LMFDB - Embedded newform 520.2.bu.b.121.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(121,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("520.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.bu (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.6
Root			$2.44974i$ of defining polynomial
Character	$\chi$	$=$	520.121
Dual form			520.2.bu.b.361.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.275748 - 0.477609i) q^{3} +1.00000i q^{5} +(-1.57306 + 0.908206i) q^{7} +(1.34793 + 2.33468i) q^{9} +O(q^{10})$	\(q+(0.275748 - 0.477609i) q^{3} +1.00000i q^{5} +(-1.57306 + 0.908206i) q^{7} +(1.34793 + 2.33468i) q^{9} +(0.759545 + 0.438523i) q^{11} +(-2.94577 + 2.07905i) q^{13} +(0.477609 + 0.275748i) q^{15} +(2.47282 + 4.28305i) q^{17} +(3.18017 - 1.83607i) q^{19} +1.00174i q^{21} +(-2.69554 + 4.66881i) q^{23} -1.00000 q^{25} +3.14124 q^{27} +(0.214596 - 0.371692i) q^{29} -2.36449i q^{31} +(0.418885 - 0.241844i) q^{33} +(-0.908206 - 1.57306i) q^{35} +(7.40500 + 4.27528i) q^{37} +(0.180686 + 1.98022i) q^{39} +(1.03931 + 0.600045i) q^{41} +(1.00825 + 1.74634i) q^{43} +(-2.33468 + 1.34793i) q^{45} -8.92633i q^{47} +(-1.85032 + 3.20485i) q^{49} +2.72750 q^{51} -5.45025 q^{53} +(-0.438523 + 0.759545i) q^{55} -2.02517i q^{57} +(3.96683 - 2.29025i) q^{59} +(-0.952525 - 1.64982i) q^{61} +(-4.24074 - 2.44839i) q^{63} +(-2.07905 - 2.94577i) q^{65} +(-4.42293 - 2.55358i) q^{67} +(1.48658 + 2.57483i) q^{69} +(13.4521 - 7.76656i) q^{71} +10.7435i q^{73} +(-0.275748 + 0.477609i) q^{75} -1.59308 q^{77} -11.2334 q^{79} +(-3.17759 + 5.50375i) q^{81} -2.60910i q^{83} +(-4.28305 + 2.47282i) q^{85} +(-0.118349 - 0.204986i) q^{87} +(0.645218 + 0.372517i) q^{89} +(2.74566 - 5.94584i) q^{91} +(-1.12930 - 0.652003i) q^{93} +(1.83607 + 3.18017i) q^{95} +(8.46798 - 4.88899i) q^{97} +2.36439i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 + 6 * q^7 - 16 * q^9	$ 16 q - 4 q^{3} + 6 q^{7} - 16 q^{9} - 6 q^{11} - 2 q^{13} + 4 q^{17} + 30 q^{19} + 6 q^{23} - 16 q^{25} + 44 q^{27} - 16 q^{29} + 24 q^{33} - 6 q^{35} - 24 q^{37} - 8 q^{39} - 24 q^{41} + 6 q^{43} + 12 q^{45} - 4 q^{49} - 40 q^{51} + 4 q^{53} - 6 q^{55} + 12 q^{59} - 2 q^{61} - 60 q^{63} - 10 q^{65} - 6 q^{67} + 52 q^{69} + 72 q^{71} + 4 q^{75} + 32 q^{77} + 36 q^{79} - 28 q^{81} - 22 q^{87} + 24 q^{89} - 22 q^{91} - 96 q^{93} + 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q - 4 * q^3 + 6 * q^7 - 16 * q^9 - 6 * q^11 - 2 * q^13 + 4 * q^17 + 30 * q^19 + 6 * q^23 - 16 * q^25 + 44 * q^27 - 16 * q^29 + 24 * q^33 - 6 * q^35 - 24 * q^37 - 8 * q^39 - 24 * q^41 + 6 * q^43 + 12 * q^45 - 4 * q^49 - 40 * q^51 + 4 * q^53 - 6 * q^55 + 12 * q^59 - 2 * q^61 - 60 * q^63 - 10 * q^65 - 6 * q^67 + 52 * q^69 + 72 * q^71 + 4 * q^75 + 32 * q^77 + 36 * q^79 - 28 * q^81 - 22 * q^87 + 24 * q^89 - 22 * q^91 - 96 * q^93 + 10 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	0.275748	−	0.477609i	0.159203	−	0.275748i	−0.775379	−	0.631497i	$-0.782441\pi$
$3$	0.275748	−	0.477609i	0.159203	−	0.275748i	0.934582	+	0.355749i	$0.115774\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−1.57306	+	0.908206i	−0.594561	+	0.343270i	−0.766899	−	0.641768i	$-0.778201\pi$
$7$	−1.57306	+	0.908206i	−0.594561	+	0.343270i	0.172338	+	0.985038i	$0.444868\pi$
$8$		0			0
$9$	1.34793	+	2.33468i	0.449309	+	0.778226i
$10$		0			0
$11$	0.759545	+	0.438523i	0.229011	+	0.132220i	0.610116	−	0.792312i	$-0.291123\pi$
$11$	0.759545	+	0.438523i	0.229011	+	0.132220i	−0.381105	+	0.924532i	$0.624456\pi$
$12$		0			0
$13$	−2.94577	+	2.07905i	−0.817009	+	0.576625i
$13$	−2.94577	+	2.07905i	−0.817009	+	0.576625i
$14$		0			0
$15$	0.477609	+	0.275748i	0.123318	+	0.0711977i
$16$		0			0
$17$	2.47282	+	4.28305i	0.599748	+	1.03879i	0.992858	+	0.119302i	$0.0380657\pi$
$17$	2.47282	+	4.28305i	0.599748	+	1.03879i	−0.393111	+	0.919491i	$0.628601\pi$
$18$		0			0
$19$	3.18017	−	1.83607i	0.729581	−	0.421224i	−0.0886879	−	0.996059i	$-0.528267\pi$
$19$	3.18017	−	1.83607i	0.729581	−	0.421224i	0.818269	+	0.574836i	$0.194934\pi$
$20$		0			0
$21$			1.00174i			0.218598i
$22$		0			0
$23$	−2.69554	+	4.66881i	−0.562058	+	0.973513i	0.435258	+	0.900306i	$0.356657\pi$
$23$	−2.69554	+	4.66881i	−0.562058	+	0.973513i	−0.997317	+	0.0732079i	$0.976676\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	3.14124			0.604531
$28$		0			0
$29$	0.214596	−	0.371692i	0.0398496	−	0.0690215i	−0.845413	−	0.534114i	$-0.820645\pi$
$29$	0.214596	−	0.371692i	0.0398496	−	0.0690215i	0.885262	+	0.465092i	$0.153979\pi$
$30$		0			0
$31$		−	2.36449i		−	0.424675i	−0.977196	−	0.212338i	$-0.931892\pi$
$31$		−	2.36449i		−	0.424675i	0.977196	−	0.212338i	$-0.0681077\pi$
$32$		0			0
$33$	0.418885	−	0.241844i	0.0729186	−	0.0420996i
$34$		0			0
$35$	−0.908206	−	1.57306i	−0.153515	−	0.265896i
$36$		0			0
$37$	7.40500	+	4.27528i	1.21737	+	0.702851i	0.964355	−	0.264610i	$-0.0852432\pi$
$37$	7.40500	+	4.27528i	1.21737	+	0.702851i	0.253019	+	0.967461i	$0.418577\pi$
$38$		0			0
$39$	0.180686	+	1.98022i	0.0289329	+	0.317089i
$40$		0			0
$41$	1.03931	+	0.600045i	0.162313	+	0.0937113i	0.578956	−	0.815359i	$-0.303460\pi$
$41$	1.03931	+	0.600045i	0.162313	+	0.0937113i	−0.416643	+	0.909070i	$0.636794\pi$
$42$		0			0
$43$	1.00825	+	1.74634i	0.153757	+	0.266315i	0.932606	−	0.360897i	$-0.117529\pi$
$43$	1.00825	+	1.74634i	0.153757	+	0.266315i	−0.778849	+	0.627212i	$0.784196\pi$
$44$		0			0
$45$	−2.33468	+	1.34793i	−0.348033	+	0.200937i
$46$		0			0
$47$		−	8.92633i		−	1.30204i	−0.759061	−	0.651020i	$-0.774341\pi$
$47$		−	8.92633i		−	1.30204i	0.759061	−	0.651020i	$-0.225659\pi$
$48$		0			0
$49$	−1.85032	+	3.20485i	−0.264332	+	0.457836i
$50$		0			0
$51$	2.72750			0.381926
$52$		0			0
$53$	−5.45025			−0.748650			−0.374325	−	0.927298i	$-0.622126\pi$
$53$	−5.45025			−0.748650			−0.374325	+	0.927298i	$0.622126\pi$
$54$		0			0
$55$	−0.438523	+	0.759545i	−0.0591305	+	0.102417i
$56$		0			0
$57$		−	2.02517i		−	0.268240i
$58$		0			0
$59$	3.96683	−	2.29025i	0.516437	−	0.298165i	−0.219039	−	0.975716i	$-0.570292\pi$
$59$	3.96683	−	2.29025i	0.516437	−	0.298165i	0.735476	+	0.677551i	$0.236959\pi$
$60$		0			0
$61$	−0.952525	−	1.64982i	−0.121958	−	0.211238i	0.798582	−	0.601887i	$-0.205584\pi$
$61$	−0.952525	−	1.64982i	−0.121958	−	0.211238i	−0.920540	+	0.390649i	$0.872251\pi$
$62$		0			0
$63$	−4.24074	−	2.44839i	−0.534283	−	0.308468i
$64$		0			0
$65$	−2.07905	−	2.94577i	−0.257875	−	0.365377i
$66$		0			0
$67$	−4.42293	−	2.55358i	−0.540347	−	0.311970i	0.204872	−	0.978789i	$-0.434322\pi$
$67$	−4.42293	−	2.55358i	−0.540347	−	0.311970i	−0.745220	+	0.666819i	$0.767655\pi$
$68$		0			0
$69$	1.48658	+	2.57483i	0.178963	+	0.309973i
$70$		0			0
$71$	13.4521	−	7.76656i	1.59647	−	0.921721i	0.604306	−	0.796752i	$-0.293450\pi$
$71$	13.4521	−	7.76656i	1.59647	−	0.921721i	0.992161	−	0.124969i	$-0.0398831\pi$
$72$		0			0
$73$			10.7435i			1.25743i	0.777635	+	0.628716i	$0.216419\pi$
$73$			10.7435i			1.25743i	−0.777635	+	0.628716i	$0.783581\pi$
$74$		0			0
$75$	−0.275748	+	0.477609i	−0.0318406	+	0.0551495i
$76$		0			0
$77$	−1.59308			−0.181548
$78$		0			0
$79$	−11.2334			−1.26386			−0.631929	−	0.775026i	$-0.717737\pi$
$79$	−11.2334			−1.26386			−0.631929	+	0.775026i	$0.717737\pi$
$80$		0			0
$81$	−3.17759	+	5.50375i	−0.353066	+	0.611528i
$82$		0			0
$83$		−	2.60910i		−	0.286386i	−0.989695	−	0.143193i	$-0.954263\pi$
$83$		−	2.60910i		−	0.286386i	0.989695	−	0.143193i	$-0.0457369\pi$
$84$		0			0
$85$	−4.28305	+	2.47282i	−0.464562	+	0.268215i
$86$		0			0
$87$	−0.118349	−	0.204986i	−0.0126883	−	0.0219768i
$88$		0			0
$89$	0.645218	+	0.372517i	0.0683930	+	0.0394867i	0.533807	−	0.845607i	$-0.320761\pi$
$89$	0.645218	+	0.372517i	0.0683930	+	0.0394867i	−0.465414	+	0.885093i	$0.654094\pi$
$90$		0			0
$91$	2.74566	−	5.94584i	0.287823	−	0.623293i
$92$		0			0
$93$	−1.12930	−	0.652003i	−0.117103	−	0.0676096i
$94$		0			0
$95$	1.83607	+	3.18017i	0.188377	+	0.326279i
$96$		0			0
$97$	8.46798	−	4.88899i	0.859794	−	0.496402i	−0.00414956	−	0.999991i	$-0.501321\pi$
$97$	8.46798	−	4.88899i	0.859794	−	0.496402i	0.863943	+	0.503589i	$0.167988\pi$
$98$		0			0
$99$			2.36439i			0.237630i
$100$		0			0
$101$	3.45444	−	5.98327i	0.343730	−	0.595358i	−0.641392	−	0.767213i	$-0.721643\pi$
$101$	3.45444	−	5.98327i	0.343730	−	0.595358i	0.985122	+	0.171855i	$0.0549761\pi$
$102$		0			0
$103$	−17.4021			−1.71468			−0.857342	−	0.514747i	$-0.827886\pi$
$103$	−17.4021			−1.71468			−0.857342	+	0.514747i	$0.827886\pi$
$104$		0			0
$105$	−1.00174			−0.0977601
$106$		0			0
$107$	3.84562	−	6.66080i	0.371770	−	0.643924i	−0.618068	−	0.786124i	$-0.712084\pi$
$107$	3.84562	−	6.66080i	0.371770	−	0.643924i	0.989838	+	0.142201i	$0.0454178\pi$
$108$		0			0
$109$		−	11.1587i		−	1.06881i	−0.845229	−	0.534404i	$-0.820536\pi$
$109$		−	11.1587i		−	1.06881i	0.845229	−	0.534404i	$-0.179464\pi$
$110$		0			0
$111$	4.08382	−	2.35780i	0.387619	−	0.223792i
$112$		0			0
$113$	−6.84621	−	11.8580i	−0.644038	−	1.11551i	−0.984523	−	0.175256i	$-0.943925\pi$
$113$	−6.84621	−	11.8580i	−0.644038	−	1.11551i	0.340485	−	0.940250i	$-0.389409\pi$
$114$		0			0
$115$	−4.66881	−	2.69554i	−0.435368	−	0.251360i
$116$		0			0
$117$	−8.82459	−	4.07500i	−0.815834	−	0.376734i
$118$		0			0
$119$	−7.77979	−	4.49167i	−0.713172	−	0.411750i
$120$		0			0
$121$	−5.11539	−	8.86012i	−0.465036	−	0.805466i
$122$		0			0
$123$	0.573174	−	0.330922i	0.0516814	−	0.0298383i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−6.56497	+	11.3709i	−0.582547	+	1.00900i	0.412630	+	0.910899i	$0.364610\pi$
$127$	−6.56497	+	11.3709i	−0.582547	+	1.00900i	−0.995176	+	0.0981016i	$0.968723\pi$
$128$		0			0
$129$	1.11209			0.0979143
$130$		0			0
$131$	19.2978			1.68606			0.843030	−	0.537866i	$-0.180770\pi$
$131$	19.2978			1.68606			0.843030	+	0.537866i	$0.180770\pi$
$132$		0			0
$133$	−3.33506	+	5.77650i	−0.289187	+	0.500886i
$134$		0			0
$135$			3.14124i			0.270355i
$136$		0			0
$137$	3.90390	−	2.25392i	0.333533	−	0.192565i	−0.323876	−	0.946100i	$-0.604986\pi$
$137$	3.90390	−	2.25392i	0.333533	−	0.192565i	0.657408	+	0.753534i	$0.271653\pi$
$138$		0			0
$139$	−4.78060	−	8.28024i	−0.405485	−	0.702321i	0.588893	−	0.808211i	$-0.299564\pi$
$139$	−4.78060	−	8.28024i	−0.405485	−	0.702321i	−0.994378	+	0.105890i	$0.966231\pi$
$140$		0			0
$141$	−4.26330	−	2.46142i	−0.359034	−	0.207289i
$142$		0			0
$143$	−3.14915	+	0.287346i	−0.263346	+	0.0240291i
$144$		0			0
$145$	0.371692	+	0.214596i	0.0308673	+	0.0178213i
$146$		0			0
$147$	1.02044	+	1.76746i	0.0841649	+	0.145778i
$148$		0			0
$149$	13.7633	−	7.94624i	1.12753	−	0.650981i	0.184220	−	0.982885i	$-0.441024\pi$
$149$	13.7633	−	7.94624i	1.12753	−	0.650981i	0.943313	+	0.331904i	$0.107691\pi$
$150$		0			0
$151$			13.4356i			1.09338i	0.837336	+	0.546689i	$0.184112\pi$
$151$			13.4356i			1.09338i	−0.837336	+	0.546689i	$0.815888\pi$
$152$		0			0
$153$	−6.66637	+	11.5465i	−0.538944	+	0.933478i
$154$		0			0
$155$	2.36449			0.189921
$156$		0			0
$157$	21.8879			1.74685			0.873424	−	0.486960i	$-0.161894\pi$
$157$	21.8879			1.74685			0.873424	+	0.486960i	$0.161894\pi$
$158$		0			0
$159$	−1.50289	+	2.60309i	−0.119187	+	0.206438i
$160$		0			0
$161$		−	9.79241i		−	0.771750i
$162$		0			0
$163$	−3.25507	+	1.87932i	−0.254957	+	0.147199i	−0.622032	−	0.782992i	$-0.713693\pi$
$163$	−3.25507	+	1.87932i	−0.254957	+	0.147199i	0.367075	+	0.930191i	$0.380359\pi$
$164$		0			0
$165$	0.241844	+	0.418885i	0.0188275	+	0.0326102i
$166$		0			0
$167$	−13.3492	−	7.70716i	−1.03299	−	0.596398i	−0.115151	−	0.993348i	$-0.536735\pi$
$167$	−13.3492	−	7.70716i	−1.03299	−	0.596398i	−0.917840	+	0.396950i	$0.870069\pi$
$168$		0			0
$169$	4.35508	−	12.2488i	0.335006	−	0.942216i
$170$		0			0
$171$	8.57327	+	4.94978i	0.655614	+	0.378519i
$172$		0			0
$173$	0.430549	+	0.745733i	0.0327340	+	0.0566970i	0.881928	−	0.471384i	$-0.156245\pi$
$173$	0.430549	+	0.745733i	0.0327340	+	0.0566970i	−0.849194	+	0.528081i	$0.822912\pi$
$174$		0			0
$175$	1.57306	−	0.908206i	0.118912	−	0.0686539i
$176$		0			0
$177$		−	2.52612i		−	0.189875i
$178$		0			0
$179$	3.90073	−	6.75627i	0.291554	−	0.504987i	−0.682623	−	0.730771i	$-0.739161\pi$
$179$	3.90073	−	6.75627i	0.291554	−	0.504987i	0.974177	+	0.225784i	$0.0724942\pi$
$180$		0			0
$181$	5.70152			0.423791			0.211895	−	0.977292i	$-0.432036\pi$
$181$	5.70152			0.423791			0.211895	+	0.977292i	$0.432036\pi$
$182$		0			0
$183$	−1.05063			−0.0776645
$184$		0			0
$185$	−4.27528	+	7.40500i	−0.314325	+	0.544426i
$186$		0			0
$187$			4.33756i			0.317194i
$188$		0			0
$189$	−4.94135	+	2.85289i	−0.359430	+	0.207517i
$190$		0			0
$191$	−0.926061	−	1.60398i	−0.0670074	−	0.116060i	0.830575	−	0.556906i	$-0.188012\pi$
$191$	−0.926061	−	1.60398i	−0.0670074	−	0.116060i	−0.897583	+	0.440846i	$0.854678\pi$
$192$		0			0
$193$	−7.47772	−	4.31726i	−0.538258	−	0.310763i	0.206115	−	0.978528i	$-0.433918\pi$
$193$	−7.47772	−	4.31726i	−0.538258	−	0.310763i	−0.744373	+	0.667765i	$0.767251\pi$
$194$		0			0
$195$	−1.98022	+	0.180686i	−0.141806	+	0.0129392i
$196$		0			0
$197$	3.66599	+	2.11656i	0.261191	+	0.150799i	0.624878	−	0.780723i	$-0.285149\pi$
$197$	3.66599	+	2.11656i	0.261191	+	0.150799i	−0.363687	+	0.931521i	$0.618482\pi$
$198$		0			0
$199$	13.8668	+	24.0179i	0.982988	+	1.70259i	0.650556	+	0.759458i	$0.274536\pi$
$199$	13.8668	+	24.0179i	0.982988	+	1.70259i	0.332432	+	0.943127i	$0.392131\pi$
$200$		0			0
$201$	−2.43923	+	1.40829i	−0.172050	+	0.0993330i
$202$		0			0
$203$			0.779591i			0.0547166i
$204$		0			0
$205$	−0.600045	+	1.03931i	−0.0419090	+	0.0725885i
$206$		0			0
$207$	−14.5335			−1.01015
$208$		0			0
$209$	3.22064			0.222776
$210$		0			0
$211$	0.0728649	−	0.126206i	0.00501623	−	0.00868836i	−0.863506	−	0.504338i	$-0.831737\pi$
$211$	0.0728649	−	0.126206i	0.00501623	−	0.00868836i	0.868523	+	0.495650i	$0.165070\pi$
$212$		0			0
$213$		−	8.56644i		−	0.586963i
$214$		0			0
$215$	−1.74634	+	1.00825i	−0.119100	+	0.0687622i
$216$		0			0
$217$	2.14745	+	3.71949i	0.145778	+	0.252495i
$218$		0			0
$219$	5.13119	+	2.96250i	0.346734	+	0.200187i
$220$		0			0
$221$	−16.1891	−	7.47575i	−1.08899	−	0.502873i
$222$		0			0
$223$	−4.24045	−	2.44822i	−0.283961	−	0.163945i	0.351254	−	0.936280i	$-0.385755\pi$
$223$	−4.24045	−	2.44822i	−0.283961	−	0.163945i	−0.635215	+	0.772335i	$0.719089\pi$
$224$		0			0
$225$	−1.34793	−	2.33468i	−0.0898618	−	0.155645i
$226$		0			0
$227$	11.9441	−	6.89595i	0.792760	−	0.457700i	−0.0481730	−	0.998839i	$-0.515340\pi$
$227$	11.9441	−	6.89595i	0.792760	−	0.457700i	0.840933	+	0.541139i	$0.182007\pi$
$228$		0			0
$229$			12.6453i			0.835628i	0.908533	+	0.417814i	$0.137204\pi$
$229$			12.6453i			0.835628i	−0.908533	+	0.417814i	$0.862796\pi$
$230$		0			0
$231$	−0.439288	+	0.760869i	−0.0289030	+	0.0500615i
$232$		0			0
$233$	10.2878			0.673975			0.336987	−	0.941509i	$-0.390592\pi$
$233$	10.2878			0.673975			0.336987	+	0.941509i	$0.390592\pi$
$234$		0			0
$235$	8.92633			0.582290
$236$		0			0
$237$	−3.09759	+	5.36518i	−0.201210	+	0.348506i
$238$		0			0
$239$			20.1730i			1.30489i	0.757838	+	0.652443i	$0.226256\pi$
$239$			20.1730i			1.30489i	−0.757838	+	0.652443i	$0.773744\pi$
$240$		0			0
$241$	0.798945	−	0.461271i	0.0514645	−	0.0297131i	−0.474047	−	0.880500i	$-0.657207\pi$
$241$	0.798945	−	0.461271i	0.0514645	−	0.0297131i	0.525512	+	0.850786i	$0.323874\pi$
$242$		0			0
$243$	6.46428	+	11.1965i	0.414684	+	0.718253i
$244$		0			0
$245$	−3.20485	−	1.85032i	−0.204751	−	0.118213i
$246$		0			0
$247$	−5.55075	+	12.0204i	−0.353186	+	0.764838i
$248$		0			0
$249$	−1.24613	−	0.719453i	−0.0789702	−	0.0455935i
$250$		0			0
$251$	8.13425	+	14.0889i	0.513430	+	0.889286i	0.999879	+	0.0155772i	$0.00495859\pi$
$251$	8.13425	+	14.0889i	0.513430	+	0.889286i	−0.486449	+	0.873709i	$0.661708\pi$
$252$		0			0
$253$	−4.09476	+	2.36411i	−0.257435	+	0.148630i
$254$		0			0
$255$			2.72750i			0.170803i
$256$		0			0
$257$	8.50538	−	14.7318i	0.530551	−	0.918941i	−0.468814	−	0.883297i	$-0.655318\pi$
$257$	8.50538	−	14.7318i	0.530551	−	0.918941i	0.999365	−	0.0356442i	$-0.0113483\pi$
$258$		0			0
$259$	−15.5313			−0.965070
$260$		0			0
$261$	1.15704			0.0716190
$262$		0			0
$263$	−9.66899	+	16.7472i	−0.596215	+	1.03268i	0.397159	+	0.917750i	$0.369996\pi$
$263$	−9.66899	+	16.7472i	−0.596215	+	1.03268i	−0.993374	+	0.114925i	$0.963337\pi$
$264$		0			0
$265$		−	5.45025i		−	0.334806i
$266$		0			0
$267$	0.355835	−	0.205441i	0.0217767	−	0.0125728i
$268$		0			0
$269$	0.285151	+	0.493896i	0.0173860	+	0.0301134i	0.874587	−	0.484868i	$-0.161132\pi$
$269$	0.285151	+	0.493896i	0.0173860	+	0.0301134i	−0.857202	+	0.514981i	$0.827799\pi$
$270$		0			0
$271$	20.3837	+	11.7686i	1.23822	+	0.714889i	0.968731	−	0.248113i	$-0.0798105\pi$
$271$	20.3837	+	11.7686i	1.23822	+	0.714889i	0.269493	+	0.963002i	$0.413144\pi$
$272$		0			0
$273$	−2.08268	−	2.95090i	−0.126049	−	0.178597i
$274$		0			0
$275$	−0.759545	−	0.438523i	−0.0458023	−	0.0264440i
$276$		0			0
$277$	7.23659	+	12.5341i	0.434804	+	0.753103i	0.997280	−	0.0737109i	$-0.0234842\pi$
$277$	7.23659	+	12.5341i	0.434804	+	0.753103i	−0.562475	+	0.826814i	$0.690151\pi$
$278$		0			0
$279$	5.52033	−	3.18716i	0.330493	−	0.190810i
$280$		0			0
$281$			24.4795i			1.46033i	0.683273	+	0.730163i	$0.260556\pi$
$281$			24.4795i			1.46033i	−0.683273	+	0.730163i	$0.739444\pi$
$282$		0			0
$283$	−8.89924	+	15.4139i	−0.529005	+	0.916263i	0.470423	+	0.882441i	$0.344101\pi$
$283$	−8.89924	+	15.4139i	−0.529005	+	0.916263i	−0.999428	+	0.0338224i	$0.989232\pi$
$284$		0			0
$285$	2.02517			0.119961
$286$		0			0
$287$	−2.17986			−0.128673
$288$		0			0
$289$	−3.72970	+	6.46003i	−0.219394	+	0.380002i
$290$		0			0
$291$		−	5.39251i		−	0.316115i
$292$		0			0
$293$	17.5760	−	10.1475i	1.02680	−	0.592824i	0.110735	−	0.993850i	$-0.464680\pi$
$293$	17.5760	−	10.1475i	1.02680	−	0.592824i	0.916067	+	0.401026i	$0.131346\pi$
$294$		0			0
$295$	2.29025	+	3.96683i	0.133344	+	0.230958i
$296$		0			0
$297$	2.38591	+	1.37751i	0.138445	+	0.0799310i
$298$		0			0
$299$	−1.76627	−	19.3574i	−0.102146	−	1.11947i
$300$		0			0
$301$	−3.17208	−	1.83140i	−0.182836	−	0.105560i
$302$		0			0
$303$	−1.90511	−	3.29975i	−0.109446	−	0.189566i
$304$		0			0
$305$	1.64982	−	0.952525i	0.0944685	−	0.0545414i
$306$		0			0
$307$			9.55636i			0.545410i	0.962098	+	0.272705i	$0.0879184\pi$
$307$			9.55636i			0.545410i	−0.962098	+	0.272705i	$0.912082\pi$
$308$		0			0
$309$	−4.79860	+	8.31142i	−0.272983	+	0.472820i
$310$		0			0
$311$	0.151461			0.00858856			0.00429428	−	0.999991i	$-0.498633\pi$
$311$	0.151461			0.00858856			0.00429428	+	0.999991i	$0.498633\pi$
$312$		0			0
$313$	28.5006			1.61095			0.805475	−	0.592630i	$-0.201910\pi$
$313$	28.5006			1.61095			0.805475	+	0.592630i	$0.201910\pi$
$314$		0			0
$315$	2.44839	−	4.24074i	0.137951	−	0.238938i
$316$		0			0
$317$		−	20.0004i		−	1.12333i	−0.827363	−	0.561667i	$-0.810160\pi$
$317$		−	20.0004i		−	1.12333i	0.827363	−	0.561667i	$-0.189840\pi$
$318$		0			0
$319$	0.325991	−	0.188211i	0.0182520	−	0.0105378i
$320$		0			0
$321$	−2.12084	−	3.67340i	−0.118374	−	0.205029i
$322$		0			0
$323$	15.7280	+	9.08056i	0.875129	+	0.505256i
$324$		0			0
$325$	2.94577	−	2.07905i	0.163402	−	0.115325i
$326$		0			0
$327$	−5.32949	−	3.07698i	−0.294721	−	0.170157i
$328$		0			0
$329$	8.10695	+	14.0417i	0.446951	+	0.774141i
$330$		0			0
$331$	8.73156	−	5.04117i	0.479930	−	0.277088i	−0.240457	−	0.970660i	$-0.577297\pi$
$331$	8.73156	−	5.04117i	0.479930	−	0.277088i	0.720387	+	0.693572i	$0.243964\pi$
$332$		0			0
$333$			23.0510i			1.26319i
$334$		0			0
$335$	2.55358	−	4.42293i	0.139517	−	0.241651i
$336$		0			0
$337$	−9.00198			−0.490369			−0.245185	−	0.969476i	$-0.578849\pi$
$337$	−9.00198			−0.490369			−0.245185	+	0.969476i	$0.578849\pi$
$338$		0			0
$339$	−7.55131			−0.410131
$340$		0			0
$341$	1.03689	−	1.79594i	0.0561505	−	0.0972555i
$342$		0			0
$343$		−	19.4368i		−	1.04949i
$344$		0			0
$345$	−2.57483	+	1.48658i	−0.138624	+	0.0800346i
$346$		0			0
$347$	0.686627	+	1.18927i	0.0368601	+	0.0638435i	0.883867	−	0.467738i	$-0.154931\pi$
$347$	0.686627	+	1.18927i	0.0368601	+	0.0638435i	−0.847007	+	0.531582i	$0.821598\pi$
$348$		0			0
$349$	−17.6180	−	10.1717i	−0.943069	−	0.544481i	−0.0521480	−	0.998639i	$-0.516607\pi$
$349$	−17.6180	−	10.1717i	−0.943069	−	0.544481i	−0.890921	+	0.454158i	$0.849940\pi$
$350$		0			0
$351$	−9.25335	+	6.53079i	−0.493907	+	0.348588i
$352$		0			0
$353$	−6.13858	−	3.54411i	−0.326724	−	0.188634i	0.327662	−	0.944795i	$-0.393739\pi$
$353$	−6.13858	−	3.54411i	−0.326724	−	0.188634i	−0.654386	+	0.756161i	$0.727073\pi$
$354$		0			0
$355$	7.76656	+	13.4521i	0.412206	+	0.713962i
$356$		0			0
$357$	−4.29052	+	2.47713i	−0.227078	+	0.131104i
$358$		0			0
$359$		−	4.81284i		−	0.254012i	−0.991902	−	0.127006i	$-0.959463\pi$
$359$		−	4.81284i		−	0.254012i	0.991902	−	0.127006i	$-0.0405368\pi$
$360$		0			0
$361$	−2.75768	+	4.77644i	−0.145141	+	0.251392i
$362$		0			0
$363$	−5.64223			−0.296140
$364$		0			0
$365$	−10.7435			−0.562341
$366$		0			0
$367$	−4.57841	+	7.93004i	−0.238991	+	0.413945i	−0.960425	−	0.278538i	$-0.910150\pi$
$367$	−4.57841	+	7.93004i	−0.238991	+	0.413945i	0.721434	+	0.692483i	$0.243483\pi$
$368$		0			0
$369$			3.23527i			0.168421i
$370$		0			0
$371$	8.57357	−	4.94995i	0.445118	−	0.256989i
$372$		0			0
$373$	−5.88828	−	10.1988i	−0.304884	−	0.528074i	0.672352	−	0.740232i	$-0.265284\pi$
$373$	−5.88828	−	10.1988i	−0.304884	−	0.528074i	−0.977235	+	0.212158i	$0.931951\pi$
$374$		0			0
$375$	−0.477609	−	0.275748i	−0.0246636	−	0.0142395i
$376$		0			0
$377$	0.140616	+	1.54107i	0.00724209	+	0.0793694i
$378$		0			0
$379$	−31.9745	−	18.4605i	−1.64242	−	0.948253i	−0.979969	−	0.199149i	$-0.936182\pi$
$379$	−31.9745	−	18.4605i	−1.64242	−	0.948253i	−0.662453	−	0.749104i	$-0.730484\pi$
$380$		0			0
$381$	3.62055	+	6.27098i	0.185486	+	0.321272i
$382$		0			0
$383$	19.1140	−	11.0355i	0.976679	−	0.563886i	0.0754134	−	0.997152i	$-0.475972\pi$
$383$	19.1140	−	11.0355i	0.976679	−	0.563886i	0.901266	+	0.433266i	$0.142639\pi$
$384$		0			0
$385$		−	1.59308i		−	0.0811908i
$386$		0			0
$387$	−2.71810	+	4.70788i	−0.138169	+	0.239315i
$388$		0			0
$389$	35.1523			1.78229			0.891146	−	0.453716i	$-0.149902\pi$
$389$	35.1523			1.78229			0.891146	+	0.453716i	$0.149902\pi$
$390$		0			0
$391$	−26.6623			−1.34837
$392$		0			0
$393$	5.32133	−	9.21682i	0.268426	−	0.464927i
$394$		0			0
$395$		−	11.2334i		−	0.565214i
$396$		0			0
$397$	8.03921	−	4.64144i	0.403476	−	0.232947i	−0.284506	−	0.958674i	$-0.591830\pi$
$397$	8.03921	−	4.64144i	0.403476	−	0.232947i	0.687983	+	0.725727i	$0.258496\pi$
$398$		0			0
$399$	1.83927	+	3.18571i	0.0920788	+	0.159485i
$400$		0			0
$401$	−24.6221	−	14.2156i	−1.22957	−	0.709893i	−0.262630	−	0.964897i	$-0.584590\pi$
$401$	−24.6221	−	14.2156i	−1.22957	−	0.709893i	−0.966940	+	0.255004i	$0.917923\pi$
$402$		0			0
$403$	4.91590	+	6.96524i	0.244879	+	0.346963i
$404$		0			0
$405$	−5.50375	−	3.17759i	−0.273483	−	0.157896i
$406$		0			0
$407$	3.74962	+	6.49453i	0.185862	+	0.321922i
$408$		0			0
$409$	17.5634	−	10.1402i	0.868452	−	0.501401i	0.00161856	−	0.999999i	$-0.499485\pi$
$409$	17.5634	−	10.1402i	0.868452	−	0.501401i	0.866834	+	0.498598i	$0.166151\pi$
$410$		0			0
$411$		−	2.48605i		−	0.122628i
$412$		0			0
$413$	−4.16004	+	7.20540i	−0.204702	+	0.354554i
$414$		0			0
$415$	2.60910			0.128076
$416$		0			0
$417$	−5.27296			−0.258218
$418$		0			0
$419$	14.6625	−	25.3962i	0.716309	−	1.24068i	−0.246143	−	0.969233i	$-0.579163\pi$
$419$	14.6625	−	25.3962i	0.716309	−	1.24068i	0.962452	−	0.271450i	$-0.0875033\pi$
$420$		0			0
$421$		−	2.92975i		−	0.142787i	−0.997448	−	0.0713936i	$-0.977255\pi$
$421$		−	2.92975i		−	0.142787i	0.997448	−	0.0713936i	$-0.0227447\pi$
$422$		0			0
$423$	20.8401	−	12.0320i	1.01328	−	0.585018i
$424$		0			0
$425$	−2.47282	−	4.28305i	−0.119950	−	0.207759i
$426$		0			0
$427$	2.99676	+	1.73018i	0.145023	+	0.0837292i
$428$		0			0
$429$	−0.731133	+	1.58330i	−0.0352994	+	0.0764424i
$430$		0			0
$431$	−30.4786	−	17.5968i	−1.46810	−	0.847609i	−0.468741	−	0.883336i	$-0.655292\pi$
$431$	−30.4786	−	17.5968i	−1.46810	−	0.847609i	−0.999362	+	0.0357266i	$0.988625\pi$
$432$		0			0
$433$	−10.3241	−	17.8819i	−0.496147	−	0.859351i	0.503843	−	0.863795i	$-0.331919\pi$
$433$	−10.3241	−	17.8819i	−0.496147	−	0.859351i	−0.999990	+	0.00444359i	$0.998586\pi$
$434$		0			0
$435$	0.204986	−	0.118349i	0.00982834	−	0.00567440i
$436$		0			0
$437$			19.7968i			0.947009i
$438$		0			0
$439$	−4.98217	+	8.62936i	−0.237786	+	0.411857i	−0.960079	−	0.279730i	$-0.909755\pi$
$439$	−4.98217	+	8.62936i	−0.237786	+	0.411857i	0.722293	+	0.691587i	$0.243088\pi$
$440$		0			0
$441$	−9.97640			−0.475067
$442$		0			0
$443$	35.1084			1.66805			0.834025	−	0.551727i	$-0.186031\pi$
$443$	35.1084			1.66805			0.834025	+	0.551727i	$0.186031\pi$
$444$		0			0
$445$	−0.372517	+	0.645218i	−0.0176590	+	0.0305863i
$446$		0			0
$447$		−	8.76463i		−	0.414553i
$448$		0			0
$449$	−27.9768	+	16.1524i	−1.32031	+	0.762280i	−0.983778	−	0.179392i	$-0.942587\pi$
$449$	−27.9768	+	16.1524i	−1.32031	+	0.762280i	−0.336531	+	0.941673i	$0.609254\pi$
$450$		0			0
$451$	0.526268	+	0.911523i	0.0247810	+	0.0429219i
$452$		0			0
$453$	6.41698	+	3.70485i	0.301496	+	0.174069i
$454$		0			0
$455$	5.94584	+	2.74566i	0.278745	+	0.128718i
$456$		0			0
$457$	17.3917	+	10.0411i	0.813550	+	0.469703i	0.848187	−	0.529697i	$-0.177694\pi$
$457$	17.3917	+	10.0411i	0.813550	+	0.469703i	−0.0346373	+	0.999400i	$0.511028\pi$
$458$		0			0
$459$	7.76772	+	13.4541i	0.362566	+	0.627983i
$460$		0			0
$461$	−18.1537	+	10.4810i	−0.845502	+	0.488151i	−0.859131	−	0.511756i	$-0.828995\pi$
$461$	−18.1537	+	10.4810i	−0.845502	+	0.488151i	0.0136287	+	0.999907i	$0.495662\pi$
$462$		0			0
$463$		−	35.1142i		−	1.63189i	−0.578127	−	0.815947i	$-0.696216\pi$
$463$		−	35.1142i		−	1.63189i	0.578127	−	0.815947i	$-0.303784\pi$
$464$		0			0
$465$	0.652003	−	1.12930i	0.0302359	−	0.0523702i
$466$		0			0
$467$	−31.6858			−1.46625			−0.733123	−	0.680096i	$-0.761938\pi$
$467$	−31.6858			−1.46625			−0.733123	+	0.680096i	$0.761938\pi$
$468$		0			0
$469$	9.27672			0.428359
$470$		0			0
$471$	6.03555	−	10.4539i	0.278103	−	0.481689i
$472$		0			0
$473$			1.76857i			0.0813188i
$474$		0			0
$475$	−3.18017	+	1.83607i	−0.145916	+	0.0842448i
$476$		0			0
$477$	−7.34654	−	12.7246i	−0.336375	−	0.582619i
$478$		0			0
$479$	−3.42202	−	1.97570i	−0.156356	−	0.0902721i	0.419781	−	0.907626i	$-0.362107\pi$
$479$	−3.42202	−	1.97570i	−0.156356	−	0.0902721i	−0.576137	+	0.817353i	$0.695440\pi$
$480$		0			0
$481$	−30.7019	+	2.80141i	−1.39989	+	0.127733i
$482$		0			0
$483$	−4.67694	−	2.70023i	−0.212808	−	0.122865i
$484$		0			0
$485$	4.88899	+	8.46798i	0.221998	+	0.384511i
$486$		0			0
$487$	15.6267	−	9.02205i	0.708111	−	0.408828i	−0.102250	−	0.994759i	$-0.532604\pi$
$487$	15.6267	−	9.02205i	0.708111	−	0.408828i	0.810361	+	0.585931i	$0.199271\pi$
$488$		0			0
$489$			2.07287i			0.0937383i
$490$		0			0
$491$	−5.77834	+	10.0084i	−0.260773	+	0.451672i	−0.966448	−	0.256864i	$-0.917311\pi$
$491$	−5.77834	+	10.0084i	−0.260773	+	0.451672i	0.705675	+	0.708536i	$0.250644\pi$
$492$		0			0
$493$	2.12264			0.0955987
$494$		0			0
$495$	−2.36439			−0.106271
$496$		0			0
$497$	−14.1073	+	24.4345i	−0.632798	+	1.09604i
$498$		0			0
$499$			2.01039i			0.0899973i	0.998987	+	0.0449987i	$0.0143284\pi$
$499$			2.01039i			0.0899973i	−0.998987	+	0.0449987i	$0.985672\pi$
$500$		0			0
$501$	−7.36202	+	4.25046i	−0.328911	+	0.189897i
$502$		0			0
$503$	−16.8145	−	29.1236i	−0.749721	−	1.29856i	−0.947956	−	0.318401i	$-0.896854\pi$
$503$	−16.8145	−	29.1236i	−0.749721	−	1.29856i	0.198235	−	0.980155i	$-0.436479\pi$
$504$		0			0
$505$	5.98327	+	3.45444i	0.266252	+	0.153721i
$506$		0			0
$507$	−4.64924	−	5.45761i	−0.206480	−	0.242381i
$508$		0			0
$509$	−18.8008	−	10.8547i	−0.833333	−	0.481125i	0.0216596	−	0.999765i	$-0.493105\pi$
$509$	−18.8008	−	10.8547i	−0.833333	−	0.481125i	−0.854992	+	0.518640i	$0.826438\pi$
$510$		0			0
$511$	−9.75732	−	16.9002i	−0.431638	−	0.747620i
$512$		0			0
$513$	9.98967	−	5.76754i	0.441054	−	0.254643i
$514$		0			0
$515$		−	17.4021i		−	0.766830i
$516$		0			0
$517$	3.91441	−	6.77995i	0.172155	−	0.298182i
$518$		0			0
$519$	0.474892			0.0208454
$520$		0			0
$521$	22.8718			1.00203			0.501016	−	0.865438i	$-0.332960\pi$
$521$	22.8718			1.00203			0.501016	+	0.865438i	$0.332960\pi$
$522$		0			0
$523$	3.36726	−	5.83226i	0.147240	−	0.255027i	−0.782966	−	0.622064i	$-0.786294\pi$
$523$	3.36726	−	5.83226i	0.147240	−	0.255027i	0.930206	+	0.367037i	$0.119628\pi$
$524$		0			0
$525$		−	1.00174i		−	0.0437196i
$526$		0			0
$527$	10.1272	−	5.84697i	0.441150	−	0.254698i
$528$		0			0
$529$	−3.03183	−	5.25129i	−0.131819	−	0.228317i
$530$		0			0
$531$	10.6940	+	6.17418i	0.464080	+	0.267936i
$532$		0			0
$533$	−4.30909	+	0.393184i	−0.186647	+	0.0170307i
$534$		0			0
$535$	6.66080	+	3.84562i	0.287972	+	0.166260i
$536$		0			0
$537$	−2.15124	−	3.72605i	−0.0928327	−	0.160791i
$538$		0			0
$539$	−2.81081	+	1.62282i	−0.121070	+	0.0698998i
$540$		0			0
$541$		−	11.2559i		−	0.483927i	−0.970285	−	0.241964i	$-0.922209\pi$
$541$		−	11.2559i		−	0.483927i	0.970285	−	0.241964i	$-0.0777915\pi$
$542$		0			0
$543$	1.57218	−	2.72310i	0.0674688	−	0.116859i
$544$		0			0
$545$	11.1587			0.477985
$546$		0			0
$547$	−10.1685			−0.434774			−0.217387	−	0.976086i	$-0.569753\pi$
$547$	−10.1685			−0.434774			−0.217387	+	0.976086i	$0.569753\pi$
$548$		0			0
$549$	2.56787	−	4.44768i	0.109594	−	0.189822i
$550$		0			0
$551$		−	1.57606i		−	0.0671423i
$552$		0			0
$553$	17.6708	−	10.2023i	0.751440	−	0.433844i
$554$		0			0
$555$	2.35780	+	4.08382i	0.100083	+	0.173349i
$556$		0			0
$557$	−16.3299	−	9.42807i	−0.691920	−	0.399480i	0.112411	−	0.993662i	$-0.464143\pi$
$557$	−16.3299	−	9.42807i	−0.691920	−	0.399480i	−0.804331	+	0.594181i	$0.797476\pi$
$558$		0			0
$559$	−6.60081	−	3.04811i	−0.279185	−	0.128921i
$560$		0			0
$561$	2.07166	+	1.19607i	0.0874655	+	0.0504982i
$562$		0			0
$563$	9.22434	+	15.9770i	0.388760	+	0.673351i	0.992283	−	0.123994i	$-0.0395704\pi$
$563$	9.22434	+	15.9770i	0.388760	+	0.673351i	−0.603523	+	0.797345i	$0.706237\pi$
$564$		0			0
$565$	11.8580	−	6.84621i	0.498869	−	0.288022i
$566$		0			0
$567$		−	11.5436i		−	0.484787i
$568$		0			0
$569$	12.8990	−	22.3417i	0.540753	−	0.936612i	−0.458108	−	0.888897i	$-0.651473\pi$
$569$	12.8990	−	22.3417i	0.540753	−	0.936612i	0.998861	−	0.0477153i	$-0.0151940\pi$
$570$		0			0
$571$	−46.0810			−1.92843			−0.964216	−	0.265118i	$-0.914589\pi$
$571$	−46.0810			−1.92843			−0.964216	+	0.265118i	$0.914589\pi$
$572$		0			0
$573$	−1.02144			−0.0426711
$574$		0			0
$575$	2.69554	−	4.66881i	0.112412	−	0.194703i
$576$		0			0
$577$			9.69085i			0.403435i	0.979444	+	0.201718i	$0.0646524\pi$
$577$			9.69085i			0.403435i	−0.979444	+	0.201718i	$0.935348\pi$
$578$		0			0
$579$	−4.12393	+	2.38095i	−0.171385	+	0.0989489i
$580$		0			0
$581$	2.36960	+	4.10427i	0.0983075	+	0.170274i
$582$		0			0
$583$	−4.13971	−	2.39006i	−0.171449	−	0.0989863i
$584$		0			0
$585$	4.07500	−	8.82459i	0.168481	−	0.364852i
$586$		0			0
$587$	−32.4680	−	18.7454i	−1.34010	−	0.773705i	−0.353275	−	0.935520i	$-0.614932\pi$
$587$	−32.4680	−	18.7454i	−1.34010	−	0.773705i	−0.986821	+	0.161815i	$0.948265\pi$
$588$		0			0
$589$	−4.34138	−	7.51949i	−0.178883	−	0.309835i
$590$		0			0
$591$	2.02178	−	1.16727i	0.0831648	−	0.0480152i
$592$		0			0
$593$			20.6021i			0.846027i	0.906123	+	0.423013i	$0.139028\pi$
$593$			20.6021i			0.846027i	−0.906123	+	0.423013i	$0.860972\pi$
$594$		0			0
$595$	4.49167	−	7.77979i	0.184140	−	0.318940i
$596$		0			0
$597$	15.2949			0.625979
$598$		0			0
$599$	1.39843			0.0571382			0.0285691	−	0.999592i	$-0.490905\pi$
$599$	1.39843			0.0571382			0.0285691	+	0.999592i	$0.490905\pi$
$600$		0			0
$601$	−19.2004	+	33.2561i	−0.783201	+	1.35654i	0.146867	+	0.989156i	$0.453081\pi$
$601$	−19.2004	+	33.2561i	−0.783201	+	1.35654i	−0.930068	+	0.367387i	$0.880252\pi$
$602$		0			0
$603$		−	13.7682i		−	0.560683i
$604$		0			0
$605$	8.86012	−	5.11539i	0.360215	−	0.207970i
$606$		0			0
$607$	3.33388	+	5.77446i	0.135318	+	0.234378i	0.925719	−	0.378212i	$-0.123461\pi$
$607$	3.33388	+	5.77446i	0.135318	+	0.234378i	−0.790401	+	0.612590i	$0.790128\pi$
$608$		0			0
$609$	0.372340	+	0.214970i	0.0150880	+	0.00871104i
$610$		0			0
$611$	18.5583	+	26.2949i	0.750789	+	1.06378i
$612$		0			0
$613$	35.3895	+	20.4322i	1.42937	+	0.825247i	0.997071	−	0.0764834i	$-0.0243692\pi$
$613$	35.3895	+	20.4322i	1.42937	+	0.825247i	0.432299	+	0.901730i	$0.357703\pi$
$614$		0			0
$615$	0.330922	+	0.573174i	0.0133441	+	0.0231126i
$616$		0			0
$617$	−10.1135	+	5.83904i	−0.407155	+	0.235071i	−0.689566	−	0.724222i	$-0.742199\pi$
$617$	−10.1135	+	5.83904i	−0.407155	+	0.235071i	0.282412	+	0.959293i	$0.408866\pi$
$618$		0			0
$619$		−	23.9724i		−	0.963534i	−0.876299	−	0.481767i	$-0.839995\pi$
$619$		−	23.9724i		−	0.963534i	0.876299	−	0.481767i	$-0.160005\pi$
$620$		0			0
$621$	−8.46732	+	14.6658i	−0.339782	+	0.588519i
$622$		0			0
$623$	−1.35329			−0.0542183
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	0.888085	−	1.53821i	0.0354667	−	0.0614301i
$628$		0			0
$629$			42.2880i			1.68613i
$630$		0			0
$631$	5.83169	−	3.36693i	0.232156	−	0.134035i	−0.379410	−	0.925228i	$-0.623873\pi$
$631$	5.83169	−	3.36693i	0.232156	−	0.134035i	0.611566	+	0.791193i	$0.290540\pi$
$632$		0			0
$633$	−0.0401846	−	0.0696019i	−0.00159720	−	0.00276643i
$634$		0			0
$635$	−11.3709	−	6.56497i	−0.451239	−	0.260523i
$636$		0			0
$637$	−1.21244	−	13.2877i	−0.0480385	−	0.526477i
$638$		0			0
$639$	36.2648	+	20.9375i	1.43461	+	0.828275i
$640$		0			0
$641$	−0.320045	−	0.554334i	−0.0126410	−	0.0218949i	0.859636	−	0.510907i	$-0.170691\pi$
$641$	−0.320045	−	0.554334i	−0.0126410	−	0.0218949i	−0.872277	+	0.489013i	$0.837357\pi$
$642$		0			0
$643$	−26.2562	+	15.1590i	−1.03544	+	0.597814i	−0.918540	−	0.395329i	$-0.870631\pi$
$643$	−26.2562	+	15.1590i	−1.03544	+	0.597814i	−0.116905	+	0.993143i	$0.537297\pi$
$644$		0			0
$645$			1.11209i			0.0437886i
$646$		0			0
$647$	3.22347	−	5.58321i	0.126728	−	0.219499i	−0.795679	−	0.605718i	$-0.792886\pi$
$647$	3.22347	−	5.58321i	0.126728	−	0.219499i	0.922407	+	0.386219i	$0.126219\pi$
$648$		0			0
$649$	4.01731			0.157693
$650$		0			0
$651$	2.36861			0.0928333
$652$		0			0
$653$	0.154888	−	0.268274i	0.00606124	−	0.0104984i	−0.862979	−	0.505240i	$-0.831404\pi$
$653$	0.154888	−	0.268274i	0.00606124	−	0.0104984i	0.869040	+	0.494742i	$0.164737\pi$
$654$		0			0
$655$			19.2978i			0.754029i
$656$		0			0
$657$	−25.0826	+	14.4815i	−0.978566	+	0.564975i
$658$		0			0
$659$	−2.55240	−	4.42088i	−0.0994273	−	0.172213i	0.812020	−	0.583629i	$-0.198368\pi$
$659$	−2.55240	−	4.42088i	−0.0994273	−	0.172213i	−0.911448	+	0.411416i	$0.865034\pi$
$660$		0			0
$661$	17.1957	+	9.92794i	0.668835	+	0.386152i	0.795635	−	0.605776i	$-0.207137\pi$
$661$	17.1957	+	9.92794i	0.668835	+	0.386152i	−0.126800	+	0.991928i	$0.540471\pi$
$662$		0			0
$663$	−8.03458	+	5.67062i	−0.312037	+	0.220228i
$664$		0			0
$665$	−5.77650	−	3.33506i	−0.224003	−	0.129328i
$666$		0			0
$667$	1.15690	+	2.00382i	0.0447955	+	0.0775881i
$668$		0			0
$669$	−2.33859	+	1.35018i	−0.0904150	+	0.0522011i
$670$		0			0
$671$		−	1.67082i		−	0.0645012i
$672$		0			0
$673$	0.192547	−	0.333501i	0.00742213	−	0.0128555i	−0.862290	−	0.506414i	$-0.830971\pi$
$673$	0.192547	−	0.333501i	0.00742213	−	0.0128555i	0.869713	+	0.493558i	$0.164304\pi$
$674$		0			0
$675$	−3.14124			−0.120906
$676$		0			0
$677$	−14.8350			−0.570157			−0.285078	−	0.958504i	$-0.592020\pi$
$677$	−14.8350			−0.570157			−0.285078	+	0.958504i	$0.592020\pi$
$678$		0			0
$679$	−8.88043	+	15.3814i	−0.340800	+	0.590282i
$680$		0			0
$681$		−	7.60617i		−	0.291469i
$682$		0			0
$683$	35.9469	−	20.7540i	1.37547	−	0.794129i	0.383861	−	0.923391i	$-0.374594\pi$
$683$	35.9469	−	20.7540i	1.37547	−	0.794129i	0.991610	+	0.129263i	$0.0412610\pi$
$684$		0			0
$685$	2.25392	+	3.90390i	0.0861178	+	0.149160i
$686$		0			0
$687$	6.03953	+	3.48692i	0.230422	+	0.133034i
$688$		0			0
$689$	16.0552	−	11.3314i	0.611653	−	0.431690i
$690$		0			0
$691$	−9.55411	−	5.51607i	−0.363455	−	0.209841i	0.307140	−	0.951664i	$-0.400628\pi$
$691$	−9.55411	−	5.51607i	−0.363455	−	0.209841i	−0.670595	+	0.741823i	$0.733961\pi$
$692$		0			0
$693$	−2.14735	−	3.71932i	−0.0815712	−	0.141285i
$694$		0			0
$695$	8.28024	−	4.78060i	0.314087	−	0.181338i
$696$		0			0
$697$			5.93522i			0.224813i
$698$		0			0
$699$	2.83683	−	4.91353i	0.107299	−	0.185847i
$700$		0			0
$701$	−29.7358			−1.12311			−0.561554	−	0.827440i	$-0.689796\pi$
$701$	−29.7358			−1.12311			−0.561554	+	0.827440i	$0.689796\pi$
$702$		0			0
$703$	31.3989			1.18423
$704$		0			0
$705$	2.46142	−	4.26330i	0.0927023	−	0.160565i
$706$		0			0
$707$			12.5494i			0.471968i
$708$		0			0
$709$	−39.3547	+	22.7214i	−1.47800	+	0.853321i	−0.999691	−	0.0248726i	$-0.992082\pi$
$709$	−39.3547	+	22.7214i	−1.47800	+	0.853321i	−0.478305	+	0.878194i	$0.658749\pi$
$710$		0			0
$711$	−15.1418	−	26.2264i	−0.567862	−	0.983567i
$712$		0			0
$713$	11.0394	+	6.37358i	0.413427	+	0.238692i
$714$		0			0
$715$	−0.287346	−	3.14915i	−0.0107461	−	0.117772i
$716$		0			0
$717$	9.63483	+	5.56267i	0.359819	+	0.207742i
$718$		0			0
$719$	26.1218	+	45.2443i	0.974179	+	1.68733i	0.682617	+	0.730777i	$0.260842\pi$
$719$	26.1218	+	45.2443i	0.974179	+	1.68733i	0.291563	+	0.956552i	$0.405825\pi$
$720$		0			0
$721$	27.3746	−	15.8047i	1.01948	−	0.588599i
$722$		0			0
$723$		−	0.508777i		−	0.0189216i
$724$		0			0
$725$	−0.214596	+	0.371692i	−0.00796991	+	0.0138043i
$726$		0			0
$727$	46.9248			1.74035			0.870173	−	0.492747i	$-0.164007\pi$
$727$	46.9248			1.74035			0.870173	+	0.492747i	$0.164007\pi$
$728$		0			0
$729$	−11.9355			−0.442056
$730$		0			0
$731$	−4.98645	+	8.63679i	−0.184431	+	0.319443i
$732$		0			0
$733$		−	36.6313i		−	1.35301i	−0.736439	−	0.676504i	$-0.763494\pi$
$733$		−	36.6313i		−	1.35301i	0.736439	−	0.676504i	$-0.236506\pi$
$734$		0			0
$735$	−1.76746	+	1.02044i	−0.0651938	+	0.0376397i
$736$		0			0
$737$	−2.23961	−	3.87912i	−0.0824971	−	0.142889i
$738$		0			0
$739$	−36.1588	−	20.8763i	−1.33012	−	0.767947i	−0.344805	−	0.938674i	$-0.612055\pi$
$739$	−36.1588	−	20.8763i	−1.33012	−	0.767947i	−0.985318	+	0.170727i	$0.945388\pi$
$740$		0			0
$741$	4.21043	+	5.96568i	0.154674	+	0.219155i
$742$		0			0
$743$	24.4237	+	14.1011i	0.896020	+	0.517318i	0.875907	−	0.482480i	$-0.160264\pi$
$743$	24.4237	+	14.1011i	0.896020	+	0.517318i	0.0201134	+	0.999798i	$0.493597\pi$
$744$		0			0
$745$	7.94624	+	13.7633i	0.291128	+	0.504248i
$746$		0			0
$747$	6.09140	−	3.51687i	0.222873	−	0.128676i
$748$		0			0
$749$			13.9704i			0.510469i
$750$		0			0
$751$	−15.9708	+	27.6623i	−0.582784	+	1.00941i	0.412364	+	0.911019i	$0.364703\pi$
$751$	−15.9708	+	27.6623i	−0.582784	+	1.00941i	−0.995148	+	0.0983921i	$0.968630\pi$
$752$		0			0
$753$	8.97201			0.326958
$754$		0			0
$755$	−13.4356			−0.488973
$756$		0			0
$757$	−5.36247	+	9.28807i	−0.194902	+	0.337581i	−0.946868	−	0.321621i	$-0.895772\pi$
$757$	−5.36247	+	9.28807i	−0.194902	+	0.337581i	0.751966	+	0.659202i	$0.229106\pi$
$758$		0			0
$759$			2.60759i			0.0946496i
$760$		0			0
$761$	0.389260	−	0.224739i	0.0141107	−	0.00814679i	−0.492928	−	0.870070i	$-0.664073\pi$
$761$	0.389260	−	0.224739i	0.0141107	−	0.00814679i	0.507039	+	0.861923i	$0.330740\pi$
$762$		0			0
$763$	10.1344	+	17.5533i	0.366889	+	0.635471i
$764$		0			0
$765$	−11.5465	−	6.66637i	−0.417464	−	0.241023i
$766$		0			0
$767$	−6.92381	+	14.9938i	−0.250004	+	0.541394i
$768$		0			0
$769$	−11.7839	−	6.80346i	−0.424940	−	0.245339i	0.272249	−	0.962227i	$-0.412233\pi$
$769$	−11.7839	−	6.80346i	−0.424940	−	0.245339i	−0.697188	+	0.716888i	$0.745566\pi$
$770$		0			0
$771$	−4.69068	−	8.12449i	−0.168931	−	0.292596i
$772$		0			0
$773$	1.70461	−	0.984159i	0.0613107	−	0.0353977i	−0.469031	−	0.883182i	$-0.655397\pi$
$773$	1.70461	−	0.984159i	0.0613107	−	0.0353977i	0.530342	+	0.847784i	$0.322064\pi$
$774$		0			0
$775$			2.36449i			0.0849351i
$776$		0			0
$777$	−4.28273	+	7.41791i	−0.153642	+	0.266116i
$778$		0			0
$779$	4.40691			0.157894
$780$		0			0
$781$	13.6233			0.487479
$782$		0			0
$783$	0.674098	−	1.16757i	0.0240903	−	0.0417256i
$784$		0			0
$785$			21.8879i			0.781214i
$786$		0			0
$787$	14.3743	−	8.29901i	0.512389	−	0.295828i	−0.221426	−	0.975177i	$-0.571071\pi$
$787$	14.3743	−	8.29901i	0.512389	−	0.295828i	0.733815	+	0.679349i	$0.237738\pi$
$788$		0			0
$789$	5.33240	+	9.23599i	0.189839	+	0.328810i
$790$		0			0
$791$	21.5390	+	12.4355i	0.765839	+	0.442157i
$792$		0			0
$793$	6.23598	+	2.87964i	0.221446	+	0.102259i
$794$		0			0
$795$	−2.60309	−	1.50289i	−0.0923221	−	0.0533022i
$796$		0			0
$797$	−12.9117	−	22.3637i	−0.457356	−	0.792164i	0.541464	−	0.840724i	$-0.317870\pi$
$797$	−12.9117	−	22.3637i	−0.457356	−	0.792164i	−0.998820	+	0.0485595i	$0.984537\pi$
$798$		0			0
$799$	38.2320	−	22.0732i	1.35255	−	0.780895i
$800$		0			0
$801$			2.00850i			0.0709669i
$802$		0			0
$803$	−4.71128	+	8.16017i	−0.166257	+	0.287966i
$804$		0			0
$805$	9.79241			0.345137
$806$		0			0
$807$	0.314519			0.0110716
$808$		0			0
$809$	−14.6415	+	25.3599i	−0.514769	+	0.891607i	0.485084	+	0.874468i	$0.338789\pi$
$809$	−14.6415	+	25.3599i	−0.514769	+	0.891607i	−0.999853	+	0.0171389i	$0.994544\pi$
$810$		0			0
$811$			31.6930i			1.11289i	0.830883	+	0.556447i	$0.187836\pi$
$811$			31.6930i			1.11289i	−0.830883	+	0.556447i	$0.812164\pi$
$812$		0			0
$813$	11.2415	−	6.49031i	0.394258	−	0.227625i
$814$		0			0
$815$	−1.87932	−	3.25507i	−0.0658295	−	0.114020i
$816$		0			0
$817$	6.41282	+	3.70244i	0.224356	+	0.129532i
$818$		0			0
$819$	17.5826	−	1.60433i	0.614384	−	0.0560597i
$820$		0			0
$821$	18.2146	+	10.5162i	0.635695	+	0.367019i	0.782954	−	0.622079i	$-0.213712\pi$
$821$	18.2146	+	10.5162i	0.635695	+	0.367019i	−0.147259	+	0.989098i	$0.547045\pi$
$822$		0			0
$823$	−16.5481	−	28.6621i	−0.576829	−	0.999097i	−0.995840	−	0.0911160i	$-0.970957\pi$
$823$	−16.5481	−	28.6621i	−0.576829	−	0.999097i	0.419011	−	0.907981i	$-0.362377\pi$
$824$		0			0
$825$	−0.418885	+	0.241844i	−0.0145837	+	0.00841991i
$826$		0			0
$827$			53.6372i			1.86515i	0.360977	+	0.932575i	$0.382443\pi$
$827$			53.6372i			1.86515i	−0.360977	+	0.932575i	$0.617557\pi$
$828$		0			0
$829$	25.5411	−	44.2386i	0.887081	−	1.53647i	0.0437704	−	0.999042i	$-0.486063\pi$
$829$	25.5411	−	44.2386i	0.887081	−	1.53647i	0.843310	−	0.537427i	$-0.180604\pi$
$830$		0			0
$831$	7.98189			0.276889
$832$		0			0
$833$	−18.3021			−0.634130
$834$		0			0
$835$	7.70716	−	13.3492i	0.266717	−	0.461968i
$836$		0			0
$837$		−	7.42743i		−	0.256730i
$838$		0			0
$839$	−17.1357	+	9.89331i	−0.591591	+	0.341555i	−0.765726	−	0.643167i	$-0.777620\pi$
$839$	−17.1357	+	9.89331i	−0.591591	+	0.341555i	0.174136	+	0.984722i	$0.444287\pi$
$840$		0			0
$841$	14.4079	+	24.9552i	0.496824	+	0.860524i
$842$		0			0
$843$	11.6916	+	6.75017i	0.402681	+	0.232488i
$844$		0			0
$845$	12.2488	+	4.35508i	0.421372	+	0.149819i
$846$		0			0
$847$	16.0936	+	9.29167i	0.552984	+	0.319265i
$848$		0			0
$849$	4.90789	+	8.50072i	0.168438	+	0.291744i
$850$		0			0
$851$	−39.9209	+	23.0483i	−1.36847	+	0.790087i
$852$		0			0
$853$			31.1517i			1.06661i	0.845922	+	0.533307i	$0.179051\pi$
$853$			31.1517i			1.06661i	−0.845922	+	0.533307i	$0.820949\pi$
$854$		0			0
$855$	−4.94978	+	8.57327i	−0.169279	+	0.293200i
$856$		0			0
$857$	13.0978			0.447413			0.223707	−	0.974657i	$-0.428184\pi$
$857$	13.0978			0.447413			0.223707	+	0.974657i	$0.428184\pi$
$858$		0			0
$859$	−50.4974			−1.72295			−0.861474	−	0.507801i	$-0.830459\pi$
$859$	−50.4974			−1.72295			−0.861474	+	0.507801i	$0.830459\pi$
$860$		0			0
$861$	−0.601091	+	1.04112i	−0.0204851	+	0.0354813i
$862$		0			0
$863$			18.1831i			0.618960i	0.950906	+	0.309480i	$0.100155\pi$
$863$			18.1831i			0.618960i	−0.950906	+	0.309480i	$0.899845\pi$
$864$		0			0
$865$	−0.745733	+	0.430549i	−0.0253557	+	0.0146391i
$866$		0			0
$867$	2.05691	+	3.56268i	0.0698564	+	0.120995i
$868$		0			0
$869$	−8.53228	−	4.92611i	−0.289438	−	0.167107i
$870$		0			0
$871$	18.3380	−	1.67325i	0.621358	−	0.0566961i
$872$		0			0
$873$	22.8284	+	13.1800i	0.772626	+	0.446076i
$874$		0			0
$875$	0.908206	+	1.57306i	0.0307030	+	0.0531791i
$876$		0			0
$877$	−23.8639	+	13.7778i	−0.805828	+	0.465245i	−0.845505	−	0.533968i	$-0.820700\pi$
$877$	−23.8639	+	13.7778i	−0.805828	+	0.465245i	0.0396771	+	0.999213i	$0.487367\pi$
$878$		0			0
$879$		−	11.1926i		−	0.377518i
$880$		0			0
$881$	25.5057	−	44.1772i	0.859309	−	1.48837i	−0.0132810	−	0.999912i	$-0.504228\pi$
$881$	25.5057	−	44.1772i	0.859309	−	1.48837i	0.872590	−	0.488454i	$-0.162439\pi$
$882$		0			0
$883$	−30.0045			−1.00973			−0.504865	−	0.863198i	$-0.668458\pi$
$883$	−30.0045			−1.00973			−0.504865	+	0.863198i	$0.668458\pi$
$884$		0			0
$885$	2.52612			0.0849148
$886$		0			0
$887$	9.73608	−	16.8634i	0.326906	−	0.566217i	−0.654991	−	0.755637i	$-0.727327\pi$
$887$	9.73608	−	16.8634i	0.326906	−	0.566217i	0.981896	+	0.189420i	$0.0606607\pi$
$888$		0			0
$889$		−	23.8494i		−	0.799882i
$890$		0			0
$891$	−4.82704	+	2.78690i	−0.161712	+	0.0933645i
$892$		0			0
$893$	−16.3894	−	28.3873i	−0.548450	−	0.949943i
$894$		0			0
$895$	6.75627	+	3.90073i	0.225837	+	0.130387i
$896$		0			0
$897$	−9.73230	−	4.49416i	−0.324952	−	0.150056i
$898$		0			0
$899$	−0.878863	−	0.507412i	−0.0293117	−	0.0169231i
$900$		0			0
$901$	−13.4775	−	23.3437i	−0.449001	−	0.777692i
$902$		0			0
$903$	−1.74939	+	1.01001i	−0.0582159	+	0.0336110i
$904$		0			0
$905$			5.70152i			0.189525i
$906$		0			0
$907$	−17.9021	+	31.0073i	−0.594428	+	1.02958i	0.399199	+	0.916864i	$0.369288\pi$
$907$	−17.9021	+	31.0073i	−0.594428	+	1.02958i	−0.993627	+	0.112716i	$0.964045\pi$
$908$		0			0
$909$	18.6254			0.617764
$910$		0			0
$911$	−23.6586			−0.783843			−0.391922	−	0.919999i	$-0.628190\pi$
$911$	−23.6586			−0.783843			−0.391922	+	0.919999i	$0.628190\pi$
$912$		0			0
$913$	1.14415	−	1.98173i	0.0378658	−	0.0655856i
$914$		0			0
$915$		−	1.05063i		−	0.0347326i
$916$		0			0
$917$	−30.3566	+	17.5264i	−1.00246	+	0.578773i
$918$		0			0
$919$	12.8747	+	22.2997i	0.424699	+	0.735600i	0.996392	−	0.0848674i	$-0.0270467\pi$
$919$	12.8747	+	22.2997i	0.424699	+	0.735600i	−0.571693	+	0.820467i	$0.693713\pi$
$920$		0			0
$921$	4.56420	+	2.63514i	0.150396	+	0.0868310i
$922$		0			0
$923$	−23.4796	+	50.8460i	−0.772840	+	1.67362i
$924$		0			0
$925$	−7.40500	−	4.27528i	−0.243475	−	0.140570i
$926$		0			0
$927$	−23.4568	−	40.6284i	−0.770423	−	1.33441i
$928$		0			0
$929$	−33.4301	+	19.3009i	−1.09680	+	0.633241i	−0.935380	−	0.353644i	$-0.884942\pi$
$929$	−33.4301	+	19.3009i	−1.09680	+	0.633241i	−0.161425	+	0.986885i	$0.551609\pi$
$930$		0			0
$931$			13.5893i			0.445371i
$932$		0			0
$933$	0.0417650	−	0.0723391i	0.00136732	−	0.00236828i
$934$		0			0
$935$	−4.33756			−0.141853
$936$		0			0
$937$	32.1250			1.04948			0.524739	−	0.851263i	$-0.324163\pi$
$937$	32.1250			1.04948			0.524739	+	0.851263i	$0.324163\pi$
$938$		0			0
$939$	7.85897	−	13.6121i	0.256468	−	0.444216i
$940$		0			0
$941$			26.6518i			0.868825i	0.900714	+	0.434412i	$0.143044\pi$
$941$			26.6518i			0.868825i	−0.900714	+	0.434412i	$0.856956\pi$
$942$		0			0
$943$	−5.60299	+	3.23489i	−0.182458	+	0.105342i
$944$		0			0
$945$	−2.85289	−	4.94135i	−0.0928045	−	0.160742i
$946$		0			0
$947$	13.9374	+	8.04678i	0.452906	+	0.261485i	0.709057	−	0.705152i	$-0.249121\pi$
$947$	13.9374	+	8.04678i	0.452906	+	0.261485i	−0.256151	+	0.966637i	$0.582454\pi$
$948$		0			0
$949$	−22.3363	−	31.6479i	−0.725067	−	1.02733i
$950$		0			0
$951$	−9.55238	−	5.51507i	−0.309757	−	0.178838i
$952$		0			0
$953$	−25.4917	−	44.1530i	−0.825759	−	1.43026i	−0.901338	−	0.433116i	$-0.857414\pi$
$953$	−25.4917	−	44.1530i	−0.825759	−	1.43026i	0.0755794	−	0.997140i	$-0.475919\pi$
$954$		0			0
$955$	1.60398	−	0.926061i	0.0519037	−	0.0299666i
$956$		0			0
$957$		−	0.207595i		−	0.00671060i
$958$		0			0
$959$	−4.09405	+	7.09109i	−0.132204	+	0.228983i
$960$		0			0
$961$	25.4092			0.819651
$962$		0			0
$963$	20.7344			0.668158
$964$		0			0
$965$	4.31726	−	7.47772i	0.138978	−	0.240716i
$966$		0			0
$967$			11.4074i			0.366837i	0.983035	+	0.183418i	$0.0587163\pi$
$967$			11.4074i			0.366837i	−0.983035	+	0.183418i	$0.941284\pi$
$968$		0			0
$969$	8.67391	−	5.00789i	0.278646	−	0.160876i
$970$		0			0
$971$	9.49209	+	16.4408i	0.304616	+	0.527610i	0.977176	−	0.212433i	$-0.0681387\pi$
$971$	9.49209	+	16.4408i	0.304616	+	0.527610i	−0.672560	+	0.740042i	$0.734805\pi$
$972$		0			0
$973$	15.0403	+	8.68354i	0.482171	+	0.278382i
$974$		0			0
$975$	−0.180686	−	1.98022i	−0.00578658	−	0.0634177i
$976$		0			0
$977$	−32.9449	−	19.0208i	−1.05400	−	0.608528i	−0.130235	−	0.991483i	$-0.541573\pi$
$977$	−32.9449	−	19.0208i	−1.05400	−	0.608528i	−0.923767	+	0.382955i	$0.874906\pi$
$978$		0			0
$979$	0.326715	+	0.565886i	0.0104418	+	0.0180858i
$980$		0			0
$981$	26.0519	−	15.0411i	0.831774	−	0.480225i
$982$		0			0
$983$		−	24.2502i		−	0.773460i	−0.922193	−	0.386730i	$-0.873605\pi$
$983$		−	24.2502i		−	0.773460i	0.922193	−	0.386730i	$-0.126395\pi$
$984$		0			0
$985$	−2.11656	+	3.66599i	−0.0674392	+	0.116808i
$986$		0			0
$987$	8.94189			0.284624
$988$		0			0
$989$	−10.8711			−0.345681
$990$		0			0
$991$	12.9946	−	22.5073i	0.412787	−	0.714968i	−0.582406	−	0.812898i	$-0.697889\pi$
$991$	12.9946	−	22.5073i	0.412787	−	0.714968i	0.995193	+	0.0979297i	$0.0312220\pi$
$992$		0			0
$993$		−	5.56036i		−	0.176453i
$994$		0			0
$995$	−24.0179	+	13.8668i	−0.761419	+	0.439606i
$996$		0			0
$997$	−2.34704	−	4.06519i	−0.0743315	−	0.128746i	0.826464	−	0.562990i	$-0.190349\pi$
$997$	−2.34704	−	4.06519i	−0.0743315	−	0.128746i	−0.900795	+	0.434244i	$0.857016\pi$
$998$		0			0
$999$	23.2609	+	13.4297i	0.735941	+	0.424896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.bu.b.121.6	✓	16
4.3	odd	2		1040.2.da.f.641.3		16
13.6	odd	12		6760.2.a.bl.1.3		8
13.7	odd	12		6760.2.a.bk.1.3		8
13.10	even	6	inner	520.2.bu.b.361.6	yes	16
52.23	odd	6		1040.2.da.f.881.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.6	✓	16	1.1	even	1	trivial
520.2.bu.b.361.6	yes	16	13.10	even	6	inner
1040.2.da.f.641.3		16	4.3	odd	2
1040.2.da.f.881.3		16	52.23	odd	6
6760.2.a.bk.1.3		8	13.7	odd	12
6760.2.a.bl.1.3		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.275748 - 0.477609i) q^{3} +1.00000i q^{5} +(-1.57306 + 0.908206i) q^{7} +(1.34793 + 2.33468i) q^{9} +O(q^{10})\)	\(q+(0.275748 - 0.477609i) q^{3} +1.00000i q^{5} +(-1.57306 + 0.908206i) q^{7} +(1.34793 + 2.33468i) q^{9} +(0.759545 + 0.438523i) q^{11} +(-2.94577 + 2.07905i) q^{13} +(0.477609 + 0.275748i) q^{15} +(2.47282 + 4.28305i) q^{17} +(3.18017 - 1.83607i) q^{19} +1.00174i q^{21} +(-2.69554 + 4.66881i) q^{23} -1.00000 q^{25} +3.14124 q^{27} +(0.214596 - 0.371692i) q^{29} -2.36449i q^{31} +(0.418885 - 0.241844i) q^{33} +(-0.908206 - 1.57306i) q^{35} +(7.40500 + 4.27528i) q^{37} +(0.180686 + 1.98022i) q^{39} +(1.03931 + 0.600045i) q^{41} +(1.00825 + 1.74634i) q^{43} +(-2.33468 + 1.34793i) q^{45} -8.92633i q^{47} +(-1.85032 + 3.20485i) q^{49} +2.72750 q^{51} -5.45025 q^{53} +(-0.438523 + 0.759545i) q^{55} -2.02517i q^{57} +(3.96683 - 2.29025i) q^{59} +(-0.952525 - 1.64982i) q^{61} +(-4.24074 - 2.44839i) q^{63} +(-2.07905 - 2.94577i) q^{65} +(-4.42293 - 2.55358i) q^{67} +(1.48658 + 2.57483i) q^{69} +(13.4521 - 7.76656i) q^{71} +10.7435i q^{73} +(-0.275748 + 0.477609i) q^{75} -1.59308 q^{77} -11.2334 q^{79} +(-3.17759 + 5.50375i) q^{81} -2.60910i q^{83} +(-4.28305 + 2.47282i) q^{85} +(-0.118349 - 0.204986i) q^{87} +(0.645218 + 0.372517i) q^{89} +(2.74566 - 5.94584i) q^{91} +(-1.12930 - 0.652003i) q^{93} +(1.83607 + 3.18017i) q^{95} +(8.46798 - 4.88899i) q^{97} +2.36439i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 + 6 * q^7 - 16 * q^9	\( 16 q - 4 q^{3} + 6 q^{7} - 16 q^{9} - 6 q^{11} - 2 q^{13} + 4 q^{17} + 30 q^{19} + 6 q^{23} - 16 q^{25} + 44 q^{27} - 16 q^{29} + 24 q^{33} - 6 q^{35} - 24 q^{37} - 8 q^{39} - 24 q^{41} + 6 q^{43} + 12 q^{45} - 4 q^{49} - 40 q^{51} + 4 q^{53} - 6 q^{55} + 12 q^{59} - 2 q^{61} - 60 q^{63} - 10 q^{65} - 6 q^{67} + 52 q^{69} + 72 q^{71} + 4 q^{75} + 32 q^{77} + 36 q^{79} - 28 q^{81} - 22 q^{87} + 24 q^{89} - 22 q^{91} - 96 q^{93} + 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q - 4 * q^3 + 6 * q^7 - 16 * q^9 - 6 * q^11 - 2 * q^13 + 4 * q^17 + 30 * q^19 + 6 * q^23 - 16 * q^25 + 44 * q^27 - 16 * q^29 + 24 * q^33 - 6 * q^35 - 24 * q^37 - 8 * q^39 - 24 * q^41 + 6 * q^43 + 12 * q^45 - 4 * q^49 - 40 * q^51 + 4 * q^53 - 6 * q^55 + 12 * q^59 - 2 * q^61 - 60 * q^63 - 10 * q^65 - 6 * q^67 + 52 * q^69 + 72 * q^71 + 4 * q^75 + 32 * q^77 + 36 * q^79 - 28 * q^81 - 22 * q^87 + 24 * q^89 - 22 * q^91 - 96 * q^93 + 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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