LMFDB - Embedded newform 3024.2.cz.g.1279.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1279,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 5]))

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

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

chi := DirichletCharacter("3024.1279");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cz (of order $6$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1279.10
Character	$\chi$	$=$	3024.1279
Dual form			3024.2.cz.g.2719.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10605 - 1.21593i) q^{5} +(-0.347128 - 2.62288i) q^{7} +O(q^{10})$	$q+(2.10605 - 1.21593i) q^{5} +(-0.347128 - 2.62288i) q^{7} +(3.88819 + 2.24485i) q^{11} +(0.395715 + 0.228466i) q^{13} +(1.45416 - 0.839559i) q^{17} +(3.17762 - 5.50381i) q^{19} +(3.03876 - 1.75443i) q^{23} +(0.456976 - 0.791506i) q^{25} +(1.38240 + 2.39439i) q^{29} -8.92570 q^{31} +(-3.92031 - 5.10184i) q^{35} +(0.463575 - 0.802935i) q^{37} +(9.08056 + 5.24267i) q^{41} +(8.87861 - 5.12607i) q^{43} -8.39449 q^{47} +(-6.75900 + 1.82095i) q^{49} +(4.91938 + 8.52062i) q^{53} +10.9183 q^{55} -6.45074 q^{59} +5.31355i q^{61} +1.11120 q^{65} -13.6441i q^{67} -1.59679i q^{71} +(9.31911 - 5.38039i) q^{73} +(4.53827 - 10.9775i) q^{77} +10.3204i q^{79} +(-0.657501 - 1.13882i) q^{83} +(2.04169 - 3.53632i) q^{85} +(-13.5161 - 7.80355i) q^{89} +(0.461876 - 1.11722i) q^{91} -15.4551i q^{95} +(-5.69780 + 3.28963i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} - 4 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 - 4 * q^7	$ 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55} - 12 q^{59} + 48 q^{73} + 48 q^{77} - 48 q^{83} - 21 q^{85} - 39 q^{89} - 9 q^{91} + 3 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	2.10605	−	1.21593i	0.941856	−	0.543781i	0.0513144	−	0.998683i	$-0.483659\pi$
$5$	2.10605	−	1.21593i	0.941856	−	0.543781i	0.890542	+	0.454902i	$0.150326\pi$
$6$		0			0
$7$	−0.347128	−	2.62288i	−0.131202	−	0.991356i
$7$	−0.347128	−	2.62288i	−0.131202	−	0.991356i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.88819	+	2.24485i	1.17233	+	0.676847i	0.954229	−	0.299078i	$-0.0966792\pi$
$11$	3.88819	+	2.24485i	1.17233	+	0.676847i	0.218105	+	0.975925i	$0.430013\pi$
$12$		0			0
$13$	0.395715	+	0.228466i	0.109752	+	0.0633652i	0.553871	−	0.832602i	$-0.313150\pi$
$13$	0.395715	+	0.228466i	0.109752	+	0.0633652i	−0.444119	+	0.895968i	$0.646483\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.45416	−	0.839559i	0.352685	−	0.203623i	−0.313182	−	0.949693i	$-0.601395\pi$
$17$	1.45416	−	0.839559i	0.352685	−	0.203623i	0.665867	+	0.746070i	$0.268062\pi$
$18$		0			0
$19$	3.17762	−	5.50381i	0.728997	−	1.26266i	−0.228310	−	0.973588i	$-0.573320\pi$
$19$	3.17762	−	5.50381i	0.728997	−	1.26266i	0.957307	−	0.289072i	$-0.0933466\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.03876	−	1.75443i	0.633625	−	0.365823i	−0.148530	−	0.988908i	$-0.547454\pi$
$23$	3.03876	−	1.75443i	0.633625	−	0.365823i	0.782154	+	0.623085i	$0.214121\pi$
$24$		0			0
$25$	0.456976	−	0.791506i	0.0913952	−	0.158301i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.38240	+	2.39439i	0.256706	+	0.444627i	0.965357	−	0.260931i	$-0.0840296\pi$
$29$	1.38240	+	2.39439i	0.256706	+	0.444627i	−0.708652	+	0.705558i	$0.750696\pi$
$30$		0			0
$31$	−8.92570			−1.60310			−0.801551	−	0.597926i	$-0.795992\pi$
$31$	−8.92570			−1.60310			−0.801551	+	0.597926i	$0.795992\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.92031	−	5.10184i	−0.662654	−	0.862369i
$36$		0			0
$37$	0.463575	−	0.802935i	0.0762113	−	0.132002i	−0.825401	−	0.564547i	$-0.809051\pi$
$37$	0.463575	−	0.802935i	0.0762113	−	0.132002i	0.901612	+	0.432545i	$0.142384\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.08056	+	5.24267i	1.41815	+	0.818767i	0.996136	−	0.0878245i	$-0.0279915\pi$
$41$	9.08056	+	5.24267i	1.41815	+	0.818767i	0.422010	+	0.906591i	$0.361325\pi$
$42$		0			0
$43$	8.87861	−	5.12607i	1.35398	−	0.781718i	0.365172	−	0.930940i	$-0.381010\pi$
$43$	8.87861	−	5.12607i	1.35398	−	0.781718i	0.988804	+	0.149222i	$0.0476769\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.39449			−1.22446			−0.612231	−	0.790679i	$-0.709728\pi$
$47$	−8.39449			−1.22446			−0.612231	+	0.790679i	$0.709728\pi$
$48$		0			0
$49$	−6.75900	+	1.82095i	−0.965572	+	0.260136i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.91938	+	8.52062i	0.675729	+	1.17040i	0.976255	+	0.216623i	$0.0695043\pi$
$53$	4.91938	+	8.52062i	0.675729	+	1.17040i	−0.300526	+	0.953773i	$0.597162\pi$
$54$		0			0
$55$	10.9183			1.47223
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.45074			−0.839815			−0.419907	−	0.907567i	$-0.637937\pi$
$59$	−6.45074			−0.839815			−0.419907	+	0.907567i	$0.637937\pi$
$60$		0			0
$61$			5.31355i			0.680331i	0.940366	+	0.340165i	$0.110483\pi$
$61$			5.31355i			0.680331i	−0.940366	+	0.340165i	$0.889517\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.11120			0.137827
$66$		0			0
$67$		−	13.6441i		−	1.66689i	−0.552601	−	0.833446i	$-0.686365\pi$
$67$		−	13.6441i		−	1.66689i	0.552601	−	0.833446i	$-0.313635\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.59679i		−	0.189504i	−0.995501	−	0.0947519i	$-0.969794\pi$
$71$		−	1.59679i		−	0.189504i	0.995501	−	0.0947519i	$-0.0302058\pi$
$72$		0			0
$73$	9.31911	−	5.38039i	1.09072	−	0.629727i	0.156951	−	0.987606i	$-0.449834\pi$
$73$	9.31911	−	5.38039i	1.09072	−	0.629727i	0.933768	+	0.357880i	$0.116500\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.53827	−	10.9775i	0.517184	−	1.25100i
$78$		0			0
$79$			10.3204i			1.16114i	0.814210	+	0.580570i	$0.197170\pi$
$79$			10.3204i			1.16114i	−0.814210	+	0.580570i	$0.802830\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.657501	−	1.13882i	−0.0721701	−	0.125002i	0.827682	−	0.561197i	$-0.189659\pi$
$83$	−0.657501	−	1.13882i	−0.0721701	−	0.125002i	−0.899852	+	0.436195i	$0.856326\pi$
$84$		0			0
$85$	2.04169	−	3.53632i	0.221453	−	0.383567i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.5161	−	7.80355i	−1.43271	−	0.827175i	−0.435382	−	0.900246i	$-0.643387\pi$
$89$	−13.5161	−	7.80355i	−1.43271	−	0.827175i	−0.997327	+	0.0730708i	$0.976720\pi$
$90$		0			0
$91$	0.461876	−	1.11722i	0.0484178	−	0.117117i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	15.4551i		−	1.58566i
$96$		0			0
$97$	−5.69780	+	3.28963i	−0.578524	+	0.334011i	−0.760547	−	0.649283i	$-0.775069\pi$
$97$	−5.69780	+	3.28963i	−0.578524	+	0.334011i	0.182022	+	0.983294i	$0.441736\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.78496	−	1.03055i	−0.177610	−	0.102543i	0.408559	−	0.912732i	$-0.366031\pi$
$101$	−1.78496	−	1.03055i	−0.177610	−	0.102543i	−0.586169	+	0.810188i	$0.699365\pi$
$102$		0			0
$103$	2.93209	+	5.07852i	0.288907	+	0.500402i	0.973549	−	0.228478i	$-0.0733748\pi$
$103$	2.93209	+	5.07852i	0.288907	+	0.500402i	−0.684642	+	0.728879i	$0.740041\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.597825	+	0.345154i	0.0577939	+	0.0333673i	0.528619	−	0.848860i	$-0.322710\pi$
$107$	0.597825	+	0.345154i	0.0577939	+	0.0333673i	−0.470825	+	0.882227i	$0.656044\pi$
$108$		0			0
$109$	2.72140	+	4.71360i	0.260663	+	0.451481i	0.966418	−	0.256975i	$-0.0827256\pi$
$109$	2.72140	+	4.71360i	0.260663	+	0.451481i	−0.705756	+	0.708455i	$0.749392\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.84129	−	15.3136i	0.831718	−	1.44058i	−0.0649566	−	0.997888i	$-0.520691\pi$
$113$	8.84129	−	15.3136i	0.831718	−	1.44058i	0.896675	−	0.442690i	$-0.145976\pi$
$114$		0			0
$115$	4.26652	−	7.38984i	0.397855	−	0.689106i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.70684	−	3.52265i	−0.248136	−	0.322921i
$120$		0			0
$121$	4.57868	+	7.93051i	0.416244	+	0.720955i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			9.93670i			0.888766i
$126$		0			0
$127$		−	6.67671i		−	0.592462i	−0.955116	−	0.296231i	$-0.904270\pi$
$127$		−	6.67671i		−	0.592462i	0.955116	−	0.296231i	$-0.0957298\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.48439	−	14.6954i	−0.741284	−	1.28394i	−0.951911	−	0.306376i	$-0.900884\pi$
$131$	−8.48439	−	14.6954i	−0.741284	−	1.28394i	0.210626	−	0.977567i	$-0.432450\pi$
$132$		0			0
$133$	−15.5389	−	6.42400i	−1.34739	−	0.557032i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.25408	+	3.90418i	−0.192579	+	0.333557i	−0.946104	−	0.323862i	$-0.895019\pi$
$137$	−2.25408	+	3.90418i	−0.192579	+	0.333557i	0.753525	+	0.657419i	$0.228352\pi$
$138$		0			0
$139$	1.31628	−	2.27987i	0.111646	−	0.193376i	−0.804788	−	0.593562i	$-0.797721\pi$
$139$	1.31628	−	2.27987i	0.111646	−	0.193376i	0.916434	+	0.400186i	$0.131055\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.02574	+	1.77664i	0.0857771	+	0.148570i
$144$		0			0
$145$	5.82283	+	3.36181i	0.483559	+	0.279183i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.50091	−	6.06375i	−0.286806	−	0.496762i	0.686240	−	0.727375i	$-0.259260\pi$
$149$	−3.50091	−	6.06375i	−0.286806	−	0.496762i	−0.973045	+	0.230613i	$0.925927\pi$
$150$		0			0
$151$	−4.00644	−	2.31312i	−0.326039	−	0.188239i	0.328042	−	0.944663i	$-0.393611\pi$
$151$	−4.00644	−	2.31312i	−0.326039	−	0.188239i	−0.654081	+	0.756424i	$0.726945\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−18.7980	+	10.8530i	−1.50989	+	0.871737i
$156$		0			0
$157$			5.18700i			0.413968i	0.978344	+	0.206984i	$0.0663648\pi$
$157$			5.18700i			0.413968i	−0.978344	+	0.206984i	$0.933635\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.65649	−	7.36129i	−0.445794	−	0.580151i
$162$		0			0
$163$	2.20250	+	1.27161i	0.172513	+	0.0996005i	0.583770	−	0.811919i	$-0.301577\pi$
$163$	2.20250	+	1.27161i	0.172513	+	0.0996005i	−0.411257	+	0.911519i	$0.634910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.67825	+	8.10297i	−0.362014	+	0.627027i	−0.988292	−	0.152573i	$-0.951244\pi$
$167$	−4.67825	+	8.10297i	−0.362014	+	0.627027i	0.626278	+	0.779600i	$0.284577\pi$
$168$		0			0
$169$	−6.39561	−	11.0775i	−0.491970	−	0.852117i
$170$		0			0
$171$		0			0
$172$		0			0
$173$			8.17956i			0.621880i	0.950429	+	0.310940i	$0.100644\pi$
$173$			8.17956i			0.621880i	−0.950429	+	0.310940i	$0.899356\pi$
$174$		0			0
$175$	−2.23465	−	0.923840i	−0.168924	−	0.0698357i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.7277	−	10.8124i	1.39977	−	0.808159i	0.405404	−	0.914137i	$-0.367131\pi$
$179$	18.7277	−	10.8124i	1.39977	−	0.808159i	0.994368	+	0.105978i	$0.0337974\pi$
$180$		0			0
$181$		−	6.15376i		−	0.457405i	−0.973496	−	0.228703i	$-0.926552\pi$
$181$		−	6.15376i		−	0.457405i	0.973496	−	0.228703i	$-0.0734484\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	2.25470i		−	0.165769i
$186$		0			0
$187$	7.53873			0.551287
$188$		0			0
$189$		0			0
$190$		0			0
$191$			0.959271i			0.0694104i	0.999398	+	0.0347052i	$0.0110492\pi$
$191$			0.959271i			0.0694104i	−0.999398	+	0.0347052i	$0.988951\pi$
$192$		0			0
$193$	9.73225			0.700542			0.350271	−	0.936648i	$-0.386089\pi$
$193$	9.73225			0.700542			0.350271	+	0.936648i	$0.386089\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.67981			−0.475917			−0.237958	−	0.971275i	$-0.576478\pi$
$197$	−6.67981			−0.475917			−0.237958	+	0.971275i	$0.576478\pi$
$198$		0			0
$199$	−7.92567	−	13.7277i	−0.561836	−	0.973128i	−0.997336	−	0.0729396i	$-0.976762\pi$
$199$	−7.92567	−	13.7277i	−0.561836	−	0.973128i	0.435501	−	0.900188i	$-0.356571\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.80033	−	4.45704i	0.407103	−	0.312823i
$204$		0			0
$205$	25.4989			1.78092
$206$		0			0
$207$		0			0
$208$		0			0
$209$	24.7104	−	14.2666i	1.70926	−	0.986839i
$210$		0			0
$211$	3.79205	+	2.18934i	0.261056	+	0.150721i	0.624816	−	0.780772i	$-0.285174\pi$
$211$	3.79205	+	2.18934i	0.261056	+	0.150721i	−0.363760	+	0.931493i	$0.618507\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	12.4659	−	21.5916i	0.850167	−	1.47253i
$216$		0			0
$217$	3.09836	+	23.4110i	0.210330	+	1.58925i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.767244			0.0516104
$222$		0			0
$223$	10.1248	+	17.5367i	0.678010	+	1.17435i	0.975579	+	0.219647i	$0.0704906\pi$
$223$	10.1248	+	17.5367i	0.678010	+	1.17435i	−0.297570	+	0.954700i	$0.596176\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.60937	+	14.9119i	−0.571424	+	0.989735i	0.424996	+	0.905195i	$0.360275\pi$
$227$	−8.60937	+	14.9119i	−0.571424	+	0.989735i	−0.996420	+	0.0845401i	$0.973058\pi$
$228$		0			0
$229$	16.4919	−	9.52161i	1.08982	−	0.629206i	0.156289	−	0.987711i	$-0.450047\pi$
$229$	16.4919	−	9.52161i	1.08982	−	0.629206i	0.933528	+	0.358506i	$0.116714\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.27568	−	14.3339i	0.542158	−	0.939045i	−0.456622	−	0.889661i	$-0.650941\pi$
$233$	8.27568	−	14.3339i	0.542158	−	0.939045i	0.998780	−	0.0493838i	$-0.0157258\pi$
$234$		0			0
$235$	−17.6792	+	10.2071i	−1.15327	+	0.665839i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.4085	+	7.16408i	0.802642	+	0.463406i	0.844394	−	0.535722i	$-0.179961\pi$
$239$	12.4085	+	7.16408i	0.802642	+	0.463406i	−0.0417519	+	0.999128i	$0.513294\pi$
$240$		0			0
$241$	20.6124	+	11.9006i	1.32776	+	0.766583i	0.984953	−	0.172823i	$-0.0552889\pi$
$241$	20.6124	+	11.9006i	1.32776	+	0.766583i	0.342807	+	0.939406i	$0.388622\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.0207	+	12.0535i	−0.767973	+	0.770070i
$246$		0			0
$247$	2.51487	−	1.45196i	0.160017	−	0.0923861i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.7179			−1.18147			−0.590733	−	0.806867i	$-0.701161\pi$
$251$	−18.7179			−1.18147			−0.590733	+	0.806867i	$0.701161\pi$
$252$		0			0
$253$	15.7537			0.990426
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.774476	−	0.447144i	0.0483105	−	0.0278921i	−0.475650	−	0.879635i	$-0.657787\pi$
$257$	0.774476	−	0.447144i	0.0483105	−	0.0278921i	0.523961	+	0.851742i	$0.324454\pi$
$258$		0			0
$259$	−2.26692	−	0.937180i	−0.140860	−	0.0582336i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.77645	−	3.91239i	−0.417854	−	0.241248i	0.276305	−	0.961070i	$-0.410890\pi$
$263$	−6.77645	−	3.91239i	−0.417854	−	0.241248i	−0.694159	+	0.719822i	$0.744223\pi$
$264$		0			0
$265$	20.7210	+	11.9633i	1.27288	+	0.734897i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−15.7164	+	9.07386i	−0.958245	+	0.553243i	−0.895632	−	0.444795i	$-0.853277\pi$
$269$	−15.7164	+	9.07386i	−0.958245	+	0.553243i	−0.0626124	+	0.998038i	$0.519943\pi$
$270$		0			0
$271$	15.8173	−	27.3965i	0.960836	−	1.66422i	0.240425	−	0.970668i	$-0.422713\pi$
$271$	15.8173	−	27.3965i	0.960836	−	1.66422i	0.720410	−	0.693548i	$-0.243954\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.55362	−	2.05168i	0.214291	−	0.123721i
$276$		0			0
$277$	−15.5598	+	26.9504i	−0.934899	+	1.61929i	−0.160084	+	0.987103i	$0.551177\pi$
$277$	−15.5598	+	26.9504i	−0.934899	+	1.61929i	−0.774814	+	0.632189i	$0.782157\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.95236	+	6.84569i	0.235778	+	0.408380i	0.959499	−	0.281714i	$-0.0909028\pi$
$281$	3.95236	+	6.84569i	0.235778	+	0.408380i	−0.723720	+	0.690093i	$0.757569\pi$
$282$		0			0
$283$	−9.93156			−0.590370			−0.295185	−	0.955440i	$-0.595381\pi$
$283$	−9.93156			−0.590370			−0.295185	+	0.955440i	$0.595381\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.5988	−	25.6371i	0.625626	−	1.51331i
$288$		0			0
$289$	−7.09028	+	12.2807i	−0.417075	+	0.722396i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.9727	−	6.33509i	−0.641032	−	0.370100i	0.143980	−	0.989581i	$-0.454010\pi$
$293$	−10.9727	−	6.33509i	−0.641032	−	0.370100i	−0.785012	+	0.619481i	$0.787343\pi$
$294$		0			0
$295$	−13.5856	+	7.84365i	−0.790985	+	0.456675i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.60331			0.0927218
$300$		0			0
$301$	−16.5271	−	21.5081i	−0.952605	−	1.23971i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.46091	+	11.1906i	0.369951	+	0.640774i
$306$		0			0
$307$	0.680046			0.0388123			0.0194061	−	0.999812i	$-0.493822\pi$
$307$	0.680046			0.0388123			0.0194061	+	0.999812i	$0.493822\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.40471			0.419883			0.209941	−	0.977714i	$-0.432673\pi$
$311$	7.40471			0.419883			0.209941	+	0.977714i	$0.432673\pi$
$312$		0			0
$313$			0.764315i			0.0432016i	0.999767	+	0.0216008i	$0.00687629\pi$
$313$			0.764315i			0.0432016i	−0.999767	+	0.0216008i	$0.993124\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.5131			1.54529			0.772644	−	0.634840i	$-0.218934\pi$
$317$	27.5131			1.54529			0.772644	+	0.634840i	$0.218934\pi$
$318$		0			0
$319$			12.4131i			0.695002i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	10.6712i		−	0.593762i
$324$		0			0
$325$	0.361665	−	0.208807i	0.0200616	−	0.0115825i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.91396	+	22.0177i	0.160652	+	1.21388i
$330$		0			0
$331$			8.40291i			0.461866i	0.972970	+	0.230933i	$0.0741778\pi$
$331$			8.40291i			0.461866i	−0.972970	+	0.230933i	$0.925822\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.5903	−	28.7352i	−0.906424	−	1.56997i
$336$		0			0
$337$	−2.06160	+	3.57079i	−0.112302	+	0.194513i	−0.916698	−	0.399580i	$-0.869156\pi$
$337$	−2.06160	+	3.57079i	−0.112302	+	0.194513i	0.804396	+	0.594094i	$0.202489\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−34.7048	−	20.0368i	−1.87937	−	1.08506i
$342$		0			0
$343$	7.12237	+	17.0960i	0.384572	+	0.923095i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			18.8928i			1.01422i	0.861881	+	0.507110i	$0.169286\pi$
$347$			18.8928i			1.01422i	−0.861881	+	0.507110i	$0.830714\pi$
$348$		0			0
$349$	−3.67063	+	2.11924i	−0.196485	+	0.113440i	−0.595015	−	0.803715i	$-0.702854\pi$
$349$	−3.67063	+	2.11924i	−0.196485	+	0.113440i	0.398530	+	0.917155i	$0.369520\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.57691	+	4.95188i	0.456503	+	0.263562i	0.710573	−	0.703624i	$-0.248436\pi$
$353$	8.57691	+	4.95188i	0.456503	+	0.263562i	−0.254070	+	0.967186i	$0.581769\pi$
$354$		0			0
$355$	−1.94158	−	3.36292i	−0.103048	−	0.178485i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.14625	+	0.661787i	0.0604967	+	0.0349278i	0.529943	−	0.848033i	$-0.322213\pi$
$359$	1.14625	+	0.661787i	0.0604967	+	0.0349278i	−0.469447	+	0.882961i	$0.655547\pi$
$360$		0			0
$361$	−10.6946	−	18.5236i	−0.562873	−	0.974925i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.0844	−	22.6628i	0.684867	−	1.18622i
$366$		0			0
$367$	18.3266	−	31.7426i	0.956642	−	1.65695i	0.226077	−	0.974109i	$-0.427410\pi$
$367$	18.3266	−	31.7426i	0.956642	−	1.65695i	0.730565	−	0.682843i	$-0.239257\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	20.6409	−	15.8607i	1.07162	−	0.823446i
$372$		0			0
$373$	−11.1831	−	19.3698i	−0.579041	−	1.00293i	−0.995590	−	0.0938155i	$-0.970094\pi$
$373$	−11.1831	−	19.3698i	−0.579041	−	1.00293i	0.416548	−	0.909114i	$-0.363240\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1.26333i			0.0650648i
$378$		0			0
$379$		−	29.0426i		−	1.49182i	−0.666048	−	0.745909i	$-0.732015\pi$
$379$		−	29.0426i		−	1.49182i	0.666048	−	0.745909i	$-0.267985\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.3588	+	17.9419i	0.529309	+	0.916790i	0.999416	+	0.0341804i	$0.0108821\pi$
$383$	10.3588	+	17.9419i	0.529309	+	0.916790i	−0.470107	+	0.882610i	$0.655785\pi$
$384$		0			0
$385$	−3.79005	−	28.6374i	−0.193159	−	1.45950i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.0995	+	33.0812i	−0.968381	+	1.67728i	−0.268137	+	0.963381i	$0.586408\pi$
$389$	−19.0995	+	33.0812i	−0.968381	+	1.67728i	−0.700244	+	0.713904i	$0.746925\pi$
$390$		0			0
$391$	2.94589	−	5.10243i	0.148980	−	0.258041i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.5489	+	21.7354i	0.631406	+	1.09363i
$396$		0			0
$397$	−22.8326	−	13.1824i	−1.14594	−	0.661606i	−0.198042	−	0.980194i	$-0.563458\pi$
$397$	−22.8326	−	13.1824i	−1.14594	−	0.661606i	−0.947894	+	0.318587i	$0.896792\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.8837	−	25.7794i	−0.743258	−	1.28736i	−0.951004	−	0.309178i	$-0.899946\pi$
$401$	−14.8837	−	25.7794i	−0.743258	−	1.28736i	0.207746	−	0.978183i	$-0.433387\pi$
$402$		0			0
$403$	−3.53204	−	2.03922i	−0.175943	−	0.101581i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.60493	−	2.08131i	0.178690	−	0.103167i
$408$		0			0
$409$		−	11.4389i		−	0.565615i	−0.959177	−	0.282808i	$-0.908734\pi$
$409$		−	11.4389i		−	0.565615i	0.959177	−	0.282808i	$-0.0912658\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.23923	+	16.9195i	0.110185	+	0.832555i
$414$		0			0
$415$	−2.76946	−	1.59895i	−0.135948	−	0.0784894i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.62952	+	6.28651i	−0.177314	+	0.307116i	−0.940960	−	0.338519i	$-0.890074\pi$
$419$	−3.62952	+	6.28651i	−0.177314	+	0.307116i	0.763646	+	0.645635i	$0.223407\pi$
$420$		0			0
$421$	3.83542	+	6.64314i	0.186927	+	0.323767i	0.944224	−	0.329304i	$-0.106814\pi$
$421$	3.83542	+	6.64314i	0.186927	+	0.323767i	−0.757297	+	0.653070i	$0.773481\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	1.53463i		−	0.0744407i
$426$		0			0
$427$	13.9368	−	1.84448i	0.674450	−	0.0892608i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.0439	+	15.0364i	−1.25449	+	0.724279i	−0.971998	−	0.234991i	$-0.924494\pi$
$431$	−26.0439	+	15.0364i	−1.25449	+	0.724279i	−0.282491	+	0.959270i	$0.591161\pi$
$432$		0			0
$433$			14.7704i			0.709819i	0.934901	+	0.354909i	$0.115488\pi$
$433$			14.7704i			0.709819i	−0.934901	+	0.354909i	$0.884512\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	22.2996i		−	1.06674i
$438$		0			0
$439$	−13.5922			−0.648719			−0.324360	−	0.945934i	$-0.605149\pi$
$439$	−13.5922			−0.648719			−0.324360	+	0.945934i	$0.605149\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			21.0890i			1.00197i	0.865457	+	0.500984i	$0.167028\pi$
$443$			21.0890i			1.00197i	−0.865457	+	0.500984i	$0.832972\pi$
$444$		0			0
$445$	−37.9543			−1.79921
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.7307			0.883959			0.441979	−	0.897025i	$-0.354276\pi$
$449$	18.7307			0.883959			0.441979	+	0.897025i	$0.354276\pi$
$450$		0			0
$451$	23.5380	+	40.7690i	1.10836	+	1.91974i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.385728	−	2.91454i	−0.0180832	−	0.136636i
$456$		0			0
$457$	29.4099			1.37574			0.687868	−	0.725836i	$-0.258547\pi$
$457$	29.4099			1.37574			0.687868	+	0.725836i	$0.258547\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.2212	+	12.8294i	−1.03494	+	0.597525i	−0.918397	−	0.395660i	$-0.870516\pi$
$461$	−22.2212	+	12.8294i	−1.03494	+	0.597525i	−0.116547	+	0.993185i	$0.537183\pi$
$462$		0			0
$463$	3.52873	+	2.03731i	0.163994	+	0.0946819i	0.579751	−	0.814794i	$-0.303150\pi$
$463$	3.52873	+	2.03731i	0.163994	+	0.0946819i	−0.415757	+	0.909476i	$0.636483\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.0531	+	19.1445i	−0.511475	+	0.885901i	0.488437	+	0.872599i	$0.337567\pi$
$467$	−11.0531	+	19.1445i	−0.511475	+	0.885901i	−0.999912	+	0.0133012i	$0.995766\pi$
$468$		0			0
$469$	−35.7868	+	4.73625i	−1.65248	+	0.218700i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	46.0290			2.11641
$474$		0			0
$475$	−2.90420	−	5.03022i	−0.133254	−	0.230802i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.5218	+	21.6883i	−0.572134	+	0.990965i	0.424213	+	0.905562i	$0.360551\pi$
$479$	−12.5218	+	21.6883i	−0.572134	+	0.990965i	−0.996347	+	0.0854021i	$0.972783\pi$
$480$		0			0
$481$	0.366888	−	0.211823i	0.0167286	−	0.00965828i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.99992	+	13.8563i	−0.363258	+	0.629181i
$486$		0			0
$487$	−36.1701	+	20.8828i	−1.63902	+	0.946290i	−0.657851	+	0.753148i	$0.728534\pi$
$487$	−36.1701	+	20.8828i	−1.63902	+	0.946290i	−0.981171	+	0.193142i	$0.938132\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	23.1251	+	13.3513i	1.04362	+	0.602534i	0.920856	−	0.389902i	$-0.127491\pi$
$491$	23.1251	+	13.3513i	1.04362	+	0.602534i	0.122763	+	0.992436i	$0.460825\pi$
$492$		0			0
$493$	4.02047	+	2.32122i	0.181073	+	0.104542i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.18818	+	0.554289i	−0.187866	+	0.0248633i
$498$		0			0
$499$	−2.19574	+	1.26771i	−0.0982950	+	0.0567507i	−0.548342	−	0.836254i	$-0.684741\pi$
$499$	−2.19574	+	1.26771i	−0.0982950	+	0.0567507i	0.450047	+	0.893005i	$0.351407\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	17.5814			0.783916			0.391958	−	0.919983i	$-0.371798\pi$
$503$	17.5814			0.783916			0.391958	+	0.919983i	$0.371798\pi$
$504$		0			0
$505$	−5.01230			−0.223045
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.4554	+	7.19111i	−0.552075	+	0.318740i	−0.749958	−	0.661485i	$-0.769927\pi$
$509$	−12.4554	+	7.19111i	−0.552075	+	0.318740i	0.197884	+	0.980226i	$0.436593\pi$
$510$		0			0
$511$	−17.3470	−	22.5752i	−0.767388	−	0.998669i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.3503	+	7.13043i	0.544218	+	0.314204i
$516$		0			0
$517$	−32.6394	−	18.8443i	−1.43548	−	0.828773i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−33.9165	+	19.5817i	−1.48591	+	0.857890i	−0.999871	−	0.0160476i	$-0.994892\pi$
$521$	−33.9165	+	19.5817i	−1.48591	+	0.857890i	−0.486038	+	0.873938i	$0.661558\pi$
$522$		0			0
$523$	−10.1114	+	17.5134i	−0.442139	+	0.765807i	−0.997848	−	0.0655699i	$-0.979113\pi$
$523$	−10.1114	+	17.5134i	−0.442139	+	0.765807i	0.555709	+	0.831377i	$0.312447\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.9794	+	7.49365i	−0.565391	+	0.326429i
$528$		0			0
$529$	−5.34397	+	9.25603i	−0.232347	+	0.402436i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.39555	+	4.14921i	0.103763	+	0.179722i
$534$		0			0
$535$	1.67873			0.0725780
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−30.3680	−	8.09273i	−1.30804	−	0.348579i
$540$		0			0
$541$	18.0846	−	31.3234i	0.777517	−	1.34670i	−0.155852	−	0.987780i	$-0.549812\pi$
$541$	18.0846	−	31.3234i	0.777517	−	1.34670i	0.933369	−	0.358919i	$-0.116854\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.4628	+	6.61806i	0.491013	+	0.283487i
$546$		0			0
$547$	−27.2261	+	15.7190i	−1.16410	+	0.672096i	−0.952284	−	0.305212i	$-0.901273\pi$
$547$	−27.2261	+	15.7190i	−1.16410	+	0.672096i	−0.211820	+	0.977309i	$0.567939\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	17.5710			0.748551
$552$		0			0
$553$	27.0693	−	3.58251i	1.15110	−	0.152344i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.22319	−	15.9750i	−0.390799	−	0.676884i	0.601756	−	0.798680i	$-0.294468\pi$
$557$	−9.22319	−	15.9750i	−0.390799	−	0.676884i	−0.992555	+	0.121796i	$0.961135\pi$
$558$		0			0
$559$	4.68454			0.198135
$560$		0			0
$561$		0			0
$562$		0			0
$563$	26.2712			1.10720			0.553599	−	0.832783i	$-0.313254\pi$
$563$	26.2712			1.10720			0.553599	+	0.832783i	$0.313254\pi$
$564$		0			0
$565$		−	43.0016i		−	1.80909i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	44.2364			1.85449			0.927244	−	0.374459i	$-0.122172\pi$
$569$	44.2364			1.85449			0.927244	+	0.374459i	$0.122172\pi$
$570$		0			0
$571$		−	25.4163i		−	1.06364i	−0.846857	−	0.531820i	$-0.821508\pi$
$571$		−	25.4163i		−	1.06364i	0.846857	−	0.531820i	$-0.178492\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	3.20692i		−	0.133738i
$576$		0			0
$577$	−15.0822	+	8.70772i	−0.627881	+	0.362507i	−0.779931	−	0.625866i	$-0.784746\pi$
$577$	−15.0822	+	8.70772i	−0.627881	+	0.362507i	0.152050	+	0.988373i	$0.451413\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.75876	+	2.11986i	−0.114453	+	0.0879468i
$582$		0			0
$583$			44.1730i			1.82946i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.224520	+	0.388879i	0.00926691	+	0.0160508i	0.870622	−	0.491953i	$-0.163717\pi$
$587$	0.224520	+	0.388879i	0.00926691	+	0.0160508i	−0.861355	+	0.508004i	$0.830384\pi$
$588$		0			0
$589$	−28.3625	+	49.1253i	−1.16866	+	2.02417i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.4137	−	11.7859i	−0.838291	−	0.483987i	0.0183921	−	0.999831i	$-0.494145\pi$
$593$	−20.4137	−	11.7859i	−0.838291	−	0.483987i	−0.856683	+	0.515843i	$0.827479\pi$
$594$		0			0
$595$	−9.98406	−	4.12756i	−0.409307	−	0.169214i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			39.6547i			1.62025i	0.586258	+	0.810125i	$0.300601\pi$
$599$			39.6547i			1.62025i	−0.586258	+	0.810125i	$0.699399\pi$
$600$		0			0
$601$	1.68404	−	0.972283i	0.0686936	−	0.0396603i	−0.465260	−	0.885174i	$-0.654039\pi$
$601$	1.68404	−	0.972283i	0.0686936	−	0.0396603i	0.533953	+	0.845514i	$0.320706\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.2859	+	11.1347i	0.784083	+	0.452691i
$606$		0			0
$607$	19.0369	+	32.9728i	0.772682	+	1.33832i	0.936088	+	0.351766i	$0.114419\pi$
$607$	19.0369	+	32.9728i	0.772682	+	1.33832i	−0.163406	+	0.986559i	$0.552248\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.32183	−	1.91786i	−0.134387	−	0.0775882i
$612$		0			0
$613$	−8.49783	−	14.7187i	−0.343224	−	0.594482i	0.641805	−	0.766868i	$-0.278186\pi$
$613$	−8.49783	−	14.7187i	−0.343224	−	0.594482i	−0.985029	+	0.172386i	$0.944852\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.72221	+	16.8394i	−0.391401	+	0.677927i	−0.992635	−	0.121146i	$-0.961343\pi$
$617$	−9.72221	+	16.8394i	−0.391401	+	0.677927i	0.601233	+	0.799074i	$0.294676\pi$
$618$		0			0
$619$	−5.57182	+	9.65067i	−0.223950	+	0.387893i	−0.956004	−	0.293354i	$-0.905229\pi$
$619$	−5.57182	+	9.65067i	−0.223950	+	0.387893i	0.732054	+	0.681247i	$0.238562\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−15.7760	+	38.1601i	−0.632050	+	1.52885i
$624$		0			0
$625$	14.3672	+	24.8848i	0.574689	+	0.995391i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.55679i		−	0.0620735i
$630$		0			0
$631$			37.9530i			1.51088i	0.655215	+	0.755442i	$0.272578\pi$
$631$			37.9530i			1.51088i	−0.655215	+	0.755442i	$0.727422\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.11841	−	14.0615i	−0.322169	−	0.558014i
$636$		0			0
$637$	−3.09067	−	0.823627i	−0.122457	−	0.0326333i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.20368	+	3.81689i	−0.0870401	+	0.150758i	−0.906259	−	0.422723i	$-0.861074\pi$
$641$	−2.20368	+	3.81689i	−0.0870401	+	0.150758i	0.819219	+	0.573481i	$0.194407\pi$
$642$		0			0
$643$	−15.7031	+	27.1985i	−0.619269	+	1.07261i	0.370350	+	0.928892i	$0.379238\pi$
$643$	−15.7031	+	27.1985i	−0.619269	+	1.07261i	−0.989619	+	0.143713i	$0.954096\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.82727	+	8.36107i	0.189779	+	0.328708i	0.945177	−	0.326560i	$-0.105889\pi$
$647$	4.82727	+	8.36107i	0.189779	+	0.328708i	−0.755397	+	0.655267i	$0.772556\pi$
$648$		0			0
$649$	−25.0817	−	14.4809i	−0.984543	−	0.568426i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.42478	+	7.66394i	0.173155	+	0.299913i	0.939521	−	0.342491i	$-0.111271\pi$
$653$	4.42478	+	7.66394i	0.173155	+	0.299913i	−0.766366	+	0.642404i	$0.777937\pi$
$654$		0			0
$655$	−35.7372	−	20.6329i	−1.39637	−	0.806193i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11.1661	+	6.44675i	−0.434969	+	0.251130i	−0.701461	−	0.712707i	$-0.747469\pi$
$659$	−11.1661	+	6.44675i	−0.434969	+	0.251130i	0.266492	+	0.963837i	$0.414135\pi$
$660$		0			0
$661$			13.9885i			0.544091i	0.962284	+	0.272046i	$0.0877001\pi$
$661$			13.9885i			0.544091i	−0.962284	+	0.272046i	$0.912300\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−40.5368	+	5.36489i	−1.57195	+	0.208042i
$666$		0			0
$667$	8.40157	+	4.85065i	0.325310	+	0.187818i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.9281	+	20.6601i	−0.460480	+	0.797574i
$672$		0			0
$673$	20.1596	+	34.9175i	0.777097	+	1.34597i	0.933608	+	0.358295i	$0.116642\pi$
$673$	20.1596	+	34.9175i	0.777097	+	1.34597i	−0.156511	+	0.987676i	$0.550025\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	20.0178i		−	0.769347i	−0.923053	−	0.384674i	$-0.874314\pi$
$677$		−	20.0178i		−	0.769347i	0.923053	−	0.384674i	$-0.125686\pi$
$678$		0			0
$679$	10.6062	+	13.8027i	0.407027	+	0.529700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.6264	+	9.02190i	−0.597927	+	0.345214i	−0.768226	−	0.640179i	$-0.778860\pi$
$683$	−15.6264	+	9.02190i	−0.597927	+	0.345214i	0.170298	+	0.985393i	$0.445527\pi$
$684$		0			0
$685$			10.9632i			0.418883i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			4.49565i			0.171271i
$690$		0			0
$691$	32.5408			1.23791			0.618956	−	0.785426i	$-0.287556\pi$
$691$	32.5408			1.23791			0.618956	+	0.785426i	$0.287556\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	6.40203i		−	0.242843i
$696$		0			0
$697$	17.6061			0.666879
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15.6096			0.589567			0.294784	−	0.955564i	$-0.404752\pi$
$701$	15.6096			0.589567			0.294784	+	0.955564i	$0.404752\pi$
$702$		0			0
$703$	−2.94613	−	5.10285i	−0.111116	−	0.192458i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.08340	+	5.03948i	−0.0783542	+	0.189529i
$708$		0			0
$709$	−40.9710			−1.53870			−0.769349	−	0.638828i	$-0.779419\pi$
$709$	−40.9710			−1.53870			−0.769349	+	0.638828i	$0.779419\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−27.1230	+	15.6595i	−1.01577	+	0.586452i
$714$		0			0
$715$	4.32055	+	2.49447i	0.161579	+	0.0932878i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.18063	+	10.7052i	−0.230499	+	0.399235i	−0.957955	−	0.286919i	$-0.907369\pi$
$719$	−6.18063	+	10.7052i	−0.230499	+	0.399235i	0.727456	+	0.686154i	$0.240702\pi$
$720$		0			0
$721$	12.3026	−	9.45341i	0.458171	−	0.352063i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.52690			0.0938467
$726$		0			0
$727$	−0.793341	−	1.37411i	−0.0294234	−	0.0509628i	0.850939	−	0.525265i	$-0.176034\pi$
$727$	−0.793341	−	1.37411i	−0.0294234	−	0.0509628i	−0.880362	+	0.474302i	$0.842700\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.60728	−	14.9082i	0.318352	−	0.551401i
$732$		0			0
$733$	16.9129	−	9.76469i	0.624694	−	0.360667i	−0.154000	−	0.988071i	$-0.549216\pi$
$733$	16.9129	−	9.76469i	0.624694	−	0.360667i	0.778694	+	0.627404i	$0.215882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	30.6289	−	53.0509i	1.12823	−	1.95415i
$738$		0			0
$739$	−10.4675	+	6.04343i	−0.385054	+	0.222311i	−0.680015	−	0.733198i	$-0.738027\pi$
$739$	−10.4675	+	6.04343i	−0.385054	+	0.222311i	0.294961	+	0.955509i	$0.404693\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	39.1566	+	22.6071i	1.43652	+	0.829373i	0.997606	−	0.0691583i	$-0.0220313\pi$
$743$	39.1566	+	22.6071i	1.43652	+	0.829373i	0.438910	+	0.898531i	$0.355365\pi$
$744$		0			0
$745$	−14.7462	−	8.51373i	−0.540259	−	0.311919i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.697777	−	1.68783i	0.0254962	−	0.0616721i
$750$		0			0
$751$	10.2452	−	5.91510i	0.373854	−	0.215845i	−0.301287	−	0.953534i	$-0.597416\pi$
$751$	10.2452	−	5.91510i	0.373854	−	0.215845i	0.675141	+	0.737689i	$0.264083\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−11.2504			−0.409443
$756$		0			0
$757$	−1.13634			−0.0413008			−0.0206504	−	0.999787i	$-0.506574\pi$
$757$	−1.13634			−0.0413008			−0.0206504	+	0.999787i	$0.506574\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.4877	−	12.9833i	0.815179	−	0.470644i	−0.0335719	−	0.999436i	$-0.510688\pi$
$761$	22.4877	−	12.9833i	0.815179	−	0.470644i	0.848751	+	0.528792i	$0.177355\pi$
$762$		0			0
$763$	11.4185	−	8.77412i	0.413379	−	0.317645i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.55266	−	1.47378i	−0.0921711	−	0.0532150i
$768$		0			0
$769$	−5.34306	−	3.08482i	−0.192676	−	0.111241i	0.400559	−	0.916271i	$-0.368816\pi$
$769$	−5.34306	−	3.08482i	−0.192676	−	0.111241i	−0.593235	+	0.805030i	$0.702149\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.9774	−	13.2660i	0.826439	−	0.477145i	−0.0261931	−	0.999657i	$-0.508338\pi$
$773$	22.9774	−	13.2660i	0.826439	−	0.477145i	0.852632	+	0.522512i	$0.175005\pi$
$774$		0			0
$775$	−4.07883	+	7.06474i	−0.146516	+	0.253773i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	57.7092	−	33.3184i	2.06765	−	1.19376i
$780$		0			0
$781$	3.58454	−	6.20861i	0.128265	−	0.222162i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.30704	+	10.9241i	0.225108	+	0.389898i
$786$		0			0
$787$	−13.7291			−0.489391			−0.244696	−	0.969600i	$-0.578688\pi$
$787$	−13.7291			−0.489391			−0.244696	+	0.969600i	$0.578688\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−43.2347	−	17.8739i	−1.53725	−	0.635522i
$792$		0			0
$793$	−1.21397	+	2.10266i	−0.0431093	+	0.0746675i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−39.5989	−	22.8624i	−1.40267	−	0.809829i	−0.408000	−	0.912982i	$-0.633774\pi$
$797$	−39.5989	−	22.8624i	−1.40267	−	0.809829i	−0.994666	+	0.103153i	$0.967107\pi$
$798$		0			0
$799$	−12.2069	+	7.04767i	−0.431850	+	0.249329i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	48.3126			1.70491
$804$		0			0
$805$	−20.8637	−	8.62536i	−0.735348	−	0.304004i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	11.8728	+	20.5642i	0.417425	+	0.723001i	0.995680	−	0.0928555i	$-0.0295995\pi$
$809$	11.8728	+	20.5642i	0.417425	+	0.723001i	−0.578255	+	0.815856i	$0.696266\pi$
$810$		0			0
$811$	−48.4581			−1.70159			−0.850797	−	0.525495i	$-0.823880\pi$
$811$	−48.4581			−1.70159			−0.850797	+	0.525495i	$0.823880\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.18478			0.216643
$816$		0			0
$817$		−	65.1549i		−	2.27948i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−37.9070			−1.32296			−0.661481	−	0.749962i	$-0.730072\pi$
$821$	−37.9070			−1.32296			−0.661481	+	0.749962i	$0.730072\pi$
$822$		0			0
$823$		−	19.0075i		−	0.662559i	−0.943533	−	0.331280i	$-0.892520\pi$
$823$		−	19.0075i		−	0.662559i	0.943533	−	0.331280i	$-0.107480\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	2.75122i		−	0.0956692i	−0.998855	−	0.0478346i	$-0.984768\pi$
$827$		−	2.75122i		−	0.0956692i	0.998855	−	0.0478346i	$-0.0152320\pi$
$828$		0			0
$829$	27.0931	−	15.6422i	0.940984	−	0.543277i	0.0507153	−	0.998713i	$-0.483850\pi$
$829$	27.0931	−	15.6422i	0.940984	−	0.543277i	0.890269	+	0.455436i	$0.150517\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.29988	+	8.32254i	−0.287574	+	0.288359i
$834$		0			0
$835$			22.7537i			0.787425i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.27568	−	2.20954i	−0.0440413	−	0.0762818i	0.843164	−	0.537656i	$-0.180690\pi$
$839$	−1.27568	−	2.20954i	−0.0440413	−	0.0762818i	−0.887206	+	0.461374i	$0.847357\pi$
$840$		0			0
$841$	10.6779	−	18.4947i	0.368204	−	0.637749i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.9390	−	15.5532i	−0.926729	−	0.535047i
$846$		0			0
$847$	19.2114	−	14.7622i	0.660111	−	0.507236i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	3.25323i		−	0.111519i
$852$		0			0
$853$	−36.1233	+	20.8558i	−1.23684	+	0.714088i	−0.968446	−	0.249222i	$-0.919825\pi$
$853$	−36.1233	+	20.8558i	−1.23684	+	0.714088i	−0.268391	+	0.963310i	$0.586492\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.9310	+	19.5901i	1.15906	+	0.669183i	0.951078	−	0.308949i	$-0.0999774\pi$
$857$	33.9310	+	19.5901i	1.15906	+	0.669183i	0.207981	+	0.978133i	$0.433311\pi$
$858$		0			0
$859$	7.69010	+	13.3196i	0.262383	+	0.454460i	0.966875	−	0.255252i	$-0.0821584\pi$
$859$	7.69010	+	13.3196i	0.262383	+	0.454460i	−0.704492	+	0.709712i	$0.748825\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	43.4544	+	25.0884i	1.47921	+	0.854020i	0.999723	−	0.0235310i	$-0.00749084\pi$
$863$	43.4544	+	25.0884i	1.47921	+	0.854020i	0.479483	+	0.877551i	$0.340824\pi$
$864$		0			0
$865$	9.94578	+	17.2266i	0.338167	+	0.585722i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−23.1678	+	40.1278i	−0.785914	+	1.36124i
$870$		0			0
$871$	3.11722	−	5.39918i	0.105623	−	0.182944i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	26.0628	−	3.44931i	0.881083	−	0.116608i
$876$		0			0
$877$	18.7034	+	32.3953i	0.631571	+	1.09391i	0.987231	+	0.159297i	$0.0509227\pi$
$877$	18.7034	+	32.3953i	0.631571	+	1.09391i	−0.355660	+	0.934615i	$0.615744\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.43451i		−	0.0820207i	−0.999159	−	0.0410104i	$-0.986942\pi$
$881$		−	2.43451i		−	0.0820207i	0.999159	−	0.0410104i	$-0.0130577\pi$
$882$		0			0
$883$			7.56709i			0.254653i	0.991861	+	0.127326i	$0.0406396\pi$
$883$			7.56709i			0.254653i	−0.991861	+	0.127326i	$0.959360\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.64424	−	4.57995i	−0.0887848	−	0.153780i	0.818213	−	0.574915i	$-0.194965\pi$
$887$	−2.64424	−	4.57995i	−0.0887848	−	0.153780i	−0.906998	+	0.421136i	$0.861632\pi$
$888$		0			0
$889$	−17.5122	+	2.31767i	−0.587341	+	0.0777322i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26.6745	+	46.2016i	−0.892629	+	1.54608i
$894$		0			0
$895$	26.2943	−	45.5431i	0.878923	−	1.52234i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.3389	−	21.3716i	−0.411526	−	0.712783i
$900$		0			0
$901$	14.3071	+	8.26022i	0.476640	+	0.275188i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.48255	−	12.9602i	−0.248728	−	0.430810i
$906$		0			0
$907$	19.4236	+	11.2142i	0.644949	+	0.372361i	0.786518	−	0.617567i	$-0.211882\pi$
$907$	19.4236	+	11.2142i	0.644949	+	0.372361i	−0.141570	+	0.989928i	$0.545215\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.0594	+	12.7360i	−0.730861	+	0.421963i	−0.818737	−	0.574168i	$-0.805325\pi$
$911$	−22.0594	+	12.7360i	−0.730861	+	0.421963i	0.0878758	+	0.996131i	$0.471992\pi$
$912$		0			0
$913$		−	5.90396i		−	0.195392i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−35.5991	+	27.3547i	−1.17559	+	0.903332i
$918$		0			0
$919$	−20.8803	−	12.0553i	−0.688779	−	0.397666i	0.114376	−	0.993438i	$-0.463513\pi$
$919$	−20.8803	−	12.0553i	−0.688779	−	0.397666i	−0.803154	+	0.595771i	$0.796847\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.364812	−	0.631873i	0.0120079	−	0.0207984i
$924$		0			0
$925$	−0.423685	−	0.733844i	−0.0139307	−	0.0241287i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	7.13159i		−	0.233980i	−0.993133	−	0.116990i	$-0.962675\pi$
$929$		−	7.13159i		−	0.233980i	0.993133	−	0.116990i	$-0.0373245\pi$
$930$		0			0
$931$	−11.4554	+	42.9866i	−0.375436	+	1.40883i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	15.8770	−	9.16658i	0.519233	−	0.299779i
$936$		0			0
$937$		−	0.272222i		−	0.00889310i	−0.999990	−	0.00444655i	$-0.998585\pi$
$937$		−	0.272222i		−	0.00889310i	0.999990	−	0.00444655i	$-0.00141539\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	38.9456i		−	1.26959i	−0.772680	−	0.634795i	$-0.781084\pi$
$941$		−	38.9456i		−	1.26959i	0.772680	−	0.634795i	$-0.218916\pi$
$942$		0			0
$943$	36.7915			1.19810
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	23.6886i		−	0.769775i	−0.922964	−	0.384887i	$-0.874240\pi$
$947$		−	23.6886i		−	0.769775i	0.922964	−	0.384887i	$-0.125760\pi$
$948$		0			0
$949$	4.91695			0.159611
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.1882			−1.39900			−0.699501	−	0.714631i	$-0.746594\pi$
$953$	−43.1882			−1.39900			−0.699501	+	0.714631i	$0.746594\pi$
$954$		0			0
$955$	1.16641	+	2.02028i	0.0377441	+	0.0653746i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.0227	+	4.55693i	0.355940	+	0.147151i
$960$		0			0
$961$	48.6681			1.56994
$962$		0			0
$963$		0			0
$964$		0			0
$965$	20.4966	−	11.8337i	0.659810	−	0.380942i
$966$		0			0
$967$	−11.0764	−	6.39497i	−0.356193	−	0.205648i	0.311216	−	0.950339i	$-0.399264\pi$
$967$	−11.0764	−	6.39497i	−0.356193	−	0.205648i	−0.667410	+	0.744691i	$0.732597\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.52582	−	4.37484i	0.0810573	−	0.140395i	−0.822647	−	0.568552i	$-0.807504\pi$
$971$	2.52582	−	4.37484i	0.0810573	−	0.140395i	0.903704	+	0.428157i	$0.140837\pi$
$972$		0			0
$973$	−6.43674	−	2.66104i	−0.206352	−	0.0853092i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.4724			−0.367034			−0.183517	−	0.983016i	$-0.558748\pi$
$977$	−11.4724			−0.367034			−0.183517	+	0.983016i	$0.558748\pi$
$978$		0			0
$979$	−35.0356	−	60.6834i	−1.11974	−	1.93945i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.2544	−	36.8137i	0.677910	−	1.17417i	−0.297699	−	0.954660i	$-0.596219\pi$
$983$	21.2544	−	36.8137i	0.677910	−	1.17417i	0.975609	−	0.219515i	$-0.0704474\pi$
$984$		0			0
$985$	−14.0680	+	8.12219i	−0.448245	+	0.258794i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.9866	−	31.1538i	0.571941	−	0.990632i
$990$		0			0
$991$	−8.80965	+	5.08625i	−0.279848	+	0.161570i	−0.633355	−	0.773862i	$-0.718322\pi$
$991$	−8.80965	+	5.08625i	−0.279848	+	0.161570i	0.353507	+	0.935432i	$0.384989\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−33.3838	−	19.2741i	−1.05834	−	0.611031i
$996$		0			0
$997$	−1.21975	−	0.704225i	−0.0386300	−	0.0223030i	0.480561	−	0.876961i	$-0.340433\pi$
$997$	−1.21975	−	0.704225i	−0.0386300	−	0.0223030i	−0.519191	+	0.854658i	$0.673767\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cz.g.1279.10		24
3.2	odd	2		1008.2.cz.h.607.10	yes	24
4.3	odd	2		3024.2.cz.h.1279.10		24
7.3	odd	6		3024.2.bf.g.1711.3		24
9.2	odd	6		1008.2.bf.g.943.3	yes	24
9.7	even	3		3024.2.bf.h.2287.10		24
12.11	even	2		1008.2.cz.g.607.3	yes	24
21.17	even	6		1008.2.bf.h.31.10	yes	24
28.3	even	6		3024.2.bf.h.1711.3		24
36.7	odd	6		3024.2.bf.g.2287.10		24
36.11	even	6		1008.2.bf.h.943.10	yes	24
63.38	even	6		1008.2.cz.g.367.3	yes	24
63.52	odd	6		3024.2.cz.h.2719.10		24
84.59	odd	6		1008.2.bf.g.31.3	✓	24
252.115	even	6	inner	3024.2.cz.g.2719.10		24
252.227	odd	6		1008.2.cz.h.367.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.3	✓	24	84.59	odd	6
1008.2.bf.g.943.3	yes	24	9.2	odd	6
1008.2.bf.h.31.10	yes	24	21.17	even	6
1008.2.bf.h.943.10	yes	24	36.11	even	6
1008.2.cz.g.367.3	yes	24	63.38	even	6
1008.2.cz.g.607.3	yes	24	12.11	even	2
1008.2.cz.h.367.10	yes	24	252.227	odd	6
1008.2.cz.h.607.10	yes	24	3.2	odd	2
3024.2.bf.g.1711.3		24	7.3	odd	6
3024.2.bf.g.2287.10		24	36.7	odd	6
3024.2.bf.h.1711.3		24	28.3	even	6
3024.2.bf.h.2287.10		24	9.7	even	3
3024.2.cz.g.1279.10		24	1.1	even	1	trivial
3024.2.cz.g.2719.10		24	252.115	even	6	inner
3024.2.cz.h.1279.10		24	4.3	odd	2
3024.2.cz.h.2719.10		24	63.52	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10605 - 1.21593i) q^{5} +(-0.347128 - 2.62288i) q^{7} +O(q^{10})\)	\(q+(2.10605 - 1.21593i) q^{5} +(-0.347128 - 2.62288i) q^{7} +(3.88819 + 2.24485i) q^{11} +(0.395715 + 0.228466i) q^{13} +(1.45416 - 0.839559i) q^{17} +(3.17762 - 5.50381i) q^{19} +(3.03876 - 1.75443i) q^{23} +(0.456976 - 0.791506i) q^{25} +(1.38240 + 2.39439i) q^{29} -8.92570 q^{31} +(-3.92031 - 5.10184i) q^{35} +(0.463575 - 0.802935i) q^{37} +(9.08056 + 5.24267i) q^{41} +(8.87861 - 5.12607i) q^{43} -8.39449 q^{47} +(-6.75900 + 1.82095i) q^{49} +(4.91938 + 8.52062i) q^{53} +10.9183 q^{55} -6.45074 q^{59} +5.31355i q^{61} +1.11120 q^{65} -13.6441i q^{67} -1.59679i q^{71} +(9.31911 - 5.38039i) q^{73} +(4.53827 - 10.9775i) q^{77} +10.3204i q^{79} +(-0.657501 - 1.13882i) q^{83} +(2.04169 - 3.53632i) q^{85} +(-13.5161 - 7.80355i) q^{89} +(0.461876 - 1.11722i) q^{91} -15.4551i q^{95} +(-5.69780 + 3.28963i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 4 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 - 4 * q^7	\( 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55} - 12 q^{59} + 48 q^{73} + 48 q^{77} - 48 q^{83} - 21 q^{85} - 39 q^{89} - 9 q^{91} + 3 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more