LMFDB - Embedded newform 900.2.w.c.469.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(109,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("900.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.6
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74098 - 1.40321i) q^{5} +1.57893i q^{7} +O(q^{10})$	$q+(1.74098 - 1.40321i) q^{5} +1.57893i q^{7} +(-1.19917 - 3.69066i) q^{11} +(0.326475 + 0.106078i) q^{13} +(3.56817 - 4.91117i) q^{17} +(2.98680 + 2.17004i) q^{19} +(-1.32236 + 0.429662i) q^{23} +(1.06200 - 4.88592i) q^{25} +(2.69395 - 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(2.21557 + 2.74888i) q^{35} +(-8.14739 - 2.64725i) q^{37} +(0.394970 - 1.21559i) q^{41} -1.42438i q^{43} +(-0.220691 - 0.303755i) q^{47} +4.50698 q^{49} +(6.64151 + 9.14125i) q^{53} +(-7.26650 - 4.74266i) q^{55} +(3.57899 - 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(0.717236 - 0.273434i) q^{65} +(-6.14771 + 8.46160i) q^{67} +(-8.19220 + 5.95198i) q^{71} +(12.5444 - 4.07594i) q^{73} +(5.82730 - 1.89340i) q^{77} +(11.1640 - 8.11114i) q^{79} +(-2.71826 + 3.74136i) q^{83} +(-0.679305 - 13.5571i) q^{85} +(-2.24626 - 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} +(8.24497 - 0.413129i) q^{95} +(3.55938 + 4.89906i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5}+O(q^{10}) $ 24 * q + 2 * q^5	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	1.74098	−	1.40321i	0.778588	−	0.627535i
$5$	1.74098	−	1.40321i	0.778588	−	0.627535i
$6$		0			0
$7$			1.57893i			0.596780i	0.954444	+	0.298390i	$0.0964496\pi$
$7$			1.57893i			0.596780i	−0.954444	+	0.298390i	$0.903550\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.19917	−	3.69066i	−0.361563	−	1.11278i	−0.952106	−	0.305769i	$-0.901086\pi$
$11$	−1.19917	−	3.69066i	−0.361563	−	1.11278i	0.590543	−	0.807006i	$-0.298914\pi$
$12$		0			0
$13$	0.326475	+	0.106078i	0.0905480	+	0.0294208i	0.353941	−	0.935268i	$-0.384841\pi$
$13$	0.326475	+	0.106078i	0.0905480	+	0.0294208i	−0.263393	+	0.964689i	$0.584841\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.56817	−	4.91117i	0.865409	−	1.19113i	−0.114844	−	0.993384i	$-0.536637\pi$
$17$	3.56817	−	4.91117i	0.865409	−	1.19113i	0.980253	−	0.197750i	$-0.0633633\pi$
$18$		0			0
$19$	2.98680	+	2.17004i	0.685219	+	0.497841i	0.875085	−	0.483969i	$-0.160805\pi$
$19$	2.98680	+	2.17004i	0.685219	+	0.497841i	−0.189866	+	0.981810i	$0.560805\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.32236	+	0.429662i	−0.275732	+	0.0895906i	−0.443619	−	0.896216i	$-0.646306\pi$
$23$	−1.32236	+	0.429662i	−0.275732	+	0.0895906i	0.167887	+	0.985806i	$0.446306\pi$
$24$		0			0
$25$	1.06200	−	4.88592i	0.212399	−	0.977183i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.69395	−	1.95727i	0.500254	−	0.363455i	−0.308860	−	0.951107i	$-0.599948\pi$
$29$	2.69395	−	1.95727i	0.500254	−	0.363455i	0.809114	+	0.587652i	$0.199948\pi$
$30$		0			0
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	0.900002	−	0.435886i	$-0.143565\pi$
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	−0.136437	+	0.990649i	$0.543565\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.21557	+	2.74888i	0.374500	+	0.464646i
$36$		0			0
$37$	−8.14739	−	2.64725i	−1.33942	−	0.435205i	−0.450301	−	0.892877i	$-0.648683\pi$
$37$	−8.14739	−	2.64725i	−1.33942	−	0.435205i	−0.889121	+	0.457672i	$0.848683\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.394970	−	1.21559i	0.0616839	−	0.189844i	−0.915466	−	0.402396i	$-0.868178\pi$
$41$	0.394970	−	1.21559i	0.0616839	−	0.189844i	0.977150	+	0.212552i	$0.0681776\pi$
$42$		0			0
$43$		−	1.42438i		−	0.217216i	−0.994085	−	0.108608i	$-0.965361\pi$
$43$		−	1.42438i		−	0.217216i	0.994085	−	0.108608i	$-0.0346394\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.220691	−	0.303755i	−0.0321911	−	0.0443072i	0.792618	−	0.609718i	$-0.208717\pi$
$47$	−0.220691	−	0.303755i	−0.0321911	−	0.0443072i	−0.824809	+	0.565411i	$0.808717\pi$
$48$		0			0
$49$	4.50698			0.643854
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.64151	+	9.14125i	0.912282	+	1.25565i	0.966382	+	0.257112i	$0.0827711\pi$
$53$	6.64151	+	9.14125i	0.912282	+	1.25565i	−0.0540999	+	0.998536i	$0.517229\pi$
$54$		0			0
$55$	−7.26650	−	4.74266i	−0.979814	−	0.639500i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.57899	−	11.0150i	0.465945	−	1.43403i	−0.391846	−	0.920031i	$-0.628163\pi$
$59$	3.57899	−	11.0150i	0.465945	−	1.43403i	0.857791	−	0.513999i	$-0.171837\pi$
$60$		0			0
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	−0.894181	−	0.447706i	$-0.852241\pi$
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	0.460252	−	0.887788i	$-0.347759\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.717236	−	0.273434i	0.0889622	−	0.0339154i
$66$		0			0
$67$	−6.14771	+	8.46160i	−0.751063	+	1.03375i	0.246842	+	0.969056i	$0.420607\pi$
$67$	−6.14771	+	8.46160i	−0.751063	+	1.03375i	−0.997905	+	0.0646937i	$0.979393\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.19220	+	5.95198i	−0.972235	+	0.706370i	−0.955960	−	0.293498i	$-0.905181\pi$
$71$	−8.19220	+	5.95198i	−0.972235	+	0.706370i	−0.0162750	+	0.999868i	$0.505181\pi$
$72$		0			0
$73$	12.5444	−	4.07594i	1.46822	−	0.477052i	0.537648	−	0.843170i	$-0.319313\pi$
$73$	12.5444	−	4.07594i	1.46822	−	0.477052i	0.930569	+	0.366117i	$0.119313\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.82730	−	1.89340i	0.664082	−	0.215773i
$78$		0			0
$79$	11.1640	−	8.11114i	1.25605	−	0.912574i	0.257494	−	0.966280i	$-0.417103\pi$
$79$	11.1640	−	8.11114i	1.25605	−	0.912574i	0.998557	+	0.0537055i	$0.0171032\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.71826	+	3.74136i	−0.298367	+	0.410668i	−0.931709	−	0.363204i	$-0.881683\pi$
$83$	−2.71826	+	3.74136i	−0.298367	+	0.410668i	0.633342	+	0.773872i	$0.281683\pi$
$84$		0			0
$85$	−0.679305	−	13.5571i	−0.0736809	−	1.47048i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.24626	−	6.91326i	−0.238103	−	0.732805i	−0.996695	−	0.0812387i	$-0.974112\pi$
$89$	−2.24626	−	6.91326i	−0.238103	−	0.732805i	0.758592	−	0.651566i	$-0.225888\pi$
$90$		0			0
$91$	−0.167490	+	0.515482i	−0.0175578	+	0.0540372i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.24497	−	0.413129i	0.845916	−	0.0423862i
$96$		0			0
$97$	3.55938	+	4.89906i	0.361400	+	0.497424i	0.950538	−	0.310608i	$-0.100533\pi$
$97$	3.55938	+	4.89906i	0.361400	+	0.497424i	−0.589138	+	0.808032i	$0.700533\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.23036			−0.321432			−0.160716	−	0.987001i	$-0.551380\pi$
$101$	−3.23036			−0.321432			−0.160716	+	0.987001i	$0.551380\pi$
$102$		0			0
$103$	4.52433	+	6.22721i	0.445796	+	0.613585i	0.971488	−	0.237090i	$-0.0761936\pi$
$103$	4.52433	+	6.22721i	0.445796	+	0.613585i	−0.525692	+	0.850675i	$0.676194\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			18.0376i			1.74376i	0.489722	+	0.871878i	$0.337098\pi$
$107$			18.0376i			1.74376i	−0.489722	+	0.871878i	$0.662902\pi$
$108$		0			0
$109$	−5.16860	+	15.9073i	−0.495062	+	1.52364i	0.321799	+	0.946808i	$0.395712\pi$
$109$	−5.16860	+	15.9073i	−0.495062	+	1.52364i	−0.816861	+	0.576835i	$0.804288\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.15793	−	0.701155i	−0.203001	−	0.0659591i	0.205751	−	0.978604i	$-0.434036\pi$
$113$	−2.15793	−	0.701155i	−0.203001	−	0.0659591i	−0.408753	+	0.912645i	$0.634036\pi$
$114$		0			0
$115$	−1.69929	+	2.60358i	−0.158460	+	0.242785i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.75440	+	5.63390i	0.710845	+	0.516459i
$120$		0			0
$121$	−3.28377	+	2.38580i	−0.298524	+	0.216891i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.00706	−	9.99646i	−0.447845	−	0.894111i
$126$		0			0
$127$	−1.43348	+	0.465767i	−0.127201	+	0.0413301i	−0.371926	−	0.928262i	$-0.621302\pi$
$127$	−1.43348	+	0.465767i	−0.127201	+	0.0413301i	0.244725	+	0.969593i	$0.421302\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−12.8948	−	9.36859i	−1.12662	−	0.818537i	−0.141421	−	0.989950i	$-0.545167\pi$
$131$	−12.8948	−	9.36859i	−1.12662	−	0.818537i	−0.985199	+	0.171412i	$0.945167\pi$
$132$		0			0
$133$	−3.42634	+	4.71595i	−0.297101	+	0.408925i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.17996	−	1.68307i	−0.442554	−	0.143795i	0.0792596	−	0.996854i	$-0.474744\pi$
$137$	−5.17996	−	1.68307i	−0.442554	−	0.143795i	−0.521814	+	0.853059i	$0.674744\pi$
$138$		0			0
$139$	3.05409	+	9.39953i	0.259045	+	0.797258i	0.993006	+	0.118066i	$0.0376694\pi$
$139$	3.05409	+	9.39953i	0.259045	+	0.797258i	−0.733961	+	0.679192i	$0.762331\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	1.33211i		−	0.111397i
$144$		0			0
$145$	1.94364	−	7.18773i	0.161410	−	0.596909i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.0649364			0.00531979			0.00265990	−	0.999996i	$-0.499153\pi$
$149$	0.0649364			0.00531979			0.00265990	+	0.999996i	$0.499153\pi$
$150$		0			0
$151$	−12.1221			−0.986481			−0.493240	−	0.869893i	$-0.664188\pi$
$151$	−12.1221			−0.986481			−0.493240	+	0.869893i	$0.664188\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.7357	−	0.588040i	0.942636	−	0.0472325i
$156$		0			0
$157$			23.4721i			1.87328i	0.350300	+	0.936638i	$0.386080\pi$
$157$			23.4721i			1.87328i	−0.350300	+	0.936638i	$0.613920\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.678406	−	2.08792i	−0.0534659	−	0.164551i
$162$		0			0
$163$	5.70240	+	1.85282i	0.446646	+	0.145124i	0.523700	−	0.851903i	$-0.324551\pi$
$163$	5.70240	+	1.85282i	0.446646	+	0.145124i	−0.0770538	+	0.997027i	$0.524551\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.76094	+	5.17649i	−0.291030	+	0.400569i	−0.929348	−	0.369204i	$-0.879630\pi$
$167$	−3.76094	+	5.17649i	−0.291030	+	0.400569i	0.638318	+	0.769773i	$0.279630\pi$
$168$		0			0
$169$	−10.4219	−	7.57194i	−0.801684	−	0.582457i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.96583	+	1.61350i	−0.377545	+	0.122672i	−0.491641	−	0.870798i	$-0.663603\pi$
$173$	−4.96583	+	1.61350i	−0.377545	+	0.122672i	0.114096	+	0.993470i	$0.463603\pi$
$174$		0			0
$175$	7.71452	+	1.67682i	0.583163	+	0.126755i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−18.8534	+	13.6978i	−1.40917	+	1.02382i	−0.415724	+	0.909491i	$0.636472\pi$
$179$	−18.8534	+	13.6978i	−1.40917	+	1.02382i	−0.993443	+	0.114329i	$0.963528\pi$
$180$		0			0
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.964454	−	0.264251i	$-0.914875\pi$
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.549350	−	0.835592i	$-0.685125\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−17.8991	+	6.82372i	−1.31596	+	0.501690i
$186$		0			0
$187$	−22.4043	−	7.27959i	−1.63836	−	0.532336i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.48188	+	7.63843i	−0.179582	+	0.552697i	−0.999813	−	0.0193354i	$-0.993845\pi$
$191$	−2.48188	+	7.63843i	−0.179582	+	0.552697i	0.820231	+	0.572033i	$0.193845\pi$
$192$		0			0
$193$			20.2575i			1.45817i	0.684424	+	0.729084i	$0.260054\pi$
$193$			20.2575i			1.45817i	−0.684424	+	0.729084i	$0.739946\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.7650	−	16.1931i	−0.838221	−	1.15371i	−0.986337	−	0.164742i	$-0.947321\pi$
$197$	−11.7650	−	16.1931i	−0.838221	−	1.15371i	0.148115	−	0.988970i	$-0.452679\pi$
$198$		0			0
$199$	22.4180			1.58917			0.794585	−	0.607153i	$-0.207689\pi$
$199$	22.4180			1.58917			0.794585	+	0.607153i	$0.207689\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.09039	+	4.25356i	0.216903	+	0.298541i
$204$		0			0
$205$	−1.01810	−	2.67054i	−0.0711072	−	0.186519i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.42719	−	13.6255i	0.306235	−	0.942495i
$210$		0			0
$211$	2.67780	+	8.24142i	0.184347	+	0.567363i	0.999937	−	0.0112687i	$-0.00358702\pi$
$211$	2.67780	+	8.24142i	0.184347	+	0.567363i	−0.815589	+	0.578631i	$0.803587\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.99871	−	2.47982i	−0.136311	−	0.169122i
$216$		0			0
$217$	−4.87698	+	6.71259i	−0.331071	+	0.455680i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.68589	−	1.22487i	0.113405	−	0.0823937i
$222$		0			0
$223$	−11.7779	+	3.82686i	−0.788705	+	0.256266i	−0.675552	−	0.737312i	$-0.736095\pi$
$223$	−11.7779	+	3.82686i	−0.788705	+	0.256266i	−0.113152	+	0.993578i	$0.536095\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.3309	+	5.63116i	−1.15029	+	0.373753i	−0.821254	−	0.570563i	$-0.806725\pi$
$227$	−17.3309	+	5.63116i	−1.15029	+	0.373753i	−0.329040	+	0.944316i	$0.606725\pi$
$228$		0			0
$229$	13.2812	−	9.64932i	0.877643	−	0.637645i	−0.0549837	−	0.998487i	$-0.517511\pi$
$229$	13.2812	−	9.64932i	0.877643	−	0.637645i	0.932627	+	0.360842i	$0.117511\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.01993	+	4.15658i	−0.197842	+	0.272307i	−0.896399	−	0.443248i	$-0.853826\pi$
$233$	−3.01993	+	4.15658i	−0.197842	+	0.272307i	0.698557	+	0.715555i	$0.253826\pi$
$234$		0			0
$235$	−0.810450	−	0.219154i	−0.0528679	−	0.0142960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.58924	+	23.3573i	0.490907	+	1.51086i	0.823239	+	0.567694i	$0.192165\pi$
$239$	7.58924	+	23.3573i	0.490907	+	1.51086i	−0.332332	+	0.943162i	$0.607835\pi$
$240$		0			0
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	−0.891331	−	0.453353i	$-0.850228\pi$
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	0.987576	+	0.157141i	$0.0502276\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.84654	−	6.32424i	0.501297	−	0.404041i
$246$		0			0
$247$	0.744923	+	1.02530i	0.0473983	+	0.0652382i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.1395			0.955594			0.477797	−	0.878470i	$-0.341435\pi$
$251$	15.1395			0.955594			0.477797	+	0.878470i	$0.341435\pi$
$252$		0			0
$253$	3.17147	+	4.36515i	0.199388	+	0.274435i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			22.7976i			1.42207i	0.703155	+	0.711036i	$0.251774\pi$
$257$			22.7976i			1.42207i	−0.703155	+	0.711036i	$0.748226\pi$
$258$		0			0
$259$	4.17982	−	12.8642i	0.259722	−	0.799341i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.98231	+	2.91853i	0.553873	+	0.179964i	0.572562	−	0.819861i	$-0.305949\pi$
$263$	8.98231	+	2.91853i	0.553873	+	0.179964i	−0.0186895	+	0.999825i	$0.505949\pi$
$264$		0			0
$265$	24.3898	+	6.59526i	1.49825	+	0.405144i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	23.7720	+	17.2714i	1.44940	+	1.05305i	0.985970	+	0.166921i	$0.0533825\pi$
$269$	23.7720	+	17.2714i	1.44940	+	1.05305i	0.463433	+	0.886132i	$0.346618\pi$
$270$		0			0
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	−0.899266	−	0.437401i	$-0.855899\pi$
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	0.138105	+	0.990418i	$0.455899\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−19.3058	+	1.93957i	−1.16418	+	0.116960i
$276$		0			0
$277$	14.6259	−	4.75225i	0.878786	−	0.285535i	0.165333	−	0.986238i	$-0.447130\pi$
$277$	14.6259	−	4.75225i	0.878786	−	0.285535i	0.713453	+	0.700703i	$0.247130\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.13314	+	2.27636i	0.186908	+	0.135796i	0.677304	−	0.735703i	$-0.263148\pi$
$281$	3.13314	+	2.27636i	0.186908	+	0.135796i	−0.490397	+	0.871499i	$0.663148\pi$
$282$		0			0
$283$	−6.98697	+	9.61673i	−0.415332	+	0.571655i	−0.964509	−	0.264051i	$-0.914941\pi$
$283$	−6.98697	+	9.61673i	−0.415332	+	0.571655i	0.549177	+	0.835706i	$0.314941\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.91934	+	0.623630i	0.113295	+	0.0368117i
$288$		0			0
$289$	−6.13443	−	18.8798i	−0.360849	−	1.11058i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			15.4596i			0.903161i	0.892230	+	0.451581i	$0.149140\pi$
$293$			15.4596i			0.903161i	−0.892230	+	0.451581i	$0.850860\pi$
$294$		0			0
$295$	−9.22543	−	24.1989i	−0.537125	−	1.40892i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.477297			−0.0276028
$300$		0			0
$301$	2.24900			0.129630
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−20.5366	−	13.4037i	−1.17592	−	0.767495i
$306$		0			0
$307$		−	26.6092i		−	1.51867i	−0.650702	−	0.759334i	$-0.725525\pi$
$307$		−	26.6092i		−	1.51867i	0.650702	−	0.759334i	$-0.274475\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.69361	+	5.21238i	0.0960356	+	0.295567i	0.987522	−	0.157480i	$-0.0503370\pi$
$311$	1.69361	+	5.21238i	0.0960356	+	0.295567i	−0.891487	+	0.453047i	$0.850337\pi$
$312$		0			0
$313$	7.08632	+	2.30248i	0.400542	+	0.130144i	0.502359	−	0.864659i	$-0.332466\pi$
$313$	7.08632	+	2.30248i	0.400542	+	0.130144i	−0.101817	+	0.994803i	$0.532466\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.74481	+	2.40152i	−0.0979981	+	0.134883i	−0.855200	−	0.518298i	$-0.826566\pi$
$317$	−1.74481	+	2.40152i	−0.0979981	+	0.134883i	0.757202	+	0.653181i	$0.226566\pi$
$318$		0			0
$319$	−10.4541	−	7.59535i	−0.585317	−	0.425258i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	21.3148	−	6.92561i	1.18599	−	0.385351i
$324$		0			0
$325$	0.865005	−	1.48248i	0.0479818	−	0.0822330i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.479608	−	0.348456i	0.0264416	−	0.0192110i
$330$		0			0
$331$	−22.1899	−	16.1219i	−1.21967	−	0.886140i	−0.223594	−	0.974682i	$-0.571779\pi$
$331$	−22.1899	−	16.1219i	−1.21967	−	0.886140i	−0.996072	+	0.0885426i	$0.971779\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.17039	+	23.3580i	0.0639455	+	1.27618i
$336$		0			0
$337$	7.14905	+	2.32287i	0.389433	+	0.126535i	0.497188	−	0.867643i	$-0.334366\pi$
$337$	7.14905	+	2.32287i	0.389433	+	0.126535i	−0.107754	+	0.994178i	$0.534366\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.30157	−	19.3943i	0.341249	−	1.05026i
$342$		0			0
$343$			18.1687i			0.981019i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.05022	−	9.70380i	−0.378476	−	0.520927i	0.576704	−	0.816953i	$-0.304339\pi$
$347$	−7.05022	−	9.70380i	−0.378476	−	0.520927i	−0.955180	+	0.296026i	$0.904339\pi$
$348$		0			0
$349$	3.50169			0.187441			0.0937207	−	0.995599i	$-0.470124\pi$
$349$	3.50169			0.187441			0.0937207	+	0.995599i	$0.470124\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.6665	−	20.1867i	−0.780617	−	1.07443i	−0.995214	−	0.0977244i	$-0.968844\pi$
$353$	−14.6665	−	20.1867i	−0.780617	−	1.07443i	0.214596	−	0.976703i	$-0.431156\pi$
$354$		0			0
$355$	−5.91053	+	21.8576i	−0.313698	+	1.16008i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.247954	−	0.763123i	0.0130865	−	0.0402761i	−0.944300	−	0.329086i	$-0.893259\pi$
$359$	0.247954	−	0.763123i	0.0130865	−	0.0402761i	0.957387	+	0.288810i	$0.0932595\pi$
$360$		0			0
$361$	−1.65941	−	5.10714i	−0.0873374	−	0.268797i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.1202	−	24.6986i	0.843769	−	1.29278i
$366$		0			0
$367$	−9.28986	+	12.7864i	−0.484927	+	0.667445i	−0.979442	−	0.201724i	$-0.935346\pi$
$367$	−9.28986	+	12.7864i	−0.484927	+	0.667445i	0.494515	+	0.869169i	$0.335346\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−14.4334	+	10.4865i	−0.749346	+	0.544431i
$372$		0			0
$373$	−3.43291	+	1.11542i	−0.177750	+	0.0577543i	−0.396540	−	0.918018i	$-0.629789\pi$
$373$	−3.43291	+	1.11542i	−0.177750	+	0.0577543i	0.218790	+	0.975772i	$0.429789\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.08713	−	0.353230i	0.0559901	−	0.0181923i
$378$		0			0
$379$	22.0967	−	16.0542i	1.13503	−	0.824647i	0.148610	−	0.988896i	$-0.452520\pi$
$379$	22.0967	−	16.0542i	1.13503	−	0.824647i	0.986419	+	0.164249i	$0.0525201\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.3334	−	15.5991i	0.579112	−	0.797079i	−0.414486	−	0.910056i	$-0.636039\pi$
$383$	11.3334	−	15.5991i	0.579112	−	0.797079i	0.993598	+	0.112977i	$0.0360386\pi$
$384$		0			0
$385$	7.48834	−	11.4733i	0.381641	−	0.584733i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.27164	−	16.2244i	−0.267283	−	0.822612i	−0.991159	−	0.132682i	$-0.957641\pi$
$389$	−5.27164	−	16.2244i	−0.267283	−	0.822612i	0.723876	−	0.689930i	$-0.242359\pi$
$390$		0			0
$391$	−2.60828	+	8.02745i	−0.131906	+	0.405966i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.05466	−	29.7868i	0.405274	−	1.49874i
$396$		0			0
$397$	16.0842	+	22.1380i	0.807243	+	1.11108i	0.991743	+	0.128243i	$0.0409336\pi$
$397$	16.0842	+	22.1380i	0.807243	+	1.11108i	−0.184499	+	0.982833i	$0.559066\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.7793			0.738042			0.369021	−	0.929421i	$-0.379693\pi$
$401$	14.7793			0.738042			0.369021	+	0.929421i	$0.379693\pi$
$402$		0			0
$403$	1.06031	+	1.45939i	0.0528177	+	0.0726974i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			33.2437i			1.64783i
$408$		0			0
$409$	−6.72523	+	20.6981i	−0.332541	+	1.02346i	0.635379	+	0.772200i	$0.280844\pi$
$409$	−6.72523	+	20.6981i	−0.332541	+	1.02346i	−0.967921	+	0.251256i	$0.919156\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.3919	+	5.65098i	0.855800	+	0.278066i
$414$		0			0
$415$	0.517499	+	10.3279i	0.0254030	+	0.506977i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.67055	+	2.66681i	0.179318	+	0.130282i	0.673824	−	0.738892i	$-0.264651\pi$
$419$	3.67055	+	2.66681i	0.179318	+	0.130282i	−0.494505	+	0.869175i	$0.664651\pi$
$420$		0			0
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	−0.646391	−	0.763006i	$-0.723722\pi$
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	0.525916	+	0.850536i	$0.323722\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−20.2062	−	22.6494i	−0.980143	−	1.09866i
$426$		0			0
$427$	16.4691	−	5.35114i	0.796996	−	0.258960i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.2881	−	11.1074i	−0.736400	−	0.535026i	0.155181	−	0.987886i	$-0.450404\pi$
$431$	−15.2881	−	11.1074i	−0.736400	−	0.535026i	−0.891582	+	0.452860i	$0.850404\pi$
$432$		0			0
$433$	−2.00963	+	2.76602i	−0.0965768	+	0.132927i	−0.854571	−	0.519335i	$-0.826180\pi$
$433$	−2.00963	+	2.76602i	−0.0965768	+	0.132927i	0.757994	+	0.652262i	$0.226180\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.88201	−	1.58626i	−0.233538	−	0.0758812i
$438$		0			0
$439$	1.84058	+	5.66473i	0.0878462	+	0.270363i	0.985323	−	0.170698i	$-0.0546023\pi$
$439$	1.84058	+	5.66473i	0.0878462	+	0.270363i	−0.897477	+	0.441061i	$0.854602\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	33.0705i		−	1.57122i	−0.618719	−	0.785612i	$-0.712348\pi$
$443$		−	33.0705i		−	1.57122i	0.618719	−	0.785612i	$-0.287652\pi$
$444$		0			0
$445$	−13.6115	−	8.88386i	−0.645245	−	0.421135i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8.68077			−0.409671			−0.204835	−	0.978796i	$-0.565666\pi$
$449$	−8.68077			−0.409671			−0.204835	+	0.978796i	$0.565666\pi$
$450$		0			0
$451$	−4.95997			−0.233556
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.431734	+	1.13247i	0.0202400	+	0.0530909i
$456$		0			0
$457$		−	13.3667i		−	0.625269i	−0.949873	−	0.312635i	$-0.898788\pi$
$457$		−	13.3667i		−	0.625269i	0.949873	−	0.312635i	$-0.101212\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.6568	+	38.9537i	0.589487	+	1.81425i	0.580453	+	0.814294i	$0.302876\pi$
$461$	12.6568	+	38.9537i	0.589487	+	1.81425i	0.00903372	+	0.999959i	$0.497124\pi$
$462$		0			0
$463$	21.9961	+	7.14695i	1.02224	+	0.332147i	0.771719	−	0.635963i	$-0.219397\pi$
$463$	21.9961	+	7.14695i	1.02224	+	0.332147i	0.250524	+	0.968110i	$0.419397\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.8034	−	24.5043i	0.823845	−	1.13392i	−0.165193	−	0.986261i	$-0.552825\pi$
$467$	17.8034	−	24.5043i	0.823845	−	1.13392i	0.989038	−	0.147664i	$-0.0471753\pi$
$468$		0			0
$469$	−13.3603	−	9.70682i	−0.616921	−	0.448219i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.25691	+	1.70807i	−0.241713	+	0.0785373i
$474$		0			0
$475$	13.7746	−	12.2887i	0.632021	−	0.563843i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.4809	−	14.1537i	0.890107	−	0.646700i	−0.0457990	−	0.998951i	$-0.514583\pi$
$479$	19.4809	−	14.1537i	0.890107	−	0.646700i	0.935906	+	0.352250i	$0.114583\pi$
$480$		0			0
$481$	−2.37911	−	1.72852i	−0.108478	−	0.0788138i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.0712	+	3.53459i	0.593533	+	0.160497i
$486$		0			0
$487$	−2.14446	−	0.696777i	−0.0971747	−	0.0315740i	0.260026	−	0.965602i	$-0.416269\pi$
$487$	−2.14446	−	0.696777i	−0.0971747	−	0.0315740i	−0.357201	+	0.934028i	$0.616269\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.84093	−	27.2096i	0.398986	−	1.22795i	−0.526828	−	0.849972i	$-0.676619\pi$
$491$	8.84093	−	27.2096i	0.398986	−	1.22795i	0.925814	−	0.377980i	$-0.123381\pi$
$492$		0			0
$493$		−	20.2143i		−	0.910406i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.39777	−	12.9349i	−0.421547	−	0.580210i
$498$		0			0
$499$	26.9489			1.20640			0.603199	−	0.797590i	$-0.293892\pi$
$499$	26.9489			1.20640			0.603199	+	0.797590i	$0.293892\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.245105	+	0.337358i	0.0109287	+	0.0150421i	0.814446	−	0.580239i	$-0.197041\pi$
$503$	0.245105	+	0.337358i	0.0109287	+	0.0150421i	−0.803518	+	0.595281i	$0.797041\pi$
$504$		0			0
$505$	−5.62397	+	4.53287i	−0.250263	+	0.201710i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.14176	−	12.7470i	0.183580	−	0.565002i	−0.816341	−	0.577571i	$-0.804001\pi$
$509$	4.14176	−	12.7470i	0.183580	−	0.565002i	0.999921	+	0.0125684i	$0.00400074\pi$
$510$		0			0
$511$	6.43563	+	19.8068i	0.284695	+	0.876202i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.6148	+	4.49283i	0.732138	+	0.197978i
$516$		0			0
$517$	−0.856410	+	1.17875i	−0.0376649	+	0.0518412i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.0496	−	12.3872i	0.746956	−	0.542695i	−0.147926	−	0.988998i	$-0.547260\pi$
$521$	17.0496	−	12.3872i	0.746956	−	0.542695i	0.894882	+	0.446303i	$0.147260\pi$
$522$		0			0
$523$	−11.2943	+	3.66974i	−0.493866	+	0.160467i	−0.545352	−	0.838207i	$-0.683604\pi$
$523$	−11.2943	+	3.66974i	−0.493866	+	0.160467i	0.0514866	+	0.998674i	$0.483604\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.3391	−	9.85777i	1.32159	−	0.429411i
$528$		0			0
$529$	−17.0434	+	12.3827i	−0.741016	+	0.538379i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.257896	−	0.354963i	0.0111707	−	0.0153752i
$534$		0			0
$535$	25.3105	+	31.4030i	1.09427	+	1.35767i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.40462	−	16.6337i	−0.232793	−	0.716464i
$540$		0			0
$541$	11.2993	−	34.7757i	0.485796	−	1.49513i	−0.345029	−	0.938592i	$-0.612131\pi$
$541$	11.2993	−	34.7757i	0.485796	−	1.49513i	0.830825	−	0.556534i	$-0.187869\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.3229	+	34.9469i	0.570691	+	1.49696i
$546$		0			0
$547$	−23.2652	−	32.0219i	−0.994750	−	1.36916i	−0.928492	−	0.371353i	$-0.878894\pi$
$547$	−23.2652	−	32.0219i	−0.994750	−	1.36916i	−0.0662579	−	0.997803i	$-0.521106\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.2936			0.523726
$552$		0			0
$553$	12.8069	+	17.6272i	0.544606	+	0.749586i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			12.1804i			0.516102i	0.966131	+	0.258051i	$0.0830802\pi$
$557$			12.1804i			0.516102i	−0.966131	+	0.258051i	$0.916920\pi$
$558$		0			0
$559$	0.151096	−	0.465026i	0.00639068	−	0.0196685i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−34.7979	−	11.3065i	−1.46656	−	0.476513i	−0.536490	−	0.843907i	$-0.680250\pi$
$563$	−34.7979	−	11.3065i	−1.46656	−	0.476513i	−0.930065	+	0.367394i	$0.880250\pi$
$564$		0			0
$565$	−4.74078	+	1.80734i	−0.199446	+	0.0760355i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	27.3735	+	19.8880i	1.14756	+	0.833749i	0.988154	−	0.153464i	$-0.0490430\pi$
$569$	27.3735	+	19.8880i	1.14756	+	0.833749i	0.159403	+	0.987214i	$0.449043\pi$
$570$		0			0
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	−0.567213	−	0.823571i	$-0.691978\pi$
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	0.607984	+	0.793949i	$0.291978\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.694947	+	6.91725i	0.0289813	+	0.288469i
$576$		0			0
$577$	15.6012	−	5.06913i	0.649485	−	0.211031i	0.0342981	−	0.999412i	$-0.489080\pi$
$577$	15.6012	−	5.06913i	0.649485	−	0.211031i	0.615187	+	0.788381i	$0.289080\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.90735	−	4.29194i	−0.245078	−	0.178060i
$582$		0			0
$583$	25.7730	−	35.4734i	1.06741	−	1.46916i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−32.0429	−	10.4114i	−1.32255	−	0.429724i	−0.439182	−	0.898398i	$-0.644732\pi$
$587$	−32.0429	−	10.4114i	−1.32255	−	0.429724i	−0.883371	+	0.468674i	$0.844732\pi$
$588$		0			0
$589$	5.99515	+	18.4512i	0.247026	+	0.760267i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			32.2208i			1.32315i	0.749878	+	0.661576i	$0.230112\pi$
$593$			32.2208i			1.32315i	−0.749878	+	0.661576i	$0.769888\pi$
$594$		0			0
$595$	21.4058	−	1.07258i	0.877551	−	0.0439713i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.7284			−0.601784			−0.300892	−	0.953658i	$-0.597284\pi$
$599$	−14.7284			−0.601784			−0.300892	+	0.953658i	$0.597284\pi$
$600$		0			0
$601$	35.5643			1.45070			0.725348	−	0.688382i	$-0.241679\pi$
$601$	35.5643			1.45070			0.725348	+	0.688382i	$0.241679\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.36918	+	8.76143i	−0.0963210	+	0.356203i
$606$		0			0
$607$			16.0986i			0.653421i	0.945124	+	0.326710i	$0.105940\pi$
$607$			16.0986i			0.653421i	−0.945124	+	0.326710i	$0.894060\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.0398283	−	0.122579i	−0.00161128	−	0.00495902i
$612$		0			0
$613$	−41.1487	−	13.3700i	−1.66198	−	0.540010i	−0.680693	−	0.732569i	$-0.738321\pi$
$613$	−41.1487	−	13.3700i	−1.66198	−	0.540010i	−0.981285	+	0.192559i	$0.938321\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.931550	−	1.28217i	0.0375028	−	0.0516182i	−0.789854	−	0.613295i	$-0.789844\pi$
$617$	0.931550	−	1.28217i	0.0375028	−	0.0516182i	0.827357	+	0.561677i	$0.189844\pi$
$618$		0			0
$619$	−10.9048	−	7.92281i	−0.438301	−	0.318444i	0.346658	−	0.937991i	$-0.387316\pi$
$619$	−10.9048	−	7.92281i	−0.438301	−	0.318444i	−0.784960	+	0.619547i	$0.787316\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.9156	−	3.54668i	0.437323	−	0.142095i
$624$		0			0
$625$	−22.7443	−	10.3776i	−0.909773	−	0.415105i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−42.0724	+	30.5674i	−1.67754	+	1.21880i
$630$		0			0
$631$	23.6944	+	17.2150i	0.943261	+	0.685319i	0.949203	−	0.314663i	$-0.101892\pi$
$631$	23.6944	+	17.2150i	0.943261	+	0.685319i	−0.00594245	+	0.999982i	$0.501892\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.84209	+	2.82237i	−0.0731011	+	0.112002i
$636$		0			0
$637$	1.47142	+	0.478092i	0.0582997	+	0.0189427i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.34325	−	16.4448i	0.211046	−	0.649532i	−0.788365	−	0.615208i	$-0.789072\pi$
$641$	5.34325	−	16.4448i	0.211046	−	0.649532i	0.999411	−	0.0343242i	$-0.0109279\pi$
$642$		0			0
$643$		−	46.8857i		−	1.84899i	−0.381190	−	0.924497i	$-0.624486\pi$
$643$		−	46.8857i		−	1.84899i	0.381190	−	0.924497i	$-0.375514\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.46236	−	11.6474i	−0.332690	−	0.457908i	0.609599	−	0.792710i	$-0.291331\pi$
$647$	−8.46236	−	11.6474i	−0.332690	−	0.457908i	−0.942288	+	0.334802i	$0.891331\pi$
$648$		0			0
$649$	−44.9444			−1.76422
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.7990	+	25.8746i	0.735661	+	1.01255i	0.998857	+	0.0478084i	$0.0152237\pi$
$653$	18.7990	+	25.8746i	0.735661	+	1.01255i	−0.263195	+	0.964743i	$0.584776\pi$
$654$		0			0
$655$	−35.5956	+	1.78358i	−1.39083	+	0.0696903i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.77517	−	17.7742i	0.224969	−	0.692383i	−0.773326	−	0.634009i	$-0.781408\pi$
$659$	5.77517	−	17.7742i	0.224969	−	0.692383i	0.998295	−	0.0583742i	$-0.0185917\pi$
$660$		0			0
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	0.946892	−	0.321551i	$-0.104204\pi$
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	−0.955055	+	0.296429i	$0.904204\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.652303	+	13.0182i	0.0252952	+	0.504826i
$666$		0			0
$667$	−2.72141	+	3.74570i	−0.105373	+	0.145034i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−34.4315	+	25.0159i	−1.32921	+	0.965730i
$672$		0			0
$673$	6.90162	−	2.24247i	0.266038	−	0.0864410i	−0.172961	−	0.984929i	$-0.555333\pi$
$673$	6.90162	−	2.24247i	0.266038	−	0.0864410i	0.438999	+	0.898488i	$0.355333\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.2918	−	10.4922i	1.24107	−	0.403249i	0.386359	−	0.922348i	$-0.373733\pi$
$677$	32.2918	−	10.4922i	1.24107	−	0.403249i	0.854714	+	0.519099i	$0.173733\pi$
$678$		0			0
$679$	−7.73528	+	5.62001i	−0.296853	+	0.215676i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.5508	+	22.7802i	−0.633298	+	0.871660i	−0.998236	−	0.0593717i	$-0.981090\pi$
$683$	−16.5508	+	22.7802i	−0.633298	+	0.871660i	0.364938	+	0.931032i	$0.381090\pi$
$684$		0			0
$685$	−11.3799	+	4.33840i	−0.434804	+	0.165762i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.19860	+	3.68892i	0.0456631	+	0.140536i
$690$		0			0
$691$	6.85416	−	21.0949i	0.260745	−	0.802489i	−0.731899	−	0.681413i	$-0.761366\pi$
$691$	6.85416	−	21.0949i	0.260745	−	0.802489i	0.992643	−	0.121076i	$-0.0386344\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18.5066	+	12.0788i	0.701996	+	0.458176i
$696$		0			0
$697$	−4.56066	−	6.27721i	−0.172747	−	0.237766i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−16.9652			−0.640768			−0.320384	−	0.947288i	$-0.603812\pi$
$701$	−16.9652			−0.640768			−0.320384	+	0.947288i	$0.603812\pi$
$702$		0			0
$703$	−18.5900	−	25.5869i	−0.701135	−	0.965030i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	5.10051i		−	0.191824i
$708$		0			0
$709$	−4.42745	+	13.6263i	−0.166276	+	0.511746i	−0.999128	−	0.0417503i	$-0.986707\pi$
$709$	−4.42745	+	13.6263i	−0.166276	+	0.511746i	0.832852	+	0.553496i	$0.186707\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.94896	−	2.25785i	−0.260241	−	0.0845573i
$714$		0			0
$715$	−1.86924	−	2.31918i	−0.0699056	−	0.0867324i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.56382	−	6.94852i	−0.356670	−	0.259136i	0.394992	−	0.918685i	$-0.370747\pi$
$719$	−9.56382	−	6.94852i	−0.356670	−	0.259136i	−0.751662	+	0.659549i	$0.770747\pi$
$720$		0			0
$721$	−9.83234	+	7.14361i	−0.366175	+	0.266042i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.70208	−	15.2410i	−0.248909	−	0.566037i
$726$		0			0
$727$	1.17583	−	0.382051i	0.0436092	−	0.0141695i	−0.287131	−	0.957891i	$-0.592702\pi$
$727$	1.17583	−	0.382051i	0.0436092	−	0.0141695i	0.330740	+	0.943722i	$0.392702\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.99538	−	5.08244i	−0.258734	−	0.187981i
$732$		0			0
$733$	−9.70319	+	13.3553i	−0.358395	+	0.493289i	−0.949701	−	0.313159i	$-0.898613\pi$
$733$	−9.70319	+	13.3553i	−0.358395	+	0.493289i	0.591305	+	0.806448i	$0.298613\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	38.6010	+	12.5422i	1.42189	+	0.461999i
$738$		0			0
$739$	5.20573	+	16.0216i	0.191496	+	0.589363i	1.00000		0.000872485i	$0.000277721\pi$
$739$	5.20573	+	16.0216i	0.191496	+	0.589363i	−0.808504	+	0.588491i	$0.799722\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			11.8940i			0.436347i	0.975910	+	0.218174i	$0.0700099\pi$
$743$			11.8940i			0.436347i	−0.975910	+	0.218174i	$0.929990\pi$
$744$		0			0
$745$	0.113053	−	0.0911194i	0.00414193	−	0.00333836i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−28.4801			−1.04064
$750$		0			0
$751$	0.821377			0.0299725			0.0149862	−	0.999888i	$-0.495230\pi$
$751$	0.821377			0.0299725			0.0149862	+	0.999888i	$0.495230\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.1042	+	17.0098i	−0.768062	+	0.619051i
$756$		0			0
$757$			32.5591i			1.18338i	0.806166	+	0.591690i	$0.201539\pi$
$757$			32.5591i			1.18338i	−0.806166	+	0.591690i	$0.798461\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.35824	+	10.3356i	0.121736	+	0.374665i	0.993292	−	0.115631i	$-0.0368889\pi$
$761$	3.35824	+	10.3356i	0.121736	+	0.374665i	−0.871556	+	0.490295i	$0.836889\pi$
$762$		0			0
$763$	−25.1165	−	8.16086i	−0.909280	−	0.295443i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.33690	−	3.21647i	0.0843807	−	0.116140i
$768$		0			0
$769$	−1.92870	−	1.40128i	−0.0695505	−	0.0505314i	0.552467	−	0.833535i	$-0.313687\pi$
$769$	−1.92870	−	1.40128i	−0.0695505	−	0.0505314i	−0.622017	+	0.783004i	$0.713687\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−35.4118	+	11.5060i	−1.27367	+	0.413841i	−0.866347	−	0.499442i	$-0.833538\pi$
$773$	−35.4118	+	11.5060i	−1.27367	+	0.413841i	−0.407325	+	0.913283i	$0.633538\pi$
$774$		0			0
$775$	19.6065	−	17.4915i	0.704285	−	0.628312i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.81757	−	2.77363i	0.136779	−	0.0993756i
$780$		0			0
$781$	31.7905	+	23.0972i	1.13755	+	0.826482i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	32.9363	+	40.8643i	1.17555	+	1.45851i
$786$		0			0
$787$	−21.7768	−	7.07570i	−0.776258	−	0.252221i	−0.106016	−	0.994364i	$-0.533809\pi$
$787$	−21.7768	−	7.07570i	−0.776258	−	0.252221i	−0.670242	+	0.742143i	$0.733809\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.10708	−	3.40723i	0.0393631	−	0.121147i
$792$		0			0
$793$		−	3.76483i		−	0.133693i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.21641	+	7.17977i	0.184775	+	0.254321i	0.891348	−	0.453319i	$-0.149760\pi$
$797$	5.21641	+	7.17977i	0.184775	+	0.254321i	−0.706574	+	0.707639i	$0.749760\pi$
$798$		0			0
$799$	−2.27925			−0.0806342
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−30.0858	−	41.4095i	−1.06170	−	1.46131i
$804$		0			0
$805$	−4.11088	−	2.68307i	−0.144890	−	0.0945658i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.5887	+	38.7442i	−0.442597	+	1.36217i	0.442502	+	0.896768i	$0.354091\pi$
$809$	−12.5887	+	38.7442i	−0.442597	+	1.36217i	−0.885098	+	0.465404i	$0.845909\pi$
$810$		0			0
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	0.830996	+	0.556279i	$0.187771\pi$
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	−0.345317	+	0.938486i	$0.612229\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.5276	−	4.77595i	0.438824	−	0.167294i
$816$		0			0
$817$	3.09096	−	4.25435i	0.108139	−	0.148841i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−40.4077	+	29.3579i	−1.41024	+	1.02460i	−0.416949	+	0.908930i	$0.636901\pi$
$821$	−40.4077	+	29.3579i	−1.41024	+	1.02460i	−0.993288	+	0.115667i	$0.963099\pi$
$822$		0			0
$823$	15.2000	−	4.93877i	0.529837	−	0.172155i	−0.0318678	−	0.999492i	$-0.510146\pi$
$823$	15.2000	−	4.93877i	0.529837	−	0.172155i	0.561705	+	0.827338i	$0.310146\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	42.9415	−	13.9525i	1.49322	−	0.485177i	0.555190	−	0.831724i	$-0.312646\pi$
$827$	42.9415	−	13.9525i	1.49322	−	0.485177i	0.938033	+	0.346546i	$0.112646\pi$
$828$		0			0
$829$	−12.4972	+	9.07975i	−0.434046	+	0.315353i	−0.783265	−	0.621688i	$-0.786447\pi$
$829$	−12.4972	+	9.07975i	−0.434046	+	0.315353i	0.349219	+	0.937041i	$0.386447\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.0817	−	22.1345i	0.557197	−	0.766916i
$834$		0			0
$835$	0.716004	+	14.2895i	0.0247783	+	0.494510i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.15711	−	22.0273i	−0.247091	−	0.760468i	−0.995285	−	0.0969885i	$-0.969079\pi$
$839$	−7.15711	−	22.0273i	−0.247091	−	0.760468i	0.748194	−	0.663480i	$-0.230921\pi$
$840$		0			0
$841$	−5.53504	+	17.0351i	−0.190863	+	0.587417i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−28.7693	+	1.44154i	−0.989694	+	0.0495904i
$846$		0			0
$847$	−3.76701	−	5.18484i	−0.129436	−	0.178153i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.9112			0.408311
$852$		0			0
$853$	0.480767	+	0.661719i	0.0164611	+	0.0226568i	0.817168	−	0.576399i	$-0.195543\pi$
$853$	0.480767	+	0.661719i	0.0164611	+	0.0226568i	−0.800707	+	0.599056i	$0.795543\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			38.5882i			1.31815i	0.752078	+	0.659074i	$0.229052\pi$
$857$			38.5882i			1.31815i	−0.752078	+	0.659074i	$0.770948\pi$
$858$		0			0
$859$	−12.4773	+	38.4012i	−0.425720	+	1.31023i	0.476583	+	0.879129i	$0.341875\pi$
$859$	−12.4773	+	38.4012i	−0.425720	+	1.31023i	−0.902303	+	0.431102i	$0.858125\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.5681	+	8.30758i	0.870349	+	0.282793i	0.709944	−	0.704258i	$-0.248720\pi$
$863$	25.5681	+	8.30758i	0.870349	+	0.282793i	0.160404	+	0.987051i	$0.448720\pi$
$864$		0			0
$865$	−6.38131	+	9.77716i	−0.216971	+	0.332433i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−43.3230	−	31.4760i	−1.46963	−	1.06775i
$870$		0			0
$871$	−2.90467	+	2.11037i	−0.0984210	+	0.0715070i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.7837	−	7.90581i	0.533588	−	0.267265i
$876$		0			0
$877$	21.5839	−	7.01303i	0.728836	−	0.236813i	0.0789861	−	0.996876i	$-0.474832\pi$
$877$	21.5839	−	7.01303i	0.728836	−	0.236813i	0.649850	+	0.760063i	$0.274832\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−24.3098	−	17.6621i	−0.819017	−	0.595051i	0.0974139	−	0.995244i	$-0.468943\pi$
$881$	−24.3098	−	17.6621i	−0.819017	−	0.595051i	−0.916431	+	0.400193i	$0.868943\pi$
$882$		0			0
$883$	20.5079	−	28.2268i	0.690147	−	0.949906i	−0.309852	−	0.950785i	$-0.600280\pi$
$883$	20.5079	−	28.2268i	0.690147	−	0.949906i	1.00000		0.000878603i	$0.000279668\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−36.9015	−	11.9900i	−1.23903	−	0.402586i	−0.385054	−	0.922894i	$-0.625817\pi$
$887$	−36.9015	−	11.9900i	−1.23903	−	0.402586i	−0.853979	+	0.520308i	$0.825817\pi$
$888$		0			0
$889$	−0.735413	−	2.26337i	−0.0246650	−	0.0759110i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	1.38616i		−	0.0463861i
$894$		0			0
$895$	−13.6024	+	50.3028i	−0.454678	+	1.68144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.4985			0.583608
$900$		0			0
$901$	68.5923			2.28514
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−56.2201	+	2.81701i	−1.86882	+	0.0936406i
$906$		0			0
$907$			10.0886i			0.334988i	0.985873	+	0.167494i	$0.0535675\pi$
$907$			10.0886i			0.334988i	−0.985873	+	0.167494i	$0.946433\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.87343	+	27.3096i	0.293990	+	0.904808i	0.983559	+	0.180588i	$0.0578001\pi$
$911$	8.87343	+	27.3096i	0.293990	+	0.904808i	−0.689569	+	0.724220i	$0.742200\pi$
$912$		0			0
$913$	17.0677	+	5.54564i	0.564859	+	0.183534i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.7924	−	20.3599i	0.488487	−	0.672344i
$918$		0			0
$919$	1.19370	+	0.867272i	0.0393764	+	0.0286086i	0.607299	−	0.794473i	$-0.292253\pi$
$919$	1.19370	+	0.867272i	0.0393764	+	0.0286086i	−0.567923	+	0.823082i	$0.692253\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.30593	+	1.07416i	−0.108816	+	0.0353564i
$924$		0			0
$925$	−21.5867	+	36.9961i	−0.709767	+	1.21642i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	33.0756	−	24.0308i	1.08517	−	0.788425i	0.106596	−	0.994302i	$-0.466005\pi$
$929$	33.0756	−	24.0308i	1.08517	−	0.788425i	0.978578	+	0.205878i	$0.0660049\pi$
$930$		0			0
$931$	13.4614	+	9.78030i	0.441181	+	0.320537i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−49.2201	+	18.7643i	−1.60967	+	0.613660i
$936$		0			0
$937$	−30.8930	−	10.0378i	−1.00923	−	0.327919i	−0.242683	−	0.970106i	$-0.578028\pi$
$937$	−30.8930	−	10.0378i	−1.00923	−	0.327919i	−0.766549	+	0.642186i	$0.778028\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.36379	−	7.27501i	0.0770575	−	0.237159i	−0.905106	−	0.425185i	$-0.860209\pi$
$941$	2.36379	−	7.27501i	0.0770575	−	0.237159i	0.982164	+	0.188026i	$0.0602090\pi$
$942$		0			0
$943$			1.77716i			0.0578722i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.6280	−	42.1558i	−0.995276	−	1.36988i	−0.928179	−	0.372134i	$-0.878626\pi$
$947$	−30.6280	−	42.1558i	−0.995276	−	1.36988i	−0.0670970	−	0.997746i	$-0.521374\pi$
$948$		0			0
$949$	4.52782			0.146979
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.47321	+	3.40408i	0.0801151	+	0.110269i	0.847194	−	0.531284i	$-0.178290\pi$
$953$	2.47321	+	3.40408i	0.0801151	+	0.110269i	−0.767079	+	0.641553i	$0.778290\pi$
$954$		0			0
$955$	6.39744	+	16.7809i	0.207016	+	0.543018i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.65746	−	8.17881i	0.0858137	−	0.264107i
$960$		0			0
$961$	−1.04615	−	3.21972i	−0.0337468	−	0.103862i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	28.4256	+	35.2679i	0.915052	+	1.13531i
$966$		0			0
$967$	29.7022	−	40.8816i	0.955158	−	1.31466i	0.00596071	−	0.999982i	$-0.498103\pi$
$967$	29.7022	−	40.8816i	0.955158	−	1.31466i	0.949198	−	0.314680i	$-0.101897\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.8283	−	9.32029i	0.411679	−	0.299102i	−0.362602	−	0.931944i	$-0.618112\pi$
$971$	12.8283	−	9.32029i	0.411679	−	0.299102i	0.774281	+	0.632842i	$0.218112\pi$
$972$		0			0
$973$	−14.8412	+	4.82220i	−0.475787	+	0.154593i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.1903	−	13.3836i	1.31780	−	0.428178i	0.436058	−	0.899918i	$-0.356374\pi$
$977$	41.1903	−	13.3836i	1.31780	−	0.428178i	0.881737	+	0.471741i	$0.156374\pi$
$978$		0			0
$979$	−22.8209	+	16.5803i	−0.729358	+	0.529909i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.5553	+	28.2920i	−0.655613	+	0.902374i	−0.999326	−	0.0367008i	$-0.988315\pi$
$983$	−20.5553	+	28.2920i	−0.655613	+	0.902374i	0.343713	+	0.939075i	$0.388315\pi$
$984$		0			0
$985$	−43.2050	−	11.6831i	−1.37662	−	0.372254i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.612002	+	1.88355i	0.0194605	+	0.0598934i
$990$		0			0
$991$	−4.75904	+	14.6468i	−0.151176	+	0.465272i	−0.997753	−	0.0669939i	$-0.978659\pi$
$991$	−4.75904	+	14.6468i	−0.151176	+	0.465272i	0.846577	+	0.532266i	$0.178659\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	39.0292	−	31.4572i	1.23731	−	0.997260i
$996$		0			0
$997$	18.1000	+	24.9124i	0.573231	+	0.788985i	0.992933	−	0.118677i	$-0.0378653\pi$
$997$	18.1000	+	24.9124i	0.573231	+	0.788985i	−0.419702	+	0.907662i	$0.637865\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.469.6		24
3.2	odd	2		300.2.o.a.169.1	✓	24
15.2	even	4		1500.2.m.c.901.2		24
15.8	even	4		1500.2.m.d.901.5		24
15.14	odd	2		1500.2.o.c.349.6		24
25.4	even	10	inner	900.2.w.c.829.6		24
75.2	even	20		7500.2.a.n.1.3		12
75.11	odd	10		7500.2.d.g.1249.22		24
75.14	odd	10		7500.2.d.g.1249.3		24
75.23	even	20		7500.2.a.m.1.10		12
75.29	odd	10		300.2.o.a.229.1	yes	24
75.47	even	20		1500.2.m.c.601.2		24
75.53	even	20		1500.2.m.d.601.5		24
75.71	odd	10		1500.2.o.c.649.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.1	✓	24	3.2	odd	2
300.2.o.a.229.1	yes	24	75.29	odd	10
900.2.w.c.469.6		24	1.1	even	1	trivial
900.2.w.c.829.6		24	25.4	even	10	inner
1500.2.m.c.601.2		24	75.47	even	20
1500.2.m.c.901.2		24	15.2	even	4
1500.2.m.d.601.5		24	75.53	even	20
1500.2.m.d.901.5		24	15.8	even	4
1500.2.o.c.349.6		24	15.14	odd	2
1500.2.o.c.649.6		24	75.71	odd	10
7500.2.a.m.1.10		12	75.23	even	20
7500.2.a.n.1.3		12	75.2	even	20
7500.2.d.g.1249.3		24	75.14	odd	10
7500.2.d.g.1249.22		24	75.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74098 - 1.40321i) q^{5} +1.57893i q^{7} +O(q^{10})\)	\(q+(1.74098 - 1.40321i) q^{5} +1.57893i q^{7} +(-1.19917 - 3.69066i) q^{11} +(0.326475 + 0.106078i) q^{13} +(3.56817 - 4.91117i) q^{17} +(2.98680 + 2.17004i) q^{19} +(-1.32236 + 0.429662i) q^{23} +(1.06200 - 4.88592i) q^{25} +(2.69395 - 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(2.21557 + 2.74888i) q^{35} +(-8.14739 - 2.64725i) q^{37} +(0.394970 - 1.21559i) q^{41} -1.42438i q^{43} +(-0.220691 - 0.303755i) q^{47} +4.50698 q^{49} +(6.64151 + 9.14125i) q^{53} +(-7.26650 - 4.74266i) q^{55} +(3.57899 - 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(0.717236 - 0.273434i) q^{65} +(-6.14771 + 8.46160i) q^{67} +(-8.19220 + 5.95198i) q^{71} +(12.5444 - 4.07594i) q^{73} +(5.82730 - 1.89340i) q^{77} +(11.1640 - 8.11114i) q^{79} +(-2.71826 + 3.74136i) q^{83} +(-0.679305 - 13.5571i) q^{85} +(-2.24626 - 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} +(8.24497 - 0.413129i) q^{95} +(3.55938 + 4.89906i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 24 * q + 2 * q^5	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

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