LMFDB - Embedded newform 315.2.b.b.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(251,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.b (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$-0.517638i$ of defining polynomial
Character	$\chi$	$=$	315.251
Dual form			315.2.b.b.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.517638i q^{2} +1.73205 q^{4} +1.00000 q^{5} +(1.00000 + 2.44949i) q^{7} -1.93185i q^{8} +O(q^{10})$	\(q-0.517638i q^{2} +1.73205 q^{4} +1.00000 q^{5} +(1.00000 + 2.44949i) q^{7} -1.93185i q^{8} -0.517638i q^{10} +0.378937i q^{11} +1.79315i q^{13} +(1.26795 - 0.517638i) q^{14} +2.46410 q^{16} -3.46410 q^{17} -1.79315i q^{19} +1.73205 q^{20} +0.196152 q^{22} -1.41421i q^{23} +1.00000 q^{25} +0.928203 q^{26} +(1.73205 + 4.24264i) q^{28} -1.41421i q^{29} -6.69213i q^{31} -5.13922i q^{32} +1.79315i q^{34} +(1.00000 + 2.44949i) q^{35} -1.46410 q^{37} -0.928203 q^{38} -1.93185i q^{40} +10.3923 q^{41} -4.92820 q^{43} +0.656339i q^{44} -0.732051 q^{46} -9.46410 q^{47} +(-5.00000 + 4.89898i) q^{49} -0.517638i q^{50} +3.10583i q^{52} +10.1769i q^{53} +0.378937i q^{55} +(4.73205 - 1.93185i) q^{56} -0.732051 q^{58} -9.46410 q^{59} -13.3843i q^{61} -3.46410 q^{62} +2.26795 q^{64} +1.79315i q^{65} -10.9282 q^{67} -6.00000 q^{68} +(1.26795 - 0.517638i) q^{70} +15.0759i q^{71} -1.79315i q^{73} +0.757875i q^{74} -3.10583i q^{76} +(-0.928203 + 0.378937i) q^{77} -10.9282 q^{79} +2.46410 q^{80} -5.37945i q^{82} +9.46410 q^{83} -3.46410 q^{85} +2.55103i q^{86} +0.732051 q^{88} -12.9282 q^{89} +(-4.39230 + 1.79315i) q^{91} -2.44949i q^{92} +4.89898i q^{94} -1.79315i q^{95} +15.1774i q^{97} +(2.53590 + 2.58819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 4 * q + 4 * q^5 + 4 * q^7	$ 4 q + 4 q^{5} + 4 q^{7} + 12 q^{14} - 4 q^{16} - 20 q^{22} + 4 q^{25} - 24 q^{26} + 4 q^{35} + 8 q^{37} + 24 q^{38} + 8 q^{43} + 4 q^{46} - 24 q^{47} - 20 q^{49} + 12 q^{56} + 4 q^{58} - 24 q^{59} + 16 q^{64} - 16 q^{67} - 24 q^{68} + 12 q^{70} + 24 q^{77} - 16 q^{79} - 4 q^{80} + 24 q^{83} - 4 q^{88} - 24 q^{89} + 24 q^{91} + 24 q^{98}+O(q^{100}) $ 4 * q + 4 * q^5 + 4 * q^7 + 12 * q^14 - 4 * q^16 - 20 * q^22 + 4 * q^25 - 24 * q^26 + 4 * q^35 + 8 * q^37 + 24 * q^38 + 8 * q^43 + 4 * q^46 - 24 * q^47 - 20 * q^49 + 12 * q^56 + 4 * q^58 - 24 * q^59 + 16 * q^64 - 16 * q^67 - 24 * q^68 + 12 * q^70 + 24 * q^77 - 16 * q^79 - 4 * q^80 + 24 * q^83 - 4 * q^88 - 24 * q^89 + 24 * q^91 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	0.517638i		−	0.366025i	−0.983111	−	0.183013i	$-0.941415\pi$
$2$		−	0.517638i		−	0.366025i	0.983111	−	0.183013i	$-0.0585849\pi$
$3$		0			0
$3$		0			0
$4$	1.73205			0.866025
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$		−	1.93185i		−	0.683013i
$9$		0			0
$10$		−	0.517638i		−	0.163692i
$11$			0.378937i			0.114254i	0.998367	+	0.0571270i	$0.0181940\pi$
$11$			0.378937i			0.114254i	−0.998367	+	0.0571270i	$0.981806\pi$
$12$		0			0
$13$			1.79315i			0.497331i	0.968589	+	0.248665i	$0.0799919\pi$
$13$			1.79315i			0.497331i	−0.968589	+	0.248665i	$0.920008\pi$
$14$	1.26795	−	0.517638i	0.338874	−	0.138345i
$15$		0			0
$16$	2.46410			0.616025
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$		−	1.79315i		−	0.411377i	−0.978618	−	0.205689i	$-0.934057\pi$
$19$		−	1.79315i		−	0.411377i	0.978618	−	0.205689i	$-0.0659434\pi$
$20$	1.73205			0.387298
$21$		0			0
$22$	0.196152			0.0418198
$23$		−	1.41421i		−	0.294884i	−0.989071	−	0.147442i	$-0.952896\pi$
$23$		−	1.41421i		−	0.294884i	0.989071	−	0.147442i	$-0.0471040\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	0.928203			0.182036
$27$		0			0
$28$	1.73205	+	4.24264i	0.327327	+	0.801784i
$29$		−	1.41421i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$29$		−	1.41421i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$30$		0			0
$31$		−	6.69213i		−	1.20194i	−0.799271	−	0.600971i	$-0.794781\pi$
$31$		−	6.69213i		−	1.20194i	0.799271	−	0.600971i	$-0.205219\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$			1.79315i			0.307523i
$35$	1.00000	+	2.44949i	0.169031	+	0.414039i
$36$		0			0
$37$	−1.46410			−0.240697			−0.120348	−	0.992732i	$-0.538401\pi$
$37$	−1.46410			−0.240697			−0.120348	+	0.992732i	$0.538401\pi$
$38$	−0.928203			−0.150574
$39$		0			0
$40$		−	1.93185i		−	0.305453i
$41$	10.3923			1.62301			0.811503	−	0.584349i	$-0.198650\pi$
$41$	10.3923			1.62301			0.811503	+	0.584349i	$0.198650\pi$
$42$		0			0
$43$	−4.92820			−0.751544			−0.375772	−	0.926712i	$-0.622622\pi$
$43$	−4.92820			−0.751544			−0.375772	+	0.926712i	$0.622622\pi$
$44$			0.656339i			0.0989468i
$45$		0			0
$46$	−0.732051			−0.107935
$47$	−9.46410			−1.38048			−0.690241	−	0.723580i	$-0.742495\pi$
$47$	−9.46410			−1.38048			−0.690241	+	0.723580i	$0.742495\pi$
$48$		0			0
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$		−	0.517638i		−	0.0732051i
$51$		0			0
$52$			3.10583i			0.430701i
$53$			10.1769i			1.39790i	0.715168	+	0.698952i	$0.246350\pi$
$53$			10.1769i			1.39790i	−0.715168	+	0.698952i	$0.753650\pi$
$54$		0			0
$55$			0.378937i			0.0510959i
$56$	4.73205	−	1.93185i	0.632347	−	0.258155i
$57$		0			0
$58$	−0.732051			−0.0961230
$59$	−9.46410			−1.23212			−0.616061	−	0.787699i	$-0.711272\pi$
$59$	−9.46410			−1.23212			−0.616061	+	0.787699i	$0.711272\pi$
$60$		0			0
$61$		−	13.3843i		−	1.71368i	−0.515583	−	0.856840i	$-0.672425\pi$
$61$		−	13.3843i		−	1.71368i	0.515583	−	0.856840i	$-0.327575\pi$
$62$	−3.46410			−0.439941
$63$		0			0
$64$	2.26795			0.283494
$65$			1.79315i			0.222413i
$66$		0			0
$67$	−10.9282			−1.33509			−0.667546	−	0.744568i	$-0.732655\pi$
$67$	−10.9282			−1.33509			−0.667546	+	0.744568i	$0.732655\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$	1.26795	−	0.517638i	0.151549	−	0.0618696i
$71$			15.0759i			1.78918i	0.446891	+	0.894589i	$0.352531\pi$
$71$			15.0759i			1.78918i	−0.446891	+	0.894589i	$0.647469\pi$
$72$		0			0
$73$		−	1.79315i		−	0.209872i	−0.994479	−	0.104936i	$-0.966536\pi$
$73$		−	1.79315i		−	0.209872i	0.994479	−	0.104936i	$-0.0334638\pi$
$74$			0.757875i			0.0881012i
$75$		0			0
$76$		−	3.10583i		−	0.356263i
$77$	−0.928203	+	0.378937i	−0.105779	+	0.0431839i
$78$		0			0
$79$	−10.9282			−1.22952			−0.614759	−	0.788715i	$-0.710747\pi$
$79$	−10.9282			−1.22952			−0.614759	+	0.788715i	$0.710747\pi$
$80$	2.46410			0.275495
$81$		0			0
$82$		−	5.37945i		−	0.594061i
$83$	9.46410			1.03882			0.519410	−	0.854525i	$-0.326152\pi$
$83$	9.46410			1.03882			0.519410	+	0.854525i	$0.326152\pi$
$84$		0			0
$85$	−3.46410			−0.375735
$86$			2.55103i			0.275084i
$87$		0			0
$88$	0.732051			0.0780369
$89$	−12.9282			−1.37039			−0.685193	−	0.728361i	$-0.740282\pi$
$89$	−12.9282			−1.37039			−0.685193	+	0.728361i	$0.740282\pi$
$90$		0			0
$91$	−4.39230	+	1.79315i	−0.460439	+	0.187973i
$92$		−	2.44949i		−	0.255377i
$93$		0			0
$94$			4.89898i			0.505291i
$95$		−	1.79315i		−	0.183973i
$96$		0			0
$97$			15.1774i			1.54103i	0.637420	+	0.770516i	$0.280002\pi$
$97$			15.1774i			1.54103i	−0.637420	+	0.770516i	$0.719998\pi$
$98$	2.53590	+	2.58819i	0.256164	+	0.261447i
$99$		0			0
$100$	1.73205			0.173205
$101$	10.3923			1.03407			0.517036	−	0.855963i	$-0.327035\pi$
$101$	10.3923			1.03407			0.517036	+	0.855963i	$0.327035\pi$
$102$		0			0
$103$		−	13.3843i		−	1.31879i	−0.751796	−	0.659395i	$-0.770812\pi$
$103$		−	13.3843i		−	1.31879i	0.751796	−	0.659395i	$-0.229188\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	5.26795			0.511668
$107$			13.2827i			1.28409i	0.766667	+	0.642045i	$0.221914\pi$
$107$			13.2827i			1.28409i	−0.766667	+	0.642045i	$0.778086\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	0.196152			0.0187024
$111$		0			0
$112$	2.46410	+	6.03579i	0.232836	+	0.570329i
$113$		−	9.41902i		−	0.886067i	−0.896505	−	0.443034i	$-0.853902\pi$
$113$		−	9.41902i		−	0.886067i	0.896505	−	0.443034i	$-0.146098\pi$
$114$		0			0
$115$		−	1.41421i		−	0.131876i
$116$		−	2.44949i		−	0.227429i
$117$		0			0
$118$			4.89898i			0.450988i
$119$	−3.46410	−	8.48528i	−0.317554	−	0.777844i
$120$		0			0
$121$	10.8564			0.986946
$122$	−6.92820			−0.627250
$123$		0			0
$124$		−	11.5911i		−	1.04091i
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.92820			0.259836			0.129918	−	0.991525i	$-0.458529\pi$
$127$	2.92820			0.259836			0.129918	+	0.991525i	$0.458529\pi$
$128$		−	11.4524i		−	1.01226i
$129$		0			0
$130$	0.928203			0.0814088
$131$	2.53590			0.221562			0.110781	−	0.993845i	$-0.464665\pi$
$131$	2.53590			0.221562			0.110781	+	0.993845i	$0.464665\pi$
$132$		0			0
$133$	4.39230	−	1.79315i	0.380861	−	0.155486i
$134$			5.65685i			0.488678i
$135$		0			0
$136$			6.69213i			0.573845i
$137$		−	21.4906i		−	1.83607i	−0.396504	−	0.918033i	$-0.629777\pi$
$137$		−	21.4906i		−	1.83607i	0.396504	−	0.918033i	$-0.370223\pi$
$138$		0			0
$139$			16.4901i			1.39867i	0.714794	+	0.699336i	$0.246521\pi$
$139$			16.4901i			1.39867i	−0.714794	+	0.699336i	$0.753479\pi$
$140$	1.73205	+	4.24264i	0.146385	+	0.358569i
$141$		0			0
$142$	7.80385			0.654884
$143$	−0.679492			−0.0568220
$144$		0			0
$145$		−	1.41421i		−	0.117444i
$146$	−0.928203			−0.0768186
$147$		0			0
$148$	−2.53590			−0.208450
$149$		−	14.7985i		−	1.21234i	−0.795336	−	0.606169i	$-0.792705\pi$
$149$		−	14.7985i		−	1.21234i	0.795336	−	0.606169i	$-0.207295\pi$
$150$		0			0
$151$	−0.535898			−0.0436108			−0.0218054	−	0.999762i	$-0.506941\pi$
$151$	−0.535898			−0.0436108			−0.0218054	+	0.999762i	$0.506941\pi$
$152$	−3.46410			−0.280976
$153$		0			0
$154$	0.196152	+	0.480473i	0.0158064	+	0.0387176i
$155$		−	6.69213i		−	0.537525i
$156$		0			0
$157$		−	3.10583i		−	0.247872i	−0.992290	−	0.123936i	$-0.960448\pi$
$157$		−	3.10583i		−	0.247872i	0.992290	−	0.123936i	$-0.0395518\pi$
$158$			5.65685i			0.450035i
$159$		0			0
$160$		−	5.13922i		−	0.406291i
$161$	3.46410	−	1.41421i	0.273009	−	0.111456i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	18.0000			1.40556
$165$		0			0
$166$		−	4.89898i		−	0.380235i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	9.78461			0.752662
$170$			1.79315i			0.137528i
$171$		0			0
$172$	−8.53590			−0.650856
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	1.00000	+	2.44949i	0.0755929	+	0.185164i
$176$			0.933740i			0.0703833i
$177$		0			0
$178$			6.69213i			0.501596i
$179$			18.6622i			1.39488i	0.716645	+	0.697438i	$0.245677\pi$
$179$			18.6622i			1.39488i	−0.716645	+	0.697438i	$0.754323\pi$
$180$		0			0
$181$			12.0716i			0.897274i	0.893714	+	0.448637i	$0.148090\pi$
$181$			12.0716i			0.897274i	−0.893714	+	0.448637i	$0.851910\pi$
$182$	0.928203	+	2.27362i	0.0688030	+	0.168532i
$183$		0			0
$184$	−2.73205			−0.201409
$185$	−1.46410			−0.107643
$186$		0			0
$187$		−	1.31268i		−	0.0959925i
$188$	−16.3923			−1.19553
$189$		0			0
$190$	−0.928203			−0.0673389
$191$		−	13.0053i		−	0.941032i	−0.882391	−	0.470516i	$-0.844068\pi$
$191$		−	13.0053i		−	0.941032i	0.882391	−	0.470516i	$-0.155932\pi$
$192$		0			0
$193$	24.3923			1.75580			0.877898	−	0.478847i	$-0.158945\pi$
$193$	24.3923			1.75580			0.877898	+	0.478847i	$0.158945\pi$
$194$	7.85641			0.564057
$195$		0			0
$196$	−8.66025	+	8.48528i	−0.618590	+	0.606092i
$197$		−	8.10634i		−	0.577553i	−0.957397	−	0.288777i	$-0.906752\pi$
$197$		−	8.10634i		−	0.577553i	0.957397	−	0.288777i	$-0.0932485\pi$
$198$		0			0
$199$		−	15.1774i		−	1.07590i	−0.842977	−	0.537949i	$-0.819199\pi$
$199$		−	15.1774i		−	1.07590i	0.842977	−	0.537949i	$-0.180801\pi$
$200$		−	1.93185i		−	0.136603i
$201$		0			0
$202$		−	5.37945i		−	0.378497i
$203$	3.46410	−	1.41421i	0.243132	−	0.0992583i
$204$		0			0
$205$	10.3923			0.725830
$206$	−6.92820			−0.482711
$207$		0			0
$208$			4.41851i			0.306368i
$209$	0.679492			0.0470014
$210$		0			0
$211$	−2.39230			−0.164693			−0.0823465	−	0.996604i	$-0.526241\pi$
$211$	−2.39230			−0.164693			−0.0823465	+	0.996604i	$0.526241\pi$
$212$			17.6269i			1.21062i
$213$		0			0
$214$	6.87564			0.470009
$215$	−4.92820			−0.336101
$216$		0			0
$217$	16.3923	−	6.69213i	1.11278	−	0.454291i
$218$		−	4.14110i		−	0.280471i
$219$		0			0
$220$			0.656339i			0.0442504i
$221$		−	6.21166i		−	0.417841i
$222$		0			0
$223$			4.89898i			0.328060i	0.986455	+	0.164030i	$0.0524494\pi$
$223$			4.89898i			0.328060i	−0.986455	+	0.164030i	$0.947551\pi$
$224$	12.5885	−	5.13922i	0.841102	−	0.343378i
$225$		0			0
$226$	−4.87564			−0.324323
$227$	11.3205			0.751369			0.375684	−	0.926748i	$-0.377408\pi$
$227$	11.3205			0.751369			0.375684	+	0.926748i	$0.377408\pi$
$228$		0			0
$229$			14.6969i			0.971201i	0.874181	+	0.485601i	$0.161399\pi$
$229$			14.6969i			0.971201i	−0.874181	+	0.485601i	$0.838601\pi$
$230$	−0.732051			−0.0482700
$231$		0			0
$232$	−2.73205			−0.179368
$233$			3.96524i			0.259771i	0.991529	+	0.129886i	$0.0414611\pi$
$233$			3.96524i			0.259771i	−0.991529	+	0.129886i	$0.958539\pi$
$234$		0			0
$235$	−9.46410			−0.617370
$236$	−16.3923			−1.06705
$237$		0			0
$238$	−4.39230	+	1.79315i	−0.284711	+	0.116233i
$239$			3.96524i			0.256490i	0.991743	+	0.128245i	$0.0409344\pi$
$239$			3.96524i			0.256490i	−0.991743	+	0.128245i	$0.959066\pi$
$240$		0			0
$241$		−	1.31268i		−	0.0845570i	−0.999106	−	0.0422785i	$-0.986538\pi$
$241$		−	1.31268i		−	0.0845570i	0.999106	−	0.0422785i	$-0.0134617\pi$
$242$		−	5.61969i		−	0.361247i
$243$		0			0
$244$		−	23.1822i		−	1.48409i
$245$	−5.00000	+	4.89898i	−0.319438	+	0.312984i
$246$		0			0
$247$	3.21539			0.204590
$248$	−12.9282			−0.820942
$249$		0			0
$250$		−	0.517638i		−	0.0327383i
$251$	−11.3205			−0.714544			−0.357272	−	0.934000i	$-0.616293\pi$
$251$	−11.3205			−0.714544			−0.357272	+	0.934000i	$0.616293\pi$
$252$		0			0
$253$	0.535898			0.0336916
$254$		−	1.51575i		−	0.0951066i
$255$		0			0
$256$	−1.39230			−0.0870191
$257$	15.4641			0.964624			0.482312	−	0.875999i	$-0.339797\pi$
$257$	15.4641			0.964624			0.482312	+	0.875999i	$0.339797\pi$
$258$		0			0
$259$	−1.46410	−	3.58630i	−0.0909748	−	0.222842i
$260$			3.10583i			0.192615i
$261$		0			0
$262$		−	1.31268i		−	0.0810975i
$263$			11.9700i			0.738105i	0.929409	+	0.369052i	$0.120318\pi$
$263$			11.9700i			0.738105i	−0.929409	+	0.369052i	$0.879682\pi$
$264$		0			0
$265$			10.1769i			0.625162i
$266$	−0.928203	−	2.27362i	−0.0569118	−	0.139405i
$267$		0			0
$268$	−18.9282			−1.15622
$269$	−8.53590			−0.520443			−0.260221	−	0.965549i	$-0.583796\pi$
$269$	−8.53590			−0.520443			−0.260221	+	0.965549i	$0.583796\pi$
$270$		0			0
$271$			26.2880i			1.59689i	0.602071	+	0.798443i	$0.294342\pi$
$271$			26.2880i			1.59689i	−0.602071	+	0.798443i	$0.705658\pi$
$272$	−8.53590			−0.517565
$273$		0			0
$274$	−11.1244			−0.672047
$275$			0.378937i			0.0228508i
$276$		0			0
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$	8.53590			0.511949
$279$		0			0
$280$	4.73205	−	1.93185i	0.282794	−	0.115450i
$281$			3.48477i			0.207884i	0.994583	+	0.103942i	$0.0331456\pi$
$281$			3.48477i			0.207884i	−0.994583	+	0.103942i	$0.966854\pi$
$282$		0			0
$283$		−	24.4949i		−	1.45607i	−0.685540	−	0.728035i	$-0.740434\pi$
$283$		−	24.4949i		−	1.45607i	0.685540	−	0.728035i	$-0.259566\pi$
$284$			26.1122i			1.54947i
$285$		0			0
$286$			0.351731i			0.0207983i
$287$	10.3923	+	25.4558i	0.613438	+	1.50261i
$288$		0			0
$289$	−5.00000			−0.294118
$290$	−0.732051			−0.0429875
$291$		0			0
$292$		−	3.10583i		−	0.181755i
$293$	10.3923			0.607125			0.303562	−	0.952812i	$-0.401824\pi$
$293$	10.3923			0.607125			0.303562	+	0.952812i	$0.401824\pi$
$294$		0			0
$295$	−9.46410			−0.551021
$296$			2.82843i			0.164399i
$297$		0			0
$298$	−7.66025			−0.443747
$299$	2.53590			0.146655
$300$		0			0
$301$	−4.92820	−	12.0716i	−0.284057	−	0.695794i
$302$			0.277401i			0.0159627i
$303$		0			0
$304$		−	4.41851i		−	0.253419i
$305$		−	13.3843i		−	0.766381i
$306$		0			0
$307$		−	14.6969i		−	0.838799i	−0.907802	−	0.419399i	$-0.862241\pi$
$307$		−	14.6969i		−	0.838799i	0.907802	−	0.419399i	$-0.137759\pi$
$308$	−1.60770	+	0.656339i	−0.0916069	+	0.0373984i
$309$		0			0
$310$	−3.46410			−0.196748
$311$	−28.3923			−1.60998			−0.804990	−	0.593288i	$-0.797829\pi$
$311$	−28.3923			−1.60998			−0.804990	+	0.593288i	$0.797829\pi$
$312$		0			0
$313$			10.2784i			0.580971i	0.956879	+	0.290486i	$0.0938169\pi$
$313$			10.2784i			0.580971i	−0.956879	+	0.290486i	$0.906183\pi$
$314$	−1.60770			−0.0907275
$315$		0			0
$316$	−18.9282			−1.06479
$317$			27.1475i			1.52475i	0.647134	+	0.762377i	$0.275968\pi$
$317$			27.1475i			1.52475i	−0.647134	+	0.762377i	$0.724032\pi$
$318$		0			0
$319$	0.535898			0.0300045
$320$	2.26795			0.126782
$321$		0			0
$322$	−0.732051	−	1.79315i	−0.0407956	−	0.0999284i
$323$			6.21166i			0.345626i
$324$		0			0
$325$			1.79315i			0.0994661i
$326$			2.07055i			0.114677i
$327$		0			0
$328$		−	20.0764i		−	1.10853i
$329$	−9.46410	−	23.1822i	−0.521773	−	1.27808i
$330$		0			0
$331$	−5.60770			−0.308227			−0.154113	−	0.988053i	$-0.549252\pi$
$331$	−5.60770			−0.308227			−0.154113	+	0.988053i	$0.549252\pi$
$332$	16.3923			0.899645
$333$		0			0
$334$		−	6.21166i		−	0.339887i
$335$	−10.9282			−0.597072
$336$		0			0
$337$	12.3923			0.675052			0.337526	−	0.941316i	$-0.390410\pi$
$337$	12.3923			0.675052			0.337526	+	0.941316i	$0.390410\pi$
$338$		−	5.06489i		−	0.275494i
$339$		0			0
$340$	−6.00000			−0.325396
$341$	2.53590			0.137327
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$			9.52056i			0.513314i
$345$		0			0
$346$			3.10583i			0.166970i
$347$		−	28.1827i		−	1.51293i	−0.654035	−	0.756464i	$-0.726925\pi$
$347$		−	28.1827i		−	1.51293i	0.654035	−	0.756464i	$-0.273075\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	1.26795	−	0.517638i	0.0677747	−	0.0276689i
$351$		0			0
$352$	1.94744			0.103799
$353$	30.0000			1.59674			0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000			1.59674			0.798369	+	0.602168i	$0.205696\pi$
$354$		0			0
$355$			15.0759i			0.800144i
$356$	−22.3923			−1.18679
$357$		0			0
$358$	9.66025			0.510560
$359$		−	20.1779i		−	1.06495i	−0.846446	−	0.532475i	$-0.821262\pi$
$359$		−	20.1779i		−	1.06495i	0.846446	−	0.532475i	$-0.178738\pi$
$360$		0			0
$361$	15.7846			0.830769
$362$	6.24871			0.328425
$363$		0			0
$364$	−7.60770	+	3.10583i	−0.398752	+	0.162790i
$365$		−	1.79315i		−	0.0938578i
$366$		0			0
$367$		−	21.8695i		−	1.14158i	−0.821096	−	0.570790i	$-0.806637\pi$
$367$		−	21.8695i		−	1.14158i	0.821096	−	0.570790i	$-0.193363\pi$
$368$		−	3.48477i		−	0.181656i
$369$		0			0
$370$			0.757875i			0.0394000i
$371$	−24.9282	+	10.1769i	−1.29421	+	0.528358i
$372$		0			0
$373$	7.07180			0.366164			0.183082	−	0.983098i	$-0.441393\pi$
$373$	7.07180			0.366164			0.183082	+	0.983098i	$0.441393\pi$
$374$	−0.679492			−0.0351357
$375$		0			0
$376$			18.2832i			0.942886i
$377$	2.53590			0.130605
$378$		0			0
$379$	11.4641			0.588871			0.294436	−	0.955671i	$-0.404868\pi$
$379$	11.4641			0.588871			0.294436	+	0.955671i	$0.404868\pi$
$380$		−	3.10583i		−	0.159326i
$381$		0			0
$382$	−6.73205			−0.344442
$383$	30.9282			1.58036			0.790179	−	0.612877i	$-0.209988\pi$
$383$	30.9282			1.58036			0.790179	+	0.612877i	$0.209988\pi$
$384$		0			0
$385$	−0.928203	+	0.378937i	−0.0473056	+	0.0193124i
$386$		−	12.6264i		−	0.642666i
$387$		0			0
$388$			26.2880i			1.33457i
$389$			30.2533i			1.53390i	0.641705	+	0.766951i	$0.278227\pi$
$389$			30.2533i			1.53390i	−0.641705	+	0.766951i	$0.721773\pi$
$390$		0			0
$391$			4.89898i			0.247752i
$392$	9.46410	+	9.65926i	0.478009	+	0.487866i
$393$		0			0
$394$	−4.19615			−0.211399
$395$	−10.9282			−0.549858
$396$		0			0
$397$			12.9038i			0.647623i	0.946122	+	0.323811i	$0.104964\pi$
$397$			12.9038i			0.647623i	−0.946122	+	0.323811i	$0.895036\pi$
$398$	−7.85641			−0.393806
$399$		0			0
$400$	2.46410			0.123205
$401$		−	21.0101i		−	1.04920i	−0.851350	−	0.524598i	$-0.824216\pi$
$401$		−	21.0101i		−	1.04920i	0.851350	−	0.524598i	$-0.175784\pi$
$402$		0			0
$403$	12.0000			0.597763
$404$	18.0000			0.895533
$405$		0			0
$406$	−0.732051	−	1.79315i	−0.0363311	−	0.0889926i
$407$		−	0.554803i		−	0.0275006i
$408$		0			0
$409$			31.6675i			1.56586i	0.622112	+	0.782929i	$0.286275\pi$
$409$			31.6675i			1.56586i	−0.622112	+	0.782929i	$0.713725\pi$
$410$		−	5.37945i		−	0.265672i
$411$		0			0
$412$		−	23.1822i		−	1.14211i
$413$	−9.46410	−	23.1822i	−0.465698	−	1.14072i
$414$		0			0
$415$	9.46410			0.464574
$416$	9.21539			0.451822
$417$		0			0
$418$		−	0.351731i		−	0.0172037i
$419$	−10.1436			−0.495547			−0.247773	−	0.968818i	$-0.579699\pi$
$419$	−10.1436			−0.495547			−0.247773	+	0.968818i	$0.579699\pi$
$420$		0			0
$421$	0.143594			0.00699832			0.00349916	−	0.999994i	$-0.498886\pi$
$421$	0.143594			0.00699832			0.00349916	+	0.999994i	$0.498886\pi$
$422$			1.23835i			0.0602818i
$423$		0			0
$424$	19.6603			0.954786
$425$	−3.46410			−0.168034
$426$		0			0
$427$	32.7846	−	13.3843i	1.58656	−	0.647710i
$428$			23.0064i			1.11205i
$429$		0			0
$430$			2.55103i			0.123021i
$431$		−	6.79367i		−	0.327239i	−0.986523	−	0.163620i	$-0.947683\pi$
$431$		−	6.79367i		−	0.327239i	0.986523	−	0.163620i	$-0.0523170\pi$
$432$		0			0
$433$			0.480473i			0.0230901i	0.999933	+	0.0115450i	$0.00367498\pi$
$433$			0.480473i			0.0230901i	−0.999933	+	0.0115450i	$0.996325\pi$
$434$	−3.46410	−	8.48528i	−0.166282	−	0.407307i
$435$		0			0
$436$	13.8564			0.663602
$437$	−2.53590			−0.121308
$438$		0			0
$439$			8.96575i			0.427912i	0.976843	+	0.213956i	$0.0686349\pi$
$439$			8.96575i			0.427912i	−0.976843	+	0.213956i	$0.931365\pi$
$440$	0.732051			0.0348992
$441$		0			0
$442$	−3.21539			−0.152941
$443$			15.5563i			0.739104i	0.929210	+	0.369552i	$0.120489\pi$
$443$			15.5563i			0.739104i	−0.929210	+	0.369552i	$0.879511\pi$
$444$		0			0
$445$	−12.9282			−0.612856
$446$	2.53590			0.120078
$447$		0			0
$448$	2.26795	+	5.55532i	0.107151	+	0.262464i
$449$		−	12.5249i		−	0.591084i	−0.955330	−	0.295542i	$-0.904500\pi$
$449$		−	12.5249i		−	0.591084i	0.955330	−	0.295542i	$-0.0955003\pi$
$450$		0			0
$451$			3.93803i			0.185435i
$452$		−	16.3142i		−	0.767357i
$453$		0			0
$454$		−	5.85993i		−	0.275020i
$455$	−4.39230	+	1.79315i	−0.205914	+	0.0840642i
$456$		0			0
$457$	26.2487			1.22786			0.613931	−	0.789359i	$-0.289587\pi$
$457$	26.2487			1.22786			0.613931	+	0.789359i	$0.289587\pi$
$458$	7.60770			0.355484
$459$		0			0
$460$		−	2.44949i		−	0.114208i
$461$	7.85641			0.365909			0.182955	−	0.983121i	$-0.441434\pi$
$461$	7.85641			0.365909			0.182955	+	0.983121i	$0.441434\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		−	3.48477i		−	0.161776i
$465$		0			0
$466$	2.05256			0.0950830
$467$	28.3923			1.31384			0.656920	−	0.753961i	$-0.271859\pi$
$467$	28.3923			1.31384			0.656920	+	0.753961i	$0.271859\pi$
$468$		0			0
$469$	−10.9282	−	26.7685i	−0.504618	−	1.23606i
$470$			4.89898i			0.225973i
$471$		0			0
$472$			18.2832i			0.841554i
$473$		−	1.86748i		−	0.0858668i
$474$		0			0
$475$		−	1.79315i		−	0.0822754i
$476$	−6.00000	−	14.6969i	−0.275010	−	0.673633i
$477$		0			0
$478$	2.05256			0.0938819
$479$	14.5359			0.664162			0.332081	−	0.943251i	$-0.392249\pi$
$479$	14.5359			0.664162			0.332081	+	0.943251i	$0.392249\pi$
$480$		0			0
$481$		−	2.62536i		−	0.119706i
$482$	−0.679492			−0.0309500
$483$		0			0
$484$	18.8038			0.854720
$485$			15.1774i			0.689171i
$486$		0			0
$487$	−11.8564			−0.537265			−0.268633	−	0.963243i	$-0.586572\pi$
$487$	−11.8564			−0.537265			−0.268633	+	0.963243i	$0.586572\pi$
$488$	−25.8564			−1.17046
$489$		0			0
$490$	2.53590	+	2.58819i	0.114560	+	0.116923i
$491$		−	13.0053i		−	0.586922i	−0.955971	−	0.293461i	$-0.905193\pi$
$491$		−	13.0053i		−	0.586922i	0.955971	−	0.293461i	$-0.0948071\pi$
$492$		0			0
$493$			4.89898i			0.220639i
$494$		−	1.66441i		−	0.0748853i
$495$		0			0
$496$		−	16.4901i		−	0.740427i
$497$	−36.9282	+	15.0759i	−1.65646	+	0.676245i
$498$		0			0
$499$	−17.6077			−0.788229			−0.394114	−	0.919061i	$-0.628949\pi$
$499$	−17.6077			−0.788229			−0.394114	+	0.919061i	$0.628949\pi$
$500$	1.73205			0.0774597
$501$		0			0
$502$			5.85993i			0.261541i
$503$	6.92820			0.308913			0.154457	−	0.988000i	$-0.450637\pi$
$503$	6.92820			0.308913			0.154457	+	0.988000i	$0.450637\pi$
$504$		0			0
$505$	10.3923			0.462451
$506$		−	0.277401i		−	0.0123320i
$507$		0			0
$508$	5.07180			0.225025
$509$	13.6077			0.603150			0.301575	−	0.953442i	$-0.402488\pi$
$509$	13.6077			0.603150			0.301575	+	0.953442i	$0.402488\pi$
$510$		0			0
$511$	4.39230	−	1.79315i	0.194304	−	0.0793243i
$512$		−	22.1841i		−	0.980408i
$513$		0			0
$514$		−	8.00481i		−	0.353077i
$515$		−	13.3843i		−	0.589781i
$516$		0			0
$517$		−	3.58630i		−	0.157725i
$518$	−1.85641	+	0.757875i	−0.0815658	+	0.0332991i
$519$		0			0
$520$	3.46410			0.151911
$521$	10.3923			0.455295			0.227648	−	0.973744i	$-0.426897\pi$
$521$	10.3923			0.455295			0.227648	+	0.973744i	$0.426897\pi$
$522$		0			0
$523$			40.1528i			1.75576i	0.478882	+	0.877879i	$0.341042\pi$
$523$			40.1528i			1.75576i	−0.478882	+	0.877879i	$0.658958\pi$
$524$	4.39230			0.191879
$525$		0			0
$526$	6.19615			0.270165
$527$			23.1822i			1.00983i
$528$		0			0
$529$	21.0000			0.913043
$530$	5.26795			0.228825
$531$		0			0
$532$	7.60770	−	3.10583i	0.329835	−	0.134655i
$533$			18.6350i			0.807170i
$534$		0			0
$535$			13.2827i			0.574262i
$536$			21.1117i			0.911885i
$537$		0			0
$538$			4.41851i			0.190495i
$539$	−1.85641	−	1.89469i	−0.0799611	−	0.0816099i
$540$		0			0
$541$	−11.8564			−0.509747			−0.254873	−	0.966974i	$-0.582034\pi$
$541$	−11.8564			−0.509747			−0.254873	+	0.966974i	$0.582034\pi$
$542$	13.6077			0.584501
$543$		0			0
$544$			17.8028i			0.763287i
$545$	8.00000			0.342682
$546$		0			0
$547$	−29.8564			−1.27657			−0.638284	−	0.769801i	$-0.720355\pi$
$547$	−29.8564			−1.27657			−0.638284	+	0.769801i	$0.720355\pi$
$548$		−	37.2228i		−	1.59008i
$549$		0			0
$550$	0.196152			0.00836397
$551$	−2.53590			−0.108033
$552$		0			0
$553$	−10.9282	−	26.7685i	−0.464714	−	1.13831i
$554$			11.3880i			0.483831i
$555$		0			0
$556$			28.5617i			1.21128i
$557$		−	28.6632i		−	1.21450i	−0.794511	−	0.607250i	$-0.792273\pi$
$557$		−	28.6632i		−	1.21450i	0.794511	−	0.607250i	$-0.207727\pi$
$558$		0			0
$559$		−	8.83701i		−	0.373766i
$560$	2.46410	+	6.03579i	0.104127	+	0.255059i
$561$		0			0
$562$	1.80385			0.0760907
$563$	−30.9282			−1.30347			−0.651734	−	0.758447i	$-0.725958\pi$
$563$	−30.9282			−1.30347			−0.651734	+	0.758447i	$0.725958\pi$
$564$		0			0
$565$		−	9.41902i		−	0.396261i
$566$	−12.6795			−0.532959
$567$		0			0
$568$	29.1244			1.22203
$569$		−	17.0721i		−	0.715700i	−0.933779	−	0.357850i	$-0.883510\pi$
$569$		−	17.0721i		−	0.715700i	0.933779	−	0.357850i	$-0.116490\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−1.17691			−0.0492093
$573$		0			0
$574$	13.1769	−	5.37945i	0.549994	−	0.224534i
$575$		−	1.41421i		−	0.0589768i
$576$		0			0
$577$			26.2880i			1.09439i	0.837007	+	0.547193i	$0.184304\pi$
$577$			26.2880i			1.09439i	−0.837007	+	0.547193i	$0.815696\pi$
$578$			2.58819i			0.107655i
$579$		0			0
$580$		−	2.44949i		−	0.101710i
$581$	9.46410	+	23.1822i	0.392637	+	0.961761i
$582$		0			0
$583$	−3.85641			−0.159716
$584$	−3.46410			−0.143346
$585$		0			0
$586$		−	5.37945i		−	0.222223i
$587$	15.7128			0.648537			0.324269	−	0.945965i	$-0.394882\pi$
$587$	15.7128			0.648537			0.324269	+	0.945965i	$0.394882\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$			4.89898i			0.201688i
$591$		0			0
$592$	−3.60770			−0.148275
$593$	9.71281			0.398857			0.199429	−	0.979912i	$-0.436091\pi$
$593$	9.71281			0.398857			0.199429	+	0.979912i	$0.436091\pi$
$594$		0			0
$595$	−3.46410	−	8.48528i	−0.142014	−	0.347863i
$596$		−	25.6317i		−	1.04992i
$597$		0			0
$598$		−	1.31268i		−	0.0536794i
$599$			26.1865i			1.06995i	0.844867	+	0.534976i	$0.179679\pi$
$599$			26.1865i			1.06995i	−0.844867	+	0.534976i	$0.820321\pi$
$600$		0			0
$601$		−	19.5959i		−	0.799334i	−0.916660	−	0.399667i	$-0.869126\pi$
$601$		−	19.5959i		−	0.799334i	0.916660	−	0.399667i	$-0.130874\pi$
$602$	−6.24871	+	2.55103i	−0.254678	+	0.103972i
$603$		0			0
$604$	−0.928203			−0.0377681
$605$	10.8564			0.441376
$606$		0			0
$607$		−	1.31268i		−	0.0532799i	−0.999645	−	0.0266400i	$-0.991519\pi$
$607$		−	1.31268i		−	0.0532799i	0.999645	−	0.0266400i	$-0.00848077\pi$
$608$	−9.21539			−0.373733
$609$		0			0
$610$	−6.92820			−0.280515
$611$		−	16.9706i		−	0.686555i
$612$		0			0
$613$	−28.9282			−1.16840			−0.584200	−	0.811610i	$-0.698591\pi$
$613$	−28.9282			−1.16840			−0.584200	+	0.811610i	$0.698591\pi$
$614$	−7.60770			−0.307022
$615$		0			0
$616$	0.732051	+	1.79315i	0.0294952	+	0.0722481i
$617$		−	13.0053i		−	0.523575i	−0.965126	−	0.261787i	$-0.915688\pi$
$617$		−	13.0053i		−	0.523575i	0.965126	−	0.261787i	$-0.0843119\pi$
$618$		0			0
$619$		−	17.4510i		−	0.701416i	−0.936485	−	0.350708i	$-0.885941\pi$
$619$		−	17.4510i		−	0.701416i	0.936485	−	0.350708i	$-0.114059\pi$
$620$		−	11.5911i		−	0.465510i
$621$		0			0
$622$			14.6969i			0.589294i
$623$	−12.9282	−	31.6675i	−0.517958	−	1.26873i
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.32051			0.212650
$627$		0			0
$628$		−	5.37945i		−	0.214664i
$629$	5.07180			0.202226
$630$		0			0
$631$	−24.7846			−0.986660			−0.493330	−	0.869842i	$-0.664220\pi$
$631$	−24.7846			−0.986660			−0.493330	+	0.869842i	$0.664220\pi$
$632$			21.1117i			0.839777i
$633$		0			0
$634$	14.0526			0.558098
$635$	2.92820			0.116202
$636$		0			0
$637$	−8.78461	−	8.96575i	−0.348059	−	0.355236i
$638$		−	0.277401i		−	0.0109824i
$639$		0			0
$640$		−	11.4524i		−	0.452696i
$641$			40.0512i			1.58193i	0.611862	+	0.790965i	$0.290421\pi$
$641$			40.0512i			1.58193i	−0.611862	+	0.790965i	$0.709579\pi$
$642$		0			0
$643$		−	28.0812i		−	1.10741i	−0.832711	−	0.553707i	$-0.813213\pi$
$643$		−	28.0812i		−	1.10741i	0.832711	−	0.553707i	$-0.186787\pi$
$644$	6.00000	−	2.44949i	0.236433	−	0.0965234i
$645$		0			0
$646$	3.21539			0.126508
$647$	−32.7846			−1.28890			−0.644448	−	0.764648i	$-0.722913\pi$
$647$	−32.7846			−1.28890			−0.644448	+	0.764648i	$0.722913\pi$
$648$		0			0
$649$		−	3.58630i		−	0.140775i
$650$	0.928203			0.0364071
$651$		0			0
$652$	−6.92820			−0.271329
$653$			7.90327i			0.309279i	0.987971	+	0.154639i	$0.0494216\pi$
$653$			7.90327i			0.309279i	−0.987971	+	0.154639i	$0.950578\pi$
$654$		0			0
$655$	2.53590			0.0990857
$656$	25.6077			0.999813
$657$		0			0
$658$	−12.0000	+	4.89898i	−0.467809	+	0.190982i
$659$			18.6622i			0.726975i	0.931599	+	0.363488i	$0.118414\pi$
$659$			18.6622i			0.726975i	−0.931599	+	0.363488i	$0.881586\pi$
$660$		0			0
$661$		−	16.0096i		−	0.622702i	−0.950295	−	0.311351i	$-0.899219\pi$
$661$		−	16.0096i		−	0.622702i	0.950295	−	0.311351i	$-0.100781\pi$
$662$			2.90276i			0.112819i
$663$		0			0
$664$		−	18.2832i		−	0.709527i
$665$	4.39230	−	1.79315i	0.170326	−	0.0695354i
$666$		0			0
$667$	−2.00000			−0.0774403
$668$	20.7846			0.804181
$669$		0			0
$670$			5.65685i			0.218543i
$671$	5.07180			0.195795
$672$		0			0
$673$	−23.6077			−0.910010			−0.455005	−	0.890489i	$-0.650362\pi$
$673$	−23.6077			−0.910010			−0.455005	+	0.890489i	$0.650362\pi$
$674$		−	6.41473i		−	0.247086i
$675$		0			0
$676$	16.9474			0.651825
$677$	−41.3205			−1.58808			−0.794038	−	0.607868i	$-0.792025\pi$
$677$	−41.3205			−1.58808			−0.794038	+	0.607868i	$0.792025\pi$
$678$		0			0
$679$	−37.1769	+	15.1774i	−1.42672	+	0.582456i
$680$			6.69213i			0.256631i
$681$		0			0
$682$		−	1.31268i		−	0.0502650i
$683$			14.2437i			0.545019i	0.962153	+	0.272509i	$0.0878536\pi$
$683$			14.2437i			0.545019i	−0.962153	+	0.272509i	$0.912146\pi$
$684$		0			0
$685$		−	21.4906i		−	0.821114i
$686$	−3.80385	+	8.79985i	−0.145232	+	0.335980i
$687$		0			0
$688$	−12.1436			−0.462970
$689$	−18.2487			−0.695221
$690$		0			0
$691$			17.4510i			0.663869i	0.943302	+	0.331934i	$0.107701\pi$
$691$			17.4510i			0.663869i	−0.943302	+	0.331934i	$0.892299\pi$
$692$	−10.3923			−0.395056
$693$		0			0
$694$	−14.5885			−0.553770
$695$			16.4901i			0.625505i
$696$		0			0
$697$	−36.0000			−1.36360
$698$		0			0
$699$		0			0
$700$	1.73205	+	4.24264i	0.0654654	+	0.160357i
$701$			32.5269i			1.22852i	0.789102	+	0.614262i	$0.210546\pi$
$701$			32.5269i			1.22852i	−0.789102	+	0.614262i	$0.789454\pi$
$702$		0			0
$703$			2.62536i			0.0990171i
$704$			0.859411i			0.0323903i
$705$		0			0
$706$		−	15.5291i		−	0.584447i
$707$	10.3923	+	25.4558i	0.390843	+	0.957366i
$708$		0			0
$709$	−45.5692			−1.71139			−0.855694	−	0.517482i	$-0.826869\pi$
$709$	−45.5692			−1.71139			−0.855694	+	0.517482i	$0.826869\pi$
$710$	7.80385			0.292873
$711$		0			0
$712$			24.9754i			0.935992i
$713$	−9.46410			−0.354433
$714$		0			0
$715$	−0.679492			−0.0254116
$716$			32.3238i			1.20800i
$717$		0			0
$718$	−10.4449			−0.389799
$719$	4.39230			0.163805			0.0819027	−	0.996640i	$-0.473900\pi$
$719$	4.39230			0.163805			0.0819027	+	0.996640i	$0.473900\pi$
$720$		0			0
$721$	32.7846	−	13.3843i	1.22096	−	0.498456i
$722$		−	8.17072i		−	0.304083i
$723$		0			0
$724$			20.9086i			0.777062i
$725$		−	1.41421i		−	0.0525226i
$726$		0			0
$727$			19.5959i			0.726772i	0.931639	+	0.363386i	$0.118379\pi$
$727$			19.5959i			0.726772i	−0.931639	+	0.363386i	$0.881621\pi$
$728$	3.46410	+	8.48528i	0.128388	+	0.314485i
$729$		0			0
$730$	−0.928203			−0.0343543
$731$	17.0718			0.631423
$732$		0			0
$733$		−	32.1480i		−	1.18741i	−0.804682	−	0.593706i	$-0.797664\pi$
$733$		−	32.1480i		−	1.18741i	0.804682	−	0.593706i	$-0.202336\pi$
$734$	−11.3205			−0.417848
$735$		0			0
$736$	−7.26795			−0.267900
$737$		−	4.14110i		−	0.152540i
$738$		0			0
$739$	25.0718			0.922281			0.461140	−	0.887327i	$-0.347440\pi$
$739$	25.0718			0.922281			0.461140	+	0.887327i	$0.347440\pi$
$740$	−2.53590			−0.0932215
$741$		0			0
$742$	5.26795	+	12.9038i	0.193392	+	0.473713i
$743$			13.2827i			0.487296i	0.969864	+	0.243648i	$0.0783441\pi$
$743$			13.2827i			0.487296i	−0.969864	+	0.243648i	$0.921656\pi$
$744$		0			0
$745$		−	14.7985i		−	0.542174i
$746$		−	3.66063i		−	0.134025i
$747$		0			0
$748$		−	2.27362i		−	0.0831319i
$749$	−32.5359	+	13.2827i	−1.18884	+	0.485340i
$750$		0			0
$751$	−26.3923			−0.963069			−0.481534	−	0.876427i	$-0.659920\pi$
$751$	−26.3923			−0.963069			−0.481534	+	0.876427i	$0.659920\pi$
$752$	−23.3205			−0.850411
$753$		0			0
$754$		−	1.31268i		−	0.0478049i
$755$	−0.535898			−0.0195033
$756$		0			0
$757$	−17.1769			−0.624306			−0.312153	−	0.950032i	$-0.601050\pi$
$757$	−17.1769			−0.624306			−0.312153	+	0.950032i	$0.601050\pi$
$758$		−	5.93426i		−	0.215542i
$759$		0			0
$760$	−3.46410			−0.125656
$761$	35.5692			1.28938			0.644692	−	0.764443i	$-0.276986\pi$
$761$	35.5692			1.28938			0.644692	+	0.764443i	$0.276986\pi$
$762$		0			0
$763$	8.00000	+	19.5959i	0.289619	+	0.709420i
$764$		−	22.5259i		−	0.814958i
$765$		0			0
$766$		−	16.0096i		−	0.578451i
$767$		−	16.9706i		−	0.612772i
$768$		0			0
$769$			39.1918i			1.41329i	0.707566	+	0.706647i	$0.249793\pi$
$769$			39.1918i			1.41329i	−0.707566	+	0.706647i	$0.750207\pi$
$770$	0.196152	+	0.480473i	0.00706884	+	0.0173151i
$771$		0			0
$772$	42.2487			1.52056
$773$	−33.7128			−1.21257			−0.606283	−	0.795249i	$-0.707340\pi$
$773$	−33.7128			−1.21257			−0.606283	+	0.795249i	$0.707340\pi$
$774$		0			0
$775$		−	6.69213i		−	0.240388i
$776$	29.3205			1.05254
$777$		0			0
$778$	15.6603			0.561447
$779$		−	18.6350i		−	0.667667i
$780$		0			0
$781$	−5.71281			−0.204421
$782$	2.53590			0.0906835
$783$		0			0
$784$	−12.3205	+	12.0716i	−0.440018	+	0.431128i
$785$		−	3.10583i		−	0.110852i
$786$		0			0
$787$		−	36.5665i		−	1.30345i	−0.758454	−	0.651727i	$-0.774045\pi$
$787$		−	36.5665i		−	1.30345i	0.758454	−	0.651727i	$-0.225955\pi$
$788$		−	14.0406i		−	0.500176i
$789$		0			0
$790$			5.65685i			0.201262i
$791$	23.0718	−	9.41902i	0.820339	−	0.334902i
$792$		0			0
$793$	24.0000			0.852265
$794$	6.67949			0.237046
$795$		0			0
$796$		−	26.2880i		−	0.931755i
$797$	−54.4974			−1.93040			−0.965199	−	0.261517i	$-0.915777\pi$
$797$	−54.4974			−1.93040			−0.965199	+	0.261517i	$0.915777\pi$
$798$		0			0
$799$	32.7846			1.15984
$800$		−	5.13922i		−	0.181699i
$801$		0			0
$802$	−10.8756			−0.384032
$803$	0.679492			0.0239787
$804$		0			0
$805$	3.46410	−	1.41421i	0.122094	−	0.0498445i
$806$		−	6.21166i		−	0.218796i
$807$		0			0
$808$		−	20.0764i		−	0.706285i
$809$			11.9700i			0.420844i	0.977611	+	0.210422i	$0.0674839\pi$
$809$			11.9700i			0.420844i	−0.977611	+	0.210422i	$0.932516\pi$
$810$		0			0
$811$		−	0.480473i		−	0.0168717i	−0.999964	−	0.00843585i	$-0.997315\pi$
$811$		−	0.480473i		−	0.0168717i	0.999964	−	0.00843585i	$-0.00268525\pi$
$812$	6.00000	−	2.44949i	0.210559	−	0.0859602i
$813$		0			0
$814$	−0.287187			−0.0100659
$815$	−4.00000			−0.140114
$816$		0			0
$817$			8.83701i			0.309168i
$818$	16.3923			0.573143
$819$		0			0
$820$	18.0000			0.628587
$821$			11.0091i			0.384220i	0.981373	+	0.192110i	$0.0615331\pi$
$821$			11.0091i			0.384220i	−0.981373	+	0.192110i	$0.938467\pi$
$822$		0			0
$823$	16.7846			0.585075			0.292537	−	0.956254i	$-0.405500\pi$
$823$	16.7846			0.585075			0.292537	+	0.956254i	$0.405500\pi$
$824$	−25.8564			−0.900751
$825$		0			0
$826$	−12.0000	+	4.89898i	−0.417533	+	0.170457i
$827$		−	21.9711i		−	0.764009i	−0.924160	−	0.382005i	$-0.875234\pi$
$827$		−	21.9711i		−	0.764009i	0.924160	−	0.382005i	$-0.124766\pi$
$828$		0			0
$829$			5.85993i			0.203524i	0.994809	+	0.101762i	$0.0324480\pi$
$829$			5.85993i			0.203524i	−0.994809	+	0.101762i	$0.967552\pi$
$830$		−	4.89898i		−	0.170046i
$831$		0			0
$832$			4.06678i			0.140990i
$833$	17.3205	−	16.9706i	0.600120	−	0.587995i
$834$		0			0
$835$	12.0000			0.415277
$836$	1.17691			0.0407044
$837$		0			0
$838$			5.25071i			0.181383i
$839$	6.92820			0.239188			0.119594	−	0.992823i	$-0.461841\pi$
$839$	6.92820			0.239188			0.119594	+	0.992823i	$0.461841\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$		−	0.0743295i		−	0.00256156i
$843$		0			0
$844$	−4.14359			−0.142628
$845$	9.78461			0.336601
$846$		0			0
$847$	10.8564	+	26.5927i	0.373031	+	0.913734i
$848$			25.0769i			0.861145i
$849$		0			0
$850$			1.79315i			0.0615046i
$851$			2.07055i			0.0709776i
$852$		0			0
$853$			33.4607i			1.14567i	0.819670	+	0.572835i	$0.194157\pi$
$853$			33.4607i			1.14567i	−0.819670	+	0.572835i	$0.805843\pi$
$854$	−6.92820	−	16.9706i	−0.237078	−	0.580721i
$855$		0			0
$856$	25.6603			0.877049
$857$	9.21539			0.314792			0.157396	−	0.987536i	$-0.449690\pi$
$857$	9.21539			0.314792			0.157396	+	0.987536i	$0.449690\pi$
$858$		0			0
$859$			22.3500i			0.762573i	0.924457	+	0.381286i	$0.124519\pi$
$859$			22.3500i			0.762573i	−0.924457	+	0.381286i	$0.875481\pi$
$860$	−8.53590			−0.291072
$861$		0			0
$862$	−3.51666			−0.119778
$863$			5.75839i			0.196018i	0.995186	+	0.0980089i	$0.0312474\pi$
$863$			5.75839i			0.196018i	−0.995186	+	0.0980089i	$0.968753\pi$
$864$		0			0
$865$	−6.00000			−0.204006
$866$	0.248711			0.00845155
$867$		0			0
$868$	28.3923	−	11.5911i	0.963698	−	0.393428i
$869$		−	4.14110i		−	0.140477i
$870$		0			0
$871$		−	19.5959i		−	0.663982i
$872$		−	15.4548i		−	0.523366i
$873$		0			0
$874$			1.31268i			0.0444020i
$875$	1.00000	+	2.44949i	0.0338062	+	0.0828079i
$876$		0			0
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	4.64102			0.156627
$879$		0			0
$880$			0.933740i			0.0314764i
$881$	50.7846			1.71098			0.855488	−	0.517822i	$-0.173257\pi$
$881$	50.7846			1.71098			0.855488	+	0.517822i	$0.173257\pi$
$882$		0			0
$883$	12.1436			0.408664			0.204332	−	0.978902i	$-0.434498\pi$
$883$	12.1436			0.408664			0.204332	+	0.978902i	$0.434498\pi$
$884$		−	10.7589i		−	0.361861i
$885$		0			0
$886$	8.05256			0.270531
$887$	18.2487			0.612732			0.306366	−	0.951914i	$-0.400887\pi$
$887$	18.2487			0.612732			0.306366	+	0.951914i	$0.400887\pi$
$888$		0			0
$889$	2.92820	+	7.17260i	0.0982088	+	0.240561i
$890$			6.69213i			0.224321i
$891$		0			0
$892$			8.48528i			0.284108i
$893$			16.9706i			0.567898i
$894$		0			0
$895$			18.6622i			0.623808i
$896$	28.0526	−	11.4524i	0.937170	−	0.382598i
$897$		0			0
$898$	−6.48334			−0.216352
$899$	−9.46410			−0.315645
$900$		0			0
$901$		−	35.2538i		−	1.17447i
$902$	2.03848			0.0678738
$903$		0			0
$904$	−18.1962			−0.605195
$905$			12.0716i			0.401273i
$906$		0			0
$907$	10.7846			0.358097			0.179049	−	0.983840i	$-0.442698\pi$
$907$	10.7846			0.358097			0.179049	+	0.983840i	$0.442698\pi$
$908$	19.6077			0.650704
$909$		0			0
$910$	0.928203	+	2.27362i	0.0307696	+	0.0753699i
$911$		−	10.7317i		−	0.355557i	−0.984071	−	0.177779i	$-0.943109\pi$
$911$		−	10.7317i		−	0.355557i	0.984071	−	0.177779i	$-0.0568911\pi$
$912$		0			0
$913$			3.58630i			0.118689i
$914$		−	13.5873i		−	0.449429i
$915$		0			0
$916$			25.4558i			0.841085i
$917$	2.53590	+	6.21166i	0.0837427	+	0.205127i
$918$		0			0
$919$	34.1051			1.12502			0.562512	−	0.826789i	$-0.309835\pi$
$919$	34.1051			1.12502			0.562512	+	0.826789i	$0.309835\pi$
$920$	−2.73205			−0.0900730
$921$		0			0
$922$		−	4.06678i		−	0.133932i
$923$	−27.0333			−0.889813
$924$		0			0
$925$	−1.46410			−0.0481394
$926$		−	4.14110i		−	0.136085i
$927$		0			0
$928$	−7.26795			−0.238582
$929$	−36.9282			−1.21158			−0.605788	−	0.795626i	$-0.707142\pi$
$929$	−36.9282			−1.21158			−0.605788	+	0.795626i	$0.707142\pi$
$930$		0			0
$931$	8.78461	+	8.96575i	0.287904	+	0.293841i
$932$			6.86800i			0.224969i
$933$		0			0
$934$		−	14.6969i		−	0.480899i
$935$		−	1.31268i		−	0.0429291i
$936$		0			0
$937$			10.2784i			0.335782i	0.985806	+	0.167891i	$0.0536956\pi$
$937$			10.2784i			0.335782i	−0.985806	+	0.167891i	$0.946304\pi$
$938$	−13.8564	+	5.65685i	−0.452428	+	0.184703i
$939$		0			0
$940$	−16.3923			−0.534658
$941$	12.9282			0.421447			0.210724	−	0.977546i	$-0.432418\pi$
$941$	12.9282			0.421447			0.210724	+	0.977546i	$0.432418\pi$
$942$		0			0
$943$		−	14.6969i		−	0.478598i
$944$	−23.3205			−0.759018
$945$		0			0
$946$	−0.966679			−0.0314294
$947$		−	39.2934i		−	1.27686i	−0.769679	−	0.638432i	$-0.779584\pi$
$947$		−	39.2934i		−	1.27686i	0.769679	−	0.638432i	$-0.220416\pi$
$948$		0			0
$949$	3.21539			0.104376
$950$	−0.928203			−0.0301149
$951$		0			0
$952$	−16.3923	+	6.69213i	−0.531278	+	0.216893i
$953$		−	21.4906i		−	0.696149i	−0.937467	−	0.348074i	$-0.886836\pi$
$953$		−	21.4906i		−	0.696149i	0.937467	−	0.348074i	$-0.113164\pi$
$954$		0			0
$955$		−	13.0053i		−	0.420842i
$956$			6.86800i			0.222127i
$957$		0			0
$958$		−	7.52433i		−	0.243100i
$959$	52.6410	−	21.4906i	1.69987	−	0.693968i
$960$		0			0
$961$	−13.7846			−0.444665
$962$	−1.35898			−0.0438154
$963$		0			0
$964$		−	2.27362i		−	0.0732285i
$965$	24.3923			0.785216
$966$		0			0
$967$	28.7846			0.925651			0.462825	−	0.886450i	$-0.346836\pi$
$967$	28.7846			0.925651			0.462825	+	0.886450i	$0.346836\pi$
$968$		−	20.9730i		−	0.674097i
$969$		0			0
$970$	7.85641			0.252254
$971$	−18.9282			−0.607435			−0.303717	−	0.952762i	$-0.598228\pi$
$971$	−18.9282			−0.607435			−0.303717	+	0.952762i	$0.598228\pi$
$972$		0			0
$973$	−40.3923	+	16.4901i	−1.29492	+	0.528648i
$974$			6.13733i			0.196653i
$975$		0			0
$976$		−	32.9802i		−	1.05567i
$977$		−	42.3992i		−	1.35647i	−0.734845	−	0.678235i	$-0.762745\pi$
$977$		−	42.3992i		−	1.35647i	0.734845	−	0.678235i	$-0.237255\pi$
$978$		0			0
$979$		−	4.89898i		−	0.156572i
$980$	−8.66025	+	8.48528i	−0.276642	+	0.271052i
$981$		0			0
$982$	−6.73205			−0.214828
$983$	9.46410			0.301858			0.150929	−	0.988545i	$-0.451774\pi$
$983$	9.46410			0.301858			0.150929	+	0.988545i	$0.451774\pi$
$984$		0			0
$985$		−	8.10634i		−	0.258290i
$986$	2.53590			0.0807595
$987$		0			0
$988$	5.56922			0.177180
$989$			6.96953i			0.221618i
$990$		0			0
$991$	13.3205			0.423140			0.211570	−	0.977363i	$-0.432142\pi$
$991$	13.3205			0.423140			0.211570	+	0.977363i	$0.432142\pi$
$992$	−34.3923			−1.09196
$993$		0			0
$994$	7.80385	+	19.1154i	0.247523	+	0.606305i
$995$		−	15.1774i		−	0.481156i
$996$		0			0
$997$			59.2682i			1.87704i	0.345220	+	0.938522i	$0.387804\pi$
$997$			59.2682i			1.87704i	−0.345220	+	0.938522i	$0.612196\pi$
$998$			9.11441i			0.288512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.b.b.251.2	yes	4
3.2	odd	2		315.2.b.a.251.3	yes	4
4.3	odd	2		5040.2.f.c.881.1		4
5.2	odd	4		1575.2.g.a.1574.6		8
5.3	odd	4		1575.2.g.a.1574.3		8
5.4	even	2		1575.2.b.c.251.3		4
7.6	odd	2		315.2.b.a.251.2	✓	4
12.11	even	2		5040.2.f.a.881.2		4
15.2	even	4		1575.2.g.c.1574.4		8
15.8	even	4		1575.2.g.c.1574.5		8
15.14	odd	2		1575.2.b.b.251.2		4
21.20	even	2	inner	315.2.b.b.251.3	yes	4
28.27	even	2		5040.2.f.a.881.3		4
35.13	even	4		1575.2.g.c.1574.3		8
35.27	even	4		1575.2.g.c.1574.6		8
35.34	odd	2		1575.2.b.b.251.3		4
84.83	odd	2		5040.2.f.c.881.4		4
105.62	odd	4		1575.2.g.a.1574.4		8
105.83	odd	4		1575.2.g.a.1574.5		8
105.104	even	2		1575.2.b.c.251.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.b.a.251.2	✓	4	7.6	odd	2
315.2.b.a.251.3	yes	4	3.2	odd	2
315.2.b.b.251.2	yes	4	1.1	even	1	trivial
315.2.b.b.251.3	yes	4	21.20	even	2	inner
1575.2.b.b.251.2		4	15.14	odd	2
1575.2.b.b.251.3		4	35.34	odd	2
1575.2.b.c.251.2		4	105.104	even	2
1575.2.b.c.251.3		4	5.4	even	2
1575.2.g.a.1574.3		8	5.3	odd	4
1575.2.g.a.1574.4		8	105.62	odd	4
1575.2.g.a.1574.5		8	105.83	odd	4
1575.2.g.a.1574.6		8	5.2	odd	4
1575.2.g.c.1574.3		8	35.13	even	4
1575.2.g.c.1574.4		8	15.2	even	4
1575.2.g.c.1574.5		8	15.8	even	4
1575.2.g.c.1574.6		8	35.27	even	4
5040.2.f.a.881.2		4	12.11	even	2
5040.2.f.a.881.3		4	28.27	even	2
5040.2.f.c.881.1		4	4.3	odd	2
5040.2.f.c.881.4		4	84.83	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.517638i q^{2} +1.73205 q^{4} +1.00000 q^{5} +(1.00000 + 2.44949i) q^{7} -1.93185i q^{8} +O(q^{10})\)	\(q-0.517638i q^{2} +1.73205 q^{4} +1.00000 q^{5} +(1.00000 + 2.44949i) q^{7} -1.93185i q^{8} -0.517638i q^{10} +0.378937i q^{11} +1.79315i q^{13} +(1.26795 - 0.517638i) q^{14} +2.46410 q^{16} -3.46410 q^{17} -1.79315i q^{19} +1.73205 q^{20} +0.196152 q^{22} -1.41421i q^{23} +1.00000 q^{25} +0.928203 q^{26} +(1.73205 + 4.24264i) q^{28} -1.41421i q^{29} -6.69213i q^{31} -5.13922i q^{32} +1.79315i q^{34} +(1.00000 + 2.44949i) q^{35} -1.46410 q^{37} -0.928203 q^{38} -1.93185i q^{40} +10.3923 q^{41} -4.92820 q^{43} +0.656339i q^{44} -0.732051 q^{46} -9.46410 q^{47} +(-5.00000 + 4.89898i) q^{49} -0.517638i q^{50} +3.10583i q^{52} +10.1769i q^{53} +0.378937i q^{55} +(4.73205 - 1.93185i) q^{56} -0.732051 q^{58} -9.46410 q^{59} -13.3843i q^{61} -3.46410 q^{62} +2.26795 q^{64} +1.79315i q^{65} -10.9282 q^{67} -6.00000 q^{68} +(1.26795 - 0.517638i) q^{70} +15.0759i q^{71} -1.79315i q^{73} +0.757875i q^{74} -3.10583i q^{76} +(-0.928203 + 0.378937i) q^{77} -10.9282 q^{79} +2.46410 q^{80} -5.37945i q^{82} +9.46410 q^{83} -3.46410 q^{85} +2.55103i q^{86} +0.732051 q^{88} -12.9282 q^{89} +(-4.39230 + 1.79315i) q^{91} -2.44949i q^{92} +4.89898i q^{94} -1.79315i q^{95} +15.1774i q^{97} +(2.53590 + 2.58819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 4 * q + 4 * q^5 + 4 * q^7	\( 4 q + 4 q^{5} + 4 q^{7} + 12 q^{14} - 4 q^{16} - 20 q^{22} + 4 q^{25} - 24 q^{26} + 4 q^{35} + 8 q^{37} + 24 q^{38} + 8 q^{43} + 4 q^{46} - 24 q^{47} - 20 q^{49} + 12 q^{56} + 4 q^{58} - 24 q^{59} + 16 q^{64} - 16 q^{67} - 24 q^{68} + 12 q^{70} + 24 q^{77} - 16 q^{79} - 4 q^{80} + 24 q^{83} - 4 q^{88} - 24 q^{89} + 24 q^{91} + 24 q^{98}+O(q^{100}) \) 4 * q + 4 * q^5 + 4 * q^7 + 12 * q^14 - 4 * q^16 - 20 * q^22 + 4 * q^25 - 24 * q^26 + 4 * q^35 + 8 * q^37 + 24 * q^38 + 8 * q^43 + 4 * q^46 - 24 * q^47 - 20 * q^49 + 12 * q^56 + 4 * q^58 - 24 * q^59 + 16 * q^64 - 16 * q^67 - 24 * q^68 + 12 * q^70 + 24 * q^77 - 16 * q^79 - 4 * q^80 + 24 * q^83 - 4 * q^88 - 24 * q^89 + 24 * q^91 + 24 * q^98

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