LMFDB - Embedded newform 1305.2.f.l.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)

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);

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")

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 = [12,0,0,16,6,0,0,0,0,2] 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 11 x^{9} + 55 x^{8} - 66 x^{7} + 328 x^{6} - 214 x^{5} + 207 x^{4} + 383 x^{3} + \cdots + 209 $ x^12 - x^11 - 11x^9 + 55x^8 - 66x^7 + 328x^6 - 214x^5 + 207x^4 + 383x^3 + 16x^2 - 107*x + 209
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 435)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.3
Root			$2.44773 + 1.33046i$ of defining polynomial
Character	$\chi$	$=$	1305.289
Dual form			1305.2.f.l.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.97264 q^{2} +1.89129 q^{4} +(-1.38075 - 1.75885i) q^{5} -0.520254i q^{7} +0.214447 q^{8} +(2.72371 + 3.46956i) q^{10} +2.16411i q^{11} -1.53375i q^{13} +1.02627i q^{14} -4.20560 q^{16} +2.47957 q^{17} +4.70989i q^{19} +(-2.61139 - 3.32649i) q^{20} -4.26900i q^{22} -1.46369i q^{23} +(-1.18708 + 4.85704i) q^{25} +3.02552i q^{26} -0.983951i q^{28} +(-2.29579 + 4.87128i) q^{29} -4.64210i q^{31} +7.86723 q^{32} -4.89129 q^{34} +(-0.915047 + 0.718339i) q^{35} -1.77536 q^{37} -9.29090i q^{38} +(-0.296097 - 0.377179i) q^{40} +9.71408i q^{41} -5.39269 q^{43} +4.09296i q^{44} +2.88733i q^{46} +3.68312 q^{47} +6.72934 q^{49} +(2.34168 - 9.58117i) q^{50} -2.90076i q^{52} -7.74965i q^{53} +(3.80634 - 2.98808i) q^{55} -0.111567i q^{56} +(4.52876 - 9.60925i) q^{58} +1.91288 q^{59} -7.66501i q^{61} +9.15717i q^{62} -7.10796 q^{64} +(-2.69763 + 2.11771i) q^{65} +7.88749i q^{67} +4.68959 q^{68} +(1.80505 - 1.41702i) q^{70} +9.78001 q^{71} +4.70676 q^{73} +3.50215 q^{74} +8.90777i q^{76} +1.12589 q^{77} +12.3714i q^{79} +(5.80687 + 7.39701i) q^{80} -19.1623i q^{82} -7.32647i q^{83} +(-3.42366 - 4.36119i) q^{85} +10.6378 q^{86} +0.464086i q^{88} -7.66235i q^{89} -0.797938 q^{91} -2.76827i q^{92} -7.26545 q^{94} +(8.28397 - 6.50316i) q^{95} +1.64507 q^{97} -13.2745 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{4} + 6 q^{5} + 2 q^{10} + 32 q^{16} + 8 q^{17} + 20 q^{20} + 12 q^{25} - 8 q^{29} + 40 q^{32} - 52 q^{34} - 14 q^{35} + 20 q^{37} - 22 q^{40} + 44 q^{43} + 32 q^{47} - 4 q^{49} - 24 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 12 * q + 16 * q^4 + 6 * q^5 + 2 * q^10 + 32 * q^16 + 8 * q^17 + 20 * q^20 + 12 * q^25 - 8 * q^29 + 40 * q^32 - 52 * q^34 - 14 * q^35 + 20 * q^37 - 22 * q^40 + 44 * q^43 + 32 * q^47 - 4 * q^49 - 24 * q^50 + 42 * q^55 - 24 * q^58 + 28 * q^59 - 4 * q^64 - 22 * q^65 - 16 * q^68 - 26 * q^70 + 16 * q^71 - 36 * q^73 + 28 * q^74 + 22 * q^80 + 30 * q^85 + 16 * q^86 + 24 * q^91 - 28 * q^94 - 16 * q^95 - 40 * q^97 + 112 * 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 $

$2$	−1.97264			−1.39486			−0.697432	−	0.716651i	$-0.745674\pi$
$2$	−1.97264			−1.39486			−0.697432	+	0.716651i	$0.745674\pi$
$3$		0			0
$3$		0			0
$4$	1.89129			0.945645
$5$	−1.38075	−	1.75885i	−0.617488	−	0.786580i
$5$	−1.38075	−	1.75885i	−0.617488	−	0.786580i
$6$		0			0
$7$		−	0.520254i		−	0.196638i	−0.995155	−	0.0983188i	$-0.968654\pi$
$7$		−	0.520254i		−	0.196638i	0.995155	−	0.0983188i	$-0.0313465\pi$
$8$	0.214447			0.0758184
$9$		0			0
$10$	2.72371	+	3.46956i	0.861312	+	1.09717i
$11$			2.16411i			0.652504i	0.945283	+	0.326252i	$0.105786\pi$
$11$			2.16411i			0.652504i	−0.945283	+	0.326252i	$0.894214\pi$
$12$		0			0
$13$		−	1.53375i		−	0.425385i	−0.977119	−	0.212692i	$-0.931777\pi$
$13$		−	1.53375i		−	0.425385i	0.977119	−	0.212692i	$-0.0682232\pi$
$14$			1.02627i			0.274283i
$15$		0			0
$16$	−4.20560			−1.05140
$17$	2.47957			0.601384			0.300692	−	0.953721i	$-0.402782\pi$
$17$	2.47957			0.601384			0.300692	+	0.953721i	$0.402782\pi$
$18$		0			0
$19$			4.70989i			1.08052i	0.841497	+	0.540262i	$0.181675\pi$
$19$			4.70989i			1.08052i	−0.841497	+	0.540262i	$0.818325\pi$
$20$	−2.61139	−	3.32649i	−0.583924	−	0.743825i
$21$		0			0
$22$		−	4.26900i		−	0.910153i
$23$		−	1.46369i		−	0.305201i	−0.988288	−	0.152600i	$-0.951235\pi$
$23$		−	1.46369i		−	0.305201i	0.988288	−	0.152600i	$-0.0487648\pi$
$24$		0			0
$25$	−1.18708	+	4.85704i	−0.237416	+	0.971408i
$26$			3.02552i			0.593354i
$27$		0			0
$28$		−	0.983951i		−	0.185949i
$29$	−2.29579	+	4.87128i	−0.426318	+	0.904573i
$29$	−2.29579	+	4.87128i	−0.426318	+	0.904573i
$30$		0			0
$31$		−	4.64210i		−	0.833746i	−0.908965	−	0.416873i	$-0.863126\pi$
$31$		−	4.64210i		−	0.833746i	0.908965	−	0.416873i	$-0.136874\pi$
$32$	7.86723			1.39074
$33$		0			0
$34$	−4.89129			−0.838849
$35$	−0.915047	+	0.718339i	−0.154671	+	0.121421i
$36$		0			0
$37$	−1.77536			−0.291868			−0.145934	−	0.989294i	$-0.546619\pi$
$37$	−1.77536			−0.291868			−0.145934	+	0.989294i	$0.546619\pi$
$38$		−	9.29090i		−	1.50718i
$39$		0			0
$40$	−0.296097	−	0.377179i	−0.0468170	−	0.0596372i
$41$			9.71408i			1.51708i	0.651624	+	0.758542i	$0.274088\pi$
$41$			9.71408i			1.51708i	−0.651624	+	0.758542i	$0.725912\pi$
$42$		0			0
$43$	−5.39269			−0.822377			−0.411188	−	0.911550i	$-0.634886\pi$
$43$	−5.39269			−0.822377			−0.411188	+	0.911550i	$0.634886\pi$
$44$			4.09296i			0.617036i
$45$		0			0
$46$			2.88733i			0.425714i
$47$	3.68312			0.537238			0.268619	−	0.963246i	$-0.413433\pi$
$47$	3.68312			0.537238			0.268619	+	0.963246i	$0.413433\pi$
$48$		0			0
$49$	6.72934			0.961334
$50$	2.34168	−	9.58117i	0.331163	−	1.35498i
$51$		0			0
$52$		−	2.90076i		−	0.402263i
$53$		−	7.74965i		−	1.06450i	−0.846588	−	0.532248i	$-0.821347\pi$
$53$		−	7.74965i		−	1.06450i	0.846588	−	0.532248i	$-0.178653\pi$
$54$		0			0
$55$	3.80634	−	2.98808i	0.513246	−	0.402913i
$56$		−	0.111567i		−	0.0149087i
$57$		0			0
$58$	4.52876	−	9.60925i	0.594655	−	1.26176i
$59$	1.91288			0.249035			0.124518	−	0.992217i	$-0.460262\pi$
$59$	1.91288			0.249035			0.124518	+	0.992217i	$0.460262\pi$
$60$		0			0
$61$		−	7.66501i		−	0.981404i	−0.871328	−	0.490702i	$-0.836740\pi$
$61$		−	7.66501i		−	0.981404i	0.871328	−	0.490702i	$-0.163260\pi$
$62$			9.15717i			1.16296i
$63$		0			0
$64$	−7.10796			−0.888495
$65$	−2.69763	+	2.11771i	−0.334599	+	0.262670i
$66$		0			0
$67$			7.88749i			0.963611i	0.876278	+	0.481805i	$0.160019\pi$
$67$			7.88749i			0.963611i	−0.876278	+	0.481805i	$0.839981\pi$
$68$	4.68959			0.568696
$69$		0			0
$70$	1.80505	−	1.41702i	0.215745	−	0.169366i
$71$	9.78001			1.16067			0.580337	−	0.814376i	$-0.302921\pi$
$71$	9.78001			1.16067			0.580337	+	0.814376i	$0.302921\pi$
$72$		0			0
$73$	4.70676			0.550885			0.275442	−	0.961318i	$-0.411176\pi$
$73$	4.70676			0.550885			0.275442	+	0.961318i	$0.411176\pi$
$74$	3.50215			0.407116
$75$		0			0
$76$			8.90777i			1.02179i
$77$	1.12589			0.128307
$78$		0			0
$79$			12.3714i			1.39189i	0.718093	+	0.695947i	$0.245015\pi$
$79$			12.3714i			1.39189i	−0.718093	+	0.695947i	$0.754985\pi$
$80$	5.80687	+	7.39701i	0.649228	+	0.827011i
$81$		0			0
$82$		−	19.1623i		−	2.11613i
$83$		−	7.32647i		−	0.804184i	−0.915599	−	0.402092i	$-0.868283\pi$
$83$		−	7.32647i		−	0.804184i	0.915599	−	0.402092i	$-0.131717\pi$
$84$		0			0
$85$	−3.42366	−	4.36119i	−0.371348	−	0.473037i
$86$	10.6378			1.14710
$87$		0			0
$88$			0.464086i			0.0494718i
$89$		−	7.66235i		−	0.812207i	−0.913827	−	0.406104i	$-0.866887\pi$
$89$		−	7.66235i		−	0.812207i	0.913827	−	0.406104i	$-0.133113\pi$
$90$		0			0
$91$	−0.797938			−0.0836466
$92$		−	2.76827i		−	0.288612i
$93$		0			0
$94$	−7.26545			−0.749374
$95$	8.28397	−	6.50316i	0.849918	−	0.667210i
$96$		0			0
$97$	1.64507			0.167031			0.0835156	−	0.996506i	$-0.473385\pi$
$97$	1.64507			0.167031			0.0835156	+	0.996506i	$0.473385\pi$
$98$	−13.2745			−1.34093
$99$		0			0
$100$	−2.24512	+	9.18607i	−0.224512	+	0.918607i
$101$		−	3.20388i		−	0.318798i	−0.987214	−	0.159399i	$-0.949044\pi$
$101$		−	3.20388i		−	0.318798i	0.987214	−	0.159399i	$-0.0509556\pi$
$102$		0			0
$103$			7.80019i			0.768575i	0.923213	+	0.384288i	$0.125553\pi$
$103$			7.80019i			0.768575i	−0.923213	+	0.384288i	$0.874447\pi$
$104$		−	0.328907i		−	0.0322520i
$105$		0			0
$106$			15.2872i			1.48483i
$107$			18.4094i			1.77971i	0.456246	+	0.889854i	$0.349194\pi$
$107$			18.4094i			1.77971i	−0.456246	+	0.889854i	$0.650806\pi$
$108$		0			0
$109$	17.4302			1.66951			0.834755	−	0.550621i	$-0.185609\pi$
$109$	17.4302			1.66951			0.834755	+	0.550621i	$0.185609\pi$
$110$	−7.50851	+	5.89440i	−0.715909	+	0.562009i
$111$		0			0
$112$			2.18798i			0.206745i
$113$	−6.78282			−0.638074			−0.319037	−	0.947742i	$-0.603359\pi$
$113$	−6.78282			−0.638074			−0.319037	+	0.947742i	$0.603359\pi$
$114$		0			0
$115$	−2.57441	+	2.02099i	−0.240065	+	0.188458i
$116$	−4.34201	+	9.21299i	−0.403145	+	0.855405i
$117$		0			0
$118$	−3.77341			−0.347370
$119$		−	1.29001i		−	0.118255i
$120$		0			0
$121$	6.31663			0.574239
$122$			15.1203i			1.36892i
$123$		0			0
$124$		−	8.77956i		−	0.788428i
$125$	10.1818	−	4.61844i	0.910692	−	0.413086i
$126$		0			0
$127$	14.0473			1.24649			0.623247	−	0.782025i	$-0.285813\pi$
$127$	14.0473			1.24649			0.623247	+	0.782025i	$0.285813\pi$
$128$	−1.71304			−0.151413
$129$		0			0
$130$	5.32143	−	4.17748i	0.466720	−	0.366389i
$131$			9.19950i			0.803764i	0.915692	+	0.401882i	$0.131644\pi$
$131$			9.19950i			0.803764i	−0.915692	+	0.401882i	$0.868356\pi$
$132$		0			0
$133$	2.45034			0.212471
$134$		−	15.5591i		−	1.34411i
$135$		0			0
$136$	0.531736			0.0455960
$137$	16.6227			1.42017			0.710086	−	0.704115i	$-0.248656\pi$
$137$	16.6227			1.42017			0.710086	+	0.704115i	$0.248656\pi$
$138$		0			0
$139$	1.13775			0.0965027			0.0482514	−	0.998835i	$-0.484635\pi$
$139$	1.13775			0.0965027			0.0482514	+	0.998835i	$0.484635\pi$
$140$	−1.73062	+	1.35859i	−0.146264	+	0.114821i
$141$		0			0
$142$	−19.2924			−1.61898
$143$	3.31920			0.277565
$144$		0			0
$145$	11.7377	−	2.68805i	0.974766	−	0.223230i
$146$	−9.28472			−0.768409
$147$		0			0
$148$	−3.35773			−0.276003
$149$	−0.981478			−0.0804058			−0.0402029	−	0.999192i	$-0.512800\pi$
$149$	−0.981478			−0.0804058			−0.0402029	+	0.999192i	$0.512800\pi$
$150$		0			0
$151$	11.4798			0.934214			0.467107	−	0.884201i	$-0.345296\pi$
$151$	11.4798			0.934214			0.467107	+	0.884201i	$0.345296\pi$
$152$			1.01002i			0.0819235i
$153$		0			0
$154$	−2.22096			−0.178970
$155$	−8.16475	+	6.40956i	−0.655808	+	0.514829i
$156$		0			0
$157$	8.00465			0.638841			0.319420	−	0.947613i	$-0.396512\pi$
$157$	8.00465			0.638841			0.319420	+	0.947613i	$0.396512\pi$
$158$		−	24.4043i		−	1.94150i
$159$		0			0
$160$	−10.8626	−	13.8372i	−0.858767	−	1.09393i
$161$	−0.761492			−0.0600140
$162$		0			0
$163$	2.46129			0.192783			0.0963915	−	0.995344i	$-0.469270\pi$
$163$	2.46129			0.192783			0.0963915	+	0.995344i	$0.469270\pi$
$164$			18.3721i			1.43462i
$165$		0			0
$166$			14.4524i			1.12173i
$167$			4.98139i			0.385471i	0.981251	+	0.192736i	$0.0617360\pi$
$167$			4.98139i			0.385471i	−0.981251	+	0.192736i	$0.938264\pi$
$168$		0			0
$169$	10.6476			0.819048
$170$	6.75363	+	8.60303i	0.517980	+	0.659822i
$171$		0			0
$172$	−10.1991			−0.777676
$173$		−	15.0543i		−	1.14456i	−0.820058	−	0.572280i	$-0.806059\pi$
$173$		−	15.0543i		−	1.14456i	0.820058	−	0.572280i	$-0.193941\pi$
$174$		0			0
$175$	2.52689	+	0.617584i	0.191015	+	0.0466850i
$176$		−	9.10139i		−	0.686043i
$177$		0			0
$178$			15.1150i			1.13292i
$179$	25.1991			1.88347			0.941736	−	0.336352i	$-0.109193\pi$
$179$	25.1991			1.88347			0.941736	+	0.336352i	$0.109193\pi$
$180$		0			0
$181$	5.27495			0.392084			0.196042	−	0.980595i	$-0.437191\pi$
$181$	5.27495			0.392084			0.196042	+	0.980595i	$0.437191\pi$
$182$	1.57404			0.116676
$183$		0			0
$184$		−	0.313884i		−	0.0231398i
$185$	2.45133	+	3.12259i	0.180225	+	0.229578i
$186$		0			0
$187$			5.36606i			0.392405i
$188$	6.96585			0.508037
$189$		0			0
$190$	−16.3413	+	12.8284i	−1.18552	+	0.930667i
$191$		−	3.31544i		−	0.239897i	−0.992780	−	0.119949i	$-0.961727\pi$
$191$		−	3.31544i		−	0.239897i	0.992780	−	0.119949i	$-0.0382730\pi$
$192$		0			0
$193$	−5.69128			−0.409667			−0.204834	−	0.978797i	$-0.565665\pi$
$193$	−5.69128			−0.409667			−0.204834	+	0.978797i	$0.565665\pi$
$194$	−3.24512			−0.232986
$195$		0			0
$196$	12.7271			0.909080
$197$			0.314623i			0.0224160i	0.999937	+	0.0112080i	$0.00356769\pi$
$197$			0.314623i			0.0224160i	−0.999937	+	0.0112080i	$0.996432\pi$
$198$		0			0
$199$	2.94247			0.208586			0.104293	−	0.994547i	$-0.466742\pi$
$199$	2.94247			0.208586			0.104293	+	0.994547i	$0.466742\pi$
$200$	−0.254566	+	1.04158i	−0.0180005	+	0.0736506i
$201$		0			0
$202$			6.32008i			0.444679i
$203$	2.53430	+	1.19440i	0.177873	+	0.0838301i
$204$		0			0
$205$	17.0856	−	13.4127i	1.19331	−	0.936782i
$206$		−	15.3869i		−	1.07206i
$207$		0			0
$208$			6.45033i			0.447250i
$209$	−10.1927			−0.705045
$210$		0			0
$211$			6.92301i			0.476600i	0.971192	+	0.238300i	$0.0765901\pi$
$211$			6.92301i			0.476600i	−0.971192	+	0.238300i	$0.923410\pi$
$212$		−	14.6568i		−	1.00664i
$213$		0			0
$214$		−	36.3151i		−	2.48245i
$215$	7.44593	+	9.48491i	0.507808	+	0.646865i
$216$		0			0
$217$	−2.41507			−0.163946
$218$	−34.3834			−2.32874
$219$		0			0
$220$	7.19888	−	5.65133i	0.485349	−	0.381013i
$221$		−	3.80303i		−	0.255820i
$222$		0			0
$223$		−	28.4693i		−	1.90644i	−0.302272	−	0.953222i	$-0.597745\pi$
$223$		−	28.4693i		−	1.90644i	0.302272	−	0.953222i	$-0.402255\pi$
$224$		−	4.09296i		−	0.273472i
$225$		0			0
$226$	13.3800			0.890026
$227$		−	7.15024i		−	0.474578i	−0.971439	−	0.237289i	$-0.923741\pi$
$227$		−	7.15024i		−	0.474578i	0.971439	−	0.237289i	$-0.0762589\pi$
$228$		0			0
$229$			9.94406i			0.657122i	0.944483	+	0.328561i	$0.106564\pi$
$229$			9.94406i			0.657122i	−0.944483	+	0.328561i	$0.893436\pi$
$230$	5.07837	−	3.98667i	0.334858	−	0.262873i
$231$		0			0
$232$	−0.492325	+	1.04463i	−0.0323227	+	0.0685833i
$233$			13.5734i			0.889222i	0.895724	+	0.444611i	$0.146658\pi$
$233$			13.5734i			0.889222i	−0.895724	+	0.444611i	$0.853342\pi$
$234$		0			0
$235$	−5.08545	−	6.47804i	−0.331738	−	0.422581i
$236$	3.61780			0.235499
$237$		0			0
$238$			2.54471i			0.164949i
$239$	−15.5469			−1.00564			−0.502821	−	0.864390i	$-0.667705\pi$
$239$	−15.5469			−1.00564			−0.502821	+	0.864390i	$0.667705\pi$
$240$		0			0
$241$	−18.2171			−1.17346			−0.586732	−	0.809781i	$-0.699586\pi$
$241$	−18.2171			−1.17346			−0.586732	+	0.809781i	$0.699586\pi$
$242$	−12.4604			−0.800985
$243$		0			0
$244$		−	14.4967i		−	0.928059i
$245$	−9.29150	−	11.8359i	−0.593612	−	0.756166i
$246$		0			0
$247$	7.22378			0.459638
$248$		−	0.995484i		−	0.0632133i
$249$		0			0
$250$	−20.0851	+	9.11050i	−1.27029	+	0.576199i
$251$			5.16558i			0.326048i	0.986622	+	0.163024i	$0.0521248\pi$
$251$			5.16558i			0.326048i	−0.986622	+	0.163024i	$0.947875\pi$
$252$		0			0
$253$	3.16759			0.199145
$254$	−27.7102			−1.73869
$255$		0			0
$256$	17.5951			1.09970
$257$			19.6922i			1.22837i	0.789163	+	0.614184i	$0.210515\pi$
$257$			19.6922i			1.22837i	−0.789163	+	0.614184i	$0.789485\pi$
$258$		0			0
$259$			0.923640i			0.0573922i
$260$	−5.10199	+	4.00521i	−0.316412	+	0.248393i
$261$		0			0
$262$		−	18.1472i		−	1.12114i
$263$	11.9634			0.737697			0.368848	−	0.929490i	$-0.379752\pi$
$263$	11.9634			0.737697			0.368848	+	0.929490i	$0.379752\pi$
$264$		0			0
$265$	−13.6304	+	10.7003i	−0.837312	+	0.657314i
$266$	−4.83363			−0.296369
$267$		0			0
$268$			14.9175i			0.911233i
$269$		−	16.5561i		−	1.00945i	−0.863282	−	0.504723i	$-0.831595\pi$
$269$		−	16.5561i		−	1.00945i	0.863282	−	0.504723i	$-0.168405\pi$
$270$		0			0
$271$			25.4539i			1.54621i	0.634277	+	0.773106i	$0.281298\pi$
$271$			25.4539i			1.54621i	−0.634277	+	0.773106i	$0.718702\pi$
$272$	−10.4281			−0.632296
$273$		0			0
$274$	−32.7905			−1.98095
$275$	−10.5112	−	2.56897i	−0.633847	−	0.154915i
$276$		0			0
$277$			30.7150i			1.84549i	0.385415	+	0.922743i	$0.374058\pi$
$277$			30.7150i			1.84549i	−0.385415	+	0.922743i	$0.625942\pi$
$278$	−2.24437			−0.134608
$279$		0			0
$280$	−0.196229	+	0.154045i	−0.0117269	+	0.00920597i
$281$	−22.7775			−1.35879			−0.679395	−	0.733773i	$-0.737758\pi$
$281$	−22.7775			−1.35879			−0.679395	+	0.733773i	$0.737758\pi$
$282$		0			0
$283$		−	30.6646i		−	1.82282i	−0.411499	−	0.911410i	$-0.634995\pi$
$283$		−	30.6646i		−	1.82282i	0.411499	−	0.911410i	$-0.365005\pi$
$284$	18.4968			1.09759
$285$		0			0
$286$	−6.54756			−0.387165
$287$	5.05379			0.298316
$288$		0			0
$289$	−10.8517			−0.638337
$290$	−23.1543	+	5.30254i	−1.35967	+	0.311376i
$291$		0			0
$292$	8.90185			0.520941
$293$	−0.956588			−0.0558845			−0.0279422	−	0.999610i	$-0.508895\pi$
$293$	−0.956588			−0.0558845			−0.0279422	+	0.999610i	$0.508895\pi$
$294$		0			0
$295$	−2.64120	−	3.36446i	−0.153776	−	0.195886i
$296$	−0.380721			−0.0221290
$297$		0			0
$298$	1.93610			0.112155
$299$	−2.24493			−0.129828
$300$		0			0
$301$			2.80557i			0.161710i
$302$	−22.6455			−1.30310
$303$		0			0
$304$		−	19.8079i		−	1.13606i
$305$	−13.4816	+	10.5834i	−0.771953	+	0.606005i
$306$		0			0
$307$	−31.8260			−1.81641			−0.908203	−	0.418530i	$-0.862545\pi$
$307$	−31.8260			−1.81641			−0.908203	+	0.418530i	$0.862545\pi$
$308$	2.12938			0.121333
$309$		0			0
$310$	16.1061	−	12.6437i	0.914763	−	0.718116i
$311$		−	1.83226i		−	0.103898i	−0.998650	−	0.0519489i	$-0.983457\pi$
$311$		−	1.83226i		−	0.103898i	0.998650	−	0.0519489i	$-0.0165433\pi$
$312$		0			0
$313$		−	16.8539i		−	0.952639i	−0.879272	−	0.476320i	$-0.841971\pi$
$313$		−	16.8539i		−	0.952639i	0.879272	−	0.476320i	$-0.158029\pi$
$314$	−15.7903			−0.891095
$315$		0			0
$316$			23.3979i			1.31624i
$317$	−29.0897			−1.63384			−0.816920	−	0.576751i	$-0.804320\pi$
$317$	−29.0897			−1.63384			−0.816920	+	0.576751i	$0.804320\pi$
$318$		0			0
$319$	−10.5420	−	4.96835i	−0.590237	−	0.278174i
$320$	9.81429	+	12.5018i	0.548635	+	0.698873i
$321$		0			0
$322$	1.50215			0.0837113
$323$			11.6785i			0.649810i
$324$		0			0
$325$	7.44947	+	1.82068i	0.413222	+	0.100993i
$326$	−4.85522			−0.268906
$327$		0			0
$328$			2.08315i			0.115023i
$329$		−	1.91616i		−	0.105641i
$330$		0			0
$331$			15.3405i			0.843191i	0.906784	+	0.421596i	$0.138530\pi$
$331$			15.3405i			0.843191i	−0.906784	+	0.421596i	$0.861470\pi$
$332$		−	13.8565i		−	0.760472i
$333$		0			0
$334$		−	9.82646i		−	0.537680i
$335$	13.8729	−	10.8906i	0.757957	−	0.595018i
$336$		0			0
$337$	21.0799			1.14830			0.574148	−	0.818751i	$-0.305333\pi$
$337$	21.0799			1.14830			0.574148	+	0.818751i	$0.305333\pi$
$338$	−21.0039			−1.14246
$339$		0			0
$340$	−6.47513	−	8.24826i	−0.351163	−	0.447325i
$341$	10.0460			0.544022
$342$		0			0
$343$		−	7.14274i		−	0.385672i
$344$	−1.15644			−0.0623513
$345$		0			0
$346$			29.6967i			1.59650i
$347$		−	24.5985i		−	1.32051i	−0.751040	−	0.660257i	$-0.770447\pi$
$347$		−	24.5985i		−	1.32051i	0.751040	−	0.660257i	$-0.229553\pi$
$348$		0			0
$349$	−22.7037			−1.21530			−0.607649	−	0.794205i	$-0.707887\pi$
$349$	−22.7037			−1.21530			−0.607649	+	0.794205i	$0.707887\pi$
$350$	−4.98464	−	1.21827i	−0.266440	−	0.0651192i
$351$		0			0
$352$			17.0255i			0.907464i
$353$		−	1.38426i		−	0.0736769i	−0.999321	−	0.0368385i	$-0.988271\pi$
$353$		−	1.38426i		−	0.0736769i	0.999321	−	0.0368385i	$-0.0117287\pi$
$354$		0			0
$355$	−13.5037	−	17.2015i	−0.716703	−	0.912963i
$356$		−	14.4917i		−	0.768059i
$357$		0			0
$358$	−49.7087			−2.62719
$359$		−	21.6876i		−	1.14463i	−0.820035	−	0.572313i	$-0.806046\pi$
$359$		−	21.6876i		−	1.14463i	0.820035	−	0.572313i	$-0.193954\pi$
$360$		0			0
$361$	−3.18307			−0.167530
$362$	−10.4056			−0.546904
$363$		0			0
$364$	−1.50913			−0.0791000
$365$	−6.49884	−	8.27847i	−0.340165	−	0.433315i
$366$		0			0
$367$	−0.210815			−0.0110044			−0.00550222	−	0.999985i	$-0.501751\pi$
$367$	−0.210815			−0.0110044			−0.00550222	+	0.999985i	$0.501751\pi$
$368$			6.15571i			0.320889i
$369$		0			0
$370$	−4.83557	−	6.15974i	−0.251389	−	0.320229i
$371$	−4.03179			−0.209320
$372$		0			0
$373$		−	5.66464i		−	0.293304i	−0.989188	−	0.146652i	$-0.953150\pi$
$373$		−	5.66464i		−	0.293304i	0.989188	−	0.146652i	$-0.0468498\pi$
$374$		−	10.5853i		−	0.547352i
$375$		0			0
$376$	0.789833			0.0407325
$377$	7.47131	+	3.52116i	0.384792	+	0.181349i
$378$		0			0
$379$		−	12.5695i		−	0.645650i	−0.946459	−	0.322825i	$-0.895367\pi$
$379$		−	12.5695i		−	0.645650i	0.946459	−	0.322825i	$-0.104633\pi$
$380$	15.6674	−	12.2994i	0.803720	−	0.630944i
$381$		0			0
$382$			6.54016i			0.334624i
$383$			23.0968i			1.18019i	0.807333	+	0.590096i	$0.200910\pi$
$383$			23.0968i			1.18019i	−0.807333	+	0.590096i	$0.799090\pi$
$384$		0			0
$385$	−1.55456	−	1.98026i	−0.0792279	−	0.100923i
$386$	11.2268			0.571430
$387$		0			0
$388$	3.11130			0.157952
$389$			20.5826i			1.04358i	0.853074	+	0.521789i	$0.174735\pi$
$389$			20.5826i			1.04358i	−0.853074	+	0.521789i	$0.825265\pi$
$390$		0			0
$391$		−	3.62933i		−	0.183543i
$392$	1.44308			0.0728868
$393$		0			0
$394$		−	0.620637i		−	0.0312672i
$395$	21.7594	−	17.0818i	1.09484	−	0.859479i
$396$		0			0
$397$		−	26.2539i		−	1.31764i	−0.752298	−	0.658822i	$-0.771055\pi$
$397$		−	26.2539i		−	1.31764i	0.752298	−	0.658822i	$-0.228945\pi$
$398$	−5.80441			−0.290949
$399$		0			0
$400$	4.99240	−	20.4268i	0.249620	−	1.02134i
$401$	17.1621			0.857034			0.428517	−	0.903534i	$-0.359036\pi$
$401$	17.1621			0.857034			0.428517	+	0.903534i	$0.359036\pi$
$402$		0			0
$403$	−7.11981			−0.354663
$404$		−	6.05946i		−	0.301469i
$405$		0			0
$406$	−4.99925	−	2.35611i	−0.248109	−	0.116932i
$407$		−	3.84208i		−	0.190445i
$408$		0			0
$409$			14.9034i			0.736925i	0.929643	+	0.368462i	$0.120116\pi$
$409$			14.9034i			0.736925i	−0.929643	+	0.368462i	$0.879884\pi$
$410$	−33.7036	+	26.4583i	−1.66450	+	1.30668i
$411$		0			0
$412$			14.7524i			0.726799i
$413$		−	0.995181i		−	0.0489697i
$414$		0			0
$415$	−12.8861	+	10.1160i	−0.632555	+	0.496574i
$416$		−	12.0663i		−	0.591601i
$417$		0			0
$418$	20.1065			0.983442
$419$	19.5741			0.956259			0.478129	−	0.878289i	$-0.341315\pi$
$419$	19.5741			0.956259			0.478129	+	0.878289i	$0.341315\pi$
$420$		0			0
$421$			8.71742i			0.424861i	0.977176	+	0.212431i	$0.0681379\pi$
$421$			8.71742i			0.424861i	−0.977176	+	0.212431i	$0.931862\pi$
$422$		−	13.6566i		−	0.664792i
$423$		0			0
$424$		−	1.66189i		−	0.0807084i
$425$	−2.94345	+	12.0434i	−0.142778	+	0.584190i
$426$		0			0
$427$	−3.98775			−0.192981
$428$			34.8176i			1.68297i
$429$		0			0
$430$	−14.6881	−	18.7103i	−0.708323	−	0.902289i
$431$	26.7125			1.28669			0.643347	−	0.765574i	$-0.277545\pi$
$431$	26.7125			1.28669			0.643347	+	0.765574i	$0.277545\pi$
$432$		0			0
$433$	−34.3298			−1.64978			−0.824892	−	0.565290i	$-0.808764\pi$
$433$	−34.3298			−1.64978			−0.824892	+	0.565290i	$0.808764\pi$
$434$	4.76406			0.228682
$435$		0			0
$436$	32.9655			1.57876
$437$	6.89383			0.329777
$438$		0			0
$439$	−30.4762			−1.45455			−0.727274	−	0.686347i	$-0.759213\pi$
$439$	−30.4762			−1.45455			−0.727274	+	0.686347i	$0.759213\pi$
$440$	0.816257	−	0.640785i	0.0389135	−	0.0305482i
$441$		0			0
$442$			7.50200i			0.356834i
$443$	17.3948			0.826451			0.413225	−	0.910629i	$-0.364402\pi$
$443$	17.3948			0.826451			0.413225	+	0.910629i	$0.364402\pi$
$444$		0			0
$445$	−13.4769	+	10.5798i	−0.638866	+	0.501528i
$446$			56.1595i			2.65923i
$447$		0			0
$448$			3.69795i			0.174712i
$449$		−	1.06526i		−	0.0502726i	−0.999684	−	0.0251363i	$-0.991998\pi$
$449$		−	1.06526i		−	0.0502726i	0.999684	−	0.0251363i	$-0.00800197\pi$
$450$		0			0
$451$	−21.0223			−0.989903
$452$	−12.8283			−0.603391
$453$		0			0
$454$			14.1048i			0.661972i
$455$	1.10175	+	1.40345i	0.0516508	+	0.0657948i
$456$		0			0
$457$		−	1.01761i		−	0.0476020i	−0.999717	−	0.0238010i	$-0.992423\pi$
$457$		−	1.01761i		−	0.0476020i	0.999717	−	0.0238010i	$-0.00757681\pi$
$458$		−	19.6160i		−	0.916596i
$459$		0			0
$460$	−4.86895	+	3.82227i	−0.227016	+	0.178214i
$461$			3.17621i			0.147931i	0.997261	+	0.0739655i	$0.0235655\pi$
$461$			3.17621i			0.147931i	−0.997261	+	0.0739655i	$0.976435\pi$
$462$		0			0
$463$			1.75704i			0.0816565i	0.999166	+	0.0408283i	$0.0129997\pi$
$463$			1.75704i			0.0816565i	−0.999166	+	0.0408283i	$0.987000\pi$
$464$	9.65519	−	20.4867i	0.448231	−	0.951069i
$465$		0			0
$466$		−	26.7753i		−	1.24034i
$467$	35.9537			1.66374			0.831870	−	0.554970i	$-0.187270\pi$
$467$	35.9537			1.66374			0.831870	+	0.554970i	$0.187270\pi$
$468$		0			0
$469$	4.10350			0.189482
$470$	10.0317	+	12.7788i	0.462730	+	0.589443i
$471$		0			0
$472$	0.410210			0.0188815
$473$		−	11.6704i		−	0.536604i
$474$		0			0
$475$	−22.8761	−	5.59103i	−1.04963	−	0.256534i
$476$		−	2.43978i		−	0.111827i
$477$		0			0
$478$	30.6683			1.40273
$479$			41.1172i			1.87869i	0.342969	+	0.939347i	$0.388567\pi$
$479$			41.1172i			1.87869i	−0.342969	+	0.939347i	$0.611433\pi$
$480$		0			0
$481$			2.72296i			0.124156i
$482$	35.9356			1.63682
$483$		0			0
$484$	11.9466			0.543026
$485$	−2.27142	−	2.89342i	−0.103140	−	0.131383i
$486$		0			0
$487$		−	9.80926i		−	0.444500i	−0.974990	−	0.222250i	$-0.928660\pi$
$487$		−	9.80926i		−	0.444500i	0.974990	−	0.222250i	$-0.0713401\pi$
$488$		−	1.64374i		−	0.0744085i
$489$		0			0
$490$	18.3287	+	23.3478i	0.828008	+	1.05475i
$491$			41.7524i			1.88426i	0.335245	+	0.942131i	$0.391181\pi$
$491$			41.7524i			1.88426i	−0.335245	+	0.942131i	$0.608819\pi$
$492$		0			0
$493$	−5.69258	+	12.0787i	−0.256381	+	0.543996i
$494$	−14.2499			−0.641132
$495$		0			0
$496$			19.5228i			0.876602i
$497$		−	5.08809i		−	0.228232i
$498$		0			0
$499$	2.50030			0.111929			0.0559644	−	0.998433i	$-0.482177\pi$
$499$	2.50030			0.111929			0.0559644	+	0.998433i	$0.482177\pi$
$500$	19.2568	−	8.73481i	0.861191	−	0.390633i
$501$		0			0
$502$		−	10.1898i		−	0.454793i
$503$	23.3850			1.04268			0.521342	−	0.853348i	$-0.325431\pi$
$503$	23.3850			1.04268			0.521342	+	0.853348i	$0.325431\pi$
$504$		0			0
$505$	−5.63513	+	4.42374i	−0.250760	+	0.196854i
$506$	−6.24850			−0.277780
$507$		0			0
$508$	26.5675			1.17874
$509$	−19.8085			−0.877997			−0.438999	−	0.898488i	$-0.644667\pi$
$509$	−19.8085			−0.877997			−0.438999	+	0.898488i	$0.644667\pi$
$510$		0			0
$511$		−	2.44871i		−	0.108325i
$512$	−31.2827			−1.38251
$513$		0			0
$514$		−	38.8456i		−	1.71340i
$515$	13.7193	−	10.7701i	0.604546	−	0.474586i
$516$		0			0
$517$			7.97068i			0.350550i
$518$		−	1.82200i		−	0.0800543i
$519$		0			0
$520$	−0.578497	+	0.454137i	−0.0253688	+	0.0199152i
$521$	26.0978			1.14337			0.571684	−	0.820474i	$-0.306291\pi$
$521$	26.0978			1.14337			0.571684	+	0.820474i	$0.306291\pi$
$522$		0			0
$523$			20.8084i			0.909888i	0.890520	+	0.454944i	$0.150341\pi$
$523$			20.8084i			0.909888i	−0.890520	+	0.454944i	$0.849659\pi$
$524$			17.3989i			0.760075i
$525$		0			0
$526$	−23.5995			−1.02899
$527$		−	11.5104i		−	0.501402i
$528$		0			0
$529$	20.8576			0.906852
$530$	26.8879	−	21.1078i	1.16794	−	0.916863i
$531$		0			0
$532$	4.63430			0.200922
$533$	14.8989			0.645345
$534$		0			0
$535$	32.3794	−	25.4188i	1.39988	−	1.09895i
$536$			1.69145i			0.0730594i
$537$		0			0
$538$			32.6592i			1.40804i
$539$			14.5630i			0.627274i
$540$		0			0
$541$		−	46.2267i		−	1.98744i	−0.111881	−	0.993722i	$-0.535688\pi$
$541$		−	46.2267i		−	1.98744i	0.111881	−	0.993722i	$-0.464312\pi$
$542$		−	50.2112i		−	2.15676i
$543$		0			0
$544$	19.5074			0.836371
$545$	−24.0667	−	30.6570i	−1.03090	−	1.31320i
$546$		0			0
$547$			24.3321i			1.04037i	0.854055	+	0.520183i	$0.174136\pi$
$547$			24.3321i			1.04037i	−0.854055	+	0.520183i	$0.825864\pi$
$548$	31.4383			1.34298
$549$		0			0
$550$	20.7347	+	5.06765i	0.884130	+	0.216085i
$551$	−22.9432	−	10.8129i	−0.977412	−	0.460646i
$552$		0			0
$553$	6.43628			0.273699
$554$		−	60.5895i		−	2.57420i
$555$		0			0
$556$	2.15181			0.0912573
$557$			32.6439i			1.38316i	0.722298	+	0.691582i	$0.243086\pi$
$557$			32.6439i			1.38316i	−0.722298	+	0.691582i	$0.756914\pi$
$558$		0			0
$559$			8.27101i			0.349827i
$560$	3.84832	−	3.02105i	0.162621	−	0.127663i
$561$		0			0
$562$	44.9316			1.89533
$563$	−5.69605			−0.240060			−0.120030	−	0.992770i	$-0.538299\pi$
$563$	−5.69605			−0.240060			−0.120030	+	0.992770i	$0.538299\pi$
$564$		0			0
$565$	9.36535	+	11.9299i	0.394003	+	0.501896i
$566$			60.4900i			2.54259i
$567$		0			0
$568$	2.09729			0.0880004
$569$		−	23.0314i		−	0.965526i	−0.875751	−	0.482763i	$-0.839633\pi$
$569$		−	23.0314i		−	0.965526i	0.875751	−	0.482763i	$-0.160367\pi$
$570$		0			0
$571$	12.1948			0.510336			0.255168	−	0.966897i	$-0.417869\pi$
$571$	12.1948			0.510336			0.255168	+	0.966897i	$0.417869\pi$
$572$	6.27756			0.262478
$573$		0			0
$574$	−9.96928			−0.416110
$575$	7.10921	+	1.73752i	0.296475	+	0.0724597i
$576$		0			0
$577$	−23.1192			−0.962466			−0.481233	−	0.876593i	$-0.659811\pi$
$577$	−23.1192			−0.962466			−0.481233	+	0.876593i	$0.659811\pi$
$578$	21.4065			0.890393
$579$		0			0
$580$	22.1994	−	5.08388i	0.921782	−	0.211096i
$581$	−3.81162			−0.158133
$582$		0			0
$583$	16.7711			0.694588
$584$	1.00935			0.0417672
$585$		0			0
$586$	1.88700			0.0779512
$587$			16.0091i			0.660767i	0.943847	+	0.330384i	$0.107178\pi$
$587$			16.0091i			0.660767i	−0.943847	+	0.330384i	$0.892822\pi$
$588$		0			0
$589$	21.8638			0.900882
$590$	5.21012	+	6.63684i	0.214497	+	0.273235i
$591$		0			0
$592$	7.46648			0.306870
$593$			20.9155i			0.858896i	0.903092	+	0.429448i	$0.141292\pi$
$593$			20.9155i			0.858896i	−0.903092	+	0.429448i	$0.858708\pi$
$594$		0			0
$595$	−2.26892	+	1.78117i	−0.0930168	+	0.0730209i
$596$	−1.85626			−0.0760353
$597$		0			0
$598$	4.42843			0.181092
$599$			39.3957i			1.60967i	0.593502	+	0.804833i	$0.297745\pi$
$599$			39.3957i			1.60967i	−0.593502	+	0.804833i	$0.702255\pi$
$600$		0			0
$601$		−	18.3996i		−	0.750533i	−0.926917	−	0.375267i	$-0.877551\pi$
$601$		−	18.3996i		−	0.750533i	0.926917	−	0.375267i	$-0.122449\pi$
$602$		−	5.53436i		−	0.225564i
$603$		0			0
$604$	21.7116			0.883434
$605$	−8.72166	−	11.1100i	−0.354586	−	0.451685i
$606$		0			0
$607$	34.8854			1.41596			0.707978	−	0.706235i	$-0.249608\pi$
$607$	34.8854			1.41596			0.707978	+	0.706235i	$0.249608\pi$
$608$			37.0538i			1.50273i
$609$		0			0
$610$	26.5942	−	20.8772i	1.07677	−	0.845295i
$611$		−	5.64897i		−	0.228533i
$612$		0			0
$613$			34.3711i			1.38824i	0.719861	+	0.694118i	$0.244205\pi$
$613$			34.3711i			1.38824i	−0.719861	+	0.694118i	$0.755795\pi$
$614$	62.7811			2.53364
$615$		0			0
$616$	0.241443			0.00972801
$617$	−32.4140			−1.30494			−0.652469	−	0.757815i	$-0.726267\pi$
$617$	−32.4140			−1.30494			−0.652469	+	0.757815i	$0.726267\pi$
$618$		0			0
$619$			37.2406i			1.49683i	0.663232	+	0.748414i	$0.269184\pi$
$619$			37.2406i			1.49683i	−0.663232	+	0.748414i	$0.730816\pi$
$620$	−15.4419	+	12.1223i	−0.620161	+	0.486845i
$621$		0			0
$622$			3.61437i			0.144923i
$623$	−3.98637			−0.159710
$624$		0			0
$625$	−22.1817	−	11.5314i	−0.887267	−	0.461256i
$626$			33.2466i			1.32880i
$627$		0			0
$628$	15.1391			0.604116
$629$	−4.40214			−0.175525
$630$		0			0
$631$	−20.0296			−0.797366			−0.398683	−	0.917089i	$-0.630533\pi$
$631$	−20.0296			−0.797366			−0.398683	+	0.917089i	$0.630533\pi$
$632$			2.65301i			0.105531i
$633$		0			0
$634$	57.3834			2.27898
$635$	−19.3957	−	24.7070i	−0.769696	−	0.980468i
$636$		0			0
$637$		−	10.3211i		−	0.408937i
$638$	20.7955	+	9.80073i	0.823301	+	0.388015i
$639$		0			0
$640$	2.36527	+	3.01297i	0.0934956	+	0.119098i
$641$		−	30.4877i		−	1.20419i	−0.798424	−	0.602096i	$-0.794332\pi$
$641$		−	30.4877i		−	1.20419i	0.798424	−	0.602096i	$-0.205668\pi$
$642$		0			0
$643$		−	9.71287i		−	0.383038i	−0.981489	−	0.191519i	$-0.938659\pi$
$643$		−	9.71287i		−	0.383038i	0.981489	−	0.191519i	$-0.0613414\pi$
$644$	−1.44020			−0.0567519
$645$		0			0
$646$		−	23.0374i		−	0.906396i
$647$		−	26.7628i		−	1.05215i	−0.850437	−	0.526077i	$-0.823663\pi$
$647$		−	26.7628i		−	1.05215i	0.850437	−	0.526077i	$-0.176337\pi$
$648$		0			0
$649$			4.13967i			0.162496i
$650$	−14.6951	−	3.59154i	−0.576389	−	0.140872i
$651$		0			0
$652$	4.65501			0.182304
$653$	−47.1066			−1.84342			−0.921712	−	0.387875i	$-0.873209\pi$
$653$	−47.1066			−1.84342			−0.921712	+	0.387875i	$0.873209\pi$
$654$		0			0
$655$	16.1805	−	12.7022i	0.632224	−	0.496315i
$656$		−	40.8536i		−	1.59506i
$657$		0			0
$658$			3.77988i			0.147355i
$659$		−	18.2896i		−	0.712460i	−0.934398	−	0.356230i	$-0.884062\pi$
$659$		−	18.2896i		−	0.712460i	0.934398	−	0.356230i	$-0.115938\pi$
$660$		0			0
$661$	27.5526			1.07167			0.535836	−	0.844322i	$-0.319997\pi$
$661$	27.5526			1.07167			0.535836	+	0.844322i	$0.319997\pi$
$662$		−	30.2613i		−	1.17614i
$663$		0			0
$664$		−	1.57114i		−	0.0609719i
$665$	−3.38330	−	4.30977i	−0.131199	−	0.167126i
$666$		0			0
$667$	7.13005	+	3.36033i	0.276077	+	0.130113i
$668$			9.42124i			0.364519i
$669$		0			0
$670$	−27.3661	+	21.4832i	−1.05725	+	0.829969i
$671$	16.5879			0.640369
$672$		0			0
$673$		−	23.9569i		−	0.923472i	−0.887017	−	0.461736i	$-0.847227\pi$
$673$		−	23.9569i		−	0.923472i	0.887017	−	0.461736i	$-0.152773\pi$
$674$	−41.5830			−1.60172
$675$		0			0
$676$	20.1377			0.774528
$677$	22.9391			0.881620			0.440810	−	0.897600i	$-0.354691\pi$
$677$	22.9391			0.881620			0.440810	+	0.897600i	$0.354691\pi$
$678$		0			0
$679$		−	0.855852i		−	0.0328446i
$680$	−0.734192	−	0.935242i	−0.0281550	−	0.0358649i
$681$		0			0
$682$	−19.8171			−0.758837
$683$			34.1942i			1.30840i	0.756320	+	0.654202i	$0.226995\pi$
$683$			34.1942i			1.30840i	−0.756320	+	0.654202i	$0.773005\pi$
$684$		0			0
$685$	−22.9517	−	29.2367i	−0.876939	−	1.11708i
$686$			14.0900i			0.537960i
$687$		0			0
$688$	22.6795			0.864648
$689$	−11.8860			−0.452821
$690$		0			0
$691$	3.83582			0.145922			0.0729608	−	0.997335i	$-0.476755\pi$
$691$	3.83582			0.145922			0.0729608	+	0.997335i	$0.476755\pi$
$692$		−	28.4721i		−	1.08235i
$693$		0			0
$694$			48.5238i			1.84194i
$695$	−1.57094	−	2.00113i	−0.0595893	−	0.0759071i
$696$		0			0
$697$			24.0868i			0.912351i
$698$	44.7860			1.69518
$699$		0			0
$700$	4.77909	+	1.16803i	0.180633	+	0.0441474i
$701$	−49.0619			−1.85304			−0.926522	−	0.376241i	$-0.877217\pi$
$701$	−49.0619			−1.85304			−0.926522	+	0.376241i	$0.877217\pi$
$702$		0			0
$703$		−	8.36177i		−	0.315370i
$704$		−	15.3824i		−	0.579746i
$705$		0			0
$706$			2.73065i			0.102769i
$707$	−1.66683			−0.0626876
$708$		0			0
$709$	−9.68605			−0.363767			−0.181884	−	0.983320i	$-0.558219\pi$
$709$	−9.68605			−0.363767			−0.181884	+	0.983320i	$0.558219\pi$
$710$	26.6379	+	33.9324i	0.999702	+	1.27346i
$711$		0			0
$712$		−	1.64317i		−	0.0615802i
$713$	−6.79461			−0.254460
$714$		0			0
$715$	−4.58297	−	5.83796i	−0.171393	−	0.218327i
$716$	47.6589			1.78110
$717$		0			0
$718$			42.7817i			1.59660i
$719$	34.8915			1.30123			0.650617	−	0.759406i	$-0.274510\pi$
$719$	34.8915			1.30123			0.650617	+	0.759406i	$0.274510\pi$
$720$		0			0
$721$	4.05808			0.151131
$722$	6.27904			0.233682
$723$		0			0
$724$	9.97646			0.370772
$725$	−20.9347	−	16.9334i	−0.777495	−	0.628889i
$726$		0			0
$727$	26.3086			0.975731			0.487866	−	0.872919i	$-0.337776\pi$
$727$	26.3086			0.975731			0.487866	+	0.872919i	$0.337776\pi$
$728$	−0.171115			−0.00634195
$729$		0			0
$730$	12.8198	+	16.3304i	0.474484	+	0.604415i
$731$	−13.3715			−0.494565
$732$		0			0
$733$	30.8872			1.14084			0.570422	−	0.821352i	$-0.306780\pi$
$733$	30.8872			1.14084			0.570422	+	0.821352i	$0.306780\pi$
$734$	0.415861			0.0153497
$735$		0			0
$736$		−	11.5152i		−	0.424456i
$737$	−17.0694			−0.628759
$738$		0			0
$739$		−	7.59328i		−	0.279323i	−0.990199	−	0.139662i	$-0.955398\pi$
$739$		−	7.59328i		−	0.279323i	0.990199	−	0.139662i	$-0.0446015\pi$
$740$	4.63617	+	5.90573i	0.170429	+	0.217099i
$741$		0			0
$742$	7.95324			0.291973
$743$	33.4121			1.22577			0.612886	−	0.790172i	$-0.290009\pi$
$743$	33.4121			1.22577			0.612886	+	0.790172i	$0.290009\pi$
$744$		0			0
$745$	1.35517	+	1.72627i	0.0496497	+	0.0632456i
$746$			11.1743i			0.409119i
$747$		0			0
$748$			10.1488i			0.371076i
$749$	9.57758			0.349957
$750$		0			0
$751$			24.7607i			0.903532i	0.892137	+	0.451766i	$0.149206\pi$
$751$			24.7607i			0.903532i	−0.892137	+	0.451766i	$0.850794\pi$
$752$	−15.4897			−0.564853
$753$		0			0
$754$	−14.7382	−	6.94597i	−0.536732	−	0.252957i
$755$	−15.8507	−	20.1912i	−0.576866	−	0.734834i
$756$		0			0
$757$	−29.8424			−1.08464			−0.542321	−	0.840172i	$-0.682454\pi$
$757$	−29.8424			−1.08464			−0.542321	+	0.840172i	$0.682454\pi$
$758$			24.7950i			0.900594i
$759$		0			0
$760$	1.77647	−	1.39458i	0.0644394	−	0.0505868i
$761$	19.7600			0.716300			0.358150	−	0.933664i	$-0.383408\pi$
$761$	19.7600			0.716300			0.358150	+	0.933664i	$0.383408\pi$
$762$		0			0
$763$		−	9.06813i		−	0.328288i
$764$		−	6.27046i		−	0.226857i
$765$		0			0
$766$		−	45.5616i		−	1.64621i
$767$		−	2.93387i		−	0.105936i
$768$		0			0
$769$			32.7782i			1.18201i	0.806667	+	0.591007i	$0.201269\pi$
$769$			32.7782i			1.18201i	−0.806667	+	0.591007i	$0.798731\pi$
$770$	3.06659	+	3.90633i	0.110512	+	0.140774i
$771$		0			0
$772$	−10.7639			−0.387400
$773$	−26.1210			−0.939507			−0.469753	−	0.882798i	$-0.655657\pi$
$773$	−26.1210			−0.939507			−0.469753	+	0.882798i	$0.655657\pi$
$774$		0			0
$775$	22.5469	+	5.51056i	0.809908	+	0.197945i
$776$	0.352779			0.0126640
$777$		0			0
$778$		−	40.6019i		−	1.45565i
$779$	−45.7523			−1.63924
$780$		0			0
$781$			21.1650i			0.757344i
$782$			7.15934i			0.256018i
$783$		0			0
$784$	−28.3009			−1.01075
$785$	−11.0524	−	14.0789i	−0.394477	−	0.502499i
$786$		0			0
$787$			37.7291i			1.34490i	0.740143	+	0.672449i	$0.234758\pi$
$787$			37.7291i			1.34490i	−0.740143	+	0.672449i	$0.765242\pi$
$788$			0.595044i			0.0211976i
$789$		0			0
$790$	−42.9234	+	33.6962i	−1.52715	+	1.19886i
$791$			3.52879i			0.125469i
$792$		0			0
$793$	−11.7562			−0.417474
$794$			51.7893i			1.83793i
$795$		0			0
$796$	5.56506			0.197248
$797$	13.7227			0.486084			0.243042	−	0.970016i	$-0.421855\pi$
$797$	13.7227			0.486084			0.243042	+	0.970016i	$0.421855\pi$
$798$		0			0
$799$	9.13256			0.323087
$800$	−9.33904	+	38.2114i	−0.330185	+	1.35098i
$801$		0			0
$802$	−33.8546			−1.19545
$803$			10.1859i			0.359454i
$804$		0			0
$805$	1.05143	+	1.33935i	0.0370579	+	0.0472058i
$806$	14.0448			0.494707
$807$		0			0
$808$		−	0.687061i		−	0.0241707i
$809$			20.1211i			0.707422i	0.935355	+	0.353711i	$0.115080\pi$
$809$			20.1211i			0.707422i	−0.935355	+	0.353711i	$0.884920\pi$
$810$		0			0
$811$	−18.6829			−0.656044			−0.328022	−	0.944670i	$-0.606382\pi$
$811$	−18.6829			−0.656044			−0.328022	+	0.944670i	$0.606382\pi$
$812$	4.79310	+	2.25895i	0.168205	+	0.0792735i
$813$		0			0
$814$			7.57903i			0.265645i
$815$	−3.39841	−	4.32903i	−0.119041	−	0.151639i
$816$		0			0
$817$		−	25.3990i		−	0.888597i
$818$		−	29.3989i		−	1.02791i
$819$		0			0
$820$	32.3138	−	25.3672i	1.12845	−	0.885863i
$821$	−23.2361			−0.810944			−0.405472	−	0.914107i	$-0.632893\pi$
$821$	−23.2361			−0.810944			−0.405472	+	0.914107i	$0.632893\pi$
$822$		0			0
$823$	−23.2939			−0.811976			−0.405988	−	0.913878i	$-0.633072\pi$
$823$	−23.2939			−0.811976			−0.405988	+	0.913878i	$0.633072\pi$
$824$			1.67273i			0.0582722i
$825$		0			0
$826$			1.96313i			0.0683060i
$827$	−7.45967			−0.259398			−0.129699	−	0.991553i	$-0.541401\pi$
$827$	−7.45967			−0.259398			−0.129699	+	0.991553i	$0.541401\pi$
$828$		0			0
$829$			13.0042i			0.451654i	0.974167	+	0.225827i	$0.0725084\pi$
$829$			13.0042i			0.451654i	−0.974167	+	0.225827i	$0.927492\pi$
$830$	25.4196	−	19.9552i	0.882328	−	0.692653i
$831$		0			0
$832$			10.9018i			0.377952i
$833$	16.6859			0.578131
$834$		0			0
$835$	8.76149	−	6.87803i	0.303204	−	0.238024i
$836$	−19.2774			−0.666722
$837$		0			0
$838$	−38.6126			−1.33385
$839$			42.3972i			1.46371i	0.681459	+	0.731857i	$0.261346\pi$
$839$			42.3972i			1.46371i	−0.681459	+	0.731857i	$0.738654\pi$
$840$		0			0
$841$	−18.4587	−	22.3669i	−0.636506	−	0.771272i
$842$		−	17.1963i		−	0.592623i
$843$		0			0
$844$			13.0934i			0.450694i
$845$	−14.7017	−	18.7275i	−0.505752	−	0.644247i
$846$		0			0
$847$		−	3.28625i		−	0.112917i
$848$			32.5920i			1.11921i
$849$		0			0
$850$	5.80636	−	23.7572i	0.199157	−	0.814865i
$851$			2.59859i			0.0890784i
$852$		0			0
$853$	−33.8135			−1.15775			−0.578876	−	0.815416i	$-0.696508\pi$
$853$	−33.8135			−1.15775			−0.578876	+	0.815416i	$0.696508\pi$
$854$	7.86638			0.269182
$855$		0			0
$856$			3.94784i			0.134935i
$857$			39.2819i			1.34184i	0.741528	+	0.670922i	$0.234102\pi$
$857$			39.2819i			1.34184i	−0.741528	+	0.670922i	$0.765898\pi$
$858$		0			0
$859$		−	11.9843i		−	0.408900i	−0.978877	−	0.204450i	$-0.934459\pi$
$859$		−	11.9843i		−	0.408900i	0.978877	−	0.204450i	$-0.0655406\pi$
$860$	14.0824	+	17.9387i	0.480206	+	0.611705i
$861$		0			0
$862$	−52.6940			−1.79476
$863$		−	36.8424i		−	1.25413i	−0.778967	−	0.627065i	$-0.784256\pi$
$863$		−	36.8424i		−	1.25413i	0.778967	−	0.627065i	$-0.215744\pi$
$864$		0			0
$865$	−26.4783	+	20.7862i	−0.900288	+	0.706752i
$866$	67.7202			2.30122
$867$		0			0
$868$	−4.56760			−0.155034
$869$	−26.7731			−0.908216
$870$		0			0
$871$	12.0974			0.409905
$872$	3.73785			0.126580
$873$		0			0
$874$	−13.5990			−0.459993
$875$	−2.40276	−	5.29715i	−0.0812282	−	0.179076i
$876$		0			0
$877$			2.27276i			0.0767456i	0.999263	+	0.0383728i	$0.0122174\pi$
$877$			2.27276i			0.0767456i	−0.999263	+	0.0383728i	$0.987783\pi$
$878$	60.1184			2.02890
$879$		0			0
$880$	−16.0079	+	12.5667i	−0.539628	+	0.423623i
$881$		−	55.3714i		−	1.86551i	−0.360512	−	0.932755i	$-0.617398\pi$
$881$		−	55.3714i		−	1.86551i	0.360512	−	0.932755i	$-0.382602\pi$
$882$		0			0
$883$			7.65846i			0.257728i	0.991662	+	0.128864i	$0.0411330\pi$
$883$			7.65846i			0.257728i	−0.991662	+	0.128864i	$0.958867\pi$
$884$		−	7.19264i		−	0.241915i
$885$		0			0
$886$	−34.3136			−1.15279
$887$	3.86090			0.129636			0.0648181	−	0.997897i	$-0.479353\pi$
$887$	3.86090			0.129636			0.0648181	+	0.997897i	$0.479353\pi$
$888$		0			0
$889$		−	7.30815i		−	0.245108i
$890$	26.5850	−	20.8700i	0.891131	−	0.699564i
$891$		0			0
$892$		−	53.8436i		−	1.80282i
$893$			17.3471i			0.580498i
$894$		0			0
$895$	−34.7936	−	44.3214i	−1.16302	−	1.48150i
$896$			0.891216i			0.0297734i
$897$		0			0
$898$			2.10136i			0.0701234i
$899$	22.6130	+	10.6573i	0.754185	+	0.355441i
$900$		0			0
$901$		−	19.2158i		−	0.640171i
$902$	41.4694			1.38078
$903$		0			0
$904$	−1.45455			−0.0483777
$905$	−7.28337	−	9.27784i	−0.242107	−	0.308406i
$906$		0			0
$907$	4.71465			0.156547			0.0782737	−	0.996932i	$-0.475059\pi$
$907$	4.71465			0.156547			0.0782737	+	0.996932i	$0.475059\pi$
$908$		−	13.5232i		−	0.448782i
$909$		0			0
$910$	−2.17335	−	2.76850i	−0.0720458	−	0.0917747i
$911$		−	6.38523i		−	0.211552i	−0.994390	−	0.105776i	$-0.966267\pi$
$911$		−	6.38523i		−	0.211552i	0.994390	−	0.105776i	$-0.0337326\pi$
$912$		0			0
$913$	15.8553			0.524733
$914$			2.00738i			0.0663983i
$915$		0			0
$916$			18.8071i			0.621404i
$917$	4.78607			0.158050
$918$		0			0
$919$	40.2376			1.32732			0.663658	−	0.748036i	$-0.269003\pi$
$919$	40.2376			1.32732			0.663658	+	0.748036i	$0.269003\pi$
$920$	−0.552074	+	0.433394i	−0.0182013	+	0.0142886i
$921$		0			0
$922$		−	6.26551i		−	0.206344i
$923$		−	15.0001i		−	0.493733i
$924$		0			0
$925$	2.10750	−	8.62301i	0.0692943	−	0.283523i
$926$		−	3.46600i		−	0.113900i
$927$		0			0
$928$	−18.0615	+	38.3234i	−0.592899	+	1.25803i
$929$	56.7497			1.86190			0.930949	−	0.365149i	$-0.118982\pi$
$929$	56.7497			1.86190			0.930949	+	0.365149i	$0.118982\pi$
$930$		0			0
$931$			31.6944i			1.03874i
$932$			25.6712i			0.840888i
$933$		0			0
$934$	−70.9236			−2.32069
$935$	9.43808	−	7.40917i	0.308658	−	0.242306i
$936$		0			0
$937$		−	42.7198i		−	1.39559i	−0.716296	−	0.697797i	$-0.754164\pi$
$937$		−	42.7198i		−	1.39559i	0.716296	−	0.697797i	$-0.245836\pi$
$938$	−8.09471			−0.264302
$939$		0			0
$940$	−9.61806	−	12.2519i	−0.313707	−	0.399611i
$941$	−32.3400			−1.05425			−0.527127	−	0.849787i	$-0.676731\pi$
$941$	−32.3400			−1.05425			−0.527127	+	0.849787i	$0.676731\pi$
$942$		0			0
$943$	14.2184			0.463016
$944$	−8.04480			−0.261836
$945$		0			0
$946$			23.0214i			0.748489i
$947$	−44.3486			−1.44114			−0.720568	−	0.693384i	$-0.756119\pi$
$947$	−44.3486			−1.44114			−0.720568	+	0.693384i	$0.756119\pi$
$948$		0			0
$949$		−	7.21898i		−	0.234338i
$950$	45.1263	+	11.0291i	1.46409	+	0.357830i
$951$		0			0
$952$		−	0.276638i		−	0.00896588i
$953$			26.0460i			0.843712i	0.906663	+	0.421856i	$0.138621\pi$
$953$			26.0460i			0.843712i	−0.906663	+	0.421856i	$0.861379\pi$
$954$		0			0
$955$	−5.83136	+	4.57779i	−0.188698	+	0.148134i
$956$	−29.4036			−0.950981
$957$		0			0
$958$		−	81.1093i		−	2.62052i
$959$		−	8.64802i		−	0.279259i
$960$		0			0
$961$	9.45088			0.304867
$962$		−	5.37140i		−	0.173181i
$963$		0			0
$964$	−34.4537			−1.10968
$965$	7.85821	+	10.0101i	0.252965	+	0.322236i
$966$		0			0
$967$	15.3861			0.494785			0.247392	−	0.968915i	$-0.420426\pi$
$967$	15.3861			0.494785			0.247392	+	0.968915i	$0.420426\pi$
$968$	1.35458			0.0435379
$969$		0			0
$970$	4.48068	+	5.70766i	0.143866	+	0.183262i
$971$		−	9.79636i		−	0.314380i	−0.987568	−	0.157190i	$-0.949756\pi$
$971$		−	9.79636i		−	0.314380i	0.987568	−	0.157190i	$-0.0502436\pi$
$972$		0			0
$973$		−	0.591919i		−	0.0189761i
$974$			19.3501i			0.620017i
$975$		0			0
$976$			32.2360i			1.03185i
$977$			26.1850i			0.837734i	0.908048	+	0.418867i	$0.137573\pi$
$977$			26.1850i			0.837734i	−0.908048	+	0.418867i	$0.862427\pi$
$978$		0			0
$979$	16.5822			0.529968
$980$	−17.5729	−	22.3851i	−0.561346	−	0.715064i
$981$		0			0
$982$		−	82.3623i		−	2.62829i
$983$	−0.127997			−0.00408247			−0.00204123	−	0.999998i	$-0.500650\pi$
$983$	−0.127997			−0.00408247			−0.00204123	+	0.999998i	$0.500650\pi$
$984$		0			0
$985$	0.553374	−	0.434415i	0.0176320	−	0.0138416i
$986$	11.2294	−	23.8268i	0.357617	−	0.758801i
$987$		0			0
$988$	13.6623			0.434654
$989$			7.89323i			0.250990i
$990$		0			0
$991$	18.1627			0.576957			0.288478	−	0.957486i	$-0.406851\pi$
$991$	18.1627			0.576957			0.288478	+	0.957486i	$0.406851\pi$
$992$		−	36.5205i		−	1.15953i
$993$		0			0
$994$			10.0369i			0.318353i
$995$	−4.06280	−	5.17535i	−0.128799	−	0.164070i
$996$		0			0
$997$	51.0941			1.61817			0.809083	−	0.587694i	$-0.199964\pi$
$997$	51.0941			1.61817			0.809083	+	0.587694i	$0.199964\pi$
$998$	−4.93218			−0.156125
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.f.l.289.3		12
3.2	odd	2		435.2.f.f.289.10	yes	12
5.4	even	2		1305.2.f.k.289.10		12
15.2	even	4		2175.2.d.j.376.18		24
15.8	even	4		2175.2.d.j.376.7		24
15.14	odd	2		435.2.f.e.289.3	✓	12
29.28	even	2		1305.2.f.k.289.9		12
87.86	odd	2		435.2.f.e.289.4	yes	12
145.144	even	2	inner	1305.2.f.l.289.4		12
435.173	even	4		2175.2.d.j.376.8		24
435.347	even	4		2175.2.d.j.376.17		24
435.434	odd	2		435.2.f.f.289.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.f.e.289.3	✓	12	15.14	odd	2
435.2.f.e.289.4	yes	12	87.86	odd	2
435.2.f.f.289.9	yes	12	435.434	odd	2
435.2.f.f.289.10	yes	12	3.2	odd	2
1305.2.f.k.289.9		12	29.28	even	2
1305.2.f.k.289.10		12	5.4	even	2
1305.2.f.l.289.3		12	1.1	even	1	trivial
1305.2.f.l.289.4		12	145.144	even	2	inner
2175.2.d.j.376.7		24	15.8	even	4
2175.2.d.j.376.8		24	435.173	even	4
2175.2.d.j.376.17		24	435.347	even	4
2175.2.d.j.376.18		24	15.2	even	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q-1.97264 q^{2} +1.89129 q^{4} +(-1.38075 - 1.75885i) q^{5} -0.520254i q^{7} +0.214447 q^{8} +(2.72371 + 3.46956i) q^{10} +2.16411i q^{11} -1.53375i q^{13} +1.02627i q^{14} -4.20560 q^{16} +2.47957 q^{17} +4.70989i q^{19} +(-2.61139 - 3.32649i) q^{20} -4.26900i q^{22} -1.46369i q^{23} +(-1.18708 + 4.85704i) q^{25} +3.02552i q^{26} -0.983951i q^{28} +(-2.29579 + 4.87128i) q^{29} -4.64210i q^{31} +7.86723 q^{32} -4.89129 q^{34} +(-0.915047 + 0.718339i) q^{35} -1.77536 q^{37} -9.29090i q^{38} +(-0.296097 - 0.377179i) q^{40} +9.71408i q^{41} -5.39269 q^{43} +4.09296i q^{44} +2.88733i q^{46} +3.68312 q^{47} +6.72934 q^{49} +(2.34168 - 9.58117i) q^{50} -2.90076i q^{52} -7.74965i q^{53} +(3.80634 - 2.98808i) q^{55} -0.111567i q^{56} +(4.52876 - 9.60925i) q^{58} +1.91288 q^{59} -7.66501i q^{61} +9.15717i q^{62} -7.10796 q^{64} +(-2.69763 + 2.11771i) q^{65} +7.88749i q^{67} +4.68959 q^{68} +(1.80505 - 1.41702i) q^{70} +9.78001 q^{71} +4.70676 q^{73} +3.50215 q^{74} +8.90777i q^{76} +1.12589 q^{77} +12.3714i q^{79} +(5.80687 + 7.39701i) q^{80} -19.1623i q^{82} -7.32647i q^{83} +(-3.42366 - 4.36119i) q^{85} +10.6378 q^{86} +0.464086i q^{88} -7.66235i q^{89} -0.797938 q^{91} -2.76827i q^{92} -7.26545 q^{94} +(8.28397 - 6.50316i) q^{95} +1.64507 q^{97} -13.2745 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{4} + 6 q^{5} + 2 q^{10} + 32 q^{16} + 8 q^{17} + 20 q^{20} + 12 q^{25} - 8 q^{29} + 40 q^{32} - 52 q^{34} - 14 q^{35} + 20 q^{37} - 22 q^{40} + 44 q^{43} + 32 q^{47} - 4 q^{49} - 24 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 12 * q + 16 * q^4 + 6 * q^5 + 2 * q^10 + 32 * q^16 + 8 * q^17 + 20 * q^20 + 12 * q^25 - 8 * q^29 + 40 * q^32 - 52 * q^34 - 14 * q^35 + 20 * q^37 - 22 * q^40 + 44 * q^43 + 32 * q^47 - 4 * q^49 - 24 * q^50 + 42 * q^55 - 24 * q^58 + 28 * q^59 - 4 * q^64 - 22 * q^65 - 16 * q^68 - 26 * q^70 + 16 * q^71 - 36 * q^73 + 28 * q^74 + 22 * q^80 + 30 * q^85 + 16 * q^86 + 24 * q^91 - 28 * q^94 - 16 * q^95 - 40 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more