LMFDB - Embedded newform 1044.2.z.c.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1044,2,Mod(109,1044)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1044, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("1044.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1044 = 2^{2} \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1044.z (of order $14$, degree $6$, 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:	$8.33638197102$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	1044.361
Dual form			1044.2.z.c.937.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25988 + 0.606724i) q^{5} +(1.39612 - 1.75068i) q^{7} +O(q^{10})$	$q+(1.25988 + 0.606724i) q^{5} +(1.39612 - 1.75068i) q^{7} +(4.39517 + 1.00317i) q^{11} +(-0.444271 + 1.94648i) q^{13} +2.28657i q^{17} +(-2.02134 + 1.61196i) q^{19} +(2.43612 - 1.17317i) q^{23} +(-1.89828 - 2.38036i) q^{25} +(3.73697 - 3.87751i) q^{29} +(0.190824 - 0.396249i) q^{31} +(2.82111 - 1.35858i) q^{35} +(-0.614322 + 0.140215i) q^{37} -1.00818i q^{41} +(-0.679751 - 1.41152i) q^{43} +(7.74412 + 1.76755i) q^{47} +(0.441923 + 1.93619i) q^{49} +(3.60829 + 1.73766i) q^{53} +(4.92872 + 3.93052i) q^{55} +8.70839 q^{59} +(1.15433 + 0.920544i) q^{61} +(-1.74070 + 2.18277i) q^{65} +(1.36788 + 5.99309i) q^{67} +(-3.27814 + 14.3625i) q^{71} +(-7.07173 - 14.6846i) q^{73} +(7.89240 - 6.29398i) q^{77} +(-5.25439 + 1.19928i) q^{79} +(3.64866 + 4.57528i) q^{83} +(-1.38732 + 2.88080i) q^{85} +(4.21497 - 8.75248i) q^{89} +(2.78740 + 3.49529i) q^{91} +(-3.52465 + 0.804479i) q^{95} +(1.25916 - 1.00414i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

$n$	$523$	$901$	$929$
$\chi(n)$	$1$	$e\left(\frac{9}{14}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	1.25988	+	0.606724i	0.563433	+	0.271335i	0.693845	−	0.720125i	$-0.255915\pi$
$5$	1.25988	+	0.606724i	0.563433	+	0.271335i	−0.130411	+	0.991460i	$0.541630\pi$
$6$		0			0
$7$	1.39612	−	1.75068i	0.527683	−	0.661694i	−0.444537	−	0.895760i	$-0.646632\pi$
$7$	1.39612	−	1.75068i	0.527683	−	0.661694i	0.972221	+	0.234066i	$0.0752033\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.39517	+	1.00317i	1.32519	+	0.302467i	0.825827	−	0.563924i	$-0.190709\pi$
$11$	4.39517	+	1.00317i	1.32519	+	0.302467i	0.499367	+	0.866391i	$0.333566\pi$
$12$		0			0
$13$	−0.444271	+	1.94648i	−0.123219	+	0.539857i	0.875206	+	0.483750i	$0.160726\pi$
$13$	−0.444271	+	1.94648i	−0.123219	+	0.539857i	−0.998425	+	0.0561063i	$0.982131\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			2.28657i			0.554575i	0.960787	+	0.277288i	$0.0894355\pi$
$17$			2.28657i			0.554575i	−0.960787	+	0.277288i	$0.910565\pi$
$18$		0			0
$19$	−2.02134	+	1.61196i	−0.463727	+	0.369810i	−0.827304	−	0.561754i	$-0.810127\pi$
$19$	−2.02134	+	1.61196i	−0.463727	+	0.369810i	0.363577	+	0.931564i	$0.381555\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.43612	−	1.17317i	0.507966	−	0.244623i	−0.162304	−	0.986741i	$-0.551893\pi$
$23$	2.43612	−	1.17317i	0.507966	−	0.244623i	0.670270	+	0.742117i	$0.266178\pi$
$24$		0			0
$25$	−1.89828	−	2.38036i	−0.379655	−	0.476073i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.73697	−	3.87751i	0.693937	−	0.720035i
$29$	3.73697	−	3.87751i	0.693937	−	0.720035i
$30$		0			0
$31$	0.190824	−	0.396249i	0.0342729	−	0.0711685i	−0.883129	−	0.469129i	$-0.844568\pi$
$31$	0.190824	−	0.396249i	0.0342729	−	0.0711685i	0.917402	+	0.397961i	$0.130282\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.82111	−	1.35858i	0.476855	−	0.229641i
$36$		0			0
$37$	−0.614322	+	0.140215i	−0.100994	+	0.0230512i	−0.272719	−	0.962094i	$-0.587923\pi$
$37$	−0.614322	+	0.140215i	−0.100994	+	0.0230512i	0.171725	+	0.985145i	$0.445066\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	1.00818i		−	0.157451i	−0.996896	−	0.0787257i	$-0.974915\pi$
$41$		−	1.00818i		−	0.157451i	0.996896	−	0.0787257i	$-0.0250851\pi$
$42$		0			0
$43$	−0.679751	−	1.41152i	−0.103661	−	0.215255i	0.842687	−	0.538404i	$-0.180973\pi$
$43$	−0.679751	−	1.41152i	−0.103661	−	0.215255i	−0.946348	+	0.323150i	$0.895258\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.74412	+	1.76755i	1.12960	+	0.257823i	0.746175	−	0.665750i	$-0.231888\pi$
$47$	7.74412	+	1.76755i	1.12960	+	0.257823i	0.383422	+	0.923573i	$0.374746\pi$
$48$		0			0
$49$	0.441923	+	1.93619i	0.0631318	+	0.276598i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.60829	+	1.73766i	0.495636	+	0.238686i	0.664966	−	0.746874i	$-0.268446\pi$
$53$	3.60829	+	1.73766i	0.495636	+	0.238686i	−0.169330	+	0.985559i	$0.554160\pi$
$54$		0			0
$55$	4.92872	+	3.93052i	0.664589	+	0.529992i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.70839			1.13374			0.566868	−	0.823809i	$-0.308155\pi$
$59$	8.70839			1.13374			0.566868	+	0.823809i	$0.308155\pi$
$60$		0			0
$61$	1.15433	+	0.920544i	0.147796	+	0.117864i	0.694597	−	0.719399i	$-0.255583\pi$
$61$	1.15433	+	0.920544i	0.147796	+	0.117864i	−0.546800	+	0.837263i	$0.684154\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.74070	+	2.18277i	−0.215908	+	0.270740i
$66$		0			0
$67$	1.36788	+	5.99309i	0.167114	+	0.732172i	0.987142	+	0.159849i	$0.0511007\pi$
$67$	1.36788	+	5.99309i	0.167114	+	0.732172i	−0.820028	+	0.572323i	$0.806042\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.27814	+	14.3625i	−0.389043	+	1.70451i	0.278918	+	0.960315i	$0.410024\pi$
$71$	−3.27814	+	14.3625i	−0.389043	+	1.70451i	−0.667962	+	0.744196i	$0.732833\pi$
$72$		0			0
$73$	−7.07173	−	14.6846i	−0.827684	−	1.71870i	−0.684507	−	0.729006i	$-0.739983\pi$
$73$	−7.07173	−	14.6846i	−0.827684	−	1.71870i	−0.143177	−	0.989697i	$-0.545732\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.89240	−	6.29398i	0.899423	−	0.717266i
$78$		0			0
$79$	−5.25439	+	1.19928i	−0.591165	+	0.134929i	−0.507630	−	0.861575i	$-0.669478\pi$
$79$	−5.25439	+	1.19928i	−0.591165	+	0.134929i	−0.0835350	+	0.996505i	$0.526621\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.64866	+	4.57528i	0.400493	+	0.502202i	0.940658	−	0.339357i	$-0.110210\pi$
$83$	3.64866	+	4.57528i	0.400493	+	0.502202i	−0.540165	+	0.841559i	$0.681638\pi$
$84$		0			0
$85$	−1.38732	+	2.88080i	−0.150476	+	0.312466i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.21497	−	8.75248i	0.446786	−	0.927761i	−0.548980	−	0.835836i	$-0.684984\pi$
$89$	4.21497	−	8.75248i	0.446786	−	0.927761i	0.995766	−	0.0919251i	$-0.0293020\pi$
$90$		0			0
$91$	2.78740	+	3.49529i	0.292199	+	0.366406i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.52465	+	0.804479i	−0.361622	+	0.0825378i
$96$		0			0
$97$	1.25916	−	1.00414i	0.127848	−	0.101955i	−0.557478	−	0.830192i	$-0.688231\pi$
$97$	1.25916	−	1.00414i	0.127848	−	0.101955i	0.685326	+	0.728236i	$0.259660\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.09772	+	2.27944i	0.109227	+	0.226813i	0.948417	−	0.317027i	$-0.102684\pi$
$101$	1.09772	+	2.27944i	0.109227	+	0.226813i	−0.839189	+	0.543839i	$0.816970\pi$
$102$		0			0
$103$	2.59702	−	11.3783i	0.255892	−	1.12114i	−0.669706	−	0.742627i	$-0.733580\pi$
$103$	2.59702	−	11.3783i	0.255892	−	1.12114i	0.925598	−	0.378509i	$-0.123563\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.72716	+	7.56717i	0.166971	+	0.731546i	0.987197	+	0.159507i	$0.0509903\pi$
$107$	1.72716	+	7.56717i	0.166971	+	0.731546i	−0.820226	+	0.572039i	$0.806153\pi$
$108$		0			0
$109$	−3.27022	+	4.10073i	−0.313231	+	0.392779i	−0.913379	−	0.407110i	$-0.866537\pi$
$109$	−3.27022	+	4.10073i	−0.313231	+	0.392779i	0.600149	+	0.799888i	$0.295108\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−12.2924	−	9.80286i	−1.15637	−	0.922175i	−0.158498	−	0.987359i	$-0.550665\pi$
$113$	−12.2924	−	9.80286i	−1.15637	−	0.922175i	−0.997873	+	0.0651838i	$0.979237\pi$
$114$		0			0
$115$	3.78100			0.352580
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.00305	+	3.19233i	0.366959	+	0.292640i
$120$		0			0
$121$	8.40052	+	4.04548i	0.763684	+	0.367771i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.50319	−	10.9672i	−0.223892	−	0.980934i
$126$		0			0
$127$	−0.237558	−	0.0542211i	−0.0210799	−	0.00481134i	0.211968	−	0.977277i	$-0.432013\pi$
$127$	−0.237558	−	0.0542211i	−0.0210799	−	0.00481134i	−0.233048	+	0.972465i	$0.574870\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.14889	−	4.46221i	−0.187749	−	0.389865i	0.785754	−	0.618539i	$-0.212275\pi$
$131$	−2.14889	−	4.46221i	−0.187749	−	0.389865i	−0.973503	+	0.228674i	$0.926561\pi$
$132$		0			0
$133$			5.78921i			0.501988i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.0247	+	2.51631i	−0.941903	+	0.214983i	−0.665788	−	0.746141i	$-0.731904\pi$
$137$	−11.0247	+	2.51631i	−0.941903	+	0.214983i	−0.276115	+	0.961125i	$0.589047\pi$
$138$		0			0
$139$	9.77002	−	4.70499i	0.828682	−	0.399072i	0.0290615	−	0.999578i	$-0.490748\pi$
$139$	9.77002	−	4.70499i	0.828682	−	0.399072i	0.799621	+	0.600505i	$0.205034\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.90530	+	8.10943i	−0.326577	+	0.678145i
$144$		0			0
$145$	7.06069	−	2.61787i	0.586358	−	0.217402i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.8909	−	13.6567i	−0.892217	−	1.11880i	−0.992304	−	0.123826i	$-0.960484\pi$
$149$	−10.8909	−	13.6567i	−0.892217	−	1.11880i	0.100087	−	0.994979i	$-0.468088\pi$
$150$		0			0
$151$	−2.17410	+	1.04699i	−0.176926	+	0.0852030i	−0.520250	−	0.854014i	$-0.674161\pi$
$151$	−2.17410	+	1.04699i	−0.176926	+	0.0852030i	0.343324	+	0.939217i	$0.388447\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.480828	−	0.383447i	0.0386210	−	0.0307992i
$156$		0			0
$157$		−	1.34054i		−	0.106986i	−0.998568	−	0.0534932i	$-0.982964\pi$
$157$		−	1.34054i		−	0.106986i	0.998568	−	0.0534932i	$-0.0170355\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.34726	−	5.90274i	0.106179	−	0.465201i
$162$		0			0
$163$	−14.6116	−	3.33500i	−1.14447	−	0.261217i	−0.392076	−	0.919933i	$-0.628243\pi$
$163$	−14.6116	−	3.33500i	−1.14447	−	0.261217i	−0.752392	+	0.658715i	$0.771100\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.76195	+	2.20942i	−0.136344	+	0.170970i	−0.845316	−	0.534267i	$-0.820588\pi$
$167$	−1.76195	+	2.20942i	−0.136344	+	0.170970i	0.708972	+	0.705237i	$0.249159\pi$
$168$		0			0
$169$	8.12119	+	3.91096i	0.624707	+	0.300843i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.8276			−1.20335			−0.601674	−	0.798742i	$-0.705499\pi$
$173$	−15.8276			−1.20335			−0.601674	+	0.798742i	$0.705499\pi$
$174$		0			0
$175$	−6.81747			−0.515352
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.98638	−	4.32761i	−0.671674	−	0.323461i	0.0667776	−	0.997768i	$-0.478728\pi$
$179$	−8.98638	−	4.32761i	−0.671674	−	0.323461i	−0.738451	+	0.674307i	$0.764442\pi$
$180$		0			0
$181$	3.61773	−	4.53649i	0.268904	−	0.337194i	−0.628985	−	0.777418i	$-0.716529\pi$
$181$	3.61773	−	4.53649i	0.268904	−	0.337194i	0.897888	+	0.440223i	$0.145101\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.859041	−	0.196071i	−0.0631580	−	0.0144154i
$186$		0			0
$187$	−2.29382	+	10.0499i	−0.167741	+	0.734920i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			26.8856i			1.94538i	0.232114	+	0.972689i	$0.425436\pi$
$191$			26.8856i			1.94538i	−0.232114	+	0.972689i	$0.574564\pi$
$192$		0			0
$193$	−16.4372	+	13.1082i	−1.18317	+	0.943549i	−0.999224	−	0.0393874i	$-0.987459\pi$
$193$	−16.4372	+	13.1082i	−1.18317	+	0.943549i	−0.183948	+	0.982936i	$0.558888\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.69653	+	2.26173i	−0.334614	+	0.161142i	−0.593644	−	0.804728i	$-0.702311\pi$
$197$	−4.69653	+	2.26173i	−0.334614	+	0.161142i	0.259030	+	0.965869i	$0.416597\pi$
$198$		0			0
$199$	−15.7615	−	19.7643i	−1.11730	−	1.40105i	−0.905816	−	0.423671i	$-0.860741\pi$
$199$	−15.7615	−	19.7643i	−1.11730	−	1.40105i	−0.211486	−	0.977381i	$-0.567830\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.57102	−	11.9557i	−0.110264	−	0.839125i
$204$		0			0
$205$	0.611687	−	1.27018i	0.0427221	−	0.0887133i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.5012	+	5.05711i	−0.726383	+	0.349808i
$210$		0			0
$211$	−9.31891	+	2.12698i	−0.641540	+	0.146427i	−0.530902	−	0.847433i	$-0.678147\pi$
$211$	−9.31891	+	2.12698i	−0.641540	+	0.146427i	−0.110639	+	0.993861i	$0.535290\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	2.19076i		−	0.149409i
$216$		0			0
$217$	−0.427292	−	0.887281i	−0.0290065	−	0.0602326i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.45077	−	1.01586i	−0.299391	−	0.0683341i
$222$		0			0
$223$	1.06991	+	4.68758i	0.0716464	+	0.313903i	0.998035	−	0.0626667i	$-0.0199605\pi$
$223$	1.06991	+	4.68758i	0.0716464	+	0.313903i	−0.926388	+	0.376570i	$0.877103\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.58815	−	1.24639i	−0.171782	−	0.0827257i	0.346017	−	0.938228i	$-0.387534\pi$
$227$	−2.58815	−	1.24639i	−0.171782	−	0.0827257i	−0.517799	+	0.855503i	$0.673248\pi$
$228$		0			0
$229$	1.91400	+	1.52636i	0.126480	+	0.100865i	0.684687	−	0.728837i	$-0.259939\pi$
$229$	1.91400	+	1.52636i	0.126480	+	0.100865i	−0.558207	+	0.829702i	$0.688510\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.24870			−0.343854			−0.171927	−	0.985110i	$-0.554999\pi$
$233$	−5.24870			−0.343854			−0.171927	+	0.985110i	$0.554999\pi$
$234$		0			0
$235$	8.68422	+	6.92543i	0.566496	+	0.451765i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.41869	+	4.28690i	−0.221137	+	0.277297i	−0.880008	−	0.474959i	$-0.842463\pi$
$239$	−3.41869	+	4.28690i	−0.221137	+	0.277297i	0.658871	+	0.752256i	$0.271034\pi$
$240$		0			0
$241$	1.38432	+	6.06512i	0.0891721	+	0.390688i	0.999743	−	0.0226642i	$-0.00721484\pi$
$241$	1.38432	+	6.06512i	0.0891721	+	0.390688i	−0.910571	+	0.413353i	$0.864358\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.617965	+	2.70748i	−0.0394803	+	0.172975i
$246$		0			0
$247$	−2.23963	−	4.65065i	−0.142504	−	0.295914i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.72932	+	2.17656i	−0.172273	+	0.137383i	−0.705831	−	0.708381i	$-0.749426\pi$
$251$	−2.72932	+	2.17656i	−0.172273	+	0.137383i	0.533558	+	0.845764i	$0.320855\pi$
$252$		0			0
$253$	11.8840	−	2.71245i	0.747143	−	0.170531i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.6921	−	19.6773i	−0.978848	−	1.22744i	−0.973790	−	0.227449i	$-0.926961\pi$
$257$	−15.6921	−	19.6773i	−0.978848	−	1.22744i	−0.00505784	−	0.999987i	$-0.501610\pi$
$258$		0			0
$259$	−0.612195	+	1.27124i	−0.0380400	+	0.0789908i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.35513	+	9.04352i	−0.268549	+	0.557647i	−0.991014	−	0.133760i	$-0.957295\pi$
$263$	−4.35513	+	9.04352i	−0.268549	+	0.557647i	0.722465	+	0.691407i	$0.243009\pi$
$264$		0			0
$265$	3.49171	+	4.37847i	0.214494	+	0.268967i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.83281	−	0.874814i	0.233691	−	0.0533384i	−0.104072	−	0.994570i	$-0.533187\pi$
$269$	3.83281	−	0.874814i	0.233691	−	0.0533384i	0.337762	+	0.941231i	$0.390330\pi$
$270$		0			0
$271$	−6.51654	+	5.19677i	−0.395852	+	0.315681i	−0.801106	−	0.598523i	$-0.795754\pi$
$271$	−6.51654	+	5.19677i	−0.395852	+	0.315681i	0.405254	+	0.914204i	$0.367183\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.95534	−	12.3664i	−0.359121	−	0.745722i
$276$		0			0
$277$	3.53350	−	15.4813i	0.212308	−	0.930180i	−0.750687	−	0.660658i	$-0.770277\pi$
$277$	3.53350	−	15.4813i	0.212308	−	0.930180i	0.962994	−	0.269522i	$-0.0868657\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.664047	+	2.90938i	0.0396137	+	0.173559i	0.990865	−	0.134858i	$-0.0430579\pi$
$281$	0.664047	+	2.90938i	0.0396137	+	0.173559i	−0.951251	+	0.308417i	$0.900201\pi$
$282$		0			0
$283$	13.9107	−	17.4434i	0.826902	−	1.03690i	−0.171757	−	0.985139i	$-0.554944\pi$
$283$	13.9107	−	17.4434i	0.826902	−	1.03690i	0.998659	−	0.0517634i	$-0.0164842\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.76500	−	1.40754i	−0.104185	−	0.0830844i
$288$		0			0
$289$	11.7716			0.692446
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−18.3169	−	14.6072i	−1.07008	−	0.853364i	−0.0804190	−	0.996761i	$-0.525626\pi$
$293$	−18.3169	−	14.6072i	−1.07008	−	0.853364i	−0.989665	+	0.143397i	$0.954197\pi$
$294$		0			0
$295$	10.9715	+	5.28359i	0.638785	+	0.307623i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.20126	+	5.26306i	0.0694706	+	0.304371i
$300$		0			0
$301$	−3.42013	−	0.780622i	−0.197133	−	0.0449943i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.895791	+	1.86013i	0.0512928	+	0.106511i
$306$		0			0
$307$			13.8568i			0.790848i	0.918499	+	0.395424i	$0.129402\pi$
$307$			13.8568i			0.790848i	−0.918499	+	0.395424i	$0.870598\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.2360	+	2.56453i	−0.637132	+	0.145421i	−0.528872	−	0.848701i	$-0.677385\pi$
$311$	−11.2360	+	2.56453i	−0.637132	+	0.145421i	−0.108260	+	0.994123i	$0.534528\pi$
$312$		0			0
$313$	−2.67800	+	1.28966i	−0.151369	+	0.0728956i	−0.508035	−	0.861337i	$-0.669628\pi$
$313$	−2.67800	+	1.28966i	−0.151369	+	0.0728956i	0.356665	+	0.934232i	$0.383914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.35708	+	19.4302i	−0.525546	+	1.09131i	0.454170	+	0.890915i	$0.349936\pi$
$317$	−9.35708	+	19.4302i	−0.525546	+	1.09131i	−0.979716	+	0.200392i	$0.935778\pi$
$318$		0			0
$319$	20.3144	−	13.2935i	1.13739	−	0.744294i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.68587	−	4.62194i	−0.205087	−	0.257172i
$324$		0			0
$325$	5.47668	−	2.63743i	0.303792	−	0.146298i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.9061	−	11.0898i	0.766669	−	0.611398i
$330$		0			0
$331$		−	18.3764i		−	1.01006i	−0.863102	−	0.505029i	$-0.831482\pi$
$331$		−	18.3764i		−	1.01006i	0.863102	−	0.505029i	$-0.168518\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.91279	+	8.38047i	−0.104507	+	0.457874i
$336$		0			0
$337$	−20.9167	−	4.77411i	−1.13941	−	0.260062i	−0.389128	−	0.921184i	$-0.627224\pi$
$337$	−20.9167	−	4.77411i	−1.13941	−	0.260062i	−0.750279	+	0.661121i	$0.770081\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.23621	−	1.55015i	0.0669444	−	0.0839456i
$342$		0			0
$343$	18.1288	+	8.73035i	0.978861	+	0.471395i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	32.7420			1.75768			0.878841	−	0.477115i	$-0.158317\pi$
$347$	32.7420			1.75768			0.878841	+	0.477115i	$0.158317\pi$
$348$		0			0
$349$	−31.1996			−1.67008			−0.835039	−	0.550191i	$-0.814555\pi$
$349$	−31.1996			−1.67008			−0.835039	+	0.550191i	$0.814555\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.7919	−	8.08654i	−0.893741	−	0.430403i	−0.0701169	−	0.997539i	$-0.522337\pi$
$353$	−16.7919	−	8.08654i	−0.893741	−	0.430403i	−0.823624	+	0.567136i	$0.808052\pi$
$354$		0			0
$355$	−12.8441	+	16.1060i	−0.681694	+	0.854817i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.44914	−	1.70022i	−0.393151	−	0.0897341i	0.0213753	−	0.999772i	$-0.493196\pi$
$359$	−7.44914	−	1.70022i	−0.393151	−	0.0897341i	−0.414526	+	0.910037i	$0.636053\pi$
$360$		0			0
$361$	−2.74051	+	12.0070i	−0.144238	+	0.631946i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	22.7914i		−	1.19295i
$366$		0			0
$367$	−3.05586	+	2.43697i	−0.159514	+	0.127209i	−0.699994	−	0.714148i	$-0.746814\pi$
$367$	−3.05586	+	2.43697i	−0.159514	+	0.127209i	0.540480	+	0.841357i	$0.318243\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.07968	−	3.89097i	0.419476	−	0.202009i
$372$		0			0
$373$	0.0980361	+	0.122933i	0.00507611	+	0.00636525i	0.784363	−	0.620302i	$-0.212990\pi$
$373$	0.0980361	+	0.122933i	0.00507611	+	0.00636525i	−0.779287	+	0.626667i	$0.784419\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.88727	+	8.99660i	0.303210	+	0.463348i
$378$		0			0
$379$	−6.58166	+	13.6670i	−0.338077	+	0.702024i	−0.998819	−	0.0485889i	$-0.984528\pi$
$379$	−6.58166	+	13.6670i	−0.338077	+	0.702024i	0.660742	+	0.750613i	$0.270242\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.13169	−	3.91601i	0.415510	−	0.200099i	−0.214436	−	0.976738i	$-0.568791\pi$
$383$	8.13169	−	3.91601i	0.415510	−	0.200099i	0.629946	+	0.776639i	$0.283077\pi$
$384$		0			0
$385$	13.7622	−	3.14112i	0.701384	−	0.160086i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			27.1487i			1.37649i	0.725477	+	0.688247i	$0.241619\pi$
$389$			27.1487i			1.37649i	−0.725477	+	0.688247i	$0.758381\pi$
$390$		0			0
$391$	2.68254	+	5.57036i	0.135662	+	0.281705i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.34750	−	1.67702i	−0.369693	−	0.0843800i
$396$		0			0
$397$	−3.07293	−	13.4634i	−0.154226	−	0.675709i	−0.991629	−	0.129122i	$-0.958784\pi$
$397$	−3.07293	−	13.4634i	−0.154226	−	0.675709i	0.837403	−	0.546587i	$-0.184073\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.3191	+	6.89573i	0.715063	+	0.344356i	0.755790	−	0.654814i	$-0.227253\pi$
$401$	14.3191	+	6.89573i	0.715063	+	0.344356i	−0.0407269	+	0.999170i	$0.512967\pi$
$402$		0			0
$403$	0.686514	+	0.547476i	0.0341977	+	0.0272717i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.84071			−0.140809
$408$		0			0
$409$	−17.3984	−	13.8747i	−0.860293	−	0.686061i	0.0904968	−	0.995897i	$-0.471155\pi$
$409$	−17.3984	−	13.8747i	−0.860293	−	0.686061i	−0.950790	+	0.309836i	$0.899726\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.1579	−	15.2456i	0.598254	−	0.750186i
$414$		0			0
$415$	1.82093	+	7.97801i	0.0893859	+	0.391625i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.99737	−	17.5136i	0.195284	−	0.855595i	−0.778414	−	0.627752i	$-0.783975\pi$
$419$	3.99737	−	17.5136i	0.195284	−	0.855595i	0.973698	−	0.227844i	$-0.0731675\pi$
$420$		0			0
$421$	−11.3899	−	23.6514i	−0.555110	−	1.15270i	−0.970063	−	0.242854i	$-0.921916\pi$
$421$	−11.3899	−	23.6514i	−0.555110	−	1.15270i	0.414953	−	0.909843i	$-0.363798\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.44287	−	4.34055i	0.264018	−	0.210547i
$426$		0			0
$427$	3.22315	−	0.735663i	0.155979	−	0.0356013i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.9868	+	26.3166i	1.01090	+	1.26762i	0.963206	+	0.268762i	$0.0866147\pi$
$431$	20.9868	+	26.3166i	1.01090	+	1.26762i	0.0476904	+	0.998862i	$0.484814\pi$
$432$		0			0
$433$	−13.8590	+	28.7785i	−0.666020	+	1.38300i	0.244545	+	0.969638i	$0.421361\pi$
$433$	−13.8590	+	28.7785i	−0.666020	+	1.38300i	−0.910565	+	0.413366i	$0.864353\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.03311	+	6.29831i	−0.145093	+	0.301289i
$438$		0			0
$439$	6.82141	+	8.55378i	0.325568	+	0.408249i	0.917498	−	0.397740i	$-0.130205\pi$
$439$	6.82141	+	8.55378i	0.325568	+	0.408249i	−0.591930	+	0.805989i	$0.701634\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.58789	−	1.73189i	0.360511	−	0.0822844i	−0.0384288	−	0.999261i	$-0.512235\pi$
$443$	7.58789	−	1.73189i	0.360511	−	0.0822844i	0.398940	+	0.916977i	$0.369378\pi$
$444$		0			0
$445$	10.6207	−	8.46971i	0.503468	−	0.401503i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.32646	+	15.2136i	0.345757	+	0.717972i	0.999240	−	0.0389690i	$-0.0124074\pi$
$449$	7.32646	+	15.2136i	0.345757	+	0.717972i	−0.653483	+	0.756941i	$0.726693\pi$
$450$		0			0
$451$	1.01138	−	4.43113i	0.0476238	−	0.208654i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.39110	+	6.09482i	0.0652159	+	0.285730i
$456$		0			0
$457$	10.9867	−	13.7769i	0.513937	−	0.644457i	−0.455372	−	0.890301i	$-0.650494\pi$
$457$	10.9867	−	13.7769i	0.513937	−	0.644457i	0.969309	+	0.245844i	$0.0790652\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	24.6633	+	19.6683i	1.14869	+	0.916046i	0.997373	−	0.0724397i	$-0.0230785\pi$
$461$	24.6633	+	19.6683i	1.14869	+	0.916046i	0.151313	+	0.988486i	$0.451650\pi$
$462$		0			0
$463$	−14.3649			−0.667594			−0.333797	−	0.942645i	$-0.608330\pi$
$463$	−14.3649			−0.667594			−0.333797	+	0.942645i	$0.608330\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.27859	+	3.41206i	0.197990	+	0.157892i	0.717466	−	0.696593i	$-0.245302\pi$
$467$	4.27859	+	3.41206i	0.197990	+	0.157892i	−0.519477	+	0.854485i	$0.673873\pi$
$468$		0			0
$469$	12.4017	+	5.97234i	0.572657	+	0.275777i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.57163	−	6.88577i	−0.0722637	−	0.316608i
$474$		0			0
$475$	7.67412	+	1.75157i	0.352113	+	0.0803675i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.9404	+	26.8711i	0.591263	+	1.22777i	0.955093	+	0.296305i	$0.0957546\pi$
$479$	12.9404	+	26.8711i	0.591263	+	1.22777i	−0.363830	+	0.931465i	$0.618531\pi$
$480$		0			0
$481$		−	1.25806i		−	0.0573626i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.19562	−	0.501136i	0.0996980	−	0.0227554i
$486$		0			0
$487$	3.36733	−	1.62162i	0.152588	−	0.0734827i	−0.356031	−	0.934474i	$-0.615870\pi$
$487$	3.36733	−	1.62162i	0.152588	−	0.0734827i	0.508619	+	0.860991i	$0.330156\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.9079	−	26.8035i	0.582524	−	1.20962i	−0.376531	−	0.926404i	$-0.622883\pi$
$491$	12.9079	−	26.8035i	0.582524	−	1.20962i	0.959055	−	0.283220i	$-0.0914026\pi$
$492$		0			0
$493$	8.86621	+	8.54484i	0.399314	+	0.384840i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.5674	+	25.7907i	0.922572	+	1.15687i
$498$		0			0
$499$	17.7560	−	8.55084i	0.794868	−	0.382788i	0.00804526	−	0.999968i	$-0.497439\pi$
$499$	17.7560	−	8.55084i	0.794868	−	0.382788i	0.786822	+	0.617180i	$0.211725\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.595757	−	0.475101i	0.0265635	−	0.0211837i	−0.610118	−	0.792311i	$-0.708878\pi$
$503$	0.595757	−	0.475101i	0.0265635	−	0.0211837i	0.636682	+	0.771127i	$0.280307\pi$
$504$		0			0
$505$			3.53782i			0.157431i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.64364	−	24.7264i	0.250150	−	1.09598i	−0.681270	−	0.732032i	$-0.738572\pi$
$509$	5.64364	−	24.7264i	0.250150	−	1.09598i	0.931420	−	0.363946i	$-0.118571\pi$
$510$		0			0
$511$	−35.5810	−	8.12113i	−1.57401	−	0.359258i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.1754	−	12.7595i	0.448382	−	0.562253i
$516$		0			0
$517$	32.2636	+	15.5373i	1.41895	+	0.683331i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.5097			1.24903			0.624517	−	0.781011i	$-0.285296\pi$
$521$	28.5097			1.24903			0.624517	+	0.781011i	$0.285296\pi$
$522$		0			0
$523$	6.46738			0.282799			0.141399	−	0.989953i	$-0.454840\pi$
$523$	6.46738			0.282799			0.141399	+	0.989953i	$0.454840\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.906052	+	0.436332i	0.0394683	+	0.0190069i
$528$		0			0
$529$	−9.78193	+	12.2662i	−0.425301	+	0.533311i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.96240	+	0.447906i	0.0850011	+	0.0194010i
$534$		0			0
$535$	−2.41518	+	10.5816i	−0.104417	+	0.457482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			8.95321i			0.385642i
$540$		0			0
$541$	−21.8278	+	17.4071i	−0.938452	+	0.748390i	−0.967942	−	0.251175i	$-0.919183\pi$
$541$	−21.8278	+	17.4071i	−0.938452	+	0.748390i	0.0294901	+	0.999565i	$0.490612\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.60809	+	3.18229i	−0.283059	+	0.136314i
$546$		0			0
$547$	−18.4618	−	23.1504i	−0.789369	−	0.989838i	−0.999925	−	0.0122558i	$-0.996099\pi$
$547$	−18.4618	−	23.1504i	−0.789369	−	0.989838i	0.210556	−	0.977582i	$-0.432473\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.30327	+	13.8616i	−0.0555212	+	0.590525i
$552$		0			0
$553$	−5.23619	+	10.8731i	−0.222666	+	0.462370i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.7251	+	7.09122i	−0.623921	+	0.300465i	−0.719005	−	0.695005i	$-0.755402\pi$
$557$	−14.7251	+	7.09122i	−0.623921	+	0.300465i	0.0950841	+	0.995469i	$0.469688\pi$
$558$		0			0
$559$	3.04949	−	0.696026i	0.128980	−	0.0294387i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	30.5482i		−	1.28745i	−0.765256	−	0.643727i	$-0.777387\pi$
$563$		−	30.5482i		−	1.28745i	0.765256	−	0.643727i	$-0.222613\pi$
$564$		0			0
$565$	−9.53926	−	19.8085i	−0.401320	−	0.833349i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.91734	+	2.03532i	0.373834	+	0.0853252i	0.405310	−	0.914179i	$-0.367164\pi$
$569$	8.91734	+	2.03532i	0.373834	+	0.0853252i	−0.0314759	+	0.999505i	$0.510021\pi$
$570$		0			0
$571$	−7.84590	−	34.3752i	−0.328341	−	1.43856i	−0.822292	−	0.569066i	$-0.807305\pi$
$571$	−7.84590	−	34.3752i	−0.328341	−	1.43856i	0.493951	−	0.869490i	$-0.335552\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.41700	−	3.57184i	−0.309310	−	0.148956i
$576$		0			0
$577$	−17.4212	−	13.8930i	−0.725255	−	0.578372i	0.189741	−	0.981834i	$-0.439235\pi$
$577$	−17.4212	−	13.8930i	−0.725255	−	0.578372i	−0.914996	+	0.403462i	$0.867807\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	13.1038			0.543637
$582$		0			0
$583$	14.1159	+	11.2570i	0.584620	+	0.466219i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.8991	−	24.9526i	0.821322	−	1.02990i	−0.177629	−	0.984098i	$-0.556843\pi$
$587$	19.8991	−	24.9526i	0.821322	−	1.02990i	0.998950	−	0.0458072i	$-0.0145860\pi$
$588$		0			0
$589$	0.253020	+	1.10855i	0.0104255	+	0.0456772i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.05026	−	39.6518i	0.371650	−	1.62830i	−0.350497	−	0.936564i	$-0.613987\pi$
$593$	9.05026	−	39.6518i	0.371650	−	1.62830i	0.722147	−	0.691740i	$-0.243155\pi$
$594$		0			0
$595$	3.10648	+	6.45068i	0.127353	+	0.264452i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.5570	+	18.7861i	−0.962513	+	0.767579i	−0.972627	−	0.232370i	$-0.925352\pi$
$599$	−23.5570	+	18.7861i	−0.962513	+	0.767579i	0.0101141	+	0.999949i	$0.496781\pi$
$600$		0			0
$601$	32.8857	−	7.50594i	1.34143	−	0.306174i	0.509224	−	0.860634i	$-0.329932\pi$
$601$	32.8857	−	7.50594i	1.34143	−	0.306174i	0.832210	+	0.554460i	$0.187075\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.12912	+	10.1936i	0.330496	+	0.414428i
$606$		0			0
$607$	−13.5369	+	28.1096i	−0.549445	+	1.14093i	0.422638	+	0.906298i	$0.361104\pi$
$607$	−13.5369	+	28.1096i	−0.549445	+	1.14093i	−0.972083	+	0.234636i	$0.924610\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.88099	+	14.2885i	−0.278375	+	0.578051i
$612$		0			0
$613$	11.5050	+	14.4269i	0.464684	+	0.582696i	0.957861	−	0.287234i	$-0.0927356\pi$
$613$	11.5050	+	14.4269i	0.464684	+	0.582696i	−0.493176	+	0.869929i	$0.664164\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.8301	−	9.09097i	1.60350	−	0.365989i	0.675146	−	0.737684i	$-0.264080\pi$
$617$	39.8301	−	9.09097i	1.60350	−	0.365989i	0.928355	+	0.371695i	$0.121223\pi$
$618$		0			0
$619$	−14.9178	+	11.8966i	−0.599598	+	0.478163i	−0.875628	−	0.482986i	$-0.839552\pi$
$619$	−14.9178	+	11.8966i	−0.599598	+	0.478163i	0.276031	+	0.961149i	$0.410981\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.43816	−	19.5985i	−0.378132	−	0.785199i
$624$		0			0
$625$	0.112909	−	0.494688i	0.00451637	−	0.0197875i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.320612	−	1.40469i	−0.0127836	−	0.0560087i
$630$		0			0
$631$	26.1618	−	32.8059i	1.04148	−	1.30598i	0.0907838	−	0.995871i	$-0.471063\pi$
$631$	26.1618	−	32.8059i	1.04148	−	1.30598i	0.950701	−	0.310110i	$-0.100366\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.266396	−	0.212444i	−0.0105716	−	0.00843058i
$636$		0			0
$637$	−3.96509			−0.157103
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.09420	+	4.06249i	0.201209	+	0.160459i	0.718911	−	0.695102i	$-0.244641\pi$
$641$	5.09420	+	4.06249i	0.201209	+	0.160459i	−0.517702	+	0.855561i	$0.673212\pi$
$642$		0			0
$643$	−15.0745	−	7.25951i	−0.594481	−	0.286287i	0.112351	−	0.993669i	$-0.464162\pi$
$643$	−15.0745	−	7.25951i	−0.594481	−	0.286287i	−0.706832	+	0.707382i	$0.749876\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.97466	+	26.1767i	0.234888	+	1.02911i	0.945524	+	0.325552i	$0.105550\pi$
$647$	5.97466	+	26.1767i	0.234888	+	1.02911i	−0.710636	+	0.703560i	$0.751593\pi$
$648$		0			0
$649$	38.2749	+	8.73599i	1.50242	+	0.342918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.35405	+	9.04128i	0.170387	+	0.353812i	0.968624	−	0.248531i	$-0.0799479\pi$
$653$	4.35405	+	9.04128i	0.170387	+	0.353812i	−0.798237	+	0.602344i	$0.794234\pi$
$654$		0			0
$655$		−	6.92561i		−	0.270606i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.1586	−	3.91633i	0.668403	−	0.152559i	0.125163	−	0.992136i	$-0.460055\pi$
$659$	17.1586	−	3.91633i	0.668403	−	0.152559i	0.543240	+	0.839578i	$0.317197\pi$
$660$		0			0
$661$	−7.53479	+	3.62856i	−0.293069	+	0.141135i	−0.574641	−	0.818405i	$-0.694858\pi$
$661$	−7.53479	+	3.62856i	−0.293069	+	0.141135i	0.281572	+	0.959540i	$0.409144\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.51245	+	7.29368i	−0.136207	+	0.282837i
$666$		0			0
$667$	4.55470	−	13.8302i	0.176359	−	0.535506i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.15000	+	5.20393i	0.160209	+	0.200896i
$672$		0			0
$673$	24.4039	−	11.7523i	0.940702	−	0.453018i	0.100285	−	0.994959i	$-0.468025\pi$
$673$	24.4039	−	11.7523i	0.940702	−	0.453018i	0.840417	+	0.541941i	$0.182310\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.3346	+	17.0138i	−0.819957	+	0.653893i	−0.940869	−	0.338770i	$-0.889989\pi$
$677$	−21.3346	+	17.0138i	−0.819957	+	0.653893i	0.120913	+	0.992663i	$0.461418\pi$
$678$		0			0
$679$		−	3.60628i		−	0.138396i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.40973	−	23.7016i	0.206998	−	0.906915i	−0.759554	−	0.650444i	$-0.774583\pi$
$683$	5.40973	−	23.7016i	0.206998	−	0.906915i	0.966552	−	0.256471i	$-0.0825600\pi$
$684$		0			0
$685$	−15.4164	−	3.51870i	−0.589032	−	0.134443i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.98538	+	6.25147i	−0.189928	+	0.238162i
$690$		0			0
$691$	36.7191	+	17.6830i	1.39686	+	0.672692i	0.972522	−	0.232811i	$-0.0747925\pi$
$691$	36.7191	+	17.6830i	1.39686	+	0.672692i	0.424338	+	0.905504i	$0.360507\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.1636			0.575190
$696$		0			0
$697$	2.30528			0.0873186
$698$		0			0
$699$		0			0
$700$		0			0
$701$	30.7555	+	14.8111i	1.16162	+	0.559406i	0.912504	−	0.409067i	$-0.134146\pi$
$701$	30.7555	+	14.8111i	1.16162	+	0.559406i	0.249115	+	0.968474i	$0.419860\pi$
$702$		0			0
$703$	1.01573	−	1.27369i	0.0383091	−	0.0480380i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.52311	+	1.26061i	0.207718	+	0.0474103i
$708$		0			0
$709$	−8.57829	+	37.5839i	−0.322164	+	1.41149i	0.511529	+	0.859266i	$0.329079\pi$
$709$	−8.57829	+	37.5839i	−0.322164	+	1.41149i	−0.833693	+	0.552228i	$0.813778\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	1.18918i		−	0.0445351i
$714$		0			0
$715$	−9.84038	+	7.84744i	−0.368009	+	0.293478i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10.3811	+	4.99927i	−0.387150	+	0.186441i	−0.617326	−	0.786707i	$-0.711784\pi$
$719$	−10.3811	+	4.99927i	−0.387150	+	0.186441i	0.230176	+	0.973149i	$0.426070\pi$
$720$		0			0
$721$	−16.2940	−	20.4320i	−0.606819	−	0.760927i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−16.3237	−	1.53475i	−0.606246	−	0.0569993i
$726$		0			0
$727$	−12.1738	+	25.2791i	−0.451501	+	0.937552i	0.543661	+	0.839305i	$0.317038\pi$
$727$	−12.1738	+	25.2791i	−0.451501	+	0.937552i	−0.995162	+	0.0982468i	$0.968677\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.22754	−	1.55430i	0.119375	−	0.0574879i
$732$		0			0
$733$	39.7109	−	9.06376i	1.46676	−	0.334778i	0.586762	−	0.809760i	$-0.300403\pi$
$733$	39.7109	−	9.06376i	1.46676	−	0.334778i	0.879995	+	0.474982i	$0.157545\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			27.7129i			1.02082i
$738$		0			0
$739$	−19.1390	−	39.7425i	−0.704038	−	1.46195i	−0.878726	−	0.477327i	$-0.841606\pi$
$739$	−19.1390	−	39.7425i	−0.704038	−	1.46195i	0.174687	−	0.984624i	$-0.444109\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−39.6633	−	9.05289i	−1.45511	−	0.332118i	−0.579431	−	0.815021i	$-0.696725\pi$
$743$	−39.6633	−	9.05289i	−1.45511	−	0.332118i	−0.875674	+	0.482903i	$0.839582\pi$
$744$		0			0
$745$	−5.43529	−	23.8136i	−0.199134	−	0.872462i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.6590	+	7.54097i	0.572167	+	0.275541i
$750$		0			0
$751$	17.1776	+	13.6987i	0.626820	+	0.499872i	0.884612	−	0.466328i	$-0.154423\pi$
$751$	17.1776	+	13.6987i	0.626820	+	0.499872i	−0.257792	+	0.966201i	$0.582995\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.37433			−0.122804
$756$		0			0
$757$	−22.6421	−	18.0565i	−0.822940	−	0.656273i	0.118686	−	0.992932i	$-0.462132\pi$
$757$	−22.6421	−	18.0565i	−0.822940	−	0.656273i	−0.941627	+	0.336659i	$0.890703\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.92645	+	6.17757i	−0.178584	+	0.223937i	−0.863064	−	0.505094i	$-0.831458\pi$
$761$	−4.92645	+	6.17757i	−0.178584	+	0.223937i	0.684480	+	0.729031i	$0.260029\pi$
$762$		0			0
$763$	2.61344	+	11.4502i	0.0946127	+	0.414526i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.86889	+	16.9507i	−0.139698	+	0.612055i
$768$		0			0
$769$	−14.6268	−	30.3728i	−0.527455	−	1.09527i	−0.979157	−	0.203103i	$-0.934897\pi$
$769$	−14.6268	−	30.3728i	−0.527455	−	1.09527i	0.451703	−	0.892169i	$-0.350817\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.94079	−	1.54773i	0.0698055	−	0.0556681i	−0.587965	−	0.808886i	$-0.700071\pi$
$773$	1.94079	−	1.54773i	0.0698055	−	0.0556681i	0.657771	+	0.753218i	$0.271499\pi$
$774$		0			0
$775$	−1.30545	+	0.297961i	−0.0468933	+	0.0107031i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.62515	+	2.03787i	0.0582271	+	0.0730144i
$780$		0			0
$781$	−28.8159	+	59.8369i	−1.03112	+	2.14113i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.813335	−	1.68891i	0.0290292	−	0.0602797i
$786$		0			0
$787$	25.4347	+	31.8941i	0.906650	+	1.13690i	0.990096	+	0.140391i	$0.0448358\pi$
$787$	25.4347	+	31.8941i	0.906650	+	1.13690i	−0.0834464	+	0.996512i	$0.526593\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−34.3233	+	7.83407i	−1.22040	+	0.278547i
$792$		0			0
$793$	−2.30466	+	1.83790i	−0.0818407	+	0.0652658i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.17561	+	2.44119i	0.0416424	+	0.0864714i	0.920752	−	0.390148i	$-0.127576\pi$
$797$	1.17561	+	2.44119i	0.0416424	+	0.0864714i	−0.879110	+	0.476620i	$0.841862\pi$
$798$		0			0
$799$	−4.04162	+	17.7075i	−0.142982	+	0.626446i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−16.3503	−	71.6355i	−0.576991	−	2.52796i
$804$		0			0
$805$	5.27872	−	6.61930i	0.186050	−	0.233300i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.2383	+	9.75973i	0.430276	+	0.343134i	0.814558	−	0.580082i	$-0.196979\pi$
$809$	12.2383	+	9.75973i	0.430276	+	0.343134i	−0.384282	+	0.923216i	$0.625551\pi$
$810$		0			0
$811$	−26.3476			−0.925190			−0.462595	−	0.886570i	$-0.653082\pi$
$811$	−26.3476			−0.925190			−0.462595	+	0.886570i	$0.653082\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.3854	−	13.0669i	−0.573954	−	0.457713i
$816$		0			0
$817$	3.64933	+	1.75742i	0.127674	+	0.0614844i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.05489	+	13.3844i	0.106616	+	0.467117i	0.999847	+	0.0175173i	$0.00557623\pi$
$821$	3.05489	+	13.3844i	0.106616	+	0.467117i	−0.893230	+	0.449600i	$0.851567\pi$
$822$		0			0
$823$	−14.6143	−	3.33563i	−0.509424	−	0.116273i	−0.0399195	−	0.999203i	$-0.512710\pi$
$823$	−14.6143	−	3.33563i	−0.509424	−	0.116273i	−0.469504	+	0.882930i	$0.655567\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−17.2997	−	35.9233i	−0.601571	−	1.24917i	−0.950120	−	0.311884i	$-0.899040\pi$
$827$	−17.2997	−	35.9233i	−0.601571	−	1.24917i	0.348549	−	0.937290i	$-0.386674\pi$
$828$		0			0
$829$			32.0784i			1.11413i	0.830469	+	0.557064i	$0.188072\pi$
$829$			32.0784i			1.11413i	−0.830469	+	0.557064i	$0.811928\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.42724	+	1.01049i	−0.153395	+	0.0350113i
$834$		0			0
$835$	−3.56034	+	1.71457i	−0.123211	+	0.0593352i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.27098	−	6.79225i	0.112927	−	0.234495i	−0.836844	−	0.547441i	$-0.815602\pi$
$839$	3.27098	−	6.79225i	0.112927	−	0.234495i	0.949771	+	0.312947i	$0.101316\pi$
$840$		0			0
$841$	−1.07016	−	28.9802i	−0.0369022	−	0.999319i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.85881	+	9.85464i	0.270351	+	0.339010i
$846$		0			0
$847$	18.8104	−	9.05863i	0.646334	−	0.311258i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.33206	+	1.06229i	−0.0456626	+	0.0364147i
$852$		0			0
$853$		−	32.0872i		−	1.09864i	−0.835611	−	0.549322i	$-0.814886\pi$
$853$		−	32.0872i		−	1.09864i	0.835611	−	0.549322i	$-0.185114\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.75512	+	33.9774i	−0.264910	+	1.16065i	0.650941	+	0.759128i	$0.274374\pi$
$857$	−7.75512	+	33.9774i	−0.264910	+	1.16065i	−0.915851	+	0.401518i	$0.868483\pi$
$858$		0			0
$859$	−40.5504	−	9.25537i	−1.38356	−	0.315789i	−0.534985	−	0.844861i	$-0.679683\pi$
$859$	−40.5504	−	9.25537i	−1.38356	−	0.315789i	−0.848577	+	0.529072i	$0.822540\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.78894	+	2.24326i	−0.0608963	+	0.0763615i	−0.811347	−	0.584565i	$-0.801265\pi$
$863$	−1.78894	+	2.24326i	−0.0608963	+	0.0763615i	0.750450	+	0.660927i	$0.229837\pi$
$864$		0			0
$865$	−19.9408	−	9.60297i	−0.678006	−	0.326511i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−24.2970			−0.824219
$870$		0			0
$871$	−12.2731			−0.415860
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−22.6947	−	10.9292i	−0.767222	−	0.369475i
$876$		0			0
$877$	−25.6436	+	32.1560i	−0.865921	+	1.08583i	0.129626	+	0.991563i	$0.458622\pi$
$877$	−25.6436	+	32.1560i	−0.865921	+	1.08583i	−0.995547	+	0.0942678i	$0.969949\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−20.0265	−	4.57091i	−0.674709	−	0.153998i	−0.128580	−	0.991699i	$-0.541042\pi$
$881$	−20.0265	−	4.57091i	−0.674709	−	0.153998i	−0.546129	+	0.837701i	$0.683899\pi$
$882$		0			0
$883$	4.29896	−	18.8350i	0.144671	−	0.633847i	−0.849643	−	0.527359i	$-0.823182\pi$
$883$	4.29896	−	18.8350i	0.144671	−	0.633847i	0.994314	−	0.106488i	$-0.0339606\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	51.8520i		−	1.74102i	−0.492150	−	0.870510i	$-0.663789\pi$
$887$		−	51.8520i		−	1.74102i	0.492150	−	0.870510i	$-0.336211\pi$
$888$		0			0
$889$	−0.426583	+	0.340188i	−0.0143071	+	0.0114096i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.5027	+	8.91044i	−0.619170	+	0.298177i
$894$		0			0
$895$	−8.69605	−	10.9045i	−0.290677	−	0.364497i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.823359	−	2.22069i	−0.0274606	−	0.0740642i
$900$		0			0
$901$	−3.97328	+	8.25061i	−0.132369	+	0.274868i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.31028	−	3.52045i	0.243002	−	0.117024i
$906$		0			0
$907$	52.9050	−	12.0752i	1.75668	−	0.400951i	0.781773	−	0.623563i	$-0.214315\pi$
$907$	52.9050	−	12.0752i	1.75668	−	0.400951i	0.974907	+	0.222612i	$0.0714582\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	0.566953i		−	0.0187840i	−0.999956	−	0.00939199i	$-0.997010\pi$
$911$		−	0.566953i		−	0.0187840i	0.999956	−	0.00939199i	$-0.00298961\pi$
$912$		0			0
$913$	11.4467	+	23.7694i	0.378831	+	0.786651i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.8120	−	2.46777i	−0.357044	−	0.0814929i
$918$		0			0
$919$	−5.65508	−	24.7765i	−0.186544	−	0.817301i	−0.978421	−	0.206621i	$-0.933753\pi$
$919$	−5.65508	−	24.7765i	−0.186544	−	0.817301i	0.791877	−	0.610680i	$-0.209104\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−26.4999	−	12.7617i	−0.872254	−	0.420055i
$924$		0			0
$925$	1.49992	+	1.19614i	0.0493170	+	0.0393290i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−46.6941			−1.53198			−0.765992	−	0.642851i	$-0.777752\pi$
$929$	−46.6941			−1.53198			−0.765992	+	0.642851i	$0.777752\pi$
$930$		0			0
$931$	−4.01434	−	3.20133i	−0.131565	−	0.104919i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.98742	+	11.2699i	−0.293920	+	0.368564i
$936$		0			0
$937$	2.21037	+	9.68425i	0.0722095	+	0.316371i	0.998114	−	0.0613870i	$-0.0195524\pi$
$937$	2.21037	+	9.68425i	0.0722095	+	0.316371i	−0.925905	+	0.377758i	$0.876695\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.42863	+	28.1657i	−0.209567	+	0.918174i	0.755288	+	0.655393i	$0.227497\pi$
$941$	−6.42863	+	28.1657i	−0.209567	+	0.918174i	−0.964855	+	0.262781i	$0.915360\pi$
$942$		0			0
$943$	−1.18277	−	2.45605i	−0.0385163	−	0.0799799i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.7585	−	13.3645i	0.544579	−	0.434287i	−0.312166	−	0.950028i	$-0.601055\pi$
$947$	16.7585	−	13.3645i	0.544579	−	0.434287i	0.856745	+	0.515741i	$0.172483\pi$
$948$		0			0
$949$	31.7251	−	7.24104i	1.02984	−	0.235054i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−23.8193	−	29.8685i	−0.771584	−	0.967536i	0.228397	−	0.973568i	$-0.426651\pi$
$953$	−23.8193	−	29.8685i	−0.771584	−	0.967536i	−0.999982	+	0.00603182i	$0.998080\pi$
$954$		0			0
$955$	−16.3122	+	33.8726i	−0.527849	+	1.09609i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−10.9865	+	22.8137i	−0.354773	+	0.736694i
$960$		0			0
$961$	19.2076	+	24.0855i	0.619599	+	0.776953i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−28.6618	+	6.54187i	−0.922657	+	0.210590i
$966$		0			0
$967$	−21.7787	+	17.3679i	−0.700356	+	0.558516i	−0.907632	−	0.419767i	$-0.862112\pi$
$967$	−21.7787	+	17.3679i	−0.700356	+	0.558516i	0.207275	+	0.978283i	$0.433540\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.20962	−	8.74136i	−0.135093	−	0.280524i	0.822437	−	0.568855i	$-0.192614\pi$
$971$	−4.20962	−	8.74136i	−0.135093	−	0.280524i	−0.957531	+	0.288332i	$0.906899\pi$
$972$		0			0
$973$	5.40318	−	23.6729i	0.173218	−	0.758918i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.5450	+	46.2008i	0.337366	+	1.47810i	0.804523	+	0.593921i	$0.202421\pi$
$977$	10.5450	+	46.2008i	0.337366	+	1.47810i	−0.467157	+	0.884174i	$0.654722\pi$
$978$		0			0
$979$	27.3057	−	34.2403i	0.872695	−	1.09432i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−25.7522	−	20.5367i	−0.821368	−	0.655019i	0.119860	−	0.992791i	$-0.461755\pi$
$983$	−25.7522	−	20.5367i	−0.821368	−	0.655019i	−0.941228	+	0.337772i	$0.890327\pi$
$984$		0			0
$985$	−7.28929			−0.232256
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.31191	−	2.64116i	−0.105313	−	0.0839840i
$990$		0			0
$991$	35.5289	+	17.1098i	1.12861	+	0.543511i	0.902543	−	0.430600i	$-0.141698\pi$
$991$	35.5289	+	17.1098i	1.12861	+	0.543511i	0.226070	+	0.974111i	$0.427412\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.86605	−	34.4634i	−0.249370	−	1.09256i
$996$		0			0
$997$	49.1867	+	11.2266i	1.55776	+	0.355548i	0.912715	−	0.408597i	$-0.133982\pi$
$997$	49.1867	+	11.2266i	1.55776	+	0.355548i	0.645045	+	0.764145i	$0.276839\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1044.2.z.c.361.3	yes	24
3.2	odd	2	inner	1044.2.z.c.361.2	✓	24
29.9	even	14	inner	1044.2.z.c.937.3	yes	24
87.38	odd	14	inner	1044.2.z.c.937.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.2.z.c.361.2	✓	24	3.2	odd	2	inner
1044.2.z.c.361.3	yes	24	1.1	even	1	trivial
1044.2.z.c.937.2	yes	24	87.38	odd	14	inner
1044.2.z.c.937.3	yes	24	29.9	even	14	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:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1044.z (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25988 + 0.606724i) q^{5} +(1.39612 - 1.75068i) q^{7} +O(q^{10})\)	\(q+(1.25988 + 0.606724i) q^{5} +(1.39612 - 1.75068i) q^{7} +(4.39517 + 1.00317i) q^{11} +(-0.444271 + 1.94648i) q^{13} +2.28657i q^{17} +(-2.02134 + 1.61196i) q^{19} +(2.43612 - 1.17317i) q^{23} +(-1.89828 - 2.38036i) q^{25} +(3.73697 - 3.87751i) q^{29} +(0.190824 - 0.396249i) q^{31} +(2.82111 - 1.35858i) q^{35} +(-0.614322 + 0.140215i) q^{37} -1.00818i q^{41} +(-0.679751 - 1.41152i) q^{43} +(7.74412 + 1.76755i) q^{47} +(0.441923 + 1.93619i) q^{49} +(3.60829 + 1.73766i) q^{53} +(4.92872 + 3.93052i) q^{55} +8.70839 q^{59} +(1.15433 + 0.920544i) q^{61} +(-1.74070 + 2.18277i) q^{65} +(1.36788 + 5.99309i) q^{67} +(-3.27814 + 14.3625i) q^{71} +(-7.07173 - 14.6846i) q^{73} +(7.89240 - 6.29398i) q^{77} +(-5.25439 + 1.19928i) q^{79} +(3.64866 + 4.57528i) q^{83} +(-1.38732 + 2.88080i) q^{85} +(4.21497 - 8.75248i) q^{89} +(2.78740 + 3.49529i) q^{91} +(-3.52465 + 0.804479i) q^{95} +(1.25916 - 1.00414i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

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