LMFDB - Embedded newform 936.2.dr.b.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(89,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 7]))

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

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

chi := DirichletCharacter("936.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dr (of order $12$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			449.1
Character	$\chi$	$=$	936.449
Dual form			936.2.dr.b.665.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65632 + 2.65632i) q^{5} +(1.47941 + 0.396406i) q^{7} +(-4.40840 + 1.18123i) q^{11} +(-2.78196 - 2.29363i) q^{13} +(-2.30001 - 3.98374i) q^{17} +(0.611448 - 2.28196i) q^{19} +(3.26044 - 5.64726i) q^{23} -9.11212i q^{25} +(6.53868 + 3.77511i) q^{29} +(3.52796 + 3.52796i) q^{31} +(-4.98277 + 2.87680i) q^{35} +(-1.56691 - 5.84780i) q^{37} +(0.0148235 + 0.0553221i) q^{41} +(-2.57798 + 1.48840i) q^{43} +(-7.10851 - 7.10851i) q^{47} +(-4.03067 - 2.32711i) q^{49} -8.48484i q^{53} +(8.57242 - 14.8479i) q^{55} +(-2.84984 + 10.6357i) q^{59} +(-0.615952 - 1.06686i) q^{61} +(13.4824 - 1.29716i) q^{65} +(-8.23130 + 2.20557i) q^{67} +(-12.9368 - 3.46642i) q^{71} +(8.01411 - 8.01411i) q^{73} -6.99007 q^{77} -12.4727 q^{79} +(-9.98438 + 9.98438i) q^{83} +(16.6917 + 4.47252i) q^{85} +(0.222542 - 0.0596300i) q^{89} +(-3.20644 - 4.49599i) q^{91} +(4.43741 + 7.68582i) q^{95} +(-2.90184 + 10.8298i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{7} - 20 q^{13} - 4 q^{19} + 4 q^{31} + 60 q^{43} + 84 q^{49} - 28 q^{61} - 24 q^{67} + 16 q^{73} + 48 q^{79} + 88 q^{85} - 116 q^{91} + 72 q^{97}+O(q^{100}) $ 32 * q + 4 * q^7 - 20 * q^13 - 4 * q^19 + 4 * q^31 + 60 * q^43 + 84 * q^49 - 28 * q^61 - 24 * q^67 + 16 * q^73 + 48 * q^79 + 88 * q^85 - 116 * q^91 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.65632	+	2.65632i	−1.18794	+	1.18794i	−0.210309	+	0.977635i	$0.567447\pi$
$5$	−2.65632	+	2.65632i	−1.18794	+	1.18794i	−0.977635	+	0.210309i	$0.932553\pi$
$6$		0			0
$7$	1.47941	+	0.396406i	0.559164	+	0.149827i	0.527322	−	0.849665i	$-0.323196\pi$
$7$	1.47941	+	0.396406i	0.559164	+	0.149827i	0.0318417	+	0.999493i	$0.489863\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.40840	+	1.18123i	−1.32918	+	0.356153i	−0.852410	−	0.522873i	$-0.824860\pi$
$11$	−4.40840	+	1.18123i	−1.32918	+	0.356153i	−0.476772	+	0.879027i	$0.658193\pi$
$12$		0			0
$13$	−2.78196	−	2.29363i	−0.771576	−	0.636137i
$13$	−2.78196	−	2.29363i	−0.771576	−	0.636137i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.30001	−	3.98374i	−0.557835	−	0.966199i	−0.997677	−	0.0681235i	$-0.978299\pi$
$17$	−2.30001	−	3.98374i	−0.557835	−	0.966199i	0.439842	−	0.898075i	$-0.355035\pi$
$18$		0			0
$19$	0.611448	−	2.28196i	0.140276	−	0.523517i	−0.859644	−	0.510893i	$-0.829315\pi$
$19$	0.611448	−	2.28196i	0.140276	−	0.523517i	0.999920	−	0.0126239i	$-0.00401841\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.26044	−	5.64726i	0.679850	−	1.17753i	−0.295176	−	0.955443i	$-0.595378\pi$
$23$	3.26044	−	5.64726i	0.679850	−	1.17753i	0.975026	−	0.222091i	$-0.0712883\pi$
$24$		0			0
$25$		−	9.11212i		−	1.82242i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.53868	+	3.77511i	1.21420	+	0.701020i	0.963672	−	0.267088i	$-0.0860616\pi$
$29$	6.53868	+	3.77511i	1.21420	+	0.701020i	0.250531	+	0.968109i	$0.419395\pi$
$30$		0			0
$31$	3.52796	+	3.52796i	0.633641	+	0.633641i	0.948979	−	0.315338i	$-0.102118\pi$
$31$	3.52796	+	3.52796i	0.633641	+	0.633641i	−0.315338	+	0.948979i	$0.602118\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.98277	+	2.87680i	−0.842242	+	0.486269i
$36$		0			0
$37$	−1.56691	−	5.84780i	−0.257599	−	0.961373i	−0.966626	−	0.256192i	$-0.917532\pi$
$37$	−1.56691	−	5.84780i	−0.257599	−	0.961373i	0.709027	−	0.705181i	$-0.249134\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0148235	+	0.0553221i	0.00231504	+	0.00863986i	0.967074	−	0.254497i	$-0.0819097\pi$
$41$	0.0148235	+	0.0553221i	0.00231504	+	0.00863986i	−0.964759	+	0.263136i	$0.915243\pi$
$42$		0			0
$43$	−2.57798	+	1.48840i	−0.393138	+	0.226978i	−0.683519	−	0.729933i	$-0.739551\pi$
$43$	−2.57798	+	1.48840i	−0.393138	+	0.226978i	0.290381	+	0.956911i	$0.406218\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.10851	−	7.10851i	−1.03688	−	1.03688i	−0.999293	−	0.0375898i	$-0.988032\pi$
$47$	−7.10851	−	7.10851i	−1.03688	−	1.03688i	−0.0375898	−	0.999293i	$-0.511968\pi$
$48$		0			0
$49$	−4.03067	−	2.32711i	−0.575810	−	0.332444i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	8.48484i		−	1.16548i	−0.812658	−	0.582741i	$-0.801980\pi$
$53$		−	8.48484i		−	1.16548i	0.812658	−	0.582741i	$-0.198020\pi$
$54$		0			0
$55$	8.57242	−	14.8479i	1.15590	−	2.00209i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.84984	+	10.6357i	−0.371018	+	1.38466i	0.488059	+	0.872810i	$0.337705\pi$
$59$	−2.84984	+	10.6357i	−0.371018	+	1.38466i	−0.859077	+	0.511846i	$0.828962\pi$
$60$		0			0
$61$	−0.615952	−	1.06686i	−0.0788646	−	0.136597i	0.823896	−	0.566741i	$-0.191796\pi$
$61$	−0.615952	−	1.06686i	−0.0788646	−	0.136597i	−0.902760	+	0.430144i	$0.858463\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	13.4824	−	1.29716i	1.67228	−	0.160893i
$66$		0			0
$67$	−8.23130	+	2.20557i	−1.00561	+	0.269453i	−0.723795	−	0.690015i	$-0.757604\pi$
$67$	−8.23130	+	2.20557i	−1.00561	+	0.269453i	−0.281818	+	0.959468i	$0.590937\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.9368	−	3.46642i	−1.53532	−	0.411388i	−0.610570	−	0.791962i	$-0.709060\pi$
$71$	−12.9368	−	3.46642i	−1.53532	−	0.411388i	−0.924751	+	0.380574i	$0.875726\pi$
$72$		0			0
$73$	8.01411	−	8.01411i	0.937981	−	0.937981i	−0.0602054	−	0.998186i	$-0.519176\pi$
$73$	8.01411	−	8.01411i	0.937981	−	0.937981i	0.998186	+	0.0602054i	$0.0191756\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.99007			−0.796592
$78$		0			0
$79$	−12.4727			−1.40329			−0.701643	−	0.712529i	$-0.747550\pi$
$79$	−12.4727			−1.40329			−0.701643	+	0.712529i	$0.747550\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.98438	+	9.98438i	−1.09593	+	1.09593i	−0.101047	+	0.994882i	$0.532219\pi$
$83$	−9.98438	+	9.98438i	−1.09593	+	1.09593i	−0.994882	+	0.101047i	$0.967781\pi$
$84$		0			0
$85$	16.6917	+	4.47252i	1.81047	+	0.485113i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.222542	−	0.0596300i	0.0235894	−	0.00632076i	−0.247005	−	0.969014i	$-0.579446\pi$
$89$	0.222542	−	0.0596300i	0.0235894	−	0.00632076i	0.270594	+	0.962693i	$0.412780\pi$
$90$		0			0
$91$	−3.20644	−	4.49599i	−0.336126	−	0.471308i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.43741	+	7.68582i	0.455269	+	0.788548i
$96$		0			0
$97$	−2.90184	+	10.8298i	−0.294638	+	1.09960i	0.646867	+	0.762603i	$0.276079\pi$
$97$	−2.90184	+	10.8298i	−0.294638	+	1.09960i	−0.941505	+	0.337000i	$0.890588\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.48124	−	6.02969i	0.346396	−	0.599976i	−0.639210	−	0.769032i	$-0.720739\pi$
$101$	3.48124	−	6.02969i	0.346396	−	0.599976i	0.985606	+	0.169056i	$0.0540719\pi$
$102$		0			0
$103$			9.56148i			0.942121i	0.882101	+	0.471060i	$0.156129\pi$
$103$			9.56148i			0.942121i	−0.882101	+	0.471060i	$0.843871\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.67644	−	1.54524i	−0.258741	−	0.149384i	0.365019	−	0.931000i	$-0.381062\pi$
$107$	−2.67644	−	1.54524i	−0.258741	−	0.149384i	−0.623760	+	0.781616i	$0.714396\pi$
$108$		0			0
$109$	−0.280559	−	0.280559i	−0.0268726	−	0.0268726i	0.693543	−	0.720415i	$-0.256049\pi$
$109$	−0.280559	−	0.280559i	−0.0268726	−	0.0268726i	−0.720415	+	0.693543i	$0.756049\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.72157	+	2.14865i	−0.350096	+	0.202128i	−0.664728	−	0.747086i	$-0.731452\pi$
$113$	−3.72157	+	2.14865i	−0.350096	+	0.202128i	0.314632	+	0.949214i	$0.398119\pi$
$114$		0			0
$115$	6.34014	+	23.6617i	0.591221	+	2.20647i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.82348	−	6.80532i	−0.167158	−	0.623842i
$120$		0			0
$121$	8.51242	−	4.91465i	0.773856	−	0.446786i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.9231	+	10.9231i	0.976993	+	0.976993i
$126$		0			0
$127$	12.2543	+	7.07503i	1.08739	+	0.627808i	0.932882	−	0.360183i	$-0.117286\pi$
$127$	12.2543	+	7.07503i	1.08739	+	0.627808i	0.154513	+	0.987991i	$0.450619\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$			0.550751i			0.0481193i	0.999711	+	0.0240597i	$0.00765917\pi$
$131$			0.550751i			0.0481193i	−0.999711	+	0.0240597i	$0.992341\pi$
$132$		0			0
$133$	1.80916	−	3.13356i	0.156874	−	0.271714i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.562445	+	2.09907i	−0.0480529	+	0.179336i	−0.985781	−	0.168034i	$-0.946258\pi$
$137$	−0.562445	+	2.09907i	−0.0480529	+	0.179336i	0.937728	+	0.347369i	$0.112925\pi$
$138$		0			0
$139$	−2.39565	−	4.14939i	−0.203196	−	0.351947i	0.746360	−	0.665542i	$-0.231800\pi$
$139$	−2.39565	−	4.14939i	−0.203196	−	0.351947i	−0.949557	+	0.313596i	$0.898466\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	14.9733	+	6.82510i	1.25213	+	0.570744i
$144$		0			0
$145$	−27.3968	+	7.34094i	−2.27518	+	0.609632i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.6637	+	2.85733i	0.873604	+	0.234081i	0.667645	−	0.744479i	$-0.267302\pi$
$149$	10.6637	+	2.85733i	0.873604	+	0.234081i	0.205958	+	0.978561i	$0.433969\pi$
$150$		0			0
$151$	3.90906	−	3.90906i	0.318115	−	0.318115i	−0.529928	−	0.848043i	$-0.677781\pi$
$151$	3.90906	−	3.90906i	0.318115	−	0.318115i	0.848043	+	0.529928i	$0.177781\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−18.7428			−1.50546
$156$		0			0
$157$	−19.5514			−1.56037			−0.780185	−	0.625549i	$-0.784875\pi$
$157$	−19.5514			−1.56037			−0.780185	+	0.625549i	$0.784875\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.06214	−	7.06214i	0.556574	−	0.556574i
$162$		0			0
$163$	−2.84178	−	0.761453i	−0.222585	−	0.0596416i	0.145803	−	0.989314i	$-0.453424\pi$
$163$	−2.84178	−	0.761453i	−0.222585	−	0.0596416i	−0.368388	+	0.929672i	$0.620090\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	20.0248	−	5.36563i	1.54957	−	0.415205i	0.620223	−	0.784425i	$-0.287042\pi$
$167$	20.0248	−	5.36563i	1.54957	−	0.415205i	0.929342	+	0.369220i	$0.120375\pi$
$168$		0			0
$169$	2.47856	+	12.7615i	0.190658	+	0.981656i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.23711	−	12.5350i	−0.550227	−	0.953022i	−0.998258	−	0.0590034i	$-0.981208\pi$
$173$	−7.23711	−	12.5350i	−0.550227	−	0.953022i	0.448030	−	0.894018i	$-0.352126\pi$
$174$		0			0
$175$	3.61210	−	13.4805i	0.273049	−	1.01903i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0952	−	20.9495i	0.904037	−	1.56584i	0.0818334	−	0.996646i	$-0.473922\pi$
$179$	12.0952	−	20.9495i	0.904037	−	1.56584i	0.822204	−	0.569193i	$-0.192744\pi$
$180$		0			0
$181$		−	7.27795i		−	0.540966i	−0.962725	−	0.270483i	$-0.912817\pi$
$181$		−	7.27795i		−	0.540966i	0.962725	−	0.270483i	$-0.0871834\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	19.6959	+	11.3714i	1.44807	+	0.836044i
$186$		0			0
$187$	14.8451	+	14.8451i	1.08558	+	1.08558i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.0353	−	10.4127i	1.30499	−	0.753435i	0.323733	−	0.946149i	$-0.395062\pi$
$191$	18.0353	−	10.4127i	1.30499	−	0.753435i	0.981255	+	0.192713i	$0.0617288\pi$
$192$		0			0
$193$	−2.88483	−	10.7663i	−0.207655	−	0.774979i	−0.988624	−	0.150409i	$-0.951941\pi$
$193$	−2.88483	−	10.7663i	−0.207655	−	0.774979i	0.780969	−	0.624570i	$-0.214726\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.57709	−	9.61784i	−0.183610	−	0.685243i	−0.994924	−	0.100631i	$-0.967914\pi$
$197$	−2.57709	−	9.61784i	−0.183610	−	0.685243i	0.811314	−	0.584611i	$-0.198753\pi$
$198$		0			0
$199$	−16.2960	+	9.40851i	−1.15519	+	0.666952i	−0.950148	−	0.311800i	$-0.899068\pi$
$199$	−16.2960	+	9.40851i	−1.15519	+	0.666952i	−0.205047	+	0.978752i	$0.565735\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.17690	+	8.17690i	0.573906	+	0.573906i
$204$		0			0
$205$	−0.186329	−	0.107577i	−0.0130138	−	0.00751353i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			10.7820i			0.745809i
$210$		0			0
$211$	−11.6782	+	20.2273i	−0.803964	+	1.39251i	0.113025	+	0.993592i	$0.463946\pi$
$211$	−11.6782	+	20.2273i	−0.803964	+	1.39251i	−0.916988	+	0.398914i	$0.869387\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.89428	−	10.8016i	0.197389	−	0.736664i
$216$		0			0
$217$	3.82079	+	6.61780i	0.259372	+	0.449246i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.73867	+	16.3580i	−0.184223	+	1.10036i
$222$		0			0
$223$	−18.9573	+	5.07960i	−1.26948	+	0.340155i	−0.829830	−	0.558016i	$-0.811563\pi$
$223$	−18.9573	+	5.07960i	−1.26948	+	0.340155i	−0.439646	+	0.898171i	$0.644896\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.11895	−	1.63957i	−0.406129	−	0.108822i	0.0499706	−	0.998751i	$-0.484087\pi$
$227$	−6.11895	−	1.63957i	−0.406129	−	0.108822i	−0.456100	+	0.889929i	$0.650754\pi$
$228$		0			0
$229$	0.150523	−	0.150523i	0.00994684	−	0.00994684i	−0.702116	−	0.712063i	$-0.747761\pi$
$229$	0.150523	−	0.150523i	0.00994684	−	0.00994684i	0.712063	+	0.702116i	$0.247761\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.2222			−1.45582			−0.727911	−	0.685671i	$-0.759509\pi$
$233$	−22.2222			−1.45582			−0.727911	+	0.685671i	$0.759509\pi$
$234$		0			0
$235$	37.7650			2.46352
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.5505	+	10.5505i	−0.682453	+	0.682453i	−0.960552	−	0.278100i	$-0.910295\pi$
$239$	−10.5505	+	10.5505i	−0.682453	+	0.682453i	0.278100	+	0.960552i	$0.410295\pi$
$240$		0			0
$241$	−1.73237	−	0.464188i	−0.111592	−	0.0299010i	0.202591	−	0.979263i	$-0.435064\pi$
$241$	−1.73237	−	0.464188i	−0.111592	−	0.0299010i	−0.314183	+	0.949363i	$0.601730\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.8883	−	4.52521i	1.07895	−	0.289105i
$246$		0			0
$247$	−6.93498	+	4.94587i	−0.441262	+	0.314698i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.0419915	−	0.0727315i	−0.00265048	−	0.00459077i	0.864697	−	0.502294i	$-0.167510\pi$
$251$	−0.0419915	−	0.0727315i	−0.00265048	−	0.00459077i	−0.867348	+	0.497703i	$0.834177\pi$
$252$		0			0
$253$	−7.70265	+	28.7467i	−0.484262	+	1.80729i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.82270	+	8.35317i	−0.300832	+	0.521056i	−0.976325	−	0.216310i	$-0.930598\pi$
$257$	−4.82270	+	8.35317i	−0.300832	+	0.521056i	0.675493	+	0.737367i	$0.263931\pi$
$258$		0			0
$259$		−	9.27242i		−	0.576160i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.59196	+	4.96057i	0.529803	+	0.305882i	0.740936	−	0.671575i	$-0.234382\pi$
$263$	8.59196	+	4.96057i	0.529803	+	0.305882i	−0.211133	+	0.977457i	$0.567715\pi$
$264$		0			0
$265$	22.5385	+	22.5385i	1.38453	+	1.38453i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.8383	+	7.41222i	−0.782767	+	0.451931i	−0.837410	−	0.546575i	$-0.815931\pi$
$269$	−12.8383	+	7.41222i	−0.782767	+	0.451931i	0.0546427	+	0.998506i	$0.482598\pi$
$270$		0			0
$271$	4.81819	+	17.9817i	0.292684	+	1.09231i	0.943039	+	0.332682i	$0.107953\pi$
$271$	4.81819	+	17.9817i	0.292684	+	1.09231i	−0.650355	+	0.759630i	$0.725380\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.7635	+	40.1699i	0.649062	+	2.42233i
$276$		0			0
$277$	26.2952	−	15.1815i	1.57992	−	0.912169i	0.585054	−	0.810994i	$-0.301073\pi$
$277$	26.2952	−	15.1815i	1.57992	−	0.912169i	0.994869	−	0.101175i	$-0.0322602\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.0621	−	10.0621i	−0.600253	−	0.600253i	0.340127	−	0.940380i	$-0.389530\pi$
$281$	−10.0621	−	10.0621i	−0.600253	−	0.600253i	−0.940380	+	0.340127i	$0.889530\pi$
$282$		0			0
$283$	20.4218	+	11.7905i	1.21395	+	0.700873i	0.963617	−	0.267287i	$-0.0861272\pi$
$283$	20.4218	+	11.7905i	1.21395	+	0.700873i	0.250331	+	0.968160i	$0.419461\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			0.0877201i			0.00517795i
$288$		0			0
$289$	−2.08012	+	3.60288i	−0.122360	+	0.211934i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.33342	−	4.97640i	0.0778994	−	0.290725i	−0.915976	−	0.401234i	$-0.868582\pi$
$293$	1.33342	−	4.97640i	0.0778994	−	0.290725i	0.993875	+	0.110509i	$0.0352482\pi$
$294$		0			0
$295$	−20.6819	−	35.8221i	−1.20415	−	2.08564i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−22.0231	+	8.23218i	−1.27363	+	0.476079i
$300$		0			0
$301$	−4.40390	+	1.18002i	−0.253836	+	0.0680152i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.47009	+	1.19776i	0.255957	+	0.0685834i
$306$		0			0
$307$	−1.74011	+	1.74011i	−0.0993135	+	0.0993135i	−0.755018	−	0.655704i	$-0.772372\pi$
$307$	−1.74011	+	1.74011i	−0.0993135	+	0.0993135i	0.655704	+	0.755018i	$0.272372\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.1143			0.743645			0.371822	−	0.928304i	$-0.378733\pi$
$311$	13.1143			0.743645			0.371822	+	0.928304i	$0.378733\pi$
$312$		0			0
$313$	−6.08751			−0.344086			−0.172043	−	0.985089i	$-0.555037\pi$
$313$	−6.08751			−0.344086			−0.172043	+	0.985089i	$0.555037\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.9406	−	16.9406i	0.951480	−	0.951480i	−0.0473961	−	0.998876i	$-0.515092\pi$
$317$	16.9406	−	16.9406i	0.951480	−	0.951480i	0.998876	+	0.0473961i	$0.0150923\pi$
$318$		0			0
$319$	−33.2844	−	8.91853i	−1.86357	−	0.499342i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.4971	+	2.81268i	−0.584072	+	0.156502i
$324$		0			0
$325$	−20.8998	+	25.3495i	−1.15931	+	1.40614i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.69853	−	13.3343i	−0.424434	−	0.735141i
$330$		0			0
$331$	−0.855151	+	3.19147i	−0.0470033	+	0.175419i	−0.985437	−	0.170040i	$-0.945610\pi$
$331$	−0.855151	+	3.19147i	−0.0470033	+	0.175419i	0.938434	+	0.345459i	$0.112277\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	16.0063	−	27.7237i	0.874517	−	1.51471i
$336$		0			0
$337$		−	5.80822i		−	0.316394i	−0.987408	−	0.158197i	$-0.949432\pi$
$337$		−	5.80822i		−	0.316394i	0.987408	−	0.158197i	$-0.0505681\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−19.7200	−	11.3853i	−1.06790	−	0.616551i
$342$		0			0
$343$	−12.6215	−	12.6215i	−0.681499	−	0.681499i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.49266	+	2.59384i	−0.241178	+	0.139244i	−0.615718	−	0.787966i	$-0.711134\pi$
$347$	−4.49266	+	2.59384i	−0.241178	+	0.139244i	0.374540	+	0.927211i	$0.377801\pi$
$348$		0			0
$349$	6.77232	+	25.2746i	0.362514	+	1.35292i	0.870760	+	0.491708i	$0.163627\pi$
$349$	6.77232	+	25.2746i	0.362514	+	1.35292i	−0.508246	+	0.861212i	$0.669706\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.89289	+	7.06437i	0.100748	+	0.375998i	0.997828	−	0.0658703i	$-0.0209824\pi$
$353$	1.89289	+	7.06437i	0.100748	+	0.375998i	−0.897080	+	0.441869i	$0.854316\pi$
$354$		0			0
$355$	43.5724	−	25.1565i	2.31258	−	1.33517i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.5073	−	11.5073i	−0.607330	−	0.607330i	0.334917	−	0.942248i	$-0.391292\pi$
$359$	−11.5073	−	11.5073i	−0.607330	−	0.607330i	−0.942248	+	0.334917i	$0.891292\pi$
$360$		0			0
$361$	11.6210	+	6.70940i	0.611633	+	0.353127i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			42.5761i			2.22854i
$366$		0			0
$367$	10.2187	−	17.6994i	0.533413	−	0.923899i	−0.465825	−	0.884877i	$-0.654242\pi$
$367$	10.2187	−	17.6994i	0.533413	−	0.923899i	0.999238	−	0.0390223i	$-0.0124243\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.36344	−	12.5525i	0.174621	−	0.651696i
$372$		0			0
$373$	−7.04216	−	12.1974i	−0.364629	−	0.631556i	0.624088	−	0.781354i	$-0.285471\pi$
$373$	−7.04216	−	12.1974i	−0.364629	−	0.631556i	−0.988717	+	0.149798i	$0.952138\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.53164	−	25.4995i	−0.490904	−	1.31329i
$378$		0			0
$379$	−14.2093	+	3.80736i	−0.729881	+	0.195571i	−0.604576	−	0.796547i	$-0.706657\pi$
$379$	−14.2093	+	3.80736i	−0.729881	+	0.195571i	−0.125305	+	0.992118i	$0.539991\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.9111	+	2.92363i	0.557532	+	0.149390i	0.526572	−	0.850130i	$-0.323477\pi$
$383$	10.9111	+	2.92363i	0.557532	+	0.149390i	0.0309600	+	0.999521i	$0.490144\pi$
$384$		0			0
$385$	18.5679	−	18.5679i	0.946307	−	0.946307i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.07825			−0.460285			−0.230143	−	0.973157i	$-0.573919\pi$
$389$	−9.07825			−0.460285			−0.230143	+	0.973157i	$0.573919\pi$
$390$		0			0
$391$	−29.9963			−1.51698
$392$		0			0
$393$		0			0
$394$		0			0
$395$	33.1315	−	33.1315i	1.66702	−	1.66702i
$396$		0			0
$397$	25.9851	+	6.96270i	1.30416	+	0.349448i	0.843021	−	0.537881i	$-0.180775\pi$
$397$	25.9851	+	6.96270i	1.30416	+	0.349448i	0.461137	+	0.887329i	$0.347442\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.0063	−	3.75297i	0.699441	−	0.187415i	0.108461	−	0.994101i	$-0.465408\pi$
$401$	14.0063	−	3.75297i	0.699441	−	0.187415i	0.590980	+	0.806686i	$0.298741\pi$
$402$		0			0
$403$	−1.72281	−	17.9065i	−0.0858193	−	0.891985i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.8152	+	23.9286i	0.684793	+	1.18610i
$408$		0			0
$409$	8.81067	−	32.8819i	0.435660	−	1.62590i	−0.303822	−	0.952729i	$-0.598263\pi$
$409$	8.81067	−	32.8819i	0.435660	−	1.62590i	0.739482	−	0.673176i	$-0.235070\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.43216	+	14.6049i	−0.414919	+	0.718661i
$414$		0			0
$415$		−	53.0435i		−	2.60380i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.2927	−	8.82923i	−0.747096	−	0.431336i	0.0775479	−	0.996989i	$-0.475291\pi$
$419$	−15.2927	−	8.82923i	−0.747096	−	0.431336i	−0.824644	+	0.565653i	$0.808624\pi$
$420$		0			0
$421$	−27.6020	−	27.6020i	−1.34524	−	1.34524i	−0.890754	−	0.454485i	$-0.849823\pi$
$421$	−27.6020	−	27.6020i	−1.34524	−	1.34524i	−0.454485	−	0.890754i	$-0.650177\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−36.3003	+	20.9580i	−1.76082	+	1.01661i
$426$		0			0
$427$	−0.488334	−	1.82249i	−0.0236322	−	0.0881964i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5.15037	+	19.2214i	0.248084	+	0.925864i	0.971808	+	0.235774i	$0.0757624\pi$
$431$	5.15037	+	19.2214i	0.248084	+	0.925864i	−0.723724	+	0.690090i	$0.757571\pi$
$432$		0			0
$433$	−31.9923	+	18.4708i	−1.53745	+	0.887648i	−0.538465	+	0.842648i	$0.680996\pi$
$433$	−31.9923	+	18.4708i	−1.53745	+	0.887648i	−0.998987	+	0.0450003i	$0.985671\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.8932	−	10.8932i	−0.521092	−	0.521092i
$438$		0			0
$439$	1.82763	+	1.05518i	0.0872280	+	0.0503611i	0.542980	−	0.839746i	$-0.317296\pi$
$439$	1.82763	+	1.05518i	0.0872280	+	0.0503611i	−0.455752	+	0.890107i	$0.650629\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	10.2789i		−	0.488363i	−0.969729	−	0.244182i	$-0.921481\pi$
$443$		−	10.2789i		−	0.488363i	0.969729	−	0.244182i	$-0.0785193\pi$
$444$		0			0
$445$	−0.432747	+	0.749541i	−0.0205142	+	0.0355316i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0763733	+	0.285029i	−0.00360428	+	0.0134514i	−0.967705	−	0.252087i	$-0.918883\pi$
$449$	−0.0763733	+	0.285029i	−0.00360428	+	0.0134514i	0.964100	+	0.265538i	$0.0855497\pi$
$450$		0			0
$451$	−0.130696	−	0.226372i	−0.00615423	−	0.0106594i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	20.4602	+	3.42547i	0.959187	+	0.160589i
$456$		0			0
$457$	32.6590	−	8.75096i	1.52773	−	0.409353i	0.605449	−	0.795884i	$-0.292994\pi$
$457$	32.6590	−	8.75096i	1.52773	−	0.409353i	0.922276	+	0.386531i	$0.126327\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.7185	−	8.23101i	−1.43070	−	0.383356i	−0.541436	−	0.840742i	$-0.682119\pi$
$461$	−30.7185	−	8.23101i	−1.43070	−	0.383356i	−0.889269	+	0.457386i	$0.848786\pi$
$462$		0			0
$463$	6.96155	−	6.96155i	0.323531	−	0.323531i	−0.526589	−	0.850120i	$-0.676529\pi$
$463$	6.96155	−	6.96155i	0.323531	−	0.323531i	0.850120	+	0.526589i	$0.176529\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.42389			−0.436086			−0.218043	−	0.975939i	$-0.569967\pi$
$467$	−9.42389			−0.436086			−0.218043	+	0.975939i	$0.569967\pi$
$468$		0			0
$469$	−13.0518			−0.602674
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.60663	−	9.60663i	0.441713	−	0.441713i
$474$		0			0
$475$	−20.7934	−	5.57159i	−0.954069	−	0.255642i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.5888	−	2.83725i	0.483812	−	0.129637i	−0.00866486	−	0.999962i	$-0.502758\pi$
$479$	10.5888	−	2.83725i	0.483812	−	0.129637i	0.492477	+	0.870325i	$0.336091\pi$
$480$		0			0
$481$	−9.05359	+	19.8622i	−0.412808	+	0.905640i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.0593	−	36.4758i	−0.956253	−	1.65628i
$486$		0			0
$487$	3.94286	−	14.7149i	0.178668	−	0.666798i	−0.817230	−	0.576312i	$-0.804491\pi$
$487$	3.94286	−	14.7149i	0.178668	−	0.666798i	0.995898	−	0.0904859i	$-0.0288420\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.8441	+	27.4428i	−0.715036	+	1.23848i	0.247910	+	0.968783i	$0.420256\pi$
$491$	−15.8441	+	27.4428i	−0.715036	+	1.23848i	−0.962946	+	0.269695i	$0.913077\pi$
$492$		0			0
$493$		−	34.7312i		−	1.56421i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.7648	−	10.2565i	−0.796859	−	0.460067i
$498$		0			0
$499$	18.1884	+	18.1884i	0.814223	+	0.814223i	0.985264	−	0.171041i	$-0.0547131\pi$
$499$	18.1884	+	18.1884i	0.814223	+	0.814223i	−0.171041	+	0.985264i	$0.554713\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−21.0862	+	12.1741i	−0.940188	+	0.542818i	−0.890019	−	0.455923i	$-0.849309\pi$
$503$	−21.0862	+	12.1741i	−0.940188	+	0.542818i	−0.0501689	+	0.998741i	$0.515976\pi$
$504$		0			0
$505$	6.76950	+	25.2641i	0.301239	+	1.12424i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.50303	+	35.4658i	0.421215	+	1.57199i	0.772053	+	0.635558i	$0.219230\pi$
$509$	9.50303	+	35.4658i	0.421215	+	1.57199i	−0.350838	+	0.936436i	$0.614103\pi$
$510$		0			0
$511$	15.0330	−	8.67930i	0.665020	−	0.383949i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.3984	−	25.3984i	−1.11919	−	1.11919i
$516$		0			0
$517$	39.7339	+	22.9404i	1.74750	+	1.00892i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			6.32648i			0.277168i	0.990351	+	0.138584i	$0.0442551\pi$
$521$			6.32648i			0.277168i	−0.990351	+	0.138584i	$0.955745\pi$
$522$		0			0
$523$	−13.8457	+	23.9814i	−0.605429	+	1.04863i	0.386555	+	0.922266i	$0.373665\pi$
$523$	−13.8457	+	23.9814i	−0.605429	+	1.04863i	−0.991984	+	0.126367i	$0.959668\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.94012	−	22.1688i	0.258756	−	0.965690i
$528$		0			0
$529$	−9.76100	−	16.9065i	−0.424391	−	0.735067i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.0856498	−	0.187903i	0.00370990	−	0.00813899i
$534$		0			0
$535$	11.2142	−	3.00482i	0.484830	−	0.129910i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	20.5176	+	5.49768i	0.883757	+	0.236802i
$540$		0			0
$541$	3.25698	−	3.25698i	0.140028	−	0.140028i	−0.633618	−	0.773646i	$-0.718431\pi$
$541$	3.25698	−	3.25698i	0.140028	−	0.140028i	0.773646	+	0.633618i	$0.218431\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.49051			0.0638464
$546$		0			0
$547$	7.51767			0.321433			0.160716	−	0.987001i	$-0.448620\pi$
$547$	7.51767			0.321433			0.160716	+	0.987001i	$0.448620\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.6127	−	12.6127i	0.537319	−	0.537319i
$552$		0			0
$553$	−18.4522	−	4.94425i	−0.784666	−	0.210251i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.3039	−	6.51221i	1.02979	−	0.275931i	0.295914	−	0.955215i	$-0.404376\pi$
$557$	24.3039	−	6.51221i	1.02979	−	0.275931i	0.733876	+	0.679283i	$0.237709\pi$
$558$		0			0
$559$	10.5857	+	1.77227i	0.447725	+	0.0749588i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.89548	−	3.28307i	−0.0798850	−	0.138365i	0.823315	−	0.567584i	$-0.192122\pi$
$563$	−1.89548	−	3.28307i	−0.0798850	−	0.138365i	−0.903200	+	0.429220i	$0.858789\pi$
$564$		0			0
$565$	4.17819	−	15.5932i	0.175778	−	0.656011i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.4549	+	28.5008i	−0.689826	+	1.19481i	0.282068	+	0.959395i	$0.408980\pi$
$569$	−16.4549	+	28.5008i	−0.689826	+	1.19481i	−0.971894	+	0.235419i	$0.924354\pi$
$570$		0			0
$571$		−	37.1542i		−	1.55486i	−0.628972	−	0.777428i	$-0.716524\pi$
$571$		−	37.1542i		−	1.55486i	0.628972	−	0.777428i	$-0.283476\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−51.4584	−	29.7095i	−2.14597	−	1.23897i
$576$		0			0
$577$	−24.4148	−	24.4148i	−1.01640	−	1.01640i	−0.999863	−	0.0165365i	$-0.994736\pi$
$577$	−24.4148	−	24.4148i	−1.01640	−	1.01640i	−0.0165365	−	0.999863i	$-0.505264\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18.7289	+	10.8131i	−0.777004	+	0.448603i
$582$		0			0
$583$	10.0225	+	37.4046i	0.415091	+	1.54914i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.9909	+	41.0187i	0.453644	+	1.69302i	0.692044	+	0.721855i	$0.256710\pi$
$587$	10.9909	+	41.0187i	0.453644	+	1.69302i	−0.238400	+	0.971167i	$0.576623\pi$
$588$		0			0
$589$	10.2078	−	5.89349i	0.420606	−	0.242837i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.74252	−	7.74252i	−0.317947	−	0.317947i	0.530031	−	0.847978i	$-0.322180\pi$
$593$	−7.74252	−	7.74252i	−0.317947	−	0.317947i	−0.847978	+	0.530031i	$0.822180\pi$
$594$		0			0
$595$	22.9209	+	13.2334i	0.939664	+	0.542516i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			1.71056i			0.0698917i	0.999389	+	0.0349459i	$0.0111259\pi$
$599$			1.71056i			0.0698917i	−0.999389	+	0.0349459i	$0.988874\pi$
$600$		0			0
$601$	−7.04234	+	12.1977i	−0.287263	+	0.497554i	−0.973155	−	0.230149i	$-0.926079\pi$
$601$	−7.04234	+	12.1977i	−0.287263	+	0.497554i	0.685892	+	0.727703i	$0.259412\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.55685	+	35.6666i	−0.388541	+	1.45006i
$606$		0			0
$607$	0.465836	+	0.806852i	0.0189077	+	0.0327491i	0.875324	−	0.483536i	$-0.160648\pi$
$607$	0.465836	+	0.806852i	0.0189077	+	0.0327491i	−0.856417	+	0.516285i	$0.827314\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.47130	+	36.0798i	0.140434	+	1.45963i
$612$		0			0
$613$	−30.8832	+	8.27513i	−1.24736	+	0.334229i	−0.821316	−	0.570473i	$-0.806760\pi$
$613$	−30.8832	+	8.27513i	−1.24736	+	0.334229i	−0.426044	+	0.904702i	$0.640093\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.0522	+	6.44478i	0.968307	+	0.259457i	0.708113	−	0.706099i	$-0.249547\pi$
$617$	24.0522	+	6.44478i	0.968307	+	0.259457i	0.260194	+	0.965556i	$0.416214\pi$
$618$		0			0
$619$	−25.9414	+	25.9414i	−1.04267	+	1.04267i	−0.0436270	+	0.999048i	$0.513891\pi$
$619$	−25.9414	+	25.9414i	−1.04267	+	1.04267i	−0.999048	+	0.0436270i	$0.986109\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.352868			0.0141374
$624$		0			0
$625$	−12.4701			−0.498803
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−19.6922	+	19.6922i	−0.785179	+	0.785179i
$630$		0			0
$631$	37.1199	+	9.94624i	1.47772	+	0.395954i	0.905570	−	0.424196i	$-0.139443\pi$
$631$	37.1199	+	9.94624i	1.47772	+	0.395954i	0.572149	+	0.820150i	$0.306110\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−51.3450	+	13.7579i	−2.03756	+	0.545964i
$636$		0			0
$637$	5.87563	+	15.7188i	0.232801	+	0.622800i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.9829	−	24.2192i	−0.552293	−	0.956599i	−0.998109	−	0.0614743i	$-0.980420\pi$
$641$	−13.9829	−	24.2192i	−0.552293	−	0.956599i	0.445816	−	0.895125i	$-0.352914\pi$
$642$		0			0
$643$	8.40853	−	31.3811i	0.331600	−	1.23755i	−0.575908	−	0.817514i	$-0.695351\pi$
$643$	8.40853	−	31.3811i	0.331600	−	1.23755i	0.907508	−	0.420034i	$-0.137982\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.6370	−	34.0122i	0.772008	−	1.33716i	−0.164452	−	0.986385i	$-0.552586\pi$
$647$	19.6370	−	34.0122i	0.772008	−	1.33716i	0.936461	−	0.350773i	$-0.114081\pi$
$648$		0			0
$649$		−	50.2530i		−	1.97260i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.7912	−	6.80764i	−0.461424	−	0.266403i	0.251219	−	0.967930i	$-0.419169\pi$
$653$	−11.7912	−	6.80764i	−0.461424	−	0.266403i	−0.712643	+	0.701527i	$0.752502\pi$
$654$		0			0
$655$	−1.46297	−	1.46297i	−0.0571631	−	0.0571631i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.3043	−	14.6094i	0.985715	−	0.569103i	0.0817242	−	0.996655i	$-0.473957\pi$
$659$	25.3043	−	14.6094i	0.985715	−	0.569103i	0.903991	+	0.427552i	$0.140624\pi$
$660$		0			0
$661$	−6.54881	−	24.4405i	−0.254719	−	0.950626i	−0.968246	−	0.249998i	$-0.919570\pi$
$661$	−6.54881	−	24.4405i	−0.254719	−	0.950626i	0.713527	−	0.700628i	$-0.247097\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.51803	+	13.1295i	0.136424	+	0.509140i
$666$		0			0
$667$	42.6380	−	24.6171i	1.65095	−	0.953177i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.97557	+	3.97557i	0.153475	+	0.153475i
$672$		0			0
$673$	30.0869	+	17.3707i	1.15976	+	0.669590i	0.951247	−	0.308429i	$-0.0998034\pi$
$673$	30.0869	+	17.3707i	1.15976	+	0.669590i	0.208516	+	0.978019i	$0.433137\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	41.0824i		−	1.57893i	−0.613798	−	0.789463i	$-0.710359\pi$
$677$		−	41.0824i		−	1.57893i	0.613798	−	0.789463i	$-0.289641\pi$
$678$		0			0
$679$	−8.58602	+	14.8714i	−0.329501	+	0.570713i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.54653	−	24.4320i	0.250496	−	0.934864i	−0.720045	−	0.693928i	$-0.755879\pi$
$683$	6.54653	−	24.4320i	0.250496	−	0.934864i	0.970541	−	0.240937i	$-0.0774546\pi$
$684$		0			0
$685$	−4.08178	−	7.06985i	−0.155957	−	0.270125i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.4611	+	23.6045i	−0.741407	+	0.899258i
$690$		0			0
$691$	−37.6468	+	10.0874i	−1.43215	+	0.383744i	−0.889778	−	0.456394i	$-0.849141\pi$
$691$	−37.6468	+	10.0874i	−1.43215	+	0.383744i	−0.542374	+	0.840137i	$0.682474\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.3857	+	4.65850i	0.659479	+	0.176707i
$696$		0			0
$697$	0.186294	−	0.186294i	0.00705641	−	0.00705641i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	34.5211			1.30384			0.651922	−	0.758286i	$-0.273963\pi$
$701$	34.5211			1.30384			0.651922	+	0.758286i	$0.273963\pi$
$702$		0			0
$703$	−14.3025			−0.539430
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.54038	−	7.54038i	0.283585	−	0.283585i
$708$		0			0
$709$	−0.117489	−	0.0314811i	−0.00441239	−	0.00118230i	0.256612	−	0.966514i	$-0.417394\pi$
$709$	−0.117489	−	0.0314811i	−0.00441239	−	0.00118230i	−0.261025	+	0.965332i	$0.584060\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	31.4260	−	8.42058i	1.17691	−	0.315353i
$714$		0			0
$715$	−57.9035	+	21.6442i	−2.16547	+	0.809447i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.22262	−	5.58175i	−0.120184	−	0.208164i	0.799656	−	0.600458i	$-0.205015\pi$
$719$	−3.22262	−	5.58175i	−0.120184	−	0.208164i	−0.919840	+	0.392294i	$0.871682\pi$
$720$		0			0
$721$	−3.79023	+	14.1453i	−0.141156	+	0.526800i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	34.3992	−	59.5812i	1.27756	−	2.21279i
$726$		0			0
$727$			22.9813i			0.852329i	0.904646	+	0.426165i	$0.140136\pi$
$727$			22.9813i			0.852329i	−0.904646	+	0.426165i	$0.859864\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11.8588	+	6.84667i	0.438613	+	0.253233i
$732$		0			0
$733$	25.2757	+	25.2757i	0.933580	+	0.933580i	0.997928	−	0.0643480i	$-0.0204968\pi$
$733$	25.2757	+	25.2757i	0.933580	+	0.933580i	−0.0643480	+	0.997928i	$0.520497\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	33.6816	−	19.4461i	1.24068	−	0.716305i
$738$		0			0
$739$	−10.9868	−	41.0035i	−0.404158	−	1.50834i	−0.805604	−	0.592454i	$-0.798159\pi$
$739$	−10.9868	−	41.0035i	−0.404158	−	1.50834i	0.401447	−	0.915882i	$-0.368508\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.240684	−	0.898244i	−0.00882983	−	0.0329534i	0.961370	−	0.275258i	$-0.0887633\pi$
$743$	−0.240684	−	0.898244i	−0.00882983	−	0.0329534i	−0.970200	+	0.242305i	$0.922097\pi$
$744$		0			0
$745$	−35.9162	+	20.7362i	−1.31587	+	0.759717i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.34700	−	3.34700i	−0.122297	−	0.122297i
$750$		0			0
$751$	−26.2440	−	15.1520i	−0.957656	−	0.552903i	−0.0622053	−	0.998063i	$-0.519813\pi$
$751$	−26.2440	−	15.1520i	−0.957656	−	0.552903i	−0.895451	+	0.445160i	$0.853147\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			20.7675i			0.755806i
$756$		0			0
$757$	5.93031	−	10.2716i	0.215541	−	0.373328i	−0.737899	−	0.674911i	$-0.764182\pi$
$757$	5.93031	−	10.2716i	0.215541	−	0.373328i	0.953440	+	0.301583i	$0.0975152\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.76242	+	32.7018i	−0.317638	+	1.18544i	0.603871	+	0.797082i	$0.293624\pi$
$761$	−8.76242	+	32.7018i	−0.317638	+	1.18544i	−0.921509	+	0.388357i	$0.873043\pi$
$762$		0			0
$763$	−0.303846	−	0.526276i	−0.0109999	−	0.0190525i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	32.3226	−	23.0517i	1.16710	−	0.832349i
$768$		0			0
$769$	−37.4338	+	10.0304i	−1.34990	+	0.361704i	−0.860097	−	0.510130i	$-0.829597\pi$
$769$	−37.4338	+	10.0304i	−1.34990	+	0.361704i	−0.489801	+	0.871834i	$0.662931\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	35.9243	+	9.62588i	1.29211	+	0.346219i	0.838460	−	0.544963i	$-0.183456\pi$
$773$	35.9243	+	9.62588i	1.29211	+	0.346219i	0.453646	+	0.891182i	$0.350123\pi$
$774$		0			0
$775$	32.1472	−	32.1472i	1.15476	−	1.15476i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.135306			0.00484785
$780$		0			0
$781$	61.1254			2.18724
$782$		0			0
$783$		0			0
$784$		0			0
$785$	51.9348	−	51.9348i	1.85363	−	1.85363i
$786$		0			0
$787$	−1.83632	−	0.492042i	−0.0654579	−	0.0175394i	0.225941	−	0.974141i	$-0.427454\pi$
$787$	−1.83632	−	0.492042i	−0.0654579	−	0.0175394i	−0.291399	+	0.956601i	$0.594121\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.35746	+	1.70348i	−0.226045	+	0.0605686i
$792$		0			0
$793$	−0.733427	+	4.38072i	−0.0260447	+	0.155564i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.06156	+	15.6951i	0.320977	+	0.555948i	0.980690	−	0.195569i	$-0.0626555\pi$
$797$	9.06156	+	15.6951i	0.320977	+	0.555948i	−0.659713	+	0.751518i	$0.729322\pi$
$798$		0			0
$799$	−11.9688	+	44.6681i	−0.423425	+	1.58024i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−25.8629	+	44.7959i	−0.912683	+	1.58081i
$804$		0			0
$805$			37.5186i			1.32236i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	29.6264	+	17.1048i	1.04161	+	0.601374i	0.920289	−	0.391240i	$-0.127954\pi$
$809$	29.6264	+	17.1048i	1.04161	+	0.601374i	0.121321	+	0.992613i	$0.461287\pi$
$810$		0			0
$811$	5.33435	+	5.33435i	0.187314	+	0.187314i	0.794534	−	0.607220i	$-0.207715\pi$
$811$	5.33435	+	5.33435i	0.187314	+	0.187314i	−0.607220	+	0.794534i	$0.707715\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.57136	−	5.52603i	0.335270	−	0.193568i
$816$		0			0
$817$	1.82016	+	6.79292i	0.0636792	+	0.237654i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.51355	+	24.3089i	0.227324	+	0.848386i	0.981460	+	0.191667i	$0.0613894\pi$
$821$	6.51355	+	24.3089i	0.227324	+	0.848386i	−0.754136	+	0.656719i	$0.771944\pi$
$822$		0			0
$823$	2.87699	−	1.66103i	0.100286	−	0.0578999i	−0.449018	−	0.893522i	$-0.648226\pi$
$823$	2.87699	−	1.66103i	0.100286	−	0.0578999i	0.549304	+	0.835623i	$0.314893\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.5396	−	23.5396i	−0.818551	−	0.818551i	0.167347	−	0.985898i	$-0.446480\pi$
$827$	−23.5396	−	23.5396i	−0.818551	−	0.818551i	−0.985898	+	0.167347i	$0.946480\pi$
$828$		0			0
$829$	0.982975	+	0.567521i	0.0341401	+	0.0197108i	0.516973	−	0.856002i	$-0.327059\pi$
$829$	0.982975	+	0.567521i	0.0341401	+	0.0197108i	−0.482833	+	0.875713i	$0.660392\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			21.4095i			0.741795i
$834$		0			0
$835$	−38.9395	+	67.4452i	−1.34756	+	2.33404i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.81885	−	10.5201i	0.0973174	−	0.363194i	−0.900043	−	0.435801i	$-0.856465\pi$
$839$	2.81885	−	10.5201i	0.0973174	−	0.363194i	0.997361	+	0.0726071i	$0.0231319\pi$
$840$		0			0
$841$	14.0029	+	24.2537i	0.482859	+	0.836336i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−40.4826	−	27.3149i	−1.39264	−	0.939662i
$846$		0			0
$847$	14.5415	−	3.89639i	0.499653	−	0.133882i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−38.1329	−	10.2177i	−1.30718	−	0.350257i
$852$		0			0
$853$	−6.22202	+	6.22202i	−0.213038	+	0.213038i	−0.805557	−	0.592519i	$-0.798134\pi$
$853$	−6.22202	+	6.22202i	−0.213038	+	0.213038i	0.592519	+	0.805557i	$0.298134\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−51.0682			−1.74446			−0.872228	−	0.489100i	$-0.837325\pi$
$857$	−51.0682			−1.74446			−0.872228	+	0.489100i	$0.837325\pi$
$858$		0			0
$859$	−39.4257			−1.34519			−0.672594	−	0.740011i	$-0.734820\pi$
$859$	−39.4257			−1.34519			−0.672594	+	0.740011i	$0.734820\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34.6691	+	34.6691i	−1.18015	+	1.18015i	−0.200445	+	0.979705i	$0.564239\pi$
$863$	−34.6691	+	34.6691i	−1.18015	+	1.18015i	−0.979705	+	0.200445i	$0.935761\pi$
$864$		0			0
$865$	52.5212	+	14.0730i	1.78578	+	0.478497i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	54.9845	−	14.7331i	1.86522	−	0.499785i
$870$		0			0
$871$	27.9579	+	12.7437i	0.947316	+	0.431805i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.8298	+	20.4897i	0.399919	+	0.692679i
$876$		0			0
$877$	6.37063	−	23.7755i	0.215121	−	0.802843i	−0.771003	−	0.636832i	$-0.780245\pi$
$877$	6.37063	−	23.7755i	0.215121	−	0.802843i	0.986124	−	0.166011i	$-0.0530887\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.7541	−	39.4112i	0.766604	−	1.32780i	−0.172790	−	0.984959i	$-0.555278\pi$
$881$	22.7541	−	39.4112i	0.766604	−	1.32780i	0.939394	−	0.342839i	$-0.111389\pi$
$882$		0			0
$883$		−	11.3895i		−	0.383288i	−0.981464	−	0.191644i	$-0.938618\pi$
$883$		−	11.3895i		−	0.383288i	0.981464	−	0.191644i	$-0.0613820\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.38602	+	3.68697i	0.214422	+	0.123796i	0.603365	−	0.797465i	$-0.293826\pi$
$887$	6.38602	+	3.68697i	0.214422	+	0.123796i	−0.388943	+	0.921262i	$0.627160\pi$
$888$		0			0
$889$	15.3245	+	15.3245i	0.513969	+	0.513969i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.5678	+	11.8748i	−0.688275	+	0.397376i
$894$		0			0
$895$	23.5199	+	87.7774i	0.786183	+	2.93408i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.74978	+	36.3867i	0.325173	+	1.21356i
$900$		0			0
$901$	−33.8014	+	19.5152i	−1.12609	+	0.650147i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	19.3326	+	19.3326i	0.642637	+	0.642637i
$906$		0			0
$907$	22.4670	+	12.9713i	0.746005	+	0.430706i	0.824248	−	0.566228i	$-0.191598\pi$
$907$	22.4670	+	12.9713i	0.746005	+	0.430706i	−0.0782439	+	0.996934i	$0.524931\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			41.7710i			1.38394i	0.721928	+	0.691968i	$0.243256\pi$
$911$			41.7710i			1.38394i	−0.721928	+	0.691968i	$0.756744\pi$
$912$		0			0
$913$	32.2213	−	55.8090i	1.06637	−	1.84701i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.218321	+	0.814785i	−0.00720960	+	0.0269066i
$918$		0			0
$919$	−26.6800	−	46.2111i	−0.880092	−	1.52436i	−0.851238	−	0.524780i	$-0.824147\pi$
$919$	−26.6800	−	46.2111i	−0.880092	−	1.52436i	−0.0288543	−	0.999584i	$-0.509186\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	28.0391	+	39.3157i	0.922917	+	1.29409i
$924$		0			0
$925$	−53.2859	+	14.2779i	−1.75203	+	0.469455i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.7725	−	2.88648i	−0.353434	−	0.0947023i	0.0777338	−	0.996974i	$-0.475232\pi$
$929$	−10.7725	−	2.88648i	−0.353434	−	0.0947023i	−0.431168	+	0.902272i	$0.641898\pi$
$930$		0			0
$931$	−7.77490	+	7.77490i	−0.254812	+	0.254812i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−78.8667			−2.57922
$936$		0			0
$937$	19.8652			0.648967			0.324483	−	0.945891i	$-0.394810\pi$
$937$	19.8652			0.648967			0.324483	+	0.945891i	$0.394810\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	13.5836	−	13.5836i	0.442814	−	0.442814i	−0.450143	−	0.892957i	$-0.648627\pi$
$941$	13.5836	−	13.5836i	0.442814	−	0.442814i	0.892957	+	0.450143i	$0.148627\pi$
$942$		0			0
$943$	0.360749	+	0.0966624i	0.0117476	+	0.00314776i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.5003	+	4.42125i	−0.536189	+	0.143671i	−0.516745	−	0.856140i	$-0.672856\pi$
$947$	−16.5003	+	4.42125i	−0.536189	+	0.143671i	−0.0194443	+	0.999811i	$0.506190\pi$
$948$		0			0
$949$	−40.6763	+	3.91353i	−1.32041	+	0.127039i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.5143	+	26.8715i	0.502556	+	0.870453i	0.999996	+	0.00295435i	$0.000940401\pi$
$953$	15.5143	+	26.8715i	0.502556	+	0.870453i	−0.497439	+	0.867499i	$0.665726\pi$
$954$		0			0
$955$	−20.2481	+	75.5670i	−0.655214	+	2.44529i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.66417	+	2.88243i	−0.0537389	+	0.0930784i
$960$		0			0
$961$		−	6.10695i		−	0.196999i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	36.2620	+	20.9359i	1.16731	+	0.673949i
$966$		0			0
$967$	32.3758	+	32.3758i	1.04113	+	1.04113i	0.999117	+	0.0420173i	$0.0133785\pi$
$967$	32.3758	+	32.3758i	1.04113	+	1.04113i	0.0420173	+	0.999117i	$0.486622\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.5211	−	10.1158i	0.562280	−	0.324632i	−0.191780	−	0.981438i	$-0.561426\pi$
$971$	17.5211	−	10.1158i	0.562280	−	0.324632i	0.754060	+	0.656806i	$0.228093\pi$
$972$		0			0
$973$	−1.89930	−	7.08829i	−0.0608888	−	0.227240i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6637	−	39.7974i	−0.341161	−	1.27323i	−0.897033	−	0.441963i	$-0.854282\pi$
$977$	−10.6637	−	39.7974i	−0.341161	−	1.27323i	0.555872	−	0.831268i	$-0.312384\pi$
$978$		0			0
$979$	−0.910618	+	0.525746i	−0.0291035	+	0.0168029i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.72603	−	4.72603i	−0.150737	−	0.150737i	0.627710	−	0.778447i	$-0.283992\pi$
$983$	−4.72603	−	4.72603i	−0.150737	−	0.150737i	−0.778447	+	0.627710i	$0.783992\pi$
$984$		0			0
$985$	32.3937	+	18.7025i	1.03215	+	0.595911i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			19.4114i			0.617245i
$990$		0			0
$991$	29.6260	−	51.3137i	0.941100	−	1.63003i	0.177722	−	0.984081i	$-0.443127\pi$
$991$	29.6260	−	51.3137i	0.941100	−	1.63003i	0.763378	−	0.645952i	$-0.223540\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	18.2955	−	68.2796i	0.580005	−	2.16461i
$996$		0			0
$997$	9.94041	+	17.2173i	0.314816	+	0.545277i	0.979398	−	0.201938i	$-0.0647239\pi$
$997$	9.94041	+	17.2173i	0.314816	+	0.545277i	−0.664583	+	0.747215i	$0.731391\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dr.b.449.1	✓	32
3.2	odd	2	inner	936.2.dr.b.449.8	yes	32
13.2	odd	12	inner	936.2.dr.b.665.8	yes	32
39.2	even	12	inner	936.2.dr.b.665.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dr.b.449.1	✓	32	1.1	even	1	trivial
936.2.dr.b.449.8	yes	32	3.2	odd	2	inner
936.2.dr.b.665.1	yes	32	39.2	even	12	inner
936.2.dr.b.665.8	yes	32	13.2	odd	12	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dr (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65632 + 2.65632i) q^{5} +(1.47941 + 0.396406i) q^{7} +(-4.40840 + 1.18123i) q^{11} +(-2.78196 - 2.29363i) q^{13} +(-2.30001 - 3.98374i) q^{17} +(0.611448 - 2.28196i) q^{19} +(3.26044 - 5.64726i) q^{23} -9.11212i q^{25} +(6.53868 + 3.77511i) q^{29} +(3.52796 + 3.52796i) q^{31} +(-4.98277 + 2.87680i) q^{35} +(-1.56691 - 5.84780i) q^{37} +(0.0148235 + 0.0553221i) q^{41} +(-2.57798 + 1.48840i) q^{43} +(-7.10851 - 7.10851i) q^{47} +(-4.03067 - 2.32711i) q^{49} -8.48484i q^{53} +(8.57242 - 14.8479i) q^{55} +(-2.84984 + 10.6357i) q^{59} +(-0.615952 - 1.06686i) q^{61} +(13.4824 - 1.29716i) q^{65} +(-8.23130 + 2.20557i) q^{67} +(-12.9368 - 3.46642i) q^{71} +(8.01411 - 8.01411i) q^{73} -6.99007 q^{77} -12.4727 q^{79} +(-9.98438 + 9.98438i) q^{83} +(16.6917 + 4.47252i) q^{85} +(0.222542 - 0.0596300i) q^{89} +(-3.20644 - 4.49599i) q^{91} +(4.43741 + 7.68582i) q^{95} +(-2.90184 + 10.8298i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{7} - 20 q^{13} - 4 q^{19} + 4 q^{31} + 60 q^{43} + 84 q^{49} - 28 q^{61} - 24 q^{67} + 16 q^{73} + 48 q^{79} + 88 q^{85} - 116 q^{91} + 72 q^{97}+O(q^{100}) \) 32 * q + 4 * q^7 - 20 * q^13 - 4 * q^19 + 4 * q^31 + 60 * q^43 + 84 * q^49 - 28 * q^61 - 24 * q^67 + 16 * q^73 + 48 * q^79 + 88 * q^85 - 116 * q^91 + 72 * q^97

Introduction

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