LMFDB - Embedded newform 936.2.dr.b.89.5

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			89.5
Character	$\chi$	$=$	936.89
Dual form			936.2.dr.b.305.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.491974 - 0.491974i) q^{5} +(0.153985 + 0.574679i) q^{7} +(-0.801922 + 2.99281i) q^{11} +(-2.04919 + 2.96661i) q^{13} +(-3.77047 + 6.53065i) q^{17} +(5.78167 - 1.54919i) q^{19} +(-3.07276 - 5.32218i) q^{23} +4.51592i q^{25} +(-0.494824 + 0.285687i) q^{29} +(4.76623 + 4.76623i) q^{31} +(0.358484 + 0.206971i) q^{35} +(4.15780 + 1.11408i) q^{37} +(6.08869 + 1.63146i) q^{41} +(-0.745493 - 0.430411i) q^{43} +(-3.56323 - 3.56323i) q^{47} +(5.75563 - 3.32302i) q^{49} +8.52682i q^{53} +(1.07786 + 1.86691i) q^{55} +(-11.4885 + 3.07834i) q^{59} +(-2.89058 + 5.00664i) q^{61} +(0.451347 + 2.46765i) q^{65} +(-0.631089 + 2.35526i) q^{67} +(-0.180758 - 0.674599i) q^{71} +(-4.84031 + 4.84031i) q^{73} -1.84339 q^{77} +16.9116 q^{79} +(-0.956248 + 0.956248i) q^{83} +(1.35794 + 5.06789i) q^{85} +(0.960598 - 3.58500i) q^{89} +(-2.02040 - 0.720815i) q^{91} +(2.08227 - 3.60660i) q^{95} +(-7.75656 + 2.07836i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$	$1$

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
$5$	0.491974	−	0.491974i	0.220017	−	0.220017i	−0.588488	−	0.808506i	$-0.700277\pi$
$5$	0.491974	−	0.491974i	0.220017	−	0.220017i	0.808506	+	0.588488i	$0.200277\pi$
$6$		0			0
$7$	0.153985	+	0.574679i	0.0582008	+	0.217208i	0.988901	−	0.148574i	$-0.0474683\pi$
$7$	0.153985	+	0.574679i	0.0582008	+	0.217208i	−0.930701	+	0.365782i	$0.880802\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.801922	+	2.99281i	−0.241789	+	0.902367i	0.733182	+	0.680033i	$0.238034\pi$
$11$	−0.801922	+	2.99281i	−0.241789	+	0.902367i	−0.974970	+	0.222335i	$0.928632\pi$
$12$		0			0
$13$	−2.04919	+	2.96661i	−0.568344	+	0.822791i
$13$	−2.04919	+	2.96661i	−0.568344	+	0.822791i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.77047	+	6.53065i	−0.914474	+	1.58392i	−0.106805	+	0.994280i	$0.534062\pi$
$17$	−3.77047	+	6.53065i	−0.914474	+	1.58392i	−0.807669	+	0.589636i	$0.799271\pi$
$18$		0			0
$19$	5.78167	−	1.54919i	1.32641	−	0.355409i	0.475032	−	0.879968i	$-0.342436\pi$
$19$	5.78167	−	1.54919i	1.32641	−	0.355409i	0.851374	+	0.524559i	$0.175770\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.07276	−	5.32218i	−0.640715	−	1.10975i	−0.985273	−	0.170986i	$-0.945305\pi$
$23$	−3.07276	−	5.32218i	−0.640715	−	1.10975i	0.344559	−	0.938765i	$-0.388029\pi$
$24$		0			0
$25$			4.51592i			0.903185i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.494824	+	0.285687i	−0.0918865	+	0.0530507i	−0.545239	−	0.838281i	$-0.683561\pi$
$29$	−0.494824	+	0.285687i	−0.0918865	+	0.0530507i	0.453353	+	0.891331i	$0.350228\pi$
$30$		0			0
$31$	4.76623	+	4.76623i	0.856041	+	0.856041i	0.990869	−	0.134828i	$-0.0430482\pi$
$31$	4.76623	+	4.76623i	0.856041	+	0.856041i	−0.134828	+	0.990869i	$0.543048\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.358484	+	0.206971i	0.0605948	+	0.0349844i
$36$		0			0
$37$	4.15780	+	1.11408i	0.683538	+	0.183153i	0.583845	−	0.811865i	$-0.301547\pi$
$37$	4.15780	+	1.11408i	0.683538	+	0.183153i	0.0996924	+	0.995018i	$0.468214\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.08869	+	1.63146i	0.950893	+	0.254791i	0.700741	−	0.713415i	$-0.252853\pi$
$41$	6.08869	+	1.63146i	0.950893	+	0.254791i	0.250152	+	0.968207i	$0.419519\pi$
$42$		0			0
$43$	−0.745493	−	0.430411i	−0.113687	−	0.0656370i	0.442078	−	0.896976i	$-0.354241\pi$
$43$	−0.745493	−	0.430411i	−0.113687	−	0.0656370i	−0.555765	+	0.831339i	$0.687575\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.56323	−	3.56323i	−0.519750	−	0.519750i	0.397746	−	0.917496i	$-0.369793\pi$
$47$	−3.56323	−	3.56323i	−0.519750	−	0.519750i	−0.917496	+	0.397746i	$0.869793\pi$
$48$		0			0
$49$	5.75563	−	3.32302i	0.822233	−	0.474717i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			8.52682i			1.17125i	0.810582	+	0.585625i	$0.199151\pi$
$53$			8.52682i			1.17125i	−0.810582	+	0.585625i	$0.800849\pi$
$54$		0			0
$55$	1.07786	+	1.86691i	0.145339	+	0.251734i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.4885	+	3.07834i	−1.49568	+	0.400765i	−0.911649	−	0.410969i	$-0.865190\pi$
$59$	−11.4885	+	3.07834i	−1.49568	+	0.400765i	−0.584027	+	0.811734i	$0.698524\pi$
$60$		0			0
$61$	−2.89058	+	5.00664i	−0.370101	+	0.641034i	−0.989581	−	0.143979i	$-0.954010\pi$
$61$	−2.89058	+	5.00664i	−0.370101	+	0.641034i	0.619480	+	0.785013i	$0.287344\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.451347	+	2.46765i	0.0559827	+	0.306074i
$66$		0			0
$67$	−0.631089	+	2.35526i	−0.0770998	+	0.287740i	−0.993701	−	0.112062i	$-0.964255\pi$
$67$	−0.631089	+	2.35526i	−0.0770998	+	0.287740i	0.916601	+	0.399802i	$0.130921\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.180758	−	0.674599i	−0.0214521	−	0.0800602i	0.954370	−	0.298627i	$-0.0965286\pi$
$71$	−0.180758	−	0.674599i	−0.0214521	−	0.0800602i	−0.975822	+	0.218567i	$0.929862\pi$
$72$		0			0
$73$	−4.84031	+	4.84031i	−0.566515	+	0.566515i	−0.931150	−	0.364635i	$-0.881194\pi$
$73$	−4.84031	+	4.84031i	−0.566515	+	0.566515i	0.364635	+	0.931150i	$0.381194\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.84339			−0.210074
$78$		0			0
$79$	16.9116			1.90271			0.951354	−	0.308101i	$-0.0996935\pi$
$79$	16.9116			1.90271			0.951354	+	0.308101i	$0.0996935\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.956248	+	0.956248i	−0.104962	+	0.104962i	−0.757637	−	0.652676i	$-0.773646\pi$
$83$	−0.956248	+	0.956248i	−0.104962	+	0.104962i	0.652676	+	0.757637i	$0.273646\pi$
$84$		0			0
$85$	1.35794	+	5.06789i	0.147289	+	0.549690i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.960598	−	3.58500i	0.101823	−	0.380009i	−0.896142	−	0.443767i	$-0.853642\pi$
$89$	0.960598	−	3.58500i	0.101823	−	0.380009i	0.997965	+	0.0637577i	$0.0203085\pi$
$90$		0			0
$91$	−2.02040	−	0.720815i	−0.211795	−	0.0755619i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.08227	−	3.60660i	0.213636	−	0.370029i
$96$		0			0
$97$	−7.75656	+	2.07836i	−0.787559	+	0.211026i	−0.630115	−	0.776502i	$-0.716992\pi$
$97$	−7.75656	+	2.07836i	−0.787559	+	0.211026i	−0.157444	+	0.987528i	$0.550326\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.76329	+	11.7144i	0.672972	+	1.16562i	0.977057	+	0.212977i	$0.0683160\pi$
$101$	6.76329	+	11.7144i	0.672972	+	1.16562i	−0.304085	+	0.952645i	$0.598351\pi$
$102$		0			0
$103$		−	18.0245i		−	1.77600i	−0.459839	−	0.888002i	$-0.652093\pi$
$103$		−	18.0245i		−	1.77600i	0.459839	−	0.888002i	$-0.347907\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.33586	−	4.23536i	0.709184	−	0.409448i	−0.101575	−	0.994828i	$-0.532388\pi$
$107$	7.33586	−	4.23536i	0.709184	−	0.409448i	0.810759	+	0.585380i	$0.199055\pi$
$108$		0			0
$109$	−10.0958	−	10.0958i	−0.967004	−	0.967004i	0.0324683	−	0.999473i	$-0.489663\pi$
$109$	−10.0958	−	10.0958i	−0.967004	−	0.967004i	−0.999473	+	0.0324683i	$0.989663\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.97212	−	1.13860i	−0.185521	−	0.107111i	0.404363	−	0.914599i	$-0.367493\pi$
$113$	−1.97212	−	1.13860i	−0.185521	−	0.107111i	−0.589884	+	0.807488i	$0.700827\pi$
$114$		0			0
$115$	−4.13009	−	1.10665i	−0.385133	−	0.103196i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.33362	−	1.16119i	−0.397263	−	0.106446i
$120$		0			0
$121$	1.21243	+	0.699996i	0.110221	+	0.0636360i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.68159	+	4.68159i	0.418734	+	0.418734i
$126$		0			0
$127$	−3.62461	+	2.09267i	−0.321632	+	0.185694i	−0.652120	−	0.758116i	$-0.726120\pi$
$127$	−3.62461	+	2.09267i	−0.321632	+	0.185694i	0.330488	+	0.943810i	$0.392787\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		−	7.24560i		−	0.633051i	−0.948584	−	0.316525i	$-0.897484\pi$
$131$		−	7.24560i		−	0.633051i	0.948584	−	0.316525i	$-0.102516\pi$
$132$		0			0
$133$	1.78058	+	3.08405i	0.154396	+	0.267421i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.571837	−	0.153223i	0.0488553	−	0.0130908i	−0.234309	−	0.972162i	$-0.575283\pi$
$137$	0.571837	−	0.153223i	0.0488553	−	0.0130908i	0.283164	+	0.959072i	$0.408616\pi$
$138$		0			0
$139$	−2.03983	+	3.53309i	−0.173016	+	0.299673i	−0.939473	−	0.342623i	$-0.888685\pi$
$139$	−2.03983	+	3.53309i	−0.173016	+	0.299673i	0.766457	+	0.642296i	$0.222018\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.23523	−	8.51185i	−0.605040	−	0.711796i
$144$		0			0
$145$	−0.102890	+	0.383991i	−0.00854456	+	0.0318887i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.27350	−	4.75275i	−0.104329	−	0.389361i	0.893939	−	0.448188i	$-0.147930\pi$
$149$	−1.27350	−	4.75275i	−0.104329	−	0.389361i	−0.998268	+	0.0588274i	$0.981264\pi$
$150$		0			0
$151$	−0.277174	+	0.277174i	−0.0225561	+	0.0225561i	−0.718295	−	0.695739i	$-0.755077\pi$
$151$	−0.277174	+	0.277174i	−0.0225561	+	0.0225561i	0.695739	+	0.718295i	$0.255077\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.68973			0.376688
$156$		0			0
$157$	0.222127			0.0177277			0.00886383	−	0.999961i	$-0.497179\pi$
$157$	0.222127			0.0177277			0.00886383	+	0.999961i	$0.497179\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.58538	−	2.58538i	0.203757	−	0.203757i
$162$		0			0
$163$	2.92522	+	10.9171i	0.229121	+	0.855090i	0.980712	+	0.195461i	$0.0626202\pi$
$163$	2.92522	+	10.9171i	0.229121	+	0.855090i	−0.751591	+	0.659630i	$0.770713\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.45231	−	20.3483i	0.421913	−	1.57460i	−0.348661	−	0.937249i	$-0.613364\pi$
$167$	5.45231	−	20.3483i	0.421913	−	1.57460i	0.770574	−	0.637351i	$-0.219970\pi$
$168$		0			0
$169$	−4.60161	−	12.1583i	−0.353970	−	0.935257i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.07135	−	10.5159i	0.461596	−	0.799508i	−0.537445	−	0.843299i	$-0.680610\pi$
$173$	6.07135	−	10.5159i	0.461596	−	0.799508i	0.999041	+	0.0437911i	$0.0139436\pi$
$174$		0			0
$175$	−2.59521	+	0.695383i	−0.196179	+	0.0525660i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.5136	+	18.2101i	0.785824	+	1.36109i	0.928506	+	0.371318i	$0.121094\pi$
$179$	10.5136	+	18.2101i	0.785824	+	1.36109i	−0.142682	+	0.989769i	$0.545573\pi$
$180$		0			0
$181$		−	18.3766i		−	1.36592i	−0.730456	−	0.682960i	$-0.760692\pi$
$181$		−	18.3766i		−	1.36592i	0.730456	−	0.682960i	$-0.239308\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.59363	−	1.49743i	0.190687	−	0.110093i
$186$		0			0
$187$	−16.5214	−	16.5214i	−1.20816	−	1.20816i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.06240	−	4.65483i	−0.583375	−	0.336812i	0.179099	−	0.983831i	$-0.442682\pi$
$191$	−8.06240	−	4.65483i	−0.583375	−	0.336812i	−0.762473	+	0.647020i	$0.776015\pi$
$192$		0			0
$193$	−16.1956	−	4.33960i	−1.16578	−	0.312371i	−0.376511	−	0.926412i	$-0.622876\pi$
$193$	−16.1956	−	4.33960i	−1.16578	−	0.312371i	−0.789274	+	0.614041i	$0.789543\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.05999	+	1.08787i	0.289263	+	0.0775077i	0.400533	−	0.916283i	$-0.368825\pi$
$197$	4.05999	+	1.08787i	0.289263	+	0.0775077i	−0.111270	+	0.993790i	$0.535492\pi$
$198$		0			0
$199$	4.01227	+	2.31648i	0.284422	+	0.164211i	0.635424	−	0.772164i	$-0.280826\pi$
$199$	4.01227	+	2.31648i	0.284422	+	0.164211i	−0.351002	+	0.936375i	$0.614159\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.240373	−	0.240373i	−0.0168709	−	0.0168709i
$204$		0			0
$205$	3.79811	−	2.19284i	0.265272	−	0.153155i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			18.5458i			1.28284i
$210$		0			0
$211$	−12.9936	−	22.5055i	−0.894515	−	1.54935i	−0.834403	−	0.551154i	$-0.814188\pi$
$211$	−12.9936	−	22.5055i	−0.894515	−	1.54935i	−0.0601118	−	0.998192i	$-0.519146\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.578514	+	0.155012i	−0.0394544	+	0.0105718i
$216$		0			0
$217$	−2.00513	+	3.47298i	−0.136117	+	0.235761i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.6475	−	24.5681i	−0.783495	−	1.65263i
$222$		0			0
$223$	7.02343	−	26.2118i	0.470324	−	1.75527i	−0.168283	−	0.985739i	$-0.553822\pi$
$223$	7.02343	−	26.2118i	0.470324	−	1.75527i	0.638606	−	0.769534i	$-0.279511\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.37723	+	20.0681i	0.356900	+	1.33197i	0.878077	+	0.478519i	$0.158826\pi$
$227$	5.37723	+	20.0681i	0.356900	+	1.33197i	−0.521178	+	0.853448i	$0.674507\pi$
$228$		0			0
$229$	−13.4738	+	13.4738i	−0.890376	+	0.890376i	−0.994558	−	0.104182i	$-0.966777\pi$
$229$	−13.4738	+	13.4738i	−0.890376	+	0.890376i	0.104182	+	0.994558i	$0.466777\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	19.0855			1.25033			0.625167	−	0.780491i	$-0.285031\pi$
$233$	19.0855			1.25033			0.625167	+	0.780491i	$0.285031\pi$
$234$		0			0
$235$	−3.50603			−0.228708
$236$		0			0
$237$		0			0
$238$		0			0
$239$	19.2245	−	19.2245i	1.24353	−	1.24353i	0.285004	−	0.958526i	$-0.408005\pi$
$239$	19.2245	−	19.2245i	1.24353	−	1.24353i	0.958526	−	0.285004i	$-0.0919950\pi$
$240$		0			0
$241$	4.90542	+	18.3073i	0.315986	+	1.17928i	0.923068	+	0.384636i	$0.125673\pi$
$241$	4.90542	+	18.3073i	0.315986	+	1.17928i	−0.607082	+	0.794639i	$0.707660\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.19678	−	4.46646i	0.0764598	−	0.285352i
$246$		0			0
$247$	−7.25190	+	20.3266i	−0.461428	+	1.29335i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.12815	+	12.3463i	−0.449925	+	0.779293i	−0.998381	−	0.0568866i	$-0.981883\pi$
$251$	−7.12815	+	12.3463i	−0.449925	+	0.779293i	0.548456	+	0.836180i	$0.315216\pi$
$252$		0			0
$253$	18.3924	−	4.92823i	1.15632	−	0.309835i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.2046	−	21.1390i	−0.761302	−	1.31861i	−0.942180	−	0.335108i	$-0.891227\pi$
$257$	−12.2046	−	21.1390i	−0.761302	−	1.31861i	0.180878	−	0.983506i	$-0.442106\pi$
$258$		0			0
$259$			2.56095i			0.159130i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.6877	−	8.47993i	0.905680	−	0.522895i	0.0266413	−	0.999645i	$-0.491519\pi$
$263$	14.6877	−	8.47993i	0.905680	−	0.522895i	0.879039	+	0.476750i	$0.158185\pi$
$264$		0			0
$265$	4.19498	+	4.19498i	0.257695	+	0.257695i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.79812	+	3.34755i	0.353518	+	0.204104i	0.666234	−	0.745743i	$-0.267905\pi$
$269$	5.79812	+	3.34755i	0.353518	+	0.204104i	−0.312716	+	0.949847i	$0.601239\pi$
$270$		0			0
$271$	1.98495	+	0.531866i	0.120577	+	0.0323086i	0.318603	−	0.947888i	$-0.396786\pi$
$271$	1.98495	+	0.531866i	0.120577	+	0.0323086i	−0.198026	+	0.980197i	$0.563453\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.5153	−	3.62142i	−0.815004	−	0.218380i
$276$		0			0
$277$	−8.85629	−	5.11318i	−0.532123	−	0.307221i	0.209758	−	0.977753i	$-0.432733\pi$
$277$	−8.85629	−	5.11318i	−0.532123	−	0.307221i	−0.741880	+	0.670532i	$0.766066\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.3399	−	13.3399i	−0.795790	−	0.795790i	0.186639	−	0.982429i	$-0.440241\pi$
$281$	−13.3399	−	13.3399i	−0.795790	−	0.795790i	−0.982429	+	0.186639i	$0.940241\pi$
$282$		0			0
$283$	6.88944	−	3.97762i	0.409535	−	0.236445i	−0.281055	−	0.959692i	$-0.590684\pi$
$283$	6.88944	−	3.97762i	0.409535	−	0.236445i	0.690590	+	0.723247i	$0.257351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			3.75026i			0.221371i
$288$		0			0
$289$	−19.9329	−	34.5249i	−1.17253	−	2.03087i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.26796	+	2.48334i	−0.541440	+	0.145078i	−0.519166	−	0.854673i	$-0.673757\pi$
$293$	−9.26796	+	2.48334i	−0.541440	+	0.145078i	−0.0222741	+	0.999752i	$0.507091\pi$
$294$		0			0
$295$	−4.13759	+	7.16651i	−0.240900	+	0.417250i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	22.0855	+	1.79048i	1.27724	+	0.103546i
$300$		0			0
$301$	0.132553	−	0.494696i	0.00764025	−	0.0285138i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.04104	+	3.88523i	0.0596100	+	0.222467i
$306$		0			0
$307$	−17.4850	+	17.4850i	−0.997923	+	0.997923i	−0.999998	−	0.00207498i	$-0.999340\pi$
$307$	−17.4850	+	17.4850i	−0.997923	+	0.997923i	0.00207498	+	0.999998i	$0.499340\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.17376			0.179968			0.0899838	−	0.995943i	$-0.471318\pi$
$311$	3.17376			0.179968			0.0899838	+	0.995943i	$0.471318\pi$
$312$		0			0
$313$	27.2645			1.54108			0.770539	−	0.637392i	$-0.219987\pi$
$313$	27.2645			1.54108			0.770539	+	0.637392i	$0.219987\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.574778	+	0.574778i	−0.0322828	+	0.0322828i	−0.723064	−	0.690781i	$-0.757267\pi$
$317$	−0.574778	+	0.574778i	−0.0322828	+	0.0322828i	0.690781	+	0.723064i	$0.257267\pi$
$318$		0			0
$319$	−0.458197	−	1.71001i	−0.0256541	−	0.0957424i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.6824	+	43.5993i	−0.650026	+	2.42593i
$324$		0			0
$325$	−13.3970	−	9.25400i	−0.743132	−	0.513320i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.49903	−	2.59639i	0.0826441	−	0.143144i
$330$		0			0
$331$	−22.0914	+	5.91938i	−1.21425	+	0.325359i	−0.808430	−	0.588592i	$-0.799682\pi$
$331$	−22.0914	+	5.91938i	−1.21425	+	0.325359i	−0.405825	+	0.913951i	$0.633016\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.848246	+	1.46920i	0.0463446	+	0.0802712i
$336$		0			0
$337$			1.04584i			0.0569708i	0.999594	+	0.0284854i	$0.00906840\pi$
$337$			1.04584i			0.0569708i	−0.999594	+	0.0284854i	$0.990932\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−18.0866	+	10.4423i	−0.979444	+	0.565482i
$342$		0			0
$343$	5.74081	+	5.74081i	0.309974	+	0.309974i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.8176	−	6.82288i	−0.634401	−	0.366272i	0.148054	−	0.988979i	$-0.452699\pi$
$347$	−11.8176	−	6.82288i	−0.634401	−	0.366272i	−0.782454	+	0.622708i	$0.786033\pi$
$348$		0			0
$349$	14.8596	+	3.98162i	0.795416	+	0.213131i	0.633571	−	0.773685i	$-0.281589\pi$
$349$	14.8596	+	3.98162i	0.795416	+	0.213131i	0.161846	+	0.986816i	$0.448255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.7410	+	3.94985i	0.784587	+	0.210229i	0.628806	−	0.777562i	$-0.283544\pi$
$353$	14.7410	+	3.94985i	0.784587	+	0.210229i	0.155781	+	0.987792i	$0.450211\pi$
$354$		0			0
$355$	−0.420814	−	0.242957i	−0.0223345	−	0.0128948i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.07022	−	3.07022i	−0.162040	−	0.162040i	0.621430	−	0.783470i	$-0.286552\pi$
$359$	−3.07022	−	3.07022i	−0.162040	−	0.162040i	−0.783470	+	0.621430i	$0.786552\pi$
$360$		0			0
$361$	14.5732	−	8.41386i	0.767012	−	0.442835i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			4.76261i			0.249286i
$366$		0			0
$367$	4.34908	+	7.53283i	0.227020	+	0.393210i	0.956924	−	0.290340i	$-0.0937683\pi$
$367$	4.34908	+	7.53283i	0.227020	+	0.393210i	−0.729903	+	0.683550i	$0.760435\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.90019	+	1.31300i	−0.254405	+	0.0681676i
$372$		0			0
$373$	4.85822	−	8.41468i	0.251549	−	0.435695i	−0.712404	−	0.701770i	$-0.752393\pi$
$373$	4.85822	−	8.41468i	0.251549	−	0.435695i	0.963952	+	0.266075i	$0.0857268\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.166468	−	2.05338i	0.00857352	−	0.105754i
$378$		0			0
$379$	−3.49735	+	13.0523i	−0.179647	+	0.670450i	0.816067	+	0.577958i	$0.196150\pi$
$379$	−3.49735	+	13.0523i	−0.179647	+	0.670450i	−0.995713	+	0.0924926i	$0.970517\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.544463	−	2.03196i	−0.0278208	−	0.103828i	0.950619	−	0.310359i	$-0.100449\pi$
$383$	−0.544463	−	2.03196i	−0.0278208	−	0.103828i	−0.978440	+	0.206531i	$0.933783\pi$
$384$		0			0
$385$	−0.906900	+	0.906900i	−0.0462199	+	0.0462199i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.2173			0.771549			0.385774	−	0.922593i	$-0.373934\pi$
$389$	15.2173			0.771549			0.385774	+	0.922593i	$0.373934\pi$
$390$		0			0
$391$	46.3431			2.34367
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.32008	−	8.32008i	0.418629	−	0.418629i
$396$		0			0
$397$	9.59315	+	35.8021i	0.481466	+	1.79686i	0.595471	+	0.803376i	$0.296965\pi$
$397$	9.59315	+	35.8021i	0.481466	+	1.79686i	−0.114005	+	0.993480i	$0.536368\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.69968	−	6.34327i	0.0848777	−	0.316768i	−0.910413	−	0.413700i	$-0.864236\pi$
$401$	1.69968	−	6.34327i	0.0848777	−	0.316768i	0.995291	+	0.0969320i	$0.0309029\pi$
$402$		0			0
$403$	−23.9065	+	4.37264i	−1.19087	+	0.217817i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.66846	+	11.5501i	−0.330543	+	0.572518i
$408$		0			0
$409$	38.8030	−	10.3972i	1.91868	−	0.514110i	0.929173	−	0.369645i	$-0.120521\pi$
$409$	38.8030	−	10.3972i	1.91868	−	0.514110i	0.989510	−	0.144465i	$-0.0461460\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.53811	−	6.12818i	−0.174099	−	0.301548i
$414$		0			0
$415$			0.940899i			0.0461869i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.22355	−	4.17052i	0.352893	−	0.203743i	−0.313066	−	0.949732i	$-0.601356\pi$
$419$	7.22355	−	4.17052i	0.352893	−	0.203743i	0.665959	+	0.745988i	$0.268023\pi$
$420$		0			0
$421$	−4.48638	−	4.48638i	−0.218653	−	0.218653i	0.589278	−	0.807931i	$-0.299412\pi$
$421$	−4.48638	−	4.48638i	−0.218653	−	0.218653i	−0.807931	+	0.589278i	$0.799412\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−29.4919	−	17.0272i	−1.43057	−	0.825939i
$426$		0			0
$427$	−3.32231	−	0.890211i	−0.160778	−	0.0430803i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.7958	+	4.23247i	0.760857	+	0.203871i	0.618329	−	0.785920i	$-0.287810\pi$
$431$	15.7958	+	4.23247i	0.760857	+	0.203871i	0.142528	+	0.989791i	$0.454477\pi$
$432$		0			0
$433$	22.0864	+	12.7516i	1.06141	+	0.612803i	0.925821	−	0.377963i	$-0.123375\pi$
$433$	22.0864	+	12.7516i	1.06141	+	0.612803i	0.135585	+	0.990766i	$0.456709\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−26.0108	−	26.0108i	−1.24426	−	1.24426i
$438$		0			0
$439$	18.6781	−	10.7838i	0.891458	−	0.514684i	0.0170390	−	0.999855i	$-0.494576\pi$
$439$	18.6781	−	10.7838i	0.891458	−	0.514684i	0.874419	+	0.485171i	$0.161243\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			40.5030i			1.92436i	0.272422	+	0.962178i	$0.412175\pi$
$443$			40.5030i			1.92436i	−0.272422	+	0.962178i	$0.587825\pi$
$444$		0			0
$445$	−1.29114	−	2.23632i	−0.0612058	−	0.106012i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−26.8751	+	7.20117i	−1.26832	+	0.339844i	−0.829386	−	0.558677i	$-0.811309\pi$
$449$	−26.8751	+	7.20117i	−1.26832	+	0.339844i	−0.438931	+	0.898521i	$0.644643\pi$
$450$		0			0
$451$	−9.76530	+	16.9140i	−0.459830	+	0.796449i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.34860	+	0.639360i	−0.0632235	+	0.0299736i
$456$		0			0
$457$	−4.83545	+	18.0461i	−0.226193	+	0.844162i	0.755731	+	0.654883i	$0.227282\pi$
$457$	−4.83545	+	18.0461i	−0.226193	+	0.844162i	−0.981923	+	0.189280i	$0.939385\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.322120	−	1.20217i	−0.0150026	−	0.0559906i	0.958019	−	0.286706i	$-0.0925602\pi$
$461$	−0.322120	−	1.20217i	−0.0150026	−	0.0559906i	−0.973021	+	0.230715i	$0.925893\pi$
$462$		0			0
$463$	−6.60597	+	6.60597i	−0.307005	+	0.307005i	−0.843747	−	0.536741i	$-0.819655\pi$
$463$	−6.60597	+	6.60597i	−0.307005	+	0.307005i	0.536741	+	0.843747i	$0.319655\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.28599			−0.0595084			−0.0297542	−	0.999557i	$-0.509472\pi$
$467$	−1.28599			−0.0595084			−0.0297542	+	0.999557i	$0.509472\pi$
$468$		0			0
$469$	−1.45069			−0.0669868
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.88597	−	1.88597i	0.0867168	−	0.0867168i
$474$		0			0
$475$	6.99604	+	26.1096i	0.321000	+	1.19799i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.97881	+	11.1171i	−0.136105	+	0.507952i	0.863885	+	0.503688i	$0.168024\pi$
$479$	−2.97881	+	11.1171i	−0.136105	+	0.507952i	−0.999991	+	0.00426412i	$0.998643\pi$
$480$		0			0
$481$	−11.8252	+	10.0516i	−0.539182	+	0.458315i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.79352	+	4.83853i	−0.126847	+	0.219706i
$486$		0			0
$487$	4.59185	−	1.23038i	0.208077	−	0.0557540i	−0.153275	−	0.988184i	$-0.548982\pi$
$487$	4.59185	−	1.23038i	0.208077	−	0.0557540i	0.361352	+	0.932430i	$0.382315\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	21.3266	+	36.9387i	0.962454	+	1.66702i	0.716306	+	0.697787i	$0.245832\pi$
$491$	21.3266	+	36.9387i	0.962454	+	1.66702i	0.246148	+	0.969232i	$0.420835\pi$
$492$		0			0
$493$		−	4.30870i		−	0.194054i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.359844	−	0.207756i	0.0161412	−	0.00931912i
$498$		0			0
$499$	−10.4562	−	10.4562i	−0.468084	−	0.468084i	0.433210	−	0.901293i	$-0.357381\pi$
$499$	−10.4562	−	10.4562i	−0.468084	−	0.468084i	−0.901293	+	0.433210i	$0.857381\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.00562	+	2.31264i	0.178602	+	0.103116i	0.586636	−	0.809851i	$-0.300452\pi$
$503$	4.00562	+	2.31264i	0.178602	+	0.103116i	−0.408034	+	0.912967i	$0.633785\pi$
$504$		0			0
$505$	9.09052	+	2.43580i	0.404523	+	0.108392i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.9580	+	3.74005i	0.618679	+	0.165775i	0.554527	−	0.832165i	$-0.312899\pi$
$509$	13.9580	+	3.74005i	0.618679	+	0.165775i	0.0641520	+	0.997940i	$0.479566\pi$
$510$		0			0
$511$	−3.52695	−	2.03629i	−0.156023	−	0.0900801i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.86758	−	8.86758i	−0.390752	−	0.390752i
$516$		0			0
$517$	13.5215	−	7.80664i	0.594675	−	0.343336i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			27.9652i			1.22518i	0.790402	+	0.612589i	$0.209872\pi$
$521$			27.9652i			1.22518i	−0.790402	+	0.612589i	$0.790128\pi$
$522$		0			0
$523$	11.8456	+	20.5172i	0.517972	+	0.897154i	0.999782	+	0.0208783i	$0.00664627\pi$
$523$	11.8456	+	20.5172i	0.517972	+	0.897154i	−0.481810	+	0.876276i	$0.660020\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−49.0976	+	13.1557i	−2.13872	+	0.573069i
$528$		0			0
$529$	−7.38372	+	12.7890i	−0.321031	+	0.556042i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.3168	+	14.7196i	−0.750074	+	0.637577i
$534$		0			0
$535$	1.52536	−	5.69274i	0.0659473	−	0.246119i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.32960	+	19.8903i	0.229562	+	0.856737i
$540$		0			0
$541$	11.4180	−	11.4180i	0.490900	−	0.490900i	−0.417690	−	0.908590i	$-0.637160\pi$
$541$	11.4180	−	11.4180i	0.490900	−	0.490900i	0.908590	+	0.417690i	$0.137160\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.93377			−0.425516
$546$		0			0
$547$	33.3431			1.42565			0.712825	−	0.701342i	$-0.247415\pi$
$547$	33.3431			1.42565			0.712825	+	0.701342i	$0.247415\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.41833	+	2.41833i	−0.103024	+	0.103024i
$552$		0			0
$553$	2.60413	+	9.71876i	0.110739	+	0.413284i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.74352	−	32.6313i	0.370475	−	1.38263i	−0.489370	−	0.872076i	$-0.662773\pi$
$557$	8.74352	−	32.6313i	0.370475	−	1.38263i	0.859845	−	0.510555i	$-0.170560\pi$
$558$		0			0
$559$	2.80452	−	1.32960i	0.118619	−	0.0562359i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.2350	−	17.7276i	0.431355	−	0.747129i	−0.565635	−	0.824656i	$-0.691369\pi$
$563$	10.2350	−	17.7276i	0.431355	−	0.747129i	0.996990	+	0.0775268i	$0.0247023\pi$
$564$		0			0
$565$	−1.53040	+	0.410068i	−0.0643842	+	0.0172517i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.16492	+	12.4100i	0.300369	+	0.520255i	0.976220	−	0.216784i	$-0.0695568\pi$
$569$	7.16492	+	12.4100i	0.300369	+	0.520255i	−0.675850	+	0.737039i	$0.736223\pi$
$570$		0			0
$571$		−	16.5106i		−	0.690949i	−0.938428	−	0.345474i	$-0.887718\pi$
$571$		−	16.5106i		−	0.690949i	0.938428	−	0.345474i	$-0.112282\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	24.0345	−	13.8764i	1.00231	−	0.578684i
$576$		0			0
$577$	−23.0566	−	23.0566i	−0.959857	−	0.959857i	0.0393676	−	0.999225i	$-0.487466\pi$
$577$	−23.0566	−	23.0566i	−0.959857	−	0.959857i	−0.999225	+	0.0393676i	$0.987466\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.696783	−	0.402288i	−0.0289074	−	0.0166897i
$582$		0			0
$583$	−25.5192	−	6.83785i	−1.05690	−	0.283195i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−35.5280	−	9.51971i	−1.46640	−	0.392920i	−0.564704	−	0.825293i	$-0.691010\pi$
$587$	−35.5280	−	9.51971i	−1.46640	−	0.392920i	−0.901695	+	0.432373i	$0.857676\pi$
$588$		0			0
$589$	34.9406	+	20.1730i	1.43970	+	0.831213i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.1226	+	17.1226i	0.703139	+	0.703139i	0.965083	−	0.261944i	$-0.0843636\pi$
$593$	17.1226	+	17.1226i	0.703139	+	0.703139i	−0.261944	+	0.965083i	$0.584364\pi$
$594$		0			0
$595$	−2.70331	+	1.56075i	−0.110825	+	0.0639847i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	35.9822i		−	1.47019i	−0.677962	−	0.735097i	$-0.737137\pi$
$599$		−	35.9822i		−	1.47019i	0.677962	−	0.735097i	$-0.262863\pi$
$600$		0			0
$601$	3.79032	+	6.56502i	0.154610	+	0.267793i	0.932917	−	0.360091i	$-0.117254\pi$
$601$	3.79032	+	6.56502i	0.154610	+	0.267793i	−0.778307	+	0.627884i	$0.783921\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.940863	−	0.252104i	0.0382515	−	0.0102495i
$606$		0			0
$607$	−16.9984	+	29.4420i	−0.689943	+	1.19502i	0.281913	+	0.959440i	$0.409031\pi$
$607$	−16.9984	+	29.4420i	−0.689943	+	1.19502i	−0.971856	+	0.235576i	$0.924302\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.8725	−	3.26898i	0.723042	−	0.132249i
$612$		0			0
$613$	−0.887521	+	3.31227i	−0.0358466	+	0.133781i	−0.981530	−	0.191307i	$-0.938727\pi$
$613$	−0.887521	+	3.31227i	−0.0358466	+	0.133781i	0.945684	+	0.325088i	$0.105394\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.49879	−	27.9859i	−0.301890	−	1.12667i	−0.935590	−	0.353089i	$-0.885131\pi$
$617$	−7.49879	−	27.9859i	−0.301890	−	1.12667i	0.633700	−	0.773579i	$-0.281535\pi$
$618$		0			0
$619$	13.4271	−	13.4271i	0.539680	−	0.539680i	−0.383755	−	0.923435i	$-0.625369\pi$
$619$	13.4271	−	13.4271i	0.539680	−	0.539680i	0.923435	+	0.383755i	$0.125369\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.20814			0.0884673
$624$		0			0
$625$	−17.9732			−0.718927
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−22.9525	+	22.9525i	−0.915177	+	0.915177i
$630$		0			0
$631$	8.66468	+	32.3370i	0.344936	+	1.28732i	0.892687	+	0.450676i	$0.148817\pi$
$631$	8.66468	+	32.3370i	0.344936	+	1.28732i	−0.547752	+	0.836641i	$0.684516\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.753674	+	2.81275i	−0.0299087	+	0.111621i
$636$		0			0
$637$	−1.93630	+	23.8843i	−0.0767190	+	0.946329i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.70705	+	13.3490i	−0.304410	+	0.527254i	−0.977130	−	0.212644i	$-0.931793\pi$
$641$	−7.70705	+	13.3490i	−0.304410	+	0.527254i	0.672720	+	0.739897i	$0.265126\pi$
$642$		0			0
$643$	−1.40639	+	0.376841i	−0.0554626	+	0.0148612i	−0.286444	−	0.958097i	$-0.592473\pi$
$643$	−1.40639	+	0.376841i	−0.0554626	+	0.0148612i	0.230981	+	0.972958i	$0.425806\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.92534	+	13.7271i	0.311577	+	0.539668i	0.978704	−	0.205276i	$-0.0658094\pi$
$647$	7.92534	+	13.7271i	0.311577	+	0.539668i	−0.667127	+	0.744944i	$0.732476\pi$
$648$		0			0
$649$		−	36.8515i		−	1.44655i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.8342	−	13.1833i	0.893572	−	0.515904i	0.0184630	−	0.999830i	$-0.494123\pi$
$653$	22.8342	−	13.1833i	0.893572	−	0.515904i	0.875109	+	0.483925i	$0.160789\pi$
$654$		0			0
$655$	−3.56465	−	3.56465i	−0.139282	−	0.139282i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.9528	+	16.7159i	1.12784	+	0.651159i	0.943391	−	0.331683i	$-0.107616\pi$
$659$	28.9528	+	16.7159i	1.12784	+	0.651159i	0.184450	+	0.982842i	$0.440950\pi$
$660$		0			0
$661$	13.9023	+	3.72512i	0.540738	+	0.144890i	0.518842	−	0.854870i	$-0.326363\pi$
$661$	13.9023	+	3.72512i	0.540738	+	0.144890i	0.0218955	+	0.999760i	$0.493030\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.39327	+	0.641275i	0.0928071	+	0.0248676i
$666$		0			0
$667$	3.04095	+	1.75569i	0.117746	+	0.0679807i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.6659	−	12.6659i	−0.488962	−	0.488962i
$672$		0			0
$673$	9.29190	−	5.36468i	0.358176	−	0.206793i	−0.310104	−	0.950703i	$-0.600364\pi$
$673$	9.29190	−	5.36468i	0.358176	−	0.206793i	0.668281	+	0.743909i	$0.267031\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			40.9483i			1.57377i	0.617099	+	0.786885i	$0.288308\pi$
$677$			40.9483i			1.57377i	−0.617099	+	0.786885i	$0.711692\pi$
$678$		0			0
$679$	−2.38878	−	4.13749i	−0.0916731	−	0.158782i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−27.1725	+	7.28084i	−1.03973	+	0.278594i	−0.738000	−	0.674801i	$-0.764229\pi$
$683$	−27.1725	+	7.28084i	−1.03973	+	0.278594i	−0.301726	+	0.953395i	$0.597563\pi$
$684$		0			0
$685$	0.205947	−	0.356711i	0.00786884	−	0.0136292i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−25.2958	−	17.4731i	−0.963693	−	0.665673i
$690$		0			0
$691$	11.0416	−	41.2076i	0.420040	−	1.56761i	−0.354480	−	0.935064i	$-0.615342\pi$
$691$	11.0416	−	41.2076i	0.420040	−	1.56761i	0.774521	−	0.632549i	$-0.217991\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.734644	+	2.74173i	0.0278666	+	0.104000i
$696$		0			0
$697$	−33.6117	+	33.6117i	−1.27314	+	1.27314i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.8413			1.05155			0.525777	−	0.850623i	$-0.323775\pi$
$701$	27.8413			1.05155			0.525777	+	0.850623i	$0.323775\pi$
$702$		0			0
$703$	25.7649			0.971743
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.69055	+	5.69055i	−0.214015	+	0.214015i
$708$		0			0
$709$	4.08132	+	15.2317i	0.153277	+	0.572038i	0.999247	+	0.0388071i	$0.0123558\pi$
$709$	4.08132	+	15.2317i	0.153277	+	0.572038i	−0.845970	+	0.533231i	$0.820978\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.7212	−	40.0122i	0.401514	−	1.49847i
$714$		0			0
$715$	−7.74715	−	0.628063i	−0.289727	−	0.0234882i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.430431	+	0.745528i	−0.0160524	+	0.0278035i	−0.873940	−	0.486034i	$-0.838443\pi$
$719$	−0.430431	+	0.745528i	−0.0160524	+	0.0278035i	0.857888	+	0.513837i	$0.171777\pi$
$720$		0			0
$721$	10.3583	−	2.77549i	0.385763	−	0.103365i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.29014	−	2.23459i	−0.0479146	−	0.0829905i
$726$		0			0
$727$		−	39.4122i		−	1.46172i	−0.682529	−	0.730858i	$-0.739120\pi$
$727$		−	39.4122i		−	1.46172i	0.682529	−	0.730858i	$-0.260880\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.62173	−	3.24571i	0.207927	−	0.120047i
$732$		0			0
$733$	−25.8535	−	25.8535i	−0.954920	−	0.954920i	0.0441065	−	0.999027i	$-0.485956\pi$
$733$	−25.8535	−	25.8535i	−0.954920	−	0.954920i	−0.999027	+	0.0441065i	$0.985956\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.54276	−	3.77746i	−0.241006	−	0.139145i
$738$		0			0
$739$	−28.3476	−	7.59571i	−1.04278	−	0.279413i	−0.303516	−	0.952826i	$-0.598161\pi$
$739$	−28.3476	−	7.59571i	−1.04278	−	0.279413i	−0.739266	+	0.673414i	$0.764827\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−31.1758	−	8.35353i	−1.14373	−	0.306461i	−0.363279	−	0.931680i	$-0.618343\pi$
$743$	−31.1758	−	8.35353i	−1.14373	−	0.306461i	−0.780449	+	0.625219i	$0.785010\pi$
$744$		0			0
$745$	−2.96476	−	1.71170i	−0.108620	−	0.0627120i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.56358	+	3.56358i	0.130210	+	0.130210i
$750$		0			0
$751$	−24.2522	+	14.0020i	−0.884974	+	0.510940i	−0.872295	−	0.488980i	$-0.837369\pi$
$751$	−24.2522	+	14.0020i	−0.884974	+	0.510940i	−0.0126790	+	0.999920i	$0.504036\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			0.272724i			0.00992546i
$756$		0			0
$757$	−24.3124	−	42.1103i	−0.883649	−	1.53053i	−0.847254	−	0.531188i	$-0.821746\pi$
$757$	−24.3124	−	42.1103i	−0.883649	−	1.53053i	−0.0363957	−	0.999337i	$-0.511588\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	49.4724	−	13.2561i	1.79337	−	0.480533i	0.800463	−	0.599383i	$-0.204587\pi$
$761$	49.4724	−	13.2561i	1.79337	−	0.480533i	0.992912	+	0.118849i	$0.0379206\pi$
$762$		0			0
$763$	4.24725	−	7.35646i	0.153761	−	0.266322i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.4099	−	40.3901i	0.520313	−	1.45840i
$768$		0			0
$769$	2.31709	−	8.64750i	0.0835564	−	0.311837i	−0.911481	−	0.411343i	$-0.865060\pi$
$769$	2.31709	−	8.64750i	0.0835564	−	0.311837i	0.995037	+	0.0995065i	$0.0317264\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.53642	−	13.1981i	−0.127196	−	0.474703i	0.872712	−	0.488235i	$-0.162359\pi$
$773$	−3.53642	−	13.1981i	−0.127196	−	0.474703i	−0.999908	+	0.0135323i	$0.995692\pi$
$774$		0			0
$775$	−21.5239	+	21.5239i	−0.773163	+	0.773163i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	37.7302			1.35183
$780$		0			0
$781$	2.16390			0.0774305
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.109281	−	0.109281i	0.00390040	−	0.00390040i
$786$		0			0
$787$	−0.507117	−	1.89259i	−0.0180768	−	0.0674634i	0.956298	−	0.292393i	$-0.0944515\pi$
$787$	−0.507117	−	1.89259i	−0.0180768	−	0.0674634i	−0.974375	+	0.224929i	$0.927785\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.350655	−	1.30866i	0.0124679	−	0.0465307i
$792$		0			0
$793$	−8.92939	−	18.8348i	−0.317092	−	0.668844i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.770404	−	1.33438i	0.0272891	−	0.0472661i	−0.852058	−	0.523447i	$-0.824646\pi$
$797$	0.770404	−	1.33438i	0.0272891	−	0.0472661i	0.879347	+	0.476181i	$0.157979\pi$
$798$		0			0
$799$	36.7052	−	9.83514i	1.29854	−	0.347942i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−10.6046	−	18.3677i	−0.374228	−	0.648181i
$804$		0			0
$805$		−	2.54388i		−	0.0896601i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.50167	−	4.33109i	0.263745	−	0.152273i	−0.362297	−	0.932063i	$-0.618007\pi$
$809$	7.50167	−	4.33109i	0.263745	−	0.152273i	0.626042	+	0.779790i	$0.284674\pi$
$810$		0			0
$811$	1.10164	+	1.10164i	0.0386840	+	0.0386840i	0.726184	−	0.687500i	$-0.241292\pi$
$811$	1.10164	+	1.10164i	0.0386840	+	0.0386840i	−0.687500	+	0.726184i	$0.741292\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.81004	+	3.93178i	0.238545	+	0.137724i
$816$		0			0
$817$	−4.97699	−	1.33358i	−0.174123	−	0.0466560i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	40.5839	+	10.8744i	1.41639	+	0.379520i	0.884200	−	0.467108i	$-0.154704\pi$
$821$	40.5839	+	10.8744i	1.41639	+	0.379520i	0.532186	+	0.846627i	$0.321371\pi$
$822$		0			0
$823$	−22.8413	−	13.1874i	−0.796198	−	0.459685i	0.0459421	−	0.998944i	$-0.485371\pi$
$823$	−22.8413	−	13.1874i	−0.796198	−	0.459685i	−0.842140	+	0.539259i	$0.818704\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.9334	−	30.9334i	−1.07566	−	1.07566i	−0.996893	−	0.0787651i	$-0.974902\pi$
$827$	−30.9334	−	30.9334i	−1.07566	−	1.07566i	−0.0787651	−	0.996893i	$-0.525098\pi$
$828$		0			0
$829$	24.2973	−	14.0280i	0.843880	−	0.487214i	−0.0147014	−	0.999892i	$-0.504680\pi$
$829$	24.2973	−	14.0280i	0.843880	−	0.487214i	0.858581	+	0.512678i	$0.171346\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			50.1174i			1.73646i
$834$		0			0
$835$	−7.32845	−	12.6932i	−0.253611	−	0.439268i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.67015	−	0.715465i	0.0921839	−	0.0247006i	−0.212432	−	0.977176i	$-0.568138\pi$
$839$	2.67015	−	0.715465i	0.0921839	−	0.0247006i	0.304616	+	0.952475i	$0.401472\pi$
$840$		0			0
$841$	−14.3368	+	24.8320i	−0.494371	+	0.856276i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.24546	−	3.71772i	−0.283652	−	0.127893i
$846$		0			0
$847$	−0.215577	+	0.804546i	−0.00740732	+	0.0276445i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.84659	−	25.5518i	−0.234698	−	0.875906i
$852$		0			0
$853$	−29.9861	+	29.9861i	−1.02671	+	1.02671i	−0.0270725	+	0.999633i	$0.508619\pi$
$853$	−29.9861	+	29.9861i	−1.02671	+	1.02671i	−0.999633	+	0.0270725i	$0.991381\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.865574			−0.0295675			−0.0147837	−	0.999891i	$-0.504706\pi$
$857$	−0.865574			−0.0295675			−0.0147837	+	0.999891i	$0.504706\pi$
$858$		0			0
$859$	16.4894			0.562611			0.281305	−	0.959618i	$-0.409233\pi$
$859$	16.4894			0.562611			0.281305	+	0.959618i	$0.409233\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.8129	−	24.8129i	0.844641	−	0.844641i	−0.144817	−	0.989458i	$-0.546259\pi$
$863$	24.8129	−	24.8129i	0.844641	−	0.844641i	0.989458	+	0.144817i	$0.0462593\pi$
$864$		0			0
$865$	−2.18660	−	8.16049i	−0.0743465	−	0.277465i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−13.5618	+	50.6134i	−0.460053	+	1.71694i
$870$		0			0
$871$	−5.69392	−	6.69858i	−0.192931	−	0.226973i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.96952	+	3.41130i	−0.0665818	+	0.115323i
$876$		0			0
$877$	−42.9777	+	11.5158i	−1.45125	+	0.388862i	−0.896460	−	0.443125i	$-0.853870\pi$
$877$	−42.9777	+	11.5158i	−1.45125	+	0.388862i	−0.554794	+	0.831988i	$0.687203\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.3106	+	19.5906i	0.381065	+	0.660024i	0.991215	−	0.132262i	$-0.0422240\pi$
$881$	11.3106	+	19.5906i	0.381065	+	0.660024i	−0.610150	+	0.792286i	$0.708891\pi$
$882$		0			0
$883$			21.8146i			0.734120i	0.930197	+	0.367060i	$0.119636\pi$
$883$			21.8146i			0.734120i	−0.930197	+	0.367060i	$0.880364\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.00797587	−	0.00460487i	0.000267804	−	0.000154616i	−0.499866	−	0.866103i	$-0.666617\pi$
$887$	0.00797587	−	0.00460487i	0.000267804	−	0.000154616i	0.500134	+	0.865948i	$0.333284\pi$
$888$		0			0
$889$	−1.76075	−	1.76075i	−0.0590535	−	0.0590535i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26.1215	−	15.0813i	−0.874124	−	0.504675i
$894$		0			0
$895$	14.1313	+	3.78647i	0.472358	+	0.126568i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.72010	−	0.996797i	−0.124072	−	0.0332450i
$900$		0			0
$901$	−55.6857	−	32.1502i	−1.85516	−	1.07108i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.04079	−	9.04079i	−0.300526	−	0.300526i
$906$		0			0
$907$	−26.0726	+	15.0530i	−0.865726	+	0.499827i	−0.865925	−	0.500173i	$-0.833270\pi$
$907$	−26.0726	+	15.0530i	−0.865726	+	0.499827i	0.000199805		1.00000i	$0.499936\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	36.1872i		−	1.19894i	−0.800398	−	0.599468i	$-0.795379\pi$
$911$		−	36.1872i		−	1.19894i	0.800398	−	0.599468i	$-0.204621\pi$
$912$		0			0
$913$	−2.09504	−	3.62871i	−0.0693356	−	0.120093i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.16389	−	1.11571i	0.137504	−	0.0368440i
$918$		0			0
$919$	17.3325	−	30.0208i	0.571747	−	0.990294i	−0.424640	−	0.905362i	$-0.639599\pi$
$919$	17.3325	−	30.0208i	0.571747	−	0.990294i	0.996387	−	0.0849319i	$-0.0270673\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.37168	+	0.846144i	0.0780649	+	0.0278512i
$924$		0			0
$925$	−5.03109	+	18.7763i	−0.165421	+	0.617361i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.4484	+	38.9940i	0.342801	+	1.27935i	0.895160	+	0.445745i	$0.147061\pi$
$929$	10.4484	+	38.9940i	0.342801	+	1.27935i	−0.552359	+	0.833606i	$0.686272\pi$
$930$		0			0
$931$	28.1292	−	28.1292i	0.921897	−	0.921897i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.2562			−0.531634
$936$		0			0
$937$	−5.04421			−0.164787			−0.0823936	−	0.996600i	$-0.526256\pi$
$937$	−5.04421			−0.164787			−0.0823936	+	0.996600i	$0.526256\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	32.5856	−	32.5856i	1.06226	−	1.06226i	0.0643312	−	0.997929i	$-0.479509\pi$
$941$	32.5856	−	32.5856i	1.06226	−	1.06226i	0.997929	−	0.0643312i	$-0.0204914\pi$
$942$		0			0
$943$	−10.0262	−	37.4182i	−0.326497	−	1.21850i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.43392	−	31.4758i	0.274066	−	1.02283i	−0.682399	−	0.730980i	$-0.739063\pi$
$947$	8.43392	−	31.4758i	0.274066	−	1.02283i	0.956465	−	0.291847i	$-0.0942699\pi$
$948$		0			0
$949$	−4.44060	−	24.2781i	−0.144148	−	0.788099i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	28.0391	−	48.5652i	0.908276	−	1.57318i	0.0918185	−	0.995776i	$-0.470732\pi$
$953$	28.0391	−	48.5652i	0.908276	−	1.57318i	0.816458	−	0.577405i	$-0.195935\pi$
$954$		0			0
$955$	−6.25655	+	1.67644i	−0.202457	+	0.0542482i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.176108	+	0.305029i	0.00568684	+	0.00984989i
$960$		0			0
$961$			14.4340i			0.465612i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.1028	+	5.83285i	−0.325220	+	0.187766i
$966$		0			0
$967$	9.64750	+	9.64750i	0.310243	+	0.310243i	0.845003	−	0.534761i	$-0.179598\pi$
$967$	9.64750	+	9.64750i	0.310243	+	0.310243i	−0.534761	+	0.845003i	$0.679598\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−34.2111	−	19.7518i	−1.09789	−	0.633865i	−0.162222	−	0.986754i	$-0.551866\pi$
$971$	−34.2111	−	19.7518i	−1.09789	−	0.633865i	−0.935665	+	0.352889i	$0.885199\pi$
$972$		0			0
$973$	−2.34449	−	0.628205i	−0.0751610	−	0.0201393i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.7352	+	8.23548i	0.983307	+	0.263476i	0.714437	−	0.699700i	$-0.246683\pi$
$977$	30.7352	+	8.23548i	0.983307	+	0.263476i	0.268870	+	0.963176i	$0.413350\pi$
$978$		0			0
$979$	9.95891	+	5.74978i	0.318288	+	0.183764i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	33.9213	+	33.9213i	1.08192	+	1.08192i	0.996330	+	0.0855907i	$0.0272777\pi$
$983$	33.9213	+	33.9213i	1.08192	+	1.08192i	0.0855907	+	0.996330i	$0.472722\pi$
$984$		0			0
$985$	2.53262	−	1.46221i	0.0806959	−	0.0465898i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			5.29020i			0.168218i
$990$		0			0
$991$	−8.60345	−	14.9016i	−0.273297	−	0.473365i	0.696407	−	0.717647i	$-0.254781\pi$
$991$	−8.60345	−	14.9016i	−0.273297	−	0.473365i	−0.969704	+	0.244282i	$0.921448\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.11358	−	0.834281i	0.0987071	−	0.0264485i
$996$		0			0
$997$	−6.59132	+	11.4165i	−0.208749	+	0.361564i	−0.951321	−	0.308203i	$-0.900273\pi$
$997$	−6.59132	+	11.4165i	−0.208749	+	0.361564i	0.742572	+	0.669767i	$0.233606\pi$
$998$		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.89.5	yes	32
3.2	odd	2	inner	936.2.dr.b.89.4	✓	32
13.6	odd	12	inner	936.2.dr.b.305.4	yes	32
39.32	even	12	inner	936.2.dr.b.305.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dr.b.89.4	✓	32	3.2	odd	2	inner
936.2.dr.b.89.5	yes	32	1.1	even	1	trivial
936.2.dr.b.305.4	yes	32	13.6	odd	12	inner
936.2.dr.b.305.5	yes	32	39.32	even	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)

\(f(q)\)	\(=\)	\(q+(0.491974 - 0.491974i) q^{5} +(0.153985 + 0.574679i) q^{7} +(-0.801922 + 2.99281i) q^{11} +(-2.04919 + 2.96661i) q^{13} +(-3.77047 + 6.53065i) q^{17} +(5.78167 - 1.54919i) q^{19} +(-3.07276 - 5.32218i) q^{23} +4.51592i q^{25} +(-0.494824 + 0.285687i) q^{29} +(4.76623 + 4.76623i) q^{31} +(0.358484 + 0.206971i) q^{35} +(4.15780 + 1.11408i) q^{37} +(6.08869 + 1.63146i) q^{41} +(-0.745493 - 0.430411i) q^{43} +(-3.56323 - 3.56323i) q^{47} +(5.75563 - 3.32302i) q^{49} +8.52682i q^{53} +(1.07786 + 1.86691i) q^{55} +(-11.4885 + 3.07834i) q^{59} +(-2.89058 + 5.00664i) q^{61} +(0.451347 + 2.46765i) q^{65} +(-0.631089 + 2.35526i) q^{67} +(-0.180758 - 0.674599i) q^{71} +(-4.84031 + 4.84031i) q^{73} -1.84339 q^{77} +16.9116 q^{79} +(-0.956248 + 0.956248i) q^{83} +(1.35794 + 5.06789i) q^{85} +(0.960598 - 3.58500i) q^{89} +(-2.02040 - 0.720815i) q^{91} +(2.08227 - 3.60660i) q^{95} +(-7.75656 + 2.07836i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{7} - 20 q^{13} - 4 q^{19} + 4 q^{31} + 60 q^{43} + 84 q^{49} - 28 q^{61} - 24 q^{67} + 16 q^{73} + 48 q^{79} + 88 q^{85} - 116 q^{91} + 72 q^{97}+O(q^{100}) \) 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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