.893619i	$0.648158\pi$
$234$		0			0
$235$	−1.64011	+	1.05403i	−0.106989	+	0.0687575i
$236$		0			0
$237$	−1.21955	+	8.48215i	−0.0792182	+	0.550975i
$238$		0			0
$239$	1.67649	+	1.07741i	0.108443	+	0.0696921i	0.593738	−	0.804658i	$-0.297651\pi$
$239$	1.67649	+	1.07741i	0.108443	+	0.0696921i	−0.485295	+	0.874350i	$0.661288\pi$
$240$		0			0
$241$	5.06443	+	11.0896i	0.326229	+	0.714341i	0.999690	−	0.0248811i	$-0.00792070\pi$
$241$	5.06443	+	11.0896i	0.326229	+	0.714341i	−0.673462	+	0.739222i	$0.735193\pi$
$242$		0			0
$243$	−2.13458	−	14.8463i	−0.136933	−	0.952393i
$244$		0			0
$245$	−6.36544	+	1.86906i	−0.406673	+	0.119410i
$246$		0			0
$247$	5.93521	−	6.84960i	0.377648	−	0.435830i
$248$		0			0
$249$	3.74475	+	4.32167i	0.237314	+	0.273875i
$250$		0			0
$251$	−11.8944	+	26.0451i	−0.750767	+	1.64395i	0.0142139	+	0.999899i	$0.495475\pi$
$251$	−11.8944	+	26.0451i	−0.750767	+	1.64395i	−0.764981	+	0.644052i	$0.777252\pi$
$252$		0			0
$253$	−4.59516	+	5.76100i	−0.288895	+	0.362191i
$254$		0			0
$255$	−1.27581	+	2.79363i	−0.0798942	+	0.174944i
$256$		0			0
$257$	−12.9658	−	14.9633i	−0.808785	−	0.933388i	0.190044	−	0.981776i	$-0.439137\pi$
$257$	−12.9658	−	14.9633i	−0.808785	−	0.933388i	−0.998829	+	0.0483880i	$0.984592\pi$
$258$		0			0
$259$	−2.94059	+	3.39362i	−0.182719	+	0.210869i
$260$		0			0
$261$	11.7602	−	3.45311i	0.727938	−	0.213742i
$262$		0			0
$263$	−2.75966	−	19.1938i	−0.170168	−	1.18354i	−0.878528	−	0.477691i	$-0.841474\pi$
$263$	−2.75966	−	19.1938i	−0.170168	−	1.18354i	0.708360	−	0.705851i	$-0.249435\pi$
$264$		0			0
$265$	−4.66041	−	10.2049i	−0.286287	−	0.626880i
$266$		0			0
$267$	14.0183	+	9.00904i	0.857908	+	0.551344i
$268$		0			0
$269$	−0.468625	+	3.25936i	−0.0285725	+	0.198726i	−0.999108	−	0.0422328i	$-0.986553\pi$
$269$	−0.468625	+	3.25936i	−0.0285725	+	0.198726i	0.970535	+	0.240959i	$0.0774620\pi$
$270$		0			0
$271$	21.8549	−	14.0453i	1.32759	−	0.853192i	0.331669	−	0.943396i	$-0.392388\pi$
$271$	21.8549	−	14.0453i	1.32759	−	0.853192i	0.995923	+	0.0902038i	$0.0287518\pi$
$272$		0			0
$273$	−4.41853	−	1.29740i	−0.267421	−	0.0785220i
$274$		0			0
$275$	1.53658			0.0926591
$276$		0			0
$277$	7.40549			0.444952			0.222476	−	0.974938i	$-0.428586\pi$
$277$	7.40549			0.444952			0.222476	+	0.974938i	$0.428586\pi$
$278$		0			0
$279$	9.51928	+	2.79511i	0.569904	+	0.167339i
$280$		0			0
$281$	11.7526	−	7.55296i	0.701103	−	0.450572i	−0.140914	−	0.990022i	$-0.545004\pi$
$281$	11.7526	−	7.55296i	0.701103	−	0.450572i	0.842018	+	0.539450i	$0.181368\pi$
$282$		0			0
$283$	−3.72093	+	25.8797i	−0.221187	+	1.53839i	0.512374	+	0.858762i	$0.328766\pi$
$283$	−3.72093	+	25.8797i	−0.221187	+	1.53839i	−0.733561	+	0.679624i	$0.762143\pi$
$284$		0			0
$285$	−1.28675	−	0.826946i	−0.0762207	−	0.0489840i
$286$		0			0
$287$	1.91605	+	4.19556i	0.113101	+	0.247656i
$288$		0			0
$289$	1.37468	+	9.56113i	0.0808637	+	0.562419i
$290$		0			0
$291$	8.88999	−	2.61034i	0.521141	−	0.153021i
$292$		0			0
$293$	−3.25396	+	3.75527i	−0.190098	+	0.219385i	−0.842796	−	0.538233i	$-0.819092\pi$
$293$	−3.25396	+	3.75527i	−0.190098	+	0.219385i	0.652697	+	0.757619i	$0.273637\pi$
$294$		0			0
$295$	8.65973	+	9.99386i	0.504189	+	0.581865i
$296$		0			0
$297$	−3.41165	+	7.47046i	−0.197964	+	0.433480i
$298$		0			0
$299$	−26.3676	+	18.5035i	−1.52488	+	1.07009i
$300$		0			0
$301$	3.20271	−	7.01295i	0.184601	−	0.404220i
$302$		0			0
$303$	−0.823090	−	0.949896i	−0.0472853	−	0.0545701i
$304$		0			0
$305$	−3.72561	+	4.29958i	−0.213328	+	0.246193i
$306$		0			0
$307$	−6.94106	+	2.03808i	−0.396147	+	0.116319i	−0.473738	−	0.880666i	$-0.657095\pi$
$307$	−6.94106	+	2.03808i	−0.396147	+	0.116319i	0.0775906	+	0.996985i	$0.475277\pi$
$308$		0			0
$309$	−0.743604	−	5.17188i	−0.0423022	−	0.294218i
$310$		0			0
$311$	−0.0315966	−	0.0691868i	−0.00179168	−	0.00392323i	0.908734	−	0.417376i	$-0.137050\pi$
$311$	−0.0315966	−	0.0691868i	−0.00179168	−	0.00392323i	−0.910526	+	0.413452i	$0.864323\pi$
$312$		0			0
$313$	−8.91255	−	5.72775i	−0.503767	−	0.323751i	0.263954	−	0.964535i	$-0.414973\pi$
$313$	−8.91255	−	5.72775i	−0.503767	−	0.323751i	−0.767721	+	0.640784i	$0.778609\pi$
$314$		0			0
$315$	0.147629	−	1.02679i	0.00831798	−	0.0578528i
$316$		0			0
$317$	−5.76475	+	3.70478i	−0.323780	+	0.208081i	−0.692426	−	0.721489i	$-0.743458\pi$
$317$	−5.76475	+	3.70478i	−0.323780	+	0.208081i	0.368645	+	0.929570i	$0.379822\pi$
$318$		0			0
$319$	−10.5362	−	3.09372i	−0.589916	−	0.173215i
$320$		0			0
$321$	−5.26812			−0.294038
$322$		0			0
$323$	3.65590			0.203419
$324$		0			0
$325$	6.44465	+	1.89232i	0.357485	+	0.104967i
$326$		0			0
$327$	−14.0627	+	9.03752i	−0.777667	+	0.499776i
$328$		0			0
$329$	0.167817	−	1.16719i	0.00925202	−	0.0643492i
$330$		0			0
$331$	−24.6133	−	15.8180i	−1.35287	−	0.869436i	−0.355011	−	0.934862i	$-0.615523\pi$
$331$	−24.6133	−	15.8180i	−1.35287	−	0.869436i	−0.997857	+	0.0654267i	$0.979159\pi$
$332$		0			0
$333$	5.28946	+	11.5823i	0.289861	+	0.634706i
$334$		0			0
$335$	−0.124267	−	0.864296i	−0.00678943	−	0.0472215i
$336$		0			0
$337$	13.7599	−	4.04026i	0.749548	−	0.220087i	0.115422	−	0.993317i	$-0.463178\pi$
$337$	13.7599	−	4.04026i	0.749548	−	0.220087i	0.634126	+	0.773229i	$0.281360\pi$
$338$		0			0
$339$	5.75946	−	6.64678i	0.312811	−	0.361003i
$340$		0			0
$341$	−5.82079	−	6.71755i	−0.315214	−	0.363776i
$342$		0			0
$343$	3.42571	−	7.50125i	0.184971	−	0.405030i
$344$		0			0
$345$	3.72424	+	3.96021i	0.200506	+	0.213211i
$346$		0			0
$347$	7.10522	−	15.5583i	0.381428	−	0.835211i	−0.617392	−	0.786656i	$-0.711811\pi$
$347$	7.10522	−	15.5583i	0.381428	−	0.835211i	0.998820	−	0.0485559i	$-0.0154619\pi$
$348$		0			0
$349$	13.7924	+	15.9172i	0.738289	+	0.852031i	0.993379	−	0.114887i	$-0.0366505\pi$
$349$	13.7924	+	15.9172i	0.738289	+	0.852031i	−0.255090	+	0.966917i	$0.582105\pi$
$350$		0			0
$351$	−23.5090	+	27.1308i	−1.25482	+	1.44814i
$352$		0			0
$353$	18.3137	−	5.37738i	0.974739	−	0.286209i	0.244688	−	0.969602i	$-0.421314\pi$
$353$	18.3137	−	5.37738i	0.974739	−	0.286209i	0.730051	+	0.683393i	$0.239496\pi$
$354$		0			0
$355$	1.10128	+	7.65959i	0.0584500	+	0.406529i
$356$		0			0
$357$	−0.771657	−	1.68969i	−0.0408404	−	0.0894281i
$358$		0			0
$359$	1.58319	+	1.01746i	0.0835578	+	0.0536993i	0.581753	−	0.813366i	$-0.302367\pi$
$359$	1.58319	+	1.01746i	0.0835578	+	0.0536993i	−0.498195	+	0.867065i	$0.666004\pi$
$360$		0			0
$361$	2.44486	−	17.0044i	0.128677	−	0.894966i
$362$		0			0
$363$	−8.23807	+	5.29429i	−0.432387	+	0.277878i
$364$		0			0
$365$	7.70613	+	2.26273i	0.403358	+	0.118436i
$366$		0			0
$367$	22.4864			1.17378			0.586891	−	0.809666i	$-0.300352\pi$
$367$	22.4864			1.17378			0.586891	+	0.809666i	$0.300352\pi$
$368$		0			0
$369$	13.0788			0.680857
$370$		0			0
$371$	6.51063	+	1.91169i	0.338015	+	0.0992501i
$372$		0			0
$373$	26.8558	−	17.2592i	1.39054	−	0.893647i	0.390900	−	0.920433i	$-0.372164\pi$
$373$	26.8558	−	17.2592i	1.39054	−	0.893647i	0.999641	+	0.0267865i	$0.00852742\pi$
$374$		0			0
$375$	0.161320	−	1.12201i	0.00833054	−	0.0579402i
$376$		0			0
$377$	−40.3807	−	25.9511i	−2.07971	−	1.33655i
$378$		0			0
$379$	2.00975	+	4.40074i	0.103234	+	0.226051i	0.954200	−	0.299170i	$-0.0967099\pi$
$379$	2.00975	+	4.40074i	0.103234	+	0.226051i	−0.850966	+	0.525221i	$0.823983\pi$
$380$		0			0
$381$	1.25838	+	8.75222i	0.0644687	+	0.448390i
$382$		0			0
$383$	26.7112	−	7.84311i	1.36488	−	0.400764i	0.484398	−	0.874848i	$-0.339039\pi$
$383$	26.7112	−	7.84311i	1.36488	−	0.400764i	0.880480	+	0.474083i	$0.157220\pi$
$384$		0			0
$385$	−0.608615	+	0.702379i	−0.0310179	+	0.0357966i
$386$		0			0
$387$	−14.3162	−	16.5218i	−0.727734	−	0.839850i
$388$		0			0
$389$	−7.23883	+	15.8508i	−0.367023	+	0.803669i	0.632552	+	0.774518i	$0.282008\pi$
$389$	−7.23883	+	15.8508i	−0.367023	+	0.803669i	−0.999575	+	0.0291506i	$0.990720\pi$
$390$		0			0
$391$	−12.6059	−	3.15038i	−0.637506	−	0.159321i
$392$		0			0
$393$	9.57709	−	20.9709i	0.483100	−	1.05784i
$394$		0			0
$395$	4.95062	+	5.71332i	0.249093	+	0.287468i
$396$		0			0
$397$	−16.1024	+	18.5832i	−0.808158	+	0.932664i	−0.998799	−	0.0489956i	$-0.984398\pi$
$397$	−16.1024	+	18.5832i	−0.808158	+	0.932664i	0.190641	+	0.981660i	$0.438943\pi$
$398$		0			0
$399$	0.887665	−	0.260642i	0.0444389	−	0.0130484i
$400$		0			0
$401$	−2.77179	−	19.2782i	−0.138417	−	0.962709i	−0.934104	−	0.357001i	$-0.883799\pi$
$401$	−2.77179	−	19.2782i	−0.138417	−	0.962709i	0.795687	−	0.605708i	$-0.207110\pi$
$402$		0			0
$403$	−16.1406	−	35.3429i	−0.804019	−	1.76056i
$404$		0			0
$405$	0.768304	+	0.493759i	0.0381773	+	0.0245351i
$406$		0			0
$407$	1.62349	−	11.2916i	0.0804736	−	0.559706i
$408$		0			0
$409$	−4.41999	+	2.84055i	−0.218554	+	0.140456i	−0.645337	−	0.763898i	$-0.723283\pi$
$409$	−4.41999	+	2.84055i	−0.218554	+	0.140456i	0.426783	+	0.904354i	$0.359647\pi$
$410$		0			0
$411$	−1.21503	−	0.356765i	−0.0599330	−	0.0175979i
$412$		0			0
$413$	−7.99824			−0.393568
$414$		0			0
$415$	5.04469			0.247634
$416$		0			0
$417$	−5.86777	−	1.72293i	−0.287346	−	0.0843723i
$418$		0			0
$419$	12.5561	−	8.06930i	0.613405	−	0.394211i	−0.196728	−	0.980458i	$-0.563032\pi$
$419$	12.5561	−	8.06930i	0.613405	−	0.394211i	0.810132	+	0.586247i	$0.199395\pi$
$420$		0			0
$421$	2.32054	−	16.1397i	0.113096	−	0.786602i	−0.851781	−	0.523899i	$-0.824477\pi$
$421$	2.32054	−	16.1397i	0.113096	−	0.786602i	0.964877	−	0.262703i	$-0.0846139\pi$
$422$		0			0
$423$	−2.81291	−	1.80775i	−0.136768	−	0.0878956i
$424$		0			0
$425$	1.12550	+	2.46451i	0.0545949	+	0.119546i
$426$		0			0
$427$	−0.489708	−	3.40600i	−0.0236987	−	0.164828i
$428$		0			0
$429$	11.2252	−	3.29601i	0.541956	−	0.159133i
$430$		0			0
$431$	3.06186	−	3.53358i	0.147485	−	0.170207i	−0.677200	−	0.735799i	$-0.736807\pi$
$431$	3.06186	−	3.53358i	0.147485	−	0.170207i	0.824685	+	0.565592i	$0.191352\pi$
$432$		0			0
$433$	−1.14944	−	1.32653i	−0.0552388	−	0.0637489i	0.727458	−	0.686153i	$-0.240702\pi$
$433$	−1.14944	−	1.32653i	−0.0552388	−	0.0637489i	−0.782696	+	0.622404i	$0.786156\pi$
$434$		0			0
$435$	−3.36519	+	7.36875i	−0.161349	+	0.353304i
$436$		0			0
$437$	2.44653	−	5.99104i	0.117034	−	0.286590i
$438$		0			0
$439$	9.49594	−	20.7932i	0.453216	−	0.992406i	−0.535765	−	0.844367i	$-0.679977\pi$
$439$	9.49594	−	20.7932i	0.453216	−	0.992406i	0.988982	−	0.148039i	$-0.0472960\pi$
$440$		0			0
$441$	−7.45108	−	8.59900i	−0.354813	−	0.409476i
$442$		0			0
$443$	−3.96981	+	4.58140i	−0.188611	+	0.217669i	−0.842178	−	0.539200i	$-0.818727\pi$
$443$	−3.96981	+	4.58140i	−0.188611	+	0.217669i	0.653566	+	0.756869i	$0.273272\pi$
$444$		0			0
$445$	14.1050	−	4.14160i	0.668641	−	0.196331i
$446$		0			0
$447$	−1.62225	−	11.2830i	−0.0767297	−	0.533667i
$448$		0			0
$449$	5.85316	+	12.8166i	0.276228	+	0.604854i	0.996000	−	0.0893565i	$-0.0284810\pi$
$449$	5.85316	+	12.8166i	0.276228	+	0.604854i	−0.719772	+	0.694210i	$0.755754\pi$
$450$		0			0
$451$	−9.85750	−	6.33503i	−0.464172	−	0.298305i
$452$		0			0
$453$	0.392852	−	2.73235i	0.0184578	−	0.128377i
$454$		0			0
$455$	−3.41762	+	2.19637i	−0.160221	+	0.102967i
$456$		0			0
$457$	20.0609	+	5.89043i	0.938412	+	0.275542i	0.714954	−	0.699171i	$-0.246448\pi$
$457$	20.0609	+	5.89043i	0.938412	+	0.275542i	0.223457	+	0.974714i	$0.428266\pi$
$458$		0			0
$459$	−14.4808			−0.675904
$460$		0			0
$461$	27.0660			1.26059			0.630295	−	0.776356i	$-0.282934\pi$
$461$	27.0660			1.26059			0.630295	+	0.776356i	$0.282934\pi$
$462$		0			0
$463$	−19.5390	−	5.73718i	−0.908056	−	0.266629i	−0.205834	−	0.978587i	$-0.565991\pi$
$463$	−19.5390	−	5.73718i	−0.908056	−	0.266629i	−0.702222	+	0.711958i	$0.747809\pi$
$464$		0			0
$465$	−5.51626	+	3.54508i	−0.255810	+	0.164399i
$466$		0			0
$467$	0.639137	−	4.44530i	0.0295757	−	0.205704i	−0.969675	−	0.244396i	$-0.921410\pi$
$467$	0.639137	−	4.44530i	0.0295757	−	0.205704i	0.999251	+	0.0386926i	$0.0123193\pi$
$468$		0			0
$469$	0.444296	+	0.285531i	0.0205157	+	0.0131846i
$470$		0			0
$471$	−8.80196	−	19.2736i	−0.405573	−	0.888081i
$472$		0			0
$473$	2.78741	+	19.3868i	0.128165	+	0.891408i
$474$		0			0
$475$	−1.29471	+	0.380160i	−0.0594052	+	0.0174429i
$476$		0			0
$477$	12.6001	−	14.5413i	0.576919	−	0.665800i
$478$		0			0
$479$	17.9184	+	20.6789i	0.818711	+	0.944843i	0.999250	−	0.0387251i	$-0.0123297\pi$
$479$	17.9184	+	20.6789i	0.818711	+	0.944843i	−0.180539	+	0.983568i	$0.557784\pi$
$480$		0			0
$481$	20.7150	−	45.3596i	0.944524	−	2.06822i
$482$		0			0
$483$	−3.28535	+	0.133795i	−0.149489	+	0.00608786i
$484$		0			0
$485$	3.39549	−	7.43510i	0.154181	−	0.337610i
$486$		0			0
$487$	8.26539	+	9.53876i	0.374540	+	0.432243i	0.911459	−	0.411392i	$-0.134957\pi$
$487$	8.26539	+	9.53876i	0.374540	+	0.432243i	−0.536918	+	0.843634i	$0.680412\pi$
$488$		0			0
$489$	−10.5100	+	12.1291i	−0.475276	+	0.548498i
$490$		0			0
$491$	−20.5430	+	6.03197i	−0.927092	+	0.272219i	−0.710219	−	0.703981i	$-0.751404\pi$
$491$	−20.5430	+	6.03197i	−0.927092	+	0.272219i	−0.216873	+	0.976200i	$0.569586\pi$
$492$		0			0
$493$	−2.75552	−	19.1651i	−0.124102	−	0.863151i
$494$		0			0
$495$	1.09476	+	2.39720i	0.0492059	+	0.107746i
$496$		0			0
$497$	−3.93745	−	2.53044i	−0.176619	−	0.113506i
$498$		0			0
$499$	2.65292	−	18.4514i	0.118761	−	0.826000i	−0.840163	−	0.542335i	$-0.817541\pi$
$499$	2.65292	−	18.4514i	0.118761	−	0.826000i	0.958923	−	0.283665i	$-0.0915504\pi$
$500$		0			0
$501$	10.6800	−	6.86363i	0.477148	−	0.306645i
$502$		0			0
$503$	−16.9785	−	4.98533i	−0.757033	−	0.222285i	−0.119633	−	0.992818i	$-0.538172\pi$
$503$	−16.9785	−	4.98533i	−0.757033	−	0.222285i	−0.637400	+	0.770533i	$0.719990\pi$
$504$		0			0
$505$	−1.10882			−0.0493417
$506$		0			0
$507$	36.4031			1.61672
$508$		0			0
$509$	24.5081	+	7.19623i	1.08630	+	0.318967i	0.775398	−	0.631473i	$-0.217549\pi$
$509$	24.5081	+	7.19623i	1.08630	+	0.318967i	0.310906	+	0.950441i	$0.399368\pi$
$510$		0			0
$511$	−4.08659	+	2.62629i	−0.180780	+	0.116180i
$512$		0			0
$513$	1.02638	−	7.13861i	0.0453157	−	0.315177i
$514$		0			0
$515$	−3.87775	−	2.49208i	−0.170874	−	0.109814i
$516$		0			0
$517$	1.24446	+	2.72499i	0.0547314	+	0.119845i
$518$		0			0
$519$	−0.679830	−	4.72832i	−0.0298412	−	0.207550i
$520$		0			0
$521$	−2.62243	+	0.770014i	−0.114891	+	0.0337349i	−0.338672	−	0.940904i	$-0.609978\pi$
$521$	−2.62243	+	0.770014i	−0.114891	+	0.0337349i	0.223782	+	0.974639i	$0.428160\pi$
$522$		0			0
$523$	−9.66115	+	11.1496i	−0.422453	+	0.487536i	−0.926583	−	0.376092i	$-0.877268\pi$
$523$	−9.66115	+	11.1496i	−0.422453	+	0.487536i	0.504130	+	0.863628i	$0.331813\pi$
$524$		0			0
$525$	0.448980	+	0.518150i	0.0195951	+	0.0226139i
$526$		0			0
$527$	6.51066	−	14.2564i	0.283609	−	0.621017i
$528$		0			0
$529$	−13.5985	+	18.5494i	−0.591239	+	0.806496i
$530$		0			0
$531$	−9.42152	+	20.6302i	−0.408859	+	0.895277i
$532$		0			0
$533$	−33.5422	−	38.7098i	−1.45288	−	1.67671i
$534$		0			0
$535$	−3.04345	+	3.51233i	−0.131580	+	0.151851i
$536$		0			0
$537$	−12.9018	+	3.78831i	−0.556754	+	0.163478i
$538$		0			0
$539$	1.45075	+	10.0902i	0.0624880	+	0.434614i
$540$		0			0
$541$	−4.75777	−	10.4181i	−0.204553	−	0.447908i	0.779356	−	0.626582i	$-0.215547\pi$
$541$	−4.75777	−	10.4181i	−0.204553	−	0.447908i	−0.983908	+	0.178674i	$0.942819\pi$
$542$		0			0
$543$	−7.28461	−	4.68153i	−0.312612	−	0.200904i
$544$		0			0
$545$	−2.09871	+	14.5968i	−0.0898988	+	0.625260i
$546$		0			0
$547$	−22.3409	+	14.3576i	−0.955230	+	0.613889i	−0.922674	−	0.385581i	$-0.874001\pi$
$547$	−22.3409	+	14.3576i	−0.955230	+	0.613889i	−0.0325556	+	0.999470i	$0.510365\pi$
$548$		0			0
$549$	−9.36210	−	2.74896i	−0.399565	−	0.117323i
$550$		0			0
$551$	9.64315			0.410812
$552$		0			0
$553$	−4.57246			−0.194441
$554$		0			0
$555$	−8.07470	−	2.37094i	−0.342752	−	0.100641i
$556$		0			0
$557$	14.6169	−	9.39368i	0.619336	−	0.398023i	−0.193012	−	0.981196i	$-0.561826\pi$
$557$	14.6169	−	9.39368i	0.619336	−	0.398023i	0.812348	+	0.583173i	$0.198189\pi$
$558$		0			0
$559$	−12.1844	+	84.7443i	−0.515345	+	3.58430i
$560$		0			0
$561$	3.96994	+	2.55133i	0.167611	+	0.107717i
$562$		0			0
$563$	9.27208	+	20.3030i	0.390772	+	0.855671i	0.998123	+	0.0612375i	$0.0195047\pi$
$563$	9.27208	+	20.3030i	0.390772	+	0.855671i	−0.607351	+	0.794433i	$0.707768\pi$
$564$		0			0
$565$	−1.10419	−	7.67982i	−0.0464537	−	0.323093i
$566$		0			0
$567$	−0.530014	+	0.155626i	−0.0222585	+	0.00653568i
$568$		0			0
$569$	9.87067	−	11.3914i	0.413800	−	0.477551i	−0.510138	−	0.860092i	$-0.670406\pi$
$569$	9.87067	−	11.3914i	0.413800	−	0.477551i	0.923938	+	0.382542i	$0.124951\pi$
$570$		0			0
$571$	23.0246	+	26.5718i	0.963550	+	1.11200i	0.993657	+	0.112450i	$0.0358697\pi$
$571$	23.0246	+	26.5718i	0.963550	+	1.11200i	−0.0301071	+	0.999547i	$0.509585\pi$
$572$		0			0
$573$	11.0413	−	24.1771i	0.461258	−	1.01001i
$574$		0			0
$575$	4.79186	−	0.195146i	0.199834	−	0.00813817i
$576$		0			0
$577$	−10.6259	+	23.2675i	−0.442362	+	0.968638i	0.548796	+	0.835956i	$0.315086\pi$
$577$	−10.6259	+	23.2675i	−0.442362	+	0.968638i	−0.991159	+	0.132682i	$0.957641\pi$
$578$		0			0
$579$	−3.22456	−	3.72134i	−0.134008	−	0.154654i
$580$		0			0
$581$	−1.99813	+	2.30596i	−0.0828963	+	0.0956674i
$582$		0			0
$583$	−16.5401	+	4.85661i	−0.685021	+	0.201140i
$584$		0			0
$585$	1.63942	+	11.4024i	0.0677818	+	0.471433i
$586$		0			0
$587$	−16.8105	−	36.8099i	−0.693844	−	1.51931i	−0.847280	−	0.531147i	$-0.821761\pi$
$587$	−16.8105	−	36.8099i	−0.693844	−	1.51931i	0.153436	−	0.988159i	$-0.450966\pi$
$588$		0			0
$589$	6.56652	+	4.22005i	0.270569	+	0.173884i
$590$		0			0
$591$	0.735624	−	5.11638i	0.0302595	−	0.210460i
$592$		0			0
$593$	13.3396	−	8.57281i	0.547790	−	0.352043i	−0.237289	−	0.971439i	$-0.576259\pi$
$593$	13.3396	−	8.57281i	0.547790	−	0.352043i	0.785079	+	0.619396i	$0.212622\pi$
$594$		0			0
$595$	−1.57234	−	0.461680i	−0.0644595	−	0.0189270i
$596$		0			0
$597$	14.0924			0.576763
$598$		0			0
$599$	21.4220			0.875281			0.437640	−	0.899150i	$-0.355814\pi$
$599$	21.4220			0.875281			0.437640	+	0.899150i	$0.355814\pi$
$600$		0			0
$601$	−8.77618	−	2.57692i	−0.357988	−	0.105115i	0.0977930	−	0.995207i	$-0.468822\pi$
$601$	−8.77618	−	2.57692i	−0.357988	−	0.105115i	−0.455781	+	0.890092i	$0.650640\pi$
$602$		0			0
$603$	1.25984	−	0.809651i	0.0513047	−	0.0329716i
$604$		0			0
$605$	−1.22945	+	8.55100i	−0.0499842	+	0.347647i
$606$		0			0
$607$	6.53254	+	4.19821i	0.265148	+	0.170400i	0.666459	−	0.745542i	$-0.267809\pi$
$607$	6.53254	+	4.19821i	0.265148	+	0.170400i	−0.401311	+	0.915942i	$0.631445\pi$
$608$		0			0
$609$	−2.03540	−	4.45690i	−0.0824785	−	0.180603i
$610$		0			0
$611$	1.86360	+	12.9616i	0.0753932	+	0.524372i
$612$		0			0
$613$	−10.9755	+	3.22269i	−0.443296	+	0.130163i	−0.495760	−	0.868459i	$-0.665111\pi$
$613$	−10.9755	+	3.22269i	−0.443296	+	0.130163i	0.0524646	+	0.998623i	$0.483292\pi$
$614$		0			0
$615$	−5.66074	+	6.53284i	−0.228263	+	0.263430i
$616$		0			0
$617$	22.4817	+	25.9453i	0.905079	+	1.04452i	0.998803	+	0.0489182i	$0.0155774\pi$
$617$	22.4817	+	25.9453i	0.905079	+	1.04452i	−0.0937241	+	0.995598i	$0.529877\pi$
$618$		0			0
$619$	−15.3477	+	33.6067i	−0.616875	+	1.35077i	0.300896	+	0.953657i	$0.402714\pi$
$619$	−15.3477	+	33.6067i	−0.616875	+	1.35077i	−0.917771	+	0.397110i	$0.870013\pi$
$620$		0			0
$621$	−9.69056	+	23.7301i	−0.388869	+	0.952257i
$622$		0			0
$623$	−3.69362	+	8.08790i	−0.147982	+	0.324035i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$		0			0
$627$	−1.53912	+	1.77624i	−0.0614664	+	0.0709360i
$628$		0			0
$629$	19.2998	−	5.66692i	0.769532	−	0.225955i
$630$		0			0
$631$	−1.05497	−	7.33746i	−0.0419976	−	0.292099i	−0.999986	−	0.00529264i	$-0.998315\pi$
$631$	−1.05497	−	7.33746i	−0.0419976	−	0.292099i	0.957988	−	0.286807i	$-0.0925938\pi$
$632$		0			0
$633$	9.84440	+	21.5562i	0.391280	+	0.856783i
$634$		0			0
$635$	6.56220	+	4.21727i	0.260413	+	0.167357i
$636$		0			0
$637$	−6.34154	+	44.1064i	−0.251261	+	1.74756i
$638$		0			0
$639$	−11.1650	+	7.17531i	−0.441681	+	0.283851i
$640$		0			0
$641$	−23.8842	−	7.01305i	−0.943371	−	0.276999i	−0.226346	−	0.974047i	$-0.572678\pi$
$641$	−23.8842	−	7.01305i	−0.943371	−	0.276999i	−0.717024	+	0.697048i	$0.754496\pi$
$642$		0			0
$643$	46.6202			1.83852			0.919261	−	0.393649i	$-0.128787\pi$
$643$	46.6202			1.83852			0.919261	+	0.393649i	$0.128787\pi$
$644$		0			0
$645$	14.4489			0.568925
$646$		0			0
$647$	−17.4305	−	5.11805i	−0.685263	−	0.201211i	−0.0794740	−	0.996837i	$-0.525324\pi$
$647$	−17.4305	−	5.11805i	−0.685263	−	0.201211i	−0.605789	+	0.795626i	$0.707142\pi$
$648$		0			0
$649$	17.0937	−	10.9855i	0.670987	−	0.431217i
$650$		0			0
$651$	0.564426	−	3.92567i	0.0221216	−	0.153859i
$652$		0			0
$653$	−1.59190	−	1.02306i	−0.0622960	−	0.0400352i	0.509122	−	0.860694i	$-0.329970\pi$
$653$	−1.59190	−	1.02306i	−0.0622960	−	0.0400352i	−0.571418	+	0.820659i	$0.693607\pi$
$654$		0			0
$655$	−8.44880	−	18.5003i	−0.330122	−	0.722866i
$656$		0			0
$657$	1.96033	+	13.6344i	0.0764796	+	0.531927i
$658$		0			0
$659$	1.82929	−	0.537127i	0.0712589	−	0.0209235i	−0.245909	−	0.969293i	$-0.579086\pi$
$659$	1.82929	−	0.537127i	0.0712589	−	0.0209235i	0.317168	+	0.948369i	$0.397268\pi$
$660$		0			0
$661$	0.337680	−	0.389704i	0.0131342	−	0.0151577i	−0.749144	−	0.662407i	$-0.769535\pi$
$661$	0.337680	−	0.389704i	0.0131342	−	0.0151577i	0.762279	+	0.647249i	$0.224081\pi$
$662$		0			0
$663$	13.5086	+	15.5897i	0.524630	+	0.605455i
$664$		0			0
$665$	0.339040	−	0.742394i	0.0131474	−	0.0287888i
$666$		0			0
$667$	−33.2505	−	8.30974i	−1.28746	−	0.321754i
$668$		0			0
$669$	7.36623	−	16.1298i	0.284795	−	0.623614i
$670$		0			0
$671$	5.72468	+	6.60664i	0.220999	+	0.255046i
$672$		0			0
$673$	−10.1441	+	11.7069i	−0.391026	+	0.451268i	−0.916794	−	0.399360i	$-0.869232\pi$
$673$	−10.1441	+	11.7069i	−0.391026	+	0.451268i	0.525768	+	0.850628i	$0.323778\pi$
$674$		0			0
$675$	5.12825	−	1.50579i	0.197386	−	0.0579579i
$676$		0			0
$677$	6.06494	+	42.1826i	0.233095	+	1.62121i	0.684585	+	0.728933i	$0.259983\pi$
$677$	6.06494	+	42.1826i	0.233095	+	1.62121i	−0.451490	+	0.892276i	$0.649107\pi$
$678$		0			0
$679$	2.05373	+	4.49703i	0.0788147	+	0.172580i
$680$		0			0
$681$	−4.88108	−	3.13688i	−0.187044	−	0.120206i
$682$		0			0
$683$	7.11009	−	49.4518i	0.272060	−	1.89222i	−0.154871	−	0.987935i	$-0.549496\pi$
$683$	7.11009	−	49.4518i	0.272060	−	1.89222i	0.426931	−	0.904284i	$-0.359595\pi$
$684$		0			0
$685$	−0.939796	+	0.603970i	−0.0359078	+	0.0230765i
$686$		0			0
$687$	−22.7669	−	6.68496i	−0.868611	−	0.255047i
$688$		0			0
$689$	−75.3528			−2.87071
$690$		0			0
$691$	−15.0571			−0.572798			−0.286399	−	0.958110i	$-0.592458\pi$
$691$	−15.0571			−0.572798			−0.286399	+	0.958110i	$0.592458\pi$
$692$		0			0
$693$	−1.52939	−	0.449070i	−0.0580968	−	0.0170588i
$694$		0			0
$695$	−4.53857	+	2.91676i	−0.172158	+	0.110639i
$696$		0			0
$697$	2.94036	−	20.4506i	0.111374	−	0.774623i
$698$		0			0
$699$	5.20768	+	3.34678i	0.196973	+	0.126587i
$700$		0			0
$701$	16.5936	+	36.3349i	0.626731	+	1.37235i	0.910521	+	0.413463i	$0.135681\pi$
$701$	16.5936	+	36.3349i	0.626731	+	1.37235i	−0.283790	+	0.958887i	$0.591592\pi$
$702$		0			0
$703$	1.42569	+	9.91590i	0.0537710	+	0.373985i
$704$		0			0
$705$	2.12044	−	0.622617i	0.0798603	−	0.0234491i
$706$		0			0
$707$	0.439185	−	0.506847i	0.0165173	−	0.0190619i
$708$		0			0
$709$	9.02378	+	10.4140i	0.338895	+	0.391106i	0.899459	−	0.437006i	$-0.143961\pi$
$709$	9.02378	+	10.4140i	0.338895	+	0.391106i	−0.560564	+	0.828111i	$0.689416\pi$
$710$		0			0
$711$	−5.38612	+	11.7940i	−0.201995	+	0.442308i
$712$		0			0
$713$	−19.0054	−	20.2096i	−0.711759	−	0.756857i
$714$		0			0
$715$	4.28740	−	9.38810i	0.160340	−	0.351095i
$716$		0			0
$717$	−1.47932	−	1.70722i	−0.0552461	−	0.0637574i
$718$		0			0
$719$	22.6723	−	26.1653i	0.845536	−	0.975800i	−0.154390	−	0.988010i	$-0.549341\pi$
$719$	22.6723	−	26.1653i	0.845536	−	0.975800i	0.999925	+	0.0122097i	$0.00388656\pi$
$720$		0			0
$721$	2.67506	−	0.785470i	0.0996246	−	0.0292524i
$722$		0			0
$723$	−1.96670	−	13.6787i	−0.0731422	−	0.508715i
$724$		0			0
$725$	2.96874	+	6.50062i	0.110256	+	0.241427i
$726$		0			0
$727$	−17.6170	−	11.3217i	−0.653378	−	0.419900i	0.171521	−	0.985180i	$-0.445132\pi$
$727$	−17.6170	−	11.3217i	−0.653378	−	0.419900i	−0.824899	+	0.565280i	$0.808768\pi$
$728$		0			0
$729$	−2.80956	+	19.5409i	−0.104058	+	0.723739i
$730$		0			0
$731$	−29.0527	+	18.6711i	−1.07455	+	0.690574i
$732$		0			0
$733$	−28.5789	−	8.39151i	−1.05558	−	0.309947i	−0.292513	−	0.956262i	$-0.594491\pi$
$733$	−28.5789	−	8.39151i	−1.05558	−	0.309947i	−0.763071	+	0.646314i	$0.776310\pi$
$734$		0			0
$735$	7.52013			0.277384
$736$		0			0
$737$	−1.34171			−0.0494227
$738$		0			0
$739$	17.9643	+	5.27480i	0.660828	+	0.194037i	0.594915	−	0.803789i	$-0.297186\pi$
$739$	17.9643	+	5.27480i	0.660828	+	0.194037i	0.0659134	+	0.997825i	$0.479004\pi$
$740$		0			0
$741$	−8.64277	+	5.55437i	−0.317500	+	0.204045i
$742$		0			0
$743$	−1.81167	+	12.6005i	−0.0664638	+	0.462266i	0.929225	+	0.369513i	$0.120476\pi$
$743$	−1.81167	+	12.6005i	−0.0664638	+	0.462266i	−0.995689	+	0.0927524i	$0.970433\pi$
$744$		0			0
$745$	−8.45970	−	5.43672i	−0.309940	−	0.199186i
$746$		0			0
$747$	3.59419	+	7.87017i	0.131504	+	0.287954i
$748$		0			0
$749$	−0.400043	−	2.78236i	−0.0146173	−	0.101665i
$750$		0			0
$751$	43.6038	−	12.8032i	1.59113	−	0.467197i	0.638067	−	0.769981i	$-0.279734\pi$
$751$	43.6038	−	12.8032i	1.59113	−	0.467197i	0.953059	+	0.302784i	$0.0979160\pi$
$752$		0			0
$753$	21.2543	−	24.5288i	0.774551	−	0.893880i
$754$		0			0
$755$	−1.59474	−	1.84043i	−0.0580385	−	0.0669800i
$756$		0			0
$757$	−11.4713	+	25.1187i	−0.416933	+	0.912955i	0.578337	+	0.815798i	$0.303702\pi$
$757$	−11.4713	+	25.1187i	−0.416933	+	0.912955i	−0.995269	+	0.0971567i	$0.969025\pi$
$758$		0			0
$759$	6.83764	−	4.79833i	0.248191	−	0.174168i
$760$		0			0
$761$	15.6959	−	34.3693i	0.568977	−	1.24589i	−0.378364	−	0.925657i	$-0.623513\pi$
$761$	15.6959	−	34.3693i	0.568977	−	1.24589i	0.947340	−	0.320228i	$-0.103760\pi$
$762$		0			0
$763$	−5.84104	−	6.74092i	−0.211460	−	0.244038i
$764$		0			0
$765$	−3.04296	+	3.51177i	−0.110019	+	0.126968i
$766$		0			0
$767$	85.2226	−	25.0236i	3.07721	−	0.903550i
$768$		0			0
$769$	5.31014	+	36.9328i	0.191489	+	1.33183i	0.828071	+	0.560624i	$0.189439\pi$
$769$	5.31014	+	36.9328i	0.191489	+	1.33183i	−0.636582	+	0.771209i	$0.719652\pi$
$770$		0			0
$771$	9.32334	+	20.4153i	0.335772	+	0.735238i
$772$		0			0
$773$	−11.3227	−	7.27669i	−0.407251	−	0.261724i	0.320939	−	0.947100i	$-0.396002\pi$
$773$	−11.3227	−	7.27669i	−0.407251	−	0.261724i	−0.728190	+	0.685376i	$0.759638\pi$
$774$		0			0
$775$	−0.823245	+	5.72579i	−0.0295718	+	0.205677i
$776$		0			0
$777$	4.28204	−	2.75190i	0.153617	−	0.0987238i
$778$		0			0
$779$	9.87317	+	2.89902i	0.353743	+	0.103868i
$780$		0			0
$781$	11.8906			0.425478
$782$		0			0
$783$	−38.1959			−1.36501
$784$		0			0
$785$	−17.9350	−	5.26618i	−0.640126	−	0.187958i
$786$		0			0
$787$	−30.8251	+	19.8101i	−1.09880	+	0.706154i	−0.958824	−	0.284001i	$-0.908338\pi$
$787$	−30.8251	+	19.8101i	−1.09880	+	0.706154i	−0.139973	+	0.990155i	$0.544702\pi$
$788$		0			0
$789$	−3.12819	+	21.7571i	−0.111367	+	0.774572i
$790$		0			0
$791$	3.94785	+	2.53713i	0.140369	+	0.0902099i
$792$		0			0
$793$	15.8741	+	34.7593i	0.563704	+	1.23434i
$794$		0			0
$795$	1.80980	+	12.5874i	0.0641870	+	0.446430i
$796$		0			0
$797$	−4.44235	+	1.30439i	−0.157356	+	0.0462039i	−0.359462	−	0.933160i	$-0.617040\pi$
$797$	−4.44235	+	1.30439i	−0.157356	+	0.0462039i	0.202106	+	0.979364i	$0.435222\pi$
$798$		0			0
$799$	−3.45906	+	3.99197i	−0.122373	+	0.141226i
$800$		0			0
$801$	16.5106	+	19.0543i	0.583374	+	0.673249i
$802$		0			0
$803$	5.12662	−	11.2257i	0.180915	−	0.396148i
$804$		0			0
$805$	−1.80878	+	2.26768i	−0.0637511	+	0.0799254i
$806$		0			0
$807$	1.55059	−	3.39531i	0.0545832	−	0.119521i
$808$		0			0
$809$	−27.8217	−	32.1080i	−0.978159	−	1.12886i	−0.991651	−	0.128947i	$-0.958840\pi$
$809$	−27.8217	−	32.1080i	−0.978159	−	1.12886i	0.0134920	−	0.999909i	$-0.495705\pi$
$810$		0			0
$811$	−6.43286	+	7.42392i	−0.225888	+	0.260689i	−0.857369	−	0.514703i	$-0.827902\pi$
$811$	−6.43286	+	7.42392i	−0.225888	+	0.260689i	0.631480	+	0.775392i	$0.282448\pi$
$812$		0			0
$813$	−28.2555	+	8.29656i	−0.990964	+	0.290973i
$814$		0			0
$815$	2.01495	+	14.0143i	0.0705805	+	0.490898i
$816$		0			0
$817$	−7.14509	−	15.6456i	−0.249975	−	0.547369i
$818$		0			0
$819$	−5.86148	−	3.76694i	−0.204817	−	0.131628i
$820$		0			0
$821$	−3.57872	+	24.8906i	−0.124898	+	0.868686i	0.826985	+	0.562225i	$0.190054\pi$
$821$	−3.57872	+	24.8906i	−0.124898	+	0.868686i	−0.951883	+	0.306462i	$0.900855\pi$
$822$		0			0
$823$	37.3002	−	23.9714i	1.30020	−	0.835590i	0.306970	−	0.951719i	$-0.400685\pi$
$823$	37.3002	−	23.9714i	1.30020	−	0.835590i	0.993234	+	0.116129i	$0.0370486\pi$
$824$		0			0
$825$	−1.67123	−	0.490716i	−0.0581846	−	0.0170845i
$826$		0			0
$827$	51.3062			1.78409			0.892045	−	0.451946i	$-0.149270\pi$
$827$	51.3062			1.78409			0.892045	+	0.451946i	$0.149270\pi$
$828$		0			0
$829$	−7.04144			−0.244559			−0.122280	−	0.992496i	$-0.539020\pi$
$829$	−7.04144			−0.244559			−0.122280	+	0.992496i	$0.539020\pi$
$830$		0			0
$831$	−8.05441	−	2.36499i	−0.279405	−	0.0820406i
$832$		0			0
$833$	−15.1209	+	9.71762i	−0.523908	+	0.336695i
$834$		0			0
$835$	1.59388	−	11.0857i	0.0551586	−	0.383637i
$836$		0			0
$837$	−26.0096	−	16.7153i	−0.899022	−	0.577766i
$838$		0			0
$839$	−8.89735	−	19.4825i	−0.307171	−	0.672610i	0.691595	−	0.722286i	$-0.256908\pi$
$839$	−8.89735	−	19.4825i	−0.307171	−	0.672610i	−0.998765	+	0.0496758i	$0.984181\pi$
$840$		0			0
$841$	−3.14110	−	21.8468i	−0.108314	−	0.753339i
$842$		0			0
$843$	−15.1946	+	4.46153i	−0.523329	+	0.153663i
$844$		0			0
$845$	21.0305	−	24.2705i	0.723470	−	0.834929i
$846$		0			0
$847$	−3.42175	−	3.94891i	−0.117573	−	0.135686i
$848$		0			0
$849$	12.3118	−	26.9592i	0.422541	−	0.925236i
$850$		0			0
$851$	3.62886	−	35.4195i	0.124396	−	1.21416i
$852$		0			0
$853$	−24.2367	+	53.0710i	−0.829849	+	1.81712i	−0.370739	+	0.928737i	$0.620895\pi$
$853$	−24.2367	+	53.0710i	−0.829849	+	1.81712i	−0.459110	+	0.888379i	$0.651832\pi$
$854$		0			0
$855$	−1.51552	−	1.74900i	−0.0518297	−	0.0598147i
$856$		0			0
$857$	−11.1538	+	12.8721i	−0.381005	+	0.439703i	−0.913567	−	0.406687i	$-0.866684\pi$
$857$	−11.1538	+	12.8721i	−0.381005	+	0.439703i	0.532562	+	0.846391i	$0.321229\pi$
$858$		0			0
$859$	0.682598	−	0.200429i	0.0232899	−	0.00683854i	−0.270067	−	0.962842i	$-0.587046\pi$
$859$	0.682598	−	0.200429i	0.0232899	−	0.00683854i	0.293357	+	0.956003i	$0.405228\pi$
$860$		0			0
$861$	−0.744070	−	5.17512i	−0.0253578	−	0.176368i
$862$		0			0
$863$	10.0100	+	21.9189i	0.340745	+	0.746128i	0.999983	−	0.00580618i	$-0.00184817\pi$
$863$	10.0100	+	21.9189i	0.340745	+	0.746128i	−0.659238	+	0.751935i	$0.729121\pi$
$864$		0			0
$865$	−3.54518	−	2.27835i	−0.120540	−	0.0774662i
$866$		0			0
$867$	1.55826	−	10.8380i	0.0529214	−	0.368077i
$868$		0			0
$869$	9.77219	−	6.28020i	0.331499	−	0.213041i
$870$		0			0
$871$	−5.62737	−	1.65234i	−0.190676	−	0.0559875i
$872$		0			0
$873$	14.0186			0.474457
$874$		0			0
$875$	0.604838			0.0204473
$876$		0			0
$877$	−43.2243	−	12.6918i	−1.45958	−	0.428572i	−0.546884	−	0.837208i	$-0.684186\pi$
$877$	−43.2243	−	12.6918i	−1.45958	−	0.428572i	−0.912697	+	0.408637i	$0.866004\pi$
$878$		0			0
$879$	4.73837	−	3.04517i	0.159821	−	0.102711i
$880$		0			0
$881$	−6.25347	+	43.4938i	−0.210685	+	1.46534i	0.560194	+	0.828362i	$0.310727\pi$
$881$	−6.25347	+	43.4938i	−0.210685	+	1.46534i	−0.770878	+	0.636982i	$0.780182\pi$
$882$		0			0
$883$	−4.84091	−	3.11106i	−0.162910	−	0.104696i	0.456646	−	0.889649i	$-0.349051\pi$
$883$	−4.84091	−	3.11106i	−0.162910	−	0.104696i	−0.619555	+	0.784953i	$0.712687\pi$
$884$		0			0
$885$	−6.22696	−	13.6351i	−0.209317	−	0.458340i
$886$		0			0
$887$	−3.34456	−	23.2619i	−0.112299	−	0.781059i	−0.965673	−	0.259760i	$-0.916357\pi$
$887$	−3.34456	−	23.2619i	−0.112299	−	0.781059i	0.853374	−	0.521299i	$-0.174553\pi$
$888$		0			0
$889$	−4.52693	+	1.32923i	−0.151828	+	0.0445808i
$890$		0			0
$891$	0.918987	−	1.06057i	0.0307872	−	0.0355303i
$892$		0			0
$893$	−1.72276	−	1.98817i	−0.0576498	−	0.0665314i
$894$		0			0
$895$	−4.92779	+	10.7903i	−0.164718	+	0.360682i
$896$		0			0
$897$	34.5874	−	11.7043i	1.15484	−	0.390795i
$898$		0			0
$899$	17.1732	−	37.6040i	0.572757	−	1.25416i
$900$		0			0
$901$	−19.9047	−	22.9712i	−0.663121	−	0.765282i
$902$		0			0
$903$	−5.72299	+	6.60468i	−0.190449	+	0.219790i
$904$		0			0
$905$	−7.32964	+	2.15218i	−0.243645	+	0.0715407i
$906$		0			0
$907$	5.94833	+	41.3715i	0.197511	+	1.37372i	0.811476	+	0.584386i	$0.198665\pi$
$907$	5.94833	+	41.3715i	0.197511	+	1.37372i	−0.613965	+	0.789334i	$0.710426\pi$
$908$		0			0
$909$	−0.789997	−	1.72985i	−0.0262025	−	0.0573755i
$910$		0			0
$911$	43.1471	+	27.7290i	1.42953	+	0.918702i	0.999877	+	0.0157075i	$0.00500006\pi$
$911$	43.1471	+	27.7290i	1.42953	+	0.918702i	0.429652	+	0.902995i	$0.358636\pi$
$912$		0			0
$913$	1.10316	−	7.67266i	0.0365094	−	0.253928i
$914$		0			0
$915$	5.42517	−	3.48655i	0.179351	−	0.115262i
$916$		0			0
$917$	11.8030	+	3.46568i	0.389771	+	0.114447i
$918$		0			0
$919$	−30.5729			−1.00851			−0.504254	−	0.863556i	$-0.668232\pi$
$919$	−30.5729			−1.00851			−0.504254	+	0.863556i	$0.668232\pi$
$920$		0			0
$921$	8.20016			0.270205
$922$		0			0
$923$	49.8710	+	14.6434i	1.64152	+	0.481995i
$924$		0			0
$925$	−6.24558	+	4.01379i	−0.205353	+	0.131973i
$926$		0			0
$927$	1.12509	−	7.82516i	0.0369528	−	0.257012i
$928$		0			0
$929$	−21.5338	−	13.8389i	−0.706502	−	0.454041i	0.137416	−	0.990513i	$-0.456120\pi$
$929$	−21.5338	−	13.8389i	−0.706502	−	0.454041i	−0.843918	+	0.536472i	$0.819757\pi$
$930$		0			0
$931$	−3.71876	−	8.14295i	−0.121877	−	0.266874i
$932$		0			0
$933$	0.0122701	+	0.0853401i	0.000401704	+	0.00279391i
$934$		0			0
$935$	3.99448	−	1.17289i	0.130634	−	0.0383575i
$936$		0			0
$937$	1.07395	−	1.23941i	0.0350845	−	0.0404897i	−0.737936	−	0.674871i	$-0.764199\pi$
$937$	1.07395	−	1.23941i	0.0350845	−	0.0404897i	0.773021	+	0.634381i	$0.218745\pi$
$938$		0			0
$939$	7.86434	+	9.07594i	0.256643	+	0.296182i
$940$		0			0
$941$	17.2124	−	37.6899i	0.561108	−	1.22866i	−0.390290	−	0.920692i	$-0.627625\pi$
$941$	17.2124	−	37.6899i	0.561108	−	1.22866i	0.951398	−	0.307963i	$-0.0996474\pi$
$942$		0			0
$943$	−31.5454	−	18.5041i	−1.02726	−	0.602575i
$944$		0			0
$945$	−1.34292	+	2.94058i	−0.0436851	+	0.0956569i
$946$		0			0
$947$	1.03339	+	1.19259i	0.0335805	+	0.0387540i	0.772291	−	0.635268i	$-0.219111\pi$
$947$	1.03339	+	1.19259i	0.0335805	+	0.0387540i	−0.738711	+	0.674022i	$0.764565\pi$
$948$		0			0
$949$	35.3266	−	40.7690i	1.14675	−	1.32342i
$950$		0			0
$951$	7.45305	−	2.18841i	0.241682	−	0.0709641i
$952$		0			0
$953$	−1.05724	−	7.35325i	−0.0342473	−	0.238195i	0.965507	−	0.260378i	$-0.0838473\pi$
$953$	−1.05724	−	7.35325i	−0.0342473	−	0.238195i	−0.999754	+	0.0221833i	$0.992938\pi$
$954$		0			0
$955$	−9.74053	−	21.3288i	−0.315196	−	0.690183i
$956$		0			0
$957$	10.4715	+	6.72963i	0.338496	+	0.217538i
$958$		0			0
$959$	0.0961604	−	0.668810i	0.00310518	−	0.0215970i
$960$		0			0
$961$	2.07153	−	1.33129i	0.0668236	−	0.0429449i
$962$		0			0
$963$	−7.64790	−	2.24563i	−0.246450	−	0.0723643i
$964$		0			0
$965$	−4.34393			−0.139836
$966$		0			0
$967$	31.5748			1.01538			0.507688	−	0.861541i	$-0.330500\pi$
$967$	31.5748			1.01538			0.507688	+	0.861541i	$0.330500\pi$
$968$		0			0
$969$	−3.97626	−	1.16753i	−0.127736	−	0.0375066i
$970$		0			0
$971$	24.7615	−	15.9132i	0.794634	−	0.510680i	−0.0792269	−	0.996857i	$-0.525245\pi$
$971$	24.7615	−	15.9132i	0.794634	−	0.510680i	0.873861	+	0.486177i	$0.161609\pi$
$972$		0			0
$973$	0.464389	−	3.22990i	0.0148876	−	0.103546i
$974$		0			0
$975$	−6.40506	−	4.11628i	−0.205126	−	0.131827i
$976$		0			0
$977$	−1.22565	−	2.68380i	−0.0392120	−	0.0858623i	0.889012	−	0.457883i	$-0.151392\pi$
$977$	−1.22565	−	2.68380i	−0.0392120	−	0.0858623i	−0.928224	+	0.372021i	$0.878665\pi$
$978$		0			0
$979$	−3.21466	−	22.3585i	−0.102741	−	0.714580i
$980$		0			0
$981$	−24.2676	+	7.12562i	−0.774806	+	0.227503i
$982$		0			0
$983$	7.69621	−	8.88190i	0.245471	−	0.283289i	−0.619622	−	0.784901i	$-0.712714\pi$
$983$	7.69621	−	8.88190i	0.245471	−	0.283289i	0.865093	+	0.501612i	$0.167259\pi$
$984$		0			0
$985$	−2.98618	−	3.44624i	−0.0951477	−	0.109806i
$986$		0			0
$987$	−0.555271	+	1.21587i	−0.0176745	+	0.0387017i
$988$		0			0
$989$	11.1548	+	60.1044i	0.354700	+	1.91121i
$990$		0			0
$991$	−5.56058	+	12.1760i	−0.176638	+	0.386782i	−0.977155	−	0.212527i	$-0.931831\pi$
$991$	−5.56058	+	12.1760i	−0.176638	+	0.386782i	0.800518	+	0.599309i	$0.204558\pi$
$992$		0			0
$993$	21.7185	+	25.0645i	0.689216	+	0.795398i
$994$		0			0
$995$	8.14132	−	9.39558i	0.258097	−	0.297860i
$996$		0			0
$997$	−50.0722	+	14.7025i	−1.58580	+	0.465634i	−0.951551	−	0.307492i	$-0.900510\pi$
$997$	−50.0722	+	14.7025i	−1.58580	+	0.465634i	−0.634253	+	0.773126i	$0.718692\pi$
$998$		0			0
$999$	−5.64707	−	39.2763i	−0.178665	−	1.24265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.121.2	✓	50
23.4	even	11	inner	460.2.m.b.441.2	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.121.2	✓	50	1.1	even	1	trivial
460.2.m.b.441.2	yes	50	23.4	even	11	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08763 - 0.319356i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0860775 - 0.598682i) q^{7} +(-1.44281 - 0.927240i) q^{9} +O(q^{10})\)	\(q+(-1.08763 - 0.319356i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0860775 - 0.598682i) q^{7} +(-1.44281 - 0.927240i) q^{9} +(0.638317 + 1.39772i) q^{11} +(0.955890 + 6.64836i) q^{13} +(1.08763 - 0.319356i) q^{15} +(-1.77424 + 2.04759i) q^{17} +(-0.883646 - 1.01978i) q^{19} +(-0.284813 + 0.623654i) q^{21} +(2.16812 + 4.27776i) q^{23} +(0.415415 - 0.909632i) q^{25} +(3.50007 + 4.03929i) q^{27} +(-4.67992 + 5.40091i) q^{29} +(-5.55035 + 1.62973i) q^{31} +(-0.247881 - 1.72405i) q^{33} +(0.251259 + 0.550180i) q^{35} +(-6.24558 - 4.01379i) q^{37} +(1.08354 - 7.53621i) q^{39} +(-6.41523 + 4.12282i) q^{41} +(12.2303 + 3.59114i) q^{43} +1.71508 q^{45} +1.94960 q^{47} +(6.36544 + 1.86906i) q^{49} +(2.58363 - 1.66040i) q^{51} +(-1.59658 + 11.1045i) q^{53} +(-1.29265 - 0.830737i) q^{55} +(0.635405 + 1.39134i) q^{57} +(-1.88194 - 13.0892i) q^{59} +(5.45871 - 1.60282i) q^{61} +(-0.679316 + 0.783972i) q^{63} +(-4.39852 - 5.07616i) q^{65} +(-0.362734 + 0.794276i) q^{67} +(-0.991980 - 5.34502i) q^{69} +(3.21463 - 7.03905i) q^{71} +(-5.25949 - 6.06978i) q^{73} +(-0.742314 + 0.856676i) q^{75} +(0.891735 - 0.261837i) q^{77} +(-1.07587 - 7.48285i) q^{79} +(-0.379392 - 0.830752i) q^{81} +(-4.24387 - 2.72737i) q^{83} +(0.385580 - 2.68177i) q^{85} +(6.81483 - 4.37962i) q^{87} +(-14.1050 - 4.14160i) q^{89} +4.06253 q^{91} +6.55719 q^{93} +(1.29471 + 0.380160i) q^{95} +(-6.87619 + 4.41906i) q^{97} +(0.375049 - 2.60852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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