LMFDB - Embedded newform 3024.2.bf.h.1711.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1711,3024)]

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, 1]))

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

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

chi := DirichletCharacter("3024.1711");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bf (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			1711.7
Character	$\chi$	$=$	3024.1711
Dual form			3024.2.bf.h.2287.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.280665i q^{5} +(-0.164674 - 2.64062i) q^{7} -2.82201i q^{11} +(-4.06955 - 2.34956i) q^{13} +(7.00051 + 4.04175i) q^{17} +(0.474304 + 0.821518i) q^{19} +0.392466i q^{23} +4.92123 q^{25} +(-1.51148 - 2.61795i) q^{29} +(-1.06355 - 1.84211i) q^{31} +(-0.741129 + 0.0462181i) q^{35} +(-2.43458 - 4.21681i) q^{37} +(0.478990 + 0.276545i) q^{41} +(4.28515 - 2.47404i) q^{43} +(1.39435 - 2.41508i) q^{47} +(-6.94577 + 0.869682i) q^{49} +(-6.21935 + 10.7722i) q^{53} -0.792039 q^{55} +(-5.70053 - 9.87361i) q^{59} +(-9.67619 - 5.58655i) q^{61} +(-0.659437 + 1.14218i) q^{65} +(7.85871 - 4.53723i) q^{67} +1.54594i q^{71} +(-0.542172 - 0.313023i) q^{73} +(-7.45187 + 0.464711i) q^{77} +(-13.3691 - 7.71866i) q^{79} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(-9.90157 + 5.71667i) q^{89} +(-5.53414 + 11.1331i) q^{91} +(0.230571 - 0.133120i) q^{95} +(-13.6260 + 7.86698i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{7} + 3 q^{13} + 3 q^{17} + 4 q^{19} - 30 q^{25} - 18 q^{29} + 17 q^{31} - 42 q^{35} - 3 q^{37} + 36 q^{41} + 24 q^{43} + 21 q^{47} - 24 q^{49} + 12 q^{53} + 30 q^{55} + 6 q^{59} - 48 q^{61}+ \cdots - 3 q^{97}+O(q^{100}) $ 24 * q + 8 * q^7 + 3 * q^13 + 3 * q^17 + 4 * q^19 - 30 * q^25 - 18 * q^29 + 17 * q^31 - 42 * q^35 - 3 * q^37 + 36 * q^41 + 24 * q^43 + 21 * q^47 - 24 * q^49 + 12 * q^53 + 30 * q^55 + 6 * q^59 - 48 * q^61 + 42 * q^67 + 48 * q^73 - 36 * q^77 - 30 * q^79 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 33 * q^95 - 3 * q^97

Character values

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

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

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
$5$		−	0.280665i		−	0.125517i	−0.998029	−	0.0627585i	$-0.980010\pi$
$5$		−	0.280665i		−	0.125517i	0.998029	−	0.0627585i	$-0.0199898\pi$
$6$		0			0
$7$	−0.164674	−	2.64062i	−0.0622408	−	0.998061i
$7$	−0.164674	−	2.64062i	−0.0622408	−	0.998061i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.82201i		−	0.850869i	−0.904989	−	0.425434i	$-0.860121\pi$
$11$		−	2.82201i		−	0.850869i	0.904989	−	0.425434i	$-0.139879\pi$
$12$		0			0
$13$	−4.06955	−	2.34956i	−1.12869	−	0.651650i	−0.185085	−	0.982722i	$-0.559256\pi$
$13$	−4.06955	−	2.34956i	−1.12869	−	0.651650i	−0.943605	+	0.331073i	$0.892589\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.00051	+	4.04175i	1.69787	+	0.980268i	0.947774	+	0.318944i	$0.103328\pi$
$17$	7.00051	+	4.04175i	1.69787	+	0.980268i	0.750100	+	0.661324i	$0.230005\pi$
$18$		0			0
$19$	0.474304	+	0.821518i	0.108813	+	0.188469i	0.915290	−	0.402797i	$-0.131962\pi$
$19$	0.474304	+	0.821518i	0.108813	+	0.188469i	−0.806477	+	0.591266i	$0.798628\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			0.392466i			0.0818348i	0.999163	+	0.0409174i	$0.0130280\pi$
$23$			0.392466i			0.0818348i	−0.999163	+	0.0409174i	$0.986972\pi$
$24$		0			0
$25$	4.92123			0.984245
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.51148	−	2.61795i	−0.280674	−	0.486142i	0.690877	−	0.722973i	$-0.257225\pi$
$29$	−1.51148	−	2.61795i	−0.280674	−	0.486142i	−0.971551	+	0.236831i	$0.923891\pi$
$30$		0			0
$31$	−1.06355	−	1.84211i	−0.191018	−	0.330854i	0.754570	−	0.656220i	$-0.227846\pi$
$31$	−1.06355	−	1.84211i	−0.191018	−	0.330854i	−0.945588	+	0.325366i	$0.894512\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.741129	+	0.0462181i	−0.125274	+	0.00781229i
$36$		0			0
$37$	−2.43458	−	4.21681i	−0.400242	−	0.693240i	0.593513	−	0.804825i	$-0.297741\pi$
$37$	−2.43458	−	4.21681i	−0.400242	−	0.693240i	−0.993755	+	0.111585i	$0.964407\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.478990	+	0.276545i	0.0748057	+	0.0431891i	0.536936	−	0.843623i	$-0.319582\pi$
$41$	0.478990	+	0.276545i	0.0748057	+	0.0431891i	−0.462131	+	0.886812i	$0.652915\pi$
$42$		0			0
$43$	4.28515	−	2.47404i	0.653480	−	0.377287i	−0.136308	−	0.990666i	$-0.543524\pi$
$43$	4.28515	−	2.47404i	0.653480	−	0.377287i	0.789788	+	0.613380i	$0.210190\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.39435	−	2.41508i	0.203387	−	0.352276i	−0.746231	−	0.665687i	$-0.768138\pi$
$47$	1.39435	−	2.41508i	0.203387	−	0.352276i	0.949618	+	0.313411i	$0.101472\pi$
$48$		0			0
$49$	−6.94577	+	0.869682i	−0.992252	+	0.124240i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.21935	+	10.7722i	−0.854293	+	1.47968i	0.0230067	+	0.999735i	$0.492676\pi$
$53$	−6.21935	+	10.7722i	−0.854293	+	1.47968i	−0.877300	+	0.479943i	$0.840657\pi$
$54$		0			0
$55$	−0.792039			−0.106799
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.70053	−	9.87361i	−0.742146	−	1.28543i	−0.951516	−	0.307598i	$-0.900475\pi$
$59$	−5.70053	−	9.87361i	−0.742146	−	1.28543i	0.209371	−	0.977836i	$-0.432859\pi$
$60$		0			0
$61$	−9.67619	−	5.58655i	−1.23891	−	0.715284i	−0.270038	−	0.962850i	$-0.587036\pi$
$61$	−9.67619	−	5.58655i	−1.23891	−	0.715284i	−0.968871	+	0.247565i	$0.920370\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.659437	+	1.14218i	−0.0817932	+	0.141670i
$66$		0			0
$67$	7.85871	−	4.53723i	0.960095	−	0.554311i	0.0638926	−	0.997957i	$-0.479648\pi$
$67$	7.85871	−	4.53723i	0.960095	−	0.554311i	0.896202	+	0.443646i	$0.146315\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.54594i			0.183469i	0.995784	+	0.0917344i	$0.0292411\pi$
$71$			1.54594i			0.183469i	−0.995784	+	0.0917344i	$0.970759\pi$
$72$		0			0
$73$	−0.542172	−	0.313023i	−0.0634564	−	0.0366366i	0.467936	−	0.883762i	$-0.344998\pi$
$73$	−0.542172	−	0.313023i	−0.0634564	−	0.0366366i	−0.531393	+	0.847126i	$0.678331\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.45187	+	0.464711i	−0.849219	+	0.0529588i
$78$		0			0
$79$	−13.3691	−	7.71866i	−1.50414	−	0.868417i	−0.999988	−	0.00480263i	$-0.998471\pi$
$79$	−13.3691	−	7.71866i	−1.50414	−	0.868417i	−0.504153	−	0.863614i	$-0.668195\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.30821	−	9.19409i	−0.582652	−	1.00918i	−0.995164	−	0.0982303i	$-0.968682\pi$
$83$	−5.30821	−	9.19409i	−0.582652	−	1.00918i	0.412512	−	0.910952i	$-0.364652\pi$
$84$		0			0
$85$	1.13438	−	1.96480i	0.123040	−	0.213112i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.90157	+	5.71667i	−1.04956	+	0.605966i	−0.922527	−	0.385932i	$-0.873880\pi$
$89$	−9.90157	+	5.71667i	−1.04956	+	0.605966i	−0.127037	+	0.991898i	$0.540547\pi$
$90$		0			0
$91$	−5.53414	+	11.1331i	−0.580136	+	1.16706i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.230571	−	0.133120i	0.0236561	−	0.0136579i
$96$		0			0
$97$	−13.6260	+	7.86698i	−1.38351	+	0.798770i	−0.992573	−	0.121647i	$-0.961182\pi$
$97$	−13.6260	+	7.86698i	−1.38351	+	0.798770i	−0.390937	+	0.920417i	$0.627849\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			7.01091i			0.697611i	0.937195	+	0.348806i	$0.113413\pi$
$101$			7.01091i			0.697611i	−0.937195	+	0.348806i	$0.886587\pi$
$102$		0			0
$103$	5.63248			0.554985			0.277493	−	0.960728i	$-0.410497\pi$
$103$	5.63248			0.554985			0.277493	+	0.960728i	$0.410497\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.00552	+	2.88994i	−0.483902	+	0.279381i	−0.722041	−	0.691850i	$-0.756796\pi$
$107$	−5.00552	+	2.88994i	−0.483902	+	0.279381i	0.238139	+	0.971231i	$0.423463\pi$
$108$		0			0
$109$	4.12859	−	7.15092i	0.395447	−	0.684934i	−0.597711	−	0.801712i	$-0.703923\pi$
$109$	4.12859	−	7.15092i	0.395447	−	0.684934i	0.993158	+	0.116777i	$0.0372564\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.47539	−	11.2157i	0.609154	−	1.05508i	−0.382227	−	0.924069i	$-0.624843\pi$
$113$	6.47539	−	11.2157i	0.609154	−	1.05508i	0.991380	−	0.131016i	$-0.0418240\pi$
$114$		0			0
$115$	0.110151			0.0102717
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.51993	−	19.1513i	0.872690	−	1.75559i
$120$		0			0
$121$	3.03625			0.276023
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	2.78454i		−	0.249057i
$126$		0			0
$127$		−	7.77236i		−	0.689685i	−0.938660	−	0.344843i	$-0.887932\pi$
$127$		−	7.77236i		−	0.689685i	0.938660	−	0.344843i	$-0.112068\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.98542			0.697690			0.348845	−	0.937180i	$-0.386574\pi$
$131$	7.98542			0.697690			0.348845	+	0.937180i	$0.386574\pi$
$132$		0			0
$133$	2.09121	−	1.38774i	0.181331	−	0.120332i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.64941			−0.738969			−0.369484	−	0.929237i	$-0.620466\pi$
$137$	−8.64941			−0.738969			−0.369484	+	0.929237i	$0.620466\pi$
$138$		0			0
$139$	7.19469	−	12.4616i	0.610246	−	1.05698i	−0.380953	−	0.924595i	$-0.624404\pi$
$139$	7.19469	−	12.4616i	0.610246	−	1.05698i	0.991199	−	0.132383i	$-0.0422627\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.63048	+	11.4843i	−0.554468	+	0.960367i
$144$		0			0
$145$	−0.734767	+	0.424218i	−0.0610191	+	0.0352294i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.06764			0.0874644			0.0437322	−	0.999043i	$-0.486075\pi$
$149$	1.06764			0.0874644			0.0437322	+	0.999043i	$0.486075\pi$
$150$		0			0
$151$			12.9439i			1.05336i	0.850064	+	0.526679i	$0.176563\pi$
$151$			12.9439i			1.05336i	−0.850064	+	0.526679i	$0.823437\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.517016	+	0.298500i	−0.0415278	+	0.0239761i
$156$		0			0
$157$	7.01702	−	4.05128i	0.560019	−	0.323327i	−0.193134	−	0.981172i	$-0.561865\pi$
$157$	7.01702	−	4.05128i	0.560019	−	0.323327i	0.753153	+	0.657845i	$0.228532\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.03635	−	0.0646288i	0.0816761	−	0.00509346i
$162$		0			0
$163$	15.8164	−	9.13162i	1.23884	−	0.715244i	0.269982	−	0.962865i	$-0.412982\pi$
$163$	15.8164	−	9.13162i	1.23884	−	0.715244i	0.968857	+	0.247621i	$0.0796489\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.41991	+	14.5837i	−0.651553	+	1.12852i	0.331194	+	0.943563i	$0.392549\pi$
$167$	−8.41991	+	14.5837i	−0.651553	+	1.12852i	−0.982746	+	0.184959i	$0.940785\pi$
$168$		0			0
$169$	4.54083	+	7.86496i	0.349295	+	0.604997i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.1823	+	9.92020i	1.30635	+	0.754219i	0.981484	−	0.191543i	$-0.0613492\pi$
$173$	17.1823	+	9.92020i	1.30635	+	0.754219i	0.324861	+	0.945762i	$0.394682\pi$
$174$		0			0
$175$	−0.810397	−	12.9951i	−0.0612603	−	0.982337i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−21.5488	−	12.4412i	−1.61063	−	0.929899i	−0.989224	−	0.146413i	$-0.953227\pi$
$179$	−21.5488	−	12.4412i	−1.61063	−	0.929899i	−0.621409	−	0.783486i	$-0.713439\pi$
$180$		0			0
$181$			7.30569i			0.543027i	0.962435	+	0.271514i	$0.0875242\pi$
$181$			7.30569i			0.543027i	−0.962435	+	0.271514i	$0.912476\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.18351	+	0.683300i	−0.0870134	+	0.0502372i
$186$		0			0
$187$	11.4059	−	19.7555i	0.834079	−	1.44467i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.11844	−	4.10983i	−0.515072	−	0.297377i	0.219844	−	0.975535i	$-0.429445\pi$
$191$	−7.11844	−	4.10983i	−0.515072	−	0.297377i	−0.734916	+	0.678158i	$0.762778\pi$
$192$		0			0
$193$	−9.78487	−	16.9479i	−0.704331	−	1.21994i	−0.966933	−	0.255032i	$-0.917914\pi$
$193$	−9.78487	−	16.9479i	−0.704331	−	1.21994i	0.262602	−	0.964904i	$-0.415419\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.3933			−1.16797			−0.583987	−	0.811763i	$-0.698508\pi$
$197$	−16.3933			−1.16797			−0.583987	+	0.811763i	$0.698508\pi$
$198$		0			0
$199$	7.86905	−	13.6296i	0.557822	−	0.966176i	−0.439856	−	0.898068i	$-0.644971\pi$
$199$	7.86905	−	13.6296i	0.557822	−	0.966176i	0.997678	−	0.0681077i	$-0.0216961\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.66413	+	4.42235i	−0.467730	+	0.310388i
$204$		0			0
$205$	0.0776164	−	0.134436i	0.00542097	−	0.00938939i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.31833	−	1.33849i	0.160363	−	0.0925854i
$210$		0			0
$211$	7.41442	+	4.28072i	0.510430	+	0.294697i	0.733010	−	0.680218i	$-0.238115\pi$
$211$	7.41442	+	4.28072i	0.510430	+	0.294697i	−0.222581	+	0.974914i	$0.571448\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.694374	−	1.20269i	−0.0473559	−	0.0820229i
$216$		0			0
$217$	−4.68919	+	3.11177i	−0.318323	+	0.211241i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.9926	−	32.8962i	−1.27758	−	2.21284i
$222$		0			0
$223$	−9.63167	−	16.6825i	−0.644984	−	1.11715i	−0.984305	−	0.176475i	$-0.943531\pi$
$223$	−9.63167	−	16.6825i	−0.644984	−	1.11715i	0.339321	−	0.940671i	$-0.389803\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−20.6399			−1.36992			−0.684960	−	0.728581i	$-0.740180\pi$
$227$	−20.6399			−1.36992			−0.684960	+	0.728581i	$0.740180\pi$
$228$		0			0
$229$			21.1950i			1.40060i	0.713848	+	0.700301i	$0.246951\pi$
$229$			21.1950i			1.40060i	−0.713848	+	0.700301i	$0.753049\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.78510	+	13.4842i	0.510019	+	0.883378i	0.999933	+	0.0116076i	$0.00369490\pi$
$233$	7.78510	+	13.4842i	0.510019	+	0.883378i	−0.489914	+	0.871771i	$0.662972\pi$
$234$		0			0
$235$	−0.677828	−	0.391344i	−0.0442167	−	0.0255285i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.36686	−	3.67591i	−0.411838	−	0.237775i	0.279741	−	0.960075i	$-0.409751\pi$
$239$	−6.36686	−	3.67591i	−0.411838	−	0.237775i	−0.691579	+	0.722301i	$0.743085\pi$
$240$		0			0
$241$			5.75441i			0.370674i	0.982675	+	0.185337i	$0.0593376\pi$
$241$			5.75441i			0.370674i	−0.982675	+	0.185337i	$0.940662\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.244089	+	1.94943i	0.0155943	+	0.124545i
$246$		0			0
$247$		−	4.45762i		−	0.283631i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.9997			1.38861			0.694305	−	0.719681i	$-0.255712\pi$
$251$	21.9997			1.38861			0.694305	+	0.719681i	$0.255712\pi$
$252$		0			0
$253$	1.10754			0.0696306
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	1.45564i		−	0.0908000i	−0.998969	−	0.0454000i	$-0.985544\pi$
$257$		−	1.45564i		−	0.0908000i	0.998969	−	0.0454000i	$-0.0144562\pi$
$258$		0			0
$259$	−10.7341	+	7.12320i	−0.666985	+	0.442614i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	21.2421i		−	1.30984i	−0.755696	−	0.654922i	$-0.772701\pi$
$263$		−	21.2421i		−	1.30984i	0.755696	−	0.654922i	$-0.227299\pi$
$264$		0			0
$265$	3.02338	+	1.74555i	0.185725	+	0.107228i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−17.4754	−	10.0894i	−1.06549	−	0.615162i	−0.138546	−	0.990356i	$-0.544243\pi$
$269$	−17.4754	−	10.0894i	−1.06549	−	0.615162i	−0.926946	+	0.375194i	$0.877576\pi$
$270$		0			0
$271$	8.69232	+	15.0555i	0.528021	+	0.914559i	0.999466	+	0.0326639i	$0.0103991\pi$
$271$	8.69232	+	15.0555i	0.528021	+	0.914559i	−0.471445	+	0.881895i	$0.656268\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	13.8878i		−	0.837464i
$276$		0			0
$277$	1.13376			0.0681208			0.0340604	−	0.999420i	$-0.489156\pi$
$277$	1.13376			0.0681208			0.0340604	+	0.999420i	$0.489156\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.37564	+	11.0429i	0.380339	+	0.658766i	0.991111	−	0.133040i	$-0.0424740\pi$
$281$	6.37564	+	11.0429i	0.380339	+	0.658766i	−0.610772	+	0.791807i	$0.709141\pi$
$282$		0			0
$283$	3.38500	+	5.86300i	0.201218	+	0.348519i	0.948921	−	0.315514i	$-0.102177\pi$
$283$	3.38500	+	5.86300i	0.201218	+	0.348519i	−0.747703	+	0.664033i	$0.768844\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.651374	−	1.31037i	0.0384494	−	0.0773488i
$288$		0			0
$289$	24.1715	+	41.8662i	1.42185	+	2.46272i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.5242	−	6.07616i	−0.614831	−	0.354973i	0.160023	−	0.987113i	$-0.448843\pi$
$293$	−10.5242	−	6.07616i	−0.614831	−	0.354973i	−0.774854	+	0.632140i	$0.782177\pi$
$294$		0			0
$295$	−2.77117	+	1.59994i	−0.161344	+	0.0931519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.922120	−	1.59716i	0.0533276	−	0.0923661i
$300$		0			0
$301$	−7.23864	−	10.9081i	−0.417228	−	0.628730i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.56795	+	2.71576i	−0.0897804	+	0.155504i
$306$		0			0
$307$	−17.3006			−0.987396			−0.493698	−	0.869634i	$-0.664355\pi$
$307$	−17.3006			−0.987396			−0.493698	+	0.869634i	$0.664355\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.2379	+	22.9288i	0.750655	+	1.30017i	0.947505	+	0.319739i	$0.103595\pi$
$311$	13.2379	+	22.9288i	0.750655	+	1.30017i	−0.196850	+	0.980434i	$0.563071\pi$
$312$		0			0
$313$	−3.86883	−	2.23367i	−0.218679	−	0.126255i	0.386659	−	0.922223i	$-0.373629\pi$
$313$	−3.86883	−	2.23367i	−0.218679	−	0.126255i	−0.605339	+	0.795968i	$0.706962\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.7017	−	25.4640i	0.825728	−	1.43020i	−0.0756338	−	0.997136i	$-0.524098\pi$
$317$	14.7017	−	25.4640i	0.825728	−	1.43020i	0.901362	−	0.433067i	$-0.142569\pi$
$318$		0			0
$319$	−7.38790	+	4.26541i	−0.413643	+	0.238817i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			7.66807i			0.426663i
$324$		0			0
$325$	−20.0272	−	11.5627i	−1.11091	−	0.641383i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.60693	−	3.28425i	−0.364252	−	0.181066i
$330$		0			0
$331$	−0.850295	−	0.490918i	−0.0467364	−	0.0269833i	0.476450	−	0.879202i	$-0.341923\pi$
$331$	−0.850295	−	0.490918i	−0.0467364	−	0.0269833i	−0.523186	+	0.852218i	$0.675257\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.27344	−	2.20566i	−0.0695755	−	0.120508i
$336$		0			0
$337$	5.58390	−	9.67160i	0.304174	−	0.526846i	−0.672903	−	0.739731i	$-0.734953\pi$
$337$	5.58390	−	9.67160i	0.304174	−	0.526846i	0.977077	+	0.212885i	$0.0682861\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.19847	+	3.00134i	−0.281513	+	0.162532i
$342$		0			0
$343$	3.44029	+	18.1979i	0.185758	+	0.982596i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.61089	+	4.39415i	−0.408574	+	0.235890i	−0.690177	−	0.723641i	$-0.742467\pi$
$347$	−7.61089	+	4.39415i	−0.408574	+	0.235890i	0.281603	+	0.959531i	$0.409134\pi$
$348$		0			0
$349$	18.2265	−	10.5231i	0.975644	−	0.563288i	0.0746915	−	0.997207i	$-0.476203\pi$
$349$	18.2265	−	10.5231i	0.975644	−	0.563288i	0.900952	+	0.433919i	$0.142869\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			2.64279i			0.140661i	0.997524	+	0.0703307i	$0.0224055\pi$
$353$			2.64279i			0.140661i	−0.997524	+	0.0703307i	$0.977595\pi$
$354$		0			0
$355$	0.433889			0.0230285
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.5571	−	11.8687i	1.08496	−	0.626405i	0.152733	−	0.988267i	$-0.451192\pi$
$359$	20.5571	−	11.8687i	1.08496	−	0.626405i	0.932231	+	0.361863i	$0.117859\pi$
$360$		0			0
$361$	9.05007	−	15.6752i	0.476320	−	0.825010i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.0878545	+	0.152168i	−0.00459852	+	0.00796486i
$366$		0			0
$367$	30.6820			1.60159			0.800793	−	0.598942i	$-0.204412\pi$
$367$	30.6820			1.60159			0.800793	+	0.598942i	$0.204412\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	29.4695	+	14.6490i	1.52998	+	0.760540i
$372$		0			0
$373$	6.58921			0.341176			0.170588	−	0.985342i	$-0.445433\pi$
$373$	6.58921			0.341176			0.170588	+	0.985342i	$0.445433\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			14.2052i			0.731605i
$378$		0			0
$379$			0.316910i			0.0162786i	0.999967	+	0.00813930i	$0.00259085\pi$
$379$			0.316910i			0.0162786i	−0.999967	+	0.00813930i	$0.997409\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.69711			0.188913			0.0944567	−	0.995529i	$-0.469889\pi$
$383$	3.69711			0.188913			0.0944567	+	0.995529i	$0.469889\pi$
$384$		0			0
$385$	0.130428	+	2.09148i	0.00664723	+	0.106591i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.59629			0.435849			0.217925	−	0.975966i	$-0.430071\pi$
$389$	8.59629			0.435849			0.217925	+	0.975966i	$0.430071\pi$
$390$		0			0
$391$	−1.58625	+	2.74746i	−0.0802200	+	0.138945i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.16635	+	3.75224i	−0.109001	+	0.188795i
$396$		0			0
$397$	−10.9255	+	6.30783i	−0.548334	+	0.316581i	−0.748450	−	0.663192i	$-0.769201\pi$
$397$	−10.9255	+	6.30783i	−0.548334	+	0.316581i	0.200116	+	0.979772i	$0.435868\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	26.1292			1.30483			0.652414	−	0.757862i	$-0.273756\pi$
$401$	26.1292			1.30483			0.652414	+	0.757862i	$0.273756\pi$
$402$		0			0
$403$			9.99544i			0.497908i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.8999	+	6.87041i	−0.589856	+	0.340554i
$408$		0			0
$409$	−0.249796	+	0.144220i	−0.0123516	+	0.00713121i	−0.506163	−	0.862438i	$-0.668937\pi$
$409$	−0.249796	+	0.144220i	−0.0123516	+	0.00713121i	0.493811	+	0.869569i	$0.335603\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−25.1337	+	16.6789i	−1.23675	+	0.820713i
$414$		0			0
$415$	−2.58046	+	1.48983i	−0.126670	+	0.0731327i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.56824	+	16.5727i	−0.467439	+	0.809629i	−0.999308	−	0.0371983i	$-0.988157\pi$
$419$	−9.56824	+	16.5727i	−0.467439	+	0.809629i	0.531869	+	0.846827i	$0.321490\pi$
$420$		0			0
$421$	−11.5319	−	19.9738i	−0.562030	−	0.973465i	−0.997319	−	0.0731740i	$-0.976687\pi$
$421$	−11.5319	−	19.9738i	−0.562030	−	0.973465i	0.435289	−	0.900291i	$-0.356646\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	34.4511	+	19.8904i	1.67112	+	0.964824i
$426$		0			0
$427$	−13.1585	+	26.4711i	−0.636787	+	1.28103i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.2196	+	7.63235i	0.636766	+	0.367637i	0.783368	−	0.621558i	$-0.213500\pi$
$431$	13.2196	+	7.63235i	0.636766	+	0.367637i	−0.146601	+	0.989196i	$0.546833\pi$
$432$		0			0
$433$		−	24.5275i		−	1.17871i	−0.807873	−	0.589357i	$-0.799381\pi$
$433$		−	24.5275i		−	1.17871i	0.807873	−	0.589357i	$-0.200619\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.322418	+	0.186148i	−0.0154233	+	0.00890467i
$438$		0			0
$439$	−9.14003	+	15.8310i	−0.436230	+	0.755572i	−0.997395	−	0.0721316i	$-0.977020\pi$
$439$	−9.14003	+	15.8310i	−0.436230	+	0.755572i	0.561165	+	0.827704i	$0.310353\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.51333	+	2.60578i	0.214435	+	0.123804i	0.603371	−	0.797461i	$-0.293824\pi$
$443$	4.51333	+	2.60578i	0.214435	+	0.123804i	−0.388936	+	0.921265i	$0.627157\pi$
$444$		0			0
$445$	1.60447	+	2.77902i	0.0760591	+	0.131738i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.38031			0.442684			0.221342	−	0.975196i	$-0.428956\pi$
$449$	9.38031			0.442684			0.221342	+	0.975196i	$0.428956\pi$
$450$		0			0
$451$	0.780414	−	1.35172i	0.0367482	−	0.0636498i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.12466	+	1.55324i	0.146486	+	0.0728169i
$456$		0			0
$457$	−14.6810	+	25.4283i	−0.686749	+	1.18948i	0.286134	+	0.958190i	$0.407630\pi$
$457$	−14.6810	+	25.4283i	−0.686749	+	1.18948i	−0.972884	+	0.231295i	$0.925704\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.10606	+	0.638584i	−0.0515144	+	0.0297418i	−0.525536	−	0.850771i	$-0.676135\pi$
$461$	−1.10606	+	0.638584i	−0.0515144	+	0.0297418i	0.474022	+	0.880513i	$0.342802\pi$
$462$		0			0
$463$	−23.8988	−	13.7980i	−1.11067	−	0.641247i	−0.171669	−	0.985155i	$-0.554916\pi$
$463$	−23.8988	−	13.7980i	−1.11067	−	0.641247i	−0.939004	+	0.343907i	$0.888249\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.00656	+	8.67162i	0.231676	+	0.401275i	0.958301	−	0.285759i	$-0.0922458\pi$
$467$	5.00656	+	8.67162i	0.231676	+	0.401275i	−0.726625	+	0.687034i	$0.758912\pi$
$468$		0			0
$469$	−13.2752	−	20.0047i	−0.612993	−	0.923733i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.98176	−	12.0928i	−0.321022	−	0.556026i
$474$		0			0
$475$	2.33416	+	4.04288i	0.107098	+	0.185500i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.7895			−0.675749			−0.337874	−	0.941191i	$-0.609708\pi$
$479$	−14.7895			−0.675749			−0.337874	+	0.941191i	$0.609708\pi$
$480$		0			0
$481$			22.8807i			1.04327i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.20798	+	3.82434i	0.100259	+	0.173654i
$486$		0			0
$487$	−12.8101	−	7.39589i	−0.580479	−	0.335140i	0.180845	−	0.983512i	$-0.442117\pi$
$487$	−12.8101	−	7.39589i	−0.580479	−	0.335140i	−0.761324	+	0.648372i	$0.775450\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.5410	−	7.24053i	−0.565966	−	0.326760i	0.189571	−	0.981867i	$-0.439290\pi$
$491$	−12.5410	−	7.24053i	−0.565966	−	0.326760i	−0.755536	+	0.655107i	$0.772624\pi$
$492$		0			0
$493$		−	24.4360i		−	1.10054i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.08223	−	0.254575i	0.183113	−	0.0114193i
$498$		0			0
$499$		−	8.69119i		−	0.389071i	−0.980895	−	0.194536i	$-0.937680\pi$
$499$		−	8.69119i		−	0.389071i	0.980895	−	0.194536i	$-0.0623200\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	40.3239			1.79795			0.898977	−	0.437995i	$-0.144311\pi$
$503$	40.3239			1.79795			0.898977	+	0.437995i	$0.144311\pi$
$504$		0			0
$505$	1.96771			0.0875621
$506$		0			0
$507$		0			0
$508$		0			0
$509$			3.37858i			0.149753i	0.997193	+	0.0748764i	$0.0238562\pi$
$509$			3.37858i			0.149753i	−0.997193	+	0.0748764i	$0.976144\pi$
$510$		0			0
$511$	−0.737294	+	1.48322i	−0.0326160	+	0.0656137i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	1.58084i		−	0.0696601i
$516$		0			0
$517$	−6.81539	−	3.93487i	−0.299741	−	0.173055i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	34.6315	+	19.9945i	1.51723	+	0.875976i	0.999795	+	0.0202566i	$0.00644831\pi$
$521$	34.6315	+	19.9945i	1.51723	+	0.875976i	0.517440	+	0.855719i	$0.326885\pi$
$522$		0			0
$523$	−6.43351	−	11.1432i	−0.281318	−	0.487257i	0.690392	−	0.723436i	$-0.257438\pi$
$523$	−6.43351	−	11.1432i	−0.281318	−	0.487257i	−0.971710	+	0.236179i	$0.924105\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	17.1943i		−	0.748997i
$528$		0			0
$529$	22.8460			0.993303
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.29952	−	2.25083i	−0.0562883	−	0.0974942i
$534$		0			0
$535$	0.811103	+	1.40487i	0.0350671	+	0.0607379i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.45425	+	19.6010i	0.105712	+	0.844276i
$540$		0			0
$541$	−2.79138	−	4.83481i	−0.120011	−	0.207865i	0.799761	−	0.600319i	$-0.204960\pi$
$541$	−2.79138	−	4.83481i	−0.120011	−	0.207865i	−0.919772	+	0.392454i	$0.871626\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.00701	−	1.15875i	−0.0859709	−	0.0496353i
$546$		0			0
$547$	−9.37486	+	5.41258i	−0.400840	+	0.231425i	−0.686846	−	0.726803i	$-0.741006\pi$
$547$	−9.37486	+	5.41258i	−0.400840	+	0.231425i	0.286006	+	0.958228i	$0.407672\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.43380	−	2.48341i	0.0610819	−	0.105797i
$552$		0			0
$553$	−18.1805	+	36.5738i	−0.773114	+	1.55528i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.38879	+	14.5298i	−0.355445	+	0.615648i	−0.987194	−	0.159525i	$-0.949004\pi$
$557$	−8.38879	+	14.5298i	−0.355445	+	0.615648i	0.631749	+	0.775173i	$0.282337\pi$
$558$		0			0
$559$	−23.2515			−0.983436
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.3360	−	24.8307i	−0.604192	−	1.04649i	−0.992179	−	0.124826i	$-0.960163\pi$
$563$	−14.3360	−	24.8307i	−0.604192	−	1.04649i	0.387987	−	0.921665i	$-0.373171\pi$
$564$		0			0
$565$	−3.14785	−	1.81741i	−0.132431	−	0.0764592i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.6286	−	28.8015i	0.697106	−	1.20742i	−0.272360	−	0.962195i	$-0.587804\pi$
$569$	16.6286	−	28.8015i	0.697106	−	1.20742i	0.969466	−	0.245227i	$-0.0788625\pi$
$570$		0			0
$571$	−28.2309	+	16.2991i	−1.18143	+	0.682097i	−0.956344	−	0.292243i	$-0.905598\pi$
$571$	−28.2309	+	16.2991i	−1.18143	+	0.682097i	−0.225082	+	0.974340i	$0.572265\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.93141i			0.0805455i
$576$		0			0
$577$	11.6155	+	6.70622i	0.483560	+	0.279183i	0.721899	−	0.691999i	$-0.243270\pi$
$577$	11.6155	+	6.70622i	0.483560	+	0.279183i	−0.238339	+	0.971182i	$0.576603\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.4040	+	15.5310i	−0.970961	+	0.644334i
$582$		0			0
$583$	30.3993	+	17.5511i	1.25901	+	0.726891i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.2883	+	29.9443i	0.713566	+	1.23593i	0.963510	+	0.267673i	$0.0862546\pi$
$587$	17.2883	+	29.9443i	0.713566	+	1.23593i	−0.249943	+	0.968260i	$0.580412\pi$
$588$		0			0
$589$	1.00889	−	1.74744i	0.0415705	−	0.0720022i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.9169	+	9.76697i	−0.694693	+	0.401081i	−0.805368	−	0.592775i	$-0.798032\pi$
$593$	−16.9169	+	9.76697i	−0.694693	+	0.401081i	0.110675	+	0.993857i	$0.464699\pi$
$594$		0			0
$595$	−5.37509	−	2.67191i	−0.220357	−	0.109538i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.5524	+	8.40186i	−0.594597	+	0.343291i	−0.766913	−	0.641751i	$-0.778208\pi$
$599$	−14.5524	+	8.40186i	−0.594597	+	0.343291i	0.172316	+	0.985042i	$0.444875\pi$
$600$		0			0
$601$	−6.18993	+	3.57376i	−0.252492	+	0.145777i	−0.620905	−	0.783886i	$-0.713235\pi$
$601$	−6.18993	+	3.57376i	−0.252492	+	0.145777i	0.368413	+	0.929662i	$0.379901\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	0.852167i		−	0.0346455i
$606$		0			0
$607$	17.8635			0.725058			0.362529	−	0.931972i	$-0.381913\pi$
$607$	17.8635			0.725058			0.362529	+	0.931972i	$0.381913\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.3488	+	6.55220i	−0.459121	+	0.265074i
$612$		0			0
$613$	9.85193	−	17.0640i	0.397916	−	0.689210i	−0.595553	−	0.803316i	$-0.703067\pi$
$613$	9.85193	−	17.0640i	0.397916	−	0.689210i	0.993469	+	0.114106i	$0.0364003\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.2946	−	26.4910i	0.615738	−	1.06649i	−0.374517	−	0.927220i	$-0.622191\pi$
$617$	15.2946	−	26.4910i	0.615738	−	1.06649i	0.990255	−	0.139269i	$-0.0444752\pi$
$618$		0			0
$619$	12.8995			0.518475			0.259237	−	0.965814i	$-0.416529\pi$
$619$	12.8995			0.518475			0.259237	+	0.965814i	$0.416529\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.7261	+	25.2049i	0.670117	+	1.00981i
$624$		0			0
$625$	23.8246			0.952985
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	39.3598i		−	1.56938i
$630$		0			0
$631$			16.8826i			0.672085i	0.941847	+	0.336042i	$0.109089\pi$
$631$			16.8826i			0.672085i	−0.941847	+	0.336042i	$0.890911\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.18143			−0.0865673
$636$		0			0
$637$	30.3095	+	12.7803i	1.20091	+	0.506372i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.2901			−0.485429			−0.242715	−	0.970098i	$-0.578038\pi$
$641$	−12.2901			−0.485429			−0.242715	+	0.970098i	$0.578038\pi$
$642$		0			0
$643$	−20.2664	+	35.1024i	−0.799228	+	1.38430i	0.120891	+	0.992666i	$0.461425\pi$
$643$	−20.2664	+	35.1024i	−0.799228	+	1.38430i	−0.920119	+	0.391638i	$0.871909\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.3850	−	21.4515i	0.486905	−	0.843344i	−0.512982	−	0.858400i	$-0.671459\pi$
$647$	12.3850	−	21.4515i	0.486905	−	0.843344i	0.999887	+	0.0150552i	$0.00479241\pi$
$648$		0			0
$649$	−27.8634	+	16.0870i	−1.09374	+	0.631469i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.6715			0.730671			0.365335	−	0.930876i	$-0.380954\pi$
$653$	18.6715			0.730671			0.365335	+	0.930876i	$0.380954\pi$
$654$		0			0
$655$		−	2.24123i		−	0.0875719i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	39.5720	−	22.8469i	1.54150	−	0.889988i	0.542761	−	0.839887i	$-0.317379\pi$
$659$	39.5720	−	22.8469i	1.54150	−	0.889988i	0.998744	−	0.0501010i	$-0.0159543\pi$
$660$		0			0
$661$	25.4400	−	14.6878i	0.989501	−	0.571289i	0.0843762	−	0.996434i	$-0.473110\pi$
$661$	25.4400	−	14.6878i	0.989501	−	0.571289i	0.905125	+	0.425145i	$0.139777\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.389489	−	0.586930i	−0.0151038	−	0.0227602i
$666$		0			0
$667$	1.02746	−	0.593203i	0.0397833	−	0.0229689i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.7653	+	27.3063i	−0.608613	+	1.05415i
$672$		0			0
$673$	13.3294	+	23.0872i	0.513810	+	0.889945i	0.999872	+	0.0160205i	$0.00509972\pi$
$673$	13.3294	+	23.0872i	0.513810	+	0.889945i	−0.486062	+	0.873925i	$0.661567\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	40.9678	+	23.6528i	1.57452	+	0.909050i	0.995604	+	0.0936633i	$0.0298577\pi$
$677$	40.9678	+	23.6528i	1.57452	+	0.909050i	0.578917	+	0.815387i	$0.303476\pi$
$678$		0			0
$679$	23.0176	+	34.6856i	0.883333	+	1.33111i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	23.6562	+	13.6579i	0.905178	+	0.522605i	0.878877	−	0.477049i	$-0.158294\pi$
$683$	23.6562	+	13.6579i	0.905178	+	0.522605i	0.0263018	+	0.999654i	$0.491627\pi$
$684$		0			0
$685$			2.42758i			0.0927532i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	50.6199	−	29.2254i	1.92846	−	1.11340i
$690$		0			0
$691$	−19.8841	+	34.4403i	−0.756427	+	1.31017i	0.188235	+	0.982124i	$0.439723\pi$
$691$	−19.8841	+	34.4403i	−0.756427	+	1.31017i	−0.944662	+	0.328046i	$0.893610\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.49752	−	2.01930i	−0.132669	−	0.0765963i
$696$		0			0
$697$	2.23545	+	3.87192i	0.0846738	+	0.146659i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	33.5286			1.26636			0.633180	−	0.774005i	$-0.281749\pi$
$701$	33.5286			1.26636			0.633180	+	0.774005i	$0.281749\pi$
$702$		0			0
$703$	2.30946	−	4.00010i	0.0871029	−	0.150867i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18.5132	−	1.15451i	0.696259	−	0.0434199i
$708$		0			0
$709$	15.1763	−	26.2860i	0.569956	−	0.987193i	−0.426613	−	0.904434i	$-0.640294\pi$
$709$	15.1763	−	26.2860i	0.569956	−	0.987193i	0.996570	−	0.0827589i	$-0.0263732\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.722967	−	0.417405i	0.0270753	−	0.0156319i
$714$		0			0
$715$	3.22324	+	1.86094i	0.120542	+	0.0695952i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	17.8512	+	30.9192i	0.665737	+	1.15309i	0.979085	+	0.203452i	$0.0652160\pi$
$719$	17.8512	+	30.9192i	0.665737	+	1.15309i	−0.313348	+	0.949638i	$0.601451\pi$
$720$		0			0
$721$	−0.927523	−	14.8733i	−0.0345427	−	0.553909i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.43832	−	12.8835i	−0.276252	−	0.478483i
$726$		0			0
$727$	4.33546	+	7.50924i	0.160793	+	0.278502i	0.935153	−	0.354243i	$-0.115261\pi$
$727$	4.33546	+	7.50924i	0.160793	+	0.278502i	−0.774360	+	0.632745i	$0.781928\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	39.9977			1.47937
$732$		0			0
$733$		−	4.04828i		−	0.149527i	−0.997201	−	0.0747633i	$-0.976180\pi$
$733$		−	4.04828i		−	0.149527i	0.997201	−	0.0747633i	$-0.0238201\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.8041	−	22.1774i	−0.471646	−	0.816915i
$738$		0			0
$739$	18.5401	+	10.7042i	0.682010	+	0.393759i	0.800612	−	0.599183i	$-0.204508\pi$
$739$	18.5401	+	10.7042i	0.682010	+	0.393759i	−0.118602	+	0.992942i	$0.537841\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−43.3251	−	25.0137i	−1.58944	−	0.917665i	−0.993399	−	0.114714i	$-0.963405\pi$
$743$	−43.3251	−	25.0137i	−1.58944	−	0.917665i	−0.596044	−	0.802952i	$-0.703262\pi$
$744$		0			0
$745$		−	0.299649i		−	0.0109783i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.45551	+	12.7418i	0.308958	+	0.465575i
$750$		0			0
$751$			21.3074i			0.777516i	0.921340	+	0.388758i	$0.127096\pi$
$751$			21.3074i			0.777516i	−0.921340	+	0.388758i	$0.872904\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.63289			0.132214
$756$		0			0
$757$	13.2589			0.481904			0.240952	−	0.970537i	$-0.422540\pi$
$757$	13.2589			0.481904			0.240952	+	0.970537i	$0.422540\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			40.2650i			1.45961i	0.683658	+	0.729803i	$0.260388\pi$
$761$			40.2650i			1.45961i	−0.683658	+	0.729803i	$0.739612\pi$
$762$		0			0
$763$	−19.5628	−	9.72447i	−0.708219	−	0.352049i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			53.5749i			1.93448i
$768$		0			0
$769$	−5.51138	−	3.18199i	−0.198745	−	0.114746i	0.397325	−	0.917678i	$-0.369939\pi$
$769$	−5.51138	−	3.18199i	−0.198745	−	0.114746i	−0.596070	+	0.802932i	$0.703272\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−42.9373	−	24.7899i	−1.54435	−	0.891629i	−0.998557	−	0.0537073i	$-0.982896\pi$
$773$	−42.9373	−	24.7899i	−1.54435	−	0.891629i	−0.545790	−	0.837922i	$-0.683770\pi$
$774$		0			0
$775$	−5.23395	−	9.06546i	−0.188009	−	0.325641i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			0.524666i			0.0187981i
$780$		0			0
$781$	4.36265			0.156108
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.13705	−	1.96943i	−0.0405831	−	0.0702919i
$786$		0			0
$787$	−14.1133	−	24.4450i	−0.503086	−	0.871370i	−0.999994	−	0.00356700i	$-0.998865\pi$
$787$	−14.1133	−	24.4450i	−0.503086	−	0.871370i	0.496908	−	0.867803i	$-0.334469\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−30.6828	−	15.2521i	−1.09095	−	0.542303i
$792$		0			0
$793$	26.2518	+	45.4695i	0.932230	+	1.61467i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.6877	−	9.05731i	−0.555688	−	0.320826i	0.195725	−	0.980659i	$-0.437294\pi$
$797$	−15.6877	−	9.05731i	−0.555688	−	0.320826i	−0.751413	+	0.659832i	$0.770627\pi$
$798$		0			0
$799$	19.5223	−	11.2712i	0.690650	−	0.398747i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.883355	+	1.53002i	−0.0311729	+	0.0539931i
$804$		0			0
$805$	−0.0181390	−	0.290868i	−0.000639317	−	0.0102517i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.56171	−	2.70496i	0.0549067	−	0.0951012i	−0.837266	−	0.546796i	$-0.815847\pi$
$809$	1.56171	−	2.70496i	0.0549067	−	0.0951012i	0.892172	+	0.451695i	$0.149181\pi$
$810$		0			0
$811$	9.66660			0.339440			0.169720	−	0.985492i	$-0.445714\pi$
$811$	9.66660			0.339440			0.169720	+	0.985492i	$0.445714\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.56292	−	4.43911i	−0.0897753	−	0.155495i
$816$		0			0
$817$	4.06493	+	2.34689i	0.142214	+	0.0821072i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.4777	−	25.0761i	0.505275	−	0.875162i	−0.494706	−	0.869060i	$-0.664724\pi$
$821$	14.4777	−	25.0761i	0.505275	−	0.875162i	0.999981	−	0.00610201i	$-0.00194234\pi$
$822$		0			0
$823$	−34.4646	+	19.8981i	−1.20136	+	0.693605i	−0.960857	−	0.277043i	$-0.910645\pi$
$823$	−34.4646	+	19.8981i	−1.20136	+	0.693605i	−0.240502	+	0.970649i	$0.577312\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			37.9694i			1.32033i	0.751123	+	0.660163i	$0.229513\pi$
$827$			37.9694i			1.32033i	−0.751123	+	0.660163i	$0.770487\pi$
$828$		0			0
$829$	38.3383	+	22.1346i	1.33154	+	0.768766i	0.985536	−	0.169466i	$-0.0542042\pi$
$829$	38.3383	+	22.1346i	1.33154	+	0.768766i	0.346006	+	0.938232i	$0.387538\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−52.1390	−	21.9848i	−1.80651	−	0.761729i
$834$		0			0
$835$	4.09313	+	2.36317i	0.141649	+	0.0817809i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−16.3128	−	28.2547i	−0.563182	−	0.975460i	−0.997216	−	0.0745634i	$-0.976244\pi$
$839$	−16.3128	−	28.2547i	−0.563182	−	0.975460i	0.434034	−	0.900896i	$-0.357090\pi$
$840$		0			0
$841$	9.93088	−	17.2008i	0.342444	−	0.593130i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.20741	−	1.27445i	0.0759374	−	0.0438425i
$846$		0			0
$847$	−0.499990	−	8.01758i	−0.0171799	−	0.275487i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.65495	−	0.955489i	0.0567311	−	0.0327537i
$852$		0			0
$853$	9.50254	−	5.48629i	0.325361	−	0.187847i	−0.328419	−	0.944532i	$-0.606516\pi$
$853$	9.50254	−	5.48629i	0.325361	−	0.187847i	0.653779	+	0.756685i	$0.273182\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			3.51579i			0.120097i	0.998195	+	0.0600485i	$0.0191255\pi$
$857$			3.51579i			0.120097i	−0.998195	+	0.0600485i	$0.980874\pi$
$858$		0			0
$859$	15.1768			0.517827			0.258913	−	0.965901i	$-0.416636\pi$
$859$	15.1768			0.517827			0.258913	+	0.965901i	$0.416636\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.7041	−	17.1496i	1.01114	−	0.583781i	0.0996133	−	0.995026i	$-0.468239\pi$
$863$	29.7041	−	17.1496i	1.01114	−	0.583781i	0.911525	+	0.411245i	$0.134906\pi$
$864$		0			0
$865$	2.78425	−	4.82246i	0.0946673	−	0.163969i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−21.7821	+	37.7278i	−0.738909	+	1.27983i
$870$		0			0
$871$	−42.6419			−1.44487
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.35291	+	0.458540i	−0.248574	+	0.0155015i
$876$		0			0
$877$	21.2826			0.718664			0.359332	−	0.933210i	$-0.383005\pi$
$877$	21.2826			0.718664			0.359332	+	0.933210i	$0.383005\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			20.5029i			0.690761i	0.938463	+	0.345380i	$0.112250\pi$
$881$			20.5029i			0.690761i	−0.938463	+	0.345380i	$0.887750\pi$
$882$		0			0
$883$		−	39.9687i		−	1.34506i	−0.740072	−	0.672528i	$-0.765209\pi$
$883$		−	39.9687i		−	1.34506i	0.740072	−	0.672528i	$-0.234791\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.3020			1.11817			0.559085	−	0.829110i	$-0.311152\pi$
$887$	33.3020			1.11817			0.559085	+	0.829110i	$0.311152\pi$
$888$		0			0
$889$	−20.5239	+	1.27990i	−0.688348	+	0.0429266i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.64538			0.0885243
$894$		0			0
$895$	−3.49181	+	6.04798i	−0.116718	+	0.202162i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.21505	+	5.56863i	−0.107228	+	0.185724i
$900$		0			0
$901$	−87.0772	+	50.2741i	−2.90096	+	1.67487i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.05045			0.0681592
$906$		0			0
$907$		−	1.71137i		−	0.0568250i	−0.999596	−	0.0284125i	$-0.990955\pi$
$907$		−	1.71137i		−	0.0568250i	0.999596	−	0.0284125i	$-0.00904519\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.22479	−	4.17123i	0.239368	−	0.138199i	−0.375518	−	0.926815i	$-0.622535\pi$
$911$	7.22479	−	4.17123i	0.239368	−	0.138199i	0.614886	+	0.788616i	$0.289202\pi$
$912$		0			0
$913$	−25.9458	+	14.9798i	−0.858682	+	0.495760i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.31499	−	21.0865i	−0.0434248	−	0.696337i
$918$		0			0
$919$	13.4897	−	7.78828i	0.444984	−	0.256911i	−0.260726	−	0.965413i	$-0.583962\pi$
$919$	13.4897	−	7.78828i	0.444984	−	0.256911i	0.705709	+	0.708501i	$0.250628\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.63226	−	6.29126i	0.119557	−	0.207079i
$924$		0			0
$925$	−11.9811	−	20.7519i	−0.393937	−	0.682318i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.11736	−	1.22246i	−0.0694684	−	0.0401076i	0.464863	−	0.885382i	$-0.346103\pi$
$929$	−2.11736	−	1.22246i	−0.0694684	−	0.0401076i	−0.534332	+	0.845275i	$0.679437\pi$
$930$		0			0
$931$	−4.00886	−	5.29358i	−0.131385	−	0.173490i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.54468	−	3.20122i	−0.181330	−	0.104691i
$936$		0			0
$937$		−	2.32069i		−	0.0758137i	−0.999281	−	0.0379069i	$-0.987931\pi$
$937$		−	2.32069i		−	0.0758137i	0.999281	−	0.0379069i	$-0.0120690\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.7718	+	7.95114i	−0.448947	+	0.259200i	−0.707386	−	0.706828i	$-0.750125\pi$
$941$	−13.7718	+	7.95114i	−0.448947	+	0.259200i	0.258438	+	0.966028i	$0.416792\pi$
$942$		0			0
$943$	−0.108534	+	0.187987i	−0.00353437	+	0.00612171i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.4689	−	18.1686i	−1.02260	−	0.590400i	−0.107746	−	0.994178i	$-0.534363\pi$
$947$	−31.4689	−	18.1686i	−1.02260	−	0.590400i	−0.914857	+	0.403778i	$0.867697\pi$
$948$		0			0
$949$	1.47093	+	2.54773i	0.0477484	+	0.0827027i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.1790			0.329730			0.164865	−	0.986316i	$-0.447281\pi$
$953$	10.1790			0.329730			0.164865	+	0.986316i	$0.447281\pi$
$954$		0			0
$955$	−1.15348	+	1.99789i	−0.0373259	+	0.0646503i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.42433	+	22.8398i	0.0459940	+	0.737536i
$960$		0			0
$961$	13.2377	−	22.9284i	0.427024	−	0.739627i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.75668	+	2.74627i	−0.153123	+	0.0884055i
$966$		0			0
$967$	−17.1689	−	9.91247i	−0.552115	−	0.318764i	0.197860	−	0.980230i	$-0.436601\pi$
$967$	−17.1689	−	9.91247i	−0.552115	−	0.318764i	−0.749974	+	0.661467i	$0.769934\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.7738	−	22.1249i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$971$	−12.7738	−	22.1249i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967780\pi$
$972$		0			0
$973$	−34.0911	−	16.9464i	−1.09291	−	0.543276i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.3985	−	19.7428i	−0.364671	−	0.631629i	0.624052	−	0.781383i	$-0.285485\pi$
$977$	−11.3985	−	19.7428i	−0.364671	−	0.631629i	−0.988723	+	0.149754i	$0.952152\pi$
$978$		0			0
$979$	16.1325	+	27.9424i	0.515598	+	0.893041i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−55.9907			−1.78583			−0.892914	−	0.450228i	$-0.851343\pi$
$983$	−55.9907			−1.78583			−0.892914	+	0.450228i	$0.851343\pi$
$984$		0			0
$985$			4.60102i			0.146601i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.970974	+	1.68178i	0.0308752	+	0.0534774i
$990$		0			0
$991$	−21.3062	−	12.3011i	−0.676814	−	0.390759i	0.121840	−	0.992550i	$-0.461121\pi$
$991$	−21.3062	−	12.3011i	−0.676814	−	0.390759i	−0.798653	+	0.601791i	$0.794454\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.82534	−	2.20856i	−0.121272	−	0.0700162i
$996$		0			0
$997$			40.4343i			1.28057i	0.768139	+	0.640283i	$0.221183\pi$
$997$			40.4343i			1.28057i	−0.768139	+	0.640283i	$0.778817\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bf.h.1711.7		24
3.2	odd	2		1008.2.bf.g.31.9	✓	24
4.3	odd	2		3024.2.bf.g.1711.7		24
7.5	odd	6		3024.2.cz.h.1279.6		24
9.2	odd	6		1008.2.cz.h.367.8	yes	24
9.7	even	3		3024.2.cz.g.2719.6		24
12.11	even	2		1008.2.bf.h.31.4	yes	24
21.5	even	6		1008.2.cz.g.607.5	yes	24
28.19	even	6		3024.2.cz.g.1279.6		24
36.7	odd	6		3024.2.cz.h.2719.6		24
36.11	even	6		1008.2.cz.g.367.5	yes	24
63.47	even	6		1008.2.bf.h.943.4	yes	24
63.61	odd	6		3024.2.bf.g.2287.6		24
84.47	odd	6		1008.2.cz.h.607.8	yes	24
252.47	odd	6		1008.2.bf.g.943.9	yes	24
252.187	even	6	inner	3024.2.bf.h.2287.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.9	✓	24	3.2	odd	2
1008.2.bf.g.943.9	yes	24	252.47	odd	6
1008.2.bf.h.31.4	yes	24	12.11	even	2
1008.2.bf.h.943.4	yes	24	63.47	even	6
1008.2.cz.g.367.5	yes	24	36.11	even	6
1008.2.cz.g.607.5	yes	24	21.5	even	6
1008.2.cz.h.367.8	yes	24	9.2	odd	6
1008.2.cz.h.607.8	yes	24	84.47	odd	6
3024.2.bf.g.1711.7		24	4.3	odd	2
3024.2.bf.g.2287.6		24	63.61	odd	6
3024.2.bf.h.1711.7		24	1.1	even	1	trivial
3024.2.bf.h.2287.6		24	252.187	even	6	inner
3024.2.cz.g.1279.6		24	28.19	even	6
3024.2.cz.g.2719.6		24	9.7	even	3
3024.2.cz.h.1279.6		24	7.5	odd	6
3024.2.cz.h.2719.6		24	36.7	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.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.280665i q^{5} +(-0.164674 - 2.64062i) q^{7} -2.82201i q^{11} +(-4.06955 - 2.34956i) q^{13} +(7.00051 + 4.04175i) q^{17} +(0.474304 + 0.821518i) q^{19} +0.392466i q^{23} +4.92123 q^{25} +(-1.51148 - 2.61795i) q^{29} +(-1.06355 - 1.84211i) q^{31} +(-0.741129 + 0.0462181i) q^{35} +(-2.43458 - 4.21681i) q^{37} +(0.478990 + 0.276545i) q^{41} +(4.28515 - 2.47404i) q^{43} +(1.39435 - 2.41508i) q^{47} +(-6.94577 + 0.869682i) q^{49} +(-6.21935 + 10.7722i) q^{53} -0.792039 q^{55} +(-5.70053 - 9.87361i) q^{59} +(-9.67619 - 5.58655i) q^{61} +(-0.659437 + 1.14218i) q^{65} +(7.85871 - 4.53723i) q^{67} +1.54594i q^{71} +(-0.542172 - 0.313023i) q^{73} +(-7.45187 + 0.464711i) q^{77} +(-13.3691 - 7.71866i) q^{79} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(-9.90157 + 5.71667i) q^{89} +(-5.53414 + 11.1331i) q^{91} +(0.230571 - 0.133120i) q^{95} +(-13.6260 + 7.86698i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{7} + 3 q^{13} + 3 q^{17} + 4 q^{19} - 30 q^{25} - 18 q^{29} + 17 q^{31} - 42 q^{35} - 3 q^{37} + 36 q^{41} + 24 q^{43} + 21 q^{47} - 24 q^{49} + 12 q^{53} + 30 q^{55} + 6 q^{59} - 48 q^{61}+ \cdots - 3 q^{97}+O(q^{100}) \) 24 * q + 8 * q^7 + 3 * q^13 + 3 * q^17 + 4 * q^19 - 30 * q^25 - 18 * q^29 + 17 * q^31 - 42 * q^35 - 3 * q^37 + 36 * q^41 + 24 * q^43 + 21 * q^47 - 24 * q^49 + 12 * q^53 + 30 * q^55 + 6 * q^59 - 48 * q^61 + 42 * q^67 + 48 * q^73 - 36 * q^77 - 30 * q^79 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 33 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more