LMFDB - Embedded newform 891.2.f.b.487.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	891.487
Dual form			891.2.f.b.730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11803 - 1.53884i) q^{2} +(1.50000 - 4.61653i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-2.30902 - 7.10642i) q^{8} -8.47214 q^{10} +(-0.809017 - 3.21644i) q^{11} +(-2.00000 + 1.45309i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-7.97214 - 5.79210i) q^{16} +(1.50000 + 1.08981i) q^{17} +(0.309017 + 0.951057i) q^{19} +(-12.7082 + 9.23305i) q^{20} +(-6.66312 - 5.56758i) q^{22} +2.38197 q^{23} +(1.69098 + 5.20431i) q^{25} +(-2.00000 + 6.15537i) q^{26} +(3.92705 + 2.85317i) q^{28} +(0.572949 - 1.76336i) q^{29} +(1.30902 - 0.951057i) q^{31} -10.8541 q^{32} +4.85410 q^{34} +(2.61803 - 1.90211i) q^{35} +(1.88197 - 5.79210i) q^{37} +(2.11803 + 1.53884i) q^{38} +(-7.47214 + 22.9969i) q^{40} +(-3.54508 - 10.9106i) q^{41} -4.85410 q^{43} +(-16.0623 - 1.08981i) q^{44} +(5.04508 - 3.66547i) q^{46} +(-1.83688 - 5.65334i) q^{47} +(4.85410 + 3.52671i) q^{49} +(11.5902 + 8.42075i) q^{50} +(3.70820 + 11.4127i) q^{52} +(5.73607 - 4.16750i) q^{53} +(-4.00000 + 9.95959i) q^{55} +7.47214 q^{56} +(-1.50000 - 4.61653i) q^{58} +(-0.190983 + 0.587785i) q^{59} +(-3.35410 - 2.43690i) q^{61} +(1.30902 - 4.02874i) q^{62} +(-7.04508 + 5.11855i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(7.28115 - 5.29007i) q^{68} +(2.61803 - 8.05748i) q^{70} +(11.3992 + 8.28199i) q^{71} +(-2.11803 + 6.51864i) q^{73} +(-4.92705 - 15.1639i) q^{74} +4.85410 q^{76} +(3.30902 + 0.224514i) q^{77} +(7.73607 - 5.62058i) q^{79} +(9.85410 + 30.3278i) q^{80} +(-24.2984 - 17.6538i) q^{82} +(11.5172 + 8.36775i) q^{83} +(-1.85410 - 5.70634i) q^{85} +(-10.2812 + 7.46969i) q^{86} +(-20.9894 + 13.1760i) q^{88} -11.2361 q^{89} +(-0.763932 - 2.35114i) q^{91} +(3.57295 - 10.9964i) q^{92} +(-12.5902 - 9.14729i) q^{94} +(1.00000 - 3.07768i) q^{95} +(-4.85410 + 3.52671i) q^{97} +15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^4 - 6 * q^5 + q^7 - 7 * q^8 - 16 * q^10 - q^11 - 8 * q^13 + q^14 - 14 * q^16 + 6 * q^17 - q^19 - 24 * q^20 - 11 * q^22 + 14 * q^23 + 9 * q^25 - 8 * q^26 + 9 * q^28 + 9 * q^29 + 3 * q^31 - 30 * q^32 + 6 * q^34 + 6 * q^35 + 12 * q^37 + 4 * q^38 - 12 * q^40 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 9 * q^46 - 23 * q^47 + 6 * q^49 + 24 * q^50 - 12 * q^52 + 14 * q^53 - 16 * q^55 + 12 * q^56 - 6 * q^58 - 3 * q^59 + 3 * q^62 - 17 * q^64 + 32 * q^65 + 24 * q^67 + 9 * q^68 + 6 * q^70 + 21 * q^71 - 4 * q^73 - 13 * q^74 + 6 * q^76 + 11 * q^77 + 22 * q^79 + 26 * q^80 - 48 * q^82 + 17 * q^83 + 6 * q^85 - 21 * q^86 - 37 * q^88 - 36 * q^89 - 12 * q^91 + 21 * q^92 - 28 * q^94 + 4 * q^95 - 6 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.526381	−	0.850249i	$-0.323549\pi$
$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.971295	−	0.237877i	$-0.0764514\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	−	4.61653i	0.750000	−	2.30826i
$5$	−2.61803	−	1.90211i	−1.17082	−	0.850651i	−0.179714	−	0.983719i	$-0.557517\pi$
$5$	−2.61803	−	1.90211i	−1.17082	−	0.850651i	−0.991107	+	0.133068i	$0.957517\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	−0.992318	−	0.123716i	$-0.960519\pi$
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	0.875520	+	0.483181i	$0.160519\pi$
$8$	−2.30902	−	7.10642i	−0.816361	−	2.51250i
$9$		0			0
$10$	−8.47214			−2.67912
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$		0			0
$13$	−2.00000	+	1.45309i	−0.554700	+	0.403013i	−0.829515	−	0.558484i	$-0.811383\pi$
$13$	−2.00000	+	1.45309i	−0.554700	+	0.403013i	0.274815	+	0.961497i	$0.411383\pi$
$14$	0.809017	+	2.48990i	0.216219	+	0.665453i
$15$		0			0
$16$	−7.97214	−	5.79210i	−1.99303	−	1.44802i
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	0.754637	−	0.656143i	$-0.227813\pi$
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	−0.390833	+	0.920461i	$0.627813\pi$
$18$		0			0
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	0.980226	−	0.197884i	$-0.0634068\pi$
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	−0.909332	+	0.416071i	$0.863407\pi$
$20$	−12.7082	+	9.23305i	−2.84164	+	2.06457i
$21$		0			0
$22$	−6.66312	−	5.56758i	−1.42058	−	1.18701i
$23$	2.38197			0.496674			0.248337	−	0.968674i	$-0.420116\pi$
$23$	2.38197			0.496674			0.248337	+	0.968674i	$0.420116\pi$
$24$		0			0
$25$	1.69098	+	5.20431i	0.338197	+	1.04086i
$26$	−2.00000	+	6.15537i	−0.392232	+	1.20717i
$27$		0			0
$28$	3.92705	+	2.85317i	0.742143	+	0.539198i
$29$	0.572949	−	1.76336i	0.106394	−	0.327447i	−0.883661	−	0.468127i	$-0.844929\pi$
$29$	0.572949	−	1.76336i	0.106394	−	0.327447i	0.990055	+	0.140680i	$0.0449289\pi$
$30$		0			0
$31$	1.30902	−	0.951057i	0.235106	−	0.170815i	−0.463994	−	0.885838i	$-0.653584\pi$
$31$	1.30902	−	0.951057i	0.235106	−	0.170815i	0.699100	+	0.715024i	$0.253584\pi$
$32$	−10.8541			−1.91875
$33$		0			0
$34$	4.85410			0.832472
$35$	2.61803	−	1.90211i	0.442529	−	0.321516i
$36$		0			0
$37$	1.88197	−	5.79210i	0.309393	−	0.952215i	−0.668608	−	0.743615i	$-0.733109\pi$
$37$	1.88197	−	5.79210i	0.309393	−	0.952215i	0.978001	−	0.208599i	$-0.0668905\pi$
$38$	2.11803	+	1.53884i	0.343590	+	0.249633i
$39$		0			0
$40$	−7.47214	+	22.9969i	−1.18145	+	3.63612i
$41$	−3.54508	−	10.9106i	−0.553649	−	1.70396i	−0.699484	−	0.714648i	$-0.746587\pi$
$41$	−3.54508	−	10.9106i	−0.553649	−	1.70396i	0.145835	−	0.989309i	$-0.453413\pi$
$42$		0			0
$43$	−4.85410			−0.740244			−0.370122	−	0.928983i	$-0.620684\pi$
$43$	−4.85410			−0.740244			−0.370122	+	0.928983i	$0.620684\pi$
$44$	−16.0623	−	1.08981i	−2.42148	−	0.164296i
$45$		0			0
$46$	5.04508	−	3.66547i	0.743857	−	0.540444i
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	−0.991002	−	0.133845i	$-0.957268\pi$
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	0.723066	−	0.690779i	$-0.242732\pi$
$48$		0			0
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$	11.5902	+	8.42075i	1.63910	+	1.19087i
$51$		0			0
$52$	3.70820	+	11.4127i	0.514235	+	1.58265i
$53$	5.73607	−	4.16750i	0.787910	−	0.572450i	−0.119433	−	0.992842i	$-0.538108\pi$
$53$	5.73607	−	4.16750i	0.787910	−	0.572450i	0.907342	+	0.420393i	$0.138108\pi$
$54$		0			0
$55$	−4.00000	+	9.95959i	−0.539360	+	1.34295i
$56$	7.47214			0.998506
$57$		0			0
$58$	−1.50000	−	4.61653i	−0.196960	−	0.606179i
$59$	−0.190983	+	0.587785i	−0.0248639	+	0.0765231i	−0.962718	−	0.270505i	$-0.912809\pi$
$59$	−0.190983	+	0.587785i	−0.0248639	+	0.0765231i	0.937855	+	0.347028i	$0.112809\pi$
$60$		0			0
$61$	−3.35410	−	2.43690i	−0.429449	−	0.312013i	0.351980	−	0.936008i	$-0.385509\pi$
$61$	−3.35410	−	2.43690i	−0.429449	−	0.312013i	−0.781428	+	0.623995i	$0.785509\pi$
$62$	1.30902	−	4.02874i	0.166245	−	0.511650i
$63$		0			0
$64$	−7.04508	+	5.11855i	−0.880636	+	0.639819i
$65$	8.00000			0.992278
$66$		0			0
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	7.28115	−	5.29007i	0.882969	−	0.641515i
$69$		0			0
$70$	2.61803	−	8.05748i	0.312915	−	0.963053i
$71$	11.3992	+	8.28199i	1.35283	+	0.982892i	0.998865	+	0.0476350i	$0.0151684\pi$
$71$	11.3992	+	8.28199i	1.35283	+	0.982892i	0.353970	+	0.935257i	$0.384832\pi$
$72$		0			0
$73$	−2.11803	+	6.51864i	−0.247897	+	0.762949i	0.747249	+	0.664544i	$0.231374\pi$
$73$	−2.11803	+	6.51864i	−0.247897	+	0.762949i	−0.995146	+	0.0984051i	$0.968626\pi$
$74$	−4.92705	−	15.1639i	−0.572758	−	1.76277i
$75$		0			0
$76$	4.85410			0.556804
$77$	3.30902	+	0.224514i	0.377097	+	0.0255857i
$78$		0			0
$79$	7.73607	−	5.62058i	0.870376	−	0.632365i	−0.0603121	−	0.998180i	$-0.519210\pi$
$79$	7.73607	−	5.62058i	0.870376	−	0.632365i	0.930688	+	0.365815i	$0.119210\pi$
$80$	9.85410	+	30.3278i	1.10172	+	3.39075i
$81$		0			0
$82$	−24.2984	−	17.6538i	−2.68331	−	1.94954i
$83$	11.5172	+	8.36775i	1.26418	+	0.918480i	0.998955	−	0.0457068i	$-0.0145540\pi$
$83$	11.5172	+	8.36775i	1.26418	+	0.918480i	0.265224	+	0.964187i	$0.414554\pi$
$84$		0			0
$85$	−1.85410	−	5.70634i	−0.201106	−	0.618939i
$86$	−10.2812	+	7.46969i	−1.10865	+	0.805478i
$87$		0			0
$88$	−20.9894	+	13.1760i	−2.23747	+	1.40457i
$89$	−11.2361			−1.19102			−0.595510	−	0.803348i	$-0.703050\pi$
$89$	−11.2361			−1.19102			−0.595510	+	0.803348i	$0.703050\pi$
$90$		0			0
$91$	−0.763932	−	2.35114i	−0.0800818	−	0.246467i
$92$	3.57295	−	10.9964i	0.372506	−	1.14645i
$93$		0			0
$94$	−12.5902	−	9.14729i	−1.29858	−	0.943471i
$95$	1.00000	−	3.07768i	0.102598	−	0.315764i
$96$		0			0
$97$	−4.85410	+	3.52671i	−0.492859	+	0.358083i	−0.806283	−	0.591530i	$-0.798524\pi$
$97$	−4.85410	+	3.52671i	−0.492859	+	0.358083i	0.313423	+	0.949613i	$0.398524\pi$
$98$	15.7082			1.58677
$99$		0			0
$100$	26.5623			2.65623
$101$	−0.381966	+	0.277515i	−0.0380070	+	0.0276137i	−0.606627	−	0.794987i	$-0.707478\pi$
$101$	−0.381966	+	0.277515i	−0.0380070	+	0.0276137i	0.568620	+	0.822601i	$0.307478\pi$
$102$		0			0
$103$	−1.78115	+	5.48183i	−0.175502	+	0.540140i	−0.999656	−	0.0262257i	$-0.991651\pi$
$103$	−1.78115	+	5.48183i	−0.175502	+	0.540140i	0.824154	+	0.566366i	$0.191651\pi$
$104$	14.9443	+	10.8576i	1.46541	+	1.06468i
$105$		0			0
$106$	5.73607	−	17.6538i	0.557136	−	1.71469i
$107$	−4.64590	−	14.2986i	−0.449136	−	1.38230i	−0.877884	−	0.478874i	$-0.841045\pi$
$107$	−4.64590	−	14.2986i	−0.449136	−	1.38230i	0.428748	−	0.903424i	$-0.358955\pi$
$108$		0			0
$109$	13.8541			1.32698			0.663491	−	0.748184i	$-0.269074\pi$
$109$	13.8541			1.32698			0.663491	+	0.748184i	$0.269074\pi$
$110$	6.85410	+	27.2501i	0.653513	+	2.59820i
$111$		0			0
$112$	7.97214	−	5.79210i	0.753296	−	0.547302i
$113$	3.94427	+	12.1392i	0.371046	+	1.14196i	0.946108	+	0.323852i	$0.104978\pi$
$113$	3.94427	+	12.1392i	0.371046	+	1.14196i	−0.575062	+	0.818110i	$0.695022\pi$
$114$		0			0
$115$	−6.23607	−	4.53077i	−0.581516	−	0.422496i
$116$	−7.28115	−	5.29007i	−0.676038	−	0.491170i
$117$		0			0
$118$	0.500000	+	1.53884i	0.0460287	+	0.141662i
$119$	−1.50000	+	1.08981i	−0.137505	+	0.0999031i
$120$		0			0
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	−10.8541			−0.982684
$123$		0			0
$124$	−2.42705	−	7.46969i	−0.217956	−	0.670798i
$125$	0.472136	−	1.45309i	0.0422291	−	0.129968i
$126$		0			0
$127$	−7.73607	−	5.62058i	−0.686465	−	0.498746i	0.189031	−	0.981971i	$-0.439465\pi$
$127$	−7.73607	−	5.62058i	−0.686465	−	0.498746i	−0.875496	+	0.483225i	$0.839465\pi$
$128$	−0.336881	+	1.03681i	−0.0297764	+	0.0916422i
$129$		0			0
$130$	16.9443	−	12.3107i	1.48611	−	1.07972i
$131$	16.7639			1.46467			0.732336	−	0.680944i	$-0.238430\pi$
$131$	16.7639			1.46467			0.732336	+	0.680944i	$0.238430\pi$
$132$		0			0
$133$	−1.00000			−0.0867110
$134$	12.7082	−	9.23305i	1.09782	−	0.797614i
$135$		0			0
$136$	4.28115	−	13.1760i	0.367106	−	1.12984i
$137$	5.16312	+	3.75123i	0.441115	+	0.320489i	0.786078	−	0.618128i	$-0.212108\pi$
$137$	5.16312	+	3.75123i	0.441115	+	0.320489i	−0.344963	+	0.938616i	$0.612108\pi$
$138$		0			0
$139$	−1.14590	+	3.52671i	−0.0971938	+	0.299132i	−0.987819	−	0.155606i	$-0.950267\pi$
$139$	−1.14590	+	3.52671i	−0.0971938	+	0.299132i	0.890625	+	0.454738i	$0.150267\pi$
$140$	−4.85410	−	14.9394i	−0.410246	−	1.26261i
$141$		0			0
$142$	36.8885			3.09562
$143$	6.29180	+	5.25731i	0.526146	+	0.439638i
$144$		0			0
$145$	−4.85410	+	3.52671i	−0.403111	+	0.292877i
$146$	5.54508	+	17.0660i	0.458914	+	1.41239i
$147$		0			0
$148$	−23.9164	−	17.3763i	−1.96592	−	1.42832i
$149$	−5.80902	−	4.22050i	−0.475893	−	0.345757i	0.323840	−	0.946112i	$-0.395026\pi$
$149$	−5.80902	−	4.22050i	−0.475893	−	0.345757i	−0.799734	+	0.600355i	$0.795026\pi$
$150$		0			0
$151$	−3.50000	−	10.7719i	−0.284826	−	0.876604i	−0.986451	−	0.164058i	$-0.947542\pi$
$151$	−3.50000	−	10.7719i	−0.284826	−	0.876604i	0.701625	−	0.712547i	$-0.252458\pi$
$152$	6.04508	−	4.39201i	0.490321	−	0.356239i
$153$		0			0
$154$	7.35410	−	4.61653i	0.592610	−	0.372010i
$155$	−5.23607			−0.420571
$156$		0			0
$157$	4.28115	+	13.1760i	0.341673	+	1.05156i	0.963341	+	0.268281i	$0.0864555\pi$
$157$	4.28115	+	13.1760i	0.341673	+	1.05156i	−0.621668	+	0.783281i	$0.713545\pi$
$158$	7.73607	−	23.8092i	0.615449	−	1.89416i
$159$		0			0
$160$	28.4164	+	20.6457i	2.24651	+	1.63219i
$161$	−0.736068	+	2.26538i	−0.0580103	+	0.178537i
$162$		0			0
$163$	−5.89919	+	4.28601i	−0.462060	+	0.335706i	−0.794339	−	0.607475i	$-0.792182\pi$
$163$	−5.89919	+	4.28601i	−0.462060	+	0.335706i	0.332279	+	0.943181i	$0.392182\pi$
$164$	−55.6869			−4.34842
$165$		0			0
$166$	37.2705			2.89275
$167$	8.28115	−	6.01661i	0.640815	−	0.465579i	−0.219315	−	0.975654i	$-0.570382\pi$
$167$	8.28115	−	6.01661i	0.640815	−	0.465579i	0.860130	+	0.510075i	$0.170382\pi$
$168$		0			0
$169$	−2.12868	+	6.55139i	−0.163744	+	0.503953i
$170$	−12.7082	−	9.23305i	−0.974675	−	0.708143i
$171$		0			0
$172$	−7.28115	+	22.4091i	−0.555183	+	1.70868i
$173$	−3.68034	−	11.3269i	−0.279811	−	0.861170i	−0.987906	−	0.155053i	$-0.950445\pi$
$173$	−3.68034	−	11.3269i	−0.279811	−	0.861170i	0.708095	−	0.706117i	$-0.249555\pi$
$174$		0			0
$175$	−5.47214			−0.413655
$176$	−12.1803	+	30.3278i	−0.918128	+	2.28604i
$177$		0			0
$178$	−23.7984	+	17.2905i	−1.78376	+	1.29598i
$179$	−7.09017	−	21.8213i	−0.529944	−	1.63100i	−0.754327	−	0.656499i	$-0.772036\pi$
$179$	−7.09017	−	21.8213i	−0.529944	−	1.63100i	0.224382	−	0.974501i	$-0.427964\pi$
$180$		0			0
$181$	17.0623	+	12.3965i	1.26823	+	0.921424i	0.999131	−	0.0416882i	$-0.0132736\pi$
$181$	17.0623	+	12.3965i	1.26823	+	0.921424i	0.269101	+	0.963112i	$0.413274\pi$
$182$	−5.23607	−	3.80423i	−0.388123	−	0.281988i
$183$		0			0
$184$	−5.50000	−	16.9273i	−0.405465	−	1.24789i
$185$	−15.9443	+	11.5842i	−1.17225	+	0.851687i
$186$		0			0
$187$	2.29180	−	5.70634i	0.167593	−	0.417289i
$188$	−28.8541			−2.10440
$189$		0			0
$190$	−2.61803	−	8.05748i	−0.189932	−	0.584551i
$191$	−3.69098	+	11.3597i	−0.267070	+	0.821957i	0.724139	+	0.689654i	$0.242237\pi$
$191$	−3.69098	+	11.3597i	−0.267070	+	0.821957i	−0.991209	+	0.132303i	$0.957763\pi$
$192$		0			0
$193$	8.89919	+	6.46564i	0.640577	+	0.465407i	0.860049	−	0.510212i	$-0.170433\pi$
$193$	8.89919	+	6.46564i	0.640577	+	0.465407i	−0.219471	+	0.975619i	$0.570433\pi$
$194$	−4.85410	+	14.9394i	−0.348504	+	1.07259i
$195$		0			0
$196$	23.5623	−	17.1190i	1.68302	−	1.22279i
$197$	3.76393			0.268169			0.134085	−	0.990970i	$-0.457191\pi$
$197$	3.76393			0.268169			0.134085	+	0.990970i	$0.457191\pi$
$198$		0			0
$199$	−13.8541			−0.982091			−0.491046	−	0.871134i	$-0.663385\pi$
$199$	−13.8541			−0.982091			−0.491046	+	0.871134i	$0.663385\pi$
$200$	33.0795	−	24.0337i	2.33908	−	1.69944i
$201$		0			0
$202$	−0.381966	+	1.17557i	−0.0268750	+	0.0827129i
$203$	1.50000	+	1.08981i	0.105279	+	0.0764899i
$204$		0			0
$205$	−11.4721	+	35.3076i	−0.801249	+	2.46599i
$206$	4.66312	+	14.3516i	0.324895	+	0.999924i
$207$		0			0
$208$	24.3607			1.68911
$209$	2.80902	−	1.76336i	0.194304	−	0.121974i
$210$		0			0
$211$	−9.32624	+	6.77591i	−0.642045	+	0.466473i	−0.860552	−	0.509363i	$-0.829881\pi$
$211$	−9.32624	+	6.77591i	−0.642045	+	0.466473i	0.218507	+	0.975835i	$0.429881\pi$
$212$	−10.6353	−	32.7319i	−0.730432	−	2.24804i
$213$		0			0
$214$	−31.8435	−	23.1356i	−2.17677	−	1.58152i
$215$	12.7082	+	9.23305i	0.866692	+	0.629689i
$216$		0			0
$217$	0.500000	+	1.53884i	0.0339422	+	0.104463i
$218$	29.3435	−	21.3193i	1.98739	−	1.44392i
$219$		0			0
$220$	39.9787	+	33.4055i	2.69536	+	2.25220i
$221$	−4.58359			−0.308326
$222$		0			0
$223$	6.95492	+	21.4050i	0.465736	+	1.43339i	0.858055	+	0.513558i	$0.171673\pi$
$223$	6.95492	+	21.4050i	0.465736	+	1.43339i	−0.392320	+	0.919829i	$0.628327\pi$
$224$	3.35410	−	10.3229i	0.224105	−	0.689725i
$225$		0			0
$226$	27.0344	+	19.6417i	1.79830	+	1.30654i
$227$	−4.44427	+	13.6781i	−0.294977	+	0.907845i	0.688253	+	0.725471i	$0.258378\pi$
$227$	−4.44427	+	13.6781i	−0.294977	+	0.907845i	−0.983229	+	0.182374i	$0.941622\pi$
$228$		0			0
$229$	9.85410	−	7.15942i	0.651177	−	0.473108i	−0.212495	−	0.977162i	$-0.568159\pi$
$229$	9.85410	−	7.15942i	0.651177	−	0.473108i	0.863672	+	0.504054i	$0.168159\pi$
$230$	−20.1803			−1.33065
$231$		0			0
$232$	−13.8541			−0.909566
$233$	−23.5623	+	17.1190i	−1.54362	+	1.12150i	−0.595603	+	0.803279i	$0.703087\pi$
$233$	−23.5623	+	17.1190i	−1.54362	+	1.12150i	−0.948015	+	0.318225i	$0.896913\pi$
$234$		0			0
$235$	−5.94427	+	18.2946i	−0.387762	+	1.19341i
$236$	2.42705	+	1.76336i	0.157988	+	0.114785i
$237$		0			0
$238$	−1.50000	+	4.61653i	−0.0972306	+	0.299245i
$239$	0.472136	+	1.45309i	0.0305399	+	0.0939923i	0.965165	−	0.261643i	$-0.0842644\pi$
$239$	0.472136	+	1.45309i	0.0305399	+	0.0939923i	−0.934625	+	0.355636i	$0.884264\pi$
$240$		0			0
$241$	26.8328			1.72845			0.864227	−	0.503102i	$-0.167808\pi$
$241$	26.8328			1.72845			0.864227	+	0.503102i	$0.167808\pi$
$242$	−12.5172	+	25.9358i	−0.804637	+	1.66722i
$243$		0			0
$244$	−16.2812	+	11.8290i	−1.04229	+	0.757271i
$245$	−6.00000	−	18.4661i	−0.383326	−	1.17976i
$246$		0			0
$247$	−2.00000	−	1.45309i	−0.127257	−	0.0924576i
$248$	−9.78115	−	7.10642i	−0.621104	−	0.451258i
$249$		0			0
$250$	−1.23607	−	3.80423i	−0.0781758	−	0.240600i
$251$	−0.354102	+	0.257270i	−0.0223507	+	0.0162387i	−0.598905	−	0.800820i	$-0.704397\pi$
$251$	−0.354102	+	0.257270i	−0.0223507	+	0.0162387i	0.576554	+	0.817059i	$0.304397\pi$
$252$		0			0
$253$	−1.92705	−	7.66145i	−0.121153	−	0.481671i
$254$	−25.0344			−1.57080
$255$		0			0
$256$	−4.50000	−	13.8496i	−0.281250	−	0.865598i
$257$	−8.06231	+	24.8132i	−0.502913	+	1.54781i	0.301339	+	0.953517i	$0.402567\pi$
$257$	−8.06231	+	24.8132i	−0.502913	+	1.54781i	−0.804251	+	0.594289i	$0.797433\pi$
$258$		0			0
$259$	4.92705	+	3.57971i	0.306152	+	0.222432i
$260$	12.0000	−	36.9322i	0.744208	−	2.29044i
$261$		0			0
$262$	35.5066	−	25.7970i	2.19360	−	1.59375i
$263$	0.708204			0.0436697			0.0218349	−	0.999762i	$-0.493049\pi$
$263$	0.708204			0.0436697			0.0218349	+	0.999762i	$0.493049\pi$
$264$		0			0
$265$	−22.9443			−1.40946
$266$	−2.11803	+	1.53884i	−0.129865	+	0.0943524i
$267$		0			0
$268$	9.00000	−	27.6992i	0.549762	−	1.69199i
$269$	−9.92705	−	7.21242i	−0.605263	−	0.439749i	0.242480	−	0.970156i	$-0.422039\pi$
$269$	−9.92705	−	7.21242i	−0.605263	−	0.439749i	−0.847743	+	0.530407i	$0.822039\pi$
$270$		0			0
$271$	4.70820	−	14.4904i	0.286003	−	0.880227i	−0.700093	−	0.714051i	$-0.746858\pi$
$271$	4.70820	−	14.4904i	0.286003	−	0.880227i	0.986096	−	0.166175i	$-0.0531418\pi$
$272$	−5.64590	−	17.3763i	−0.342333	−	1.05359i
$273$		0			0
$274$	16.7082			1.00938
$275$	15.3713	−	9.64932i	0.926926	−	0.581876i
$276$		0			0
$277$	11.9443	−	8.67802i	0.717662	−	0.521412i	−0.167975	−	0.985791i	$-0.553723\pi$
$277$	11.9443	−	8.67802i	0.717662	−	0.521412i	0.885636	+	0.464380i	$0.153723\pi$
$278$	3.00000	+	9.23305i	0.179928	+	0.553762i
$279$		0			0
$280$	−19.5623	−	14.2128i	−1.16907	−	0.849380i
$281$	−5.11803	−	3.71847i	−0.305316	−	0.221825i	0.424568	−	0.905396i	$-0.360426\pi$
$281$	−5.11803	−	3.71847i	−0.305316	−	0.221825i	−0.729884	+	0.683571i	$0.760426\pi$
$282$		0			0
$283$	−5.25329	−	16.1680i	−0.312276	−	0.961086i	−0.976861	−	0.213874i	$-0.931392\pi$
$283$	−5.25329	−	16.1680i	−0.312276	−	0.961086i	0.664586	−	0.747212i	$-0.268608\pi$
$284$	55.3328	−	40.2016i	3.28340	−	2.38553i
$285$		0			0
$286$	21.4164	+	1.45309i	1.26638	+	0.0859227i
$287$	11.4721			0.677179
$288$		0			0
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$	−4.85410	+	14.9394i	−0.285043	+	0.877271i
$291$		0			0
$292$	26.9164	+	19.5559i	1.57516	+	1.14442i
$293$	−2.10739	+	6.48588i	−0.123115	+	0.378909i	−0.993553	−	0.113369i	$-0.963836\pi$
$293$	−2.10739	+	6.48588i	−0.123115	+	0.378909i	0.870438	+	0.492278i	$0.163836\pi$
$294$		0			0
$295$	1.61803	−	1.17557i	0.0942056	−	0.0684444i
$296$	−45.5066			−2.64502
$297$		0			0
$298$	−18.7984			−1.08896
$299$	−4.76393	+	3.46120i	−0.275505	+	0.200166i
$300$		0			0
$301$	1.50000	−	4.61653i	0.0864586	−	0.266092i
$302$	−23.9894	−	17.4293i	−1.38043	−	1.00294i
$303$		0			0
$304$	3.04508	−	9.37181i	0.174648	−	0.537510i
$305$	4.14590	+	12.7598i	0.237393	+	0.730622i
$306$		0			0
$307$	1.14590			0.0653999			0.0326999	−	0.999465i	$-0.489589\pi$
$307$	1.14590			0.0653999			0.0326999	+	0.999465i	$0.489589\pi$
$308$	6.00000	−	14.9394i	0.341882	−	0.851251i
$309$		0			0
$310$	−11.0902	+	8.05748i	−0.629879	+	0.457634i
$311$	−2.21885	−	6.82891i	−0.125819	−	0.387232i	0.868230	−	0.496162i	$-0.165258\pi$
$311$	−2.21885	−	6.82891i	−0.125819	−	0.387232i	−0.994049	+	0.108930i	$0.965258\pi$
$312$		0			0
$313$	4.42705	+	3.21644i	0.250232	+	0.181804i	0.705829	−	0.708382i	$-0.250574\pi$
$313$	4.42705	+	3.21644i	0.250232	+	0.181804i	−0.455598	+	0.890186i	$0.650574\pi$
$314$	29.3435	+	21.3193i	1.65595	+	1.20312i
$315$		0			0
$316$	−14.3435	−	44.1446i	−0.806883	−	2.48333i
$317$	−2.47214	+	1.79611i	−0.138849	+	0.100880i	−0.655042	−	0.755593i	$-0.727349\pi$
$317$	−2.47214	+	1.79611i	−0.138849	+	0.100880i	0.516193	+	0.856473i	$0.327349\pi$
$318$		0			0
$319$	−6.13525	−	0.416272i	−0.343508	−	0.0233067i
$320$	28.1803			1.57533
$321$		0			0
$322$	1.92705	+	5.93085i	0.107390	+	0.330514i
$323$	−0.572949	+	1.76336i	−0.0318797	+	0.0981157i
$324$		0			0
$325$	−10.9443	−	7.95148i	−0.607079	−	0.441069i
$326$	−5.89919	+	18.1558i	−0.326726	+	1.00556i
$327$		0			0
$328$	−69.3500	+	50.3858i	−3.82922	+	2.78209i
$329$	5.94427			0.327718
$330$		0			0
$331$	−12.4164			−0.682467			−0.341234	−	0.939978i	$-0.610845\pi$
$331$	−12.4164			−0.682467			−0.341234	+	0.939978i	$0.610845\pi$
$332$	55.9058	−	40.6179i	3.06823	−	2.22920i
$333$		0			0
$334$	8.28115	−	25.4868i	0.453125	−	1.39457i
$335$	−15.7082	−	11.4127i	−0.858231	−	0.623541i
$336$		0			0
$337$	−0.781153	+	2.40414i	−0.0425521	+	0.130962i	−0.970076	−	0.242803i	$-0.921933\pi$
$337$	−0.781153	+	2.40414i	−0.0425521	+	0.130962i	0.927524	+	0.373765i	$0.121933\pi$
$338$	5.57295	+	17.1518i	0.303128	+	0.932933i
$339$		0			0
$340$	−29.1246			−1.57950
$341$	−4.11803	−	3.44095i	−0.223004	−	0.186338i
$342$		0			0
$343$	−10.5172	+	7.64121i	−0.567877	+	0.412586i
$344$	11.2082	+	34.4953i	0.604306	+	1.85986i
$345$		0			0
$346$	−25.2254	−	18.3273i	−1.35613	−	0.985284i
$347$	−21.7533	−	15.8047i	−1.16778	−	0.848440i	−0.177037	−	0.984204i	$-0.556651\pi$
$347$	−21.7533	−	15.8047i	−1.16778	−	0.848440i	−0.990741	+	0.135764i	$0.956651\pi$
$348$		0			0
$349$	−3.35410	−	10.3229i	−0.179541	−	0.552570i	0.820271	−	0.571975i	$-0.193823\pi$
$349$	−3.35410	−	10.3229i	−0.179541	−	0.552570i	−0.999812	+	0.0194052i	$0.993823\pi$
$350$	−11.5902	+	8.42075i	−0.619521	+	0.450108i
$351$		0			0
$352$	8.78115	+	34.9116i	0.468037	+	1.86079i
$353$	10.4164			0.554409			0.277205	−	0.960811i	$-0.410592\pi$
$353$	10.4164			0.554409			0.277205	+	0.960811i	$0.410592\pi$
$354$		0			0
$355$	−14.0902	−	43.3651i	−0.747829	−	2.30158i
$356$	−16.8541	+	51.8716i	−0.893266	+	2.74919i
$357$		0			0
$358$	−48.5967	−	35.3076i	−2.56842	−	1.86606i
$359$	−4.98936	+	15.3557i	−0.263328	+	0.810441i	0.728746	+	0.684784i	$0.240104\pi$
$359$	−4.98936	+	15.3557i	−0.263328	+	0.810441i	−0.992074	+	0.125656i	$0.959896\pi$
$360$		0			0
$361$	14.5623	−	10.5801i	0.766437	−	0.556849i
$362$	55.2148			2.90202
$363$		0			0
$364$	−12.0000			−0.628971
$365$	17.9443	−	13.0373i	0.939246	−	0.682402i
$366$		0			0
$367$	0.218847	−	0.673542i	0.0114237	−	0.0351586i	−0.945182	−	0.326544i	$-0.894116\pi$
$367$	0.218847	−	0.673542i	0.0114237	−	0.0351586i	0.956606	+	0.291385i	$0.0941160\pi$
$368$	−18.9894	−	13.7966i	−0.989889	−	0.719196i
$369$		0			0
$370$	−15.9443	+	49.0714i	−0.828903	+	2.55110i
$371$	2.19098	+	6.74315i	0.113750	+	0.350087i
$372$		0			0
$373$	25.6525			1.32823			0.664117	−	0.747628i	$-0.268807\pi$
$373$	25.6525			1.32823			0.664117	+	0.747628i	$0.268807\pi$
$374$	−3.92705	−	15.6129i	−0.203063	−	0.807325i
$375$		0			0
$376$	−35.9336	+	26.1073i	−1.85314	+	1.34638i
$377$	1.41641	+	4.35926i	0.0729487	+	0.224513i
$378$		0			0
$379$	7.11803	+	5.17155i	0.365629	+	0.265645i	0.755396	−	0.655269i	$-0.227445\pi$
$379$	7.11803	+	5.17155i	0.365629	+	0.265645i	−0.389767	+	0.920913i	$0.627445\pi$
$380$	−12.7082	−	9.23305i	−0.651917	−	0.473646i
$381$		0			0
$382$	9.66312	+	29.7400i	0.494408	+	1.52163i
$383$	−10.6353	+	7.72696i	−0.543436	+	0.394829i	−0.825360	−	0.564607i	$-0.809028\pi$
$383$	−10.6353	+	7.72696i	−0.543436	+	0.394829i	0.281923	+	0.959437i	$0.409028\pi$
$384$		0			0
$385$	−8.23607	−	6.88191i	−0.419749	−	0.350735i
$386$	28.7984			1.46580
$387$		0			0
$388$	9.00000	+	27.6992i	0.456906	+	1.40621i
$389$	2.67376	−	8.22899i	0.135565	−	0.417227i	−0.860112	−	0.510105i	$-0.829607\pi$
$389$	2.67376	−	8.22899i	0.135565	−	0.417227i	0.995677	+	0.0928781i	$0.0296067\pi$
$390$		0			0
$391$	3.57295	+	2.59590i	0.180692	+	0.131280i
$392$	13.8541	−	42.6385i	0.699738	−	2.15357i
$393$		0			0
$394$	7.97214	−	5.79210i	0.401630	−	0.291802i
$395$	−30.9443			−1.55698
$396$		0			0
$397$	38.1246			1.91342			0.956710	−	0.291044i	$-0.0940026\pi$
$397$	38.1246			1.91342			0.956710	+	0.291044i	$0.0940026\pi$
$398$	−29.3435	+	21.3193i	−1.47085	+	1.06864i
$399$		0			0
$400$	16.6631	−	51.2838i	0.833156	−	2.56419i
$401$	4.50000	+	3.26944i	0.224719	+	0.163268i	0.694448	−	0.719542i	$-0.255648\pi$
$401$	4.50000	+	3.26944i	0.224719	+	0.163268i	−0.469729	+	0.882811i	$0.655648\pi$
$402$		0			0
$403$	−1.23607	+	3.80423i	−0.0615729	+	0.189502i
$404$	0.708204	+	2.17963i	0.0352345	+	0.108441i
$405$		0			0
$406$	4.85410			0.240905
$407$	−20.1525	−	1.36733i	−0.998921	−	0.0677759i
$408$		0			0
$409$	−7.07295	+	5.13880i	−0.349735	+	0.254097i	−0.748758	−	0.662844i	$-0.769349\pi$
$409$	−7.07295	+	5.13880i	−0.349735	+	0.254097i	0.399023	+	0.916941i	$0.369349\pi$
$410$	30.0344	+	92.4365i	1.48330	+	4.56511i
$411$		0			0
$412$	22.6353	+	16.4455i	1.11516	+	0.810210i
$413$	−0.500000	−	0.363271i	−0.0246034	−	0.0178754i
$414$		0			0
$415$	−14.2361	−	43.8141i	−0.698821	−	2.15075i
$416$	21.7082	−	15.7719i	1.06433	−	0.773283i
$417$		0			0
$418$	3.23607	−	8.05748i	0.158281	−	0.394104i
$419$	−3.09017			−0.150965			−0.0754823	−	0.997147i	$-0.524050\pi$
$419$	−3.09017			−0.150965			−0.0754823	+	0.997147i	$0.524050\pi$
$420$		0			0
$421$	1.78115	+	5.48183i	0.0868081	+	0.267168i	0.985032	−	0.172370i	$-0.0551424\pi$
$421$	1.78115	+	5.48183i	0.0868081	+	0.267168i	−0.898224	+	0.439537i	$0.855142\pi$
$422$	−9.32624	+	28.7032i	−0.453994	+	1.39725i
$423$		0			0
$424$	−42.8607	−	31.1401i	−2.08150	−	1.51230i
$425$	−3.13525	+	9.64932i	−0.152082	+	0.468061i
$426$		0			0
$427$	3.35410	−	2.43690i	0.162316	−	0.117930i
$428$	−72.9787			−3.52756
$429$		0			0
$430$	41.1246			1.98320
$431$	−19.4721	+	14.1473i	−0.937940	+	0.681453i	−0.947924	−	0.318497i	$-0.896822\pi$
$431$	−19.4721	+	14.1473i	−0.937940	+	0.681453i	0.00998408	+	0.999950i	$0.496822\pi$
$432$		0			0
$433$	−8.57295	+	26.3848i	−0.411990	+	1.26797i	0.502926	+	0.864329i	$0.332257\pi$
$433$	−8.57295	+	26.3848i	−0.411990	+	1.26797i	−0.914916	+	0.403644i	$0.867743\pi$
$434$	3.42705	+	2.48990i	0.164504	+	0.119519i
$435$		0			0
$436$	20.7812	−	63.9578i	0.995237	−	3.06302i
$437$	0.736068	+	2.26538i	0.0352109	+	0.108368i
$438$		0			0
$439$	12.7082			0.606529			0.303265	−	0.952906i	$-0.401923\pi$
$439$	12.7082			0.606529			0.303265	+	0.952906i	$0.401923\pi$
$440$	80.0132	+	5.42882i	3.81448	+	0.258809i
$441$		0			0
$442$	−9.70820	+	7.05342i	−0.461772	+	0.335497i
$443$	1.00000	+	3.07768i	0.0475114	+	0.146225i	0.971998	−	0.234990i	$-0.0755057\pi$
$443$	1.00000	+	3.07768i	0.0475114	+	0.146225i	−0.924486	+	0.381215i	$0.875506\pi$
$444$		0			0
$445$	29.4164	+	21.3723i	1.39447	+	1.01314i
$446$	47.6697	+	34.6341i	2.25723	+	1.63997i
$447$		0			0
$448$	−2.69098	−	8.28199i	−0.127137	−	0.391287i
$449$	1.19098	−	0.865300i	0.0562060	−	0.0408360i	−0.559328	−	0.828947i	$-0.688941\pi$
$449$	1.19098	−	0.865300i	0.0562060	−	0.0408360i	0.615533	+	0.788111i	$0.288941\pi$
$450$		0			0
$451$	−32.2254	+	20.2295i	−1.51744	+	0.952568i
$452$	61.9574			2.91423
$453$		0			0
$454$	11.6353	+	35.8096i	0.546070	+	1.68063i
$455$	−2.47214	+	7.60845i	−0.115896	+	0.356690i
$456$		0			0
$457$	0.809017	+	0.587785i	0.0378442	+	0.0274954i	0.606547	−	0.795048i	$-0.292554\pi$
$457$	0.809017	+	0.587785i	0.0378442	+	0.0274954i	−0.568702	+	0.822543i	$0.692554\pi$
$458$	9.85410	−	30.3278i	0.460452	−	1.41713i
$459$		0			0
$460$	−30.2705	+	21.9928i	−1.41137	+	1.02542i
$461$	−22.8541			−1.06442			−0.532211	−	0.846612i	$-0.678639\pi$
$461$	−22.8541			−1.06442			−0.532211	+	0.846612i	$0.678639\pi$
$462$		0			0
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$	−14.7812	+	10.7391i	−0.686198	+	0.498552i
$465$		0			0
$466$	−23.5623	+	72.5173i	−1.09150	+	3.35930i
$467$	4.23607	+	3.07768i	0.196022	+	0.142418i	0.681467	−	0.731849i	$-0.261342\pi$
$467$	4.23607	+	3.07768i	0.196022	+	0.142418i	−0.485445	+	0.874267i	$0.661342\pi$
$468$		0			0
$469$	−1.85410	+	5.70634i	−0.0856145	+	0.263494i
$470$	15.5623	+	47.8959i	0.717836	+	2.20927i
$471$		0			0
$472$	4.61803			0.212562
$473$	3.92705	+	15.6129i	0.180566	+	0.717883i
$474$		0			0
$475$	−4.42705	+	3.21644i	−0.203127	+	0.147580i
$476$	2.78115	+	8.55951i	0.127474	+	0.392324i
$477$		0			0
$478$	3.23607	+	2.35114i	0.148014	+	0.107539i
$479$	13.1353	+	9.54332i	0.600165	+	0.436045i	0.845937	−	0.533282i	$-0.179042\pi$
$479$	13.1353	+	9.54332i	0.600165	+	0.436045i	−0.245772	+	0.969328i	$0.579042\pi$
$480$		0			0
$481$	4.65248	+	14.3188i	0.212135	+	0.652883i
$482$	56.8328	−	41.2915i	2.58866	−	1.88077i
$483$		0			0
$484$	9.48936	+	52.5451i	0.431334	+	2.38842i
$485$	19.4164			0.881654
$486$		0			0
$487$	10.5000	+	32.3157i	0.475800	+	1.46436i	0.844875	+	0.534963i	$0.179675\pi$
$487$	10.5000	+	32.3157i	0.475800	+	1.46436i	−0.369075	+	0.929400i	$0.620325\pi$
$488$	−9.57295	+	29.4625i	−0.433347	+	1.33371i
$489$		0			0
$490$	−41.1246	−	29.8788i	−1.85782	−	1.34979i
$491$	−2.57295	+	7.91872i	−0.116116	+	0.357367i	−0.992178	−	0.124831i	$-0.960161\pi$
$491$	−2.57295	+	7.91872i	−0.116116	+	0.357367i	0.876063	+	0.482198i	$0.160161\pi$
$492$		0			0
$493$	2.78115	−	2.02063i	0.125257	−	0.0910044i
$494$	−6.47214			−0.291195
$495$		0			0
$496$	−15.9443			−0.715919
$497$	−11.3992	+	8.28199i	−0.511323	+	0.371498i
$498$		0			0
$499$	3.57953	−	11.0167i	0.160242	−	0.493173i	−0.838413	−	0.545036i	$-0.816516\pi$
$499$	3.57953	−	11.0167i	0.160242	−	0.493173i	0.998654	+	0.0518631i	$0.0165159\pi$
$500$	−6.00000	−	4.35926i	−0.268328	−	0.194952i
$501$		0			0
$502$	−0.354102	+	1.08981i	−0.0158043	+	0.0486408i
$503$	−5.70820	−	17.5680i	−0.254516	−	0.783320i	−0.993925	−	0.110063i	$-0.964895\pi$
$503$	−5.70820	−	17.5680i	−0.254516	−	0.783320i	0.739408	−	0.673257i	$-0.235105\pi$
$504$		0			0
$505$	1.52786			0.0679891
$506$	−15.8713	−	13.2618i	−0.705566	−	0.589559i
$507$		0			0
$508$	−37.5517	+	27.2829i	−1.66609	+	1.21048i
$509$	−1.48936	−	4.58377i	−0.0660146	−	0.203172i	0.912608	−	0.408835i	$-0.134065\pi$
$509$	−1.48936	−	4.58377i	−0.0660146	−	0.203172i	−0.978623	+	0.205663i	$0.934065\pi$
$510$		0			0
$511$	−5.54508	−	4.02874i	−0.245300	−	0.178221i
$512$	−32.6074	−	23.6907i	−1.44106	−	1.04699i
$513$		0			0
$514$	21.1074	+	64.9619i	0.931007	+	2.86535i
$515$	15.0902	−	10.9637i	0.664952	−	0.483116i
$516$		0			0
$517$	−16.6976	+	10.4819i	−0.734358	+	0.460992i
$518$	15.9443			0.700551
$519$		0			0
$520$	−18.4721	−	56.8514i	−0.810057	−	2.49310i
$521$	1.34752	−	4.14725i	0.0590361	−	0.181694i	−0.917190	−	0.398451i	$-0.869548\pi$
$521$	1.34752	−	4.14725i	0.0590361	−	0.181694i	0.976226	+	0.216757i	$0.0695478\pi$
$522$		0			0
$523$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$523$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$524$	25.1459	−	77.3911i	1.09850	−	3.38085i
$525$		0			0
$526$	1.50000	−	1.08981i	0.0654031	−	0.0475181i
$527$	3.00000			0.130682
$528$		0			0
$529$	−17.3262			−0.753315
$530$	−48.5967	+	35.3076i	−2.11091	+	1.53366i
$531$		0			0
$532$	−1.50000	+	4.61653i	−0.0650332	+	0.200152i
$533$	22.9443	+	16.6700i	0.993827	+	0.722057i
$534$		0			0
$535$	−15.0344	+	46.2713i	−0.649996	+	2.00048i
$536$	−13.8541	−	42.6385i	−0.598406	−	1.84170i
$537$		0			0
$538$	−32.1246			−1.38499
$539$	7.41641	−	18.4661i	0.319447	−	0.795391i
$540$		0			0
$541$	18.6803	−	13.5721i	0.803131	−	0.583508i	−0.108700	−	0.994075i	$-0.534669\pi$
$541$	18.6803	−	13.5721i	0.803131	−	0.583508i	0.911831	+	0.410566i	$0.134669\pi$
$542$	−12.3262	−	37.9363i	−0.529457	−	1.62950i
$543$		0			0
$544$	−16.2812	−	11.8290i	−0.698049	−	0.507162i
$545$	−36.2705	−	26.3521i	−1.55366	−	1.12880i
$546$		0			0
$547$	−5.15248	−	15.8577i	−0.220304	−	0.678026i	−0.998734	−	0.0502950i	$-0.983984\pi$
$547$	−5.15248	−	15.8577i	−0.220304	−	0.678026i	0.778430	−	0.627731i	$-0.216016\pi$
$548$	25.0623	−	18.2088i	1.07061	−	0.777843i
$549$		0			0
$550$	17.7082	−	44.0916i	0.755080	−	1.88007i
$551$	1.85410			0.0789874
$552$		0			0
$553$	2.95492	+	9.09429i	0.125656	+	0.386729i
$554$	11.9443	−	36.7607i	0.507463	−	1.56181i
$555$		0			0
$556$	14.5623	+	10.5801i	0.617579	+	0.448698i
$557$	9.47214	−	29.1522i	0.401347	−	1.23522i	−0.522560	−	0.852603i	$-0.675023\pi$
$557$	9.47214	−	29.1522i	0.401347	−	1.23522i	0.923907	−	0.382617i	$-0.124977\pi$
$558$		0			0
$559$	9.70820	−	7.05342i	0.410613	−	0.298328i
$560$	−31.8885			−1.34754
$561$		0			0
$562$	−16.5623			−0.698639
$563$	−34.2254	+	24.8662i	−1.44243	+	1.04799i	−0.454902	+	0.890542i	$0.650326\pi$
$563$	−34.2254	+	24.8662i	−1.44243	+	1.04799i	−0.987528	+	0.157445i	$0.949674\pi$
$564$		0			0
$565$	12.7639	−	39.2833i	0.536983	−	1.65266i
$566$	−36.0066	−	26.1603i	−1.51347	−	1.09960i
$567$		0			0
$568$	32.5344	−	100.131i	1.36511	−	4.20139i
$569$	4.38854	+	13.5065i	0.183977	+	0.566224i	0.999929	−	0.0118958i	$-0.00378663\pi$
$569$	4.38854	+	13.5065i	0.183977	+	0.566224i	−0.815952	+	0.578120i	$0.803787\pi$
$570$		0			0
$571$	−27.4721			−1.14967			−0.574837	−	0.818268i	$-0.694934\pi$
$571$	−27.4721			−1.14967			−0.574837	+	0.818268i	$0.694934\pi$
$572$	33.7082	−	21.1603i	1.40941	−	0.884755i
$573$		0			0
$574$	24.2984	−	17.6538i	1.01419	−	0.736855i
$575$	4.02786	+	12.3965i	0.167974	+	0.516969i
$576$		0			0
$577$	−6.94427	−	5.04531i	−0.289094	−	0.210039i	0.433780	−	0.901019i	$-0.357179\pi$
$577$	−6.94427	−	5.04531i	−0.289094	−	0.210039i	−0.722874	+	0.690980i	$0.757179\pi$
$578$	−28.7254	−	20.8702i	−1.19482	−	0.868088i
$579$		0			0
$580$	9.00000	+	27.6992i	0.373705	+	1.15014i
$581$	−11.5172	+	8.36775i	−0.477815	+	0.347153i
$582$		0			0
$583$	−18.0451	−	15.0781i	−0.747351	−	0.624473i
$584$	51.2148			2.11928
$585$		0			0
$586$	5.51722	+	16.9803i	0.227914	+	0.701448i
$587$	−4.14590	+	12.7598i	−0.171120	+	0.526652i	−0.999435	−	0.0336102i	$-0.989300\pi$
$587$	−4.14590	+	12.7598i	−0.171120	+	0.526652i	0.828315	+	0.560262i	$0.189300\pi$
$588$		0			0
$589$	1.30902	+	0.951057i	0.0539371	+	0.0391876i
$590$	1.61803	−	4.97980i	0.0666134	−	0.205015i
$591$		0			0
$592$	−48.5517	+	35.2748i	−1.99546	+	1.44979i
$593$	6.94427			0.285167			0.142584	−	0.989783i	$-0.454459\pi$
$593$	6.94427			0.285167			0.142584	+	0.989783i	$0.454459\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	−28.1976	+	20.4867i	−1.15502	+	0.839169i
$597$		0			0
$598$	−4.76393	+	14.6619i	−0.194812	+	0.599569i
$599$	−25.3713	−	18.4333i	−1.03664	−	0.753166i	−0.0670165	−	0.997752i	$-0.521348\pi$
$599$	−25.3713	−	18.4333i	−1.03664	−	0.753166i	−0.969628	+	0.244586i	$0.921348\pi$
$600$		0			0
$601$	−2.63525	+	8.11048i	−0.107494	+	0.330833i	−0.990308	−	0.138890i	$-0.955646\pi$
$601$	−2.63525	+	8.11048i	−0.107494	+	0.330833i	0.882813	+	0.469724i	$0.155646\pi$
$602$	−3.92705	−	12.0862i	−0.160055	−	0.492598i
$603$		0			0
$604$	−54.9787			−2.23705
$605$	35.2705	+	4.80828i	1.43395	+	0.195485i
$606$		0			0
$607$	24.6074	−	17.8783i	0.998783	−	0.725658i	0.0369562	−	0.999317i	$-0.488234\pi$
$607$	24.6074	−	17.8783i	0.998783	−	0.725658i	0.961827	+	0.273658i	$0.0882338\pi$
$608$	−3.35410	−	10.3229i	−0.136027	−	0.418647i
$609$		0			0
$610$	28.4164	+	20.6457i	1.15055	+	0.835921i
$611$	11.8885	+	8.63753i	0.480959	+	0.349437i
$612$		0			0
$613$	4.06231	+	12.5025i	0.164075	+	0.504971i	0.998967	−	0.0454430i	$-0.0144699\pi$
$613$	4.06231	+	12.5025i	0.164075	+	0.504971i	−0.834892	+	0.550414i	$0.814470\pi$
$614$	2.42705	−	1.76336i	0.0979478	−	0.0711632i
$615$		0			0
$616$	−6.04508	−	24.0337i	−0.243563	−	0.968345i
$617$	42.1591			1.69726			0.848630	−	0.528987i	$-0.177428\pi$
$617$	42.1591			1.69726			0.848630	+	0.528987i	$0.177428\pi$
$618$		0			0
$619$	2.29837	+	7.07367i	0.0923794	+	0.284315i	0.986562	−	0.163388i	$-0.0522423\pi$
$619$	2.29837	+	7.07367i	0.0923794	+	0.284315i	−0.894182	+	0.447703i	$0.852242\pi$
$620$	−7.85410	+	24.1724i	−0.315428	+	0.970789i
$621$		0			0
$622$	−15.2082	−	11.0494i	−0.609793	−	0.443041i
$623$	3.47214	−	10.6861i	0.139108	−	0.428131i
$624$		0			0
$625$	18.1353	−	13.1760i	0.725410	−	0.527041i
$626$	14.3262			0.572592
$627$		0			0
$628$	67.2492			2.68354
$629$	9.13525	−	6.63715i	0.364246	−	0.264641i
$630$		0			0
$631$	7.69098	−	23.6704i	0.306173	−	0.942304i	−0.673064	−	0.739585i	$-0.735022\pi$
$631$	7.69098	−	23.6704i	0.306173	−	0.942304i	0.979237	−	0.202720i	$-0.0649780\pi$
$632$	−57.8050	−	41.9978i	−2.29936	−	1.67058i
$633$		0			0
$634$	−2.47214	+	7.60845i	−0.0981811	+	0.302170i
$635$	9.56231	+	29.4298i	0.379469	+	1.16788i
$636$		0			0
$637$	−14.8328			−0.587698
$638$	−13.6353	+	8.55951i	−0.539825	+	0.338874i
$639$		0			0
$640$	2.85410	−	2.07363i	0.112818	−	0.0819673i
$641$	10.9549	+	33.7158i	0.432693	+	1.33169i	0.895432	+	0.445198i	$0.146867\pi$
$641$	10.9549	+	33.7158i	0.432693	+	1.33169i	−0.462739	+	0.886495i	$0.653133\pi$
$642$		0			0
$643$	0.118034	+	0.0857567i	0.00465481	+	0.00338191i	0.590110	−	0.807323i	$-0.299084\pi$
$643$	0.118034	+	0.0857567i	0.00465481	+	0.00338191i	−0.585455	+	0.810705i	$0.699084\pi$
$644$	9.35410	+	6.79615i	0.368603	+	0.267806i
$645$		0			0
$646$	1.50000	+	4.61653i	0.0590167	+	0.181635i
$647$	−14.7082	+	10.6861i	−0.578239	+	0.420115i	−0.838089	−	0.545534i	$-0.816327\pi$
$647$	−14.7082	+	10.6861i	−0.578239	+	0.420115i	0.259850	+	0.965649i	$0.416327\pi$
$648$		0			0
$649$	2.04508	+	0.138757i	0.0802766	+	0.00544670i
$650$	−35.4164			−1.38915
$651$		0			0
$652$	10.9377	+	33.6628i	0.428353	+	1.31834i
$653$	13.3992	−	41.2385i	0.524351	−	1.61379i	−0.241246	−	0.970464i	$-0.577556\pi$
$653$	13.3992	−	41.2385i	0.524351	−	1.61379i	0.765596	−	0.643321i	$-0.222444\pi$
$654$		0			0
$655$	−43.8885	−	31.8869i	−1.71487	−	1.24592i
$656$	−34.9336	+	107.515i	−1.36393	+	4.19774i
$657$		0			0
$658$	12.5902	−	9.14729i	0.490816	−	0.356599i
$659$	−36.9787			−1.44049			−0.720243	−	0.693722i	$-0.755970\pi$
$659$	−36.9787			−1.44049			−0.720243	+	0.693722i	$0.755970\pi$
$660$		0			0
$661$	−17.7082			−0.688769			−0.344385	−	0.938829i	$-0.611912\pi$
$661$	−17.7082			−0.688769			−0.344385	+	0.938829i	$0.611912\pi$
$662$	−26.2984	+	19.1069i	−1.02212	+	0.742610i
$663$		0			0
$664$	32.8713	−	101.168i	1.27565	−	3.92606i
$665$	2.61803	+	1.90211i	0.101523	+	0.0737608i
$666$		0			0
$667$	1.36475	−	4.20025i	0.0528431	−	0.162634i
$668$	−15.3541	−	47.2551i	−0.594068	−	1.82835i
$669$		0			0
$670$	−50.8328			−1.96384
$671$	−5.12461	+	12.7598i	−0.197833	+	0.492585i
$672$		0			0
$673$	7.63525	−	5.54734i	0.294317	−	0.213834i	−0.430821	−	0.902438i	$-0.641776\pi$
$673$	7.63525	−	5.54734i	0.294317	−	0.213834i	0.725138	+	0.688603i	$0.241776\pi$
$674$	2.04508	+	6.29412i	0.0787737	+	0.242441i
$675$		0			0
$676$	27.0517	+	19.6542i	1.04045	+	0.755930i
$677$	−19.3713	−	14.0741i	−0.744500	−	0.540911i	0.149617	−	0.988744i	$-0.452196\pi$
$677$	−19.3713	−	14.0741i	−0.744500	−	0.540911i	−0.894117	+	0.447833i	$0.852196\pi$
$678$		0			0
$679$	−1.85410	−	5.70634i	−0.0711539	−	0.218989i
$680$	−36.2705	+	26.3521i	−1.39091	+	1.01056i
$681$		0			0
$682$	−14.0172	−	0.951057i	−0.536747	−	0.0364178i
$683$	−14.4721			−0.553761			−0.276880	−	0.960904i	$-0.589301\pi$
$683$	−14.4721			−0.553761			−0.276880	+	0.960904i	$0.589301\pi$
$684$		0			0
$685$	−6.38197	−	19.6417i	−0.243842	−	0.750470i
$686$	−10.5172	+	32.3687i	−0.401549	+	1.23584i
$687$		0			0
$688$	38.6976	+	28.1154i	1.47533	+	1.07189i
$689$	−5.41641	+	16.6700i	−0.206349	+	0.635076i
$690$		0			0
$691$	27.9894	−	20.3355i	1.06477	−	0.773597i	0.0898012	−	0.995960i	$-0.471377\pi$
$691$	27.9894	−	20.3355i	1.06477	−	0.773597i	0.974964	+	0.222362i	$0.0713768\pi$
$692$	−57.8115			−2.19766
$693$		0			0
$694$	−70.3951			−2.67216
$695$	9.70820	−	7.05342i	0.368253	−	0.267552i
$696$		0			0
$697$	6.57295	−	20.2295i	0.248968	−	0.766245i
$698$	−22.9894	−	16.7027i	−0.870160	−	0.632208i
$699$		0			0
$700$	−8.20820	+	25.2623i	−0.310241	+	0.954823i
$701$	12.8926	+	39.6794i	0.486947	+	1.49867i	0.829141	+	0.559040i	$0.188830\pi$
$701$	12.8926	+	39.6794i	0.486947	+	1.49867i	−0.342194	+	0.939629i	$0.611170\pi$
$702$		0			0
$703$	6.09017			0.229695
$704$	22.1631	+	18.5191i	0.835304	+	0.697965i
$705$		0			0
$706$	22.0623	−	16.0292i	0.830326	−	0.603267i
$707$	−0.145898	−	0.449028i	−0.00548706	−	0.0168874i
$708$		0			0
$709$	24.4615	+	17.7723i	0.918671	+	0.667453i	0.943193	−	0.332246i	$-0.107806\pi$
$709$	24.4615	+	17.7723i	0.918671	+	0.667453i	−0.0245221	+	0.999699i	$0.507806\pi$
$710$	−96.5755	−	70.1662i	−3.62441	−	2.63329i
$711$		0			0
$712$	25.9443	+	79.8483i	0.972303	+	2.99244i
$713$	3.11803	−	2.26538i	0.116771	−	0.0848393i
$714$		0			0
$715$	−6.47214	−	25.7315i	−0.242044	−	0.962305i
$716$	−111.374			−4.16224
$717$		0			0
$718$	13.0623	+	40.2016i	0.487481	+	1.50031i
$719$	9.14590	−	28.1482i	0.341084	−	1.04975i	−0.622562	−	0.782570i	$-0.713908\pi$
$719$	9.14590	−	28.1482i	0.341084	−	1.04975i	0.963647	−	0.267180i	$-0.0860917\pi$
$720$		0			0
$721$	−4.66312	−	3.38795i	−0.173664	−	0.126174i
$722$	14.5623	−	44.8182i	0.541953	−	1.66796i
$723$		0			0
$724$	82.8222	−	60.1738i	3.07806	−	2.23634i
$725$	10.1459			0.376809
$726$		0			0
$727$	−34.8328			−1.29188			−0.645939	−	0.763389i	$-0.723534\pi$
$727$	−34.8328			−1.29188			−0.645939	+	0.763389i	$0.723534\pi$
$728$	−14.9443	+	10.8576i	−0.553872	+	0.402411i
$729$		0			0
$730$	17.9443	−	55.2268i	0.664147	−	2.04404i
$731$	−7.28115	−	5.29007i	−0.269303	−	0.195660i
$732$		0			0
$733$	12.2148	−	37.5932i	0.451163	−	1.38854i	−0.424418	−	0.905466i	$-0.639521\pi$
$733$	12.2148	−	37.5932i	0.451163	−	1.38854i	0.875581	−	0.483071i	$-0.160479\pi$
$734$	−0.572949	−	1.76336i	−0.0211479	−	0.0650866i
$735$		0			0
$736$	−25.8541			−0.952995
$737$	−4.85410	−	19.2986i	−0.178803	−	0.710875i
$738$		0			0
$739$	19.8541	−	14.4248i	0.730345	−	0.530627i	−0.159328	−	0.987226i	$-0.550933\pi$
$739$	19.8541	−	14.4248i	0.730345	−	0.530627i	0.889673	+	0.456599i	$0.150933\pi$
$740$	29.5623	+	90.9834i	1.08673	+	3.34462i
$741$		0			0
$742$	15.0172	+	10.9106i	0.551300	+	0.400543i
$743$	−1.90983	−	1.38757i	−0.0700649	−	0.0509051i	0.552201	−	0.833711i	$-0.313788\pi$
$743$	−1.90983	−	1.38757i	−0.0700649	−	0.0509051i	−0.622266	+	0.782806i	$0.713788\pi$
$744$		0			0
$745$	7.18034	+	22.0988i	0.263067	+	0.809638i
$746$	54.3328	−	39.4751i	1.98927	−	1.44529i
$747$		0			0
$748$	−22.9058	−	19.1396i	−0.837518	−	0.699815i
$749$	15.0344			0.549347
$750$		0			0
$751$	15.2188	+	46.8388i	0.555344	+	1.70917i	0.695034	+	0.718977i	$0.255389\pi$
$751$	15.2188	+	46.8388i	0.555344	+	1.70917i	−0.139691	+	0.990195i	$0.544611\pi$
$752$	−18.1008	+	55.7086i	−0.660069	+	2.03148i
$753$		0			0
$754$	9.70820	+	7.05342i	0.353552	+	0.256871i
$755$	−11.3262	+	34.8586i	−0.412204	+	1.26863i
$756$		0			0
$757$	−8.89919	+	6.46564i	−0.323446	+	0.234998i	−0.737645	−	0.675189i	$-0.764062\pi$
$757$	−8.89919	+	6.46564i	−0.323446	+	0.234998i	0.414198	+	0.910187i	$0.364062\pi$
$758$	23.0344			0.836649
$759$		0			0
$760$	−24.1803			−0.877113
$761$	32.3435	−	23.4989i	1.17245	−	0.851834i	0.181149	−	0.983456i	$-0.442018\pi$
$761$	32.3435	−	23.4989i	1.17245	−	0.851834i	0.991300	+	0.131621i	$0.0420182\pi$
$762$		0			0
$763$	−4.28115	+	13.1760i	−0.154988	+	0.477004i
$764$	46.9058	+	34.0790i	1.69699	+	1.23294i
$765$		0			0
$766$	−10.6353	+	32.7319i	−0.384267	+	1.18265i
$767$	−0.472136	−	1.45309i	−0.0170478	−	0.0524679i
$768$		0			0
$769$	8.79837			0.317277			0.158639	−	0.987337i	$-0.449289\pi$
$769$	8.79837			0.317277			0.158639	+	0.987337i	$0.449289\pi$
$770$	−28.0344	−	1.90211i	−1.01029	−	0.0685474i
$771$		0			0
$772$	43.1976	−	31.3849i	1.55471	−	1.12957i
$773$	−2.36475	−	7.27794i	−0.0850540	−	0.261769i	0.899480	−	0.436961i	$-0.143945\pi$
$773$	−2.36475	−	7.27794i	−0.0850540	−	0.261769i	−0.984534	+	0.175192i	$0.943945\pi$
$774$		0			0
$775$	7.16312	+	5.20431i	0.257307	+	0.186944i
$776$	36.2705	+	26.3521i	1.30204	+	0.945984i
$777$		0			0
$778$	−7.00000	−	21.5438i	−0.250962	−	0.772382i
$779$	9.28115	−	6.74315i	0.332532	−	0.241599i
$780$		0			0
$781$	17.4164	−	43.3651i	0.623208	−	1.55172i
$782$	11.5623			0.413467
$783$		0			0
$784$	−18.2705	−	56.2308i	−0.652518	−	2.00824i
$785$	13.8541	−	42.6385i	0.494474	−	1.52183i
$786$		0			0
$787$	−29.1246	−	21.1603i	−1.03818	−	0.754282i	−0.0682508	−	0.997668i	$-0.521742\pi$
$787$	−29.1246	−	21.1603i	−1.03818	−	0.754282i	−0.969929	+	0.243386i	$0.921742\pi$
$788$	5.64590	−	17.3763i	0.201127	−	0.619005i
$789$		0			0
$790$	−65.5410	+	47.6183i	−2.33184	+	1.69418i
$791$	−12.7639			−0.453833
$792$		0			0
$793$	10.2492			0.363961
$794$	80.7492	−	58.6677i	2.86568	−	2.08204i
$795$		0			0
$796$	−20.7812	+	63.9578i	−0.736568	+	2.26692i
$797$	7.50000	+	5.44907i	0.265664	+	0.193016i	0.712640	−	0.701530i	$-0.247499\pi$
$797$	7.50000	+	5.44907i	0.265664	+	0.193016i	−0.446977	+	0.894546i	$0.647499\pi$
$798$		0			0
$799$	3.40576	−	10.4819i	0.120487	−	0.370822i
$800$	−18.3541	−	56.4881i	−0.648915	−	1.99716i
$801$		0			0
$802$	14.5623			0.514213
$803$	22.6803	+	1.53884i	0.800372	+	0.0543045i
$804$		0			0
$805$	6.23607	−	4.53077i	0.219793	−	0.159689i
$806$	3.23607	+	9.95959i	0.113986	+	0.350812i
$807$		0			0
$808$	2.85410	+	2.07363i	0.100407	+	0.0729499i
$809$	5.59017	+	4.06150i	0.196540	+	0.142795i	0.681703	−	0.731629i	$-0.261240\pi$
$809$	5.59017	+	4.06150i	0.196540	+	0.142795i	−0.485163	+	0.874424i	$0.661240\pi$
$810$		0			0
$811$	−15.9721	−	49.1572i	−0.560858	−	1.72614i	−0.679950	−	0.733259i	$-0.737998\pi$
$811$	−15.9721	−	49.1572i	−0.560858	−	1.72614i	0.119092	−	0.992883i	$-0.462002\pi$
$812$	7.28115	−	5.29007i	0.255518	−	0.185645i
$813$		0			0
$814$	−44.7877	+	28.1154i	−1.56981	+	0.985445i
$815$	23.5967			0.826558
$816$		0			0
$817$	−1.50000	−	4.61653i	−0.0524784	−	0.161512i
$818$	−7.07295	+	21.7683i	−0.247300	+	0.761111i
$819$		0			0
$820$	145.790	+	105.923i	5.09122	+	3.69899i
$821$	−4.08359	+	12.5680i	−0.142518	+	0.438626i	−0.996684	−	0.0813754i	$-0.974069\pi$
$821$	−4.08359	+	12.5680i	−0.142518	+	0.438626i	0.854165	+	0.520002i	$0.174069\pi$
$822$		0			0
$823$	45.0689	−	32.7445i	1.57100	−	1.14140i	0.644814	−	0.764340i	$-0.276935\pi$
$823$	45.0689	−	32.7445i	1.57100	−	1.14140i	0.926189	−	0.377061i	$-0.123065\pi$
$824$	43.0689			1.50038
$825$		0			0
$826$	−1.61803			−0.0562986
$827$	22.6246	−	16.4377i	0.786735	−	0.571596i	−0.120258	−	0.992743i	$-0.538372\pi$
$827$	22.6246	−	16.4377i	0.786735	−	0.571596i	0.906993	+	0.421146i	$0.138372\pi$
$828$		0			0
$829$	−7.27458	+	22.3888i	−0.252656	+	0.777597i	0.741626	+	0.670814i	$0.234055\pi$
$829$	−7.27458	+	22.3888i	−0.252656	+	0.777597i	−0.994282	+	0.106783i	$0.965945\pi$
$830$	−97.5755	−	70.8927i	−3.38689	−	2.46072i
$831$		0			0
$832$	6.65248	−	20.4742i	0.230633	−	0.709816i
$833$	3.43769	+	10.5801i	0.119109	+	0.366580i
$834$		0			0
$835$	−33.1246			−1.14632
$836$	−3.92705	−	15.6129i	−0.135820	−	0.539985i
$837$		0			0
$838$	−6.54508	+	4.75528i	−0.226096	+	0.164269i
$839$	−9.48936	−	29.2052i	−0.327609	−	1.00828i	−0.970249	−	0.242109i	$-0.922161\pi$
$839$	−9.48936	−	29.2052i	−0.327609	−	1.00828i	0.642640	−	0.766168i	$-0.277839\pi$
$840$		0			0
$841$	20.6803	+	15.0251i	0.713115	+	0.518108i
$842$	12.2082	+	8.86978i	0.420722	+	0.305673i
$843$		0			0
$844$	17.2918	+	53.2187i	0.595208	+	1.83186i
$845$	18.0344	−	13.1028i	0.620404	−	0.450750i
$846$		0			0
$847$	−1.95492	−	10.8249i	−0.0671717	−	0.371948i
$848$	−69.8673			−2.39925
$849$		0			0
$850$	8.20820	+	25.2623i	0.281539	+	0.866488i
$851$	4.48278	−	13.7966i	0.153668	−	0.472941i
$852$		0			0
$853$	44.9508	+	32.6587i	1.53909	+	1.11821i	0.950904	+	0.309485i	$0.100157\pi$
$853$	44.9508	+	32.6587i	1.53909	+	1.11821i	0.588184	+	0.808727i	$0.299843\pi$
$854$	3.35410	−	10.3229i	0.114775	−	0.353241i
$855$		0			0
$856$	−90.8845	+	66.0314i	−3.10637	+	2.25691i
$857$	−19.3607			−0.661348			−0.330674	−	0.943745i	$-0.607276\pi$
$857$	−19.3607			−0.661348			−0.330674	+	0.943745i	$0.607276\pi$
$858$		0			0
$859$	−12.4377			−0.424369			−0.212184	−	0.977230i	$-0.568058\pi$
$859$	−12.4377			−0.424369			−0.212184	+	0.977230i	$0.568058\pi$
$860$	61.6869	−	44.8182i	2.10351	−	1.52829i
$861$		0			0
$862$	−19.4721	+	59.9291i	−0.663224	+	2.04119i
$863$	33.5344	+	24.3642i	1.14153	+	0.829367i	0.987331	−	0.158674i	$-0.0507217\pi$
$863$	33.5344	+	24.3642i	1.14153	+	0.829367i	0.154195	+	0.988041i	$0.450722\pi$
$864$		0			0
$865$	−11.9098	+	36.6547i	−0.404946	+	1.24630i
$866$	22.4443	+	69.0764i	0.762687	+	2.34731i
$867$		0			0
$868$	7.85410			0.266586
$869$	−24.3369	−	20.3355i	−0.825572	−	0.689833i
$870$		0			0
$871$	−12.0000	+	8.71851i	−0.406604	+	0.295415i
$872$	−31.9894	−	98.4531i	−1.08330	−	3.33404i
$873$		0			0
$874$	5.04508	+	3.66547i	0.170653	+	0.123986i
$875$	1.23607	+	0.898056i	0.0417867	+	0.0303598i
$876$		0			0
$877$	−11.6180	−	35.7566i	−0.392313	−	1.20742i	−0.931034	−	0.364932i	$-0.881092\pi$
$877$	−11.6180	−	35.7566i	−0.392313	−	1.20742i	0.538721	−	0.842484i	$-0.318908\pi$
$878$	26.9164	−	19.5559i	0.908385	−	0.659980i
$879$		0			0
$880$	89.5755	−	56.2308i	3.01959	−	1.89554i
$881$	24.1803			0.814656			0.407328	−	0.913282i	$-0.366461\pi$
$881$	24.1803			0.814656			0.407328	+	0.913282i	$0.366461\pi$
$882$		0			0
$883$	−1.34346	−	4.13474i	−0.0452110	−	0.139145i	0.925903	−	0.377762i	$-0.123306\pi$
$883$	−1.34346	−	4.13474i	−0.0452110	−	0.139145i	−0.971114	+	0.238616i	$0.923306\pi$
$884$	−6.87539	+	21.1603i	−0.231244	+	0.711697i
$885$		0			0
$886$	6.85410	+	4.97980i	0.230268	+	0.167300i
$887$	7.73607	−	23.8092i	0.259752	−	0.799434i	−0.733104	−	0.680116i	$-0.761929\pi$
$887$	7.73607	−	23.8092i	0.259752	−	0.799434i	0.992856	−	0.119318i	$-0.0380707\pi$
$888$		0			0
$889$	7.73607	−	5.62058i	0.259459	−	0.188508i
$890$	95.1935			3.19089
$891$		0			0
$892$	109.249			3.65793
$893$	4.80902	−	3.49396i	0.160928	−	0.116921i
$894$		0			0
$895$	−22.9443	+	70.6152i	−0.766942	+	2.36041i
$896$	−0.881966	−	0.640786i	−0.0294644	−	0.0214072i
$897$		0			0
$898$	1.19098	−	3.66547i	0.0397436	−	0.122318i
$899$	−0.927051	−	2.85317i	−0.0309189	−	0.0951585i
$900$		0			0
$901$	13.1459			0.437953
$902$	−37.1246	+	92.4365i	−1.23611	+	3.07780i
$903$		0			0
$904$	77.1591	−	56.0593i	2.56627	−	1.86451i
$905$	−21.0902	−	64.9089i	−0.701061	−	2.15764i
$906$		0			0
$907$	33.5066	+	24.3440i	1.11257	+	0.808328i	0.983066	−	0.183251i	$-0.0586623\pi$
$907$	33.5066	+	24.3440i	1.11257	+	0.808328i	0.129502	+	0.991579i	$0.458662\pi$
$908$	56.4787	+	41.0342i	1.87431	+	1.36177i
$909$		0			0
$910$	6.47214	+	19.9192i	0.214549	+	0.660315i
$911$	−2.57295	+	1.86936i	−0.0852456	+	0.0619346i	−0.629592	−	0.776926i	$-0.716778\pi$
$911$	−2.57295	+	1.86936i	−0.0852456	+	0.0619346i	0.544346	+	0.838861i	$0.316778\pi$
$912$		0			0
$913$	17.5967	−	43.8141i	0.582367	−	1.45004i
$914$	2.61803			0.0865969
$915$		0			0
$916$	−18.2705	−	56.2308i	−0.603675	−	1.85792i
$917$	−5.18034	+	15.9434i	−0.171070	+	0.526499i
$918$		0			0
$919$	−45.1976	−	32.8380i	−1.49093	−	1.08322i	−0.973824	−	0.227303i	$-0.927009\pi$
$919$	−45.1976	−	32.8380i	−1.49093	−	1.08322i	−0.517106	−	0.855922i	$-0.672991\pi$
$920$	−17.7984	+	54.7778i	−0.586795	+	1.80597i
$921$		0			0
$922$	−48.4058	+	35.1688i	−1.59416	+	1.15822i
$923$	−34.8328			−1.14654
$924$		0			0
$925$	33.3262			1.09576
$926$	36.0066	−	26.1603i	1.18325	−	0.859681i
$927$		0			0
$928$	−6.21885	+	19.1396i	−0.204144	+	0.628290i
$929$	11.9164	+	8.65778i	0.390965	+	0.284052i	0.765851	−	0.643018i	$-0.222318\pi$
$929$	11.9164	+	8.65778i	0.390965	+	0.284052i	−0.374886	+	0.927071i	$0.622318\pi$
$930$		0			0
$931$	−1.85410	+	5.70634i	−0.0607657	+	0.187018i
$932$	43.6869	+	134.455i	1.43101	+	4.40420i
$933$		0			0
$934$	13.7082			0.448546
$935$	−16.8541	+	10.5801i	−0.551188	+	0.346007i
$936$		0			0
$937$	−4.88197	+	3.54696i	−0.159487	+	0.115874i	−0.664666	−	0.747140i	$-0.731426\pi$
$937$	−4.88197	+	3.54696i	−0.159487	+	0.115874i	0.505179	+	0.863014i	$0.331426\pi$
$938$	4.85410	+	14.9394i	0.158492	+	0.487788i
$939$		0			0
$940$	75.5410	+	54.8838i	2.46388	+	1.79011i
$941$	34.1074	+	24.7805i	1.11187	+	0.807820i	0.982957	−	0.183836i	$-0.0588515\pi$
$941$	34.1074	+	24.7805i	1.11187	+	0.807820i	0.128912	+	0.991656i	$0.458851\pi$
$942$		0			0
$943$	−8.44427	−	25.9888i	−0.274983	−	0.846312i
$944$	4.92705	−	3.57971i	0.160362	−	0.116510i
$945$		0			0
$946$	32.3435	+	27.0256i	1.05158	+	0.878678i
$947$	23.2918			0.756882			0.378441	−	0.925625i	$-0.376460\pi$
$947$	23.2918			0.756882			0.378441	+	0.925625i	$0.376460\pi$
$948$		0			0
$949$	−5.23607	−	16.1150i	−0.169970	−	0.523114i
$950$	−4.42705	+	13.6251i	−0.143633	+	0.442055i
$951$		0			0
$952$	11.2082	+	8.14324i	0.363260	+	0.263924i
$953$	−14.6803	+	45.1814i	−0.475543	+	1.46357i	0.369681	+	0.929159i	$0.379467\pi$
$953$	−14.6803	+	45.1814i	−0.475543	+	1.46357i	−0.845224	+	0.534412i	$0.820533\pi$
$954$		0			0
$955$	31.2705	−	22.7194i	1.01189	−	0.735181i
$956$	7.41641			0.239864
$957$		0			0
$958$	42.5066			1.37333
$959$	−5.16312	+	3.75123i	−0.166726	+	0.121133i
$960$		0			0
$961$	−8.77051	+	26.9929i	−0.282920	+	0.870737i
$962$	31.8885	+	23.1684i	1.02813	+	0.746979i
$963$		0			0
$964$	40.2492	−	123.874i	1.29634	−	3.98972i
$965$	−11.0000	−	33.8545i	−0.354103	−	1.08982i
$966$		0			0
$967$	−32.4853			−1.04466			−0.522328	−	0.852744i	$-0.674936\pi$
$967$	−32.4853			−1.04466			−0.522328	+	0.852744i	$0.674936\pi$
$968$	59.3607	+	56.8514i	1.90792	+	1.82727i
$969$		0			0
$970$	41.1246	−	29.8788i	1.32043	−	0.959350i
$971$	−7.50000	−	23.0826i	−0.240686	−	0.740757i	−0.996316	−	0.0857575i	$-0.972669\pi$
$971$	−7.50000	−	23.0826i	−0.240686	−	0.740757i	0.755630	−	0.654999i	$-0.227331\pi$
$972$		0			0
$973$	−3.00000	−	2.17963i	−0.0961756	−	0.0698757i
$974$	71.9681	+	52.2879i	2.30601	+	1.67541i
$975$		0			0
$976$	12.6246	+	38.8546i	0.404104	+	1.24370i
$977$	−16.3713	+	11.8945i	−0.523765	+	0.380538i	−0.818020	−	0.575189i	$-0.804928\pi$
$977$	−16.3713	+	11.8945i	−0.523765	+	0.380538i	0.294255	+	0.955727i	$0.404928\pi$
$978$		0			0
$979$	9.09017	+	36.1401i	0.290523	+	1.15504i
$980$	−94.2492			−3.01068
$981$		0			0
$982$	6.73607	+	20.7315i	0.214957	+	0.661568i
$983$	15.9894	−	49.2102i	0.509981	−	1.56956i	−0.282251	−	0.959341i	$-0.591081\pi$
$983$	15.9894	−	49.2102i	0.509981	−	1.56956i	0.792232	−	0.610220i	$-0.208919\pi$
$984$		0			0
$985$	−9.85410	−	7.15942i	−0.313978	−	0.228118i
$986$	2.78115	−	8.55951i	0.0885700	−	0.272590i
$987$		0			0
$988$	−9.70820	+	7.05342i	−0.308859	+	0.224399i
$989$	−11.5623			−0.367660
$990$		0			0
$991$	−28.5967			−0.908406			−0.454203	−	0.890898i	$-0.650076\pi$
$991$	−28.5967			−0.908406			−0.454203	+	0.890898i	$0.650076\pi$
$992$	−14.2082	+	10.3229i	−0.451111	+	0.327751i
$993$		0			0
$994$	−11.3992	+	35.0831i	−0.361560	+	1.11277i
$995$	36.2705	+	26.3521i	1.14985	+	0.835417i
$996$		0			0
$997$	2.97214	−	9.14729i	0.0941285	−	0.289698i	−0.892897	−	0.450261i	$-0.851331\pi$
$997$	2.97214	−	9.14729i	0.0941285	−	0.289698i	0.987026	+	0.160563i	$0.0513310\pi$
$998$	−9.37132	−	28.8420i	−0.296644	−	0.912976i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.b.487.1		4
3.2	odd	2		891.2.f.a.487.1		4
9.2	odd	6		297.2.n.a.91.1		8
9.4	even	3		99.2.m.a.25.1	yes	8
9.5	odd	6		297.2.n.a.289.1		8
9.7	even	3		99.2.m.a.58.1	yes	8
11.2	odd	10		9801.2.a.bc.1.2		2
11.4	even	5	inner	891.2.f.b.730.1		4
11.9	even	5		9801.2.a.n.1.1		2
33.2	even	10		9801.2.a.m.1.1		2
33.20	odd	10		9801.2.a.bb.1.2		2
33.26	odd	10		891.2.f.a.730.1		4
99.4	even	15		99.2.m.a.70.1	yes	8
99.13	odd	30		1089.2.e.d.727.1		4
99.31	even	15		1089.2.e.g.727.2		4
99.59	odd	30		297.2.n.a.235.1		8
99.70	even	15		99.2.m.a.4.1	✓	8
99.79	odd	30		1089.2.e.d.364.1		4
99.92	odd	30		297.2.n.a.37.1		8
99.97	even	15		1089.2.e.g.364.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.4.1	✓	8	99.70	even	15
99.2.m.a.25.1	yes	8	9.4	even	3
99.2.m.a.58.1	yes	8	9.7	even	3
99.2.m.a.70.1	yes	8	99.4	even	15
297.2.n.a.37.1		8	99.92	odd	30
297.2.n.a.91.1		8	9.2	odd	6
297.2.n.a.235.1		8	99.59	odd	30
297.2.n.a.289.1		8	9.5	odd	6
891.2.f.a.487.1		4	3.2	odd	2
891.2.f.a.730.1		4	33.26	odd	10
891.2.f.b.487.1		4	1.1	even	1	trivial
891.2.f.b.730.1		4	11.4	even	5	inner
1089.2.e.d.364.1		4	99.79	odd	30
1089.2.e.d.727.1		4	99.13	odd	30
1089.2.e.g.364.2		4	99.97	even	15
1089.2.e.g.727.2		4	99.31	even	15
9801.2.a.m.1.1		2	33.2	even	10
9801.2.a.n.1.1		2	11.9	even	5
9801.2.a.bb.1.2		2	33.20	odd	10
9801.2.a.bc.1.2		2	11.2	odd	10

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11803 - 1.53884i) q^{2} +(1.50000 - 4.61653i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-2.30902 - 7.10642i) q^{8} -8.47214 q^{10} +(-0.809017 - 3.21644i) q^{11} +(-2.00000 + 1.45309i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-7.97214 - 5.79210i) q^{16} +(1.50000 + 1.08981i) q^{17} +(0.309017 + 0.951057i) q^{19} +(-12.7082 + 9.23305i) q^{20} +(-6.66312 - 5.56758i) q^{22} +2.38197 q^{23} +(1.69098 + 5.20431i) q^{25} +(-2.00000 + 6.15537i) q^{26} +(3.92705 + 2.85317i) q^{28} +(0.572949 - 1.76336i) q^{29} +(1.30902 - 0.951057i) q^{31} -10.8541 q^{32} +4.85410 q^{34} +(2.61803 - 1.90211i) q^{35} +(1.88197 - 5.79210i) q^{37} +(2.11803 + 1.53884i) q^{38} +(-7.47214 + 22.9969i) q^{40} +(-3.54508 - 10.9106i) q^{41} -4.85410 q^{43} +(-16.0623 - 1.08981i) q^{44} +(5.04508 - 3.66547i) q^{46} +(-1.83688 - 5.65334i) q^{47} +(4.85410 + 3.52671i) q^{49} +(11.5902 + 8.42075i) q^{50} +(3.70820 + 11.4127i) q^{52} +(5.73607 - 4.16750i) q^{53} +(-4.00000 + 9.95959i) q^{55} +7.47214 q^{56} +(-1.50000 - 4.61653i) q^{58} +(-0.190983 + 0.587785i) q^{59} +(-3.35410 - 2.43690i) q^{61} +(1.30902 - 4.02874i) q^{62} +(-7.04508 + 5.11855i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(7.28115 - 5.29007i) q^{68} +(2.61803 - 8.05748i) q^{70} +(11.3992 + 8.28199i) q^{71} +(-2.11803 + 6.51864i) q^{73} +(-4.92705 - 15.1639i) q^{74} +4.85410 q^{76} +(3.30902 + 0.224514i) q^{77} +(7.73607 - 5.62058i) q^{79} +(9.85410 + 30.3278i) q^{80} +(-24.2984 - 17.6538i) q^{82} +(11.5172 + 8.36775i) q^{83} +(-1.85410 - 5.70634i) q^{85} +(-10.2812 + 7.46969i) q^{86} +(-20.9894 + 13.1760i) q^{88} -11.2361 q^{89} +(-0.763932 - 2.35114i) q^{91} +(3.57295 - 10.9964i) q^{92} +(-12.5902 - 9.14729i) q^{94} +(1.00000 - 3.07768i) q^{95} +(-4.85410 + 3.52671i) q^{97} +15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^4 - 6 * q^5 + q^7 - 7 * q^8 - 16 * q^10 - q^11 - 8 * q^13 + q^14 - 14 * q^16 + 6 * q^17 - q^19 - 24 * q^20 - 11 * q^22 + 14 * q^23 + 9 * q^25 - 8 * q^26 + 9 * q^28 + 9 * q^29 + 3 * q^31 - 30 * q^32 + 6 * q^34 + 6 * q^35 + 12 * q^37 + 4 * q^38 - 12 * q^40 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 9 * q^46 - 23 * q^47 + 6 * q^49 + 24 * q^50 - 12 * q^52 + 14 * q^53 - 16 * q^55 + 12 * q^56 - 6 * q^58 - 3 * q^59 + 3 * q^62 - 17 * q^64 + 32 * q^65 + 24 * q^67 + 9 * q^68 + 6 * q^70 + 21 * q^71 - 4 * q^73 - 13 * q^74 + 6 * q^76 + 11 * q^77 + 22 * q^79 + 26 * q^80 - 48 * q^82 + 17 * q^83 + 6 * q^85 - 21 * q^86 - 37 * q^88 - 36 * q^89 - 12 * q^91 + 21 * q^92 - 28 * q^94 + 4 * q^95 - 6 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more