LMFDB - Embedded newform 460.2.x.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	460.33
Dual form			460.2.x.a.237.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.486808 - 2.23782i) q^{3} +(0.0638162 + 2.23516i) q^{5} +(1.23306 + 2.25818i) q^{7} +(-2.04197 + 0.932535i) q^{9} +O(q^{10})$	\(q+(-0.486808 - 2.23782i) q^{3} +(0.0638162 + 2.23516i) q^{5} +(1.23306 + 2.25818i) q^{7} +(-2.04197 + 0.932535i) q^{9} +(0.879344 + 0.761956i) q^{11} +(4.16960 + 2.27677i) q^{13} +(4.97082 - 1.23090i) q^{15} +(-2.50905 + 3.35170i) q^{17} +(-0.0362513 + 0.252133i) q^{19} +(4.45315 - 3.85868i) q^{21} +(4.61338 - 1.31024i) q^{23} +(-4.99185 + 0.285278i) q^{25} +(-1.03643 - 1.38451i) q^{27} +(-1.34948 + 0.194026i) q^{29} +(8.60919 - 5.53279i) q^{31} +(1.27705 - 2.33874i) q^{33} +(-4.96871 + 2.90020i) q^{35} +(-1.66154 + 4.45477i) q^{37} +(3.06522 - 10.4392i) q^{39} +(2.79496 - 6.12010i) q^{41} +(6.28917 - 1.36812i) q^{43} +(-2.21467 - 4.50461i) q^{45} +(-1.71936 + 1.71936i) q^{47} +(0.205531 - 0.319813i) q^{49} +(8.72192 + 3.98317i) q^{51} +(-7.04584 + 3.84732i) q^{53} +(-1.64698 + 2.01410i) q^{55} +(0.581876 - 0.0416166i) q^{57} +(0.664449 + 2.26290i) q^{59} +(-0.532294 - 0.828266i) q^{61} +(-4.62371 - 3.46126i) q^{63} +(-4.82286 + 9.46501i) q^{65} +(-0.626287 + 8.75664i) q^{67} +(-5.17791 - 9.68608i) q^{69} +(-4.15239 - 4.79212i) q^{71} +(-11.8709 + 8.88643i) q^{73} +(3.06848 + 11.0320i) q^{75} +(-0.636352 + 2.92526i) q^{77} +(0.671175 - 0.197075i) q^{79} +(-7.00389 + 8.08292i) q^{81} +(-12.2947 - 4.58568i) q^{83} +(-7.65169 - 5.39423i) q^{85} +(1.09113 + 2.92544i) q^{87} +(8.57741 + 5.51237i) q^{89} +12.2231i q^{91} +(-16.5724 - 16.5724i) q^{93} +(-0.565870 - 0.0649371i) q^{95} +(14.5308 - 5.41971i) q^{97} +(-2.50614 - 0.735870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.486808	−	2.23782i	−0.281059	−	1.29201i	−0.873670	−	0.486518i	$-0.838267\pi$
$3$	−0.486808	−	2.23782i	−0.281059	−	1.29201i	0.592611	−	0.805488i	$-0.298097\pi$
$4$		0			0
$5$	0.0638162	+	2.23516i	0.0285395	+	0.999593i
$5$	0.0638162	+	2.23516i	0.0285395	+	0.999593i
$6$		0			0
$7$	1.23306	+	2.25818i	0.466054	+	0.853513i	0.999968	+	0.00797503i	$0.00253856\pi$
$7$	1.23306	+	2.25818i	0.466054	+	0.853513i	−0.533915	+	0.845538i	$0.679280\pi$
$8$		0			0
$9$	−2.04197	+	0.932535i	−0.680656	+	0.310845i
$10$		0			0
$11$	0.879344	+	0.761956i	0.265132	+	0.229738i	0.777274	−	0.629163i	$-0.216602\pi$
$11$	0.879344	+	0.761956i	0.265132	+	0.229738i	−0.512141	+	0.858901i	$0.671148\pi$
$12$		0			0
$13$	4.16960	+	2.27677i	1.15644	+	0.631464i	0.938765	−	0.344558i	$-0.111971\pi$
$13$	4.16960	+	2.27677i	1.15644	+	0.631464i	0.217674	+	0.976022i	$0.430153\pi$
$14$		0			0
$15$	4.97082	−	1.23090i	1.28346	−	0.317818i
$16$		0			0
$17$	−2.50905	+	3.35170i	−0.608534	+	0.812906i	−0.993950	−	0.109837i	$-0.964967\pi$
$17$	−2.50905	+	3.35170i	−0.608534	+	0.812906i	0.385416	+	0.922743i	$0.374058\pi$
$18$		0			0
$19$	−0.0362513	+	0.252133i	−0.00831661	+	0.0578433i	−0.993557	−	0.113332i	$-0.963847\pi$
$19$	−0.0362513	+	0.252133i	−0.00831661	+	0.0578433i	0.985241	+	0.171176i	$0.0547566\pi$
$20$		0			0
$21$	4.45315	−	3.85868i	0.971757	−	0.842032i
$22$		0			0
$23$	4.61338	−	1.31024i	0.961956	−	0.273204i
$23$	4.61338	−	1.31024i	0.961956	−	0.273204i
$24$		0			0
$25$	−4.99185	+	0.285278i	−0.998371	+	0.0570557i
$26$		0			0
$27$	−1.03643	−	1.38451i	−0.199461	−	0.266449i
$28$		0			0
$29$	−1.34948	+	0.194026i	−0.250592	+	0.0360297i	−0.266466	−	0.963844i	$-0.585856\pi$
$29$	−1.34948	+	0.194026i	−0.250592	+	0.0360297i	0.0158740	+	0.999874i	$0.494947\pi$
$30$		0			0
$31$	8.60919	−	5.53279i	1.54626	−	0.993719i	0.560002	−	0.828492i	$-0.310801\pi$
$31$	8.60919	−	5.53279i	1.54626	−	0.993719i	0.986255	−	0.165228i	$-0.0528358\pi$
$32$		0			0
$33$	1.27705	−	2.33874i	0.222306	−	0.407123i
$34$		0			0
$35$	−4.96871	+	2.90020i	−0.839865	+	0.490223i
$36$		0			0
$37$	−1.66154	+	4.45477i	−0.273156	+	0.732359i	0.725853	+	0.687850i	$0.241445\pi$
$37$	−1.66154	+	4.45477i	−0.273156	+	0.732359i	−0.999009	+	0.0445096i	$0.985827\pi$
$38$		0			0
$39$	3.06522	−	10.4392i	0.490828	−	1.67161i
$40$		0			0
$41$	2.79496	−	6.12010i	0.436499	−	0.955799i	−0.555729	−	0.831364i	$-0.687561\pi$
$41$	2.79496	−	6.12010i	0.436499	−	0.955799i	0.992228	−	0.124436i	$-0.0397120\pi$
$42$		0			0
$43$	6.28917	−	1.36812i	0.959089	−	0.208637i	0.294337	−	0.955702i	$-0.404901\pi$
$43$	6.28917	−	1.36812i	0.959089	−	0.208637i	0.664752	+	0.747064i	$0.268537\pi$
$44$		0			0
$45$	−2.21467	−	4.50461i	−0.330144	−	0.671507i
$46$		0			0
$47$	−1.71936	+	1.71936i	−0.250794	+	0.250794i	−0.821296	−	0.570502i	$-0.806749\pi$
$47$	−1.71936	+	1.71936i	−0.250794	+	0.250794i	0.570502	+	0.821296i	$0.306749\pi$
$48$		0			0
$49$	0.205531	−	0.319813i	0.0293616	−	0.0456875i
$50$		0			0
$51$	8.72192	+	3.98317i	1.22131	+	0.557755i
$52$		0			0
$53$	−7.04584	+	3.84732i	−0.967821	+	0.528470i	−0.883735	−	0.467988i	$-0.844979\pi$
$53$	−7.04584	+	3.84732i	−0.967821	+	0.528470i	−0.0840862	+	0.996458i	$0.526797\pi$
$54$		0			0
$55$	−1.64698	+	2.01410i	−0.222078	+	0.271581i
$56$		0			0
$57$	0.581876	−	0.0416166i	0.0770714	−	0.00551225i
$58$		0			0
$59$	0.664449	+	2.26290i	0.0865039	+	0.294605i	0.991370	−	0.131090i	$-0.0418477\pi$
$59$	0.664449	+	2.26290i	0.0865039	+	0.294605i	−0.904867	+	0.425695i	$0.860030\pi$
$60$		0			0
$61$	−0.532294	−	0.828266i	−0.0681533	−	0.106049i	0.805504	−	0.592590i	$-0.201895\pi$
$61$	−0.532294	−	0.828266i	−0.0681533	−	0.106049i	−0.873657	+	0.486542i	$0.838258\pi$
$62$		0			0
$63$	−4.62371	−	3.46126i	−0.582532	−	0.436078i
$64$		0			0
$65$	−4.82286	+	9.46501i	−0.598202	+	1.17399i
$66$		0			0
$67$	−0.626287	+	8.75664i	−0.0765132	+	1.06979i	0.803644	+	0.595111i	$0.202892\pi$
$67$	−0.626287	+	8.75664i	−0.0765132	+	1.06979i	−0.880157	+	0.474683i	$0.842563\pi$
$68$		0			0
$69$	−5.17791	−	9.68608i	−0.623348	−	1.16607i
$70$		0			0
$71$	−4.15239	−	4.79212i	−0.492798	−	0.568719i	0.453813	−	0.891097i	$-0.350063\pi$
$71$	−4.15239	−	4.79212i	−0.492798	−	0.568719i	−0.946611	+	0.322378i	$0.895518\pi$
$72$		0			0
$73$	−11.8709	+	8.88643i	−1.38938	+	1.04008i	−0.396877	+	0.917872i	$0.629906\pi$
$73$	−11.8709	+	8.88643i	−1.38938	+	1.04008i	−0.992505	+	0.122206i	$0.961003\pi$
$74$		0			0
$75$	3.06848	+	11.0320i	0.354317	+	1.27387i
$76$		0			0
$77$	−0.636352	+	2.92526i	−0.0725190	+	0.333364i
$78$		0			0
$79$	0.671175	−	0.197075i	0.0755131	−	0.0221726i	−0.243758	−	0.969836i	$-0.578380\pi$
$79$	0.671175	−	0.197075i	0.0755131	−	0.0221726i	0.319271	+	0.947663i	$0.396562\pi$
$80$		0			0
$81$	−7.00389	+	8.08292i	−0.778210	+	0.898102i
$82$		0			0
$83$	−12.2947	−	4.58568i	−1.34952	−	0.503344i	−0.432299	−	0.901730i	$-0.642298\pi$
$83$	−12.2947	−	4.58568i	−1.34952	−	0.503344i	−0.917218	+	0.398387i	$0.869570\pi$
$84$		0			0
$85$	−7.65169	−	5.39423i	−0.829942	−	0.585086i
$86$		0			0
$87$	1.09113	+	2.92544i	0.116982	+	0.313640i
$88$		0			0
$89$	8.57741	+	5.51237i	0.909204	+	0.584310i	0.909506	−	0.415690i	$-0.136460\pi$
$89$	8.57741	+	5.51237i	0.909204	+	0.584310i	−0.000302485		1.00000i	$0.500096\pi$
$90$		0			0
$91$			12.2231i			1.28133i
$92$		0			0
$93$	−16.5724	−	16.5724i	−1.71848	−	1.71848i
$94$		0			0
$95$	−0.565870	−	0.0649371i	−0.0580571	−	0.00666240i
$96$		0			0
$97$	14.5308	−	5.41971i	1.47538	−	0.550288i	0.522234	−	0.852802i	$-0.325099\pi$
$97$	14.5308	−	5.41971i	1.47538	−	0.550288i	0.953145	+	0.302515i	$0.0978261\pi$
$98$		0			0
$99$	−2.50614	−	0.735870i	−0.251877	−	0.0739577i
$100$		0			0
$101$	0.507307	+	1.11085i	0.0504789	+	0.110533i	0.933191	−	0.359381i	$-0.117012\pi$
$101$	0.507307	+	1.11085i	0.0504789	+	0.110533i	−0.882712	+	0.469914i	$0.844285\pi$
$102$		0			0
$103$	0.543305	+	7.59640i	0.0535335	+	0.748496i	0.951347	+	0.308121i	$0.0997000\pi$
$103$	0.543305	+	7.59640i	0.0535335	+	0.748496i	−0.897814	+	0.440375i	$0.854845\pi$
$104$		0			0
$105$	8.90893	+	9.70724i	0.869422	+	0.947330i
$106$		0			0
$107$	−0.177345	−	0.0385791i	−0.0171446	−	0.00372958i	0.203985	−	0.978974i	$-0.434611\pi$
$107$	−0.177345	−	0.0385791i	−0.0171446	−	0.00372958i	−0.221129	+	0.975244i	$0.570974\pi$
$108$		0			0
$109$	−2.06213	−	14.3424i	−0.197516	−	1.37376i	−0.811461	−	0.584406i	$-0.801327\pi$
$109$	−2.06213	−	14.3424i	−0.197516	−	1.37376i	0.613945	−	0.789349i	$-0.289582\pi$
$110$		0			0
$111$	10.7778	+	1.54962i	1.02299	+	0.147083i
$112$		0			0
$113$	11.8792	+	0.849617i	1.11750	+	0.0799252i	0.617846	−	0.786299i	$-0.288006\pi$
$113$	11.8792	+	0.849617i	1.11750	+	0.0799252i	0.499655	+	0.866225i	$0.333460\pi$
$114$		0			0
$115$	3.22300	+	10.2280i	0.300546	+	0.953767i
$116$		0			0
$117$	−10.6374	−	0.760799i	−0.983424	−	0.0703359i
$118$		0			0
$119$	−10.6626	−	1.53304i	−0.977435	−	0.140534i
$120$		0			0
$121$	−1.37279	−	9.54799i	−0.124799	−	0.867999i
$122$		0			0
$123$	−15.0563	−	3.27530i	−1.35758	−	0.295324i
$124$		0			0
$125$	−0.956203	−	11.1394i	−0.0855254	−	0.996336i
$126$		0			0
$127$	−0.158077	−	2.21021i	−0.0140271	−	0.196125i	−0.999634	−	0.0270687i	$-0.991383\pi$
$127$	−0.158077	−	2.21021i	−0.0140271	−	0.196125i	0.985606	−	0.169056i	$-0.0540718\pi$
$128$		0			0
$129$	−6.12324	−	13.4080i	−0.539121	−	1.18051i
$130$		0			0
$131$	−15.5540	−	4.56706i	−1.35896	−	0.399026i	−0.480563	−	0.876960i	$-0.659568\pi$
$131$	−15.5540	−	4.56706i	−1.35896	−	0.399026i	−0.878396	+	0.477934i	$0.841386\pi$
$132$		0			0
$133$	−0.614063	+	0.229034i	−0.0532460	+	0.0198597i
$134$		0			0
$135$	3.02845	−	2.40494i	0.260648	−	0.206984i
$136$		0			0
$137$	−11.3944	−	11.3944i	−0.973491	−	0.973491i	0.0261670	−	0.999658i	$-0.491670\pi$
$137$	−11.3944	−	11.3944i	−0.973491	−	0.973491i	−0.999658	+	0.0261670i	$0.991670\pi$
$138$		0			0
$139$		−	8.15032i		−	0.691301i	−0.938363	−	0.345650i	$-0.887658\pi$
$139$		−	8.15032i		−	0.691301i	0.938363	−	0.345650i	$-0.112342\pi$
$140$		0			0
$141$	4.68461	+	3.01061i	0.394515	+	0.253539i
$142$		0			0
$143$	1.93171	+	5.17912i	0.161538	+	0.433100i
$144$		0			0
$145$	−0.519797	−	3.00392i	−0.0431668	−	0.249462i
$146$		0			0
$147$	−0.815738	−	0.304255i	−0.0672809	−	0.0250945i
$148$		0			0
$149$	−11.1085	+	12.8199i	−0.910041	+	1.05024i	0.0884906	+	0.996077i	$0.471796\pi$
$149$	−11.1085	+	12.8199i	−0.910041	+	1.05024i	−0.998532	+	0.0541666i	$0.982750\pi$
$150$		0			0
$151$	15.5893	−	4.57743i	1.26864	−	0.372506i	0.422935	−	0.906160i	$-0.361000\pi$
$151$	15.5893	−	4.57743i	1.26864	−	0.372506i	0.845703	+	0.533654i	$0.179182\pi$
$152$		0			0
$153$	1.99782	−	9.18383i	0.161514	−	0.742469i
$154$		0			0
$155$	12.9161	+	18.8898i	1.03744	+	1.51727i
$156$		0			0
$157$	9.72286	−	7.27844i	0.775968	−	0.580883i	−0.136208	−	0.990680i	$-0.543492\pi$
$157$	9.72286	−	7.27844i	0.775968	−	0.580883i	0.912177	+	0.409798i	$0.134401\pi$
$158$		0			0
$159$	12.0396	+	13.8944i	0.954802	+	1.10190i
$160$		0			0
$161$	8.64735	+	8.80225i	0.681506	+	0.693715i
$162$		0			0
$163$	1.28726	−	17.9983i	0.100826	−	1.40974i	−0.655329	−	0.755343i	$-0.727470\pi$
$163$	1.28726	−	17.9983i	0.100826	−	1.40974i	0.756156	−	0.654392i	$-0.227075\pi$
$164$		0			0
$165$	5.30895	+	2.70516i	0.413301	+	0.210596i
$166$		0			0
$167$	−15.5768	−	11.6606i	−1.20537	−	0.902326i	−0.208240	−	0.978078i	$-0.566773\pi$
$167$	−15.5768	−	11.6606i	−1.20537	−	0.902326i	−0.997127	+	0.0757517i	$0.975864\pi$
$168$		0			0
$169$	5.17354	+	8.05018i	0.397964	+	0.619245i
$170$		0			0
$171$	−0.161099	−	0.548653i	−0.0123195	−	0.0419565i
$172$		0			0
$173$	4.37672	−	0.313029i	0.332756	−	0.0237992i	0.0960382	−	0.995378i	$-0.469383\pi$
$173$	4.37672	−	0.313029i	0.332756	−	0.0237992i	0.236718	+	0.971578i	$0.423928\pi$
$174$		0			0
$175$	−6.79948	−	10.9208i	−0.513992	−	0.825532i
$176$		0			0
$177$	4.74052	−	2.58852i	0.356319	−	0.194565i
$178$		0			0
$179$	−5.02842	−	2.29640i	−0.375842	−	0.171641i	0.218533	−	0.975830i	$-0.429873\pi$
$179$	−5.02842	−	2.29640i	−0.375842	−	0.171641i	−0.594374	+	0.804188i	$0.702600\pi$
$180$		0			0
$181$	−4.58232	+	7.13022i	−0.340601	+	0.529985i	−0.968728	−	0.248125i	$-0.920185\pi$
$181$	−4.58232	+	7.13022i	−0.340601	+	0.529985i	0.628127	+	0.778111i	$0.283822\pi$
$182$		0			0
$183$	−1.59439	+	1.59439i	−0.117860	+	0.117860i
$184$		0			0
$185$	−10.0631	−	3.42952i	−0.739857	−	0.252144i
$186$		0			0
$187$	−4.76016	+	1.03551i	−0.348098	+	0.0757240i
$188$		0			0
$189$	1.84849	−	4.04763i	0.134458	−	0.294422i
$190$		0			0
$191$	0.389028	−	1.32491i	0.0281491	−	0.0958669i	−0.944220	−	0.329314i	$-0.893182\pi$
$191$	0.389028	−	1.32491i	0.0281491	−	0.0958669i	0.972369	+	0.233447i	$0.0750006\pi$
$192$		0			0
$193$	−0.178934	+	0.479740i	−0.0128799	+	0.0345325i	−0.943231	−	0.332139i	$-0.892230\pi$
$193$	−0.178934	+	0.479740i	−0.0128799	+	0.0345325i	0.930351	+	0.366671i	$0.119503\pi$
$194$		0			0
$195$	23.5288	+	6.18506i	1.68493	+	0.442921i
$196$		0			0
$197$	−7.98687	+	14.6269i	−0.569041	+	1.04212i	0.421749	+	0.906713i	$0.361416\pi$
$197$	−7.98687	+	14.6269i	−0.569041	+	1.04212i	−0.990790	+	0.135408i	$0.956765\pi$
$198$		0			0
$199$	14.2806	−	9.17760i	1.01233	−	0.650583i	0.0743320	−	0.997234i	$-0.476318\pi$
$199$	14.2806	−	9.17760i	1.01233	−	0.650583i	0.937994	+	0.346651i	$0.112681\pi$
$200$		0			0
$201$	19.9007	−	2.86129i	1.40369	−	0.201820i
$202$		0			0
$203$	−2.10214	−	2.80813i	−0.147541	−	0.197092i
$204$		0			0
$205$	13.8578	+	5.85661i	0.967867	+	0.409043i
$206$		0			0
$207$	−8.19852	+	6.97760i	−0.569837	+	0.484977i
$208$		0			0
$209$	−0.223992	+	0.194090i	−0.0154938	+	0.0134255i
$210$		0			0
$211$	−2.40391	+	16.7196i	−0.165492	+	1.15102i	0.722569	+	0.691299i	$0.242961\pi$
$211$	−2.40391	+	16.7196i	−0.165492	+	1.15102i	−0.888061	+	0.459725i	$0.847948\pi$
$212$		0			0
$213$	−8.70248	+	11.6252i	−0.596284	+	0.796542i
$214$		0			0
$215$	3.45932	+	13.9700i	0.235924	+	0.952744i
$216$		0			0
$217$	23.1097	+	12.6189i	1.56879	+	0.856625i
$218$		0			0
$219$	25.6651	+	22.2389i	1.73429	+	1.50277i
$220$		0			0
$221$	−18.0928	+	8.26270i	−1.21705	+	0.555809i
$222$		0			0
$223$	−9.94864	−	18.2196i	−0.666210	−	1.22007i	−0.964117	−	0.265478i	$-0.914470\pi$
$223$	−9.94864	−	18.2196i	−0.666210	−	1.22007i	0.297907	−	0.954595i	$-0.403712\pi$
$224$		0			0
$225$	9.92717	−	5.23761i	0.661811	−	0.349174i
$226$		0			0
$227$	−4.92229	−	22.6274i	−0.326704	−	1.50183i	−0.788603	−	0.614902i	$-0.789195\pi$
$227$	−4.92229	−	22.6274i	−0.326704	−	1.50183i	0.461899	−	0.886932i	$-0.347168\pi$
$228$		0			0
$229$	−19.7231			−1.30334			−0.651669	−	0.758503i	$-0.725931\pi$
$229$	−19.7231			−1.30334			−0.651669	+	0.758503i	$0.725931\pi$
$230$		0			0
$231$	6.85599			0.451091
$232$		0			0
$233$	4.66991	+	21.4672i	0.305936	+	1.40636i	0.831459	+	0.555585i	$0.187506\pi$
$233$	4.66991	+	21.4672i	0.305936	+	1.40636i	−0.525524	+	0.850779i	$0.676131\pi$
$234$		0			0
$235$	−3.95275	−	3.73331i	−0.257849	−	0.243534i
$236$		0			0
$237$	−0.767752	−	1.40603i	−0.0498708	−	0.0913316i
$238$		0			0
$239$	15.0679	−	6.88126i	0.974659	−	0.445112i	0.136561	−	0.990632i	$-0.456395\pi$
$239$	15.0679	−	6.88126i	0.974659	−	0.445112i	0.838098	+	0.545520i	$0.183668\pi$
$240$		0			0
$241$	−11.8652	−	10.2812i	−0.764302	−	0.662272i	0.182819	−	0.983147i	$-0.441478\pi$
$241$	−11.8652	−	10.2812i	−0.764302	−	0.662272i	−0.947122	+	0.320875i	$0.896023\pi$
$242$		0			0
$243$	16.9439	+	9.25209i	1.08695	+	0.593522i
$244$		0			0
$245$	0.727948	+	0.438985i	0.0465069	+	0.0280457i
$246$		0			0
$247$	−0.725203	+	0.968758i	−0.0461436	+	0.0616406i
$248$		0			0
$249$	−4.27678	+	29.7456i	−0.271030	+	1.88505i
$250$		0			0
$251$	4.49291	−	3.89313i	0.283590	−	0.245732i	−0.501436	−	0.865195i	$-0.667195\pi$
$251$	4.49291	−	3.89313i	0.283590	−	0.245732i	0.785026	+	0.619462i	$0.212649\pi$
$252$		0			0
$253$	5.05510	+	2.36304i	0.317811	+	0.148563i
$254$		0			0
$255$	−8.34641	+	19.7491i	−0.522672	+	1.23673i
$256$		0			0
$257$	2.72844	+	3.64476i	0.170195	+	0.227354i	0.877527	−	0.479528i	$-0.159192\pi$
$257$	2.72844	+	3.64476i	0.170195	+	0.227354i	−0.707331	+	0.706882i	$0.750101\pi$
$258$		0			0
$259$	−12.1085	+	1.74094i	−0.752384	+	0.108176i
$260$		0			0
$261$	2.57466	−	1.65463i	0.159367	−	0.102419i
$262$		0			0
$263$	−4.50513	+	8.25052i	−0.277798	+	0.508749i	−0.978907	−	0.204305i	$-0.934507\pi$
$263$	−4.50513	+	8.25052i	−0.277798	+	0.508749i	0.701109	+	0.713054i	$0.252688\pi$
$264$		0			0
$265$	−9.04901	−	15.5030i	−0.555876	−	0.952344i
$266$		0			0
$267$	8.16014	−	21.8782i	0.499392	−	1.33892i
$268$		0			0
$269$	7.32412	−	24.9437i	0.446560	−	1.52084i	−0.361858	−	0.932233i	$-0.617857\pi$
$269$	7.32412	−	24.9437i	0.446560	−	1.52084i	0.808418	−	0.588609i	$-0.200324\pi$
$270$		0			0
$271$	9.24085	−	20.2346i	0.561342	−	1.22917i	−0.389939	−	0.920841i	$-0.627504\pi$
$271$	9.24085	−	20.2346i	0.561342	−	1.22917i	0.951281	−	0.308326i	$-0.0997688\pi$
$272$		0			0
$273$	27.3532	−	5.95032i	1.65549	−	0.360130i
$274$		0			0
$275$	−4.60693	−	3.55272i	−0.277808	−	0.214237i
$276$		0			0
$277$	3.98532	−	3.98532i	0.239455	−	0.239455i	−0.577170	−	0.816624i	$-0.695843\pi$
$277$	3.98532	−	3.98532i	0.239455	−	0.239455i	0.816624	+	0.577170i	$0.195843\pi$
$278$		0			0
$279$	−12.4202	+	19.3262i	−0.743576	+	1.15703i
$280$		0			0
$281$	−11.7867	−	5.38281i	−0.703137	−	0.321112i	0.0315653	−	0.999502i	$-0.489951\pi$
$281$	−11.7867	−	5.38281i	−0.703137	−	0.321112i	−0.734702	+	0.678390i	$0.762678\pi$
$282$		0			0
$283$	−11.3609	+	6.20354i	−0.675337	+	0.368762i	−0.780030	−	0.625743i	$-0.784796\pi$
$283$	−11.3609	+	6.20354i	−0.675337	+	0.368762i	0.104692	+	0.994505i	$0.466614\pi$
$284$		0			0
$285$	0.130153	+	1.29793i	0.00770958	+	0.0768827i
$286$		0			0
$287$	17.2667	−	1.23494i	1.01922	−	0.0728960i
$288$		0			0
$289$	−0.149091	−	0.507758i	−0.00877007	−	0.0298681i
$290$		0			0
$291$	−19.2020	−	29.8790i	−1.12564	−	1.75154i
$292$		0			0
$293$	−1.67489	−	1.25381i	−0.0978481	−	0.0732482i	0.549233	−	0.835669i	$-0.314920\pi$
$293$	−1.67489	−	1.25381i	−0.0978481	−	0.0732482i	−0.647082	+	0.762421i	$0.724011\pi$
$294$		0			0
$295$	−5.01554	+	1.62956i	−0.292016	+	0.0948765i
$296$		0			0
$297$	0.143556	−	2.00717i	0.00832996	−	0.116468i
$298$		0			0
$299$	22.2191	+	5.04045i	1.28496	+	0.291496i
$300$		0			0
$301$	10.8444	+	12.5151i	0.625061	+	0.721359i
$302$		0			0
$303$	2.23892	−	1.67603i	0.128622	−	0.0962855i
$304$		0			0
$305$	1.81734	−	1.24262i	0.104060	−	0.0711521i
$306$		0			0
$307$	4.73737	−	21.7774i	0.270376	−	1.24290i	−0.618879	−	0.785487i	$-0.712413\pi$
$307$	4.73737	−	21.7774i	0.270376	−	1.24290i	0.889255	−	0.457412i	$-0.151224\pi$
$308$		0			0
$309$	16.7349	−	4.91381i	0.952015	−	0.279537i
$310$		0			0
$311$	−1.22356	+	1.41207i	−0.0693819	+	0.0800710i	−0.789379	−	0.613906i	$-0.789598\pi$
$311$	−1.22356	+	1.41207i	−0.0693819	+	0.0800710i	0.719997	+	0.693977i	$0.244143\pi$
$312$		0			0
$313$	22.5743	+	8.41977i	1.27597	+	0.475914i	0.893920	−	0.448226i	$-0.147944\pi$
$313$	22.5743	+	8.41977i	1.27597	+	0.475914i	0.382054	+	0.924140i	$0.375217\pi$
$314$		0			0
$315$	7.44140	−	10.5556i	0.419275	−	0.594740i
$316$		0			0
$317$	11.7419	+	31.4812i	0.659489	+	1.76816i	0.640031	+	0.768349i	$0.278921\pi$
$317$	11.7419	+	31.4812i	0.659489	+	1.76816i	0.0194581	+	0.999811i	$0.493806\pi$
$318$		0			0
$319$	−1.33450	−	0.857629i	−0.0747175	−	0.0480180i
$320$		0			0
$321$			0.415648i			0.0231992i
$322$		0			0
$323$	−0.754117	−	0.754117i	−0.0419602	−	0.0419602i
$324$		0			0
$325$	−21.4636	−	10.1758i	−1.19058	−	0.564453i
$326$		0			0
$327$	−31.0919	+	11.5967i	−1.71939	+	0.641298i
$328$		0			0
$329$	−6.00269	−	1.76255i	−0.330939	−	0.0971725i
$330$		0			0
$331$	2.14408	+	4.69489i	0.117849	+	0.258054i	0.959359	−	0.282188i	$-0.0910600\pi$
$331$	2.14408	+	4.69489i	0.117849	+	0.258054i	−0.841510	+	0.540242i	$0.818333\pi$
$332$		0			0
$333$	−0.761412	−	10.6459i	−0.0417251	−	0.583394i
$334$		0			0
$335$	−19.6124	−	0.841035i	−1.07154	−	0.0459507i
$336$		0			0
$337$	17.6065	+	3.83007i	0.959090	+	0.208637i	0.664752	−	0.747064i	$-0.268537\pi$
$337$	17.6065	+	3.83007i	0.959090	+	0.208637i	0.294338	+	0.955701i	$0.404901\pi$
$338$		0			0
$339$	−3.88160	−	26.9971i	−0.210820	−	1.46628i
$340$		0			0
$341$	11.7862	+	1.69460i	0.638258	+	0.0917677i
$342$		0			0
$343$	18.9401	+	1.35462i	1.02267	+	0.0731426i
$344$		0			0
$345$	21.3195	−	12.1916i	1.14780	−	0.656373i
$346$		0			0
$347$	−21.2251	−	1.51805i	−1.13942	−	0.0814932i	−0.511154	−	0.859489i	$-0.670782\pi$
$347$	−21.2251	−	1.51805i	−1.13942	−	0.0814932i	−0.628269	+	0.777996i	$0.716236\pi$
$348$		0			0
$349$	−14.4063	−	2.07132i	−0.771153	−	0.110875i	−0.254503	−	0.967072i	$-0.581912\pi$
$349$	−14.4063	−	2.07132i	−0.771153	−	0.110875i	−0.516650	+	0.856197i	$0.672821\pi$
$350$		0			0
$351$	−1.16929	−	8.13256i	−0.0624119	−	0.434084i
$352$		0			0
$353$	6.74770	+	1.46787i	0.359144	+	0.0781270i	0.388517	−	0.921442i	$-0.372987\pi$
$353$	6.74770	+	1.46787i	0.359144	+	0.0781270i	−0.0293732	+	0.999569i	$0.509351\pi$
$354$		0			0
$355$	10.4461	−	9.58706i	0.554424	−	0.508828i
$356$		0			0
$357$	1.75994	+	24.6072i	0.0931460	+	1.30235i
$358$		0			0
$359$	−11.9493	−	26.1653i	−0.630660	−	1.38095i	−0.907506	−	0.420038i	$-0.862017\pi$
$359$	−11.9493	−	26.1653i	−0.630660	−	1.38095i	0.276846	−	0.960914i	$-0.410711\pi$
$360$		0			0
$361$	18.1681	+	5.33464i	0.956216	+	0.280770i
$362$		0			0
$363$	−20.6984	+	7.72011i	−1.08638	+	0.405201i
$364$		0			0
$365$	−20.6201	−	25.9662i	−1.07931	−	1.35913i
$366$		0			0
$367$	9.96153	+	9.96153i	0.519988	+	0.519988i	0.917568	−	0.397580i	$-0.130150\pi$
$367$	9.96153	+	9.96153i	0.519988	+	0.519988i	−0.397580	+	0.917568i	$0.630150\pi$
$368$		0			0
$369$			15.1034i			0.786254i
$370$		0			0
$371$	−17.3759	−	11.1668i	−0.902113	−	0.579753i
$372$		0			0
$373$	−7.18971	−	19.2763i	−0.372269	−	0.998091i	−0.979121	−	0.203277i	$-0.934841\pi$
$373$	−7.18971	−	19.2763i	−0.372269	−	0.998091i	0.606852	−	0.794815i	$-0.292432\pi$
$374$		0			0
$375$	−24.4624	+	7.56255i	−1.26324	+	0.390528i
$376$		0			0
$377$	−6.06854	−	2.26345i	−0.312546	−	0.116574i
$378$		0			0
$379$	−13.3417	+	15.3971i	−0.685316	+	0.790896i	−0.986691	−	0.162609i	$-0.948009\pi$
$379$	−13.3417	+	15.3971i	−0.685316	+	0.790896i	0.301375	+	0.953506i	$0.402554\pi$
$380$		0			0
$381$	−4.86910	+	1.42970i	−0.249452	+	0.0732457i
$382$		0			0
$383$	−1.65358	+	7.60140i	−0.0844942	+	0.388413i	−0.999900	−	0.0141180i	$-0.995506\pi$
$383$	−1.65358	+	7.60140i	−0.0844942	+	0.388413i	0.915406	+	0.402531i	$0.131870\pi$
$384$		0			0
$385$	−6.57903	−	1.23567i	−0.335298	−	0.0629754i
$386$		0			0
$387$	−11.5664	+	8.65853i	−0.587956	+	0.440138i
$388$		0			0
$389$	1.10656	+	1.27703i	0.0561047	+	0.0647482i	0.783108	−	0.621886i	$-0.213633\pi$
$389$	1.10656	+	1.27703i	0.0561047	+	0.0647482i	−0.727004	+	0.686634i	$0.759088\pi$
$390$		0			0
$391$	−7.18367	+	18.7501i	−0.363294	+	0.948234i
$392$		0			0
$393$	−2.64846	+	37.0303i	−0.133597	+	1.86793i
$394$		0			0
$395$	0.483325	+	1.48761i	0.0243187	+	0.0748495i
$396$		0			0
$397$	12.2625	+	9.17962i	0.615439	+	0.460712i	0.860955	−	0.508680i	$-0.169867\pi$
$397$	12.2625	+	9.17962i	0.615439	+	0.460712i	−0.245516	+	0.969393i	$0.578957\pi$
$398$		0			0
$399$	0.811467	+	1.26267i	0.0406242	+	0.0632124i
$400$		0			0
$401$	−4.60299	−	15.6763i	−0.229862	−	0.782839i	−0.990955	−	0.134196i	$-0.957155\pi$
$401$	−4.60299	−	15.6763i	−0.229862	−	0.782839i	0.761093	−	0.648643i	$-0.224663\pi$
$402$		0			0
$403$	48.4938	−	3.46835i	2.41565	−	0.172771i
$404$		0			0
$405$	−18.5136	−	15.1390i	−0.919946	−	0.752261i
$406$		0			0
$407$	−4.85541	+	2.65125i	−0.240674	+	0.131418i
$408$		0			0
$409$	−17.4650	−	7.97600i	−0.863589	−	0.394388i	−0.0661657	−	0.997809i	$-0.521077\pi$
$409$	−17.4650	−	7.97600i	−0.863589	−	0.394388i	−0.797423	+	0.603421i	$0.793804\pi$
$410$		0			0
$411$	−19.9518	+	31.0456i	−0.984148	+	1.53136i
$412$		0			0
$413$	−4.29075	+	4.29075i	−0.211134	+	0.211134i
$414$		0			0
$415$	9.46511	−	27.7732i	0.464624	−	1.36333i
$416$		0			0
$417$	−18.2390	+	3.96764i	−0.893166	+	0.194296i
$418$		0			0
$419$	−4.28986	+	9.39348i	−0.209573	+	0.458902i	−0.985004	−	0.172531i	$-0.944806\pi$
$419$	−4.28986	+	9.39348i	−0.209573	+	0.458902i	0.775431	+	0.631433i	$0.217533\pi$
$420$		0			0
$421$	−6.08457	+	20.7221i	−0.296544	+	1.00994i	0.667592	+	0.744527i	$0.267325\pi$
$421$	−6.08457	+	20.7221i	−0.296544	+	1.00994i	−0.964136	+	0.265408i	$0.914493\pi$
$422$		0			0
$423$	1.90751	−	5.11423i	0.0927462	−	0.248662i
$424$		0			0
$425$	11.5686	−	17.4470i	0.561161	−	0.846302i
$426$		0			0
$427$	1.21403	−	2.22332i	0.0587508	−	0.107594i
$428$		0			0
$429$	10.6496	−	6.84407i	0.514166	−	0.330435i
$430$		0			0
$431$	−30.4242	+	4.37435i	−1.46548	+	0.210705i	−0.828421	−	0.560106i	$-0.810760\pi$
$431$	−30.4242	+	4.37435i	−1.46548	+	0.210705i	−0.637064	+	0.770811i	$0.719851\pi$
$432$		0			0
$433$	−15.4808	−	20.6800i	−0.743961	−	0.993815i	−0.999634	−	0.0270518i	$-0.991388\pi$
$433$	−15.4808	−	20.6800i	−0.743961	−	0.993815i	0.255673	−	0.966763i	$-0.417703\pi$
$434$		0			0
$435$	−6.46919	+	2.62554i	−0.310174	+	0.125885i
$436$		0			0
$437$	0.163114	+	1.21068i	0.00780280	+	0.0579148i
$438$		0			0
$439$	−11.0709	+	9.59297i	−0.528384	+	0.457848i	−0.877736	−	0.479144i	$-0.840947\pi$
$439$	−11.0709	+	9.59297i	−0.528384	+	0.457848i	0.349352	+	0.936992i	$0.386402\pi$
$440$		0			0
$441$	−0.121451	+	0.844712i	−0.00578339	+	0.0402244i
$442$		0			0
$443$	−20.0414	+	26.7722i	−0.952198	+	1.27199i	0.0100883	+	0.999949i	$0.496789\pi$
$443$	−20.0414	+	26.7722i	−0.952198	+	1.27199i	−0.962286	+	0.272039i	$0.912302\pi$
$444$		0			0
$445$	−11.7736	+	19.5236i	−0.558124	+	0.925509i
$446$		0			0
$447$	34.0962	+	18.6180i	1.61270	+	0.880599i
$448$		0			0
$449$	26.6822	+	23.1203i	1.25921	+	1.09111i	0.991836	+	0.127521i	$0.0407019\pi$
$449$	26.6822	+	23.1203i	1.25921	+	1.09111i	0.267376	+	0.963592i	$0.413844\pi$
$450$		0			0
$451$	7.12098	−	3.25204i	0.335314	−	0.153133i
$452$		0			0
$453$	−17.8325	−	32.6577i	−0.837842	−	1.53439i
$454$		0			0
$455$	−27.3206	+	0.780033i	−1.28081	+	0.0365685i
$456$		0			0
$457$	−0.984706	−	4.52662i	−0.0460626	−	0.211746i	0.948363	−	0.317187i	$-0.102738\pi$
$457$	−0.984706	−	4.52662i	−0.0460626	−	0.211746i	−0.994426	+	0.105441i	$0.966375\pi$
$458$		0			0
$459$	7.24091			0.337977
$460$		0			0
$461$	1.80350			0.0839972			0.0419986	−	0.999118i	$-0.486627\pi$
$461$	1.80350			0.0839972			0.0419986	+	0.999118i	$0.486627\pi$
$462$		0			0
$463$	6.84376	+	31.4603i	0.318056	+	1.46208i	0.807407	+	0.589995i	$0.200870\pi$
$463$	6.84376	+	31.4603i	0.318056	+	1.46208i	−0.489351	+	0.872087i	$0.662766\pi$
$464$		0			0
$465$	35.9844	−	38.0996i	1.66874	−	1.76683i
$466$		0			0
$467$	−3.20247	−	5.86489i	−0.148193	−	0.271395i	0.793029	−	0.609184i	$-0.208503\pi$
$467$	−3.20247	−	5.86489i	−0.148193	−	0.271395i	−0.941222	+	0.337789i	$0.890321\pi$
$468$		0			0
$469$	−20.5464	+	9.38321i	−0.948743	+	0.433276i
$470$		0			0
$471$	−21.0210	−	18.2148i	−0.968597	−	0.839294i
$472$		0			0
$473$	6.57280	+	3.58902i	0.302217	+	0.165023i
$474$		0			0
$475$	0.109033	−	1.26895i	0.00500277	−	0.0582236i
$476$		0			0
$477$	10.7996	−	14.4266i	0.494480	−	0.660548i
$478$		0			0
$479$	3.62645	−	25.2225i	0.165697	−	1.15245i	−0.721958	−	0.691937i	$-0.756758\pi$
$479$	3.62645	−	25.2225i	0.165697	−	1.15245i	0.887655	−	0.460509i	$-0.152333\pi$
$480$		0			0
$481$	−17.0705	+	14.7916i	−0.778346	+	0.674441i
$482$		0			0
$483$	15.4883	−	23.6362i	0.704741	−	1.07549i
$484$		0			0
$485$	13.0412	+	32.1327i	0.592170	+	1.45907i
$486$		0			0
$487$	−8.40720	−	11.2307i	−0.380967	−	0.508912i	0.568541	−	0.822655i	$-0.307508\pi$
$487$	−8.40720	−	11.2307i	−0.380967	−	0.508912i	−0.949508	+	0.313743i	$0.898417\pi$
$488$		0			0
$489$	−40.9036	+	5.88105i	−1.84973	+	0.265950i
$490$		0			0
$491$	29.1742	−	18.7491i	1.31661	−	0.846136i	0.321697	−	0.946843i	$-0.395747\pi$
$491$	29.1742	−	18.7491i	1.31661	−	0.846136i	0.994916	+	0.100707i	$0.0321106\pi$
$492$		0			0
$493$	2.73559	−	5.00987i	0.123205	−	0.225633i
$494$		0			0
$495$	1.48485	−	5.64858i	0.0667392	−	0.253885i
$496$		0			0
$497$	5.70132	−	15.2858i	0.255739	−	0.685664i
$498$		0			0
$499$	−10.7872	+	36.7377i	−0.482900	+	1.64461i	0.252964	+	0.967476i	$0.418595\pi$
$499$	−10.7872	+	36.7377i	−0.482900	+	1.64461i	−0.735864	+	0.677130i	$0.763224\pi$
$500$		0			0
$501$	−18.5115	+	40.5345i	−0.827033	+	1.81095i
$502$		0			0
$503$	−6.67779	+	1.45266i	−0.297748	+	0.0647711i	−0.358958	−	0.933354i	$-0.616868\pi$
$503$	−6.67779	+	1.45266i	−0.297748	+	0.0647711i	0.0612098	+	0.998125i	$0.480504\pi$
$504$		0			0
$505$	−2.45054	+	1.20480i	−0.109048	+	0.0536129i
$506$		0			0
$507$	15.4963	−	15.4963i	0.688217	−	0.688217i
$508$		0			0
$509$	16.3502	−	25.4414i	0.724711	−	1.12767i	−0.261981	−	0.965073i	$-0.584376\pi$
$509$	16.3502	−	25.4414i	0.724711	−	1.12767i	0.986692	−	0.162599i	$-0.0519878\pi$
$510$		0			0
$511$	−34.7047	−	15.8491i	−1.53525	−	0.701124i
$512$		0			0
$513$	0.386652	−	0.211128i	0.0170711	−	0.00932153i
$514$		0			0
$515$	−16.9445	+	1.69915i	−0.746663	+	0.0748733i
$516$		0			0
$517$	−2.82198	+	0.201832i	−0.124111	+	0.00887656i
$518$		0			0
$519$	−2.83113	−	9.64193i	−0.124273	−	0.423234i
$520$		0			0
$521$	−3.43642	−	5.34717i	−0.150552	−	0.234264i	0.757783	−	0.652507i	$-0.226283\pi$
$521$	−3.43642	−	5.34717i	−0.150552	−	0.234264i	−0.908335	+	0.418243i	$0.862646\pi$
$522$		0			0
$523$	−8.35087	−	6.25138i	−0.365158	−	0.273354i	0.400905	−	0.916120i	$-0.368696\pi$
$523$	−8.35087	−	6.25138i	−0.365158	−	0.273354i	−0.766063	+	0.642766i	$0.777787\pi$
$524$		0			0
$525$	−21.1287	+	20.5323i	−0.922131	+	0.896105i
$526$		0			0
$527$	−3.05664	+	42.7375i	−0.133149	+	1.86167i
$528$		0			0
$529$	19.5665	−	12.0893i	0.850719	−	0.525620i
$530$		0			0
$531$	−3.46702	−	4.00115i	−0.150456	−	0.173635i
$532$		0			0
$533$	25.5879	−	19.1549i	1.10834	−	0.829690i
$534$		0			0
$535$	0.0749128	−	0.398856i	0.00323876	−	0.0172441i
$536$		0			0
$537$	−2.69106	+	12.3706i	−0.116128	+	0.533831i
$538$		0			0
$539$	0.424416	−	0.124620i	0.0182809	−	0.00536775i
$540$		0			0
$541$	−13.9928	+	16.1485i	−0.601597	+	0.694280i	−0.972104	−	0.234550i	$-0.924639\pi$
$541$	−13.9928	+	16.1485i	−0.601597	+	0.694280i	0.370507	+	0.928830i	$0.379184\pi$
$542$		0			0
$543$	18.1869	+	6.78335i	0.780474	+	0.291102i
$544$		0			0
$545$	31.9260	−	5.52446i	1.36756	−	0.236642i
$546$		0			0
$547$	−10.0567	−	26.9631i	−0.429994	−	1.15286i	−0.953647	−	0.300926i	$-0.902704\pi$
$547$	−10.0567	−	26.9631i	−0.429994	−	1.15286i	0.523654	−	0.851931i	$-0.324569\pi$
$548$		0			0
$549$	1.85931	+	1.19491i	0.0793536	+	0.0509975i
$550$		0			0
$551$		−	0.347282i		−	0.0147947i
$552$		0			0
$553$	1.27263	+	1.27263i	0.0541178	+	0.0541178i
$554$		0			0
$555$	−2.77584	+	24.1890i	−0.117828	+	1.02677i
$556$		0			0
$557$	41.8580	−	15.6122i	1.77358	−	0.661511i	0.773980	−	0.633210i	$-0.218263\pi$
$557$	41.8580	−	15.6122i	1.77358	−	0.661511i	0.999599	−	0.0283015i	$-0.00900985\pi$
$558$		0			0
$559$	29.3382	+	8.61448i	1.24087	+	0.364354i
$560$		0			0
$561$	4.63457	+	10.1483i	0.195672	+	0.428462i
$562$		0			0
$563$	1.12036	+	15.6647i	0.0472177	+	0.660190i	0.964857	+	0.262776i	$0.0846379\pi$
$563$	1.12036	+	15.6647i	0.0472177	+	0.660190i	−0.917639	+	0.397414i	$0.869908\pi$
$564$		0			0
$565$	−1.14094	+	26.6061i	−0.0479998	+	1.11933i
$566$		0			0
$567$	−26.8889	−	5.84933i	−1.12923	−	0.245649i
$568$		0			0
$569$	4.02665	+	28.0060i	0.168806	+	1.17407i	0.881357	+	0.472451i	$0.156631\pi$
$569$	4.02665	+	28.0060i	0.168806	+	1.17407i	−0.712551	+	0.701620i	$0.752460\pi$
$570$		0			0
$571$	−9.67484	−	1.39103i	−0.404879	−	0.0582129i	−0.0631331	−	0.998005i	$-0.520109\pi$
$571$	−9.67484	−	1.39103i	−0.404879	−	0.0582129i	−0.341746	+	0.939792i	$0.611018\pi$
$572$		0			0
$573$	−3.15429	−	0.225599i	−0.131772	−	0.00942454i
$574$		0			0
$575$	−22.6555	+	7.85663i	−0.944801	+	0.327644i
$576$		0			0
$577$	−4.69877	−	0.336062i	−0.195612	−	0.0139905i	−0.0268107	−	0.999641i	$-0.508535\pi$
$577$	−4.69877	−	0.336062i	−0.195612	−	0.0139905i	−0.168801	+	0.985650i	$0.553990\pi$
$578$		0			0
$579$	1.16068	+	0.166881i	0.0482362	+	0.00693532i
$580$		0			0
$581$	−4.80480	−	33.4181i	−0.199336	−	1.38642i
$582$		0			0
$583$	−9.12721	−	1.98550i	−0.378011	−	0.0822312i
$584$		0			0
$585$	1.02167	−	23.8247i	0.0422408	−	0.985031i
$586$		0			0
$587$	−2.75348	−	38.4987i	−0.113648	−	1.58901i	−0.659877	−	0.751374i	$-0.729392\pi$
$587$	−2.75348	−	38.4987i	−0.113648	−	1.58901i	0.546229	−	0.837636i	$-0.316063\pi$
$588$		0			0
$589$	1.08291	+	2.37123i	0.0446204	+	0.0977049i
$590$		0			0
$591$	36.6204	+	10.7527i	1.50636	+	0.442308i
$592$		0			0
$593$	19.2780	−	7.19032i	0.791653	−	0.295271i	0.0790790	−	0.996868i	$-0.474802\pi$
$593$	19.2780	−	7.19032i	0.791653	−	0.295271i	0.712574	+	0.701597i	$0.247529\pi$
$594$		0			0
$595$	2.74615	−	23.9303i	0.112581	−	0.981048i
$596$		0			0
$597$	−27.4897	−	27.4897i	−1.12508	−	1.12508i
$598$		0			0
$599$			26.8232i			1.09597i	0.836490	+	0.547983i	$0.184604\pi$
$599$			26.8232i			1.09597i	−0.836490	+	0.547983i	$0.815396\pi$
$600$		0			0
$601$	31.8650	+	20.4784i	1.29980	+	0.835332i	0.993190	−	0.116503i	$-0.0371685\pi$
$601$	31.8650	+	20.4784i	1.29980	+	0.835332i	0.306611	+	0.951835i	$0.400805\pi$
$602$		0			0
$603$	−6.88702	−	18.4648i	−0.280461	−	0.751945i
$604$		0			0
$605$	21.2537	−	3.67773i	0.864084	−	0.149521i
$606$		0			0
$607$	−8.24471	−	3.07512i	−0.334642	−	0.124815i	0.176525	−	0.984296i	$-0.443514\pi$
$607$	−8.24471	−	3.07512i	−0.334642	−	0.124815i	−0.511168	+	0.859481i	$0.670787\pi$
$608$		0			0
$609$	−5.26075	+	6.07123i	−0.213176	+	0.246019i
$610$		0			0
$611$	−11.0836	+	3.25444i	−0.448395	+	0.131661i
$612$		0			0
$613$	−6.76158	+	31.0825i	−0.273098	+	1.25541i	0.612319	+	0.790611i	$0.290237\pi$
$613$	−6.76158	+	31.0825i	−0.273098	+	1.25541i	−0.885416	+	0.464799i	$0.846127\pi$
$614$		0			0
$615$	6.35997	−	33.8622i	0.256459	−	1.36546i
$616$		0			0
$617$	−4.54828	+	3.40480i	−0.183107	+	0.137072i	−0.686899	−	0.726753i	$-0.741029\pi$
$617$	−4.54828	+	3.40480i	−0.183107	+	0.137072i	0.503792	+	0.863825i	$0.331938\pi$
$618$		0			0
$619$	19.9222	+	22.9915i	0.800741	+	0.924104i	0.998422	−	0.0561620i	$-0.0178863\pi$
$619$	19.9222	+	22.9915i	0.800741	+	0.924104i	−0.197681	+	0.980266i	$0.563341\pi$
$620$		0			0
$621$	−6.59548	−	5.02929i	−0.264668	−	0.201818i
$622$		0			0
$623$	−1.87146	+	26.1665i	−0.0749786	+	1.04834i
$624$		0			0
$625$	24.8372	−	2.84814i	0.993489	−	0.113925i
$626$		0			0
$627$	0.543380	+	0.406769i	0.0217005	+	0.0162448i
$628$		0			0
$629$	−10.7621	−	16.7462i	−0.429115	−	0.667715i
$630$		0			0
$631$	−10.3019	−	35.0850i	−0.410112	−	1.39671i	−0.863026	−	0.505159i	$-0.831434\pi$
$631$	−10.3019	−	35.0850i	−0.410112	−	1.39671i	0.452915	−	0.891554i	$-0.350384\pi$
$632$		0			0
$633$	38.5857	−	2.75970i	1.53364	−	0.109688i
$634$		0			0
$635$	4.93008	−	0.494375i	0.195644	−	0.0196187i
$636$		0			0
$637$	1.58512	−	0.865543i	0.0628049	−	0.0342941i
$638$		0			0
$639$	12.9479	+	5.91309i	0.512209	+	0.233918i
$640$		0			0
$641$	−8.86764	+	13.7983i	−0.350251	+	0.545001i	−0.971022	−	0.238991i	$-0.923183\pi$
$641$	−8.86764	+	13.7983i	−0.350251	+	0.545001i	0.620771	+	0.783992i	$0.286820\pi$
$642$		0			0
$643$	−32.4127	+	32.4127i	−1.27823	+	1.27823i	−0.336577	+	0.941656i	$0.609269\pi$
$643$	−32.4127	+	32.4127i	−1.27823	+	1.27823i	−0.941656	+	0.336577i	$0.890731\pi$
$644$		0			0
$645$	29.5783	−	14.5420i	1.16464	−	0.572593i
$646$		0			0
$647$	31.6287	−	6.88040i	1.24345	−	0.270496i	0.457738	−	0.889087i	$-0.348660\pi$
$647$	31.6287	−	6.88040i	1.24345	−	0.270496i	0.785713	+	0.618591i	$0.212296\pi$
$648$		0			0
$649$	−1.13996	+	2.49615i	−0.0447472	+	0.0979826i
$650$		0			0
$651$	16.9888	−	57.8584i	0.665842	−	2.26765i
$652$		0			0
$653$	12.7161	−	34.0931i	0.497618	−	1.33416i	−0.409125	−	0.912479i	$-0.634166\pi$
$653$	12.7161	−	34.0931i	0.497618	−	1.33416i	0.906742	−	0.421686i	$-0.138561\pi$
$654$		0			0
$655$	9.21551	−	35.0571i	0.360080	−	1.36979i
$656$		0			0
$657$	15.9530	−	29.2158i	0.622387	−	1.13982i
$658$		0			0
$659$	32.5712	−	20.9322i	1.26879	−	0.815403i	0.279330	−	0.960195i	$-0.409888\pi$
$659$	32.5712	−	20.9322i	1.26879	−	0.815403i	0.989462	+	0.144792i	$0.0462512\pi$
$660$		0			0
$661$	27.5592	−	3.96242i	1.07193	−	0.154120i	0.416319	−	0.909219i	$-0.363320\pi$
$661$	27.5592	−	3.96242i	1.07193	−	0.154120i	0.655611	+	0.755098i	$0.272411\pi$
$662$		0			0
$663$	27.2982	+	36.4661i	1.06017	+	1.41622i
$664$		0			0
$665$	−0.551113	−	1.35791i	−0.0213713	−	0.0526575i
$666$		0			0
$667$	−5.97144	+	2.66326i	−0.231215	+	0.103122i
$668$		0			0
$669$	−35.9291	+	31.1327i	−1.38910	+	1.20366i
$670$		0			0
$671$	0.163033	−	1.13392i	0.00629380	−	0.0437743i
$672$		0			0
$673$	−4.67785	+	6.24887i	−0.180318	+	0.240876i	−0.881589	−	0.472019i	$-0.843525\pi$
$673$	−4.67785	+	6.24887i	−0.180318	+	0.240876i	0.701271	+	0.712895i	$0.252616\pi$
$674$		0			0
$675$	5.56868	+	6.61559i	0.214339	+	0.254634i
$676$		0			0
$677$	−16.7820	−	9.16366i	−0.644984	−	0.352188i	0.123233	−	0.992378i	$-0.460674\pi$
$677$	−16.7820	−	9.16366i	−0.644984	−	0.352188i	−0.768217	+	0.640190i	$0.778856\pi$
$678$		0			0
$679$	30.1561	+	26.1304i	1.15728	+	1.00279i
$680$		0			0
$681$	−48.2399	+	22.0304i	−1.84856	+	0.844208i
$682$		0			0
$683$	7.31521	+	13.3968i	0.279909	+	0.512615i	0.979375	−	0.202051i	$-0.0647607\pi$
$683$	7.31521	+	13.3968i	0.279909	+	0.512615i	−0.699466	+	0.714666i	$0.746579\pi$
$684$		0			0
$685$	24.7412	−	26.1955i	0.945311	−	1.00088i
$686$		0			0
$687$	9.60137	+	44.1368i	0.366315	+	1.68392i
$688$		0			0
$689$	−38.1378			−1.45294
$690$		0			0
$691$	−7.78028			−0.295976			−0.147988	−	0.988989i	$-0.547280\pi$
$691$	−7.78028			−0.295976			−0.147988	+	0.988989i	$0.547280\pi$
$692$		0			0
$693$	−1.42850	−	6.56671i	−0.0542642	−	0.249449i
$694$		0			0
$695$	18.2172	−	0.520122i	0.691019	−	0.0197294i
$696$		0			0
$697$	13.5000	+	24.7235i	0.511350	+	0.936468i
$698$		0			0
$699$	45.7665	−	20.9008i	1.73105	−	0.790542i
$700$		0			0
$701$	−11.8526	−	10.2703i	−0.447666	−	0.387905i	0.401647	−	0.915795i	$-0.368438\pi$
$701$	−11.8526	−	10.2703i	−0.447666	−	0.387905i	−0.849313	+	0.527890i	$0.822983\pi$
$702$		0			0
$703$	−1.06296	−	0.580421i	−0.0400903	−	0.0218910i
$704$		0			0
$705$	−6.43024	+	10.6630i	−0.242177	+	0.401590i
$706$		0			0
$707$	−1.88296	+	2.51534i	−0.0708159	+	0.0945989i
$708$		0			0
$709$	0.173269	−	1.20511i	0.00650725	−	0.0452589i	−0.986309	−	0.164907i	$-0.947268\pi$
$709$	0.173269	−	1.20511i	0.00650725	−	0.0452589i	0.992816	+	0.119648i	$0.0381767\pi$
$710$		0			0
$711$	−1.18674	+	1.02831i	−0.0445062	+	0.0385648i
$712$		0			0
$713$	32.4682	−	36.8050i	1.21594	−	1.37836i
$714$		0			0
$715$	−11.4529	+	4.64819i	−0.428313	+	0.173833i
$716$		0			0
$717$	−22.7342	−	30.3693i	−0.849024	−	1.13416i
$718$		0			0
$719$	1.03007	−	0.148101i	0.0384150	−	0.00552325i	−0.123081	−	0.992397i	$-0.539277\pi$
$719$	1.03007	−	0.148101i	0.0384150	−	0.00552325i	0.161496	+	0.986873i	$0.448368\pi$
$720$		0			0
$721$	−16.4841	+	10.5937i	−0.613902	+	0.394531i
$722$		0			0
$723$	−17.2315	+	31.5571i	−0.640846	+	1.17362i
$724$		0			0
$725$	6.68105	−	1.35353i	0.248128	−	0.0502687i
$726$		0			0
$727$	13.4459	−	36.0499i	0.498681	−	1.33702i	−0.407144	−	0.913364i	$-0.633475\pi$
$727$	13.4459	−	36.0499i	0.498681	−	1.33702i	0.905825	−	0.423652i	$-0.139252\pi$
$728$		0			0
$729$	3.41649	−	11.6355i	0.126537	−	0.430944i
$730$		0			0
$731$	−11.1943	+	24.5121i	−0.414036	+	0.906612i
$732$		0			0
$733$	−35.3479	+	7.68946i	−1.30560	+	0.284017i	−0.810972	−	0.585086i	$-0.801061\pi$
$733$	−35.3479	+	7.68946i	−1.30560	+	0.284017i	−0.494632	+	0.869102i	$0.664697\pi$
$734$		0			0
$735$	0.628000	−	1.84272i	0.0231641	−	0.0679697i
$736$		0			0
$737$	−7.22290	+	7.22290i	−0.266059	+	0.266059i
$738$		0			0
$739$	−14.3480	+	22.3259i	−0.527799	+	0.821271i	−0.998124	−	0.0612224i	$-0.980500\pi$
$739$	−14.3480	+	22.3259i	−0.527799	+	0.821271i	0.470326	+	0.882493i	$0.344136\pi$
$740$		0			0
$741$	2.52094	+	1.15128i	0.0926091	+	0.0422932i
$742$		0			0
$743$	−17.4851	+	9.54760i	−0.641467	+	0.350267i	−0.766836	−	0.641843i	$-0.778170\pi$
$743$	−17.4851	+	9.54760i	−0.641467	+	0.350267i	0.125370	+	0.992110i	$0.459988\pi$
$744$		0			0
$745$	−29.3633	−	24.0111i	−1.07579	−	0.879697i
$746$		0			0
$747$	29.3816	−	2.10142i	1.07502	−	0.0768868i
$748$		0			0
$749$	−0.131559	−	0.448049i	−0.00480706	−	0.0163713i
$750$		0			0
$751$	17.0805	+	26.5778i	0.623277	+	0.969838i	0.999069	+	0.0431343i	$0.0137343\pi$
$751$	17.0805	+	26.5778i	0.623277	+	0.969838i	−0.375792	+	0.926704i	$0.622629\pi$
$752$		0			0
$753$	−10.8993	−	8.15913i	−0.397193	−	0.297335i
$754$		0			0
$755$	11.2261	+	34.5524i	0.408560	+	1.25749i
$756$		0			0
$757$	0.266262	−	3.72284i	0.00967747	−	0.135309i	−0.990316	−	0.138829i	$-0.955666\pi$
$757$	0.266262	−	3.72284i	0.00967747	−	0.135309i	0.999994	+	0.00352051i	$0.00112061\pi$
$758$		0			0
$759$	2.82720	−	12.4627i	0.102621	−	0.452369i
$760$		0			0
$761$	18.4195	+	21.2573i	0.667707	+	0.770575i	0.984016	−	0.178081i	$-0.0569889\pi$
$761$	18.4195	+	21.2573i	0.667707	+	0.770575i	−0.316309	+	0.948656i	$0.602443\pi$
$762$		0			0
$763$	29.8451	−	22.3418i	1.08047	−	0.808826i
$764$		0			0
$765$	20.6548	+	3.87936i	0.746776	+	0.140259i
$766$		0			0
$767$	−2.38164	+	10.9482i	−0.0859959	+	0.395317i
$768$		0			0
$769$	−18.7856	+	5.51596i	−0.677427	+	0.198911i	−0.602308	−	0.798264i	$-0.705752\pi$
$769$	−18.7856	+	5.51596i	−0.677427	+	0.198911i	−0.0751195	+	0.997175i	$0.523934\pi$
$770$		0			0
$771$	6.82811	−	7.88005i	0.245908	−	0.283793i
$772$		0			0
$773$	29.0669	+	10.8414i	1.04546	+	0.389938i	0.812754	−	0.582608i	$-0.197968\pi$
$773$	29.0669	+	10.8414i	1.04546	+	0.389938i	0.232711	+	0.972546i	$0.425240\pi$
$774$		0			0
$775$	−41.3975	+	30.0749i	−1.48704	+	1.08032i
$776$		0			0
$777$	9.79041	+	26.2491i	0.351229	+	0.941681i
$778$		0			0
$779$	1.44176	+	0.926562i	0.0516564	+	0.0331975i
$780$		0			0
$781$		−	7.37786i		−	0.264001i
$782$		0			0
$783$	1.66727	+	1.66727i	0.0595834	+	0.0595834i
$784$		0			0
$785$	16.8889	+	21.2676i	0.602792	+	0.759074i
$786$		0			0
$787$	17.7463	−	6.61904i	0.632588	−	0.235943i	−0.0126556	−	0.999920i	$-0.504029\pi$
$787$	17.7463	−	6.61904i	0.632588	−	0.235943i	0.645244	+	0.763977i	$0.276756\pi$
$788$		0			0
$789$	20.6563	+	6.06525i	0.735385	+	0.215928i
$790$		0			0
$791$	12.7292	+	27.8730i	0.452598	+	0.991051i
$792$		0			0
$793$	−0.333680	−	4.66545i	−0.0118493	−	0.165675i
$794$		0			0
$795$	−30.2879	+	27.7971i	−1.07420	+	0.985860i
$796$		0			0
$797$	34.7238	+	7.55371i	1.22998	+	0.267566i	0.780176	−	0.625560i	$-0.215130\pi$
$797$	34.7238	+	7.55371i	1.22998	+	0.267566i	0.449806	+	0.893126i	$0.351493\pi$
$798$		0			0
$799$	−1.44881	−	10.0767i	−0.0512553	−	0.356488i
$800$		0			0
$801$	−22.6553	−	3.25734i	−0.800484	−	0.115092i
$802$		0			0
$803$	−17.2097	−	1.23086i	−0.607316	−	0.0434361i
$804$		0			0
$805$	−19.1226	+	19.8899i	−0.673982	+	0.701027i
$806$		0			0
$807$	−59.3849	−	4.24729i	−2.09045	−	0.149512i
$808$		0			0
$809$	25.9022	+	3.72417i	0.910672	+	0.130935i	0.581699	−	0.813404i	$-0.302388\pi$
$809$	25.9022	+	3.72417i	0.910672	+	0.130935i	0.328973	+	0.944339i	$0.393297\pi$
$810$		0			0
$811$	2.80564	+	19.5137i	0.0985195	+	0.685218i	0.977896	+	0.209091i	$0.0670505\pi$
$811$	2.80564	+	19.5137i	0.0985195	+	0.685218i	−0.879377	+	0.476127i	$0.842040\pi$
$812$		0			0
$813$	−49.7800	−	10.8290i	−1.74586	−	0.379789i
$814$		0			0
$815$	40.3112	+	1.72865i	1.41204	+	0.0605521i
$816$		0			0
$817$	0.116959	+	1.63530i	0.00409188	+	0.0572120i
$818$		0			0
$819$	−11.3985	−	24.9592i	−0.398296	−	0.872146i
$820$		0			0
$821$	54.1926	+	15.9124i	1.89134	+	0.555346i	0.993322	+	0.115379i	$0.0368083\pi$
$821$	54.1926	+	15.9124i	1.89134	+	0.555346i	0.898014	+	0.439967i	$0.145010\pi$
$822$		0			0
$823$	−3.79242	+	1.41450i	−0.132195	+	0.0493063i	−0.414691	−	0.909962i	$-0.636110\pi$
$823$	−3.79242	+	1.41450i	−0.132195	+	0.0493063i	0.282496	+	0.959269i	$0.408838\pi$
$824$		0			0
$825$	−5.70766	+	12.0390i	−0.198715	+	0.419143i
$826$		0			0
$827$	12.7745	+	12.7745i	0.444214	+	0.444214i	0.893425	−	0.449212i	$-0.148295\pi$
$827$	12.7745	+	12.7745i	0.444214	+	0.444214i	−0.449212	+	0.893425i	$0.648295\pi$
$828$		0			0
$829$			35.7697i			1.24233i	0.783679	+	0.621167i	$0.213341\pi$
$829$			35.7697i			1.24233i	−0.783679	+	0.621167i	$0.786659\pi$
$830$		0			0
$831$	−10.8585	−	6.97835i	−0.376678	−	0.242076i
$832$		0			0
$833$	0.556228	+	1.49130i	0.0192721	+	0.0516706i
$834$		0			0
$835$	25.0693	−	35.5607i	0.867558	−	1.23063i
$836$		0			0
$837$	−16.5830	−	6.18515i	−0.573193	−	0.213790i
$838$		0			0
$839$	15.2611	−	17.6123i	0.526872	−	0.608043i	−0.428466	−	0.903558i	$-0.640946\pi$
$839$	15.2611	−	17.6123i	0.526872	−	0.608043i	0.955338	+	0.295515i	$0.0954913\pi$
$840$		0			0
$841$	−26.0418	+	7.64658i	−0.897995	+	0.263675i
$842$		0			0
$843$	−6.30791	+	28.9970i	−0.217256	+	0.998709i
$844$		0			0
$845$	−17.6633	+	12.0774i	−0.607635	+	0.415475i
$846$		0			0
$847$	19.8684	−	14.8733i	0.682686	−	0.511052i
$848$		0			0
$849$	19.4130	+	22.4038i	0.666252	+	0.768896i
$850$		0			0
$851$	−1.82851	+	22.7286i	−0.0626806	+	0.779125i
$852$		0			0
$853$	1.79703	−	25.1258i	0.0615292	−	0.860291i	−0.869172	−	0.494510i	$-0.835347\pi$
$853$	1.79703	−	25.1258i	0.0615292	−	0.860291i	0.930701	−	0.365781i	$-0.119198\pi$
$854$		0			0
$855$	1.21604	−	0.395094i	0.0415878	−	0.0135119i
$856$		0			0
$857$	−11.4325	−	8.55830i	−0.390528	−	0.292346i	0.385913	−	0.922535i	$-0.373886\pi$
$857$	−11.4325	−	8.55830i	−0.390528	−	0.292346i	−0.776442	+	0.630189i	$0.782977\pi$
$858$		0			0
$859$	−27.3077	−	42.4916i	−0.931726	−	1.44979i	−0.892749	−	0.450555i	$-0.851226\pi$
$859$	−27.3077	−	42.4916i	−0.931726	−	1.44979i	−0.0389775	−	0.999240i	$-0.512410\pi$
$860$		0			0
$861$	−11.1691	−	38.0385i	−0.380643	−	1.29635i
$862$		0			0
$863$	−11.3587	+	0.812394i	−0.386656	+	0.0276542i	−0.263314	−	0.964710i	$-0.584816\pi$
$863$	−11.3587	+	0.812394i	−0.386656	+	0.0276542i	−0.123342	+	0.992364i	$0.539361\pi$
$864$		0			0
$865$	0.978975	+	9.76268i	0.0332861	+	0.331941i
$866$		0			0
$867$	−1.06369	+	0.580820i	−0.0361249	+	0.0197257i
$868$		0			0
$869$	0.740357	+	0.338109i	0.0251149	+	0.0114696i
$870$		0			0
$871$	−22.5483	+	35.0858i	−0.764019	+	1.18884i
$872$		0			0
$873$	−24.6173	+	24.6173i	−0.833171	+	0.833171i
$874$		0			0
$875$	23.9757	−	15.8948i	0.810527	−	0.537343i
$876$		0			0
$877$	−24.1315	+	5.24949i	−0.814863	+	0.177263i	−0.600637	−	0.799522i	$-0.705086\pi$
$877$	−24.1315	+	5.24949i	−0.814863	+	0.177263i	−0.214226	+	0.976784i	$0.568723\pi$
$878$		0			0
$879$	−1.99045	+	4.35847i	−0.0671361	+	0.147007i
$880$		0			0
$881$	6.36966	−	21.6931i	0.214599	−	0.730858i	−0.779880	−	0.625929i	$-0.784720\pi$
$881$	6.36966	−	21.6931i	0.214599	−	0.730858i	0.994480	−	0.104930i	$-0.0334617\pi$
$882$		0			0
$883$	8.67845	−	23.2678i	0.292053	−	0.783024i	−0.705204	−	0.709005i	$-0.749145\pi$
$883$	8.67845	−	23.2678i	0.292053	−	0.783024i	0.997257	−	0.0740197i	$-0.0235828\pi$
$884$		0			0
$885$	6.08827	+	10.4306i	0.204655	+	0.350621i
$886$		0			0
$887$	1.20190	−	2.20112i	0.0403559	−	0.0739064i	−0.856723	−	0.515777i	$-0.827503\pi$
$887$	1.20190	−	2.20112i	0.0403559	−	0.0739064i	0.897079	+	0.441871i	$0.145685\pi$
$888$		0			0
$889$	4.79615	−	3.08230i	0.160858	−	0.103377i
$890$		0			0
$891$	−12.3177	+	1.77101i	−0.412657	+	0.0593311i
$892$		0			0
$893$	−0.371178	−	0.495835i	−0.0124210	−	0.0165925i
$894$		0			0
$895$	4.81193	−	11.3859i	0.160845	−	0.380587i
$896$		0			0
$897$	0.463191	−	52.1760i	0.0154655	−	1.74211i
$898$		0			0
$899$	−10.5444	+	9.13680i	−0.351676	+	0.304729i
$900$		0			0
$901$	4.78331	−	33.2686i	0.159355	−	1.10834i
$902$		0			0
$903$	22.7274	−	30.3603i	0.756322	−	1.01033i
$904$		0			0
$905$	−16.2296	−	9.78717i	−0.539490	−	0.325337i
$906$		0			0
$907$	34.8183	+	19.0123i	1.15612	+	0.631291i	0.938683	−	0.344782i	$-0.112047\pi$
$907$	34.8183	+	19.0123i	1.15612	+	0.631291i	0.217441	+	0.976073i	$0.430229\pi$
$908$		0			0
$909$	−2.07181	−	1.79523i	−0.0687175	−	0.0595441i
$910$		0			0
$911$	−24.1333	+	11.0213i	−0.799571	+	0.365152i	−0.772928	−	0.634493i	$-0.781209\pi$
$911$	−24.1333	+	11.0213i	−0.799571	+	0.365152i	−0.0266425	+	0.999645i	$0.508482\pi$
$912$		0			0
$913$	−7.31717	−	13.4004i	−0.242163	−	0.443489i
$914$		0			0
$915$	−3.66545	−	3.46196i	−0.121176	−	0.114449i
$916$		0			0
$917$	−8.86576	−	40.7553i	−0.292773	−	1.34586i
$918$		0			0
$919$	−11.9818			−0.395243			−0.197622	−	0.980278i	$-0.563322\pi$
$919$	−11.9818			−0.395243			−0.197622	+	0.980278i	$0.563322\pi$
$920$		0			0
$921$	−51.0400			−1.68183
$922$		0			0
$923$	−6.40325	−	29.4353i	−0.210766	−	0.968873i
$924$		0			0
$925$	7.02333	−	22.7116i	0.230926	−	0.746752i
$926$		0			0
$927$	−8.19332	−	15.0049i	−0.269104	−	0.492827i
$928$		0			0
$929$	−45.3987	+	20.7329i	−1.48948	+	0.680225i	−0.983265	−	0.182180i	$-0.941684\pi$
$929$	−45.3987	+	20.7329i	−1.48948	+	0.680225i	−0.506219	+	0.862405i	$0.668957\pi$
$930$		0			0
$931$	0.0731846	+	0.0634148i	0.00239853	+	0.00207834i
$932$		0			0
$933$	3.75560	+	2.05071i	0.122953	+	0.0671373i
$934$		0			0
$935$	−2.61830	−	10.5736i	−0.0856277	−	0.345795i
$936$		0			0
$937$	−11.4424	+	15.2852i	−0.373806	+	0.499346i	−0.947514	−	0.319714i	$-0.896413\pi$
$937$	−11.4424	+	15.2852i	−0.373806	+	0.499346i	0.573709	+	0.819060i	$0.305504\pi$
$938$		0			0
$939$	7.85260	−	54.6160i	0.256260	−	1.78233i
$940$		0			0
$941$	41.5853	−	36.0339i	1.35564	−	1.17467i	0.388201	−	0.921575i	$-0.373097\pi$
$941$	41.5853	−	36.0339i	1.35564	−	1.17467i	0.967441	−	0.253096i	$-0.0814488\pi$
$942$		0			0
$943$	4.87539	−	31.8964i	0.158765	−	1.03869i
$944$		0			0
$945$	9.16506	+	3.87337i	0.298140	+	0.126001i
$946$		0			0
$947$	9.97228	+	13.3214i	0.324056	+	0.432888i	0.932754	−	0.360514i	$-0.117399\pi$
$947$	9.97228	+	13.3214i	0.324056	+	0.432888i	−0.608698	+	0.793402i	$0.708308\pi$
$948$		0			0
$949$	−69.7292	+	10.0255i	−2.26351	+	0.325443i
$950$		0			0
$951$	64.7332	−	41.6015i	2.09912	−	1.34902i
$952$		0			0
$953$	−25.8005	+	47.2500i	−0.835759	+	1.53058i	0.0118328	+	0.999930i	$0.496233\pi$
$953$	−25.8005	+	47.2500i	−0.835759	+	1.53058i	−0.847592	+	0.530649i	$0.821948\pi$
$954$		0			0
$955$	2.98620	+	0.784988i	0.0966312	+	0.0254016i
$956$		0			0
$957$	−1.26958	+	3.40387i	−0.0410396	+	0.110031i
$958$		0			0
$959$	11.6807	−	39.7807i	0.377188	−	1.28459i
$960$		0			0
$961$	30.6286	−	67.0672i	0.988018	−	2.16346i
$962$		0			0
$963$	0.398109	−	0.0866034i	0.0128289	−	0.00279076i
$964$		0			0
$965$	−1.08371	−	0.369330i	−0.0348860	−	0.0118892i
$966$		0			0
$967$	−3.34516	+	3.34516i	−0.107573	+	0.107573i	−0.758845	−	0.651272i	$-0.774236\pi$
$967$	−3.34516	+	3.34516i	−0.107573	+	0.107573i	0.651272	+	0.758845i	$0.274236\pi$
$968$		0			0
$969$	−1.32047	+	2.05469i	−0.0424196	+	0.0660062i
$970$		0			0
$971$	−11.6705	−	5.32972i	−0.374523	−	0.171039i	0.219256	−	0.975667i	$-0.429637\pi$
$971$	−11.6705	−	5.32972i	−0.374523	−	0.171039i	−0.593778	+	0.804629i	$0.702364\pi$
$972$		0			0
$973$	18.4049	−	10.0498i	0.590035	−	0.322183i
$974$		0			0
$975$	−12.3231	+	52.9853i	−0.394654	+	1.69689i
$976$		0			0
$977$	−55.2542	+	3.95186i	−1.76774	+	0.126431i	−0.916931	−	0.399047i	$-0.869341\pi$
$977$	−55.2542	+	3.95186i	−1.76774	+	0.126431i	−0.850807	+	0.525478i	$0.823887\pi$
$978$		0			0
$979$	3.34232	+	11.3829i	0.106821	+	0.363799i
$980$		0			0
$981$	17.5856	+	27.3637i	0.561465	+	0.873657i
$982$		0			0
$983$	−21.9442	−	16.4272i	−0.699912	−	0.523947i	0.189028	−	0.981972i	$-0.439466\pi$
$983$	−21.9442	−	16.4272i	−0.699912	−	0.523947i	−0.888940	+	0.458024i	$0.848557\pi$
$984$		0			0
$985$	−33.2030	−	16.9185i	−1.05794	−	0.539068i
$986$		0			0
$987$	−1.02211	+	14.2910i	−0.0325342	+	0.454887i
$988$		0			0
$989$	27.2217	−	14.5520i	0.865601	−	0.462727i
$990$		0			0
$991$	15.4299	+	17.8070i	0.490146	+	0.565659i	0.945905	−	0.324445i	$-0.105177\pi$
$991$	15.4299	+	17.8070i	0.490146	+	0.565659i	−0.455758	+	0.890103i	$0.650632\pi$
$992$		0			0
$993$	9.46256	−	7.08358i	0.300285	−	0.224791i
$994$		0			0
$995$	21.4247	+	31.3337i	0.679209	+	0.993347i
$996$		0			0
$997$	−6.77373	+	31.1383i	−0.214526	+	0.986161i	0.736353	+	0.676598i	$0.236546\pi$
$997$	−6.77373	+	31.1383i	−0.214526	+	0.986161i	−0.950879	+	0.309563i	$0.899817\pi$
$998$		0			0
$999$	7.88974	−	2.31664i	0.249620	−	0.0732951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.33.2	✓	240
5.2	odd	4	inner	460.2.x.a.217.2	yes	240
23.7	odd	22	inner	460.2.x.a.53.2	yes	240
115.7	even	44	inner	460.2.x.a.237.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.2	✓	240	1.1	even	1	trivial
460.2.x.a.53.2	yes	240	23.7	odd	22	inner
460.2.x.a.217.2	yes	240	5.2	odd	4	inner
460.2.x.a.237.2	yes	240	115.7	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.486808 - 2.23782i) q^{3} +(0.0638162 + 2.23516i) q^{5} +(1.23306 + 2.25818i) q^{7} +(-2.04197 + 0.932535i) q^{9} +O(q^{10})\)	\(q+(-0.486808 - 2.23782i) q^{3} +(0.0638162 + 2.23516i) q^{5} +(1.23306 + 2.25818i) q^{7} +(-2.04197 + 0.932535i) q^{9} +(0.879344 + 0.761956i) q^{11} +(4.16960 + 2.27677i) q^{13} +(4.97082 - 1.23090i) q^{15} +(-2.50905 + 3.35170i) q^{17} +(-0.0362513 + 0.252133i) q^{19} +(4.45315 - 3.85868i) q^{21} +(4.61338 - 1.31024i) q^{23} +(-4.99185 + 0.285278i) q^{25} +(-1.03643 - 1.38451i) q^{27} +(-1.34948 + 0.194026i) q^{29} +(8.60919 - 5.53279i) q^{31} +(1.27705 - 2.33874i) q^{33} +(-4.96871 + 2.90020i) q^{35} +(-1.66154 + 4.45477i) q^{37} +(3.06522 - 10.4392i) q^{39} +(2.79496 - 6.12010i) q^{41} +(6.28917 - 1.36812i) q^{43} +(-2.21467 - 4.50461i) q^{45} +(-1.71936 + 1.71936i) q^{47} +(0.205531 - 0.319813i) q^{49} +(8.72192 + 3.98317i) q^{51} +(-7.04584 + 3.84732i) q^{53} +(-1.64698 + 2.01410i) q^{55} +(0.581876 - 0.0416166i) q^{57} +(0.664449 + 2.26290i) q^{59} +(-0.532294 - 0.828266i) q^{61} +(-4.62371 - 3.46126i) q^{63} +(-4.82286 + 9.46501i) q^{65} +(-0.626287 + 8.75664i) q^{67} +(-5.17791 - 9.68608i) q^{69} +(-4.15239 - 4.79212i) q^{71} +(-11.8709 + 8.88643i) q^{73} +(3.06848 + 11.0320i) q^{75} +(-0.636352 + 2.92526i) q^{77} +(0.671175 - 0.197075i) q^{79} +(-7.00389 + 8.08292i) q^{81} +(-12.2947 - 4.58568i) q^{83} +(-7.65169 - 5.39423i) q^{85} +(1.09113 + 2.92544i) q^{87} +(8.57741 + 5.51237i) q^{89} +12.2231i q^{91} +(-16.5724 - 16.5724i) q^{93} +(-0.565870 - 0.0649371i) q^{95} +(14.5308 - 5.41971i) q^{97} +(-2.50614 - 0.735870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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