LMFDB - Embedded newform 3024.2.cz.g.1279.6

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			1279.6
Character	$\chi$	$=$	3024.1279
Dual form			3024.2.cz.g.2719.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.243063 - 0.140332i) q^{5} +(-2.20451 - 1.46292i) q^{7} +(-2.44393 - 1.41101i) q^{11} +(4.06955 + 2.34956i) q^{13} +(7.00051 - 4.04175i) q^{17} +(0.474304 - 0.821518i) q^{19} +(-0.339885 + 0.196233i) q^{23} +(-2.46061 + 4.26191i) q^{25} +(-1.51148 - 2.61795i) q^{29} +2.12709 q^{31} +(-0.741129 - 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-0.478990 - 0.276545i) q^{41} +(-4.28515 + 2.47404i) q^{43} -2.78870 q^{47} +(2.71972 + 6.45005i) q^{49} +(-6.21935 - 10.7722i) q^{53} -0.792039 q^{55} +11.4011 q^{59} -11.1731i q^{61} +1.31887 q^{65} -9.07446i q^{67} -1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(3.32348 + 6.68586i) q^{77} -15.4373i q^{79} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(-9.90157 - 5.71667i) q^{89} +(-5.53414 - 11.1331i) q^{91} -0.266241i q^{95} +(13.6260 - 7.86698i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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
$5$	0.243063	−	0.140332i	0.108701	−	0.0627585i	−0.444664	−	0.895698i	$-0.646677\pi$
$5$	0.243063	−	0.140332i	0.108701	−	0.0627585i	0.553365	+	0.832939i	$0.313344\pi$
$6$		0			0
$7$	−2.20451	−	1.46292i	−0.833226	−	0.552933i
$7$	−2.20451	−	1.46292i	−0.833226	−	0.552933i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.44393	−	1.41101i	−0.736874	−	0.425434i	0.0840577	−	0.996461i	$-0.473212\pi$
$11$	−2.44393	−	1.41101i	−0.736874	−	0.425434i	−0.820932	+	0.571027i	$0.806545\pi$
$12$		0			0
$13$	4.06955	+	2.34956i	1.12869	+	0.651650i	0.943605	−	0.331073i	$-0.107411\pi$
$13$	4.06955	+	2.34956i	1.12869	+	0.651650i	0.185085	+	0.982722i	$0.440744\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.00051	−	4.04175i	1.69787	−	0.980268i	0.750100	−	0.661324i	$-0.230005\pi$
$17$	7.00051	−	4.04175i	1.69787	−	0.980268i	0.947774	−	0.318944i	$-0.103328\pi$
$18$		0			0
$19$	0.474304	−	0.821518i	0.108813	−	0.188469i	−0.806477	−	0.591266i	$-0.798628\pi$
$19$	0.474304	−	0.821518i	0.108813	−	0.188469i	0.915290	+	0.402797i	$0.131962\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.339885	+	0.196233i	−0.0708710	+	0.0409174i	−0.535017	−	0.844841i	$-0.679695\pi$
$23$	−0.339885	+	0.196233i	−0.0708710	+	0.0409174i	0.464146	+	0.885759i	$0.346361\pi$
$24$		0			0
$25$	−2.46061	+	4.26191i	−0.492123	+	0.852382i
$26$		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
$31$	2.12709			0.382037			0.191018	−	0.981586i	$-0.438821\pi$
$31$	2.12709			0.382037			0.191018	+	0.981586i	$0.438821\pi$
$32$		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	−0.993755	−	0.111585i	$-0.964407\pi$
$37$	−2.43458	+	4.21681i	−0.400242	+	0.693240i	0.593513	+	0.804825i	$0.297741\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.478990	−	0.276545i	−0.0748057	−	0.0431891i	0.462131	−	0.886812i	$-0.347085\pi$
$41$	−0.478990	−	0.276545i	−0.0748057	−	0.0431891i	−0.536936	+	0.843623i	$0.680418\pi$
$42$		0			0
$43$	−4.28515	+	2.47404i	−0.653480	+	0.377287i	−0.789788	−	0.613380i	$-0.789810\pi$
$43$	−4.28515	+	2.47404i	−0.653480	+	0.377287i	0.136308	+	0.990666i	$0.456476\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.78870			−0.406773			−0.203387	−	0.979098i	$-0.565195\pi$
$47$	−2.78870			−0.406773			−0.203387	+	0.979098i	$0.565195\pi$
$48$		0			0
$49$	2.71972	+	6.45005i	0.388531	+	0.921436i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.21935	−	10.7722i	−0.854293	−	1.47968i	−0.877300	−	0.479943i	$-0.840657\pi$
$53$	−6.21935	−	10.7722i	−0.854293	−	1.47968i	0.0230067	−	0.999735i	$-0.492676\pi$
$54$		0			0
$55$	−0.792039			−0.106799
$56$		0			0
$57$		0			0
$58$		0			0
$59$	11.4011			1.48429			0.742146	−	0.670238i	$-0.233808\pi$
$59$	11.4011			1.48429			0.742146	+	0.670238i	$0.233808\pi$
$60$		0			0
$61$		−	11.1731i		−	1.43057i	−0.698833	−	0.715284i	$-0.746297\pi$
$61$		−	11.1731i		−	1.43057i	0.698833	−	0.715284i	$-0.253703\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.31887			0.163586
$66$		0			0
$67$		−	9.07446i		−	1.10862i	−0.832310	−	0.554311i	$-0.812982\pi$
$67$		−	9.07446i		−	1.10862i	0.832310	−	0.554311i	$-0.187018\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.54594i		−	0.183469i	−0.995784	−	0.0917344i	$-0.970759\pi$
$71$		−	1.54594i		−	0.183469i	0.995784	−	0.0917344i	$-0.0292411\pi$
$72$		0			0
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	−0.531393	−	0.847126i	$-0.678331\pi$
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	0.467936	+	0.883762i	$0.344998\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.32348	+	6.68586i	0.378746	+	0.761925i
$78$		0			0
$79$		−	15.4373i		−	1.73683i	−0.495835	−	0.868417i	$-0.665138\pi$
$79$		−	15.4373i		−	1.73683i	0.495835	−	0.868417i	$-0.334862\pi$
$80$		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	−0.127037	−	0.991898i	$-0.540547\pi$
$89$	−9.90157	−	5.71667i	−1.04956	−	0.605966i	−0.922527	+	0.385932i	$0.873880\pi$
$90$		0			0
$91$	−5.53414	−	11.1331i	−0.580136	−	1.16706i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	0.266241i		−	0.0273157i
$96$		0			0
$97$	13.6260	−	7.86698i	1.38351	−	0.798770i	0.390937	−	0.920417i	$-0.372151\pi$
$97$	13.6260	−	7.86698i	1.38351	−	0.798770i	0.992573	+	0.121647i	$0.0388175\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.07162	+	3.50545i	0.604149	+	0.348806i	0.770672	−	0.637232i	$-0.219921\pi$
$101$	6.07162	+	3.50545i	0.604149	+	0.348806i	−0.166523	+	0.986038i	$0.553254\pi$
$102$		0			0
$103$	−2.81624	−	4.87787i	−0.277493	−	0.480631i	0.693268	−	0.720680i	$-0.256170\pi$
$103$	−2.81624	−	4.87787i	−0.277493	−	0.480631i	−0.970761	+	0.240048i	$0.922837\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.00552	−	2.88994i	−0.483902	−	0.279381i	0.238139	−	0.971231i	$-0.423463\pi$
$107$	−5.00552	−	2.88994i	−0.483902	−	0.279381i	−0.722041	+	0.691850i	$0.756796\pi$
$108$		0			0
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	0.993158	−	0.116777i	$-0.0372564\pi$
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	−0.597711	+	0.801712i	$0.703923\pi$
$110$		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
$115$	−0.0550756	+	0.0953938i	−0.00513583	+	0.00889552i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−21.3455	−	1.33114i	−1.95673	−	0.122025i
$120$		0			0
$121$	−1.51812	−	2.62947i	−0.138011	−	0.239043i
$122$		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	$0.112068\pi$
$127$			7.77236i			0.689685i	−0.938660	+	0.344843i	$0.887932\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.99271	−	6.91558i	−0.348845	−	0.604217i	0.637200	−	0.770699i	$-0.280093\pi$
$131$	−3.99271	−	6.91558i	−0.348845	−	0.604217i	−0.986045	+	0.166482i	$0.946759\pi$
$132$		0			0
$133$	−2.24742	+	1.11717i	−0.194876	+	0.0968713i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.32470	−	7.49061i	0.369484	−	0.639966i	−0.620001	−	0.784601i	$-0.712868\pi$
$137$	4.32470	−	7.49061i	0.369484	−	0.639966i	0.989485	+	0.144636i	$0.0462010\pi$
$138$		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
$149$	−0.533820	−	0.924603i	−0.0437322	−	0.0757464i	0.843331	−	0.537395i	$-0.180592\pi$
$149$	−0.533820	−	0.924603i	−0.0437322	−	0.0757464i	−0.887063	+	0.461648i	$0.847258\pi$
$150$		0			0
$151$	11.2097	+	6.47194i	0.912235	+	0.526679i	0.881150	−	0.472838i	$-0.156770\pi$
$151$	11.2097	+	6.47194i	0.912235	+	0.526679i	0.0310854	+	0.999517i	$0.490104\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.517016	−	0.298500i	0.0415278	−	0.0239761i
$156$		0			0
$157$		−	8.10255i		−	0.646654i	−0.946287	−	0.323327i	$-0.895199\pi$
$157$		−	8.10255i		−	0.646654i	0.946287	−	0.323327i	$-0.104801\pi$
$158$		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	0.968857	−	0.247621i	$-0.0796489\pi$
$163$	15.8164	+	9.13162i	1.23884	+	0.715244i	0.269982	+	0.962865i	$0.412982\pi$
$164$		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
$173$			19.8404i			1.50844i	0.656623	+	0.754219i	$0.271984\pi$
$173$			19.8404i			1.50844i	−0.656623	+	0.754219i	$0.728016\pi$
$174$		0			0
$175$	11.6593	−	5.79573i	0.881359	−	0.438116i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−21.5488	+	12.4412i	−1.61063	+	0.929899i	−0.621409	+	0.783486i	$0.713439\pi$
$179$	−21.5488	+	12.4412i	−1.61063	+	0.929899i	−0.989224	+	0.146413i	$0.953227\pi$
$180$		0			0
$181$		−	7.30569i		−	0.543027i	−0.962435	−	0.271514i	$-0.912476\pi$
$181$		−	7.30569i		−	0.543027i	0.962435	−	0.271514i	$-0.0875242\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			1.36660i			0.100474i
$186$		0			0
$187$	−22.8117			−1.66816
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	8.21966i		−	0.594754i	−0.954760	−	0.297377i	$-0.903888\pi$
$191$		−	8.21966i		−	0.594754i	0.954760	−	0.297377i	$-0.0961118\pi$
$192$		0			0
$193$	19.5697			1.40866			0.704331	−	0.709872i	$-0.251247\pi$
$193$	19.5697			1.40866			0.704331	+	0.709872i	$0.251247\pi$
$194$		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	0.997678	+	0.0681077i	$0.0216961\pi$
$199$	7.86905	+	13.6296i	0.557822	+	0.966176i	−0.439856	+	0.898068i	$0.644971\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.497801	+	7.98248i	−0.0349388	+	0.560260i
$204$		0			0
$205$	−0.155233			−0.0108419
$206$		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	0.222581	−	0.974914i	$-0.428552\pi$
$211$	−7.41442	−	4.28072i	−0.510430	−	0.294697i	−0.733010	+	0.680218i	$0.761885\pi$
$212$		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
$221$	37.9853			2.55517
$222$		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
$227$	10.3200	−	17.8747i	0.684960	−	1.18639i	−0.288489	−	0.957483i	$-0.593153\pi$
$227$	10.3200	−	17.8747i	0.684960	−	1.18639i	0.973449	−	0.228902i	$-0.0735137\pi$
$228$		0			0
$229$	−18.3554	+	10.5975i	−1.21296	+	0.700301i	−0.963402	−	0.268060i	$-0.913618\pi$
$229$	−18.3554	+	10.5975i	−1.21296	+	0.700301i	−0.249555	+	0.968361i	$0.580284\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.78510	−	13.4842i	0.510019	−	0.883378i	−0.489914	−	0.871771i	$-0.662972\pi$
$233$	7.78510	−	13.4842i	0.510019	−	0.883378i	0.999933	−	0.0116076i	$-0.00369490\pi$
$234$		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	0.691579	−	0.722301i	$-0.256915\pi$
$239$	6.36686	+	3.67591i	0.411838	+	0.237775i	−0.279741	+	0.960075i	$0.590249\pi$
$240$		0			0
$241$	4.98346	+	2.87720i	0.321013	+	0.185337i	0.651844	−	0.758353i	$-0.273996\pi$
$241$	4.98346	+	2.87720i	0.321013	+	0.185337i	−0.330831	+	0.943690i	$0.607329\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.56621	+	1.18610i	0.100062	+	0.0757773i
$246$		0			0
$247$	3.86041	−	2.22881i	0.245632	−	0.141816i
$248$		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
$257$	1.26062	−	0.727818i	0.0786351	−	0.0454000i	−0.460167	−	0.887832i	$-0.652210\pi$
$257$	1.26062	−	0.727818i	0.0786351	−	0.0454000i	0.538802	+	0.842432i	$0.318877\pi$
$258$		0			0
$259$	11.5359	−	5.73440i	0.716807	−	0.356318i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−18.3962	−	10.6211i	−1.13436	−	0.654922i	−0.189331	−	0.981913i	$-0.560632\pi$
$263$	−18.3962	−	10.6211i	−1.13436	−	0.654922i	−0.945028	+	0.326991i	$0.893965\pi$
$264$		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	−0.926946	−	0.375194i	$-0.877576\pi$
$269$	−17.4754	+	10.0894i	−1.06549	+	0.615162i	−0.138546	+	0.990356i	$0.544243\pi$
$270$		0			0
$271$	8.69232	−	15.0555i	0.528021	−	0.914559i	−0.471445	−	0.881895i	$-0.656268\pi$
$271$	8.69232	−	15.0555i	0.528021	−	0.914559i	0.999466	−	0.0326639i	$-0.0103991\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.0272	−	6.94388i	0.725265	−	0.418732i
$276$		0			0
$277$	−0.566878	+	0.981861i	−0.0340604	+	0.0589943i	−0.882553	−	0.470213i	$-0.844177\pi$
$277$	−0.566878	+	0.981861i	−0.0340604	+	0.0589943i	0.848493	+	0.529207i	$0.177511\pi$
$278$		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
$283$	−6.77001			−0.402435			−0.201218	−	0.979547i	$-0.564490\pi$
$283$	−6.77001			−0.402435			−0.201218	+	0.979547i	$0.564490\pi$
$284$		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	0.774854	−	0.632140i	$-0.217823\pi$
$293$	10.5242	+	6.07616i	0.614831	+	0.354973i	−0.160023	+	0.987113i	$0.551157\pi$
$294$		0			0
$295$	2.77117	−	1.59994i	0.161344	−	0.0931519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.84424			−0.106655
$300$		0			0
$301$	13.0660	+	0.814817i	0.753111	+	0.0469653i
$302$		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
$311$	−26.4759			−1.50131			−0.750655	−	0.660694i	$-0.770262\pi$
$311$	−26.4759			−1.50131			−0.750655	+	0.660694i	$0.770262\pi$
$312$		0			0
$313$		−	4.46734i		−	0.252509i	−0.991998	−	0.126255i	$-0.959704\pi$
$313$		−	4.46734i		−	0.252509i	0.991998	−	0.126255i	$-0.0402956\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.4033			−1.65146			−0.825728	−	0.564069i	$-0.809235\pi$
$317$	−29.4033			−1.65146			−0.825728	+	0.564069i	$0.809235\pi$
$318$		0			0
$319$			8.53081i			0.477634i
$320$		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
$329$	6.14771	+	4.07965i	0.338934	+	0.224918i
$330$		0			0
$331$		−	0.981836i		−	0.0539666i	−0.999636	−	0.0269833i	$-0.991410\pi$
$331$		−	0.981836i		−	0.0539666i	0.999636	−	0.0269833i	$-0.00859009\pi$
$332$		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
$347$			8.78830i			0.471781i	0.971780	+	0.235890i	$0.0758006\pi$
$347$			8.78830i			0.471781i	−0.971780	+	0.235890i	$0.924199\pi$
$348$		0			0
$349$	−18.2265	+	10.5231i	−0.975644	+	0.563288i	−0.900952	−	0.433919i	$-0.857131\pi$
$349$	−18.2265	+	10.5231i	−0.975644	+	0.563288i	−0.0746915	+	0.997207i	$0.523797\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.28872	+	1.32139i	0.121816	+	0.0703307i	0.559670	−	0.828716i	$-0.310928\pi$
$353$	2.28872	+	1.32139i	0.121816	+	0.0703307i	−0.437854	+	0.899046i	$0.644261\pi$
$354$		0			0
$355$	−0.216945	−	0.375759i	−0.0115142	−	0.0199432i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.5571	+	11.8687i	1.08496	+	0.626405i	0.932231	−	0.361863i	$-0.117859\pi$
$359$	20.5571	+	11.8687i	1.08496	+	0.626405i	0.152733	+	0.988267i	$0.451192\pi$
$360$		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
$367$	−15.3410	+	26.5714i	−0.800793	+	1.38701i	0.118303	+	0.992978i	$0.462255\pi$
$367$	−15.3410	+	26.5714i	−0.800793	+	1.38701i	−0.919095	+	0.394036i	$0.871079\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.04833	+	32.8459i	−0.106344	+	1.70527i
$372$		0			0
$373$	−3.29461	−	5.70642i	−0.170588	−	0.295467i	0.768037	−	0.640405i	$-0.221233\pi$
$373$	−3.29461	−	5.70642i	−0.170588	−	0.295467i	−0.938626	+	0.344937i	$0.887900\pi$
$374$		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	$-0.997409\pi$
$379$		−	0.316910i		−	0.0162786i	0.999967	−	0.00813930i	$-0.00259085\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.84855	−	3.20179i	−0.0944567	−	0.163604i	0.814925	−	0.579566i	$-0.196778\pi$
$383$	−1.84855	−	3.20179i	−0.0944567	−	0.163604i	−0.909382	+	0.415963i	$0.863445\pi$
$384$		0			0
$385$	1.74606	+	1.15869i	0.0889873	+	0.0590524i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.29814	+	7.44460i	−0.217925	+	0.377456i	−0.954173	−	0.299255i	$-0.903262\pi$
$389$	−4.29814	+	7.44460i	−0.217925	+	0.377456i	0.736249	+	0.676711i	$0.236595\pi$
$390$		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	0.200116	−	0.979772i	$-0.435868\pi$
$397$	−10.9255	−	6.30783i	−0.548334	−	0.316581i	−0.748450	+	0.663192i	$0.769201\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.0646	−	22.6285i	−0.652414	−	1.13001i	−0.982535	−	0.186076i	$-0.940423\pi$
$401$	−13.0646	−	22.6285i	−0.652414	−	1.13001i	0.330121	−	0.943939i	$-0.392910\pi$
$402$		0			0
$403$	8.65631	+	4.99772i	0.431201	+	0.248954i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.8999	−	6.87041i	0.589856	−	0.340554i
$408$		0			0
$409$			0.288440i			0.0142624i	0.999975	+	0.00713121i	$0.00226995\pi$
$409$			0.288440i			0.0142624i	−0.999975	+	0.00713121i	$0.997730\pi$
$410$		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
$425$			39.7807i			1.92965i
$426$		0			0
$427$	−16.3454	+	24.6312i	−0.791008	+	1.19199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.2196	−	7.63235i	0.636766	−	0.367637i	−0.146601	−	0.989196i	$-0.546833\pi$
$431$	13.2196	−	7.63235i	0.636766	−	0.367637i	0.783368	+	0.621558i	$0.213500\pi$
$432$		0			0
$433$			24.5275i			1.17871i	0.807873	+	0.589357i	$0.200619\pi$
$433$			24.5275i			1.17871i	−0.807873	+	0.589357i	$0.799381\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			0.372296i			0.0178093i
$438$		0			0
$439$	18.2801			0.872460			0.436230	−	0.899835i	$-0.356313\pi$
$439$	18.2801			0.872460			0.436230	+	0.899835i	$0.356313\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			5.21155i			0.247608i	0.992307	+	0.123804i	$0.0395094\pi$
$443$			5.21155i			0.247608i	−0.992307	+	0.123804i	$0.960491\pi$
$444$		0			0
$445$	−3.20894			−0.152118
$446$		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
$455$	−2.90747	−	1.92941i	−0.136304	−	0.0904522i
$456$		0			0
$457$	29.3621			1.37350			0.686749	−	0.726894i	$-0.259037\pi$
$457$	29.3621			1.37350			0.686749	+	0.726894i	$0.259037\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.10606	−	0.638584i	0.0515144	−	0.0297418i	−0.474022	−	0.880513i	$-0.657198\pi$
$461$	1.10606	−	0.638584i	0.0515144	−	0.0297418i	0.525536	+	0.850771i	$0.323865\pi$
$462$		0			0
$463$	23.8988	+	13.7980i	1.11067	+	0.641247i	0.939004	−	0.343907i	$-0.111751\pi$
$463$	23.8988	+	13.7980i	1.11067	+	0.641247i	0.171669	+	0.985155i	$0.445084\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.00656	−	8.67162i	0.231676	−	0.401275i	−0.726625	−	0.687034i	$-0.758912\pi$
$467$	5.00656	−	8.67162i	0.231676	−	0.401275i	0.958301	+	0.285759i	$0.0922458\pi$
$468$		0			0
$469$	−13.2752	+	20.0047i	−0.612993	+	0.923733i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.9635			0.642043
$474$		0			0
$475$	2.33416	+	4.04288i	0.107098	+	0.185500i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.39474	−	12.8081i	0.337874	−	0.585216i	−0.646158	−	0.763203i	$-0.723625\pi$
$479$	7.39474	−	12.8081i	0.337874	−	0.585216i	0.984033	+	0.177988i	$0.0569588\pi$
$480$		0			0
$481$	−19.8153	+	11.4404i	−0.903499	+	0.521636i
$482$		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	−0.761324	−	0.648372i	$-0.775450\pi$
$487$	−12.8101	+	7.39589i	−0.580479	+	0.335140i	0.180845	+	0.983512i	$0.442117\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.5410	+	7.24053i	0.565966	+	0.326760i	0.755536	−	0.655107i	$-0.227376\pi$
$491$	12.5410	+	7.24053i	0.565966	+	0.326760i	−0.189571	+	0.981867i	$0.560710\pi$
$492$		0			0
$493$	−21.1622	−	12.2180i	−0.953099	−	0.550272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.26158	+	3.40803i	−0.101446	+	0.152871i
$498$		0			0
$499$	7.52679	−	4.34559i	0.336945	−	0.194536i	−0.321975	−	0.946748i	$-0.604347\pi$
$499$	7.52679	−	4.34559i	0.336945	−	0.194536i	0.658920	+	0.752213i	$0.271013\pi$
$500$		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
$509$	−2.92593	+	1.68929i	−0.129690	+	0.0748764i	−0.563441	−	0.826156i	$-0.690523\pi$
$509$	−2.92593	+	1.68929i	−0.129690	+	0.0748764i	0.433752	+	0.901033i	$0.357190\pi$
$510$		0			0
$511$	1.65315	+	0.103093i	0.0731311	+	0.00456058i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.36905	−	0.790420i	−0.0603274	−	0.0348300i
$516$		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	0.517440	−	0.855719i	$-0.326885\pi$
$521$	34.6315	−	19.9945i	1.51723	−	0.875976i	0.999795	−	0.0202566i	$-0.00644831\pi$
$522$		0			0
$523$	−6.43351	+	11.1432i	−0.281318	+	0.487257i	−0.971710	−	0.236179i	$-0.924105\pi$
$523$	−6.43351	+	11.1432i	−0.281318	+	0.487257i	0.690392	+	0.723436i	$0.257438\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.8907	−	8.59716i	0.648650	−	0.374498i
$528$		0			0
$529$	−11.4230	+	19.7852i	−0.496652	+	0.860226i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.29952	−	2.25083i	−0.0562883	−	0.0974942i
$534$		0			0
$535$	−1.62221			−0.0701341
$536$		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	−0.919772	−	0.392454i	$-0.871626\pi$
$541$	−2.79138	+	4.83481i	−0.120011	+	0.207865i	0.799761	+	0.600319i	$0.204960\pi$
$542$		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	−0.286006	−	0.958228i	$-0.592328\pi$
$547$	9.37486	−	5.41258i	0.400840	−	0.231425i	0.686846	+	0.726803i	$0.258994\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.86760			−0.122164
$552$		0			0
$553$	−22.5836	+	34.0317i	−0.960352	+	1.44717i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.38879	−	14.5298i	−0.355445	−	0.615648i	0.631749	−	0.775173i	$-0.282337\pi$
$557$	−8.38879	−	14.5298i	−0.355445	−	0.615648i	−0.987194	+	0.159525i	$0.949004\pi$
$558$		0			0
$559$	−23.2515			−0.983436
$560$		0			0
$561$		0			0
$562$		0			0
$563$	28.6721			1.20838			0.604192	−	0.796839i	$-0.293496\pi$
$563$	28.6721			1.20838			0.604192	+	0.796839i	$0.293496\pi$
$564$		0			0
$565$		−	3.63483i		−	0.152918i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−33.2571			−1.39421			−0.697106	−	0.716968i	$-0.745529\pi$
$569$	−33.2571			−1.39421			−0.697106	+	0.716968i	$0.745529\pi$
$570$		0			0
$571$			32.5982i			1.36419i	0.731262	+	0.682097i	$0.238932\pi$
$571$			32.5982i			1.36419i	−0.731262	+	0.682097i	$0.761068\pi$
$572$		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	−0.238339	−	0.971182i	$-0.576603\pi$
$577$	11.6155	−	6.70622i	0.483560	−	0.279183i	0.721899	+	0.691999i	$0.243270\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.74825	+	28.0339i	−0.0725295	+	1.16304i
$582$		0			0
$583$			35.1021i			1.45378i
$584$		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	0.110675	−	0.993857i	$-0.464699\pi$
$593$	−16.9169	−	9.76697i	−0.694693	−	0.401081i	−0.805368	+	0.592775i	$0.798032\pi$
$594$		0			0
$595$	−5.37509	+	2.67191i	−0.220357	+	0.109538i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			16.8037i			0.686581i	0.939229	+	0.343291i	$0.111542\pi$
$599$			16.8037i			0.686581i	−0.939229	+	0.343291i	$0.888458\pi$
$600$		0			0
$601$	6.18993	−	3.57376i	0.252492	−	0.145777i	−0.368413	−	0.929662i	$-0.620099\pi$
$601$	6.18993	−	3.57376i	0.252492	−	0.145777i	0.620905	+	0.783886i	$0.286765\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.737999	−	0.426084i	−0.0300039	−	0.0173228i
$606$		0			0
$607$	−8.93176	−	15.4703i	−0.362529	−	0.627919i	0.625847	−	0.779946i	$-0.284753\pi$
$607$	−8.93176	−	15.4703i	−0.362529	−	0.627919i	−0.988376	+	0.152027i	$0.951420\pi$
$608$		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	0.993469	−	0.114106i	$-0.0364003\pi$
$613$	9.85193	+	17.0640i	0.397916	+	0.689210i	−0.595553	+	0.803316i	$0.703067\pi$
$614$		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
$619$	−6.44975	+	11.1713i	−0.259237	+	0.449012i	−0.966038	−	0.258401i	$-0.916805\pi$
$619$	−6.44975	+	11.1713i	−0.259237	+	0.449012i	0.706800	+	0.707413i	$0.250138\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.4650	+	27.0877i	0.539466	+	1.08525i
$624$		0			0
$625$	−11.9123	−	20.6327i	−0.476492	−	0.825309i
$626$		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	$-0.890911\pi$
$631$		−	16.8826i		−	0.672085i	0.941847	−	0.336042i	$-0.109089\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.09071	+	1.88917i	0.0432836	+	0.0749694i
$636$		0			0
$637$	−4.08674	+	32.6389i	−0.161922	+	1.29320i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.14505	−	10.6435i	0.242715	−	0.420394i	−0.718772	−	0.695246i	$-0.755295\pi$
$641$	6.14505	−	10.6435i	0.242715	−	0.420394i	0.961487	+	0.274852i	$0.0886288\pi$
$642$		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	0.999887	−	0.0150552i	$-0.00479241\pi$
$647$	12.3850	+	21.4515i	0.486905	+	0.843344i	−0.512982	+	0.858400i	$0.671459\pi$
$648$		0			0
$649$	−27.8634	−	16.0870i	−1.09374	−	0.631469i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.33573	−	16.1700i	−0.365335	−	0.632779i	0.623495	−	0.781828i	$-0.285712\pi$
$653$	−9.33573	−	16.1700i	−0.365335	−	0.632779i	−0.988830	+	0.149048i	$0.952379\pi$
$654$		0			0
$655$	−1.94096	−	1.12061i	−0.0758395	−	0.0437860i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−39.5720	+	22.8469i	−1.54150	+	0.889988i	−0.542761	+	0.839887i	$0.682621\pi$
$659$	−39.5720	+	22.8469i	−1.54150	+	0.889988i	−0.998744	+	0.0501010i	$0.984046\pi$
$660$		0			0
$661$		−	29.3756i		−	1.14258i	−0.820749	−	0.571289i	$-0.806444\pi$
$661$		−	29.3756i		−	1.14258i	0.820749	−	0.571289i	$-0.193556\pi$
$662$		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
$677$			47.3055i			1.81810i	0.416687	+	0.909050i	$0.363191\pi$
$677$			47.3055i			1.81810i	−0.416687	+	0.909050i	$0.636809\pi$
$678$		0			0
$679$	−41.5474	−	2.59097i	−1.59444	−	0.0994323i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	23.6562	−	13.6579i	0.905178	−	0.522605i	0.0263018	−	0.999654i	$-0.491627\pi$
$683$	23.6562	−	13.6579i	0.905178	−	0.522605i	0.878877	+	0.477049i	$0.158294\pi$
$684$		0			0
$685$		−	2.42758i		−	0.0927532i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	58.4508i		−	2.22680i
$690$		0			0
$691$	39.7682			1.51285			0.756427	−	0.654078i	$-0.226943\pi$
$691$	39.7682			1.51285			0.756427	+	0.654078i	$0.226943\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	4.03859i		−	0.153193i
$696$		0			0
$697$	−4.47090			−0.169348
$698$		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
$707$	−8.25674	−	16.6101i	−0.310527	−	0.624688i
$708$		0			0
$709$	−30.3525			−1.13991			−0.569956	−	0.821675i	$-0.693040\pi$
$709$	−30.3525			−1.13991			−0.569956	+	0.821675i	$0.693040\pi$
$710$		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	−0.313348	−	0.949638i	$-0.601451\pi$
$719$	17.8512	−	30.9192i	0.665737	−	1.15309i	0.979085	−	0.203452i	$-0.0652160\pi$
$720$		0			0
$721$	−0.927523	+	14.8733i	−0.0345427	+	0.553909i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.8766			0.552505
$726$		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
$731$	−19.9989	+	34.6390i	−0.739684	+	1.28117i
$732$		0			0
$733$	3.50591	−	2.02414i	0.129494	−	0.0747633i	−0.433854	−	0.900983i	$-0.642847\pi$
$733$	3.50591	−	2.02414i	0.129494	−	0.0747633i	0.563348	+	0.826220i	$0.309513\pi$
$734$		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	−0.118602	−	0.992942i	$-0.537841\pi$
$739$	18.5401	−	10.7042i	0.682010	−	0.393759i	0.800612	+	0.599183i	$0.204508\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	43.3251	+	25.0137i	1.58944	+	0.917665i	0.993399	+	0.114714i	$0.0365951\pi$
$743$	43.3251	+	25.0137i	1.58944	+	0.917665i	0.596044	+	0.802952i	$0.296738\pi$
$744$		0			0
$745$	−0.259503	−	0.149824i	−0.00950746	−	0.00548914i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.80695	+	13.6936i	0.248721	+	0.500352i
$750$		0			0
$751$	−18.4527	+	10.6537i	−0.673349	+	0.388758i	−0.797344	−	0.603525i	$-0.793763\pi$
$751$	−18.4527	+	10.6537i	−0.673349	+	0.388758i	0.123995	+	0.992283i	$0.460429\pi$
$752$		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
$761$	−34.8705	+	20.1325i	−1.26406	+	0.729803i	−0.973857	−	0.227163i	$-0.927055\pi$
$761$	−34.8705	+	20.1325i	−1.26406	+	0.729803i	−0.290199	+	0.956966i	$0.593722\pi$
$762$		0			0
$763$	1.35974	−	21.8041i	0.0492259	−	0.789361i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	46.3972	+	26.7874i	1.67531	+	0.967238i
$768$		0			0
$769$	5.51138	+	3.18199i	0.198745	+	0.114746i	0.596070	−	0.802932i	$-0.296728\pi$
$769$	5.51138	+	3.18199i	0.198745	+	0.114746i	−0.397325	+	0.917678i	$0.630061\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−42.9373	+	24.7899i	−1.54435	+	0.891629i	−0.545790	+	0.837922i	$0.683770\pi$
$773$	−42.9373	+	24.7899i	−1.54435	+	0.891629i	−0.998557	+	0.0537073i	$0.982896\pi$
$774$		0			0
$775$	−5.23395	+	9.06546i	−0.188009	+	0.325641i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.454374	+	0.262333i	−0.0162796	+	0.00939905i
$780$		0			0
$781$	−2.18132	+	3.77816i	−0.0780539	+	0.135193i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.13705	−	1.96943i	−0.0405831	−	0.0702919i
$786$		0			0
$787$	28.2267			1.00617			0.503086	−	0.864236i	$-0.332198\pi$
$787$	28.2267			1.00617			0.503086	+	0.864236i	$0.332198\pi$
$788$		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	0.751413	−	0.659832i	$-0.229373\pi$
$797$	15.6877	+	9.05731i	0.555688	+	0.320826i	−0.195725	+	0.980659i	$0.562706\pi$
$798$		0			0
$799$	−19.5223	+	11.2712i	−0.690650	+	0.398747i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.76671			0.0623458
$804$		0			0
$805$	0.260968	−	0.129725i	0.00919793	−	0.00457221i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.56171	+	2.70496i	0.0549067	+	0.0951012i	0.892172	−	0.451695i	$-0.149181\pi$
$809$	1.56171	+	2.70496i	0.0549067	+	0.0951012i	−0.837266	+	0.546796i	$0.815847\pi$
$810$		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
$815$	5.12585			0.179551
$816$		0			0
$817$			4.69378i			0.164214i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.9554			−1.01055			−0.505275	−	0.862958i	$-0.668609\pi$
$821$	−28.9554			−1.01055			−0.505275	+	0.862958i	$0.668609\pi$
$822$		0			0
$823$			39.7963i			1.38721i	0.720355	+	0.693605i	$0.243979\pi$
$823$			39.7963i			1.38721i	−0.720355	+	0.693605i	$0.756021\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	37.9694i		−	1.32033i	−0.751123	−	0.660163i	$-0.770487\pi$
$827$		−	37.9694i		−	1.32033i	0.751123	−	0.660163i	$-0.229513\pi$
$828$		0			0
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.346006	−	0.938232i	$-0.387538\pi$
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.985536	+	0.169466i	$0.0542042\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	45.1089	+	34.1613i	1.56293	+	1.18362i
$834$		0			0
$835$			4.72634i			0.163562i
$836$		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
$851$		−	1.91098i		−	0.0655075i
$852$		0			0
$853$	−9.50254	+	5.48629i	−0.325361	+	0.187847i	−0.653779	−	0.756685i	$-0.726818\pi$
$853$	−9.50254	+	5.48629i	−0.325361	+	0.187847i	0.328419	+	0.944532i	$0.393484\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.04476	+	1.75789i	0.104007	+	0.0600485i	0.551101	−	0.834438i	$-0.314208\pi$
$857$	3.04476	+	1.75789i	0.104007	+	0.0600485i	−0.447094	+	0.894487i	$0.647541\pi$
$858$		0			0
$859$	−7.58841	−	13.1435i	−0.258913	−	0.448451i	0.707038	−	0.707176i	$-0.250031\pi$
$859$	−7.58841	−	13.1435i	−0.258913	−	0.448451i	−0.965951	+	0.258725i	$0.916698\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.7041	+	17.1496i	1.01114	+	0.583781i	0.911525	−	0.411245i	$-0.134906\pi$
$863$	29.7041	+	17.1496i	1.01114	+	0.583781i	0.0996133	+	0.995026i	$0.468239\pi$
$864$		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
$871$	21.3210	−	36.9290i	0.722433	−	1.25129i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.07356	−	6.13854i	0.137712	−	0.207520i
$876$		0			0
$877$	−10.6413	−	18.4313i	−0.359332	−	0.622381i	0.628517	−	0.777795i	$-0.283662\pi$
$877$	−10.6413	−	18.4313i	−0.359332	−	0.622381i	−0.987849	+	0.155414i	$0.950329\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	20.5029i		−	0.690761i	−0.938463	−	0.345380i	$-0.887750\pi$
$881$		−	20.5029i		−	0.690761i	0.938463	−	0.345380i	$-0.112250\pi$
$882$		0			0
$883$			39.9687i			1.34506i	0.740072	+	0.672528i	$0.234791\pi$
$883$			39.9687i			1.34506i	−0.740072	+	0.672528i	$0.765209\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.6510	−	28.8404i	−0.559085	−	0.968364i	−0.997573	−	0.0696271i	$-0.977819\pi$
$887$	−16.6510	−	28.8404i	−0.559085	−	0.968364i	0.438488	−	0.898737i	$-0.355514\pi$
$888$		0			0
$889$	11.3704	−	17.1342i	0.381350	−	0.574664i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.32269	+	2.29097i	−0.0442621	+	0.0766643i
$894$		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
$905$	−1.02522	−	1.77574i	−0.0340796	−	0.0590276i
$906$		0			0
$907$	−1.48209	−	0.855683i	−0.0492119	−	0.0284125i	0.475192	−	0.879882i	$-0.342379\pi$
$907$	−1.48209	−	0.855683i	−0.0492119	−	0.0284125i	−0.524404	+	0.851470i	$0.675712\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.22479	+	4.17123i	−0.239368	+	0.138199i	−0.614886	−	0.788616i	$-0.710798\pi$
$911$	−7.22479	+	4.17123i	−0.239368	+	0.138199i	0.375518	+	0.926815i	$0.377465\pi$
$912$		0			0
$913$			29.9597i			0.991520i
$914$		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	0.705709	−	0.708501i	$-0.250628\pi$
$919$	13.4897	+	7.78828i	0.444984	+	0.256911i	−0.260726	+	0.965413i	$0.583962\pi$
$920$		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
$929$		−	2.44492i		−	0.0802152i	−0.999195	−	0.0401076i	$-0.987230\pi$
$929$		−	2.44492i		−	0.0802152i	0.999195	−	0.0401076i	$-0.0127701\pi$
$930$		0			0
$931$	6.58881	+	0.824987i	0.215939	+	0.0270379i
$932$		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	$0.0120690\pi$
$937$			2.32069i			0.0758137i	−0.999281	+	0.0379069i	$0.987931\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			15.9023i			0.518400i	0.965824	+	0.259200i	$0.0834588\pi$
$941$			15.9023i			0.518400i	−0.965824	+	0.259200i	$0.916541\pi$
$942$		0			0
$943$	0.217069			0.00706874
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	36.3372i		−	1.18080i	−0.807111	−	0.590400i	$-0.798970\pi$
$947$		−	36.3372i		−	1.18080i	0.807111	−	0.590400i	$-0.201030\pi$
$948$		0			0
$949$	−2.94186			−0.0954969
$950$		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
$959$	−20.4920	+	10.1864i	−0.661722	+	0.328936i
$960$		0			0
$961$	−26.4755			−0.854048
$962$		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	0.749974	−	0.661467i	$-0.230066\pi$
$967$	17.1689	+	9.91247i	0.552115	+	0.318764i	−0.197860	+	0.980230i	$0.563399\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.7738	+	22.1249i	−0.409931	+	0.710021i	−0.994882	−	0.101048i	$-0.967780\pi$
$971$	−12.7738	+	22.1249i	−0.409931	+	0.710021i	0.584951	+	0.811069i	$0.301114\pi$
$972$		0			0
$973$	−34.0911	+	16.9464i	−1.09291	+	0.543276i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.7971			0.729343			0.364671	−	0.931136i	$-0.381181\pi$
$977$	22.7971			0.729343			0.364671	+	0.931136i	$0.381181\pi$
$978$		0			0
$979$	16.1325	+	27.9424i	0.515598	+	0.893041i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.9954	−	48.4894i	0.892914	−	1.54657i	0.0565482	−	0.998400i	$-0.481991\pi$
$983$	27.9954	−	48.4894i	0.892914	−	1.54657i	0.836366	−	0.548172i	$-0.184676\pi$
$984$		0			0
$985$	−3.98460	+	2.30051i	−0.126960	+	0.0733003i
$986$		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	−0.798653	−	0.601791i	$-0.794454\pi$
$991$	−21.3062	+	12.3011i	−0.676814	+	0.390759i	0.121840	+	0.992550i	$0.461121\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.82534	+	2.20856i	0.121272	+	0.0700162i
$996$		0			0
$997$	35.0171	+	20.2171i	1.10900	+	0.640283i	0.938571	−	0.345087i	$-0.112150\pi$
$997$	35.0171	+	20.2171i	1.10900	+	0.640283i	0.170432	+	0.985370i	$0.445484\pi$
$998$		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.1279.6		24
3.2	odd	2		1008.2.cz.h.607.8	yes	24
4.3	odd	2		3024.2.cz.h.1279.6		24
7.3	odd	6		3024.2.bf.g.1711.7		24
9.2	odd	6		1008.2.bf.g.943.9	yes	24
9.7	even	3		3024.2.bf.h.2287.6		24
12.11	even	2		1008.2.cz.g.607.5	yes	24
21.17	even	6		1008.2.bf.h.31.4	yes	24
28.3	even	6		3024.2.bf.h.1711.7		24
36.7	odd	6		3024.2.bf.g.2287.6		24
36.11	even	6		1008.2.bf.h.943.4	yes	24
63.38	even	6		1008.2.cz.g.367.5	yes	24
63.52	odd	6		3024.2.cz.h.2719.6		24
84.59	odd	6		1008.2.bf.g.31.9	✓	24
252.115	even	6	inner	3024.2.cz.g.2719.6		24
252.227	odd	6		1008.2.cz.h.367.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.9	✓	24	84.59	odd	6
1008.2.bf.g.943.9	yes	24	9.2	odd	6
1008.2.bf.h.31.4	yes	24	21.17	even	6
1008.2.bf.h.943.4	yes	24	36.11	even	6
1008.2.cz.g.367.5	yes	24	63.38	even	6
1008.2.cz.g.607.5	yes	24	12.11	even	2
1008.2.cz.h.367.8	yes	24	252.227	odd	6
1008.2.cz.h.607.8	yes	24	3.2	odd	2
3024.2.bf.g.1711.7		24	7.3	odd	6
3024.2.bf.g.2287.6		24	36.7	odd	6
3024.2.bf.h.1711.7		24	28.3	even	6
3024.2.bf.h.2287.6		24	9.7	even	3
3024.2.cz.g.1279.6		24	1.1	even	1	trivial
3024.2.cz.g.2719.6		24	252.115	even	6	inner
3024.2.cz.h.1279.6		24	4.3	odd	2
3024.2.cz.h.2719.6		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)

\(f(q)\)	\(=\)	\(q+(0.243063 - 0.140332i) q^{5} +(-2.20451 - 1.46292i) q^{7} +(-2.44393 - 1.41101i) q^{11} +(4.06955 + 2.34956i) q^{13} +(7.00051 - 4.04175i) q^{17} +(0.474304 - 0.821518i) q^{19} +(-0.339885 + 0.196233i) q^{23} +(-2.46061 + 4.26191i) q^{25} +(-1.51148 - 2.61795i) q^{29} +2.12709 q^{31} +(-0.741129 - 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-0.478990 - 0.276545i) q^{41} +(-4.28515 + 2.47404i) q^{43} -2.78870 q^{47} +(2.71972 + 6.45005i) q^{49} +(-6.21935 - 10.7722i) q^{53} -0.792039 q^{55} +11.4011 q^{59} -11.1731i q^{61} +1.31887 q^{65} -9.07446i q^{67} -1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(3.32348 + 6.68586i) q^{77} -15.4373i q^{79} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(-9.90157 - 5.71667i) q^{89} +(-5.53414 - 11.1331i) q^{91} -0.266241i q^{95} +(13.6260 - 7.86698i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55}+ \cdots + 3 q^{97}+O(q^{100}) \) 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

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