LMFDB - Embedded newform 2340.2.dj.d.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2340,2,Mod(361,2340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2340, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("2340.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.dj (of order $6$, degree $2$, 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:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	2340.901
Dual form			2340.2.dj.d.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{5} +(0.716063 - 0.413419i) q^{7} +O(q^{10})$	$q-1.00000i q^{5} +(0.716063 - 0.413419i) q^{7} +(-1.50000 - 0.866025i) q^{11} +(3.32235 - 1.40072i) q^{13} +(-0.716063 - 1.24026i) q^{17} +(-0.926118 + 0.534695i) q^{19} +(-1.54290 + 2.67238i) q^{23} -1.00000 q^{25} +(3.72756 - 6.45632i) q^{29} -5.84325i q^{31} +(-0.413419 - 0.716063i) q^{35} +(0.851811 + 0.491793i) q^{37} +(3.69615 + 2.13397i) q^{41} +(-4.77046 - 8.26268i) q^{43} +3.46410i q^{47} +(-3.15817 + 5.47011i) q^{49} -0.334308 q^{53} +(-0.866025 + 1.50000i) q^{55} +(9.98052 - 5.76225i) q^{59} +(-1.35824 - 2.35255i) q^{61} +(-1.40072 - 3.32235i) q^{65} +(-11.9122 - 6.87752i) q^{67} +(-8.46704 + 4.88845i) q^{71} -11.1806i q^{73} -1.43213 q^{77} -0.252387 q^{79} +5.67165i q^{83} +(-1.24026 + 0.716063i) q^{85} +(-3.98052 - 2.29815i) q^{89} +(1.79992 - 2.37653i) q^{91} +(0.534695 + 0.926118i) q^{95} +(8.25698 - 4.76717i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{7}+O(q^{10}) $ 8 * q + 6 * q^7	$ 8 q + 6 q^{7} - 12 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{23} - 8 q^{25} + 6 q^{35} + 6 q^{37} - 12 q^{41} + 10 q^{43} - 4 q^{49} - 24 q^{53} + 24 q^{59} - 4 q^{61} - 54 q^{67} + 36 q^{71} - 12 q^{77} - 16 q^{79} + 18 q^{85} + 24 q^{89} - 30 q^{97}+O(q^{100}) $ 8 * q + 6 * q^7 - 12 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^23 - 8 * q^25 + 6 * q^35 + 6 * q^37 - 12 * q^41 + 10 * q^43 - 4 * q^49 - 24 * q^53 + 24 * q^59 - 4 * q^61 - 54 * q^67 + 36 * q^71 - 12 * q^77 - 16 * q^79 + 18 * q^85 + 24 * q^89 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	0.716063	−	0.413419i	0.270646	−	0.156258i	−0.358535	−	0.933516i	$-0.616724\pi$
$7$	0.716063	−	0.413419i	0.270646	−	0.156258i	0.629181	+	0.777259i	$0.283390\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	0.256520	−	0.966539i	$-0.417424\pi$
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	−0.708787	+	0.705422i	$0.750757\pi$
$12$		0			0
$13$	3.32235	−	1.40072i	0.921453	−	0.388490i
$13$	3.32235	−	1.40072i	0.921453	−	0.388490i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.716063	−	1.24026i	−0.173671	−	0.300807i	0.766030	−	0.642805i	$-0.222230\pi$
$17$	−0.716063	−	1.24026i	−0.173671	−	0.300807i	−0.939700	+	0.341999i	$0.888896\pi$
$18$		0			0
$19$	−0.926118	+	0.534695i	−0.212466	+	0.122667i	−0.602457	−	0.798151i	$-0.705811\pi$
$19$	−0.926118	+	0.534695i	−0.212466	+	0.122667i	0.389991	+	0.920819i	$0.372478\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.54290	+	2.67238i	−0.321717	+	0.557231i	−0.980842	−	0.194803i	$-0.937593\pi$
$23$	−1.54290	+	2.67238i	−0.321717	+	0.557231i	0.659125	+	0.752033i	$0.270927\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.72756	−	6.45632i	0.692190	−	1.19891i	−0.278928	−	0.960312i	$-0.589979\pi$
$29$	3.72756	−	6.45632i	0.692190	−	1.19891i	0.971119	−	0.238597i	$-0.0766874\pi$
$30$		0			0
$31$		−	5.84325i		−	1.04948i	−0.851263	−	0.524740i	$-0.824163\pi$
$31$		−	5.84325i		−	1.04948i	0.851263	−	0.524740i	$-0.175837\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.413419	−	0.716063i	−0.0698806	−	0.121037i
$36$		0			0
$37$	0.851811	+	0.491793i	0.140037	+	0.0808503i	0.568382	−	0.822765i	$-0.307570\pi$
$37$	0.851811	+	0.491793i	0.140037	+	0.0808503i	−0.428345	+	0.903615i	$0.640903\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.69615	+	2.13397i	0.577242	+	0.333271i	0.760037	−	0.649880i	$-0.225181\pi$
$41$	3.69615	+	2.13397i	0.577242	+	0.333271i	−0.182795	+	0.983151i	$0.558514\pi$
$42$		0			0
$43$	−4.77046	−	8.26268i	−0.727488	−	1.26005i	−0.957942	−	0.286963i	$-0.907354\pi$
$43$	−4.77046	−	8.26268i	−0.727488	−	1.26005i	0.230453	−	0.973083i	$-0.425979\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.46410i			0.505291i	0.967559	+	0.252646i	$0.0813007\pi$
$47$			3.46410i			0.505291i	−0.967559	+	0.252646i	$0.918699\pi$
$48$		0			0
$49$	−3.15817	+	5.47011i	−0.451167	+	0.781444i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.334308			−0.0459207			−0.0229603	−	0.999736i	$-0.507309\pi$
$53$	−0.334308			−0.0459207			−0.0229603	+	0.999736i	$0.507309\pi$
$54$		0			0
$55$	−0.866025	+	1.50000i	−0.116775	+	0.202260i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	9.98052	−	5.76225i	1.29935	−	0.750181i	0.319060	−	0.947734i	$-0.396633\pi$
$59$	9.98052	−	5.76225i	1.29935	−	0.750181i	0.980292	+	0.197553i	$0.0632995\pi$
$60$		0			0
$61$	−1.35824	−	2.35255i	−0.173905	−	0.301213i	0.765877	−	0.642988i	$-0.222305\pi$
$61$	−1.35824	−	2.35255i	−0.173905	−	0.301213i	−0.939782	+	0.341775i	$0.888972\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.40072	−	3.32235i	−0.173738	−	0.412086i
$66$		0			0
$67$	−11.9122	−	6.87752i	−1.45531	−	0.840223i	−0.456534	−	0.889706i	$-0.650909\pi$
$67$	−11.9122	−	6.87752i	−1.45531	−	0.840223i	−0.998775	+	0.0494832i	$0.984243\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.46704	+	4.88845i	−1.00485	+	0.580152i	−0.909680	−	0.415309i	$-0.863673\pi$
$71$	−8.46704	+	4.88845i	−1.00485	+	0.580152i	−0.0951721	+	0.995461i	$0.530340\pi$
$72$		0			0
$73$		−	11.1806i		−	1.30859i	−0.756240	−	0.654295i	$-0.772966\pi$
$73$		−	11.1806i		−	1.30859i	0.756240	−	0.654295i	$-0.227034\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.43213			−0.163206
$78$		0			0
$79$	−0.252387			−0.0283958			−0.0141979	−	0.999899i	$-0.504519\pi$
$79$	−0.252387			−0.0283958			−0.0141979	+	0.999899i	$0.504519\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			5.67165i			0.622544i	0.950321	+	0.311272i	$0.100755\pi$
$83$			5.67165i			0.622544i	−0.950321	+	0.311272i	$0.899245\pi$
$84$		0			0
$85$	−1.24026	+	0.716063i	−0.134525	+	0.0776679i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.98052	−	2.29815i	−0.421934	−	0.243604i	0.273971	−	0.961738i	$-0.411663\pi$
$89$	−3.98052	−	2.29815i	−0.421934	−	0.243604i	−0.695904	+	0.718135i	$0.744996\pi$
$90$		0			0
$91$	1.79992	−	2.37653i	0.188683	−	0.249128i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.534695	+	0.926118i	0.0548585	+	0.0950177i
$96$		0			0
$97$	8.25698	−	4.76717i	0.838370	−	0.484033i	−0.0183401	−	0.999832i	$-0.505838\pi$
$97$	8.25698	−	4.76717i	0.838370	−	0.484033i	0.856710	+	0.515799i	$0.172505\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.90072	−	5.02419i	0.288632	−	0.499926i	−0.684851	−	0.728683i	$-0.740133\pi$
$101$	2.90072	−	5.02419i	0.288632	−	0.499926i	0.973484	+	0.228757i	$0.0734661\pi$
$102$		0			0
$103$	10.0760			0.992814			0.496407	−	0.868090i	$-0.334652\pi$
$103$	10.0760			0.992814			0.496407	+	0.868090i	$0.334652\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.13977	−	14.0985i	0.786902	−	1.36295i	−0.140955	−	0.990016i	$-0.545017\pi$
$107$	8.13977	−	14.0985i	0.786902	−	1.36295i	0.927856	−	0.372938i	$-0.121649\pi$
$108$		0			0
$109$		−	3.12979i		−	0.299780i	−0.988703	−	0.149890i	$-0.952108\pi$
$109$		−	3.12979i		−	0.299780i	0.988703	−	0.149890i	$-0.0478919\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.08538	−	8.80813i	−0.478392	−	0.828599i	0.521301	−	0.853373i	$-0.325447\pi$
$113$	−5.08538	−	8.80813i	−0.478392	−	0.828599i	−0.999693	+	0.0247735i	$0.992114\pi$
$114$		0			0
$115$	2.67238	+	1.54290i	0.249201	+	0.143876i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.02549	−	0.592068i	−0.0940068	−	0.0542748i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	2.98401	−	5.16846i	0.264788	−	0.458627i	−0.702720	−	0.711467i	$-0.748031\pi$
$127$	2.98401	−	5.16846i	0.264788	−	0.458627i	0.967508	+	0.252840i	$0.0813646\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.6267			−1.45268			−0.726342	−	0.687334i	$-0.758781\pi$
$131$	−16.6267			−1.45268			−0.726342	+	0.687334i	$0.758781\pi$
$132$		0			0
$133$	−0.442106	+	0.765750i	−0.0383355	+	0.0663990i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.350349	−	0.202274i	0.0299324	−	0.0172815i	−0.484959	−	0.874537i	$-0.661166\pi$
$137$	0.350349	−	0.202274i	0.0299324	−	0.0172815i	0.514892	+	0.857255i	$0.327832\pi$
$138$		0			0
$139$	4.65817	+	8.06819i	0.395101	+	0.684335i	0.993114	−	0.117152i	$-0.0373763\pi$
$139$	4.65817	+	8.06819i	0.395101	+	0.684335i	−0.598013	+	0.801486i	$0.704043\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.19658	−	0.776156i	−0.518184	−	0.0649054i
$144$		0			0
$145$	−6.45632	−	3.72756i	−0.536168	−	0.309557i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.41179	+	5.43390i	−0.771044	+	0.445162i	−0.833247	−	0.552901i	$-0.813521\pi$
$149$	−9.41179	+	5.43390i	−0.771044	+	0.445162i	0.0622030	+	0.998064i	$0.480187\pi$
$150$		0			0
$151$			0.991015i			0.0806477i	0.999187	+	0.0403238i	$0.0128390\pi$
$151$			0.991015i			0.0806477i	−0.999187	+	0.0403238i	$0.987161\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.84325			−0.469341
$156$		0			0
$157$	17.5729			1.40247			0.701235	−	0.712930i	$-0.252632\pi$
$157$	17.5729			1.40247			0.701235	+	0.712930i	$0.252632\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.55146i			0.201083i
$162$		0			0
$163$	−14.9666	+	8.64098i	−1.17228	+	0.676814i	−0.954215	−	0.299122i	$-0.903306\pi$
$163$	−14.9666	+	8.64098i	−1.17228	+	0.676814i	−0.218061	+	0.975935i	$0.569973\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.64965	+	1.52978i	0.205036	+	0.118378i	0.599002	−	0.800747i	$-0.295564\pi$
$167$	2.64965	+	1.52978i	0.205036	+	0.118378i	−0.393966	+	0.919125i	$0.628897\pi$
$168$		0			0
$169$	9.07597	−	9.30735i	0.698151	−	0.715950i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.71006	+	2.96190i	0.130013	+	0.225189i	0.923681	−	0.383161i	$-0.125165\pi$
$173$	1.71006	+	2.96190i	0.130013	+	0.225189i	−0.793668	+	0.608351i	$0.791831\pi$
$174$		0			0
$175$	−0.716063	+	0.413419i	−0.0541293	+	0.0312516i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.19109	−	8.99123i	0.388000	−	0.672036i	−0.604180	−	0.796848i	$-0.706499\pi$
$179$	5.19109	−	8.99123i	0.388000	−	0.672036i	0.992180	+	0.124811i	$0.0398326\pi$
$180$		0			0
$181$	−10.3492			−0.769247			−0.384624	−	0.923073i	$-0.625669\pi$
$181$	−10.3492			−0.769247			−0.384624	+	0.923073i	$0.625669\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.491793	−	0.851811i	0.0361574	−	0.0626264i
$186$		0			0
$187$			2.48052i			0.181393i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.75296	−	13.4285i	−0.560984	−	0.971653i	−0.997411	−	0.0719134i	$-0.977089\pi$
$191$	−7.75296	−	13.4285i	−0.560984	−	0.971653i	0.436427	−	0.899740i	$-0.356244\pi$
$192$		0			0
$193$	4.82401	+	2.78514i	0.347239	+	0.200479i	0.663469	−	0.748204i	$-0.269084\pi$
$193$	4.82401	+	2.78514i	0.347239	+	0.200479i	−0.316229	+	0.948683i	$0.602417\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.5405	+	12.4364i	1.53470	+	0.886058i	0.999136	+	0.0415608i	$0.0132330\pi$
$197$	21.5405	+	12.4364i	1.53470	+	0.886058i	0.535561	+	0.844497i	$0.320100\pi$
$198$		0			0
$199$	−9.32443	−	16.1504i	−0.660991	−	1.14487i	−0.980356	−	0.197239i	$-0.936803\pi$
$199$	−9.32443	−	16.1504i	−0.660991	−	1.14487i	0.319364	−	0.947632i	$-0.396531\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	6.16418i		−	0.432640i
$204$		0			0
$205$	2.13397	−	3.69615i	0.149043	−	0.258150i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.85224			0.128122
$210$		0			0
$211$	−4.82235	+	8.35255i	−0.331984	+	0.575013i	−0.982901	−	0.184136i	$-0.941051\pi$
$211$	−4.82235	+	8.35255i	−0.331984	+	0.575013i	0.650917	+	0.759149i	$0.274385\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.26268	+	4.77046i	−0.563510	+	0.325343i
$216$		0			0
$217$	−2.41571	−	4.18414i	−0.163989	−	0.284038i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.11626	−	3.11756i	−0.276890	−	0.209710i
$222$		0			0
$223$	−1.00558	−	0.580573i	−0.0673387	−	0.0388780i	0.465953	−	0.884810i	$-0.345712\pi$
$223$	−1.00558	−	0.580573i	−0.0673387	−	0.0388780i	−0.533291	+	0.845932i	$0.679045\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	23.5957	−	13.6230i	1.56610	−	0.904191i	0.569488	−	0.822000i	$-0.307142\pi$
$227$	23.5957	−	13.6230i	1.56610	−	0.904191i	0.996617	−	0.0821911i	$-0.0261918\pi$
$228$		0			0
$229$		−	24.3432i		−	1.60864i	−0.594193	−	0.804322i	$-0.702529\pi$
$229$		−	24.3432i		−	1.60864i	0.594193	−	0.804322i	$-0.297471\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	23.0238			1.50834			0.754171	−	0.656678i	$-0.228039\pi$
$233$	23.0238			1.50834			0.754171	+	0.656678i	$0.228039\pi$
$234$		0			0
$235$	3.46410			0.225973
$236$		0			0
$237$		0			0
$238$		0			0
$239$			23.7057i			1.53340i	0.642008	+	0.766698i	$0.278102\pi$
$239$			23.7057i			1.53340i	−0.642008	+	0.766698i	$0.721898\pi$
$240$		0			0
$241$	−9.37968	+	5.41536i	−0.604198	+	0.348834i	−0.770691	−	0.637209i	$-0.780089\pi$
$241$	−9.37968	+	5.41536i	−0.604198	+	0.348834i	0.166493	+	0.986043i	$0.446756\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.47011	+	3.15817i	0.349472	+	0.201768i
$246$		0			0
$247$	−2.32793	+	3.07367i	−0.148123	+	0.195573i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.560405	+	0.970649i	0.0353724	+	0.0612668i	0.883170	−	0.469054i	$-0.155405\pi$
$251$	0.560405	+	0.970649i	0.0353724	+	0.0612668i	−0.847797	+	0.530321i	$0.822072\pi$
$252$		0			0
$253$	4.62870	−	2.67238i	0.291004	−	0.168011i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.31534	+	14.4026i	−0.518697	+	0.898409i	0.481067	+	0.876684i	$0.340249\pi$
$257$	−8.31534	+	14.4026i	−0.518697	+	0.898409i	−0.999764	+	0.0217255i	$0.993084\pi$
$258$		0			0
$259$	0.813267			0.0505340
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.2510	−	21.2193i	0.755427	−	1.30844i	−0.189734	−	0.981836i	$-0.560763\pi$
$263$	12.2510	−	21.2193i	0.755427	−	1.30844i	0.945162	−	0.326603i	$-0.105904\pi$
$264$		0			0
$265$			0.334308i			0.0205364i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.26643	−	5.65763i	−0.199158	−	0.344952i	0.749098	−	0.662460i	$-0.230487\pi$
$269$	−3.26643	−	5.65763i	−0.199158	−	0.344952i	−0.948256	+	0.317508i	$0.897154\pi$
$270$		0			0
$271$	4.89831	+	2.82804i	0.297551	+	0.171791i	0.641342	−	0.767255i	$-0.278378\pi$
$271$	4.89831	+	2.82804i	0.297551	+	0.171791i	−0.343791	+	0.939046i	$0.611711\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.50000	+	0.866025i	0.0904534	+	0.0522233i
$276$		0			0
$277$	1.85782	+	3.21784i	0.111626	+	0.193341i	0.916426	−	0.400205i	$-0.131061\pi$
$277$	1.85782	+	3.21784i	0.111626	+	0.193341i	−0.804800	+	0.593546i	$0.797728\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			9.70447i			0.578920i	0.957190	+	0.289460i	$0.0934758\pi$
$281$			9.70447i			0.578920i	−0.957190	+	0.289460i	$0.906524\pi$
$282$		0			0
$283$	−12.0988	+	20.9558i	−0.719200	+	1.24569i	0.242117	+	0.970247i	$0.422158\pi$
$283$	−12.0988	+	20.9558i	−0.719200	+	1.24569i	−0.961317	+	0.275444i	$0.911175\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.52890			0.208305
$288$		0			0
$289$	7.47451	−	12.9462i	0.439677	−	0.761543i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.14218	−	1.81414i	0.183568	−	0.105983i	−0.405400	−	0.914139i	$-0.632868\pi$
$293$	3.14218	−	1.81414i	0.183568	−	0.105983i	0.588968	+	0.808156i	$0.299534\pi$
$294$		0			0
$295$	−5.76225	−	9.98052i	−0.335491	−	0.581088i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.38279	+	11.0398i	−0.0799689	+	0.638446i
$300$		0			0
$301$	−6.83190	−	3.94440i	−0.393784	−	0.227351i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.35255	+	1.35824i	−0.134707	+	0.0777729i
$306$		0			0
$307$			9.40129i			0.536560i	0.963341	+	0.268280i	$0.0864552\pi$
$307$			9.40129i			0.536560i	−0.963341	+	0.268280i	$0.913545\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−25.5370			−1.44807			−0.724034	−	0.689764i	$-0.757714\pi$
$311$	−25.5370			−1.44807			−0.724034	+	0.689764i	$0.757714\pi$
$312$		0			0
$313$	5.25656			0.297118			0.148559	−	0.988904i	$-0.452536\pi$
$313$	5.25656			0.297118			0.148559	+	0.988904i	$0.452536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	14.1536i		−	0.794947i	−0.917614	−	0.397474i	$-0.869887\pi$
$317$		−	14.1536i		−	0.794947i	0.917614	−	0.397474i	$-0.130113\pi$
$318$		0			0
$319$	−11.1827	+	6.45632i	−0.626110	+	0.361485i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.32632	+	0.765750i	0.0737983	+	0.0426075i
$324$		0			0
$325$	−3.32235	+	1.40072i	−0.184291	+	0.0776980i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.43213	+	2.48052i	0.0789557	+	0.136755i
$330$		0			0
$331$	−16.0945	+	9.29214i	−0.884632	+	0.510742i	−0.872183	−	0.489180i	$-0.837296\pi$
$331$	−16.0945	+	9.29214i	−0.884632	+	0.510742i	−0.0124490	+	0.999923i	$0.503963\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.87752	+	11.9122i	−0.375759	+	0.650834i
$336$		0			0
$337$	22.4060			1.22053			0.610267	−	0.792196i	$-0.291062\pi$
$337$	22.4060			1.22053			0.610267	+	0.792196i	$0.291062\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.06040	+	8.76488i	−0.274036	+	0.474645i
$342$		0			0
$343$			11.0105i			0.594509i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.0862	+	17.4699i	0.541457	+	0.937831i	0.998821	+	0.0485514i	$0.0154605\pi$
$347$	10.0862	+	17.4699i	0.541457	+	0.937831i	−0.457364	+	0.889280i	$0.651206\pi$
$348$		0			0
$349$	24.7634	+	14.2972i	1.32556	+	0.765310i	0.984609	−	0.174773i	$-0.0559192\pi$
$349$	24.7634	+	14.2972i	1.32556	+	0.765310i	0.340947	+	0.940083i	$0.389252\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.66167	−	5.57817i	−0.514239	−	0.296896i	0.220336	−	0.975424i	$-0.429285\pi$
$353$	−9.66167	−	5.57817i	−0.514239	−	0.296896i	−0.734574	+	0.678528i	$0.762618\pi$
$354$		0			0
$355$	4.88845	+	8.46704i	0.259452	+	0.449384i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			11.0490i			0.583145i	0.956549	+	0.291572i	$0.0941784\pi$
$359$			11.0490i			0.583145i	−0.956549	+	0.291572i	$0.905822\pi$
$360$		0			0
$361$	−8.92820	+	15.4641i	−0.469905	+	0.813900i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.1806			−0.585219
$366$		0			0
$367$	−12.2026	+	21.1355i	−0.636970	+	1.10326i	0.349124	+	0.937076i	$0.386479\pi$
$367$	−12.2026	+	21.1355i	−0.636970	+	1.10326i	−0.986094	+	0.166188i	$0.946854\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.239385	+	0.138209i	−0.0124283	+	0.00717546i
$372$		0			0
$373$	2.65566	+	4.59974i	0.137505	+	0.238165i	0.926552	−	0.376168i	$-0.122758\pi$
$373$	2.65566	+	4.59974i	0.137505	+	0.238165i	−0.789047	+	0.614333i	$0.789425\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.34074	−	26.6714i	0.172057	−	1.37365i
$378$		0			0
$379$	29.0469	+	16.7703i	1.49204	+	0.861430i	0.999958	−	0.00911888i	$-0.00290267\pi$
$379$	29.0469	+	16.7703i	1.49204	+	0.861430i	0.492082	+	0.870549i	$0.336236\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−20.6138	+	11.9014i	−1.05331	+	0.608131i	−0.923575	−	0.383417i	$-0.874747\pi$
$383$	−20.6138	+	11.9014i	−1.05331	+	0.608131i	−0.129739	+	0.991548i	$0.541414\pi$
$384$		0			0
$385$			1.43213i			0.0729879i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	26.2787			1.33238			0.666191	−	0.745781i	$-0.267923\pi$
$389$	26.2787			1.33238			0.666191	+	0.745781i	$0.267923\pi$
$390$		0			0
$391$	4.41926			0.223492
$392$		0			0
$393$		0			0
$394$		0			0
$395$			0.252387i			0.0126990i
$396$		0			0
$397$	28.8317	−	16.6460i	1.44702	−	0.835439i	0.448719	−	0.893673i	$-0.351880\pi$
$397$	28.8317	−	16.6460i	1.44702	−	0.835439i	0.998303	+	0.0582340i	$0.0185469\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.2709	−	7.08460i	−0.612779	−	0.353788i	0.161273	−	0.986910i	$-0.448440\pi$
$401$	−12.2709	−	7.08460i	−0.612779	−	0.353788i	−0.774052	+	0.633122i	$0.781773\pi$
$402$		0			0
$403$	−8.18476	−	19.4133i	−0.407712	−	0.967046i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.851811	−	1.47538i	−0.0422227	−	0.0731319i
$408$		0			0
$409$	5.93213	−	3.42491i	0.293325	−	0.169351i	−0.346116	−	0.938192i	$-0.612499\pi$
$409$	5.93213	−	3.42491i	0.293325	−	0.169351i	0.639440	+	0.768841i	$0.279166\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.76445	−	8.25227i	0.234443	−	0.406068i
$414$		0			0
$415$	5.67165			0.278410
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.19109	+	14.1874i	−0.400161	+	0.693099i	−0.993745	−	0.111673i	$-0.964379\pi$
$419$	−8.19109	+	14.1874i	−0.400161	+	0.693099i	0.593584	+	0.804772i	$0.297712\pi$
$420$		0			0
$421$			21.7045i			1.05781i	0.848681	+	0.528906i	$0.177397\pi$
$421$			21.7045i			1.05781i	−0.848681	+	0.528906i	$0.822603\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.716063	+	1.24026i	0.0347342	+	0.0601613i
$426$		0			0
$427$	−1.94518	−	1.12305i	−0.0941337	−	0.0543481i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−28.0495	−	16.1944i	−1.35110	−	0.780056i	−0.362693	−	0.931909i	$-0.618143\pi$
$431$	−28.0495	−	16.1944i	−1.35110	−	0.780056i	−0.988403	+	0.151853i	$0.951476\pi$
$432$		0			0
$433$	14.3987	+	24.9393i	0.691959	+	1.19851i	0.971195	+	0.238286i	$0.0765855\pi$
$433$	14.3987	+	24.9393i	0.691959	+	1.19851i	−0.279236	+	0.960223i	$0.590081\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	3.29992i		−	0.157857i
$438$		0			0
$439$	−8.79992	+	15.2419i	−0.419997	+	0.727457i	−0.995939	−	0.0900341i	$-0.971302\pi$
$439$	−8.79992	+	15.2419i	−0.419997	+	0.727457i	0.575941	+	0.817491i	$0.304636\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.4043			0.684370			0.342185	−	0.939633i	$-0.388833\pi$
$443$	14.4043			0.684370			0.342185	+	0.939633i	$0.388833\pi$
$444$		0			0
$445$	−2.29815	+	3.98052i	−0.108943	+	0.188695i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.58821	−	1.49430i	0.122145	−	0.0705206i	−0.437683	−	0.899130i	$-0.644201\pi$
$449$	2.58821	−	1.49430i	0.122145	−	0.0705206i	0.559828	+	0.828609i	$0.310867\pi$
$450$		0			0
$451$	−3.69615	−	6.40192i	−0.174045	−	0.301455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.37653	−	1.79992i	−0.111413	−	0.0843818i
$456$		0			0
$457$	−23.0540	−	13.3102i	−1.07842	−	0.622626i	−0.147950	−	0.988995i	$-0.547267\pi$
$457$	−23.0540	−	13.3102i	−1.07842	−	0.622626i	−0.930470	+	0.366369i	$0.880601\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.26488	+	4.19438i	−0.338359	+	0.195352i	−0.659546	−	0.751664i	$-0.729252\pi$
$461$	−7.26488	+	4.19438i	−0.338359	+	0.195352i	0.321187	+	0.947016i	$0.395918\pi$
$462$		0			0
$463$			21.3014i			0.989960i	0.868904	+	0.494980i	$0.164825\pi$
$463$			21.3014i			0.989960i	−0.868904	+	0.494980i	$0.835175\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.12392			−0.0982833			−0.0491417	−	0.998792i	$-0.515649\pi$
$467$	−2.12392			−0.0982833			−0.0491417	+	0.998792i	$0.515649\pi$
$468$		0			0
$469$	−11.3732			−0.525165
$470$		0			0
$471$		0			0
$472$		0			0
$473$			16.5254i			0.759837i
$474$		0			0
$475$	0.926118	−	0.534695i	0.0424932	−	0.0245335i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	25.1617	+	14.5271i	1.14967	+	0.663762i	0.948806	−	0.315858i	$-0.102292\pi$
$479$	25.1617	+	14.5271i	1.14967	+	0.663762i	0.200862	+	0.979619i	$0.435626\pi$
$480$		0			0
$481$	3.51887	+	0.440759i	0.160447	+	0.0200969i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.76717	−	8.25698i	−0.216466	−	0.374930i
$486$		0			0
$487$	−26.2570	+	15.1595i	−1.18982	+	0.686941i	−0.958265	−	0.285881i	$-0.907714\pi$
$487$	−26.2570	+	15.1595i	−1.18982	+	0.686941i	−0.231552	+	0.972822i	$0.574380\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.0759	+	33.0405i	−0.860884	+	1.49110i	0.0101919	+	0.999948i	$0.496756\pi$
$491$	−19.0759	+	33.0405i	−0.860884	+	1.49110i	−0.871076	+	0.491148i	$0.836578\pi$
$492$		0			0
$493$	−10.6767			−0.480853
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.04196	+	7.00087i	−0.181306	+	0.314032i
$498$		0			0
$499$			16.5179i			0.739444i	0.929142	+	0.369722i	$0.120547\pi$
$499$			16.5179i			0.739444i	−0.929142	+	0.369722i	$0.879453\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.88081	+	10.1859i	0.262212	+	0.454165i	0.966830	−	0.255423i	$-0.0822146\pi$
$503$	5.88081	+	10.1859i	0.262212	+	0.454165i	−0.704617	+	0.709588i	$0.748881\pi$
$504$		0			0
$505$	−5.02419	−	2.90072i	−0.223574	−	0.129080i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.5930	−	15.9308i	−1.22304	−	0.706122i	−0.257474	−	0.966285i	$-0.582890\pi$
$509$	−27.5930	−	15.9308i	−1.22304	−	0.706122i	−0.965565	+	0.260164i	$0.916223\pi$
$510$		0			0
$511$	−4.62227	−	8.00601i	−0.204477	−	0.354165i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	10.0760i		−	0.444000i
$516$		0			0
$517$	3.00000	−	5.19615i	0.131940	−	0.228527i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	19.5013			0.854367			0.427183	−	0.904165i	$-0.359506\pi$
$521$	19.5013			0.854367			0.427183	+	0.904165i	$0.359506\pi$
$522$		0			0
$523$	22.2830	−	38.5952i	0.974365	−	1.68765i	0.292352	−	0.956311i	$-0.405562\pi$
$523$	22.2830	−	38.5952i	0.974365	−	1.68765i	0.682014	−	0.731340i	$-0.261105\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.24714	+	4.18414i	−0.315690	+	0.182264i
$528$		0			0
$529$	6.73891	+	11.6721i	0.292996	+	0.507484i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15.2690	+	1.91253i	0.661374	+	0.0828407i
$534$		0			0
$535$	−14.0985	−	8.13977i	−0.609531	−	0.351913i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.47451	−	5.47011i	0.408096	−	0.235614i
$540$		0			0
$541$			3.74450i			0.160989i	0.996755	+	0.0804943i	$0.0256499\pi$
$541$			3.74450i			0.160989i	−0.996755	+	0.0804943i	$0.974350\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.12979			−0.134066
$546$		0			0
$547$	38.3803			1.64102			0.820511	−	0.571630i	$-0.193689\pi$
$547$	38.3803			1.64102			0.820511	+	0.571630i	$0.193689\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			7.97242i			0.339637i
$552$		0			0
$553$	−0.180725	+	0.104342i	−0.00768522	+	0.00443706i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.0763	+	13.3231i	0.977772	+	0.564517i	0.901597	−	0.432577i	$-0.142396\pi$
$557$	23.0763	+	13.3231i	0.977772	+	0.564517i	0.0761755	+	0.997094i	$0.475729\pi$
$558$		0			0
$559$	−27.4228	−	20.7694i	−1.15986	−	0.878452i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.34675	+	14.4570i	0.351774	+	0.609290i	0.986560	−	0.163398i	$-0.0522454\pi$
$563$	8.34675	+	14.4570i	0.351774	+	0.609290i	−0.634787	+	0.772687i	$0.718912\pi$
$564$		0			0
$565$	−8.80813	+	5.08538i	−0.370561	+	0.213943i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.9620	−	38.0393i	0.920694	−	1.59469i	0.122350	−	0.992487i	$-0.460957\pi$
$569$	21.9620	−	38.0393i	0.920694	−	1.59469i	0.798344	−	0.602202i	$-0.205710\pi$
$570$		0			0
$571$	−11.4641			−0.479758			−0.239879	−	0.970803i	$-0.577108\pi$
$571$	−11.4641			−0.479758			−0.239879	+	0.970803i	$0.577108\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.54290	−	2.67238i	0.0643434	−	0.111446i
$576$		0			0
$577$			44.9354i			1.87069i	0.353743	+	0.935343i	$0.384909\pi$
$577$			44.9354i			1.87069i	−0.353743	+	0.935343i	$0.615091\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.34477	+	4.06126i	0.0972773	+	0.168489i
$582$		0			0
$583$	0.501461	+	0.289519i	0.0207684	+	0.0119906i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.2364	+	12.2608i	0.876520	+	0.506059i	0.869509	−	0.493916i	$-0.164435\pi$
$587$	21.2364	+	12.2608i	0.876520	+	0.506059i	0.00701059	+	0.999975i	$0.497768\pi$
$588$		0			0
$589$	3.12436	+	5.41154i	0.128737	+	0.222979i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			18.7655i			0.770607i	0.922790	+	0.385303i	$0.125903\pi$
$593$			18.7655i			0.770607i	−0.922790	+	0.385303i	$0.874097\pi$
$594$		0			0
$595$	−0.592068	+	1.02549i	−0.0242724	+	0.0420411i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	35.9293			1.46803			0.734015	−	0.679133i	$-0.237644\pi$
$599$	35.9293			1.46803			0.734015	+	0.679133i	$0.237644\pi$
$600$		0			0
$601$	19.8863	−	34.4441i	0.811179	−	1.40500i	−0.100860	−	0.994901i	$-0.532160\pi$
$601$	19.8863	−	34.4441i	0.811179	−	1.40500i	0.912039	−	0.410103i	$-0.134507\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.92820	+	4.00000i	−0.281672	+	0.162623i
$606$		0			0
$607$	−16.7306	−	28.9783i	−0.679076	−	1.17619i	−0.975260	−	0.221063i	$-0.929047\pi$
$607$	−16.7306	−	28.9783i	−0.679076	−	1.17619i	0.296184	−	0.955131i	$-0.404286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.85224	+	11.5089i	0.196300	+	0.465602i
$612$		0			0
$613$	17.1212	+	9.88495i	0.691520	+	0.399249i	0.804181	−	0.594384i	$-0.202604\pi$
$613$	17.1212	+	9.88495i	0.691520	+	0.399249i	−0.112661	+	0.993633i	$0.535937\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.8950	−	9.75436i	0.680169	−	0.392696i	−0.119750	−	0.992804i	$-0.538209\pi$
$617$	16.8950	−	9.75436i	0.680169	−	0.392696i	0.799919	+	0.600108i	$0.204876\pi$
$618$		0			0
$619$			40.4640i			1.62639i	0.581994	+	0.813193i	$0.302273\pi$
$619$			40.4640i			1.62639i	−0.581994	+	0.813193i	$0.697727\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.80040			−0.152260
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.40862i		−	0.0561653i
$630$		0			0
$631$	−16.9707	+	9.79806i	−0.675594	+	0.390054i	−0.798193	−	0.602402i	$-0.794211\pi$
$631$	−16.9707	+	9.79806i	−0.675594	+	0.390054i	0.122599	+	0.992456i	$0.460877\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.16846	−	2.98401i	−0.205104	−	0.118417i
$636$		0			0
$637$	−2.83044	+	22.5973i	−0.112146	+	0.895338i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.5238	−	26.8881i	−0.613155	−	1.06202i	−0.990705	−	0.136026i	$-0.956567\pi$
$641$	−15.5238	−	26.8881i	−0.613155	−	1.06202i	0.377550	−	0.925989i	$-0.376767\pi$
$642$		0			0
$643$	−5.14990	+	2.97329i	−0.203092	+	0.117255i	−0.598097	−	0.801424i	$-0.704076\pi$
$643$	−5.14990	+	2.97329i	−0.203092	+	0.117255i	0.395005	+	0.918679i	$0.370743\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.2510	+	36.8078i	−0.835462	+	1.44706i	0.0581916	+	0.998305i	$0.481467\pi$
$647$	−21.2510	+	36.8078i	−0.835462	+	1.44706i	−0.893654	+	0.448757i	$0.851867\pi$
$648$		0			0
$649$	−19.9610			−0.783539
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.3054	+	26.5097i	−0.598945	+	1.03740i	0.394032	+	0.919097i	$0.371080\pi$
$653$	−15.3054	+	26.5097i	−0.598945	+	1.03740i	−0.992977	+	0.118307i	$0.962253\pi$
$654$		0			0
$655$			16.6267i			0.649660i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.7191	−	22.0302i	−0.495467	−	0.858175i	0.504519	−	0.863401i	$-0.331670\pi$
$659$	−12.7191	−	22.0302i	−0.495467	−	0.858175i	−0.999986	+	0.00522582i	$0.998337\pi$
$660$		0			0
$661$	−0.288909	−	0.166802i	−0.0112373	−	0.00648784i	0.494371	−	0.869251i	$-0.335398\pi$
$661$	−0.288909	−	0.166802i	−0.0112373	−	0.00648784i	−0.505608	+	0.862763i	$0.668732\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.765750	+	0.442106i	0.0296945	+	0.0171441i
$666$		0			0
$667$	11.5025	+	19.9229i	0.445379	+	0.771419i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			4.70510i			0.181638i
$672$		0			0
$673$	4.90706	−	8.49928i	0.189153	−	0.327623i	−0.755815	−	0.654785i	$-0.772759\pi$
$673$	4.90706	−	8.49928i	0.189153	−	0.327623i	0.944968	+	0.327162i	$0.106092\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.2414			0.893241			0.446620	−	0.894724i	$-0.352627\pi$
$677$	23.2414			0.893241			0.446620	+	0.894724i	$0.352627\pi$
$678$		0			0
$679$	3.94168	−	6.82719i	0.151268	−	0.262004i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.56144	+	2.63355i	−0.174539	+	0.100770i	−0.584724	−	0.811232i	$-0.698797\pi$
$683$	−4.56144	+	2.63355i	−0.174539	+	0.100770i	0.410186	+	0.912002i	$0.365464\pi$
$684$		0			0
$685$	−0.202274	−	0.350349i	−0.00772850	−	0.0133862i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.11069	+	0.468271i	−0.0423138	+	0.0178397i
$690$		0			0
$691$	17.1334	+	9.89199i	0.651787	+	0.376309i	0.789140	−	0.614213i	$-0.210526\pi$
$691$	17.1334	+	9.89199i	0.651787	+	0.376309i	−0.137354	+	0.990522i	$0.543860\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.06819	−	4.65817i	0.306044	−	0.176694i
$696$		0			0
$697$		−	6.11224i		−	0.231518i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.1256			−0.684595			−0.342298	−	0.939592i	$-0.611205\pi$
$701$	−18.1256			−0.684595			−0.342298	+	0.939592i	$0.611205\pi$
$702$		0			0
$703$	−1.05184			−0.0396708
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	4.79685i		−	0.180404i
$708$		0			0
$709$	−22.3514	+	12.9046i	−0.839424	+	0.484642i	−0.857068	−	0.515203i	$-0.827717\pi$
$709$	−22.3514	+	12.9046i	−0.839424	+	0.484642i	0.0176445	+	0.999844i	$0.494383\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.6154	+	9.01556i	0.584802	+	0.337635i
$714$		0			0
$715$	−0.776156	+	6.19658i	−0.0290266	+	0.231739i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.51338	+	7.81741i	0.168321	+	0.291540i	0.937830	−	0.347096i	$-0.112832\pi$
$719$	4.51338	+	7.81741i	0.168321	+	0.291540i	−0.769509	+	0.638636i	$0.779499\pi$
$720$		0			0
$721$	7.21503	−	4.16560i	0.268702	−	0.155135i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.72756	+	6.45632i	−0.138438	+	0.239782i
$726$		0			0
$727$	24.8934			0.923245			0.461623	−	0.887076i	$-0.347267\pi$
$727$	24.8934			0.923245			0.461623	+	0.887076i	$0.347267\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.83190	+	11.8332i	−0.252687	+	0.437667i
$732$		0			0
$733$			13.2793i			0.490484i	0.969462	+	0.245242i	$0.0788674\pi$
$733$			13.2793i			0.490484i	−0.969462	+	0.245242i	$0.921133\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.9122	+	20.6326i	0.438792	+	0.760010i
$738$		0			0
$739$	16.9656	+	9.79508i	0.624089	+	0.360318i	0.778459	−	0.627695i	$-0.216002\pi$
$739$	16.9656	+	9.79508i	0.624089	+	0.360318i	−0.154370	+	0.988013i	$0.549335\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−44.3804	−	25.6230i	−1.62816	−	0.940017i	−0.984642	−	0.174583i	$-0.944142\pi$
$743$	−44.3804	−	25.6230i	−1.62816	−	0.940017i	−0.643515	−	0.765434i	$-0.722525\pi$
$744$		0			0
$745$	5.43390	+	9.41179i	0.199083	+	0.344821i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	13.4606i		−	0.491838i
$750$		0			0
$751$	−10.5992	+	18.3584i	−0.386772	+	0.669908i	−0.992013	−	0.126134i	$-0.959743\pi$
$751$	−10.5992	+	18.3584i	−0.386772	+	0.669908i	0.605242	+	0.796042i	$0.293077\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.991015			0.0360667
$756$		0			0
$757$	16.4747	−	28.5350i	0.598783	−	1.03712i	−0.394218	−	0.919017i	$-0.628984\pi$
$757$	16.4747	−	28.5350i	0.598783	−	1.03712i	0.993001	−	0.118106i	$-0.0376823\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−45.2367	+	26.1174i	−1.63983	+	0.946756i	−0.658939	+	0.752197i	$0.728994\pi$
$761$	−45.2367	+	26.1174i	−1.63983	+	0.946756i	−0.980891	+	0.194559i	$0.937672\pi$
$762$		0			0
$763$	−1.29392	−	2.24113i	−0.0468429	−	0.0811343i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	25.0874	−	33.1241i	0.905854	−	1.19604i
$768$		0			0
$769$	23.2717	+	13.4359i	0.839200	+	0.484513i	0.856992	−	0.515329i	$-0.172330\pi$
$769$	23.2717	+	13.4359i	0.839200	+	0.484513i	−0.0177920	+	0.999842i	$0.505664\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.3533	+	5.97746i	−0.372381	+	0.214994i	−0.674498	−	0.738276i	$-0.735640\pi$
$773$	−10.3533	+	5.97746i	−0.372381	+	0.214994i	0.302117	+	0.953271i	$0.402307\pi$
$774$		0			0
$775$			5.84325i			0.209896i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.56410			−0.163526
$780$		0			0
$781$	16.9341			0.605949
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	17.5729i		−	0.627204i
$786$		0			0
$787$	29.8724	−	17.2468i	1.06484	−	0.614783i	0.138070	−	0.990422i	$-0.455910\pi$
$787$	29.8724	−	17.2468i	1.06484	−	0.614783i	0.926766	+	0.375639i	$0.122577\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.28290	−	4.20479i	−0.258950	−	0.149505i
$792$		0			0
$793$	−7.80782	−	5.91346i	−0.277264	−	0.209993i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.6025	−	28.7563i	−0.588089	−	1.01860i	−0.994483	−	0.104902i	$-0.966547\pi$
$797$	−16.6025	−	28.7563i	−0.588089	−	1.01860i	0.406393	−	0.913698i	$-0.366786\pi$
$798$		0			0
$799$	4.29638	−	2.48052i	0.151995	−	0.0877543i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.68268	+	16.7709i	−0.341694	+	0.591832i
$804$		0			0
$805$	2.55146			0.0899272
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.35139	+	7.53682i	−0.152987	+	0.264980i	−0.932324	−	0.361624i	$-0.882222\pi$
$809$	−4.35139	+	7.53682i	−0.152987	+	0.264980i	0.779338	+	0.626604i	$0.215556\pi$
$810$		0			0
$811$			7.69132i			0.270079i	0.990840	+	0.135039i	$0.0431161\pi$
$811$			7.69132i			0.270079i	−0.990840	+	0.135039i	$0.956884\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.64098	+	14.9666i	0.302680	+	0.524258i
$816$		0			0
$817$	8.83602	+	5.10148i	0.309133	+	0.178478i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.532962	+	0.307706i	0.0186005	+	0.0107390i	0.509271	−	0.860606i	$-0.329915\pi$
$821$	0.532962	+	0.307706i	0.0186005	+	0.0107390i	−0.490671	+	0.871345i	$0.663248\pi$
$822$		0			0
$823$	−11.1688	−	19.3449i	−0.389319	−	0.674320i	0.603039	−	0.797712i	$-0.293956\pi$
$823$	−11.1688	−	19.3449i	−0.389319	−	0.674320i	−0.992358	+	0.123391i	$0.960623\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	33.8701i		−	1.17778i	−0.808213	−	0.588890i	$-0.799565\pi$
$827$		−	33.8701i		−	1.17778i	0.808213	−	0.588890i	$-0.200435\pi$
$828$		0			0
$829$	−17.2646	+	29.9033i	−0.599626	+	1.03858i	0.393250	+	0.919432i	$0.371351\pi$
$829$	−17.2646	+	29.9033i	−0.599626	+	1.03858i	−0.992876	+	0.119151i	$0.961983\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.04579			0.313418
$834$		0			0
$835$	1.52978	−	2.64965i	0.0529401	−	0.0916949i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.9386	−	14.9757i	0.895501	−	0.517018i	0.0197630	−	0.999805i	$-0.493709\pi$
$839$	25.9386	−	14.9757i	0.895501	−	0.517018i	0.875738	+	0.482787i	$0.160376\pi$
$840$		0			0
$841$	−13.2894	−	23.0179i	−0.458255	−	0.793720i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.30735	−	9.07597i	−0.320183	−	0.312223i
$846$		0			0
$847$	−5.72850	−	3.30735i	−0.196834	−	0.113642i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.62852	+	1.51758i	−0.0901045	+	0.0520219i
$852$		0			0
$853$		−	54.1009i		−	1.85238i	−0.377059	−	0.926189i	$-0.623065\pi$
$853$		−	54.1009i		−	1.85238i	0.377059	−	0.926189i	$-0.376935\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.4383			0.561521			0.280761	−	0.959778i	$-0.409413\pi$
$857$	16.4383			0.561521			0.280761	+	0.959778i	$0.409413\pi$
$858$		0			0
$859$	32.7187			1.11635			0.558174	−	0.829724i	$-0.311502\pi$
$859$	32.7187			1.11635			0.558174	+	0.829724i	$0.311502\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	55.7922i		−	1.89919i	−0.313482	−	0.949594i	$-0.601496\pi$
$863$		−	55.7922i		−	1.89919i	0.313482	−	0.949594i	$-0.398504\pi$
$864$		0			0
$865$	2.96190	−	1.71006i	0.100708	−	0.0581436i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.378581	+	0.218574i	0.0128425	+	0.00741461i
$870$		0			0
$871$	−49.2100	−	6.16382i	−1.66742	−	0.208853i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.413419	+	0.716063i	0.0139761	+	0.0242073i
$876$		0			0
$877$	−33.5084	+	19.3461i	−1.13150	+	0.653271i	−0.944311	−	0.329054i	$-0.893270\pi$
$877$	−33.5084	+	19.3461i	−1.13150	+	0.653271i	−0.187187	+	0.982324i	$0.559937\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.71058	−	4.69485i	0.0913216	−	0.158174i	−0.816746	−	0.576998i	$-0.804224\pi$
$881$	2.71058	−	4.69485i	0.0913216	−	0.158174i	0.908067	+	0.418824i	$0.137558\pi$
$882$		0			0
$883$	21.2583			0.715397			0.357699	−	0.933837i	$-0.383561\pi$
$883$	21.2583			0.715397			0.357699	+	0.933837i	$0.383561\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.283085	−	0.490318i	0.00950507	−	0.0164633i	−0.861234	−	0.508209i	$-0.830308\pi$
$887$	0.283085	−	0.490318i	0.00950507	−	0.0164633i	0.870739	+	0.491746i	$0.163641\pi$
$888$		0			0
$889$		−	4.93459i		−	0.165501i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.85224	−	3.20817i	−0.0619827	−	0.107357i
$894$		0			0
$895$	−8.99123	−	5.19109i	−0.300544	−	0.173519i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−37.7259	−	21.7811i	−1.25823	−	0.726439i
$900$		0			0
$901$	0.239385	+	0.414628i	0.00797508	+	0.0138132i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			10.3492i			0.344018i
$906$		0			0
$907$	18.5258	−	32.0876i	0.615139	−	1.06545i	−0.375222	−	0.926935i	$-0.622433\pi$
$907$	18.5258	−	32.0876i	0.615139	−	1.06545i	0.990360	−	0.138516i	$-0.0442333\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	27.9952			0.927522			0.463761	−	0.885960i	$-0.346500\pi$
$911$	27.9952			0.927522			0.463761	+	0.885960i	$0.346500\pi$
$912$		0			0
$913$	4.91179	−	8.50747i	0.162557	−	0.281556i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.9058	+	6.87381i	−0.393164	+	0.226993i
$918$		0			0
$919$	−18.4721	−	31.9945i	−0.609337	−	1.05540i	−0.991350	−	0.131246i	$-0.958102\pi$
$919$	−18.4721	−	31.9945i	−0.609337	−	1.05540i	0.382013	−	0.924157i	$-0.375231\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21.2831	+	28.1011i	−0.700541	+	0.924958i
$924$		0			0
$925$	−0.851811	−	0.491793i	−0.0280074	−	0.0161701i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.5432	+	6.66449i	−0.378721	+	0.218655i	−0.677262	−	0.735742i	$-0.736834\pi$
$929$	−11.5432	+	6.66449i	−0.378721	+	0.218655i	0.298541	+	0.954397i	$0.403500\pi$
$930$		0			0
$931$		−	6.75462i		−	0.221374i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.48052			0.0811215
$936$		0			0
$937$	13.0922			0.427702			0.213851	−	0.976866i	$-0.431399\pi$
$937$	13.0922			0.427702			0.213851	+	0.976866i	$0.431399\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			43.0399i			1.40306i	0.712639	+	0.701531i	$0.247500\pi$
$941$			43.0399i			1.40306i	−0.712639	+	0.701531i	$0.752500\pi$
$942$		0			0
$943$	−11.4056	+	6.58502i	−0.371417	+	0.214438i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.3311	+	15.2023i	0.855646	+	0.494008i	0.862552	−	0.505969i	$-0.168865\pi$
$947$	26.3311	+	15.2023i	0.855646	+	0.494008i	−0.00690573	+	0.999976i	$0.502198\pi$
$948$		0			0
$949$	−15.6609	−	37.1458i	−0.508374	−	1.20580i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.7011	+	18.5349i	0.346643	+	0.600404i	0.985651	−	0.168796i	$-0.0539881\pi$
$953$	10.7011	+	18.5349i	0.346643	+	0.600404i	−0.639008	+	0.769201i	$0.720655\pi$
$954$		0			0
$955$	−13.4285	+	7.75296i	−0.434537	+	0.250880i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.167248	−	0.289682i	0.00540072	−	0.00935433i
$960$		0			0
$961$	−3.14359			−0.101406
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.78514	−	4.82401i	0.0896569	−	0.155290i
$966$		0			0
$967$			41.8892i			1.34707i	0.739157	+	0.673533i	$0.235224\pi$
$967$			41.8892i			1.34707i	−0.739157	+	0.673533i	$0.764776\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.4126	−	24.9634i	−0.462524	−	0.801114i	0.536562	−	0.843861i	$-0.319723\pi$
$971$	−14.4126	−	24.9634i	−0.462524	−	0.801114i	−0.999086	+	0.0427462i	$0.986389\pi$
$972$		0			0
$973$	6.67109	+	3.85155i	0.213865	+	0.123475i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	47.1705	+	27.2339i	1.50912	+	0.871289i	0.999944	+	0.0106254i	$0.00338225\pi$
$977$	47.1705	+	27.2339i	1.50912	+	0.871289i	0.509174	+	0.860664i	$0.329951\pi$
$978$		0			0
$979$	3.98052	+	6.89445i	0.127218	+	0.220348i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	56.5991i		−	1.80523i	−0.430447	−	0.902616i	$-0.641644\pi$
$983$		−	56.5991i		−	1.80523i	0.430447	−	0.902616i	$-0.358356\pi$
$984$		0			0
$985$	12.4364	−	21.5405i	0.396257	−	0.686337i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	29.4414			0.936182
$990$		0			0
$991$	−11.3462	+	19.6522i	−0.360425	+	0.624274i	−0.988031	−	0.154257i	$-0.950702\pi$
$991$	−11.3462	+	19.6522i	−0.360425	+	0.624274i	0.627606	+	0.778531i	$0.284035\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.1504	+	9.32443i	−0.512002	+	0.295604i
$996$		0			0
$997$	−23.3614	−	40.4631i	−0.739862	−	1.28148i	−0.952557	−	0.304360i	$-0.901557\pi$
$997$	−23.3614	−	40.4631i	−0.739862	−	1.28148i	0.212695	−	0.977119i	$-0.431776\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.dj.d.901.2		8
3.2	odd	2		260.2.x.a.121.3	yes	8
12.11	even	2		1040.2.da.c.641.2		8
13.10	even	6	inner	2340.2.dj.d.361.4		8
15.2	even	4		1300.2.ba.c.849.2		8
15.8	even	4		1300.2.ba.b.849.3		8
15.14	odd	2		1300.2.y.b.901.2		8
39.17	odd	6		3380.2.f.i.3041.3		8
39.20	even	12		3380.2.a.p.1.2		4
39.23	odd	6		260.2.x.a.101.3	✓	8
39.32	even	12		3380.2.a.q.1.2		4
39.35	odd	6		3380.2.f.i.3041.4		8
156.23	even	6		1040.2.da.c.881.2		8
195.23	even	12		1300.2.ba.c.49.2		8
195.62	even	12		1300.2.ba.b.49.3		8
195.179	odd	6		1300.2.y.b.101.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.3	✓	8	39.23	odd	6
260.2.x.a.121.3	yes	8	3.2	odd	2
1040.2.da.c.641.2		8	12.11	even	2
1040.2.da.c.881.2		8	156.23	even	6
1300.2.y.b.101.2		8	195.179	odd	6
1300.2.y.b.901.2		8	15.14	odd	2
1300.2.ba.b.49.3		8	195.62	even	12
1300.2.ba.b.849.3		8	15.8	even	4
1300.2.ba.c.49.2		8	195.23	even	12
1300.2.ba.c.849.2		8	15.2	even	4
2340.2.dj.d.361.4		8	13.10	even	6	inner
2340.2.dj.d.901.2		8	1.1	even	1	trivial
3380.2.a.p.1.2		4	39.20	even	12
3380.2.a.q.1.2		4	39.32	even	12
3380.2.f.i.3041.3		8	39.17	odd	6
3380.2.f.i.3041.4		8	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.dj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{5} +(0.716063 - 0.413419i) q^{7} +O(q^{10})\)	\(q-1.00000i q^{5} +(0.716063 - 0.413419i) q^{7} +(-1.50000 - 0.866025i) q^{11} +(3.32235 - 1.40072i) q^{13} +(-0.716063 - 1.24026i) q^{17} +(-0.926118 + 0.534695i) q^{19} +(-1.54290 + 2.67238i) q^{23} -1.00000 q^{25} +(3.72756 - 6.45632i) q^{29} -5.84325i q^{31} +(-0.413419 - 0.716063i) q^{35} +(0.851811 + 0.491793i) q^{37} +(3.69615 + 2.13397i) q^{41} +(-4.77046 - 8.26268i) q^{43} +3.46410i q^{47} +(-3.15817 + 5.47011i) q^{49} -0.334308 q^{53} +(-0.866025 + 1.50000i) q^{55} +(9.98052 - 5.76225i) q^{59} +(-1.35824 - 2.35255i) q^{61} +(-1.40072 - 3.32235i) q^{65} +(-11.9122 - 6.87752i) q^{67} +(-8.46704 + 4.88845i) q^{71} -11.1806i q^{73} -1.43213 q^{77} -0.252387 q^{79} +5.67165i q^{83} +(-1.24026 + 0.716063i) q^{85} +(-3.98052 - 2.29815i) q^{89} +(1.79992 - 2.37653i) q^{91} +(0.534695 + 0.926118i) q^{95} +(8.25698 - 4.76717i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{7}+O(q^{10}) \) 8 * q + 6 * q^7	\( 8 q + 6 q^{7} - 12 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{23} - 8 q^{25} + 6 q^{35} + 6 q^{37} - 12 q^{41} + 10 q^{43} - 4 q^{49} - 24 q^{53} + 24 q^{59} - 4 q^{61} - 54 q^{67} + 36 q^{71} - 12 q^{77} - 16 q^{79} + 18 q^{85} + 24 q^{89} - 30 q^{97}+O(q^{100}) \) 8 * q + 6 * q^7 - 12 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^23 - 8 * q^25 + 6 * q^35 + 6 * q^37 - 12 * q^41 + 10 * q^43 - 4 * q^49 - 24 * q^53 + 24 * q^59 - 4 * q^61 - 54 * q^67 + 36 * q^71 - 12 * q^77 - 16 * q^79 + 18 * q^85 + 24 * q^89 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more