LMFDB - Embedded newform 756.2.k.f.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(109,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("756.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	756.109
Dual form			756.2.k.f.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14400 + 3.71351i) q^{5} +(1.40545 - 2.24159i) q^{7} +O(q^{10})$	$q+(2.14400 + 3.71351i) q^{5} +(1.40545 - 2.24159i) q^{7} +(1.90545 - 3.30033i) q^{11} +3.28799 q^{13} +(0.405446 - 0.702253i) q^{17} +(-3.54944 - 6.14781i) q^{19} +(3.23855 + 5.60933i) q^{23} +(-6.69344 + 11.5934i) q^{25} +3.81089 q^{29} +(-1.64400 + 2.84748i) q^{31} +(11.3374 + 0.413181i) q^{35} +(2.88255 + 4.99272i) q^{37} +2.09888 q^{41} -8.76509 q^{43} +(-1.66690 - 2.88715i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-4.93199 + 8.54245i) q^{53} +16.3411 q^{55} +(-1.73855 + 3.01126i) q^{59} +(-2.97710 - 5.15649i) q^{61} +(7.04944 + 12.2100i) q^{65} +(1.76145 - 3.05092i) q^{67} +6.05308 q^{71} +(5.19344 - 8.99530i) q^{73} +(-4.71998 - 8.90966i) q^{77} +(2.57234 + 4.45543i) q^{79} -1.71201 q^{83} +3.47710 q^{85} +(-6.26509 - 10.8515i) q^{89} +(4.62110 - 7.37033i) q^{91} +(15.2200 - 26.3618i) q^{95} +1.04580 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 2 q^{7}+O(q^{10}) $ 6 * q + q^5 + 2 * q^7	$ 6 q + q^{5} + 2 q^{7} + 5 q^{11} - 4 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} + 10 q^{29} + 2 q^{31} + 26 q^{35} - 24 q^{41} - 18 q^{43} - 9 q^{47} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 31 q^{77} + 8 q^{79} - 34 q^{83} + 10 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q + q^5 + 2 * q^7 + 5 * q^11 - 4 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 + 10 * q^29 + 2 * q^31 + 26 * q^35 - 24 * q^41 - 18 * q^43 - 9 * q^47 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 31 * q^77 + 8 * q^79 - 34 * q^83 + 10 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	2.14400	+	3.71351i	0.958824	+	1.66073i	0.725364	+	0.688366i	$0.241672\pi$
$5$	2.14400	+	3.71351i	0.958824	+	1.66073i	0.233461	+	0.972366i	$0.424995\pi$
$6$		0			0
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.90545	−	3.30033i	0.574514	−	0.995087i	−0.421581	−	0.906791i	$-0.638525\pi$
$11$	1.90545	−	3.30033i	0.574514	−	0.995087i	0.996094	−	0.0882959i	$-0.0281421\pi$
$12$		0			0
$13$	3.28799			0.911925			0.455962	−	0.889999i	$-0.349295\pi$
$13$	3.28799			0.911925			0.455962	+	0.889999i	$0.349295\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.405446	−	0.702253i	0.0983351	−	0.170321i	−0.812661	−	0.582737i	$-0.801982\pi$
$17$	0.405446	−	0.702253i	0.0983351	−	0.170321i	0.910996	+	0.412416i	$0.135315\pi$
$18$		0			0
$19$	−3.54944	−	6.14781i	−0.814298	−	1.41041i	−0.909831	−	0.414979i	$-0.863789\pi$
$19$	−3.54944	−	6.14781i	−0.814298	−	1.41041i	0.0955331	−	0.995426i	$-0.469544\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.23855	+	5.60933i	0.675284	+	1.16963i	0.976386	+	0.216035i	$0.0693124\pi$
$23$	3.23855	+	5.60933i	0.675284	+	1.16963i	−0.301101	+	0.953592i	$0.597354\pi$
$24$		0			0
$25$	−6.69344	+	11.5934i	−1.33869	+	2.31868i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.81089			0.707665			0.353832	−	0.935309i	$-0.384878\pi$
$29$	3.81089			0.707665			0.353832	+	0.935309i	$0.384878\pi$
$30$		0			0
$31$	−1.64400	+	2.84748i	−0.295270	+	0.511423i	−0.975048	−	0.221995i	$-0.928743\pi$
$31$	−1.64400	+	2.84748i	−0.295270	+	0.511423i	0.679777	+	0.733419i	$0.262076\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	11.3374	+	0.413181i	1.91638	+	0.0698403i
$36$		0			0
$37$	2.88255	+	4.99272i	0.473888	+	0.820797i	0.999553	−	0.0298939i	$-0.00951695\pi$
$37$	2.88255	+	4.99272i	0.473888	+	0.820797i	−0.525665	+	0.850691i	$0.676184\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.09888			0.327791			0.163895	−	0.986478i	$-0.447594\pi$
$41$	2.09888			0.327791			0.163895	+	0.986478i	$0.447594\pi$
$42$		0			0
$43$	−8.76509			−1.33666			−0.668332	−	0.743863i	$-0.732991\pi$
$43$	−8.76509			−1.33666			−0.668332	+	0.743863i	$0.732991\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.66690	−	2.88715i	−0.243142	−	0.421134i	0.718466	−	0.695562i	$-0.244845\pi$
$47$	−1.66690	−	2.88715i	−0.243142	−	0.421134i	−0.961608	+	0.274428i	$0.911511\pi$
$48$		0			0
$49$	−3.04944	−	6.30087i	−0.435635	−	0.900124i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.93199	+	8.54245i	−0.677461	+	1.17340i	0.298282	+	0.954478i	$0.403586\pi$
$53$	−4.93199	+	8.54245i	−0.677461	+	1.17340i	−0.975743	+	0.218919i	$0.929747\pi$
$54$		0			0
$55$	16.3411			2.20343
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.73855	+	3.01126i	−0.226340	+	0.392032i	−0.956721	−	0.291008i	$-0.906009\pi$
$59$	−1.73855	+	3.01126i	−0.226340	+	0.392032i	0.730381	+	0.683040i	$0.239343\pi$
$60$		0			0
$61$	−2.97710	−	5.15649i	−0.381179	−	0.660221i	0.610052	−	0.792361i	$-0.291148\pi$
$61$	−2.97710	−	5.15649i	−0.381179	−	0.660221i	−0.991231	+	0.132140i	$0.957815\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.04944	+	12.2100i	0.874376	+	1.51446i
$66$		0			0
$67$	1.76145	−	3.05092i	0.215195	−	0.372729i	−0.738138	−	0.674650i	$-0.764295\pi$
$67$	1.76145	−	3.05092i	0.215195	−	0.372729i	0.953333	+	0.301921i	$0.0976278\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.05308			0.718369			0.359184	−	0.933267i	$-0.383055\pi$
$71$	6.05308			0.718369			0.359184	+	0.933267i	$0.383055\pi$
$72$		0			0
$73$	5.19344	−	8.99530i	0.607846	−	1.05282i	−0.383749	−	0.923438i	$-0.625367\pi$
$73$	5.19344	−	8.99530i	0.607846	−	1.05282i	0.991595	−	0.129383i	$-0.0412995\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.71998	−	8.90966i	−0.537892	−	1.01535i
$78$		0			0
$79$	2.57234	+	4.45543i	0.289411	+	0.501275i	0.973669	−	0.227965i	$-0.0732072\pi$
$79$	2.57234	+	4.45543i	0.289411	+	0.501275i	−0.684258	+	0.729240i	$0.739874\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.71201			−0.187917			−0.0939586	−	0.995576i	$-0.529952\pi$
$83$	−1.71201			−0.187917			−0.0939586	+	0.995576i	$0.529952\pi$
$84$		0			0
$85$	3.47710			0.377144
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.26509	−	10.8515i	−0.664098	−	1.15025i	−0.979529	−	0.201304i	$-0.935482\pi$
$89$	−6.26509	−	10.8515i	−0.664098	−	1.15025i	0.315430	−	0.948949i	$-0.397851\pi$
$90$		0			0
$91$	4.62110	−	7.37033i	0.484422	−	0.772620i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.2200	−	26.3618i	1.56154	−	2.70466i
$96$		0			0
$97$	1.04580			0.106185			0.0530925	−	0.998590i	$-0.483092\pi$
$97$	1.04580			0.106185			0.0530925	+	0.998590i	$0.483092\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.95489	+	15.5103i	−0.891045	+	1.54333i	−0.0524199	+	0.998625i	$0.516693\pi$
$101$	−8.95489	+	15.5103i	−0.891045	+	1.54333i	−0.838625	+	0.544710i	$0.816640\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.45056	+	5.97654i	0.333578	+	0.577774i	0.983211	−	0.182474i	$-0.0584106\pi$
$107$	3.45056	+	5.97654i	0.333578	+	0.577774i	−0.649633	+	0.760248i	$0.725077\pi$
$108$		0			0
$109$	2.81089	−	4.86861i	0.269235	−	0.466328i	−0.699430	−	0.714701i	$-0.746563\pi$
$109$	2.81089	−	4.86861i	0.269235	−	0.466328i	0.968664	+	0.248373i	$0.0798959\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−20.1520			−1.89574			−0.947869	−	0.318661i	$-0.896767\pi$
$113$	−20.1520			−1.89574			−0.947869	+	0.318661i	$0.896767\pi$
$114$		0			0
$115$	−13.8869	+	24.0528i	−1.29496	+	2.24293i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.00433	−	1.89582i	−0.0920668	−	0.173790i
$120$		0			0
$121$	−1.76145	−	3.05092i	−0.160132	−	0.277356i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−35.9629			−3.21662
$126$		0			0
$127$	−2.14468			−0.190310			−0.0951550	−	0.995462i	$-0.530335\pi$
$127$	−2.14468			−0.190310			−0.0951550	+	0.995462i	$0.530335\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.69344	+	2.93312i	0.147956	+	0.256268i	0.930472	−	0.366363i	$-0.119397\pi$
$131$	1.69344	+	2.93312i	0.147956	+	0.256268i	−0.782516	+	0.622631i	$0.786064\pi$
$132$		0			0
$133$	−18.7694	−	0.684031i	−1.62752	−	0.0593130i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.47710	−	11.2187i	0.553376	−	0.958475i	−0.444652	−	0.895703i	$-0.646673\pi$
$137$	6.47710	−	11.2187i	0.553376	−	0.958475i	0.998028	−	0.0627719i	$-0.0199941\pi$
$138$		0			0
$139$	−17.2880			−1.46635			−0.733174	−	0.680041i	$-0.761962\pi$
$139$	−17.2880			−1.46635			−0.733174	+	0.680041i	$0.761962\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.26509	−	10.8515i	0.523913	−	0.907444i
$144$		0			0
$145$	8.17054	+	14.1518i	0.678526	+	1.17524i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.784350	+	1.35853i	0.0642565	+	0.111295i	0.896364	−	0.443319i	$-0.146199\pi$
$149$	0.784350	+	1.35853i	0.0642565	+	0.111295i	−0.832107	+	0.554614i	$0.812866\pi$
$150$		0			0
$151$	0.693438	−	1.20107i	0.0564312	−	0.0977417i	−0.836430	−	0.548074i	$-0.815361\pi$
$151$	0.693438	−	1.20107i	0.0564312	−	0.0977417i	0.892861	+	0.450332i	$0.148695\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.0989			−1.13245
$156$		0			0
$157$	8.43199	−	14.6046i	0.672946	−	1.16558i	−0.304119	−	0.952634i	$-0.598362\pi$
$157$	8.43199	−	14.6046i	0.672946	−	1.16558i	0.977065	−	0.212942i	$-0.0683047\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.1254	+	0.624118i	1.34967	+	0.0491874i
$162$		0			0
$163$	−8.64833	−	14.9793i	−0.677389	−	1.17327i	−0.975764	−	0.218824i	$-0.929778\pi$
$163$	−8.64833	−	14.9793i	−0.677389	−	1.17327i	0.298375	−	0.954449i	$-0.403555\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.9556			−1.07991			−0.539957	−	0.841692i	$-0.681560\pi$
$167$	−13.9556			−1.07991			−0.539957	+	0.841692i	$0.681560\pi$
$168$		0			0
$169$	−2.18911			−0.168393
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.57165	−	7.91834i	−0.347576	−	0.602020i	0.638242	−	0.769836i	$-0.279662\pi$
$173$	−4.57165	−	7.91834i	−0.347576	−	0.602020i	−0.985818	+	0.167816i	$0.946329\pi$
$174$		0			0
$175$	16.5803	+	31.2978i	1.25335	+	2.36589i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.53087	+	14.7759i	−0.637627	+	1.10440i	0.348325	+	0.937374i	$0.386751\pi$
$179$	−8.53087	+	14.7759i	−0.637627	+	1.10440i	−0.985952	+	0.167029i	$0.946583\pi$
$180$		0			0
$181$	−16.4400			−1.22197			−0.610986	−	0.791641i	$-0.709227\pi$
$181$	−16.4400			−1.22197			−0.610986	+	0.791641i	$0.709227\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.3603	+	21.4087i	−0.908750	+	1.57400i
$186$		0			0
$187$	−1.54511	−	2.67621i	−0.112990	−	0.195704i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.48143	−	2.56591i	−0.107193	−	0.185663i	0.807439	−	0.589951i	$-0.200853\pi$
$191$	−1.48143	−	2.56591i	−0.107193	−	0.185663i	−0.914632	+	0.404288i	$0.867519\pi$
$192$		0			0
$193$	8.71565	−	15.0959i	0.627366	−	1.08663i	−0.360712	−	0.932677i	$-0.617466\pi$
$193$	8.71565	−	15.0959i	0.627366	−	1.08663i	0.988078	−	0.153953i	$-0.0492004\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.2880			0.732989			0.366495	−	0.930420i	$-0.380558\pi$
$197$	10.2880			0.732989			0.366495	+	0.930420i	$0.380558\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.35600	−	8.54245i	0.375918	−	0.599563i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−27.0531			−1.87130
$210$		0			0
$211$	16.4327			1.13127			0.565636	−	0.824655i	$-0.308631\pi$
$211$	16.4327			1.13127			0.565636	+	0.824655i	$0.308631\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−18.7923	−	32.5493i	−1.28163	−	2.21984i
$216$		0			0
$217$	4.07234	+	7.68715i	0.276449	+	0.521838i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.33310	−	2.30900i	0.0896743	−	0.155320i
$222$		0			0
$223$	4.13602			0.276969			0.138484	−	0.990365i	$-0.455777\pi$
$223$	4.13602			0.276969			0.138484	+	0.990365i	$0.455777\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.6483	−	18.4434i	0.706754	−	1.22413i	−0.259300	−	0.965797i	$-0.583492\pi$
$227$	10.6483	−	18.4434i	0.706754	−	1.22413i	0.966055	−	0.258338i	$-0.0831747\pi$
$228$		0			0
$229$	2.92766	+	5.07085i	0.193465	+	0.335091i	0.946396	−	0.323008i	$-0.104694\pi$
$229$	2.92766	+	5.07085i	0.193465	+	0.335091i	−0.752931	+	0.658099i	$0.771361\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.02290	+	6.96787i	0.263549	+	0.456480i	0.967182	−	0.254083i	$-0.0817736\pi$
$233$	4.02290	+	6.96787i	0.263549	+	0.456480i	−0.703633	+	0.710563i	$0.748440\pi$
$234$		0			0
$235$	7.14764	−	12.3801i	0.466260	−	0.807587i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.0989			−0.911981			−0.455991	−	0.889985i	$-0.650715\pi$
$239$	−14.0989			−0.911981			−0.455991	+	0.889985i	$0.650715\pi$
$240$		0			0
$241$	13.3640	−	23.1471i	0.860849	−	1.49103i	−0.0102608	−	0.999947i	$-0.503266\pi$
$241$	13.3640	−	23.1471i	0.860849	−	1.49103i	0.871110	−	0.491088i	$-0.163400\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.8603	−	24.8332i	1.07717	−	1.58653i
$246$		0			0
$247$	−11.6705	−	20.2140i	−0.742579	−	1.28618i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$		0			0
$253$	24.6835			1.55184
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.26509	+	10.8515i	0.390806	+	0.676895i	0.992556	−	0.121789i	$-0.0388631\pi$
$257$	6.26509	+	10.8515i	0.390806	+	0.676895i	−0.601750	+	0.798684i	$0.705530\pi$
$258$		0			0
$259$	15.2429	+	0.555510i	0.947147	+	0.0345177i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.45056	−	5.97654i	0.212771	−	0.368529i	−0.739810	−	0.672816i	$-0.765085\pi$
$263$	3.45056	−	5.97654i	0.212771	−	0.368529i	0.952581	+	0.304286i	$0.0984180\pi$
$264$		0			0
$265$	−42.2967			−2.59826
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.9054	+	18.8888i	−0.664917	+	1.15167i	0.314391	+	0.949294i	$0.398200\pi$
$269$	−10.9054	+	18.8888i	−0.664917	+	1.15167i	−0.979308	+	0.202376i	$0.935134\pi$
$270$		0			0
$271$	−3.76145	−	6.51502i	−0.228492	−	0.395759i	0.728870	−	0.684653i	$-0.240046\pi$
$271$	−3.76145	−	6.51502i	−0.228492	−	0.395759i	−0.957361	+	0.288893i	$0.906713\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	25.5080	+	44.1811i	1.53819	+	2.66422i
$276$		0			0
$277$	−4.61745	+	7.99766i	−0.277436	+	0.480533i	−0.970747	−	0.240106i	$-0.922818\pi$
$277$	−4.61745	+	7.99766i	−0.277436	+	0.480533i	0.693311	+	0.720639i	$0.256151\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.6749			−0.815774			−0.407887	−	0.913032i	$-0.633734\pi$
$281$	−13.6749			−0.815774			−0.407887	+	0.913032i	$0.633734\pi$
$282$		0			0
$283$	−1.07165	+	1.85616i	−0.0637032	+	0.110337i	−0.896118	−	0.443816i	$-0.853624\pi$
$283$	−1.07165	+	1.85616i	−0.0637032	+	0.110337i	0.832415	+	0.554153i	$0.186958\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.94987	−	4.70484i	0.174125	−	0.277718i
$288$		0			0
$289$	8.17123	+	14.1530i	0.480660	+	0.832528i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.29665			0.543116			0.271558	−	0.962422i	$-0.412461\pi$
$293$	9.29665			0.543116			0.271558	+	0.962422i	$0.412461\pi$
$294$		0			0
$295$	−14.9098			−0.868081
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.6483	+	18.4434i	0.615809	+	1.06661i
$300$		0			0
$301$	−12.3189	+	19.6477i	−0.710048	+	1.13248i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.7658	−	22.1110i	0.730966	−	1.26607i
$306$		0			0
$307$	−10.3869			−0.592810			−0.296405	−	0.955062i	$-0.595788\pi$
$307$	−10.3869			−0.592810			−0.296405	+	0.955062i	$0.595788\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.28799	+	2.23087i	−0.0730353	+	0.126501i	−0.900230	−	0.435414i	$-0.856602\pi$
$311$	−1.28799	+	2.23087i	−0.0730353	+	0.126501i	0.827195	+	0.561915i	$0.189935\pi$
$312$		0			0
$313$	5.74219	+	9.94577i	0.324568	+	0.562168i	0.981425	−	0.191847i	$-0.0614478\pi$
$313$	5.74219	+	9.94577i	0.324568	+	0.562168i	−0.656857	+	0.754015i	$0.728114\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.59820	+	13.1605i	0.426757	+	0.739165i	0.996583	−	0.0826006i	$-0.0263226\pi$
$317$	7.59820	+	13.1605i	0.426757	+	0.739165i	−0.569826	+	0.821766i	$0.692989\pi$
$318$		0			0
$319$	7.26145	−	12.5772i	0.406563	−	0.704188i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.75643			−0.320296
$324$		0			0
$325$	−22.0080	+	38.1189i	−1.22078	+	2.11446i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.81453	−	0.321236i	−0.485961	−	0.0177103i
$330$		0			0
$331$	−7.76578	−	13.4507i	−0.426846	−	0.739319i	0.569745	−	0.821822i	$-0.307042\pi$
$331$	−7.76578	−	13.4507i	−0.426846	−	0.739319i	−0.996591	+	0.0825028i	$0.973709\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	15.1062			0.825338
$336$		0			0
$337$	−3.00866			−0.163892			−0.0819461	−	0.996637i	$-0.526114\pi$
$337$	−3.00866			−0.163892			−0.0819461	+	0.996637i	$0.526114\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.26509	+	10.8515i	0.339274	+	0.587639i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.4327	−	19.8020i	0.613738	−	1.06303i	−0.376866	−	0.926268i	$-0.622998\pi$
$347$	11.4327	−	19.8020i	0.613738	−	1.06303i	0.990604	−	0.136758i	$-0.0436683\pi$
$348$		0			0
$349$	9.04442			0.484137			0.242068	−	0.970259i	$-0.422174\pi$
$349$	9.04442			0.484137			0.242068	+	0.970259i	$0.422174\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.09820	+	15.7585i	−0.484248	+	0.838742i	−0.999836	−	0.0180942i	$-0.994240\pi$
$353$	−9.09820	+	15.7585i	−0.484248	+	0.838742i	0.515588	+	0.856837i	$0.327573\pi$
$354$		0			0
$355$	12.9778	+	22.4782i	0.688789	+	1.19302i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.1934	+	21.1197i	0.643545	+	1.11465i	0.984636	+	0.174622i	$0.0558704\pi$
$359$	12.1934	+	21.1197i	0.643545	+	1.11465i	−0.341090	+	0.940030i	$0.610796\pi$
$360$		0			0
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	44.5388			2.33127
$366$		0			0
$367$	4.43268	−	7.67762i	0.231384	−	0.400769i	−0.726832	−	0.686816i	$-0.759008\pi$
$367$	4.43268	−	7.67762i	0.231384	−	0.400769i	0.958216	+	0.286047i	$0.0923413\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.2170	+	23.0614i	0.634276	+	1.19729i
$372$		0			0
$373$	1.57598	+	2.72968i	0.0816014	+	0.141338i	0.903938	−	0.427664i	$-0.140663\pi$
$373$	1.57598	+	2.72968i	0.0816014	+	0.141338i	−0.822337	+	0.569001i	$0.807330\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.5302			0.645337
$378$		0			0
$379$	−2.28799			−0.117526			−0.0587631	−	0.998272i	$-0.518716\pi$
$379$	−2.28799			−0.117526			−0.0587631	+	0.998272i	$0.518716\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.1254	−	24.4660i	−0.721776	−	1.25015i	−0.960287	−	0.279012i	$-0.909993\pi$
$383$	−14.1254	−	24.4660i	−0.721776	−	1.25015i	0.238512	−	0.971140i	$-0.423340\pi$
$384$		0			0
$385$	22.9665	−	36.6300i	1.17048	−	1.86684i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.360335	−	0.624118i	0.0182697	−	0.0316440i	−0.856746	−	0.515739i	$-0.827518\pi$
$389$	0.360335	−	0.624118i	0.0182697	−	0.0316440i	0.875016	+	0.484095i	$0.160851\pi$
$390$		0			0
$391$	5.25223			0.265617
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.0302	+	19.1048i	−0.554989	+	0.961269i
$396$		0			0
$397$	−10.5753	−	18.3169i	−0.530759	−	0.919301i	−0.999356	−	0.0358892i	$-0.988574\pi$
$397$	−10.5753	−	18.3169i	−0.530759	−	0.919301i	0.468597	−	0.883412i	$-0.344760\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.2472	−	24.6769i	−0.711472	−	1.23231i	−0.964305	−	0.264795i	$-0.914696\pi$
$401$	−14.2472	−	24.6769i	−0.711472	−	1.23231i	0.252833	−	0.967510i	$-0.418638\pi$
$402$		0			0
$403$	−5.40545	+	9.36251i	−0.269264	+	0.466380i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.9701			1.08902
$408$		0			0
$409$	5.38186	−	9.32165i	0.266116	−	0.460926i	−0.701740	−	0.712434i	$-0.747593\pi$
$409$	5.38186	−	9.32165i	0.266116	−	0.460926i	0.967855	+	0.251508i	$0.0809263\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.30656	+	8.12927i	0.211912	+	0.400015i
$414$		0			0
$415$	−3.67054	−	6.35756i	−0.180180	−	0.312080i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−34.0604			−1.66396			−0.831979	−	0.554807i	$-0.812792\pi$
$419$	−34.0604			−1.66396			−0.831979	+	0.554807i	$0.812792\pi$
$420$		0			0
$421$	20.5833			1.00317			0.501584	−	0.865109i	$-0.332751\pi$
$421$	20.5833			1.00317			0.501584	+	0.865109i	$0.332751\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.42766	+	9.40098i	0.263280	+	0.456014i
$426$		0			0
$427$	−15.7429	−	0.573732i	−0.761851	−	0.0277649i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.9814	−	20.7524i	0.577125	−	0.999610i	−0.418682	−	0.908133i	$-0.637508\pi$
$431$	11.9814	−	20.7524i	0.577125	−	0.999610i	0.995807	−	0.0914772i	$-0.0291589\pi$
$432$		0			0
$433$	29.9642			1.43999			0.719995	−	0.693980i	$-0.244144\pi$
$433$	29.9642			1.43999			0.719995	+	0.693980i	$0.244144\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.9901	−	39.8200i	1.09977	−	1.90485i
$438$		0			0
$439$	−14.4098	−	24.9585i	−0.687741	−	1.19120i	−0.972567	−	0.232623i	$-0.925269\pi$
$439$	−14.4098	−	24.9585i	−0.687741	−	1.19120i	0.284826	−	0.958579i	$-0.408064\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.0043	+	27.7203i	0.760389	+	1.31703i	0.942650	+	0.333782i	$0.108325\pi$
$443$	16.0043	+	27.7203i	0.760389	+	1.31703i	−0.182262	+	0.983250i	$0.558342\pi$
$444$		0			0
$445$	26.8647	−	46.5310i	1.27351	−	2.20578i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	32.0087			1.51058			0.755291	−	0.655390i	$-0.227496\pi$
$449$	32.0087			1.51058			0.755291	+	0.655390i	$0.227496\pi$
$450$		0			0
$451$	3.99931	−	6.92701i	0.188320	−	0.326180i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	37.2774	+	1.35853i	1.74759	+	0.0636891i
$456$		0			0
$457$	10.4277	+	18.0612i	0.487785	+	0.844869i	0.999901	−	0.0140474i	$-0.00447158\pi$
$457$	10.4277	+	18.0612i	0.487785	+	0.844869i	−0.512116	+	0.858916i	$0.671138\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.2509			−1.17605			−0.588025	−	0.808843i	$-0.700094\pi$
$461$	−25.2509			−1.17605			−0.588025	+	0.808843i	$0.700094\pi$
$462$		0			0
$463$	−21.1520			−0.983015			−0.491508	−	0.870873i	$-0.663554\pi$
$463$	−21.1520			−0.983015			−0.491508	+	0.870873i	$0.663554\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.95853	+	13.7846i	0.368277	+	0.637874i	0.989296	−	0.145921i	$-0.0466145\pi$
$467$	7.95853	+	13.7846i	0.368277	+	0.637874i	−0.621019	+	0.783795i	$0.713281\pi$
$468$		0			0
$469$	−4.36329	−	8.23635i	−0.201478	−	0.380319i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.7014	+	28.9277i	−0.767932	+	1.33010i
$474$		0			0
$475$	95.0319			4.36036
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.977789	+	1.69358i	−0.0446763	+	0.0773816i	−0.887499	−	0.460810i	$-0.847559\pi$
$479$	−0.977789	+	1.69358i	−0.0446763	+	0.0773816i	0.842823	+	0.538192i	$0.180892\pi$
$480$		0			0
$481$	9.47779	+	16.4160i	0.432150	+	0.748506i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.24219	+	3.88359i	0.101813	+	0.176345i
$486$		0			0
$487$	−9.98143	+	17.2883i	−0.452302	+	0.783410i	−0.998529	−	0.0542276i	$-0.982730\pi$
$487$	−9.98143	+	17.2883i	−0.452302	+	0.783410i	0.546227	+	0.837637i	$0.316064\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−22.0975			−0.997247			−0.498623	−	0.866819i	$-0.666161\pi$
$491$	−22.0975			−0.997247			−0.498623	+	0.866819i	$0.666161\pi$
$492$		0			0
$493$	1.54511	−	2.67621i	0.0695883	−	0.120531i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.50728	−	13.5685i	0.381604	−	0.608632i
$498$		0			0
$499$	16.5574	+	28.6783i	0.741212	+	1.28382i	0.951944	+	0.306272i	$0.0990819\pi$
$499$	16.5574	+	28.6783i	0.741212	+	1.28382i	−0.210732	+	0.977544i	$0.567585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.76509			0.212465			0.106232	−	0.994341i	$-0.466121\pi$
$503$	4.76509			0.212465			0.106232	+	0.994341i	$0.466121\pi$
$504$		0			0
$505$	−76.7970			−3.41742
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.38255	−	9.32284i	−0.238577	−	0.413228i	0.721729	−	0.692176i	$-0.243348\pi$
$509$	−5.38255	−	9.32284i	−0.238577	−	0.413228i	−0.960306	+	0.278948i	$0.910014\pi$
$510$		0			0
$511$	−12.8647	−	24.2840i	−0.569099	−	1.07426i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.0080	+	25.9946i	−0.661330	+	1.14546i
$516$		0			0
$517$	−12.7047			−0.558753
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.617454	+	1.06946i	−0.0270512	+	0.0468540i	−0.879234	−	0.476390i	$-0.841945\pi$
$521$	−0.617454	+	1.06946i	−0.0270512	+	0.0468540i	0.852183	+	0.523244i	$0.175278\pi$
$522$		0			0
$523$	4.28435	+	7.42071i	0.187342	+	0.324485i	0.944363	−	0.328905i	$-0.106680\pi$
$523$	4.28435	+	7.42071i	0.187342	+	0.324485i	−0.757022	+	0.653390i	$0.773346\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.33310	+	2.30900i	0.0580709	+	0.100582i
$528$		0			0
$529$	−9.47641	+	16.4136i	−0.412018	+	0.713636i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.90112			0.298920
$534$		0			0
$535$	−14.7960	+	25.6274i	−0.639685	+	1.10797i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.6055	−	1.94180i	−1.14598	−	0.0836390i
$540$		0			0
$541$	7.50433	+	12.9979i	0.322636	+	0.558823i	0.981031	−	0.193850i	$-0.0620976\pi$
$541$	7.50433	+	12.9979i	0.322636	+	0.558823i	−0.658395	+	0.752673i	$0.728764\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	24.1062			1.03259
$546$		0			0
$547$	12.2509			0.523809			0.261904	−	0.965094i	$-0.415650\pi$
$547$	12.2509			0.523809			0.261904	+	0.965094i	$0.415650\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.5265	−	23.4287i	−0.576250	−	0.998094i
$552$		0			0
$553$	13.6025	+	0.495729i	0.578438	+	0.0210806i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.8905	−	22.3270i	0.546189	−	0.946027i	−0.452342	−	0.891844i	$-0.649411\pi$
$557$	12.8905	−	22.3270i	0.546189	−	0.946027i	0.998531	−	0.0541823i	$-0.0172552\pi$
$558$		0			0
$559$	−28.8196			−1.21894
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.3418	+	21.3766i	−0.520143	+	0.900915i	0.479582	+	0.877497i	$0.340788\pi$
$563$	−12.3418	+	21.3766i	−0.520143	+	0.900915i	−0.999726	+	0.0234179i	$0.992545\pi$
$564$		0			0
$565$	−43.2057	−	74.8345i	−1.81768	−	3.14831i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.11677	−	10.5945i	−0.256428	−	0.444147i	0.708854	−	0.705355i	$-0.249212\pi$
$569$	−6.11677	−	10.5945i	−0.256428	−	0.444147i	−0.965282	+	0.261208i	$0.915879\pi$
$570$		0			0
$571$	−17.6563	+	30.5816i	−0.738893	+	1.27980i	0.214101	+	0.976812i	$0.431318\pi$
$571$	−17.6563	+	30.5816i	−0.738893	+	1.27980i	−0.952994	+	0.302989i	$0.902015\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−86.7081			−3.61598
$576$		0			0
$577$	−4.52221	+	7.83270i	−0.188262	+	0.326080i	−0.944671	−	0.328020i	$-0.893619\pi$
$577$	−4.52221	+	7.83270i	−0.188262	+	0.326080i	0.756409	+	0.654099i	$0.226952\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.40613	+	3.83762i	−0.0998233	+	0.159211i
$582$		0			0
$583$	18.7953	+	32.5544i	0.778421	+	1.34826i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	35.8196			1.47843			0.739216	−	0.673469i	$-0.235196\pi$
$587$	35.8196			1.47843			0.739216	+	0.673469i	$0.235196\pi$
$588$		0			0
$589$	23.3411			0.961752
$590$		0			0
$591$		0			0
$592$		0			0
$593$	22.0309	+	38.1586i	0.904700	+	1.56699i	0.821320	+	0.570468i	$0.193238\pi$
$593$	22.0309	+	38.1586i	0.904700	+	1.56699i	0.0833794	+	0.996518i	$0.473429\pi$
$594$		0			0
$595$	4.88688	−	7.79423i	0.200342	−	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−15.0316	+	26.0354i	−0.614173	+	1.06378i	0.376356	+	0.926475i	$0.377177\pi$
$599$	−15.0316	+	26.0354i	−0.614173	+	1.06378i	−0.990529	+	0.137304i	$0.956156\pi$
$600$		0			0
$601$	29.1964			1.19095			0.595473	−	0.803375i	$-0.296965\pi$
$601$	29.1964			1.19095			0.595473	+	0.803375i	$0.296965\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.55308	−	13.0823i	0.307077	−	0.531872i
$606$		0			0
$607$	8.07165	+	13.9805i	0.327618	+	0.567452i	0.982039	−	0.188679i	$-0.0604207\pi$
$607$	8.07165	+	13.9805i	0.327618	+	0.567452i	−0.654420	+	0.756131i	$0.727087\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.48074	−	9.49292i	−0.221727	−	0.384043i
$612$		0			0
$613$	−23.5581	+	40.8038i	−0.951503	+	1.64805i	−0.209327	+	0.977846i	$0.567127\pi$
$613$	−23.5581	+	40.8038i	−0.951503	+	1.64805i	−0.742175	+	0.670206i	$0.766206\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	38.0146			1.53041			0.765204	−	0.643787i	$-0.222638\pi$
$617$	38.0146			1.53041			0.765204	+	0.643787i	$0.222638\pi$
$618$		0			0
$619$	−6.09091	+	10.5498i	−0.244814	+	0.424031i	−0.962079	−	0.272769i	$-0.912060\pi$
$619$	−6.09091	+	10.5498i	−0.244814	+	0.424031i	0.717265	+	0.696800i	$0.245394\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−33.1298	−	1.20738i	−1.32732	−	0.0483726i
$624$		0			0
$625$	−43.6370	−	75.5816i	−1.74548	−	3.02326i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.67487			0.186399
$630$		0			0
$631$	−10.8640			−0.432488			−0.216244	−	0.976339i	$-0.569381\pi$
$631$	−10.8640			−0.432488			−0.216244	+	0.976339i	$0.569381\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.59820	−	7.96431i	−0.182474	−	0.316054i
$636$		0			0
$637$	−10.0265	−	20.7172i	−0.397266	−	0.820845i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.2200	−	26.3618i	0.601153	−	1.04123i	−0.391494	−	0.920181i	$-0.628042\pi$
$641$	15.2200	−	26.3618i	0.601153	−	1.04123i	0.992647	−	0.121047i	$-0.0386251\pi$
$642$		0			0
$643$	−37.8640			−1.49321			−0.746605	−	0.665268i	$-0.768317\pi$
$643$	−37.8640			−1.49321			−0.746605	+	0.665268i	$0.768317\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.0982	−	31.3470i	0.711513	−	1.23238i	−0.252775	−	0.967525i	$-0.581343\pi$
$647$	18.0982	−	31.3470i	0.711513	−	1.23238i	0.964289	−	0.264853i	$-0.0853233\pi$
$648$		0			0
$649$	6.62543	+	11.4756i	0.260071	+	0.450456i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.0488	−	19.1370i	−0.432371	−	0.748889i	0.564706	−	0.825292i	$-0.308990\pi$
$653$	−11.0488	−	19.1370i	−0.432371	−	0.748889i	−0.997077	+	0.0764035i	$0.975656\pi$
$654$		0			0
$655$	−7.26145	+	12.5772i	−0.283728	+	0.491432i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−44.0677			−1.71663			−0.858316	−	0.513121i	$-0.828489\pi$
$659$	−44.0677			−1.71663			−0.858316	+	0.513121i	$0.828489\pi$
$660$		0			0
$661$	−2.95351	+	5.11563i	−0.114878	+	0.198975i	−0.917731	−	0.397202i	$-0.869981\pi$
$661$	−2.95351	+	5.11563i	−0.114878	+	0.198975i	0.802853	+	0.596177i	$0.203314\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−37.7014	−	71.1670i	−1.46200	−	2.75974i
$666$		0			0
$667$	12.3418	+	21.3766i	0.477875	+	0.827704i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−22.6908			−0.875969
$672$		0			0
$673$	−2.19777			−0.0847178			−0.0423589	−	0.999102i	$-0.513487\pi$
$673$	−2.19777			−0.0847178			−0.0423589	+	0.999102i	$0.513487\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.0316	−	26.0354i	−0.577710	−	1.00062i	−0.995741	−	0.0921903i	$-0.970613\pi$
$677$	−15.0316	−	26.0354i	−0.577710	−	1.00062i	0.418032	−	0.908432i	$-0.362720\pi$
$678$		0			0
$679$	1.46982	−	2.34425i	0.0564064	−	0.0899642i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.14764	−	7.18392i	0.158705	−	0.274885i	−0.775697	−	0.631106i	$-0.782601\pi$
$683$	4.14764	−	7.18392i	0.158705	−	0.274885i	0.934402	+	0.356221i	$0.115935\pi$
$684$		0			0
$685$	55.5475			2.12236
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.2163	+	28.0875i	−0.617793	+	1.07005i
$690$		0			0
$691$	0.598196	+	1.03611i	0.0227564	+	0.0394153i	0.877179	−	0.480163i	$-0.159422\pi$
$691$	0.598196	+	1.03611i	0.0227564	+	0.0394153i	−0.854423	+	0.519578i	$0.826089\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−37.0654	−	64.1991i	−1.40597	−	2.43521i
$696$		0			0
$697$	0.850985	−	1.47395i	0.0322333	−	0.0558298i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31.8813			−1.20414			−0.602070	−	0.798443i	$-0.705657\pi$
$701$	−31.8813			−1.20414			−0.602070	+	0.798443i	$0.705657\pi$
$702$		0			0
$703$	20.4629	−	35.4427i	0.771771	−	1.33675i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.1822	+	41.8721i	0.834246	+	1.57476i
$708$		0			0
$709$	10.7163	+	18.5612i	0.402461	+	0.697082i	0.994022	−	0.109178i	$-0.0348217\pi$
$709$	10.7163	+	18.5612i	0.402461	+	0.697082i	−0.591562	+	0.806260i	$0.701488\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−21.2967			−0.797566
$714$		0			0
$715$	53.7293			2.00936
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.6304	+	37.4650i	0.806680	+	1.39721i	0.915151	+	0.403110i	$0.132071\pi$
$719$	21.6304	+	37.4650i	0.806680	+	1.39721i	−0.108472	+	0.994100i	$0.534596\pi$
$720$		0			0
$721$	18.5080	+	0.674503i	0.689273	+	0.0251198i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.5080	+	44.1811i	−0.947342	+	1.64085i
$726$		0			0
$727$	12.1818			0.451799			0.225899	−	0.974151i	$-0.427468\pi$
$727$	12.1818			0.451799			0.225899	+	0.974151i	$0.427468\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.55377	+	6.15532i	−0.131441	+	0.227663i
$732$		0			0
$733$	−6.72431	−	11.6468i	−0.248368	−	0.430186i	0.714705	−	0.699426i	$-0.246561\pi$
$733$	−6.72431	−	11.6468i	−0.248368	−	0.430186i	−0.963073	+	0.269240i	$0.913228\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.71270	−	11.6267i	−0.247265	−	0.428276i
$738$		0			0
$739$	4.93632	−	8.54995i	0.181585	−	0.314515i	−0.760835	−	0.648945i	$-0.775210\pi$
$739$	4.93632	−	8.54995i	0.181585	−	0.314515i	0.942421	+	0.334430i	$0.108544\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.5687			−0.827965			−0.413983	−	0.910285i	$-0.635863\pi$
$743$	−22.5687			−0.827965			−0.413983	+	0.910285i	$0.635863\pi$
$744$		0			0
$745$	−3.36329	+	5.82539i	−0.123221	+	0.213426i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	18.2465	+	0.664975i	0.666713	+	0.0242977i
$750$		0			0
$751$	0.287992	+	0.498817i	0.0105090	+	0.0182021i	0.871232	−	0.490871i	$-0.163321\pi$
$751$	0.287992	+	0.498817i	0.0105090	+	0.0182021i	−0.860723	+	0.509073i	$0.829988\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.94692			0.216430
$756$		0			0
$757$	22.8196			0.829391			0.414695	−	0.909960i	$-0.363888\pi$
$757$	22.8196			0.829391			0.414695	+	0.909960i	$0.363888\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.89052	−	17.1309i	−0.358531	−	0.620994i	0.629185	−	0.777256i	$-0.283389\pi$
$761$	−9.89052	−	17.1309i	−0.358531	−	0.620994i	−0.987716	+	0.156262i	$0.950056\pi$
$762$		0			0
$763$	−6.96286	−	13.1434i	−0.252072	−	0.475824i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.71634	+	9.90099i	−0.206405	+	0.357504i
$768$		0			0
$769$	−28.7207			−1.03569			−0.517847	−	0.855473i	$-0.673266\pi$
$769$	−28.7207			−1.03569			−0.517847	+	0.855473i	$0.673266\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.10253	+	7.10578i	−0.147558	+	0.255577i	−0.930324	−	0.366738i	$-0.880475\pi$
$773$	−4.10253	+	7.10578i	−0.147558	+	0.255577i	0.782767	+	0.622315i	$0.213808\pi$
$774$		0			0
$775$	−22.0080	−	38.1189i	−0.790550	−	1.36927i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.44987	−	12.9036i	−0.266919	−	0.462318i
$780$		0			0
$781$	11.5338	−	19.9772i	0.412713	−	0.714839i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	72.3126			2.58095
$786$		0			0
$787$	26.3182	−	45.5844i	0.938142	−	1.62491i	0.169208	−	0.985580i	$-0.445879\pi$
$787$	26.3182	−	45.5844i	0.938142	−	1.62491i	0.768934	−	0.639329i	$-0.220788\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−28.3225	+	45.1724i	−1.00703	+	1.60615i
$792$		0			0
$793$	−9.78868	−	16.9545i	−0.347606	−	0.602072i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.5329			−0.621049			−0.310524	−	0.950565i	$-0.600505\pi$
$797$	−17.5329			−0.621049			−0.310524	+	0.950565i	$0.600505\pi$
$798$		0			0
$799$	−2.70335			−0.0956375
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.7916	−	34.2801i	−0.698432	−	1.20972i
$804$		0			0
$805$	34.3992	+	64.9336i	1.21241	+	2.28861i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.57530	−	6.19259i	0.125701	−	0.217720i	−0.796306	−	0.604894i	$-0.793215\pi$
$809$	3.57530	−	6.19259i	0.125701	−	0.217720i	0.922007	+	0.387174i	$0.126549\pi$
$810$		0			0
$811$	−31.6835			−1.11256			−0.556280	−	0.830995i	$-0.687772\pi$
$811$	−31.6835			−1.11256			−0.556280	+	0.830995i	$0.687772\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	37.0840	−	64.2313i	1.29899	−	2.24992i
$816$		0			0
$817$	31.1112	+	53.8862i	1.08844	+	1.88524i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.53451	+	13.0502i	0.262956	+	0.455454i	0.967026	−	0.254677i	$-0.0819691\pi$
$821$	7.53451	+	13.0502i	0.262956	+	0.455454i	−0.704070	+	0.710131i	$0.748636\pi$
$822$		0			0
$823$	10.4778	−	18.1481i	0.365233	−	0.632602i	−0.623581	−	0.781759i	$-0.714323\pi$
$823$	10.4778	−	18.1481i	0.365233	−	0.632602i	0.988813	+	0.149157i	$0.0476561\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.7897			1.27930			0.639652	−	0.768665i	$-0.279079\pi$
$827$	36.7897			1.27930			0.639652	+	0.768665i	$0.279079\pi$
$828$		0			0
$829$	−23.1527	+	40.1016i	−0.804125	+	1.39279i	0.112755	+	0.993623i	$0.464032\pi$
$829$	−23.1527	+	40.1016i	−0.804125	+	1.39279i	−0.916880	+	0.399163i	$0.869301\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.66119	−	0.413181i	−0.196149	−	0.0143159i
$834$		0			0
$835$	−29.9207	−	51.8242i	−1.03545	−	1.79345i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.6377			−0.885113			−0.442556	−	0.896741i	$-0.645928\pi$
$839$	−25.6377			−0.885113			−0.442556	+	0.896741i	$0.645928\pi$
$840$		0			0
$841$	−14.4771			−0.499210
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.69344	−	8.12927i	−0.161459	−	0.279656i
$846$		0			0
$847$	−9.31453	−	0.339458i	−0.320051	−	0.0116639i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.6705	+	32.3383i	−0.640018	+	1.10854i
$852$		0			0
$853$	−5.43130			−0.185964			−0.0929821	−	0.995668i	$-0.529640\pi$
$853$	−5.43130			−0.185964			−0.0929821	+	0.995668i	$0.529640\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.61745	+	6.26561i	−0.123570	+	0.214029i	−0.921173	−	0.389153i	$-0.872768\pi$
$857$	−3.61745	+	6.26561i	−0.123570	+	0.214029i	0.797603	+	0.603183i	$0.206101\pi$
$858$		0			0
$859$	2.71565	+	4.70364i	0.0926568	+	0.160486i	0.908628	−	0.417606i	$-0.137131\pi$
$859$	2.71565	+	4.70364i	0.0926568	+	0.160486i	−0.815971	+	0.578092i	$0.803797\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.35600	−	9.27687i	−0.182320	−	0.315788i	0.760350	−	0.649514i	$-0.225028\pi$
$863$	−5.35600	−	9.27687i	−0.182320	−	0.315788i	−0.942670	+	0.333725i	$0.891694\pi$
$864$		0			0
$865$	19.6032	−	33.9538i	0.666529	−	1.15446i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	19.6058			0.665083
$870$		0			0
$871$	5.79163	−	10.0314i	0.196242	−	0.339901i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−50.5439	+	80.6140i	−1.70869	+	2.72525i
$876$		0			0
$877$	6.90840	+	11.9657i	0.233280	+	0.404053i	0.958771	−	0.284178i	$-0.0917208\pi$
$877$	6.90840	+	11.9657i	0.233280	+	0.404053i	−0.725491	+	0.688231i	$0.758387\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.6662			0.797335			0.398667	−	0.917096i	$-0.369473\pi$
$881$	23.6662			0.797335			0.398667	+	0.917096i	$0.369473\pi$
$882$		0			0
$883$	18.9615			0.638105			0.319052	−	0.947737i	$-0.396635\pi$
$883$	18.9615			0.638105			0.319052	+	0.947737i	$0.396635\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.1978	−	17.6631i	−0.342408	−	0.593067i	0.642472	−	0.766309i	$-0.277909\pi$
$887$	−10.1978	−	17.6631i	−0.342408	−	0.593067i	−0.984879	+	0.173242i	$0.944576\pi$
$888$		0			0
$889$	−3.01424	+	4.80750i	−0.101094	+	0.161238i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11.8331	+	20.4955i	−0.395980	+	0.685857i
$894$		0			0
$895$	−73.1606			−2.44549
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.26509	+	10.8515i	−0.208953	+	0.361916i
$900$		0			0
$901$	3.99931	+	6.92701i	0.133236	+	0.230772i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−35.2472	−	61.0500i	−1.17166	−	2.02937i
$906$		0			0
$907$	−20.0073	+	34.6536i	−0.664331	+	1.15065i	0.315135	+	0.949047i	$0.397950\pi$
$907$	−20.0073	+	34.6536i	−0.664331	+	1.15065i	−0.979466	+	0.201608i	$0.935383\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.8268			0.424972			0.212486	−	0.977164i	$-0.431844\pi$
$911$	12.8268			0.424972			0.212486	+	0.977164i	$0.431844\pi$
$912$		0			0
$913$	−3.26214	+	5.65019i	−0.107961	+	0.186994i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.95489	+	0.326351i	0.295716	+	0.0107771i
$918$		0			0
$919$	21.9771	+	38.0655i	0.724958	+	1.25566i	0.958991	+	0.283435i	$0.0914740\pi$
$919$	21.9771	+	38.0655i	0.724958	+	1.25566i	−0.234034	+	0.972228i	$0.575193\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.9025			0.655099
$924$		0			0
$925$	−77.1766			−2.53755
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20.1175	+	34.8445i	0.660032	+	1.14321i	0.980607	+	0.195986i	$0.0627907\pi$
$929$	20.1175	+	34.8445i	0.660032	+	1.14321i	−0.320574	+	0.947223i	$0.603876\pi$
$930$		0			0
$931$	−27.9127	+	41.1120i	−0.914803	+	1.34739i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.62543	−	11.4756i	0.216675	−	0.375291i
$936$		0			0
$937$	−3.06175			−0.100023			−0.0500114	−	0.998749i	$-0.515926\pi$
$937$	−3.06175			−0.100023			−0.0500114	+	0.998749i	$0.515926\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.0946	−	17.4843i	0.329073	−	0.569971i	−0.653255	−	0.757138i	$-0.726597\pi$
$941$	10.0946	−	17.4843i	0.329073	−	0.569971i	0.982328	+	0.187167i	$0.0599304\pi$
$942$		0			0
$943$	6.79734	+	11.7733i	0.221352	+	0.383393i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.572342	−	0.991326i	−0.0185986	−	0.0322138i	0.856576	−	0.516020i	$-0.172587\pi$
$947$	−0.572342	−	0.991326i	−0.0185986	−	0.0322138i	−0.875175	+	0.483807i	$0.839254\pi$
$948$		0			0
$949$	17.0760	−	29.5765i	0.554310	−	0.960093i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−42.9701			−1.39194			−0.695970	−	0.718071i	$-0.745025\pi$
$953$	−42.9701			−1.39194			−0.695970	+	0.718071i	$0.745025\pi$
$954$		0			0
$955$	6.35236	−	11.0026i	0.205558	−	0.356036i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.0444	−	30.2862i	−0.518101	−	0.977993i
$960$		0			0
$961$	10.0946	+	17.4843i	0.325631	+	0.564009i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	74.7453			2.40614
$966$		0			0
$967$	9.99862			0.321534			0.160767	−	0.986992i	$-0.448603\pi$
$967$	9.99862			0.321534			0.160767	+	0.986992i	$0.448603\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	16.3145	+	28.2576i	0.523558	+	0.906830i	0.999624	+	0.0274199i	$0.00872911\pi$
$971$	16.3145	+	28.2576i	0.523558	+	0.906830i	−0.476066	+	0.879410i	$0.657938\pi$
$972$		0			0
$973$	−24.2973	+	38.7526i	−0.778937	+	1.24235i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.7479	−	35.9364i	0.663784	−	1.14971i	−0.315829	−	0.948816i	$-0.602283\pi$
$977$	20.7479	−	35.9364i	0.663784	−	1.14971i	0.979613	−	0.200892i	$-0.0643840\pi$
$978$		0			0
$979$	−47.7512			−1.52613
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.7163	−	30.6856i	0.565063	−	0.978719i	−0.431980	−	0.901883i	$-0.642185\pi$
$983$	17.7163	−	30.6856i	0.565063	−	0.978719i	0.997044	−	0.0768356i	$-0.0244816\pi$
$984$		0			0
$985$	22.0574	+	38.2046i	0.702808	+	1.21730i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−28.3862	−	49.1663i	−0.902628	−	1.56340i
$990$		0			0
$991$	24.2960	−	42.0818i	0.771787	−	1.33677i	−0.164796	−	0.986328i	$-0.552697\pi$
$991$	24.2960	−	42.0818i	0.771787	−	1.33677i	0.936583	−	0.350446i	$-0.113970\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.0159			0.951569
$996$		0			0
$997$	−23.5130	+	40.7257i	−0.744664	+	1.28980i	0.205688	+	0.978618i	$0.434057\pi$
$997$	−23.5130	+	40.7257i	−0.744664	+	1.28980i	−0.950352	+	0.311178i	$0.899276\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.k.f.109.3	yes	6
3.2	odd	2		756.2.k.e.109.1	✓	6
7.2	even	3	inner	756.2.k.f.541.3	yes	6
7.3	odd	6		5292.2.a.w.1.3		3
7.4	even	3		5292.2.a.u.1.1		3
9.2	odd	6		2268.2.l.k.109.3		6
9.4	even	3		2268.2.i.k.865.3		6
9.5	odd	6		2268.2.i.j.865.1		6
9.7	even	3		2268.2.l.j.109.1		6
21.2	odd	6		756.2.k.e.541.1	yes	6
21.11	odd	6		5292.2.a.x.1.3		3
21.17	even	6		5292.2.a.v.1.1		3
63.2	odd	6		2268.2.i.j.2053.1		6
63.16	even	3		2268.2.i.k.2053.3		6
63.23	odd	6		2268.2.l.k.541.3		6
63.58	even	3		2268.2.l.j.541.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.1	✓	6	3.2	odd	2
756.2.k.e.541.1	yes	6	21.2	odd	6
756.2.k.f.109.3	yes	6	1.1	even	1	trivial
756.2.k.f.541.3	yes	6	7.2	even	3	inner
2268.2.i.j.865.1		6	9.5	odd	6
2268.2.i.j.2053.1		6	63.2	odd	6
2268.2.i.k.865.3		6	9.4	even	3
2268.2.i.k.2053.3		6	63.16	even	3
2268.2.l.j.109.1		6	9.7	even	3
2268.2.l.j.541.1		6	63.58	even	3
2268.2.l.k.109.3		6	9.2	odd	6
2268.2.l.k.541.3		6	63.23	odd	6
5292.2.a.u.1.1		3	7.4	even	3
5292.2.a.v.1.1		3	21.17	even	6
5292.2.a.w.1.3		3	7.3	odd	6
5292.2.a.x.1.3		3	21.11	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14400 + 3.71351i) q^{5} +(1.40545 - 2.24159i) q^{7} +O(q^{10})\)	\(q+(2.14400 + 3.71351i) q^{5} +(1.40545 - 2.24159i) q^{7} +(1.90545 - 3.30033i) q^{11} +3.28799 q^{13} +(0.405446 - 0.702253i) q^{17} +(-3.54944 - 6.14781i) q^{19} +(3.23855 + 5.60933i) q^{23} +(-6.69344 + 11.5934i) q^{25} +3.81089 q^{29} +(-1.64400 + 2.84748i) q^{31} +(11.3374 + 0.413181i) q^{35} +(2.88255 + 4.99272i) q^{37} +2.09888 q^{41} -8.76509 q^{43} +(-1.66690 - 2.88715i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-4.93199 + 8.54245i) q^{53} +16.3411 q^{55} +(-1.73855 + 3.01126i) q^{59} +(-2.97710 - 5.15649i) q^{61} +(7.04944 + 12.2100i) q^{65} +(1.76145 - 3.05092i) q^{67} +6.05308 q^{71} +(5.19344 - 8.99530i) q^{73} +(-4.71998 - 8.90966i) q^{77} +(2.57234 + 4.45543i) q^{79} -1.71201 q^{83} +3.47710 q^{85} +(-6.26509 - 10.8515i) q^{89} +(4.62110 - 7.37033i) q^{91} +(15.2200 - 26.3618i) q^{95} +1.04580 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q + q^5 + 2 * q^7	\( 6 q + q^{5} + 2 q^{7} + 5 q^{11} - 4 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} + 10 q^{29} + 2 q^{31} + 26 q^{35} - 24 q^{41} - 18 q^{43} - 9 q^{47} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 31 q^{77} + 8 q^{79} - 34 q^{83} + 10 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q + q^5 + 2 * q^7 + 5 * q^11 - 4 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 + 10 * q^29 + 2 * q^31 + 26 * q^35 - 24 * q^41 - 18 * q^43 - 9 * q^47 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 31 * q^77 + 8 * q^79 - 34 * q^83 + 10 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 + 28 * q^97

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