LMFDB - Embedded newform 476.2.bl.a.129.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.5
Character	$\chi$	$=$	476.129
Dual form			476.2.bl.a.369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.492526 - 0.998743i) q^{3} +(-3.01462 + 2.64375i) q^{5} +(2.62862 - 0.300610i) q^{7} +(1.07138 - 1.39625i) q^{9} +O(q^{10})$	\(q+(-0.492526 - 0.998743i) q^{3} +(-3.01462 + 2.64375i) q^{5} +(2.62862 - 0.300610i) q^{7} +(1.07138 - 1.39625i) q^{9} +(-4.08011 + 0.267425i) q^{11} +(-4.36738 - 4.36738i) q^{13} +(4.12520 + 1.70871i) q^{15} +(-3.63362 + 1.94853i) q^{17} +(0.826921 + 6.28109i) q^{19} +(-1.59489 - 2.47726i) q^{21} +(-6.53831 - 3.22434i) q^{23} +(1.44588 - 10.9826i) q^{25} +(-5.19873 - 1.03409i) q^{27} +(-0.361977 - 1.81978i) q^{29} +(-2.27602 + 1.12241i) q^{31} +(2.27665 + 3.94327i) q^{33} +(-7.12954 + 7.85563i) q^{35} +(-0.379265 + 5.78647i) q^{37} +(-2.21084 + 6.51294i) q^{39} +(-0.175632 + 0.882961i) q^{41} +(-0.668963 - 1.61502i) q^{43} +(0.461531 + 7.04160i) q^{45} +(-0.151120 + 0.563987i) q^{47} +(6.81927 - 1.58038i) q^{49} +(3.73574 + 2.66936i) q^{51} +(-1.96982 - 2.56712i) q^{53} +(11.5930 - 11.5930i) q^{55} +(5.86591 - 3.91948i) q^{57} +(-4.58770 - 0.603982i) q^{59} +(-0.828262 - 2.43998i) q^{61} +(2.39652 - 3.99227i) q^{63} +(24.7122 + 1.61973i) q^{65} +(7.57605 + 4.37403i) q^{67} +8.11817i q^{69} +(-3.54023 - 2.36550i) q^{71} +(-2.01695 - 0.684662i) q^{73} +(-11.6809 + 3.96513i) q^{75} +(-10.6447 + 1.92948i) q^{77} +(0.497769 - 1.00938i) q^{79} +(0.161206 + 0.601630i) q^{81} +(1.61401 - 3.89656i) q^{83} +(5.80256 - 15.4805i) q^{85} +(-1.63921 + 1.25781i) q^{87} +(15.9892 + 4.28431i) q^{89} +(-12.7931 - 10.1673i) q^{91} +(2.24199 + 1.72034i) q^{93} +(-19.0985 - 16.7489i) q^{95} +(-3.12741 + 0.622081i) q^{97} +(-3.99795 + 5.98335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.492526	−	0.998743i	−0.284360	−	0.576625i	0.707088	−	0.707125i	$-0.250008\pi$
$3$	−0.492526	−	0.998743i	−0.284360	−	0.576625i	−0.991448	+	0.130500i	$0.958342\pi$
$4$		0			0
$5$	−3.01462	+	2.64375i	−1.34818	+	1.18232i	−0.382085	+	0.924127i	$0.624794\pi$
$5$	−3.01462	+	2.64375i	−1.34818	+	1.18232i	−0.966093	+	0.258193i	$0.916873\pi$
$6$		0			0
$7$	2.62862	−	0.300610i	0.993524	−	0.113620i
$7$	2.62862	−	0.300610i	0.993524	−	0.113620i
$8$		0			0
$9$	1.07138	−	1.39625i	0.357126	−	0.465416i
$10$		0			0
$11$	−4.08011	+	0.267425i	−1.23020	+	0.0806315i	−0.666599	−	0.745416i	$-0.732251\pi$
$11$	−4.08011	+	0.267425i	−1.23020	+	0.0806315i	−0.563600	+	0.826048i	$0.690584\pi$
$12$		0			0
$13$	−4.36738	−	4.36738i	−1.21129	−	1.21129i	−0.970602	−	0.240692i	$-0.922626\pi$
$13$	−4.36738	−	4.36738i	−1.21129	−	1.21129i	−0.240692	−	0.970602i	$-0.577374\pi$
$14$		0			0
$15$	4.12520	+	1.70871i	1.06512	+	0.441188i
$16$		0			0
$17$	−3.63362	+	1.94853i	−0.881283	+	0.472588i
$17$	−3.63362	+	1.94853i	−0.881283	+	0.472588i
$18$		0			0
$19$	0.826921	+	6.28109i	0.189709	+	1.44098i	0.775925	+	0.630825i	$0.217284\pi$
$19$	0.826921	+	6.28109i	0.189709	+	1.44098i	−0.586216	+	0.810155i	$0.699383\pi$
$20$		0			0
$21$	−1.59489	−	2.47726i	−0.348034	−	0.540582i
$22$		0			0
$23$	−6.53831	−	3.22434i	−1.36333	−	0.672321i	−0.394238	−	0.919009i	$-0.628991\pi$
$23$	−6.53831	−	3.22434i	−1.36333	−	0.672321i	−0.969095	+	0.246687i	$0.920658\pi$
$24$		0			0
$25$	1.44588	−	10.9826i	0.289176	−	2.19651i
$26$		0			0
$27$	−5.19873	−	1.03409i	−1.00050	−	0.199011i
$28$		0			0
$29$	−0.361977	−	1.81978i	−0.0672175	−	0.337925i	0.932513	−	0.361136i	$-0.117611\pi$
$29$	−0.361977	−	1.81978i	−0.0672175	−	0.337925i	−0.999731	+	0.0232110i	$0.992611\pi$
$30$		0			0
$31$	−2.27602	+	1.12241i	−0.408784	+	0.201590i	−0.635042	−	0.772477i	$-0.719017\pi$
$31$	−2.27602	+	1.12241i	−0.408784	+	0.201590i	0.226258	+	0.974067i	$0.427351\pi$
$32$		0			0
$33$	2.27665	+	3.94327i	0.396313	+	0.686435i
$34$		0			0
$35$	−7.12954	+	7.85563i	−1.20511	+	1.32784i
$36$		0			0
$37$	−0.379265	+	5.78647i	−0.0623508	+	0.951289i	0.846027	+	0.533140i	$0.178988\pi$
$37$	−0.379265	+	5.78647i	−0.0623508	+	0.951289i	−0.908378	+	0.418150i	$0.862679\pi$
$38$		0			0
$39$	−2.21084	+	6.51294i	−0.354018	+	1.04290i
$40$		0			0
$41$	−0.175632	+	0.882961i	−0.0274291	+	0.137895i	−0.992073	−	0.125660i	$-0.959895\pi$
$41$	−0.175632	+	0.882961i	−0.0274291	+	0.137895i	0.964644	+	0.263555i	$0.0848952\pi$
$42$		0			0
$43$	−0.668963	−	1.61502i	−0.102016	−	0.246288i	0.864628	−	0.502413i	$-0.167554\pi$
$43$	−0.668963	−	1.61502i	−0.102016	−	0.246288i	−0.966644	+	0.256125i	$0.917554\pi$
$44$		0			0
$45$	0.461531	+	7.04160i	0.0688010	+	1.04970i
$46$		0			0
$47$	−0.151120	+	0.563987i	−0.0220431	+	0.0822660i	−0.976071	−	0.217451i	$-0.930226\pi$
$47$	−0.151120	+	0.563987i	−0.0220431	+	0.0822660i	0.954028	+	0.299717i	$0.0968924\pi$
$48$		0			0
$49$	6.81927	−	1.58038i	0.974181	−	0.225768i
$50$		0			0
$51$	3.73574	+	2.66936i	0.523108	+	0.373784i
$52$		0			0
$53$	−1.96982	−	2.56712i	−0.270576	−	0.352621i	0.638226	−	0.769849i	$-0.279668\pi$
$53$	−1.96982	−	2.56712i	−0.270576	−	0.352621i	−0.908802	+	0.417228i	$0.863002\pi$
$54$		0			0
$55$	11.5930	−	11.5930i	1.56320	−	1.56320i
$56$		0			0
$57$	5.86591	−	3.91948i	0.776959	−	0.519147i
$58$		0			0
$59$	−4.58770	−	0.603982i	−0.597268	−	0.0786318i	−0.174170	−	0.984716i	$-0.555724\pi$
$59$	−4.58770	−	0.603982i	−0.597268	−	0.0786318i	−0.423098	+	0.906084i	$0.639057\pi$
$60$		0			0
$61$	−0.828262	−	2.43998i	−0.106048	−	0.312407i	0.880934	−	0.473240i	$-0.156916\pi$
$61$	−0.828262	−	2.43998i	−0.106048	−	0.312407i	−0.986982	+	0.160832i	$0.948582\pi$
$62$		0			0
$63$	2.39652	−	3.99227i	0.301933	−	0.502978i
$64$		0			0
$65$	24.7122	+	1.61973i	3.06518	+	0.200902i
$66$		0			0
$67$	7.57605	+	4.37403i	0.925562	+	0.534373i	0.885405	−	0.464820i	$-0.153881\pi$
$67$	7.57605	+	4.37403i	0.925562	+	0.534373i	0.0401565	+	0.999193i	$0.487214\pi$
$68$		0			0
$69$			8.11817i			0.977312i
$70$		0			0
$71$	−3.54023	−	2.36550i	−0.420148	−	0.280734i	0.327472	−	0.944861i	$-0.393803\pi$
$71$	−3.54023	−	2.36550i	−0.420148	−	0.280734i	−0.747620	+	0.664127i	$0.768803\pi$
$72$		0			0
$73$	−2.01695	−	0.684662i	−0.236066	−	0.0801337i	0.200899	−	0.979612i	$-0.435614\pi$
$73$	−2.01695	−	0.684662i	−0.236066	−	0.0801337i	−0.436966	+	0.899478i	$0.643947\pi$
$74$		0			0
$75$	−11.6809	+	3.96513i	−1.34879	+	0.457854i
$76$		0			0
$77$	−10.6447	+	1.92948i	−1.21307	+	0.219885i
$78$		0			0
$79$	0.497769	−	1.00938i	0.0560034	−	0.113564i	−0.867072	−	0.498183i	$-0.834001\pi$
$79$	0.497769	−	1.00938i	0.0560034	−	0.113564i	0.923075	+	0.384620i	$0.125667\pi$
$80$		0			0
$81$	0.161206	+	0.601630i	0.0179118	+	0.0668477i
$82$		0			0
$83$	1.61401	−	3.89656i	0.177161	−	0.427704i	−0.810208	−	0.586142i	$-0.800646\pi$
$83$	1.61401	−	3.89656i	0.177161	−	0.427704i	0.987369	+	0.158439i	$0.0506460\pi$
$84$		0			0
$85$	5.80256	−	15.4805i	0.629376	−	1.67909i
$86$		0			0
$87$	−1.63921	+	1.25781i	−0.175742	+	0.134852i
$88$		0			0
$89$	15.9892	+	4.28431i	1.69486	+	0.454136i	0.971636	−	0.236481i	$-0.0759942\pi$
$89$	15.9892	+	4.28431i	1.69486	+	0.454136i	0.723221	+	0.690617i	$0.242661\pi$
$90$		0			0
$91$	−12.7931	−	10.1673i	−1.34108	−	1.06582i
$92$		0			0
$93$	2.24199	+	1.72034i	0.232484	+	0.178391i
$94$		0			0
$95$	−19.0985	−	16.7489i	−1.95946	−	1.71840i
$96$		0			0
$97$	−3.12741	+	0.622081i	−0.317541	+	0.0631628i	−0.351287	−	0.936268i	$-0.614256\pi$
$97$	−3.12741	+	0.622081i	−0.317541	+	0.0631628i	0.0337468	+	0.999430i	$0.489256\pi$
$98$		0			0
$99$	−3.99795	+	5.98335i	−0.401809	+	0.601350i
$100$		0			0
$101$	5.75109	−	9.96118i	0.572255	−	0.991174i	−0.424079	−	0.905625i	$-0.639402\pi$
$101$	5.75109	−	9.96118i	0.572255	−	0.991174i	0.996334	−	0.0855490i	$-0.0272644\pi$
$102$		0			0
$103$	−9.37465	+	5.41246i	−0.923711	+	0.533305i	−0.884817	−	0.465938i	$-0.845717\pi$
$103$	−9.37465	+	5.41246i	−0.923711	+	0.533305i	−0.0388943	+	0.999243i	$0.512384\pi$
$104$		0			0
$105$	11.3572	+	3.25148i	1.10835	+	0.317312i
$106$		0			0
$107$	4.69519	+	5.35384i	0.453901	+	0.517575i	0.932849	−	0.360269i	$-0.117315\pi$
$107$	4.69519	+	5.35384i	0.453901	+	0.517575i	−0.478948	+	0.877843i	$0.658982\pi$
$108$		0			0
$109$	8.71355	−	9.93590i	0.834606	−	0.951686i	−0.164793	−	0.986328i	$-0.552696\pi$
$109$	8.71355	−	9.93590i	0.834606	−	0.951686i	0.999400	+	0.0346420i	$0.0110291\pi$
$110$		0			0
$111$	5.96599	−	2.47119i	0.566267	−	0.234555i
$112$		0			0
$113$	3.41041	+	5.10403i	0.320824	+	0.480147i	0.956469	−	0.291835i	$-0.0942657\pi$
$113$	3.41041	+	5.10403i	0.320824	+	0.480147i	−0.635645	+	0.771982i	$0.719266\pi$
$114$		0			0
$115$	28.2349	−	7.56551i	2.63291	−	0.705487i
$116$		0			0
$117$	−10.7771	+	1.41883i	−0.996339	+	0.131171i
$118$		0			0
$119$	−8.96566	+	6.21425i	−0.821881	+	0.569659i
$120$		0			0
$121$	5.66988	−	0.746454i	0.515444	−	0.0678595i
$122$		0			0
$123$	0.968354	−	0.259470i	0.0873136	−	0.0233956i
$124$		0			0
$125$	13.5381	+	20.2612i	1.21089	+	1.81222i
$126$		0			0
$127$	−11.2888	+	4.67598i	−1.00172	+	0.414926i	−0.822428	−	0.568870i	$-0.807381\pi$
$127$	−11.2888	+	4.67598i	−1.00172	+	0.414926i	−0.179293	+	0.983796i	$0.557381\pi$
$128$		0			0
$129$	−1.28351	+	1.46356i	−0.113007	+	0.128859i
$130$		0			0
$131$	7.00927	+	7.99254i	0.612402	+	0.698311i	0.972049	−	0.234777i	$-0.0754361\pi$
$131$	7.00927	+	7.99254i	0.612402	+	0.698311i	−0.359647	+	0.933089i	$0.617103\pi$
$132$		0			0
$133$	4.06182	+	16.2620i	0.352204	+	1.41009i
$134$		0			0
$135$	18.4061	−	10.6268i	1.58414	−	0.914605i
$136$		0			0
$137$	7.84119	−	13.5813i	0.669918	−	1.16033i	−0.308008	−	0.951384i	$-0.599663\pi$
$137$	7.84119	−	13.5813i	0.669918	−	1.16033i	0.977927	−	0.208949i	$-0.0670041\pi$
$138$		0			0
$139$	−7.18225	+	10.7490i	−0.609190	+	0.911718i	−0.999962	−	0.00877008i	$-0.997208\pi$
$139$	−7.18225	+	10.7490i	−0.609190	+	0.911718i	0.390771	+	0.920488i	$0.372208\pi$
$140$		0			0
$141$	0.637709	−	0.126848i	0.0537048	−	0.0106825i
$142$		0			0
$143$	18.9873	+	16.6514i	1.58780	+	1.39246i
$144$		0			0
$145$	5.90227	+	4.52897i	0.490157	+	0.376111i
$146$		0			0
$147$	−4.93706	−	6.03232i	−0.407202	−	0.497537i
$148$		0			0
$149$	−6.72331	−	1.80151i	−0.550795	−	0.147585i	−0.0273211	−	0.999627i	$-0.508698\pi$
$149$	−6.72331	−	1.80151i	−0.550795	−	0.147585i	−0.523474	+	0.852042i	$0.675364\pi$
$150$		0			0
$151$	−9.62978	+	7.38919i	−0.783660	+	0.601324i	−0.921163	−	0.389178i	$-0.872759\pi$
$151$	−9.62978	+	7.38919i	−0.783660	+	0.601324i	0.137503	+	0.990501i	$0.456092\pi$
$152$		0			0
$153$	−1.17235	+	7.16105i	−0.0947791	+	0.578937i
$154$		0			0
$155$	3.89395	−	9.40084i	0.312770	−	0.755094i
$156$		0			0
$157$	−4.73626	−	17.6760i	−0.377995	−	1.41070i	−0.848919	−	0.528523i	$-0.822746\pi$
$157$	−4.73626	−	17.6760i	−0.377995	−	1.41070i	0.470924	−	0.882174i	$-0.343920\pi$
$158$		0			0
$159$	−1.59371	+	3.23172i	−0.126389	+	0.256292i
$160$		0			0
$161$	−18.1560	−	6.51007i	−1.43089	−	0.513066i
$162$		0			0
$163$	0.408057	−	0.138517i	0.0319615	−	0.0108495i	−0.305413	−	0.952220i	$-0.598794\pi$
$163$	0.408057	−	0.138517i	0.0319615	−	0.0108495i	0.337374	+	0.941371i	$0.390461\pi$
$164$		0			0
$165$	−17.2882	−	5.86856i	−1.34589	−	0.456867i
$166$		0			0
$167$	10.1896	+	6.80845i	0.788492	+	0.526854i	0.883393	−	0.468633i	$-0.155253\pi$
$167$	10.1896	+	6.80845i	0.788492	+	0.526854i	−0.0949008	+	0.995487i	$0.530253\pi$
$168$		0			0
$169$			25.1480i			1.93446i
$170$		0			0
$171$	9.65589	+	5.57483i	0.738404	+	0.426318i
$172$		0			0
$173$	−9.48511	−	0.621687i	−0.721140	−	0.0472660i	−0.299586	−	0.954069i	$-0.596848\pi$
$173$	−9.48511	−	0.621687i	−0.721140	−	0.0472660i	−0.421554	+	0.906803i	$0.638515\pi$
$174$		0			0
$175$	0.499200	−	29.3036i	0.0377360	−	2.21514i
$176$		0			0
$177$	1.65634	+	4.87941i	0.124498	+	0.366759i
$178$		0			0
$179$	13.3991	+	1.76402i	1.00149	+	0.131849i	0.613401	−	0.789772i	$-0.289801\pi$
$179$	13.3991	+	1.76402i	1.00149	+	0.131849i	0.388092	+	0.921621i	$0.373134\pi$
$180$		0			0
$181$	−17.4804	+	11.6800i	−1.29931	+	0.868171i	−0.996394	−	0.0848460i	$-0.972960\pi$
$181$	−17.4804	+	11.6800i	−1.29931	+	0.868171i	−0.302916	+	0.953017i	$0.597960\pi$
$182$		0			0
$183$	−2.02897	+	2.02897i	−0.149986	+	0.149986i
$184$		0			0
$185$	−14.1546	−	18.4467i	−1.04067	−	1.35623i
$186$		0			0
$187$	14.3045	−	8.92194i	1.04605	−	0.652437i
$188$		0			0
$189$	−13.9763	−	1.15544i	−1.01663	−	0.0840460i
$190$		0			0
$191$	−4.96262	+	18.5208i	−0.359083	+	1.34011i	0.516185	+	0.856477i	$0.327352\pi$
$191$	−4.96262	+	18.5208i	−0.359083	+	1.34011i	−0.875268	+	0.483638i	$0.839315\pi$
$192$		0			0
$193$	−0.0528128	−	0.805767i	−0.00380155	−	0.0580004i	0.995537	−	0.0943757i	$-0.0300855\pi$
$193$	−0.0528128	−	0.805767i	−0.00380155	−	0.0580004i	−0.999338	+	0.0363753i	$0.988419\pi$
$194$		0			0
$195$	−10.5537	−	25.4789i	−0.755768	−	1.82458i
$196$		0			0
$197$	−0.372285	+	1.87160i	−0.0265242	+	0.133346i	−0.991779	−	0.127966i	$-0.959155\pi$
$197$	−0.372285	+	1.87160i	−0.0265242	+	0.133346i	0.965254	+	0.261312i	$0.0841552\pi$
$198$		0			0
$199$	−4.25263	+	12.5278i	−0.301461	+	0.888075i	0.685635	+	0.727946i	$0.259525\pi$
$199$	−4.25263	+	12.5278i	−0.301461	+	0.888075i	−0.987096	+	0.160130i	$0.948809\pi$
$200$		0			0
$201$	0.637138	−	9.72085i	0.0449403	−	0.685656i
$202$		0			0
$203$	−1.49855	−	4.67470i	−0.105177	−	0.328100i
$204$		0			0
$205$	−1.80486	−	3.12612i	−0.126057	−	0.218337i
$206$		0			0
$207$	−11.5070	+	5.67461i	−0.799790	+	0.394413i
$208$		0			0
$209$	−5.05364	−	25.4064i	−0.349568	−	1.75740i
$210$		0			0
$211$	0.948031	+	0.188575i	0.0652652	+	0.0129820i	0.227615	−	0.973751i	$-0.426907\pi$
$211$	0.948031	+	0.188575i	0.0652652	+	0.0129820i	−0.162350	+	0.986733i	$0.551907\pi$
$212$		0			0
$213$	−0.618879	+	4.70085i	−0.0424049	+	0.322097i
$214$		0			0
$215$	6.28637	+	3.10009i	0.428727	+	0.211425i
$216$		0			0
$217$	−5.64537	+	3.63457i	−0.383233	+	0.246731i
$218$		0			0
$219$	0.309598	+	2.35163i	0.0209207	+	0.158908i
$220$		0			0
$221$	24.3794	+	7.35944i	1.63994	+	0.495049i
$222$		0			0
$223$	−21.3532	−	8.84480i	−1.42992	−	0.592292i	−0.472587	−	0.881284i	$-0.656680\pi$
$223$	−21.3532	−	8.84480i	−1.42992	−	0.592292i	−0.957331	+	0.288992i	$0.906680\pi$
$224$		0			0
$225$	−13.7853	−	13.7853i	−0.919019	−	0.919019i
$226$		0			0
$227$	−11.6689	+	0.764818i	−0.774490	+	0.0507627i	−0.447522	−	0.894273i	$-0.647693\pi$
$227$	−11.6689	+	0.764818i	−0.774490	+	0.0507627i	−0.326967	+	0.945036i	$0.606027\pi$
$228$		0			0
$229$	−0.146807	+	0.191322i	−0.00970126	+	0.0126429i	−0.798179	−	0.602421i	$-0.794203\pi$
$229$	−0.146807	+	0.191322i	−0.00970126	+	0.0126429i	0.788478	+	0.615064i	$0.210870\pi$
$230$		0			0
$231$	7.16982	+	9.68096i	0.471740	+	0.636961i
$232$		0			0
$233$	−11.8082	+	10.3555i	−0.773578	+	0.678409i	−0.952189	−	0.305510i	$-0.901173\pi$
$233$	−11.8082	+	10.3555i	−0.773578	+	0.678409i	0.178611	+	0.983920i	$0.442840\pi$
$234$		0			0
$235$	−1.03547	−	2.09973i	−0.0675468	−	0.136971i
$236$		0			0
$237$	−1.25327			−0.0814087
$238$		0			0
$239$	−12.1566			−0.786343			−0.393172	−	0.919465i	$-0.628622\pi$
$239$	−12.1566			−0.786343			−0.393172	+	0.919465i	$0.628622\pi$
$240$		0			0
$241$	−2.90165	−	5.88396i	−0.186912	−	0.379019i	0.783167	−	0.621812i	$-0.213603\pi$
$241$	−2.90165	−	5.88396i	−0.186912	−	0.379019i	−0.970078	+	0.242793i	$0.921937\pi$
$242$		0			0
$243$	−11.4341	+	10.0274i	−0.733497	+	0.643260i
$244$		0			0
$245$	−16.3794	+	22.7927i	−1.04644	+	1.45617i
$246$		0			0
$247$	23.8204	−	31.0434i	1.51566	−	1.97524i
$248$		0			0
$249$	−4.68661	+	0.307177i	−0.297002	+	0.0194665i
$250$		0			0
$251$	−4.87769	−	4.87769i	−0.307877	−	0.307877i	0.536209	−	0.844086i	$-0.319856\pi$
$251$	−4.87769	−	4.87769i	−0.307877	−	0.307877i	−0.844086	+	0.536209i	$0.819856\pi$
$252$		0			0
$253$	27.5393	+	11.4072i	1.73138	+	0.717162i
$254$		0			0
$255$	−18.3189	+	1.82926i	−1.14718	+	0.114553i
$256$		0			0
$257$	−3.60878	−	27.4114i	−0.225109	−	1.70988i	−0.614595	−	0.788843i	$-0.710681\pi$
$257$	−3.60878	−	27.4114i	−0.225109	−	1.70988i	0.389486	−	0.921033i	$-0.372653\pi$
$258$		0			0
$259$	0.742528	+	15.3244i	0.0461384	+	0.952213i
$260$		0			0
$261$	−2.92868	−	1.44427i	−0.181281	−	0.0893978i
$262$		0			0
$263$	0.697477	−	5.29786i	0.0430083	−	0.326680i	−0.956393	−	0.292083i	$-0.905652\pi$
$263$	0.697477	−	5.29786i	0.0430083	−	0.326680i	0.999401	−	0.0345975i	$-0.0110149\pi$
$264$		0			0
$265$	12.7251	+	2.53117i	0.781695	+	0.155489i
$266$		0			0
$267$	−3.59619	−	18.0793i	−0.220083	−	1.10643i
$268$		0			0
$269$	11.7001	−	5.76986i	0.713369	−	0.351794i	−0.0491229	−	0.998793i	$-0.515643\pi$
$269$	11.7001	−	5.76986i	0.713369	−	0.351794i	0.762491	+	0.646998i	$0.223976\pi$
$270$		0			0
$271$	0.503461	+	0.872020i	0.0305831	+	0.0529714i	0.880912	−	0.473280i	$-0.156930\pi$
$271$	0.503461	+	0.872020i	0.0305831	+	0.0529714i	−0.850329	+	0.526252i	$0.823597\pi$
$272$		0			0
$273$	−3.85361	+	17.7846i	−0.233231	+	1.07637i
$274$		0			0
$275$	−2.96235	+	45.1967i	−0.178636	+	2.72546i
$276$		0			0
$277$	9.69625	−	28.5642i	0.582591	−	1.71626i	−0.109069	−	0.994034i	$-0.534787\pi$
$277$	9.69625	−	28.5642i	0.582591	−	1.71626i	0.691660	−	0.722223i	$-0.256880\pi$
$278$		0			0
$279$	−0.871316	+	4.38040i	−0.0521643	+	0.262248i
$280$		0			0
$281$	−0.861265	−	2.07928i	−0.0513788	−	0.124039i	0.896106	−	0.443840i	$-0.146384\pi$
$281$	−0.861265	−	2.07928i	−0.0513788	−	0.124039i	−0.947485	+	0.319801i	$0.896384\pi$
$282$		0			0
$283$	−1.35604	−	20.6891i	−0.0806080	−	1.22984i	−0.826176	−	0.563412i	$-0.809488\pi$
$283$	−1.35604	−	20.6891i	−0.0806080	−	1.22984i	0.745568	−	0.666429i	$-0.232178\pi$
$284$		0			0
$285$	−7.32137	+	27.3237i	−0.433680	+	1.61852i
$286$		0			0
$287$	−0.196242	+	2.37376i	−0.0115838	+	0.140119i
$288$		0			0
$289$	9.40645	−	14.1605i	0.553320	−	0.832969i
$290$		0			0
$291$	2.16163	+	2.81709i	0.126717	+	0.165141i
$292$		0			0
$293$	13.4682	−	13.4682i	0.786823	−	0.786823i	−0.194149	−	0.980972i	$-0.562195\pi$
$293$	13.4682	−	13.4682i	0.786823	−	0.786823i	0.980972	+	0.194149i	$0.0621946\pi$
$294$		0			0
$295$	15.4269	−	10.3079i	0.898191	−	0.600152i
$296$		0			0
$297$	21.4879	+	2.82894i	1.24686	+	0.164152i
$298$		0			0
$299$	14.4734	+	42.6372i	0.837018	+	2.46577i
$300$		0			0
$301$	−2.24394	−	4.04417i	−0.129338	−	0.233102i
$302$		0			0
$303$	−12.7812	−	0.837725i	−0.734262	−	0.0481260i
$304$		0			0
$305$	8.94759	+	5.16589i	0.512337	+	0.295798i
$306$		0			0
$307$		−	14.3135i		−	0.816912i	−0.912778	−	0.408456i	$-0.866067\pi$
$307$		−	14.3135i		−	0.816912i	0.912778	−	0.408456i	$-0.133933\pi$
$308$		0			0
$309$	10.0229	+	6.69709i	0.570183	+	0.380984i
$310$		0			0
$311$	8.98261	+	3.04919i	0.509357	+	0.172904i	0.564274	−	0.825587i	$-0.309156\pi$
$311$	8.98261	+	3.04919i	0.509357	+	0.172904i	−0.0549169	+	0.998491i	$0.517489\pi$
$312$		0			0
$313$	−29.8310	+	10.1263i	−1.68615	+	0.572370i	−0.989435	−	0.144980i	$-0.953688\pi$
$313$	−29.8310	+	10.1263i	−1.68615	+	0.572370i	−0.696713	+	0.717350i	$0.745355\pi$
$314$		0			0
$315$	3.32997	+	18.3709i	0.187622	+	1.03509i
$316$		0			0
$317$	−2.64890	+	5.37143i	−0.148777	+	0.301690i	−0.958485	−	0.285143i	$-0.907959\pi$
$317$	−2.64890	+	5.37143i	−0.148777	+	0.301690i	0.809708	+	0.586833i	$0.199625\pi$
$318$		0			0
$319$	1.96356	+	7.32811i	0.109938	+	0.410296i
$320$		0			0
$321$	3.03461	−	7.32619i	0.169375	−	0.408908i
$322$		0			0
$323$	−15.2436	−	21.2118i	−0.848177	−	1.18026i
$324$		0			0
$325$	−54.2797	+	41.6503i	−3.01090	+	2.31034i
$326$		0			0
$327$	−14.2151	−	3.80891i	−0.786094	−	0.210633i
$328$		0			0
$329$	−0.227696	+	1.52794i	−0.0125533	+	0.0842378i
$330$		0			0
$331$	−13.4139	−	10.2928i	−0.737294	−	0.565745i	0.170402	−	0.985375i	$-0.445493\pi$
$331$	−13.4139	−	10.2928i	−0.737294	−	0.565745i	−0.907696	+	0.419629i	$0.862160\pi$
$332$		0			0
$333$	7.67300	+	6.72904i	0.420478	+	0.368749i
$334$		0			0
$335$	−34.4027	+	6.84313i	−1.87962	+	0.373880i
$336$		0			0
$337$	16.0333	−	23.9956i	0.873391	−	1.30712i	−0.0773084	−	0.997007i	$-0.524633\pi$
$337$	16.0333	−	23.9956i	0.873391	−	1.30712i	0.950699	−	0.310115i	$-0.100367\pi$
$338$		0			0
$339$	3.41791	−	5.91999i	0.185635	−	0.321529i
$340$		0			0
$341$	8.98623	−	5.18820i	0.486632	−	0.280957i
$342$		0			0
$343$	17.4502	−	6.20415i	0.942221	−	0.334993i
$344$		0			0
$345$	−21.4624	−	24.4732i	−1.15550	−	1.31759i
$346$		0			0
$347$	−6.97527	+	7.95378i	−0.374452	+	0.426981i	−0.908118	−	0.418715i	$-0.862481\pi$
$347$	−6.97527	+	7.95378i	−0.374452	+	0.426981i	0.533666	+	0.845696i	$0.320814\pi$
$348$		0			0
$349$	−28.5458	+	11.8240i	−1.52802	+	0.632926i	−0.979179	−	0.203000i	$-0.934931\pi$
$349$	−28.5458	+	11.8240i	−1.52802	+	0.632926i	−0.548841	+	0.835927i	$0.684931\pi$
$350$		0			0
$351$	18.1886	+	27.2211i	0.970834	+	1.45296i
$352$		0			0
$353$	−15.3504	+	4.11314i	−0.817021	+	0.218920i	−0.643044	−	0.765829i	$-0.722329\pi$
$353$	−15.3504	+	4.11314i	−0.817021	+	0.218920i	−0.173978	+	0.984750i	$0.555662\pi$
$354$		0			0
$355$	16.9262	−	2.22838i	0.898351	−	0.118270i
$356$		0			0
$357$	10.6223	+	5.89372i	0.562190	+	0.311928i
$358$		0			0
$359$	17.6438	−	2.32285i	0.931204	−	0.122595i	0.350364	−	0.936614i	$-0.386058\pi$
$359$	17.6438	−	2.32285i	0.931204	−	0.122595i	0.580839	+	0.814018i	$0.302724\pi$
$360$		0			0
$361$	−20.4156	+	5.47036i	−1.07451	+	0.287913i
$362$		0			0
$363$	−3.53808	−	5.29511i	−0.185701	−	0.277921i
$364$		0			0
$365$	7.89041	−	3.26831i	0.413003	−	0.171071i
$366$		0			0
$367$	14.4737	−	16.5041i	0.755522	−	0.861508i	−0.238448	−	0.971155i	$-0.576639\pi$
$367$	14.4737	−	16.5041i	0.755522	−	0.861508i	0.993971	+	0.109647i	$0.0349721\pi$
$368$		0			0
$369$	1.04466	+	1.19121i	0.0543830	+	0.0620119i
$370$		0			0
$371$	−5.94961	−	6.15583i	−0.308888	−	0.319595i
$372$		0			0
$373$	7.10915	−	4.10447i	0.368098	−	0.212521i	−0.304529	−	0.952503i	$-0.598499\pi$
$373$	7.10915	−	4.10447i	0.368098	−	0.212521i	0.672627	+	0.739982i	$0.265166\pi$
$374$		0			0
$375$	13.5679	−	23.5003i	0.700643	−	1.21355i
$376$		0			0
$377$	−6.36679	+	9.52858i	−0.327906	+	0.490747i
$378$		0			0
$379$	−2.14353	+	0.426375i	−0.110106	+	0.0219014i	−0.249836	−	0.968288i	$-0.580377\pi$
$379$	−2.14353	+	0.426375i	−0.110106	+	0.0219014i	0.139730	+	0.990190i	$0.455377\pi$
$380$		0			0
$381$	10.2301	+	8.97159i	0.524106	+	0.459628i
$382$		0			0
$383$	−24.2637	−	18.6182i	−1.23982	−	0.951345i	−0.240006	−	0.970771i	$-0.577149\pi$
$383$	−24.2637	−	18.6182i	−1.23982	−	0.951345i	−0.999811	+	0.0194259i	$0.993816\pi$
$384$		0			0
$385$	26.9885	−	33.9584i	1.37546	−	1.73068i
$386$		0			0
$387$	−2.97168	−	0.796258i	−0.151059	−	0.0404761i
$388$		0			0
$389$	−26.5375	+	20.3629i	−1.34550	+	1.03244i	−0.350097	+	0.936713i	$0.613851\pi$
$389$	−26.5375	+	20.3629i	−1.34550	+	1.03244i	−0.995407	+	0.0957285i	$0.969482\pi$
$390$		0			0
$391$	30.0405	−	1.02408i	1.51921	−	0.0517898i
$392$		0			0
$393$	4.53025	−	10.9370i	0.228521	−	0.551698i
$394$		0			0
$395$	1.16795	+	4.35886i	0.0587661	+	0.219318i
$396$		0			0
$397$	7.03636	−	14.2683i	0.353145	−	0.716107i	−0.645728	−	0.763567i	$-0.723446\pi$
$397$	7.03636	−	14.2683i	0.353145	−	0.716107i	0.998873	+	0.0474604i	$0.0151128\pi$
$398$		0			0
$399$	14.2410	−	12.0662i	0.712942	−	0.604064i
$400$		0			0
$401$	−6.63348	+	2.25176i	−0.331260	+	0.112448i	−0.482114	−	0.876108i	$-0.660131\pi$
$401$	−6.63348	+	2.25176i	−0.331260	+	0.112448i	0.150854	+	0.988556i	$0.451798\pi$
$402$		0			0
$403$	14.8422	+	5.03825i	0.739343	+	0.250973i
$404$		0			0
$405$	−2.07653	−	1.38749i	−0.103184	−	0.0689452i
$406$		0			0
$407$		−	23.7108i		−	1.17530i
$408$		0			0
$409$	32.7250	+	18.8938i	1.61815	+	0.934238i	0.987399	+	0.158251i	$0.0505856\pi$
$409$	32.7250	+	18.8938i	1.61815	+	0.934238i	0.630749	+	0.775987i	$0.282748\pi$
$410$		0			0
$411$	−17.4263	−	1.14218i	−0.859574	−	0.0563395i
$412$		0			0
$413$	−12.2409	−	0.208529i	−0.602334	−	0.0102610i
$414$		0			0
$415$	5.43591	+	16.0137i	0.266839	+	0.786081i
$416$		0			0
$417$	14.2729	+	1.87907i	0.698948	+	0.0920183i
$418$		0			0
$419$	16.5450	−	11.0550i	0.808274	−	0.540072i	−0.0813925	−	0.996682i	$-0.525937\pi$
$419$	16.5450	−	11.0550i	0.808274	−	0.540072i	0.889667	+	0.456611i	$0.150937\pi$
$420$		0			0
$421$	−12.8961	+	12.8961i	−0.628517	+	0.628517i	−0.947695	−	0.319178i	$-0.896593\pi$
$421$	−12.8961	+	12.8961i	−0.628517	+	0.628517i	0.319178	+	0.947695i	$0.396593\pi$
$422$		0			0
$423$	0.625559	+	0.815244i	0.0304157	+	0.0396385i
$424$		0			0
$425$	16.1461	+	42.7238i	0.783200	+	2.07241i
$426$		0			0
$427$	−2.91067	−	6.16479i	−0.140857	−	0.298335i
$428$		0			0
$429$	7.27877	−	27.1647i	0.351422	−	1.31153i
$430$		0			0
$431$	1.98710	+	30.3173i	0.0957152	+	1.46033i	0.727990	+	0.685588i	$0.240455\pi$
$431$	1.98710	+	30.3173i	0.0957152	+	1.46033i	−0.632275	+	0.774744i	$0.717879\pi$
$432$		0			0
$433$	−1.17534	−	2.83752i	−0.0564832	−	0.136362i	0.893119	−	0.449821i	$-0.148512\pi$
$433$	−1.17534	−	2.83752i	−0.0564832	−	0.136362i	−0.949602	+	0.313459i	$0.898512\pi$
$434$		0			0
$435$	1.61626	−	8.12549i	0.0774938	−	0.389587i
$436$		0			0
$437$	14.8457	−	43.7340i	0.710166	−	2.09208i
$438$		0			0
$439$	−0.500158	+	7.63093i	−0.0238712	+	0.364205i	0.969166	+	0.246407i	$0.0792500\pi$
$439$	−0.500158	+	7.63093i	−0.0238712	+	0.364205i	−0.993038	+	0.117797i	$0.962417\pi$
$440$		0			0
$441$	5.09941	−	11.2146i	0.242829	−	0.534027i
$442$		0			0
$443$	3.66638	+	6.35035i	0.174195	+	0.301714i	0.939882	−	0.341498i	$-0.110934\pi$
$443$	3.66638	+	6.35035i	0.174195	+	0.301714i	−0.765687	+	0.643213i	$0.777601\pi$
$444$		0			0
$445$	−59.5281	+	29.3560i	−2.82190	+	1.39161i
$446$		0			0
$447$	1.51216	+	7.60215i	0.0715228	+	0.359569i
$448$		0			0
$449$	−17.8855	−	3.55766i	−0.844071	−	0.167896i	−0.245931	−	0.969287i	$-0.579094\pi$
$449$	−17.8855	−	3.55766i	−0.844071	−	0.167896i	−0.598141	+	0.801391i	$0.704094\pi$
$450$		0			0
$451$	0.480472	−	3.64955i	0.0226245	−	0.171850i
$452$		0			0
$453$	12.1228	+	5.97831i	0.569579	+	0.280885i
$454$		0			0
$455$	65.4460	−	3.17111i	3.06815	−	0.148664i
$456$		0			0
$457$	4.32588	+	32.8583i	0.202356	+	1.53705i	0.727544	+	0.686061i	$0.240662\pi$
$457$	4.32588	+	32.8583i	0.202356	+	1.53705i	−0.525188	+	0.850987i	$0.676005\pi$
$458$		0			0
$459$	20.9052	−	6.37240i	0.975771	−	0.297438i
$460$		0			0
$461$	19.8738	+	8.23201i	0.925617	+	0.383403i	0.794014	−	0.607900i	$-0.207988\pi$
$461$	19.8738	+	8.23201i	0.925617	+	0.383403i	0.131603	+	0.991303i	$0.457988\pi$
$462$		0			0
$463$	24.6795	+	24.6795i	1.14695	+	1.14695i	0.987149	+	0.159805i	$0.0510864\pi$
$463$	24.6795	+	24.6795i	1.14695	+	1.14695i	0.159805	+	0.987149i	$0.448914\pi$
$464$		0			0
$465$	−11.3069	+	0.741093i	−0.524345	+	0.0343674i
$466$		0			0
$467$	4.53209	−	5.90634i	0.209720	−	0.273313i	−0.676635	−	0.736319i	$-0.736562\pi$
$467$	4.53209	−	5.90634i	0.209720	−	0.273313i	0.886355	+	0.463006i	$0.153229\pi$
$468$		0			0
$469$	21.2294	+	9.22023i	0.980283	+	0.425750i
$470$		0			0
$471$	−15.3210	+	13.4362i	−0.705956	+	0.619106i
$472$		0			0
$473$	3.16134	+	6.41055i	0.145358	+	0.294758i
$474$		0			0
$475$	70.1780			3.21999
$476$		0			0
$477$	−5.69475			−0.260745
$478$		0			0
$479$	−1.93497	−	3.92374i	−0.0884111	−	0.179280i	0.848176	−	0.529714i	$-0.177701\pi$
$479$	−1.93497	−	3.92374i	−0.0884111	−	0.179280i	−0.936587	+	0.350434i	$0.886034\pi$
$480$		0			0
$481$	26.9281	−	23.6153i	1.22782	−	1.07677i
$482$		0			0
$483$	2.44040	+	21.3396i	0.111042	+	0.970984i
$484$		0			0
$485$	7.78333	−	10.1434i	0.353423	−	0.460589i
$486$		0			0
$487$	−20.0891	+	1.31671i	−0.910322	+	0.0596657i	−0.513364	−	0.858171i	$-0.671601\pi$
$487$	−20.0891	+	1.31671i	−0.910322	+	0.0596657i	−0.396958	+	0.917837i	$0.629934\pi$
$488$		0			0
$489$	−0.339321	−	0.339321i	−0.0153446	−	0.0153446i
$490$		0			0
$491$	−17.2814	−	7.15819i	−0.779899	−	0.323045i	−0.0430241	−	0.999074i	$-0.513699\pi$
$491$	−17.2814	−	7.15819i	−0.779899	−	0.323045i	−0.736875	+	0.676029i	$0.763699\pi$
$492$		0			0
$493$	4.86120	+	5.90708i	0.218937	+	0.266042i
$494$		0			0
$495$	−3.76620	−	28.6071i	−0.169278	−	1.28579i
$496$		0			0
$497$	−10.0170	−	5.15378i	−0.449324	−	0.231179i
$498$		0			0
$499$	5.54186	+	2.73295i	0.248088	+	0.122343i	0.562082	−	0.827082i	$-0.310001\pi$
$499$	5.54186	+	2.73295i	0.248088	+	0.122343i	−0.313994	+	0.949425i	$0.601667\pi$
$500$		0			0
$501$	1.78127	−	13.5301i	0.0795813	−	0.604480i
$502$		0			0
$503$	−30.4712	−	6.06110i	−1.35864	−	0.270251i	−0.538605	−	0.842559i	$-0.681048\pi$
$503$	−30.4712	−	6.06110i	−1.35864	−	0.270251i	−0.820039	+	0.572308i	$0.806048\pi$
$504$		0			0
$505$	8.99752	+	45.2336i	0.400384	+	2.01287i
$506$		0			0
$507$	25.1164	−	12.3860i	1.11546	−	0.550084i
$508$		0			0
$509$	−15.5279	−	26.8951i	−0.688262	−	1.19210i	−0.972400	−	0.233321i	$-0.925041\pi$
$509$	−15.5279	−	26.8951i	−0.688262	−	1.19210i	0.284138	−	0.958784i	$-0.408293\pi$
$510$		0			0
$511$	−5.50761	−	1.19340i	−0.243642	−	0.0527929i
$512$		0			0
$513$	2.19628	−	33.5088i	0.0969683	−	1.47945i
$514$		0			0
$515$	13.9518	−	41.1007i	0.614790	−	1.81111i
$516$		0			0
$517$	0.465762	−	2.34154i	0.0204842	−	0.102981i
$518$		0			0
$519$	4.05075	+	9.77939i	0.177808	+	0.429267i
$520$		0			0
$521$	−1.26431	−	19.2896i	−0.0553903	−	0.845093i	−0.931674	−	0.363297i	$-0.881651\pi$
$521$	−1.26431	−	19.2896i	−0.0553903	−	0.845093i	0.876283	−	0.481796i	$-0.160015\pi$
$522$		0			0
$523$	7.15038	−	26.6856i	0.312664	−	1.16688i	−0.613480	−	0.789710i	$-0.710231\pi$
$523$	7.15038	−	26.6856i	0.312664	−	1.16688i	0.926144	−	0.377169i	$-0.123103\pi$
$524$		0			0
$525$	−29.5126	+	13.9342i	−1.28804	+	0.608138i
$526$		0			0
$527$	6.08314	−	8.51329i	0.264986	−	0.370845i
$528$		0			0
$529$	18.3517	+	23.9164i	0.797899	+	1.03984i
$530$		0			0
$531$	−5.75847	+	5.75847i	−0.249896	+	0.249896i
$532$		0			0
$533$	4.62328	−	3.08918i	0.200256	−	0.133807i
$534$		0			0
$535$	−28.3084	−	3.72687i	−1.22388	−	0.161127i
$536$		0			0
$537$	−4.83758	−	14.2510i	−0.208757	−	0.614978i
$538$		0			0
$539$	−27.4007	+	8.27176i	−1.18023	+	0.356290i
$540$		0			0
$541$	−24.8114	−	1.62622i	−1.06672	−	0.0699168i	−0.478085	−	0.878313i	$-0.658669\pi$
$541$	−24.8114	−	1.62622i	−1.06672	−	0.0699168i	−0.588638	+	0.808397i	$0.700336\pi$
$542$		0			0
$543$	20.2749	+	11.7057i	0.870081	+	0.502341i
$544$		0			0
$545$			52.9894i			2.26981i
$546$		0			0
$547$	3.85024	+	2.57265i	0.164624	+	0.109999i	0.635153	−	0.772386i	$-0.280937\pi$
$547$	3.85024	+	2.57265i	0.164624	+	0.109999i	−0.470529	+	0.882385i	$0.655937\pi$
$548$		0			0
$549$	−4.29420	−	1.45768i	−0.183272	−	0.0622124i
$550$		0			0
$551$	11.1309	−	3.77843i	0.474192	−	0.160966i
$552$		0			0
$553$	1.00502	−	2.80290i	0.0427376	−	0.119191i
$554$		0			0
$555$	−11.4520	+	23.2223i	−0.486109	+	0.985731i
$556$		0			0
$557$	−4.66092	−	17.3948i	−0.197489	−	0.737040i	−0.991608	−	0.129278i	$-0.958734\pi$
$557$	−4.66092	−	17.3948i	−0.197489	−	0.737040i	0.794119	−	0.607762i	$-0.207933\pi$
$558$		0			0
$559$	−4.13179	+	9.97501i	−0.174756	+	0.421898i
$560$		0			0
$561$	−15.9561	−	9.89223i	−0.673665	−	0.417650i
$562$		0			0
$563$	−30.2246	+	23.1922i	−1.27382	+	0.977434i	−0.273939	+	0.961747i	$0.588327\pi$
$563$	−30.2246	+	23.1922i	−1.27382	+	0.977434i	−0.999877	+	0.0156866i	$0.995007\pi$
$564$		0			0
$565$	−23.7748	−	6.37045i	−1.00022	−	0.268007i
$566$		0			0
$567$	0.604605	+	1.53299i	0.0253910	+	0.0643797i
$568$		0			0
$569$	−16.5298	−	12.6838i	−0.692967	−	0.531732i	0.201153	−	0.979560i	$-0.435531\pi$
$569$	−16.5298	−	12.6838i	−0.692967	−	0.531732i	−0.894120	+	0.447828i	$0.852198\pi$
$570$		0			0
$571$	−22.1537	−	19.4283i	−0.927105	−	0.813050i	0.0555566	−	0.998456i	$-0.482307\pi$
$571$	−22.1537	−	19.4283i	−0.927105	−	0.813050i	−0.982662	+	0.185406i	$0.940640\pi$
$572$		0			0
$573$	20.9417	−	4.16556i	0.874852	−	0.174019i
$574$		0			0
$575$	−44.8651	+	67.1454i	−1.87101	+	2.80016i
$576$		0			0
$577$	−10.4542	+	18.1072i	−0.435214	+	0.753813i	−0.997313	−	0.0732568i	$-0.976661\pi$
$577$	−10.4542	+	18.1072i	−0.435214	+	0.753813i	0.562099	+	0.827070i	$0.309994\pi$
$578$		0			0
$579$	−0.778743	+	0.449607i	−0.0323634	+	0.0186850i
$580$		0			0
$581$	3.07127	−	10.7278i	0.127418	−	0.445063i
$582$		0			0
$583$	8.72359	+	9.94735i	0.361294	+	0.411977i
$584$		0			0
$585$	28.7377	−	32.7690i	1.18816	−	1.35483i
$586$		0			0
$587$	−5.40833	+	2.24020i	−0.223225	+	0.0924630i	−0.491493	−	0.870881i	$-0.663549\pi$
$587$	−5.40833	+	2.24020i	−0.223225	+	0.0924630i	0.268268	+	0.963344i	$0.413549\pi$
$588$		0			0
$589$	−8.93201	−	13.3677i	−0.368037	−	0.550807i
$590$		0			0
$591$	2.05261	−	0.549996i	0.0844332	−	0.0226238i
$592$		0			0
$593$	32.1348	−	4.23063i	1.31962	−	0.173731i	0.562385	−	0.826875i	$-0.309884\pi$
$593$	32.1348	−	4.23063i	1.31962	−	0.173731i	0.757234	+	0.653144i	$0.226550\pi$
$594$		0			0
$595$	10.5991	−	42.4365i	0.434522	−	1.73973i
$596$		0			0
$597$	14.6066	−	1.92300i	0.597810	−	0.0787031i
$598$		0			0
$599$	17.6953	−	4.74145i	0.723011	−	0.193730i	0.121496	−	0.992592i	$-0.461231\pi$
$599$	17.6953	−	4.74145i	0.723011	−	0.193730i	0.601515	+	0.798862i	$0.294564\pi$
$600$		0			0
$601$	2.67407	+	4.00202i	0.109077	+	0.163246i	0.881992	−	0.471264i	$-0.156202\pi$
$601$	2.67407	+	4.00202i	0.109077	+	0.163246i	−0.772915	+	0.634510i	$0.781202\pi$
$602$		0			0
$603$	14.2240	−	5.89179i	0.579248	−	0.239932i
$604$		0			0
$605$	−15.1191	+	17.2400i	−0.614679	+	0.700907i
$606$		0			0
$607$	3.14873	+	3.59044i	0.127803	+	0.145731i	0.812202	−	0.583376i	$-0.198269\pi$
$607$	3.14873	+	3.59044i	0.127803	+	0.145731i	−0.684399	+	0.729108i	$0.739935\pi$
$608$		0			0
$609$	−3.93075	+	3.79907i	−0.159282	+	0.153946i
$610$		0			0
$611$	3.12315	−	1.80315i	0.126349	−	0.0729476i
$612$		0			0
$613$	−15.6095	+	27.0364i	−0.630461	+	1.09199i	0.356997	+	0.934106i	$0.383801\pi$
$613$	−15.6095	+	27.0364i	−0.630461	+	1.09199i	−0.987458	+	0.157884i	$0.949533\pi$
$614$		0			0
$615$	−2.23325	+	3.34229i	−0.0900531	+	0.134774i
$616$		0			0
$617$	−39.3791	+	7.83299i	−1.58534	+	0.315344i	−0.907561	−	0.419920i	$-0.862058\pi$
$617$	−39.3791	+	7.83299i	−1.58534	+	0.315344i	−0.677781	+	0.735264i	$0.737058\pi$
$618$		0			0
$619$	−18.2060	−	15.9662i	−0.731761	−	0.641737i	0.210123	−	0.977675i	$-0.432613\pi$
$619$	−18.2060	−	15.9662i	−0.731761	−	0.641737i	−0.941884	+	0.335938i	$0.890947\pi$
$620$		0			0
$621$	30.6567	+	23.5237i	1.23021	+	0.943974i
$622$		0			0
$623$	43.3175	+	6.45527i	1.73548	+	0.258625i
$624$		0			0
$625$	−40.8785	−	10.9534i	−1.63514	−	0.438135i
$626$		0			0
$627$	−22.8854	+	17.5606i	−0.913955	+	0.701302i
$628$		0			0
$629$	−9.89701	−	21.7649i	−0.394620	−	0.867822i
$630$		0			0
$631$	5.99587	−	14.4753i	0.238692	−	0.576253i	−0.758456	−	0.651724i	$-0.774046\pi$
$631$	5.99587	−	14.4753i	0.238692	−	0.576253i	0.997148	+	0.0754711i	$0.0240461\pi$
$632$		0			0
$633$	−0.278592	−	1.03972i	−0.0110730	−	0.0413251i
$634$		0			0
$635$	21.6693	−	43.9411i	0.859922	−	1.74375i
$636$		0			0
$637$	−36.6845	−	22.8802i	−1.45349	−	0.906547i
$638$		0			0
$639$	−7.09575	+	2.40868i	−0.280704	+	0.0952860i
$640$		0			0
$641$	26.5676	+	9.01849i	1.04936	+	0.356209i	0.792265	−	0.610178i	$-0.208902\pi$
$641$	26.5676	+	9.01849i	1.04936	+	0.356209i	0.257093	+	0.966387i	$0.417235\pi$
$642$		0			0
$643$	22.7141	+	15.1771i	0.895756	+	0.598525i	0.915959	−	0.401271i	$-0.131431\pi$
$643$	22.7141	+	15.1771i	0.895756	+	0.598525i	−0.0202037	+	0.999796i	$0.506431\pi$
$644$		0			0
$645$		−	7.80534i		−	0.307335i
$646$		0			0
$647$	39.0581	+	22.5502i	1.53553	+	0.886539i	0.999092	+	0.0425995i	$0.0135639\pi$
$647$	39.0581	+	22.5502i	1.53553	+	0.886539i	0.536438	+	0.843940i	$0.319769\pi$
$648$		0			0
$649$	18.8798	+	1.23745i	0.741098	+	0.0485742i
$650$		0			0
$651$	6.41049	+	3.84815i	0.251247	+	0.150821i
$652$		0			0
$653$	2.86964	+	8.45370i	0.112298	+	0.330819i	0.988520	−	0.151088i	$-0.0482777\pi$
$653$	2.86964	+	8.45370i	0.112298	+	0.330819i	−0.876222	+	0.481907i	$0.839944\pi$
$654$		0			0
$655$	−42.2605	−	5.56370i	−1.65126	−	0.217392i
$656$		0			0
$657$	−3.11687	+	2.08263i	−0.121601	+	0.0812511i
$658$		0			0
$659$	−17.7751	+	17.7751i	−0.692419	+	0.692419i	−0.962764	−	0.270345i	$-0.912862\pi$
$659$	−17.7751	+	17.7751i	−0.692419	+	0.692419i	0.270345	+	0.962764i	$0.412862\pi$
$660$		0			0
$661$	−5.28440	−	6.88676i	−0.205539	−	0.267864i	0.679197	−	0.733956i	$-0.262328\pi$
$661$	−5.28440	−	6.88676i	−0.205539	−	0.267864i	−0.884736	+	0.466092i	$0.845662\pi$
$662$		0			0
$663$	−4.65729	−	27.9735i	−0.180874	−	1.08640i
$664$		0			0
$665$	−55.2375	−	38.2853i	−2.14202	−	1.48464i
$666$		0			0
$667$	−3.50088	+	13.0655i	−0.135555	+	0.505896i
$668$		0			0
$669$	1.68333	+	25.6827i	0.0650814	+	0.992950i
$670$		0			0
$671$	4.03191	+	9.73389i	0.155650	+	0.375773i
$672$		0			0
$673$	1.51940	−	7.63855i	0.0585686	−	0.294444i	−0.940389	−	0.340102i	$-0.889538\pi$
$673$	1.51940	−	7.63855i	0.0585686	−	0.294444i	0.998957	+	0.0456577i	$0.0145384\pi$
$674$		0			0
$675$	−18.8737	+	55.6002i	−0.726450	+	2.14005i
$676$		0			0
$677$	−0.208069	+	3.17453i	−0.00799676	+	0.122007i	−0.999991	−	0.00427732i	$-0.998638\pi$
$677$	−0.208069	+	3.17453i	−0.00799676	+	0.122007i	0.991994	+	0.126284i	$0.0403052\pi$
$678$		0			0
$679$	−8.03377	+	2.57535i	−0.308308	+	0.0988327i
$680$		0			0
$681$	6.51107	+	11.2775i	0.249505	+	0.432155i
$682$		0			0
$683$	29.5078	−	14.5516i	1.12908	−	0.556803i	0.220868	−	0.975304i	$-0.429111\pi$
$683$	29.5078	−	14.5516i	1.12908	−	0.556803i	0.908216	+	0.418501i	$0.137444\pi$
$684$		0			0
$685$	12.2675	+	61.6727i	0.468716	+	2.35639i
$686$		0			0
$687$	0.263388	+	0.0523911i	0.0100489	+	0.00199884i
$688$		0			0
$689$	−2.60863	+	19.8145i	−0.0993810	+	0.754874i
$690$		0			0
$691$	−31.5278	−	15.5478i	−1.19937	−	0.591466i	−0.270809	−	0.962633i	$-0.587291\pi$
$691$	−31.5278	−	15.5478i	−1.19937	−	0.591466i	−0.928566	+	0.371167i	$0.878958\pi$
$692$		0			0
$693$	−8.71042	+	16.9298i	−0.330882	+	0.643109i
$694$		0			0
$695$	−6.76591	−	51.3922i	−0.256645	−	1.94942i
$696$		0			0
$697$	−1.08230	−	3.55057i	−0.0409949	−	0.134488i
$698$		0			0
$699$	16.1583	+	6.69298i	0.611162	+	0.253152i
$700$		0			0
$701$	29.4598	+	29.4598i	1.11268	+	1.11268i	0.992787	+	0.119893i	$0.0382551\pi$
$701$	29.4598	+	29.4598i	1.11268	+	1.11268i	0.119893	+	0.992787i	$0.461745\pi$
$702$		0			0
$703$	−36.6589	+	2.40275i	−1.38262	+	0.0906215i
$704$		0			0
$705$	−1.58709	+	2.06834i	−0.0597734	+	0.0778983i
$706$		0			0
$707$	12.1230	−	27.9130i	0.455932	−	1.04978i
$708$		0			0
$709$	−5.76412	+	5.05500i	−0.216476	+	0.189844i	−0.760715	−	0.649086i	$-0.775152\pi$
$709$	−5.76412	+	5.05500i	−0.216476	+	0.189844i	0.544239	+	0.838930i	$0.316818\pi$
$710$		0			0
$711$	−0.876039	−	1.77643i	−0.0328540	−	0.0666214i
$712$		0			0
$713$	18.5003			0.692843
$714$		0			0
$715$	−101.262			−3.78698
$716$		0			0
$717$	5.98742	+	12.1413i	0.223604	+	0.453425i
$718$		0			0
$719$	0.424879	−	0.372609i	0.0158453	−	0.0138960i	−0.651387	−	0.758746i	$-0.725812\pi$
$719$	0.424879	−	0.372609i	0.0158453	−	0.0138960i	0.667232	+	0.744850i	$0.267479\pi$
$720$		0			0
$721$	−23.0153	+	17.0454i	−0.857136	+	0.634804i
$722$		0			0
$723$	−4.44743	+	5.79601i	−0.165402	+	0.215556i
$724$		0			0
$725$	−20.5093	+	1.34425i	−0.761695	+	0.0499241i
$726$		0			0
$727$	−11.1346	−	11.1346i	−0.412958	−	0.412958i	0.469810	−	0.882768i	$-0.344323\pi$
$727$	−11.1346	−	11.1346i	−0.412958	−	0.412958i	−0.882768	+	0.469810i	$0.844323\pi$
$728$		0			0
$729$	17.3727	+	7.19602i	0.643435	+	0.266519i
$730$		0			0
$731$	5.57767	+	4.56487i	0.206298	+	0.168838i
$732$		0			0
$733$	−1.49360	−	11.3450i	−0.0551674	−	0.419038i	−0.996637	−	0.0819408i	$-0.973888\pi$
$733$	−1.49360	−	11.3450i	−0.0551674	−	0.419038i	0.941470	−	0.337097i	$-0.109445\pi$
$734$		0			0
$735$	30.8313	+	5.13280i	1.13723	+	0.189326i
$736$		0			0
$737$	−32.0808	−	15.8205i	−1.18171	−	0.582756i
$738$		0			0
$739$	−5.93531	+	45.0832i	−0.218334	+	1.65841i	0.434323	+	0.900757i	$0.356988\pi$
$739$	−5.93531	+	45.0832i	−0.218334	+	1.65841i	−0.652657	+	0.757654i	$0.726346\pi$
$740$		0			0
$741$	−42.7365	−	8.50082i	−1.56997	−	0.312285i
$742$		0			0
$743$	−4.72756	−	23.7670i	−0.173437	−	0.871928i	−0.965283	−	0.261207i	$-0.915880\pi$
$743$	−4.72756	−	23.7670i	−0.173437	−	0.871928i	0.791846	−	0.610721i	$-0.209120\pi$
$744$		0			0
$745$	25.0309	−	12.3439i	0.917063	−	0.452245i
$746$		0			0
$747$	−3.71135	−	6.42825i	−0.135791	−	0.235197i
$748$		0			0
$749$	13.9513	+	12.6618i	0.509769	+	0.462651i
$750$		0			0
$751$	0.166728	−	2.54378i	0.00608400	−	0.0928239i	−0.993737	−	0.111744i	$-0.964356\pi$
$751$	0.166728	−	2.54378i	0.00608400	−	0.0928239i	0.999821	+	0.0189204i	$0.00602291\pi$
$752$		0			0
$753$	−2.46917	+	7.27394i	−0.0899816	+	0.265077i
$754$		0			0
$755$	9.49494	−	47.7343i	0.345556	−	1.73723i
$756$		0			0
$757$	−13.3125	−	32.1393i	−0.483853	−	1.16812i	−0.957765	−	0.287552i	$-0.907159\pi$
$757$	−13.3125	−	32.1393i	−0.483853	−	1.16812i	0.473912	−	0.880572i	$-0.342841\pi$
$758$		0			0
$759$	−2.17100	−	33.1230i	−0.0788022	−	1.20229i
$760$		0			0
$761$	4.67679	−	17.4540i	0.169534	−	0.632708i	−0.827885	−	0.560898i	$-0.810456\pi$
$761$	4.67679	−	17.4540i	0.169534	−	0.632708i	0.997418	−	0.0718098i	$-0.0228775\pi$
$762$		0			0
$763$	19.9178	−	28.7371i	0.721071	−	1.04035i
$764$		0			0
$765$	−15.3978	−	24.6872i	−0.556709	−	0.892569i
$766$		0			0
$767$	17.3984	+	22.6740i	0.628220	+	0.818712i
$768$		0			0
$769$	−4.81003	+	4.81003i	−0.173454	+	0.173454i	−0.788495	−	0.615041i	$-0.789139\pi$
$769$	−4.81003	+	4.81003i	−0.173454	+	0.173454i	0.615041	+	0.788495i	$0.289139\pi$
$770$		0			0
$771$	−25.5995	+	17.1051i	−0.921944	+	0.616023i
$772$		0			0
$773$	16.1121	+	2.12120i	0.579511	+	0.0762941i	0.414583	−	0.910012i	$-0.363927\pi$
$773$	16.1121	+	2.12120i	0.579511	+	0.0762941i	0.164928	+	0.986306i	$0.447261\pi$
$774$		0			0
$775$	9.03605	+	26.6193i	0.324584	+	0.956195i
$776$		0			0
$777$	14.9394	−	8.28927i	0.535950	−	0.297376i
$778$		0			0
$779$	−5.69119	−	0.373020i	−0.203908	−	0.0133648i
$780$		0			0
$781$	15.0771	+	8.70477i	0.539501	+	0.311481i
$782$		0			0
$783$			9.83489i			0.351470i
$784$		0			0
$785$	61.0088	+	40.7648i	2.17750	+	1.45496i
$786$		0			0
$787$	14.1339	+	4.79781i	0.503819	+	0.171024i	0.561766	−	0.827296i	$-0.310122\pi$
$787$	14.1339	+	4.79781i	0.503819	+	0.171024i	−0.0579470	+	0.998320i	$0.518455\pi$
$788$		0			0
$789$	−5.63473	+	1.91273i	−0.200602	+	0.0680951i
$790$		0			0
$791$	10.4990	+	12.3913i	0.373301	+	0.440586i
$792$		0			0
$793$	−7.03899	+	14.2737i	−0.249962	+	0.506872i
$794$		0			0
$795$	−3.73943	−	13.9558i	−0.132624	−	0.494959i
$796$		0			0
$797$	4.21387	−	10.1732i	0.149263	−	0.360353i	−0.831509	−	0.555512i	$-0.812522\pi$
$797$	4.21387	−	10.1732i	0.149263	−	0.360353i	0.980772	+	0.195159i	$0.0625223\pi$
$798$		0			0
$799$	−0.549834	−	2.34378i	−0.0194517	−	0.0829170i
$800$		0			0
$801$	23.1125	−	17.7348i	0.816639	−	0.626629i
$802$		0			0
$803$	8.41247	+	2.25412i	0.296870	+	0.0795460i
$804$		0			0
$805$	71.9444	−	28.3745i	2.53571	−	1.00007i
$806$		0			0
$807$	−11.5252	−	8.84361i	−0.405707	−	0.311310i
$808$		0			0
$809$	−22.4890	−	19.7223i	−0.790671	−	0.693400i	0.165499	−	0.986210i	$-0.447076\pi$
$809$	−22.4890	−	19.7223i	−0.790671	−	0.693400i	−0.956171	+	0.292810i	$0.905410\pi$
$810$		0			0
$811$	5.23108	−	1.04053i	0.183688	−	0.0365378i	−0.102389	−	0.994744i	$-0.532649\pi$
$811$	5.23108	−	1.04053i	0.183688	−	0.0365378i	0.286077	+	0.958207i	$0.407649\pi$
$812$		0			0
$813$	0.622956	−	0.932320i	0.0218480	−	0.0326979i
$814$		0			0
$815$	−0.863932	+	1.49637i	−0.0302622	+	0.0524157i
$816$		0			0
$817$	9.59089	−	5.53730i	0.335543	−	0.193726i
$818$		0			0
$819$	−27.9023	+	6.96925i	−0.974984	+	0.243525i
$820$		0			0
$821$	7.40478	+	8.44354i	0.258429	+	0.294682i	0.866475	−	0.499220i	$-0.166380\pi$
$821$	7.40478	+	8.44354i	0.258429	+	0.294682i	−0.608047	+	0.793901i	$0.708047\pi$
$822$		0			0
$823$	−19.7393	+	22.5083i	−0.688067	+	0.784590i	−0.985413	−	0.170180i	$-0.945565\pi$
$823$	−19.7393	+	22.5083i	−0.688067	+	0.784590i	0.297346	+	0.954770i	$0.403899\pi$
$824$		0			0
$825$	46.5989	−	19.3019i	1.62237	−	0.672006i
$826$		0			0
$827$	6.20691	+	9.28930i	0.215836	+	0.323021i	0.923550	−	0.383478i	$-0.125274\pi$
$827$	6.20691	+	9.28930i	0.215836	+	0.323021i	−0.707715	+	0.706498i	$0.750274\pi$
$828$		0			0
$829$	−26.7318	+	7.16278i	−0.928435	+	0.248773i	−0.691187	−	0.722676i	$-0.742912\pi$
$829$	−26.7318	+	7.16278i	−0.928435	+	0.248773i	−0.237248	+	0.971449i	$0.576245\pi$
$830$		0			0
$831$	−33.3040	+	4.38455i	−1.15530	+	0.152098i
$832$		0			0
$833$	−21.6992	+	19.0301i	−0.751834	+	0.659353i
$834$		0			0
$835$	−48.7175	+	6.41378i	−1.68594	+	0.221958i
$836$		0			0
$837$	12.9931	−	3.48148i	0.449106	−	0.120338i
$838$		0			0
$839$	−26.8118	−	40.1267i	−0.925647	−	1.38533i	−0.922778	−	0.385333i	$-0.874087\pi$
$839$	−26.8118	−	40.1267i	−0.925647	−	1.38533i	−0.00286944	−	0.999996i	$-0.500913\pi$
$840$		0			0
$841$	23.6119	−	9.78038i	0.814204	−	0.337254i
$842$		0			0
$843$	−1.65247	+	1.88428i	−0.0569141	+	0.0648981i
$844$		0			0
$845$	−66.4851	−	75.8117i	−2.28716	−	2.60800i
$846$		0			0
$847$	14.6796	−	3.66657i	0.504396	−	0.125985i
$848$		0			0
$849$	−19.9952	+	11.5443i	−0.686235	+	0.396198i
$850$		0			0
$851$	21.1373	−	36.6109i	0.724577	−	1.25500i
$852$		0			0
$853$	1.01518	−	1.51932i	0.0347591	−	0.0520207i	−0.813683	−	0.581309i	$-0.802541\pi$
$853$	1.01518	−	1.51932i	0.0347591	−	0.0520207i	0.848442	+	0.529288i	$0.177541\pi$
$854$		0			0
$855$	−43.8473	+	8.72176i	−1.49954	+	0.298278i
$856$		0			0
$857$	18.2636	+	16.0167i	0.623871	+	0.547121i	0.911854	−	0.410515i	$-0.134651\pi$
$857$	18.2636	+	16.0167i	0.623871	+	0.547121i	−0.287982	+	0.957636i	$0.592984\pi$
$858$		0			0
$859$	27.5185	+	21.1157i	0.938921	+	0.720459i	0.960200	−	0.279314i	$-0.0901072\pi$
$859$	27.5185	+	21.1157i	0.938921	+	0.720459i	−0.0212790	+	0.999774i	$0.506774\pi$
$860$		0			0
$861$	2.46743	−	0.973144i	0.0840899	−	0.0331647i
$862$		0			0
$863$	−42.0315	−	11.2623i	−1.43077	−	0.383373i	−0.541478	−	0.840715i	$-0.682135\pi$
$863$	−42.0315	−	11.2623i	−1.43077	−	0.383373i	−0.889291	+	0.457341i	$0.848802\pi$
$864$		0			0
$865$	30.2376	−	23.2021i	1.02811	−	0.788895i
$866$		0			0
$867$	−18.7756	−	2.42023i	−0.637652	−	0.0821954i
$868$		0			0
$869$	−1.76102	+	4.25148i	−0.0597385	+	0.144222i
$870$		0			0
$871$	−13.9844	−	52.1906i	−0.473844	−	1.76841i
$872$		0			0
$873$	−2.48206	+	5.03312i	−0.0840051	+	0.170345i
$874$		0			0
$875$	41.6773	+	49.1894i	1.40895	+	1.66290i
$876$		0			0
$877$	−55.8544	+	18.9600i	−1.88607	+	0.640235i	−0.913910	+	0.405917i	$0.866952\pi$
$877$	−55.8544	+	18.9600i	−1.88607	+	0.640235i	−0.972160	+	0.234318i	$0.924714\pi$
$878$		0			0
$879$	−20.0848	−	6.81786i	−0.677442	−	0.229961i
$880$		0			0
$881$	13.0899	+	8.74641i	0.441011	+	0.294674i	0.756183	−	0.654361i	$-0.227062\pi$
$881$	13.0899	+	8.74641i	0.441011	+	0.294674i	−0.315172	+	0.949035i	$0.602062\pi$
$882$		0			0
$883$			38.3134i			1.28935i	0.764457	+	0.644675i	$0.223007\pi$
$883$			38.3134i			1.28935i	−0.764457	+	0.644675i	$0.776993\pi$
$884$		0			0
$885$	−17.8932	−	10.3306i	−0.601472	−	0.347260i
$886$		0			0
$887$	2.37297	+	0.155533i	0.0796766	+	0.00522228i	0.105189	−	0.994452i	$-0.466455\pi$
$887$	2.37297	+	0.155533i	0.0796766	+	0.00522228i	−0.0255127	+	0.999674i	$0.508122\pi$
$888$		0			0
$889$	−28.2683	+	15.6849i	−0.948089	+	0.526055i
$890$		0			0
$891$	−0.818629	−	2.41160i	−0.0274251	−	0.0807918i
$892$		0			0
$893$	−3.66742	−	0.482825i	−0.122725	−	0.0161571i
$894$		0			0
$895$	−45.0566	+	30.1059i	−1.50608	+	1.00633i
$896$		0			0
$897$	35.4551	−	35.4551i	1.18381	−	1.18381i
$898$		0			0
$899$	2.86640	+	3.73557i	0.0955999	+	0.124588i
$900$		0			0
$901$	12.1597	+	5.48969i	0.405098	+	0.182888i
$902$		0			0
$903$	−2.93389	+	4.23298i	−0.0976337	+	0.140865i
$904$		0			0
$905$	21.8177	−	81.4248i	0.725245	−	2.70665i
$906$		0			0
$907$	3.29866	+	50.3279i	0.109530	+	1.67111i	0.600266	+	0.799801i	$0.295061\pi$
$907$	3.29866	+	50.3279i	0.109530	+	1.67111i	−0.490735	+	0.871309i	$0.663272\pi$
$908$		0			0
$909$	−7.74667	−	18.7021i	−0.256941	−	0.620310i
$910$		0			0
$911$	10.7237	−	53.9118i	0.355293	−	1.78618i	−0.227731	−	0.973724i	$-0.573131\pi$
$911$	10.7237	−	53.9118i	0.355293	−	1.78618i	0.583024	−	0.812455i	$-0.301869\pi$
$912$		0			0
$913$	−5.54330	+	16.3300i	−0.183456	+	0.540445i
$914$		0			0
$915$	0.752483	−	11.4807i	0.0248763	−	0.379539i
$916$		0			0
$917$	20.8273	+	18.9023i	0.687779	+	0.624208i
$918$		0			0
$919$	19.7716	+	34.2453i	0.652204	+	1.12965i	0.982587	+	0.185803i	$0.0594886\pi$
$919$	19.7716	+	34.2453i	0.652204	+	1.12965i	−0.330383	+	0.943847i	$0.607178\pi$
$920$		0			0
$921$	−14.2955	+	7.04975i	−0.471052	+	0.232297i
$922$		0			0
$923$	5.13046	+	25.7926i	0.168871	+	0.848973i
$924$		0			0
$925$	63.0019	+	12.5318i	2.07149	+	0.412045i
$926$		0			0
$927$	−2.48667	+	18.8881i	−0.0816728	+	0.620367i
$928$		0			0
$929$	7.50558	+	3.70134i	0.246250	+	0.121437i	0.561226	−	0.827663i	$-0.310330\pi$
$929$	7.50558	+	3.70134i	0.246250	+	0.121437i	−0.314976	+	0.949100i	$0.601996\pi$
$930$		0			0
$931$	15.5655	+	41.5256i	0.510138	+	1.36094i
$932$		0			0
$933$	−1.37881	−	10.4731i	−0.0451403	−	0.342875i
$934$		0			0
$935$	−19.5352	+	64.7138i	−0.638870	+	2.11637i
$936$		0			0
$937$	33.3849	+	13.8285i	1.09064	+	0.451757i	0.854229	−	0.519897i	$-0.174030\pi$
$937$	33.3849	+	13.8285i	1.09064	+	0.451757i	0.236408	+	0.971654i	$0.424030\pi$
$938$		0			0
$939$	24.8061	+	24.8061i	0.809515	+	0.809515i
$940$		0			0
$941$	25.4650	−	1.66907i	0.830136	−	0.0544100i	0.355592	−	0.934641i	$-0.384279\pi$
$941$	25.4650	−	1.66907i	0.830136	−	0.0544100i	0.474545	+	0.880231i	$0.342613\pi$
$942$		0			0
$943$	3.99530	−	5.20678i	0.130105	−	0.169556i
$944$		0			0
$945$	45.1880	−	33.4667i	1.46997	−	1.08867i
$946$		0			0
$947$	13.8346	−	12.1326i	0.449564	−	0.394257i	−0.404406	−	0.914580i	$-0.632522\pi$
$947$	13.8346	−	12.1326i	0.449564	−	0.394257i	0.853970	+	0.520323i	$0.174188\pi$
$948$		0			0
$949$	5.81861	+	11.7990i	0.188880	+	0.383011i
$950$		0			0
$951$	6.66933			0.216268
$952$		0			0
$953$	−1.39178			−0.0450843			−0.0225421	−	0.999746i	$-0.507176\pi$
$953$	−1.39178			−0.0450843			−0.0225421	+	0.999746i	$0.507176\pi$
$954$		0			0
$955$	−34.0038	−	68.9529i	−1.10034	−	2.23126i
$956$		0			0
$957$	6.35180	−	5.57038i	0.205324	−	0.180065i
$958$		0			0
$959$	16.5288	−	38.0573i	0.533743	−	1.22893i
$960$		0			0
$961$	−14.9512	+	19.4847i	−0.482295	+	0.628540i
$962$		0			0
$963$	12.5056	−	0.819660i	0.402987	−	0.0264132i
$964$		0			0
$965$	2.28946	+	2.28946i	0.0737002	+	0.0737002i
$966$		0			0
$967$	25.3126	+	10.4848i	0.813998	+	0.337169i	0.750548	−	0.660816i	$-0.229790\pi$
$967$	25.3126	+	10.4848i	0.813998	+	0.337169i	0.0634501	+	0.997985i	$0.479790\pi$
$968$		0			0
$969$	−13.6773	+	25.6718i	−0.439378	+	0.824698i
$970$		0			0
$971$	5.13485	+	39.0030i	0.164785	+	1.25167i	0.851350	+	0.524599i	$0.175785\pi$
$971$	5.13485	+	39.0030i	0.164785	+	1.25167i	−0.686565	+	0.727069i	$0.740882\pi$
$972$		0			0
$973$	−15.6481	+	30.4141i	−0.501656	+	0.975030i
$974$		0			0
$975$	68.3321	+	33.6977i	2.18838	+	1.07919i
$976$		0			0
$977$	1.82533	−	13.8648i	0.0583975	−	0.443573i	−0.937121	−	0.349005i	$-0.886520\pi$
$977$	1.82533	−	13.8648i	0.0583975	−	0.443573i	0.995518	−	0.0945683i	$-0.0301471\pi$
$978$		0			0
$979$	−66.3836	−	13.2045i	−2.12163	−	0.422018i
$980$		0			0
$981$	−4.53746	−	22.8114i	−0.144870	−	0.728311i
$982$		0			0
$983$	−16.0452	+	7.91264i	−0.511764	+	0.252374i	−0.679788	−	0.733409i	$-0.737928\pi$
$983$	−16.0452	+	7.91264i	−0.511764	+	0.252374i	0.168024	+	0.985783i	$0.446261\pi$
$984$		0			0
$985$	−3.82576	−	6.62640i	−0.121899	−	0.211135i
$986$		0			0
$987$	1.63816	−	0.525137i	0.0521433	−	0.0167153i
$988$		0			0
$989$	−0.833481	+	12.7165i	−0.0265031	+	0.404360i
$990$		0			0
$991$	−1.91706	+	5.64748i	−0.0608975	+	0.179398i	−0.973121	−	0.230295i	$-0.926031\pi$
$991$	−1.91706	+	5.64748i	−0.0608975	+	0.179398i	0.912223	+	0.409693i	$0.134364\pi$
$992$		0			0
$993$	−3.67322	+	18.4665i	−0.116566	+	0.586017i
$994$		0			0
$995$	−20.3004	−	49.0096i	−0.643567	−	1.55371i
$996$		0			0
$997$	−3.87719	−	59.1545i	−0.122792	−	1.87344i	−0.405311	−	0.914179i	$-0.632837\pi$
$997$	−3.87719	−	59.1545i	−0.122792	−	1.87344i	0.282519	−	0.959262i	$-0.408830\pi$
$998$		0			0
$999$	7.95544	−	29.6901i	0.251699	−	0.939353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.129.5	yes	192
7.5	odd	6	inner	476.2.bl.a.61.5	✓	192
17.12	odd	16	inner	476.2.bl.a.437.5	yes	192
119.12	even	48	inner	476.2.bl.a.369.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.61.5	✓	192	7.5	odd	6	inner
476.2.bl.a.129.5	yes	192	1.1	even	1	trivial
476.2.bl.a.369.5	yes	192	119.12	even	48	inner
476.2.bl.a.437.5	yes	192	17.12	odd	16	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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.492526 - 0.998743i) q^{3} +(-3.01462 + 2.64375i) q^{5} +(2.62862 - 0.300610i) q^{7} +(1.07138 - 1.39625i) q^{9} +O(q^{10})\)	\(q+(-0.492526 - 0.998743i) q^{3} +(-3.01462 + 2.64375i) q^{5} +(2.62862 - 0.300610i) q^{7} +(1.07138 - 1.39625i) q^{9} +(-4.08011 + 0.267425i) q^{11} +(-4.36738 - 4.36738i) q^{13} +(4.12520 + 1.70871i) q^{15} +(-3.63362 + 1.94853i) q^{17} +(0.826921 + 6.28109i) q^{19} +(-1.59489 - 2.47726i) q^{21} +(-6.53831 - 3.22434i) q^{23} +(1.44588 - 10.9826i) q^{25} +(-5.19873 - 1.03409i) q^{27} +(-0.361977 - 1.81978i) q^{29} +(-2.27602 + 1.12241i) q^{31} +(2.27665 + 3.94327i) q^{33} +(-7.12954 + 7.85563i) q^{35} +(-0.379265 + 5.78647i) q^{37} +(-2.21084 + 6.51294i) q^{39} +(-0.175632 + 0.882961i) q^{41} +(-0.668963 - 1.61502i) q^{43} +(0.461531 + 7.04160i) q^{45} +(-0.151120 + 0.563987i) q^{47} +(6.81927 - 1.58038i) q^{49} +(3.73574 + 2.66936i) q^{51} +(-1.96982 - 2.56712i) q^{53} +(11.5930 - 11.5930i) q^{55} +(5.86591 - 3.91948i) q^{57} +(-4.58770 - 0.603982i) q^{59} +(-0.828262 - 2.43998i) q^{61} +(2.39652 - 3.99227i) q^{63} +(24.7122 + 1.61973i) q^{65} +(7.57605 + 4.37403i) q^{67} +8.11817i q^{69} +(-3.54023 - 2.36550i) q^{71} +(-2.01695 - 0.684662i) q^{73} +(-11.6809 + 3.96513i) q^{75} +(-10.6447 + 1.92948i) q^{77} +(0.497769 - 1.00938i) q^{79} +(0.161206 + 0.601630i) q^{81} +(1.61401 - 3.89656i) q^{83} +(5.80256 - 15.4805i) q^{85} +(-1.63921 + 1.25781i) q^{87} +(15.9892 + 4.28431i) q^{89} +(-12.7931 - 10.1673i) q^{91} +(2.24199 + 1.72034i) q^{93} +(-19.0985 - 16.7489i) q^{95} +(-3.12741 + 0.622081i) q^{97} +(-3.99795 + 5.98335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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