LMFDB - Embedded newform 720.2.bm.h.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (of order $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39033 - 0.258835i) q^{2} +(1.86601 + 0.719729i) q^{4} +(-2.19925 + 0.404088i) q^{5} -1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} +O(q^{10})$	\(q+(-1.39033 - 0.258835i) q^{2} +(1.86601 + 0.719729i) q^{4} +(-2.19925 + 0.404088i) q^{5} -1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} +(3.16227 + 0.00742837i) q^{10} +(0.331965 - 0.331965i) q^{11} +(0.0310184 - 0.0310184i) q^{13} +(2.52438 + 0.469959i) q^{14} +(2.96398 + 2.68604i) q^{16} -1.00474i q^{17} +(-2.08203 - 2.08203i) q^{19} +(-4.39466 - 0.828833i) q^{20} +(-0.547464 + 0.375616i) q^{22} +6.22794 q^{23} +(4.67343 - 1.77739i) q^{25} +(-0.0511543 + 0.0350971i) q^{26} +(-3.38806 - 1.30679i) q^{28} +(6.28959 + 6.28959i) q^{29} +7.11301 q^{31} +(-3.42566 - 4.50165i) q^{32} +(-0.260063 + 1.39692i) q^{34} +(3.99313 - 0.733693i) q^{35} +(0.0723513 + 0.0723513i) q^{37} +(2.35580 + 3.43360i) q^{38} +(5.89548 + 2.28984i) q^{40} -3.06050i q^{41} +(-3.78495 - 3.78495i) q^{43} +(0.858375 - 0.380525i) q^{44} +(-8.65886 - 1.61201i) q^{46} +10.0476i q^{47} -3.70333 q^{49} +(-6.95763 + 1.26150i) q^{50} +(0.0802055 - 0.0355558i) q^{52} +(7.04636 + 7.04636i) q^{53} +(-0.595932 + 0.864219i) q^{55} +(4.37227 + 2.69382i) q^{56} +(-7.11661 - 10.3725i) q^{58} +(6.68042 - 6.68042i) q^{59} +(2.89442 + 2.89442i) q^{61} +(-9.88940 - 1.84109i) q^{62} +(3.59760 + 7.14544i) q^{64} +(-0.0556832 + 0.0807515i) q^{65} +(0.150837 - 0.150837i) q^{67} +(0.723143 - 1.87486i) q^{68} +(-5.74165 - 0.0134875i) q^{70} -14.5503i q^{71} +15.0323 q^{73} +(-0.0818648 - 0.119319i) q^{74} +(-2.38659 - 5.38358i) q^{76} +(-0.602741 + 0.602741i) q^{77} +15.5985 q^{79} +(-7.60394 - 4.70957i) q^{80} +(-0.792162 + 4.25508i) q^{82} +(5.48985 - 5.48985i) q^{83} +(0.406005 + 2.20969i) q^{85} +(4.28263 + 6.24198i) q^{86} +(-1.29191 + 0.306877i) q^{88} -14.3520i q^{89} +(-0.0563193 + 0.0563193i) q^{91} +(11.6214 + 4.48242i) q^{92} +(2.60066 - 13.9694i) q^{94} +(5.42023 + 3.73758i) q^{95} +13.5585i q^{97} +(5.14883 + 0.958550i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.39033	−	0.258835i	−0.983108	−	0.183024i
$2$	−1.39033	−	0.258835i	−0.983108	−	0.183024i
$3$		0			0
$3$		0			0
$4$	1.86601	+	0.719729i	0.933005	+	0.359864i
$5$	−2.19925	+	0.404088i	−0.983536	+	0.180714i
$5$	−2.19925	+	0.404088i	−0.983536	+	0.180714i
$6$		0			0
$7$	−1.81567			−0.686260			−0.343130	−	0.939288i	$-0.611487\pi$
$7$	−1.81567			−0.686260			−0.343130	+	0.939288i	$0.611487\pi$
$8$	−2.40807	−	1.48364i	−0.851381	−	0.524548i
$9$		0			0
$10$	3.16227	+	0.00742837i	0.999997	+	0.00234906i
$11$	0.331965	−	0.331965i	0.100091	−	0.100091i	−0.655288	−	0.755379i	$-0.727453\pi$
$11$	0.331965	−	0.331965i	0.100091	−	0.100091i	0.755379	+	0.655288i	$0.227453\pi$
$12$		0			0
$13$	0.0310184	−	0.0310184i	0.00860296	−	0.00860296i	−0.702792	−	0.711395i	$-0.748064\pi$
$13$	0.0310184	−	0.0310184i	0.00860296	−	0.00860296i	0.711395	+	0.702792i	$0.248064\pi$
$14$	2.52438	+	0.469959i	0.674668	+	0.125602i
$15$		0			0
$16$	2.96398	+	2.68604i	0.740995	+	0.671510i
$17$		−	1.00474i		−	0.243686i	−0.992549	−	0.121843i	$-0.961120\pi$
$17$		−	1.00474i		−	0.243686i	0.992549	−	0.121843i	$-0.0388805\pi$
$18$		0			0
$19$	−2.08203	−	2.08203i	−0.477650	−	0.477650i	0.426729	−	0.904379i	$-0.359666\pi$
$19$	−2.08203	−	2.08203i	−0.477650	−	0.477650i	−0.904379	+	0.426729i	$0.859666\pi$
$20$	−4.39466	−	0.828833i	−0.982676	−	0.185333i
$21$		0			0
$22$	−0.547464	+	0.375616i	−0.116720	+	0.0800815i
$23$	6.22794			1.29861			0.649307	−	0.760526i	$-0.275059\pi$
$23$	6.22794			1.29861			0.649307	+	0.760526i	$0.275059\pi$
$24$		0			0
$25$	4.67343	−	1.77739i	0.934685	−	0.355477i
$26$	−0.0511543	+	0.0350971i	−0.0100322	+	0.00688310i
$27$		0			0
$28$	−3.38806	−	1.30679i	−0.640284	−	0.246961i
$29$	6.28959	+	6.28959i	1.16795	+	1.16795i	0.982690	+	0.185258i	$0.0593120\pi$
$29$	6.28959	+	6.28959i	1.16795	+	1.16795i	0.185258	+	0.982690i	$0.440688\pi$
$30$		0			0
$31$	7.11301			1.27753			0.638767	−	0.769400i	$-0.279445\pi$
$31$	7.11301			1.27753			0.638767	+	0.769400i	$0.279445\pi$
$32$	−3.42566	−	4.50165i	−0.605576	−	0.795787i
$33$		0			0
$34$	−0.260063	+	1.39692i	−0.0446004	+	0.239570i
$35$	3.99313	−	0.733693i	0.674961	−	0.124017i
$36$		0			0
$37$	0.0723513	+	0.0723513i	0.0118945	+	0.0118945i	0.713029	−	0.701135i	$-0.247323\pi$
$37$	0.0723513	+	0.0723513i	0.0118945	+	0.0118945i	−0.701135	+	0.713029i	$0.747323\pi$
$38$	2.35580	+	3.43360i	0.382161	+	0.557003i
$39$		0			0
$40$	5.89548	+	2.28984i	0.932157	+	0.362055i
$41$		−	3.06050i		−	0.477969i	−0.971023	−	0.238985i	$-0.923185\pi$
$41$		−	3.06050i		−	0.477969i	0.971023	−	0.238985i	$-0.0768145\pi$
$42$		0			0
$43$	−3.78495	−	3.78495i	−0.577199	−	0.577199i	0.356932	−	0.934131i	$-0.383823\pi$
$43$	−3.78495	−	3.78495i	−0.577199	−	0.577199i	−0.934131	+	0.356932i	$0.883823\pi$
$44$	0.858375	−	0.380525i	0.129405	−	0.0573663i
$45$		0			0
$46$	−8.65886	−	1.61201i	−1.27668	−	0.237677i
$47$			10.0476i			1.46559i	0.680450	+	0.732795i	$0.261785\pi$
$47$			10.0476i			1.46559i	−0.680450	+	0.732795i	$0.738215\pi$
$48$		0			0
$49$	−3.70333			−0.529047
$50$	−6.95763	+	1.26150i	−0.983958	+	0.178403i
$51$		0			0
$52$	0.0802055	−	0.0355558i	0.0111225	−	0.00493070i
$53$	7.04636	+	7.04636i	0.967892	+	0.967892i	0.999500	−	0.0316087i	$-0.0100630\pi$
$53$	7.04636	+	7.04636i	0.967892	+	0.967892i	−0.0316087	+	0.999500i	$0.510063\pi$
$54$		0			0
$55$	−0.595932	+	0.864219i	−0.0803555	+	0.116531i
$56$	4.37227	+	2.69382i	0.584269	+	0.359976i
$57$		0			0
$58$	−7.11661	−	10.3725i	−0.934457	−	1.36198i
$59$	6.68042	−	6.68042i	0.869717	−	0.869717i	−0.122724	−	0.992441i	$-0.539163\pi$
$59$	6.68042	−	6.68042i	0.869717	−	0.869717i	0.992441	+	0.122724i	$0.0391629\pi$
$60$		0			0
$61$	2.89442	+	2.89442i	0.370592	+	0.370592i	0.867693	−	0.497101i	$-0.165602\pi$
$61$	2.89442	+	2.89442i	0.370592	+	0.370592i	−0.497101	+	0.867693i	$0.665602\pi$
$62$	−9.88940	−	1.84109i	−1.25596	−	0.233819i
$63$		0			0
$64$	3.59760	+	7.14544i	0.449699	+	0.893180i
$65$	−0.0556832	+	0.0807515i	−0.00690665	+	0.0100160i
$66$		0			0
$67$	0.150837	−	0.150837i	0.0184276	−	0.0184276i	−0.697833	−	0.716261i	$-0.745852\pi$
$67$	0.150837	−	0.150837i	0.0184276	−	0.0184276i	0.716261	+	0.697833i	$0.245852\pi$
$68$	0.723143	−	1.87486i	0.0876940	−	0.227360i
$69$		0			0
$70$	−5.74165	−	0.0134875i	−0.686258	−	0.00161206i
$71$		−	14.5503i		−	1.72680i	−0.504520	−	0.863400i	$-0.668331\pi$
$71$		−	14.5503i		−	1.72680i	0.504520	−	0.863400i	$-0.331669\pi$
$72$		0			0
$73$	15.0323			1.75939			0.879697	−	0.475534i	$-0.157745\pi$
$73$	15.0323			1.75939			0.879697	+	0.475534i	$0.157745\pi$
$74$	−0.0818648	−	0.119319i	−0.00951659	−	0.0138705i
$75$		0			0
$76$	−2.38659	−	5.38358i	−0.273760	−	0.617539i
$77$	−0.602741	+	0.602741i	−0.0686887	+	0.0686887i
$78$		0			0
$79$	15.5985			1.75497			0.877487	−	0.479601i	$-0.159219\pi$
$79$	15.5985			1.75497			0.877487	+	0.479601i	$0.159219\pi$
$80$	−7.60394	−	4.70957i	−0.850147	−	0.526546i
$81$		0			0
$82$	−0.792162	+	4.25508i	−0.0874797	+	0.469895i
$83$	5.48985	−	5.48985i	0.602590	−	0.602590i	−0.338409	−	0.940999i	$-0.609889\pi$
$83$	5.48985	−	5.48985i	0.602590	−	0.602590i	0.940999	+	0.338409i	$0.109889\pi$
$84$		0			0
$85$	0.406005	+	2.20969i	0.0440375	+	0.239674i
$86$	4.28263	+	6.24198i	0.461808	+	0.673090i
$87$		0			0
$88$	−1.29191	+	0.306877i	−0.137718	+	0.0327132i
$89$		−	14.3520i		−	1.52131i	−0.649157	−	0.760655i	$-0.724878\pi$
$89$		−	14.3520i		−	1.52131i	0.649157	−	0.760655i	$-0.275122\pi$
$90$		0			0
$91$	−0.0563193	+	0.0563193i	−0.00590387	+	0.00590387i
$92$	11.6214	+	4.48242i	1.21161	+	0.467325i
$93$		0			0
$94$	2.60066	−	13.9694i	0.268238	−	1.44083i
$95$	5.42023	+	3.73758i	0.556104	+	0.383468i
$96$		0			0
$97$			13.5585i			1.37666i	0.725399	+	0.688329i	$0.241655\pi$
$97$			13.5585i			1.37666i	−0.725399	+	0.688329i	$0.758345\pi$
$98$	5.14883	+	0.958550i	0.520111	+	0.0968281i
$99$		0			0
$100$	9.99989	+	0.0469810i	0.999989	+	0.00469810i
$101$	−10.5132	+	10.5132i	−1.04610	+	1.04610i	−0.0472186	+	0.998885i	$0.515036\pi$
$101$	−10.5132	+	10.5132i	−1.04610	+	1.04610i	−0.998885	+	0.0472186i	$0.984964\pi$
$102$		0			0
$103$	6.14387			0.605373			0.302687	−	0.953090i	$-0.402116\pi$
$103$	6.14387			0.605373			0.302687	+	0.953090i	$0.402116\pi$
$104$	−0.120715	+	0.0286742i	−0.0118371	+	0.00281174i
$105$		0			0
$106$	−7.97289	−	11.6206i	−0.774395	−	1.12869i
$107$	−6.91512	−	6.91512i	−0.668510	−	0.668510i	0.288861	−	0.957371i	$-0.406723\pi$
$107$	−6.91512	−	6.91512i	−0.668510	−	0.668510i	−0.957371	+	0.288861i	$0.906723\pi$
$108$		0			0
$109$	−6.15941	−	6.15941i	−0.589964	−	0.589964i	0.347657	−	0.937622i	$-0.386977\pi$
$109$	−6.15941	−	6.15941i	−0.589964	−	0.589964i	−0.937622	+	0.347657i	$0.886977\pi$
$110$	1.05223	−	1.04730i	0.100326	−	0.0998559i
$111$		0			0
$112$	−5.38162	−	4.87697i	−0.508516	−	0.460831i
$113$			2.13102i			0.200470i	0.994964	+	0.100235i	$0.0319594\pi$
$113$			2.13102i			0.200470i	−0.994964	+	0.100235i	$0.968041\pi$
$114$		0			0
$115$	−13.6968	+	2.51664i	−1.27723	+	0.234678i
$116$	7.20964	+	16.2632i	0.669398	+	1.51000i
$117$		0			0
$118$	−11.0171	+	7.55884i	−1.01421	+	0.695847i
$119$			1.82429i			0.167232i
$120$		0			0
$121$			10.7796i			0.979963i
$122$	−3.27501	−	4.77336i	−0.296505	−	0.432159i
$123$		0			0
$124$	13.2729	+	5.11944i	1.19195	+	0.459739i
$125$	−9.55982	+	5.79740i	−0.855056	+	0.518535i
$126$		0			0
$127$		−	10.5491i		−	0.936077i	−0.883708	−	0.468039i	$-0.844961\pi$
$127$		−	10.5491i		−	0.936077i	0.883708	−	0.468039i	$-0.155039\pi$
$128$	−3.15234	−	10.8657i	−0.278630	−	0.960398i
$129$		0			0
$130$	0.0983190	−	0.0978582i	0.00862315	−	0.00858273i
$131$	−5.82338	−	5.82338i	−0.508791	−	0.508791i	0.405364	−	0.914155i	$-0.367145\pi$
$131$	−5.82338	−	5.82338i	−0.508791	−	0.508791i	−0.914155	+	0.405364i	$0.867145\pi$
$132$		0			0
$133$	3.78028	+	3.78028i	0.327792	+	0.327792i
$134$	−0.248754	+	0.170670i	−0.0214890	+	0.0147437i
$135$		0			0
$136$	−1.49068	+	2.41949i	−0.127825	+	0.207470i
$137$	15.6554			1.33753			0.668764	−	0.743475i	$-0.266824\pi$
$137$	15.6554			1.33753			0.668764	+	0.743475i	$0.266824\pi$
$138$		0			0
$139$	−1.14177	+	1.14177i	−0.0968440	+	0.0968440i	−0.753869	−	0.657025i	$-0.771815\pi$
$139$	−1.14177	+	1.14177i	−0.0968440	+	0.0968440i	0.657025	+	0.753869i	$0.271815\pi$
$140$	7.97927	+	1.50489i	0.674371	+	0.127186i
$141$		0			0
$142$	−3.76611	+	20.2296i	−0.316045	+	1.69763i
$143$		−	0.0205941i		−	0.00172216i
$144$		0			0
$145$	−16.3740	−	11.2908i	−1.35978	−	0.937654i
$146$	−20.8997	−	3.89087i	−1.72968	−	0.322011i
$147$		0			0
$148$	0.0829349	+	0.187081i	0.00681720	+	0.0153780i
$149$	1.81817	−	1.81817i	0.148951	−	0.148951i	−0.628698	−	0.777649i	$-0.716412\pi$
$149$	1.81817	−	1.81817i	0.148951	−	0.148951i	0.777649	+	0.628698i	$0.216412\pi$
$150$		0			0
$151$		−	11.2409i		−	0.914774i	−0.889268	−	0.457387i	$-0.848785\pi$
$151$		−	11.2409i		−	0.914774i	0.889268	−	0.457387i	$-0.151215\pi$
$152$	1.92468	+	8.10266i	0.156112	+	0.657212i
$153$		0			0
$154$	0.994016	−	0.681995i	0.0801001	−	0.0549567i
$155$	−15.6433	+	2.87429i	−1.25650	+	0.230868i
$156$		0			0
$157$	−14.8194	+	14.8194i	−1.18272	+	1.18272i	−0.203681	+	0.979037i	$0.565291\pi$
$157$	−14.8194	+	14.8194i	−1.18272	+	1.18272i	−0.979037	+	0.203681i	$0.934709\pi$
$158$	−21.6871	−	4.03744i	−1.72533	−	0.321202i
$159$		0			0
$160$	9.35295	+	8.51600i	0.739416	+	0.673249i
$161$	−11.3079			−0.891187
$162$		0			0
$163$	6.87622	−	6.87622i	0.538587	−	0.538587i	−0.384527	−	0.923114i	$-0.625635\pi$
$163$	6.87622	−	6.87622i	0.538587	−	0.538587i	0.923114	+	0.384527i	$0.125635\pi$
$164$	2.20273	−	5.71091i	0.172004	−	0.445947i
$165$		0			0
$166$	−9.05365	+	6.21172i	−0.702699	+	0.482123i
$167$	−12.8174			−0.991838			−0.495919	−	0.868369i	$-0.665169\pi$
$167$	−12.8174			−0.991838			−0.495919	+	0.868369i	$0.665169\pi$
$168$		0			0
$169$			12.9981i			0.999852i
$170$	0.00746361	−	3.17727i	0.000572433	−	0.243686i
$171$		0			0
$172$	−4.33861	−	9.78688i	−0.330816	−	0.746243i
$173$	−5.88931	+	5.88931i	−0.447756	+	0.447756i	−0.894608	−	0.446852i	$-0.852545\pi$
$173$	−5.88931	+	5.88931i	−0.447756	+	0.447756i	0.446852	+	0.894608i	$0.352545\pi$
$174$		0			0
$175$	−8.48542	+	3.22715i	−0.641437	+	0.243950i
$176$	1.87561	−	0.0922665i	0.141379	−	0.00695485i
$177$		0			0
$178$	−3.71479	+	19.9540i	−0.278436	+	1.49561i
$179$	10.1383	+	10.1383i	0.757769	+	0.757769i	0.975916	−	0.218147i	$-0.0700011\pi$
$179$	10.1383	+	10.1383i	0.757769	+	0.757769i	−0.218147	+	0.975916i	$0.570001\pi$
$180$		0			0
$181$	−10.8678	+	10.8678i	−0.807798	+	0.807798i	−0.984300	−	0.176503i	$-0.943522\pi$
$181$	−10.8678	+	10.8678i	−0.807798	+	0.807798i	0.176503	+	0.984300i	$0.443522\pi$
$182$	0.0928796	−	0.0637248i	0.00688469	−	0.00472360i
$183$		0			0
$184$	−14.9973	−	9.24005i	−1.10562	−	0.681185i
$185$	−0.188355	−	0.129882i	−0.0138481	−	0.00954915i
$186$		0			0
$187$	−0.333540	−	0.333540i	−0.0243909	−	0.0243909i
$188$	−7.23153	+	18.7489i	−0.527414	+	1.36740i
$189$		0			0
$190$	−6.56847	−	6.59940i	−0.476527	−	0.478771i
$191$	1.57307			0.113823			0.0569116	−	0.998379i	$-0.481875\pi$
$191$	1.57307			0.113823			0.0569116	+	0.998379i	$0.481875\pi$
$192$		0			0
$193$		−	3.91815i		−	0.282034i	−0.990007	−	0.141017i	$-0.954963\pi$
$193$		−	3.91815i		−	0.282034i	0.990007	−	0.141017i	$-0.0450373\pi$
$194$	3.50941	−	18.8507i	0.251961	−	1.35340i
$195$		0			0
$196$	−6.91045	−	2.66539i	−0.493603	−	0.190385i
$197$	−2.72966	−	2.72966i	−0.194480	−	0.194480i	0.603149	−	0.797629i	$-0.293913\pi$
$197$	−2.72966	−	2.72966i	−0.194480	−	0.194480i	−0.797629	+	0.603149i	$0.793913\pi$
$198$		0			0
$199$		−	19.6851i		−	1.39544i	−0.716371	−	0.697719i	$-0.754198\pi$
$199$		−	19.6851i		−	1.39544i	0.716371	−	0.697719i	$-0.245802\pi$
$200$	−13.8909	−	2.65364i	−0.982238	−	0.187640i
$201$		0			0
$202$	17.3380	−	11.8956i	1.21989	−	0.836971i
$203$	−11.4198	−	11.4198i	−0.801516	−	0.801516i
$204$		0			0
$205$	1.23671	+	6.73080i	0.0863756	+	0.470100i
$206$	−8.54198	−	1.59025i	−0.595148	−	0.110798i
$207$		0			0
$208$	0.175255	−	0.00862127i	0.0121517	−	0.000597778i
$209$	−1.38232			−0.0956172
$210$		0			0
$211$	1.93798	+	1.93798i	0.133416	+	0.133416i	0.770661	−	0.637245i	$-0.219926\pi$
$211$	1.93798	+	1.93798i	0.133416	+	0.133416i	−0.637245	+	0.770661i	$0.719926\pi$
$212$	8.07710	+	18.2200i	0.554738	+	1.25136i
$213$		0			0
$214$	7.82439	+	11.4041i	0.534864	+	0.779571i
$215$	9.85351	+	6.79460i	0.672004	+	0.463388i
$216$		0			0
$217$	−12.9149			−0.876721
$218$	6.96931	+	10.1578i	0.472021	+	0.687976i
$219$		0			0
$220$	−1.73402	+	1.18373i	−0.116907	+	0.0798071i
$221$	−0.0311656	−	0.0311656i	−0.00209642	−	0.00209642i
$222$		0			0
$223$			9.22040i			0.617443i	0.951152	+	0.308722i	$0.0999012\pi$
$223$			9.22040i			0.617443i	−0.951152	+	0.308722i	$0.900099\pi$
$224$	6.21988	+	8.17353i	0.415583	+	0.546117i
$225$		0			0
$226$	0.551582	−	2.96281i	0.0366907	−	0.197083i
$227$	−11.0458	+	11.0458i	−0.733132	+	0.733132i	−0.971239	−	0.238107i	$-0.923473\pi$
$227$	−11.0458	+	11.0458i	−0.733132	+	0.733132i	0.238107	+	0.971239i	$0.423473\pi$
$228$		0			0
$229$	5.23103	−	5.23103i	0.345676	−	0.345676i	−0.512820	−	0.858496i	$-0.671399\pi$
$229$	5.23103	−	5.23103i	0.345676	−	0.345676i	0.858496	+	0.512820i	$0.171399\pi$
$230$	19.6944	+	0.0462634i	1.29861	+	0.00305052i
$231$		0			0
$232$	−5.81425	−	24.4773i	−0.381724	−	1.60701i
$233$	14.5509			0.953262			0.476631	−	0.879103i	$-0.341858\pi$
$233$	14.5509			0.953262			0.476631	+	0.879103i	$0.341858\pi$
$234$		0			0
$235$	−4.06011	−	22.0972i	−0.264852	−	1.44146i
$236$	17.2738	−	7.65764i	1.12443	−	0.498470i
$237$		0			0
$238$	0.472189	−	2.53635i	0.0306075	−	0.164407i
$239$	8.23404			0.532616			0.266308	−	0.963888i	$-0.414196\pi$
$239$	8.23404			0.532616			0.266308	+	0.963888i	$0.414196\pi$
$240$		0			0
$241$	−6.81789			−0.439179			−0.219589	−	0.975592i	$-0.570472\pi$
$241$	−6.81789			−0.439179			−0.219589	+	0.975592i	$0.570472\pi$
$242$	2.79013	−	14.9871i	0.179357	−	0.963410i
$243$		0			0
$244$	3.31781	+	7.48421i	0.212401	+	0.479127i
$245$	8.14456	−	1.49647i	0.520337	−	0.0956061i
$246$		0			0
$247$	−0.129162			−0.00821841
$248$	−17.1286	−	10.5532i	−1.08767	−	0.670128i
$249$		0			0
$250$	14.7918	−	5.58585i	0.935517	−	0.353280i
$251$	−12.1421	+	12.1421i	−0.766403	+	0.766403i	−0.977471	−	0.211068i	$-0.932306\pi$
$251$	−12.1421	+	12.1421i	−0.766403	+	0.766403i	0.211068	+	0.977471i	$0.432306\pi$
$252$		0			0
$253$	2.06746	−	2.06746i	0.129980	−	0.129980i
$254$	−2.73046	+	14.6666i	−0.171324	+	0.920266i
$255$		0			0
$256$	1.57037	+	15.9227i	0.0981481	+	0.995172i
$257$		−	13.9667i		−	0.871217i	−0.900136	−	0.435609i	$-0.856533\pi$
$257$		−	13.9667i		−	0.871217i	0.900136	−	0.435609i	$-0.143467\pi$
$258$		0			0
$259$	−0.131366	−	0.131366i	−0.00816271	−	0.00816271i
$260$	−0.162024	+	0.110606i	−0.0100483	+	0.00685951i
$261$		0			0
$262$	6.58910	+	9.60368i	0.407076	+	0.593317i
$263$	3.31340			0.204313			0.102157	−	0.994768i	$-0.467426\pi$
$263$	3.31340			0.204313			0.102157	+	0.994768i	$0.467426\pi$
$264$		0			0
$265$	−18.3441	−	12.6494i	−1.12687	−	0.777045i
$266$	−4.27736	−	6.23429i	−0.262262	−	0.382249i
$267$		0			0
$268$	0.390024	−	0.172901i	0.0238245	−	0.0105616i
$269$	14.5006	+	14.5006i	0.884120	+	0.884120i	0.993950	−	0.109831i	$-0.0350308\pi$
$269$	14.5006	+	14.5006i	0.884120	+	0.884120i	−0.109831	+	0.993950i	$0.535031\pi$
$270$		0			0
$271$	−7.51560			−0.456540			−0.228270	−	0.973598i	$-0.573307\pi$
$271$	−7.51560			−0.456540			−0.228270	+	0.973598i	$0.573307\pi$
$272$	2.69878	−	2.97804i	0.163638	−	0.180570i
$273$		0			0
$274$	−21.7661	−	4.05215i	−1.31494	−	0.244799i
$275$	0.961384	−	2.14144i	0.0579737	−	0.129134i
$276$		0			0
$277$	−11.7421	−	11.7421i	−0.705512	−	0.705512i	0.260076	−	0.965588i	$-0.416252\pi$
$277$	−11.7421	−	11.7421i	−0.705512	−	0.705512i	−0.965588	+	0.260076i	$0.916252\pi$
$278$	1.88297	−	1.29191i	0.112933	−	0.0774834i
$279$		0			0
$280$	−10.7043	−	4.15760i	−0.639702	−	0.248464i
$281$			32.4999i			1.93878i	0.245523	+	0.969391i	$0.421040\pi$
$281$			32.4999i			1.93878i	−0.245523	+	0.969391i	$0.578960\pi$
$282$		0			0
$283$	3.88285	+	3.88285i	0.230811	+	0.230811i	0.813031	−	0.582220i	$-0.197816\pi$
$283$	3.88285	+	3.88285i	0.230811	+	0.230811i	−0.582220	+	0.813031i	$0.697816\pi$
$284$	10.4723	−	27.1509i	0.621414	−	1.61111i
$285$		0			0
$286$	−0.00533046	+	0.0286325i	−0.000315197	+	0.00169307i
$287$			5.55686i			0.328011i
$288$		0			0
$289$	15.9905			0.940617
$290$	19.8427	+	19.9361i	1.16520	+	1.17069i
$291$		0			0
$292$	28.0504	+	10.8192i	1.64152	+	0.633143i
$293$	−10.6693	−	10.6693i	−0.623305	−	0.623305i	0.323070	−	0.946375i	$-0.395285\pi$
$293$	−10.6693	−	10.6693i	−0.623305	−	0.623305i	−0.946375	+	0.323070i	$0.895285\pi$
$294$		0			0
$295$	−11.9925	+	17.3914i	−0.698228	+	1.01257i
$296$	−0.0668833	−	0.281570i	−0.00388751	−	0.0163660i
$297$		0			0
$298$	−2.99846	+	2.05725i	−0.173696	+	0.119173i
$299$	0.193181	−	0.193181i	0.0111719	−	0.0111719i
$300$		0			0
$301$	6.87223	+	6.87223i	0.396109	+	0.396109i
$302$	−2.90954	+	15.6286i	−0.167425	+	0.899322i
$303$		0			0
$304$	−0.578680	−	11.7635i	−0.0331896	−	0.674683i
$305$	−7.53516	−	5.19596i	−0.431462	−	0.297520i
$306$		0			0
$307$	16.3961	−	16.3961i	0.935778	−	0.935778i	−0.0622811	−	0.998059i	$-0.519838\pi$
$307$	16.3961	−	16.3961i	0.935778	−	0.935778i	0.998059	+	0.0622811i	$0.0198375\pi$
$308$	−1.55853	+	0.690910i	−0.0888054	+	0.0393682i
$309$		0			0
$310$	22.4933	+	0.0528381i	1.27753	+	0.00300100i
$311$		−	10.1406i		−	0.575023i	−0.957777	−	0.287512i	$-0.907172\pi$
$311$		−	10.1406i		−	0.575023i	0.957777	−	0.287512i	$-0.0928280\pi$
$312$		0			0
$313$	23.3811			1.32158			0.660790	−	0.750571i	$-0.270221\pi$
$313$	23.3811			1.32158			0.660790	+	0.750571i	$0.270221\pi$
$314$	24.4396	−	16.7680i	1.37921	−	0.946275i
$315$		0			0
$316$	29.1070	+	11.2267i	1.63740	+	0.631552i
$317$	10.8253	−	10.8253i	0.608009	−	0.608009i	−0.334416	−	0.942425i	$-0.608539\pi$
$317$	10.8253	−	10.8253i	0.608009	−	0.608009i	0.942425	+	0.334416i	$0.108539\pi$
$318$		0			0
$319$	4.17585			0.233803
$320$	−10.7994	−	14.2609i	−0.603705	−	0.797207i
$321$		0			0
$322$	15.7217	+	2.92688i	0.876134	+	0.163108i
$323$	−2.09191	+	2.09191i	−0.116397	+	0.116397i
$324$		0			0
$325$	0.0898306	−	0.200094i	0.00498290	−	0.0110992i
$326$	−11.3400	+	7.78038i	−0.628064	+	0.430915i
$327$		0			0
$328$	−4.54069	+	7.36989i	−0.250718	+	0.406934i
$329$		−	18.2431i		−	1.00578i
$330$		0			0
$331$	12.1611	−	12.1611i	0.668432	−	0.668432i	−0.288921	−	0.957353i	$-0.593296\pi$
$331$	12.1611	−	12.1611i	0.668432	−	0.668432i	0.957353	+	0.288921i	$0.0932964\pi$
$332$	14.1953	−	6.29291i	0.779069	−	0.345368i
$333$		0			0
$334$	17.8203	+	3.31758i	0.975085	+	0.181530i
$335$	−0.270776	+	0.392679i	−0.0147941	+	0.0214543i
$336$		0			0
$337$			1.91202i			0.104154i	0.998643	+	0.0520772i	$0.0165842\pi$
$337$			1.91202i			0.104154i	−0.998643	+	0.0520772i	$0.983416\pi$
$338$	3.36435	−	18.0716i	0.182997	−	0.982963i
$339$		0			0
$340$	−0.832765	+	4.41551i	−0.0451630	+	0.239465i
$341$	2.36127	−	2.36127i	0.127870	−	0.127870i
$342$		0			0
$343$	19.4338			1.04932
$344$	3.49890	+	14.7299i	0.188648	+	0.794185i
$345$		0			0
$346$	9.71241	−	6.66370i	0.522143	−	0.358243i
$347$	0.274551	+	0.274551i	0.0147386	+	0.0147386i	0.714438	−	0.699699i	$-0.246683\pi$
$347$	0.274551	+	0.274551i	0.0147386	+	0.0147386i	−0.699699	+	0.714438i	$0.746683\pi$
$348$		0			0
$349$	−1.33045	−	1.33045i	−0.0712172	−	0.0712172i	0.670601	−	0.741818i	$-0.266036\pi$
$349$	−1.33045	−	1.33045i	−0.0712172	−	0.0712172i	−0.741818	+	0.670601i	$0.766036\pi$
$350$	12.6328	−	2.29047i	0.675251	−	0.122431i
$351$		0			0
$352$	−2.63159	−	0.357192i	−0.140264	−	0.0190384i
$353$		−	27.5571i		−	1.46672i	−0.679841	−	0.733359i	$-0.737951\pi$
$353$		−	27.5571i		−	1.46672i	0.679841	−	0.733359i	$-0.262049\pi$
$354$		0			0
$355$	5.87960	+	31.9997i	0.312057	+	1.69837i
$356$	10.3295	−	26.7810i	0.547465	−	1.41939i
$357$		0			0
$358$	−11.4714	−	16.7196i	−0.606280	−	0.883659i
$359$			9.65759i			0.509708i	0.966980	+	0.254854i	$0.0820274\pi$
$359$			9.65759i			0.509708i	−0.966980	+	0.254854i	$0.917973\pi$
$360$		0			0
$361$		−	10.3303i		−	0.543701i
$362$	17.9227	−	12.2968i	0.941999	−	0.646307i
$363$		0			0
$364$	−0.145627	+	0.0645578i	−0.00763293	+	0.00338375i
$365$	−33.0598	+	6.07437i	−1.73043	+	0.317947i
$366$		0			0
$367$			5.40212i			0.281988i	0.990010	+	0.140994i	$0.0450299\pi$
$367$			5.40212i			0.281988i	−0.990010	+	0.140994i	$0.954970\pi$
$368$	18.4595	+	16.7285i	0.962267	+	0.872033i
$369$		0			0
$370$	0.228257	+	0.229332i	0.0118665	+	0.0119224i
$371$	−12.7939	−	12.7939i	−0.664225	−	0.664225i
$372$		0			0
$373$	6.54862	+	6.54862i	0.339075	+	0.339075i	0.856019	−	0.516944i	$-0.172931\pi$
$373$	6.54862	+	6.54862i	0.339075	+	0.339075i	−0.516944	+	0.856019i	$0.672931\pi$
$374$	0.377398	+	0.550061i	0.0195148	+	0.0284430i
$375$		0			0
$376$	14.9070	−	24.1953i	0.768772	−	1.24778i
$377$	0.390186			0.0200956
$378$		0			0
$379$	−24.8255	+	24.8255i	−1.27520	+	1.27520i	−0.331877	+	0.943323i	$0.607682\pi$
$379$	−24.8255	+	24.8255i	−1.27520	+	1.27520i	−0.943323	+	0.331877i	$0.892318\pi$
$380$	7.42415	+	10.8755i	0.380851	+	0.557899i
$381$		0			0
$382$	−2.18708	−	0.407164i	−0.111901	−	0.0208323i
$383$		−	0.293274i		−	0.0149856i	−0.999972	−	0.00749279i	$-0.997615\pi$
$383$		−	0.293274i		−	0.0149856i	0.999972	−	0.00749279i	$-0.00238505\pi$
$384$		0			0
$385$	1.08202	−	1.56914i	0.0551448	−	0.0799707i
$386$	−1.01415	+	5.44750i	−0.0516190	+	0.277270i
$387$		0			0
$388$	−9.75844	+	25.3003i	−0.495410	+	1.28443i
$389$	0.442101	−	0.442101i	0.0224154	−	0.0224154i	−0.695810	−	0.718226i	$-0.744955\pi$
$389$	0.442101	−	0.442101i	0.0224154	−	0.0224154i	0.718226	+	0.695810i	$0.244955\pi$
$390$		0			0
$391$		−	6.25748i		−	0.316454i
$392$	8.91787	+	5.49442i	0.450421	+	0.277510i
$393$		0			0
$394$	3.08859	+	4.50165i	0.155601	+	0.226790i
$395$	−34.3051	+	6.30319i	−1.72608	+	0.317148i
$396$		0			0
$397$	24.4503	−	24.4503i	1.22712	−	1.22712i	0.262078	−	0.965047i	$-0.415592\pi$
$397$	24.4503	−	24.4503i	1.22712	−	1.22712i	0.965047	−	0.262078i	$-0.0844076\pi$
$398$	−5.09518	+	27.3687i	−0.255398	+	1.37187i
$399$		0			0
$400$	18.6261	+	7.28487i	0.931304	+	0.364244i
$401$	17.3106			0.864451			0.432226	−	0.901765i	$-0.357728\pi$
$401$	17.3106			0.864451			0.432226	+	0.901765i	$0.357728\pi$
$402$		0			0
$403$	0.220634	−	0.220634i	0.0109906	−	0.0109906i
$404$	−27.1844	+	12.0511i	−1.35247	+	0.599564i
$405$		0			0
$406$	12.9214	+	18.8332i	0.641281	+	0.934674i
$407$	0.0480362			0.00238107
$408$		0			0
$409$		−	7.62314i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$409$		−	7.62314i		−	0.376940i	0.982079	−	0.188470i	$-0.0603528\pi$
$410$	0.0227345	−	9.67811i	0.00112278	−	0.477968i
$411$		0			0
$412$	11.4645	+	4.42192i	0.564816	+	0.217852i
$413$	−12.1295	+	12.1295i	−0.596852	+	0.596852i
$414$		0			0
$415$	−9.85519	+	14.2920i	−0.483772	+	0.701565i
$416$	−0.245893	−	0.0333756i	−0.0120559	−	0.00163637i
$417$		0			0
$418$	1.92188	+	0.357793i	0.0940021	+	0.0175002i
$419$	−3.21455	−	3.21455i	−0.157041	−	0.157041i	0.624213	−	0.781254i	$-0.285420\pi$
$419$	−3.21455	−	3.21455i	−0.157041	−	0.157041i	−0.781254	+	0.624213i	$0.785420\pi$
$420$		0			0
$421$	−8.12907	+	8.12907i	−0.396187	+	0.396187i	−0.876886	−	0.480699i	$-0.840383\pi$
$421$	−8.12907	+	8.12907i	−0.396187	+	0.396187i	0.480699	+	0.876886i	$0.340383\pi$
$422$	−2.19280	−	3.19603i	−0.106744	−	0.155580i
$423$		0			0
$424$	−6.51383	−	27.4224i	−0.316339	−	1.33175i
$425$	−1.78582	−	4.69560i	−0.0866249	−	0.227770i
$426$		0			0
$427$	−5.25532	−	5.25532i	−0.254323	−	0.254323i
$428$	−7.92666	−	17.8807i	−0.383150	−	0.864295i
$429$		0			0
$430$	−11.9409	−	11.9971i	−0.575842	−	0.578553i
$431$	34.3410			1.65415			0.827074	−	0.562093i	$-0.190004\pi$
$431$	34.3410			1.65415			0.827074	+	0.562093i	$0.190004\pi$
$432$		0			0
$433$		−	31.2038i		−	1.49956i	−0.661687	−	0.749780i	$-0.730159\pi$
$433$		−	31.2038i		−	1.49956i	0.661687	−	0.749780i	$-0.269841\pi$
$434$	17.9559	+	3.34283i	0.861912	+	0.160461i
$435$		0			0
$436$	−7.06041	−	15.9266i	−0.338132	−	0.762747i
$437$	−12.9667	−	12.9667i	−0.620283	−	0.620283i
$438$		0			0
$439$			25.1727i			1.20143i	0.799464	+	0.600714i	$0.205117\pi$
$439$			25.1727i			1.20143i	−0.799464	+	0.600714i	$0.794883\pi$
$440$	2.71724	−	1.19695i	0.129539	−	0.0570622i
$441$		0			0
$442$	0.0352636	+	0.0513970i	0.00167732	+	0.00244471i
$443$	4.89367	+	4.89367i	0.232505	+	0.232505i	0.813738	−	0.581232i	$-0.197429\pi$
$443$	4.89367	+	4.89367i	0.232505	+	0.232505i	−0.581232	+	0.813738i	$0.697429\pi$
$444$		0			0
$445$	5.79948	+	31.5637i	0.274922	+	1.49626i
$446$	2.38656	−	12.8194i	0.113007	−	0.607014i
$447$		0			0
$448$	−6.53206	−	12.9738i	−0.308611	−	0.612954i
$449$	−36.7865			−1.73606			−0.868031	−	0.496511i	$-0.834614\pi$
$449$	−36.7865			−1.73606			−0.868031	+	0.496511i	$0.834614\pi$
$450$		0			0
$451$	−1.01598	−	1.01598i	−0.0478405	−	0.0478405i
$452$	−1.53376	+	3.97651i	−0.0721419	+	0.187039i
$453$		0			0
$454$	18.2162	−	12.4982i	0.854929	−	0.586568i
$455$	0.101102	−	0.146618i	0.00473976	−	0.00687358i
$456$		0			0
$457$	−3.78613			−0.177108			−0.0885539	−	0.996071i	$-0.528225\pi$
$457$	−3.78613			−0.177108			−0.0885539	+	0.996071i	$0.528225\pi$
$458$	−8.62680	+	5.91886i	−0.403104	+	0.276570i
$459$		0			0
$460$	−27.3697	−	5.16192i	−1.27612	−	0.240676i
$461$	24.6710	+	24.6710i	1.14904	+	1.14904i	0.986741	+	0.162303i	$0.0518921\pi$
$461$	24.6710	+	24.6710i	1.14904	+	1.14904i	0.162303	+	0.986741i	$0.448108\pi$
$462$		0			0
$463$			3.86935i			0.179824i	0.995950	+	0.0899120i	$0.0286586\pi$
$463$			3.86935i			0.179824i	−0.995950	+	0.0899120i	$0.971341\pi$
$464$	1.74813	+	35.5363i	0.0811550	+	1.64973i
$465$		0			0
$466$	−20.2305	−	3.76628i	−0.937160	−	0.174470i
$467$	12.5440	−	12.5440i	0.580469	−	0.580469i	−0.354563	−	0.935032i	$-0.615370\pi$
$467$	12.5440	−	12.5440i	0.580469	−	0.580469i	0.935032	+	0.354563i	$0.115370\pi$
$468$		0			0
$469$	−0.273870	+	0.273870i	−0.0126461	+	0.0126461i
$470$	−0.0746371	+	31.7731i	−0.00344275	+	1.46559i
$471$		0			0
$472$	−25.9983	+	6.17555i	−1.19667	+	0.284253i
$473$	−2.51294			−0.115545
$474$		0			0
$475$	−13.4308	−	6.02964i	−0.616246	−	0.276659i
$476$	−1.31299	+	3.40414i	−0.0601809	+	0.156028i
$477$		0			0
$478$	−11.4480	−	2.13126i	−0.523619	−	0.0974814i
$479$	−26.9702			−1.23230			−0.616150	−	0.787629i	$-0.711308\pi$
$479$	−26.9702			−1.23230			−0.616150	+	0.787629i	$0.711308\pi$
$480$		0			0
$481$	0.00448844			0.000204655
$482$	9.47908	+	1.76471i	0.431760	+	0.0803801i
$483$		0			0
$484$	−7.75839	+	20.1148i	−0.352654	+	0.914310i
$485$	−5.47883	−	29.8186i	−0.248781	−	1.35399i
$486$		0			0
$487$	−25.1835			−1.14117			−0.570586	−	0.821238i	$-0.693284\pi$
$487$	−25.1835			−1.14117			−0.570586	+	0.821238i	$0.693284\pi$
$488$	−2.67567	−	11.2642i	−0.121122	−	0.509908i
$489$		0			0
$490$	−11.7109	−	0.0275097i	−0.529045	−	0.00124276i
$491$	17.0641	−	17.0641i	0.770094	−	0.770094i	−0.208029	−	0.978123i	$-0.566705\pi$
$491$	17.0641	−	17.0641i	0.770094	−	0.770094i	0.978123	+	0.208029i	$0.0667048\pi$
$492$		0			0
$493$	6.31943	−	6.31943i	0.284613	−	0.284613i
$494$	0.179578	+	0.0334317i	0.00807959	+	0.00150416i
$495$		0			0
$496$	21.0828	+	19.1058i	0.946647	+	0.857878i
$497$			26.4186i			1.18503i
$498$		0			0
$499$	11.2471	+	11.2471i	0.503488	+	0.503488i	0.912520	−	0.409032i	$-0.134133\pi$
$499$	11.2471	+	11.2471i	0.503488	+	0.503488i	−0.409032	+	0.912520i	$0.634133\pi$
$500$	−22.0113	+	3.93752i	−0.984374	+	0.176091i
$501$		0			0
$502$	20.0243	−	13.7387i	0.893728	−	0.613188i
$503$	37.0584			1.65235			0.826176	−	0.563412i	$-0.190512\pi$
$503$	37.0584			1.65235			0.826176	+	0.563412i	$0.190512\pi$
$504$		0			0
$505$	18.8729	−	27.3695i	0.839834	−	1.21793i
$506$	−3.40957	+	2.33931i	−0.151574	+	0.103995i
$507$		0			0
$508$	7.59246	−	19.6846i	0.336861	−	0.873365i
$509$	−6.60068	−	6.60068i	−0.292570	−	0.292570i	0.545525	−	0.838095i	$-0.316330\pi$
$509$	−6.60068	−	6.60068i	−0.292570	−	0.292570i	−0.838095	+	0.545525i	$0.816330\pi$
$510$		0			0
$511$	−27.2937			−1.20740
$512$	1.93803	−	22.5443i	0.0856498	−	0.996325i
$513$		0			0
$514$	−3.61506	+	19.4182i	−0.159453	+	0.856501i
$515$	−13.5119	+	2.48267i	−0.595406	+	0.109399i
$516$		0			0
$517$	3.33545	+	3.33545i	0.146693	+	0.146693i
$518$	0.148640	+	0.216644i	0.00653086	+	0.00951879i
$519$		0			0
$520$	0.253895	−	0.111841i	0.0111341	−	0.00490456i
$521$			11.8337i			0.518442i	0.965818	+	0.259221i	$0.0834657\pi$
$521$			11.8337i			0.518442i	−0.965818	+	0.259221i	$0.916534\pi$
$522$		0			0
$523$	−8.02817	−	8.02817i	−0.351047	−	0.351047i	0.509452	−	0.860499i	$-0.329848\pi$
$523$	−8.02817	−	8.02817i	−0.351047	−	0.351047i	−0.860499	+	0.509452i	$0.829848\pi$
$524$	−6.67522	−	15.0577i	−0.291608	−	0.657800i
$525$		0			0
$526$	−4.60671	−	0.857623i	−0.200862	−	0.0373941i
$527$		−	7.14676i		−	0.311318i
$528$		0			0
$529$	15.7872			0.686400
$530$	22.2301	+	22.3348i	0.965615	+	0.970163i
$531$		0			0
$532$	4.33327	+	9.77482i	0.187871	+	0.423792i
$533$	−0.0949317	−	0.0949317i	−0.00411195	−	0.00411195i
$534$		0			0
$535$	18.0024	+	12.4138i	0.778312	+	0.536694i
$536$	−0.587013	+	0.139437i	−0.0253551	+	0.00602276i
$537$		0			0
$538$	−16.4073	−	23.9139i	−0.707371	−	1.03100i
$539$	−1.22938	+	1.22938i	−0.0529530	+	0.0529530i
$540$		0			0
$541$	10.9990	+	10.9990i	0.472882	+	0.472882i	0.902846	−	0.429964i	$-0.141474\pi$
$541$	10.9990	+	10.9990i	0.472882	+	0.472882i	−0.429964	+	0.902846i	$0.641474\pi$
$542$	10.4491	+	1.94530i	0.448829	+	0.0835577i
$543$		0			0
$544$	−4.52301	+	3.44191i	−0.193922	+	0.147571i
$545$	16.0350	+	11.0571i	0.686866	+	0.473636i
$546$		0			0
$547$	21.3064	−	21.3064i	0.910997	−	0.910997i	−0.0853539	−	0.996351i	$-0.527202\pi$
$547$	21.3064	−	21.3064i	0.910997	−	0.910997i	0.996351	+	0.0853539i	$0.0272021\pi$
$548$	29.2131	+	11.2676i	1.24792	+	0.481329i
$549$		0			0
$550$	−1.89092	+	2.72846i	−0.0806290	+	0.116342i
$551$		−	26.1902i		−	1.11574i
$552$		0			0
$553$	−28.3219			−1.20437
$554$	13.2860	+	19.3645i	0.564469	+	0.822720i
$555$		0			0
$556$	−2.95233	+	1.30879i	−0.125207	+	0.0555052i
$557$	−18.9715	+	18.9715i	−0.803846	+	0.803846i	−0.983694	−	0.179848i	$-0.942439\pi$
$557$	−18.9715	+	18.9715i	−0.803846	+	0.803846i	0.179848	+	0.983694i	$0.442439\pi$
$558$		0			0
$559$	−0.234806			−0.00993124
$560$	13.8063	+	8.55105i	0.583422	+	0.361348i
$561$		0			0
$562$	8.41210	−	45.1854i	0.354843	−	1.90603i
$563$	−0.478449	+	0.478449i	−0.0201642	+	0.0201642i	−0.717117	−	0.696953i	$-0.754539\pi$
$563$	−0.478449	+	0.478449i	−0.0201642	+	0.0201642i	0.696953	+	0.717117i	$0.254539\pi$
$564$		0			0
$565$	−0.861121	−	4.68666i	−0.0362276	−	0.197169i
$566$	−4.39341	−	6.40344i	−0.184669	−	0.269157i
$567$		0			0
$568$	−21.5874	+	35.0381i	−0.905789	+	1.47016i
$569$		−	11.7904i		−	0.494278i	−0.968980	−	0.247139i	$-0.920510\pi$
$569$		−	11.7904i		−	0.494278i	0.968980	−	0.247139i	$-0.0794904\pi$
$570$		0			0
$571$	−6.72738	+	6.72738i	−0.281532	+	0.281532i	−0.833720	−	0.552188i	$-0.813793\pi$
$571$	−6.72738	+	6.72738i	−0.281532	+	0.281532i	0.552188	+	0.833720i	$0.313793\pi$
$572$	0.0148221	−	0.0384287i	0.000619745	−	0.00160679i
$573$		0			0
$574$	1.43831	−	7.72585i	0.0600338	−	0.322471i
$575$	29.1058	−	11.0694i	1.21380	−	0.461628i
$576$		0			0
$577$			27.7420i			1.15491i	0.816421	+	0.577457i	$0.195955\pi$
$577$			27.7420i			1.15491i	−0.816421	+	0.577457i	$0.804045\pi$
$578$	−22.2320	−	4.13889i	−0.924729	−	0.172155i
$579$		0			0
$580$	−22.4276	−	32.8536i	−0.931255	−	1.36417i
$581$	−9.96778	+	9.96778i	−0.413533	+	0.413533i
$582$		0			0
$583$	4.67829			0.193755
$584$	−36.1988	−	22.3026i	−1.49792	−	0.922886i
$585$		0			0
$586$	12.0722	+	17.5953i	0.498697	+	0.726856i
$587$	9.78016	+	9.78016i	0.403670	+	0.403670i	0.879524	−	0.475854i	$-0.157861\pi$
$587$	9.78016	+	9.78016i	0.403670	+	0.403670i	−0.475854	+	0.879524i	$0.657861\pi$
$588$		0			0
$589$	−14.8095	−	14.8095i	−0.610214	−	0.610214i
$590$	21.1749	−	21.0757i	0.871758	−	0.867672i
$591$		0			0
$592$	0.0201093	+	0.408786i	0.000826489	+	0.0168010i
$593$			12.8018i			0.525707i	0.964836	+	0.262854i	$0.0846637\pi$
$593$			12.8018i			0.525707i	−0.964836	+	0.262854i	$0.915336\pi$
$594$		0			0
$595$	−0.737174	−	4.01207i	−0.0302212	−	0.164479i
$596$	4.70132	−	2.08414i	0.192574	−	0.0853696i
$597$		0			0
$598$	−0.318586	+	0.218582i	−0.0130279	+	0.00893849i
$599$			35.6315i			1.45586i	0.685650	+	0.727932i	$0.259518\pi$
$599$			35.6315i			1.45586i	−0.685650	+	0.727932i	$0.740482\pi$
$600$		0			0
$601$		−	43.3118i		−	1.76672i	−0.468692	−	0.883362i	$-0.655275\pi$
$601$		−	43.3118i		−	1.76672i	0.468692	−	0.883362i	$-0.344725\pi$
$602$	−7.77586	−	11.3334i	−0.316921	−	0.461915i
$603$		0			0
$604$	8.09042	−	20.9757i	0.329195	−	0.853488i
$605$	−4.35591	−	23.7071i	−0.177093	−	0.963829i
$606$		0			0
$607$			18.4382i			0.748385i	0.927351	+	0.374192i	$0.122080\pi$
$607$			18.4382i			0.748385i	−0.927351	+	0.374192i	$0.877920\pi$
$608$	−2.24025	+	16.5049i	−0.0908541	+	0.669361i
$609$		0			0
$610$	9.13143	+	9.17443i	0.369721	+	0.371462i
$611$	0.311660	+	0.311660i	0.0126084	+	0.0126084i
$612$		0			0
$613$	9.81446	+	9.81446i	0.396402	+	0.396402i	0.876962	−	0.480560i	$-0.159566\pi$
$613$	9.81446	+	9.81446i	0.396402	+	0.396402i	−0.480560	+	0.876962i	$0.659566\pi$
$614$	−27.0399	+	18.5521i	−1.09124	+	0.748701i
$615$		0			0
$616$	2.34569	−	0.557188i	0.0945107	−	0.0224497i
$617$	−9.02339			−0.363268			−0.181634	−	0.983366i	$-0.558139\pi$
$617$	−9.02339			−0.363268			−0.181634	+	0.983366i	$0.558139\pi$
$618$		0			0
$619$	−15.6705	+	15.6705i	−0.629850	+	0.629850i	−0.948030	−	0.318181i	$-0.896928\pi$
$619$	−15.6705	+	15.6705i	−0.629850	+	0.629850i	0.318181	+	0.948030i	$0.396928\pi$
$620$	−31.2593	−	5.89550i	−1.25540	−	0.236769i
$621$		0			0
$622$	−2.62475	+	14.0988i	−0.105243	+	0.565310i
$623$			26.0586i			1.04401i
$624$		0			0
$625$	18.6818	−	16.6130i	0.747272	−	0.664518i
$626$	−32.5074	−	6.05185i	−1.29926	−	0.241881i
$627$		0			0
$628$	−38.3191	+	16.9872i	−1.52910	+	0.677864i
$629$	0.0726945	−	0.0726945i	0.00289852	−	0.00289852i
$630$		0			0
$631$			7.32472i			0.291593i	0.989315	+	0.145796i	$0.0465744\pi$
$631$			7.32472i			0.291593i	−0.989315	+	0.145796i	$0.953426\pi$
$632$	−37.5624	−	23.1427i	−1.49415	−	0.920567i
$633$		0			0
$634$	−17.8526	+	12.2487i	−0.709019	+	0.486459i
$635$	4.26275	+	23.2000i	0.169162	+	0.920666i
$636$		0			0
$637$	−0.114871	+	0.114871i	−0.00455137	+	0.00455137i
$638$	−5.80579	−	1.08085i	−0.229853	−	0.0427914i
$639$		0			0
$640$	11.3235	+	22.6225i	0.447600	+	0.894234i
$641$	22.8353			0.901939			0.450970	−	0.892539i	$-0.351078\pi$
$641$	22.8353			0.901939			0.450970	+	0.892539i	$0.351078\pi$
$642$		0			0
$643$	−15.9787	+	15.9787i	−0.630138	+	0.630138i	−0.948102	−	0.317965i	$-0.897001\pi$
$643$	−15.9787	+	15.9787i	−0.630138	+	0.630138i	0.317965	+	0.948102i	$0.397001\pi$
$644$	−21.1006	−	8.13862i	−0.831482	−	0.320707i
$645$		0			0
$646$	3.44989	−	2.36697i	0.135734	−	0.0931273i
$647$	−7.57070			−0.297635			−0.148817	−	0.988865i	$-0.547547\pi$
$647$	−7.57070			−0.297635			−0.148817	+	0.988865i	$0.547547\pi$
$648$		0			0
$649$		−	4.43534i		−	0.174102i
$650$	−0.176685	+	0.254944i	−0.00693015	+	0.00999974i
$651$		0			0
$652$	17.7801	−	7.88208i	0.696323	−	0.308686i
$653$	8.64398	−	8.64398i	0.338265	−	0.338265i	−0.517449	−	0.855714i	$-0.673118\pi$
$653$	8.64398	−	8.64398i	0.338265	−	0.338265i	0.855714	+	0.517449i	$0.173118\pi$
$654$		0			0
$655$	15.1602	+	10.4539i	0.592359	+	0.408468i
$656$	8.22062	−	9.07125i	0.320961	−	0.354173i
$657$		0			0
$658$	−4.72195	+	25.3639i	−0.184081	+	0.988787i
$659$	−22.8915	−	22.8915i	−0.891728	−	0.891728i	0.102958	−	0.994686i	$-0.467169\pi$
$659$	−22.8915	−	22.8915i	−0.891728	−	0.891728i	−0.994686	+	0.102958i	$0.967169\pi$
$660$		0			0
$661$	16.8355	−	16.8355i	0.654824	−	0.654824i	−0.299326	−	0.954151i	$-0.596762\pi$
$661$	16.8355	−	16.8355i	0.654824	−	0.654824i	0.954151	+	0.299326i	$0.0967619\pi$
$662$	−20.0555	+	13.7601i	−0.779480	+	0.534802i
$663$		0			0
$664$	−21.3649	+	5.07495i	−0.829120	+	0.196946i
$665$	−9.84137	−	6.78623i	−0.381632	−	0.263159i
$666$		0			0
$667$	39.1712	+	39.1712i	1.51671	+	1.51671i
$668$	−23.9173	−	9.22503i	−0.925390	−	0.356927i
$669$		0			0
$670$	0.478106	−	0.475865i	0.0184709	−	0.0183843i
$671$	1.92169			0.0741861
$672$		0			0
$673$			5.34019i			0.205849i	0.994689	+	0.102925i	$0.0328200\pi$
$673$			5.34019i			0.205849i	−0.994689	+	0.102925i	$0.967180\pi$
$674$	0.494897	−	2.65833i	0.0190627	−	0.102395i
$675$		0			0
$676$	−9.35509	+	24.2545i	−0.359811	+	0.932867i
$677$	−0.117760	−	0.117760i	−0.00452590	−	0.00452590i	0.704840	−	0.709366i	$-0.251019\pi$
$677$	−0.117760	−	0.117760i	−0.00452590	−	0.00452590i	−0.709366	+	0.704840i	$0.751019\pi$
$678$		0			0
$679$		−	24.6178i		−	0.944745i
$680$	2.30070	−	5.92345i	0.0882278	−	0.227154i
$681$		0			0
$682$	−3.89412	+	2.67176i	−0.149113	+	0.102307i
$683$	11.0216	+	11.0216i	0.421729	+	0.421729i	0.885799	−	0.464070i	$-0.153611\pi$
$683$	11.0216	+	11.0216i	0.421729	+	0.421729i	−0.464070	+	0.885799i	$0.653611\pi$
$684$		0			0
$685$	−34.4301	+	6.32615i	−1.31551	+	0.241710i
$686$	−27.0192	−	5.03013i	−1.03160	−	0.192051i
$687$		0			0
$688$	−1.05199	−	21.3850i	−0.0401067	−	0.815297i
$689$	0.437134			0.0166535
$690$		0			0
$691$	−33.0825	−	33.0825i	−1.25852	−	1.25852i	−0.951801	−	0.306716i	$-0.900770\pi$
$691$	−33.0825	−	33.0825i	−1.25852	−	1.25852i	−0.306716	−	0.951801i	$-0.599230\pi$
$692$	−15.2282	+	6.75080i	−0.578890	+	0.256627i
$693$		0			0
$694$	−0.310651	−	0.452778i	−0.0117922	−	0.0171872i
$695$	2.04967	−	2.97243i	0.0777485	−	0.112751i
$696$		0			0
$697$	−3.07501			−0.116474
$698$	1.50539	+	2.19412i	0.0569798	+	0.0830486i
$699$		0			0
$700$	−18.1565	−	0.0853022i	−0.686253	−	0.00322412i
$701$	−3.90473	−	3.90473i	−0.147480	−	0.147480i	0.629511	−	0.776991i	$-0.283255\pi$
$701$	−3.90473	−	3.90473i	−0.147480	−	0.147480i	−0.776991	+	0.629511i	$0.783255\pi$
$702$		0			0
$703$		−	0.301275i		−	0.0113628i
$704$	3.56631	+	1.17776i	0.134411	+	0.0443885i
$705$		0			0
$706$	−7.13274	+	38.3134i	−0.268444	+	1.44194i
$707$	19.0886	−	19.0886i	0.717899	−	0.717899i
$708$		0			0
$709$	7.84907	−	7.84907i	0.294778	−	0.294778i	−0.544186	−	0.838964i	$-0.683162\pi$
$709$	7.84907	−	7.84907i	0.294778	−	0.294778i	0.838964	+	0.544186i	$0.183162\pi$
$710$	0.108085	−	46.0119i	0.00405635	−	1.72680i
$711$		0			0
$712$	−21.2933	+	34.5606i	−0.797999	+	1.29521i
$713$	44.2994			1.65903
$714$		0			0
$715$	0.00832183	+	0.0452916i	0.000311219	+	0.00169381i
$716$	11.6213	+	26.2149i	0.434308	+	0.979697i
$717$		0			0
$718$	2.49972	−	13.4272i	0.0932886	−	0.501098i
$719$	−24.3830			−0.909331			−0.454665	−	0.890662i	$-0.650241\pi$
$719$	−24.3830			−0.909331			−0.454665	+	0.890662i	$0.650241\pi$
$720$		0			0
$721$	−11.1553			−0.415444
$722$	−2.67384	+	14.3625i	−0.0995102	+	0.534517i
$723$		0			0
$724$	−28.1013	+	12.4576i	−1.04438	+	0.462981i
$725$	40.5730	+	18.2149i	1.50684	+	0.676485i
$726$		0			0
$727$	−25.7991			−0.956834			−0.478417	−	0.878133i	$-0.658789\pi$
$727$	−25.7991			−0.956834			−0.478417	+	0.878133i	$0.658789\pi$
$728$	0.219179	−	0.0520630i	0.00812330	−	0.00192958i
$729$		0			0
$730$	47.5361	+	0.111665i	1.75939	+	0.00413292i
$731$	−3.80290	+	3.80290i	−0.140655	+	0.140655i
$732$		0			0
$733$	−15.0948	+	15.0948i	−0.557537	+	0.557537i	−0.928606	−	0.371068i	$-0.878992\pi$
$733$	−15.0948	+	15.0948i	−0.557537	+	0.557537i	0.371068	+	0.928606i	$0.378992\pi$
$734$	1.39826	−	7.51070i	0.0516105	−	0.277225i
$735$		0			0
$736$	−21.3348	−	28.0360i	−0.786410	−	1.03342i
$737$		−	0.100145i		−	0.00368889i
$738$		0			0
$739$	−17.9291	−	17.9291i	−0.659531	−	0.659531i	0.295738	−	0.955269i	$-0.404434\pi$
$739$	−17.9291	−	17.9291i	−0.659531	−	0.659531i	−0.955269	+	0.295738i	$0.904434\pi$
$740$	−0.257992	−	0.377926i	−0.00948398	−	0.0138928i
$741$		0			0
$742$	14.4762	+	21.0992i	0.531437	+	0.774575i
$743$	−8.25344			−0.302789			−0.151395	−	0.988473i	$-0.548376\pi$
$743$	−8.25344			−0.302789			−0.151395	+	0.988473i	$0.548376\pi$
$744$		0			0
$745$	−3.26392	+	4.73333i	−0.119581	+	0.173416i
$746$	−7.40970	−	10.7997i	−0.271289	−	0.395406i
$747$		0			0
$748$	−0.382331	−	0.862447i	−0.0139794	−	0.0315342i
$749$	12.5556	+	12.5556i	0.458772	+	0.458772i
$750$		0			0
$751$	6.07037			0.221511			0.110755	−	0.993848i	$-0.464673\pi$
$751$	6.07037			0.221511			0.110755	+	0.993848i	$0.464673\pi$
$752$	−26.9882	+	29.7808i	−0.984159	+	1.08600i
$753$		0			0
$754$	−0.542486	−	0.100994i	−0.0197562	−	0.00367797i
$755$	4.54233	+	24.7216i	0.165312	+	0.899713i
$756$		0			0
$757$	−21.4003	−	21.4003i	−0.777806	−	0.777806i	0.201651	−	0.979457i	$-0.435369\pi$
$757$	−21.4003	−	21.4003i	−0.777806	−	0.777806i	−0.979457	+	0.201651i	$0.935369\pi$
$758$	40.9412	−	28.0898i	1.48705	−	1.02027i
$759$		0			0
$760$	−7.50704	−	17.0421i	−0.272309	−	0.618180i
$761$			20.8862i			0.757125i	0.925576	+	0.378563i	$0.123582\pi$
$761$			20.8862i			0.757125i	−0.925576	+	0.378563i	$0.876418\pi$
$762$		0			0
$763$	11.1835	+	11.1835i	0.404869	+	0.404869i
$764$	2.93536	+	1.13218i	0.106198	+	0.0409609i
$765$		0			0
$766$	−0.0759093	+	0.407746i	−0.00274272	+	0.0147324i
$767$		−	0.414432i		−	0.0149643i
$768$		0			0
$769$	−8.06017			−0.290657			−0.145329	−	0.989383i	$-0.546424\pi$
$769$	−8.06017			−0.290657			−0.145329	+	0.989383i	$0.546424\pi$
$770$	−1.91050	+	1.90155i	−0.0688498	+	0.0685271i
$771$		0			0
$772$	2.82000	−	7.31130i	0.101494	−	0.263139i
$773$	11.9200	+	11.9200i	0.428731	+	0.428731i	0.888196	−	0.459465i	$-0.151959\pi$
$773$	11.9200	+	11.9200i	0.428731	+	0.428731i	−0.459465	+	0.888196i	$0.651959\pi$
$774$		0			0
$775$	33.2421	−	12.6426i	1.19409	−	0.454134i
$776$	20.1160	−	32.6498i	0.722123	−	1.17206i
$777$		0			0
$778$	−0.729095	+	0.500233i	−0.0261393	+	0.0179342i
$779$	−6.37204	+	6.37204i	−0.228302	+	0.228302i
$780$		0			0
$781$	−4.83018	−	4.83018i	−0.172838	−	0.172838i
$782$	−1.61965	+	8.69994i	−0.0579187	+	0.311109i
$783$		0			0
$784$	−10.9766	−	9.94729i	−0.392021	−	0.355260i
$785$	26.6033	−	38.5800i	0.949512	−	1.37698i
$786$		0			0
$787$	−38.1416	+	38.1416i	−1.35960	+	1.35960i	−0.485194	+	0.874407i	$0.661251\pi$
$787$	−38.1416	+	38.1416i	−1.35960	+	1.35960i	−0.874407	+	0.485194i	$0.838749\pi$
$788$	−3.12896	−	7.05819i	−0.111464	−	0.251437i
$789$		0			0
$790$	49.3268	+	0.115872i	1.75497	+	0.00412253i
$791$		−	3.86924i		−	0.137574i
$792$		0			0
$793$	0.179561			0.00637638
$794$	−40.3224	+	27.6653i	−1.43099	+	0.981804i
$795$		0			0
$796$	14.1679	−	36.7325i	0.502168	−	1.30195i
$797$	22.2285	−	22.2285i	0.787373	−	0.787373i	−0.193690	−	0.981063i	$-0.562046\pi$
$797$	22.2285	−	22.2285i	0.787373	−	0.787373i	0.981063	+	0.193690i	$0.0620456\pi$
$798$		0			0
$799$	10.0952			0.357144
$800$	−24.0107	−	14.9494i	−0.848907	−	0.528542i
$801$		0			0
$802$	−24.0674	−	4.48059i	−0.849849	−	0.158215i
$803$	4.99019	−	4.99019i	0.176100	−	0.176100i
$804$		0			0
$805$	24.8689	−	4.56939i	0.876515	−	0.161050i
$806$	−0.363861	+	0.249646i	−0.0128165	+	0.00879340i
$807$		0			0
$808$	40.9144	−	9.71867i	1.43936	−	0.341901i
$809$		−	41.1080i		−	1.44528i	−0.691225	−	0.722639i	$-0.742929\pi$
$809$		−	41.1080i		−	1.44528i	0.691225	−	0.722639i	$-0.257071\pi$
$810$		0			0
$811$	10.2679	−	10.2679i	0.360555	−	0.360555i	−0.503462	−	0.864017i	$-0.667941\pi$
$811$	10.2679	−	10.2679i	0.360555	−	0.360555i	0.864017	+	0.503462i	$0.167941\pi$
$812$	−13.0903	−	29.5287i	−0.459381	−	1.03626i
$813$		0			0
$814$	−0.0667860	−	0.0124334i	−0.00234085	−	0.000435792i
$815$	−12.3439	+	17.9011i	−0.432390	+	0.627050i
$816$		0			0
$817$			15.7607i			0.551398i
$818$	−1.97313	+	10.5986i	−0.0689890	+	0.370573i
$819$		0			0
$820$	−2.53664	+	13.4498i	−0.0885832	+	0.469689i
$821$	6.82793	−	6.82793i	0.238296	−	0.238296i	−0.577848	−	0.816144i	$-0.696107\pi$
$821$	6.82793	−	6.82793i	0.238296	−	0.238296i	0.816144	+	0.577848i	$0.196107\pi$
$822$		0			0
$823$	40.4181			1.40889			0.704444	−	0.709760i	$-0.251197\pi$
$823$	40.4181			1.40889			0.704444	+	0.709760i	$0.251197\pi$
$824$	−14.7949	−	9.11532i	−0.515403	−	0.317547i
$825$		0			0
$826$	20.0034	−	13.7244i	0.696009	−	0.477532i
$827$	23.8197	+	23.8197i	0.828291	+	0.828291i	0.987280	−	0.158989i	$-0.0508236\pi$
$827$	23.8197	+	23.8197i	0.828291	+	0.828291i	−0.158989	+	0.987280i	$0.550824\pi$
$828$		0			0
$829$	−13.6687	−	13.6687i	−0.474734	−	0.474734i	0.428709	−	0.903443i	$-0.358969\pi$
$829$	−13.6687	−	13.6687i	−0.474734	−	0.474734i	−0.903443	+	0.428709i	$0.858969\pi$
$830$	17.4012	−	17.3196i	0.604003	−	0.601172i
$831$		0			0
$832$	0.333232	+	0.110048i	0.0115527	+	0.00381525i
$833$			3.72090i			0.128921i
$834$		0			0
$835$	28.1886	−	5.17935i	0.975508	−	0.179239i
$836$	−2.57943	−	0.994897i	−0.0892113	−	0.0344092i
$837$		0			0
$838$	3.63723	+	5.30130i	0.125646	+	0.183130i
$839$		−	0.00707031i		−	0.000244094i	−1.00000		0.000122047i	$-0.999961\pi$
$839$		−	0.00707031i		−	0.000244094i	1.00000		0.000122047i	$-3.88488e-5\pi$
$840$		0			0
$841$			50.1179i			1.72820i
$842$	13.4061	−	9.19797i	0.462006	−	0.316983i
$843$		0			0
$844$	2.22146	+	5.01110i	0.0764659	+	0.172489i
$845$	−5.25237	−	28.5861i	−0.180687	−	0.983390i
$846$		0			0
$847$		−	19.5722i		−	0.672510i
$848$	1.95847	+	39.8121i	0.0672540	+	1.36715i
$849$		0			0
$850$	1.26748	+	6.99064i	0.0434743	+	0.239777i
$851$	0.450599	+	0.450599i	0.0154463	+	0.0154463i
$852$		0			0
$853$	−24.8778	−	24.8778i	−0.851800	−	0.851800i	0.138555	−	0.990355i	$-0.455754\pi$
$853$	−24.8778	−	24.8778i	−0.851800	−	0.851800i	−0.990355	+	0.138555i	$0.955754\pi$
$854$	5.94634	+	8.66686i	0.203480	+	0.296574i
$855$		0			0
$856$	6.39250	+	26.9117i	0.218491	+	0.919822i
$857$	−17.0079			−0.580979			−0.290490	−	0.956878i	$-0.593818\pi$
$857$	−17.0079			−0.580979			−0.290490	+	0.956878i	$0.593818\pi$
$858$		0			0
$859$	−10.6241	+	10.6241i	−0.362490	+	0.362490i	−0.864729	−	0.502239i	$-0.832510\pi$
$859$	−10.6241	+	10.6241i	−0.362490	+	0.362490i	0.502239	+	0.864729i	$0.332510\pi$
$860$	13.4965	+	19.7706i	0.460226	+	0.674173i
$861$		0			0
$862$	−47.7452	−	8.88864i	−1.62621	−	0.302748i
$863$			8.48545i			0.288848i	0.989516	+	0.144424i	$0.0461329\pi$
$863$			8.48545i			0.288848i	−0.989516	+	0.144424i	$0.953867\pi$
$864$		0			0
$865$	10.5723	−	15.3319i	0.359468	−	0.521300i
$866$	−8.07663	+	43.3835i	−0.274455	+	1.47423i
$867$		0			0
$868$	−24.0993	−	9.29523i	−0.817985	−	0.315501i
$869$	5.17817	−	5.17817i	0.175658	−	0.175658i
$870$		0			0
$871$		−	0.00935742i		−	0.000317064i
$872$	5.69391	+	23.9707i	0.192820	+	0.811749i
$873$		0			0
$874$	14.6717	+	21.3842i	0.496279	+	0.723332i
$875$	17.3575	−	10.5262i	0.586791	−	0.355850i
$876$		0			0
$877$	37.8615	−	37.8615i	1.27849	−	1.27849i	0.336982	−	0.941511i	$-0.390594\pi$
$877$	37.8615	−	37.8615i	1.27849	−	1.27849i	0.941511	−	0.336982i	$-0.109406\pi$
$878$	6.51557	−	34.9983i	0.219890	−	1.18113i
$879$		0			0
$880$	−4.08766	+	0.960830i	−0.137795	+	0.0323896i
$881$	−13.4706			−0.453836			−0.226918	−	0.973914i	$-0.572865\pi$
$881$	−13.4706			−0.453836			−0.226918	+	0.973914i	$0.572865\pi$
$882$		0			0
$883$	9.55258	−	9.55258i	0.321470	−	0.321470i	−0.527861	−	0.849331i	$-0.677006\pi$
$883$	9.55258	−	9.55258i	0.321470	−	0.321470i	0.849331	+	0.527861i	$0.177006\pi$
$884$	−0.0357245	−	0.0805860i	−0.00120154	−	0.00271040i
$885$		0			0
$886$	−5.53714	−	8.07045i	−0.186024	−	0.271132i
$887$	0.288617			0.00969081			0.00484540	−	0.999988i	$-0.498458\pi$
$887$	0.288617			0.00969081			0.00484540	+	0.999988i	$0.498458\pi$
$888$		0			0
$889$			19.1536i			0.642393i
$890$	0.106612	−	45.3849i	0.00357364	−	1.52130i
$891$		0			0
$892$	−6.63618	+	17.2053i	−0.222196	+	0.576078i
$893$	20.9193	−	20.9193i	0.700039	−	0.700039i
$894$		0			0
$895$	−26.3934	−	18.1998i	−0.882233	−	0.608354i
$896$	5.72362	+	19.7285i	0.191213	+	0.659083i
$897$		0			0
$898$	51.1452	+	9.52161i	1.70674	+	0.317740i
$899$	44.7379	+	44.7379i	1.49209	+	1.49209i
$900$		0			0
$901$	7.07979	−	7.07979i	0.235862	−	0.235862i
$902$	1.14957	+	1.67551i	0.0382765	+	0.0557884i
$903$		0			0
$904$	3.16168	−	5.13165i	0.105156	−	0.170676i
$905$	19.5095	−	28.2926i	0.648518	−	0.940478i
$906$		0			0
$907$	38.0634	+	38.0634i	1.26387	+	1.26387i	0.949200	+	0.314672i	$0.101895\pi$
$907$	38.0634	+	38.0634i	1.26387	+	1.26387i	0.314672	+	0.949200i	$0.398105\pi$
$908$	−28.5614	+	12.6615i	−0.947844	+	0.420188i
$909$		0			0
$910$	−0.178515	+	0.177679i	−0.00591772	+	0.00588999i
$911$	−27.9067			−0.924591			−0.462295	−	0.886726i	$-0.652974\pi$
$911$	−27.9067			−0.924591			−0.462295	+	0.886726i	$0.652974\pi$
$912$		0			0
$913$		−	3.64488i		−	0.120628i
$914$	5.26395	+	0.979982i	0.174116	+	0.0324149i
$915$		0			0
$916$	13.5261	−	5.99623i	0.446914	−	0.198121i
$917$	10.5734	+	10.5734i	0.349163	+	0.349163i
$918$		0			0
$919$			27.9263i			0.921202i	0.887607	+	0.460601i	$0.152366\pi$
$919$			27.9263i			0.921202i	−0.887607	+	0.460601i	$0.847634\pi$
$920$	36.7167	+	14.2610i	1.21051	+	0.470170i
$921$		0			0
$922$	−27.9150	−	40.6865i	−0.919332	−	1.33994i
$923$	−0.451327	−	0.451327i	−0.0148556	−	0.0148556i
$924$		0			0
$925$	0.466724	+	0.209532i	0.0153458	+	0.00688938i
$926$	1.00152	−	5.37966i	0.0329121	−	0.176787i
$927$		0			0
$928$	6.76756	−	49.8595i	0.222156	−	1.63672i
$929$	24.8391			0.814943			0.407472	−	0.913218i	$-0.366411\pi$
$929$	24.8391			0.814943			0.407472	+	0.913218i	$0.366411\pi$
$930$		0			0
$931$	7.71043	+	7.71043i	0.252699	+	0.252699i
$932$	27.1521	+	10.4727i	0.889398	+	0.343045i
$933$		0			0
$934$	−20.6871	+	14.1935i	−0.676904	+	0.464425i
$935$	0.868319	+	0.598759i	0.0283971	+	0.0195815i
$936$		0			0
$937$	14.2052			0.464062			0.232031	−	0.972708i	$-0.425463\pi$
$937$	14.2052			0.464062			0.232031	+	0.972708i	$0.425463\pi$
$938$	0.451655	−	0.309881i	0.0147471	−	0.0101180i
$939$		0			0
$940$	8.32776	−	44.1557i	0.271622	−	1.44020i
$941$	−0.916857	−	0.916857i	−0.0298887	−	0.0298887i	0.692005	−	0.721893i	$-0.256728\pi$
$941$	−0.916857	−	0.916857i	−0.0298887	−	0.0298887i	−0.721893	+	0.692005i	$0.756728\pi$
$942$		0			0
$943$		−	19.0606i		−	0.620698i
$944$	37.7445	−	1.85676i	1.22848	−	0.0604324i
$945$		0			0
$946$	3.49381	+	0.650436i	0.113593	+	0.0211475i
$947$	−20.1404	+	20.1404i	−0.654474	+	0.654474i	−0.954067	−	0.299593i	$-0.903149\pi$
$947$	−20.1404	+	20.1404i	−0.654474	+	0.654474i	0.299593	+	0.954067i	$0.403149\pi$
$948$		0			0
$949$	0.466277	−	0.466277i	0.0151360	−	0.0151360i
$950$	17.1125	+	11.8595i	0.555201	+	0.384773i
$951$		0			0
$952$	2.70660	−	4.39301i	0.0877212	−	0.142378i
$953$	−49.1705			−1.59279			−0.796394	−	0.604777i	$-0.793262\pi$
$953$	−49.1705			−1.59279			−0.796394	+	0.604777i	$0.793262\pi$
$954$		0			0
$955$	−3.45957	+	0.635658i	−0.111949	+	0.0205694i
$956$	15.3648	+	5.92628i	0.496933	+	0.191669i
$957$		0			0
$958$	37.4973	+	6.98082i	1.21148	+	0.225540i
$959$	−28.4250			−0.917892
$960$		0			0
$961$	19.5949			0.632095
$962$	−0.00624040	−	0.00116176i	−0.000201198	−	3.74568e-5i
$963$		0			0
$964$	−12.7222	−	4.90703i	−0.409756	−	0.158045i
$965$	1.58328	+	8.61700i	0.0509675	+	0.277391i
$966$		0			0
$967$	−52.7223			−1.69543			−0.847717	−	0.530449i	$-0.822023\pi$
$967$	−52.7223			−1.69543			−0.847717	+	0.530449i	$0.822023\pi$
$968$	15.9931	−	25.9580i	0.514038	−	0.834322i
$969$		0			0
$970$	−0.100718	+	42.8756i	−0.00323385	+	1.37665i
$971$	36.7211	−	36.7211i	1.17843	−	1.17843i	0.198292	−	0.980143i	$-0.436461\pi$
$971$	36.7211	−	36.7211i	1.17843	−	1.17843i	0.980143	−	0.198292i	$-0.0635394\pi$
$972$		0			0
$973$	2.07309	−	2.07309i	0.0664602	−	0.0664602i
$974$	35.0132	+	6.51835i	1.12190	+	0.208862i
$975$		0			0
$976$	0.804476	+	16.3535i	0.0257506	+	0.523464i
$977$			44.2340i			1.41517i	0.706628	+	0.707585i	$0.250215\pi$
$977$			44.2340i			1.41517i	−0.706628	+	0.707585i	$0.749785\pi$
$978$		0			0
$979$	−4.76436	−	4.76436i	−0.152270	−	0.152270i
$980$	16.2749	+	3.06944i	0.519882	+	0.0980496i
$981$		0			0
$982$	−28.1415	+	19.3079i	−0.898031	+	0.616140i
$983$	−55.1017			−1.75747			−0.878736	−	0.477308i	$-0.841612\pi$
$983$	−55.1017			−1.75747			−0.878736	+	0.477308i	$0.841612\pi$
$984$		0			0
$985$	7.10624	+	4.90019i	0.226424	+	0.156133i
$986$	−10.4217	+	7.15038i	−0.331896	+	0.227714i
$987$		0			0
$988$	−0.241018	−	0.0929619i	−0.00766781	−	0.00295751i
$989$	−23.5724	−	23.5724i	−0.749559	−	0.749559i
$990$		0			0
$991$	−0.865019			−0.0274782			−0.0137391	−	0.999906i	$-0.504373\pi$
$991$	−0.865019			−0.0274782			−0.0137391	+	0.999906i	$0.504373\pi$
$992$	−24.3667	−	32.0203i	−0.773645	−	1.01665i
$993$		0			0
$994$	6.83804	−	36.7304i	0.216889	−	1.16502i
$995$	7.95451	+	43.2925i	0.252175	+	1.37246i
$996$		0			0
$997$	−41.8219	−	41.8219i	−1.32451	−	1.32451i	−0.910080	−	0.414433i	$-0.863980\pi$
$997$	−41.8219	−	41.8219i	−1.32451	−	1.32451i	−0.414433	−	0.910080i	$-0.636020\pi$
$998$	−12.7260	−	18.5482i	−0.402833	−	0.587134i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.2		48
3.2	odd	2		240.2.bl.a.109.23	yes	48
5.4	even	2	inner	720.2.bm.h.109.23		48
12.11	even	2		960.2.bl.a.529.24		48
15.14	odd	2		240.2.bl.a.109.2	✓	48
16.5	even	4	inner	720.2.bm.h.469.23		48
24.5	odd	2		1920.2.bl.a.289.21		48
24.11	even	2		1920.2.bl.b.289.4		48
48.5	odd	4		240.2.bl.a.229.2	yes	48
48.11	even	4		960.2.bl.a.49.7		48
48.29	odd	4		1920.2.bl.a.1249.4		48
48.35	even	4		1920.2.bl.b.1249.21		48
60.59	even	2		960.2.bl.a.529.7		48
80.69	even	4	inner	720.2.bm.h.469.2		48
120.29	odd	2		1920.2.bl.a.289.4		48
120.59	even	2		1920.2.bl.b.289.21		48
240.29	odd	4		1920.2.bl.a.1249.21		48
240.59	even	4		960.2.bl.a.49.24		48
240.149	odd	4		240.2.bl.a.229.23	yes	48
240.179	even	4		1920.2.bl.b.1249.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.2	✓	48	15.14	odd	2
240.2.bl.a.109.23	yes	48	3.2	odd	2
240.2.bl.a.229.2	yes	48	48.5	odd	4
240.2.bl.a.229.23	yes	48	240.149	odd	4
720.2.bm.h.109.2		48	1.1	even	1	trivial
720.2.bm.h.109.23		48	5.4	even	2	inner
720.2.bm.h.469.2		48	80.69	even	4	inner
720.2.bm.h.469.23		48	16.5	even	4	inner
960.2.bl.a.49.7		48	48.11	even	4
960.2.bl.a.49.24		48	240.59	even	4
960.2.bl.a.529.7		48	60.59	even	2
960.2.bl.a.529.24		48	12.11	even	2
1920.2.bl.a.289.4		48	120.29	odd	2
1920.2.bl.a.289.21		48	24.5	odd	2
1920.2.bl.a.1249.4		48	48.29	odd	4
1920.2.bl.a.1249.21		48	240.29	odd	4
1920.2.bl.b.289.4		48	24.11	even	2
1920.2.bl.b.289.21		48	120.59	even	2
1920.2.bl.b.1249.4		48	240.179	even	4
1920.2.bl.b.1249.21		48	48.35	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39033 - 0.258835i) q^{2} +(1.86601 + 0.719729i) q^{4} +(-2.19925 + 0.404088i) q^{5} -1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} +O(q^{10})\)	\(q+(-1.39033 - 0.258835i) q^{2} +(1.86601 + 0.719729i) q^{4} +(-2.19925 + 0.404088i) q^{5} -1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} +(3.16227 + 0.00742837i) q^{10} +(0.331965 - 0.331965i) q^{11} +(0.0310184 - 0.0310184i) q^{13} +(2.52438 + 0.469959i) q^{14} +(2.96398 + 2.68604i) q^{16} -1.00474i q^{17} +(-2.08203 - 2.08203i) q^{19} +(-4.39466 - 0.828833i) q^{20} +(-0.547464 + 0.375616i) q^{22} +6.22794 q^{23} +(4.67343 - 1.77739i) q^{25} +(-0.0511543 + 0.0350971i) q^{26} +(-3.38806 - 1.30679i) q^{28} +(6.28959 + 6.28959i) q^{29} +7.11301 q^{31} +(-3.42566 - 4.50165i) q^{32} +(-0.260063 + 1.39692i) q^{34} +(3.99313 - 0.733693i) q^{35} +(0.0723513 + 0.0723513i) q^{37} +(2.35580 + 3.43360i) q^{38} +(5.89548 + 2.28984i) q^{40} -3.06050i q^{41} +(-3.78495 - 3.78495i) q^{43} +(0.858375 - 0.380525i) q^{44} +(-8.65886 - 1.61201i) q^{46} +10.0476i q^{47} -3.70333 q^{49} +(-6.95763 + 1.26150i) q^{50} +(0.0802055 - 0.0355558i) q^{52} +(7.04636 + 7.04636i) q^{53} +(-0.595932 + 0.864219i) q^{55} +(4.37227 + 2.69382i) q^{56} +(-7.11661 - 10.3725i) q^{58} +(6.68042 - 6.68042i) q^{59} +(2.89442 + 2.89442i) q^{61} +(-9.88940 - 1.84109i) q^{62} +(3.59760 + 7.14544i) q^{64} +(-0.0556832 + 0.0807515i) q^{65} +(0.150837 - 0.150837i) q^{67} +(0.723143 - 1.87486i) q^{68} +(-5.74165 - 0.0134875i) q^{70} -14.5503i q^{71} +15.0323 q^{73} +(-0.0818648 - 0.119319i) q^{74} +(-2.38659 - 5.38358i) q^{76} +(-0.602741 + 0.602741i) q^{77} +15.5985 q^{79} +(-7.60394 - 4.70957i) q^{80} +(-0.792162 + 4.25508i) q^{82} +(5.48985 - 5.48985i) q^{83} +(0.406005 + 2.20969i) q^{85} +(4.28263 + 6.24198i) q^{86} +(-1.29191 + 0.306877i) q^{88} -14.3520i q^{89} +(-0.0563193 + 0.0563193i) q^{91} +(11.6214 + 4.48242i) q^{92} +(2.60066 - 13.9694i) q^{94} +(5.42023 + 3.73758i) q^{95} +13.5585i q^{97} +(5.14883 + 0.958550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

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