LMFDB - Embedded newform 1134.2.d.a.1133.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(1133,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1134.1133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.d (of order $2$, degree $1$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1133.14
Root			$-1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	1134.1133
Dual form			1134.2.d.a.1133.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +1.79035 q^{5} +(2.28052 - 1.34136i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +1.79035 q^{5} +(2.28052 - 1.34136i) q^{7} -1.00000i q^{8} +1.79035i q^{10} -2.40150i q^{11} +4.89133i q^{13} +(1.34136 + 2.28052i) q^{14} +1.00000 q^{16} +3.66466 q^{17} -3.01701i q^{19} -1.79035 q^{20} +2.40150 q^{22} -3.76638i q^{23} -1.79465 q^{25} -4.89133 q^{26} +(-2.28052 + 1.34136i) q^{28} -6.56103i q^{29} +4.64661i q^{31} +1.00000i q^{32} +3.66466i q^{34} +(4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +3.01701 q^{38} -1.79035i q^{40} +8.08188 q^{41} +6.96254 q^{43} +2.40150i q^{44} +3.76638 q^{46} -5.13604 q^{47} +(3.40150 - 6.11799i) q^{49} -1.79465i q^{50} -4.89133i q^{52} -4.29953i q^{55} +(-1.34136 - 2.28052i) q^{56} +6.56103 q^{58} -14.5900 q^{59} +11.3283i q^{61} -4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +0.570231 q^{67} -3.66466 q^{68} +(2.40150 + 4.08292i) q^{70} -5.96254i q^{71} +12.3814i q^{73} +9.36404i q^{74} +3.01701i q^{76} +(-3.22128 - 5.47667i) q^{77} +3.03663 q^{79} +1.79035 q^{80} +8.08188i q^{82} +14.0054 q^{83} +6.56103 q^{85} +6.96254i q^{86} -2.40150 q^{88} -3.74863 q^{89} +(6.56103 + 11.1547i) q^{91} +3.76638i q^{92} -5.13604i q^{94} -5.40150i q^{95} +5.51087i q^{97} +(6.11799 + 3.40150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 - 4 * q^7	$ 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.79035			0.800669			0.400334	−	0.916369i	$-0.368894\pi$
$5$	1.79035			0.800669			0.400334	+	0.916369i	$0.368894\pi$
$6$		0			0
$7$	2.28052	−	1.34136i	0.861954	−	0.506987i
$7$	2.28052	−	1.34136i	0.861954	−	0.506987i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			1.79035i			0.566158i
$11$		−	2.40150i		−	0.724081i	−0.932162	−	0.362040i	$-0.882080\pi$
$11$		−	2.40150i		−	0.724081i	0.932162	−	0.362040i	$-0.117920\pi$
$12$		0			0
$13$			4.89133i			1.35661i	0.734781	+	0.678305i	$0.237285\pi$
$13$			4.89133i			1.35661i	−0.734781	+	0.678305i	$0.762715\pi$
$14$	1.34136	+	2.28052i	0.358494	+	0.609493i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.66466			0.888812			0.444406	−	0.895826i	$-0.353415\pi$
$17$	3.66466			0.888812			0.444406	+	0.895826i	$0.353415\pi$
$18$		0			0
$19$		−	3.01701i		−	0.692150i	−0.938207	−	0.346075i	$-0.887514\pi$
$19$		−	3.01701i		−	0.692150i	0.938207	−	0.346075i	$-0.112486\pi$
$20$	−1.79035			−0.400334
$21$		0			0
$22$	2.40150			0.512002
$23$		−	3.76638i		−	0.785345i	−0.919678	−	0.392673i	$-0.871551\pi$
$23$		−	3.76638i		−	0.785345i	0.919678	−	0.392673i	$-0.128449\pi$
$24$		0			0
$25$	−1.79465			−0.358930
$26$	−4.89133			−0.959268
$27$		0			0
$28$	−2.28052	+	1.34136i	−0.430977	+	0.253493i
$29$		−	6.56103i		−	1.21835i	−0.793035	−	0.609176i	$-0.791500\pi$
$29$		−	6.56103i		−	1.21835i	0.793035	−	0.609176i	$-0.208500\pi$
$30$		0			0
$31$			4.64661i			0.834556i	0.908779	+	0.417278i	$0.137016\pi$
$31$			4.64661i			0.834556i	−0.908779	+	0.417278i	$0.862984\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			3.66466i			0.628485i
$35$	4.08292	−	2.40150i	0.690140	−	0.405928i
$36$		0			0
$37$	9.36404			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$37$	9.36404			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$38$	3.01701			0.489424
$39$		0			0
$40$		−	1.79035i		−	0.283079i
$41$	8.08188			1.26218			0.631088	−	0.775711i	$-0.282608\pi$
$41$	8.08188			1.26218			0.631088	+	0.775711i	$0.282608\pi$
$42$		0			0
$43$	6.96254			1.06178			0.530888	−	0.847442i	$-0.321858\pi$
$43$	6.96254			1.06178			0.530888	+	0.847442i	$0.321858\pi$
$44$			2.40150i			0.362040i
$45$		0			0
$46$	3.76638			0.555323
$47$	−5.13604			−0.749169			−0.374584	−	0.927193i	$-0.622215\pi$
$47$	−5.13604			−0.749169			−0.374584	+	0.927193i	$0.622215\pi$
$48$		0			0
$49$	3.40150	−	6.11799i	0.485929	−	0.873998i
$50$		−	1.79465i		−	0.253802i
$51$		0			0
$52$		−	4.89133i		−	0.678305i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	4.29953i		−	0.579749i
$56$	−1.34136	−	2.28052i	−0.179247	−	0.304747i
$57$		0			0
$58$	6.56103			0.861506
$59$	−14.5900			−1.89946			−0.949729	−	0.313073i	$-0.898641\pi$
$59$	−14.5900			−1.89946			−0.949729	+	0.313073i	$0.898641\pi$
$60$		0			0
$61$			11.3283i			1.45044i	0.688518	+	0.725219i	$0.258262\pi$
$61$			11.3283i			1.45044i	−0.688518	+	0.725219i	$0.741738\pi$
$62$	−4.64661			−0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$			8.75718i			1.08619i
$66$		0			0
$67$	0.570231			0.0696648			0.0348324	−	0.999393i	$-0.488910\pi$
$67$	0.570231			0.0696648			0.0348324	+	0.999393i	$0.488910\pi$
$68$	−3.66466			−0.444406
$69$		0			0
$70$	2.40150	+	4.08292i	0.287035	+	0.488002i
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$		0			0
$73$			12.3814i			1.44913i	0.689204	+	0.724567i	$0.257960\pi$
$73$			12.3814i			1.44913i	−0.689204	+	0.724567i	$0.742040\pi$
$74$			9.36404i			1.08855i
$75$		0			0
$76$			3.01701i			0.346075i
$77$	−3.22128	−	5.47667i	−0.367099	−	0.624124i
$78$		0			0
$79$	3.03663			0.341647			0.170824	−	0.985302i	$-0.445357\pi$
$79$	3.03663			0.341647			0.170824	+	0.985302i	$0.445357\pi$
$80$	1.79035			0.200167
$81$		0			0
$82$			8.08188i			0.892494i
$83$	14.0054			1.53729			0.768646	−	0.639674i	$-0.220931\pi$
$83$	14.0054			1.53729			0.768646	+	0.639674i	$0.220931\pi$
$84$		0			0
$85$	6.56103			0.711644
$86$			6.96254i			0.750790i
$87$		0			0
$88$	−2.40150			−0.256001
$89$	−3.74863			−0.397354			−0.198677	−	0.980065i	$-0.563664\pi$
$89$	−3.74863			−0.397354			−0.198677	+	0.980065i	$0.563664\pi$
$90$		0			0
$91$	6.56103	+	11.1547i	0.687783	+	1.16934i
$92$			3.76638i			0.392673i
$93$		0			0
$94$		−	5.13604i		−	0.529742i
$95$		−	5.40150i		−	0.554183i
$96$		0			0
$97$			5.51087i			0.559545i	0.960066	+	0.279772i	$0.0902590\pi$
$97$			5.51087i			0.559545i	−0.960066	+	0.279772i	$0.909741\pi$
$98$	6.11799	+	3.40150i	0.618010	+	0.343604i
$99$		0			0
$100$	1.79465			0.179465
$101$	0.250324			0.0249082			0.0124541	−	0.999922i	$-0.496036\pi$
$101$	0.250324			0.0249082			0.0124541	+	0.999922i	$0.496036\pi$
$102$		0			0
$103$		−	0.167931i		−	0.0165468i	−0.999966	−	0.00827339i	$-0.997366\pi$
$103$		−	0.167931i		−	0.0165468i	0.999966	−	0.00827339i	$-0.00263353\pi$
$104$	4.89133			0.479634
$105$		0			0
$106$		0			0
$107$			7.99080i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$107$			7.99080i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$108$		0			0
$109$	−18.9533			−1.81540			−0.907700	−	0.419619i	$-0.862164\pi$
$109$	−18.9533			−1.81540			−0.907700	+	0.419619i	$0.862164\pi$
$110$	4.29953			0.409944
$111$		0			0
$112$	2.28052	−	1.34136i	0.215488	−	0.126747i
$113$			1.15953i			0.109079i	0.998512	+	0.0545396i	$0.0173691\pi$
$113$			1.15953i			0.109079i	−0.998512	+	0.0545396i	$0.982631\pi$
$114$		0			0
$115$		−	6.74314i		−	0.628801i
$116$			6.56103i			0.609176i
$117$		0			0
$118$		−	14.5900i		−	1.34312i
$119$	8.35733	−	4.91564i	0.766115	−	0.450616i
$120$		0			0
$121$	5.23278			0.475707
$122$	−11.3283			−1.02561
$123$		0			0
$124$		−	4.64661i		−	0.417278i
$125$	−12.1648			−1.08805
$126$		0			0
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−8.75718			−0.768056
$131$	10.4918			0.916671			0.458335	−	0.888779i	$-0.348446\pi$
$131$	10.4918			0.916671			0.458335	+	0.888779i	$0.348446\pi$
$132$		0			0
$133$	−4.04690	−	6.88034i	−0.350911	−	0.596601i
$134$			0.570231i			0.0492604i
$135$		0			0
$136$		−	3.66466i		−	0.314242i
$137$		−	4.72056i		−	0.403305i	−0.979457	−	0.201652i	$-0.935369\pi$
$137$		−	4.72056i		−	0.403305i	0.979457	−	0.201652i	$-0.0646311\pi$
$138$		0			0
$139$			2.36375i			0.200491i	0.994963	+	0.100245i	$0.0319628\pi$
$139$			2.36375i			0.200491i	−0.994963	+	0.100245i	$0.968037\pi$
$140$	−4.08292	+	2.40150i	−0.345070	+	0.202964i
$141$		0			0
$142$	5.96254			0.500365
$143$	11.7465			0.982295
$144$		0			0
$145$		−	11.7465i		−	0.975497i
$146$	−12.3814			−1.02469
$147$		0			0
$148$	−9.36404			−0.769719
$149$			17.3640i			1.42252i	0.702930	+	0.711259i	$0.251875\pi$
$149$			17.3640i			1.42252i	−0.702930	+	0.711259i	$0.748125\pi$
$150$		0			0
$151$	−11.2328			−0.914110			−0.457055	−	0.889438i	$-0.651096\pi$
$151$	−11.2328			−0.914110			−0.457055	+	0.889438i	$0.651096\pi$
$152$	−3.01701			−0.244712
$153$		0			0
$154$	5.47667	−	3.22128i	0.441322	−	0.259578i
$155$			8.31905i			0.668203i
$156$		0			0
$157$		−	13.8431i		−	1.10480i	−0.833580	−	0.552399i	$-0.813713\pi$
$157$		−	13.8431i		−	1.10480i	0.833580	−	0.552399i	$-0.186287\pi$
$158$			3.03663i			0.241581i
$159$		0			0
$160$			1.79035i			0.141540i
$161$	−5.05208	−	8.58930i	−0.398159	−	0.676931i
$162$		0			0
$163$	−4.33577			−0.339604			−0.169802	−	0.985478i	$-0.554313\pi$
$163$	−4.33577			−0.339604			−0.169802	+	0.985478i	$0.554313\pi$
$164$	−8.08188			−0.631088
$165$		0			0
$166$			14.0054i			1.08703i
$167$	12.4151			0.960711			0.480355	−	0.877074i	$-0.340508\pi$
$167$	12.4151			0.960711			0.480355	+	0.877074i	$0.340508\pi$
$168$		0			0
$169$	−10.9251			−0.840390
$170$			6.56103i			0.503208i
$171$		0			0
$172$	−6.96254			−0.530888
$173$	−17.4182			−1.32428			−0.662139	−	0.749381i	$-0.730351\pi$
$173$	−17.4182			−1.32428			−0.662139	+	0.749381i	$0.730351\pi$
$174$		0			0
$175$	−4.09272	+	2.40727i	−0.309381	+	0.181973i
$176$		−	2.40150i		−	0.181020i
$177$		0			0
$178$		−	3.74863i		−	0.280972i
$179$		−	13.1221i		−	0.980789i	−0.871501	−	0.490395i	$-0.836853\pi$
$179$		−	13.1221i		−	0.980789i	0.871501	−	0.490395i	$-0.163147\pi$
$180$		0			0
$181$		−	13.3577i		−	0.992873i	−0.868073	−	0.496437i	$-0.834641\pi$
$181$		−	13.3577i		−	0.992873i	0.868073	−	0.496437i	$-0.165359\pi$
$182$	−11.1547	+	6.56103i	−0.826845	+	0.486336i
$183$		0			0
$184$	−3.76638			−0.277661
$185$	16.7649			1.23258
$186$		0			0
$187$		−	8.80071i		−	0.643572i
$188$	5.13604			0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$		−	9.25333i		−	0.669547i	−0.942299	−	0.334774i	$-0.891340\pi$
$191$		−	9.25333i		−	0.669547i	0.942299	−	0.334774i	$-0.108660\pi$
$192$		0			0
$193$	−24.5602			−1.76788			−0.883941	−	0.467599i	$-0.845119\pi$
$193$	−24.5602			−1.76788			−0.883941	+	0.467599i	$0.845119\pi$
$194$	−5.51087			−0.395658
$195$		0			0
$196$	−3.40150	+	6.11799i	−0.242965	+	0.436999i
$197$			12.4861i			0.889598i	0.895630	+	0.444799i	$0.146725\pi$
$197$			12.4861i			0.889598i	−0.895630	+	0.444799i	$0.853275\pi$
$198$		0			0
$199$		−	0.179145i		−	0.0126993i	−0.999980	−	0.00634964i	$-0.997979\pi$
$199$		−	0.179145i		−	0.0126993i	0.999980	−	0.00634964i	$-0.00202117\pi$
$200$			1.79465i			0.126901i
$201$		0			0
$202$			0.250324i			0.0176127i
$203$	−8.80071	−	14.9625i	−0.617689	−	1.05016i
$204$		0			0
$205$	14.4694			1.01059
$206$	0.167931			0.0117003
$207$		0			0
$208$			4.89133i			0.339152i
$209$	−7.24536			−0.501172
$210$		0			0
$211$	−15.1221			−1.04105			−0.520523	−	0.853848i	$-0.674263\pi$
$211$	−15.1221			−1.04105			−0.520523	+	0.853848i	$0.674263\pi$
$212$		0			0
$213$		0			0
$214$	−7.99080			−0.546240
$215$	12.4654			0.850131
$216$		0			0
$217$	6.23278	+	10.5967i	0.423109	+	0.719348i
$218$		−	18.9533i		−	1.28368i
$219$		0			0
$220$			4.29953i			0.289874i
$221$			17.9251i			1.20577i
$222$		0			0
$223$		−	8.39524i		−	0.562187i	−0.959680	−	0.281093i	$-0.909303\pi$
$223$		−	8.39524i		−	0.562187i	0.959680	−	0.281093i	$-0.0906971\pi$
$224$	1.34136	+	2.28052i	0.0896234	+	0.152373i
$225$		0			0
$226$	−1.15953			−0.0771306
$227$	−2.42522			−0.160967			−0.0804836	−	0.996756i	$-0.525646\pi$
$227$	−2.42522			−0.160967			−0.0804836	+	0.996756i	$0.525646\pi$
$228$		0			0
$229$		−	2.01975i		−	0.133469i	−0.997771	−	0.0667344i	$-0.978742\pi$
$229$		−	2.01975i		−	0.133469i	0.997771	−	0.0667344i	$-0.0212580\pi$
$230$	6.74314			0.444630
$231$		0			0
$232$	−6.56103			−0.430753
$233$		−	12.7289i		−	0.833899i	−0.908930	−	0.416950i	$-0.863099\pi$
$233$		−	12.7289i		−	0.833899i	0.908930	−	0.416950i	$-0.136901\pi$
$234$		0			0
$235$	−9.19531			−0.599836
$236$	14.5900			0.949729
$237$		0			0
$238$	4.91564	+	8.35733i	0.318633	+	0.541725i
$239$		−	17.4495i		−	1.12871i	−0.825531	−	0.564356i	$-0.809124\pi$
$239$		−	17.4495i		−	1.12871i	0.825531	−	0.564356i	$-0.190876\pi$
$240$		0			0
$241$			11.4332i			0.736476i	0.929732	+	0.368238i	$0.120039\pi$
$241$			11.4332i			0.736476i	−0.929732	+	0.368238i	$0.879961\pi$
$242$			5.23278i			0.336376i
$243$		0			0
$244$		−	11.3283i		−	0.725219i
$245$	6.08988	−	10.9533i	0.389068	−	0.699783i
$246$		0			0
$247$	14.7572			0.938977
$248$	4.64661			0.295060
$249$		0			0
$250$		−	12.1648i		−	0.769369i
$251$	−27.3560			−1.72669			−0.863347	−	0.504611i	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$			1.40150i			0.0879382i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.49673			−0.218120			−0.109060	−	0.994035i	$-0.534784\pi$
$257$	−3.49673			−0.218120			−0.109060	+	0.994035i	$0.534784\pi$
$258$		0			0
$259$	21.3548	−	12.5606i	1.32693	−	0.780475i
$260$		−	8.75718i		−	0.543097i
$261$		0			0
$262$			10.4918i			0.648184i
$263$		−	9.64348i		−	0.594643i	−0.954777	−	0.297321i	$-0.903907\pi$
$263$		−	9.64348i		−	0.594643i	0.954777	−	0.297321i	$-0.0960932\pi$
$264$		0			0
$265$		0			0
$266$	6.88034	−	4.04690i	0.421861	−	0.248131i
$267$		0			0
$268$	−0.570231			−0.0348324
$269$	−6.91107			−0.421376			−0.210688	−	0.977553i	$-0.567570\pi$
$269$	−6.91107			−0.421376			−0.210688	+	0.977553i	$0.567570\pi$
$270$		0			0
$271$		−	20.6312i		−	1.25326i	−0.779318	−	0.626629i	$-0.784434\pi$
$271$		−	20.6312i		−	1.25326i	0.779318	−	0.626629i	$-0.215566\pi$
$272$	3.66466			0.222203
$273$		0			0
$274$	4.72056			0.285179
$275$			4.30986i			0.259894i
$276$		0			0
$277$	−15.5144			−0.932168			−0.466084	−	0.884740i	$-0.654336\pi$
$277$	−15.5144			−0.932168			−0.466084	+	0.884740i	$0.654336\pi$
$278$	−2.36375			−0.141768
$279$		0			0
$280$	−2.40150	−	4.08292i	−0.143517	−	0.244001i
$281$			13.5977i			0.811168i	0.914058	+	0.405584i	$0.132932\pi$
$281$			13.5977i			0.811168i	−0.914058	+	0.405584i	$0.867068\pi$
$282$		0			0
$283$			5.44783i			0.323840i	0.986804	+	0.161920i	$0.0517687\pi$
$283$			5.44783i			0.323840i	−0.986804	+	0.161920i	$0.948231\pi$
$284$			5.96254i			0.353811i
$285$		0			0
$286$			11.7465i			0.694587i
$287$	18.4308	−	10.8407i	1.08794	−	0.639907i
$288$		0			0
$289$	−3.57023			−0.210014
$290$	11.7465			0.689781
$291$		0			0
$292$		−	12.3814i		−	0.724567i
$293$	−24.4622			−1.42910			−0.714550	−	0.699585i	$-0.753368\pi$
$293$	−24.4622			−1.42910			−0.714550	+	0.699585i	$0.753368\pi$
$294$		0			0
$295$	−26.1212			−1.52084
$296$		−	9.36404i		−	0.544274i
$297$		0			0
$298$	−17.3640			−1.00587
$299$	18.4226			1.06541
$300$		0			0
$301$	15.8782	−	9.33927i	0.915203	−	0.538307i
$302$		−	11.2328i		−	0.646374i
$303$		0			0
$304$		−	3.01701i		−	0.173037i
$305$			20.2816i			1.16132i
$306$		0			0
$307$			31.2223i			1.78195i	0.454053	+	0.890975i	$0.349978\pi$
$307$			31.2223i			1.78195i	−0.454053	+	0.890975i	$0.650022\pi$
$308$	3.22128	+	5.47667i	0.183550	+	0.312062i
$309$		0			0
$310$	−8.31905			−0.472491
$311$	10.9100			0.618651			0.309325	−	0.950956i	$-0.399897\pi$
$311$	10.9100			0.618651			0.309325	+	0.950956i	$0.399897\pi$
$312$		0			0
$313$			3.42405i			0.193539i	0.995307	+	0.0967694i	$0.0308509\pi$
$313$			3.42405i			0.193539i	−0.995307	+	0.0967694i	$0.969149\pi$
$314$	13.8431			0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$			19.0471i			1.06979i	0.844917	+	0.534897i	$0.179650\pi$
$317$			19.0471i			1.06979i	−0.844917	+	0.534897i	$0.820350\pi$
$318$		0			0
$319$	−15.7563			−0.882186
$320$	−1.79035			−0.100084
$321$		0			0
$322$	8.58930	−	5.05208i	0.478663	−	0.281541i
$323$		−	11.0563i		−	0.615191i
$324$		0			0
$325$		−	8.77821i		−	0.486927i
$326$		−	4.33577i		−	0.240136i
$327$		0			0
$328$		−	8.08188i		−	0.446247i
$329$	−11.7128	+	6.88929i	−0.645749	+	0.379819i
$330$		0			0
$331$	0.0732502			0.00402620			0.00201310	−	0.999998i	$-0.499359\pi$
$331$	0.0732502			0.00402620			0.00201310	+	0.999998i	$0.499359\pi$
$332$	−14.0054			−0.768646
$333$		0			0
$334$			12.4151i			0.679325i
$335$	1.02091			0.0557784
$336$		0			0
$337$	−2.23278			−0.121627			−0.0608136	−	0.998149i	$-0.519370\pi$
$337$	−2.23278			−0.121627			−0.0608136	+	0.998149i	$0.519370\pi$
$338$		−	10.9251i		−	0.594246i
$339$		0			0
$340$	−6.56103			−0.355822
$341$	11.1589			0.604286
$342$		0			0
$343$	−0.449242	−	18.5148i	−0.0242568	−	0.999706i
$344$		−	6.96254i		−	0.375395i
$345$		0			0
$346$		−	17.4182i		−	0.936406i
$347$		−	31.8409i		−	1.70931i	−0.519195	−	0.854656i	$-0.673768\pi$
$347$		−	31.8409i		−	1.70931i	0.519195	−	0.854656i	$-0.326232\pi$
$348$		0			0
$349$		−	14.7354i		−	0.788770i	−0.918945	−	0.394385i	$-0.870958\pi$
$349$		−	14.7354i		−	0.788770i	0.918945	−	0.394385i	$-0.129042\pi$
$350$	−2.40727	−	4.09272i	−0.128674	−	0.218765i
$351$		0			0
$352$	2.40150			0.128001
$353$	2.15957			0.114943			0.0574713	−	0.998347i	$-0.481696\pi$
$353$	2.15957			0.114943			0.0574713	+	0.998347i	$0.481696\pi$
$354$		0			0
$355$		−	10.6750i		−	0.566571i
$356$	3.74863			0.198677
$357$		0			0
$358$	13.1221			0.693523
$359$			32.6448i			1.72293i	0.507820	+	0.861463i	$0.330451\pi$
$359$			32.6448i			1.72293i	−0.507820	+	0.861463i	$0.669549\pi$
$360$		0			0
$361$	9.89765			0.520929
$362$	13.3577			0.702067
$363$		0			0
$364$	−6.56103	−	11.1547i	−0.343891	−	0.584668i
$365$			22.1670i			1.16028i
$366$		0			0
$367$			29.7003i			1.55034i	0.631751	+	0.775171i	$0.282336\pi$
$367$			29.7003i			1.55034i	−0.631751	+	0.775171i	$0.717664\pi$
$368$		−	3.76638i		−	0.196336i
$369$		0			0
$370$			16.7649i			0.871566i
$371$		0			0
$372$		0			0
$373$	−2.01672			−0.104422			−0.0522109	−	0.998636i	$-0.516627\pi$
$373$	−2.01672			−0.104422			−0.0522109	+	0.998636i	$0.516627\pi$
$374$	8.80071			0.455074
$375$		0			0
$376$			5.13604i			0.264871i
$377$	32.0921			1.65283
$378$		0			0
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$			5.40150i			0.277091i
$381$		0			0
$382$	9.25333			0.473441
$383$	0.836511			0.0427437			0.0213719	−	0.999772i	$-0.493197\pi$
$383$	0.836511			0.0427437			0.0213719	+	0.999772i	$0.493197\pi$
$384$		0			0
$385$	−5.76722	−	9.80515i	−0.293925	−	0.499717i
$386$		−	24.5602i		−	1.25008i
$387$		0			0
$388$		−	5.51087i		−	0.279772i
$389$			24.8219i			1.25852i	0.777195	+	0.629260i	$0.216642\pi$
$389$			24.8219i			1.25852i	−0.777195	+	0.629260i	$0.783358\pi$
$390$		0			0
$391$		−	13.8025i		−	0.698024i
$392$	−6.11799	−	3.40150i	−0.309005	−	0.171802i
$393$		0			0
$394$	−12.4861			−0.629041
$395$	5.43662			0.273546
$396$		0			0
$397$			3.03390i			0.152267i	0.997098	+	0.0761336i	$0.0242575\pi$
$397$			3.03390i			0.152267i	−0.997098	+	0.0761336i	$0.975742\pi$
$398$	0.179145			0.00897975
$399$		0			0
$400$	−1.79465			−0.0897324
$401$		−	13.0771i		−	0.653038i	−0.945191	−	0.326519i	$-0.894124\pi$
$401$		−	13.0771i		−	0.653038i	0.945191	−	0.326519i	$-0.105876\pi$
$402$		0			0
$403$	−22.7281			−1.13217
$404$	−0.250324			−0.0124541
$405$		0			0
$406$	14.9625	−	8.80071i	0.742578	−	0.436772i
$407$		−	22.4878i		−	1.11468i
$408$		0			0
$409$		−	5.56709i		−	0.275275i	−0.990483	−	0.137637i	$-0.956049\pi$
$409$		−	5.56709i		−	0.275275i	0.990483	−	0.137637i	$-0.0439508\pi$
$410$			14.4694i			0.714592i
$411$		0			0
$412$			0.167931i			0.00827339i
$413$	−33.2728	+	19.5705i	−1.63725	+	0.963000i
$414$		0			0
$415$	25.0746			1.23086
$416$	−4.89133			−0.239817
$417$		0			0
$418$		−	7.24536i		−	0.354382i
$419$	−16.3988			−0.801132			−0.400566	−	0.916268i	$-0.631186\pi$
$419$	−16.3988			−0.801132			−0.400566	+	0.916268i	$0.631186\pi$
$420$		0			0
$421$	15.4578			0.753369			0.376684	−	0.926342i	$-0.377064\pi$
$421$	15.4578			0.753369			0.376684	+	0.926342i	$0.377064\pi$
$422$		−	15.1221i		−	0.736131i
$423$		0			0
$424$		0			0
$425$	−6.57678			−0.319021
$426$		0			0
$427$	15.1953	+	25.8343i	0.735353	+	1.25021i
$428$		−	7.99080i		−	0.386250i
$429$		0			0
$430$			12.4654i			0.601134i
$431$		−	25.0266i		−	1.20549i	−0.797935	−	0.602744i	$-0.794074\pi$
$431$		−	25.0266i		−	1.20549i	0.797935	−	0.602744i	$-0.205926\pi$
$432$		0			0
$433$			2.25168i			0.108209i	0.998535	+	0.0541044i	$0.0172304\pi$
$433$			2.25168i			0.108209i	−0.998535	+	0.0541044i	$0.982770\pi$
$434$	−10.5967	+	6.23278i	−0.508656	+	0.299183i
$435$		0			0
$436$	18.9533			0.907700
$437$	−11.3632			−0.543576
$438$		0			0
$439$			18.7400i			0.894412i	0.894431	+	0.447206i	$0.147581\pi$
$439$			18.7400i			0.894412i	−0.894431	+	0.447206i	$0.852419\pi$
$440$	−4.29953			−0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$		−	1.20451i		−	0.0572281i	−0.999591	−	0.0286141i	$-0.990891\pi$
$443$		−	1.20451i		−	0.0572281i	0.999591	−	0.0286141i	$-0.00910938\pi$
$444$		0			0
$445$	−6.71136			−0.318149
$446$	8.39524			0.397526
$447$		0			0
$448$	−2.28052	+	1.34136i	−0.107744	+	0.0633733i
$449$			26.8022i			1.26487i	0.774612	+	0.632436i	$0.217945\pi$
$449$			26.8022i			1.26487i	−0.774612	+	0.632436i	$0.782055\pi$
$450$		0			0
$451$		−	19.4087i		−	0.913918i
$452$		−	1.15953i		−	0.0545396i
$453$		0			0
$454$		−	2.42522i		−	0.113821i
$455$	11.7465	+	19.9709i	0.550686	+	0.936250i
$456$		0			0
$457$	13.8488			0.647821			0.323911	−	0.946088i	$-0.395002\pi$
$457$	13.8488			0.647821			0.323911	+	0.946088i	$0.395002\pi$
$458$	2.01975			0.0943766
$459$		0			0
$460$			6.74314i			0.314401i
$461$	−4.80483			−0.223783			−0.111892	−	0.993720i	$-0.535691\pi$
$461$	−4.80483			−0.223783			−0.111892	+	0.993720i	$0.535691\pi$
$462$		0			0
$463$	−21.0388			−0.977755			−0.488877	−	0.872353i	$-0.662593\pi$
$463$	−21.0388			−0.977755			−0.488877	+	0.872353i	$0.662593\pi$
$464$		−	6.56103i		−	0.304588i
$465$		0			0
$466$	12.7289			0.589656
$467$	5.82302			0.269457			0.134729	−	0.990883i	$-0.456984\pi$
$467$	5.82302			0.269457			0.134729	+	0.990883i	$0.456984\pi$
$468$		0			0
$469$	1.30042	−	0.764885i	0.0600478	−	0.0353191i
$470$		−	9.19531i		−	0.424148i
$471$		0			0
$472$			14.5900i			0.671560i
$473$		−	16.7206i		−	0.768812i
$474$		0			0
$475$			5.41447i			0.248433i
$476$	−8.35733	+	4.91564i	−0.383057	+	0.225308i
$477$		0			0
$478$	17.4495			0.798121
$479$	−26.9561			−1.23166			−0.615828	−	0.787881i	$-0.711178\pi$
$479$	−26.9561			−1.23166			−0.615828	+	0.787881i	$0.711178\pi$
$480$		0			0
$481$			45.8026i			2.08842i
$482$	−11.4332			−0.520767
$483$		0			0
$484$	−5.23278			−0.237854
$485$			9.86639i			0.448010i
$486$		0			0
$487$	−13.6268			−0.617487			−0.308744	−	0.951145i	$-0.599909\pi$
$487$	−13.6268			−0.617487			−0.308744	+	0.951145i	$0.599909\pi$
$488$	11.3283			0.512807
$489$		0			0
$490$	10.9533	+	6.08988i	0.494821	+	0.275113i
$491$			38.9630i			1.75838i	0.476475	+	0.879188i	$0.341914\pi$
$491$			38.9630i			1.75838i	−0.476475	+	0.879188i	$0.658086\pi$
$492$		0			0
$493$		−	24.0440i		−	1.08289i
$494$			14.7572i			0.663957i
$495$		0			0
$496$			4.64661i			0.208639i
$497$	−7.99791	−	13.5977i	−0.358755	−	0.609938i
$498$		0			0
$499$	26.0097			1.16435			0.582176	−	0.813063i	$-0.302201\pi$
$499$	26.0097			1.16435			0.582176	+	0.813063i	$0.302201\pi$
$500$	12.1648			0.544026
$501$		0			0
$502$		−	27.3560i		−	1.22096i
$503$	10.5271			0.469378			0.234689	−	0.972070i	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$		−	9.04499i		−	0.402099i
$507$		0			0
$508$	−1.40150			−0.0621817
$509$	−0.938871			−0.0416147			−0.0208074	−	0.999784i	$-0.506624\pi$
$509$	−0.938871			−0.0416147			−0.0208074	+	0.999784i	$0.506624\pi$
$510$		0			0
$511$	16.6079	+	28.2360i	0.734692	+	1.24909i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	3.49673i		−	0.154234i
$515$		−	0.300656i		−	0.0132485i
$516$		0			0
$517$			12.3342i			0.542459i
$518$	12.5606	+	21.3548i	0.551879	+	0.938278i
$519$		0			0
$520$	8.75718			0.384028
$521$	−39.5054			−1.73076			−0.865382	−	0.501112i	$-0.832924\pi$
$521$	−39.5054			−1.73076			−0.865382	+	0.501112i	$0.832924\pi$
$522$		0			0
$523$			24.3292i			1.06384i	0.846794	+	0.531922i	$0.178530\pi$
$523$			24.3292i			1.06384i	−0.846794	+	0.531922i	$0.821470\pi$
$524$	−10.4918			−0.458335
$525$		0			0
$526$	9.64348			0.420476
$527$			17.0283i			0.741763i
$528$		0			0
$529$	8.81436			0.383233
$530$		0			0
$531$		0			0
$532$	4.04690	+	6.88034i	0.175455	+	0.298301i
$533$			39.5311i			1.71228i
$534$		0			0
$535$			14.3063i			0.618516i
$536$		−	0.570231i		−	0.0246302i
$537$		0			0
$538$		−	6.91107i		−	0.297958i
$539$	−14.6924	−	8.16873i	−0.632845	−	0.351852i
$540$		0			0
$541$	42.7281			1.83702			0.918512	−	0.395394i	$-0.129392\pi$
$541$	42.7281			1.83702			0.918512	+	0.395394i	$0.129392\pi$
$542$	20.6312			0.886187
$543$		0			0
$544$			3.66466i			0.157121i
$545$	−33.9331			−1.45353
$546$		0			0
$547$	24.4953			1.04734			0.523672	−	0.851920i	$-0.324562\pi$
$547$	24.4953			1.04734			0.523672	+	0.851920i	$0.324562\pi$
$548$			4.72056i			0.201652i
$549$		0			0
$550$	−4.30986			−0.183773
$551$	−19.7947			−0.843283
$552$		0			0
$553$	6.92507	−	4.07321i	0.294484	−	0.173210i
$554$		−	15.5144i		−	0.659142i
$555$		0			0
$556$		−	2.36375i		−	0.100245i
$557$		−	2.54431i		−	0.107806i	−0.998546	−	0.0539030i	$-0.982834\pi$
$557$		−	2.54431i		−	0.107806i	0.998546	−	0.0539030i	$-0.0171662\pi$
$558$		0			0
$559$			34.0560i			1.44042i
$560$	4.08292	−	2.40150i	0.172535	−	0.101482i
$561$		0			0
$562$	−13.5977			−0.573583
$563$	15.8141			0.666487			0.333243	−	0.942841i	$-0.391857\pi$
$563$	15.8141			0.666487			0.333243	+	0.942841i	$0.391857\pi$
$564$		0			0
$565$			2.07596i			0.0873363i
$566$	−5.44783			−0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$		−	6.38311i		−	0.267594i	−0.991009	−	0.133797i	$-0.957283\pi$
$569$		−	6.38311i		−	0.267594i	0.991009	−	0.133797i	$-0.0427170\pi$
$570$		0			0
$571$	−7.82375			−0.327414			−0.163707	−	0.986509i	$-0.552345\pi$
$571$	−7.82375			−0.327414			−0.163707	+	0.986509i	$0.552345\pi$
$572$	−11.7465			−0.491148
$573$		0			0
$574$	10.8407	+	18.4308i	0.452482	+	0.769289i
$575$			6.75933i			0.281884i
$576$		0			0
$577$		−	14.3197i		−	0.596138i	−0.954544	−	0.298069i	$-0.903657\pi$
$577$		−	14.3197i		−	0.596138i	0.954544	−	0.298069i	$-0.0963425\pi$
$578$		−	3.57023i		−	0.148502i
$579$		0			0
$580$			11.7465i			0.487749i
$581$	31.9395	−	18.7863i	1.32508	−	0.779387i
$582$		0			0
$583$		0			0
$584$	12.3814			0.512346
$585$		0			0
$586$		−	24.4622i		−	1.01053i
$587$	4.75150			0.196115			0.0980577	−	0.995181i	$-0.468737\pi$
$587$	4.75150			0.196115			0.0980577	+	0.995181i	$0.468737\pi$
$588$		0			0
$589$	14.0189			0.577637
$590$		−	26.1212i		−	1.07539i
$591$		0			0
$592$	9.36404			0.384860
$593$	3.58070			0.147042			0.0735208	−	0.997294i	$-0.476576\pi$
$593$	3.58070			0.147042			0.0735208	+	0.997294i	$0.476576\pi$
$594$		0			0
$595$	14.9625	−	8.80071i	0.613404	−	0.360794i
$596$		−	17.3640i		−	0.711259i
$597$		0			0
$598$			18.4226i			0.753357i
$599$			15.0655i			0.615561i	0.951457	+	0.307780i	$0.0995862\pi$
$599$			15.0655i			0.615561i	−0.951457	+	0.307780i	$0.900414\pi$
$600$		0			0
$601$		−	22.9444i		−	0.935920i	−0.883750	−	0.467960i	$-0.844989\pi$
$601$		−	22.9444i		−	0.935920i	0.883750	−	0.467960i	$-0.155011\pi$
$602$	9.33927	+	15.8782i	0.380640	+	0.647146i
$603$		0			0
$604$	11.2328			0.457055
$605$	9.36850			0.380884
$606$		0			0
$607$		−	24.4832i		−	0.993741i	−0.867825	−	0.496870i	$-0.834482\pi$
$607$		−	24.4832i		−	0.993741i	0.867825	−	0.496870i	$-0.165518\pi$
$608$	3.01701			0.122356
$609$		0			0
$610$	−20.2816			−0.821178
$611$		−	25.1221i		−	1.01633i
$612$		0			0
$613$	−0.880086			−0.0355463			−0.0177732	−	0.999842i	$-0.505658\pi$
$613$	−0.880086			−0.0355463			−0.0177732	+	0.999842i	$0.505658\pi$
$614$	−31.2223			−1.26003
$615$		0			0
$616$	−5.47667	+	3.22128i	−0.220661	+	0.129789i
$617$			13.5801i			0.546714i	0.961913	+	0.273357i	$0.0881341\pi$
$617$			13.5801i			0.546714i	−0.961913	+	0.273357i	$0.911866\pi$
$618$		0			0
$619$		−	35.4869i		−	1.42634i	−0.700992	−	0.713169i	$-0.747259\pi$
$619$		−	35.4869i		−	1.42634i	0.700992	−	0.713169i	$-0.252741\pi$
$620$		−	8.31905i		−	0.334101i
$621$		0			0
$622$			10.9100i			0.437452i
$623$	−8.54881	+	5.02826i	−0.342501	+	0.201453i
$624$		0			0
$625$	−12.8060			−0.512240
$626$	−3.42405			−0.136853
$627$		0			0
$628$			13.8431i			0.552399i
$629$	34.3161			1.36827
$630$		0			0
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$		−	3.03663i		−	0.120790i
$633$		0			0
$634$	−19.0471			−0.756458
$635$	2.50918			0.0995739
$636$		0			0
$637$	29.9251	+	16.6379i	1.18567	+	0.659216i
$638$		−	15.7563i		−	0.623800i
$639$		0			0
$640$		−	1.79035i		−	0.0707698i
$641$			1.07708i			0.0425420i	0.999774	+	0.0212710i	$0.00677128\pi$
$641$			1.07708i			0.0425420i	−0.999774	+	0.0212710i	$0.993229\pi$
$642$		0			0
$643$		−	38.4661i		−	1.51695i	−0.651700	−	0.758477i	$-0.725944\pi$
$643$		−	38.4661i		−	1.51695i	0.651700	−	0.758477i	$-0.274056\pi$
$644$	5.05208	+	8.58930i	0.199080	+	0.338466i
$645$		0			0
$646$	11.0563			0.435006
$647$	−8.95210			−0.351943			−0.175972	−	0.984395i	$-0.556307\pi$
$647$	−8.95210			−0.351943			−0.175972	+	0.984395i	$0.556307\pi$
$648$		0			0
$649$			35.0380i			1.37536i
$650$	8.77821			0.344310
$651$		0			0
$652$	4.33577			0.169802
$653$			11.3846i			0.445513i	0.974874	+	0.222757i	$0.0715055\pi$
$653$			11.3846i			0.445513i	−0.974874	+	0.222757i	$0.928494\pi$
$654$		0			0
$655$	18.7839			0.733949
$656$	8.08188			0.315544
$657$		0			0
$658$	−6.88929	−	11.7128i	−0.268572	−	0.456614i
$659$			36.3007i			1.41407i	0.707177	+	0.707036i	$0.249968\pi$
$659$			36.3007i			1.41407i	−0.707177	+	0.707036i	$0.750032\pi$
$660$		0			0
$661$			36.0758i			1.40319i	0.712578	+	0.701593i	$0.247527\pi$
$661$			36.0758i			1.40319i	−0.712578	+	0.701593i	$0.752473\pi$
$662$			0.0732502i			0.00284695i
$663$		0			0
$664$		−	14.0054i		−	0.543515i
$665$	−7.24536	−	12.3182i	−0.280963	−	0.477680i
$666$		0			0
$667$	−24.7114			−0.956828
$668$	−12.4151			−0.480355
$669$		0			0
$670$			1.02091i			0.0394413i
$671$	27.2049			1.05023
$672$		0			0
$673$	−9.57023			−0.368905			−0.184453	−	0.982841i	$-0.559051\pi$
$673$	−9.57023			−0.368905			−0.184453	+	0.982841i	$0.559051\pi$
$674$		−	2.23278i		−	0.0860034i
$675$		0			0
$676$	10.9251			0.420195
$677$	−15.6282			−0.600639			−0.300320	−	0.953839i	$-0.597093\pi$
$677$	−15.6282			−0.600639			−0.300320	+	0.953839i	$0.597093\pi$
$678$		0			0
$679$	7.39207	+	12.5676i	0.283682	+	0.482302i
$680$		−	6.56103i		−	0.251604i
$681$		0			0
$682$			11.1589i			0.427294i
$683$			11.1313i			0.425926i	0.977060	+	0.212963i	$0.0683114\pi$
$683$			11.1313i			0.425926i	−0.977060	+	0.212963i	$0.931689\pi$
$684$		0			0
$685$		−	8.45145i		−	0.322913i
$686$	18.5148	−	0.449242i	0.706899	−	0.0171522i
$687$		0			0
$688$	6.96254			0.265444
$689$		0			0
$690$		0			0
$691$			3.02419i			0.115046i	0.998344	+	0.0575228i	$0.0183202\pi$
$691$			3.02419i			0.115046i	−0.998344	+	0.0575228i	$0.981680\pi$
$692$	17.4182			0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$			4.23194i			0.160527i
$696$		0			0
$697$	29.6174			1.12184
$698$	14.7354			0.557745
$699$		0			0
$700$	4.09272	−	2.40727i	0.154690	−	0.0909863i
$701$			50.1486i			1.89409i	0.321103	+	0.947044i	$0.395946\pi$
$701$			50.1486i			1.89409i	−0.321103	+	0.947044i	$0.604054\pi$
$702$		0			0
$703$		−	28.2514i		−	1.06552i
$704$			2.40150i			0.0905101i
$705$		0			0
$706$			2.15957i			0.0812766i
$707$	0.570868	−	0.335775i	0.0214697	−	0.0126281i
$708$		0			0
$709$	−3.60770			−0.135490			−0.0677449	−	0.997703i	$-0.521580\pi$
$709$	−3.60770			−0.135490			−0.0677449	+	0.997703i	$0.521580\pi$
$710$	10.6750			0.400626
$711$		0			0
$712$			3.74863i			0.140486i
$713$	17.5009			0.655414
$714$		0			0
$715$	21.0304			0.786493
$716$			13.1221i			0.490395i
$717$		0			0
$718$	−32.6448			−1.21829
$719$	−34.3161			−1.27977			−0.639887	−	0.768469i	$-0.721019\pi$
$719$	−34.3161			−1.27977			−0.639887	+	0.768469i	$0.721019\pi$
$720$		0			0
$721$	−0.225257	−	0.382970i	−0.00838899	−	0.0142626i
$722$			9.89765i			0.368352i
$723$		0			0
$724$			13.3577i			0.496437i
$725$			11.7747i			0.437303i
$726$		0			0
$727$			22.4886i			0.834057i	0.908893	+	0.417029i	$0.136929\pi$
$727$			22.4886i			0.834057i	−0.908893	+	0.417029i	$0.863071\pi$
$728$	11.1547	−	6.56103i	0.413422	−	0.243168i
$729$		0			0
$730$	−22.1670			−0.820439
$731$	25.5154			0.943720
$732$		0			0
$733$		−	31.1845i		−	1.15182i	−0.817512	−	0.575912i	$-0.804647\pi$
$733$		−	31.1845i		−	1.15182i	0.817512	−	0.575912i	$-0.195353\pi$
$734$	−29.7003			−1.09626
$735$		0			0
$736$	3.76638			0.138831
$737$		−	1.36941i		−	0.0504429i
$738$		0			0
$739$	4.08628			0.150316			0.0751581	−	0.997172i	$-0.476054\pi$
$739$	4.08628			0.150316			0.0751581	+	0.997172i	$0.476054\pi$
$740$	−16.7649			−0.616290
$741$		0			0
$742$		0			0
$743$			2.05821i			0.0755083i	0.999287	+	0.0377542i	$0.0120204\pi$
$743$			2.05821i			0.0755083i	−0.999287	+	0.0377542i	$0.987980\pi$
$744$		0			0
$745$			31.0877i			1.13897i
$746$		−	2.01672i		−	0.0738374i
$747$		0			0
$748$			8.80071i			0.321786i
$749$	10.7185	+	18.2231i	0.391647	+	0.665859i
$750$		0			0
$751$	23.8105			0.868859			0.434429	−	0.900706i	$-0.356950\pi$
$751$	23.8105			0.868859			0.434429	+	0.900706i	$0.356950\pi$
$752$	−5.13604			−0.187292
$753$		0			0
$754$			32.0921i			1.16873i
$755$	−20.1106			−0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$		−	18.8709i		−	0.685421i
$759$		0			0
$760$	−5.40150			−0.195933
$761$	−27.8735			−1.01041			−0.505207	−	0.862998i	$-0.668584\pi$
$761$	−27.8735			−1.01041			−0.505207	+	0.862998i	$0.668584\pi$
$762$		0			0
$763$	−43.2234	+	25.4233i	−1.56479	+	0.920384i
$764$			9.25333i			0.334774i
$765$		0			0
$766$			0.836511i			0.0302244i
$767$		−	71.3645i		−	2.57682i
$768$		0			0
$769$			7.17261i			0.258651i	0.991602	+	0.129326i	$0.0412812\pi$
$769$			7.17261i			0.258651i	−0.991602	+	0.129326i	$0.958719\pi$
$770$	9.80515	−	5.76722i	0.353353	−	0.207836i
$771$		0			0
$772$	24.5602			0.883941
$773$	−2.14153			−0.0770255			−0.0385128	−	0.999258i	$-0.512262\pi$
$773$	−2.14153			−0.0770255			−0.0385128	+	0.999258i	$0.512262\pi$
$774$		0			0
$775$		−	8.33903i		−	0.299547i
$776$	5.51087			0.197829
$777$		0			0
$778$	−24.8219			−0.889907
$779$		−	24.3831i		−	0.873615i
$780$		0			0
$781$	−14.3191			−0.512376
$782$	13.8025			0.493578
$783$		0			0
$784$	3.40150	−	6.11799i	0.121482	−	0.218500i
$785$		−	24.7839i		−	0.884577i
$786$		0			0
$787$		−	18.3552i		−	0.654292i	−0.944974	−	0.327146i	$-0.893913\pi$
$787$		−	18.3552i		−	0.654292i	0.944974	−	0.327146i	$-0.106087\pi$
$788$		−	12.4861i		−	0.444799i
$789$		0			0
$790$			5.43662i			0.193426i
$791$	1.55534	+	2.64432i	0.0553017	+	0.0940212i
$792$		0			0
$793$	−55.4103			−1.96768
$794$	−3.03390			−0.107669
$795$		0			0
$796$			0.179145i			0.00634964i
$797$	−24.8452			−0.880062			−0.440031	−	0.897982i	$-0.645033\pi$
$797$	−24.8452			−0.880062			−0.440031	+	0.897982i	$0.645033\pi$
$798$		0			0
$799$	−18.8219			−0.665870
$800$		−	1.79465i		−	0.0634504i
$801$		0			0
$802$	13.0771			0.461768
$803$	29.7340			1.04929
$804$		0			0
$805$	−9.04499	−	15.3778i	−0.318794	−	0.541998i
$806$		−	22.7281i		−	0.800562i
$807$		0			0
$808$		−	0.250324i		−	0.00880637i
$809$		−	37.7861i		−	1.32849i	−0.747516	−	0.664244i	$-0.768754\pi$
$809$		−	37.7861i		−	1.32849i	0.747516	−	0.664244i	$-0.231246\pi$
$810$		0			0
$811$			36.5165i			1.28227i	0.767429	+	0.641134i	$0.221536\pi$
$811$			36.5165i			1.28227i	−0.767429	+	0.641134i	$0.778464\pi$
$812$	8.80071	+	14.9625i	0.308844	+	0.525082i
$813$		0			0
$814$	22.4878			0.788196
$815$	−7.76255			−0.271910
$816$		0			0
$817$		−	21.0060i		−	0.734909i
$818$	5.56709			0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$		−	6.37558i		−	0.222509i	−0.993792	−	0.111255i	$-0.964513\pi$
$821$		−	6.37558i		−	0.222509i	0.993792	−	0.111255i	$-0.0354869\pi$
$822$		0			0
$823$	28.0587			0.978064			0.489032	−	0.872266i	$-0.337350\pi$
$823$	28.0587			0.978064			0.489032	+	0.872266i	$0.337350\pi$
$824$	−0.167931			−0.00585017
$825$		0			0
$826$	−19.5705	−	33.2728i	−0.680944	−	1.15771i
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$		0			0
$829$			51.9246i			1.80342i	0.432346	+	0.901708i	$0.357686\pi$
$829$			51.9246i			1.80342i	−0.432346	+	0.901708i	$0.642314\pi$
$830$			25.0746i			0.870351i
$831$		0			0
$832$		−	4.89133i		−	0.169576i
$833$	12.4654	−	22.4204i	0.431900	−	0.776820i
$834$		0			0
$835$	22.2274			0.769211
$836$	7.24536			0.250586
$837$		0			0
$838$		−	16.3988i		−	0.566486i
$839$	6.66075			0.229955			0.114977	−	0.993368i	$-0.463320\pi$
$839$	6.66075			0.229955			0.114977	+	0.993368i	$0.463320\pi$
$840$		0			0
$841$	−14.0471			−0.484384
$842$			15.4578i			0.532712i
$843$		0			0
$844$	15.1221			0.520523
$845$	−19.5597			−0.672874
$846$		0			0
$847$	11.9334	−	7.01904i	0.410038	−	0.241177i
$848$		0			0
$849$		0			0
$850$		−	6.57678i		−	0.225582i
$851$		−	35.2686i		−	1.20899i
$852$		0			0
$853$		−	22.2034i		−	0.760229i	−0.924939	−	0.380115i	$-0.875885\pi$
$853$		−	22.2034i		−	0.760229i	0.924939	−	0.380115i	$-0.124115\pi$
$854$	−25.8343	+	15.1953i	−0.884033	+	0.519973i
$855$		0			0
$856$	7.99080			0.273120
$857$	15.2966			0.522522			0.261261	−	0.965268i	$-0.415862\pi$
$857$	15.2966			0.522522			0.261261	+	0.965268i	$0.415862\pi$
$858$		0			0
$859$		−	4.25646i		−	0.145229i	−0.997360	−	0.0726143i	$-0.976866\pi$
$859$		−	4.25646i		−	0.145229i	0.997360	−	0.0726143i	$-0.0231342\pi$
$860$	−12.4654			−0.425066
$861$		0			0
$862$	25.0266			0.852409
$863$		−	23.6624i		−	0.805476i	−0.915315	−	0.402738i	$-0.868059\pi$
$863$		−	23.6624i		−	0.805476i	0.915315	−	0.402738i	$-0.131941\pi$
$864$		0			0
$865$	−31.1846			−1.06031
$866$	−2.25168			−0.0765151
$867$		0			0
$868$	−6.23278	−	10.5967i	−0.211554	−	0.359674i
$869$		−	7.29247i		−	0.247380i
$870$		0			0
$871$			2.78919i			0.0945079i
$872$			18.9533i			0.641841i
$873$		0			0
$874$		−	11.3632i		−	0.384367i
$875$	−27.7420	+	16.3174i	−0.937851	+	0.551628i
$876$		0			0
$877$	−20.3923			−0.688599			−0.344300	−	0.938860i	$-0.611884\pi$
$877$	−20.3923			−0.688599			−0.344300	+	0.938860i	$0.611884\pi$
$878$	−18.7400			−0.632445
$879$		0			0
$880$		−	4.29953i		−	0.144937i
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		0			0
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$		−	17.9251i		−	0.602885i
$885$		0			0
$886$	1.20451			0.0404664
$887$	9.72119			0.326405			0.163203	−	0.986593i	$-0.447818\pi$
$887$	9.72119			0.326405			0.163203	+	0.986593i	$0.447818\pi$
$888$		0			0
$889$	3.19615	−	1.87992i	0.107196	−	0.0630506i
$890$		−	6.71136i		−	0.224965i
$891$		0			0
$892$			8.39524i			0.281093i
$893$			15.4955i			0.518537i
$894$		0			0
$895$		−	23.4931i		−	0.785287i
$896$	−1.34136	−	2.28052i	−0.0448117	−	0.0761867i
$897$		0			0
$898$	−26.8022			−0.894400
$899$	30.4865			1.01678
$900$		0			0
$901$		0			0
$902$	19.4087			0.646238
$903$		0			0
$904$	1.15953			0.0385653
$905$		−	23.9150i		−	0.794963i
$906$		0			0
$907$	−16.0863			−0.534136			−0.267068	−	0.963678i	$-0.586055\pi$
$907$	−16.0863			−0.534136			−0.267068	+	0.963678i	$0.586055\pi$
$908$	2.42522			0.0804836
$909$		0			0
$910$	−19.9709	+	11.7465i	−0.662029	+	0.389394i
$911$			31.1870i			1.03327i	0.856206	+	0.516635i	$0.172816\pi$
$911$			31.1870i			1.03327i	−0.856206	+	0.516635i	$0.827184\pi$
$912$		0			0
$913$		−	33.6340i		−	1.11312i
$914$			13.8488i			0.458079i
$915$		0			0
$916$			2.01975i			0.0667344i
$917$	23.9267	−	14.0733i	0.790128	−	0.464740i
$918$		0			0
$919$	25.7664			0.849955			0.424977	−	0.905204i	$-0.360282\pi$
$919$	25.7664			0.849955			0.424977	+	0.905204i	$0.360282\pi$
$920$	−6.74314			−0.222315
$921$		0			0
$922$		−	4.80483i		−	0.158239i
$923$	29.1647			0.959968
$924$		0			0
$925$	−16.8052			−0.552550
$926$		−	21.0388i		−	0.691377i
$927$		0			0
$928$	6.56103			0.215376
$929$	54.7487			1.79625			0.898124	−	0.439743i	$-0.144931\pi$
$929$	54.7487			1.79625			0.898124	+	0.439743i	$0.144931\pi$
$930$		0			0
$931$	−18.4580	−	10.2624i	−0.604938	−	0.336336i
$932$			12.7289i			0.416950i
$933$		0			0
$934$			5.82302i			0.190535i
$935$		−	15.7563i		−	0.515288i
$936$		0			0
$937$		−	58.2065i		−	1.90152i	−0.309924	−	0.950761i	$-0.600304\pi$
$937$		−	58.2065i		−	1.90152i	0.309924	−	0.950761i	$-0.399696\pi$
$938$	0.764885	+	1.30042i	0.0249744	+	0.0424602i
$939$		0			0
$940$	9.19531			0.299918
$941$	−33.3316			−1.08658			−0.543289	−	0.839545i	$-0.682821\pi$
$941$	−33.3316			−1.08658			−0.543289	+	0.839545i	$0.682821\pi$
$942$		0			0
$943$		−	30.4394i		−	0.991245i
$944$	−14.5900			−0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$		−	7.61522i		−	0.247461i	−0.992316	−	0.123731i	$-0.960514\pi$
$947$		−	7.61522i		−	0.247461i	0.992316	−	0.123731i	$-0.0394859\pi$
$948$		0			0
$949$	−60.5615			−1.96591
$950$	−5.41447			−0.175669
$951$		0			0
$952$	−4.91564	−	8.35733i	−0.159317	−	0.270862i
$953$		−	55.7861i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$953$		−	55.7861i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$954$		0			0
$955$		−	16.5667i		−	0.536085i
$956$			17.4495i			0.564356i
$957$		0			0
$958$		−	26.9561i		−	0.870912i
$959$	−6.33197	−	10.7653i	−0.204470	−	0.347630i
$960$		0			0
$961$	9.40903			0.303517
$962$	−45.8026			−1.47673
$963$		0			0
$964$		−	11.4332i		−	0.368238i
$965$	−43.9713			−1.41549
$966$		0			0
$967$	26.6739			0.857775			0.428887	−	0.903358i	$-0.358906\pi$
$967$	26.6739			0.857775			0.428887	+	0.903358i	$0.358906\pi$
$968$		−	5.23278i		−	0.168188i
$969$		0			0
$970$	−9.86639			−0.316791
$971$	−8.59942			−0.275968			−0.137984	−	0.990434i	$-0.544062\pi$
$971$	−8.59942			−0.275968			−0.137984	+	0.990434i	$0.544062\pi$
$972$		0			0
$973$	3.17064	+	5.39057i	0.101646	+	0.172814i
$974$		−	13.6268i		−	0.436630i
$975$		0			0
$976$			11.3283i			0.362610i
$977$			14.7771i			0.472761i	0.971661	+	0.236380i	$0.0759612\pi$
$977$			14.7771i			0.472761i	−0.971661	+	0.236380i	$0.924039\pi$
$978$		0			0
$979$			9.00235i			0.287716i
$980$	−6.08988	+	10.9533i	−0.194534	+	0.349891i
$981$		0			0
$982$	−38.9630			−1.24336
$983$	−20.5135			−0.654280			−0.327140	−	0.944976i	$-0.606085\pi$
$983$	−20.5135			−0.654280			−0.327140	+	0.944976i	$0.606085\pi$
$984$		0			0
$985$			22.3545i			0.712273i
$986$	24.0440			0.765716
$987$		0			0
$988$	−14.7572			−0.469489
$989$		−	26.2236i		−	0.833861i
$990$		0			0
$991$	−9.29294			−0.295200			−0.147600	−	0.989047i	$-0.547155\pi$
$991$	−9.29294			−0.295200			−0.147600	+	0.989047i	$0.547155\pi$
$992$	−4.64661			−0.147530
$993$		0			0
$994$	13.5977	−	7.99791i	0.431291	−	0.253678i
$995$		−	0.320733i		−	0.0101679i
$996$		0			0
$997$		−	0.0199668i		−	0.000632354i	−1.00000		0.000316177i	$-0.999899\pi$
$997$		−	0.0199668i		−	0.000632354i	1.00000		0.000316177i	$-0.000100642\pi$
$998$			26.0097i			0.823322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.d.a.1133.14		16
3.2	odd	2	inner	1134.2.d.a.1133.3		16
7.6	odd	2	inner	1134.2.d.a.1133.11		16
9.2	odd	6		378.2.m.a.125.4		16
9.4	even	3		378.2.m.a.251.1		16
9.5	odd	6		126.2.m.a.83.5	yes	16
9.7	even	3		126.2.m.a.41.8	yes	16
21.20	even	2	inner	1134.2.d.a.1133.6		16
36.7	odd	6		1008.2.cc.b.545.1		16
36.11	even	6		3024.2.cc.b.881.6		16
36.23	even	6		1008.2.cc.b.209.8		16
36.31	odd	6		3024.2.cc.b.2897.3		16
63.2	odd	6		2646.2.t.a.2285.5		16
63.4	even	3		2646.2.t.a.1979.8		16
63.5	even	6		882.2.l.a.227.2		16
63.11	odd	6		2646.2.l.b.1097.4		16
63.13	odd	6		378.2.m.a.251.4		16
63.16	even	3		882.2.t.b.815.2		16
63.20	even	6		378.2.m.a.125.1		16
63.23	odd	6		882.2.l.a.227.3		16
63.25	even	3		882.2.l.a.509.6		16
63.31	odd	6		2646.2.t.a.1979.5		16
63.32	odd	6		882.2.t.b.803.3		16
63.34	odd	6		126.2.m.a.41.5	✓	16
63.38	even	6		2646.2.l.b.1097.1		16
63.40	odd	6		2646.2.l.b.521.8		16
63.41	even	6		126.2.m.a.83.8	yes	16
63.47	even	6		2646.2.t.a.2285.8		16
63.52	odd	6		882.2.l.a.509.7		16
63.58	even	3		2646.2.l.b.521.5		16
63.59	even	6		882.2.t.b.803.2		16
63.61	odd	6		882.2.t.b.815.3		16
252.83	odd	6		3024.2.cc.b.881.3		16
252.139	even	6		3024.2.cc.b.2897.6		16
252.167	odd	6		1008.2.cc.b.209.1		16
252.223	even	6		1008.2.cc.b.545.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	63.34	odd	6
126.2.m.a.41.8	yes	16	9.7	even	3
126.2.m.a.83.5	yes	16	9.5	odd	6
126.2.m.a.83.8	yes	16	63.41	even	6
378.2.m.a.125.1		16	63.20	even	6
378.2.m.a.125.4		16	9.2	odd	6
378.2.m.a.251.1		16	9.4	even	3
378.2.m.a.251.4		16	63.13	odd	6
882.2.l.a.227.2		16	63.5	even	6
882.2.l.a.227.3		16	63.23	odd	6
882.2.l.a.509.6		16	63.25	even	3
882.2.l.a.509.7		16	63.52	odd	6
882.2.t.b.803.2		16	63.59	even	6
882.2.t.b.803.3		16	63.32	odd	6
882.2.t.b.815.2		16	63.16	even	3
882.2.t.b.815.3		16	63.61	odd	6
1008.2.cc.b.209.1		16	252.167	odd	6
1008.2.cc.b.209.8		16	36.23	even	6
1008.2.cc.b.545.1		16	36.7	odd	6
1008.2.cc.b.545.8		16	252.223	even	6
1134.2.d.a.1133.3		16	3.2	odd	2	inner
1134.2.d.a.1133.6		16	21.20	even	2	inner
1134.2.d.a.1133.11		16	7.6	odd	2	inner
1134.2.d.a.1133.14		16	1.1	even	1	trivial
2646.2.l.b.521.5		16	63.58	even	3
2646.2.l.b.521.8		16	63.40	odd	6
2646.2.l.b.1097.1		16	63.38	even	6
2646.2.l.b.1097.4		16	63.11	odd	6
2646.2.t.a.1979.5		16	63.31	odd	6
2646.2.t.a.1979.8		16	63.4	even	3
2646.2.t.a.2285.5		16	63.2	odd	6
2646.2.t.a.2285.8		16	63.47	even	6
3024.2.cc.b.881.3		16	252.83	odd	6
3024.2.cc.b.881.6		16	36.11	even	6
3024.2.cc.b.2897.3		16	36.31	odd	6
3024.2.cc.b.2897.6		16	252.139	even	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.79035 q^{5} +(2.28052 - 1.34136i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.79035 q^{5} +(2.28052 - 1.34136i) q^{7} -1.00000i q^{8} +1.79035i q^{10} -2.40150i q^{11} +4.89133i q^{13} +(1.34136 + 2.28052i) q^{14} +1.00000 q^{16} +3.66466 q^{17} -3.01701i q^{19} -1.79035 q^{20} +2.40150 q^{22} -3.76638i q^{23} -1.79465 q^{25} -4.89133 q^{26} +(-2.28052 + 1.34136i) q^{28} -6.56103i q^{29} +4.64661i q^{31} +1.00000i q^{32} +3.66466i q^{34} +(4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +3.01701 q^{38} -1.79035i q^{40} +8.08188 q^{41} +6.96254 q^{43} +2.40150i q^{44} +3.76638 q^{46} -5.13604 q^{47} +(3.40150 - 6.11799i) q^{49} -1.79465i q^{50} -4.89133i q^{52} -4.29953i q^{55} +(-1.34136 - 2.28052i) q^{56} +6.56103 q^{58} -14.5900 q^{59} +11.3283i q^{61} -4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +0.570231 q^{67} -3.66466 q^{68} +(2.40150 + 4.08292i) q^{70} -5.96254i q^{71} +12.3814i q^{73} +9.36404i q^{74} +3.01701i q^{76} +(-3.22128 - 5.47667i) q^{77} +3.03663 q^{79} +1.79035 q^{80} +8.08188i q^{82} +14.0054 q^{83} +6.56103 q^{85} +6.96254i q^{86} -2.40150 q^{88} -3.74863 q^{89} +(6.56103 + 11.1547i) q^{91} +3.76638i q^{92} -5.13604i q^{94} -5.40150i q^{95} +5.51087i q^{97} +(6.11799 + 3.40150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 - 4 * q^7	\( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

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