LMFDB - Embedded newform 1512.2.q.d.793.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$, degree $2$, not 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.11
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70368 + 2.95086i) q^{5} +(-0.410295 - 2.61374i) q^{7} +O(q^{10})$	$q+(1.70368 + 2.95086i) q^{5} +(-0.410295 - 2.61374i) q^{7} +(2.69819 - 4.67340i) q^{11} +(1.89598 - 3.28393i) q^{13} +(-0.411976 - 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +(-2.74950 - 4.76227i) q^{23} +(-3.30506 + 5.72452i) q^{25} +(-0.400332 - 0.693396i) q^{29} -9.90732 q^{31} +(7.01378 - 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(-1.84467 + 3.19507i) q^{41} +(-4.36356 - 7.55790i) q^{43} +10.4991 q^{47} +(-6.66332 + 2.14481i) q^{49} +(4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +1.66069 q^{59} +0.948811 q^{61} +12.9206 q^{65} +0.539184 q^{67} +3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(-13.3221 - 5.13490i) q^{77} +7.82899 q^{79} +(3.79623 + 6.57527i) q^{83} +(1.40375 - 2.43137i) q^{85} +(3.73498 - 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +1.59199 q^{95} +(-3.22500 - 5.58587i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	1.70368	+	2.95086i	0.761909	+	1.31967i	0.941865	+	0.335991i	$0.109071\pi$
$5$	1.70368	+	2.95086i	0.761909	+	1.31967i	−0.179956	+	0.983675i	$0.557596\pi$
$6$		0			0
$7$	−0.410295	−	2.61374i	−0.155077	−	0.987902i
$7$	−0.410295	−	2.61374i	−0.155077	−	0.987902i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.69819	−	4.67340i	0.813535	−	1.40908i	−0.0968406	−	0.995300i	$-0.530874\pi$
$11$	2.69819	−	4.67340i	0.813535	−	1.40908i	0.910375	−	0.413784i	$-0.135793\pi$
$12$		0			0
$13$	1.89598	−	3.28393i	0.525850	−	0.910800i	−0.473696	−	0.880688i	$-0.657080\pi$
$13$	1.89598	−	3.28393i	0.525850	−	0.910800i	0.999547	−	0.0301113i	$-0.00958618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.411976	−	0.713564i	−0.0999190	−	0.173065i	0.811732	−	0.584030i	$-0.198525\pi$
$17$	−0.411976	−	0.713564i	−0.0999190	−	0.173065i	−0.911651	+	0.410965i	$0.865192\pi$
$18$		0			0
$19$	0.233611	−	0.404626i	0.0535940	−	0.0928275i	−0.837984	−	0.545695i	$-0.816266\pi$
$19$	0.233611	−	0.404626i	0.0535940	−	0.0928275i	0.891578	+	0.452868i	$0.149599\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.74950	−	4.76227i	−0.573309	−	0.993001i	−0.996223	−	0.0868310i	$-0.972326\pi$
$23$	−2.74950	−	4.76227i	−0.573309	−	0.993001i	0.422914	−	0.906170i	$-0.361007\pi$
$24$		0			0
$25$	−3.30506	+	5.72452i	−0.661011	+	1.14490i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.400332	−	0.693396i	−0.0743399	−	0.128760i	0.826459	−	0.562997i	$-0.190352\pi$
$29$	−0.400332	−	0.693396i	−0.0743399	−	0.128760i	−0.900799	+	0.434236i	$0.857018\pi$
$30$		0			0
$31$	−9.90732			−1.77941			−0.889703	−	0.456539i	$-0.849089\pi$
$31$	−9.90732			−1.77941			−0.889703	+	0.456539i	$0.849089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.01378	−	5.66371i	1.18555	−	0.957342i
$36$		0			0
$37$	4.34210	−	7.52074i	0.713837	−	1.23640i	−0.249569	−	0.968357i	$-0.580289\pi$
$37$	4.34210	−	7.52074i	0.713837	−	1.23640i	0.963406	−	0.268045i	$-0.0863777\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.84467	+	3.19507i	−0.288090	+	0.498986i	−0.973354	−	0.229309i	$-0.926354\pi$
$41$	−1.84467	+	3.19507i	−0.288090	+	0.498986i	0.685264	+	0.728295i	$0.259687\pi$
$42$		0			0
$43$	−4.36356	−	7.55790i	−0.665436	−	1.15257i	−0.979167	−	0.203057i	$-0.934912\pi$
$43$	−4.36356	−	7.55790i	−0.665436	−	1.15257i	0.313731	−	0.949512i	$-0.398421\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.4991			1.53146			0.765728	−	0.643164i	$-0.222379\pi$
$47$	10.4991			1.53146			0.765728	+	0.643164i	$0.222379\pi$
$48$		0			0
$49$	−6.66332	+	2.14481i	−0.951902	+	0.306402i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.71820	+	8.17217i	0.648095	+	1.12253i	0.983577	+	0.180487i	$0.0577673\pi$
$53$	4.71820	+	8.17217i	0.648095	+	1.12253i	−0.335483	+	0.942046i	$0.608899\pi$
$54$		0			0
$55$	18.3874			2.47936
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.66069			0.216203			0.108102	−	0.994140i	$-0.465523\pi$
$59$	1.66069			0.216203			0.108102	+	0.994140i	$0.465523\pi$
$60$		0			0
$61$	0.948811			0.121483			0.0607414	−	0.998154i	$-0.480654\pi$
$61$	0.948811			0.121483			0.0607414	+	0.998154i	$0.480654\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.9206			1.60260
$66$		0			0
$67$	0.539184			0.0658718			0.0329359	−	0.999457i	$-0.489514\pi$
$67$	0.539184			0.0658718			0.0329359	+	0.999457i	$0.489514\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.86901			0.459167			0.229583	−	0.973289i	$-0.426264\pi$
$71$	3.86901			0.459167			0.229583	+	0.973289i	$0.426264\pi$
$72$		0			0
$73$	2.58943	+	4.48502i	0.303070	+	0.524932i	0.976830	−	0.214018i	$-0.0686551\pi$
$73$	2.58943	+	4.48502i	0.303070	+	0.524932i	−0.673760	+	0.738950i	$0.735322\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−13.3221	−	5.13490i	−1.51820	−	0.585176i
$78$		0			0
$79$	7.82899			0.880830			0.440415	−	0.897794i	$-0.354831\pi$
$79$	7.82899			0.880830			0.440415	+	0.897794i	$0.354831\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.79623	+	6.57527i	0.416691	+	0.721729i	0.995604	−	0.0936595i	$-0.0298565\pi$
$83$	3.79623	+	6.57527i	0.416691	+	0.721729i	−0.578914	+	0.815389i	$0.696523\pi$
$84$		0			0
$85$	1.40375	−	2.43137i	0.152258	−	0.263719i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.73498	−	6.46917i	0.395907	−	0.685730i	−0.597310	−	0.802011i	$-0.703764\pi$
$89$	3.73498	−	6.46917i	0.395907	−	0.685730i	0.993216	+	0.116280i	$0.0370971\pi$
$90$		0			0
$91$	−9.36128	−	3.60823i	−0.981328	−	0.378245i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.59199			0.163335
$96$		0			0
$97$	−3.22500	−	5.58587i	−0.327450	−	0.567159i	0.654555	−	0.756014i	$-0.272856\pi$
$97$	−3.22500	−	5.58587i	−0.327450	−	0.567159i	−0.982005	+	0.188855i	$0.939522\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.09973	+	14.0291i	−0.805953	+	1.39595i	0.109692	+	0.993966i	$0.465014\pi$
$101$	−8.09973	+	14.0291i	−0.805953	+	1.39595i	−0.915646	+	0.401987i	$0.868320\pi$
$102$		0			0
$103$	7.84930	+	13.5954i	0.773414	+	1.33959i	0.935681	+	0.352846i	$0.114786\pi$
$103$	7.84930	+	13.5954i	0.773414	+	1.33959i	−0.162267	+	0.986747i	$0.551881\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.85024	+	4.93675i	−0.275543	+	0.477254i	−0.970272	−	0.242017i	$-0.922191\pi$
$107$	−2.85024	+	4.93675i	−0.275543	+	0.477254i	0.694729	+	0.719271i	$0.255524\pi$
$108$		0			0
$109$	−2.19196	−	3.79659i	−0.209952	−	0.363648i	0.741747	−	0.670680i	$-0.233997\pi$
$109$	−2.19196	−	3.79659i	−0.209952	−	0.363648i	−0.951699	+	0.307032i	$0.900664\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.96607	−	8.60149i	0.467169	−	0.809160i	−0.532128	−	0.846664i	$-0.678607\pi$
$113$	4.96607	−	8.60149i	0.467169	−	0.809160i	0.999296	+	0.0375041i	$0.0119407\pi$
$114$		0			0
$115$	9.36852	−	16.2268i	0.873619	−	1.51315i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.69604	+	1.36957i	−0.155476	+	0.125549i
$120$		0			0
$121$	−9.06045	−	15.6932i	−0.823677	−	1.42665i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.48623			−0.490703
$126$		0			0
$127$	16.1122			1.42973			0.714864	−	0.699263i	$-0.246488\pi$
$127$	16.1122			1.42973			0.714864	+	0.699263i	$0.246488\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.97039	+	12.0731i	0.609006	+	1.05483i	0.991405	+	0.130832i	$0.0417648\pi$
$131$	6.97039	+	12.0731i	0.609006	+	1.05483i	−0.382399	+	0.923997i	$0.624902\pi$
$132$		0			0
$133$	−1.15344	−	0.444583i	−0.100016	−	0.0385502i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.57598	+	9.65787i	−0.476388	+	0.825128i	−0.999634	−	0.0270537i	$-0.991388\pi$
$137$	−5.57598	+	9.65787i	−0.476388	+	0.825128i	0.523246	+	0.852182i	$0.324721\pi$
$138$		0			0
$139$	3.17737	−	5.50337i	0.269501	−	0.466790i	−0.699232	−	0.714895i	$-0.746474\pi$
$139$	3.17737	−	5.50337i	0.269501	−	0.466790i	0.968733	+	0.248105i	$0.0798078\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.2314	−	17.7214i	−0.855595	−	1.48193i
$144$		0			0
$145$	1.36408	−	2.36265i	0.113280	−	0.196207i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.76521	−	9.98564i	−0.472304	−	0.818055i	0.527193	−	0.849745i	$-0.323244\pi$
$149$	−5.76521	−	9.98564i	−0.472304	−	0.818055i	−0.999498	+	0.0316900i	$0.989911\pi$
$150$		0			0
$151$	0.347317	−	0.601571i	0.0282643	−	0.0489551i	−0.851547	−	0.524278i	$-0.824335\pi$
$151$	0.347317	−	0.601571i	0.0282643	−	0.0489551i	0.879812	+	0.475323i	$0.157669\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.8789	−	29.2351i	−1.35575	−	2.34822i
$156$		0			0
$157$	−4.04845			−0.323102			−0.161551	−	0.986864i	$-0.551650\pi$
$157$	−4.04845			−0.323102			−0.161551	+	0.986864i	$0.551650\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.3192	+	9.14041i	−0.892081	+	0.720365i
$162$		0			0
$163$	−5.05968	+	8.76363i	−0.396305	+	0.686420i	−0.993267	−	0.115849i	$-0.963041\pi$
$163$	−5.05968	+	8.76363i	−0.396305	+	0.686420i	0.596962	+	0.802270i	$0.296374\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.76377	+	15.1793i	−0.678161	+	1.17461i	0.297374	+	0.954761i	$0.403889\pi$
$167$	−8.76377	+	15.1793i	−0.678161	+	1.17461i	−0.975534	+	0.219847i	$0.929444\pi$
$168$		0			0
$169$	−0.689486	−	1.19422i	−0.0530374	−	0.0918634i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.83515			0.595695			0.297848	−	0.954613i	$-0.403731\pi$
$173$	7.83515			0.595695			0.297848	+	0.954613i	$0.403731\pi$
$174$		0			0
$175$	16.3185	+	6.28982i	1.23356	+	0.475466i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.61920	−	8.00069i	−0.345255	−	0.597999i	0.640145	−	0.768254i	$-0.278874\pi$
$179$	−4.61920	−	8.00069i	−0.345255	−	0.597999i	−0.985400	+	0.170255i	$0.945541\pi$
$180$		0			0
$181$	9.45977			0.703139			0.351569	−	0.936162i	$-0.385648\pi$
$181$	9.45977			0.703139			0.351569	+	0.936162i	$0.385648\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	29.5902			2.17552
$186$		0			0
$187$	−4.44636			−0.325150
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0452967			−0.00327756			−0.00163878	−	0.999999i	$-0.500522\pi$
$191$	−0.0452967			−0.00327756			−0.00163878	+	0.999999i	$0.500522\pi$
$192$		0			0
$193$	−18.8198			−1.35468			−0.677340	−	0.735670i	$-0.736868\pi$
$193$	−18.8198			−1.35468			−0.677340	+	0.735670i	$0.736868\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.3886			1.59512			0.797561	−	0.603239i	$-0.206123\pi$
$197$	22.3886			1.59512			0.797561	+	0.603239i	$0.206123\pi$
$198$		0			0
$199$	−11.3709	−	19.6949i	−0.806060	−	1.39614i	−0.915573	−	0.402152i	$-0.868262\pi$
$199$	−11.3709	−	19.6949i	−0.806060	−	1.39614i	0.109513	−	0.993985i	$-0.465071\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.64811	+	1.33086i	−0.115674	+	0.0934083i
$204$		0			0
$205$	−12.5709			−0.877993
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.26065	−	2.18351i	−0.0872011	−	0.151037i
$210$		0			0
$211$	−2.95868	+	5.12458i	−0.203684	+	0.352791i	−0.949713	−	0.313123i	$-0.898625\pi$
$211$	−2.95868	+	5.12458i	−0.203684	+	0.352791i	0.746029	+	0.665914i	$0.231958\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	14.8682	−	25.7525i	1.01400	−	1.75631i
$216$		0			0
$217$	4.06492	+	25.8952i	0.275945	+	1.75788i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.12440			−0.210170
$222$		0			0
$223$	−1.20124	−	2.08062i	−0.0804412	−	0.139328i	0.822998	−	0.568044i	$-0.192300\pi$
$223$	−1.20124	−	2.08062i	−0.0804412	−	0.139328i	−0.903440	+	0.428716i	$0.858966\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.48851	+	6.04227i	−0.231540	+	0.401040i	−0.958262	−	0.285893i	$-0.907710\pi$
$227$	−3.48851	+	6.04227i	−0.231540	+	0.401040i	0.726721	+	0.686933i	$0.241043\pi$
$228$		0			0
$229$	9.60782	+	16.6412i	0.634903	+	1.09968i	0.986536	+	0.163546i	$0.0522931\pi$
$229$	9.60782	+	16.6412i	0.634903	+	1.09968i	−0.351633	+	0.936138i	$0.614374\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.9002	+	22.3439i	−0.845122	+	1.46379i	0.0403930	+	0.999184i	$0.487139\pi$
$233$	−12.9002	+	22.3439i	−0.845122	+	1.46379i	−0.885515	+	0.464611i	$0.846194\pi$
$234$		0			0
$235$	17.8872	+	30.9815i	1.16683	+	2.02101i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.65732	−	11.5308i	0.430626	−	0.745866i	−0.566301	−	0.824198i	$-0.691626\pi$
$239$	6.65732	−	11.5308i	0.430626	−	0.745866i	0.996927	+	0.0783322i	$0.0249595\pi$
$240$		0			0
$241$	−0.928238	+	1.60776i	−0.0597931	+	0.103565i	−0.894372	−	0.447323i	$-0.852377\pi$
$241$	−0.928238	+	1.60776i	−0.0597931	+	0.103565i	0.834579	+	0.550888i	$0.185711\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.6812	−	16.0084i	−1.12961	−	1.02274i
$246$		0			0
$247$	−0.885843	−	1.53432i	−0.0563648	−	0.0976267i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.6947			−0.738165			−0.369083	−	0.929397i	$-0.620328\pi$
$251$	−11.6947			−0.738165			−0.369083	+	0.929397i	$0.620328\pi$
$252$		0			0
$253$	−29.6746			−1.86563
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.46594	+	2.53908i	0.0914429	+	0.158384i	0.908118	−	0.418713i	$-0.137519\pi$
$257$	1.46594	+	2.53908i	0.0914429	+	0.158384i	−0.816676	+	0.577097i	$0.804185\pi$
$258$		0			0
$259$	−21.4388	−	8.26342i	−1.33214	−	0.513464i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.1420	+	24.4946i	−0.872032	+	1.51040i	−0.0121407	+	0.999926i	$0.503865\pi$
$263$	−14.1420	+	24.4946i	−0.872032	+	1.51040i	−0.859891	+	0.510477i	$0.829469\pi$
$264$		0			0
$265$	−16.0766	+	27.8455i	−0.987579	+	1.71054i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.79128	−	8.29874i	−0.292129	−	0.505983i	0.682184	−	0.731181i	$-0.261030\pi$
$269$	−4.79128	−	8.29874i	−0.292129	−	0.505983i	−0.974313	+	0.225198i	$0.927697\pi$
$270$		0			0
$271$	9.14220	−	15.8348i	0.555349	−	0.961893i	−0.442527	−	0.896755i	$-0.645918\pi$
$271$	9.14220	−	15.8348i	0.555349	−	0.961893i	0.997876	−	0.0651381i	$-0.0207488\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	17.8353	+	30.8917i	1.07551	+	1.86284i
$276$		0			0
$277$	−2.32776	+	4.03180i	−0.139862	+	0.242248i	−0.927444	−	0.373962i	$-0.877999\pi$
$277$	−2.32776	+	4.03180i	−0.139862	+	0.242248i	0.787582	+	0.616209i	$0.211332\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.06669	+	15.7040i	0.540873	+	0.936820i	0.998854	+	0.0478580i	$0.0152395\pi$
$281$	9.06669	+	15.7040i	0.540873	+	0.936820i	−0.457981	+	0.888962i	$0.651427\pi$
$282$		0			0
$283$	−16.6194			−0.987920			−0.493960	−	0.869485i	$-0.664451\pi$
$283$	−16.6194			−0.987920			−0.493960	+	0.869485i	$0.664451\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.10796	+	3.51059i	0.537626	+	0.207223i
$288$		0			0
$289$	8.16055	−	14.1345i	0.480032	−	0.831441i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.94284	+	3.36510i	−0.113502	+	0.196591i	−0.917180	−	0.398473i	$-0.869540\pi$
$293$	−1.94284	+	3.36510i	−0.113502	+	0.196591i	0.803678	+	0.595064i	$0.202873\pi$
$294$		0			0
$295$	2.82928	+	4.90046i	0.164727	+	0.285316i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.8520			−1.20590
$300$		0			0
$301$	−17.9641	+	14.5062i	−1.03543	+	0.836123i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.61647	+	2.79981i	0.0925588	+	0.160317i
$306$		0			0
$307$	−3.48452			−0.198872			−0.0994361	−	0.995044i	$-0.531704\pi$
$307$	−3.48452			−0.198872			−0.0994361	+	0.995044i	$0.531704\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.9855			0.736338			0.368169	−	0.929759i	$-0.379985\pi$
$311$	12.9855			0.736338			0.368169	+	0.929759i	$0.379985\pi$
$312$		0			0
$313$	15.0439			0.850329			0.425164	−	0.905116i	$-0.360216\pi$
$313$	15.0439			0.850329			0.425164	+	0.905116i	$0.360216\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.45839			0.475070			0.237535	−	0.971379i	$-0.423660\pi$
$317$	8.45839			0.475070			0.237535	+	0.971379i	$0.423660\pi$
$318$		0			0
$319$	−4.32069			−0.241912
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.384968			−0.0214202
$324$		0			0
$325$	12.5326	+	21.7072i	0.695186	+	1.20410i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.30774	−	27.4421i	−0.237494	−	1.51293i
$330$		0			0
$331$	10.0245			0.550996			0.275498	−	0.961302i	$-0.411157\pi$
$331$	10.0245			0.550996			0.275498	+	0.961302i	$0.411157\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.918597	+	1.59106i	0.0501883	+	0.0869287i
$336$		0			0
$337$	−9.33242	+	16.1642i	−0.508369	+	0.880522i	0.491584	+	0.870830i	$0.336418\pi$
$337$	−9.33242	+	16.1642i	−0.508369	+	0.880522i	−0.999953	+	0.00969119i	$0.996915\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−26.7318	+	46.3009i	−1.44761	+	2.50733i
$342$		0			0
$343$	8.33992	+	16.5362i	0.450313	+	0.892871i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.8048			−0.848446			−0.424223	−	0.905558i	$-0.639453\pi$
$347$	−15.8048			−0.848446			−0.424223	+	0.905558i	$0.639453\pi$
$348$		0			0
$349$	4.51578	+	7.82156i	0.241724	+	0.418678i	0.961205	−	0.275833i	$-0.0889538\pi$
$349$	4.51578	+	7.82156i	0.241724	+	0.418678i	−0.719481	+	0.694512i	$0.755620\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.23939	−	12.5390i	0.385314	−	0.667383i	−0.606499	−	0.795084i	$-0.707427\pi$
$353$	7.23939	−	12.5390i	0.385314	−	0.667383i	0.991813	+	0.127701i	$0.0407599\pi$
$354$		0			0
$355$	6.59155	+	11.4169i	0.349843	+	0.605947i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.85517	+	13.6056i	−0.414580	+	0.718074i	−0.995384	−	0.0959695i	$-0.969405\pi$
$359$	−7.85517	+	13.6056i	−0.414580	+	0.718074i	0.580804	+	0.814043i	$0.302738\pi$
$360$		0			0
$361$	9.39085	+	16.2654i	0.494255	+	0.856075i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.82312	+	15.2821i	−0.461823	+	0.799902i
$366$		0			0
$367$	9.42947	−	16.3323i	0.492214	−	0.852540i	−0.507746	−	0.861507i	$-0.669521\pi$
$367$	9.42947	−	16.3323i	0.492214	−	0.852540i	0.999960	+	0.00896710i	$0.00285436\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	19.4241	−	15.6852i	1.00845	−	0.814334i
$372$		0			0
$373$	16.8568	+	29.1969i	0.872814	+	1.51176i	0.859073	+	0.511853i	$0.171041\pi$
$373$	16.8568	+	29.1969i	0.872814	+	1.51176i	0.0137417	+	0.999906i	$0.495626\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.03609			−0.156367
$378$		0			0
$379$	−33.7263			−1.73241			−0.866203	−	0.499693i	$-0.833446\pi$
$379$	−33.7263			−1.73241			−0.866203	+	0.499693i	$0.833446\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.16201	−	15.8691i	−0.468157	−	0.810871i	0.531181	−	0.847258i	$-0.321748\pi$
$383$	−9.16201	−	15.8691i	−0.468157	−	0.810871i	−0.999338	+	0.0363870i	$0.988415\pi$
$384$		0			0
$385$	−7.54427	−	48.0600i	−0.384491	−	2.44936i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.13744	−	3.70216i	0.108373	−	0.187707i	−0.806739	−	0.590909i	$-0.798769\pi$
$389$	2.13744	−	3.70216i	0.108373	−	0.187707i	0.915111	+	0.403202i	$0.132103\pi$
$390$		0			0
$391$	−2.26545	+	3.92388i	−0.114569	+	0.198439i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.3381	+	23.1023i	0.671112	+	1.16240i
$396$		0			0
$397$	17.9312	−	31.0577i	0.899939	−	1.55874i	0.0723687	−	0.997378i	$-0.476944\pi$
$397$	17.9312	−	31.0577i	0.899939	−	1.55874i	0.827570	−	0.561362i	$-0.189723\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.7007	−	20.2663i	−0.584307	−	1.01205i	−0.994961	−	0.100259i	$-0.968033\pi$
$401$	−11.7007	−	20.2663i	−0.584307	−	1.01205i	0.410654	−	0.911791i	$-0.365300\pi$
$402$		0			0
$403$	−18.7841	+	32.5350i	−0.935702	+	1.62068i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−23.4316	−	40.5848i	−1.16146	−	2.01171i
$408$		0			0
$409$	34.8032			1.72091			0.860453	−	0.509530i	$-0.170181\pi$
$409$	34.8032			1.72091			0.860453	+	0.509530i	$0.170181\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.681372	−	4.34062i	−0.0335281	−	0.213588i
$414$		0			0
$415$	−12.9351	+	22.4043i	−0.634961	+	1.09978i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.90894	−	5.03843i	0.142111	−	0.246143i	−0.786180	−	0.617997i	$-0.787944\pi$
$419$	2.90894	−	5.03843i	0.142111	−	0.246143i	0.928291	+	0.371854i	$0.121278\pi$
$420$		0			0
$421$	−17.7765	−	30.7898i	−0.866375	−	1.50061i	−0.865676	−	0.500605i	$-0.833111\pi$
$421$	−17.7765	−	30.7898i	−0.866375	−	1.50061i	−0.000699237	−	1.00000i	$-0.500223\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.44642			0.264190
$426$		0			0
$427$	−0.389292	−	2.47995i	−0.0188392	−	0.120013i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.48374	−	4.30196i	−0.119637	−	0.207218i	0.799987	−	0.600018i	$-0.204840\pi$
$431$	−2.48374	−	4.30196i	−0.119637	−	0.207218i	−0.919624	+	0.392800i	$0.871507\pi$
$432$		0			0
$433$	22.9062			1.10080			0.550401	−	0.834900i	$-0.314475\pi$
$433$	22.9062			1.10080			0.550401	+	0.834900i	$0.314475\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.56925			−0.122904
$438$		0			0
$439$	−8.05894			−0.384632			−0.192316	−	0.981333i	$-0.561600\pi$
$439$	−8.05894			−0.384632			−0.192316	+	0.981333i	$0.561600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.77766			−0.179482			−0.0897410	−	0.995965i	$-0.528604\pi$
$443$	−3.77766			−0.179482			−0.0897410	+	0.995965i	$0.528604\pi$
$444$		0			0
$445$	25.4528			1.20658
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.5069			−1.58129			−0.790644	−	0.612276i	$-0.790254\pi$
$449$	−33.5069			−1.58129			−0.790644	+	0.612276i	$0.790254\pi$
$450$		0			0
$451$	9.95457	+	17.2418i	0.468742	+	0.811885i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.30125	−	33.7711i	−0.248527	−	1.58321i
$456$		0			0
$457$	0.739506			0.0345926			0.0172963	−	0.999850i	$-0.494494\pi$
$457$	0.739506			0.0345926			0.0172963	+	0.999850i	$0.494494\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.30465	+	5.72383i	0.153913	+	0.266585i	0.932663	−	0.360750i	$-0.117479\pi$
$461$	3.30465	+	5.72383i	0.153913	+	0.266585i	−0.778750	+	0.627335i	$0.784146\pi$
$462$		0			0
$463$	5.96606	−	10.3335i	0.277266	−	0.480239i	−0.693438	−	0.720516i	$-0.743905\pi$
$463$	5.96606	−	10.3335i	0.277266	−	0.480239i	0.970704	+	0.240277i	$0.0772383\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.11184	+	8.85396i	−0.236548	+	0.409713i	−0.959721	−	0.280954i	$-0.909349\pi$
$467$	−5.11184	+	8.85396i	−0.236548	+	0.409713i	0.723174	+	0.690666i	$0.242683\pi$
$468$		0			0
$469$	−0.221225	−	1.40929i	−0.0102152	−	0.0650749i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−47.0948			−2.16542
$474$		0			0
$475$	1.54419	+	2.67462i	0.0708524	+	0.122720i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.01896	−	1.76488i	0.0465573	−	0.0806395i	−0.841808	−	0.539778i	$-0.818508\pi$
$479$	1.01896	−	1.76488i	0.0465573	−	0.0806395i	0.888365	+	0.459138i	$0.151842\pi$
$480$		0			0
$481$	−16.4651	−	28.5184i	−0.750743	−	1.30033i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.9888	−	19.0331i	0.498974	−	0.864248i
$486$		0			0
$487$	−17.5958	−	30.4767i	−0.797340	−	1.38103i	−0.921343	−	0.388751i	$-0.872907\pi$
$487$	−17.5958	−	30.4767i	−0.797340	−	1.38103i	0.124003	−	0.992282i	$-0.460427\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.5708	+	30.4335i	−0.792958	+	1.37344i	0.131170	+	0.991360i	$0.458127\pi$
$491$	−17.5708	+	30.4335i	−0.792958	+	1.37344i	−0.924128	+	0.382083i	$0.875207\pi$
$492$		0			0
$493$	−0.329855	+	0.571326i	−0.0148559	+	0.0257312i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.58744	−	10.1126i	−0.0712062	−	0.453612i
$498$		0			0
$499$	2.32633	+	4.02932i	0.104141	+	0.180377i	0.913387	−	0.407093i	$-0.133457\pi$
$499$	2.32633	+	4.02932i	0.104141	+	0.180377i	−0.809246	+	0.587470i	$0.800124\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0660			0.537997			0.268999	−	0.963141i	$-0.413307\pi$
$503$	12.0660			0.537997			0.268999	+	0.963141i	$0.413307\pi$
$504$		0			0
$505$	−55.1974			−2.45625
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.1739	+	19.3537i	0.495273	+	0.857838i	0.999985	−	0.00544958i	$-0.00173466\pi$
$509$	11.1739	+	19.3537i	0.495273	+	0.857838i	−0.504712	+	0.863288i	$0.668401\pi$
$510$		0			0
$511$	10.6603	−	8.60829i	0.471583	−	0.380808i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−26.7454	+	46.3244i	−1.17854	+	2.04130i
$516$		0			0
$517$	28.3287	−	49.0667i	1.24589	−	2.15795i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.854260	−	1.47962i	−0.0374258	−	0.0648234i	0.846706	−	0.532061i	$-0.178582\pi$
$521$	−0.854260	−	1.47962i	−0.0374258	−	0.0648234i	−0.884132	+	0.467238i	$0.845249\pi$
$522$		0			0
$523$	10.6036	−	18.3659i	0.463662	−	0.803087i	−0.535478	−	0.844549i	$-0.679868\pi$
$523$	10.6036	−	18.3659i	0.463662	−	0.803087i	0.999140	+	0.0414627i	$0.0132018\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.08158	+	7.06951i	0.177796	+	0.307952i
$528$		0			0
$529$	−3.61945	+	6.26907i	−0.157367	+	0.272568i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.99494	+	12.1156i	0.302984	+	0.524784i
$534$		0			0
$535$	−19.4236			−0.839754
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.95532	+	36.9275i	−0.342660	+	1.59058i
$540$		0			0
$541$	4.79443	−	8.30419i	0.206129	−	0.357025i	−0.744363	−	0.667775i	$-0.767247\pi$
$541$	4.79443	−	8.30419i	0.206129	−	0.357025i	0.950492	+	0.310750i	$0.100580\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.46882	−	12.9364i	0.319929	−	0.554133i
$546$		0			0
$547$	5.65927	+	9.80214i	0.241973	+	0.419109i	0.961276	−	0.275587i	$-0.0888722\pi$
$547$	5.65927	+	9.80214i	0.241973	+	0.419109i	−0.719303	+	0.694696i	$0.755539\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.374088			−0.0159367
$552$		0			0
$553$	−3.21220	−	20.4630i	−0.136596	−	0.870174i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.68102	−	2.91162i	−0.0712272	−	0.123369i	0.828212	−	0.560415i	$-0.189358\pi$
$557$	−1.68102	−	2.91162i	−0.0712272	−	0.123369i	−0.899439	+	0.437045i	$0.856025\pi$
$558$		0			0
$559$	−33.0929			−1.39968
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.0914			−0.804606			−0.402303	−	0.915506i	$-0.631790\pi$
$563$	−19.0914			−0.804606			−0.402303	+	0.915506i	$0.631790\pi$
$564$		0			0
$565$	33.8424			1.42376
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.62726			−0.110140			−0.0550702	−	0.998482i	$-0.517538\pi$
$569$	−2.62726			−0.110140			−0.0550702	+	0.998482i	$0.517538\pi$
$570$		0			0
$571$	9.98226			0.417745			0.208872	−	0.977943i	$-0.433021\pi$
$571$	9.98226			0.417745			0.208872	+	0.977943i	$0.433021\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.3489			1.51586
$576$		0			0
$577$	6.05761	+	10.4921i	0.252182	+	0.436791i	0.964126	−	0.265444i	$-0.0855187\pi$
$577$	6.05761	+	10.4921i	0.252182	+	0.436791i	−0.711945	+	0.702236i	$0.752185\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.6285	−	12.6202i	0.648379	−	0.523573i
$582$		0			0
$583$	50.9224			2.10899
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.1857	+	26.3025i	0.626782	+	1.08562i	0.988193	+	0.153212i	$0.0489618\pi$
$587$	15.1857	+	26.3025i	0.626782	+	1.08562i	−0.361411	+	0.932407i	$0.617705\pi$
$588$		0			0
$589$	−2.31446	+	4.00875i	−0.0953655	+	0.165178i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.5788	−	35.6434i	0.845068	−	1.46370i	−0.0404940	−	0.999180i	$-0.512893\pi$
$593$	20.5788	−	35.6434i	0.845068	−	1.46370i	0.885562	−	0.464521i	$-0.153774\pi$
$594$		0			0
$595$	−6.93093	−	2.67147i	−0.284141	−	0.109520i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.11041			0.331382			0.165691	−	0.986178i	$-0.447014\pi$
$599$	8.11041			0.331382			0.165691	+	0.986178i	$0.447014\pi$
$600$		0			0
$601$	15.8320	+	27.4218i	0.645801	+	1.11856i	0.984116	+	0.177527i	$0.0568098\pi$
$601$	15.8320	+	27.4218i	0.645801	+	1.11856i	−0.338315	+	0.941033i	$0.609857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	30.8722	−	53.4723i	1.25513	−	2.17396i
$606$		0			0
$607$	−11.5131	−	19.9412i	−0.467300	−	0.809388i	0.532002	−	0.846743i	$-0.321440\pi$
$607$	−11.5131	−	19.9412i	−0.467300	−	0.809388i	−0.999302	+	0.0373552i	$0.988107\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	19.9062	−	34.4785i	0.805317	−	1.39485i
$612$		0			0
$613$	11.4750	+	19.8752i	0.463470	+	0.802753i	0.999131	−	0.0416796i	$-0.0132709\pi$
$613$	11.4750	+	19.8752i	0.463470	+	0.802753i	−0.535661	+	0.844433i	$0.679938\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.1183	+	19.2574i	−0.447605	+	0.775274i	−0.998230	−	0.0594788i	$-0.981056\pi$
$617$	−11.1183	+	19.2574i	−0.447605	+	0.775274i	0.550625	+	0.834753i	$0.314389\pi$
$618$		0			0
$619$	−2.75302	+	4.76836i	−0.110653	+	0.191657i	−0.916034	−	0.401101i	$-0.868628\pi$
$619$	−2.75302	+	4.76836i	−0.110653	+	0.191657i	0.805381	+	0.592758i	$0.201961\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.4412	−	7.10800i	−0.738831	−	0.284776i
$624$		0			0
$625$	7.17850	+	12.4335i	0.287140	+	0.497341i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.15538			−0.285303
$630$		0			0
$631$	32.9276			1.31083			0.655413	−	0.755271i	$-0.272495\pi$
$631$	32.9276			1.31083			0.655413	+	0.755271i	$0.272495\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	27.4501	+	47.5449i	1.08932	+	1.88676i
$636$		0			0
$637$	−5.59009	+	25.9484i	−0.221488	+	1.02811i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.945880	+	1.63831i	−0.0373600	+	0.0647095i	−0.884101	−	0.467296i	$-0.845228\pi$
$641$	−0.945880	+	1.63831i	−0.0373600	+	0.0647095i	0.846741	+	0.532006i	$0.178562\pi$
$642$		0			0
$643$	−22.8742	+	39.6193i	−0.902070	+	1.56243i	−0.0772675	+	0.997010i	$0.524620\pi$
$643$	−22.8742	+	39.6193i	−0.902070	+	1.56243i	−0.824803	+	0.565421i	$0.808714\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.98067	+	15.5550i	0.353066	+	0.611529i	0.986785	−	0.162035i	$-0.0518056\pi$
$647$	8.98067	+	15.5550i	0.353066	+	0.611529i	−0.633719	+	0.773564i	$0.718472\pi$
$648$		0			0
$649$	4.48085	−	7.76106i	0.175889	−	0.304648i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.0741	−	19.1809i	−0.433363	−	0.750607i	0.563797	−	0.825913i	$-0.309340\pi$
$653$	−11.0741	−	19.1809i	−0.433363	−	0.750607i	−0.997160	+	0.0753063i	$0.976007\pi$
$654$		0			0
$655$	−23.7506	+	41.1373i	−0.928015	+	1.60737i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.39543	−	9.34515i	−0.210176	−	0.364035i	0.741594	−	0.670850i	$-0.234070\pi$
$659$	−5.39543	−	9.34515i	−0.210176	−	0.364035i	−0.951769	+	0.306814i	$0.900737\pi$
$660$		0			0
$661$	−5.13907			−0.199887			−0.0999434	−	0.994993i	$-0.531866\pi$
$661$	−5.13907			−0.199887			−0.0999434	+	0.994993i	$0.531866\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.653187	−	4.16106i	−0.0253295	−	0.161359i
$666$		0			0
$667$	−2.20142	+	3.81298i	−0.0852395	+	0.147639i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.56007	−	4.43417i	0.0988304	−	0.171179i
$672$		0			0
$673$	10.9290	+	18.9295i	0.421281	+	0.729680i	0.996065	−	0.0886254i	$-0.0282474\pi$
$673$	10.9290	+	18.9295i	0.421281	+	0.729680i	−0.574784	+	0.818305i	$0.694914\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.7296			0.450807			0.225403	−	0.974266i	$-0.427630\pi$
$677$	11.7296			0.450807			0.225403	+	0.974266i	$0.427630\pi$
$678$		0			0
$679$	−13.2768	+	10.7212i	−0.509518	+	0.411442i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.260358	−	0.450954i	−0.00996234	−	0.0172553i	0.861001	−	0.508603i	$-0.169838\pi$
$683$	−0.260358	−	0.450954i	−0.00996234	−	0.0172553i	−0.870964	+	0.491348i	$0.836504\pi$
$684$		0			0
$685$	−37.9987			−1.45186
$686$		0			0
$687$		0			0
$688$		0			0
$689$	35.7825			1.36320
$690$		0			0
$691$	−46.1912			−1.75720			−0.878599	−	0.477561i	$-0.841521\pi$
$691$	−46.1912			−1.75720			−0.878599	+	0.477561i	$0.841521\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.6529			0.821342
$696$		0			0
$697$	3.03985			0.115143
$698$		0			0
$699$		0			0
$700$		0			0
$701$	32.7166			1.23569			0.617844	−	0.786301i	$-0.288006\pi$
$701$	32.7166			1.23569			0.617844	+	0.786301i	$0.288006\pi$
$702$		0			0
$703$	−2.02872	−	3.51385i	−0.0765148	−	0.132527i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	39.9919	+	15.4145i	1.50405	+	0.579723i
$708$		0			0
$709$	−33.4551			−1.25643			−0.628216	−	0.778039i	$-0.716215\pi$
$709$	−33.4551			−1.25643			−0.628216	+	0.778039i	$0.716215\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	27.2401	+	47.1813i	1.02015	+	1.76695i
$714$		0			0
$715$	34.8622	−	60.3831i	1.30377	−	2.25820i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.42685	−	16.3278i	0.351562	−	0.608924i	−0.634961	−	0.772544i	$-0.718984\pi$
$719$	9.42685	−	16.3278i	0.351562	−	0.608924i	0.986523	+	0.163621i	$0.0523173\pi$
$720$		0			0
$721$	32.3143	−	26.0942i	1.20345	−	0.971798i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.29248			0.196558
$726$		0			0
$727$	19.3107	+	33.4471i	0.716194	+	1.24048i	0.962497	+	0.271291i	$0.0874507\pi$
$727$	19.3107	+	33.4471i	0.716194	+	1.24048i	−0.246303	+	0.969193i	$0.579216\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.59537	+	6.22736i	−0.132979	+	0.230327i
$732$		0			0
$733$	9.35591	+	16.2049i	0.345569	+	0.598542i	0.985457	−	0.169926i	$-0.0543527\pi$
$733$	9.35591	+	16.2049i	0.345569	+	0.598542i	−0.639888	+	0.768468i	$0.721019\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.45482	−	2.51982i	0.0535890	−	0.0928189i
$738$		0			0
$739$	−7.15949	−	12.4006i	−0.263366	−	0.456163i	0.703768	−	0.710430i	$-0.251499\pi$
$739$	−7.15949	−	12.4006i	−0.263366	−	0.456163i	−0.967134	+	0.254266i	$0.918166\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.2068	−	24.6069i	0.521197	−	0.902740i	−0.478499	−	0.878088i	$-0.658819\pi$
$743$	14.2068	−	24.6069i	0.521197	−	0.902740i	0.999696	−	0.0246519i	$-0.00784775\pi$
$744$		0			0
$745$	19.6442	−	34.0247i	0.719706	−	1.24657i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.0729	+	5.42426i	0.514211	+	0.198198i
$750$		0			0
$751$	−15.7209	−	27.2294i	−0.573663	−	0.993614i	−0.996185	−	0.0872612i	$-0.972189\pi$
$751$	−15.7209	−	27.2294i	−0.573663	−	0.993614i	0.422522	−	0.906353i	$-0.361145\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.36687			0.0861392
$756$		0			0
$757$	0.405916			0.0147533			0.00737663	−	0.999973i	$-0.497652\pi$
$757$	0.405916			0.0147533			0.00737663	+	0.999973i	$0.497652\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.65688	+	4.60184i	0.0963117	+	0.166817i	0.910155	−	0.414267i	$-0.135962\pi$
$761$	2.65688	+	4.60184i	0.0963117	+	0.166817i	−0.813844	+	0.581084i	$0.802629\pi$
$762$		0			0
$763$	−9.02397	+	7.28696i	−0.326690	+	0.263806i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.14863	−	5.45359i	0.113691	−	0.196918i
$768$		0			0
$769$	11.9430	−	20.6858i	0.430674	−	0.745949i	−0.566258	−	0.824228i	$-0.691609\pi$
$769$	11.9430	−	20.6858i	0.430674	−	0.745949i	0.996931	+	0.0782793i	$0.0249426\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.8525	−	22.2613i	−0.462274	−	0.800682i	0.536800	−	0.843710i	$-0.319633\pi$
$773$	−12.8525	−	22.2613i	−0.462274	−	0.800682i	−0.999074	+	0.0430274i	$0.986300\pi$
$774$		0			0
$775$	32.7442	−	56.7147i	1.17621	−	2.03725i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.861872	+	1.49281i	0.0308798	+	0.0534853i
$780$		0			0
$781$	10.4393	−	18.0814i	0.373548	−	0.647004i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.89727	−	11.9464i	−0.246174	−	0.426386i
$786$		0			0
$787$	−16.1109			−0.574292			−0.287146	−	0.957887i	$-0.592707\pi$
$787$	−16.1109			−0.574292			−0.287146	+	0.957887i	$0.592707\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−24.5196	−	9.45089i	−0.871818	−	0.336035i
$792$		0			0
$793$	1.79893	−	3.11583i	0.0638818	−	0.110646i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.556852	+	0.964495i	−0.0197247	+	0.0341642i	−0.875719	−	0.482821i	$-0.839612\pi$
$797$	−0.556852	+	0.964495i	−0.0197247	+	0.0341642i	0.855995	+	0.516985i	$0.172946\pi$
$798$		0			0
$799$	−4.32540	−	7.49181i	−0.153022	−	0.265041i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	27.9471			0.986231
$804$		0			0
$805$	−46.2565	−	17.8292i	−1.63033	−	0.628395i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.1461	−	17.5736i	−0.356718	−	0.617853i	0.630693	−	0.776033i	$-0.282771\pi$
$809$	−10.1461	−	17.5736i	−0.356718	−	0.617853i	−0.987410	+	0.158179i	$0.949438\pi$
$810$		0			0
$811$	9.72686			0.341556			0.170778	−	0.985310i	$-0.445372\pi$
$811$	9.72686			0.341556			0.170778	+	0.985310i	$0.445372\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−34.4803			−1.20779
$816$		0			0
$817$	−4.07749			−0.142653
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.07104			0.142080			0.0710401	−	0.997473i	$-0.477368\pi$
$821$	4.07104			0.142080			0.0710401	+	0.997473i	$0.477368\pi$
$822$		0			0
$823$	−2.61200			−0.0910485			−0.0455242	−	0.998963i	$-0.514496\pi$
$823$	−2.61200			−0.0910485			−0.0455242	+	0.998963i	$0.514496\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0054			−1.04339			−0.521695	−	0.853132i	$-0.674700\pi$
$827$	−30.0054			−1.04339			−0.521695	+	0.853132i	$0.674700\pi$
$828$		0			0
$829$	−14.0676	−	24.3658i	−0.488588	−	0.846260i	0.511325	−	0.859387i	$-0.329155\pi$
$829$	−14.0676	−	24.3658i	−0.488588	−	0.846260i	−0.999914	+	0.0131272i	$0.995821\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.27559	+	3.87109i	0.148140	+	0.134125i
$834$		0			0
$835$	−59.7226			−2.06679
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.61277	−	6.25750i	−0.124727	−	0.216033i	0.796899	−	0.604112i	$-0.206472\pi$
$839$	−3.61277	−	6.25750i	−0.124727	−	0.216033i	−0.921626	+	0.388079i	$0.873139\pi$
$840$		0			0
$841$	14.1795	−	24.5596i	0.488947	−	0.846881i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.34933	−	4.06915i	0.0808193	−	0.139983i
$846$		0			0
$847$	−37.3005	+	30.1205i	−1.28166	+	1.03495i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−47.7544			−1.63700
$852$		0			0
$853$	16.0767	+	27.8457i	0.550457	+	0.953419i	0.998242	+	0.0592779i	$0.0188798\pi$
$853$	16.0767	+	27.8457i	0.550457	+	0.953419i	−0.447785	+	0.894141i	$0.647787\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.48585	+	6.03767i	−0.119074	+	0.206243i	−0.919401	−	0.393321i	$-0.871326\pi$
$857$	−3.48585	+	6.03767i	−0.119074	+	0.206243i	0.800327	+	0.599564i	$0.204659\pi$
$858$		0			0
$859$	−17.3523	−	30.0551i	−0.592054	−	1.02547i	−0.993955	−	0.109785i	$-0.964984\pi$
$859$	−17.3523	−	30.0551i	−0.592054	−	1.02547i	0.401901	−	0.915683i	$-0.368350\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.9863	−	45.0095i	0.884583	−	1.53214i	0.0383914	−	0.999263i	$-0.487777\pi$
$863$	25.9863	−	45.0095i	0.884583	−	1.53214i	0.846191	−	0.532879i	$-0.178890\pi$
$864$		0			0
$865$	13.3486	+	23.1204i	0.453866	+	0.786119i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	21.1241	−	36.5880i	0.716586	−	1.24116i
$870$		0			0
$871$	1.02228	−	1.77064i	0.0346387	−	0.0599960i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.25097	+	14.3396i	0.0760968	+	0.484767i
$876$		0			0
$877$	−20.3822	−	35.3029i	−0.688257	−	1.19210i	−0.972401	−	0.233314i	$-0.925043\pi$
$877$	−20.3822	−	35.3029i	−0.688257	−	1.19210i	0.284145	−	0.958781i	$-0.408290\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.07339			0.204618			0.102309	−	0.994753i	$-0.467377\pi$
$881$	6.07339			0.204618			0.102309	+	0.994753i	$0.467377\pi$
$882$		0			0
$883$	10.0958			0.339751			0.169875	−	0.985466i	$-0.445664\pi$
$883$	10.0958			0.339751			0.169875	+	0.985466i	$0.445664\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.55215	−	11.3487i	−0.220000	−	0.381051i	0.734808	−	0.678275i	$-0.237272\pi$
$887$	−6.55215	−	11.3487i	−0.220000	−	0.381051i	−0.954808	+	0.297225i	$0.903939\pi$
$888$		0			0
$889$	−6.61077	−	42.1132i	−0.221718	−	1.41243i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.45271	−	4.24822i	0.0820768	−	0.142161i
$894$		0			0
$895$	15.7393	−	27.2612i	0.526106	−	0.911242i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.96622	+	6.86969i	0.132281	+	0.229117i
$900$		0			0
$901$	3.88758	−	6.73348i	0.129514	−	0.224325i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.1164	+	27.9145i	0.535728	+	0.927908i
$906$		0			0
$907$	6.41698	−	11.1145i	0.213072	−	0.369052i	−0.739602	−	0.673044i	$-0.764986\pi$
$907$	6.41698	−	11.1145i	0.213072	−	0.369052i	0.952674	+	0.303992i	$0.0983197\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.5089	+	30.3262i	0.580094	+	1.00475i	0.995468	+	0.0951015i	$0.0303176\pi$
$911$	17.5089	+	30.3262i	0.580094	+	1.00475i	−0.415373	+	0.909651i	$0.636349\pi$
$912$		0			0
$913$	40.9718			1.35597
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.6960	−	23.1723i	0.947626	−	0.765218i
$918$		0			0
$919$	4.12422	−	7.14336i	0.136046	−	0.235638i	−0.789951	−	0.613170i	$-0.789894\pi$
$919$	4.12422	−	7.14336i	0.136046	−	0.235638i	0.925996	+	0.377532i	$0.123227\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.33557	−	12.7056i	0.241453	−	0.418209i
$924$		0			0
$925$	28.7018	+	49.7129i	0.943709	+	1.63455i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	56.8512			1.86523			0.932614	−	0.360876i	$-0.117522\pi$
$929$	56.8512			1.86523			0.932614	+	0.360876i	$0.117522\pi$
$930$		0			0
$931$	−0.688776	+	3.19720i	−0.0225737	+	0.104784i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.57518	−	13.1206i	−0.247735	−	0.429089i
$936$		0			0
$937$	−46.6213			−1.52305			−0.761526	−	0.648134i	$-0.775550\pi$
$937$	−46.6213			−1.52305			−0.761526	+	0.648134i	$0.775550\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−25.3402			−0.826067			−0.413033	−	0.910716i	$-0.635531\pi$
$941$	−25.3402			−0.826067			−0.413033	+	0.910716i	$0.635531\pi$
$942$		0			0
$943$	20.2877			0.660658
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.9572			−0.973478			−0.486739	−	0.873548i	$-0.661814\pi$
$947$	−29.9572			−0.973478			−0.486739	+	0.873548i	$0.661814\pi$
$948$		0			0
$949$	19.6380			0.637478
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−38.6721			−1.25271			−0.626356	−	0.779537i	$-0.715454\pi$
$953$	−38.6721			−1.25271			−0.626356	+	0.779537i	$0.715454\pi$
$954$		0			0
$955$	−0.0771711	−	0.133664i	−0.00249720	−	0.00432528i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.5310	+	10.6116i	0.889023	+	0.342666i
$960$		0			0
$961$	67.1549			2.16629
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.0630	−	55.5347i	−1.03214	−	1.78773i
$966$		0			0
$967$	16.2161	−	28.0870i	0.521473	−	0.903218i	−0.478215	−	0.878243i	$-0.658716\pi$
$967$	16.2161	−	28.0870i	0.521473	−	0.903218i	0.999688	−	0.0249755i	$-0.00795076\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.53128	+	14.7766i	−0.273782	+	0.474204i	−0.969827	−	0.243794i	$-0.921608\pi$
$971$	−8.53128	+	14.7766i	−0.273782	+	0.474204i	0.696045	+	0.717998i	$0.254941\pi$
$972$		0			0
$973$	−15.6881	−	6.04683i	−0.502936	−	0.193853i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.5513			0.465538			0.232769	−	0.972532i	$-0.425221\pi$
$977$	14.5513			0.465538			0.232769	+	0.972532i	$0.425221\pi$
$978$		0			0
$979$	−20.1553	−	34.9101i	−0.644168	−	1.11573i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.1926	+	28.0463i	−0.516463	+	0.894540i	0.483355	+	0.875425i	$0.339418\pi$
$983$	−16.1926	+	28.0463i	−0.516463	+	0.894540i	−0.999817	+	0.0191149i	$0.993915\pi$
$984$		0			0
$985$	38.1430	+	66.0657i	1.21534	+	2.10503i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.9952	+	41.5608i	−0.763002	+	1.32156i
$990$		0			0
$991$	12.7165	+	22.0256i	0.403952	+	0.699665i	0.994199	−	0.107558i	$-0.0343030\pi$
$991$	12.7165	+	22.0256i	0.403952	+	0.699665i	−0.590247	+	0.807223i	$0.700970\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	38.7447	−	67.1078i	1.22829	−	2.12746i
$996$		0			0
$997$	0.696665	−	1.20666i	0.0220636	−	0.0382153i	−0.854783	−	0.518986i	$-0.826310\pi$
$997$	0.696665	−	1.20666i	0.0220636	−	0.0382153i	0.876846	+	0.480771i	$0.159643\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.793.11		22
3.2	odd	2		504.2.q.c.121.6	yes	22
4.3	odd	2		3024.2.q.l.2305.11		22
7.4	even	3		1512.2.t.c.361.1		22
9.2	odd	6		504.2.t.c.457.3	yes	22
9.7	even	3		1512.2.t.c.289.1		22
12.11	even	2		1008.2.q.l.625.6		22
21.11	odd	6		504.2.t.c.193.3	yes	22
28.11	odd	6		3024.2.t.k.1873.1		22
36.7	odd	6		3024.2.t.k.289.1		22
36.11	even	6		1008.2.t.l.961.9		22
63.11	odd	6		504.2.q.c.25.6	✓	22
63.25	even	3	inner	1512.2.q.d.1369.11		22
84.11	even	6		1008.2.t.l.193.9		22
252.11	even	6		1008.2.q.l.529.6		22
252.151	odd	6		3024.2.q.l.2881.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.6	✓	22	63.11	odd	6
504.2.q.c.121.6	yes	22	3.2	odd	2
504.2.t.c.193.3	yes	22	21.11	odd	6
504.2.t.c.457.3	yes	22	9.2	odd	6
1008.2.q.l.529.6		22	252.11	even	6
1008.2.q.l.625.6		22	12.11	even	2
1008.2.t.l.193.9		22	84.11	even	6
1008.2.t.l.961.9		22	36.11	even	6
1512.2.q.d.793.11		22	1.1	even	1	trivial
1512.2.q.d.1369.11		22	63.25	even	3	inner
1512.2.t.c.289.1		22	9.7	even	3
1512.2.t.c.361.1		22	7.4	even	3
3024.2.q.l.2305.11		22	4.3	odd	2
3024.2.q.l.2881.11		22	252.151	odd	6
3024.2.t.k.289.1		22	36.7	odd	6
3024.2.t.k.1873.1		22	28.11	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70368 + 2.95086i) q^{5} +(-0.410295 - 2.61374i) q^{7} +O(q^{10})\)	\(q+(1.70368 + 2.95086i) q^{5} +(-0.410295 - 2.61374i) q^{7} +(2.69819 - 4.67340i) q^{11} +(1.89598 - 3.28393i) q^{13} +(-0.411976 - 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +(-2.74950 - 4.76227i) q^{23} +(-3.30506 + 5.72452i) q^{25} +(-0.400332 - 0.693396i) q^{29} -9.90732 q^{31} +(7.01378 - 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(-1.84467 + 3.19507i) q^{41} +(-4.36356 - 7.55790i) q^{43} +10.4991 q^{47} +(-6.66332 + 2.14481i) q^{49} +(4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +1.66069 q^{59} +0.948811 q^{61} +12.9206 q^{65} +0.539184 q^{67} +3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(-13.3221 - 5.13490i) q^{77} +7.82899 q^{79} +(3.79623 + 6.57527i) q^{83} +(1.40375 - 2.43137i) q^{85} +(3.73498 - 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +1.59199 q^{95} +(-3.22500 - 5.58587i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more