LMFDB - Embedded newform 1500.2.i.b.557.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.10
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.b.1193.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587422 - 1.62940i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(-2.30987 - 1.91429i) q^{9} +O(q^{10})$	$q+(0.587422 - 1.62940i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(-2.30987 - 1.91429i) q^{9} -3.38918i q^{11} +(-0.729890 + 0.729890i) q^{13} +(-4.39236 + 4.39236i) q^{17} -5.19476i q^{19} +(-3.71542 + 1.74636i) q^{21} +(3.36368 + 3.36368i) q^{23} +(-4.47600 + 2.63920i) q^{27} -6.24434 q^{29} +3.21054 q^{31} +(-5.52233 - 1.99088i) q^{33} +(1.02020 + 1.02020i) q^{37} +(0.760527 + 1.61803i) q^{39} +3.22165i q^{41} +(-1.41400 + 1.41400i) q^{43} +(-8.14896 + 8.14896i) q^{47} -1.38197i q^{49} +(4.57673 + 9.73707i) q^{51} +(-1.42668 - 1.42668i) q^{53} +(-8.46433 - 3.05152i) q^{57} +3.16268 q^{59} -10.2752 q^{61} +(0.663003 + 7.07974i) q^{63} +(-11.1377 - 11.1377i) q^{67} +(7.45668 - 3.50488i) q^{69} -16.4514i q^{71} +(9.57853 - 9.57853i) q^{73} +(-5.68031 + 5.68031i) q^{77} +13.1535i q^{79} +(1.67101 + 8.84351i) q^{81} +(1.91041 + 1.91041i) q^{83} +(-3.66806 + 10.1745i) q^{87} +3.69168 q^{89} +2.44661 q^{91} +(1.88594 - 5.23125i) q^{93} +(-1.81931 - 1.81931i) q^{97} +(-6.48787 + 7.82857i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) $ 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.587422	−	1.62940i	0.339148	−	0.940733i
$3$	0.587422	−	1.62940i	0.339148	−	0.940733i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.67601	−	1.67601i	−0.633473	−	0.633473i	0.315464	−	0.948937i	$-0.397840\pi$
$7$	−1.67601	−	1.67601i	−0.633473	−	0.633473i	−0.948937	+	0.315464i	$0.897840\pi$
$8$		0			0
$9$	−2.30987	−	1.91429i	−0.769957	−	0.638096i
$10$		0			0
$11$		−	3.38918i		−	1.02188i	−0.859617	−	0.510939i	$-0.829298\pi$
$11$		−	3.38918i		−	1.02188i	0.859617	−	0.510939i	$-0.170702\pi$
$12$		0			0
$13$	−0.729890	+	0.729890i	−0.202435	+	0.202435i	−0.801043	−	0.598607i	$-0.795721\pi$
$13$	−0.729890	+	0.729890i	−0.202435	+	0.202435i	0.598607	+	0.801043i	$0.295721\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.39236	+	4.39236i	−1.06530	+	1.06530i	−0.0675905	+	0.997713i	$0.521531\pi$
$17$	−4.39236	+	4.39236i	−1.06530	+	1.06530i	−0.997713	+	0.0675905i	$0.978469\pi$
$18$		0			0
$19$		−	5.19476i		−	1.19176i	−0.803073	−	0.595880i	$-0.796803\pi$
$19$		−	5.19476i		−	1.19176i	0.803073	−	0.595880i	$-0.203197\pi$
$20$		0			0
$21$	−3.71542	+	1.74636i	−0.810770	+	0.381088i
$22$		0			0
$23$	3.36368	+	3.36368i	0.701377	+	0.701377i	0.964706	−	0.263329i	$-0.0848206\pi$
$23$	3.36368	+	3.36368i	0.701377	+	0.701377i	−0.263329	+	0.964706i	$0.584821\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.47600	+	2.63920i	−0.861407	+	0.507915i
$28$		0			0
$29$	−6.24434			−1.15954			−0.579772	−	0.814778i	$-0.696859\pi$
$29$	−6.24434			−1.15954			−0.579772	+	0.814778i	$0.696859\pi$
$30$		0			0
$31$	3.21054			0.576630			0.288315	−	0.957536i	$-0.406905\pi$
$31$	3.21054			0.576630			0.288315	+	0.957536i	$0.406905\pi$
$32$		0			0
$33$	−5.52233	−	1.99088i	−0.961313	−	0.346568i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.02020	+	1.02020i	0.167720	+	0.167720i	0.785976	−	0.618257i	$-0.212161\pi$
$37$	1.02020	+	1.02020i	0.167720	+	0.167720i	−0.618257	+	0.785976i	$0.712161\pi$
$38$		0			0
$39$	0.760527	+	1.61803i	0.121782	+	0.259093i
$40$		0			0
$41$			3.22165i			0.503136i	0.967840	+	0.251568i	$0.0809463\pi$
$41$			3.22165i			0.503136i	−0.967840	+	0.251568i	$0.919054\pi$
$42$		0			0
$43$	−1.41400	+	1.41400i	−0.215633	+	0.215633i	−0.806655	−	0.591022i	$-0.798724\pi$
$43$	−1.41400	+	1.41400i	−0.215633	+	0.215633i	0.591022	+	0.806655i	$0.298724\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.14896	+	8.14896i	−1.18865	+	1.18865i	−0.211207	+	0.977441i	$0.567739\pi$
$47$	−8.14896	+	8.14896i	−1.18865	+	1.18865i	−0.977441	+	0.211207i	$0.932261\pi$
$48$		0			0
$49$		−	1.38197i		−	0.197424i
$50$		0			0
$51$	4.57673	+	9.73707i	0.640870	+	1.36346i
$52$		0			0
$53$	−1.42668	−	1.42668i	−0.195969	−	0.195969i	0.602301	−	0.798269i	$-0.294251\pi$
$53$	−1.42668	−	1.42668i	−0.195969	−	0.195969i	−0.798269	+	0.602301i	$0.794251\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.46433	−	3.05152i	−1.12113	−	0.404184i
$58$		0			0
$59$	3.16268			0.411746			0.205873	−	0.978579i	$-0.433997\pi$
$59$	3.16268			0.411746			0.205873	+	0.978579i	$0.433997\pi$
$60$		0			0
$61$	−10.2752			−1.31560			−0.657801	−	0.753192i	$-0.728513\pi$
$61$	−10.2752			−1.31560			−0.657801	+	0.753192i	$0.728513\pi$
$62$		0			0
$63$	0.663003	+	7.07974i	0.0835305	+	0.891964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−11.1377	−	11.1377i	−1.36069	−	1.36069i	−0.873044	−	0.487641i	$-0.837858\pi$
$67$	−11.1377	−	11.1377i	−1.36069	−	1.36069i	−0.487641	−	0.873044i	$-0.662142\pi$
$68$		0			0
$69$	7.45668	−	3.50488i	0.897679	−	0.421937i
$70$		0			0
$71$		−	16.4514i		−	1.95243i	−0.216812	−	0.976213i	$-0.569566\pi$
$71$		−	16.4514i		−	1.95243i	0.216812	−	0.976213i	$-0.430434\pi$
$72$		0			0
$73$	9.57853	−	9.57853i	1.12108	−	1.12108i	0.129504	−	0.991579i	$-0.458662\pi$
$73$	9.57853	−	9.57853i	1.12108	−	1.12108i	0.991579	−	0.129504i	$-0.0413384\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.68031	+	5.68031i	−0.647332	+	0.647332i
$78$		0			0
$79$			13.1535i			1.47988i	0.672673	+	0.739940i	$0.265146\pi$
$79$			13.1535i			1.47988i	−0.672673	+	0.739940i	$0.734854\pi$
$80$		0			0
$81$	1.67101	+	8.84351i	0.185667	+	0.982613i
$82$		0			0
$83$	1.91041	+	1.91041i	0.209695	+	0.209695i	0.804138	−	0.594443i	$-0.202627\pi$
$83$	1.91041	+	1.91041i	0.209695	+	0.209695i	−0.594443	+	0.804138i	$0.702627\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.66806	+	10.1745i	−0.393258	+	1.09082i
$88$		0			0
$89$	3.69168			0.391317			0.195658	−	0.980672i	$-0.437316\pi$
$89$	3.69168			0.391317			0.195658	+	0.980672i	$0.437316\pi$
$90$		0			0
$91$	2.44661			0.256474
$92$		0			0
$93$	1.88594	−	5.23125i	0.195563	−	0.542455i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.81931	−	1.81931i	−0.184723	−	0.184723i	0.608687	−	0.793410i	$-0.291696\pi$
$97$	−1.81931	−	1.81931i	−0.184723	−	0.184723i	−0.793410	+	0.608687i	$0.791696\pi$
$98$		0			0
$99$	−6.48787	+	7.82857i	−0.652055	+	0.786801i
$100$		0			0
$101$		−	11.6052i		−	1.15476i	−0.816476	−	0.577380i	$-0.804075\pi$
$101$		−	11.6052i		−	1.15476i	0.816476	−	0.577380i	$-0.195925\pi$
$102$		0			0
$103$	−2.96234	+	2.96234i	−0.291888	+	0.291888i	−0.837826	−	0.545938i	$-0.816174\pi$
$103$	−2.96234	+	2.96234i	−0.291888	+	0.291888i	0.545938	+	0.837826i	$0.316174\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.903252	−	0.903252i	0.0873207	−	0.0873207i	−0.662097	−	0.749418i	$-0.730333\pi$
$107$	0.903252	−	0.903252i	0.0873207	−	0.0873207i	0.749418	+	0.662097i	$0.230333\pi$
$108$		0			0
$109$			8.79702i			0.842602i	0.906921	+	0.421301i	$0.138426\pi$
$109$			8.79702i			0.842602i	−0.906921	+	0.421301i	$0.861574\pi$
$110$		0			0
$111$	2.26160	−	1.06302i	0.214661	−	0.100898i
$112$		0			0
$113$	−10.8851	−	10.8851i	−1.02398	−	1.02398i	−0.999705	−	0.0242797i	$-0.992271\pi$
$113$	−10.8851	−	10.8851i	−1.02398	−	1.02398i	−0.0242797	−	0.999705i	$-0.507729\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.08317	−	0.288732i	0.285039	−	0.0266933i
$118$		0			0
$119$	14.7233			1.34968
$120$		0			0
$121$	−0.486560			−0.0442328
$122$		0			0
$123$	5.24934	+	1.89247i	0.473317	+	0.170638i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.42699	+	8.42699i	0.747774	+	0.747774i	0.974061	−	0.226287i	$-0.0726586\pi$
$127$	8.42699	+	8.42699i	0.747774	+	0.747774i	−0.226287	+	0.974061i	$0.572659\pi$
$128$		0			0
$129$	1.47335	+	3.13458i	0.129721	+	0.275984i
$130$		0			0
$131$		−	8.14002i		−	0.711197i	−0.934639	−	0.355598i	$-0.884277\pi$
$131$		−	8.14002i		−	0.711197i	0.934639	−	0.355598i	$-0.115723\pi$
$132$		0			0
$133$	−8.70649	+	8.70649i	−0.754948	+	0.754948i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.1387	+	15.1387i	−1.29339	+	1.29339i	−0.360714	+	0.932677i	$0.617467\pi$
$137$	−15.1387	+	15.1387i	−1.29339	+	1.29339i	−0.932677	+	0.360714i	$0.882533\pi$
$138$		0			0
$139$		−	13.6669i		−	1.15921i	−0.814897	−	0.579606i	$-0.803207\pi$
$139$		−	13.6669i		−	1.15921i	0.814897	−	0.579606i	$-0.196793\pi$
$140$		0			0
$141$	8.49102	+	18.0648i	0.715073	+	1.52133i
$142$		0			0
$143$	2.47373	+	2.47373i	0.206864	+	0.206864i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.25177	−	0.811797i	−0.185723	−	0.0669559i
$148$		0			0
$149$	6.48787			0.531507			0.265754	−	0.964041i	$-0.414379\pi$
$149$	6.48787			0.531507			0.265754	+	0.964041i	$0.414379\pi$
$150$		0			0
$151$	9.20451			0.749053			0.374526	−	0.927216i	$-0.377805\pi$
$151$	9.20451			0.749053			0.374526	+	0.927216i	$0.377805\pi$
$152$		0			0
$153$	18.5540	−	1.73754i	1.50000	−	0.140472i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.93255	−	9.93255i	−0.792704	−	0.792704i	0.189229	−	0.981933i	$-0.439401\pi$
$157$	−9.93255	−	9.93255i	−0.792704	−	0.792704i	−0.981933	+	0.189229i	$0.939401\pi$
$158$		0			0
$159$	−3.16268	+	1.48656i	−0.250817	+	0.117892i
$160$		0			0
$161$		−	11.2751i		−	0.888606i
$162$		0			0
$163$	−13.3828	+	13.3828i	−1.04822	+	1.04822i	−0.0494450	+	0.998777i	$0.515745\pi$
$163$	−13.3828	+	13.3828i	−1.04822	+	1.04822i	−0.998777	+	0.0494450i	$0.984255\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.1412	−	11.1412i	0.862135	−	0.862135i	−0.129450	−	0.991586i	$-0.541321\pi$
$167$	11.1412	−	11.1412i	0.862135	−	0.862135i	0.991586	+	0.129450i	$0.0413213\pi$
$168$		0			0
$169$			11.9345i			0.918040i
$170$		0			0
$171$	−9.94427	+	11.9992i	−0.760457	+	0.917604i
$172$		0			0
$173$	−3.57992	−	3.57992i	−0.272176	−	0.272176i	0.557799	−	0.829976i	$-0.311646\pi$
$173$	−3.57992	−	3.57992i	−0.272176	−	0.272176i	−0.829976	+	0.557799i	$0.811646\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.85783	−	5.15326i	0.139643	−	0.387343i
$178$		0			0
$179$	−14.8098			−1.10694			−0.553469	−	0.832870i	$-0.686696\pi$
$179$	−14.8098			−1.10694			−0.553469	+	0.832870i	$0.686696\pi$
$180$		0			0
$181$	−8.07439			−0.600165			−0.300082	−	0.953913i	$-0.597014\pi$
$181$	−8.07439			−0.600165			−0.300082	+	0.953913i	$0.597014\pi$
$182$		0			0
$183$	−6.03587	+	16.7424i	−0.446184	+	1.23763i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	14.8865	+	14.8865i	1.08861	+	1.08861i
$188$		0			0
$189$	11.9252	+	3.07850i	0.867429	+	0.223928i
$190$		0			0
$191$		−	5.11733i		−	0.370277i	−0.982712	−	0.185138i	$-0.940727\pi$
$191$		−	5.11733i		−	0.370277i	0.982712	−	0.185138i	$-0.0592733\pi$
$192$		0			0
$193$	7.84708	−	7.84708i	0.564845	−	0.564845i	−0.365835	−	0.930680i	$-0.619216\pi$
$193$	7.84708	−	7.84708i	0.564845	−	0.564845i	0.930680	+	0.365835i	$0.119216\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.8242	−	13.8242i	0.984933	−	0.984933i	−0.0149551	−	0.999888i	$-0.504761\pi$
$197$	13.8242	−	13.8242i	0.984933	−	0.984933i	0.999888	+	0.0149551i	$0.00476053\pi$
$198$		0			0
$199$		−	6.77368i		−	0.480174i	−0.970751	−	0.240087i	$-0.922824\pi$
$199$		−	6.77368i		−	0.480174i	0.970751	−	0.240087i	$-0.0771759\pi$
$200$		0			0
$201$	−24.6902	+	11.6052i	−1.74152	+	0.818567i
$202$		0			0
$203$	10.4656	+	10.4656i	0.734540	+	0.734540i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.33062	−	14.2087i	−0.0924843	−	0.987575i
$208$		0			0
$209$	−17.6060			−1.21783
$210$		0			0
$211$	−3.75926			−0.258798			−0.129399	−	0.991593i	$-0.541305\pi$
$211$	−3.75926			−0.258798			−0.129399	+	0.991593i	$0.541305\pi$
$212$		0			0
$213$	−26.8059	−	9.66394i	−1.83671	−	0.662162i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.38091	−	5.38091i	−0.365280	−	0.365280i
$218$		0			0
$219$	−9.98060	−	21.2339i	−0.674426	−	1.43485i
$220$		0			0
$221$		−	6.41188i		−	0.431310i
$222$		0			0
$223$	19.8357	−	19.8357i	1.32829	−	1.32829i	0.421436	−	0.906858i	$-0.361526\pi$
$223$	19.8357	−	19.8357i	1.32829	−	1.32829i	0.906858	−	0.421436i	$-0.138474\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.43891	−	2.43891i	0.161876	−	0.161876i	−0.621521	−	0.783397i	$-0.713485\pi$
$227$	2.43891	−	2.43891i	0.161876	−	0.161876i	0.783397	+	0.621521i	$0.213485\pi$
$228$		0			0
$229$		−	13.4542i		−	0.889077i	−0.895760	−	0.444538i	$-0.853368\pi$
$229$		−	13.4542i		−	0.889077i	0.895760	−	0.444538i	$-0.146632\pi$
$230$		0			0
$231$	5.91874	+	12.5922i	0.389425	+	0.828508i
$232$		0			0
$233$	−19.0392	−	19.0392i	−1.24730	−	1.24730i	−0.956909	−	0.290387i	$-0.906216\pi$
$233$	−19.0392	−	19.0392i	−1.24730	−	1.24730i	−0.290387	−	0.956909i	$-0.593784\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	21.4322	+	7.72663i	1.39217	+	0.501899i
$238$		0			0
$239$	7.68702			0.497232			0.248616	−	0.968602i	$-0.420024\pi$
$239$	7.68702			0.497232			0.248616	+	0.968602i	$0.420024\pi$
$240$		0			0
$241$	18.2181			1.17353			0.586766	−	0.809757i	$-0.300401\pi$
$241$	18.2181			1.17353			0.586766	+	0.809757i	$0.300401\pi$
$242$		0			0
$243$	15.3912	+	2.47214i	0.987345	+	0.158588i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.79161	+	3.79161i	0.241254	+	0.241254i
$248$		0			0
$249$	4.23503	−	1.99060i	0.268384	−	0.126149i
$250$		0			0
$251$		−	1.62963i		−	0.102861i	−0.998677	−	0.0514306i	$-0.983622\pi$
$251$		−	1.62963i		−	0.102861i	0.998677	−	0.0514306i	$-0.0163781\pi$
$252$		0			0
$253$	11.4001	−	11.4001i	0.716721	−	0.716721i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.8672	−	13.8672i	0.865014	−	0.865014i	−0.126901	−	0.991915i	$-0.540503\pi$
$257$	13.8672	−	13.8672i	0.865014	−	0.865014i	0.991915	+	0.126901i	$0.0405031\pi$
$258$		0			0
$259$		−	3.41973i		−	0.212492i
$260$		0			0
$261$	14.4236	+	11.9535i	0.892800	+	0.739901i
$262$		0			0
$263$	11.6330	+	11.6330i	0.717321	+	0.717321i	0.968056	−	0.250735i	$-0.0806723\pi$
$263$	11.6330	+	11.6330i	0.717321	+	0.717321i	−0.250735	+	0.968056i	$0.580672\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.16857	−	6.01521i	0.132714	−	0.368125i
$268$		0			0
$269$	−28.3471			−1.72836			−0.864178	−	0.503187i	$-0.832161\pi$
$269$	−28.3471			−1.72836			−0.864178	+	0.503187i	$0.832161\pi$
$270$		0			0
$271$	5.77503			0.350808			0.175404	−	0.984497i	$-0.443877\pi$
$271$	5.77503			0.350808			0.175404	+	0.984497i	$0.443877\pi$
$272$		0			0
$273$	1.43719	−	3.98650i	0.0869828	−	0.241274i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	12.2271	+	12.2271i	0.734656	+	0.734656i	0.971538	−	0.236882i	$-0.0761256\pi$
$277$	12.2271	+	12.2271i	0.734656	+	0.734656i	−0.236882	+	0.971538i	$0.576126\pi$
$278$		0			0
$279$	−7.41593	−	6.14590i	−0.443980	−	0.367945i
$280$		0			0
$281$		−	22.1392i		−	1.32072i	−0.750951	−	0.660358i	$-0.770405\pi$
$281$		−	22.1392i		−	1.32072i	0.750951	−	0.660358i	$-0.229595\pi$
$282$		0			0
$283$	−8.37111	+	8.37111i	−0.497611	+	0.497611i	−0.910693	−	0.413083i	$-0.864452\pi$
$283$	−8.37111	+	8.37111i	−0.497611	+	0.497611i	0.413083	+	0.910693i	$0.364452\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.39952	−	5.39952i	0.318723	−	0.318723i
$288$		0			0
$289$		−	21.5856i		−	1.26974i
$290$		0			0
$291$	−4.03309	+	1.89568i	−0.236424	+	0.111127i
$292$		0			0
$293$	3.69239	+	3.69239i	0.215712	+	0.215712i	0.806688	−	0.590977i	$-0.201258\pi$
$293$	3.69239	+	3.69239i	0.215712	+	0.215712i	−0.590977	+	0.806688i	$0.701258\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	8.94474	+	15.1700i	0.519027	+	0.880252i
$298$		0			0
$299$	−4.91024			−0.283966
$300$		0			0
$301$	4.73976			0.273195
$302$		0			0
$303$	−18.9095	−	6.81715i	−1.08632	−	0.391635i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−3.20390	−	3.20390i	−0.182856	−	0.182856i	0.609743	−	0.792599i	$-0.291273\pi$
$307$	−3.20390	−	3.20390i	−0.182856	−	0.182856i	−0.792599	+	0.609743i	$0.791273\pi$
$308$		0			0
$309$	3.08669	+	6.56698i	0.175596	+	0.373582i
$310$		0			0
$311$		−	14.4433i		−	0.819006i	−0.912309	−	0.409503i	$-0.865702\pi$
$311$		−	14.4433i		−	0.819006i	0.912309	−	0.409503i	$-0.134298\pi$
$312$		0			0
$313$	−11.2479	+	11.2479i	−0.635768	+	0.635768i	−0.949509	−	0.313741i	$-0.898418\pi$
$313$	−11.2479	+	11.2479i	−0.635768	+	0.635768i	0.313741	+	0.949509i	$0.398418\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.9655	−	17.9655i	1.00904	−	1.00904i	0.00908410	−	0.999959i	$-0.497108\pi$
$317$	17.9655	−	17.9655i	1.00904	−	1.00904i	0.999959	−	0.00908410i	$-0.00289160\pi$
$318$		0			0
$319$			21.1632i			1.18491i
$320$		0			0
$321$	−0.941167	−	2.00235i	−0.0525308	−	0.111760i
$322$		0			0
$323$	22.8173	+	22.8173i	1.26959	+	1.26959i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	14.3338	+	5.16756i	0.792663	+	0.285767i
$328$		0			0
$329$	27.3155			1.50595
$330$		0			0
$331$	−22.2428			−1.22257			−0.611287	−	0.791409i	$-0.709348\pi$
$331$	−22.2428			−1.22257			−0.611287	+	0.791409i	$0.709348\pi$
$332$		0			0
$333$	−0.403574	−	4.30948i	−0.0221157	−	0.236158i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	24.0821	+	24.0821i	1.31183	+	1.31183i	0.920063	+	0.391770i	$0.128137\pi$
$337$	24.0821	+	24.0821i	1.31183	+	1.31183i	0.391770	+	0.920063i	$0.371863\pi$
$338$		0			0
$339$	−24.1303	+	11.3420i	−1.31058	+	0.616014i
$340$		0			0
$341$		−	10.8811i		−	0.589245i
$342$		0			0
$343$	−14.0483	+	14.0483i	−0.758536	+	0.758536i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.4568	−	14.4568i	0.776082	−	0.776082i	−0.203080	−	0.979162i	$-0.565095\pi$
$347$	14.4568	−	14.4568i	0.776082	−	0.776082i	0.979162	+	0.203080i	$0.0650951\pi$
$348$		0			0
$349$		−	17.0804i		−	0.914294i	−0.889391	−	0.457147i	$-0.848871\pi$
$349$		−	17.0804i		−	0.914294i	0.889391	−	0.457147i	$-0.151129\pi$
$350$		0			0
$351$	1.34066	−	5.19332i	0.0715593	−	0.277199i
$352$		0			0
$353$	−7.22927	−	7.22927i	−0.384775	−	0.384775i	0.488044	−	0.872819i	$-0.337711\pi$
$353$	−7.22927	−	7.22927i	−0.384775	−	0.384775i	−0.872819	+	0.488044i	$0.837711\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.64879	−	23.9901i	0.457742	−	1.26969i
$358$		0			0
$359$	19.1391			1.01012			0.505060	−	0.863084i	$-0.331470\pi$
$359$	19.1391			1.01012			0.505060	+	0.863084i	$0.331470\pi$
$360$		0			0
$361$	−7.98558			−0.420293
$362$		0			0
$363$	−0.285816	+	0.792800i	−0.0150015	+	0.0416112i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−18.9167	−	18.9167i	−0.987443	−	0.987443i	0.0124792	−	0.999922i	$-0.496028\pi$
$367$	−18.9167	−	18.9167i	−0.987443	−	0.987443i	−0.999922	+	0.0124792i	$0.996028\pi$
$368$		0			0
$369$	6.16716	−	7.44158i	0.321049	−	0.387393i
$370$		0			0
$371$			4.78225i			0.248282i
$372$		0			0
$373$	11.3056	−	11.3056i	0.585381	−	0.585381i	−0.350996	−	0.936377i	$-0.614157\pi$
$373$	11.3056	−	11.3056i	0.585381	−	0.585381i	0.936377	+	0.350996i	$0.114157\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.55768	−	4.55768i	0.234733	−	0.234733i
$378$		0			0
$379$			4.31732i			0.221766i	0.993833	+	0.110883i	$0.0353679\pi$
$379$			4.31732i			0.221766i	−0.993833	+	0.110883i	$0.964632\pi$
$380$		0			0
$381$	18.6811	−	8.78071i	0.957062	−	0.449850i
$382$		0			0
$383$	−0.801078	−	0.801078i	−0.0409332	−	0.0409332i	0.686344	−	0.727277i	$-0.259214\pi$
$383$	−0.801078	−	0.801078i	−0.0409332	−	0.0409332i	−0.727277	+	0.686344i	$0.759214\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.97295	−	0.559354i	0.303622	−	0.0284336i
$388$		0			0
$389$	−17.0526			−0.864599			−0.432300	−	0.901730i	$-0.642298\pi$
$389$	−17.0526			−0.864599			−0.432300	+	0.901730i	$0.642298\pi$
$390$		0			0
$391$	−29.5490			−1.49436
$392$		0			0
$393$	−13.2633	−	4.78163i	−0.669046	−	0.241201i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.33101	+	9.33101i	0.468310	+	0.468310i	0.901367	−	0.433057i	$-0.142565\pi$
$397$	9.33101	+	9.33101i	0.468310	+	0.468310i	−0.433057	+	0.901367i	$0.642565\pi$
$398$		0			0
$399$	9.07195	+	19.3007i	0.454165	+	0.966244i
$400$		0			0
$401$		−	12.6512i		−	0.631770i	−0.948797	−	0.315885i	$-0.897699\pi$
$401$		−	12.6512i		−	0.631770i	0.948797	−	0.315885i	$-0.102301\pi$
$402$		0			0
$403$	−2.34334	+	2.34334i	−0.116730	+	0.116730i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.45764	−	3.45764i	0.171389	−	0.171389i
$408$		0			0
$409$			8.72179i			0.431265i	0.976475	+	0.215632i	$0.0691813\pi$
$409$			8.72179i			0.431265i	−0.976475	+	0.215632i	$0.930819\pi$
$410$		0			0
$411$	15.7742	+	33.5599i	0.778084	+	1.65539i
$412$		0			0
$413$	−5.30069	−	5.30069i	−0.260830	−	0.260830i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−22.2688	−	8.02824i	−1.09051	−	0.393144i
$418$		0			0
$419$	31.4904			1.53841			0.769203	−	0.639004i	$-0.220653\pi$
$419$	31.4904			1.53841			0.769203	+	0.639004i	$0.220653\pi$
$420$		0			0
$421$	33.4864			1.63203			0.816014	−	0.578032i	$-0.196179\pi$
$421$	33.4864			1.63203			0.816014	+	0.578032i	$0.196179\pi$
$422$		0			0
$423$	34.4225	−	3.22359i	1.67368	−	0.156737i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	17.2213	+	17.2213i	0.833399	+	0.833399i
$428$		0			0
$429$	5.48381	−	2.57757i	0.264761	−	0.124446i
$430$		0			0
$431$			29.4346i			1.41781i	0.705302	+	0.708907i	$0.250812\pi$
$431$			29.4346i			1.41781i	−0.705302	+	0.708907i	$0.749188\pi$
$432$		0			0
$433$	−15.1389	+	15.1389i	−0.727527	+	0.727527i	−0.970127	−	0.242599i	$-0.922000\pi$
$433$	−15.1389	+	15.1389i	−0.727527	+	0.727527i	0.242599	+	0.970127i	$0.422000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.4735	−	17.4735i	0.835873	−	0.835873i
$438$		0			0
$439$			23.1844i			1.10653i	0.833006	+	0.553265i	$0.186618\pi$
$439$			23.1844i			1.10653i	−0.833006	+	0.553265i	$0.813382\pi$
$440$		0			0
$441$	−2.64548	+	3.19216i	−0.125975	+	0.152008i
$442$		0			0
$443$	−3.22496	−	3.22496i	−0.153223	−	0.153223i	0.626333	−	0.779556i	$-0.284555\pi$
$443$	−3.22496	−	3.22496i	−0.153223	−	0.153223i	−0.779556	+	0.626333i	$0.784555\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	3.81112	−	10.5713i	0.180260	−	0.500006i
$448$		0			0
$449$	−29.3543			−1.38531			−0.692657	−	0.721267i	$-0.743560\pi$
$449$	−29.3543			−1.38531			−0.692657	+	0.721267i	$0.743560\pi$
$450$		0			0
$451$	10.9187			0.514144
$452$		0			0
$453$	5.40693	−	14.9978i	0.254040	−	0.704659i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−25.4123	−	25.4123i	−1.18874	−	1.18874i	−0.977417	−	0.211321i	$-0.932223\pi$
$457$	−25.4123	−	25.4123i	−1.18874	−	1.18874i	−0.211321	−	0.977417i	$-0.567777\pi$
$458$		0			0
$459$	8.06789	−	31.2525i	0.376577	−	1.45874i
$460$		0			0
$461$			20.2905i			0.945024i	0.881324	+	0.472512i	$0.156653\pi$
$461$			20.2905i			0.945024i	−0.881324	+	0.472512i	$0.843347\pi$
$462$		0			0
$463$	−13.9519	+	13.9519i	−0.648400	+	0.648400i	−0.952606	−	0.304206i	$-0.901609\pi$
$463$	−13.9519	+	13.9519i	−0.648400	+	0.648400i	0.304206	+	0.952606i	$0.401609\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.07171	−	1.07171i	0.0495930	−	0.0495930i	−0.681875	−	0.731468i	$-0.738835\pi$
$467$	1.07171	−	1.07171i	0.0495930	−	0.0495930i	0.731468	+	0.681875i	$0.238835\pi$
$468$		0			0
$469$			37.3338i			1.72391i
$470$		0			0
$471$	−22.0187	+	10.3495i	−1.01457	+	0.476878i
$472$		0			0
$473$	4.79230	+	4.79230i	0.220350	+	0.220350i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.564369	+	6.02650i	0.0258407	+	0.275935i
$478$		0			0
$479$	27.4385			1.25370			0.626848	−	0.779142i	$-0.284345\pi$
$479$	27.4385			1.25370			0.626848	+	0.779142i	$0.284345\pi$
$480$		0			0
$481$	−1.48926			−0.0679046
$482$		0			0
$483$	−18.3717	−	6.62327i	−0.835941	−	0.301369i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.84607	+	4.84607i	0.219596	+	0.219596i	0.808328	−	0.588732i	$-0.200373\pi$
$487$	4.84607	+	4.84607i	0.219596	+	0.219596i	−0.588732	+	0.808328i	$0.700373\pi$
$488$		0			0
$489$	13.9445	+	29.6673i	0.630594	+	1.34160i
$490$		0			0
$491$		−	30.9142i		−	1.39514i	−0.716518	−	0.697569i	$-0.754265\pi$
$491$		−	30.9142i		−	1.39514i	0.716518	−	0.697569i	$-0.245735\pi$
$492$		0			0
$493$	27.4274	−	27.4274i	1.23527	−	1.23527i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.5728	+	27.5728i	−1.23681	+	1.23681i
$498$		0			0
$499$		−	4.33310i		−	0.193976i	−0.995286	−	0.0969881i	$-0.969079\pi$
$499$		−	4.33310i		−	0.193976i	0.995286	−	0.0969881i	$-0.0309209\pi$
$500$		0			0
$501$	−11.6089	−	24.6981i	−0.518648	−	1.10343i
$502$		0			0
$503$	9.81340	+	9.81340i	0.437558	+	0.437558i	0.891189	−	0.453632i	$-0.149872\pi$
$503$	9.81340	+	9.81340i	0.437558	+	0.437558i	−0.453632	+	0.891189i	$0.649872\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	19.4461	+	7.01060i	0.863631	+	0.311352i
$508$		0			0
$509$	3.45628			0.153197			0.0765986	−	0.997062i	$-0.475594\pi$
$509$	3.45628			0.153197			0.0765986	+	0.997062i	$0.475594\pi$
$510$		0			0
$511$	−32.1075			−1.42035
$512$		0			0
$513$	13.7100	+	23.2518i	0.605313	+	1.02659i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	27.6183	+	27.6183i	1.21465	+	1.21465i
$518$		0			0
$519$	−7.93604	+	3.73019i	−0.348354	+	0.163737i
$520$		0			0
$521$			19.8876i			0.871291i	0.900118	+	0.435646i	$0.143480\pi$
$521$			19.8876i			0.871291i	−0.900118	+	0.435646i	$0.856520\pi$
$522$		0			0
$523$	13.9917	−	13.9917i	0.611815	−	0.611815i	−0.331604	−	0.943419i	$-0.607590\pi$
$523$	13.9917	−	13.9917i	0.611815	−	0.611815i	0.943419	+	0.331604i	$0.107590\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.1018	+	14.1018i	−0.614286	+	0.614286i
$528$		0			0
$529$		−	0.371266i		−	0.0161420i
$530$		0			0
$531$	−7.30538	−	6.05428i	−0.317027	−	0.262733i
$532$		0			0
$533$	−2.35145	−	2.35145i	−0.101852	−	0.101852i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.69961	+	24.1311i	−0.375416	+	1.04133i
$538$		0			0
$539$	−4.68374			−0.201743
$540$		0			0
$541$	−26.8910			−1.15614			−0.578068	−	0.815989i	$-0.696193\pi$
$541$	−26.8910			−1.15614			−0.578068	+	0.815989i	$0.696193\pi$
$542$		0			0
$543$	−4.74308	+	13.1564i	−0.203545	+	0.564595i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.272821	+	0.272821i	0.0116650	+	0.0116650i	0.712915	−	0.701250i	$-0.247374\pi$
$547$	0.272821	+	0.272821i	0.0116650	+	0.0116650i	−0.701250	+	0.712915i	$0.747374\pi$
$548$		0			0
$549$	23.7343	+	19.6697i	1.01296	+	0.839480i
$550$		0			0
$551$			32.4379i			1.38190i
$552$		0			0
$553$	22.0454	−	22.0454i	0.937464	−	0.937464i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.9654	−	16.9654i	0.718845	−	0.718845i	−0.249523	−	0.968369i	$-0.580274\pi$
$557$	16.9654	−	16.9654i	0.718845	−	0.718845i	0.968369	+	0.249523i	$0.0802740\pi$
$558$		0			0
$559$		−	2.06413i		−	0.0873032i
$560$		0			0
$561$	33.0007	−	15.5114i	1.39329	−	0.654891i
$562$		0			0
$563$	−31.1856	−	31.1856i	−1.31432	−	1.31432i	−0.918200	−	0.396117i	$-0.870358\pi$
$563$	−31.1856	−	31.1856i	−1.31432	−	1.31432i	−0.396117	−	0.918200i	$-0.629642\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.0212	−	17.6225i	0.504843	−	0.740074i
$568$		0			0
$569$	−33.2298			−1.39307			−0.696533	−	0.717525i	$-0.745275\pi$
$569$	−33.2298			−1.39307			−0.696533	+	0.717525i	$0.745275\pi$
$570$		0			0
$571$	41.0773			1.71903			0.859515	−	0.511110i	$-0.170765\pi$
$571$	41.0773			1.71903			0.859515	+	0.511110i	$0.170765\pi$
$572$		0			0
$573$	−8.33816	−	3.00603i	−0.348331	−	0.125579i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−31.9917	−	31.9917i	−1.33183	−	1.33183i	−0.903732	−	0.428098i	$-0.859184\pi$
$577$	−31.9917	−	31.9917i	−1.33183	−	1.33183i	−0.428098	−	0.903732i	$-0.640816\pi$
$578$		0			0
$579$	−8.17646	−	17.3956i	−0.339802	−	0.722935i
$580$		0			0
$581$		−	6.40374i		−	0.265672i
$582$		0			0
$583$	−4.83526	+	4.83526i	−0.200256	+	0.200256i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.1334	+	22.1334i	−0.913543	+	0.913543i	−0.996549	−	0.0830059i	$-0.973548\pi$
$587$	−22.1334	+	22.1334i	−0.913543	+	0.913543i	0.0830059	+	0.996549i	$0.473548\pi$
$588$		0			0
$589$		−	16.6780i		−	0.687205i
$590$		0			0
$591$	−14.4045	−	30.6457i	−0.592521	−	1.26060i
$592$		0			0
$593$	−13.3487	−	13.3487i	−0.548165	−	0.548165i	0.377745	−	0.925910i	$-0.376700\pi$
$593$	−13.3487	−	13.3487i	−0.548165	−	0.548165i	−0.925910	+	0.377745i	$0.876700\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.0370	−	3.97901i	−0.451715	−	0.162850i
$598$		0			0
$599$	36.1207			1.47585			0.737925	−	0.674883i	$-0.235806\pi$
$599$	36.1207			1.47585			0.737925	+	0.674883i	$0.235806\pi$
$600$		0			0
$601$	20.3591			0.830467			0.415233	−	0.909715i	$-0.363700\pi$
$601$	20.3591			0.830467			0.415233	+	0.909715i	$0.363700\pi$
$602$		0			0
$603$	4.40589	+	47.0474i	0.179422	+	1.91592i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−13.6754	−	13.6754i	−0.555066	−	0.555066i	0.372832	−	0.927899i	$-0.378387\pi$
$607$	−13.6754	−	13.6754i	−0.555066	−	0.555066i	−0.927899	+	0.372832i	$0.878387\pi$
$608$		0			0
$609$	23.2003	−	10.9049i	0.940125	−	0.441888i
$610$		0			0
$611$		−	11.8957i		−	0.481248i
$612$		0			0
$613$	−7.25452	+	7.25452i	−0.293007	+	0.293007i	−0.838267	−	0.545260i	$-0.816431\pi$
$613$	−7.25452	+	7.25452i	−0.293007	+	0.293007i	0.545260	+	0.838267i	$0.316431\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.1068	+	22.1068i	−0.889986	+	0.889986i	−0.994521	−	0.104535i	$-0.966665\pi$
$617$	−22.1068	+	22.1068i	−0.889986	+	0.889986i	0.104535	+	0.994521i	$0.466665\pi$
$618$		0			0
$619$		−	16.9399i		−	0.680872i	−0.940268	−	0.340436i	$-0.889425\pi$
$619$		−	16.9399i		−	0.680872i	0.940268	−	0.340436i	$-0.110575\pi$
$620$		0			0
$621$	−23.9333	−	6.17842i	−0.960410	−	0.247931i
$622$		0			0
$623$	−6.18730	−	6.18730i	−0.247889	−	0.247889i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−10.3422	+	28.6872i	−0.413026	+	1.14566i
$628$		0			0
$629$	−8.96216			−0.357345
$630$		0			0
$631$	36.6867			1.46047			0.730237	−	0.683194i	$-0.239410\pi$
$631$	36.6867			1.46047			0.730237	+	0.683194i	$0.239410\pi$
$632$		0			0
$633$	−2.20827	+	6.12532i	−0.0877709	+	0.243460i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.00868	+	1.00868i	0.0399655	+	0.0399655i
$638$		0			0
$639$	−31.4928	+	38.0007i	−1.24584	+	1.50328i
$640$		0			0
$641$		−	9.91349i		−	0.391560i	−0.980648	−	0.195780i	$-0.937276\pi$
$641$		−	9.91349i		−	0.391560i	0.980648	−	0.195780i	$-0.0627238\pi$
$642$		0			0
$643$	−2.45098	+	2.45098i	−0.0966571	+	0.0966571i	−0.753782	−	0.657125i	$-0.771772\pi$
$643$	−2.45098	+	2.45098i	−0.0966571	+	0.0966571i	0.657125	+	0.753782i	$0.271772\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.2971	+	10.2971i	−0.404822	+	0.404822i	−0.879928	−	0.475106i	$-0.842410\pi$
$647$	−10.2971	+	10.2971i	−0.404822	+	0.404822i	0.475106	+	0.879928i	$0.342410\pi$
$648$		0			0
$649$		−	10.7189i		−	0.420754i
$650$		0			0
$651$	−11.9285	+	5.60677i	−0.467515	+	0.219747i
$652$		0			0
$653$	5.94781	+	5.94781i	0.232756	+	0.232756i	0.813842	−	0.581086i	$-0.197372\pi$
$653$	5.94781	+	5.94781i	0.232756	+	0.232756i	−0.581086	+	0.813842i	$0.697372\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−40.4612	+	3.78911i	−1.57854	+	0.147827i
$658$		0			0
$659$	−2.80819			−0.109392			−0.0546958	−	0.998503i	$-0.517419\pi$
$659$	−2.80819			−0.109392			−0.0546958	+	0.998503i	$0.517419\pi$
$660$		0			0
$661$	10.2070			0.397006			0.198503	−	0.980100i	$-0.436392\pi$
$661$	10.2070			0.397006			0.198503	+	0.980100i	$0.436392\pi$
$662$		0			0
$663$	−10.4475	−	3.76648i	−0.405747	−	0.146278i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.0040	−	21.0040i	−0.813278	−	0.813278i
$668$		0			0
$669$	−20.6683	−	43.9721i	−0.799081	−	1.70006i
$670$		0			0
$671$			34.8245i			1.34438i
$672$		0			0
$673$	−29.2490	+	29.2490i	−1.12747	+	1.12747i	−0.136878	+	0.990588i	$0.543707\pi$
$673$	−29.2490	+	29.2490i	−1.12747	+	1.12747i	−0.990588	+	0.136878i	$0.956293\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.6023	−	17.6023i	0.676512	−	0.676512i	−0.282697	−	0.959209i	$-0.591229\pi$
$677$	17.6023	−	17.6023i	0.676512	−	0.676512i	0.959209	+	0.282697i	$0.0912292\pi$
$678$		0			0
$679$			6.09838i			0.234035i
$680$		0			0
$681$	−2.54129	−	5.40663i	−0.0973823	−	0.207182i
$682$		0			0
$683$	18.7136	+	18.7136i	0.716056	+	0.716056i	0.967795	−	0.251739i	$-0.0810026\pi$
$683$	18.7136	+	18.7136i	0.716056	+	0.716056i	−0.251739	+	0.967795i	$0.581003\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−21.9222	−	7.90328i	−0.836384	−	0.301529i
$688$		0			0
$689$	2.08263			0.0793419
$690$		0			0
$691$	−12.6595			−0.481591			−0.240795	−	0.970576i	$-0.577408\pi$
$691$	−12.6595			−0.481591			−0.240795	+	0.970576i	$0.577408\pi$
$692$		0			0
$693$	23.9945	−	2.24704i	0.911477	−	0.0853579i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−14.1506	−	14.1506i	−0.535993	−	0.535993i
$698$		0			0
$699$	−42.2064	+	19.8383i	−1.59639	+	0.750354i
$700$		0			0
$701$			2.72331i			0.102858i	0.998677	+	0.0514290i	$0.0163776\pi$
$701$			2.72331i			0.102858i	−0.998677	+	0.0514290i	$0.983622\pi$
$702$		0			0
$703$	5.29969	−	5.29969i	0.199882	−	0.199882i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.4504	+	19.4504i	−0.731509	+	0.731509i
$708$		0			0
$709$		−	10.4686i		−	0.393156i	−0.980488	−	0.196578i	$-0.937017\pi$
$709$		−	10.4686i		−	0.393156i	0.980488	−	0.196578i	$-0.0629830\pi$
$710$		0			0
$711$	25.1795	−	30.3828i	0.944305	−	1.13944i
$712$		0			0
$713$	10.7992	+	10.7992i	0.404435	+	0.404435i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.51552	−	12.5252i	0.168635	−	0.467762i
$718$		0			0
$719$	−30.5817			−1.14051			−0.570253	−	0.821469i	$-0.693155\pi$
$719$	−30.5817			−1.14051			−0.570253	+	0.821469i	$0.693155\pi$
$720$		0			0
$721$	9.92985			0.369807
$722$		0			0
$723$	10.7017	−	29.6845i	0.398001	−	1.10398i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	9.30986	+	9.30986i	0.345283	+	0.345283i	0.858349	−	0.513066i	$-0.171490\pi$
$727$	9.30986	+	9.30986i	0.345283	+	0.345283i	−0.513066	+	0.858349i	$0.671490\pi$
$728$		0			0
$729$	13.0692	−	23.6262i	0.484045	−	0.875043i
$730$		0			0
$731$		−	12.4216i		−	0.459429i
$732$		0			0
$733$	−22.3320	+	22.3320i	−0.824850	+	0.824850i	−0.986799	−	0.161949i	$-0.948222\pi$
$733$	−22.3320	+	22.3320i	−0.824850	+	0.824850i	0.161949	+	0.986799i	$0.448222\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−37.7477	+	37.7477i	−1.39045	+	1.39045i
$738$		0			0
$739$		−	20.9382i		−	0.770226i	−0.922869	−	0.385113i	$-0.874162\pi$
$739$		−	20.9382i		−	0.770226i	0.922869	−	0.385113i	$-0.125838\pi$
$740$		0			0
$741$	8.40531	−	3.95076i	0.308777	−	0.145135i
$742$		0			0
$743$	7.98872	+	7.98872i	0.293078	+	0.293078i	0.838295	−	0.545217i	$-0.183553\pi$
$743$	7.98872	+	7.98872i	0.293078	+	0.293078i	−0.545217	+	0.838295i	$0.683553\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.755727	−	8.06987i	−0.0276506	−	0.295261i
$748$		0			0
$749$	−3.02772			−0.110631
$750$		0			0
$751$	−8.91874			−0.325450			−0.162725	−	0.986671i	$-0.552028\pi$
$751$	−8.91874			−0.325450			−0.162725	+	0.986671i	$0.552028\pi$
$752$		0			0
$753$	−2.65531	−	0.957279i	−0.0967649	−	0.0348852i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	7.08933	+	7.08933i	0.257666	+	0.257666i	0.824104	−	0.566438i	$-0.191679\pi$
$757$	7.08933	+	7.08933i	0.257666	+	0.257666i	−0.566438	+	0.824104i	$0.691679\pi$
$758$		0			0
$759$	−11.8787	−	25.2720i	−0.431168	−	0.917317i
$760$		0			0
$761$			53.1546i			1.92685i	0.267975	+	0.963426i	$0.413645\pi$
$761$			53.1546i			1.92685i	−0.267975	+	0.963426i	$0.586355\pi$
$762$		0			0
$763$	14.7439	−	14.7439i	0.533766	−	0.533766i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.30841	+	2.30841i	−0.0833518	+	0.0833518i
$768$		0			0
$769$			36.2547i			1.30738i	0.756763	+	0.653690i	$0.226780\pi$
$769$			36.2547i			1.30738i	−0.756763	+	0.653690i	$0.773220\pi$
$770$		0			0
$771$	−14.4493	−	30.7411i	−0.520379	−	1.10712i
$772$		0			0
$773$	−15.9613	−	15.9613i	−0.574090	−	0.574090i	0.359179	−	0.933269i	$-0.383057\pi$
$773$	−15.9613	−	15.9613i	−0.574090	−	0.574090i	−0.933269	+	0.359179i	$0.883057\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.57210	−	2.00882i	−0.199898	−	0.0720662i
$778$		0			0
$779$	16.7357			0.599618
$780$		0			0
$781$	−55.7569			−1.99514
$782$		0			0
$783$	27.9497	−	16.4801i	0.998840	−	0.588950i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.29858	−	4.29858i	−0.153228	−	0.153228i	0.626330	−	0.779558i	$-0.284556\pi$
$787$	−4.29858	−	4.29858i	−0.153228	−	0.153228i	−0.779558	+	0.626330i	$0.784556\pi$
$788$		0			0
$789$	25.7882	−	12.1213i	0.918085	−	0.431529i
$790$		0			0
$791$			36.4872i			1.29733i
$792$		0			0
$793$	7.49975	−	7.49975i	0.266324	−	0.266324i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.66209	+	7.66209i	−0.271405	+	0.271405i	−0.829666	−	0.558261i	$-0.811469\pi$
$797$	−7.66209	+	7.66209i	−0.271405	+	0.271405i	0.558261	+	0.829666i	$0.311469\pi$
$798$		0			0
$799$		−	71.5863i		−	2.53254i
$800$		0			0
$801$	−8.52730	−	7.06693i	−0.301297	−	0.249698i
$802$		0			0
$803$	−32.4634	−	32.4634i	−1.14561	−	1.14561i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−16.6517	+	46.1887i	−0.586169	+	1.62592i
$808$		0			0
$809$	−24.3424			−0.855834			−0.427917	−	0.903818i	$-0.640753\pi$
$809$	−24.3424			−0.855834			−0.427917	+	0.903818i	$0.640753\pi$
$810$		0			0
$811$	−36.9463			−1.29736			−0.648680	−	0.761061i	$-0.724679\pi$
$811$	−36.9463			−1.29736			−0.648680	+	0.761061i	$0.724679\pi$
$812$		0			0
$813$	3.39238	−	9.40983i	0.118976	−	0.330017i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.34539	+	7.34539i	0.256983	+	0.256983i
$818$		0			0
$819$	−5.65135	−	4.68351i	−0.197474	−	0.163655i
$820$		0			0
$821$			14.7144i			0.513536i	0.966473	+	0.256768i	$0.0826577\pi$
$821$			14.7144i			0.513536i	−0.966473	+	0.256768i	$0.917342\pi$
$822$		0			0
$823$	2.65228	−	2.65228i	0.0924527	−	0.0924527i	−0.659368	−	0.751821i	$-0.729176\pi$
$823$	2.65228	−	2.65228i	0.0924527	−	0.0924527i	0.751821	+	0.659368i	$0.229176\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.0622	+	24.0622i	−0.836724	+	0.836724i	−0.988426	−	0.151702i	$-0.951525\pi$
$827$	−24.0622	+	24.0622i	−0.836724	+	0.836724i	0.151702	+	0.988426i	$0.451525\pi$
$828$		0			0
$829$			2.65799i			0.0923157i	0.998934	+	0.0461578i	$0.0146977\pi$
$829$			2.65799i			0.0923157i	−0.998934	+	0.0461578i	$0.985302\pi$
$830$		0			0
$831$	27.1053	−	12.7403i	0.940272	−	0.441958i
$832$		0			0
$833$	6.07009	+	6.07009i	0.210316	+	0.210316i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−14.3704	+	8.47327i	−0.496713	+	0.292879i
$838$		0			0
$839$	−25.2693			−0.872394			−0.436197	−	0.899851i	$-0.643675\pi$
$839$	−25.2693			−0.872394			−0.436197	+	0.899851i	$0.643675\pi$
$840$		0			0
$841$	9.99179			0.344544
$842$		0			0
$843$	−36.0736	−	13.0051i	−1.24244	−	0.447918i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.815481	+	0.815481i	0.0280203	+	0.0280203i
$848$		0			0
$849$	8.72249	+	18.5572i	0.299355	+	0.636882i
$850$		0			0
$851$			6.86325i			0.235269i
$852$		0			0
$853$	−14.7848	+	14.7848i	−0.506224	+	0.506224i	−0.913365	−	0.407142i	$-0.866526\pi$
$853$	−14.7848	+	14.7848i	−0.506224	+	0.506224i	0.407142	+	0.913365i	$0.366526\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.3037	+	15.3037i	−0.522765	+	0.522765i	−0.918406	−	0.395640i	$-0.870523\pi$
$857$	−15.3037	+	15.3037i	−0.522765	+	0.522765i	0.395640	+	0.918406i	$0.370523\pi$
$858$		0			0
$859$			36.6774i			1.25142i	0.780058	+	0.625708i	$0.215190\pi$
$859$			36.6774i			1.25142i	−0.780058	+	0.625708i	$0.784810\pi$
$860$		0			0
$861$	−5.62616	−	11.9698i	−0.191739	−	0.407928i
$862$		0			0
$863$	−6.43133	−	6.43133i	−0.218925	−	0.218925i	0.589120	−	0.808045i	$-0.299474\pi$
$863$	−6.43133	−	6.43133i	−0.218925	−	0.218925i	−0.808045	+	0.589120i	$0.799474\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−35.1716	−	12.6799i	−1.19449	−	0.430631i
$868$		0			0
$869$	44.5795			1.51226
$870$		0			0
$871$	16.2586			0.550901
$872$		0			0
$873$	0.719690	+	7.68507i	0.0243578	+	0.260100i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.5515	−	21.5515i	−0.727742	−	0.727742i	0.242428	−	0.970169i	$-0.422056\pi$
$877$	−21.5515	−	21.5515i	−0.727742	−	0.727742i	−0.970169	+	0.242428i	$0.922056\pi$
$878$		0			0
$879$	8.18535	−	3.84738i	0.276085	−	0.129769i
$880$		0			0
$881$			31.4532i			1.05969i	0.848096	+	0.529843i	$0.177749\pi$
$881$			31.4532i			1.05969i	−0.848096	+	0.529843i	$0.822251\pi$
$882$		0			0
$883$	38.9909	−	38.9909i	1.31215	−	1.31215i	0.392318	−	0.919830i	$-0.371673\pi$
$883$	38.9909	−	38.9909i	1.31215	−	1.31215i	0.919830	−	0.392318i	$-0.128327\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.84513	+	2.84513i	−0.0955301	+	0.0955301i	−0.753257	−	0.657727i	$-0.771518\pi$
$887$	−2.84513	+	2.84513i	−0.0955301	+	0.0955301i	0.657727	+	0.753257i	$0.271518\pi$
$888$		0			0
$889$		−	28.2475i		−	0.947390i
$890$		0			0
$891$	29.9723	−	5.66335i	1.00411	−	0.189729i
$892$		0			0
$893$	42.3319	+	42.3319i	1.41658	+	1.41658i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.88438	+	8.00073i	−0.0963067	+	0.267137i
$898$		0			0
$899$	−20.0477			−0.668629
$900$		0			0
$901$	12.5329			0.417533
$902$		0			0
$903$	2.78424	−	7.72295i	0.0926536	−	0.257004i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	2.19452	+	2.19452i	0.0728678	+	0.0728678i	0.742601	−	0.669734i	$-0.233592\pi$
$907$	2.19452	+	2.19452i	0.0728678	+	0.0728678i	−0.669734	+	0.742601i	$0.733592\pi$
$908$		0			0
$909$	−22.2157	+	26.8065i	−0.736848	+	0.889116i
$910$		0			0
$911$			34.1466i			1.13133i	0.824636	+	0.565664i	$0.191380\pi$
$911$			34.1466i			1.13133i	−0.824636	+	0.565664i	$0.808620\pi$
$912$		0			0
$913$	6.47473	−	6.47473i	0.214282	−	0.214282i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.6428	+	13.6428i	−0.450524	+	0.450524i
$918$		0			0
$919$			36.7948i			1.21375i	0.794797	+	0.606875i	$0.207577\pi$
$919$			36.7948i			1.21375i	−0.794797	+	0.606875i	$0.792423\pi$
$920$		0			0
$921$	−7.10246	+	3.33838i	−0.234034	+	0.110003i
$922$		0			0
$923$	12.0077	+	12.0077i	0.395240	+	0.395240i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.5134	−	1.17185i	0.410994	−	0.0384887i
$928$		0			0
$929$	−52.8490			−1.73392			−0.866959	−	0.498379i	$-0.833929\pi$
$929$	−52.8490			−1.73392			−0.866959	+	0.498379i	$0.833929\pi$
$930$		0			0
$931$	−7.17899			−0.235282
$932$		0			0
$933$	−23.5339	−	8.48433i	−0.770466	−	0.277764i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−13.0962	−	13.0962i	−0.427833	−	0.427833i	0.460056	−	0.887890i	$-0.347829\pi$
$937$	−13.0962	−	13.0962i	−0.427833	−	0.427833i	−0.887890	+	0.460056i	$0.847829\pi$
$938$		0			0
$939$	11.7200	+	24.9345i	0.382468	+	0.813707i
$940$		0			0
$941$			42.1838i			1.37515i	0.726112	+	0.687577i	$0.241326\pi$
$941$			42.1838i			1.37515i	−0.726112	+	0.687577i	$0.758674\pi$
$942$		0			0
$943$	−10.8366	+	10.8366i	−0.352888	+	0.352888i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.4385	−	21.4385i	0.696658	−	0.696658i	−0.267030	−	0.963688i	$-0.586042\pi$
$947$	21.4385	−	21.4385i	0.696658	−	0.696658i	0.963688	+	0.267030i	$0.0860424\pi$
$948$		0			0
$949$			13.9826i			0.453893i
$950$		0			0
$951$	−18.7196	−	39.8263i	−0.607025	−	1.29145i
$952$		0			0
$953$	28.3158	+	28.3158i	0.917240	+	0.917240i	0.996828	−	0.0795883i	$-0.0253606\pi$
$953$	28.3158	+	28.3158i	0.917240	+	0.917240i	−0.0795883	+	0.996828i	$0.525361\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	34.4833	+	12.4317i	1.11469	+	0.401861i
$958$		0			0
$959$	50.7454			1.63866
$960$		0			0
$961$	−20.6924			−0.667498
$962$		0			0
$963$	−3.81548	+	0.357312i	−0.122952	+	0.0115142i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−12.2465	−	12.2465i	−0.393819	−	0.393819i	0.482227	−	0.876046i	$-0.339828\pi$
$967$	−12.2465	−	12.2465i	−0.393819	−	0.393819i	−0.876046	+	0.482227i	$0.839828\pi$
$968$		0			0
$969$	50.5818	−	23.7750i	1.62492	−	0.763764i
$970$		0			0
$971$		−	29.3186i		−	0.940879i	−0.882432	−	0.470439i	$-0.844095\pi$
$971$		−	29.3186i		−	0.940879i	0.882432	−	0.470439i	$-0.155905\pi$
$972$		0			0
$973$	−22.9059	+	22.9059i	−0.734329	+	0.734329i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.5780	+	20.5780i	−0.658347	+	0.658347i	−0.954989	−	0.296642i	$-0.904133\pi$
$977$	−20.5780	+	20.5780i	−0.658347	+	0.658347i	0.296642	+	0.954989i	$0.404133\pi$
$978$		0			0
$979$		−	12.5118i		−	0.399878i
$980$		0			0
$981$	16.8400	−	20.3200i	0.537661	−	0.648767i
$982$		0			0
$983$	−18.9594	−	18.9594i	−0.604710	−	0.604710i	0.336849	−	0.941559i	$-0.390639\pi$
$983$	−18.9594	−	18.9594i	−0.604710	−	0.604710i	−0.941559	+	0.336849i	$0.890639\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	16.0457	−	44.5078i	0.510741	−	1.41670i
$988$		0			0
$989$	−9.51249			−0.302479
$990$		0			0
$991$	29.8368			0.947798			0.473899	−	0.880579i	$-0.342846\pi$
$991$	29.8368			0.947798			0.473899	+	0.880579i	$0.342846\pi$
$992$		0			0
$993$	−13.0659	+	36.2423i	−0.414634	+	1.15012i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.58487	+	2.58487i	0.0818637	+	0.0818637i	0.746853	−	0.664989i	$-0.231564\pi$
$997$	2.58487	+	2.58487i	0.0818637	+	0.0818637i	−0.664989	+	0.746853i	$0.731564\pi$
$998$		0			0
$999$	−7.25892	−	1.87390i	−0.229662	−	0.0592876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.b.557.10	yes	32
3.2	odd	2	inner	1500.2.i.b.557.15	yes	32
5.2	odd	4	inner	1500.2.i.b.1193.2	yes	32
5.3	odd	4	inner	1500.2.i.b.1193.15	yes	32
5.4	even	2	inner	1500.2.i.b.557.7	yes	32
15.2	even	4	inner	1500.2.i.b.1193.7	yes	32
15.8	even	4	inner	1500.2.i.b.1193.10	yes	32
15.14	odd	2	inner	1500.2.i.b.557.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.b.557.2	✓	32	15.14	odd	2	inner
1500.2.i.b.557.7	yes	32	5.4	even	2	inner
1500.2.i.b.557.10	yes	32	1.1	even	1	trivial
1500.2.i.b.557.15	yes	32	3.2	odd	2	inner
1500.2.i.b.1193.2	yes	32	5.2	odd	4	inner
1500.2.i.b.1193.7	yes	32	15.2	even	4	inner
1500.2.i.b.1193.10	yes	32	15.8	even	4	inner
1500.2.i.b.1193.15	yes	32	5.3	odd	4	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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587422 - 1.62940i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(-2.30987 - 1.91429i) q^{9} +O(q^{10})\)	\(q+(0.587422 - 1.62940i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(-2.30987 - 1.91429i) q^{9} -3.38918i q^{11} +(-0.729890 + 0.729890i) q^{13} +(-4.39236 + 4.39236i) q^{17} -5.19476i q^{19} +(-3.71542 + 1.74636i) q^{21} +(3.36368 + 3.36368i) q^{23} +(-4.47600 + 2.63920i) q^{27} -6.24434 q^{29} +3.21054 q^{31} +(-5.52233 - 1.99088i) q^{33} +(1.02020 + 1.02020i) q^{37} +(0.760527 + 1.61803i) q^{39} +3.22165i q^{41} +(-1.41400 + 1.41400i) q^{43} +(-8.14896 + 8.14896i) q^{47} -1.38197i q^{49} +(4.57673 + 9.73707i) q^{51} +(-1.42668 - 1.42668i) q^{53} +(-8.46433 - 3.05152i) q^{57} +3.16268 q^{59} -10.2752 q^{61} +(0.663003 + 7.07974i) q^{63} +(-11.1377 - 11.1377i) q^{67} +(7.45668 - 3.50488i) q^{69} -16.4514i q^{71} +(9.57853 - 9.57853i) q^{73} +(-5.68031 + 5.68031i) q^{77} +13.1535i q^{79} +(1.67101 + 8.84351i) q^{81} +(1.91041 + 1.91041i) q^{83} +(-3.66806 + 10.1745i) q^{87} +3.69168 q^{89} +2.44661 q^{91} +(1.88594 - 5.23125i) q^{93} +(-1.81931 - 1.81931i) q^{97} +(-6.48787 + 7.82857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) \) 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

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