LMFDB - Embedded newform 1305.2.f.i.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1305,2,Mod(289,1305)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1305.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,-4,-3,0,0,-12,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.3
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1305.289
Dual form			1305.2.f.i.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000 q^{4} +(0.280776 - 2.21837i) q^{5} +3.46410i q^{7} -3.00000 q^{8} +(0.280776 - 2.21837i) q^{10} +0.972638i q^{11} -4.43674i q^{13} +3.46410i q^{14} -1.00000 q^{16} -2.00000 q^{17} -3.46410i q^{19} +(-0.280776 + 2.21837i) q^{20} +0.972638i q^{22} -3.46410i q^{23} +(-4.84233 - 1.24573i) q^{25} -4.43674i q^{26} -3.46410i q^{28} +(-4.12311 - 3.46410i) q^{29} -7.90084i q^{31} +5.00000 q^{32} -2.00000 q^{34} +(7.68466 + 0.972638i) q^{35} -7.12311 q^{37} -3.46410i q^{38} +(-0.842329 + 6.65511i) q^{40} +8.87348i q^{41} -5.43845 q^{43} -0.972638i q^{44} -3.46410i q^{46} -11.6847 q^{47} -5.00000 q^{49} +(-4.84233 - 1.24573i) q^{50} +4.43674i q^{52} -4.43674i q^{53} +(2.15767 + 0.273094i) q^{55} -10.3923i q^{56} +(-4.12311 - 3.46410i) q^{58} +1.12311 q^{59} +1.94528i q^{61} -7.90084i q^{62} +7.00000 q^{64} +(-9.84233 - 1.24573i) q^{65} -12.3376i q^{67} +2.00000 q^{68} +(7.68466 + 0.972638i) q^{70} +2.24621 q^{71} +7.12311 q^{73} -7.12311 q^{74} +3.46410i q^{76} -3.36932 q^{77} +14.8290i q^{79} +(-0.280776 + 2.21837i) q^{80} +8.87348i q^{82} -10.3923i q^{83} +(-0.561553 + 4.43674i) q^{85} -5.43845 q^{86} -2.91791i q^{88} +8.87348i q^{89} +15.3693 q^{91} +3.46410i q^{92} -11.6847 q^{94} +(-7.68466 - 0.972638i) q^{95} -8.24621 q^{97} -5.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{4} - 3 q^{5} - 12 q^{8} - 3 q^{10} - 4 q^{16} - 8 q^{17} + 3 q^{20} - 7 q^{25} + 20 q^{32} - 8 q^{34} + 6 q^{35} - 12 q^{37} + 9 q^{40} - 30 q^{43} - 22 q^{47} - 20 q^{49} - 7 q^{50}+ \cdots - 20 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 - 12 * q^8 - 3 * q^10 - 4 * q^16 - 8 * q^17 + 3 * q^20 - 7 * q^25 + 20 * q^32 - 8 * q^34 + 6 * q^35 - 12 * q^37 + 9 * q^40 - 30 * q^43 - 22 * q^47 - 20 * q^49 - 7 * q^50 + 21 * q^55 - 12 * q^59 + 28 * q^64 - 27 * q^65 + 8 * q^68 + 6 * q^70 - 24 * q^71 + 12 * q^73 - 12 * q^74 + 36 * q^77 + 3 * q^80 + 6 * q^85 - 30 * q^86 + 12 * q^91 - 22 * q^94 - 6 * q^95 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.280776	−	2.21837i	0.125567	−	0.992085i
$5$	0.280776	−	2.21837i	0.125567	−	0.992085i
$6$		0			0
$7$			3.46410i			1.30931i	0.755929	+	0.654654i	$0.227186\pi$
$7$			3.46410i			1.30931i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	0.280776	−	2.21837i	0.0887893	−	0.701510i
$11$			0.972638i			0.293261i	0.989191	+	0.146631i	$0.0468429\pi$
$11$			0.972638i			0.293261i	−0.989191	+	0.146631i	$0.953157\pi$
$12$		0			0
$13$		−	4.43674i		−	1.23053i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$		−	4.43674i		−	1.23053i	0.788320	−	0.615265i	$-0.210951\pi$
$14$			3.46410i			0.925820i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−0.280776	+	2.21837i	−0.0627835	+	0.496043i
$21$		0			0
$22$			0.972638i			0.207367i
$23$		−	3.46410i		−	0.722315i	−0.932505	−	0.361158i	$-0.882382\pi$
$23$		−	3.46410i		−	0.722315i	0.932505	−	0.361158i	$-0.117618\pi$
$24$		0			0
$25$	−4.84233	−	1.24573i	−0.968466	−	0.249146i
$26$		−	4.43674i		−	0.870116i
$27$		0			0
$28$		−	3.46410i		−	0.654654i
$29$	−4.12311	−	3.46410i	−0.765641	−	0.643268i
$29$	−4.12311	−	3.46410i	−0.765641	−	0.643268i
$30$		0			0
$31$		−	7.90084i		−	1.41903i	−0.704689	−	0.709516i	$-0.748913\pi$
$31$		−	7.90084i		−	1.41903i	0.704689	−	0.709516i	$-0.251087\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−2.00000			−0.342997
$35$	7.68466	+	0.972638i	1.29894	+	0.164406i
$36$		0			0
$37$	−7.12311			−1.17103			−0.585516	−	0.810661i	$-0.699108\pi$
$37$	−7.12311			−1.17103			−0.585516	+	0.810661i	$0.699108\pi$
$38$		−	3.46410i		−	0.561951i
$39$		0			0
$40$	−0.842329	+	6.65511i	−0.133184	+	1.05227i
$41$			8.87348i			1.38580i	0.721031	+	0.692902i	$0.243668\pi$
$41$			8.87348i			1.38580i	−0.721031	+	0.692902i	$0.756332\pi$
$42$		0			0
$43$	−5.43845			−0.829355			−0.414678	−	0.909968i	$-0.636106\pi$
$43$	−5.43845			−0.829355			−0.414678	+	0.909968i	$0.636106\pi$
$44$		−	0.972638i		−	0.146631i
$45$		0			0
$46$		−	3.46410i		−	0.510754i
$47$	−11.6847			−1.70438			−0.852191	−	0.523230i	$-0.824727\pi$
$47$	−11.6847			−1.70438			−0.852191	+	0.523230i	$0.824727\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$	−4.84233	−	1.24573i	−0.684809	−	0.176173i
$51$		0			0
$52$			4.43674i			0.615265i
$53$		−	4.43674i		−	0.609433i	−0.952443	−	0.304717i	$-0.901438\pi$
$53$		−	4.43674i		−	0.609433i	0.952443	−	0.304717i	$-0.0985617\pi$
$54$		0			0
$55$	2.15767	+	0.273094i	0.290940	+	0.0368240i
$56$		−	10.3923i		−	1.38873i
$57$		0			0
$58$	−4.12311	−	3.46410i	−0.541390	−	0.454859i
$59$	1.12311			0.146216			0.0731079	−	0.997324i	$-0.476708\pi$
$59$	1.12311			0.146216			0.0731079	+	0.997324i	$0.476708\pi$
$60$		0			0
$61$			1.94528i			0.249067i	0.992215	+	0.124534i	$0.0397434\pi$
$61$			1.94528i			0.249067i	−0.992215	+	0.124534i	$0.960257\pi$
$62$		−	7.90084i		−	1.00341i
$63$		0			0
$64$	7.00000			0.875000
$65$	−9.84233	−	1.24573i	−1.22079	−	0.154514i
$66$		0			0
$67$		−	12.3376i		−	1.50728i	−0.657290	−	0.753638i	$-0.728297\pi$
$67$		−	12.3376i		−	1.50728i	0.657290	−	0.753638i	$-0.271703\pi$
$68$	2.00000			0.242536
$69$		0			0
$70$	7.68466	+	0.972638i	0.918492	+	0.116252i
$71$	2.24621			0.266576			0.133288	−	0.991077i	$-0.457446\pi$
$71$	2.24621			0.266576			0.133288	+	0.991077i	$0.457446\pi$
$72$		0			0
$73$	7.12311			0.833696			0.416848	−	0.908976i	$-0.363135\pi$
$73$	7.12311			0.833696			0.416848	+	0.908976i	$0.363135\pi$
$74$	−7.12311			−0.828044
$75$		0			0
$76$			3.46410i			0.397360i
$77$	−3.36932			−0.383969
$78$		0			0
$79$			14.8290i			1.66840i	0.551464	+	0.834199i	$0.314070\pi$
$79$			14.8290i			1.66840i	−0.551464	+	0.834199i	$0.685930\pi$
$80$	−0.280776	+	2.21837i	−0.0313918	+	0.248021i
$81$		0			0
$82$			8.87348i			0.979912i
$83$		−	10.3923i		−	1.14070i	−0.821401	−	0.570352i	$-0.806807\pi$
$83$		−	10.3923i		−	1.14070i	0.821401	−	0.570352i	$-0.193193\pi$
$84$		0			0
$85$	−0.561553	+	4.43674i	−0.0609090	+	0.481232i
$86$	−5.43845			−0.586443
$87$		0			0
$88$		−	2.91791i		−	0.311051i
$89$			8.87348i			0.940587i	0.882510	+	0.470293i	$0.155852\pi$
$89$			8.87348i			0.940587i	−0.882510	+	0.470293i	$0.844148\pi$
$90$		0			0
$91$	15.3693			1.61114
$92$			3.46410i			0.361158i
$93$		0			0
$94$	−11.6847			−1.20518
$95$	−7.68466	−	0.972638i	−0.788429	−	0.0997906i
$96$		0			0
$97$	−8.24621			−0.837276			−0.418638	−	0.908153i	$-0.637492\pi$
$97$	−8.24621			−0.837276			−0.418638	+	0.908153i	$0.637492\pi$
$98$	−5.00000			−0.505076
$99$		0			0
$100$	4.84233	+	1.24573i	0.484233	+	0.124573i
$101$			6.92820i			0.689382i	0.938716	+	0.344691i	$0.112016\pi$
$101$			6.92820i			0.689382i	−0.938716	+	0.344691i	$0.887984\pi$
$102$		0			0
$103$		−	1.51883i		−	0.149654i	−0.997197	−	0.0748272i	$-0.976159\pi$
$103$		−	1.51883i		−	0.149654i	0.997197	−	0.0748272i	$-0.0238405\pi$
$104$			13.3102i			1.30517i
$105$		0			0
$106$		−	4.43674i		−	0.430934i
$107$		−	14.2829i		−	1.38078i	−0.723439	−	0.690388i	$-0.757440\pi$
$107$		−	14.2829i		−	1.38078i	0.723439	−	0.690388i	$-0.242560\pi$
$108$		0			0
$109$	−5.68466			−0.544492			−0.272246	−	0.962228i	$-0.587766\pi$
$109$	−5.68466			−0.544492			−0.272246	+	0.962228i	$0.587766\pi$
$110$	2.15767	+	0.273094i	0.205726	+	0.0260385i
$111$		0			0
$112$		−	3.46410i		−	0.327327i
$113$	5.36932			0.505103			0.252551	−	0.967583i	$-0.418730\pi$
$113$	5.36932			0.505103			0.252551	+	0.967583i	$0.418730\pi$
$114$		0			0
$115$	−7.68466	−	0.972638i	−0.716598	−	0.0906990i
$116$	4.12311	+	3.46410i	0.382821	+	0.321634i
$117$		0			0
$118$	1.12311			0.103390
$119$		−	6.92820i		−	0.635107i
$120$		0			0
$121$	10.0540			0.913998
$122$			1.94528i			0.176117i
$123$		0			0
$124$			7.90084i			0.709516i
$125$	−4.12311	+	10.3923i	−0.368782	+	0.929516i
$126$		0			0
$127$	2.24621			0.199319			0.0996595	−	0.995022i	$-0.468225\pi$
$127$	2.24621			0.199319			0.0996595	+	0.995022i	$0.468225\pi$
$128$	−3.00000			−0.265165
$129$		0			0
$130$	−9.84233	−	1.24573i	−0.863229	−	0.109258i
$131$		−	14.2829i		−	1.24790i	−0.781465	−	0.623949i	$-0.785527\pi$
$131$		−	14.2829i		−	1.24790i	0.781465	−	0.623949i	$-0.214473\pi$
$132$		0			0
$133$	12.0000			1.04053
$134$		−	12.3376i		−	1.06580i
$135$		0			0
$136$	6.00000			0.514496
$137$	13.3693			1.14222			0.571109	−	0.820874i	$-0.306513\pi$
$137$	13.3693			1.14222			0.571109	+	0.820874i	$0.306513\pi$
$138$		0			0
$139$	19.3693			1.64288			0.821442	−	0.570292i	$-0.193170\pi$
$139$	19.3693			1.64288			0.821442	+	0.570292i	$0.193170\pi$
$140$	−7.68466	−	0.972638i	−0.649472	−	0.0822029i
$141$		0			0
$142$	2.24621			0.188498
$143$	4.31534			0.360867
$144$		0			0
$145$	−8.84233	+	8.17394i	−0.734315	+	0.678808i
$146$	7.12311			0.589512
$147$		0			0
$148$	7.12311			0.585516
$149$	13.6847			1.12109			0.560545	−	0.828124i	$-0.310592\pi$
$149$	13.6847			1.12109			0.560545	+	0.828124i	$0.310592\pi$
$150$		0			0
$151$	15.3693			1.25074			0.625369	−	0.780329i	$-0.284949\pi$
$151$	15.3693			1.25074			0.625369	+	0.780329i	$0.284949\pi$
$152$			10.3923i			0.842927i
$153$		0			0
$154$	−3.36932			−0.271507
$155$	−17.5270	−	2.21837i	−1.40780	−	0.178184i
$156$		0			0
$157$	−22.4924			−1.79509			−0.897545	−	0.440922i	$-0.854651\pi$
$157$	−22.4924			−1.79509			−0.897545	+	0.440922i	$0.854651\pi$
$158$			14.8290i			1.17974i
$159$		0			0
$160$	1.40388	−	11.0918i	0.110987	−	0.876888i
$161$	12.0000			0.945732
$162$		0			0
$163$	5.43845			0.425972			0.212986	−	0.977055i	$-0.431681\pi$
$163$	5.43845			0.425972			0.212986	+	0.977055i	$0.431681\pi$
$164$		−	8.87348i		−	0.692902i
$165$		0			0
$166$		−	10.3923i		−	0.806599i
$167$		−	8.44703i		−	0.653651i	−0.945085	−	0.326825i	$-0.894021\pi$
$167$		−	8.44703i		−	0.653651i	0.945085	−	0.326825i	$-0.105979\pi$
$168$		0			0
$169$	−6.68466			−0.514204
$170$	−0.561553	+	4.43674i	−0.0430691	+	0.340282i
$171$		0			0
$172$	5.43845			0.414678
$173$			10.8188i			0.822535i	0.911515	+	0.411267i	$0.134914\pi$
$173$			10.8188i			0.822535i	−0.911515	+	0.411267i	$0.865086\pi$
$174$		0			0
$175$	4.31534	−	16.7743i	0.326209	−	1.26802i
$176$		−	0.972638i		−	0.0733153i
$177$		0			0
$178$			8.87348i			0.665095i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−13.6847			−1.01717			−0.508586	−	0.861011i	$-0.669832\pi$
$181$	−13.6847			−1.01717			−0.508586	+	0.861011i	$0.669832\pi$
$182$	15.3693			1.13925
$183$		0			0
$184$			10.3923i			0.766131i
$185$	−2.00000	+	15.8017i	−0.147043	+	1.16176i
$186$		0			0
$187$		−	1.94528i		−	0.142253i
$188$	11.6847			0.852191
$189$		0			0
$190$	−7.68466	−	0.972638i	−0.557504	−	0.0705626i
$191$		−	3.46410i		−	0.250654i	−0.992116	−	0.125327i	$-0.960002\pi$
$191$		−	3.46410i		−	0.250654i	0.992116	−	0.125327i	$-0.0399979\pi$
$192$		0			0
$193$	−8.24621			−0.593575			−0.296788	−	0.954944i	$-0.595915\pi$
$193$	−8.24621			−0.593575			−0.296788	+	0.954944i	$0.595915\pi$
$194$	−8.24621			−0.592043
$195$		0			0
$196$	5.00000			0.357143
$197$		−	10.8188i		−	0.770804i	−0.922749	−	0.385402i	$-0.874063\pi$
$197$		−	10.8188i		−	0.770804i	0.922749	−	0.385402i	$-0.125937\pi$
$198$		0			0
$199$	−15.3693			−1.08950			−0.544751	−	0.838598i	$-0.683376\pi$
$199$	−15.3693			−1.08950			−0.544751	+	0.838598i	$0.683376\pi$
$200$	14.5270	+	3.73720i	1.02721	+	0.264260i
$201$		0			0
$202$			6.92820i			0.487467i
$203$	12.0000	−	14.2829i	0.842235	−	1.00246i
$204$		0			0
$205$	19.6847	+	2.49146i	1.37484	+	0.174011i
$206$		−	1.51883i		−	0.105822i
$207$		0			0
$208$			4.43674i			0.307633i
$209$	3.36932			0.233061
$210$		0			0
$211$		−	14.8290i		−	1.02087i	−0.859915	−	0.510437i	$-0.829484\pi$
$211$		−	14.8290i		−	1.02087i	0.859915	−	0.510437i	$-0.170516\pi$
$212$			4.43674i			0.304717i
$213$		0			0
$214$		−	14.2829i		−	0.976356i
$215$	−1.52699	+	12.0645i	−0.104140	+	0.822791i
$216$		0			0
$217$	27.3693			1.85795
$218$	−5.68466			−0.385014
$219$		0			0
$220$	−2.15767	−	0.273094i	−0.145470	−	0.0184120i
$221$			8.87348i			0.596895i
$222$		0			0
$223$			12.3376i			0.826186i	0.910689	+	0.413093i	$0.135551\pi$
$223$			12.3376i			0.826186i	−0.910689	+	0.413093i	$0.864449\pi$
$224$			17.3205i			1.15728i
$225$		0			0
$226$	5.36932			0.357162
$227$			12.3376i			0.818874i	0.912338	+	0.409437i	$0.134275\pi$
$227$			12.3376i			0.818874i	−0.912338	+	0.409437i	$0.865725\pi$
$228$		0			0
$229$			15.8017i			1.04420i	0.852883	+	0.522102i	$0.174852\pi$
$229$			15.8017i			1.04420i	−0.852883	+	0.522102i	$0.825148\pi$
$230$	−7.68466	−	0.972638i	−0.506711	−	0.0641339i
$231$		0			0
$232$	12.3693	+	10.3923i	0.812085	+	0.682288i
$233$		−	2.49146i		−	0.163221i	−0.996664	−	0.0816106i	$-0.973994\pi$
$233$		−	2.49146i		−	0.163221i	0.996664	−	0.0816106i	$-0.0260064\pi$
$234$		0			0
$235$	−3.28078	+	25.9209i	−0.214014	+	1.69089i
$236$	−1.12311			−0.0731079
$237$		0			0
$238$		−	6.92820i		−	0.449089i
$239$	−13.1231			−0.848863			−0.424432	−	0.905460i	$-0.639526\pi$
$239$	−13.1231			−0.848863			−0.424432	+	0.905460i	$0.639526\pi$
$240$		0			0
$241$	−1.68466			−0.108518			−0.0542592	−	0.998527i	$-0.517280\pi$
$241$	−1.68466			−0.108518			−0.0542592	+	0.998527i	$0.517280\pi$
$242$	10.0540			0.646294
$243$		0			0
$244$		−	1.94528i		−	0.124534i
$245$	−1.40388	+	11.0918i	−0.0896907	+	0.708632i
$246$		0			0
$247$	−15.3693			−0.977926
$248$			23.7025i			1.50511i
$249$		0			0
$250$	−4.12311	+	10.3923i	−0.260768	+	0.657267i
$251$		−	16.7743i		−	1.05879i	−0.848377	−	0.529393i	$-0.822420\pi$
$251$		−	16.7743i		−	1.05879i	0.848377	−	0.529393i	$-0.177580\pi$
$252$		0			0
$253$	3.36932			0.211827
$254$	2.24621			0.140940
$255$		0			0
$256$	−17.0000			−1.06250
$257$			11.3649i			0.708926i	0.935070	+	0.354463i	$0.115336\pi$
$257$			11.3649i			0.708926i	−0.935070	+	0.354463i	$0.884664\pi$
$258$		0			0
$259$		−	24.6752i		−	1.53324i
$260$	9.84233	+	1.24573i	0.610395	+	0.0772570i
$261$		0			0
$262$		−	14.2829i		−	0.882398i
$263$	3.68466			0.227206			0.113603	−	0.993526i	$-0.463761\pi$
$263$	3.68466			0.227206			0.113603	+	0.993526i	$0.463761\pi$
$264$		0			0
$265$	−9.84233	−	1.24573i	−0.604609	−	0.0765247i
$266$	12.0000			0.735767
$267$		0			0
$268$			12.3376i			0.753638i
$269$			15.8017i			0.963446i	0.876324	+	0.481723i	$0.159989\pi$
$269$			15.8017i			0.963446i	−0.876324	+	0.481723i	$0.840011\pi$
$270$		0			0
$271$			14.8290i			0.900800i	0.892827	+	0.450400i	$0.148719\pi$
$271$			14.8290i			0.900800i	−0.892827	+	0.450400i	$0.851281\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	13.3693			0.807670
$275$	1.21165	−	4.70983i	0.0730650	−	0.284014i
$276$		0			0
$277$			10.8188i			0.650036i	0.945708	+	0.325018i	$0.105370\pi$
$277$			10.8188i			0.650036i	−0.945708	+	0.325018i	$0.894630\pi$
$278$	19.3693			1.16169
$279$		0			0
$280$	−23.0540	−	2.91791i	−1.37774	−	0.174379i
$281$	−13.6847			−0.816358			−0.408179	−	0.912902i	$-0.633836\pi$
$281$	−13.6847			−0.816358			−0.408179	+	0.912902i	$0.633836\pi$
$282$		0			0
$283$			14.2829i			0.849028i	0.905421	+	0.424514i	$0.139555\pi$
$283$			14.2829i			0.849028i	−0.905421	+	0.424514i	$0.860445\pi$
$284$	−2.24621			−0.133288
$285$		0			0
$286$	4.31534			0.255171
$287$	−30.7386			−1.81444
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−8.84233	+	8.17394i	−0.519239	+	0.479990i
$291$		0			0
$292$	−7.12311			−0.416848
$293$	1.36932			0.0799963			0.0399982	−	0.999200i	$-0.487265\pi$
$293$	1.36932			0.0799963			0.0399982	+	0.999200i	$0.487265\pi$
$294$		0			0
$295$	0.315342	−	2.49146i	0.0183599	−	0.145059i
$296$	21.3693			1.24207
$297$		0			0
$298$	13.6847			0.792731
$299$	−15.3693			−0.888831
$300$		0			0
$301$		−	18.8393i		−	1.08588i
$302$	15.3693			0.884405
$303$		0			0
$304$			3.46410i			0.198680i
$305$	4.31534	+	0.546188i	0.247096	+	0.0312746i
$306$		0			0
$307$	−3.19224			−0.182191			−0.0910953	−	0.995842i	$-0.529037\pi$
$307$	−3.19224			−0.182191			−0.0910953	+	0.995842i	$0.529037\pi$
$308$	3.36932			0.191985
$309$		0			0
$310$	−17.5270	−	2.21837i	−0.995466	−	0.125995i
$311$			0.426450i			0.0241818i	0.999927	+	0.0120909i	$0.00384874\pi$
$311$			0.426450i			0.0241818i	−0.999927	+	0.0120909i	$0.996151\pi$
$312$		0			0
$313$			2.49146i			0.140826i	0.997518	+	0.0704129i	$0.0224317\pi$
$313$			2.49146i			0.140826i	−0.997518	+	0.0704129i	$0.977568\pi$
$314$	−22.4924			−1.26932
$315$		0			0
$316$		−	14.8290i		−	0.834199i
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		0			0
$319$	3.36932	−	4.01029i	0.188646	−	0.224533i
$320$	1.96543	−	15.5286i	0.109871	−	0.868074i
$321$		0			0
$322$	12.0000			0.668734
$323$			6.92820i			0.385496i
$324$		0			0
$325$	−5.52699	+	21.4842i	−0.306582	+	1.19173i
$326$	5.43845			0.301208
$327$		0			0
$328$		−	26.6204i		−	1.46987i
$329$		−	40.4768i		−	2.23156i
$330$		0			0
$331$		−	5.95557i		−	0.327347i	−0.986515	−	0.163674i	$-0.947666\pi$
$331$		−	5.95557i		−	0.327347i	0.986515	−	0.163674i	$-0.0523344\pi$
$332$			10.3923i			0.570352i
$333$		0			0
$334$		−	8.44703i		−	0.462201i
$335$	−27.3693	−	3.46410i	−1.49535	−	0.189264i
$336$		0			0
$337$	−3.75379			−0.204482			−0.102241	−	0.994760i	$-0.532601\pi$
$337$	−3.75379			−0.204482			−0.102241	+	0.994760i	$0.532601\pi$
$338$	−6.68466			−0.363597
$339$		0			0
$340$	0.561553	−	4.43674i	0.0304545	−	0.240616i
$341$	7.68466			0.416148
$342$		0			0
$343$			6.92820i			0.374088i
$344$	16.3153			0.879664
$345$		0			0
$346$			10.8188i			0.581620i
$347$			26.1940i			1.40617i	0.711107	+	0.703083i	$0.248194\pi$
$347$			26.1940i			1.40617i	−0.711107	+	0.703083i	$0.751806\pi$
$348$		0			0
$349$	10.3153			0.552168			0.276084	−	0.961134i	$-0.410963\pi$
$349$	10.3153			0.552168			0.276084	+	0.961134i	$0.410963\pi$
$350$	4.31534	−	16.7743i	0.230665	−	0.896625i
$351$		0			0
$352$			4.86319i			0.259209i
$353$		−	17.7470i		−	0.944575i	−0.881444	−	0.472288i	$-0.843428\pi$
$353$		−	17.7470i		−	0.944575i	0.881444	−	0.472288i	$-0.156572\pi$
$354$		0			0
$355$	0.630683	−	4.98293i	0.0334732	−	0.264466i
$356$		−	8.87348i		−	0.470293i
$357$		0			0
$358$	12.0000			0.634220
$359$			21.7572i			1.14830i	0.818749	+	0.574152i	$0.194668\pi$
$359$			21.7572i			1.14830i	−0.818749	+	0.574152i	$0.805332\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$	−13.6847			−0.719250
$363$		0			0
$364$	−15.3693			−0.805571
$365$	2.00000	−	15.8017i	0.104685	−	0.827098i
$366$		0			0
$367$	28.4924			1.48729			0.743646	−	0.668573i	$-0.233095\pi$
$367$	28.4924			1.48729			0.743646	+	0.668573i	$0.233095\pi$
$368$			3.46410i			0.180579i
$369$		0			0
$370$	−2.00000	+	15.8017i	−0.103975	+	0.821490i
$371$	15.3693			0.797935
$372$		0			0
$373$		−	36.0401i		−	1.86609i	−0.359765	−	0.933043i	$-0.617143\pi$
$373$		−	36.0401i		−	1.86609i	0.359765	−	0.933043i	$-0.382857\pi$
$374$		−	1.94528i		−	0.100588i
$375$		0			0
$376$	35.0540			1.80777
$377$	−15.3693	+	18.2931i	−0.791560	+	0.942145i
$378$		0			0
$379$			0.426450i			0.0219053i	0.999940	+	0.0109526i	$0.00348640\pi$
$379$			0.426450i			0.0219053i	−0.999940	+	0.0109526i	$0.996514\pi$
$380$	7.68466	+	0.972638i	0.394215	+	0.0498953i
$381$		0			0
$382$		−	3.46410i		−	0.177239i
$383$		−	17.3205i		−	0.885037i	−0.896759	−	0.442518i	$-0.854085\pi$
$383$		−	17.3205i		−	0.885037i	0.896759	−	0.442518i	$-0.145915\pi$
$384$		0			0
$385$	−0.946025	+	7.47439i	−0.0482139	+	0.380930i
$386$	−8.24621			−0.419721
$387$		0			0
$388$	8.24621			0.418638
$389$		−	10.8188i		−	0.548533i	−0.961654	−	0.274266i	$-0.911565\pi$
$389$		−	10.8188i		−	0.548533i	0.961654	−	0.274266i	$-0.0884350\pi$
$390$		0			0
$391$			6.92820i			0.350374i
$392$	15.0000			0.757614
$393$		0			0
$394$		−	10.8188i		−	0.545041i
$395$	32.8963	+	4.16365i	1.65519	+	0.209496i
$396$		0			0
$397$			0.546188i			0.0274124i	0.999906	+	0.0137062i	$0.00436295\pi$
$397$			0.546188i			0.0274124i	−0.999906	+	0.0137062i	$0.995637\pi$
$398$	−15.3693			−0.770394
$399$		0			0
$400$	4.84233	+	1.24573i	0.242116	+	0.0622866i
$401$	−15.9309			−0.795550			−0.397775	−	0.917483i	$-0.630217\pi$
$401$	−15.9309			−0.795550			−0.397775	+	0.917483i	$0.630217\pi$
$402$		0			0
$403$	−35.0540			−1.74616
$404$		−	6.92820i		−	0.344691i
$405$		0			0
$406$	12.0000	−	14.2829i	0.595550	−	0.708846i
$407$		−	6.92820i		−	0.343418i
$408$		0			0
$409$		−	3.89055i		−	0.192375i	−0.995363	−	0.0961877i	$-0.969335\pi$
$409$		−	3.89055i		−	0.192375i	0.995363	−	0.0961877i	$-0.0306649\pi$
$410$	19.6847	+	2.49146i	0.972156	+	0.123045i
$411$		0			0
$412$			1.51883i			0.0748272i
$413$			3.89055i			0.191442i
$414$		0			0
$415$	−23.0540	−	2.91791i	−1.13168	−	0.143235i
$416$		−	22.1837i		−	1.08765i
$417$		0			0
$418$	3.36932			0.164799
$419$	−14.2462			−0.695973			−0.347986	−	0.937500i	$-0.613134\pi$
$419$	−14.2462			−0.695973			−0.347986	+	0.937500i	$0.613134\pi$
$420$		0			0
$421$		−	37.4392i		−	1.82467i	−0.409439	−	0.912337i	$-0.634276\pi$
$421$		−	37.4392i		−	1.82467i	0.409439	−	0.912337i	$-0.365724\pi$
$422$		−	14.8290i		−	0.721867i
$423$		0			0
$424$			13.3102i			0.646401i
$425$	9.68466	+	2.49146i	0.469775	+	0.120854i
$426$		0			0
$427$	−6.73863			−0.326105
$428$			14.2829i			0.690388i
$429$		0			0
$430$	−1.52699	+	12.0645i	−0.0736379	+	0.581801i
$431$	−8.63068			−0.415725			−0.207863	−	0.978158i	$-0.566651\pi$
$431$	−8.63068			−0.415725			−0.207863	+	0.978158i	$0.566651\pi$
$432$		0			0
$433$	−16.8769			−0.811052			−0.405526	−	0.914084i	$-0.632912\pi$
$433$	−16.8769			−0.811052			−0.405526	+	0.914084i	$0.632912\pi$
$434$	27.3693			1.31377
$435$		0			0
$436$	5.68466			0.272246
$437$	−12.0000			−0.574038
$438$		0			0
$439$	15.3693			0.733537			0.366769	−	0.930312i	$-0.380464\pi$
$439$	15.3693			0.733537			0.366769	+	0.930312i	$0.380464\pi$
$440$	−6.47301	−	0.819281i	−0.308589	−	0.0390577i
$441$		0			0
$442$			8.87348i			0.422068i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$		0			0
$445$	19.6847	+	2.49146i	0.933142	+	0.118107i
$446$			12.3376i			0.584201i
$447$		0			0
$448$			24.2487i			1.14564i
$449$			17.7470i			0.837531i	0.908094	+	0.418765i	$0.137537\pi$
$449$			17.7470i			0.837531i	−0.908094	+	0.418765i	$0.862463\pi$
$450$		0			0
$451$	−8.63068			−0.406403
$452$	−5.36932			−0.252551
$453$		0			0
$454$			12.3376i			0.579031i
$455$	4.31534	−	34.0948i	0.202306	−	1.59839i
$456$		0			0
$457$			3.89055i			0.181992i	0.995851	+	0.0909962i	$0.0290051\pi$
$457$			3.89055i			0.181992i	−0.995851	+	0.0909962i	$0.970995\pi$
$458$			15.8017i			0.738364i
$459$		0			0
$460$	7.68466	+	0.972638i	0.358299	+	0.0453495i
$461$		−	34.6410i		−	1.61339i	−0.590966	−	0.806696i	$-0.701253\pi$
$461$		−	34.6410i		−	1.61339i	0.590966	−	0.806696i	$-0.298747\pi$
$462$		0			0
$463$			7.35465i			0.341800i	0.985288	+	0.170900i	$0.0546675\pi$
$463$			7.35465i			0.341800i	−0.985288	+	0.170900i	$0.945333\pi$
$464$	4.12311	+	3.46410i	0.191410	+	0.160817i
$465$		0			0
$466$		−	2.49146i		−	0.115415i
$467$	−8.31534			−0.384788			−0.192394	−	0.981318i	$-0.561625\pi$
$467$	−8.31534			−0.384788			−0.192394	+	0.981318i	$0.561625\pi$
$468$		0			0
$469$	42.7386			1.97349
$470$	−3.28078	+	25.9209i	−0.151331	+	1.19564i
$471$		0			0
$472$	−3.36932			−0.155085
$473$		−	5.28964i		−	0.243218i
$474$		0			0
$475$	−4.31534	+	16.7743i	−0.198001	+	0.769659i
$476$			6.92820i			0.317554i
$477$		0			0
$478$	−13.1231			−0.600237
$479$			2.91791i			0.133323i	0.997776	+	0.0666614i	$0.0212347\pi$
$479$			2.91791i			0.133323i	−0.997776	+	0.0666614i	$0.978765\pi$
$480$		0			0
$481$			31.6034i			1.44099i
$482$	−1.68466			−0.0767341
$483$		0			0
$484$	−10.0540			−0.456999
$485$	−2.31534	+	18.2931i	−0.105134	+	0.830649i
$486$		0			0
$487$		−	32.0298i		−	1.45141i	−0.688006	−	0.725705i	$-0.741514\pi$
$487$		−	32.0298i		−	1.45141i	0.688006	−	0.725705i	$-0.258486\pi$
$488$		−	5.83583i		−	0.264176i
$489$		0			0
$490$	−1.40388	+	11.0918i	−0.0634209	+	0.501079i
$491$		−	29.5384i		−	1.33305i	−0.745484	−	0.666524i	$-0.767782\pi$
$491$		−	29.5384i		−	1.33305i	0.745484	−	0.666524i	$-0.232218\pi$
$492$		0			0
$493$	8.24621	+	6.92820i	0.371391	+	0.312031i
$494$	−15.3693			−0.691498
$495$		0			0
$496$			7.90084i			0.354758i
$497$			7.78110i			0.349030i
$498$		0			0
$499$	−4.63068			−0.207298			−0.103649	−	0.994614i	$-0.533052\pi$
$499$	−4.63068			−0.207298			−0.103649	+	0.994614i	$0.533052\pi$
$500$	4.12311	−	10.3923i	0.184391	−	0.464758i
$501$		0			0
$502$		−	16.7743i		−	0.748675i
$503$	4.94602			0.220532			0.110266	−	0.993902i	$-0.464830\pi$
$503$	4.94602			0.220532			0.110266	+	0.993902i	$0.464830\pi$
$504$		0			0
$505$	15.3693	+	1.94528i	0.683926	+	0.0865636i
$506$	3.36932			0.149784
$507$		0			0
$508$	−2.24621			−0.0996595
$509$	29.0540			1.28779			0.643897	−	0.765112i	$-0.277316\pi$
$509$	29.0540			1.28779			0.643897	+	0.765112i	$0.277316\pi$
$510$		0			0
$511$			24.6752i			1.09156i
$512$	−11.0000			−0.486136
$513$		0			0
$514$			11.3649i			0.501286i
$515$	−3.36932	−	0.426450i	−0.148470	−	0.0187916i
$516$		0			0
$517$		−	11.3649i		−	0.499830i
$518$		−	24.6752i		−	1.08416i
$519$		0			0
$520$	29.5270	+	3.73720i	1.29484	+	0.163887i
$521$	−22.3153			−0.977653			−0.488826	−	0.872381i	$-0.662575\pi$
$521$	−22.3153			−0.977653			−0.488826	+	0.872381i	$0.662575\pi$
$522$		0			0
$523$		−	26.1940i		−	1.14538i	−0.819771	−	0.572692i	$-0.805899\pi$
$523$		−	26.1940i		−	1.14538i	0.819771	−	0.572692i	$-0.194101\pi$
$524$			14.2829i			0.623949i
$525$		0			0
$526$	3.68466			0.160659
$527$			15.8017i			0.688332i
$528$		0			0
$529$	11.0000			0.478261
$530$	−9.84233	−	1.24573i	−0.427523	−	0.0541111i
$531$		0			0
$532$	−12.0000			−0.520266
$533$	39.3693			1.70527
$534$		0			0
$535$	−31.6847	−	4.01029i	−1.36985	−	0.173380i
$536$			37.0127i			1.59871i
$537$		0			0
$538$			15.8017i			0.681259i
$539$		−	4.86319i		−	0.209472i
$540$		0			0
$541$		−	38.5316i		−	1.65660i	−0.560284	−	0.828301i	$-0.689308\pi$
$541$		−	38.5316i		−	1.65660i	0.560284	−	0.828301i	$-0.310692\pi$
$542$			14.8290i			0.636962i
$543$		0			0
$544$	−10.0000			−0.428746
$545$	−1.59612	+	12.6107i	−0.0683702	+	0.540182i
$546$		0			0
$547$		−	7.35465i		−	0.314462i	−0.987562	−	0.157231i	$-0.949743\pi$
$547$		−	7.35465i		−	0.314462i	0.987562	−	0.157231i	$-0.0502568\pi$
$548$	−13.3693			−0.571109
$549$		0			0
$550$	1.21165	−	4.70983i	0.0516648	−	0.200828i
$551$	−12.0000	+	14.2829i	−0.511217	+	0.608470i
$552$		0			0
$553$	−51.3693			−2.18445
$554$			10.8188i			0.459645i
$555$		0			0
$556$	−19.3693			−0.821442
$557$		−	6.92820i		−	0.293557i	−0.989169	−	0.146779i	$-0.953109\pi$
$557$		−	6.92820i		−	0.293557i	0.989169	−	0.146779i	$-0.0468905\pi$
$558$		0			0
$559$			24.1290i			1.02055i
$560$	−7.68466	−	0.972638i	−0.324736	−	0.0411015i
$561$		0			0
$562$	−13.6847			−0.577252
$563$	−15.6847			−0.661030			−0.330515	−	0.943801i	$-0.607222\pi$
$563$	−15.6847			−0.661030			−0.330515	+	0.943801i	$0.607222\pi$
$564$		0			0
$565$	1.50758	−	11.9111i	0.0634243	−	0.501105i
$566$			14.2829i			0.600353i
$567$		0			0
$568$	−6.73863			−0.282747
$569$			3.89055i			0.163100i	0.996669	+	0.0815502i	$0.0259871\pi$
$569$			3.89055i			0.163100i	−0.996669	+	0.0815502i	$0.974013\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	−4.31534			−0.180433
$573$		0			0
$574$	−30.7386			−1.28301
$575$	−4.31534	+	16.7743i	−0.179962	+	0.699538i
$576$		0			0
$577$	44.2462			1.84199			0.920997	−	0.389570i	$-0.127376\pi$
$577$	44.2462			1.84199			0.920997	+	0.389570i	$0.127376\pi$
$578$	−13.0000			−0.540729
$579$		0			0
$580$	8.84233	−	8.17394i	0.367158	−	0.339404i
$581$	36.0000			1.49353
$582$		0			0
$583$	4.31534			0.178723
$584$	−21.3693			−0.884269
$585$		0			0
$586$	1.36932			0.0565660
$587$			13.4300i			0.554314i	0.960825	+	0.277157i	$0.0893921\pi$
$587$			13.4300i			0.554314i	−0.960825	+	0.277157i	$0.910608\pi$
$588$		0			0
$589$	−27.3693			−1.12773
$590$	0.315342	−	2.49146i	0.0129824	−	0.102572i
$591$		0			0
$592$	7.12311			0.292758
$593$		−	6.38202i		−	0.262078i	−0.991377	−	0.131039i	$-0.958169\pi$
$593$		−	6.38202i		−	0.262078i	0.991377	−	0.131039i	$-0.0418313\pi$
$594$		0			0
$595$	−15.3693	−	1.94528i	−0.630081	−	0.0797485i
$596$	−13.6847			−0.560545
$597$		0			0
$598$	−15.3693			−0.628498
$599$		−	0.972638i		−	0.0397409i	−0.999803	−	0.0198705i	$-0.993675\pi$
$599$		−	0.972638i		−	0.0397409i	0.999803	−	0.0198705i	$-0.00632538\pi$
$600$		0			0
$601$			8.87348i			0.361957i	0.983487	+	0.180978i	$0.0579264\pi$
$601$			8.87348i			0.361957i	−0.983487	+	0.180978i	$0.942074\pi$
$602$		−	18.8393i		−	0.767834i
$603$		0			0
$604$	−15.3693			−0.625369
$605$	2.82292	−	22.3034i	0.114768	−	0.906764i
$606$		0			0
$607$	−0.177081			−0.00718749			−0.00359375	−	0.999994i	$-0.501144\pi$
$607$	−0.177081			−0.00718749			−0.00359375	+	0.999994i	$0.501144\pi$
$608$		−	17.3205i		−	0.702439i
$609$		0			0
$610$	4.31534	+	0.546188i	0.174723	+	0.0221145i
$611$			51.8418i			2.09729i
$612$		0			0
$613$			14.4026i			0.581715i	0.956766	+	0.290858i	$0.0939406\pi$
$613$			14.4026i			0.581715i	−0.956766	+	0.290858i	$0.906059\pi$
$614$	−3.19224			−0.128828
$615$		0			0
$616$	10.1080			0.407261
$617$	13.3693			0.538228			0.269114	−	0.963108i	$-0.413269\pi$
$617$	13.3693			0.538228			0.269114	+	0.963108i	$0.413269\pi$
$618$		0			0
$619$		−	10.9385i		−	0.439655i	−0.975539	−	0.219828i	$-0.929451\pi$
$619$		−	10.9385i		−	0.439655i	0.975539	−	0.219828i	$-0.0705495\pi$
$620$	17.5270	+	2.21837i	0.703901	+	0.0890919i
$621$		0			0
$622$			0.426450i			0.0170991i
$623$	−30.7386			−1.23152
$624$		0			0
$625$	21.8963	+	12.0645i	0.875852	+	0.482579i
$626$			2.49146i			0.0995789i
$627$		0			0
$628$	22.4924			0.897545
$629$	14.2462			0.568034
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	44.4871i		−	1.76960i
$633$		0			0
$634$	2.00000			0.0794301
$635$	0.630683	−	4.98293i	0.0250279	−	0.197741i
$636$		0			0
$637$			22.1837i			0.878950i
$638$	3.36932	−	4.01029i	0.133393	−	0.158769i
$639$		0			0
$640$	−0.842329	+	6.65511i	−0.0332960	+	0.263066i
$641$			4.98293i			0.196814i	0.995146	+	0.0984069i	$0.0313747\pi$
$641$			4.98293i			0.196814i	−0.995146	+	0.0984069i	$0.968625\pi$
$642$		0			0
$643$		−	35.0675i		−	1.38293i	−0.722412	−	0.691463i	$-0.756967\pi$
$643$		−	35.0675i		−	1.38293i	0.722412	−	0.691463i	$-0.243033\pi$
$644$	−12.0000			−0.472866
$645$		0			0
$646$			6.92820i			0.272587i
$647$		−	48.9239i		−	1.92340i	−0.274111	−	0.961698i	$-0.588384\pi$
$647$		−	48.9239i		−	1.92340i	0.274111	−	0.961698i	$-0.411616\pi$
$648$		0			0
$649$			1.09238i			0.0428795i
$650$	−5.52699	+	21.4842i	−0.216786	+	0.842678i
$651$		0			0
$652$	−5.43845			−0.212986
$653$	−28.7386			−1.12463			−0.562315	−	0.826923i	$-0.690089\pi$
$653$	−28.7386			−1.12463			−0.562315	+	0.826923i	$0.690089\pi$
$654$		0			0
$655$	−31.6847	−	4.01029i	−1.23802	−	0.156695i
$656$		−	8.87348i		−	0.346451i
$657$		0			0
$658$		−	40.4768i		−	1.57795i
$659$		−	35.6137i		−	1.38731i	−0.720307	−	0.693655i	$-0.755999\pi$
$659$		−	35.6137i		−	1.38731i	0.720307	−	0.693655i	$-0.244001\pi$
$660$		0			0
$661$	−24.7386			−0.962221			−0.481111	−	0.876660i	$-0.659766\pi$
$661$	−24.7386			−0.962221			−0.481111	+	0.876660i	$0.659766\pi$
$662$		−	5.95557i		−	0.231470i
$663$		0			0
$664$			31.1769i			1.20990i
$665$	3.36932	−	26.6204i	0.130657	−	1.03230i
$666$		0			0
$667$	−12.0000	+	14.2829i	−0.464642	+	0.553034i
$668$			8.44703i			0.326825i
$669$		0			0
$670$	−27.3693	−	3.46410i	−1.05737	−	0.133830i
$671$	−1.89205			−0.0730418
$672$		0			0
$673$			29.1119i			1.12218i	0.827754	+	0.561091i	$0.189618\pi$
$673$			29.1119i			1.12218i	−0.827754	+	0.561091i	$0.810382\pi$
$674$	−3.75379			−0.144591
$675$		0			0
$676$	6.68466			0.257102
$677$	−13.3693			−0.513825			−0.256912	−	0.966435i	$-0.582705\pi$
$677$	−13.3693			−0.513825			−0.256912	+	0.966435i	$0.582705\pi$
$678$		0			0
$679$		−	28.5657i		−	1.09625i
$680$	1.68466	−	13.3102i	0.0646037	−	0.510424i
$681$		0			0
$682$	7.68466			0.294261
$683$			16.2281i			0.620952i	0.950581	+	0.310476i	$0.100488\pi$
$683$			16.2281i			0.620952i	−0.950581	+	0.310476i	$0.899512\pi$
$684$		0			0
$685$	3.75379	−	29.6581i	0.143425	−	1.13318i
$686$			6.92820i			0.264520i
$687$		0			0
$688$	5.43845			0.207339
$689$	−19.6847			−0.749926
$690$		0			0
$691$	18.7386			0.712851			0.356426	−	0.934324i	$-0.383995\pi$
$691$	18.7386			0.712851			0.356426	+	0.934324i	$0.383995\pi$
$692$		−	10.8188i		−	0.411267i
$693$		0			0
$694$			26.1940i			0.994310i
$695$	5.43845	−	42.9683i	0.206292	−	1.62988i
$696$		0			0
$697$		−	17.7470i		−	0.672214i
$698$	10.3153			0.390441
$699$		0			0
$700$	−4.31534	+	16.7743i	−0.163105	+	0.634010i
$701$	50.8078			1.91898			0.959491	−	0.281738i	$-0.0909109\pi$
$701$	50.8078			1.91898			0.959491	+	0.281738i	$0.0909109\pi$
$702$		0			0
$703$			24.6752i			0.930641i
$704$			6.80847i			0.256604i
$705$		0			0
$706$		−	17.7470i		−	0.667916i
$707$	−24.0000			−0.902613
$708$		0			0
$709$	−6.31534			−0.237178			−0.118589	−	0.992943i	$-0.537837\pi$
$709$	−6.31534			−0.237178			−0.118589	+	0.992943i	$0.537837\pi$
$710$	0.630683	−	4.98293i	0.0236691	−	0.187006i
$711$		0			0
$712$		−	26.6204i		−	0.997643i
$713$	−27.3693			−1.02499
$714$		0			0
$715$	1.21165	−	9.57302i	0.0453130	−	0.358011i
$716$	−12.0000			−0.448461
$717$		0			0
$718$			21.7572i			0.811973i
$719$	−26.2462			−0.978819			−0.489409	−	0.872054i	$-0.662788\pi$
$719$	−26.2462			−0.978819			−0.489409	+	0.872054i	$0.662788\pi$
$720$		0			0
$721$	5.26137			0.195944
$722$	7.00000			0.260513
$723$		0			0
$724$	13.6847			0.508586
$725$	15.6501	+	21.9106i	0.581230	+	0.813739i
$726$		0			0
$727$	4.49242			0.166615			0.0833074	−	0.996524i	$-0.473452\pi$
$727$	4.49242			0.166615			0.0833074	+	0.996524i	$0.473452\pi$
$728$	−46.1080			−1.70887
$729$		0			0
$730$	2.00000	−	15.8017i	0.0740233	−	0.584847i
$731$	10.8769			0.402296
$732$		0			0
$733$	16.8769			0.623362			0.311681	−	0.950187i	$-0.399108\pi$
$733$	16.8769			0.623362			0.311681	+	0.950187i	$0.399108\pi$
$734$	28.4924			1.05167
$735$		0			0
$736$		−	17.3205i		−	0.638442i
$737$	12.0000			0.442026
$738$		0			0
$739$		−	27.5931i		−	1.01503i	−0.861644	−	0.507514i	$-0.830565\pi$
$739$		−	27.5931i		−	1.01503i	0.861644	−	0.507514i	$-0.169435\pi$
$740$	2.00000	−	15.8017i	0.0735215	−	0.580881i
$741$		0			0
$742$	15.3693			0.564225
$743$	−32.0000			−1.17397			−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000			−1.17397			−0.586983	+	0.809599i	$0.699684\pi$
$744$		0			0
$745$	3.84233	−	30.3576i	0.140772	−	1.11222i
$746$		−	36.0401i		−	1.31952i
$747$		0			0
$748$			1.94528i			0.0711263i
$749$	49.4773			1.80786
$750$		0			0
$751$		−	6.50175i		−	0.237252i	−0.992939	−	0.118626i	$-0.962151\pi$
$751$		−	6.50175i		−	0.237252i	0.992939	−	0.118626i	$-0.0378490\pi$
$752$	11.6847			0.426096
$753$		0			0
$754$	−15.3693	+	18.2931i	−0.559718	+	0.666197i
$755$	4.31534	−	34.0948i	0.157051	−	1.24084i
$756$		0			0
$757$	−15.7538			−0.572581			−0.286291	−	0.958143i	$-0.592422\pi$
$757$	−15.7538			−0.572581			−0.286291	+	0.958143i	$0.592422\pi$
$758$			0.426450i			0.0154894i
$759$		0			0
$760$	23.0540	+	2.91791i	0.836256	+	0.105844i
$761$	1.50758			0.0546496			0.0273248	−	0.999627i	$-0.491301\pi$
$761$	1.50758			0.0546496			0.0273248	+	0.999627i	$0.491301\pi$
$762$		0			0
$763$		−	19.6922i		−	0.712907i
$764$			3.46410i			0.125327i
$765$		0			0
$766$		−	17.3205i		−	0.625815i
$767$		−	4.98293i		−	0.179923i
$768$		0			0
$769$		−	32.6957i		−	1.17904i	−0.807754	−	0.589519i	$-0.799317\pi$
$769$		−	32.6957i		−	1.17904i	0.807754	−	0.589519i	$-0.200683\pi$
$770$	−0.946025	+	7.47439i	−0.0340924	+	0.269358i
$771$		0			0
$772$	8.24621			0.296788
$773$	26.0000			0.935155			0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000			0.935155			0.467578	+	0.883952i	$0.345127\pi$
$774$		0			0
$775$	−9.84233	+	38.2585i	−0.353547	+	1.37428i
$776$	24.7386			0.888065
$777$		0			0
$778$		−	10.8188i		−	0.387871i
$779$	30.7386			1.10133
$780$		0			0
$781$			2.18475i			0.0781765i
$782$			6.92820i			0.247752i
$783$		0			0
$784$	5.00000			0.178571
$785$	−6.31534	+	49.8965i	−0.225404	+	1.78088i
$786$		0			0
$787$		−	12.3376i		−	0.439787i	−0.975524	−	0.219894i	$-0.929429\pi$
$787$		−	12.3376i		−	0.439787i	0.975524	−	0.219894i	$-0.0705710\pi$
$788$			10.8188i			0.385402i
$789$		0			0
$790$	32.8963	+	4.16365i	1.17040	+	0.148136i
$791$			18.5999i			0.661335i
$792$		0			0
$793$	8.63068			0.306485
$794$			0.546188i			0.0193835i
$795$		0			0
$796$	15.3693			0.544751
$797$	34.0000			1.20434			0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000			1.20434			0.602171	+	0.798367i	$0.294303\pi$
$798$		0			0
$799$	23.3693			0.826747
$800$	−24.2116	−	6.22866i	−0.856011	−	0.220216i
$801$		0			0
$802$	−15.9309			−0.562539
$803$			6.92820i			0.244491i
$804$		0			0
$805$	3.36932	−	26.6204i	0.118753	−	0.938247i
$806$	−35.0540			−1.23472
$807$		0			0
$808$		−	20.7846i		−	0.731200i
$809$		−	31.6034i		−	1.11112i	−0.831478	−	0.555558i	$-0.812505\pi$
$809$		−	31.6034i		−	1.11112i	0.831478	−	0.555558i	$-0.187495\pi$
$810$		0			0
$811$	4.63068			0.162605			0.0813026	−	0.996689i	$-0.474092\pi$
$811$	4.63068			0.162605			0.0813026	+	0.996689i	$0.474092\pi$
$812$	−12.0000	+	14.2829i	−0.421117	+	0.501230i
$813$		0			0
$814$		−	6.92820i		−	0.242833i
$815$	1.52699	−	12.0645i	0.0534880	−	0.422601i
$816$		0			0
$817$			18.8393i			0.659105i
$818$		−	3.89055i		−	0.136030i
$819$		0			0
$820$	−19.6847	−	2.49146i	−0.687418	−	0.0870057i
$821$	−47.7926			−1.66797			−0.833987	−	0.551784i	$-0.813947\pi$
$821$	−47.7926			−1.66797			−0.833987	+	0.551784i	$0.813947\pi$
$822$		0			0
$823$	21.7538			0.758289			0.379145	−	0.925337i	$-0.376218\pi$
$823$	21.7538			0.758289			0.379145	+	0.925337i	$0.376218\pi$
$824$			4.55648i			0.158732i
$825$		0			0
$826$			3.89055i			0.135370i
$827$	−15.0540			−0.523478			−0.261739	−	0.965139i	$-0.584296\pi$
$827$	−15.0540			−0.523478			−0.261739	+	0.965139i	$0.584296\pi$
$828$		0			0
$829$		−	23.5828i		−	0.819064i	−0.912296	−	0.409532i	$-0.865692\pi$
$829$		−	23.5828i		−	0.819064i	0.912296	−	0.409532i	$-0.134308\pi$
$830$	−23.0540	−	2.91791i	−0.800215	−	0.101282i
$831$		0			0
$832$		−	31.0572i		−	1.07671i
$833$	10.0000			0.346479
$834$		0			0
$835$	−18.7386	−	2.37173i	−0.648477	−	0.0820770i
$836$	−3.36932			−0.116530
$837$		0			0
$838$	−14.2462			−0.492127
$839$		−	18.7196i		−	0.646272i	−0.946352	−	0.323136i	$-0.895263\pi$
$839$		−	18.7196i		−	0.646272i	0.946352	−	0.323136i	$-0.104737\pi$
$840$		0			0
$841$	5.00000	+	28.5657i	0.172414	+	0.985025i
$842$		−	37.4392i		−	1.29024i
$843$		0			0
$844$			14.8290i			0.510437i
$845$	−1.87689	+	14.8290i	−0.0645671	+	0.510135i
$846$		0			0
$847$			34.8280i			1.19670i
$848$			4.43674i			0.152358i
$849$		0			0
$850$	9.68466	+	2.49146i	0.332181	+	0.0854565i
$851$			24.6752i			0.845854i
$852$		0			0
$853$	−37.8617			−1.29636			−0.648181	−	0.761487i	$-0.724470\pi$
$853$	−37.8617			−1.29636			−0.648181	+	0.761487i	$0.724470\pi$
$854$	−6.73863			−0.230591
$855$		0			0
$856$			42.8486i			1.46453i
$857$			20.2384i			0.691331i	0.938358	+	0.345666i	$0.112347\pi$
$857$			20.2384i			0.691331i	−0.938358	+	0.345666i	$0.887653\pi$
$858$		0			0
$859$			52.2682i			1.78337i	0.452657	+	0.891685i	$0.350476\pi$
$859$			52.2682i			1.78337i	−0.452657	+	0.891685i	$0.649524\pi$
$860$	1.52699	−	12.0645i	0.0520698	−	0.411396i
$861$		0			0
$862$	−8.63068			−0.293962
$863$			15.3752i			0.523379i	0.965152	+	0.261689i	$0.0842796\pi$
$863$			15.3752i			0.523379i	−0.965152	+	0.261689i	$0.915720\pi$
$864$		0			0
$865$	24.0000	+	3.03765i	0.816024	+	0.103283i
$866$	−16.8769			−0.573500
$867$		0			0
$868$	−27.3693			−0.928975
$869$	−14.4233			−0.489277
$870$		0			0
$871$	−54.7386			−1.85475
$872$	17.0540			0.577520
$873$		0			0
$874$	−12.0000			−0.405906
$875$	−36.0000	−	14.2829i	−1.21702	−	0.482849i
$876$		0			0
$877$			41.0230i			1.38525i	0.721298	+	0.692625i	$0.243546\pi$
$877$			41.0230i			1.38525i	−0.721298	+	0.692625i	$0.756454\pi$
$878$	15.3693			0.518689
$879$		0			0
$880$	−2.15767	−	0.273094i	−0.0727351	−	0.00920599i
$881$		−	45.4598i		−	1.53158i	−0.643092	−	0.765789i	$-0.722349\pi$
$881$		−	45.4598i		−	1.53158i	0.643092	−	0.765789i	$-0.277651\pi$
$882$		0			0
$883$			35.9204i			1.20882i	0.796675	+	0.604408i	$0.206590\pi$
$883$			35.9204i			1.20882i	−0.796675	+	0.604408i	$0.793410\pi$
$884$		−	8.87348i		−	0.298447i
$885$		0			0
$886$	−4.00000			−0.134383
$887$	−3.68466			−0.123719			−0.0618594	−	0.998085i	$-0.519703\pi$
$887$	−3.68466			−0.123719			−0.0618594	+	0.998085i	$0.519703\pi$
$888$		0			0
$889$			7.78110i			0.260970i
$890$	19.6847	+	2.49146i	0.659831	+	0.0835141i
$891$		0			0
$892$		−	12.3376i		−	0.413093i
$893$			40.4768i			1.35451i
$894$		0			0
$895$	3.36932	−	26.6204i	0.112624	−	0.889823i
$896$		−	10.3923i		−	0.347183i
$897$		0			0
$898$			17.7470i			0.592224i
$899$	−27.3693	+	32.5760i	−0.912818	+	1.08647i
$900$		0			0
$901$			8.87348i			0.295618i
$902$	−8.63068			−0.287370
$903$		0			0
$904$	−16.1080			−0.535742
$905$	−3.84233	+	30.3576i	−0.127723	+	1.00912i
$906$		0			0
$907$	40.4924			1.34453			0.672264	−	0.740311i	$-0.265322\pi$
$907$	40.4924			1.34453			0.672264	+	0.740311i	$0.265322\pi$
$908$		−	12.3376i		−	0.409437i
$909$		0			0
$910$	4.31534	−	34.0948i	0.143052	−	1.13023i
$911$		−	9.84612i		−	0.326216i	−0.986608	−	0.163108i	$-0.947848\pi$
$911$		−	9.84612i		−	0.326216i	0.986608	−	0.163108i	$-0.0521520\pi$
$912$		0			0
$913$	10.1080			0.334524
$914$			3.89055i			0.128688i
$915$		0			0
$916$		−	15.8017i		−	0.522102i
$917$	49.4773			1.63388
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	23.0540	+	2.91791i	0.760067	+	0.0962008i
$921$		0			0
$922$		−	34.6410i		−	1.14084i
$923$		−	9.96585i		−	0.328030i
$924$		0			0
$925$	34.4924	+	8.87348i	1.13410	+	0.291758i
$926$			7.35465i			0.241689i
$927$		0			0
$928$	−20.6155	−	17.3205i	−0.676738	−	0.568574i
$929$	−48.7386			−1.59906			−0.799531	−	0.600624i	$-0.794919\pi$
$929$	−48.7386			−1.59906			−0.799531	+	0.600624i	$0.794919\pi$
$930$		0			0
$931$			17.3205i			0.567657i
$932$			2.49146i			0.0816106i
$933$		0			0
$934$	−8.31534			−0.272086
$935$	−4.31534	−	0.546188i	−0.141127	−	0.0178622i
$936$		0			0
$937$		−	31.6034i		−	1.03244i	−0.856457	−	0.516218i	$-0.827339\pi$
$937$		−	31.6034i		−	1.03244i	0.856457	−	0.516218i	$-0.172661\pi$
$938$	42.7386			1.39547
$939$		0			0
$940$	3.28078	−	25.9209i	0.107007	−	0.845446i
$941$	−32.4233			−1.05697			−0.528485	−	0.848943i	$-0.677240\pi$
$941$	−32.4233			−1.05697			−0.528485	+	0.848943i	$0.677240\pi$
$942$		0			0
$943$	30.7386			1.00099
$944$	−1.12311			−0.0365540
$945$		0			0
$946$		−	5.28964i		−	0.171981i
$947$	23.6847			0.769648			0.384824	−	0.922990i	$-0.374262\pi$
$947$	23.6847			0.769648			0.384824	+	0.922990i	$0.374262\pi$
$948$		0			0
$949$		−	31.6034i		−	1.02589i
$950$	−4.31534	+	16.7743i	−0.140008	+	0.544231i
$951$		0			0
$952$			20.7846i			0.673633i
$953$		−	10.2726i		−	0.332761i	−0.986062	−	0.166381i	$-0.946792\pi$
$953$		−	10.2726i		−	0.332761i	0.986062	−	0.166381i	$-0.0532080\pi$
$954$		0			0
$955$	−7.68466	−	0.972638i	−0.248670	−	0.0314738i
$956$	13.1231			0.424432
$957$		0			0
$958$			2.91791i			0.0942735i
$959$			46.3127i			1.49551i
$960$		0			0
$961$	−31.4233			−1.01365
$962$			31.6034i			1.01893i
$963$		0			0
$964$	1.68466			0.0542592
$965$	−2.31534	+	18.2931i	−0.0745335	+	0.588877i
$966$		0			0
$967$	−45.9309			−1.47704			−0.738519	−	0.674233i	$-0.764474\pi$
$967$	−45.9309			−1.47704			−0.738519	+	0.674233i	$0.764474\pi$
$968$	−30.1619			−0.969441
$969$		0			0
$970$	−2.31534	+	18.2931i	−0.0743411	+	0.587358i
$971$		−	45.8862i		−	1.47256i	−0.676678	−	0.736279i	$-0.736581\pi$
$971$		−	45.8862i		−	1.47256i	0.676678	−	0.736279i	$-0.263419\pi$
$972$		0			0
$973$			67.0973i			2.15104i
$974$		−	32.0298i		−	1.02630i
$975$		0			0
$976$		−	1.94528i		−	0.0622668i
$977$		−	6.38202i		−	0.204179i	−0.994775	−	0.102089i	$-0.967447\pi$
$977$		−	6.38202i		−	0.204179i	0.994775	−	0.102089i	$-0.0325528\pi$
$978$		0			0
$979$	−8.63068			−0.275838
$980$	1.40388	−	11.0918i	0.0448454	−	0.354316i
$981$		0			0
$982$		−	29.5384i		−	0.942607i
$983$	27.0540			0.862888			0.431444	−	0.902140i	$-0.358004\pi$
$983$	27.0540			0.862888			0.431444	+	0.902140i	$0.358004\pi$
$984$		0			0
$985$	−24.0000	−	3.03765i	−0.764704	−	0.0967876i
$986$	8.24621	+	6.92820i	0.262613	+	0.220639i
$987$		0			0
$988$	15.3693			0.488963
$989$			18.8393i			0.599056i
$990$		0			0
$991$	−30.7386			−0.976445			−0.488222	−	0.872719i	$-0.662355\pi$
$991$	−30.7386			−0.976445			−0.488222	+	0.872719i	$0.662355\pi$
$992$		−	39.5042i		−	1.25426i
$993$		0			0
$994$			7.78110i			0.246802i
$995$	−4.31534	+	34.0948i	−0.136806	+	1.08088i
$996$		0			0
$997$	−59.6155			−1.88804			−0.944021	−	0.329884i	$-0.892990\pi$
$997$	−59.6155			−1.88804			−0.944021	+	0.329884i	$0.892990\pi$
$998$	−4.63068			−0.146582
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.f.i.289.3		4
3.2	odd	2		145.2.d.a.144.4	yes	4
5.4	even	2		1305.2.f.e.289.4		4
12.11	even	2		2320.2.j.a.289.2		4
15.2	even	4		725.2.c.f.376.1		8
15.8	even	4		725.2.c.f.376.8		8
15.14	odd	2		145.2.d.c.144.1	yes	4
29.28	even	2		1305.2.f.e.289.3		4
60.59	even	2		2320.2.j.c.289.3		4
87.86	odd	2		145.2.d.c.144.2	yes	4
145.144	even	2	inner	1305.2.f.i.289.4		4
348.347	even	2		2320.2.j.c.289.4		4
435.173	even	4		725.2.c.f.376.2		8
435.347	even	4		725.2.c.f.376.7		8
435.434	odd	2		145.2.d.a.144.3	✓	4
1740.1739	even	2		2320.2.j.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.d.a.144.3	✓	4	435.434	odd	2
145.2.d.a.144.4	yes	4	3.2	odd	2
145.2.d.c.144.1	yes	4	15.14	odd	2
145.2.d.c.144.2	yes	4	87.86	odd	2
725.2.c.f.376.1		8	15.2	even	4
725.2.c.f.376.2		8	435.173	even	4
725.2.c.f.376.7		8	435.347	even	4
725.2.c.f.376.8		8	15.8	even	4
1305.2.f.e.289.3		4	29.28	even	2
1305.2.f.e.289.4		4	5.4	even	2
1305.2.f.i.289.3		4	1.1	even	1	trivial
1305.2.f.i.289.4		4	145.144	even	2	inner
2320.2.j.a.289.1		4	1740.1739	even	2
2320.2.j.a.289.2		4	12.11	even	2
2320.2.j.c.289.3		4	60.59	even	2
2320.2.j.c.289.4		4	348.347	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{4} +(0.280776 - 2.21837i) q^{5} +3.46410i q^{7} -3.00000 q^{8} +(0.280776 - 2.21837i) q^{10} +0.972638i q^{11} -4.43674i q^{13} +3.46410i q^{14} -1.00000 q^{16} -2.00000 q^{17} -3.46410i q^{19} +(-0.280776 + 2.21837i) q^{20} +0.972638i q^{22} -3.46410i q^{23} +(-4.84233 - 1.24573i) q^{25} -4.43674i q^{26} -3.46410i q^{28} +(-4.12311 - 3.46410i) q^{29} -7.90084i q^{31} +5.00000 q^{32} -2.00000 q^{34} +(7.68466 + 0.972638i) q^{35} -7.12311 q^{37} -3.46410i q^{38} +(-0.842329 + 6.65511i) q^{40} +8.87348i q^{41} -5.43845 q^{43} -0.972638i q^{44} -3.46410i q^{46} -11.6847 q^{47} -5.00000 q^{49} +(-4.84233 - 1.24573i) q^{50} +4.43674i q^{52} -4.43674i q^{53} +(2.15767 + 0.273094i) q^{55} -10.3923i q^{56} +(-4.12311 - 3.46410i) q^{58} +1.12311 q^{59} +1.94528i q^{61} -7.90084i q^{62} +7.00000 q^{64} +(-9.84233 - 1.24573i) q^{65} -12.3376i q^{67} +2.00000 q^{68} +(7.68466 + 0.972638i) q^{70} +2.24621 q^{71} +7.12311 q^{73} -7.12311 q^{74} +3.46410i q^{76} -3.36932 q^{77} +14.8290i q^{79} +(-0.280776 + 2.21837i) q^{80} +8.87348i q^{82} -10.3923i q^{83} +(-0.561553 + 4.43674i) q^{85} -5.43845 q^{86} -2.91791i q^{88} +8.87348i q^{89} +15.3693 q^{91} +3.46410i q^{92} -11.6847 q^{94} +(-7.68466 - 0.972638i) q^{95} -8.24621 q^{97} -5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{4} - 3 q^{5} - 12 q^{8} - 3 q^{10} - 4 q^{16} - 8 q^{17} + 3 q^{20} - 7 q^{25} + 20 q^{32} - 8 q^{34} + 6 q^{35} - 12 q^{37} + 9 q^{40} - 30 q^{43} - 22 q^{47} - 20 q^{49} - 7 q^{50}+ \cdots - 20 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 - 12 * q^8 - 3 * q^10 - 4 * q^16 - 8 * q^17 + 3 * q^20 - 7 * q^25 + 20 * q^32 - 8 * q^34 + 6 * q^35 - 12 * q^37 + 9 * q^40 - 30 * q^43 - 22 * q^47 - 20 * q^49 - 7 * q^50 + 21 * q^55 - 12 * q^59 + 28 * q^64 - 27 * q^65 + 8 * q^68 + 6 * q^70 - 24 * q^71 + 12 * q^73 - 12 * q^74 + 36 * q^77 + 3 * q^80 + 6 * q^85 - 30 * q^86 + 12 * q^91 - 22 * q^94 - 6 * q^95 - 20 * q^98

Introduction

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