LMFDB - Embedded newform 864.2.v.a.325.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			325.10
Character	$\chi$	$=$	864.325
Dual form			864.2.v.a.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.934820 - 1.06118i) q^{2} +(-0.252222 + 1.98403i) q^{4} +(0.930451 + 0.385405i) q^{5} +(-0.938500 - 0.938500i) q^{7} +(2.34121 - 1.58706i) q^{8} +O(q^{10})$	\(q+(-0.934820 - 1.06118i) q^{2} +(-0.252222 + 1.98403i) q^{4} +(0.930451 + 0.385405i) q^{5} +(-0.938500 - 0.938500i) q^{7} +(2.34121 - 1.58706i) q^{8} +(-0.460818 - 1.34766i) q^{10} +(-0.846222 + 2.04296i) q^{11} +(-5.64483 + 2.33816i) q^{13} +(-0.118592 + 1.87325i) q^{14} +(-3.87277 - 1.00083i) q^{16} -7.71645i q^{17} +(-3.36643 + 1.39442i) q^{19} +(-0.999337 + 1.74884i) q^{20} +(2.95902 - 1.01180i) q^{22} +(5.65026 - 5.65026i) q^{23} +(-2.81833 - 2.81833i) q^{25} +(7.75812 + 3.80444i) q^{26} +(2.09872 - 1.62530i) q^{28} +(-0.949070 - 2.29126i) q^{29} +5.39395 q^{31} +(2.55827 + 5.04532i) q^{32} +(-8.18857 + 7.21350i) q^{34} +(-0.511525 - 1.23493i) q^{35} +(-4.01544 - 1.66325i) q^{37} +(4.62674 + 2.26887i) q^{38} +(2.79004 - 0.574368i) q^{40} +(-6.02596 + 6.02596i) q^{41} +(3.38507 - 8.17229i) q^{43} +(-3.83986 - 2.19421i) q^{44} +(-11.2779 - 0.713987i) q^{46} -6.68653i q^{47} -5.23844i q^{49} +(-0.356135 + 5.62540i) q^{50} +(-3.21524 - 11.7893i) q^{52} +(0.589451 - 1.42306i) q^{53} +(-1.57474 + 1.57474i) q^{55} +(-3.68668 - 0.707766i) q^{56} +(-1.54424 + 3.14905i) q^{58} +(-7.21416 - 2.98820i) q^{59} +(-3.05674 - 7.37963i) q^{61} +(-5.04238 - 5.72397i) q^{62} +(2.96249 - 7.43126i) q^{64} -6.15337 q^{65} +(3.77223 + 9.10696i) q^{67} +(15.3097 + 1.94626i) q^{68} +(-0.832305 + 1.69726i) q^{70} +(-1.95353 - 1.95353i) q^{71} +(-8.58563 + 8.58563i) q^{73} +(1.98870 + 5.81596i) q^{74} +(-1.91749 - 7.03081i) q^{76} +(2.71150 - 1.12314i) q^{77} +11.7674i q^{79} +(-3.21769 - 2.42381i) q^{80} +(12.0278 + 0.761461i) q^{82} +(-6.05690 + 2.50885i) q^{83} +(2.97396 - 7.17978i) q^{85} +(-11.8367 + 4.04744i) q^{86} +(1.26112 + 6.12599i) q^{88} +(-5.36845 - 5.36845i) q^{89} +(7.49204 + 3.10330i) q^{91} +(9.78518 + 12.6354i) q^{92} +(-7.09564 + 6.25071i) q^{94} -3.66972 q^{95} -8.31108 q^{97} +(-5.55894 + 4.89700i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.934820	−	1.06118i	−0.661018	−	0.750370i
$2$	−0.934820	−	1.06118i	−0.661018	−	0.750370i
$3$		0			0
$3$		0			0
$4$	−0.252222	+	1.98403i	−0.126111	+	0.992016i
$5$	0.930451	+	0.385405i	0.416110	+	0.172359i	0.580909	−	0.813969i	$-0.302697\pi$
$5$	0.930451	+	0.385405i	0.416110	+	0.172359i	−0.164798	+	0.986327i	$0.552697\pi$
$6$		0			0
$7$	−0.938500	−	0.938500i	−0.354720	−	0.354720i	0.507143	−	0.861862i	$-0.330702\pi$
$7$	−0.938500	−	0.938500i	−0.354720	−	0.354720i	−0.861862	+	0.507143i	$0.830702\pi$
$8$	2.34121	−	1.58706i	0.827741	−	0.561110i
$9$		0			0
$10$	−0.460818	−	1.34766i	−0.145724	−	0.426169i
$11$	−0.846222	+	2.04296i	−0.255145	+	0.615976i	−0.998605	−	0.0528055i	$-0.983184\pi$
$11$	−0.846222	+	2.04296i	−0.255145	+	0.615976i	0.743459	+	0.668781i	$0.233184\pi$
$12$		0			0
$13$	−5.64483	+	2.33816i	−1.56559	+	0.648490i	−0.986050	−	0.166451i	$-0.946769\pi$
$13$	−5.64483	+	2.33816i	−1.56559	+	0.648490i	−0.579543	+	0.814941i	$0.696769\pi$
$14$	−0.118592	+	1.87325i	−0.0316951	+	0.500647i
$15$		0			0
$16$	−3.87277	−	1.00083i	−0.968192	−	0.250209i
$17$		−	7.71645i		−	1.87151i	−0.352645	−	0.935757i	$-0.614718\pi$
$17$		−	7.71645i		−	1.87151i	0.352645	−	0.935757i	$-0.385282\pi$
$18$		0			0
$19$	−3.36643	+	1.39442i	−0.772312	+	0.319902i	−0.733809	−	0.679356i	$-0.762259\pi$
$19$	−3.36643	+	1.39442i	−0.772312	+	0.319902i	−0.0385035	+	0.999258i	$0.512259\pi$
$20$	−0.999337	+	1.74884i	−0.223459	+	0.391052i
$21$		0			0
$22$	2.95902	−	1.01180i	0.630865	−	0.215717i
$23$	5.65026	−	5.65026i	1.17816	−	1.17816i	0.197948	−	0.980212i	$-0.436572\pi$
$23$	5.65026	−	5.65026i	1.17816	−	1.17816i	0.980212	−	0.197948i	$-0.0634278\pi$
$24$		0			0
$25$	−2.81833	−	2.81833i	−0.563666	−	0.563666i
$26$	7.75812	+	3.80444i	1.52149	+	0.746111i
$27$		0			0
$28$	2.09872	−	1.62530i	0.396622	−	0.307154i
$29$	−0.949070	−	2.29126i	−0.176238	−	0.425476i	0.810934	−	0.585138i	$-0.198960\pi$
$29$	−0.949070	−	2.29126i	−0.176238	−	0.425476i	−0.987172	+	0.159662i	$0.948960\pi$
$30$		0			0
$31$	5.39395			0.968782			0.484391	−	0.874852i	$-0.339041\pi$
$31$	5.39395			0.968782			0.484391	+	0.874852i	$0.339041\pi$
$32$	2.55827	+	5.04532i	0.452243	+	0.891895i
$33$		0			0
$34$	−8.18857	+	7.21350i	−1.40433	+	1.23710i
$35$	−0.511525	−	1.23493i	−0.0864636	−	0.208741i
$36$		0			0
$37$	−4.01544	−	1.66325i	−0.660134	−	0.273436i	0.0273609	−	0.999626i	$-0.491290\pi$
$37$	−4.01544	−	1.66325i	−0.660134	−	0.273436i	−0.687495	+	0.726189i	$0.741290\pi$
$38$	4.62674	+	2.26887i	0.750557	+	0.368059i
$39$		0			0
$40$	2.79004	−	0.574368i	0.441144	−	0.0908155i
$41$	−6.02596	+	6.02596i	−0.941096	+	0.941096i	−0.998359	−	0.0572629i	$-0.981763\pi$
$41$	−6.02596	+	6.02596i	−0.941096	+	0.941096i	0.0572629	+	0.998359i	$0.481763\pi$
$42$		0			0
$43$	3.38507	−	8.17229i	0.516219	−	1.24626i	−0.423991	−	0.905666i	$-0.639371\pi$
$43$	3.38507	−	8.17229i	0.516219	−	1.24626i	0.940210	−	0.340596i	$-0.110629\pi$
$44$	−3.83986	−	2.19421i	−0.578881	−	0.330790i
$45$		0			0
$46$	−11.2779	−	0.713987i	−1.66284	−	0.105272i
$47$		−	6.68653i		−	0.975331i	−0.873031	−	0.487666i	$-0.837849\pi$
$47$		−	6.68653i		−	0.975331i	0.873031	−	0.487666i	$-0.162151\pi$
$48$		0			0
$49$		−	5.23844i		−	0.748348i
$50$	−0.356135	+	5.62540i	−0.0503650	+	0.795552i
$51$		0			0
$52$	−3.21524	−	11.7893i	−0.445874	−	1.63488i
$53$	0.589451	−	1.42306i	0.0809673	−	0.195472i	−0.878212	−	0.478272i	$-0.841263\pi$
$53$	0.589451	−	1.42306i	0.0809673	−	0.195472i	0.959179	+	0.282800i	$0.0912632\pi$
$54$		0			0
$55$	−1.57474	+	1.57474i	−0.212337	+	0.212337i
$56$	−3.68668	−	0.707766i	−0.492653	−	0.0945792i
$57$		0			0
$58$	−1.54424	+	3.14905i	−0.202768	+	0.413491i
$59$	−7.21416	−	2.98820i	−0.939204	−	0.389031i	−0.140041	−	0.990146i	$-0.544723\pi$
$59$	−7.21416	−	2.98820i	−0.939204	−	0.389031i	−0.799163	+	0.601115i	$0.794723\pi$
$60$		0			0
$61$	−3.05674	−	7.37963i	−0.391376	−	0.944865i	−0.989641	−	0.143566i	$-0.954143\pi$
$61$	−3.05674	−	7.37963i	−0.391376	−	0.944865i	0.598265	−	0.801298i	$-0.295857\pi$
$62$	−5.04238	−	5.72397i	−0.640382	−	0.726946i
$63$		0			0
$64$	2.96249	−	7.43126i	0.370311	−	0.928908i
$65$	−6.15337			−0.763232
$66$		0			0
$67$	3.77223	+	9.10696i	0.460851	+	1.11259i	0.968049	+	0.250762i	$0.0806813\pi$
$67$	3.77223	+	9.10696i	0.460851	+	1.11259i	−0.507198	+	0.861830i	$0.669319\pi$
$68$	15.3097	+	1.94626i	1.85657	+	0.236019i
$69$		0			0
$70$	−0.832305	+	1.69726i	−0.0994795	+	0.202861i
$71$	−1.95353	−	1.95353i	−0.231842	−	0.231842i	0.581619	−	0.813461i	$-0.302419\pi$
$71$	−1.95353	−	1.95353i	−0.231842	−	0.231842i	−0.813461	+	0.581619i	$0.802419\pi$
$72$		0			0
$73$	−8.58563	+	8.58563i	−1.00487	+	1.00487i	−0.00488401	+	0.999988i	$0.501555\pi$
$73$	−8.58563	+	8.58563i	−1.00487	+	1.00487i	−0.999988	+	0.00488401i	$0.998445\pi$
$74$	1.98870	+	5.81596i	0.231182	+	0.676091i
$75$		0			0
$76$	−1.91749	−	7.03081i	−0.219951	−	0.806489i
$77$	2.71150	−	1.12314i	0.309004	−	0.127994i
$78$		0			0
$79$			11.7674i			1.32394i	0.749531	+	0.661969i	$0.230279\pi$
$79$			11.7674i			1.32394i	−0.749531	+	0.661969i	$0.769721\pi$
$80$	−3.21769	−	2.42381i	−0.359749	−	0.270991i
$81$		0			0
$82$	12.0278	+	0.761461i	1.32825	+	0.0840894i
$83$	−6.05690	+	2.50885i	−0.664831	+	0.275382i	−0.689470	−	0.724314i	$-0.742156\pi$
$83$	−6.05690	+	2.50885i	−0.664831	+	0.275382i	0.0246390	+	0.999696i	$0.492156\pi$
$84$		0			0
$85$	2.97396	−	7.17978i	0.322571	−	0.778756i
$86$	−11.8367	+	4.04744i	−1.27639	+	0.436446i
$87$		0			0
$88$	1.26112	+	6.12599i	0.134436	+	0.653033i
$89$	−5.36845	−	5.36845i	−0.569055	−	0.569055i	0.362809	−	0.931864i	$-0.381818\pi$
$89$	−5.36845	−	5.36845i	−0.569055	−	0.569055i	−0.931864	+	0.362809i	$0.881818\pi$
$90$		0			0
$91$	7.49204	+	3.10330i	0.785379	+	0.325315i
$92$	9.78518	+	12.6354i	1.02018	+	1.31733i
$93$		0			0
$94$	−7.09564	+	6.25071i	−0.731860	+	0.644711i
$95$	−3.66972			−0.376505
$96$		0			0
$97$	−8.31108			−0.843862			−0.421931	−	0.906628i	$-0.638648\pi$
$97$	−8.31108			−0.843862			−0.421931	+	0.906628i	$0.638648\pi$
$98$	−5.55894	+	4.89700i	−0.561538	+	0.494671i
$99$		0			0
$100$	6.30251	−	4.88082i	0.630251	−	0.488082i
$101$	3.21953	+	1.33357i	0.320355	+	0.132695i	0.537066	−	0.843540i	$-0.319533\pi$
$101$	3.21953	+	1.33357i	0.320355	+	0.132695i	−0.216711	+	0.976236i	$0.569533\pi$
$102$		0			0
$103$	0.343343	+	0.343343i	0.0338306	+	0.0338306i	0.723820	−	0.689989i	$-0.242385\pi$
$103$	0.343343	+	0.343343i	0.0338306	+	0.0338306i	−0.689989	+	0.723820i	$0.742385\pi$
$104$	−9.50489	+	14.4328i	−0.932032	+	1.41525i
$105$		0			0
$106$	−2.06116	+	0.704790i	−0.200198	+	0.0684553i
$107$	1.86534	−	4.50334i	0.180330	−	0.435354i	−0.807705	−	0.589587i	$-0.799291\pi$
$107$	1.86534	−	4.50334i	0.180330	−	0.435354i	0.988035	+	0.154233i	$0.0492906\pi$
$108$		0			0
$109$	−6.74343	+	2.79322i	−0.645904	+	0.267542i	−0.681493	−	0.731824i	$-0.738669\pi$
$109$	−6.74343	+	2.79322i	−0.645904	+	0.267542i	0.0355895	+	0.999366i	$0.488669\pi$
$110$	3.14318	+	0.198989i	0.299690	+	0.0189729i
$111$		0			0
$112$	2.69531	+	4.57388i	0.254683	+	0.432191i
$113$			2.17091i			0.204222i	0.994773	+	0.102111i	$0.0325596\pi$
$113$			2.17091i			0.204222i	−0.994773	+	0.102111i	$0.967440\pi$
$114$		0			0
$115$	7.43493	−	3.07965i	0.693311	−	0.287179i
$116$	4.78531	−	1.30508i	0.444304	−	0.121174i
$117$		0			0
$118$	3.57291	+	10.4490i	0.328913	+	0.961907i
$119$	−7.24189	+	7.24189i	−0.663863	+	0.663863i
$120$		0			0
$121$	4.32058	+	4.32058i	0.392780	+	0.392780i
$122$	−4.97364	+	10.1424i	−0.450292	+	0.918249i
$123$		0			0
$124$	−1.36047	+	10.7018i	−0.122174	+	0.961048i
$125$	−3.46315	−	8.36078i	−0.309753	−	0.747810i
$126$		0			0
$127$	−0.995355			−0.0883235			−0.0441617	−	0.999024i	$-0.514062\pi$
$127$	−0.995355			−0.0883235			−0.0441617	+	0.999024i	$0.514062\pi$
$128$	−10.6553	+	3.80315i	−0.941807	+	0.336154i
$129$		0			0
$130$	5.75230	+	6.52986i	0.504510	+	0.572707i
$131$	4.10132	+	9.90147i	0.358334	+	0.865096i	0.995535	+	0.0943974i	$0.0300924\pi$
$131$	4.10132	+	9.90147i	0.358334	+	0.865096i	−0.637200	+	0.770698i	$0.719908\pi$
$132$		0			0
$133$	4.46806	+	1.85073i	0.387430	+	0.160479i
$134$	6.13780	−	12.5164i	0.530225	−	1.08125i
$135$		0			0
$136$	−12.2465	−	18.0658i	−1.05013	−	1.54913i
$137$	12.7750	−	12.7750i	1.09144	−	1.09144i	0.0960676	−	0.995375i	$-0.469374\pi$
$137$	12.7750	−	12.7750i	1.09144	−	1.09144i	0.995375	−	0.0960676i	$-0.0306265\pi$
$138$		0			0
$139$	−1.10035	+	2.65647i	−0.0933302	+	0.225319i	−0.963650	−	0.267168i	$-0.913912\pi$
$139$	−1.10035	+	2.65647i	−0.0933302	+	0.225319i	0.870320	+	0.492487i	$0.163912\pi$
$140$	2.57916	−	0.703405i	0.217979	−	0.0594486i
$141$		0			0
$142$	−0.246855	+	3.89926i	−0.0207156	+	0.327219i
$143$		−	13.5108i		−	1.12983i
$144$		0			0
$145$		−	2.49768i		−	0.207421i
$146$	17.1370	+	1.08491i	1.41826	+	0.0897879i
$147$		0			0
$148$	4.31272	−	7.54725i	0.354504	−	0.620380i
$149$	0.247702	−	0.598004i	0.0202925	−	0.0489904i	−0.913408	−	0.407044i	$-0.866560\pi$
$149$	0.247702	−	0.598004i	0.0202925	−	0.0489904i	0.933701	+	0.358054i	$0.116560\pi$
$150$		0			0
$151$	13.5472	−	13.5472i	1.10246	−	1.10246i	0.108344	−	0.994113i	$-0.465445\pi$
$151$	13.5472	−	13.5472i	1.10246	−	1.10246i	0.994113	−	0.108344i	$-0.0345549\pi$
$152$	−5.66848	+	8.60735i	−0.459774	+	0.698148i
$153$		0			0
$154$	−3.72662	−	1.82746i	−0.300300	−	0.147261i
$155$	5.01881	+	2.07886i	0.403120	+	0.166978i
$156$		0			0
$157$	4.17046	+	10.0684i	0.332839	+	0.803544i	0.998365	+	0.0571689i	$0.0182074\pi$
$157$	4.17046	+	10.0684i	0.332839	+	0.803544i	−0.665526	+	0.746375i	$0.731793\pi$
$158$	12.4874	−	11.0004i	0.993444	−	0.875147i
$159$		0			0
$160$	0.435854	+	5.68039i	0.0344573	+	0.449075i
$161$	−10.6055			−0.835834
$162$		0			0
$163$	−2.29505	−	5.54074i	−0.179762	−	0.433985i	0.808154	−	0.588971i	$-0.200467\pi$
$163$	−2.29505	−	5.54074i	−0.179762	−	0.433985i	−0.987917	+	0.154986i	$0.950467\pi$
$164$	−10.4358	−	13.4756i	−0.814900	−	1.05227i
$165$		0			0
$166$	8.32446	+	4.08216i	0.646103	+	0.316837i
$167$	−6.22675	−	6.22675i	−0.481840	−	0.481840i	0.423879	−	0.905719i	$-0.360668\pi$
$167$	−6.22675	−	6.22675i	−0.481840	−	0.481840i	−0.905719	+	0.423879i	$0.860668\pi$
$168$		0			0
$169$	17.2047	−	17.2047i	1.32344	−	1.32344i
$170$	−10.3992	+	3.55588i	−0.797581	+	0.272724i
$171$		0			0
$172$	15.3603	+	8.77733i	1.17121	+	0.669265i
$173$	−0.963826	+	0.399230i	−0.0732783	+	0.0303529i	−0.419022	−	0.907976i	$-0.637627\pi$
$173$	−0.963826	+	0.399230i	−0.0732783	+	0.0303529i	0.345743	+	0.938329i	$0.387627\pi$
$174$		0			0
$175$			5.29001i			0.399887i
$176$	5.32188	−	7.06498i	0.401152	−	0.532543i
$177$		0			0
$178$	−0.678377	+	10.7154i	−0.0508465	+	0.803157i
$179$	−9.89224	+	4.09750i	−0.739381	+	0.306261i	−0.720400	−	0.693558i	$-0.756042\pi$
$179$	−9.89224	+	4.09750i	−0.739381	+	0.306261i	−0.0189802	+	0.999820i	$0.506042\pi$
$180$		0			0
$181$	1.31664	−	3.17865i	0.0978651	−	0.236267i	−0.867363	−	0.497676i	$-0.834187\pi$
$181$	1.31664	−	3.17865i	0.0978651	−	0.236267i	0.965228	+	0.261408i	$0.0841870\pi$
$182$	−3.71053	−	10.8515i	−0.275043	−	0.804364i
$183$		0			0
$184$	4.26112	−	22.1957i	0.314134	−	1.63629i
$185$	−3.09514	−	3.09514i	−0.227559	−	0.227559i
$186$		0			0
$187$	15.7644	+	6.52983i	1.15281	+	0.477508i
$188$	13.2663	+	1.68649i	0.967544	+	0.123000i
$189$		0			0
$190$	3.43052	+	3.89424i	0.248876	+	0.282518i
$191$	21.8507			1.58106			0.790531	−	0.612422i	$-0.209805\pi$
$191$	21.8507			1.58106			0.790531	+	0.612422i	$0.209805\pi$
$192$		0			0
$193$	−14.5286			−1.04579			−0.522897	−	0.852396i	$-0.675149\pi$
$193$	−14.5286			−1.04579			−0.522897	+	0.852396i	$0.675149\pi$
$194$	7.76936	+	8.81958i	0.557808	+	0.633209i
$195$		0			0
$196$	10.3932	+	1.32125i	0.742373	+	0.0943750i
$197$	15.9169	+	6.59300i	1.13403	+	0.469732i	0.869150	−	0.494548i	$-0.164667\pi$
$197$	15.9169	+	6.59300i	1.13403	+	0.469732i	0.264883	+	0.964280i	$0.414667\pi$
$198$		0			0
$199$	12.3938	+	12.3938i	0.878574	+	0.878574i	0.993387	−	0.114813i	$-0.0366270\pi$
$199$	12.3938	+	12.3938i	0.878574	+	0.878574i	−0.114813	+	0.993387i	$0.536627\pi$
$200$	−11.0712	−	2.12543i	−0.782849	−	0.150291i
$201$		0			0
$202$	−1.59451	−	4.66316i	−0.112190	−	0.328099i
$203$	−1.25964	+	3.04105i	−0.0884096	+	0.213440i
$204$		0			0
$205$	−7.92929	+	3.28442i	−0.553806	+	0.229394i
$206$	0.0433860	−	0.685313i	0.00302285	−	0.0477480i
$207$		0			0
$208$	24.2012	−	3.40563i	1.67805	−	0.236138i
$209$		−	8.05747i		−	0.557347i
$210$		0			0
$211$	−10.6796	+	4.42362i	−0.735212	+	0.304535i	−0.718692	−	0.695329i	$-0.755259\pi$
$211$	−10.6796	+	4.42362i	−0.735212	+	0.304535i	−0.0165202	+	0.999864i	$0.505259\pi$
$212$	2.67473	+	1.52842i	0.183701	+	0.104972i
$213$		0			0
$214$	−6.52263	+	2.23034i	−0.445878	+	0.152463i
$215$	6.29929	−	6.29929i	0.429608	−	0.429608i
$216$		0			0
$217$	−5.06222	−	5.06222i	−0.343646	−	0.343646i
$218$	9.26802	+	4.54486i	0.627710	+	0.307817i
$219$		0			0
$220$	−2.72714	−	3.52151i	−0.183864	−	0.237420i
$221$	18.0423	+	43.5580i	1.21366	+	2.93003i
$222$		0			0
$223$	12.0545			0.807226			0.403613	−	0.914930i	$-0.367754\pi$
$223$	12.0545			0.807226			0.403613	+	0.914930i	$0.367754\pi$
$224$	2.33409	−	7.13597i	0.155953	−	0.476792i
$225$		0			0
$226$	2.30373	−	2.02941i	0.153242	−	0.134994i
$227$	3.72637	+	8.99626i	0.247328	+	0.597103i	0.997975	−	0.0636001i	$-0.0202582\pi$
$227$	3.72637	+	8.99626i	0.247328	+	0.597103i	−0.750647	+	0.660703i	$0.770258\pi$
$228$		0			0
$229$	−26.6130	−	11.0235i	−1.75864	−	0.728452i	−0.996733	−	0.0807641i	$-0.974264\pi$
$229$	−26.6130	−	11.0235i	−1.75864	−	0.728452i	−0.761906	−	0.647688i	$-0.775736\pi$
$230$	−10.2184	−	5.01091i	−0.673781	−	0.330410i
$231$		0			0
$232$	−5.85833	−	3.85807i	−0.384618	−	0.253295i
$233$	−11.3815	+	11.3815i	−0.745628	+	0.745628i	−0.973655	−	0.228027i	$-0.926773\pi$
$233$	−11.3815	+	11.3815i	−0.745628	+	0.745628i	0.228027	+	0.973655i	$0.426773\pi$
$234$		0			0
$235$	2.57703	−	6.22149i	0.168107	−	0.405845i
$236$	7.74826	−	13.5594i	0.504369	−	0.882644i
$237$		0			0
$238$	14.4548	+	0.915111i	0.936968	+	0.0593179i
$239$		−	12.1171i		−	0.783790i	−0.920010	−	0.391895i	$-0.871820\pi$
$239$		−	12.1171i		−	0.783790i	0.920010	−	0.391895i	$-0.128180\pi$
$240$		0			0
$241$		−	1.31602i		−	0.0847721i	−0.999101	−	0.0423860i	$-0.986504\pi$
$241$		−	1.31602i		−	0.0847721i	0.999101	−	0.0423860i	$-0.0134959\pi$
$242$	0.545964	−	8.62390i	0.0350959	−	0.554365i
$243$		0			0
$244$	15.4124	−	4.20337i	0.986678	−	0.269093i
$245$	2.01892	−	4.87411i	0.128984	−	0.311395i
$246$		0			0
$247$	15.7425	−	15.7425i	1.00167	−	1.00167i
$248$	12.6283	−	8.56052i	0.801901	−	0.543594i
$249$		0			0
$250$	−5.63490	+	11.4909i	−0.356382	+	0.726746i
$251$	−9.63552	−	3.99117i	−0.608189	−	0.251920i	0.0572650	−	0.998359i	$-0.481762\pi$
$251$	−9.63552	−	3.99117i	−0.608189	−	0.251920i	−0.665454	+	0.746439i	$0.731762\pi$
$252$		0			0
$253$	6.76188	+	16.3246i	0.425116	+	1.02632i
$254$	0.930478	+	1.05625i	0.0583834	+	0.0662753i
$255$		0			0
$256$	13.9967	+	7.75200i	0.874791	+	0.484500i
$257$	−8.53035			−0.532109			−0.266054	−	0.963958i	$-0.585720\pi$
$257$	−8.53035			−0.532109			−0.266054	+	0.963958i	$0.585720\pi$
$258$		0			0
$259$	2.20753	+	5.32945i	0.137169	+	0.331156i
$260$	1.55202	−	12.2085i	0.0962521	−	0.757139i
$261$		0			0
$262$	6.67328	−	13.6084i	0.412277	−	0.840727i
$263$	−6.53095	−	6.53095i	−0.402715	−	0.402715i	0.476473	−	0.879189i	$-0.341915\pi$
$263$	−6.53095	−	6.53095i	−0.402715	−	0.402715i	−0.879189	+	0.476473i	$0.841915\pi$
$264$		0			0
$265$	1.09691	−	1.09691i	0.0673827	−	0.0673827i
$266$	−2.21287	−	6.47153i	−0.135680	−	0.396795i
$267$		0			0
$268$	−19.0199	+	5.18724i	−1.16183	+	0.316861i
$269$	22.7725	−	9.43267i	1.38846	−	0.575120i	0.441732	−	0.897147i	$-0.354364\pi$
$269$	22.7725	−	9.43267i	1.38846	−	0.575120i	0.946731	+	0.322027i	$0.104364\pi$
$270$		0			0
$271$			30.4157i			1.84762i	0.382847	+	0.923812i	$0.374944\pi$
$271$			30.4157i			1.84762i	−0.382847	+	0.923812i	$0.625056\pi$
$272$	−7.72289	+	29.8840i	−0.468269	+	1.81199i
$273$		0			0
$274$	−25.4990	−	1.61430i	−1.54045	−	0.0975232i
$275$	8.14267	−	3.37281i	0.491022	−	0.203388i
$276$		0			0
$277$	11.9512	−	28.8527i	0.718077	−	1.73359i	0.0393221	−	0.999227i	$-0.487480\pi$
$277$	11.9512	−	28.8527i	0.718077	−	1.73359i	0.678755	−	0.734365i	$-0.262520\pi$
$278$	3.84763	−	1.31565i	0.230766	−	0.0789077i
$279$		0			0
$280$	−3.15749	−	2.07941i	−0.188696	−	0.124268i
$281$	−23.3117	−	23.3117i	−1.39066	−	1.39066i	−0.823844	−	0.566816i	$-0.808175\pi$
$281$	−23.3117	−	23.3117i	−1.39066	−	1.39066i	−0.566816	−	0.823844i	$-0.691825\pi$
$282$		0			0
$283$	22.7460	+	9.42171i	1.35211	+	0.560063i	0.936879	−	0.349653i	$-0.113701\pi$
$283$	22.7460	+	9.42171i	1.35211	+	0.560063i	0.415232	+	0.909716i	$0.363701\pi$
$284$	4.36860	−	3.38315i	0.259228	−	0.200753i
$285$		0			0
$286$	−14.3374	+	12.6301i	−0.847788	+	0.746835i
$287$	11.3107			0.667651
$288$		0			0
$289$	−42.5436			−2.50257
$290$	−2.65050	+	2.33488i	−0.155643	+	0.137109i
$291$		0			0
$292$	−14.8687	−	19.1997i	−0.870124	−	1.12357i
$293$	10.6254	+	4.40120i	0.620744	+	0.257121i	0.670815	−	0.741625i	$-0.265945\pi$
$293$	10.6254	+	4.40120i	0.620744	+	0.257121i	−0.0500704	+	0.998746i	$0.515945\pi$
$294$		0			0
$295$	−5.56075	−	5.56075i	−0.323759	−	0.323759i
$296$	−12.0406	+	2.47873i	−0.699848	+	0.144073i
$297$		0			0
$298$	−0.866149	+	0.296170i	−0.0501747	+	0.0171567i
$299$	−18.6835	+	45.1060i	−1.08050	+	2.60855i
$300$		0			0
$301$	−10.8466	+	4.49280i	−0.625187	+	0.258961i
$302$	−27.0403	−	1.71188i	−1.55600	−	0.0985074i
$303$		0			0
$304$	14.4330	−	2.03103i	0.827789	−	0.116488i
$305$		−	8.04447i		−	0.460625i
$306$		0			0
$307$	−3.33416	+	1.38105i	−0.190290	+	0.0788209i	−0.475794	−	0.879557i	$-0.657839\pi$
$307$	−3.33416	+	1.38105i	−0.190290	+	0.0788209i	0.285504	+	0.958378i	$0.407839\pi$
$308$	1.54444	+	5.66298i	0.0880028	+	0.322678i
$309$		0			0
$310$	−2.48563	−	7.26924i	−0.141174	−	0.412865i
$311$	15.7937	−	15.7937i	0.895577	−	0.895577i	−0.0994642	−	0.995041i	$-0.531713\pi$
$311$	15.7937	−	15.7937i	0.895577	−	0.895577i	0.995041	+	0.0994642i	$0.0317129\pi$
$312$		0			0
$313$	22.6900	+	22.6900i	1.28251	+	1.28251i	0.939234	+	0.343279i	$0.111538\pi$
$313$	22.6900	+	22.6900i	1.28251	+	1.28251i	0.343279	+	0.939234i	$0.388462\pi$
$314$	6.78577	−	13.8377i	0.382943	−	0.780909i
$315$		0			0
$316$	−23.3469	−	2.96801i	−1.31337	−	0.166963i
$317$	−0.135667	−	0.327529i	−0.00761982	−	0.0183959i	0.920024	−	0.391862i	$-0.128169\pi$
$317$	−0.135667	−	0.327529i	−0.00761982	−	0.0183959i	−0.927644	+	0.373467i	$0.878169\pi$
$318$		0			0
$319$	5.48407			0.307049
$320$	5.62050	−	5.77267i	0.314195	−	0.322702i
$321$		0			0
$322$	9.91427	+	11.2544i	0.552501	+	0.627185i
$323$	10.7600	+	25.9769i	0.598701	+	1.44539i
$324$		0			0
$325$	22.4987	+	9.31927i	1.24800	+	0.516940i
$326$	−3.73429	+	7.61507i	−0.206823	+	0.421760i
$327$		0			0
$328$	−4.54445	+	23.6716i	−0.250925	+	1.30704i
$329$	−6.27531	+	6.27531i	−0.345969	+	0.345969i
$330$		0			0
$331$	−0.599578	+	1.44751i	−0.0329558	+	0.0795622i	−0.939501	−	0.342547i	$-0.888710\pi$
$331$	−0.599578	+	1.44751i	−0.0329558	+	0.0795622i	0.906545	+	0.422110i	$0.138710\pi$
$332$	−3.44995	−	12.6499i	−0.189341	−	0.694252i
$333$		0			0
$334$	−0.786835	+	12.4286i	−0.0430537	+	0.680064i
$335$			9.92741i			0.542393i
$336$		0			0
$337$		−	9.16524i		−	0.499262i	−0.968341	−	0.249631i	$-0.919691\pi$
$337$		−	9.16524i		−	0.499262i	0.968341	−	0.249631i	$-0.0803094\pi$
$338$	−34.3406	−	2.17404i	−1.86788	−	0.118252i
$339$		0			0
$340$	13.4948	+	7.71134i	0.731859	+	0.418206i
$341$	−4.56448	+	11.0196i	−0.247180	+	0.596746i
$342$		0			0
$343$	−11.4858	+	11.4858i	−0.620173	+	0.620173i
$344$	−5.04476	−	24.5053i	−0.271995	−	1.32124i
$345$		0			0
$346$	1.32466	+	0.649588i	0.0712141	+	0.0349221i
$347$	0.809488	+	0.335301i	0.0434556	+	0.0179999i	0.404305	−	0.914624i	$-0.367513\pi$
$347$	0.809488	+	0.335301i	0.0434556	+	0.0179999i	−0.360850	+	0.932624i	$0.617513\pi$
$348$		0			0
$349$	1.88249	+	4.54472i	0.100767	+	0.243273i	0.966221	−	0.257716i	$-0.0829697\pi$
$349$	1.88249	+	4.54472i	0.100767	+	0.243273i	−0.865454	+	0.500989i	$0.832970\pi$
$350$	5.61367	−	4.94521i	0.300063	−	0.264333i
$351$		0			0
$352$	−12.4722	+	0.956990i	−0.664773	+	0.0510078i
$353$	6.05956			0.322518			0.161259	−	0.986912i	$-0.448445\pi$
$353$	6.05956			0.322518			0.161259	+	0.986912i	$0.448445\pi$
$354$		0			0
$355$	−1.06476	−	2.57057i	−0.0565118	−	0.136432i
$356$	12.0052	−	9.29714i	0.636275	−	0.492747i
$357$		0			0
$358$	13.5957	+	6.66706i	0.718553	+	0.352365i
$359$	11.1337	+	11.1337i	0.587616	+	0.587616i	0.936985	−	0.349369i	$-0.113604\pi$
$359$	11.1337	+	11.1337i	0.587616	+	0.587616i	−0.349369	+	0.936985i	$0.613604\pi$
$360$		0			0
$361$	−4.04659	+	4.04659i	−0.212978	+	0.212978i
$362$	−4.60395	+	1.57427i	−0.241978	+	0.0827418i
$363$		0			0
$364$	−8.04671	+	14.0817i	−0.421762	+	0.738083i
$365$	−11.2975	+	4.67956i	−0.591336	+	0.244939i
$366$		0			0
$367$		−	33.7822i		−	1.76341i	−0.471797	−	0.881707i	$-0.656394\pi$
$367$		−	33.7822i		−	1.76341i	0.471797	−	0.881707i	$-0.343606\pi$
$368$	−27.5371	+	16.2272i	−1.43547	+	0.845900i
$369$		0			0
$370$	−0.391113	+	6.17792i	−0.0203330	+	0.321175i
$371$	−1.88874	+	0.782343i	−0.0980586	+	0.0406172i
$372$		0			0
$373$	0.132294	−	0.319386i	0.00684991	−	0.0165372i	−0.920418	−	0.390937i	$-0.872151\pi$
$373$	0.132294	−	0.319386i	0.00684991	−	0.0165372i	0.927267	+	0.374400i	$0.122151\pi$
$374$	−7.80753	−	22.8331i	−0.403718	−	1.18067i
$375$		0			0
$376$	−10.6119	−	15.6545i	−0.547268	−	0.807322i
$377$	10.7147	+	10.7147i	0.551834	+	0.551834i
$378$		0			0
$379$	0.705525	+	0.292238i	0.0362404	+	0.0150112i	0.400730	−	0.916196i	$-0.368757\pi$
$379$	0.705525	+	0.292238i	0.0362404	+	0.0150112i	−0.364490	+	0.931207i	$0.618757\pi$
$380$	0.925584	−	7.28083i	0.0474815	−	0.373499i
$381$		0			0
$382$	−20.4265	−	23.1876i	−1.04511	−	1.18638i
$383$	0.0618011			0.00315789			0.00157894	−	0.999999i	$-0.499497\pi$
$383$	0.0618011			0.00315789			0.00157894	+	0.999999i	$0.499497\pi$
$384$		0			0
$385$	2.95578			0.150640
$386$	13.5817	+	15.4176i	0.691289	+	0.784733i
$387$		0			0
$388$	2.09624	−	16.4894i	0.106420	−	0.837125i
$389$	22.0157	+	9.11918i	1.11624	+	0.462361i	0.863082	−	0.505064i	$-0.168531\pi$
$389$	22.0157	+	9.11918i	1.11624	+	0.462361i	0.253156	+	0.967425i	$0.418531\pi$
$390$		0			0
$391$	−43.6000	−	43.6000i	−2.20494	−	2.20494i
$392$	−8.31371	−	12.2643i	−0.419906	−	0.619438i
$393$		0			0
$394$	−7.88307	−	23.0541i	−0.397143	−	1.16145i
$395$	−4.53523	+	10.9490i	−0.228192	+	0.550904i
$396$		0			0
$397$	2.50388	−	1.03714i	0.125666	−	0.0520525i	−0.318964	−	0.947767i	$-0.603335\pi$
$397$	2.50388	−	1.03714i	0.125666	−	0.0520525i	0.444630	+	0.895714i	$0.353335\pi$
$398$	1.56613	−	24.7381i	0.0785028	−	1.24001i
$399$		0			0
$400$	8.09406	+	13.7354i	0.404703	+	0.686771i
$401$			14.8862i			0.743380i	0.928357	+	0.371690i	$0.121222\pi$
$401$			14.8862i			0.743380i	−0.928357	+	0.371690i	$0.878778\pi$
$402$		0			0
$403$	−30.4479	+	12.6119i	−1.51672	+	0.628246i
$404$	−3.45789	+	6.05129i	−0.172036	+	0.301063i
$405$		0			0
$406$	4.40465	−	1.50612i	0.218599	−	0.0747475i
$407$	6.79590	−	6.79590i	0.336860	−	0.336860i
$408$		0			0
$409$	12.5375	+	12.5375i	0.619938	+	0.619938i	0.945515	−	0.325578i	$-0.105559\pi$
$409$	12.5375	+	12.5375i	0.619938	+	0.619938i	−0.325578	+	0.945515i	$0.605559\pi$
$410$	10.8978	+	5.34409i	0.538206	+	0.263926i
$411$		0			0
$412$	−0.767802	+	0.594604i	−0.0378269	+	0.0292941i
$413$	3.96606	+	9.57492i	0.195157	+	0.471151i
$414$		0			0
$415$	−6.60257			−0.324107
$416$	−26.2378	−	22.4983i	−1.28641	−	1.10307i
$417$		0			0
$418$	−8.55046	+	7.53229i	−0.418217	+	0.368416i
$419$	−15.1946	−	36.6829i	−0.742303	−	1.79208i	−0.596244	−	0.802803i	$-0.703341\pi$
$419$	−15.1946	−	36.6829i	−0.742303	−	1.79208i	−0.146060	−	0.989276i	$-0.546659\pi$
$420$		0			0
$421$	−11.0470	−	4.57581i	−0.538397	−	0.223011i	0.0968796	−	0.995296i	$-0.469114\pi$
$421$	−11.0470	−	4.57581i	−0.538397	−	0.223011i	−0.635276	+	0.772285i	$0.719114\pi$
$422$	14.6778	+	7.19770i	0.714502	+	0.350378i
$423$		0			0
$424$	−0.878456	−	4.26717i	−0.0426616	−	0.207232i
$425$	−21.7475	+	21.7475i	−1.05491	+	1.05491i
$426$		0			0
$427$	−4.05703	+	9.79454i	−0.196333	+	0.473991i
$428$	8.46428	+	4.83674i	0.409137	+	0.233793i
$429$		0			0
$430$	−12.5734	−	0.796001i	−0.606343	−	0.0383866i
$431$			27.7654i			1.33741i	0.743527	+	0.668706i	$0.233152\pi$
$431$			27.7654i			1.33741i	−0.743527	+	0.668706i	$0.766848\pi$
$432$		0			0
$433$		−	5.43486i		−	0.261183i	−0.991436	−	0.130591i	$-0.958312\pi$
$433$		−	5.43486i		−	0.261183i	0.991436	−	0.130591i	$-0.0416876\pi$
$434$	−0.639681	+	10.1042i	−0.0307057	+	0.485018i
$435$		0			0
$436$	−3.84100	−	14.0837i	−0.183950	−	0.674487i
$437$	−11.1424	+	26.9001i	−0.533012	+	1.28680i
$438$		0			0
$439$	−7.46141	+	7.46141i	−0.356114	+	0.356114i	−0.862378	−	0.506265i	$-0.831026\pi$
$439$	−7.46141	+	7.46141i	−0.356114	+	0.356114i	0.506265	+	0.862378i	$0.331026\pi$
$440$	−1.18758	+	6.18598i	−0.0566157	+	0.294905i
$441$		0			0
$442$	29.3567	−	59.8652i	1.39636	−	2.84749i
$443$	33.3044	+	13.7951i	1.58234	+	0.655427i	0.988782	−	0.149365i	$-0.0477229\pi$
$443$	33.3044	+	13.7951i	1.58234	+	0.655427i	0.593558	+	0.804791i	$0.297723\pi$
$444$		0			0
$445$	−2.92605	−	7.06411i	−0.138708	−	0.334871i
$446$	−11.2687	−	12.7920i	−0.533591	−	0.605718i
$447$		0			0
$448$	−9.75453	+	4.19395i	−0.460858	+	0.198145i
$449$	−7.32090			−0.345494			−0.172747	−	0.984966i	$-0.555264\pi$
$449$	−7.32090			−0.345494			−0.172747	+	0.984966i	$0.555264\pi$
$450$		0			0
$451$	−7.21149	−	17.4101i	−0.339576	−	0.819809i
$452$	−4.30715	−	0.547551i	−0.202591	−	0.0257546i
$453$		0			0
$454$	6.06320	−	12.3643i	0.284560	−	0.580283i
$455$	5.77494	+	5.77494i	0.270733	+	0.270733i
$456$		0			0
$457$	−13.2198	+	13.2198i	−0.618398	+	0.618398i	−0.945120	−	0.326723i	$-0.894056\pi$
$457$	−13.2198	+	13.2198i	−0.618398	+	0.618398i	0.326723	+	0.945120i	$0.394056\pi$
$458$	13.1805	+	38.5463i	0.615883	+	1.80115i
$459$		0			0
$460$	4.23487	+	15.5279i	0.197452	+	0.723992i
$461$	−3.91240	+	1.62057i	−0.182219	+	0.0754774i	−0.471927	−	0.881637i	$-0.656442\pi$
$461$	−3.91240	+	1.62057i	−0.182219	+	0.0754774i	0.289709	+	0.957115i	$0.406442\pi$
$462$		0			0
$463$			19.9447i			0.926910i	0.886121	+	0.463455i	$0.153390\pi$
$463$			19.9447i			0.926910i	−0.886121	+	0.463455i	$0.846610\pi$
$464$	1.38236	+	9.82337i	0.0641744	+	0.456038i
$465$		0			0
$466$	22.7176	+	1.43821i	1.05237	+	0.0666238i
$467$	−23.4125	+	9.69779i	−1.08340	+	0.448760i	−0.851702	−	0.524027i	$-0.824429\pi$
$467$	−23.4125	+	9.69779i	−1.08340	+	0.448760i	−0.231701	+	0.972787i	$0.574429\pi$
$468$		0			0
$469$	5.00665	−	12.0871i	0.231185	−	0.558131i
$470$	−9.01120	+	3.08128i	−0.415656	+	0.142129i
$471$		0			0
$472$	−21.6323	+	4.45330i	−0.995707	+	0.204980i
$473$	13.8311	+	13.8311i	0.635956	+	0.635956i
$474$		0			0
$475$	13.4177	+	5.55778i	0.615645	+	0.255008i
$476$	−12.5416	−	16.1947i	−0.574842	−	0.742283i
$477$		0			0
$478$	−12.8585	+	11.3273i	−0.588133	+	0.518099i
$479$	−15.7464			−0.719470			−0.359735	−	0.933054i	$-0.617133\pi$
$479$	−15.7464			−0.719470			−0.359735	+	0.933054i	$0.617133\pi$
$480$		0			0
$481$	26.5554			1.21082
$482$	−1.39654	+	1.23024i	−0.0636104	+	0.0560358i
$483$		0			0
$484$	−9.66192	+	7.48243i	−0.439178	+	0.340110i
$485$	−7.73305	−	3.20313i	−0.351140	−	0.145447i
$486$		0			0
$487$	−21.8941	−	21.8941i	−0.992116	−	0.992116i	0.00785353	−	0.999969i	$-0.497500\pi$
$487$	−21.8941	−	21.8941i	−0.992116	−	0.992116i	−0.999969	+	0.00785353i	$0.997500\pi$
$488$	−18.8684	−	12.4260i	−0.854131	−	0.562498i
$489$		0			0
$490$	−7.05965	+	2.41397i	−0.318923	+	0.109052i
$491$	3.16126	−	7.63197i	0.142666	−	0.344426i	−0.836354	−	0.548189i	$-0.815317\pi$
$491$	3.16126	−	7.63197i	0.142666	−	0.344426i	0.979020	+	0.203763i	$0.0653173\pi$
$492$		0			0
$493$	−17.6804	+	7.32345i	−0.796284	+	0.329832i
$494$	−31.4222	−	1.98928i	−1.41375	−	0.0895021i
$495$		0			0
$496$	−20.8895	−	5.39845i	−0.937967	−	0.242398i
$497$			3.66678i			0.164478i
$498$		0			0
$499$	−23.1527	+	9.59016i	−1.03646	+	0.429314i	−0.835039	−	0.550191i	$-0.814555\pi$
$499$	−23.1527	+	9.59016i	−1.03646	+	0.429314i	−0.201418	+	0.979505i	$0.564555\pi$
$500$	17.4615	−	4.76222i	0.780903	−	0.212973i
$501$		0			0
$502$	4.77212	+	13.9561i	0.212990	+	0.622891i
$503$	5.59362	−	5.59362i	0.249407	−	0.249407i	−0.571320	−	0.820727i	$-0.693569\pi$
$503$	5.59362	−	5.59362i	0.249407	−	0.249407i	0.820727	+	0.571320i	$0.193569\pi$
$504$		0			0
$505$	2.48165	+	2.48165i	0.110432	+	0.110432i
$506$	11.0023	−	22.4362i	0.489111	−	0.997410i
$507$		0			0
$508$	0.251051	−	1.97482i	0.0111386	−	0.0876183i
$509$	−13.2327	−	31.9466i	−0.586530	−	1.41601i	−0.886800	−	0.462154i	$-0.847077\pi$
$509$	−13.2327	−	31.9466i	−0.586530	−	1.41601i	0.300270	−	0.953854i	$-0.402923\pi$
$510$		0			0
$511$	16.1152			0.712896
$512$	−4.85807	−	22.0998i	−0.214698	−	0.976680i
$513$		0			0
$514$	7.97435	+	9.05227i	0.351733	+	0.399279i
$515$	0.187137	+	0.451790i	0.00824626	+	0.0199082i
$516$		0			0
$517$	13.6603	+	5.65829i	0.600780	+	0.248851i
$518$	3.59188	−	7.32467i	0.157818	−	0.321828i
$519$		0			0
$520$	−14.4063	+	9.76577i	−0.631759	+	0.428257i
$521$	15.3045	−	15.3045i	0.670500	−	0.670500i	−0.287331	−	0.957831i	$-0.592768\pi$
$521$	15.3045	−	15.3045i	0.670500	−	0.670500i	0.957831	+	0.287331i	$0.0927680\pi$
$522$		0			0
$523$	11.5084	−	27.7838i	0.503229	−	1.21490i	−0.444487	−	0.895785i	$-0.646614\pi$
$523$	11.5084	−	27.7838i	0.503229	−	1.21490i	0.947716	−	0.319116i	$-0.103386\pi$
$524$	−20.6793	+	5.63979i	−0.903379	+	0.246375i
$525$		0			0
$526$	−0.825274	+	13.0358i	−0.0359837	+	0.568388i
$527$		−	41.6222i		−	1.81309i
$528$		0			0
$529$		−	40.8509i		−	1.77613i
$530$	−2.18944	−	0.138610i	−0.0951031	−	0.00602081i
$531$		0			0
$532$	−4.79885	+	8.39798i	−0.208057	+	0.364099i
$533$	19.9258	−	48.1051i	0.863082	−	2.08367i
$534$		0			0
$535$	3.47122	−	3.47122i	0.150074	−	0.150074i
$536$	23.2848	+	15.3345i	1.00575	+	0.662350i
$537$		0			0
$538$	−31.2980	−	15.3479i	−1.34935	−	0.661697i
$539$	10.7019	+	4.43288i	0.460964	+	0.190938i
$540$		0			0
$541$	−3.65267	−	8.81833i	−0.157041	−	0.379130i	0.825702	−	0.564106i	$-0.190779\pi$
$541$	−3.65267	−	8.81833i	−0.157041	−	0.379130i	−0.982743	+	0.184976i	$0.940779\pi$
$542$	32.2767	−	28.4332i	1.38640	−	1.22131i
$543$		0			0
$544$	38.9320	−	19.7408i	1.66919	−	0.846379i
$545$	−7.35096			−0.314880
$546$		0			0
$547$	−6.85086	−	16.5394i	−0.292921	−	0.707175i	−1.00000		3.99033e-5i	$-0.999987\pi$
$547$	−6.85086	−	16.5394i	−0.292921	−	0.707175i	0.707079	−	0.707135i	$-0.250013\pi$
$548$	22.1239	+	28.5682i	0.945085	+	1.22037i
$549$		0			0
$550$	−11.1911	−	5.48791i	−0.477190	−	0.234005i
$551$	6.38996	+	6.38996i	0.272221	+	0.272221i
$552$		0			0
$553$	11.0437	−	11.0437i	0.469627	−	0.469627i
$554$	−41.7902	+	14.2897i	−1.77550	+	0.607111i
$555$		0			0
$556$	−4.99300	−	2.85315i	−0.211750	−	0.121000i
$557$	3.33392	−	1.38096i	0.141263	−	0.0585130i	−0.310932	−	0.950432i	$-0.600641\pi$
$557$	3.33392	−	1.38096i	0.141263	−	0.0585130i	0.452195	+	0.891919i	$0.350641\pi$
$558$		0			0
$559$			54.0460i			2.28590i
$560$	0.745057	+	5.29455i	0.0314844	+	0.223736i
$561$		0			0
$562$	−2.94575	+	46.5303i	−0.124259	+	1.96276i
$563$	−15.8181	+	6.55208i	−0.666654	+	0.276137i	−0.690236	−	0.723585i	$-0.742493\pi$
$563$	−15.8181	+	6.55208i	−0.666654	+	0.276137i	0.0235814	+	0.999722i	$0.492493\pi$
$564$		0			0
$565$	−0.836679	+	2.01992i	−0.0351993	+	0.0849787i
$566$	−11.2653	−	32.9453i	−0.473515	−	1.38480i
$567$		0			0
$568$	−7.67399	−	1.47325i	−0.321994	−	0.0618161i
$569$	−14.2778	−	14.2778i	−0.598558	−	0.598558i	0.341371	−	0.939929i	$-0.389109\pi$
$569$	−14.2778	−	14.2778i	−0.598558	−	0.598558i	−0.939929	+	0.341371i	$0.889109\pi$
$570$		0			0
$571$	−20.4753	−	8.48116i	−0.856866	−	0.354926i	−0.0893852	−	0.995997i	$-0.528490\pi$
$571$	−20.4753	−	8.48116i	−0.856866	−	0.354926i	−0.767481	+	0.641071i	$0.778490\pi$
$572$	26.8058	+	3.40771i	1.12081	+	0.142484i
$573$		0			0
$574$	−10.5735	−	12.0028i	−0.441329	−	0.500985i
$575$	−31.8486			−1.32818
$576$		0			0
$577$	−32.9749			−1.37276			−0.686382	−	0.727241i	$-0.740802\pi$
$577$	−32.9749			−1.37276			−0.686382	+	0.727241i	$0.740802\pi$
$578$	39.7706	+	45.1466i	1.65424	+	1.87785i
$579$		0			0
$580$	4.95548	+	0.629970i	0.205765	+	0.0261581i
$581$	8.03895	+	3.32984i	0.333512	+	0.138145i
$582$		0			0
$583$	2.40845	+	2.40845i	0.0997478	+	0.0997478i
$584$	−6.47482	+	33.7266i	−0.267930	+	1.39562i
$585$		0			0
$586$	−5.26239	−	15.3899i	−0.217387	−	0.635749i
$587$	−6.25478	+	15.1004i	−0.258162	+	0.623259i	−0.998817	−	0.0486267i	$-0.984516\pi$
$587$	−6.25478	+	15.1004i	−0.258162	+	0.623259i	0.740655	+	0.671886i	$0.234516\pi$
$588$		0			0
$589$	−18.1584	+	7.52144i	−0.748202	+	0.309916i
$590$	−0.702677	+	11.0993i	−0.0289287	+	0.456950i
$591$		0			0
$592$	13.8862	+	10.4602i	0.570720	+	0.429910i
$593$		−	2.82225i		−	0.115896i	−0.998320	−	0.0579479i	$-0.981544\pi$
$593$		−	2.82225i		−	0.115896i	0.998320	−	0.0579479i	$-0.0184557\pi$
$594$		0			0
$595$	−9.52929	+	3.94716i	−0.390663	+	0.161818i
$596$	1.12398	+	0.642278i	0.0460402	+	0.0263087i
$597$		0			0
$598$	65.3314	−	22.3393i	2.67160	−	0.913524i
$599$	4.80895	−	4.80895i	0.196488	−	0.196488i	−0.602004	−	0.798493i	$-0.705631\pi$
$599$	4.80895	−	4.80895i	0.196488	−	0.196488i	0.798493	+	0.602004i	$0.205631\pi$
$600$		0			0
$601$	1.97562	+	1.97562i	0.0805873	+	0.0805873i	0.746251	−	0.665664i	$-0.231852\pi$
$601$	1.97562	+	1.97562i	0.0805873	+	0.0805873i	−0.665664	+	0.746251i	$0.731852\pi$
$602$	14.9073	+	7.31026i	0.607576	+	0.297944i
$603$		0			0
$604$	23.4612	+	30.2950i	0.954624	+	1.23269i
$605$	2.35491	+	5.68526i	0.0957408	+	0.231139i
$606$		0			0
$607$	−2.25264			−0.0914320			−0.0457160	−	0.998954i	$-0.514557\pi$
$607$	−2.25264			−0.0914320			−0.0457160	+	0.998954i	$0.514557\pi$
$608$	−15.6475	−	13.4174i	−0.634592	−	0.544148i
$609$		0			0
$610$	−8.53666	+	7.52013i	−0.345639	+	0.304481i
$611$	15.6342	+	37.7443i	0.632492	+	1.52697i
$612$		0			0
$613$	38.1764	+	15.8132i	1.54193	+	0.638688i	0.981834	−	0.189740i	$-0.0607644\pi$
$613$	38.1764	+	15.8132i	1.54193	+	0.638688i	0.560095	+	0.828428i	$0.310764\pi$
$614$	4.58239	+	2.24712i	0.184930	+	0.0906863i
$615$		0			0
$616$	4.56568	−	6.93281i	0.183957	−	0.279331i
$617$	11.7568	−	11.7568i	0.473312	−	0.473312i	−0.429673	−	0.902985i	$-0.641371\pi$
$617$	11.7568	−	11.7568i	0.473312	−	0.473312i	0.902985	+	0.429673i	$0.141371\pi$
$618$		0			0
$619$	14.6215	−	35.2995i	0.587689	−	1.41881i	−0.298017	−	0.954561i	$-0.596325\pi$
$619$	14.6215	−	35.2995i	0.587689	−	1.41881i	0.885706	−	0.464247i	$-0.153675\pi$
$620$	−5.39038	+	9.43314i	−0.216483	+	0.378844i
$621$		0			0
$622$	−31.5242	−	1.99575i	−1.26401	−	0.0800221i
$623$			10.0766i			0.403710i
$624$		0			0
$625$			10.8146i			0.432584i
$626$	2.86719	−	45.2893i	0.114596	−	1.81012i
$627$		0			0
$628$	−21.0279	+	5.73485i	−0.839103	+	0.228846i
$629$	−12.8344	+	30.9849i	−0.511740	+	1.23545i
$630$		0			0
$631$	0.538322	−	0.538322i	0.0214302	−	0.0214302i	−0.696310	−	0.717741i	$-0.745176\pi$
$631$	0.538322	−	0.538322i	0.0214302	−	0.0214302i	0.717741	+	0.696310i	$0.245176\pi$
$632$	18.6756	+	27.5499i	0.742875	+	1.09588i
$633$		0			0
$634$	−0.220744	+	0.450149i	−0.00876688	+	0.0178777i
$635$	−0.926129	−	0.383615i	−0.0367523	−	0.0152233i
$636$		0			0
$637$	12.2483	+	29.5701i	0.485296	+	1.17161i
$638$	−5.12662	−	5.81961i	−0.202965	−	0.230400i
$639$		0			0
$640$	−11.3800	−	0.567973i	−0.449835	−	0.0224511i
$641$	13.2510			0.523384			0.261692	−	0.965151i	$-0.415719\pi$
$641$	13.2510			0.523384			0.261692	+	0.965151i	$0.415719\pi$
$642$		0			0
$643$	4.36388	+	10.5353i	0.172095	+	0.415473i	0.986269	−	0.165147i	$-0.0528100\pi$
$643$	4.36388	+	10.5353i	0.172095	+	0.415473i	−0.814174	+	0.580621i	$0.802810\pi$
$644$	2.67495	−	21.0417i	0.105408	−	0.829160i
$645$		0			0
$646$	17.5076	−	35.7020i	0.688828	−	1.40468i
$647$	0.948610	+	0.948610i	0.0372937	+	0.0372937i	0.725508	−	0.688214i	$-0.241605\pi$
$647$	0.948610	+	0.948610i	0.0372937	+	0.0372937i	−0.688214	+	0.725508i	$0.741605\pi$
$648$		0			0
$649$	12.2096	−	12.2096i	0.479267	−	0.479267i
$650$	−11.1428	−	32.5871i	−0.437056	−	1.27817i
$651$		0			0
$652$	11.5719	−	3.15596i	0.453190	−	0.123597i
$653$	42.6127	−	17.6508i	1.66756	−	0.690727i	0.668947	−	0.743310i	$-0.266745\pi$
$653$	42.6127	−	17.6508i	1.66756	−	0.690727i	0.998617	+	0.0525829i	$0.0167454\pi$
$654$		0			0
$655$			10.7935i			0.421737i
$656$	29.3681	−	17.3061i	1.14663	−	0.675691i
$657$		0			0
$658$	12.5255	+	0.792971i	0.488297	+	0.0309132i
$659$	7.85964	−	3.25557i	0.306168	−	0.126819i	−0.224310	−	0.974518i	$-0.572013\pi$
$659$	7.85964	−	3.25557i	0.306168	−	0.126819i	0.530477	+	0.847699i	$0.322013\pi$
$660$		0			0
$661$	−4.31440	+	10.4159i	−0.167811	+	0.405131i	−0.985305	−	0.170806i	$-0.945363\pi$
$661$	−4.31440	+	10.4159i	−0.167811	+	0.405131i	0.817494	+	0.575937i	$0.195363\pi$
$662$	2.09657	−	0.716898i	0.0814855	−	0.0278630i
$663$		0			0
$664$	−10.1987	+	15.4864i	−0.395788	+	0.600988i
$665$	3.44403	+	3.44403i	0.133554	+	0.133554i
$666$		0			0
$667$	−18.3087	−	7.58371i	−0.708915	−	0.293642i
$668$	13.9246	−	10.7835i	0.538759	−	0.417228i
$669$		0			0
$670$	10.5348	−	9.28035i	0.406995	−	0.358531i
$671$	17.6630			0.681871
$672$		0			0
$673$	−6.74887			−0.260150			−0.130075	−	0.991504i	$-0.541522\pi$
$673$	−6.74887			−0.260150			−0.130075	+	0.991504i	$0.541522\pi$
$674$	−9.72601	+	8.56785i	−0.374632	+	0.330021i
$675$		0			0
$676$	29.7952	+	38.4740i	1.14597	+	1.47977i
$677$	−11.8633	−	4.91394i	−0.455944	−	0.188858i	0.142878	−	0.989740i	$-0.454364\pi$
$677$	−11.8633	−	4.91394i	−0.455944	−	0.188858i	−0.598822	+	0.800882i	$0.704364\pi$
$678$		0			0
$679$	7.79995	+	7.79995i	0.299334	+	0.299334i
$680$	−4.43208	−	21.5292i	−0.169963	−	0.825607i
$681$		0			0
$682$	15.9608	−	5.45762i	0.611171	−	0.208983i
$683$	14.3773	−	34.7099i	0.550132	−	1.32814i	−0.367247	−	0.930123i	$-0.619700\pi$
$683$	14.3773	−	34.7099i	0.550132	−	1.32814i	0.917379	−	0.398014i	$-0.130300\pi$
$684$		0			0
$685$	16.8101	−	6.96296i	0.642280	−	0.266041i
$686$	22.9256	+	1.45138i	0.875305	+	0.0554141i
$687$		0			0
$688$	−21.2887	+	28.2615i	−0.811624	+	1.07746i
$689$			9.41116i			0.358537i
$690$		0			0
$691$	−45.7721	+	18.9594i	−1.74125	+	0.721250i	−0.742579	+	0.669759i	$0.766398\pi$
$691$	−45.7721	+	18.9594i	−1.74125	+	0.721250i	−0.998673	+	0.0514917i	$0.983602\pi$
$692$	−0.548986	−	2.01296i	−0.0208693	−	0.0765211i
$693$		0			0
$694$	−0.400910	−	1.17246i	−0.0152183	−	0.0445060i
$695$	−2.04764	+	2.04764i	−0.0776713	+	0.0776713i
$696$		0			0
$697$	46.4990	+	46.4990i	1.76128	+	1.76128i
$698$	3.06300	−	6.24616i	0.115936	−	0.236421i
$699$		0			0
$700$	−10.4956	−	1.33426i	−0.396695	−	0.0504302i
$701$	13.2680	+	32.0317i	0.501124	+	1.20982i	0.948872	+	0.315661i	$0.102226\pi$
$701$	13.2680	+	32.0317i	0.501124	+	1.20982i	−0.447748	+	0.894160i	$0.647774\pi$
$702$		0			0
$703$	15.8370			0.597302
$704$	12.6749	+	12.3407i	0.477702	+	0.465109i
$705$		0			0
$706$	−5.66459	−	6.43030i	−0.213190	−	0.242008i
$707$	−1.76997	−	4.27309i	−0.0665666	−	0.160706i
$708$		0			0
$709$	22.1634	+	9.18039i	0.832365	+	0.344777i	0.757838	−	0.652442i	$-0.226256\pi$
$709$	22.1634	+	9.18039i	0.832365	+	0.344777i	0.0745263	+	0.997219i	$0.476256\pi$
$710$	−1.73248	+	3.53293i	−0.0650189	+	0.132588i
$711$		0			0
$712$	−21.0887	−	4.04860i	−0.790332	−	0.151728i
$713$	30.4772	−	30.4772i	1.14138	−	1.14138i
$714$		0			0
$715$	5.20712	−	12.5711i	0.194735	−	0.470132i
$716$	−5.63453	−	20.6600i	−0.210572	−	0.772101i
$717$		0			0
$718$	1.40690	−	22.2230i	0.0525050	−	0.829354i
$719$		−	30.9298i		−	1.15349i	−0.816925	−	0.576744i	$-0.804323\pi$
$719$		−	30.9298i		−	1.15349i	0.816925	−	0.576744i	$-0.195677\pi$
$720$		0			0
$721$		−	0.644454i		−	0.0240007i
$722$	8.07700	+	0.511341i	0.300595	+	0.0190301i
$723$		0			0
$724$	5.97446	+	3.41398i	0.222039	+	0.126880i
$725$	−3.78273	+	9.13232i	−0.140487	+	0.339166i
$726$		0			0
$727$	−1.17119	+	1.17119i	−0.0434369	+	0.0434369i	−0.728492	−	0.685055i	$-0.759778\pi$
$727$	−1.17119	+	1.17119i	−0.0434369	+	0.0434369i	0.685055	+	0.728492i	$0.259778\pi$
$728$	22.4655	−	4.62484i	0.832628	−	0.171408i
$729$		0			0
$730$	15.5270	+	7.61413i	0.574679	+	0.281812i
$731$	−63.0611	−	26.1207i	−2.33240	−	0.966111i
$732$		0			0
$733$	2.77936	+	6.70998i	0.102658	+	0.247839i	0.966860	−	0.255306i	$-0.0821762\pi$
$733$	2.77936	+	6.70998i	0.102658	+	0.247839i	−0.864202	+	0.503145i	$0.832176\pi$
$734$	−35.8491	+	31.5803i	−1.32321	+	1.16565i
$735$		0			0
$736$	42.9623	+	14.0525i	1.58361	+	0.517980i
$737$	−21.7973			−0.802913
$738$		0			0
$739$	1.42163	+	3.43212i	0.0522956	+	0.126253i	0.947868	−	0.318663i	$-0.103234\pi$
$739$	1.42163	+	3.43212i	0.0522956	+	0.126253i	−0.895573	+	0.444915i	$0.853234\pi$
$740$	6.92153	−	5.36020i	0.254440	−	0.197045i
$741$		0			0
$742$	2.59584	+	1.27295i	0.0952964	+	0.0467316i
$743$	−15.7962	−	15.7962i	−0.579505	−	0.579505i	0.355262	−	0.934767i	$-0.384392\pi$
$743$	−15.7962	−	15.7962i	−0.579505	−	0.579505i	−0.934767	+	0.355262i	$0.884392\pi$
$744$		0			0
$745$	0.460948	−	0.460948i	0.0168878	−	0.0168878i
$746$	−0.462598	+	0.158180i	−0.0169369	+	0.00579138i
$747$		0			0
$748$	−16.9315	+	29.6301i	−0.619078	+	1.08338i
$749$	−5.97701	+	2.47576i	−0.218395	+	0.0904622i
$750$		0			0
$751$		−	13.5578i		−	0.494731i	−0.968922	−	0.247366i	$-0.920435\pi$
$751$		−	13.5578i		−	0.494731i	0.968922	−	0.247366i	$-0.0795649\pi$
$752$	−6.69211	+	25.8954i	−0.244036	+	0.944308i
$753$		0			0
$754$	1.35394	−	21.3865i	0.0493077	−	0.778851i
$755$	17.8262	−	7.38386i	0.648762	−	0.268726i
$756$		0			0
$757$	16.6598	−	40.2204i	0.605512	−	1.46184i	−0.262322	−	0.964980i	$-0.584488\pi$
$757$	16.6598	−	40.2204i	0.605512	−	1.46184i	0.867834	−	0.496855i	$-0.165512\pi$
$758$	−0.349421	−	1.02188i	−0.0126915	−	0.0371164i
$759$		0			0
$760$	−8.59156	+	5.82406i	−0.311649	+	0.211261i
$761$	−4.92005	−	4.92005i	−0.178352	−	0.178352i	0.612285	−	0.790637i	$-0.290250\pi$
$761$	−4.92005	−	4.92005i	−0.178352	−	0.178352i	−0.790637	+	0.612285i	$0.790250\pi$
$762$		0			0
$763$	8.95015	+	3.70727i	0.324017	+	0.134212i
$764$	−5.51123	+	43.3525i	−0.199389	+	1.56844i
$765$		0			0
$766$	−0.0577729	−	0.0655823i	−0.00208742	−	0.00236958i
$767$	47.7096			1.72269
$768$		0			0
$769$	30.1958			1.08889			0.544444	−	0.838797i	$-0.316741\pi$
$769$	30.1958			1.08889			0.544444	+	0.838797i	$0.316741\pi$
$770$	−2.76312	−	3.13662i	−0.0995760	−	0.113036i
$771$		0			0
$772$	3.66445	−	28.8253i	0.131886	−	1.03744i
$773$	−28.5054	−	11.8073i	−1.02527	−	0.424679i	−0.194265	−	0.980949i	$-0.562232\pi$
$773$	−28.5054	−	11.8073i	−1.02527	−	0.424679i	−0.831002	+	0.556270i	$0.812232\pi$
$774$		0			0
$775$	−15.2019	−	15.2019i	−0.546070	−	0.546070i
$776$	−19.4579	+	13.1902i	−0.698499	+	0.473500i
$777$		0			0
$778$	−10.9035	−	31.8875i	−0.390911	−	1.14322i
$779$	11.8832	−	28.6887i	0.425761	−	1.02788i
$780$		0			0
$781$	5.64411	−	2.33787i	0.201962	−	0.0836554i
$782$	−5.50945	+	87.0257i	−0.197017	+	3.11203i
$783$		0			0
$784$	−5.24281	+	20.2872i	−0.187243	+	0.724544i
$785$			10.9754i			0.391730i
$786$		0			0
$787$	12.1718	−	5.04174i	0.433879	−	0.179719i	−0.155044	−	0.987908i	$-0.549552\pi$
$787$	12.1718	−	5.04174i	0.433879	−	0.179719i	0.588923	+	0.808189i	$0.299552\pi$
$788$	−17.0953	+	29.9168i	−0.608996	+	1.06574i
$789$		0			0
$790$	15.8585	−	5.42264i	0.564221	−	0.192929i
$791$	2.03740	−	2.03740i	0.0724414	−	0.0724414i
$792$		0			0
$793$	34.5096	+	34.5096i	1.22547	+	1.22547i
$794$	−3.44127	−	1.68753i	−0.122126	−	0.0598883i
$795$		0			0
$796$	−27.7157	+	21.4637i	−0.982357	+	0.760761i
$797$	−1.91098	−	4.61351i	−0.0676903	−	0.163419i	0.886414	−	0.462893i	$-0.153189\pi$
$797$	−1.91098	−	4.61351i	−0.0676903	−	0.163419i	−0.954104	+	0.299474i	$0.903189\pi$
$798$		0			0
$799$	−51.5963			−1.82535
$800$	7.00932	−	21.4294i	0.247817	−	0.757645i
$801$		0			0
$802$	15.7970	−	13.9159i	0.557810	−	0.491387i
$803$	−10.2748	−	24.8054i	−0.362588	−	0.875365i
$804$		0			0
$805$	−9.86793	−	4.08743i	−0.347799	−	0.144063i
$806$	41.8469	+	20.5209i	1.47400	+	0.722819i
$807$		0			0
$808$	9.65404	−	1.98742i	0.339628	−	0.0699170i
$809$	−18.3954	+	18.3954i	−0.646746	+	0.646746i	−0.952205	−	0.305459i	$-0.901190\pi$
$809$	−18.3954	+	18.3954i	−0.646746	+	0.646746i	0.305459	+	0.952205i	$0.401190\pi$
$810$		0			0
$811$	17.3184	−	41.8102i	0.608130	−	1.46816i	−0.256901	−	0.966438i	$-0.582701\pi$
$811$	17.3184	−	41.8102i	0.608130	−	1.46816i	0.865031	−	0.501718i	$-0.167299\pi$
$812$	−5.71583	−	3.26619i	−0.200586	−	0.114621i
$813$		0			0
$814$	−13.5646	−	0.858755i	−0.475441	−	0.0300993i
$815$		−	6.03992i		−	0.211569i
$816$		0			0
$817$			32.2317i			1.12764i
$818$	1.58428	−	25.0248i	0.0553930	−	0.874973i
$819$		0			0
$820$	−4.51645	−	16.5604i	−0.157721	−	0.578313i
$821$	8.21305	−	19.8281i	0.286638	−	0.692004i	−0.713323	−	0.700835i	$-0.752811\pi$
$821$	8.21305	−	19.8281i	0.286638	−	0.692004i	0.999961	+	0.00883070i	$0.00281093\pi$
$822$		0			0
$823$	22.0587	−	22.0587i	0.768918	−	0.768918i	−0.208998	−	0.977916i	$-0.567020\pi$
$823$	22.0587	−	22.0587i	0.768918	−	0.768918i	0.977916	+	0.208998i	$0.0670202\pi$
$824$	1.34874	+	0.258931i	0.0469856	+	0.00902027i
$825$		0			0
$826$	6.45319	−	13.1595i	0.224535	−	0.457879i
$827$	−5.61721	−	2.32672i	−0.195329	−	0.0809081i	0.282875	−	0.959157i	$-0.408712\pi$
$827$	−5.61721	−	2.32672i	−0.195329	−	0.0809081i	−0.478204	+	0.878249i	$0.658712\pi$
$828$		0			0
$829$	15.9329	+	38.4654i	0.553373	+	1.33596i	0.914931	+	0.403610i	$0.132245\pi$
$829$	15.9329	+	38.4654i	0.553373	+	1.33596i	−0.361558	+	0.932349i	$0.617755\pi$
$830$	6.17221	+	7.00654i	0.214241	+	0.243201i
$831$		0			0
$832$	0.652794	+	48.8750i	0.0226315	+	1.69443i
$833$	−40.4221			−1.40054
$834$		0			0
$835$	−3.39386	−	8.19351i	−0.117449	−	0.283548i
$836$	15.9863	+	2.03227i	0.552897	+	0.0702877i
$837$		0			0
$838$	−24.7232	+	50.4162i	−0.854047	+	1.74160i
$839$	−19.8239	−	19.8239i	−0.684399	−	0.684399i	0.276590	−	0.960988i	$-0.410796\pi$
$839$	−19.8239	−	19.8239i	−0.684399	−	0.684399i	−0.960988	+	0.276590i	$0.910796\pi$
$840$		0			0
$841$	16.1570	−	16.1570i	0.557137	−	0.557137i
$842$	5.47116	+	16.0004i	0.188549	+	0.551411i
$843$		0			0
$844$	−6.08299	−	22.3044i	−0.209385	−	0.767747i
$845$	22.6389	−	9.37733i	0.778801	−	0.322590i
$846$		0			0
$847$		−	8.10973i		−	0.278654i
$848$	−3.70705	+	4.92124i	−0.127301	+	0.168996i
$849$		0			0
$850$	43.4081	+	2.74810i	1.48889	+	0.0942589i
$851$	−32.0861	+	13.2905i	−1.09990	+	0.455592i
$852$		0			0
$853$	−0.282320	+	0.681580i	−0.00966645	+	0.0233369i	−0.928639	−	0.370984i	$-0.879020\pi$
$853$	−0.282320	+	0.681580i	−0.00966645	+	0.0233369i	0.918973	+	0.394321i	$0.129020\pi$
$854$	14.1864	−	4.85088i	0.485449	−	0.165994i
$855$		0			0
$856$	−2.77991	−	13.5036i	−0.0950154	−	0.461545i
$857$	−28.6025	−	28.6025i	−0.977043	−	0.977043i	0.0226993	−	0.999742i	$-0.492774\pi$
$857$	−28.6025	−	28.6025i	−0.977043	−	0.977043i	−0.999742	+	0.0226993i	$0.992774\pi$
$858$		0			0
$859$	40.1822	+	16.6440i	1.37100	+	0.567886i	0.942059	−	0.335447i	$-0.108887\pi$
$859$	40.1822	+	16.6440i	1.37100	+	0.567886i	0.428939	+	0.903333i	$0.358887\pi$
$860$	10.9092	+	14.0868i	0.372000	+	0.480356i
$861$		0			0
$862$	29.4642	−	25.9557i	1.00355	−	0.884053i
$863$	−24.3873			−0.830152			−0.415076	−	0.909787i	$-0.636245\pi$
$863$	−24.3873			−0.830152			−0.415076	+	0.909787i	$0.636245\pi$
$864$		0			0
$865$	−1.05066			−0.0357234
$866$	−5.76738	+	5.08062i	−0.195984	+	0.172646i
$867$		0			0
$868$	11.3204	−	8.76681i	0.384240	−	0.297565i
$869$	−24.0404	−	9.95785i	−0.815514	−	0.337797i
$870$		0			0
$871$	−42.5871	−	42.5871i	−1.44301	−	1.44301i
$872$	−11.3548	+	17.2417i	−0.384521	+	0.583879i
$873$		0			0
$874$	38.9620	−	13.3226i	1.31791	−	0.450644i
$875$	−4.59642	+	11.0968i	−0.155388	+	0.375139i
$876$		0			0
$877$	−27.2085	+	11.2701i	−0.918765	+	0.380565i	−0.791405	−	0.611292i	$-0.790650\pi$
$877$	−27.2085	+	11.2701i	−0.918765	+	0.380565i	−0.127360	+	0.991857i	$0.540650\pi$
$878$	14.8930	+	0.942851i	0.502615	+	0.0318197i
$879$		0			0
$880$	7.67463	−	4.52254i	0.258712	−	0.152455i
$881$		−	39.5282i		−	1.33174i	−0.746069	−	0.665869i	$-0.768061\pi$
$881$		−	39.5282i		−	1.33174i	0.746069	−	0.665869i	$-0.231939\pi$
$882$		0			0
$883$	−4.08879	+	1.69363i	−0.137599	+	0.0569952i	−0.450420	−	0.892817i	$-0.648726\pi$
$883$	−4.08879	+	1.69363i	−0.137599	+	0.0569952i	0.312822	+	0.949812i	$0.398726\pi$
$884$	−90.9712	+	24.8103i	−3.05969	+	0.834459i
$885$		0			0
$886$	−16.4945	−	48.2381i	−0.554142	−	1.62059i
$887$	−8.25045	+	8.25045i	−0.277023	+	0.277023i	−0.831919	−	0.554896i	$-0.812758\pi$
$887$	−8.25045	+	8.25045i	−0.277023	+	0.277023i	0.554896	+	0.831919i	$0.312758\pi$
$888$		0			0
$889$	0.934141	+	0.934141i	0.0313301	+	0.0313301i
$890$	−4.76099	+	9.70875i	−0.159589	+	0.325438i
$891$		0			0
$892$	−3.04040	+	23.9164i	−0.101800	+	0.800781i
$893$	9.32384	+	22.5097i	0.312011	+	0.753260i
$894$		0			0
$895$	−10.7834			−0.360451
$896$	13.5693	+	6.43077i	0.453318	+	0.214837i
$897$		0			0
$898$	6.84372	+	7.76882i	0.228378	+	0.259249i
$899$	−5.11924	−	12.3589i	−0.170736	−	0.412193i
$900$		0			0
$901$	−10.9810	−	4.54847i	−0.365829	−	0.151532i
$902$	−11.7338	+	23.9280i	−0.390694	+	0.796716i
$903$		0			0
$904$	3.44536	+	5.08254i	0.114591	+	0.169043i
$905$	2.45014	−	2.45014i	0.0814453	−	0.0814453i
$906$		0			0
$907$	−19.7593	+	47.7031i	−0.656096	+	1.58396i	0.147688	+	0.989034i	$0.452817\pi$
$907$	−19.7593	+	47.7031i	−0.656096	+	1.58396i	−0.803784	+	0.594921i	$0.797183\pi$
$908$	−18.7888	+	5.12419i	−0.623527	+	0.170052i
$909$		0			0
$910$	0.729743	−	11.5268i	0.0241907	−	0.382110i
$911$			51.4196i			1.70361i	0.523862	+	0.851803i	$0.324491\pi$
$911$			51.4196i			1.70361i	−0.523862	+	0.851803i	$0.675509\pi$
$912$		0			0
$913$		−	14.4970i		−	0.479782i
$914$	26.3868	+	1.67051i	0.872799	+	0.0552554i
$915$		0			0
$916$	28.5833	−	50.0208i	0.944420	−	1.65273i
$917$	5.44344	−	13.1416i	0.179758	−	0.433975i
$918$		0			0
$919$	15.9328	−	15.9328i	0.525575	−	0.525575i	−0.393675	−	0.919250i	$-0.628796\pi$
$919$	15.9328	−	15.9328i	0.525575	−	0.525575i	0.919250	+	0.393675i	$0.128796\pi$
$920$	12.5191	−	19.0098i	0.412743	−	0.626733i
$921$		0			0
$922$	5.37711	+	2.63683i	0.177086	+	0.0868395i
$923$	15.5950	+	6.45967i	0.513317	+	0.212623i
$924$		0			0
$925$	6.62925	+	16.0044i	0.217968	+	0.526222i
$926$	21.1650	−	18.6447i	0.695526	−	0.612704i
$927$		0			0
$928$	9.13214	−	10.6500i	0.299777	−	0.349604i
$929$	25.5885			0.839532			0.419766	−	0.907632i	$-0.362112\pi$
$929$	25.5885			0.839532			0.419766	+	0.907632i	$0.362112\pi$
$930$		0			0
$931$	7.30458	+	17.6348i	0.239398	+	0.577958i
$932$	−19.7106	−	25.4520i	−0.645643	−	0.833707i
$933$		0			0
$934$	32.1776	+	15.7793i	1.05288	+	0.516315i
$935$	12.1514	+	12.1514i	0.397392	+	0.397392i
$936$		0			0
$937$	6.19246	−	6.19246i	0.202299	−	0.202299i	−0.598685	−	0.800984i	$-0.704310\pi$
$937$	6.19246	−	6.19246i	0.202299	−	0.202299i	0.800984	+	0.598685i	$0.204310\pi$
$938$	−17.5070	+	5.98631i	−0.571623	+	0.195460i
$939$		0			0
$940$	11.6937	+	6.68210i	0.381405	+	0.217946i
$941$	−22.7706	+	9.43189i	−0.742300	+	0.307471i	−0.721596	−	0.692315i	$-0.756591\pi$
$941$	−22.7706	+	9.43189i	−0.742300	+	0.307471i	−0.0207048	+	0.999786i	$0.506591\pi$
$942$		0			0
$943$			68.0964i			2.21753i
$944$	24.9481	+	18.7928i	0.811990	+	0.611653i
$945$		0			0
$946$	1.74775	−	27.6070i	0.0568243	−	0.897581i
$947$	35.7353	−	14.8021i	1.16124	−	0.481002i	0.282954	−	0.959134i	$-0.408686\pi$
$947$	35.7353	−	14.8021i	1.16124	−	0.481002i	0.878288	+	0.478131i	$0.158686\pi$
$948$		0			0
$949$	28.3898	−	68.5390i	0.921571	−	2.22487i
$950$	−6.64528	−	19.4341i	−0.215601	−	0.630526i
$951$		0			0
$952$	−5.46144	+	28.4481i	−0.177006	+	0.922007i
$953$	2.65738	+	2.65738i	0.0860809	+	0.0860809i	0.748836	−	0.662755i	$-0.230613\pi$
$953$	2.65738	+	2.65738i	0.0860809	+	0.0860809i	−0.662755	+	0.748836i	$0.730613\pi$
$954$		0			0
$955$	20.3310	+	8.42138i	0.657896	+	0.272509i
$956$	24.0407	+	3.05620i	0.777532	+	0.0988447i
$957$		0			0
$958$	14.7200	+	16.7098i	0.475583	+	0.539869i
$959$	−23.9787			−0.774312
$960$		0			0
$961$	−1.90528			−0.0614607
$962$	−24.8245	−	28.1802i	−0.800375	−	0.908565i
$963$		0			0
$964$	2.61102	+	0.331929i	0.0840952	+	0.0106907i
$965$	−13.5182	−	5.59942i	−0.435166	−	0.180252i
$966$		0			0
$967$	−5.32503	−	5.32503i	−0.171241	−	0.171241i	0.616283	−	0.787525i	$-0.288638\pi$
$967$	−5.32503	−	5.32503i	−0.171241	−	0.171241i	−0.787525	+	0.616283i	$0.788638\pi$
$968$	16.9724	+	3.25835i	0.545513	+	0.104727i
$969$		0			0
$970$	3.82990	+	11.2005i	0.122971	+	0.359628i
$971$	−9.21695	+	22.2517i	−0.295786	+	0.714090i	0.704206	+	0.709996i	$0.251303\pi$
$971$	−9.21695	+	22.2517i	−0.295786	+	0.714090i	−0.999992	+	0.00409432i	$0.998697\pi$
$972$		0			0
$973$	3.52578	−	1.46042i	0.113031	−	0.0468190i
$974$	−2.76662	+	43.7007i	−0.0886481	+	1.40026i
$975$		0			0
$976$	4.45227	+	31.6389i	0.142514	+	1.01274i
$977$		−	21.7322i		−	0.695274i	−0.937629	−	0.347637i	$-0.886984\pi$
$977$		−	21.7322i		−	0.695274i	0.937629	−	0.347637i	$-0.113016\pi$
$978$		0			0
$979$	15.5104	−	6.42463i	0.495715	−	0.205332i
$980$	9.16117	+	5.23496i	0.292643	+	0.167225i
$981$		0			0
$982$	−11.0541	+	3.77984i	−0.352752	+	0.120619i
$983$	−30.7394	+	30.7394i	−0.980436	+	0.980436i	−0.999812	−	0.0193762i	$-0.993832\pi$
$983$	−30.7394	+	30.7394i	−0.980436	+	0.980436i	0.0193762	+	0.999812i	$0.493832\pi$
$984$		0			0
$985$	12.2689	+	12.2689i	0.390921	+	0.390921i
$986$	24.2995	+	11.9160i	0.773854	+	0.379483i
$987$		0			0
$988$	27.2631	+	35.2043i	0.867354	+	1.12000i
$989$	−27.0490	−	65.3021i	−0.860109	−	2.07649i
$990$		0			0
$991$	12.5981			0.400192			0.200096	−	0.979776i	$-0.435875\pi$
$991$	12.5981			0.400192			0.200096	+	0.979776i	$0.435875\pi$
$992$	13.7992	+	27.2142i	0.438125	+	0.864052i
$993$		0			0
$994$	3.89113	−	3.42778i	0.123419	−	0.108723i
$995$	6.75519	+	16.3085i	0.214154	+	0.517013i
$996$		0			0
$997$	0.0205884	+	0.00852802i	0.000652043	+	0.000270085i	0.383009	−	0.923744i	$-0.374888\pi$
$997$	0.0205884	+	0.00852802i	0.000652043	+	0.000270085i	−0.382357	+	0.924015i	$0.624888\pi$
$998$	31.8205	+	15.6042i	1.00726	+	0.493942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.325.10	yes	128
3.2	odd	2	inner	864.2.v.a.325.23	yes	128
32.13	even	8	inner	864.2.v.a.109.10	✓	128
96.77	odd	8	inner	864.2.v.a.109.23	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.10	✓	128	32.13	even	8	inner
864.2.v.a.109.23	yes	128	96.77	odd	8	inner
864.2.v.a.325.10	yes	128	1.1	even	1	trivial
864.2.v.a.325.23	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.934820 - 1.06118i) q^{2} +(-0.252222 + 1.98403i) q^{4} +(0.930451 + 0.385405i) q^{5} +(-0.938500 - 0.938500i) q^{7} +(2.34121 - 1.58706i) q^{8} +O(q^{10})\)	\(q+(-0.934820 - 1.06118i) q^{2} +(-0.252222 + 1.98403i) q^{4} +(0.930451 + 0.385405i) q^{5} +(-0.938500 - 0.938500i) q^{7} +(2.34121 - 1.58706i) q^{8} +(-0.460818 - 1.34766i) q^{10} +(-0.846222 + 2.04296i) q^{11} +(-5.64483 + 2.33816i) q^{13} +(-0.118592 + 1.87325i) q^{14} +(-3.87277 - 1.00083i) q^{16} -7.71645i q^{17} +(-3.36643 + 1.39442i) q^{19} +(-0.999337 + 1.74884i) q^{20} +(2.95902 - 1.01180i) q^{22} +(5.65026 - 5.65026i) q^{23} +(-2.81833 - 2.81833i) q^{25} +(7.75812 + 3.80444i) q^{26} +(2.09872 - 1.62530i) q^{28} +(-0.949070 - 2.29126i) q^{29} +5.39395 q^{31} +(2.55827 + 5.04532i) q^{32} +(-8.18857 + 7.21350i) q^{34} +(-0.511525 - 1.23493i) q^{35} +(-4.01544 - 1.66325i) q^{37} +(4.62674 + 2.26887i) q^{38} +(2.79004 - 0.574368i) q^{40} +(-6.02596 + 6.02596i) q^{41} +(3.38507 - 8.17229i) q^{43} +(-3.83986 - 2.19421i) q^{44} +(-11.2779 - 0.713987i) q^{46} -6.68653i q^{47} -5.23844i q^{49} +(-0.356135 + 5.62540i) q^{50} +(-3.21524 - 11.7893i) q^{52} +(0.589451 - 1.42306i) q^{53} +(-1.57474 + 1.57474i) q^{55} +(-3.68668 - 0.707766i) q^{56} +(-1.54424 + 3.14905i) q^{58} +(-7.21416 - 2.98820i) q^{59} +(-3.05674 - 7.37963i) q^{61} +(-5.04238 - 5.72397i) q^{62} +(2.96249 - 7.43126i) q^{64} -6.15337 q^{65} +(3.77223 + 9.10696i) q^{67} +(15.3097 + 1.94626i) q^{68} +(-0.832305 + 1.69726i) q^{70} +(-1.95353 - 1.95353i) q^{71} +(-8.58563 + 8.58563i) q^{73} +(1.98870 + 5.81596i) q^{74} +(-1.91749 - 7.03081i) q^{76} +(2.71150 - 1.12314i) q^{77} +11.7674i q^{79} +(-3.21769 - 2.42381i) q^{80} +(12.0278 + 0.761461i) q^{82} +(-6.05690 + 2.50885i) q^{83} +(2.97396 - 7.17978i) q^{85} +(-11.8367 + 4.04744i) q^{86} +(1.26112 + 6.12599i) q^{88} +(-5.36845 - 5.36845i) q^{89} +(7.49204 + 3.10330i) q^{91} +(9.78518 + 12.6354i) q^{92} +(-7.09564 + 6.25071i) q^{94} -3.66972 q^{95} -8.31108 q^{97} +(-5.55894 + 4.89700i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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