LMFDB - Embedded newform 1512.2.t.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (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			289.1
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +O(q^{10})$	$q-3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} -5.39638 q^{11} +(1.89598 + 3.28393i) q^{13} +(-0.411976 - 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +5.49899 q^{23} +6.61011 q^{25} +(-0.400332 + 0.693396i) q^{29} +(4.95366 - 8.57999i) q^{31} +(7.01378 - 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(-1.84467 - 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(-5.24957 - 9.09252i) q^{47} +(1.47420 - 6.84301i) q^{49} +(4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +(-0.830344 + 1.43820i) q^{59} +(-0.474405 - 0.821694i) q^{61} +(-6.46029 - 11.1896i) q^{65} +(-0.269592 + 0.466947i) q^{67} +3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(11.1080 - 8.96985i) q^{77} +(-3.91449 - 6.78010i) q^{79} +(3.79623 - 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(3.73498 - 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +(-0.795996 + 1.37871i) q^{95} +(-3.22500 + 5.58587i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−3.40736			−1.52382			−0.761909	−	0.647684i	$-0.775738\pi$
$5$	−3.40736			−1.52382			−0.761909	+	0.647684i	$0.775738\pi$
$6$		0			0
$7$	−2.05842	+	1.66220i	−0.778010	+	0.628252i
$7$	−2.05842	+	1.66220i	−0.778010	+	0.628252i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.39638			−1.62707			−0.813535	−	0.581516i	$-0.802460\pi$
$11$	−5.39638			−1.62707			−0.813535	+	0.581516i	$0.802460\pi$
$12$		0			0
$13$	1.89598	+	3.28393i	0.525850	+	0.910800i	0.999547	+	0.0301113i	$0.00958618\pi$
$13$	1.89598	+	3.28393i	0.525850	+	0.910800i	−0.473696	+	0.880688i	$0.657080\pi$
$14$		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
$23$	5.49899			1.14662			0.573309	−	0.819339i	$-0.305659\pi$
$23$	5.49899			1.14662			0.573309	+	0.819339i	$0.305659\pi$
$24$		0			0
$25$	6.61011			1.32202
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.400332	+	0.693396i	−0.0743399	+	0.128760i	−0.900799	−	0.434236i	$-0.857018\pi$
$29$	−0.400332	+	0.693396i	−0.0743399	+	0.128760i	0.826459	+	0.562997i	$0.190352\pi$
$30$		0			0
$31$	4.95366	−	8.57999i	0.889703	−	1.54101i	0.0494772	−	0.998775i	$-0.484244\pi$
$31$	4.95366	−	8.57999i	0.889703	−	1.54101i	0.840226	−	0.542236i	$-0.182422\pi$
$32$		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	0.685264	−	0.728295i	$-0.259687\pi$
$41$	−1.84467	−	3.19507i	−0.288090	−	0.498986i	−0.973354	+	0.229309i	$0.926354\pi$
$42$		0			0
$43$	−4.36356	+	7.55790i	−0.665436	+	1.15257i	0.313731	+	0.949512i	$0.398421\pi$
$43$	−4.36356	+	7.55790i	−0.665436	+	1.15257i	−0.979167	+	0.203057i	$0.934912\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.24957	−	9.09252i	−0.765728	−	1.32628i	−0.939861	−	0.341558i	$-0.889045\pi$
$47$	−5.24957	−	9.09252i	−0.765728	−	1.32628i	0.174133	−	0.984722i	$-0.444288\pi$
$48$		0			0
$49$	1.47420	−	6.84301i	0.210599	−	0.977572i
$50$		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
$59$	−0.830344	+	1.43820i	−0.108102	+	0.187238i	−0.915001	−	0.403451i	$-0.867811\pi$
$59$	−0.830344	+	1.43820i	−0.108102	+	0.187238i	0.806900	+	0.590689i	$0.201144\pi$
$60$		0			0
$61$	−0.474405	−	0.821694i	−0.0607414	−	0.105207i	0.834056	−	0.551680i	$-0.186013\pi$
$61$	−0.474405	−	0.821694i	−0.0607414	−	0.105207i	−0.894797	+	0.446473i	$0.852680\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.46029	−	11.1896i	−0.801301	−	1.38789i
$66$		0			0
$67$	−0.269592	+	0.466947i	−0.0329359	+	0.0570467i	−0.882024	−	0.471205i	$-0.843819\pi$
$67$	−0.269592	+	0.466947i	−0.0329359	+	0.0570467i	0.849088	+	0.528252i	$0.177152\pi$
$68$		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
$77$	11.1080	−	8.96985i	1.26588	−	1.02221i
$78$		0			0
$79$	−3.91449	−	6.78010i	−0.440415	−	0.762821i	0.557305	−	0.830308i	$-0.311835\pi$
$79$	−3.91449	−	6.78010i	−0.440415	−	0.762821i	−0.997720	+	0.0674866i	$0.978502\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.79623	−	6.57527i	0.416691	−	0.721729i	−0.578914	−	0.815389i	$-0.696523\pi$
$83$	3.79623	−	6.57527i	0.416691	−	0.721729i	0.995604	+	0.0936595i	$0.0298565\pi$
$84$		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
$95$	−0.795996	+	1.37871i	−0.0816675	+	0.141452i
$96$		0			0
$97$	−3.22500	+	5.58587i	−0.327450	+	0.567159i	−0.982005	−	0.188855i	$-0.939522\pi$
$97$	−3.22500	+	5.58587i	−0.327450	+	0.567159i	0.654555	+	0.756014i	$0.272856\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.1995			1.61191			0.805953	−	0.591979i	$-0.201653\pi$
$101$	16.1995			1.61191			0.805953	+	0.591979i	$0.201653\pi$
$102$		0			0
$103$	−15.6986			−1.54683			−0.773414	−	0.633901i	$-0.781453\pi$
$103$	−15.6986			−1.54683			−0.773414	+	0.633901i	$0.781453\pi$
$104$		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	0.999296	−	0.0375041i	$-0.0119407\pi$
$113$	4.96607	+	8.60149i	0.467169	+	0.809160i	−0.532128	+	0.846664i	$0.678607\pi$
$114$		0			0
$115$	−18.7370			−1.74724
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.03411	+	0.784029i	0.186466	+	0.0718718i
$120$		0			0
$121$	18.1209			1.64735
$122$		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
$131$	−13.9408			−1.21801			−0.609006	−	0.793166i	$-0.708431\pi$
$131$	−13.9408			−1.21801			−0.609006	+	0.793166i	$0.708431\pi$
$132$		0			0
$133$	0.191699	+	1.22120i	0.0166224	+	0.105891i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.1520			0.952776			0.476388	−	0.879235i	$-0.341946\pi$
$137$	11.1520			0.952776			0.476388	+	0.879235i	$0.341946\pi$
$138$		0			0
$139$	3.17737	+	5.50337i	0.269501	+	0.466790i	0.968733	−	0.248105i	$-0.0798078\pi$
$139$	3.17737	+	5.50337i	0.269501	+	0.466790i	−0.699232	+	0.714895i	$0.746474\pi$
$140$		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
$149$	11.5304			0.944609			0.472304	−	0.881435i	$-0.343422\pi$
$149$	11.5304			0.944609			0.472304	+	0.881435i	$0.343422\pi$
$150$		0			0
$151$	−0.694634			−0.0565285			−0.0282643	−	0.999600i	$-0.508998\pi$
$151$	−0.694634			−0.0565285			−0.0282643	+	0.999600i	$0.508998\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.8789	+	29.2351i	−1.35575	+	2.34822i
$156$		0			0
$157$	2.02423	−	3.50606i	0.161551	−	0.279814i	−0.773874	−	0.633339i	$-0.781684\pi$
$157$	2.02423	−	3.50606i	0.161551	−	0.279814i	0.935425	+	0.353525i	$0.115017\pi$
$158$		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	−0.975534	−	0.219847i	$-0.929444\pi$
$167$	−8.76377	−	15.1793i	−0.678161	−	1.17461i	0.297374	−	0.954761i	$-0.403889\pi$
$168$		0			0
$169$	−0.689486	+	1.19422i	−0.0530374	+	0.0918634i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.91758	−	6.78544i	−0.297848	−	0.515887i	0.677796	−	0.735250i	$-0.262935\pi$
$173$	−3.91758	−	6.78544i	−0.297848	−	0.515887i	−0.975643	+	0.219363i	$0.929602\pi$
$174$		0			0
$175$	−13.6064	+	10.9873i	−1.02855	+	0.830563i
$176$		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
$185$	−14.7951	+	25.6259i	−1.08776	+	1.88405i
$186$		0			0
$187$	2.22318	+	3.85066i	0.162575	+	0.281588i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.0226484	+	0.0392281i	0.00163878	+	0.00283845i	0.866844	−	0.498580i	$-0.166145\pi$
$191$	0.0226484	+	0.0392281i	0.00163878	+	0.00283845i	−0.865205	+	0.501419i	$0.832812\pi$
$192$		0			0
$193$	9.40991	−	16.2984i	0.677340	−	1.17319i	−0.298438	−	0.954429i	$-0.596466\pi$
$193$	9.40991	−	16.2984i	0.677340	−	1.17319i	0.975779	−	0.218759i	$-0.0702009\pi$
$194$		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
$203$	−0.328509	−	2.09273i	−0.0230568	−	0.146881i
$204$		0			0
$205$	6.28547	+	10.8868i	0.438997	+	0.760364i
$206$		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	0.746029	−	0.665914i	$-0.231958\pi$
$211$	−2.95868	−	5.12458i	−0.203684	−	0.352791i	−0.949713	+	0.313123i	$0.898625\pi$
$212$		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
$221$	1.56220	−	2.70581i	0.105085	−	0.182012i
$222$		0			0
$223$	−1.20124	+	2.08062i	−0.0804412	+	0.139328i	−0.903440	−	0.428716i	$-0.858966\pi$
$223$	−1.20124	+	2.08062i	−0.0804412	+	0.139328i	0.822998	+	0.568044i	$0.192300\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.97702			0.463081			0.231540	−	0.972825i	$-0.425623\pi$
$227$	6.97702			0.463081			0.231540	+	0.972825i	$0.425623\pi$
$228$		0			0
$229$	−19.2156			−1.26981			−0.634903	−	0.772592i	$-0.718960\pi$
$229$	−19.2156			−1.26981			−0.634903	+	0.772592i	$0.718960\pi$
$230$		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	0.996927	−	0.0783322i	$-0.0249595\pi$
$239$	6.65732	+	11.5308i	0.430626	+	0.745866i	−0.566301	+	0.824198i	$0.691626\pi$
$240$		0			0
$241$	1.85648			0.119586			0.0597931	−	0.998211i	$-0.480956\pi$
$241$	1.85648			0.119586			0.0597931	+	0.998211i	$0.480956\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.02312	+	23.3166i	−0.320915	+	1.48964i
$246$		0			0
$247$	1.77169			0.112730
$248$		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
$257$	−2.93188			−0.182886			−0.0914429	−	0.995810i	$-0.529148\pi$
$257$	−2.93188			−0.182886			−0.0914429	+	0.995810i	$0.529148\pi$
$258$		0			0
$259$	3.56309	+	22.6983i	0.221399	+	1.41040i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	28.2840			1.74406			0.872032	−	0.489449i	$-0.162802\pi$
$263$	28.2840			1.74406			0.872032	+	0.489449i	$0.162802\pi$
$264$		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
$275$	−35.6707			−2.15102
$276$		0			0
$277$	4.65553			0.279723			0.139862	−	0.990171i	$-0.455334\pi$
$277$	4.65553			0.279723			0.139862	+	0.990171i	$0.455334\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.06669	−	15.7040i	0.540873	−	0.936820i	−0.457981	−	0.888962i	$-0.651427\pi$
$281$	9.06669	−	15.7040i	0.540873	−	0.936820i	0.998854	−	0.0478580i	$-0.0152395\pi$
$282$		0			0
$283$	8.30969	−	14.3928i	0.493960	−	0.855564i	−0.506016	−	0.862524i	$-0.668882\pi$
$283$	8.30969	−	14.3928i	0.493960	−	0.855564i	0.999976	+	0.00696045i	$0.00221560\pi$
$284$		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	0.803678	−	0.595064i	$-0.202873\pi$
$293$	−1.94284	−	3.36510i	−0.113502	−	0.196591i	−0.917180	+	0.398473i	$0.869540\pi$
$294$		0			0
$295$	2.82928	−	4.90046i	0.164727	−	0.285316i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.4260	+	18.0583i	0.602950	+	1.04434i
$300$		0			0
$301$	−3.58069	−	22.8104i	−0.206388	−	1.31477i
$302$		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
$311$	−6.49273	+	11.2457i	−0.368169	+	0.637687i	−0.989279	−	0.146036i	$-0.953349\pi$
$311$	−6.49273	+	11.2457i	−0.368169	+	0.637687i	0.621110	+	0.783723i	$0.286682\pi$
$312$		0			0
$313$	−7.52193	−	13.0284i	−0.425164	−	0.736406i	0.571271	−	0.820761i	$-0.306450\pi$
$313$	−7.52193	−	13.0284i	−0.425164	−	0.736406i	−0.996436	+	0.0843548i	$0.973117\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.22919	−	7.32518i	−0.237535	−	0.411423i	0.722471	−	0.691401i	$-0.243006\pi$
$317$	−4.22919	−	7.32518i	−0.237535	−	0.411423i	−0.960006	+	0.279978i	$0.909673\pi$
$318$		0			0
$319$	2.16035	−	3.74183i	0.120956	−	0.209502i
$320$		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
$329$	25.9194	+	9.99041i	1.42898	+	0.550789i
$330$		0			0
$331$	−5.01224	−	8.68146i	−0.275498	−	0.477176i	0.694763	−	0.719239i	$-0.255509\pi$
$331$	−5.01224	−	8.68146i	−0.275498	−	0.477176i	−0.970261	+	0.242063i	$0.922176\pi$
$332$		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	−0.999953	−	0.00969119i	$-0.996915\pi$
$337$	−9.33242	−	16.1642i	−0.508369	−	0.880522i	0.491584	−	0.870830i	$-0.336418\pi$
$338$		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
$347$	7.90240	−	13.6874i	0.424223	−	0.734776i	−0.572125	−	0.820167i	$-0.693881\pi$
$347$	7.90240	−	13.6874i	0.424223	−	0.734776i	0.996348	+	0.0853910i	$0.0272139\pi$
$348$		0			0
$349$	4.51578	−	7.82156i	0.241724	−	0.418678i	−0.719481	−	0.694512i	$-0.755620\pi$
$349$	4.51578	−	7.82156i	0.241724	−	0.418678i	0.961205	+	0.275833i	$0.0889538\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.4788			−0.770627			−0.385314	−	0.922786i	$-0.625907\pi$
$353$	−14.4788			−0.770627			−0.385314	+	0.922786i	$0.625907\pi$
$354$		0			0
$355$	−13.1831			−0.699687
$356$		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
$367$	−18.8589			−0.984428			−0.492214	−	0.870474i	$-0.663812\pi$
$367$	−18.8589			−0.984428			−0.492214	+	0.870474i	$0.663812\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−23.2958	−	8.97917i	−1.20946	−	0.466175i
$372$		0			0
$373$	−33.7137			−1.74563			−0.872814	−	0.488052i	$-0.837708\pi$
$373$	−33.7137			−1.74563			−0.872814	+	0.488052i	$0.837708\pi$
$374$		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
$383$	18.3240			0.936314			0.468157	−	0.883645i	$-0.344918\pi$
$383$	18.3240			0.936314			0.468157	+	0.883645i	$0.344918\pi$
$384$		0			0
$385$	−37.8490	+	30.5635i	−1.92897	+	1.55766i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.27488			−0.216745			−0.108373	−	0.994110i	$-0.534564\pi$
$389$	−4.27488			−0.216745			−0.108373	+	0.994110i	$0.534564\pi$
$390$		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
$401$	23.4015			1.16861			0.584307	−	0.811533i	$-0.301366\pi$
$401$	23.4015			1.16861			0.584307	+	0.811533i	$0.301366\pi$
$402$		0			0
$403$	37.5682			1.87140
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−23.4316	+	40.5848i	−1.16146	+	2.01171i
$408$		0			0
$409$	−17.4016	+	30.1404i	−0.860453	+	1.49035i	0.0110389	+	0.999939i	$0.496486\pi$
$409$	−17.4016	+	30.1404i	−0.860453	+	1.49035i	−0.871492	+	0.490410i	$0.836847\pi$
$410$		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	0.928291	−	0.371854i	$-0.121278\pi$
$419$	2.90894	+	5.03843i	0.142111	+	0.246143i	−0.786180	+	0.617997i	$0.787944\pi$
$420$		0			0
$421$	−17.7765	+	30.7898i	−0.866375	+	1.50061i	−0.000699237		1.00000i	$0.500223\pi$
$421$	−17.7765	+	30.7898i	−0.866375	+	1.50061i	−0.865676	+	0.500605i	$0.833111\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.72321	−	4.71674i	−0.132095	−	0.228795i
$426$		0			0
$427$	2.34234	+	0.902837i	0.113354	+	0.0436913i
$428$		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
$437$	1.28462	−	2.22503i	0.0614519	−	0.106438i
$438$		0			0
$439$	4.02947	+	6.97925i	0.192316	+	0.333101i	0.946017	−	0.324116i	$-0.105067\pi$
$439$	4.02947	+	6.97925i	0.192316	+	0.333101i	−0.753701	+	0.657217i	$0.771733\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.88883	+	3.27155i	0.0897410	+	0.155436i	0.907402	−	0.420265i	$-0.138063\pi$
$443$	1.88883	+	3.27155i	0.0897410	+	0.155436i	−0.817661	+	0.575701i	$0.804729\pi$
$444$		0			0
$445$	−12.7264	+	22.0428i	−0.603290	+	1.04493i
$446$		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
$455$	31.8973	+	12.2945i	1.49537	+	0.576376i
$456$		0			0
$457$	−0.369753	−	0.640431i	−0.0172963	−	0.0299581i	0.857248	−	0.514904i	$-0.172173\pi$
$457$	−0.369753	−	0.640431i	−0.0172963	−	0.0299581i	−0.874544	+	0.484946i	$0.838839\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.30465	−	5.72383i	0.153913	−	0.266585i	−0.778750	−	0.627335i	$-0.784146\pi$
$461$	3.30465	−	5.72383i	0.153913	−	0.266585i	0.932663	+	0.360750i	$0.117479\pi$
$462$		0			0
$463$	5.96606	+	10.3335i	0.277266	+	0.480239i	0.970704	−	0.240277i	$-0.0772383\pi$
$463$	5.96606	+	10.3335i	0.277266	+	0.480239i	−0.693438	+	0.720516i	$0.743905\pi$
$464$		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
$473$	23.5474	−	40.7853i	1.08271	−	1.87531i
$474$		0			0
$475$	1.54419	−	2.67462i	0.0708524	−	0.122720i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.03791			−0.0931145			−0.0465573	−	0.998916i	$-0.514825\pi$
$479$	−2.03791			−0.0931145			−0.0465573	+	0.998916i	$0.514825\pi$
$480$		0			0
$481$	32.9302			1.50149
$482$		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	−0.924128	−	0.382083i	$-0.875207\pi$
$491$	−17.5708	−	30.4335i	−0.792958	−	1.37344i	0.131170	−	0.991360i	$-0.458127\pi$
$492$		0			0
$493$	0.659710			0.0297118
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.96405	+	6.43106i	−0.357236	+	0.288472i
$498$		0			0
$499$	−4.65266			−0.208282			−0.104141	−	0.994563i	$-0.533209\pi$
$499$	−4.65266			−0.208282			−0.104141	+	0.994563i	$0.533209\pi$
$500$		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
$509$	−22.3477			−0.990546			−0.495273	−	0.868737i	$-0.664932\pi$
$509$	−22.3477			−0.990546			−0.495273	+	0.868737i	$0.664932\pi$
$510$		0			0
$511$	−12.7851	−	4.92792i	−0.565581	−	0.217998i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	53.4908			2.35709
$516$		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
$527$	−8.16316			−0.355593
$528$		0			0
$529$	7.23889			0.314735
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.99494	−	12.1156i	0.302984	−	0.524784i
$534$		0			0
$535$	9.71179	−	16.8213i	0.419877	−	0.727248i
$536$		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	−0.719303	−	0.694696i	$-0.755539\pi$
$547$	5.65927	−	9.80214i	0.241973	−	0.419109i	0.961276	+	0.275587i	$0.0888722\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.187044	+	0.323969i	0.00796834	+	0.0138016i
$552$		0			0
$553$	19.3275	+	7.44964i	0.821891	+	0.316791i
$554$		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
$563$	9.54570	−	16.5336i	0.402303	−	0.696810i	−0.591700	−	0.806158i	$-0.701543\pi$
$563$	9.54570	−	16.5336i	0.402303	−	0.696810i	0.994003	+	0.109348i	$0.0348764\pi$
$564$		0			0
$565$	−16.9212	−	29.3084i	−0.711880	−	1.23301i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.31363	+	2.27527i	0.0550702	+	0.0953844i	0.892246	−	0.451549i	$-0.149128\pi$
$569$	1.31363	+	2.27527i	0.0550702	+	0.0953844i	−0.837176	+	0.546933i	$0.815795\pi$
$570$		0			0
$571$	−4.99113	+	8.64489i	−0.208872	+	0.361777i	−0.951360	−	0.308083i	$-0.900313\pi$
$571$	−4.99113	+	8.64489i	−0.208872	+	0.361777i	0.742487	+	0.669860i	$0.233646\pi$
$572$		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
$581$	3.11515	+	19.8448i	0.129238	+	0.823299i
$582$		0			0
$583$	−25.4612	−	44.1001i	−1.05450	−	1.82644i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.1857	−	26.3025i	0.626782	−	1.08562i	−0.361411	−	0.932407i	$-0.617705\pi$
$587$	15.1857	−	26.3025i	0.626782	−	1.08562i	0.988193	−	0.153212i	$-0.0489618\pi$
$588$		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
$599$	−4.05521	+	7.02382i	−0.165691	+	0.286986i	−0.936901	−	0.349596i	$-0.886319\pi$
$599$	−4.05521	+	7.02382i	−0.165691	+	0.286986i	0.771209	+	0.636582i	$0.219652\pi$
$600$		0			0
$601$	15.8320	−	27.4218i	0.645801	−	1.11856i	−0.338315	−	0.941033i	$-0.609857\pi$
$601$	15.8320	−	27.4218i	0.645801	−	1.11856i	0.984116	−	0.177527i	$-0.0568098\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−61.7445			−2.51027
$606$		0			0
$607$	23.0261			0.934601			0.467300	−	0.884099i	$-0.345227\pi$
$607$	23.0261			0.934601			0.467300	+	0.884099i	$0.345227\pi$
$608$		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	0.550625	−	0.834753i	$-0.314389\pi$
$617$	−11.1183	−	19.2574i	−0.447605	−	0.775274i	−0.998230	+	0.0594788i	$0.981056\pi$
$618$		0			0
$619$	5.50603			0.221306			0.110653	−	0.993859i	$-0.464706\pi$
$619$	5.50603			0.221306			0.110653	+	0.993859i	$0.464706\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.06488	+	19.5245i	0.122792	+	0.782234i
$624$		0			0
$625$	−14.3570			−0.574280
$626$		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
$635$	−54.9002			−2.17865
$636$		0			0
$637$	25.2670	−	8.13305i	1.00112	−	0.322243i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.89176			0.0747201			0.0373600	−	0.999302i	$-0.488105\pi$
$641$	1.89176			0.0747201			0.0373600	+	0.999302i	$0.488105\pi$
$642$		0			0
$643$	−22.8742	−	39.6193i	−0.902070	−	1.56243i	−0.824803	−	0.565421i	$-0.808714\pi$
$643$	−22.8742	−	39.6193i	−0.902070	−	1.56243i	−0.0772675	−	0.997010i	$-0.524620\pi$
$644$		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
$653$	22.1482			0.866726			0.433363	−	0.901219i	$-0.357327\pi$
$653$	22.1482			0.866726			0.433363	+	0.901219i	$0.357327\pi$
$654$		0			0
$655$	47.5013			1.85603
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.39543	+	9.34515i	−0.210176	+	0.364035i	−0.951769	−	0.306814i	$-0.900737\pi$
$659$	−5.39543	+	9.34515i	−0.210176	+	0.364035i	0.741594	+	0.670850i	$0.234070\pi$
$660$		0			0
$661$	2.56954	−	4.45057i	0.0999434	−	0.173107i	−0.811718	−	0.584050i	$-0.801467\pi$
$661$	2.56954	−	4.45057i	0.0999434	−	0.173107i	0.911661	+	0.410943i	$0.134800\pi$
$662$		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	−0.574784	−	0.818305i	$-0.694914\pi$
$673$	10.9290	−	18.9295i	0.421281	−	0.729680i	0.996065	+	0.0886254i	$0.0282474\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.86482	−	10.1582i	−0.225403	−	0.390410i	0.731037	−	0.682338i	$-0.239037\pi$
$677$	−5.86482	−	10.1582i	−0.225403	−	0.390410i	−0.956440	+	0.291928i	$0.905703\pi$
$678$		0			0
$679$	−2.64641	−	16.8587i	−0.101560	−	0.646976i
$680$		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
$689$	−17.8912	+	30.9885i	−0.681602	+	1.18057i
$690$		0			0
$691$	23.0956	+	40.0028i	0.878599	+	1.52178i	0.852879	+	0.522108i	$0.174854\pi$
$691$	23.0956	+	40.0028i	0.878599	+	1.52178i	0.0257196	+	0.999669i	$0.491812\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.8265	−	18.7520i	−0.410671	−	0.711303i
$696$		0			0
$697$	−1.51993	+	2.63259i	−0.0575713	+	0.0997164i
$698$		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
$707$	−33.3453	+	26.9267i	−1.25408	+	1.01268i
$708$		0			0
$709$	16.7275	+	28.9730i	0.628216	+	1.08810i	0.987910	+	0.155032i	$0.0495480\pi$
$709$	16.7275	+	28.9730i	0.628216	+	1.08810i	−0.359693	+	0.933071i	$0.617119\pi$
$710$		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
$725$	−2.64624	+	4.58342i	−0.0982789	+	0.170224i
$726$		0			0
$727$	19.3107	−	33.4471i	0.716194	−	1.24048i	−0.246303	−	0.969193i	$-0.579216\pi$
$727$	19.3107	−	33.4471i	0.716194	−	1.24048i	0.962497	−	0.271291i	$-0.0874507\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.19073			0.265959
$732$		0			0
$733$	−18.7118			−0.691137			−0.345569	−	0.938394i	$-0.612314\pi$
$733$	−18.7118			−0.691137			−0.345569	+	0.938394i	$0.612314\pi$
$734$		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	0.999696	+	0.0246519i	$0.00784775\pi$
$743$	14.2068	+	24.6069i	0.521197	+	0.902740i	−0.478499	+	0.878088i	$0.658819\pi$
$744$		0			0
$745$	−39.2883			−1.43941
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.33888	−	14.8996i	−0.0854607	−	0.544419i
$750$		0			0
$751$	31.4418			1.14733			0.573663	−	0.819091i	$-0.305522\pi$
$751$	31.4418			1.14733			0.573663	+	0.819091i	$0.305522\pi$
$752$		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
$761$	−5.31375			−0.192623			−0.0963117	−	0.995351i	$-0.530705\pi$
$761$	−5.31375			−0.192623			−0.0963117	+	0.995351i	$0.530705\pi$
$762$		0			0
$763$	10.8227	+	4.17151i	0.391807	+	0.151019i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.29727			−0.227381
$768$		0			0
$769$	11.9430	+	20.6858i	0.430674	+	0.745949i	0.996931	−	0.0782793i	$-0.0249426\pi$
$769$	11.9430	+	20.6858i	0.430674	+	0.745949i	−0.566258	+	0.824228i	$0.691609\pi$
$770$		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
$779$	−1.72374			−0.0617595
$780$		0			0
$781$	−20.8786			−0.747096
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.89727	+	11.9464i	−0.246174	+	0.426386i
$786$		0			0
$787$	8.05546	−	13.9525i	0.287146	−	0.497352i	−0.685981	−	0.727619i	$-0.740627\pi$
$787$	8.05546	−	13.9525i	0.287146	−	0.497352i	0.973127	+	0.230268i	$0.0739602\pi$
$788$		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	0.855995	−	0.516985i	$-0.172946\pi$
$797$	−0.556852	−	0.964495i	−0.0197247	−	0.0341642i	−0.875719	+	0.482821i	$0.839612\pi$
$798$		0			0
$799$	−4.32540	+	7.49181i	−0.153022	+	0.265041i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13.9735	−	24.2029i	−0.493116	−	0.854101i
$804$		0			0
$805$	38.5687	−	31.1447i	1.35937	−	1.09771i
$806$		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
$815$	17.2402	−	29.8608i	0.603897	−	1.04598i
$816$		0			0
$817$	2.03875	+	3.53121i	0.0713267	+	0.123542i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.03552	−	3.52562i	−0.0710401	−	0.123045i	0.828317	−	0.560259i	$-0.189299\pi$
$821$	−2.03552	−	3.52562i	−0.0710401	−	0.123045i	−0.899357	+	0.437214i	$0.855965\pi$
$822$		0			0
$823$	1.30600	−	2.26206i	0.0455242	−	0.0788503i	−0.842365	−	0.538907i	$-0.818838\pi$
$823$	1.30600	−	2.26206i	0.0455242	−	0.0788503i	0.887890	+	0.460056i	$0.152171\pi$
$824$		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
$833$	−5.49026	+	1.76722i	−0.190226	+	0.0612307i
$834$		0			0
$835$	29.8613	+	51.7213i	1.03339	+	1.78989i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.61277	+	6.25750i	−0.124727	+	0.216033i	−0.921626	−	0.388079i	$-0.873139\pi$
$839$	−3.61277	+	6.25750i	−0.124727	+	0.216033i	0.796899	+	0.604112i	$0.206472\pi$
$840$		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
$851$	23.8772	−	41.3565i	0.818499	−	1.41768i
$852$		0			0
$853$	16.0767	−	27.8457i	0.550457	−	0.953419i	−0.447785	−	0.894141i	$-0.647787\pi$
$853$	16.0767	−	27.8457i	0.550457	−	0.953419i	0.998242	−	0.0592779i	$-0.0188798\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.97170			0.238149			0.119074	−	0.992885i	$-0.462007\pi$
$857$	6.97170			0.238149			0.119074	+	0.992885i	$0.462007\pi$
$858$		0			0
$859$	34.7047			1.18411			0.592054	−	0.805898i	$-0.298317\pi$
$859$	34.7047			1.18411			0.592054	+	0.805898i	$0.298317\pi$
$860$		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
$871$	−2.04456			−0.0692774
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.2930	−	9.11920i	0.381772	−	0.308285i
$876$		0			0
$877$	40.7643			1.37651			0.688257	−	0.725467i	$-0.258376\pi$
$877$	40.7643			1.37651			0.688257	+	0.725467i	$0.258376\pi$
$878$		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
$887$	13.1043			0.440000			0.220000	−	0.975500i	$-0.429394\pi$
$887$	13.1043			0.440000			0.220000	+	0.975500i	$0.429394\pi$
$888$		0			0
$889$	−33.1657	+	26.7817i	−1.11234	+	0.898230i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.90542			−0.164154
$894$		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
$905$	−32.2328			−1.07146
$906$		0			0
$907$	−12.8340			−0.426144			−0.213072	−	0.977036i	$-0.568347\pi$
$907$	−12.8340			−0.426144			−0.213072	+	0.977036i	$0.568347\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.5089	−	30.3262i	0.580094	−	1.00475i	−0.415373	−	0.909651i	$-0.636349\pi$
$911$	17.5089	−	30.3262i	0.580094	−	1.00475i	0.995468	−	0.0951015i	$-0.0303176\pi$
$912$		0			0
$913$	−20.4859	+	35.4826i	−0.677985	+	1.17430i
$914$		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
$929$	−28.4256	−	49.2346i	−0.932614	−	1.61533i	−0.778835	−	0.627229i	$-0.784189\pi$
$929$	−28.4256	−	49.2346i	−0.932614	−	1.61533i	−0.153779	−	0.988105i	$-0.549144\pi$
$930$		0			0
$931$	−2.42447	−	2.19510i	−0.0794587	−	0.0719414i
$932$		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
$941$	12.6701	−	21.9453i	0.413033	−	0.715395i	−0.582186	−	0.813055i	$-0.697803\pi$
$941$	12.6701	−	21.9453i	0.413033	−	0.715395i	0.995220	+	0.0976604i	$0.0311359\pi$
$942$		0			0
$943$	−10.1438	−	17.5697i	−0.330329	−	0.572147i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.9786	+	25.9437i	0.486739	+	0.843056i	0.999884	−	0.0152455i	$-0.00485299\pi$
$947$	14.9786	+	25.9437i	0.486739	+	0.843056i	−0.513145	+	0.858302i	$0.671520\pi$
$948$		0			0
$949$	−9.81902	+	17.0070i	−0.318739	+	0.552072i
$950$		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
$959$	−22.9554	+	18.5368i	−0.741269	+	0.598583i
$960$		0			0
$961$	−33.5775	−	58.1579i	−1.08314	−	1.87606i
$962$		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	0.999688	+	0.0249755i	$0.00795076\pi$
$967$	16.2161	+	28.0870i	0.521473	+	0.903218i	−0.478215	+	0.878243i	$0.658716\pi$
$968$		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
$977$	−7.27566	+	12.6018i	−0.232769	+	0.403168i	−0.958622	−	0.284682i	$-0.908112\pi$
$977$	−7.27566	+	12.6018i	−0.232769	+	0.403168i	0.725853	+	0.687850i	$0.241445\pi$
$978$		0			0
$979$	−20.1553	+	34.9101i	−0.644168	+	1.11573i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	32.3851			1.03293			0.516463	−	0.856310i	$-0.327249\pi$
$983$	32.3851			1.03293			0.516463	+	0.856310i	$0.327249\pi$
$984$		0			0
$985$	−76.2860			−2.43068
$986$		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
$997$	−1.39333			−0.0441272			−0.0220636	−	0.999757i	$-0.507024\pi$
$997$	−1.39333			−0.0441272			−0.0220636	+	0.999757i	$0.507024\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.289.1		22
3.2	odd	2		504.2.t.c.457.3	yes	22
4.3	odd	2		3024.2.t.k.289.1		22
7.4	even	3		1512.2.q.d.1369.11		22
9.4	even	3		1512.2.q.d.793.11		22
9.5	odd	6		504.2.q.c.121.6	yes	22
12.11	even	2		1008.2.t.l.961.9		22
21.11	odd	6		504.2.q.c.25.6	✓	22
28.11	odd	6		3024.2.q.l.2881.11		22
36.23	even	6		1008.2.q.l.625.6		22
36.31	odd	6		3024.2.q.l.2305.11		22
63.4	even	3	inner	1512.2.t.c.361.1		22
63.32	odd	6		504.2.t.c.193.3	yes	22
84.11	even	6		1008.2.q.l.529.6		22
252.67	odd	6		3024.2.t.k.1873.1		22
252.95	even	6		1008.2.t.l.193.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.6	✓	22	21.11	odd	6
504.2.q.c.121.6	yes	22	9.5	odd	6
504.2.t.c.193.3	yes	22	63.32	odd	6
504.2.t.c.457.3	yes	22	3.2	odd	2
1008.2.q.l.529.6		22	84.11	even	6
1008.2.q.l.625.6		22	36.23	even	6
1008.2.t.l.193.9		22	252.95	even	6
1008.2.t.l.961.9		22	12.11	even	2
1512.2.q.d.793.11		22	9.4	even	3
1512.2.q.d.1369.11		22	7.4	even	3
1512.2.t.c.289.1		22	1.1	even	1	trivial
1512.2.t.c.361.1		22	63.4	even	3	inner
3024.2.q.l.2305.11		22	36.31	odd	6
3024.2.q.l.2881.11		22	28.11	odd	6
3024.2.t.k.289.1		22	4.3	odd	2
3024.2.t.k.1873.1		22	252.67	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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +O(q^{10})\)	\(q-3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} -5.39638 q^{11} +(1.89598 + 3.28393i) q^{13} +(-0.411976 - 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +5.49899 q^{23} +6.61011 q^{25} +(-0.400332 + 0.693396i) q^{29} +(4.95366 - 8.57999i) q^{31} +(7.01378 - 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(-1.84467 - 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(-5.24957 - 9.09252i) q^{47} +(1.47420 - 6.84301i) q^{49} +(4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +(-0.830344 + 1.43820i) q^{59} +(-0.474405 - 0.821694i) q^{61} +(-6.46029 - 11.1896i) q^{65} +(-0.269592 + 0.466947i) q^{67} +3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(11.1080 - 8.96985i) q^{77} +(-3.91449 - 6.78010i) q^{79} +(3.79623 - 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(3.73498 - 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +(-0.795996 + 1.37871i) q^{95} +(-3.22500 + 5.58587i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more