LMFDB - Embedded newform 460.2.m.a.41.2

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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	460.41
Dual form			460.2.m.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.329283 - 0.380013i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(-0.847137 - 1.85497i) q^{7} +(0.390962 + 2.71920i) q^{9} +O(q^{10})$	\(q+(0.329283 - 0.380013i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(-0.847137 - 1.85497i) q^{7} +(0.390962 + 2.71920i) q^{9} +(4.95488 - 1.45488i) q^{11} +(0.773111 - 1.69288i) q^{13} +(0.329283 + 0.380013i) q^{15} +(0.687204 - 0.441639i) q^{17} +(5.37737 + 3.45583i) q^{19} +(-0.983860 - 0.288887i) q^{21} +(4.01575 - 2.62178i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(2.43109 + 1.56237i) q^{27} +(-1.82922 + 1.17557i) q^{29} +(-2.33171 - 2.69094i) q^{31} +(1.07868 - 2.36199i) q^{33} +(1.95665 - 0.574525i) q^{35} +(-0.0791837 - 0.550735i) q^{37} +(-0.388742 - 0.851227i) q^{39} +(0.207389 - 1.44242i) q^{41} +(-6.92394 + 7.99065i) q^{43} -2.74716 q^{45} +1.60379 q^{47} +(1.86075 - 2.14742i) q^{49} +(0.0584560 - 0.406570i) q^{51} +(-2.53532 - 5.55157i) q^{53} +(0.734922 + 5.11150i) q^{55} +(3.08393 - 0.905525i) q^{57} +(-2.28512 + 5.00371i) q^{59} +(-0.676314 - 0.780507i) q^{61} +(4.71284 - 3.02876i) q^{63} +(1.56562 + 1.00616i) q^{65} +(4.15251 + 1.21929i) q^{67} +(0.326011 - 2.38934i) q^{69} +(-0.396395 - 0.116392i) q^{71} +(-5.14265 - 3.30498i) q^{73} +(-0.423007 + 0.271850i) q^{75} +(-6.89623 - 7.95868i) q^{77} +(-4.50110 + 9.85604i) q^{79} +(-6.51342 + 1.91251i) q^{81} +(-2.02608 - 14.0917i) q^{83} +(0.339345 + 0.743061i) q^{85} +(-0.155600 + 1.08222i) q^{87} +(-8.47579 + 9.78158i) q^{89} -3.79517 q^{91} -1.79038 q^{93} +(-4.18593 + 4.83082i) q^{95} +(-2.60153 + 18.0940i) q^{97} +(5.89329 + 12.9045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$3$	0.329283	−	0.380013i	0.190112	−	0.219400i	−0.652690	−	0.757625i	$-0.726359\pi$
$3$	0.329283	−	0.380013i	0.190112	−	0.219400i	0.842801	+	0.538225i	$0.180905\pi$
$4$		0			0
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$		0			0
$7$	−0.847137	−	1.85497i	−0.320188	−	0.701113i	0.679275	−	0.733884i	$-0.262294\pi$
$7$	−0.847137	−	1.85497i	−0.320188	−	0.701113i	−0.999463	+	0.0327703i	$0.989567\pi$
$8$		0			0
$9$	0.390962	+	2.71920i	0.130321	+	0.906400i
$10$		0			0
$11$	4.95488	−	1.45488i	1.49395	−	0.438664i	0.570152	−	0.821539i	$-0.306884\pi$
$11$	4.95488	−	1.45488i	1.49395	−	0.438664i	0.923800	+	0.382875i	$0.125066\pi$
$12$		0			0
$13$	0.773111	−	1.69288i	0.214422	−	0.469519i	−0.771605	−	0.636102i	$-0.780546\pi$
$13$	0.773111	−	1.69288i	0.214422	−	0.469519i	0.986028	+	0.166582i	$0.0532731\pi$
$14$		0			0
$15$	0.329283	+	0.380013i	0.0850205	+	0.0981188i
$16$		0			0
$17$	0.687204	−	0.441639i	0.166671	−	0.107113i	−0.454646	−	0.890672i	$-0.650234\pi$
$17$	0.687204	−	0.441639i	0.166671	−	0.107113i	0.621317	+	0.783559i	$0.286598\pi$
$18$		0			0
$19$	5.37737	+	3.45583i	1.23365	+	0.792821i	0.984456	−	0.175632i	$-0.0561968\pi$
$19$	5.37737	+	3.45583i	1.23365	+	0.792821i	0.249197	+	0.968453i	$0.419833\pi$
$20$		0			0
$21$	−0.983860	−	0.288887i	−0.214696	−	0.0630404i
$22$		0			0
$23$	4.01575	−	2.62178i	0.837343	−	0.546678i
$23$	4.01575	−	2.62178i	0.837343	−	0.546678i
$24$		0			0
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$		0			0
$27$	2.43109	+	1.56237i	0.467863	+	0.300677i
$28$		0			0
$29$	−1.82922	+	1.17557i	−0.339678	+	0.218298i	−0.699347	−	0.714782i	$-0.746526\pi$
$29$	−1.82922	+	1.17557i	−0.339678	+	0.218298i	0.359669	+	0.933080i	$0.382889\pi$
$30$		0			0
$31$	−2.33171	−	2.69094i	−0.418788	−	0.483307i	0.506679	−	0.862135i	$-0.330873\pi$
$31$	−2.33171	−	2.69094i	−0.418788	−	0.483307i	−0.925467	+	0.378828i	$0.876327\pi$
$32$		0			0
$33$	1.07868	−	2.36199i	0.187775	−	0.411169i
$34$		0			0
$35$	1.95665	−	0.574525i	0.330734	−	0.0971124i
$36$		0			0
$37$	−0.0791837	−	0.550735i	−0.0130177	−	0.0905403i	0.982277	−	0.187436i	$-0.0600177\pi$
$37$	−0.0791837	−	0.550735i	−0.0130177	−	0.0905403i	−0.995295	+	0.0968958i	$0.969109\pi$
$38$		0			0
$39$	−0.388742	−	0.851227i	−0.0622486	−	0.136305i
$40$		0			0
$41$	0.207389	−	1.44242i	0.0323887	−	0.225268i	−0.967198	−	0.254025i	$-0.918246\pi$
$41$	0.207389	−	1.44242i	0.0323887	−	0.225268i	0.999586	+	0.0287564i	$0.00915470\pi$
$42$		0			0
$43$	−6.92394	+	7.99065i	−1.05589	+	1.21856i	−0.0808066	+	0.996730i	$0.525750\pi$
$43$	−6.92394	+	7.99065i	−1.05589	+	1.21856i	−0.975085	+	0.221834i	$0.928796\pi$
$44$		0			0
$45$	−2.74716			−0.409523
$46$		0			0
$47$	1.60379			0.233938			0.116969	−	0.993136i	$-0.462682\pi$
$47$	1.60379			0.233938			0.116969	+	0.993136i	$0.462682\pi$
$48$		0			0
$49$	1.86075	−	2.14742i	0.265821	−	0.306774i
$50$		0			0
$51$	0.0584560	−	0.406570i	0.00818548	−	0.0569312i
$52$		0			0
$53$	−2.53532	−	5.55157i	−0.348252	−	0.762566i	−0.999992	−	0.00412306i	$-0.998688\pi$
$53$	−2.53532	−	5.55157i	−0.348252	−	0.762566i	0.651739	−	0.758443i	$-0.274040\pi$
$54$		0			0
$55$	0.734922	+	5.11150i	0.0990969	+	0.689234i
$56$		0			0
$57$	3.08393	−	0.905525i	0.408477	−	0.119940i
$58$		0			0
$59$	−2.28512	+	5.00371i	−0.297497	+	0.651427i	−0.998066	−	0.0621569i	$-0.980202\pi$
$59$	−2.28512	+	5.00371i	−0.297497	+	0.651427i	0.700570	+	0.713584i	$0.252929\pi$
$60$		0			0
$61$	−0.676314	−	0.780507i	−0.0865931	−	0.0999337i	0.710799	−	0.703395i	$-0.248333\pi$
$61$	−0.676314	−	0.780507i	−0.0865931	−	0.0999337i	−0.797393	+	0.603461i	$0.793788\pi$
$62$		0			0
$63$	4.71284	−	3.02876i	0.593762	−	0.381588i
$64$		0			0
$65$	1.56562	+	1.00616i	0.194191	+	0.124799i
$66$		0			0
$67$	4.15251	+	1.21929i	0.507310	+	0.148960i	0.525364	−	0.850877i	$-0.323929\pi$
$67$	4.15251	+	1.21929i	0.507310	+	0.148960i	−0.0180546	+	0.999837i	$0.505747\pi$
$68$		0			0
$69$	0.326011	−	2.38934i	0.0392471	−	0.287643i
$70$		0			0
$71$	−0.396395	−	0.116392i	−0.0470435	−	0.0138132i	0.258126	−	0.966111i	$-0.416895\pi$
$71$	−0.396395	−	0.116392i	−0.0470435	−	0.0138132i	−0.305170	+	0.952298i	$0.598713\pi$
$72$		0			0
$73$	−5.14265	−	3.30498i	−0.601902	−	0.386819i	0.203911	−	0.978989i	$-0.434635\pi$
$73$	−5.14265	−	3.30498i	−0.601902	−	0.386819i	−0.805812	+	0.592171i	$0.798271\pi$
$74$		0			0
$75$	−0.423007	+	0.271850i	−0.0488446	+	0.0313905i
$76$		0			0
$77$	−6.89623	−	7.95868i	−0.785899	−	0.906975i
$78$		0			0
$79$	−4.50110	+	9.85604i	−0.506414	+	1.10889i	0.467918	+	0.883772i	$0.345004\pi$
$79$	−4.50110	+	9.85604i	−0.506414	+	1.10889i	−0.974331	+	0.225119i	$0.927723\pi$
$80$		0			0
$81$	−6.51342	+	1.91251i	−0.723713	+	0.212501i
$82$		0			0
$83$	−2.02608	−	14.0917i	−0.222391	−	1.54677i	−0.728954	−	0.684563i	$-0.759993\pi$
$83$	−2.02608	−	14.0917i	−0.222391	−	1.54677i	0.506562	−	0.862203i	$-0.330916\pi$
$84$		0			0
$85$	0.339345	+	0.743061i	0.0368071	+	0.0805963i
$86$		0			0
$87$	−0.155600	+	1.08222i	−0.0166821	+	0.116026i
$88$		0			0
$89$	−8.47579	+	9.78158i	−0.898432	+	1.03685i	0.100689	+	0.994918i	$0.467895\pi$
$89$	−8.47579	+	9.78158i	−0.898432	+	1.03685i	−0.999121	+	0.0419279i	$0.986650\pi$
$90$		0			0
$91$	−3.79517			−0.397842
$92$		0			0
$93$	−1.79038			−0.185654
$94$		0			0
$95$	−4.18593	+	4.83082i	−0.429467	+	0.495632i
$96$		0			0
$97$	−2.60153	+	18.0940i	−0.264145	+	1.83717i	0.236637	+	0.971598i	$0.423955\pi$
$97$	−2.60153	+	18.0940i	−0.264145	+	1.83717i	−0.500783	+	0.865573i	$0.666954\pi$
$98$		0			0
$99$	5.89329	+	12.9045i	0.592298	+	1.29695i
$100$		0			0
$101$	−1.22251	−	8.50275i	−0.121644	−	0.846055i	−0.955693	−	0.294364i	$-0.904892\pi$
$101$	−1.22251	−	8.50275i	−0.121644	−	0.846055i	0.834049	−	0.551690i	$-0.186017\pi$
$102$		0			0
$103$	5.08228	−	1.49229i	0.500772	−	0.147040i	−0.0215847	−	0.999767i	$-0.506871\pi$
$103$	5.08228	−	1.49229i	0.500772	−	0.147040i	0.522357	+	0.852727i	$0.325053\pi$
$104$		0			0
$105$	0.425965	−	0.932733i	0.0415699	−	0.0910254i
$106$		0			0
$107$	−7.77359	−	8.97120i	−0.751501	−	0.867279i	0.243211	−	0.969973i	$-0.421799\pi$
$107$	−7.77359	−	8.97120i	−0.751501	−	0.867279i	−0.994713	+	0.102694i	$0.967254\pi$
$108$		0			0
$109$	−14.4592	+	9.29236i	−1.38494	+	0.890046i	−0.999466	−	0.0326726i	$-0.989598\pi$
$109$	−14.4592	+	9.29236i	−1.38494	+	0.890046i	−0.385473	+	0.922719i	$0.625962\pi$
$110$		0			0
$111$	−0.235360	−	0.151257i	−0.0223394	−	0.0143567i
$112$		0			0
$113$	−9.05703	−	2.65938i	−0.852014	−	0.250174i	−0.173566	−	0.984822i	$-0.555529\pi$
$113$	−9.05703	−	2.65938i	−0.852014	−	0.250174i	−0.678448	+	0.734649i	$0.737347\pi$
$114$		0			0
$115$	2.02359	+	4.34800i	0.188701	+	0.405453i
$116$		0			0
$117$	4.90553	+	1.44039i	0.453516	+	0.133164i
$118$		0			0
$119$	−1.40138	−	0.900615i	−0.128465	−	0.0825592i
$120$		0			0
$121$	13.1804	−	8.47050i	1.19821	−	0.770046i
$122$		0			0
$123$	−0.479848	−	0.553774i	−0.0432665	−	0.0499322i
$124$		0			0
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$		0			0
$127$	8.54876	−	2.51014i	0.758579	−	0.222739i	0.120504	−	0.992713i	$-0.461549\pi$
$127$	8.54876	−	2.51014i	0.758579	−	0.222739i	0.638075	+	0.769974i	$0.279731\pi$
$128$		0			0
$129$	0.756615	+	5.26237i	0.0666162	+	0.463326i
$130$		0			0
$131$	−3.02063	−	6.61426i	−0.263914	−	0.577890i	0.730563	−	0.682845i	$-0.239258\pi$
$131$	−3.02063	−	6.61426i	−0.263914	−	0.577890i	−0.994477	+	0.104955i	$0.966530\pi$
$132$		0			0
$133$	1.85509	−	12.9024i	0.160857	−	1.11878i
$134$		0			0
$135$	−1.89244	+	2.18399i	−0.162875	+	0.187968i
$136$		0			0
$137$	−18.2823			−1.56196			−0.780982	−	0.624553i	$-0.785281\pi$
$137$	−18.2823			−1.56196			−0.780982	+	0.624553i	$0.785281\pi$
$138$		0			0
$139$	5.19550			0.440676			0.220338	−	0.975424i	$-0.429284\pi$
$139$	5.19550			0.440676			0.220338	+	0.975424i	$0.429284\pi$
$140$		0			0
$141$	0.528102	−	0.609462i	0.0444742	−	0.0513260i
$142$		0			0
$143$	1.36773	−	9.51279i	0.114376	−	0.795499i
$144$		0			0
$145$	−0.903278	−	1.97790i	−0.0750131	−	0.164256i
$146$		0			0
$147$	−0.203333	−	1.41421i	−0.0167707	−	0.116642i
$148$		0			0
$149$	0.326269	−	0.0958011i	0.0267290	−	0.00784833i	−0.268341	−	0.963324i	$-0.586475\pi$
$149$	0.326269	−	0.0958011i	0.0267290	−	0.00784833i	0.295070	+	0.955476i	$0.404657\pi$
$150$		0			0
$151$	−4.41140	+	9.65961i	−0.358994	+	0.786088i	0.640836	+	0.767678i	$0.278588\pi$
$151$	−4.41140	+	9.65961i	−0.358994	+	0.786088i	−0.999831	+	0.0184103i	$0.994139\pi$
$152$		0			0
$153$	1.46958	+	1.69598i	0.118808	+	0.137112i
$154$		0			0
$155$	2.99539	−	1.92502i	0.240595	−	0.154621i
$156$		0			0
$157$	−20.2295	−	13.0007i	−1.61449	−	1.03757i	−0.959414	−	0.282001i	$-0.909002\pi$
$157$	−20.2295	−	13.0007i	−1.61449	−	1.03757i	−0.655072	−	0.755566i	$-0.727362\pi$
$158$		0			0
$159$	−2.94450	−	0.864584i	−0.233514	−	0.0685659i
$160$		0			0
$161$	−8.26522	−	5.22811i	−0.651390	−	0.412033i
$162$		0			0
$163$	5.55239	+	1.63033i	0.434897	+	0.127697i	0.491851	−	0.870680i	$-0.336321\pi$
$163$	5.55239	+	1.63033i	0.434897	+	0.127697i	−0.0569537	+	0.998377i	$0.518139\pi$
$164$		0			0
$165$	2.18443	+	1.40385i	0.170058	+	0.109289i
$166$		0			0
$167$	9.05165	−	5.81714i	0.700437	−	0.450144i	−0.141345	−	0.989960i	$-0.545143\pi$
$167$	9.05165	−	5.81714i	0.700437	−	0.450144i	0.841783	+	0.539817i	$0.181506\pi$
$168$		0			0
$169$	6.24506	+	7.20718i	0.480389	+	0.554399i
$170$		0			0
$171$	−7.29474	+	15.9732i	−0.557843	+	1.22150i
$172$		0			0
$173$	7.04012	−	2.06717i	0.535250	−	0.157164i	−0.00292639	−	0.999996i	$-0.500932\pi$
$173$	7.04012	−	2.06717i	0.535250	−	0.157164i	0.538177	+	0.842832i	$0.319113\pi$
$174$		0			0
$175$	0.290216	+	2.01850i	0.0219383	+	0.152584i
$176$		0			0
$177$	1.14902	+	2.51601i	0.0863658	+	0.189115i
$178$		0			0
$179$	1.38089	−	9.60431i	0.103213	−	0.717859i	−0.870845	−	0.491558i	$-0.836428\pi$
$179$	1.38089	−	9.60431i	0.103213	−	0.717859i	0.974057	−	0.226301i	$-0.0726634\pi$
$180$		0			0
$181$	12.3974	−	14.3074i	0.921491	−	1.06346i	−0.0763037	−	0.997085i	$-0.524312\pi$
$181$	12.3974	−	14.3074i	0.921491	−	1.06346i	0.997795	−	0.0663729i	$-0.0211427\pi$
$182$		0			0
$183$	−0.519301			−0.0383878
$184$		0			0
$185$	0.556398			0.0409072
$186$		0			0
$187$	2.76248	−	3.18807i	0.202013	−	0.233135i
$188$		0			0
$189$	0.838678	−	5.83314i	0.0610049	−	0.424298i
$190$		0			0
$191$	11.3966	+	24.9550i	0.824626	+	1.80568i	0.523272	+	0.852166i	$0.324711\pi$
$191$	11.3966	+	24.9550i	0.824626	+	1.80568i	0.301354	+	0.953512i	$0.402561\pi$
$192$		0			0
$193$	2.60069	+	18.0882i	0.187202	+	1.30202i	0.839211	+	0.543805i	$0.183017\pi$
$193$	2.60069	+	18.0882i	0.187202	+	1.30202i	−0.652010	+	0.758211i	$0.726074\pi$
$194$		0			0
$195$	0.897887	−	0.263643i	0.0642990	−	0.0188799i
$196$		0			0
$197$	−4.53893	+	9.93886i	−0.323385	+	0.708115i	−0.999591	−	0.0285981i	$-0.990896\pi$
$197$	−4.53893	+	9.93886i	−0.323385	+	0.708115i	0.676206	+	0.736713i	$0.263623\pi$
$198$		0			0
$199$	2.29908	+	2.65328i	0.162978	+	0.188086i	0.831364	−	0.555728i	$-0.187560\pi$
$199$	2.29908	+	2.65328i	0.162978	+	0.188086i	−0.668387	+	0.743814i	$0.733015\pi$
$200$		0			0
$201$	1.83069	−	1.17652i	0.129127	−	0.0829850i
$202$		0			0
$203$	3.73025	+	2.39728i	0.261812	+	0.168256i
$204$		0			0
$205$	1.39822	+	0.410555i	0.0976562	+	0.0286744i
$206$		0			0
$207$	8.69915	+	9.89463i	0.604632	+	0.687724i
$208$		0			0
$209$	31.6721	+	9.29975i	2.19080	+	0.643277i
$210$		0			0
$211$	1.47913	+	0.950580i	0.101828	+	0.0654406i	0.590564	−	0.806991i	$-0.298905\pi$
$211$	1.47913	+	0.950580i	0.101828	+	0.0654406i	−0.488736	+	0.872432i	$0.662542\pi$
$212$		0			0
$213$	−0.174757	+	0.112309i	−0.0119741	+	0.00769531i
$214$		0			0
$215$	−6.92394	−	7.99065i	−0.472209	−	0.544958i
$216$		0			0
$217$	−3.01634	+	6.60486i	−0.204762	+	0.448367i
$218$		0			0
$219$	−2.94932	+	0.865999i	−0.199297	+	0.0585188i
$220$		0			0
$221$	−0.216356	−	1.50479i	−0.0145537	−	0.101223i
$222$		0			0
$223$	−0.572783	−	1.25422i	−0.0383564	−	0.0839887i	0.889484	−	0.456966i	$-0.151064\pi$
$223$	−0.572783	−	1.25422i	−0.0383564	−	0.0839887i	−0.927840	+	0.372978i	$0.878337\pi$
$224$		0			0
$225$	0.390962	−	2.71920i	0.0260641	−	0.181280i
$226$		0			0
$227$	15.5051	−	17.8938i	1.02911	−	1.18766i	0.0470875	−	0.998891i	$-0.485006\pi$
$227$	15.5051	−	17.8938i	1.02911	−	1.18766i	0.982022	−	0.188765i	$-0.0604485\pi$
$228$		0			0
$229$	0.556469			0.0367725			0.0183863	−	0.999831i	$-0.494147\pi$
$229$	0.556469			0.0367725			0.0183863	+	0.999831i	$0.494147\pi$
$230$		0			0
$231$	−5.29521			−0.348399
$232$		0			0
$233$	8.18763	−	9.44902i	0.536389	−	0.619026i	−0.421268	−	0.906936i	$-0.638415\pi$
$233$	8.18763	−	9.44902i	0.536389	−	0.619026i	0.957657	+	0.287910i	$0.0929604\pi$
$234$		0			0
$235$	−0.228244	+	1.58747i	−0.0148890	+	0.103555i
$236$		0			0
$237$	2.26328	+	4.95590i	0.147016	+	0.321920i
$238$		0			0
$239$	−3.17500	−	22.0826i	−0.205374	−	1.42841i	−0.788005	−	0.615669i	$-0.788886\pi$
$239$	−3.17500	−	22.0826i	−0.205374	−	1.42841i	0.582632	−	0.812736i	$-0.302023\pi$
$240$		0			0
$241$	15.3930	−	4.51981i	0.991553	−	0.291146i	0.254568	−	0.967055i	$-0.418067\pi$
$241$	15.3930	−	4.51981i	0.991553	−	0.291146i	0.736985	+	0.675909i	$0.236249\pi$
$242$		0			0
$243$	−5.01943	+	10.9910i	−0.321996	+	0.705074i
$244$		0			0
$245$	1.86075	+	2.14742i	0.118879	+	0.137193i
$246$		0			0
$247$	10.0076	−	6.43149i	0.636768	−	0.409226i
$248$		0			0
$249$	−6.02218	−	3.87022i	−0.381640	−	0.245265i
$250$		0			0
$251$	−29.7141	−	8.72486i	−1.87554	−	0.550708i	−0.997380	−	0.0723403i	$-0.976953\pi$
$251$	−29.7141	−	8.72486i	−1.87554	−	0.550708i	−0.878160	−	0.478368i	$-0.841229\pi$
$252$		0			0
$253$	16.0832	−	18.8330i	1.01114	−	1.18402i
$254$		0			0
$255$	0.394113	+	0.115722i	0.0246803	+	0.00724679i
$256$		0			0
$257$	21.8619	+	14.0498i	1.36371	+	0.876402i	0.998512	−	0.0545292i	$-0.0173658\pi$
$257$	21.8619	+	14.0498i	1.36371	+	0.876402i	0.365195	+	0.930931i	$0.381002\pi$
$258$		0			0
$259$	−0.954518	+	0.613432i	−0.0593109	+	0.0381168i
$260$		0			0
$261$	−3.91176	−	4.51441i	−0.242132	−	0.279435i
$262$		0			0
$263$	1.54736	−	3.38826i	0.0954146	−	0.208929i	−0.855906	−	0.517131i	$-0.827000\pi$
$263$	1.54736	−	3.38826i	0.0954146	−	0.208929i	0.951321	+	0.308202i	$0.0997273\pi$
$264$		0			0
$265$	5.85587	−	1.71944i	0.359723	−	0.105624i
$266$		0			0
$267$	0.926193	+	6.44182i	0.0566821	+	0.394233i
$268$		0			0
$269$	5.79490	+	12.6891i	0.353321	+	0.773666i	0.999941	+	0.0108535i	$0.00345484\pi$
$269$	5.79490	+	12.6891i	0.353321	+	0.773666i	−0.646620	+	0.762813i	$0.723818\pi$
$270$		0			0
$271$	2.13569	−	14.8540i	0.129734	−	0.902318i	−0.816156	−	0.577831i	$-0.803899\pi$
$271$	2.13569	−	14.8540i	0.129734	−	0.902318i	0.945890	−	0.324487i	$-0.105192\pi$
$272$		0			0
$273$	−1.24968	+	1.44221i	−0.0756343	+	0.0872866i
$274$		0			0
$275$	−5.16406			−0.311405
$276$		0			0
$277$	−3.87509			−0.232831			−0.116416	−	0.993201i	$-0.537140\pi$
$277$	−3.87509			−0.232831			−0.116416	+	0.993201i	$0.537140\pi$
$278$		0			0
$279$	6.40560	−	7.39245i	0.383493	−	0.442574i
$280$		0			0
$281$	1.68704	−	11.7336i	0.100641	−	0.699971i	−0.875561	−	0.483107i	$-0.839508\pi$
$281$	1.68704	−	11.7336i	0.100641	−	0.699971i	0.976202	−	0.216864i	$-0.0695827\pi$
$282$		0			0
$283$	0.222697	+	0.487639i	0.0132380	+	0.0289871i	0.916136	−	0.400869i	$-0.131292\pi$
$283$	0.222697	+	0.487639i	0.0132380	+	0.0289871i	−0.902898	+	0.429856i	$0.858564\pi$
$284$		0			0
$285$	0.457418	+	3.18141i	0.0270951	+	0.188451i
$286$		0			0
$287$	−2.85133	+	0.837227i	−0.168309	+	0.0494200i
$288$		0			0
$289$	−6.78485	+	14.8568i	−0.399109	+	0.873927i
$290$		0			0
$291$	6.01932	+	6.94667i	0.352859	+	0.407221i
$292$		0			0
$293$	−19.0883	+	12.2673i	−1.11515	+	0.716662i	−0.962409	−	0.271605i	$-0.912446\pi$
$293$	−19.0883	+	12.2673i	−1.11515	+	0.716662i	−0.152739	+	0.988267i	$0.548809\pi$
$294$		0			0
$295$	−4.62757	−	2.97396i	−0.269428	−	0.173151i
$296$		0			0
$297$	14.3188	+	4.20438i	0.830861	+	0.243963i
$298$		0			0
$299$	−1.33372	−	8.82510i	−0.0771310	−	0.510369i
$300$		0			0
$301$	20.6880	+	6.07453i	1.19243	+	0.350130i
$302$		0			0
$303$	−3.63370	−	2.33524i	−0.208751	−	0.134156i
$304$		0			0
$305$	0.868812	−	0.558352i	0.0497481	−	0.0319711i
$306$		0			0
$307$	−9.48462	−	10.9458i	−0.541316	−	0.624712i	0.417521	−	0.908667i	$-0.362899\pi$
$307$	−9.48462	−	10.9458i	−0.541316	−	0.624712i	−0.958838	+	0.283955i	$0.908353\pi$
$308$		0			0
$309$	1.10642	−	2.42272i	0.0629419	−	0.137824i
$310$		0			0
$311$	9.93898	−	2.91835i	0.563588	−	0.165484i	0.0124856	−	0.999922i	$-0.496026\pi$
$311$	9.93898	−	2.91835i	0.563588	−	0.165484i	0.551102	+	0.834438i	$0.314207\pi$
$312$		0			0
$313$	2.65668	+	18.4776i	0.150164	+	1.04442i	0.915942	+	0.401310i	$0.131445\pi$
$313$	2.65668	+	18.4776i	0.150164	+	1.04442i	−0.765778	+	0.643105i	$0.777646\pi$
$314$		0			0
$315$	2.32722	+	5.09591i	0.131124	+	0.287122i
$316$		0			0
$317$	2.50055	−	17.3917i	0.140445	−	0.976815i	−0.790710	−	0.612191i	$-0.790288\pi$
$317$	2.50055	−	17.3917i	0.140445	−	0.976815i	0.931155	−	0.364624i	$-0.118803\pi$
$318$		0			0
$319$	−7.35325	+	8.48610i	−0.411703	+	0.475131i
$320$		0			0
$321$	−5.96888			−0.333150
$322$		0			0
$323$	5.22158			0.290536
$324$		0			0
$325$	−1.21873	+	1.40649i	−0.0676031	+	0.0780182i
$326$		0			0
$327$	−1.22995	+	8.55449i	−0.0680164	+	0.473064i
$328$		0			0
$329$	−1.35863	−	2.97499i	−0.0749039	−	0.164017i
$330$		0			0
$331$	4.12915	+	28.7188i	0.226958	+	1.57853i	0.710813	+	0.703381i	$0.248327\pi$
$331$	4.12915	+	28.7188i	0.226958	+	1.57853i	−0.483854	+	0.875149i	$0.660764\pi$
$332$		0			0
$333$	1.46660	−	0.430633i	0.0803692	−	0.0235985i
$334$		0			0
$335$	−1.79784	+	3.93672i	−0.0982265	+	0.215086i
$336$		0			0
$337$	0.353263	+	0.407687i	0.0192434	+	0.0222081i	0.765290	−	0.643686i	$-0.222596\pi$
$337$	0.353263	+	0.407687i	0.0192434	+	0.0222081i	−0.746046	+	0.665894i	$0.768050\pi$
$338$		0			0
$339$	−3.99292	+	2.56610i	−0.216866	+	0.139371i
$340$		0			0
$341$	−15.4684	−	9.94091i	−0.837659	−	0.538331i
$342$		0			0
$343$	−19.2563	−	5.65415i	−1.03974	−	0.305295i
$344$		0			0
$345$	2.31863	+	0.662732i	0.124831	+	0.0356803i
$346$		0			0
$347$	7.33312	+	2.15320i	0.393663	+	0.115590i	0.472572	−	0.881292i	$-0.343326\pi$
$347$	7.33312	+	2.15320i	0.393663	+	0.115590i	−0.0789095	+	0.996882i	$0.525144\pi$
$348$		0			0
$349$	−22.5810	−	14.5119i	−1.20873	−	0.776805i	−0.228286	−	0.973594i	$-0.573312\pi$
$349$	−22.5810	−	14.5119i	−1.20873	−	0.776805i	−0.980446	+	0.196789i	$0.936948\pi$
$350$		0			0
$351$	4.52439	−	2.90765i	0.241494	−	0.155199i
$352$		0			0
$353$	−1.30178	−	1.50233i	−0.0692866	−	0.0799611i	0.720048	−	0.693924i	$-0.244120\pi$
$353$	−1.30178	−	1.50233i	−0.0692866	−	0.0799611i	−0.789335	+	0.613963i	$0.789574\pi$
$354$		0			0
$355$	0.171620	−	0.375796i	0.00910867	−	0.0199452i
$356$		0			0
$357$	−0.803697	+	0.235987i	−0.0425361	+	0.0124897i
$358$		0			0
$359$	−3.52681	−	24.5295i	−0.186138	−	1.29462i	−0.841894	−	0.539644i	$-0.818559\pi$
$359$	−3.52681	−	24.5295i	−0.186138	−	1.29462i	0.655756	−	0.754973i	$-0.272350\pi$
$360$		0			0
$361$	9.08049	+	19.8835i	0.477921	+	1.04650i
$362$		0			0
$363$	1.12117	−	7.79790i	0.0588461	−	0.409283i
$364$		0			0
$365$	4.00322	−	4.61996i	0.209538	−	0.241820i
$366$		0			0
$367$	−23.8482			−1.24487			−0.622433	−	0.782673i	$-0.713856\pi$
$367$	−23.8482			−1.24487			−0.622433	+	0.782673i	$0.713856\pi$
$368$		0			0
$369$	4.00331			0.208404
$370$		0			0
$371$	−8.15024	+	9.40588i	−0.423139	+	0.488329i
$372$		0			0
$373$	−4.56885	+	31.7770i	−0.236566	+	1.64535i	0.432126	+	0.901813i	$0.357763\pi$
$373$	−4.56885	+	31.7770i	−0.236566	+	1.64535i	−0.668692	+	0.743539i	$0.733146\pi$
$374$		0			0
$375$	−0.208883	−	0.457389i	−0.0107867	−	0.0236195i
$376$		0			0
$377$	0.575902	+	4.00549i	0.0296605	+	0.206293i
$378$		0			0
$379$	11.3523	−	3.33333i	0.583127	−	0.171222i	0.0231533	−	0.999732i	$-0.492629\pi$
$379$	11.3523	−	3.33333i	0.583127	−	0.171222i	0.559974	+	0.828510i	$0.310811\pi$
$380$		0			0
$381$	1.86107	−	4.07518i	0.0953457	−	0.208778i
$382$		0			0
$383$	5.75799	+	6.64507i	0.294219	+	0.339547i	0.883543	−	0.468350i	$-0.155151\pi$
$383$	5.75799	+	6.64507i	0.294219	+	0.339547i	−0.589324	+	0.807897i	$0.700606\pi$
$384$		0			0
$385$	8.85910	−	5.69340i	0.451502	−	0.290163i
$386$		0			0
$387$	−24.4352	−	15.7035i	−1.24211	−	0.798256i
$388$		0			0
$389$	−27.5522	−	8.09006i	−1.39695	−	0.410182i	−0.505316	−	0.862935i	$-0.668624\pi$
$389$	−27.5522	−	8.09006i	−1.39695	−	0.410182i	−0.891636	+	0.452752i	$0.850442\pi$
$390$		0			0
$391$	1.60176	−	3.57521i	0.0810047	−	0.180806i
$392$		0			0
$393$	−3.50814	−	1.03008i	−0.176962	−	0.0519608i
$394$		0			0
$395$	−9.11515	−	5.85795i	−0.458633	−	0.294745i
$396$		0			0
$397$	−29.6357	+	19.0457i	−1.48737	+	0.955876i	−0.490965	+	0.871180i	$0.663356\pi$
$397$	−29.6357	+	19.0457i	−1.48737	+	0.955876i	−0.996407	+	0.0846961i	$0.973008\pi$
$398$		0			0
$399$	−4.29224	−	4.95351i	−0.214881	−	0.247985i
$400$		0			0
$401$	−1.74850	+	3.82868i	−0.0873159	+	0.191195i	−0.948253	−	0.317517i	$-0.897151\pi$
$401$	−1.74850	+	3.82868i	−0.0873159	+	0.191195i	0.860937	+	0.508712i	$0.169878\pi$
$402$		0			0
$403$	−6.35810	+	1.86691i	−0.316720	+	0.0929973i
$404$		0			0
$405$	−0.966089	−	6.71930i	−0.0480054	−	0.333885i
$406$		0			0
$407$	−1.19360	−	2.61362i	−0.0591646	−	0.129552i
$408$		0			0
$409$	4.07089	−	28.3137i	0.201293	−	1.40002i	−0.599162	−	0.800628i	$-0.704499\pi$
$409$	4.07089	−	28.3137i	0.201293	−	1.40002i	0.800455	−	0.599393i	$-0.204591\pi$
$410$		0			0
$411$	−6.02006	+	6.94751i	−0.296947	+	0.342696i
$412$		0			0
$413$	11.2175			0.551979
$414$		0			0
$415$	14.2366			0.698848
$416$		0			0
$417$	1.71079	−	1.97435i	0.0837776	−	0.0966845i
$418$		0			0
$419$	0.714304	−	4.96809i	0.0348960	−	0.242707i	−0.964906	−	0.262595i	$-0.915422\pi$
$419$	0.714304	−	4.96809i	0.0348960	−	0.242707i	0.999802	+	0.0198877i	$0.00633086\pi$
$420$		0			0
$421$	1.51626	+	3.32015i	0.0738981	+	0.161814i	0.942976	−	0.332861i	$-0.108014\pi$
$421$	1.51626	+	3.32015i	0.0738981	+	0.161814i	−0.869078	+	0.494676i	$0.835287\pi$
$422$		0			0
$423$	0.627023	+	4.36104i	0.0304869	+	0.212041i
$424$		0			0
$425$	−0.783792	+	0.230142i	−0.0380195	+	0.0111635i
$426$		0			0
$427$	−0.874889	+	1.91574i	−0.0423388	+	0.0927091i
$428$		0			0
$429$	−3.16461	−	3.65215i	−0.152789	−	0.176328i
$430$		0			0
$431$	−12.4652	+	8.01092i	−0.600429	+	0.385873i	−0.805257	−	0.592925i	$-0.797973\pi$
$431$	−12.4652	+	8.01092i	−0.600429	+	0.385873i	0.204828	+	0.978798i	$0.434337\pi$
$432$		0			0
$433$	3.17361	+	2.03956i	0.152514	+	0.0980148i	0.614672	−	0.788783i	$-0.289288\pi$
$433$	3.17361	+	2.03956i	0.152514	+	0.0980148i	−0.462158	+	0.886798i	$0.652925\pi$
$434$		0			0
$435$	−1.04906	−	0.308032i	−0.0502987	−	0.0147690i
$436$		0			0
$437$	30.6546	−	0.220513i	1.46641	−	0.0105486i
$438$		0			0
$439$	−3.29916	−	0.968720i	−0.157460	−	0.0462345i	0.202052	−	0.979375i	$-0.435239\pi$
$439$	−3.29916	−	0.968720i	−0.157460	−	0.0462345i	−0.359513	+	0.933140i	$0.617057\pi$
$440$		0			0
$441$	6.56674	+	4.22019i	0.312702	+	0.200961i
$442$		0			0
$443$	−11.4987	+	7.38979i	−0.546321	+	0.351099i	−0.784507	−	0.620120i	$-0.787084\pi$
$443$	−11.4987	+	7.38979i	−0.546321	+	0.351099i	0.238185	+	0.971220i	$0.423447\pi$
$444$		0			0
$445$	−8.47579	−	9.78158i	−0.401791	−	0.463692i
$446$		0			0
$447$	0.0710290	−	0.155532i	0.00335956	−	0.00735640i
$448$		0			0
$449$	38.7322	−	11.3728i	1.82789	−	0.536716i	0.828169	−	0.560478i	$-0.189383\pi$
$449$	38.7322	−	11.3728i	1.82789	−	0.536716i	0.999718	+	0.0237623i	$0.00756450\pi$
$450$		0			0
$451$	−1.07097	−	7.44874i	−0.0504299	−	0.350748i
$452$		0			0
$453$	2.21818	+	4.85713i	0.104219	+	0.228208i
$454$		0			0
$455$	0.540109	−	3.75654i	0.0253207	−	0.176109i
$456$		0			0
$457$	−22.3145	+	25.7523i	−1.04383	+	1.20464i	−0.0654432	+	0.997856i	$0.520846\pi$
$457$	−22.3145	+	25.7523i	−1.04383	+	1.20464i	−0.978386	+	0.206787i	$0.933699\pi$
$458$		0			0
$459$	2.36065			0.110186
$460$		0			0
$461$	−5.55797			−0.258861			−0.129430	−	0.991589i	$-0.541315\pi$
$461$	−5.55797			−0.258861			−0.129430	+	0.991589i	$0.541315\pi$
$462$		0			0
$463$	−20.7022	+	23.8916i	−0.962114	+	1.11034i	0.0317241	+	0.999497i	$0.489900\pi$
$463$	−20.7022	+	23.8916i	−0.962114	+	1.11034i	−0.993838	+	0.110842i	$0.964645\pi$
$464$		0			0
$465$	0.254798	−	1.77216i	0.0118160	−	0.0821820i
$466$		0			0
$467$	5.93445	+	12.9946i	0.274614	+	0.601320i	0.995814	−	0.0914068i	$-0.0291364\pi$
$467$	5.93445	+	12.9946i	0.274614	+	0.601320i	−0.721200	+	0.692727i	$0.756409\pi$
$468$		0			0
$469$	−1.25600	−	8.73569i	−0.0579968	−	0.403377i
$470$		0			0
$471$	−11.6016	+	3.40655i	−0.534575	+	0.156965i
$472$		0			0
$473$	−22.6818	+	49.6663i	−1.04291	+	2.28366i
$474$		0			0
$475$	−4.18593	−	4.83082i	−0.192064	−	0.221653i
$476$		0			0
$477$	14.1046	−	9.06448i	0.645806	−	0.415034i
$478$		0			0
$479$	6.42979	+	4.13217i	0.293785	+	0.188804i	0.679227	−	0.733928i	$-0.262315\pi$
$479$	6.42979	+	4.13217i	0.293785	+	0.188804i	−0.385443	+	0.922732i	$0.625951\pi$
$480$		0			0
$481$	−0.993544	−	0.291731i	−0.0453017	−	0.0133018i
$482$		0			0
$483$	−4.70834	+	1.41936i	−0.214237	+	0.0645832i
$484$		0			0
$485$	−17.5396	−	5.15010i	−0.796434	−	0.233854i
$486$		0			0
$487$	−27.2128	−	17.4886i	−1.23313	−	0.792485i	−0.248755	−	0.968566i	$-0.580021\pi$
$487$	−27.2128	−	17.4886i	−1.23313	−	0.792485i	−0.984376	+	0.176081i	$0.943658\pi$
$488$		0			0
$489$	2.44785	−	1.57314i	0.110696	−	0.0711399i
$490$		0			0
$491$	−10.4483	−	12.0580i	−0.471525	−	0.544169i	0.469310	−	0.883033i	$-0.344503\pi$
$491$	−10.4483	−	12.0580i	−0.471525	−	0.544169i	−0.940835	+	0.338864i	$0.889957\pi$
$492$		0			0
$493$	−0.737870	+	1.61571i	−0.0332320	+	0.0727680i
$494$		0			0
$495$	−13.6119	+	3.99680i	−0.611808	+	0.179643i
$496$		0			0
$497$	0.119897	+	0.833902i	0.00537812	+	0.0374056i
$498$		0			0
$499$	−13.1002	−	28.6854i	−0.586444	−	1.28413i	−0.937567	−	0.347804i	$-0.886928\pi$
$499$	−13.1002	−	28.6854i	−0.586444	−	1.28413i	0.351124	−	0.936329i	$-0.385800\pi$
$500$		0			0
$501$	0.769965	−	5.35522i	0.0343995	−	0.239254i
$502$		0			0
$503$	−17.0861	+	19.7184i	−0.761830	+	0.879198i	−0.995659	−	0.0930794i	$-0.970329\pi$
$503$	−17.0861	+	19.7184i	−0.761830	+	0.879198i	0.233829	+	0.972278i	$0.424874\pi$
$504$		0			0
$505$	8.59018			0.382258
$506$		0			0
$507$	4.79521			0.212963
$508$		0			0
$509$	−10.0322	+	11.5778i	−0.444671	+	0.513178i	−0.933194	−	0.359373i	$-0.882990\pi$
$509$	−10.0322	+	11.5778i	−0.444671	+	0.513178i	0.488523	+	0.872551i	$0.337536\pi$
$510$		0			0
$511$	−1.77411	+	12.3392i	−0.0784822	+	0.545856i
$512$		0			0
$513$	7.67360	+	16.8028i	0.338798	+	0.741863i
$514$		0			0
$515$	0.753819	+	5.24293i	0.0332172	+	0.231031i
$516$		0			0
$517$	7.94661	−	2.33334i	0.349492	−	0.102620i
$518$		0			0
$519$	1.53264	−	3.35602i	0.0672755	−	0.147313i
$520$		0			0
$521$	8.48353	+	9.79051i	0.371670	+	0.428930i	0.910516	−	0.413474i	$-0.135685\pi$
$521$	8.48353	+	9.79051i	0.371670	+	0.428930i	−0.538846	+	0.842405i	$0.681139\pi$
$522$		0			0
$523$	3.36065	−	2.15976i	0.146951	−	0.0944396i	−0.465099	−	0.885259i	$-0.653981\pi$
$523$	3.36065	−	2.15976i	0.146951	−	0.0944396i	0.612050	+	0.790819i	$0.290345\pi$
$524$		0			0
$525$	0.862618	+	0.554371i	0.0376477	+	0.0241947i
$526$		0			0
$527$	−2.79079	−	0.819449i	−0.121569	−	0.0356958i
$528$		0			0
$529$	9.25258	−	21.0568i	0.402286	−	0.915514i
$530$		0			0
$531$	−14.4995	−	4.25743i	−0.629224	−	0.184757i
$532$		0			0
$533$	−2.28150	−	1.46623i	−0.0988229	−	0.0635096i
$534$		0			0
$535$	9.98619	−	6.41773i	0.431740	−	0.277463i
$536$		0			0
$537$	−3.19505	−	3.68729i	−0.137877	−	0.159118i
$538$		0			0
$539$	6.09554	−	13.3474i	0.262553	−	0.574912i
$540$		0			0
$541$	21.1098	−	6.19840i	0.907582	−	0.266490i	0.205559	−	0.978645i	$-0.434099\pi$
$541$	21.1098	−	6.19840i	0.907582	−	0.266490i	0.702023	+	0.712155i	$0.252280\pi$
$542$		0			0
$543$	−1.35473	−	9.42234i	−0.0581369	−	0.404351i
$544$		0			0
$545$	−7.14002	−	15.6345i	−0.305845	−	0.669707i
$546$		0			0
$547$	4.93221	−	34.3043i	0.210886	−	1.46674i	−0.559321	−	0.828951i	$-0.688938\pi$
$547$	4.93221	−	34.3043i	0.210886	−	1.46674i	0.770207	−	0.637793i	$-0.220153\pi$
$548$		0			0
$549$	1.85794	−	2.14418i	0.0792951	−	0.0915114i
$550$		0			0
$551$	−13.8990			−0.592115
$552$		0			0
$553$	22.0957			0.939606
$554$		0			0
$555$	0.183212	−	0.211438i	0.00777693	−	0.00897506i
$556$		0			0
$557$	−2.68578	+	18.6800i	−0.113800	+	0.791497i	0.850365	+	0.526193i	$0.176381\pi$
$557$	−2.68578	+	18.6800i	−0.113800	+	0.791497i	−0.964165	+	0.265303i	$0.914528\pi$
$558$		0			0
$559$	8.17422	+	17.8990i	0.345733	+	0.757049i
$560$		0			0
$561$	−0.301870	−	2.09955i	−0.0127450	−	0.0886433i
$562$		0			0
$563$	44.9326	−	13.1934i	1.89368	−	0.556035i	0.901240	−	0.433320i	$-0.142658\pi$
$563$	44.9326	−	13.1934i	1.89368	−	0.556035i	0.992442	−	0.122716i	$-0.0391603\pi$
$564$		0			0
$565$	3.92126	−	8.58637i	0.164969	−	0.361231i
$566$		0			0
$567$	9.06541	+	10.4620i	0.380712	+	0.439365i
$568$		0			0
$569$	−11.8294	+	7.60230i	−0.495915	+	0.318705i	−0.764580	−	0.644529i	$-0.777054\pi$
$569$	−11.8294	+	7.60230i	−0.495915	+	0.318705i	0.268666	+	0.963233i	$0.413417\pi$
$570$		0			0
$571$	27.4155	+	17.6189i	1.14730	+	0.737327i	0.969100	−	0.246667i	$-0.0793354\pi$
$571$	27.4155	+	17.6189i	1.14730	+	0.737327i	0.178203	+	0.983994i	$0.442972\pi$
$572$		0			0
$573$	13.2359	+	3.88641i	0.552937	+	0.162357i
$574$		0			0
$575$	−4.59173	+	1.38421i	−0.191488	+	0.0577254i
$576$		0			0
$577$	−6.62015	−	1.94385i	−0.275600	−	0.0809236i	0.141012	−	0.990008i	$-0.454964\pi$
$577$	−6.62015	−	1.94385i	−0.275600	−	0.0809236i	−0.416612	+	0.909084i	$0.636783\pi$
$578$		0			0
$579$	7.73010	+	4.96783i	0.321252	+	0.206456i
$580$		0			0
$581$	−24.4234	+	15.6959i	−1.01325	+	0.651177i
$582$		0			0
$583$	−20.6391	−	23.8188i	−0.854783	−	0.986472i
$584$		0			0
$585$	−2.12386	+	4.65061i	−0.0878109	+	0.192279i
$586$		0			0
$587$	8.98073	−	2.63698i	0.370674	−	0.108840i	−0.0910895	−	0.995843i	$-0.529035\pi$
$587$	8.98073	−	2.63698i	0.370674	−	0.108840i	0.461764	+	0.887003i	$0.347217\pi$
$588$		0			0
$589$	−3.23906	−	22.5282i	−0.133463	−	0.928257i
$590$		0			0
$591$	2.28230	+	4.99755i	0.0938814	+	0.205572i
$592$		0			0
$593$	−0.159893	+	1.11208i	−0.00656601	+	0.0456676i	−0.992841	−	0.119443i	$-0.961889\pi$
$593$	−0.159893	+	1.11208i	−0.00656601	+	0.0456676i	0.986275	+	0.165111i	$0.0527982\pi$
$594$		0			0
$595$	1.09089	−	1.25895i	0.0447220	−	0.0516119i
$596$		0			0
$597$	1.76533			0.0722501
$598$		0			0
$599$	7.19246			0.293876			0.146938	−	0.989146i	$-0.453058\pi$
$599$	7.19246			0.293876			0.146938	+	0.989146i	$0.453058\pi$
$600$		0			0
$601$	5.00113	−	5.77161i	0.204000	−	0.235429i	−0.644526	−	0.764583i	$-0.722945\pi$
$601$	5.00113	−	5.77161i	0.204000	−	0.235429i	0.848526	+	0.529154i	$0.177491\pi$
$602$		0			0
$603$	−1.69201	+	11.7682i	−0.0689040	+	0.479238i
$604$		0			0
$605$	6.50853	+	14.2517i	0.264609	+	0.579413i
$606$		0			0
$607$	5.24301	+	36.4659i	0.212807	+	1.48011i	0.763723	+	0.645544i	$0.223369\pi$
$607$	5.24301	+	36.4659i	0.212807	+	1.48011i	−0.550916	+	0.834561i	$0.685721\pi$
$608$		0			0
$609$	2.13930	−	0.628156i	0.0866890	−	0.0254542i
$610$		0			0
$611$	1.23991	−	2.71503i	0.0501614	−	0.109838i
$612$		0			0
$613$	−14.3462	−	16.5564i	−0.579437	−	0.668706i	0.388047	−	0.921640i	$-0.373150\pi$
$613$	−14.3462	−	16.5564i	−0.579437	−	0.668706i	−0.967484	+	0.252934i	$0.918604\pi$
$614$		0			0
$615$	0.616427	−	0.396154i	0.0248567	−	0.0159745i
$616$		0			0
$617$	−0.711146	−	0.457026i	−0.0286297	−	0.0183992i	0.526248	−	0.850331i	$-0.323598\pi$
$617$	−0.711146	−	0.457026i	−0.0286297	−	0.0183992i	−0.554877	+	0.831932i	$0.687235\pi$
$618$		0			0
$619$	−12.9114	−	3.79113i	−0.518953	−	0.152378i	0.0117584	−	0.999931i	$-0.496257\pi$
$619$	−12.9114	−	3.79113i	−0.518953	−	0.152378i	−0.530712	+	0.847552i	$0.678075\pi$
$620$		0			0
$621$	13.8588	−	0.0996929i	0.556135	−	0.00400054i
$622$		0			0
$623$	25.3247	+	7.43601i	1.01461	+	0.297917i
$624$		0			0
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$		0			0
$627$	13.9631	−	8.97353i	0.557632	−	0.358368i
$628$		0			0
$629$	−0.297641	−	0.343497i	−0.0118677	−	0.0136961i
$630$		0			0
$631$	−2.58301	+	5.65600i	−0.102828	+	0.225162i	−0.954052	−	0.299640i	$-0.903133\pi$
$631$	−2.58301	+	5.65600i	−0.102828	+	0.225162i	0.851224	+	0.524802i	$0.175861\pi$
$632$		0			0
$633$	0.848285	−	0.249079i	0.0337163	−	0.00990000i
$634$		0			0
$635$	1.26798	+	8.81897i	0.0503181	+	0.349970i
$636$		0			0
$637$	−2.19675	−	4.81021i	−0.0870383	−	0.190587i
$638$		0			0
$639$	0.161518	−	1.12338i	0.00638956	−	0.0444404i
$640$		0			0
$641$	−20.7252	+	23.9181i	−0.818596	+	0.944710i	−0.999246	−	0.0388377i	$-0.987634\pi$
$641$	−20.7252	+	23.9181i	−0.818596	+	0.944710i	0.180650	+	0.983547i	$0.442180\pi$
$642$		0			0
$643$	8.22655			0.324423			0.162212	−	0.986756i	$-0.448137\pi$
$643$	8.22655			0.324423			0.162212	+	0.986756i	$0.448137\pi$
$644$		0			0
$645$	−5.31649			−0.209336
$646$		0			0
$647$	29.7511	−	34.3346i	1.16964	−	1.34983i	0.244751	−	0.969586i	$-0.421294\pi$
$647$	29.7511	−	34.3346i	1.16964	−	1.34983i	0.924885	−	0.380246i	$-0.124161\pi$
$648$		0			0
$649$	−4.04267	+	28.1174i	−0.158688	+	1.10370i
$650$		0			0
$651$	1.51670	+	3.32111i	0.0594442	+	0.130165i
$652$		0			0
$653$	−5.01926	−	34.9097i	−0.196419	−	1.36612i	−0.814570	−	0.580065i	$-0.803027\pi$
$653$	−5.01926	−	34.9097i	−0.196419	−	1.36612i	0.618151	−	0.786059i	$-0.287882\pi$
$654$		0			0
$655$	6.97681	−	2.04858i	0.272607	−	0.0800445i
$656$		0			0
$657$	6.97632	−	15.2760i	0.272172	−	0.595974i
$658$		0			0
$659$	−11.5821	−	13.3665i	−0.451176	−	0.520685i	0.483904	−	0.875121i	$-0.339218\pi$
$659$	−11.5821	−	13.3665i	−0.451176	−	0.520685i	−0.935080	+	0.354436i	$0.884673\pi$
$660$		0			0
$661$	35.0648	−	22.5348i	1.36386	−	0.876503i	0.365344	−	0.930873i	$-0.380951\pi$
$661$	35.0648	−	22.5348i	1.36386	−	0.876503i	0.998521	+	0.0543702i	$0.0173151\pi$
$662$		0			0
$663$	−0.643081	−	0.413283i	−0.0249752	−	0.0160506i
$664$		0			0
$665$	12.5071	+	3.67241i	0.485004	+	0.142410i
$666$		0			0
$667$	−4.26362	+	9.51660i	−0.165088	+	0.368484i
$668$		0			0
$669$	−0.665227	−	0.195328i	−0.0257192	−	0.00755182i
$670$		0			0
$671$	−4.48660	−	2.88336i	−0.173203	−	0.111311i
$672$		0			0
$673$	−7.80311	+	5.01476i	−0.300788	+	0.193305i	−0.682325	−	0.731049i	$-0.739031\pi$
$673$	−7.80311	+	5.01476i	−0.300788	+	0.193305i	0.381537	+	0.924353i	$0.375395\pi$
$674$		0			0
$675$	−1.89244	−	2.18399i	−0.0728401	−	0.0840620i
$676$		0			0
$677$	−17.9722	+	39.3536i	−0.690727	+	1.51248i	0.160137	+	0.987095i	$0.448806\pi$
$677$	−17.9722	+	39.3536i	−0.690727	+	1.51248i	−0.850864	+	0.525386i	$0.823921\pi$
$678$		0			0
$679$	35.7678	−	10.5024i	1.37264	−	0.403044i
$680$		0			0
$681$	−1.69432	−	11.7843i	−0.0649266	−	0.451574i
$682$		0			0
$683$	17.9307	+	39.2628i	0.686101	+	1.50235i	0.856047	+	0.516898i	$0.172913\pi$
$683$	17.9307	+	39.2628i	0.686101	+	1.50235i	−0.169947	+	0.985453i	$0.554360\pi$
$684$		0			0
$685$	2.60185	−	18.0962i	0.0994114	−	0.691422i
$686$		0			0
$687$	0.183236	−	0.211465i	0.00699088	−	0.00806791i
$688$		0			0
$689$	−11.3582			−0.432713
$690$		0			0
$691$	−12.1223			−0.461153			−0.230576	−	0.973054i	$-0.574061\pi$
$691$	−12.1223			−0.461153			−0.230576	+	0.973054i	$0.574061\pi$
$692$		0			0
$693$	18.9451	−	21.8638i	0.719664	−	0.830536i
$694$		0			0
$695$	−0.739396	+	5.14261i	−0.0280469	+	0.195070i
$696$		0			0
$697$	−0.494511	−	1.08283i	−0.0187309	−	0.0410150i
$698$		0			0
$699$	−0.894704	−	6.22280i	−0.0338408	−	0.235368i
$700$		0			0
$701$	29.2788	−	8.59704i	1.10585	−	0.324706i	0.322674	−	0.946510i	$-0.395418\pi$
$701$	29.2788	−	8.59704i	1.10585	−	0.324706i	0.783172	+	0.621805i	$0.213600\pi$
$702$		0			0
$703$	1.47744	−	3.23515i	0.0557228	−	0.122016i
$704$		0			0
$705$	0.528102	+	0.609462i	0.0198895	+	0.0229537i
$706$		0			0
$707$	−14.7367	+	9.47071i	−0.554231	+	0.356183i
$708$		0			0
$709$	2.71801	+	1.74676i	0.102077	+	0.0656008i	0.590683	−	0.806903i	$-0.298858\pi$
$709$	2.71801	+	1.74676i	0.102077	+	0.0656008i	−0.488606	+	0.872504i	$0.662495\pi$
$710$		0			0
$711$	−28.5603	−	8.38606i	−1.07110	−	0.314502i
$712$		0			0
$713$	−16.4186	−	4.69293i	−0.614883	−	0.175751i
$714$		0			0
$715$	9.22131	+	2.70762i	0.344857	+	0.101259i
$716$		0			0
$717$	−9.43714	−	6.06488i	−0.352437	−	0.226497i
$718$		0			0
$719$	19.3740	−	12.4509i	0.722530	−	0.464342i	−0.126986	−	0.991904i	$-0.540530\pi$
$719$	19.3740	−	12.4509i	0.722530	−	0.464342i	0.849516	+	0.527563i	$0.176894\pi$
$720$		0			0
$721$	−7.07355	−	8.16331i	−0.263433	−	0.304018i
$722$		0			0
$723$	3.35108	−	7.33785i	0.124628	−	0.272897i
$724$		0			0
$725$	2.08632	−	0.612599i	0.0774840	−	0.0227513i
$726$		0			0
$727$	2.37341	+	16.5074i	0.0880250	+	0.612227i	0.985310	+	0.170776i	$0.0546273\pi$
$727$	2.37341	+	16.5074i	0.0880250	+	0.612227i	−0.897285	+	0.441452i	$0.854464\pi$
$728$		0			0
$729$	−5.93609	−	12.9982i	−0.219855	−	0.481416i
$730$		0			0
$731$	−1.22917	+	8.54909i	−0.0454626	+	0.316200i
$732$		0			0
$733$	17.5131	−	20.2112i	0.646860	−	0.746516i	−0.333712	−	0.942675i	$-0.608301\pi$
$733$	17.5131	−	20.2112i	0.646860	−	0.746516i	0.980572	+	0.196159i	$0.0628468\pi$
$734$		0			0
$735$	1.42876			0.0527005
$736$		0			0
$737$	22.3491			0.823240
$738$		0			0
$739$	−14.1958	+	16.3828i	−0.522201	+	0.602652i	−0.954181	−	0.299231i	$-0.903270\pi$
$739$	−14.1958	+	16.3828i	−0.522201	+	0.602652i	0.431980	+	0.901883i	$0.357815\pi$
$740$		0			0
$741$	0.851281	−	5.92079i	0.0312726	−	0.217506i
$742$		0			0
$743$	6.04276	+	13.2318i	0.221687	+	0.485427i	0.987497	−	0.157640i	$-0.0503887\pi$
$743$	6.04276	+	13.2318i	0.221687	+	0.485427i	−0.765809	+	0.643068i	$0.777661\pi$
$744$		0			0
$745$	0.0483931	+	0.336581i	0.00177299	+	0.0123314i
$746$		0			0
$747$	37.5261	−	11.0187i	1.37301	−	0.403151i
$748$		0			0
$749$	−10.0560	+	22.0196i	−0.367439	+	0.804580i
$750$		0			0
$751$	22.1421	+	25.5534i	0.807977	+	0.932455i	0.998790	−	0.0491710i	$-0.0156579\pi$
$751$	22.1421	+	25.5534i	0.807977	+	0.932455i	−0.190813	+	0.981626i	$0.561112\pi$
$752$		0			0
$753$	−13.0999	+	8.41880i	−0.477387	+	0.306798i
$754$		0			0
$755$	−8.93348	−	5.74120i	−0.325123	−	0.208944i
$756$		0			0
$757$	17.1821	+	5.04513i	0.624495	+	0.183368i	0.578644	−	0.815580i	$-0.303582\pi$
$757$	17.1821	+	5.04513i	0.624495	+	0.183368i	0.0458509	+	0.998948i	$0.485400\pi$
$758$		0			0
$759$	−1.86087	−	12.3132i	−0.0675454	−	0.446942i
$760$		0			0
$761$	38.0258	+	11.1654i	1.37843	+	0.404745i	0.885224	−	0.465165i	$-0.154005\pi$
$761$	38.0258	+	11.1654i	1.37843	+	0.404745i	0.493211	+	0.869910i	$0.335823\pi$
$762$		0			0
$763$	29.4860	+	18.9495i	1.06746	+	0.686017i
$764$		0			0
$765$	−1.88786	+	1.21325i	−0.0682558	+	0.0438653i
$766$		0			0
$767$	6.70401	+	7.73684i	0.242068	+	0.279361i
$768$		0			0
$769$	13.7474	−	30.1027i	0.495745	−	1.08553i	−0.482084	−	0.876125i	$-0.660120\pi$
$769$	13.7474	−	30.1027i	0.495745	−	1.08553i	0.977829	−	0.209405i	$-0.0671526\pi$
$770$		0			0
$771$	12.5378	−	3.68144i	0.451539	−	0.132584i
$772$		0			0
$773$	4.10393	+	28.5435i	0.147608	+	1.02664i	0.920120	+	0.391637i	$0.128091\pi$
$773$	4.10393	+	28.5435i	0.147608	+	1.02664i	−0.772512	+	0.635001i	$0.781000\pi$
$774$		0			0
$775$	1.47914	+	3.23886i	0.0531322	+	0.116343i
$776$		0			0
$777$	−0.0811947	+	0.564721i	−0.00291284	+	0.0202593i
$778$		0			0
$779$	6.09996	−	7.03973i	0.218554	−	0.252224i
$780$		0			0
$781$	−2.13343			−0.0763401
$782$		0			0
$783$	−6.28366			−0.224560
$784$		0			0
$785$	15.7473	−	18.1734i	0.562045	−	0.648635i
$786$		0			0
$787$	2.15774	−	15.0074i	0.0769151	−	0.534956i	−0.914539	−	0.404498i	$-0.867446\pi$
$787$	2.15774	−	15.0074i	0.0769151	−	0.534956i	0.991454	−	0.130458i	$-0.0416447\pi$
$788$		0			0
$789$	−0.778060	−	1.70371i	−0.0276997	−	0.0606538i
$790$		0			0
$791$	2.73946	+	19.0534i	0.0974041	+	0.677461i
$792$		0			0
$793$	−1.84417	+	0.541497i	−0.0654883	+	0.0192291i
$794$		0			0
$795$	1.27483	−	2.79149i	0.0452135	−	0.0990039i
$796$		0			0
$797$	5.03954	+	5.81593i	0.178510	+	0.206011i	0.837952	−	0.545744i	$-0.183753\pi$
$797$	5.03954	+	5.81593i	0.178510	+	0.206011i	−0.659442	+	0.751755i	$0.729208\pi$
$798$		0			0
$799$	1.10213	−	0.708299i	0.0389907	−	0.0250578i
$800$		0			0
$801$	−29.9118	−	19.2232i	−1.05688	−	0.679217i
$802$		0			0
$803$	−30.2896	−	8.89382i	−1.06890	−	0.313856i
$804$		0			0
$805$	6.35116	−	7.43705i	0.223849	−	0.262122i
$806$		0			0
$807$	6.73017	+	1.97616i	0.236913	+	0.0695640i
$808$		0			0
$809$	34.5544	+	22.2067i	1.21487	+	0.780747i	0.981467	−	0.191634i	$-0.0613785\pi$
$809$	34.5544	+	22.2067i	1.21487	+	0.780747i	0.233400	+	0.972381i	$0.425015\pi$
$810$		0			0
$811$	16.6818	−	10.7208i	0.585778	−	0.376457i	−0.213927	−	0.976850i	$-0.568625\pi$
$811$	16.6818	−	10.7208i	0.585778	−	0.376457i	0.799705	+	0.600393i	$0.204989\pi$
$812$		0			0
$813$	−4.94148	−	5.70277i	−0.173305	−	0.200005i
$814$		0			0
$815$	−2.40392	+	5.26386i	−0.0842058	+	0.184385i
$816$		0			0
$817$	−64.8469	+	19.0408i	−2.26871	+	0.666152i
$818$		0			0
$819$	−1.48377	−	10.3198i	−0.0518470	−	0.360604i
$820$		0			0
$821$	−3.74456	−	8.19945i	−0.130686	−	0.286163i	0.832965	−	0.553325i	$-0.186641\pi$
$821$	−3.74456	−	8.19945i	−0.130686	−	0.286163i	−0.963652	+	0.267162i	$0.913914\pi$
$822$		0			0
$823$	−4.15398	+	28.8916i	−0.144799	+	1.00710i	0.779766	+	0.626071i	$0.215338\pi$
$823$	−4.15398	+	28.8916i	−0.144799	+	1.00710i	−0.924565	+	0.381026i	$0.875571\pi$
$824$		0			0
$825$	−1.70044	+	1.96241i	−0.0592016	+	0.0683223i
$826$		0			0
$827$	−1.01185			−0.0351856			−0.0175928	−	0.999845i	$-0.505600\pi$
$827$	−1.01185			−0.0351856			−0.0175928	+	0.999845i	$0.505600\pi$
$828$		0			0
$829$	−48.4160			−1.68156			−0.840778	−	0.541380i	$-0.817902\pi$
$829$	−48.4160			−1.68156			−0.840778	+	0.541380i	$0.817902\pi$
$830$		0			0
$831$	−1.27600	+	1.47258i	−0.0442639	+	0.0510833i
$832$		0			0
$833$	0.330329	−	2.29749i	0.0114452	−	0.0796034i
$834$		0			0
$835$	4.46975	+	9.78738i	0.154682	+	0.338706i
$836$		0			0
$837$	−1.46437	−	10.1849i	−0.0506159	−	0.352042i
$838$		0			0
$839$	17.7321	−	5.20663i	0.612181	−	0.179753i	0.0390786	−	0.999236i	$-0.487558\pi$
$839$	17.7321	−	5.20663i	0.612181	−	0.179753i	0.573103	+	0.819483i	$0.305740\pi$
$840$		0			0
$841$	−10.0829	+	22.0786i	−0.347688	+	0.761330i
$842$		0			0
$843$	−3.90342	−	4.50479i	−0.134441	−	0.155153i
$844$		0			0
$845$	−8.02259	+	5.15580i	−0.275985	+	0.177365i
$846$		0			0
$847$	−26.8781	−	17.2735i	−0.923543	−	0.593525i
$848$		0			0
$849$	0.258640	+	0.0759434i	0.00887649	+	0.00260637i
$850$		0			0
$851$	−1.76189	−	2.00401i	−0.0603967	−	0.0686967i
$852$		0			0
$853$	17.9839	+	5.28056i	0.615758	+	0.180803i	0.574714	−	0.818354i	$-0.305113\pi$
$853$	17.9839	+	5.28056i	0.615758	+	0.180803i	0.0410442	+	0.999157i	$0.486932\pi$
$854$		0			0
$855$	−14.7725	−	9.49372i	−0.505209	−	0.324678i
$856$		0			0
$857$	−21.6890	+	13.9387i	−0.740883	+	0.476137i	−0.855844	−	0.517233i	$-0.826962\pi$
$857$	−21.6890	+	13.9387i	−0.740883	+	0.476137i	0.114961	+	0.993370i	$0.463326\pi$
$858$		0			0
$859$	−17.3756	−	20.0525i	−0.592849	−	0.684184i	0.377468	−	0.926023i	$-0.376795\pi$
$859$	−17.3756	−	20.0525i	−0.592849	−	0.684184i	−0.970316	+	0.241839i	$0.922249\pi$
$860$		0			0
$861$	−0.620738	+	1.35923i	−0.0211547	+	0.0463224i
$862$		0			0
$863$	11.6635	−	3.42470i	0.397029	−	0.116578i	−0.0771225	−	0.997022i	$-0.524573\pi$
$863$	11.6635	−	3.42470i	0.397029	−	0.116578i	0.474151	+	0.880444i	$0.342755\pi$
$864$		0			0
$865$	1.04421	+	7.26265i	0.0355042	+	0.246937i
$866$		0			0
$867$	3.41162	+	7.47040i	0.115865	+	0.253708i
$868$		0			0
$869$	−7.96303	+	55.3841i	−0.270127	+	1.87878i
$870$		0			0
$871$	5.27445	−	6.08704i	0.178718	−	0.206251i
$872$		0			0
$873$	−50.2184			−1.69964
$874$		0			0
$875$	−2.03925			−0.0689394
$876$		0			0
$877$	16.8502	−	19.4462i	0.568991	−	0.656651i	−0.396210	−	0.918160i	$-0.629675\pi$
$877$	16.8502	−	19.4462i	0.568991	−	0.656651i	0.965201	+	0.261509i	$0.0842202\pi$
$878$		0			0
$879$	−1.62371	+	11.2932i	−0.0547665	+	0.380910i
$880$		0			0
$881$	−0.416190	−	0.911328i	−0.0140218	−	0.0307034i	0.902492	−	0.430708i	$-0.141736\pi$
$881$	−0.416190	−	0.911328i	−0.0140218	−	0.0307034i	−0.916513	+	0.400004i	$0.869009\pi$
$882$		0			0
$883$	−3.15566	−	21.9481i	−0.106197	−	0.738613i	−0.971444	−	0.237268i	$-0.923748\pi$
$883$	−3.15566	−	21.9481i	−0.106197	−	0.738613i	0.865248	−	0.501345i	$-0.167161\pi$
$884$		0			0
$885$	−2.65392	+	0.779262i	−0.0892106	+	0.0261946i
$886$		0			0
$887$	22.6938	−	49.6924i	0.761982	−	1.66851i	0.0184307	−	0.999830i	$-0.494133\pi$
$887$	22.6938	−	49.6924i	0.761982	−	1.66851i	0.743552	−	0.668679i	$-0.233140\pi$
$888$		0			0
$889$	−11.8982	−	13.7313i	−0.399053	−	0.460532i
$890$		0			0
$891$	−29.4907	+	18.9525i	−0.987976	+	0.634934i
$892$		0			0
$893$	8.62420	+	5.54244i	0.288598	+	0.185471i
$894$		0			0
$895$	9.31003	+	2.73367i	0.311200	+	0.0913765i
$896$		0			0
$897$	−3.79282	−	2.39912i	−0.126639	−	0.0801044i
$898$		0			0
$899$	7.42860	+	2.18123i	0.247758	+	0.0727482i
$900$		0			0
$901$	−4.19407	−	2.69536i	−0.139725	−	0.0897956i
$902$		0			0
$903$	9.12059	−	5.86145i	0.303514	−	0.195057i
$904$		0			0
$905$	12.3974	+	14.3074i	0.412103	+	0.475593i
$906$		0			0
$907$	−20.9133	+	45.7938i	−0.694416	+	1.52056i	0.152196	+	0.988350i	$0.451365\pi$
$907$	−20.9133	+	45.7938i	−0.694416	+	1.52056i	−0.846613	+	0.532209i	$0.821362\pi$
$908$		0			0
$909$	22.6427	−	6.64850i	0.751012	−	0.220517i
$910$		0			0
$911$	3.68527	+	25.6316i	0.122098	+	0.849213i	0.955172	+	0.296051i	$0.0956698\pi$
$911$	3.68527	+	25.6316i	0.122098	+	0.849213i	−0.833074	+	0.553162i	$0.813421\pi$
$912$		0			0
$913$	−30.5408	−	66.8750i	−1.01075	−	2.21324i
$914$		0			0
$915$	0.0739043	−	0.514015i	0.00244320	−	0.0169928i
$916$		0			0
$917$	−9.71037	+	11.2064i	−0.320665	+	0.370067i
$918$		0			0
$919$	−1.47121			−0.0485307			−0.0242654	−	0.999706i	$-0.507725\pi$
$919$	−1.47121			−0.0485307			−0.0242654	+	0.999706i	$0.507725\pi$
$920$		0			0
$921$	−7.28268			−0.239973
$922$		0			0
$923$	−0.503495	+	0.581064i	−0.0165727	+	0.0191260i
$924$		0			0
$925$	−0.0791837	+	0.550735i	−0.00260354	+	0.0181081i
$926$		0			0
$927$	6.04482	+	13.2363i	0.198538	+	0.434738i
$928$		0			0
$929$	−2.29047	−	15.9305i	−0.0751477	−	0.522664i	−0.992274	−	0.124067i	$-0.960406\pi$
$929$	−2.29047	−	15.9305i	−0.0751477	−	0.522664i	0.917126	−	0.398597i	$-0.130503\pi$
$930$		0			0
$931$	17.4270	−	5.11704i	0.571148	−	0.167704i
$932$		0			0
$933$	2.16373	−	4.73790i	0.0708372	−	0.155112i
$934$		0			0
$935$	2.76248	+	3.18807i	0.0903427	+	0.104261i
$936$		0			0
$937$	41.5464	−	26.7002i	1.35726	−	0.872258i	0.359124	−	0.933290i	$-0.383075\pi$
$937$	41.5464	−	26.7002i	1.35726	−	0.872258i	0.998136	+	0.0610315i	$0.0194390\pi$
$938$		0			0
$939$	7.89652	+	5.07478i	0.257693	+	0.165609i
$940$		0			0
$941$	−4.67526	−	1.37278i	−0.152409	−	0.0447513i	0.204638	−	0.978838i	$-0.434398\pi$
$941$	−4.67526	−	1.37278i	−0.152409	−	0.0447513i	−0.357047	+	0.934086i	$0.616216\pi$
$942$		0			0
$943$	−2.94888	−	6.33613i	−0.0960288	−	0.206333i
$944$		0			0
$945$	5.65441	+	1.66028i	0.183938	+	0.0540090i
$946$		0			0
$947$	−39.5978	−	25.4480i	−1.28676	−	0.826948i	−0.295051	−	0.955482i	$-0.595337\pi$
$947$	−39.5978	−	25.4480i	−1.28676	−	0.826948i	−0.991705	+	0.128534i	$0.958973\pi$
$948$		0			0
$949$	−9.57076	+	6.15075i	−0.310680	+	0.199662i
$950$		0			0
$951$	−5.78568	−	6.67703i	−0.187614	−	0.216518i
$952$		0			0
$953$	−8.58110	+	18.7900i	−0.277969	+	0.608668i	−0.996196	−	0.0871415i	$-0.972227\pi$
$953$	−8.58110	+	18.7900i	−0.277969	+	0.608668i	0.718227	+	0.695809i	$0.244954\pi$
$954$		0			0
$955$	−26.3229	+	7.72909i	−0.851788	+	0.250107i
$956$		0			0
$957$	0.803528	+	5.58866i	0.0259744	+	0.180656i
$958$		0			0
$959$	15.4876	+	33.9132i	0.500122	+	1.09511i
$960$		0			0
$961$	2.60749	−	18.1355i	0.0841125	−	0.585015i
$962$		0			0
$963$	21.3553	−	24.6454i	0.688166	−	0.794186i
$964$		0			0
$965$	−18.2742			−0.588267
$966$		0			0
$967$	−22.9596			−0.738331			−0.369165	−	0.929364i	$-0.620356\pi$
$967$	−22.9596			−0.738331			−0.369165	+	0.929364i	$0.620356\pi$
$968$		0			0
$969$	1.71938	−	1.98427i	0.0552343	−	0.0637438i
$970$		0			0
$971$	0.638993	−	4.44430i	0.0205063	−	0.142624i	−0.976996	−	0.213257i	$-0.931593\pi$
$971$	0.638993	−	4.44430i	0.0205063	−	0.142624i	0.997502	+	0.0706329i	$0.0225019\pi$
$972$		0			0
$973$	−4.40130	−	9.63750i	−0.141099	−	0.308964i
$974$		0			0
$975$	0.133177	+	0.926268i	0.00426508	+	0.0296643i
$976$		0			0
$977$	−30.7173	+	9.01940i	−0.982732	+	0.288556i	−0.733352	−	0.679850i	$-0.762045\pi$
$977$	−30.7173	+	9.01940i	−0.982732	+	0.288556i	−0.249380	+	0.968406i	$0.580227\pi$
$978$		0			0
$979$	−27.7655	+	60.7979i	−0.887388	+	1.94311i
$980$		0			0
$981$	−30.9208	−	35.6845i	−0.987225	−	1.13932i
$982$		0			0
$983$	23.7538	−	15.2656i	0.757627	−	0.486897i	−0.103913	−	0.994586i	$-0.533136\pi$
$983$	23.7538	−	15.2656i	0.757627	−	0.486897i	0.861540	+	0.507689i	$0.169500\pi$
$984$		0			0
$985$	−9.19174	−	5.90717i	−0.292873	−	0.188218i
$986$		0			0
$987$	−1.57791	−	0.463316i	−0.0502254	−	0.0147475i
$988$		0			0
$989$	−6.85514	+	50.2415i	−0.217981	+	1.59759i
$990$		0			0
$991$	−24.9651	−	7.33040i	−0.793041	−	0.232858i	−0.139971	−	0.990156i	$-0.544701\pi$
$991$	−24.9651	−	7.33040i	−0.793041	−	0.232858i	−0.653070	+	0.757298i	$0.726519\pi$
$992$		0			0
$993$	12.2732	+	7.88749i	0.389478	+	0.250302i
$994$		0			0
$995$	−2.95347	+	1.89808i	−0.0936313	+	0.0601732i
$996$		0			0
$997$	−8.64887	−	9.98133i	−0.273913	−	0.316112i	0.602081	−	0.798435i	$-0.294339\pi$
$997$	−8.64887	−	9.98133i	−0.273913	−	0.316112i	−0.875993	+	0.482323i	$0.839793\pi$
$998$		0			0
$999$	0.667946	−	1.46260i	0.0211329	−	0.0462746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.41.2	✓	30
23.9	even	11	inner	460.2.m.a.101.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.41.2	✓	30	1.1	even	1	trivial
460.2.m.a.101.2	yes	30	23.9	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)

\(f(q)\)	\(=\)	\(q+(0.329283 - 0.380013i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(-0.847137 - 1.85497i) q^{7} +(0.390962 + 2.71920i) q^{9} +O(q^{10})\)	\(q+(0.329283 - 0.380013i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(-0.847137 - 1.85497i) q^{7} +(0.390962 + 2.71920i) q^{9} +(4.95488 - 1.45488i) q^{11} +(0.773111 - 1.69288i) q^{13} +(0.329283 + 0.380013i) q^{15} +(0.687204 - 0.441639i) q^{17} +(5.37737 + 3.45583i) q^{19} +(-0.983860 - 0.288887i) q^{21} +(4.01575 - 2.62178i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(2.43109 + 1.56237i) q^{27} +(-1.82922 + 1.17557i) q^{29} +(-2.33171 - 2.69094i) q^{31} +(1.07868 - 2.36199i) q^{33} +(1.95665 - 0.574525i) q^{35} +(-0.0791837 - 0.550735i) q^{37} +(-0.388742 - 0.851227i) q^{39} +(0.207389 - 1.44242i) q^{41} +(-6.92394 + 7.99065i) q^{43} -2.74716 q^{45} +1.60379 q^{47} +(1.86075 - 2.14742i) q^{49} +(0.0584560 - 0.406570i) q^{51} +(-2.53532 - 5.55157i) q^{53} +(0.734922 + 5.11150i) q^{55} +(3.08393 - 0.905525i) q^{57} +(-2.28512 + 5.00371i) q^{59} +(-0.676314 - 0.780507i) q^{61} +(4.71284 - 3.02876i) q^{63} +(1.56562 + 1.00616i) q^{65} +(4.15251 + 1.21929i) q^{67} +(0.326011 - 2.38934i) q^{69} +(-0.396395 - 0.116392i) q^{71} +(-5.14265 - 3.30498i) q^{73} +(-0.423007 + 0.271850i) q^{75} +(-6.89623 - 7.95868i) q^{77} +(-4.50110 + 9.85604i) q^{79} +(-6.51342 + 1.91251i) q^{81} +(-2.02608 - 14.0917i) q^{83} +(0.339345 + 0.743061i) q^{85} +(-0.155600 + 1.08222i) q^{87} +(-8.47579 + 9.78158i) q^{89} -3.79517 q^{91} -1.79038 q^{93} +(-4.18593 + 4.83082i) q^{95} +(-2.60153 + 18.0940i) q^{97} +(5.89329 + 12.9045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more