LMFDB - Embedded newform 3024.2.q.k.2881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.3
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.k.2305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26145 + 2.18490i) q^{5} +(-2.63136 + 0.275550i) q^{7} +O(q^{10})$	$q+(-1.26145 + 2.18490i) q^{5} +(-2.63136 + 0.275550i) q^{7} +(2.85648 + 4.94757i) q^{11} +(-2.45245 - 4.24777i) q^{13} +(-2.49483 + 4.32118i) q^{17} +(0.00383929 + 0.00664984i) q^{19} +(-0.333877 + 0.578292i) q^{23} +(-0.682524 - 1.18217i) q^{25} +(-3.85082 + 6.66981i) q^{29} +7.76605 q^{31} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-5.21159 - 9.02673i) q^{41} +(-4.42935 + 7.67185i) q^{43} +2.16104 q^{47} +(6.84814 - 1.45015i) q^{49} +(3.69858 - 6.40613i) q^{53} -14.4133 q^{55} -0.523594 q^{59} -8.99082 q^{61} +12.3746 q^{65} +5.09582 q^{67} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(-8.87975 - 12.2318i) q^{77} -6.16230 q^{79} +(-0.258726 + 0.448126i) q^{83} +(-6.29422 - 10.9019i) q^{85} +(-1.19093 - 2.06274i) q^{89} +(7.62377 + 10.5017i) q^{91} -0.0193723 q^{95} +(4.32994 - 7.49968i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 + 5 * q^7	$ 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.26145	+	2.18490i	−0.564139	+	0.977117i	0.432991	+	0.901398i	$0.357458\pi$
$5$	−1.26145	+	2.18490i	−0.564139	+	0.977117i	−0.997129	+	0.0757184i	$0.975875\pi$
$6$		0			0
$7$	−2.63136	+	0.275550i	−0.994562	+	0.104148i
$7$	−2.63136	+	0.275550i	−0.994562	+	0.104148i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.85648	+	4.94757i	0.861262	+	1.49175i	0.870712	+	0.491794i	$0.163659\pi$
$11$	2.85648	+	4.94757i	0.861262	+	1.49175i	−0.00944971	+	0.999955i	$0.503008\pi$
$12$		0			0
$13$	−2.45245	−	4.24777i	−0.680188	−	1.17812i	−0.974923	−	0.222541i	$-0.928565\pi$
$13$	−2.45245	−	4.24777i	−0.680188	−	1.17812i	0.294735	−	0.955579i	$-0.404769\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.49483	+	4.32118i	−0.605086	+	1.04804i	0.386952	+	0.922100i	$0.373528\pi$
$17$	−2.49483	+	4.32118i	−0.605086	+	1.04804i	−0.992038	+	0.125939i	$0.959806\pi$
$18$		0			0
$19$	0.00383929	+	0.00664984i	0.000880793	+	0.00152558i	0.866465	−	0.499237i	$-0.166386\pi$
$19$	0.00383929	+	0.00664984i	0.000880793	+	0.00152558i	−0.865585	+	0.500763i	$0.833053\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.333877	+	0.578292i	−0.0696181	+	0.120582i	−0.898733	−	0.438496i	$-0.855511\pi$
$23$	−0.333877	+	0.578292i	−0.0696181	+	0.120582i	0.829115	+	0.559078i	$0.188845\pi$
$24$		0			0
$25$	−0.682524	−	1.18217i	−0.136505	−	0.236433i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.85082	+	6.66981i	−0.715079	+	1.23855i	0.247851	+	0.968798i	$0.420276\pi$
$29$	−3.85082	+	6.66981i	−0.715079	+	1.23855i	−0.962929	+	0.269754i	$0.913058\pi$
$30$		0			0
$31$	7.76605			1.39482			0.697412	−	0.716671i	$-0.254335\pi$
$31$	7.76605			1.39482			0.697412	+	0.716671i	$0.254335\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.71729	−	6.09686i	0.459306	−	1.03056i
$36$		0			0
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	−0.999564	−	0.0295319i	$-0.990598\pi$
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	0.474207	−	0.880414i	$-0.342735\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.21159	−	9.02673i	−0.813913	−	1.40974i	−0.910106	−	0.414376i	$-0.864000\pi$
$41$	−5.21159	−	9.02673i	−0.813913	−	1.40974i	0.0961931	−	0.995363i	$-0.469333\pi$
$42$		0			0
$43$	−4.42935	+	7.67185i	−0.675469	+	1.16995i	0.300863	+	0.953668i	$0.402725\pi$
$43$	−4.42935	+	7.67185i	−0.675469	+	1.16995i	−0.976332	+	0.216279i	$0.930608\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.16104			0.315220			0.157610	−	0.987501i	$-0.449621\pi$
$47$	2.16104			0.315220			0.157610	+	0.987501i	$0.449621\pi$
$48$		0			0
$49$	6.84814	−	1.45015i	0.978306	−	0.207164i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.69858	−	6.40613i	0.508039	−	0.879950i	−0.491917	−	0.870642i	$-0.663704\pi$
$53$	3.69858	−	6.40613i	0.508039	−	0.879950i	0.999957	−	0.00930815i	$-0.00296292\pi$
$54$		0			0
$55$	−14.4133			−1.94348
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.523594			−0.0681661			−0.0340831	−	0.999419i	$-0.510851\pi$
$59$	−0.523594			−0.0681661			−0.0340831	+	0.999419i	$0.510851\pi$
$60$		0			0
$61$	−8.99082			−1.15116			−0.575578	−	0.817747i	$-0.695223\pi$
$61$	−8.99082			−1.15116			−0.575578	+	0.817747i	$0.695223\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.3746			1.53488
$66$		0			0
$67$	5.09582			0.622554			0.311277	−	0.950319i	$-0.399243\pi$
$67$	5.09582			0.622554			0.311277	+	0.950319i	$0.399243\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.68471			−0.674651			−0.337325	−	0.941388i	$-0.609522\pi$
$71$	−5.68471			−0.674651			−0.337325	+	0.941388i	$0.609522\pi$
$72$		0			0
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	−0.941187	−	0.337887i	$-0.890288\pi$
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	0.763212	+	0.646148i	$0.223621\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.87975	−	12.2318i	−1.01194	−	1.39394i
$78$		0			0
$79$	−6.16230			−0.693313			−0.346657	−	0.937992i	$-0.612683\pi$
$79$	−6.16230			−0.693313			−0.346657	+	0.937992i	$0.612683\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.258726	+	0.448126i	−0.0283988	+	0.0491882i	−0.879876	−	0.475204i	$-0.842374\pi$
$83$	−0.258726	+	0.448126i	−0.0283988	+	0.0491882i	0.851477	+	0.524392i	$0.175708\pi$
$84$		0			0
$85$	−6.29422	−	10.9019i	−0.682704	−	1.18248i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.19093	−	2.06274i	−0.126238	−	0.218650i	0.795978	−	0.605325i	$-0.206957\pi$
$89$	−1.19093	−	2.06274i	−0.126238	−	0.218650i	−0.922216	+	0.386675i	$0.873624\pi$
$90$		0			0
$91$	7.62377	+	10.5017i	0.799188	+	1.10087i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0193723			−0.00198756
$96$		0			0
$97$	4.32994	−	7.49968i	0.439639	−	0.761477i	−0.558022	−	0.829826i	$-0.688440\pi$
$97$	4.32994	−	7.49968i	0.439639	−	0.761477i	0.997662	+	0.0683485i	$0.0217730\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.66783	−	8.08492i	−0.464466	−	0.804479i	0.534711	−	0.845035i	$-0.320420\pi$
$101$	−4.66783	−	8.08492i	−0.464466	−	0.804479i	−0.999177	+	0.0405558i	$0.987087\pi$
$102$		0			0
$103$	8.10926	−	14.0456i	0.799029	−	1.38396i	−0.121220	−	0.992626i	$-0.538681\pi$
$103$	8.10926	−	14.0456i	0.799029	−	1.38396i	0.920249	−	0.391333i	$-0.127986\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	0.997312	−	0.0732767i	$-0.0233456\pi$
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	−0.562115	+	0.827059i	$0.690012\pi$
$108$		0			0
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	−0.631378	−	0.775476i	$-0.717510\pi$
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	0.987270	+	0.159051i	$0.0508435\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.14642	−	12.3780i	−0.672278	−	1.16442i	−0.977256	−	0.212061i	$-0.931982\pi$
$113$	−7.14642	−	12.3780i	−0.672278	−	1.16442i	0.304978	−	0.952359i	$-0.401351\pi$
$114$		0			0
$115$	−0.842339	−	1.45897i	−0.0785486	−	0.136050i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.37411	−	12.0580i	0.492644	−	1.10536i
$120$		0			0
$121$	−10.8190	+	18.7390i	−0.983544	+	1.70355i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.17064			−0.820247
$126$		0			0
$127$	1.96011			0.173932			0.0869660	−	0.996211i	$-0.472283\pi$
$127$	1.96011			0.173932			0.0869660	+	0.996211i	$0.472283\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.99412	−	3.45392i	0.174227	−	0.301771i	−0.765666	−	0.643238i	$-0.777591\pi$
$131$	1.99412	−	3.45392i	0.174227	−	0.301771i	0.939894	+	0.341467i	$0.110924\pi$
$132$		0			0
$133$	−0.0119349	−	0.0164402i	−0.00103489	−	0.00142555i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.70422	−	6.41589i	−0.316473	−	0.548147i	0.663277	−	0.748374i	$-0.269165\pi$
$137$	−3.70422	−	6.41589i	−0.316473	−	0.548147i	−0.979749	+	0.200227i	$0.935832\pi$
$138$		0			0
$139$	−6.92660	−	11.9972i	−0.587507	−	1.01759i	−0.994558	−	0.104186i	$-0.966776\pi$
$139$	−6.92660	−	11.9972i	−0.587507	−	1.01759i	0.407051	−	0.913405i	$-0.366557\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	14.0108	−	24.2674i	1.17164	−	2.02934i
$144$		0			0
$145$	−9.71524	−	16.8273i	−0.806807	−	1.39743i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.05202	+	12.2144i	−0.577724	+	1.00065i	0.418016	+	0.908440i	$0.362726\pi$
$149$	−7.05202	+	12.2144i	−0.577724	+	1.00065i	−0.995740	+	0.0922071i	$0.970608\pi$
$150$		0			0
$151$	−5.30027	−	9.18034i	−0.431330	−	0.747086i	0.565658	−	0.824640i	$-0.308622\pi$
$151$	−5.30027	−	9.18034i	−0.431330	−	0.747086i	−0.996988	+	0.0775543i	$0.975289\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.79650	+	16.9680i	−0.786874	+	1.36291i
$156$		0			0
$157$	−0.259558			−0.0207150			−0.0103575	−	0.999946i	$-0.503297\pi$
$157$	−0.259558			−0.0207150			−0.0103575	+	0.999946i	$0.503297\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.719203	−	1.61370i	0.0566811	−	0.127177i
$162$		0			0
$163$	−6.31882	−	10.9445i	−0.494928	−	0.857241i	0.505055	−	0.863087i	$-0.331472\pi$
$163$	−6.31882	−	10.9445i	−0.494928	−	0.857241i	−0.999983	+	0.00584647i	$0.998139\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.74959	−	9.95859i	−0.444917	−	0.770619i	0.553129	−	0.833095i	$-0.313433\pi$
$167$	−5.74959	−	9.95859i	−0.444917	−	0.770619i	−0.998046	+	0.0624765i	$0.980100\pi$
$168$		0			0
$169$	−5.52905	+	9.57659i	−0.425311	+	0.736661i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	15.8094			1.20197			0.600984	−	0.799261i	$-0.294775\pi$
$173$	15.8094			1.20197			0.600984	+	0.799261i	$0.294775\pi$
$174$		0			0
$175$	2.12171	+	2.92264i	0.160387	+	0.220931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	0.351265	+	0.936276i	$0.385752\pi$
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	−0.986471	+	0.163934i	$0.947582\pi$
$180$		0			0
$181$	6.35841			0.472617			0.236308	−	0.971678i	$-0.424062\pi$
$181$	6.35841			0.472617			0.236308	+	0.971678i	$0.424062\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	16.1245			1.18550
$186$		0			0
$187$	−28.5058			−2.08455
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.14094			−0.299628			−0.149814	−	0.988714i	$-0.547867\pi$
$191$	−4.14094			−0.299628			−0.149814	+	0.988714i	$0.547867\pi$
$192$		0			0
$193$	−7.69586			−0.553960			−0.276980	−	0.960876i	$-0.589334\pi$
$193$	−7.69586			−0.553960			−0.276980	+	0.960876i	$0.589334\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.29508			−0.234765			−0.117383	−	0.993087i	$-0.537450\pi$
$197$	−3.29508			−0.234765			−0.117383	+	0.993087i	$0.537450\pi$
$198$		0			0
$199$	−8.08840	+	14.0095i	−0.573371	+	0.993108i	0.422845	+	0.906202i	$0.361031\pi$
$199$	−8.08840	+	14.0095i	−0.573371	+	0.993108i	−0.996216	+	0.0869063i	$0.972302\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.29503	−	18.6118i	0.582197	−	1.30629i
$204$		0			0
$205$	26.2967			1.83664
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0219337	+	0.0379903i	−0.00151719	+	0.00262784i
$210$		0			0
$211$	13.9633	+	24.1851i	0.961273	+	1.66497i	0.719312	+	0.694687i	$0.244457\pi$
$211$	13.9633	+	24.1851i	0.961273	+	1.66497i	0.241961	+	0.970286i	$0.422209\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.1748	−	19.3554i	−0.762116	−	1.32002i
$216$		0			0
$217$	−20.4353	+	2.13994i	−1.38724	+	0.145268i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	24.4738			1.64629
$222$		0			0
$223$	10.1652	−	17.6066i	0.680711	−	1.17903i	−0.294054	−	0.955789i	$-0.595004\pi$
$223$	10.1652	−	17.6066i	0.680711	−	1.17903i	0.974764	−	0.223237i	$-0.0716623\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.84470	+	4.92716i	0.188809	+	0.327027i	0.944853	−	0.327493i	$-0.106204\pi$
$227$	2.84470	+	4.92716i	0.188809	+	0.327027i	−0.756044	+	0.654520i	$0.772871\pi$
$228$		0			0
$229$	−7.42708	+	12.8641i	−0.490795	+	0.850082i	−0.999944	−	0.0105964i	$-0.996627\pi$
$229$	−7.42708	+	12.8641i	−0.490795	+	0.850082i	0.509149	+	0.860679i	$0.329960\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.70652	−	11.6160i	−0.439358	−	0.760991i	0.558282	−	0.829652i	$-0.311461\pi$
$233$	−6.70652	−	11.6160i	−0.439358	−	0.760991i	−0.997640	+	0.0686603i	$0.978128\pi$
$234$		0			0
$235$	−2.72605	+	4.72166i	−0.177828	+	0.308007i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.33123	−	16.1622i	−0.603587	−	1.04544i	−0.992273	−	0.124073i	$-0.960404\pi$
$239$	−9.33123	−	16.1622i	−0.603587	−	1.04544i	0.388686	−	0.921370i	$-0.372929\pi$
$240$		0			0
$241$	10.7080	+	18.5468i	0.689762	+	1.19470i	0.971915	+	0.235333i	$0.0756181\pi$
$241$	10.7080	+	18.5468i	0.689762	+	1.19470i	−0.282153	+	0.959369i	$0.591049\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.47018	+	16.7918i	−0.349477	+	1.07279i
$246$		0			0
$247$	0.0188313	−	0.0326168i	0.00119821	−	0.00207536i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.462898			−0.0292179			−0.0146089	−	0.999893i	$-0.504650\pi$
$251$	−0.462898			−0.0292179			−0.0146089	+	0.999893i	$0.504650\pi$
$252$		0			0
$253$	−3.81485			−0.239838
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.401256	−	0.694996i	0.0250297	−	0.0433527i	−0.853239	−	0.521520i	$-0.825365\pi$
$257$	0.401256	−	0.694996i	0.0250297	−	0.0433527i	0.878269	+	0.478167i	$0.158699\pi$
$258$		0			0
$259$	9.93401	+	13.6840i	0.617270	+	0.850282i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.100693	−	0.174406i	−0.00620902	−	0.0107543i	0.862904	−	0.505368i	$-0.168643\pi$
$263$	−0.100693	−	0.174406i	−0.00620902	−	0.0107543i	−0.869113	+	0.494613i	$0.835310\pi$
$264$		0			0
$265$	9.33117	+	16.1621i	0.573209	+	0.992828i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.1773	−	19.3596i	0.681490	−	1.18038i	−0.293036	−	0.956101i	$-0.594666\pi$
$269$	11.1773	−	19.3596i	0.681490	−	1.18038i	0.974526	−	0.224274i	$-0.0720011\pi$
$270$		0			0
$271$	1.78925	+	3.09907i	0.108689	+	0.188255i	0.915240	−	0.402910i	$-0.132001\pi$
$271$	1.78925	+	3.09907i	0.108689	+	0.188255i	−0.806550	+	0.591166i	$0.798668\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.89924	−	6.75367i	0.235133	−	0.407262i
$276$		0			0
$277$	5.05336	+	8.75267i	0.303627	+	0.525897i	0.976955	−	0.213447i	$-0.0684690\pi$
$277$	5.05336	+	8.75267i	0.303627	+	0.525897i	−0.673328	+	0.739344i	$0.735136\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.7114	+	22.0167i	−0.758296	+	1.31341i	0.185422	+	0.982659i	$0.440635\pi$
$281$	−12.7114	+	22.0167i	−0.758296	+	1.31341i	−0.943719	+	0.330749i	$0.892699\pi$
$282$		0			0
$283$	−3.87666			−0.230443			−0.115222	−	0.993340i	$-0.536758\pi$
$283$	−3.87666			−0.230443			−0.115222	+	0.993340i	$0.536758\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.2009	+	22.3166i	0.956308	+	1.31730i
$288$		0			0
$289$	−3.94838	−	6.83879i	−0.232257	−	0.402282i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.428834	−	0.742762i	−0.0250527	−	0.0433926i	0.853227	−	0.521539i	$-0.174642\pi$
$293$	−0.428834	−	0.742762i	−0.0250527	−	0.0433926i	−0.878280	+	0.478147i	$0.841309\pi$
$294$		0			0
$295$	0.660489	−	1.14400i	0.0384551	−	0.0666063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.27527			0.189414
$300$		0			0
$301$	9.54124	−	21.4079i	0.549948	−	1.23393i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.3415	−	19.6440i	0.649412	−	1.12481i
$306$		0			0
$307$	0.717950			0.0409756			0.0204878	−	0.999790i	$-0.493478\pi$
$307$	0.717950			0.0409756			0.0204878	+	0.999790i	$0.493478\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.45213			−0.535981			−0.267990	−	0.963422i	$-0.586360\pi$
$311$	−9.45213			−0.535981			−0.267990	+	0.963422i	$0.586360\pi$
$312$		0			0
$313$	−23.2635			−1.31493			−0.657464	−	0.753486i	$-0.728371\pi$
$313$	−23.2635			−1.31493			−0.657464	+	0.753486i	$0.728371\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.2354			−0.743375			−0.371687	−	0.928358i	$-0.621221\pi$
$317$	−13.2354			−0.743375			−0.371687	+	0.928358i	$0.621221\pi$
$318$		0			0
$319$	−43.9992			−2.46348
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.0383135			−0.00213182
$324$		0			0
$325$	−3.34772	+	5.79841i	−0.185698	+	0.321638i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.68649	+	0.595476i	−0.313506	+	0.0328297i
$330$		0			0
$331$	30.4330			1.67275			0.836375	−	0.548158i	$-0.184671\pi$
$331$	30.4330			1.67275			0.836375	+	0.548158i	$0.184671\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.42813	+	11.1339i	−0.351206	+	0.608307i
$336$		0			0
$337$	−0.767420	−	1.32921i	−0.0418041	−	0.0724067i	0.844366	−	0.535766i	$-0.179977\pi$
$337$	−0.767420	−	1.32921i	−0.0418041	−	0.0724067i	−0.886170	+	0.463360i	$0.846644\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	22.1836	+	38.4231i	1.20131	+	2.08073i
$342$		0			0
$343$	−17.6204	+	5.70287i	−0.951410	+	0.307926i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.6072			−1.53571			−0.767856	−	0.640622i	$-0.778677\pi$
$347$	−28.6072			−1.53571			−0.767856	+	0.640622i	$0.778677\pi$
$348$		0			0
$349$	−9.05123	+	15.6772i	−0.484501	+	0.839181i	−0.999841	−	0.0178047i	$-0.994332\pi$
$349$	−9.05123	+	15.6772i	−0.484501	+	0.839181i	0.515340	+	0.856986i	$0.327666\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.29541	+	12.6360i	0.388295	+	0.672547i	0.992220	−	0.124494i	$-0.0397307\pi$
$353$	7.29541	+	12.6360i	0.388295	+	0.672547i	−0.603925	+	0.797041i	$0.706397\pi$
$354$		0			0
$355$	7.17099	−	12.4205i	0.380596	−	0.659212i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	0.836746	−	0.547592i	$-0.184455\pi$
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	−0.892601	+	0.450847i	$0.851122\pi$
$360$		0			0
$361$	9.49997	−	16.4544i	0.499998	−	0.866023i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.83638	−	6.64480i	−0.200805	−	0.347805i
$366$		0			0
$367$	3.33104	+	5.76954i	0.173879	+	0.301167i	0.939773	−	0.341800i	$-0.111036\pi$
$367$	3.33104	+	5.76954i	0.173879	+	0.301167i	−0.765894	+	0.642967i	$0.777703\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.96710	+	17.8760i	−0.413631	+	0.928076i
$372$		0			0
$373$	6.24916	−	10.8239i	0.323569	−	0.560438i	−0.657653	−	0.753321i	$-0.728451\pi$
$373$	6.24916	−	10.8239i	0.323569	−	0.560438i	0.981222	+	0.192883i	$0.0617838\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	37.7758			1.94555
$378$		0			0
$379$	19.5504			1.00423			0.502117	−	0.864800i	$-0.332555\pi$
$379$	19.5504			1.00423			0.502117	+	0.864800i	$0.332555\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.33740	−	2.31644i	0.0683379	−	0.118365i	−0.829832	−	0.558013i	$-0.811564\pi$
$383$	1.33740	−	2.31644i	0.0683379	−	0.118365i	0.898170	+	0.439649i	$0.144897\pi$
$384$		0			0
$385$	37.9265	−	3.97158i	1.93292	−	0.202411i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.98155	−	3.43214i	−0.100469	−	0.174017i	0.811409	−	0.584478i	$-0.198701\pi$
$389$	−1.98155	−	3.43214i	−0.100469	−	0.174017i	−0.911878	+	0.410462i	$0.865368\pi$
$390$		0			0
$391$	−1.66593	−	2.88548i	−0.0842499	−	0.145925i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.77345	−	13.4640i	0.391125	−	0.677448i
$396$		0			0
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	0.999809	+	0.0195431i	$0.00622114\pi$
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	−0.482980	+	0.875632i	$0.660446\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.91979	+	3.32517i	−0.0958696	+	0.166051i	−0.909971	−	0.414671i	$-0.863897\pi$
$401$	−1.91979	+	3.32517i	−0.0958696	+	0.166051i	0.814102	+	0.580722i	$0.197230\pi$
$402$		0			0
$403$	−19.0459	−	32.9884i	−0.948742	−	1.64327i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.2565	−	31.6212i	0.904940	−	1.56740i
$408$		0			0
$409$	−29.4227			−1.45486			−0.727428	−	0.686184i	$-0.759285\pi$
$409$	−29.4227			−1.45486			−0.727428	+	0.686184i	$0.759285\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.37777	−	0.144276i	0.0677954	−	0.00709938i
$414$		0			0
$415$	−0.652741	−	1.13058i	−0.0320418	−	0.0554980i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.40821	+	7.63525i	0.215355	+	0.373006i	0.953382	−	0.301765i	$-0.0975757\pi$
$419$	4.40821	+	7.63525i	0.215355	+	0.373006i	−0.738027	+	0.674771i	$0.764242\pi$
$420$		0			0
$421$	−17.6437	+	30.5597i	−0.859899	+	1.48939i	0.0121255	+	0.999926i	$0.496140\pi$
$421$	−17.6437	+	30.5597i	−0.859899	+	1.48939i	−0.872024	+	0.489462i	$0.837193\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.81113			0.330388
$426$		0			0
$427$	23.6581	−	2.47742i	1.14490	−	0.119891i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	0.372995	+	0.927833i	$0.378331\pi$
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	−0.990025	+	0.140893i	$0.955003\pi$
$432$		0			0
$433$	16.8556			0.810030			0.405015	−	0.914310i	$-0.367266\pi$
$433$	16.8556			0.810030			0.405015	+	0.914310i	$0.367266\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.00512739			−0.000245277
$438$		0			0
$439$	−30.9192			−1.47569			−0.737846	−	0.674969i	$-0.764157\pi$
$439$	−30.9192			−1.47569			−0.737846	+	0.674969i	$0.764157\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.31087			−0.442373			−0.221186	−	0.975232i	$-0.570993\pi$
$443$	−9.31087			−0.442373			−0.221186	+	0.975232i	$0.570993\pi$
$444$		0			0
$445$	6.00918			0.284862
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−23.8055			−1.12345			−0.561724	−	0.827324i	$-0.689862\pi$
$449$	−23.8055			−1.12345			−0.561724	+	0.827324i	$0.689862\pi$
$450$		0			0
$451$	29.7736	−	51.5694i	1.40198	−	2.42831i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−32.5621	+	3.40983i	−1.52653	+	0.159855i
$456$		0			0
$457$	−13.8110			−0.646053			−0.323027	−	0.946390i	$-0.604700\pi$
$457$	−13.8110			−0.646053			−0.323027	+	0.946390i	$0.604700\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.00256407	−	0.00444110i	0.000119421	−	0.000206843i	−0.865966	−	0.500103i	$-0.833295\pi$
$461$	0.00256407	−	0.00444110i	0.000119421	−	0.000206843i	0.866085	+	0.499897i	$0.166629\pi$
$462$		0			0
$463$	−12.9682	−	22.4616i	−0.602685	−	1.04388i	−0.992413	−	0.122951i	$-0.960764\pi$
$463$	−12.9682	−	22.4616i	−0.602685	−	1.04388i	0.389728	−	0.920930i	$-0.372569\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	−0.997702	−	0.0677588i	$-0.978415\pi$
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	0.440170	−	0.897914i	$-0.354918\pi$
$468$		0			0
$469$	−13.4090	+	1.40416i	−0.619168	+	0.0648379i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−50.6094			−2.32702
$474$		0			0
$475$	0.00524081	−	0.00907735i	0.000240465	−	0.000416497i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.39114	−	12.8018i	−0.337710	−	0.584931i	0.646292	−	0.763091i	$-0.276319\pi$
$479$	−7.39114	−	12.8018i	−0.337710	−	0.584931i	−0.984002	+	0.178160i	$0.942986\pi$
$480$		0			0
$481$	−15.6742	+	27.1486i	−0.714683	+	1.23787i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.9240	+	18.9210i	0.496035	+	0.859158i
$486$		0			0
$487$	−9.38360	+	16.2529i	−0.425211	+	0.736488i	−0.996440	−	0.0843033i	$-0.973134\pi$
$487$	−9.38360	+	16.2529i	−0.425211	+	0.736488i	0.571229	+	0.820791i	$0.306467\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	18.2871	+	31.6741i	0.825284	+	1.42943i	0.901702	+	0.432358i	$0.142318\pi$
$491$	18.2871	+	31.6741i	0.825284	+	1.42943i	−0.0764182	+	0.997076i	$0.524348\pi$
$492$		0			0
$493$	−19.2143	−	33.2801i	−0.865368	−	1.49886i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.9585	−	1.56642i	0.670982	−	0.0702637i
$498$		0			0
$499$	2.31591	−	4.01127i	0.103674	−	0.179569i	−0.809521	−	0.587090i	$-0.800273\pi$
$499$	2.31591	−	4.01127i	0.103674	−	0.179569i	0.913196	+	0.407521i	$0.133607\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.4143			0.731879			0.365940	−	0.930639i	$-0.380748\pi$
$503$	16.4143			0.731879			0.365940	+	0.930639i	$0.380748\pi$
$504$		0			0
$505$	23.5530			1.04809
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.24169	−	9.07888i	0.232334	−	0.402414i	−0.726161	−	0.687525i	$-0.758697\pi$
$509$	5.24169	−	9.07888i	0.232334	−	0.402414i	0.958495	+	0.285111i	$0.0920305\pi$
$510$		0			0
$511$	3.27556	−	7.34947i	0.144902	−	0.325121i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	20.4589	+	35.4358i	0.901526	+	1.56149i
$516$		0			0
$517$	6.17298	+	10.6919i	0.271487	+	0.470230i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.0087	−	19.0675i	0.482298	−	0.835364i	−0.517496	−	0.855686i	$-0.673136\pi$
$521$	11.0087	−	19.0675i	0.482298	−	0.835364i	0.999793	+	0.0203215i	$0.00646899\pi$
$522$		0			0
$523$	1.18541	+	2.05320i	0.0518346	+	0.0897801i	0.890778	−	0.454438i	$-0.150160\pi$
$523$	1.18541	+	2.05320i	0.0518346	+	0.0897801i	−0.838944	+	0.544218i	$0.816826\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−19.3750	+	33.5585i	−0.843988	+	1.46183i
$528$		0			0
$529$	11.2771	+	19.5324i	0.490307	+	0.849236i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.5623	+	44.2753i	−1.10723	+	1.91777i
$534$		0			0
$535$	−22.7147			−0.982044
$536$		0			0
$537$		0			0
$538$		0			0
$539$	26.7363	+	29.7394i	1.15161	+	1.28097i
$540$		0			0
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	0.972850	−	0.231436i	$-0.0743423\pi$
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	−0.686854	+	0.726795i	$0.741009\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.37418	+	16.2366i	0.401546	+	0.695498i
$546$		0			0
$547$	2.43685	−	4.22074i	0.104192	−	0.180466i	−0.809216	−	0.587512i	$-0.800108\pi$
$547$	2.43685	−	4.22074i	0.104192	−	0.180466i	0.913408	+	0.407046i	$0.133441\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.0591375			−0.00251934
$552$		0			0
$553$	16.2153	−	1.69802i	0.689543	−	0.0722074i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.09601	+	12.2907i	−0.300668	+	0.520772i	−0.976287	−	0.216479i	$-0.930543\pi$
$557$	−7.09601	+	12.2907i	−0.300668	+	0.520772i	0.675620	+	0.737250i	$0.263876\pi$
$558$		0			0
$559$	43.4511			1.83778
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.03971			0.296688			0.148344	−	0.988936i	$-0.452606\pi$
$563$	7.03971			0.296688			0.148344	+	0.988936i	$0.452606\pi$
$564$		0			0
$565$	36.0595			1.51703
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.3016			0.767244			0.383622	−	0.923490i	$-0.374677\pi$
$569$	18.3016			0.767244			0.383622	+	0.923490i	$0.374677\pi$
$570$		0			0
$571$	30.4383			1.27380			0.636902	−	0.770944i	$-0.280215\pi$
$571$	30.4383			1.27380			0.636902	+	0.770944i	$0.280215\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.911516			0.0380128
$576$		0			0
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	−0.724008	−	0.689791i	$-0.757702\pi$
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	0.959381	+	0.282114i	$0.0910356\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.557320	−	1.25047i	0.0231215	−	0.0518784i
$582$		0			0
$583$	42.2597			1.75022
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.89755	+	17.1431i	−0.408516	+	0.707570i	−0.994724	−	0.102591i	$-0.967287\pi$
$587$	−9.89755	+	17.1431i	−0.408516	+	0.707570i	0.586208	+	0.810161i	$0.300620\pi$
$588$		0			0
$589$	0.0298161	+	0.0516430i	0.00122855	+	0.00212791i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.69067	−	4.66038i	−0.110493	−	0.191379i	0.805476	−	0.592628i	$-0.201910\pi$
$593$	−2.69067	−	4.66038i	−0.110493	−	0.191379i	−0.915969	+	0.401249i	$0.868576\pi$
$594$		0			0
$595$	19.5664	+	26.9525i	0.802145	+	1.10495i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.25959			0.0923243			0.0461622	−	0.998934i	$-0.485301\pi$
$599$	2.25959			0.0923243			0.0461622	+	0.998934i	$0.485301\pi$
$600$		0			0
$601$	18.1873	−	31.5013i	0.741875	−	1.28496i	−0.209766	−	0.977752i	$-0.567270\pi$
$601$	18.1873	−	31.5013i	0.741875	−	1.28496i	0.951641	−	0.307213i	$-0.0993964\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−27.2953	−	47.2768i	−1.10971	−	1.92207i
$606$		0			0
$607$	8.10803	−	14.0435i	0.329095	−	0.570009i	−0.653238	−	0.757153i	$-0.726590\pi$
$607$	8.10803	−	14.0435i	0.329095	−	0.570009i	0.982333	+	0.187144i	$0.0599231\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.29985	−	9.17961i	−0.214409	−	0.371367i
$612$		0			0
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.0158822	−	0.999874i	$-0.494944\pi$
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.857975	−	0.513691i	$-0.171722\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.92248	+	10.2580i	0.238430	+	0.412973i	0.960264	−	0.279093i	$-0.0900339\pi$
$617$	5.92248	+	10.2580i	0.238430	+	0.412973i	−0.721834	+	0.692066i	$0.756701\pi$
$618$		0			0
$619$	20.1644	+	34.9257i	0.810475	+	1.40378i	0.912532	+	0.409006i	$0.134124\pi$
$619$	20.1644	+	34.9257i	0.810475	+	1.40378i	−0.102057	+	0.994779i	$0.532542\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.70215	+	5.09967i	0.148323	+	0.204314i
$624$		0			0
$625$	14.9809	−	25.9478i	0.599238	−	1.03791i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	31.8902			1.27154
$630$		0			0
$631$	−13.9489			−0.555298			−0.277649	−	0.960683i	$-0.589555\pi$
$631$	−13.9489			−0.555298			−0.277649	+	0.960683i	$0.589555\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.47259	+	4.28265i	−0.0981217	+	0.169952i
$636$		0			0
$637$	−22.9546	−	25.5329i	−0.909496	−	1.01165i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.76975	+	15.1896i	0.346384	+	0.599955i	0.985604	−	0.169069i	$-0.0540761\pi$
$641$	8.76975	+	15.1896i	0.346384	+	0.599955i	−0.639220	+	0.769024i	$0.720743\pi$
$642$		0			0
$643$	13.5329	+	23.4397i	0.533686	+	0.924371i	0.999226	+	0.0393443i	$0.0125269\pi$
$643$	13.5329	+	23.4397i	0.533686	+	0.924371i	−0.465540	+	0.885027i	$0.654140\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	−0.552828	−	0.833295i	$-0.686452\pi$
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	0.998069	+	0.0621160i	$0.0197849\pi$
$648$		0			0
$649$	−1.49564	−	2.59052i	−0.0587089	−	0.101687i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.392054	+	0.679058i	−0.0153423	+	0.0265736i	−0.873595	−	0.486654i	$-0.838217\pi$
$653$	−0.392054	+	0.679058i	−0.0153423	+	0.0265736i	0.858252	+	0.513228i	$0.171550\pi$
$654$		0			0
$655$	5.03098	+	8.71392i	0.196577	+	0.340481i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.7219	+	28.9632i	−0.651392	+	1.12824i	0.331393	+	0.943493i	$0.392481\pi$
$659$	−16.7219	+	28.9632i	−0.651392	+	1.12824i	−0.982785	+	0.184752i	$0.940852\pi$
$660$		0			0
$661$	3.06516			0.119221			0.0596104	−	0.998222i	$-0.481014\pi$
$661$	3.06516			0.119221			0.0596104	+	0.998222i	$0.481014\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.0509756	−	0.00533805i	0.00197675	−	0.000207001i
$666$		0			0
$667$	−2.57140	−	4.45379i	−0.0995649	−	0.172451i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−25.6821	−	44.4827i	−0.991447	−	1.71724i
$672$		0			0
$673$	14.4618	−	25.0487i	0.557463	−	0.965555i	−0.440244	−	0.897878i	$-0.645108\pi$
$673$	14.4618	−	25.0487i	0.557463	−	0.965555i	0.997707	−	0.0676766i	$-0.0215586\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.7164			0.450296			0.225148	−	0.974325i	$-0.427713\pi$
$677$	11.7164			0.450296			0.225148	+	0.974325i	$0.427713\pi$
$678$		0			0
$679$	−9.32711	+	20.9275i	−0.357942	+	0.803124i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	−0.131441	−	0.991324i	$-0.541960\pi$
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	0.924232	−	0.381831i	$-0.124706\pi$
$684$		0			0
$685$	18.6908			0.714138
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−36.2824			−1.38225
$690$		0			0
$691$	6.91350			0.263002			0.131501	−	0.991316i	$-0.458020\pi$
$691$	6.91350			0.263002			0.131501	+	0.991316i	$0.458020\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	34.9503			1.32574
$696$		0			0
$697$	52.0081			1.96995
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−39.1954			−1.48039			−0.740195	−	0.672392i	$-0.765267\pi$
$701$	−39.1954			−1.48039			−0.740195	+	0.672392i	$0.765267\pi$
$702$		0			0
$703$	0.0245378	−	0.0425008i	0.000925462	−	0.00160295i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.5106	+	19.9881i	0.545726	+	0.751731i
$708$		0			0
$709$	20.4871			0.769409			0.384705	−	0.923040i	$-0.374303\pi$
$709$	20.4871			0.769409			0.384705	+	0.923040i	$0.374303\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.59290	+	4.49104i	−0.0971050	+	0.168191i
$714$		0			0
$715$	35.3479	+	61.2243i	1.32193	+	2.28966i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	0.985688	+	0.168582i	$0.0539187\pi$
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	−0.346848	+	0.937921i	$0.612748\pi$
$720$		0			0
$721$	−17.4681	+	39.1937i	−0.650547	+	1.45965i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.5131			0.390447
$726$		0			0
$727$	−7.18914	+	12.4520i	−0.266631	+	0.461818i	−0.967990	−	0.250991i	$-0.919244\pi$
$727$	−7.18914	+	12.4520i	−0.266631	+	0.461818i	0.701359	+	0.712808i	$0.252577\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−22.1010	−	38.2800i	−0.817433	−	1.41584i
$732$		0			0
$733$	−19.7887	+	34.2750i	−0.730911	+	1.26597i	0.225584	+	0.974224i	$0.427571\pi$
$733$	−19.7887	+	34.2750i	−0.730911	+	1.26597i	−0.956494	+	0.291751i	$0.905762\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.5561	+	25.2119i	0.536182	+	0.928694i
$738$		0			0
$739$	−10.8407	+	18.7767i	−0.398783	+	0.690712i	−0.993576	−	0.113167i	$-0.963901\pi$
$739$	−10.8407	+	18.7767i	−0.398783	+	0.690712i	0.594793	+	0.803879i	$0.297234\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.5692	+	28.6987i	0.607864	+	1.05285i	0.991592	+	0.129406i	$0.0413069\pi$
$743$	16.5692	+	28.6987i	0.607864	+	1.05285i	−0.383727	+	0.923446i	$0.625360\pi$
$744$		0			0
$745$	−17.7916	−	30.8159i	−0.651832	−	1.12901i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−13.9941	−	19.2768i	−0.511335	−	0.704358i
$750$		0			0
$751$	−12.9662	+	22.4581i	−0.473144	+	0.819509i	−0.999527	−	0.0307381i	$-0.990214\pi$
$751$	−12.9662	+	22.4581i	−0.473144	+	0.819509i	0.526384	+	0.850247i	$0.323548\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	26.7442			0.973320
$756$		0			0
$757$	−30.5846			−1.11162			−0.555808	−	0.831311i	$-0.687591\pi$
$757$	−30.5846			−1.11162			−0.555808	+	0.831311i	$0.687591\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.2648	+	31.6355i	−0.662097	+	1.14679i	0.317967	+	0.948102i	$0.397000\pi$
$761$	−18.2648	+	31.6355i	−0.662097	+	1.14679i	−0.980064	+	0.198684i	$0.936333\pi$
$762$		0			0
$763$	−8.00382	+	17.9584i	−0.289758	+	0.650138i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.28409	+	2.22411i	0.0463658	+	0.0803079i
$768$		0			0
$769$	−21.3107	−	36.9113i	−0.768485	−	1.33105i	−0.938384	−	0.345593i	$-0.887678\pi$
$769$	−21.3107	−	36.9113i	−0.768485	−	1.33105i	0.169900	−	0.985461i	$-0.445656\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−16.1309	+	27.9395i	−0.580187	+	1.00491i	0.415270	+	0.909698i	$0.363687\pi$
$773$	−16.1309	+	27.9395i	−0.580187	+	1.00491i	−0.995457	+	0.0952148i	$0.969646\pi$
$774$		0			0
$775$	−5.30051	−	9.18076i	−0.190400	−	0.329783i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.0400175	−	0.0693124i	0.00143378	−	0.00248337i
$780$		0			0
$781$	−16.2383	−	28.1255i	−0.581051	−	1.00641i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.327420	−	0.567107i	0.0116861	−	0.0202409i
$786$		0			0
$787$	−30.7676			−1.09675			−0.548373	−	0.836234i	$-0.684753\pi$
$787$	−30.7676			−1.09675			−0.548373	+	0.836234i	$0.684753\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	22.2156	+	30.6017i	0.789895	+	1.08807i
$792$		0			0
$793$	22.0496	+	38.1910i	0.783003	+	1.35620i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.59378	+	6.22460i	0.127298	+	0.220487i	0.922629	−	0.385689i	$-0.126036\pi$
$797$	3.59378	+	6.22460i	0.127298	+	0.220487i	−0.795331	+	0.606176i	$0.792703\pi$
$798$		0			0
$799$	−5.39144	+	9.33824i	−0.190735	+	0.330363i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.3745			−0.613133
$804$		0			0
$805$	2.61852	+	3.60699i	0.0922908	+	0.127130i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	23.3886	−	40.5103i	0.822301	−	1.42427i	−0.0816637	−	0.996660i	$-0.526023\pi$
$809$	23.3886	−	40.5103i	0.822301	−	1.42427i	0.903965	−	0.427607i	$-0.140643\pi$
$810$		0			0
$811$	−17.6946			−0.621341			−0.310671	−	0.950518i	$-0.600554\pi$
$811$	−17.6946			−0.621341			−0.310671	+	0.950518i	$0.600554\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	31.8836			1.11683
$816$		0			0
$817$	−0.0680221			−0.00237979
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.2215			0.601034			0.300517	−	0.953776i	$-0.402841\pi$
$821$	17.2215			0.601034			0.300517	+	0.953776i	$0.402841\pi$
$822$		0			0
$823$	−11.5434			−0.402378			−0.201189	−	0.979552i	$-0.564480\pi$
$823$	−11.5434			−0.402378			−0.201189	+	0.979552i	$0.564480\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.1448			−0.700503			−0.350251	−	0.936656i	$-0.613904\pi$
$827$	−20.1448			−0.700503			−0.350251	+	0.936656i	$0.613904\pi$
$828$		0			0
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	−0.927269	−	0.374397i	$-0.877850\pi$
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	0.787871	+	0.615840i	$0.211183\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.8186	+	33.2099i	−0.374843	+	1.15066i
$834$		0			0
$835$	29.0114			1.00398
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.59341	+	7.95603i	−0.158582	+	0.274673i	−0.934358	−	0.356337i	$-0.884026\pi$
$839$	−4.59341	+	7.95603i	−0.158582	+	0.274673i	0.775775	+	0.631009i	$0.217359\pi$
$840$		0			0
$841$	−15.1576	−	26.2537i	−0.522675	−	0.905299i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.9493	−	24.1608i	−0.479869	−	0.831158i
$846$		0			0
$847$	23.3051	−	52.2904i	0.800774	−	1.79672i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.26778			0.146298
$852$		0			0
$853$	−10.7925	+	18.6931i	−0.369527	+	0.640040i	−0.989492	−	0.144590i	$-0.953814\pi$
$853$	−10.7925	+	18.6931i	−0.369527	+	0.640040i	0.619964	+	0.784630i	$0.287147\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.0326	+	20.8410i	0.411024	+	0.711915i	0.995002	−	0.0998547i	$-0.0318378\pi$
$857$	12.0326	+	20.8410i	0.411024	+	0.711915i	−0.583978	+	0.811770i	$0.698504\pi$
$858$		0			0
$859$	−8.15861	+	14.1311i	−0.278368	+	0.482148i	−0.970979	−	0.239163i	$-0.923127\pi$
$859$	−8.15861	+	14.1311i	−0.278368	+	0.482148i	0.692611	+	0.721311i	$0.256460\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	0.653811	−	0.756658i	$-0.273169\pi$
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	−0.982190	+	0.187888i	$0.939836\pi$
$864$		0			0
$865$	−19.9428	+	34.5420i	−0.678077	+	1.17446i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−17.6025	−	30.4884i	−0.597124	−	1.03425i
$870$		0			0
$871$	−12.4973	−	21.6459i	−0.423453	−	0.733443i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.1313	−	2.52697i	0.815786	−	0.0854273i
$876$		0			0
$877$	−15.1464	+	26.2343i	−0.511457	+	0.885870i	0.488454	+	0.872589i	$0.337561\pi$
$877$	−15.1464	+	26.2343i	−0.511457	+	0.885870i	−0.999912	+	0.0132808i	$0.995772\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.4943			−0.656779			−0.328390	−	0.944542i	$-0.606506\pi$
$881$	−19.4943			−0.656779			−0.328390	+	0.944542i	$0.606506\pi$
$882$		0			0
$883$	−47.5302			−1.59952			−0.799759	−	0.600321i	$-0.795040\pi$
$883$	−47.5302			−1.59952			−0.799759	+	0.600321i	$0.795040\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.05946	−	3.56709i	0.0691499	−	0.119771i	−0.829377	−	0.558689i	$-0.811305\pi$
$887$	2.05946	−	3.56709i	0.0691499	−	0.119771i	0.898527	+	0.438918i	$0.144638\pi$
$888$		0			0
$889$	−5.15777	+	0.540110i	−0.172986	+	0.0181147i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.00829686	+	0.0143706i	0.000277644	+	0.000480893i
$894$		0			0
$895$	−21.4409	−	37.1367i	−0.716689	−	1.24134i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.9056	+	51.7981i	−0.997408	+	1.72756i
$900$		0			0
$901$	18.4547	+	31.9645i	0.614815	+	1.06489i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.02083	+	13.8925i	−0.266621	+	0.461802i
$906$		0			0
$907$	4.07084	+	7.05090i	0.135170	+	0.234121i	0.925662	−	0.378351i	$-0.123509\pi$
$907$	4.07084	+	7.05090i	0.135170	+	0.234121i	−0.790492	+	0.612472i	$0.790175\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.6454	+	42.6871i	−0.816540	+	1.41429i	0.0916774	+	0.995789i	$0.470777\pi$
$911$	−24.6454	+	42.6871i	−0.816540	+	1.41429i	−0.908217	+	0.418499i	$0.862556\pi$
$912$		0			0
$913$	−2.95618			−0.0978354
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.29553	+	9.63801i	−0.141851	+	0.318275i
$918$		0			0
$919$	4.71585	+	8.16809i	0.155561	+	0.269440i	0.933263	−	0.359193i	$-0.116948\pi$
$919$	4.71585	+	8.16809i	0.155561	+	0.269440i	−0.777702	+	0.628633i	$0.783615\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.9415	+	24.1473i	0.458889	+	0.794819i
$924$		0			0
$925$	−4.36218	+	7.55552i	−0.143428	+	0.248424i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−29.4739			−0.967006			−0.483503	−	0.875343i	$-0.660636\pi$
$929$	−29.4739			−0.967006			−0.483503	+	0.875343i	$0.660636\pi$
$930$		0			0
$931$	0.0359352	+	0.0399715i	0.00117773	+	0.00131001i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	35.9587	−	62.2823i	1.17597	−	2.03685i
$936$		0			0
$937$	−54.3451			−1.77538			−0.887688	−	0.460445i	$-0.847690\pi$
$937$	−54.3451			−1.77538			−0.887688	+	0.460445i	$0.847690\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.98173			0.0972017			0.0486008	−	0.998818i	$-0.484524\pi$
$941$	2.98173			0.0972017			0.0486008	+	0.998818i	$0.484524\pi$
$942$		0			0
$943$	6.96011			0.226652
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.3292			0.985567			0.492783	−	0.870152i	$-0.335979\pi$
$947$	30.3292			0.985567			0.492783	+	0.870152i	$0.335979\pi$
$948$		0			0
$949$	14.9170			0.484226
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.380127			−0.0123135			−0.00615676	−	0.999981i	$-0.501960\pi$
$953$	−0.380127			−0.0123135			−0.00615676	+	0.999981i	$0.501960\pi$
$954$		0			0
$955$	5.22360	−	9.04754i	0.169032	−	0.292771i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.5150	+	15.8618i	0.371840	+	0.512206i
$960$		0			0
$961$	29.3115			0.945533
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.70796	−	16.8147i	0.312510	−	0.541284i
$966$		0			0
$967$	22.6744	+	39.2732i	0.729160	+	1.26294i	0.957239	+	0.289300i	$0.0934224\pi$
$967$	22.6744	+	39.2732i	0.729160	+	1.26294i	−0.228078	+	0.973643i	$0.573244\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.852996	−	0.521917i	$-0.825217\pi$
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.0254951	−	0.999675i	$-0.508116\pi$
$972$		0			0
$973$	21.5323	+	29.6604i	0.690292	+	0.950870i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.71311			−0.0868001			−0.0434001	−	0.999058i	$-0.513819\pi$
$977$	−2.71311			−0.0868001			−0.0434001	+	0.999058i	$0.513819\pi$
$978$		0			0
$979$	6.80371	−	11.7844i	0.217448	−	0.376630i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.3828	−	37.0361i	−0.682006	−	1.18127i	−0.974368	−	0.224961i	$-0.927774\pi$
$983$	−21.3828	−	37.0361i	−0.682006	−	1.18127i	0.292362	−	0.956308i	$-0.405559\pi$
$984$		0			0
$985$	4.15659	−	7.19943i	0.132440	−	0.229393i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.95771	−	5.12291i	−0.0940498	−	0.162899i
$990$		0			0
$991$	−29.6731	+	51.3954i	−0.942598	+	1.63263i	−0.182107	+	0.983279i	$0.558292\pi$
$991$	−29.6731	+	51.3954i	−0.942598	+	1.63263i	−0.760491	+	0.649349i	$0.775042\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.4063	−	35.3447i	−0.646922	−	1.12050i
$996$		0			0
$997$	−22.0320	−	38.1606i	−0.697762	−	1.20856i	−0.969241	−	0.246114i	$-0.920846\pi$
$997$	−22.0320	−	38.1606i	−0.697762	−	1.20856i	0.271479	−	0.962444i	$-0.412487\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.k.2881.3		22
3.2	odd	2		1008.2.q.k.529.9		22
4.3	odd	2		1512.2.q.c.1369.3		22
7.2	even	3		3024.2.t.l.289.9		22
9.4	even	3		3024.2.t.l.1873.9		22
9.5	odd	6		1008.2.t.k.193.2		22
12.11	even	2		504.2.q.d.25.3	✓	22
21.2	odd	6		1008.2.t.k.961.2		22
28.23	odd	6		1512.2.t.d.289.9		22
36.23	even	6		504.2.t.d.193.10	yes	22
36.31	odd	6		1512.2.t.d.361.9		22
63.23	odd	6		1008.2.q.k.625.9		22
63.58	even	3	inner	3024.2.q.k.2305.3		22
84.23	even	6		504.2.t.d.457.10	yes	22
252.23	even	6		504.2.q.d.121.3	yes	22
252.247	odd	6		1512.2.q.c.793.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.3	✓	22	12.11	even	2
504.2.q.d.121.3	yes	22	252.23	even	6
504.2.t.d.193.10	yes	22	36.23	even	6
504.2.t.d.457.10	yes	22	84.23	even	6
1008.2.q.k.529.9		22	3.2	odd	2
1008.2.q.k.625.9		22	63.23	odd	6
1008.2.t.k.193.2		22	9.5	odd	6
1008.2.t.k.961.2		22	21.2	odd	6
1512.2.q.c.793.3		22	252.247	odd	6
1512.2.q.c.1369.3		22	4.3	odd	2
1512.2.t.d.289.9		22	28.23	odd	6
1512.2.t.d.361.9		22	36.31	odd	6
3024.2.q.k.2305.3		22	63.58	even	3	inner
3024.2.q.k.2881.3		22	1.1	even	1	trivial
3024.2.t.l.289.9		22	7.2	even	3
3024.2.t.l.1873.9		22	9.4	even	3

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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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26145 + 2.18490i) q^{5} +(-2.63136 + 0.275550i) q^{7} +O(q^{10})\)	\(q+(-1.26145 + 2.18490i) q^{5} +(-2.63136 + 0.275550i) q^{7} +(2.85648 + 4.94757i) q^{11} +(-2.45245 - 4.24777i) q^{13} +(-2.49483 + 4.32118i) q^{17} +(0.00383929 + 0.00664984i) q^{19} +(-0.333877 + 0.578292i) q^{23} +(-0.682524 - 1.18217i) q^{25} +(-3.85082 + 6.66981i) q^{29} +7.76605 q^{31} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-5.21159 - 9.02673i) q^{41} +(-4.42935 + 7.67185i) q^{43} +2.16104 q^{47} +(6.84814 - 1.45015i) q^{49} +(3.69858 - 6.40613i) q^{53} -14.4133 q^{55} -0.523594 q^{59} -8.99082 q^{61} +12.3746 q^{65} +5.09582 q^{67} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(-8.87975 - 12.2318i) q^{77} -6.16230 q^{79} +(-0.258726 + 0.448126i) q^{83} +(-6.29422 - 10.9019i) q^{85} +(-1.19093 - 2.06274i) q^{89} +(7.62377 + 10.5017i) q^{91} -0.0193723 q^{95} +(4.32994 - 7.49968i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 + 5 * q^7	\( 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

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