LMFDB - Embedded newform 1305.2.c.f.784.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (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:	$10.4204774638$
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:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.1
Root			$-1.93185i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.f.784.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.93185i q^{2} -1.73205 q^{4} +(-1.73205 - 1.41421i) q^{5} -2.44949i q^{7} -0.517638i q^{8} +(-2.73205 + 3.34607i) q^{10} +4.73205 q^{11} -6.69213i q^{13} -4.73205 q^{14} -4.46410 q^{16} +1.41421i q^{17} +6.73205 q^{19} +(3.00000 + 2.44949i) q^{20} -9.14162i q^{22} -3.48477i q^{23} +(1.00000 + 4.89898i) q^{25} -12.9282 q^{26} +4.24264i q^{28} +1.00000 q^{29} -5.26795 q^{31} +7.58871i q^{32} +2.73205 q^{34} +(-3.46410 + 4.24264i) q^{35} +0.656339i q^{37} -13.0053i q^{38} +(-0.732051 + 0.896575i) q^{40} -6.92820 q^{41} -0.656339i q^{43} -8.19615 q^{44} -6.73205 q^{46} +1.41421i q^{47} +1.00000 q^{49} +(9.46410 - 1.93185i) q^{50} +11.5911i q^{52} +8.76268i q^{53} +(-8.19615 - 6.69213i) q^{55} -1.26795 q^{56} -1.93185i q^{58} +10.3923 q^{59} -10.9282 q^{61} +10.1769i q^{62} +5.73205 q^{64} +(-9.46410 + 11.5911i) q^{65} -4.24264i q^{67} -2.44949i q^{68} +(8.19615 + 6.69213i) q^{70} +3.46410 q^{71} +7.34847i q^{73} +1.26795 q^{74} -11.6603 q^{76} -11.5911i q^{77} -6.19615 q^{79} +(7.73205 + 6.31319i) q^{80} +13.3843i q^{82} +4.52004i q^{83} +(2.00000 - 2.44949i) q^{85} -1.26795 q^{86} -2.44949i q^{88} -10.3923 q^{89} -16.3923 q^{91} +6.03579i q^{92} +2.73205 q^{94} +(-11.6603 - 9.52056i) q^{95} +6.03579i q^{97} -1.93185i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{10} + 12 q^{11} - 12 q^{14} - 4 q^{16} + 20 q^{19} + 12 q^{20} + 4 q^{25} - 24 q^{26} + 4 q^{29} - 28 q^{31} + 4 q^{34} + 4 q^{40} - 12 q^{44} - 20 q^{46} + 4 q^{49} + 24 q^{50} - 12 q^{55} - 12 q^{56}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q - 4 * q^10 + 12 * q^11 - 12 * q^14 - 4 * q^16 + 20 * q^19 + 12 * q^20 + 4 * q^25 - 24 * q^26 + 4 * q^29 - 28 * q^31 + 4 * q^34 + 4 * q^40 - 12 * q^44 - 20 * q^46 + 4 * q^49 + 24 * q^50 - 12 * q^55 - 12 * q^56 - 16 * q^61 + 16 * q^64 - 24 * q^65 + 12 * q^70 + 12 * q^74 - 12 * q^76 - 4 * q^79 + 24 * q^80 + 8 * q^85 - 12 * q^86 - 24 * q^91 + 4 * q^94 - 12 * q^95

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 $

$2$		−	1.93185i		−	1.36603i	−0.730406	−	0.683013i	$-0.760669\pi$
$2$		−	1.93185i		−	1.36603i	0.730406	−	0.683013i	$-0.239331\pi$
$3$		0			0
$3$		0			0
$4$	−1.73205			−0.866025
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$6$		0			0
$7$		−	2.44949i		−	0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$7$		−	2.44949i		−	0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$8$		−	0.517638i		−	0.183013i
$9$		0			0
$10$	−2.73205	+	3.34607i	−0.863950	+	1.05812i
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$		0			0
$13$		−	6.69213i		−	1.85606i	−0.372502	−	0.928032i	$-0.621500\pi$
$13$		−	6.69213i		−	1.85606i	0.372502	−	0.928032i	$-0.378500\pi$
$14$	−4.73205			−1.26469
$15$		0			0
$16$	−4.46410			−1.11603
$17$			1.41421i			0.342997i	0.985184	+	0.171499i	$0.0548609\pi$
$17$			1.41421i			0.342997i	−0.985184	+	0.171499i	$0.945139\pi$
$18$		0			0
$19$	6.73205			1.54444			0.772219	−	0.635356i	$-0.219147\pi$
$19$	6.73205			1.54444			0.772219	+	0.635356i	$0.219147\pi$
$20$	3.00000	+	2.44949i	0.670820	+	0.547723i
$21$		0			0
$22$		−	9.14162i		−	1.94900i
$23$		−	3.48477i		−	0.726624i	−0.931668	−	0.363312i	$-0.881646\pi$
$23$		−	3.48477i		−	0.726624i	0.931668	−	0.363312i	$-0.118354\pi$
$24$		0			0
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$	−12.9282			−2.53543
$27$		0			0
$28$			4.24264i			0.801784i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$		0			0
$31$	−5.26795			−0.946152			−0.473076	−	0.881022i	$-0.656856\pi$
$31$	−5.26795			−0.946152			−0.473076	+	0.881022i	$0.656856\pi$
$32$			7.58871i			1.34151i
$33$		0			0
$34$	2.73205			0.468543
$35$	−3.46410	+	4.24264i	−0.585540	+	0.717137i
$36$		0			0
$37$			0.656339i			0.107901i	0.998544	+	0.0539507i	$0.0171814\pi$
$37$			0.656339i			0.107901i	−0.998544	+	0.0539507i	$0.982819\pi$
$38$		−	13.0053i		−	2.10974i
$39$		0			0
$40$	−0.732051	+	0.896575i	−0.115747	+	0.141761i
$41$	−6.92820			−1.08200			−0.541002	−	0.841021i	$-0.681955\pi$
$41$	−6.92820			−1.08200			−0.541002	+	0.841021i	$0.681955\pi$
$42$		0			0
$43$		−	0.656339i		−	0.100091i	−0.998747	−	0.0500454i	$-0.984063\pi$
$43$		−	0.656339i		−	0.100091i	0.998747	−	0.0500454i	$-0.0159366\pi$
$44$	−8.19615			−1.23562
$45$		0			0
$46$	−6.73205			−0.992587
$47$			1.41421i			0.206284i	0.994667	+	0.103142i	$0.0328896\pi$
$47$			1.41421i			0.206284i	−0.994667	+	0.103142i	$0.967110\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	9.46410	−	1.93185i	1.33843	−	0.273205i
$51$		0			0
$52$			11.5911i			1.60740i
$53$			8.76268i			1.20365i	0.798629	+	0.601824i	$0.205559\pi$
$53$			8.76268i			1.20365i	−0.798629	+	0.601824i	$0.794441\pi$
$54$		0			0
$55$	−8.19615	−	6.69213i	−1.10517	−	0.902367i
$56$	−1.26795			−0.169437
$57$		0			0
$58$		−	1.93185i		−	0.253665i
$59$	10.3923			1.35296			0.676481	−	0.736460i	$-0.263504\pi$
$59$	10.3923			1.35296			0.676481	+	0.736460i	$0.263504\pi$
$60$		0			0
$61$	−10.9282			−1.39921			−0.699607	−	0.714528i	$-0.746641\pi$
$61$	−10.9282			−1.39921			−0.699607	+	0.714528i	$0.746641\pi$
$62$			10.1769i			1.29247i
$63$		0			0
$64$	5.73205			0.716506
$65$	−9.46410	+	11.5911i	−1.17388	+	1.43770i
$66$		0			0
$67$		−	4.24264i		−	0.518321i	−0.965834	−	0.259161i	$-0.916554\pi$
$67$		−	4.24264i		−	0.518321i	0.965834	−	0.259161i	$-0.0834459\pi$
$68$		−	2.44949i		−	0.297044i
$69$		0			0
$70$	8.19615	+	6.69213i	0.979628	+	0.799863i
$71$	3.46410			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$72$		0			0
$73$			7.34847i			0.860073i	0.902811	+	0.430037i	$0.141499\pi$
$73$			7.34847i			0.860073i	−0.902811	+	0.430037i	$0.858501\pi$
$74$	1.26795			0.147396
$75$		0			0
$76$	−11.6603			−1.33752
$77$		−	11.5911i		−	1.32093i
$78$		0			0
$79$	−6.19615			−0.697122			−0.348561	−	0.937286i	$-0.613330\pi$
$79$	−6.19615			−0.697122			−0.348561	+	0.937286i	$0.613330\pi$
$80$	7.73205	+	6.31319i	0.864470	+	0.705836i
$81$		0			0
$82$			13.3843i			1.47804i
$83$			4.52004i			0.496139i	0.968742	+	0.248070i	$0.0797961\pi$
$83$			4.52004i			0.496139i	−0.968742	+	0.248070i	$0.920204\pi$
$84$		0			0
$85$	2.00000	−	2.44949i	0.216930	−	0.265684i
$86$	−1.26795			−0.136726
$87$		0			0
$88$		−	2.44949i		−	0.261116i
$89$	−10.3923			−1.10158			−0.550791	−	0.834643i	$-0.685674\pi$
$89$	−10.3923			−1.10158			−0.550791	+	0.834643i	$0.685674\pi$
$90$		0			0
$91$	−16.3923			−1.71838
$92$			6.03579i			0.629275i
$93$		0			0
$94$	2.73205			0.281790
$95$	−11.6603	−	9.52056i	−1.19632	−	0.976789i
$96$		0			0
$97$			6.03579i			0.612842i	0.951896	+	0.306421i	$0.0991315\pi$
$97$			6.03579i			0.612842i	−0.951896	+	0.306421i	$0.900869\pi$
$98$		−	1.93185i		−	0.195146i
$99$		0			0
$100$	−1.73205	−	8.48528i	−0.173205	−	0.848528i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$		−	0.656339i		−	0.0646710i	−0.999477	−	0.0323355i	$-0.989705\pi$
$103$		−	0.656339i		−	0.0646710i	0.999477	−	0.0323355i	$-0.0102945\pi$
$104$	−3.46410			−0.339683
$105$		0			0
$106$	16.9282			1.64421
$107$		−	3.96524i		−	0.383334i	−0.981460	−	0.191667i	$-0.938611\pi$
$107$		−	3.96524i		−	0.383334i	0.981460	−	0.191667i	$-0.0613894\pi$
$108$		0			0
$109$	9.85641			0.944073			0.472036	−	0.881579i	$-0.343519\pi$
$109$	9.85641			0.944073			0.472036	+	0.881579i	$0.343519\pi$
$110$	−12.9282	+	15.8338i	−1.23266	+	1.50969i
$111$		0			0
$112$			10.9348i			1.03324i
$113$		−	1.69161i		−	0.159134i	−0.996830	−	0.0795669i	$-0.974646\pi$
$113$		−	1.69161i		−	0.159134i	0.996830	−	0.0795669i	$-0.0253537\pi$
$114$		0			0
$115$	−4.92820	+	6.03579i	−0.459557	+	0.562840i
$116$	−1.73205			−0.160817
$117$		0			0
$118$		−	20.0764i		−	1.84818i
$119$	3.46410			0.317554
$120$		0			0
$121$	11.3923			1.03566
$122$			21.1117i			1.91136i
$123$		0			0
$124$	9.12436			0.819391
$125$	5.19615	−	9.89949i	0.464758	−	0.885438i
$126$		0			0
$127$		−	4.24264i		−	0.376473i	−0.982124	−	0.188237i	$-0.939723\pi$
$127$		−	4.24264i		−	0.376473i	0.982124	−	0.188237i	$-0.0602772\pi$
$128$			4.10394i			0.362740i
$129$		0			0
$130$	22.3923	+	18.2832i	1.96394	+	1.60355i
$131$	1.26795			0.110781			0.0553906	−	0.998465i	$-0.482360\pi$
$131$	1.26795			0.110781			0.0553906	+	0.998465i	$0.482360\pi$
$132$		0			0
$133$		−	16.4901i		−	1.42987i
$134$	−8.19615			−0.708040
$135$		0			0
$136$	0.732051			0.0627728
$137$			5.00052i			0.427223i	0.976919	+	0.213611i	$0.0685226\pi$
$137$			5.00052i			0.427223i	−0.976919	+	0.213611i	$0.931477\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	6.00000	−	7.34847i	0.507093	−	0.621059i
$141$		0			0
$142$		−	6.69213i		−	0.561591i
$143$		−	31.6675i		−	2.64817i
$144$		0			0
$145$	−1.73205	−	1.41421i	−0.143839	−	0.117444i
$146$	14.1962			1.17488
$147$		0			0
$148$		−	1.13681i		−	0.0934454i
$149$	12.9282			1.05912			0.529560	−	0.848273i	$-0.322357\pi$
$149$	12.9282			1.05912			0.529560	+	0.848273i	$0.322357\pi$
$150$		0			0
$151$	22.7846			1.85419			0.927093	−	0.374832i	$-0.122300\pi$
$151$	22.7846			1.85419			0.927093	+	0.374832i	$0.122300\pi$
$152$		−	3.48477i		−	0.282652i
$153$		0			0
$154$	−22.3923			−1.80442
$155$	9.12436	+	7.45001i	0.732886	+	0.598399i
$156$		0			0
$157$		−	6.03579i		−	0.481709i	−0.970561	−	0.240854i	$-0.922572\pi$
$157$		−	6.03579i		−	0.481709i	0.970561	−	0.240854i	$-0.0774276\pi$
$158$			11.9700i			0.952286i
$159$		0			0
$160$	10.7321	−	13.1440i	0.848443	−	1.03913i
$161$	−8.53590			−0.672723
$162$		0			0
$163$		−	5.55532i		−	0.435126i	−0.976046	−	0.217563i	$-0.930189\pi$
$163$		−	5.55532i		−	0.435126i	0.976046	−	0.217563i	$-0.0698108\pi$
$164$	12.0000			0.937043
$165$		0			0
$166$	8.73205			0.677739
$167$		−	8.38375i		−	0.648754i	−0.945928	−	0.324377i	$-0.894845\pi$
$167$		−	8.38375i		−	0.648754i	0.945928	−	0.324377i	$-0.105155\pi$
$168$		0			0
$169$	−31.7846			−2.44497
$170$	−4.73205	−	3.86370i	−0.362932	−	0.296333i
$171$		0			0
$172$			1.13681i			0.0866811i
$173$		−	9.52056i		−	0.723835i	−0.932210	−	0.361917i	$-0.882122\pi$
$173$		−	9.52056i		−	0.723835i	0.932210	−	0.361917i	$-0.117878\pi$
$174$		0			0
$175$	12.0000	−	2.44949i	0.907115	−	0.185164i
$176$	−21.1244			−1.59231
$177$		0			0
$178$			20.0764i			1.50479i
$179$	9.46410			0.707380			0.353690	−	0.935363i	$-0.384927\pi$
$179$	9.46410			0.707380			0.353690	+	0.935363i	$0.384927\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$			31.6675i			2.34735i
$183$		0			0
$184$	−1.80385			−0.132981
$185$	0.928203	−	1.13681i	0.0682429	−	0.0835801i
$186$		0			0
$187$			6.69213i			0.489377i
$188$		−	2.44949i		−	0.178647i
$189$		0			0
$190$	−18.3923	+	22.5259i	−1.33432	+	1.63420i
$191$	9.12436			0.660215			0.330108	−	0.943943i	$-0.392915\pi$
$191$	9.12436			0.660215			0.330108	+	0.943943i	$0.392915\pi$
$192$		0			0
$193$			9.14162i			0.658028i	0.944325	+	0.329014i	$0.106716\pi$
$193$			9.14162i			0.658028i	−0.944325	+	0.329014i	$0.893284\pi$
$194$	11.6603			0.837157
$195$		0			0
$196$	−1.73205			−0.123718
$197$			16.7675i			1.19463i	0.802005	+	0.597317i	$0.203767\pi$
$197$			16.7675i			1.19463i	−0.802005	+	0.597317i	$0.796233\pi$
$198$		0			0
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	2.53590	−	0.517638i	0.179315	−	0.0366025i
$201$		0			0
$202$		−	11.5911i		−	0.815548i
$203$		−	2.44949i		−	0.171920i
$204$		0			0
$205$	12.0000	+	9.79796i	0.838116	+	0.684319i
$206$	−1.26795			−0.0883422
$207$		0			0
$208$			29.8744i			2.07141i
$209$	31.8564			2.20355
$210$		0			0
$211$	−11.2679			−0.775718			−0.387859	−	0.921719i	$-0.626785\pi$
$211$	−11.2679			−0.775718			−0.387859	+	0.921719i	$0.626785\pi$
$212$		−	15.1774i		−	1.04239i
$213$		0			0
$214$	−7.66025			−0.523644
$215$	−0.928203	+	1.13681i	−0.0633029	+	0.0775299i
$216$		0			0
$217$			12.9038i			0.875966i
$218$		−	19.0411i		−	1.28963i
$219$		0			0
$220$	14.1962	+	11.5911i	0.957104	+	0.781472i
$221$	9.46410			0.636624
$222$		0			0
$223$			23.8386i			1.59635i	0.602427	+	0.798174i	$0.294200\pi$
$223$			23.8386i			1.59635i	−0.602427	+	0.798174i	$0.705800\pi$
$224$	18.5885			1.24199
$225$		0			0
$226$	−3.26795			−0.217381
$227$		−	10.6574i		−	0.707354i	−0.935368	−	0.353677i	$-0.884931\pi$
$227$		−	10.6574i		−	0.707354i	0.935368	−	0.353677i	$-0.115069\pi$
$228$		0			0
$229$	22.7846			1.50565			0.752825	−	0.658221i	$-0.228691\pi$
$229$	22.7846			1.50565			0.752825	+	0.658221i	$0.228691\pi$
$230$	11.6603	+	9.52056i	0.768854	+	0.627767i
$231$		0			0
$232$		−	0.517638i		−	0.0339846i
$233$		−	26.0106i		−	1.70401i	−0.523530	−	0.852007i	$-0.675385\pi$
$233$		−	26.0106i		−	1.70401i	0.523530	−	0.852007i	$-0.324615\pi$
$234$		0			0
$235$	2.00000	−	2.44949i	0.130466	−	0.159787i
$236$	−18.0000			−1.17170
$237$		0			0
$238$		−	6.69213i		−	0.433786i
$239$	−10.3923			−0.672222			−0.336111	−	0.941822i	$-0.609112\pi$
$239$	−10.3923			−0.672222			−0.336111	+	0.941822i	$0.609112\pi$
$240$		0			0
$241$	4.53590			0.292183			0.146091	−	0.989271i	$-0.453331\pi$
$241$	4.53590			0.292183			0.146091	+	0.989271i	$0.453331\pi$
$242$		−	22.0082i		−	1.41474i
$243$		0			0
$244$	18.9282			1.21175
$245$	−1.73205	−	1.41421i	−0.110657	−	0.0903508i
$246$		0			0
$247$		−	45.0518i		−	2.86657i
$248$			2.72689i			0.173158i
$249$		0			0
$250$	−19.1244	−	10.0382i	−1.20953	−	0.634871i
$251$	9.12436			0.575924			0.287962	−	0.957642i	$-0.407022\pi$
$251$	9.12436			0.575924			0.287962	+	0.957642i	$0.407022\pi$
$252$		0			0
$253$		−	16.4901i		−	1.03672i
$254$	−8.19615			−0.514272
$255$		0			0
$256$	19.3923			1.21202
$257$		−	4.62158i		−	0.288286i	−0.989557	−	0.144143i	$-0.953957\pi$
$257$		−	4.62158i		−	0.288286i	0.989557	−	0.144143i	$-0.0460425\pi$
$258$		0			0
$259$	1.60770			0.0998973
$260$	16.3923	−	20.0764i	1.01661	−	1.24508i
$261$		0			0
$262$		−	2.44949i		−	0.151330i
$263$			24.5964i			1.51668i	0.651859	+	0.758341i	$0.273990\pi$
$263$			24.5964i			1.51668i	−0.651859	+	0.758341i	$0.726010\pi$
$264$		0			0
$265$	12.3923	−	15.1774i	0.761253	−	0.932341i
$266$	−31.8564			−1.95324
$267$		0			0
$268$			7.34847i			0.448879i
$269$	−12.0000			−0.731653			−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000			−0.731653			−0.365826	+	0.930683i	$0.619214\pi$
$270$		0			0
$271$	−23.2679			−1.41343			−0.706714	−	0.707500i	$-0.749823\pi$
$271$	−23.2679			−1.41343			−0.706714	+	0.707500i	$0.749823\pi$
$272$		−	6.31319i		−	0.382794i
$273$		0			0
$274$	9.66025			0.583597
$275$	4.73205	+	23.1822i	0.285353	+	1.39794i
$276$		0			0
$277$		−	23.6627i		−	1.42175i	−0.703317	−	0.710877i	$-0.748298\pi$
$277$		−	23.6627i		−	1.42175i	0.703317	−	0.710877i	$-0.251702\pi$
$278$		−	15.4548i		−	0.926918i
$279$		0			0
$280$	2.19615	+	1.79315i	0.131245	+	0.107161i
$281$	8.78461			0.524046			0.262023	−	0.965062i	$-0.415610\pi$
$281$	8.78461			0.524046			0.262023	+	0.965062i	$0.415610\pi$
$282$		0			0
$283$			1.96902i			0.117046i	0.998286	+	0.0585229i	$0.0186391\pi$
$283$			1.96902i			0.117046i	−0.998286	+	0.0585229i	$0.981361\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−61.1769			−3.61747
$287$			16.9706i			1.00174i
$288$		0			0
$289$	15.0000			0.882353
$290$	−2.73205	+	3.34607i	−0.160432	+	0.196488i
$291$		0			0
$292$		−	12.7279i		−	0.744845i
$293$		−	25.8348i		−	1.50928i	−0.656137	−	0.754642i	$-0.727811\pi$
$293$		−	25.8348i		−	1.50928i	0.656137	−	0.754642i	$-0.272189\pi$
$294$		0			0
$295$	−18.0000	−	14.6969i	−1.04800	−	0.855689i
$296$	0.339746			0.0197473
$297$		0			0
$298$		−	24.9754i		−	1.44678i
$299$	−23.3205			−1.34866
$300$		0			0
$301$	−1.60770			−0.0926660
$302$		−	44.0165i		−	2.53286i
$303$		0			0
$304$	−30.0526			−1.72363
$305$	18.9282	+	15.4548i	1.08383	+	0.884940i
$306$		0			0
$307$			18.9396i			1.08094i	0.841364	+	0.540469i	$0.181753\pi$
$307$			18.9396i			1.08094i	−0.841364	+	0.540469i	$0.818247\pi$
$308$			20.0764i			1.14396i
$309$		0			0
$310$	14.3923	−	17.6269i	0.817428	−	1.00114i
$311$	−24.5885			−1.39428			−0.697142	−	0.716933i	$-0.745545\pi$
$311$	−24.5885			−1.39428			−0.697142	+	0.716933i	$0.745545\pi$
$312$		0			0
$313$		−	18.7637i		−	1.06059i	−0.847814	−	0.530294i	$-0.822082\pi$
$313$		−	18.7637i		−	1.06059i	0.847814	−	0.530294i	$-0.177918\pi$
$314$	−11.6603			−0.658026
$315$		0			0
$316$	10.7321			0.603725
$317$		−	25.3543i		−	1.42404i	−0.702159	−	0.712020i	$-0.747781\pi$
$317$		−	25.3543i		−	1.42404i	0.702159	−	0.712020i	$-0.252219\pi$
$318$		0			0
$319$	4.73205			0.264944
$320$	−9.92820	−	8.10634i	−0.555003	−	0.453158i
$321$		0			0
$322$			16.4901i			0.918957i
$323$			9.52056i			0.529738i
$324$		0			0
$325$	32.7846	−	6.69213i	1.81856	−	0.371213i
$326$	−10.7321			−0.594393
$327$		0			0
$328$			3.58630i			0.198020i
$329$	3.46410			0.190982
$330$		0			0
$331$	−7.80385			−0.428938			−0.214469	−	0.976731i	$-0.568802\pi$
$331$	−7.80385			−0.428938			−0.214469	+	0.976731i	$0.568802\pi$
$332$		−	7.82894i		−	0.429669i
$333$		0			0
$334$	−16.1962			−0.886214
$335$	−6.00000	+	7.34847i	−0.327815	+	0.401490i
$336$		0			0
$337$			23.0064i			1.25324i	0.779327	+	0.626618i	$0.215561\pi$
$337$			23.0064i			1.25324i	−0.779327	+	0.626618i	$0.784439\pi$
$338$			61.4032i			3.33989i
$339$		0			0
$340$	−3.46410	+	4.24264i	−0.187867	+	0.230089i
$341$	−24.9282			−1.34994
$342$		0			0
$343$		−	19.5959i		−	1.05808i
$344$	−0.339746			−0.0183179
$345$		0			0
$346$	−18.3923			−0.988776
$347$			6.79367i			0.364703i	0.983233	+	0.182352i	$0.0583709\pi$
$347$			6.79367i			0.364703i	−0.983233	+	0.182352i	$0.941629\pi$
$348$		0			0
$349$	−18.7846			−1.00552			−0.502759	−	0.864427i	$-0.667682\pi$
$349$	−18.7846			−1.00552			−0.502759	+	0.864427i	$0.667682\pi$
$350$	−4.73205	−	23.1822i	−0.252939	−	1.23914i
$351$		0			0
$352$			35.9101i			1.91402i
$353$		−	12.1459i		−	0.646462i	−0.946320	−	0.323231i	$-0.895231\pi$
$353$		−	12.1459i		−	0.646462i	0.946320	−	0.323231i	$-0.104769\pi$
$354$		0			0
$355$	−6.00000	−	4.89898i	−0.318447	−	0.260011i
$356$	18.0000			0.953998
$357$		0			0
$358$		−	18.2832i		−	0.966299i
$359$	−10.7321			−0.566416			−0.283208	−	0.959059i	$-0.591399\pi$
$359$	−10.7321			−0.566416			−0.283208	+	0.959059i	$0.591399\pi$
$360$		0			0
$361$	26.3205			1.38529
$362$			30.9096i			1.62457i
$363$		0			0
$364$	28.3923			1.48816
$365$	10.3923	−	12.7279i	0.543958	−	0.666210i
$366$		0			0
$367$		−	25.1512i		−	1.31288i	−0.754377	−	0.656442i	$-0.772061\pi$
$367$		−	25.1512i		−	1.31288i	0.754377	−	0.656442i	$-0.227939\pi$
$368$			15.5563i			0.810931i
$369$		0			0
$370$	−2.19615	−	1.79315i	−0.114173	−	0.0932215i
$371$	21.4641			1.11436
$372$		0			0
$373$			19.5959i			1.01464i	0.861758	+	0.507319i	$0.169363\pi$
$373$			19.5959i			1.01464i	−0.861758	+	0.507319i	$0.830637\pi$
$374$	12.9282			0.668501
$375$		0			0
$376$	0.732051			0.0377526
$377$		−	6.69213i		−	0.344662i
$378$		0			0
$379$	5.80385			0.298124			0.149062	−	0.988828i	$-0.452375\pi$
$379$	5.80385			0.298124			0.149062	+	0.988828i	$0.452375\pi$
$380$	20.1962	+	16.4901i	1.03604	+	0.845924i
$381$		0			0
$382$		−	17.6269i		−	0.901871i
$383$		−	23.5612i		−	1.20392i	−0.798527	−	0.601959i	$-0.794387\pi$
$383$		−	23.5612i		−	1.20392i	0.798527	−	0.601959i	$-0.205613\pi$
$384$		0			0
$385$	−16.3923	+	20.0764i	−0.835429	+	1.02319i
$386$	17.6603			0.898883
$387$		0			0
$388$		−	10.4543i		−	0.530737i
$389$	20.7846			1.05382			0.526911	−	0.849921i	$-0.323350\pi$
$389$	20.7846			1.05382			0.526911	+	0.849921i	$0.323350\pi$
$390$		0			0
$391$	4.92820			0.249230
$392$		−	0.517638i		−	0.0261447i
$393$		0			0
$394$	32.3923			1.63190
$395$	10.7321	+	8.76268i	0.539988	+	0.440898i
$396$		0			0
$397$			4.89898i			0.245873i	0.992415	+	0.122936i	$0.0392311\pi$
$397$			4.89898i			0.245873i	−0.992415	+	0.122936i	$0.960769\pi$
$398$		−	27.0459i		−	1.35569i
$399$		0			0
$400$	−4.46410	−	21.8695i	−0.223205	−	1.09348i
$401$	−10.1436			−0.506547			−0.253273	−	0.967395i	$-0.581507\pi$
$401$	−10.1436			−0.506547			−0.253273	+	0.967395i	$0.581507\pi$
$402$		0			0
$403$			35.2538i			1.75612i
$404$	−10.3923			−0.517036
$405$		0			0
$406$	−4.73205			−0.234848
$407$			3.10583i			0.153950i
$408$		0			0
$409$	−22.9282			−1.13373			−0.566863	−	0.823812i	$-0.691843\pi$
$409$	−22.9282			−1.13373			−0.566863	+	0.823812i	$0.691843\pi$
$410$	18.9282	−	23.1822i	0.934797	−	1.14489i
$411$		0			0
$412$			1.13681i			0.0560067i
$413$		−	25.4558i		−	1.25260i
$414$		0			0
$415$	6.39230	−	7.82894i	0.313786	−	0.384308i
$416$	50.7846			2.48992
$417$		0			0
$418$		−	61.5419i		−	3.01011i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	−1.46410			−0.0713559			−0.0356780	−	0.999363i	$-0.511359\pi$
$421$	−1.46410			−0.0713559			−0.0356780	+	0.999363i	$0.511359\pi$
$422$			21.7680i			1.05965i
$423$		0			0
$424$	4.53590			0.220283
$425$	−6.92820	+	1.41421i	−0.336067	+	0.0685994i
$426$		0			0
$427$			26.7685i			1.29542i
$428$			6.86800i			0.331977i
$429$		0			0
$430$	2.19615	+	1.79315i	0.105908	+	0.0864734i
$431$	−25.1769			−1.21273			−0.606365	−	0.795187i	$-0.707373\pi$
$431$	−25.1769			−1.21273			−0.606365	+	0.795187i	$0.707373\pi$
$432$		0			0
$433$		−	22.5259i		−	1.08252i	−0.840854	−	0.541262i	$-0.817947\pi$
$433$		−	22.5259i		−	1.08252i	0.840854	−	0.541262i	$-0.182053\pi$
$434$	24.9282			1.19659
$435$		0			0
$436$	−17.0718			−0.817591
$437$		−	23.4596i		−	1.12223i
$438$		0			0
$439$	20.9282			0.998849			0.499424	−	0.866358i	$-0.333545\pi$
$439$	20.9282			0.998849			0.499424	+	0.866358i	$0.333545\pi$
$440$	−3.46410	+	4.24264i	−0.165145	+	0.202260i
$441$		0			0
$442$		−	18.2832i		−	0.869645i
$443$			21.0101i			0.998221i	0.866538	+	0.499111i	$0.166340\pi$
$443$			21.0101i			0.998221i	−0.866538	+	0.499111i	$0.833660\pi$
$444$		0			0
$445$	18.0000	+	14.6969i	0.853282	+	0.696702i
$446$	46.0526			2.18065
$447$		0			0
$448$		−	14.0406i		−	0.663356i
$449$	1.85641			0.0876092			0.0438046	−	0.999040i	$-0.486052\pi$
$449$	1.85641			0.0876092			0.0438046	+	0.999040i	$0.486052\pi$
$450$		0			0
$451$	−32.7846			−1.54377
$452$			2.92996i			0.137814i
$453$		0			0
$454$	−20.5885			−0.966264
$455$	28.3923	+	23.1822i	1.33105	+	1.08680i
$456$		0			0
$457$			18.7637i			0.877730i	0.898553	+	0.438865i	$0.144619\pi$
$457$			18.7637i			0.877730i	−0.898553	+	0.438865i	$0.855381\pi$
$458$		−	44.0165i		−	2.05676i
$459$		0			0
$460$	8.53590	−	10.4543i	0.397988	−	0.487434i
$461$	−11.0718			−0.515665			−0.257832	−	0.966190i	$-0.583008\pi$
$461$	−11.0718			−0.515665			−0.257832	+	0.966190i	$0.583008\pi$
$462$		0			0
$463$		−	32.3238i		−	1.50222i	−0.660179	−	0.751108i	$-0.729520\pi$
$463$		−	32.3238i		−	1.50222i	0.660179	−	0.751108i	$-0.270480\pi$
$464$	−4.46410			−0.207241
$465$		0			0
$466$	−50.2487			−2.32773
$467$		−	18.1817i		−	0.841349i	−0.907212	−	0.420674i	$-0.861793\pi$
$467$		−	18.1817i		−	0.841349i	0.907212	−	0.420674i	$-0.138207\pi$
$468$		0			0
$469$	−10.3923			−0.479872
$470$	−4.73205	−	3.86370i	−0.218273	−	0.178219i
$471$		0			0
$472$		−	5.37945i		−	0.247609i
$473$		−	3.10583i		−	0.142806i
$474$		0			0
$475$	6.73205	+	32.9802i	0.308888	+	1.51323i
$476$	−6.00000			−0.275010
$477$		0			0
$478$			20.0764i			0.918273i
$479$	−11.6603			−0.532771			−0.266385	−	0.963867i	$-0.585829\pi$
$479$	−11.6603			−0.532771			−0.266385	+	0.963867i	$0.585829\pi$
$480$		0			0
$481$	4.39230			0.200272
$482$		−	8.76268i		−	0.399129i
$483$		0			0
$484$	−19.7321			−0.896911
$485$	8.53590	−	10.4543i	0.387595	−	0.474705i
$486$		0			0
$487$			6.03579i			0.273508i	0.990605	+	0.136754i	$0.0436670\pi$
$487$			6.03579i			0.273508i	−0.990605	+	0.136754i	$0.956333\pi$
$488$			5.65685i			0.256074i
$489$		0			0
$490$	−2.73205	+	3.34607i	−0.123421	+	0.151160i
$491$	−10.7321			−0.484331			−0.242165	−	0.970235i	$-0.577858\pi$
$491$	−10.7321			−0.484331			−0.242165	+	0.970235i	$0.577858\pi$
$492$		0			0
$493$			1.41421i			0.0636930i
$494$	−87.0333			−3.91581
$495$		0			0
$496$	23.5167			1.05593
$497$		−	8.48528i		−	0.380617i
$498$		0			0
$499$	14.9282			0.668278			0.334139	−	0.942524i	$-0.391554\pi$
$499$	14.9282			0.668278			0.334139	+	0.942524i	$0.391554\pi$
$500$	−9.00000	+	17.1464i	−0.402492	+	0.766812i
$501$		0			0
$502$		−	17.6269i		−	0.786727i
$503$			41.5670i			1.85338i	0.375826	+	0.926690i	$0.377359\pi$
$503$			41.5670i			1.85338i	−0.375826	+	0.926690i	$0.622641\pi$
$504$		0			0
$505$	−10.3923	−	8.48528i	−0.462451	−	0.377590i
$506$	−31.8564			−1.41619
$507$		0			0
$508$			7.34847i			0.326036i
$509$	26.5359			1.17618			0.588092	−	0.808794i	$-0.299879\pi$
$509$	26.5359			1.17618			0.588092	+	0.808794i	$0.299879\pi$
$510$		0			0
$511$	18.0000			0.796273
$512$		−	29.2552i		−	1.29291i
$513$		0			0
$514$	−8.92820			−0.393806
$515$	−0.928203	+	1.13681i	−0.0409015	+	0.0500939i
$516$		0			0
$517$			6.69213i			0.294320i
$518$		−	3.10583i		−	0.136462i
$519$		0			0
$520$	6.00000	+	4.89898i	0.263117	+	0.214834i
$521$	16.3923			0.718160			0.359080	−	0.933307i	$-0.383091\pi$
$521$	16.3923			0.718160			0.359080	+	0.933307i	$0.383091\pi$
$522$		0			0
$523$			40.8091i			1.78446i	0.451583	+	0.892229i	$0.350860\pi$
$523$			40.8091i			1.78446i	−0.451583	+	0.892229i	$0.649140\pi$
$524$	−2.19615			−0.0959394
$525$		0			0
$526$	47.5167			2.07182
$527$		−	7.45001i		−	0.324527i
$528$		0			0
$529$	10.8564			0.472018
$530$	−29.3205	−	23.9401i	−1.27360	−	1.03989i
$531$		0			0
$532$			28.5617i			1.23831i
$533$			46.3644i			2.00827i
$534$		0			0
$535$	−5.60770	+	6.86800i	−0.242442	+	0.296929i
$536$	−2.19615			−0.0948593
$537$		0			0
$538$			23.1822i			0.999456i
$539$	4.73205			0.203824
$540$		0			0
$541$	21.6077			0.928987			0.464494	−	0.885576i	$-0.346236\pi$
$541$	21.6077			0.928987			0.464494	+	0.885576i	$0.346236\pi$
$542$			44.9502i			1.93078i
$543$		0			0
$544$	−10.7321			−0.460133
$545$	−17.0718	−	13.9391i	−0.731275	−	0.597084i
$546$		0			0
$547$		−	2.44949i		−	0.104733i	−0.998628	−	0.0523663i	$-0.983324\pi$
$547$		−	2.44949i		−	0.104733i	0.998628	−	0.0523663i	$-0.0166763\pi$
$548$		−	8.66115i		−	0.369986i
$549$		0			0
$550$	44.7846	−	9.14162i	1.90962	−	0.389800i
$551$	6.73205			0.286795
$552$		0			0
$553$			15.1774i			0.645409i
$554$	−45.7128			−1.94215
$555$		0			0
$556$	−13.8564			−0.587643
$557$			28.8391i			1.22195i	0.791650	+	0.610975i	$0.209223\pi$
$557$			28.8391i			1.22195i	−0.791650	+	0.610975i	$0.790777\pi$
$558$		0			0
$559$	−4.39230			−0.185775
$560$	15.4641	−	18.9396i	0.653478	−	0.800343i
$561$		0			0
$562$		−	16.9706i		−	0.715860i
$563$			16.1112i			0.679004i	0.940605	+	0.339502i	$0.110259\pi$
$563$			16.1112i			0.679004i	−0.940605	+	0.339502i	$0.889741\pi$
$564$		0			0
$565$	−2.39230	+	2.92996i	−0.100645	+	0.123264i
$566$	3.80385			0.159888
$567$		0			0
$568$		−	1.79315i		−	0.0752389i
$569$	14.5359			0.609377			0.304688	−	0.952452i	$-0.401448\pi$
$569$	14.5359			0.609377			0.304688	+	0.952452i	$0.401448\pi$
$570$		0			0
$571$	−4.67949			−0.195831			−0.0979153	−	0.995195i	$-0.531217\pi$
$571$	−4.67949			−0.195831			−0.0979153	+	0.995195i	$0.531217\pi$
$572$			54.8497i			2.29338i
$573$		0			0
$574$	32.7846			1.36840
$575$	17.0718	−	3.48477i	0.711943	−	0.145325i
$576$		0			0
$577$			0.656339i			0.0273237i	0.999907	+	0.0136619i	$0.00434884\pi$
$577$			0.656339i			0.0273237i	−0.999907	+	0.0136619i	$0.995651\pi$
$578$		−	28.9778i		−	1.20532i
$579$		0			0
$580$	3.00000	+	2.44949i	0.124568	+	0.101710i
$581$	11.0718			0.459336
$582$		0			0
$583$			41.4655i			1.71732i
$584$	3.80385			0.157404
$585$		0			0
$586$	−49.9090			−2.06172
$587$		−	15.5563i		−	0.642079i	−0.947066	−	0.321040i	$-0.895968\pi$
$587$		−	15.5563i		−	0.642079i	0.947066	−	0.321040i	$-0.104032\pi$
$588$		0			0
$589$	−35.4641			−1.46127
$590$	−28.3923	+	34.7733i	−1.16889	+	1.43160i
$591$		0			0
$592$		−	2.92996i		−	0.120421i
$593$			28.3586i			1.16455i	0.812993	+	0.582274i	$0.197837\pi$
$593$			28.3586i			1.16455i	−0.812993	+	0.582274i	$0.802163\pi$
$594$		0			0
$595$	−6.00000	−	4.89898i	−0.245976	−	0.200839i
$596$	−22.3923			−0.917225
$597$		0			0
$598$			45.0518i			1.84230i
$599$	4.73205			0.193346			0.0966732	−	0.995316i	$-0.469180\pi$
$599$	4.73205			0.193346			0.0966732	+	0.995316i	$0.469180\pi$
$600$		0			0
$601$	−24.7846			−1.01099			−0.505493	−	0.862831i	$-0.668689\pi$
$601$	−24.7846			−1.01099			−0.505493	+	0.862831i	$0.668689\pi$
$602$			3.10583i			0.126584i
$603$		0			0
$604$	−39.4641			−1.60577
$605$	−19.7321	−	16.1112i	−0.802222	−	0.655011i
$606$		0			0
$607$		−	26.1122i		−	1.05986i	−0.848041	−	0.529930i	$-0.822218\pi$
$607$		−	26.1122i		−	1.05986i	0.848041	−	0.529930i	$-0.177782\pi$
$608$			51.0876i			2.07187i
$609$		0			0
$610$	29.8564	−	36.5665i	1.20885	−	1.48053i
$611$	9.46410			0.382877
$612$		0			0
$613$		−	1.31268i		−	0.0530185i	−0.999649	−	0.0265093i	$-0.991561\pi$
$613$		−	1.31268i		−	0.0530185i	0.999649	−	0.0265093i	$-0.00843915\pi$
$614$	36.5885			1.47659
$615$		0			0
$616$	−6.00000			−0.241747
$617$		−	7.55154i		−	0.304014i	−0.988379	−	0.152007i	$-0.951426\pi$
$617$		−	7.55154i		−	0.304014i	0.988379	−	0.152007i	$-0.0485736\pi$
$618$		0			0
$619$	34.1962			1.37446			0.687230	−	0.726440i	$-0.258827\pi$
$619$	34.1962			1.37446			0.687230	+	0.726440i	$0.258827\pi$
$620$	−15.8038	−	12.9038i	−0.634698	−	0.518229i
$621$		0			0
$622$			47.5013i			1.90463i
$623$			25.4558i			1.01987i
$624$		0			0
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	−36.2487			−1.44879
$627$		0			0
$628$			10.4543i			0.417172i
$629$	−0.928203			−0.0370099
$630$		0			0
$631$	36.3923			1.44875			0.724377	−	0.689404i	$-0.242127\pi$
$631$	36.3923			1.44875			0.724377	+	0.689404i	$0.242127\pi$
$632$			3.20736i			0.127582i
$633$		0			0
$634$	−48.9808			−1.94527
$635$	−6.00000	+	7.34847i	−0.238103	+	0.291615i
$636$		0			0
$637$		−	6.69213i		−	0.265152i
$638$		−	9.14162i		−	0.361920i
$639$		0			0
$640$	5.80385	−	7.10823i	0.229417	−	0.280978i
$641$	34.6410			1.36824			0.684119	−	0.729370i	$-0.260187\pi$
$641$	34.6410			1.36824			0.684119	+	0.729370i	$0.260187\pi$
$642$		0			0
$643$			18.9396i			0.746904i	0.927649	+	0.373452i	$0.121826\pi$
$643$			18.9396i			0.746904i	−0.927649	+	0.373452i	$0.878174\pi$
$644$	14.7846			0.582595
$645$		0			0
$646$	18.3923			0.723636
$647$		−	19.9749i		−	0.785293i	−0.919690	−	0.392646i	$-0.871560\pi$
$647$		−	19.9749i		−	0.785293i	0.919690	−	0.392646i	$-0.128440\pi$
$648$		0			0
$649$	49.1769			1.93036
$650$	−12.9282	−	63.3350i	−0.507086	−	2.48420i
$651$		0			0
$652$			9.62209i			0.376830i
$653$		−	1.69161i		−	0.0661980i	−0.999452	−	0.0330990i	$-0.989462\pi$
$653$		−	1.69161i		−	0.0661980i	0.999452	−	0.0330990i	$-0.0105377\pi$
$654$		0			0
$655$	−2.19615	−	1.79315i	−0.0858108	−	0.0700642i
$656$	30.9282			1.20754
$657$		0			0
$658$		−	6.69213i		−	0.260886i
$659$	−26.4449			−1.03015			−0.515073	−	0.857146i	$-0.672235\pi$
$659$	−26.4449			−1.03015			−0.515073	+	0.857146i	$0.672235\pi$
$660$		0			0
$661$	40.7846			1.58634			0.793169	−	0.609002i	$-0.208430\pi$
$661$	40.7846			1.58634			0.793169	+	0.609002i	$0.208430\pi$
$662$			15.0759i			0.585941i
$663$		0			0
$664$	2.33975			0.0907998
$665$	−23.3205	+	28.5617i	−0.904331	+	1.10757i
$666$		0			0
$667$		−	3.48477i		−	0.134931i
$668$			14.5211i			0.561837i
$669$		0			0
$670$	14.1962	+	11.5911i	0.548445	+	0.447804i
$671$	−51.7128			−1.99635
$672$		0			0
$673$		−	12.4233i		−	0.478884i	−0.970911	−	0.239442i	$-0.923036\pi$
$673$		−	12.4233i		−	0.478884i	0.970911	−	0.239442i	$-0.0769644\pi$
$674$	44.4449			1.71195
$675$		0			0
$676$	55.0526			2.11741
$677$			46.9464i			1.80430i	0.431424	+	0.902149i	$0.358011\pi$
$677$			46.9464i			1.80430i	−0.431424	+	0.902149i	$0.641989\pi$
$678$		0			0
$679$	14.7846			0.567381
$680$	−1.26795	−	1.03528i	−0.0486236	−	0.0397010i
$681$		0			0
$682$			48.1576i			1.84405i
$683$			31.7690i			1.21561i	0.794087	+	0.607804i	$0.207949\pi$
$683$			31.7690i			1.21561i	−0.794087	+	0.607804i	$0.792051\pi$
$684$		0			0
$685$	7.07180	−	8.66115i	0.270199	−	0.330925i
$686$	−37.8564			−1.44536
$687$		0			0
$688$			2.92996i			0.111704i
$689$	58.6410			2.23404
$690$		0			0
$691$	−13.7128			−0.521660			−0.260830	−	0.965385i	$-0.583996\pi$
$691$	−13.7128			−0.521660			−0.260830	+	0.965385i	$0.583996\pi$
$692$			16.4901i			0.626859i
$693$		0			0
$694$	13.1244			0.498194
$695$	−13.8564	−	11.3137i	−0.525603	−	0.429153i
$696$		0			0
$697$		−	9.79796i		−	0.371124i
$698$			36.2891i			1.37356i
$699$		0			0
$700$	−20.7846	+	4.24264i	−0.785584	+	0.160357i
$701$	27.7128			1.04670			0.523349	−	0.852118i	$-0.324682\pi$
$701$	27.7128			1.04670			0.523349	+	0.852118i	$0.324682\pi$
$702$		0			0
$703$			4.41851i			0.166647i
$704$	27.1244			1.02229
$705$		0			0
$706$	−23.4641			−0.883083
$707$		−	14.6969i		−	0.552735i
$708$		0			0
$709$	0.392305			0.0147333			0.00736666	−	0.999973i	$-0.497655\pi$
$709$	0.392305			0.0147333			0.00736666	+	0.999973i	$0.497655\pi$
$710$	−9.46410	+	11.5911i	−0.355181	+	0.435007i
$711$		0			0
$712$			5.37945i			0.201604i
$713$			18.3576i			0.687496i
$714$		0			0
$715$	−44.7846	+	54.8497i	−1.67485	+	2.05126i
$716$	−16.3923			−0.612609
$717$		0			0
$718$			20.7327i			0.773739i
$719$	7.85641			0.292995			0.146497	−	0.989211i	$-0.453200\pi$
$719$	7.85641			0.292995			0.146497	+	0.989211i	$0.453200\pi$
$720$		0			0
$721$	−1.60770			−0.0598737
$722$		−	50.8473i		−	1.89234i
$723$		0			0
$724$	27.7128			1.02994
$725$	1.00000	+	4.89898i	0.0371391	+	0.181944i
$726$		0			0
$727$			46.6690i			1.73086i	0.501031	+	0.865430i	$0.332954\pi$
$727$			46.6690i			1.73086i	−0.501031	+	0.865430i	$0.667046\pi$
$728$			8.48528i			0.314485i
$729$		0			0
$730$	−24.5885	−	20.0764i	−0.910060	−	0.743061i
$731$	0.928203			0.0343308
$732$		0			0
$733$			12.7279i			0.470117i	0.971981	+	0.235058i	$0.0755281\pi$
$733$			12.7279i			0.470117i	−0.971981	+	0.235058i	$0.924472\pi$
$734$	−48.5885			−1.79343
$735$		0			0
$736$	26.4449			0.974771
$737$		−	20.0764i		−	0.739523i
$738$		0			0
$739$	−32.9808			−1.21322			−0.606608	−	0.795001i	$-0.707470\pi$
$739$	−32.9808			−1.21322			−0.606608	+	0.795001i	$0.707470\pi$
$740$	−1.60770	+	1.96902i	−0.0591000	+	0.0723825i
$741$		0			0
$742$		−	41.4655i		−	1.52224i
$743$			9.89949i			0.363177i	0.983375	+	0.181589i	$0.0581239\pi$
$743$			9.89949i			0.363177i	−0.983375	+	0.181589i	$0.941876\pi$
$744$		0			0
$745$	−22.3923	−	18.2832i	−0.820391	−	0.669846i
$746$	37.8564			1.38602
$747$		0			0
$748$		−	11.5911i		−	0.423813i
$749$	−9.71281			−0.354898
$750$		0			0
$751$	−15.9090			−0.580526			−0.290263	−	0.956947i	$-0.593743\pi$
$751$	−15.9090			−0.580526			−0.290263	+	0.956947i	$0.593743\pi$
$752$		−	6.31319i		−	0.230218i
$753$		0			0
$754$	−12.9282			−0.470817
$755$	−39.4641	−	32.2223i	−1.43625	−	1.17269i
$756$		0			0
$757$		−	6.03579i		−	0.219375i	−0.993966	−	0.109687i	$-0.965015\pi$
$757$		−	6.03579i		−	0.219375i	0.993966	−	0.109687i	$-0.0349849\pi$
$758$		−	11.2122i		−	0.407244i
$759$		0			0
$760$	−4.92820	+	6.03579i	−0.178765	+	0.218941i
$761$	−47.5692			−1.72438			−0.862191	−	0.506583i	$-0.830909\pi$
$761$	−47.5692			−1.72438			−0.862191	+	0.506583i	$0.830909\pi$
$762$		0			0
$763$		−	24.1432i		−	0.874041i
$764$	−15.8038			−0.571763
$765$		0			0
$766$	−45.5167			−1.64458
$767$		−	69.5467i		−	2.51118i
$768$		0			0
$769$	32.9282			1.18742			0.593711	−	0.804679i	$-0.297662\pi$
$769$	32.9282			1.18742			0.593711	+	0.804679i	$0.297662\pi$
$770$	38.7846	+	31.6675i	1.39770	+	1.14122i
$771$		0			0
$772$		−	15.8338i		−	0.569869i
$773$		−	8.38375i		−	0.301542i	−0.988569	−	0.150771i	$-0.951824\pi$
$773$		−	8.38375i		−	0.301542i	0.988569	−	0.150771i	$-0.0481757\pi$
$774$		0			0
$775$	−5.26795	−	25.8076i	−0.189230	−	0.927035i
$776$	3.12436			0.112158
$777$		0			0
$778$		−	40.1528i		−	1.43955i
$779$	−46.6410			−1.67109
$780$		0			0
$781$	16.3923			0.586563
$782$		−	9.52056i		−	0.340454i
$783$		0			0
$784$	−4.46410			−0.159432
$785$	−8.53590	+	10.4543i	−0.304659	+	0.373130i
$786$		0			0
$787$		−	49.7749i		−	1.77428i	−0.461498	−	0.887141i	$-0.652688\pi$
$787$		−	49.7749i		−	1.77428i	0.461498	−	0.887141i	$-0.347312\pi$
$788$		−	29.0421i		−	1.03458i
$789$		0			0
$790$	16.9282	−	20.7327i	0.602278	−	0.737637i
$791$	−4.14359			−0.147329
$792$		0			0
$793$			73.1330i			2.59703i
$794$	9.46410			0.335868
$795$		0			0
$796$	−24.2487			−0.859473
$797$		−	34.6718i		−	1.22814i	−0.789252	−	0.614069i	$-0.789532\pi$
$797$		−	34.6718i		−	1.22814i	0.789252	−	0.614069i	$-0.210468\pi$
$798$		0			0
$799$	−2.00000			−0.0707549
$800$	−37.1769	+	7.58871i	−1.31440	+	0.268301i
$801$		0			0
$802$			19.5959i			0.691956i
$803$			34.7733i			1.22712i
$804$		0			0
$805$	14.7846	+	12.0716i	0.521089	+	0.425467i
$806$	68.1051			2.39890
$807$		0			0
$808$		−	3.10583i		−	0.109263i
$809$	34.3923			1.20917			0.604585	−	0.796541i	$-0.293339\pi$
$809$	34.3923			1.20917			0.604585	+	0.796541i	$0.293339\pi$
$810$		0			0
$811$	4.78461			0.168010			0.0840052	−	0.996465i	$-0.473229\pi$
$811$	4.78461			0.168010			0.0840052	+	0.996465i	$0.473229\pi$
$812$			4.24264i			0.148888i
$813$		0			0
$814$	6.00000			0.210300
$815$	−7.85641	+	9.62209i	−0.275198	+	0.337047i
$816$		0			0
$817$		−	4.41851i		−	0.154584i
$818$			44.2939i			1.54870i
$819$		0			0
$820$	−20.7846	−	16.9706i	−0.725830	−	0.592638i
$821$	−50.7846			−1.77240			−0.886198	−	0.463308i	$-0.846663\pi$
$821$	−50.7846			−1.77240			−0.886198	+	0.463308i	$0.846663\pi$
$822$		0			0
$823$		−	1.61729i		−	0.0563750i	−0.999603	−	0.0281875i	$-0.991026\pi$
$823$		−	1.61729i		−	0.0563750i	0.999603	−	0.0281875i	$-0.00897355\pi$
$824$	−0.339746			−0.0118356
$825$		0			0
$826$	−49.1769			−1.71108
$827$			33.0817i			1.15036i	0.818025	+	0.575182i	$0.195069\pi$
$827$			33.0817i			1.15036i	−0.818025	+	0.575182i	$0.804931\pi$
$828$		0			0
$829$	−24.7846			−0.860805			−0.430403	−	0.902637i	$-0.641628\pi$
$829$	−24.7846			−0.860805			−0.430403	+	0.902637i	$0.641628\pi$
$830$	−15.1244	−	12.3490i	−0.524974	−	0.428640i
$831$		0			0
$832$		−	38.3596i		−	1.32988i
$833$			1.41421i			0.0489996i
$834$		0			0
$835$	−11.8564	+	14.5211i	−0.410308	+	0.502522i
$836$	−55.1769			−1.90833
$837$		0			0
$838$			11.5911i			0.400408i
$839$	−10.9808			−0.379098			−0.189549	−	0.981871i	$-0.560703\pi$
$839$	−10.9808			−0.379098			−0.189549	+	0.981871i	$0.560703\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			2.82843i			0.0974740i
$843$		0			0
$844$	19.5167			0.671791
$845$	55.0526	+	44.9502i	1.89387	+	1.54633i
$846$		0			0
$847$		−	27.9053i		−	0.958839i
$848$		−	39.1175i		−	1.34330i
$849$		0			0
$850$	2.73205	+	13.3843i	0.0937086	+	0.459076i
$851$	2.28719			0.0784038
$852$		0			0
$853$		−	6.86800i		−	0.235156i	−0.993064	−	0.117578i	$-0.962487\pi$
$853$		−	6.86800i		−	0.235156i	0.993064	−	0.117578i	$-0.0375130\pi$
$854$	51.7128			1.76958
$855$		0			0
$856$	−2.05256			−0.0701550
$857$		−	30.4292i		−	1.03944i	−0.854337	−	0.519720i	$-0.826036\pi$
$857$		−	30.4292i		−	1.03944i	0.854337	−	0.519720i	$-0.173964\pi$
$858$		0			0
$859$	15.2679			0.520936			0.260468	−	0.965483i	$-0.416123\pi$
$859$	15.2679			0.520936			0.260468	+	0.965483i	$0.416123\pi$
$860$	1.60770	−	1.96902i	0.0548219	−	0.0671429i
$861$		0			0
$862$			48.6381i			1.65662i
$863$			13.0053i			0.442706i	0.975194	+	0.221353i	$0.0710474\pi$
$863$			13.0053i			0.442706i	−0.975194	+	0.221353i	$0.928953\pi$
$864$		0			0
$865$	−13.4641	+	16.4901i	−0.457793	+	0.560680i
$866$	−43.5167			−1.47876
$867$		0			0
$868$		−	22.3500i		−	0.758609i
$869$	−29.3205			−0.994630
$870$		0			0
$871$	−28.3923			−0.962037
$872$		−	5.10205i		−	0.172777i
$873$		0			0
$874$	−45.3205			−1.53299
$875$	−24.2487	−	12.7279i	−0.819756	−	0.430282i
$876$		0			0
$877$		−	0.480473i		−	0.0162244i	−0.999967	−	0.00811222i	$-0.997418\pi$
$877$		−	0.480473i		−	0.0162244i	0.999967	−	0.00811222i	$-0.00258223\pi$
$878$		−	40.4302i		−	1.36445i
$879$		0			0
$880$	36.5885	+	29.8744i	1.23340	+	1.00706i
$881$	57.4641			1.93601			0.968007	−	0.250922i	$-0.0807337\pi$
$881$	57.4641			1.93601			0.968007	+	0.250922i	$0.0807337\pi$
$882$		0			0
$883$		−	52.4002i		−	1.76341i	−0.471803	−	0.881704i	$-0.656397\pi$
$883$		−	52.4002i		−	1.76341i	0.471803	−	0.881704i	$-0.343603\pi$
$884$	−16.3923			−0.551333
$885$		0			0
$886$	40.5885			1.36360
$887$		−	18.1817i		−	0.610482i	−0.952275	−	0.305241i	$-0.901263\pi$
$887$		−	18.1817i		−	0.610482i	0.952275	−	0.305241i	$-0.0987370\pi$
$888$		0			0
$889$	−10.3923			−0.348547
$890$	28.3923	−	34.7733i	0.951712	−	1.16560i
$891$		0			0
$892$		−	41.2896i		−	1.38248i
$893$			9.52056i			0.318593i
$894$		0			0
$895$	−16.3923	−	13.3843i	−0.547934	−	0.447386i
$896$	10.0526			0.335832
$897$		0			0
$898$		−	3.58630i		−	0.119676i
$899$	−5.26795			−0.175696
$900$		0			0
$901$	−12.3923			−0.412848
$902$			63.3350i			2.10882i
$903$		0			0
$904$	−0.875644			−0.0291235
$905$	27.7128	+	22.6274i	0.921205	+	0.752161i
$906$		0			0
$907$		−	3.28169i		−	0.108967i	−0.998515	−	0.0544834i	$-0.982649\pi$
$907$		−	3.28169i		−	0.108967i	0.998515	−	0.0544834i	$-0.0173512\pi$
$908$			18.4591i			0.612587i
$909$		0			0
$910$	44.7846	−	54.8497i	1.48460	−	1.81825i
$911$	20.1962			0.669128			0.334564	−	0.942373i	$-0.391411\pi$
$911$	20.1962			0.669128			0.334564	+	0.942373i	$0.391411\pi$
$912$		0			0
$913$			21.3891i			0.707875i
$914$	36.2487			1.19900
$915$		0			0
$916$	−39.4641			−1.30393
$917$		−	3.10583i		−	0.102563i
$918$		0			0
$919$	59.9615			1.97795			0.988974	−	0.148089i	$-0.0473121\pi$
$919$	59.9615			1.97795			0.988974	+	0.148089i	$0.0473121\pi$
$920$	3.12436	+	2.55103i	0.103007	+	0.0841048i
$921$		0			0
$922$			21.3891i			0.704411i
$923$		−	23.1822i		−	0.763052i
$924$		0			0
$925$	−3.21539	+	0.656339i	−0.105721	+	0.0215803i
$926$	−62.4449			−2.05207
$927$		0			0
$928$			7.58871i			0.249111i
$929$	28.1436			0.923361			0.461681	−	0.887046i	$-0.347247\pi$
$929$	28.1436			0.923361			0.461681	+	0.887046i	$0.347247\pi$
$930$		0			0
$931$	6.73205			0.220634
$932$			45.0518i			1.47572i
$933$		0			0
$934$	−35.1244			−1.14930
$935$	9.46410	−	11.5911i	0.309509	−	0.379070i
$936$		0			0
$937$		−	56.6429i		−	1.85044i	−0.379429	−	0.925221i	$-0.623879\pi$
$937$		−	56.6429i		−	1.85044i	0.379429	−	0.925221i	$-0.376121\pi$
$938$			20.0764i			0.655517i
$939$		0			0
$940$	−3.46410	+	4.24264i	−0.112987	+	0.138380i
$941$	−19.8564			−0.647300			−0.323650	−	0.946177i	$-0.604910\pi$
$941$	−19.8564			−0.647300			−0.323650	+	0.946177i	$0.604910\pi$
$942$		0			0
$943$			24.1432i			0.786210i
$944$	−46.3923			−1.50994
$945$		0			0
$946$	−6.00000			−0.195077
$947$			30.8081i			1.00113i	0.865699	+	0.500564i	$0.166874\pi$
$947$			30.8081i			1.00113i	−0.865699	+	0.500564i	$0.833126\pi$
$948$		0			0
$949$	49.1769			1.59635
$950$	63.7128	−	13.0053i	2.06712	−	0.421948i
$951$		0			0
$952$		−	1.79315i		−	0.0581164i
$953$			5.65685i			0.183243i	0.995794	+	0.0916217i	$0.0292051\pi$
$953$			5.65685i			0.183243i	−0.995794	+	0.0916217i	$0.970795\pi$
$954$		0			0
$955$	−15.8038	−	12.9038i	−0.511400	−	0.417557i
$956$	18.0000			0.582162
$957$		0			0
$958$			22.5259i			0.727778i
$959$	12.2487			0.395532
$960$		0			0
$961$	−3.24871			−0.104797
$962$		−	8.48528i		−	0.273576i
$963$		0			0
$964$	−7.85641			−0.253038
$965$	12.9282	−	15.8338i	0.416174	−	0.509706i
$966$		0			0
$967$		−	27.4249i		−	0.881924i	−0.897526	−	0.440962i	$-0.854637\pi$
$967$		−	27.4249i		−	0.881924i	0.897526	−	0.440962i	$-0.145363\pi$
$968$		−	5.89709i		−	0.189540i
$969$		0			0
$970$	−20.1962	−	16.4901i	−0.648459	−	0.529465i
$971$	4.48334			0.143877			0.0719386	−	0.997409i	$-0.477081\pi$
$971$	4.48334			0.143877			0.0719386	+	0.997409i	$0.477081\pi$
$972$		0			0
$973$		−	19.5959i		−	0.628216i
$974$	11.6603			0.373619
$975$		0			0
$976$	48.7846			1.56156
$977$		−	8.20788i		−	0.262593i	−0.991343	−	0.131297i	$-0.958086\pi$
$977$		−	8.20788i		−	0.262593i	0.991343	−	0.131297i	$-0.0419140\pi$
$978$		0			0
$979$	−49.1769			−1.57170
$980$	3.00000	+	2.44949i	0.0958315	+	0.0782461i
$981$		0			0
$982$			20.7327i			0.661608i
$983$		−	0.859411i		−	0.0274109i	−0.999906	−	0.0137055i	$-0.995637\pi$
$983$		−	0.859411i		−	0.0274109i	0.999906	−	0.0137055i	$-0.00436272\pi$
$984$		0			0
$985$	23.7128	−	29.0421i	0.755553	−	0.925360i
$986$	2.73205			0.0870062
$987$		0			0
$988$			78.0319i			2.48253i
$989$	−2.28719			−0.0727283
$990$		0			0
$991$	−6.78461			−0.215520			−0.107760	−	0.994177i	$-0.534368\pi$
$991$	−6.78461			−0.215520			−0.107760	+	0.994177i	$0.534368\pi$
$992$		−	39.9769i		−	1.26927i
$993$		0			0
$994$	−16.3923			−0.519932
$995$	−24.2487	−	19.7990i	−0.768736	−	0.627670i
$996$		0			0
$997$		−	41.2896i		−	1.30765i	−0.756644	−	0.653827i	$-0.773162\pi$
$997$		−	41.2896i		−	1.30765i	0.756644	−	0.653827i	$-0.226838\pi$
$998$		−	28.8391i		−	0.912885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.f.784.1		4
3.2	odd	2		145.2.b.b.59.4	yes	4
5.2	odd	4		6525.2.a.bj.1.4		4
5.3	odd	4		6525.2.a.bj.1.1		4
5.4	even	2	inner	1305.2.c.f.784.4		4
12.11	even	2		2320.2.d.f.929.2		4
15.2	even	4		725.2.a.f.1.1		4
15.8	even	4		725.2.a.f.1.4		4
15.14	odd	2		145.2.b.b.59.1	✓	4
60.59	even	2		2320.2.d.f.929.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.b.59.1	✓	4	15.14	odd	2
145.2.b.b.59.4	yes	4	3.2	odd	2
725.2.a.f.1.1		4	15.2	even	4
725.2.a.f.1.4		4	15.8	even	4
1305.2.c.f.784.1		4	1.1	even	1	trivial
1305.2.c.f.784.4		4	5.4	even	2	inner
2320.2.d.f.929.2		4	12.11	even	2
2320.2.d.f.929.4		4	60.59	even	2
6525.2.a.bj.1.1		4	5.3	odd	4
6525.2.a.bj.1.4		4	5.2	odd	4

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

\(f(q)\)	\(=\)	\(q-1.93185i q^{2} -1.73205 q^{4} +(-1.73205 - 1.41421i) q^{5} -2.44949i q^{7} -0.517638i q^{8} +(-2.73205 + 3.34607i) q^{10} +4.73205 q^{11} -6.69213i q^{13} -4.73205 q^{14} -4.46410 q^{16} +1.41421i q^{17} +6.73205 q^{19} +(3.00000 + 2.44949i) q^{20} -9.14162i q^{22} -3.48477i q^{23} +(1.00000 + 4.89898i) q^{25} -12.9282 q^{26} +4.24264i q^{28} +1.00000 q^{29} -5.26795 q^{31} +7.58871i q^{32} +2.73205 q^{34} +(-3.46410 + 4.24264i) q^{35} +0.656339i q^{37} -13.0053i q^{38} +(-0.732051 + 0.896575i) q^{40} -6.92820 q^{41} -0.656339i q^{43} -8.19615 q^{44} -6.73205 q^{46} +1.41421i q^{47} +1.00000 q^{49} +(9.46410 - 1.93185i) q^{50} +11.5911i q^{52} +8.76268i q^{53} +(-8.19615 - 6.69213i) q^{55} -1.26795 q^{56} -1.93185i q^{58} +10.3923 q^{59} -10.9282 q^{61} +10.1769i q^{62} +5.73205 q^{64} +(-9.46410 + 11.5911i) q^{65} -4.24264i q^{67} -2.44949i q^{68} +(8.19615 + 6.69213i) q^{70} +3.46410 q^{71} +7.34847i q^{73} +1.26795 q^{74} -11.6603 q^{76} -11.5911i q^{77} -6.19615 q^{79} +(7.73205 + 6.31319i) q^{80} +13.3843i q^{82} +4.52004i q^{83} +(2.00000 - 2.44949i) q^{85} -1.26795 q^{86} -2.44949i q^{88} -10.3923 q^{89} -16.3923 q^{91} +6.03579i q^{92} +2.73205 q^{94} +(-11.6603 - 9.52056i) q^{95} +6.03579i q^{97} -1.93185i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{10} + 12 q^{11} - 12 q^{14} - 4 q^{16} + 20 q^{19} + 12 q^{20} + 4 q^{25} - 24 q^{26} + 4 q^{29} - 28 q^{31} + 4 q^{34} + 4 q^{40} - 12 q^{44} - 20 q^{46} + 4 q^{49} + 24 q^{50} - 12 q^{55} - 12 q^{56}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q - 4 * q^10 + 12 * q^11 - 12 * q^14 - 4 * q^16 + 20 * q^19 + 12 * q^20 + 4 * q^25 - 24 * q^26 + 4 * q^29 - 28 * q^31 + 4 * q^34 + 4 * q^40 - 12 * q^44 - 20 * q^46 + 4 * q^49 + 24 * q^50 - 12 * q^55 - 12 * q^56 - 16 * q^61 + 16 * q^64 - 24 * q^65 + 12 * q^70 + 12 * q^74 - 12 * q^76 - 4 * q^79 + 24 * q^80 + 8 * q^85 - 12 * q^86 - 24 * q^91 + 4 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more