LMFDB - Embedded newform 1512.2.t.c.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.5
Character	$\chi$	$=$	1512.361
Dual form			1512.2.t.c.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +O(q^{10})$	$q-0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} -4.61052 q^{11} +(0.244554 - 0.423580i) q^{13} +(-2.75579 + 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +0.0539537 q^{23} -4.72332 q^{25} +(3.28471 + 5.68929i) q^{29} +(-3.03820 - 5.26231i) q^{31} +(-1.28325 - 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-2.52284 + 4.36968i) q^{41} +(2.84893 + 4.93449i) q^{43} +(-4.59810 + 7.96415i) q^{47} +(4.90354 + 4.99552i) q^{49} +(4.37138 - 7.57145i) q^{53} +2.42515 q^{55} +(-3.31538 - 5.74241i) q^{59} +(0.232812 - 0.403243i) q^{61} +(-0.128636 + 0.222805i) q^{65} +(-2.59679 - 4.49777i) q^{67} -1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(-11.2479 - 4.72039i) q^{77} +(-8.18509 + 14.1770i) q^{79} +(-4.49251 - 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(7.05145 + 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +(-0.966699 - 1.67437i) q^{95} +(5.22413 + 9.04847i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.526004			−0.235236			−0.117618	−	0.993059i	$-0.537526\pi$
$5$	−0.526004			−0.235236			−0.117618	+	0.993059i	$0.537526\pi$
$6$		0			0
$7$	2.43963	+	1.02383i	0.922092	+	0.386971i
$7$	2.43963	+	1.02383i	0.922092	+	0.386971i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.61052			−1.39012			−0.695062	−	0.718950i	$-0.744623\pi$
$11$	−4.61052			−1.39012			−0.695062	+	0.718950i	$0.744623\pi$
$12$		0			0
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	−0.830118	−	0.557588i	$-0.811727\pi$
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	0.897945	+	0.440109i	$0.145060\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.75579	+	4.77318i	−0.668378	+	1.15767i	0.309979	+	0.950743i	$0.399678\pi$
$17$	−2.75579	+	4.77318i	−0.668378	+	1.15767i	−0.978357	+	0.206922i	$0.933655\pi$
$18$		0			0
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	0.996099	−	0.0882484i	$-0.0281269\pi$
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	−0.574475	+	0.818522i	$0.694794\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.0539537			0.0112501			0.00562506	−	0.999984i	$-0.498209\pi$
$23$	0.0539537			0.0112501			0.00562506	+	0.999984i	$0.498209\pi$
$24$		0			0
$25$	−4.72332			−0.944664
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.28471	+	5.68929i	0.609956	+	1.05647i	0.991247	+	0.132019i	$0.0421461\pi$
$29$	3.28471	+	5.68929i	0.609956	+	1.05647i	−0.381292	+	0.924455i	$0.624521\pi$
$30$		0			0
$31$	−3.03820	−	5.26231i	−0.545676	−	0.945139i	−0.998564	−	0.0535717i	$-0.982939\pi$
$31$	−3.03820	−	5.26231i	−0.545676	−	0.945139i	0.452888	−	0.891568i	$-0.350394\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.28325	−	0.538539i	−0.216909	−	0.0910297i
$36$		0			0
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	0.883830	−	0.467808i	$-0.154956\pi$
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	−0.847049	+	0.531515i	$0.821623\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.52284	+	4.36968i	−0.394001	+	0.682430i	−0.992973	−	0.118340i	$-0.962243\pi$
$41$	−2.52284	+	4.36968i	−0.394001	+	0.682430i	0.598972	+	0.800770i	$0.295576\pi$
$42$		0			0
$43$	2.84893	+	4.93449i	0.434458	+	0.752503i	0.997251	−	0.0740947i	$-0.0236067\pi$
$43$	2.84893	+	4.93449i	0.434458	+	0.752503i	−0.562794	+	0.826598i	$0.690273\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.59810	+	7.96415i	−0.670702	+	1.16169i	0.307003	+	0.951709i	$0.400674\pi$
$47$	−4.59810	+	7.96415i	−0.670702	+	1.16169i	−0.977705	+	0.209982i	$0.932659\pi$
$48$		0			0
$49$	4.90354	+	4.99552i	0.700506	+	0.713646i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.37138	−	7.57145i	0.600455	−	1.04002i	−0.392297	−	0.919839i	$-0.628320\pi$
$53$	4.37138	−	7.57145i	0.600455	−	1.04002i	0.992752	−	0.120180i	$-0.0383471\pi$
$54$		0			0
$55$	2.42515			0.327008
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.31538	−	5.74241i	−0.431626	−	0.747598i	0.565388	−	0.824825i	$-0.308727\pi$
$59$	−3.31538	−	5.74241i	−0.431626	−	0.747598i	−0.997014	+	0.0772273i	$0.975393\pi$
$60$		0			0
$61$	0.232812	−	0.403243i	0.0298086	−	0.0516299i	−0.850736	−	0.525593i	$-0.823844\pi$
$61$	0.232812	−	0.403243i	0.0298086	−	0.0516299i	0.880545	+	0.473963i	$0.157177\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.128636	+	0.222805i	−0.0159554	+	0.0276355i
$66$		0			0
$67$	−2.59679	−	4.49777i	−0.317248	−	0.549490i	0.662665	−	0.748916i	$-0.269425\pi$
$67$	−2.59679	−	4.49777i	−0.317248	−	0.549490i	−0.979913	+	0.199426i	$0.936092\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.76328			−0.209263			−0.104632	−	0.994511i	$-0.533366\pi$
$71$	−1.76328			−0.209263			−0.104632	+	0.994511i	$0.533366\pi$
$72$		0			0
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	0.377692	+	0.925931i	$0.376718\pi$
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	−0.990726	+	0.135875i	$0.956616\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.2479	−	4.72039i	−1.28182	−	0.537938i
$78$		0			0
$79$	−8.18509	+	14.1770i	−0.920895	+	1.59504i	−0.122860	+	0.992424i	$0.539207\pi$
$79$	−8.18509	+	14.1770i	−0.920895	+	1.59504i	−0.798034	+	0.602612i	$0.794127\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.49251	−	7.78126i	−0.493117	−	0.854104i	0.506851	−	0.862034i	$-0.330809\pi$
$83$	−4.49251	−	7.78126i	−0.493117	−	0.854104i	−0.999969	+	0.00792925i	$0.997476\pi$
$84$		0			0
$85$	1.44956	−	2.51071i	0.157227	−	0.272325i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.05145	+	12.2135i	0.747452	+	1.29463i	0.949040	+	0.315155i	$0.102056\pi$
$89$	7.05145	+	12.2135i	0.747452	+	1.29463i	−0.201588	+	0.979470i	$0.564610\pi$
$90$		0			0
$91$	1.03029	−	0.782994i	0.108004	−	0.0820801i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.966699	−	1.67437i	−0.0991813	−	0.171787i
$96$		0			0
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	0.999370	+	0.0355020i	$0.0113030\pi$
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	−0.468939	+	0.883230i	$0.655364\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.96508			0.991562			0.495781	−	0.868448i	$-0.334882\pi$
$101$	9.96508			0.991562			0.495781	+	0.868448i	$0.334882\pi$
$102$		0			0
$103$	11.6511			1.14801			0.574006	−	0.818851i	$-0.305389\pi$
$103$	11.6511			1.14801			0.574006	+	0.818851i	$0.305389\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.45556	−	4.25316i	−0.237388	−	0.411168i	0.722576	−	0.691292i	$-0.242958\pi$
$107$	−2.45556	−	4.25316i	−0.237388	−	0.411168i	−0.959964	+	0.280123i	$0.909625\pi$
$108$		0			0
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.160858	+	0.986978i	$0.551426\pi$
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.774319	+	0.632796i	$0.781907\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.48658	+	9.50304i	−0.516134	+	0.893971i	0.483690	+	0.875239i	$0.339296\pi$
$113$	−5.48658	+	9.50304i	−0.516134	+	0.893971i	−0.999825	+	0.0187317i	$0.994037\pi$
$114$		0			0
$115$	−0.0283799			−0.00264644
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.6100	+	8.82330i	−1.06429	+	0.808830i
$120$		0			0
$121$	10.2569			0.932444
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.11451			0.457456
$126$		0			0
$127$	−16.6107			−1.47396			−0.736979	−	0.675915i	$-0.763748\pi$
$127$	−16.6107			−1.47396			−0.736979	+	0.675915i	$0.763748\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.81696			−0.508230			−0.254115	−	0.967174i	$-0.581784\pi$
$131$	−5.81696			−0.508230			−0.254115	+	0.967174i	$0.581784\pi$
$132$		0			0
$133$	1.22454	+	9.64740i	0.106181	+	0.836536i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.22626			0.788253			0.394126	−	0.919056i	$-0.371047\pi$
$137$	9.22626			0.788253			0.394126	+	0.919056i	$0.371047\pi$
$138$		0			0
$139$	6.88477	−	11.9248i	0.583959	−	1.01145i	−0.411046	−	0.911615i	$-0.634836\pi$
$139$	6.88477	−	11.9248i	0.583959	−	1.01145i	0.995004	−	0.0998314i	$-0.0318303\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.12752	+	1.95292i	−0.0942880	+	0.163312i
$144$		0			0
$145$	−1.72777	−	2.99259i	−0.143484	−	0.248521i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.30086			0.680033			0.340016	−	0.940420i	$-0.389567\pi$
$149$	8.30086			0.680033			0.340016	+	0.940420i	$0.389567\pi$
$150$		0			0
$151$	−14.4979			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$151$	−14.4979			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.59811	+	2.76800i	0.128363	+	0.222331i
$156$		0			0
$157$	6.24434	+	10.8155i	0.498352	+	0.863172i	0.999998	−	0.00190155i	$-0.000605282\pi$
$157$	6.24434	+	10.8155i	0.498352	+	0.863172i	−0.501646	+	0.865073i	$0.667272\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.131627	+	0.0552394i	0.0103736	+	0.00435348i
$162$		0			0
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	0.752169	−	0.658970i	$-0.229007\pi$
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	−0.946769	+	0.321913i	$0.895674\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.0088	−	17.3357i	0.774504	−	1.34148i	−0.160569	−	0.987025i	$-0.551333\pi$
$167$	10.0088	−	17.3357i	0.774504	−	1.34148i	0.935073	−	0.354456i	$-0.115334\pi$
$168$		0			0
$169$	6.38039	+	11.0512i	0.490799	+	0.850089i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.52742	−	7.84173i	0.344214	−	0.596196i	−0.640997	−	0.767543i	$-0.721479\pi$
$173$	4.52742	−	7.84173i	0.344214	−	0.596196i	0.985211	+	0.171348i	$0.0548122\pi$
$174$		0			0
$175$	−11.5231	−	4.83588i	−0.871067	−	0.365558i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.69175	−	13.3225i	0.574908	−	0.995770i	−0.421143	−	0.906994i	$-0.638371\pi$
$179$	7.69175	−	13.3225i	0.574908	−	0.995770i	0.996052	−	0.0887763i	$-0.0282956\pi$
$180$		0			0
$181$	−9.54973			−0.709826			−0.354913	−	0.934899i	$-0.615489\pi$
$181$	−9.54973			−0.709826			−0.354913	+	0.934899i	$0.615489\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.117683	−	0.203834i	−0.00865225	−	0.0149861i
$186$		0			0
$187$	12.7056	−	22.0068i	0.929129	−	1.60930i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.52163	+	9.56375i	−0.399531	+	0.692009i	−0.993668	−	0.112355i	$-0.964160\pi$
$191$	−5.52163	+	9.56375i	−0.399531	+	0.692009i	0.594137	+	0.804364i	$0.297494\pi$
$192$		0			0
$193$	−13.3496	−	23.1221i	−0.960923	−	1.66437i	−0.720192	−	0.693775i	$-0.755946\pi$
$193$	−13.3496	−	23.1221i	−0.960923	−	1.66437i	−0.240731	−	0.970592i	$-0.577387\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.8386			−0.914715			−0.457357	−	0.889283i	$-0.651204\pi$
$197$	−12.8386			−0.914715			−0.457357	+	0.889283i	$0.651204\pi$
$198$		0			0
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	−0.242586	−	0.970130i	$-0.577996\pi$
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	0.961450	−	0.274979i	$-0.0886710\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.18860	+	17.2427i	0.153610	+	1.21020i
$204$		0			0
$205$	1.32702	−	2.29847i	0.0926833	−	0.160532i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.47329	−	14.6762i	−0.586109	−	1.01517i
$210$		0			0
$211$	4.77903	−	8.27752i	0.329002	−	0.569848i	−0.653312	−	0.757088i	$-0.726621\pi$
$211$	4.77903	−	8.27752i	0.329002	−	0.569848i	0.982314	+	0.187241i	$0.0599545\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.49855	−	2.59556i	−0.102200	−	0.177016i
$216$		0			0
$217$	−2.02435	−	15.9487i	−0.137422	−	1.08267i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.34788	+	2.33460i	0.0906683	+	0.157042i
$222$		0			0
$223$	11.9155	+	20.6383i	0.797921	+	1.38204i	0.920968	+	0.389639i	$0.127400\pi$
$223$	11.9155	+	20.6383i	0.797921	+	1.38204i	−0.123046	+	0.992401i	$0.539266\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.67134			0.177303			0.0886514	−	0.996063i	$-0.471744\pi$
$227$	2.67134			0.177303			0.0886514	+	0.996063i	$0.471744\pi$
$228$		0			0
$229$	6.32516			0.417978			0.208989	−	0.977918i	$-0.432983\pi$
$229$	6.32516			0.417978			0.208989	+	0.977918i	$0.432983\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.63381	−	8.02600i	−0.303571	−	0.525801i	0.673371	−	0.739305i	$-0.264846\pi$
$233$	−4.63381	−	8.02600i	−0.303571	−	0.525801i	−0.976942	+	0.213504i	$0.931512\pi$
$234$		0			0
$235$	2.41862	−	4.18918i	0.157774	−	0.273272i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.69219	+	2.93096i	−0.109459	+	0.189588i	−0.915551	−	0.402202i	$-0.868245\pi$
$239$	−1.69219	+	2.93096i	−0.109459	+	0.189588i	0.806092	+	0.591790i	$0.201578\pi$
$240$		0			0
$241$	13.1596			0.847687			0.423844	−	0.905735i	$-0.360681\pi$
$241$	13.1596			0.847687			0.423844	+	0.905735i	$0.360681\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.57929	−	2.62767i	−0.164784	−	0.167876i
$246$		0			0
$247$	1.79778			0.114390
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.30235			0.145323			0.0726614	−	0.997357i	$-0.476851\pi$
$251$	2.30235			0.145323			0.0726614	+	0.997357i	$0.476851\pi$
$252$		0			0
$253$	−0.248755			−0.0156391
$254$		0			0
$255$		0			0
$256$		0			0
$257$	29.1323			1.81722			0.908610	−	0.417646i	$-0.137145\pi$
$257$	29.1323			1.81722			0.908610	+	0.417646i	$0.137145\pi$
$258$		0			0
$259$	0.149072	+	1.17445i	0.00926286	+	0.0729767i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.71837			0.167622			0.0838110	−	0.996482i	$-0.473291\pi$
$263$	2.71837			0.167622			0.0838110	+	0.996482i	$0.473291\pi$
$264$		0			0
$265$	−2.29936	+	3.98261i	−0.141249	+	0.244650i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.80840	+	4.86428i	−0.171231	+	0.296581i	−0.938850	−	0.344325i	$-0.888108\pi$
$269$	−2.80840	+	4.86428i	−0.171231	+	0.296581i	0.767620	+	0.640906i	$0.221441\pi$
$270$		0			0
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	0.557221	−	0.830364i	$-0.311867\pi$
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	−0.997727	+	0.0673860i	$0.978534\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.7770			1.31320
$276$		0			0
$277$	−1.74791			−0.105022			−0.0525108	−	0.998620i	$-0.516722\pi$
$277$	−1.74791			−0.105022			−0.0525108	+	0.998620i	$0.516722\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.35657	−	9.27786i	−0.319546	−	0.553471i	0.660847	−	0.750521i	$-0.270197\pi$
$281$	−5.35657	−	9.27786i	−0.319546	−	0.553471i	−0.980393	+	0.197050i	$0.936864\pi$
$282$		0			0
$283$	6.29833	+	10.9090i	0.374397	+	0.648474i	0.990237	−	0.139397i	$-0.0445165\pi$
$283$	6.29833	+	10.9090i	0.374397	+	0.648474i	−0.615840	+	0.787871i	$0.711183\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.6286	+	8.07743i	−0.627386	+	0.476796i
$288$		0			0
$289$	−6.68881	−	11.5854i	−0.393459	−	0.681491i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.57575	−	2.72928i	0.0920562	−	0.159446i	−0.816320	−	0.577600i	$-0.803989\pi$
$293$	1.57575	−	2.72928i	0.0920562	−	0.159446i	0.908376	+	0.418154i	$0.137323\pi$
$294$		0			0
$295$	1.74391	+	3.02053i	0.101534	+	0.175862i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.0131946	−	0.0228537i	0.000763063	−	0.00132166i
$300$		0			0
$301$	1.89824	+	14.9551i	0.109413	+	0.861999i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.122460	+	0.212107i	−0.00701206	+	0.0121452i
$306$		0			0
$307$	−20.3884			−1.16363			−0.581813	−	0.813322i	$-0.697657\pi$
$307$	−20.3884			−1.16363			−0.581813	+	0.813322i	$0.697657\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.3507	+	19.6600i	0.643640	+	1.11482i	0.984614	+	0.174744i	$0.0559099\pi$
$311$	11.3507	+	19.6600i	0.643640	+	1.11482i	−0.340974	+	0.940073i	$0.610757\pi$
$312$		0			0
$313$	8.35389	−	14.4694i	0.472190	−	0.817857i	−0.527304	−	0.849677i	$-0.676797\pi$
$313$	8.35389	−	14.4694i	0.472190	−	0.817857i	0.999494	+	0.0318201i	$0.0101304\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.16401	−	8.94433i	0.290040	−	0.502364i	−0.683779	−	0.729689i	$-0.739665\pi$
$317$	5.16401	−	8.94433i	0.290040	−	0.502364i	0.973819	+	0.227325i	$0.0729981\pi$
$318$		0			0
$319$	−15.1442	−	26.2306i	−0.847914	−	1.46863i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−20.2586			−1.12722
$324$		0			0
$325$	−1.15511	+	2.00070i	−0.0640738	+	0.110979i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−19.3716	+	14.7219i	−1.06799	+	0.811643i
$330$		0			0
$331$	11.3158	−	19.5995i	0.621970	−	1.07728i	−0.367148	−	0.930162i	$-0.619666\pi$
$331$	11.3158	−	19.5995i	0.621970	−	1.07728i	0.989118	−	0.147122i	$-0.0470008\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.36592	+	2.36585i	0.0746283	+	0.129260i
$336$		0			0
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	−0.620014	−	0.784590i	$-0.712873\pi$
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	0.989482	+	0.144653i	$0.0462066\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.0077	+	24.2620i	0.758558	+	1.31386i
$342$		0			0
$343$	6.84824	+	17.2076i	0.369770	+	0.929123i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.5131	−	28.6015i	−0.886470	−	1.53541i	−0.844019	−	0.536313i	$-0.819817\pi$
$347$	−16.5131	−	28.6015i	−0.886470	−	1.53541i	−0.0424511	−	0.999099i	$-0.513517\pi$
$348$		0			0
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	−0.998621	−	0.0525019i	$-0.983280\pi$
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	0.453842	−	0.891082i	$-0.350053\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.50763			0.293141			0.146571	−	0.989200i	$-0.453176\pi$
$353$	5.50763			0.293141			0.146571	+	0.989200i	$0.453176\pi$
$354$		0			0
$355$	0.927495			0.0492263
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.4656	+	18.1270i	0.552354	+	0.956704i	0.998104	+	0.0615472i	$0.0196035\pi$
$359$	10.4656	+	18.1270i	0.552354	+	0.956704i	−0.445751	+	0.895157i	$0.647063\pi$
$360$		0			0
$361$	2.74486	−	4.75424i	0.144467	−	0.250223i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.75509	−	4.77195i	0.144208	−	0.249775i
$366$		0			0
$367$	4.28637			0.223747			0.111873	−	0.993722i	$-0.464315\pi$
$367$	4.28637			0.223747			0.111873	+	0.993722i	$0.464315\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.4164	−	13.9959i	0.956132	−	0.726633i
$372$		0			0
$373$	−11.2892			−0.584534			−0.292267	−	0.956337i	$-0.594410\pi$
$373$	−11.2892			−0.584534			−0.292267	+	0.956337i	$0.594410\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.21316			0.165486
$378$		0			0
$379$	−20.5828			−1.05727			−0.528634	−	0.848850i	$-0.677295\pi$
$379$	−20.5828			−1.05727			−0.528634	+	0.848850i	$0.677295\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	21.6215			1.10481			0.552405	−	0.833576i	$-0.313710\pi$
$383$	21.6215			1.10481			0.552405	+	0.833576i	$0.313710\pi$
$384$		0			0
$385$	5.91646	+	2.48295i	0.301531	+	0.126543i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.6848			0.744550			0.372275	−	0.928123i	$-0.378578\pi$
$389$	14.6848			0.744550			0.372275	+	0.928123i	$0.378578\pi$
$390$		0			0
$391$	−0.148685	+	0.257531i	−0.00751934	+	0.0130239i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.30539	−	7.45716i	0.216628	−	0.375210i
$396$		0			0
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	0.776592	−	0.630003i	$-0.216947\pi$
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	−0.933895	+	0.357547i	$0.883613\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−29.3901			−1.46767			−0.733836	−	0.679327i	$-0.762272\pi$
$401$	−29.3901			−1.46767			−0.733836	+	0.679327i	$0.762272\pi$
$402$		0			0
$403$	−2.97201			−0.148046
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.03152	−	1.78664i	−0.0511303	−	0.0885603i
$408$		0			0
$409$	0.816425	+	1.41409i	0.0403696	+	0.0699222i	0.885504	−	0.464631i	$-0.153813\pi$
$409$	0.816425	+	1.41409i	0.0403696	+	0.0699222i	−0.845135	+	0.534554i	$0.820480\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.20904	−	17.4037i	−0.108700	−	0.856381i
$414$		0			0
$415$	2.36308	+	4.09298i	0.115999	+	0.200916i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.01823	−	15.6200i	0.440569	−	0.763088i	−0.557162	−	0.830404i	$-0.688110\pi$
$419$	9.01823	−	15.6200i	0.440569	−	0.763088i	0.997732	+	0.0673151i	$0.0214433\pi$
$420$		0			0
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	0.905581	+	0.424172i	$0.139435\pi$
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	−0.0854466	+	0.996343i	$0.527232\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.0165	−	22.5452i	0.631393	−	1.09360i
$426$		0			0
$427$	0.980827	−	0.745401i	0.0474655	−	0.0360725i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.1545	−	19.3202i	0.537295	−	0.930622i	−0.461754	−	0.887008i	$-0.652780\pi$
$431$	11.1545	−	19.3202i	0.537295	−	0.930622i	0.999048	−	0.0436135i	$-0.0138870\pi$
$432$		0			0
$433$	7.32414			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$433$	7.32414			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0991570	+	0.171745i	0.00474332	+	0.00821567i
$438$		0			0
$439$	12.3364	−	21.3673i	0.588785	−	1.01981i	−0.405607	−	0.914048i	$-0.632940\pi$
$439$	12.3364	−	21.3673i	0.588785	−	1.01981i	0.994392	−	0.105758i	$-0.0337270\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.2682	−	26.4452i	0.725412	−	1.25645i	−0.233393	−	0.972383i	$-0.574983\pi$
$443$	15.2682	−	26.4452i	0.725412	−	1.25645i	0.958804	−	0.284067i	$-0.0916839\pi$
$444$		0			0
$445$	−3.70909	−	6.42434i	−0.175828	−	0.304543i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	41.4782			1.95748			0.978738	−	0.205116i	$-0.0657572\pi$
$449$	41.4782			1.95748			0.978738	+	0.205116i	$0.0657572\pi$
$450$		0			0
$451$	11.6316	−	20.1465i	0.547710	−	0.948662i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.541939	+	0.411858i	−0.0254065	+	0.0193082i
$456$		0			0
$457$	5.81446	−	10.0709i	0.271989	−	0.471099i	−0.697382	−	0.716700i	$-0.745652\pi$
$457$	5.81446	−	10.0709i	0.271989	−	0.471099i	0.969371	+	0.245601i	$0.0789852\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.60886	+	9.71483i	0.261231	+	0.452465i	0.966569	−	0.256406i	$-0.0825383\pi$
$461$	5.60886	+	9.71483i	0.261231	+	0.452465i	−0.705339	+	0.708871i	$0.749205\pi$
$462$		0			0
$463$	−19.9362	+	34.5305i	−0.926514	+	1.60477i	−0.137405	+	0.990515i	$0.543876\pi$
$463$	−19.9362	+	34.5305i	−0.926514	+	1.60477i	−0.789108	+	0.614254i	$0.789457\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.7818	−	20.4067i	−0.545198	−	0.944311i	−0.998594	−	0.0530016i	$-0.983121\pi$
$467$	−11.7818	−	20.4067i	−0.545198	−	0.944311i	0.453397	−	0.891309i	$-0.350212\pi$
$468$		0			0
$469$	−1.73024	−	13.6315i	−0.0798950	−	0.629446i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−13.1350	−	22.7506i	−0.603950	−	1.04607i
$474$		0			0
$475$	−8.68059	−	15.0352i	−0.398293	−	0.689864i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.2297			−0.650172			−0.325086	−	0.945685i	$-0.605393\pi$
$479$	−14.2297			−0.650172			−0.325086	+	0.945685i	$0.605393\pi$
$480$		0			0
$481$	0.218857			0.00997902
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.74792	−	4.75953i	−0.124776	−	0.216119i
$486$		0			0
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	0.353242	+	0.935532i	$0.385079\pi$
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	−0.986815	+	0.161850i	$0.948254\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.2543	+	29.8853i	−0.778676	+	1.34871i	0.154030	+	0.988066i	$0.450775\pi$
$491$	−17.2543	+	29.8853i	−0.778676	+	1.34871i	−0.932705	+	0.360639i	$0.882558\pi$
$492$		0			0
$493$	−36.2080			−1.63072
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.30175	−	1.80530i	−0.192960	−	0.0809789i
$498$		0			0
$499$	26.2873			1.17678			0.588390	−	0.808577i	$-0.299762\pi$
$499$	26.2873			1.17678			0.588390	+	0.808577i	$0.299762\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.09068			−0.271570			−0.135785	−	0.990738i	$-0.543356\pi$
$503$	−6.09068			−0.271570			−0.135785	+	0.990738i	$0.543356\pi$
$504$		0			0
$505$	−5.24167			−0.233251
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.17231			0.362231			0.181116	−	0.983462i	$-0.442029\pi$
$509$	8.17231			0.362231			0.181116	+	0.983462i	$0.442029\pi$
$510$		0			0
$511$	−22.0664	+	16.7699i	−0.976162	+	0.741856i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.12850			−0.270054
$516$		0			0
$517$	21.1996	−	36.7189i	0.932360	−	1.61489i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.0485	+	22.6007i	−0.571666	+	0.990155i	0.424729	+	0.905321i	$0.360370\pi$
$521$	−13.0485	+	22.6007i	−0.571666	+	0.990155i	−0.996395	+	0.0848346i	$0.972964\pi$
$522$		0			0
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	0.993181	+	0.116581i	$0.0371935\pi$
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	−0.395628	+	0.918411i	$0.629473\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	33.4906			1.45887
$528$		0			0
$529$	−22.9971			−0.999873
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.23394	+	2.13725i	0.0534478	+	0.0925744i
$534$		0			0
$535$	1.29164	+	2.23718i	0.0558423	+	0.0967217i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−22.6079	−	23.0320i	−0.973790	−	0.992057i
$540$		0			0
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	0.714271	−	0.699869i	$-0.246758\pi$
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	−0.963240	+	0.268643i	$0.913425\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.13566	−	8.89522i	0.219987	−	0.381029i
$546$		0			0
$547$	20.3651	+	35.2734i	0.870750	+	1.50818i	0.861222	+	0.508228i	$0.169699\pi$
$547$	20.3651	+	35.2734i	0.870750	+	1.50818i	0.00952755	+	0.999955i	$0.496967\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.0734	+	20.9117i	−0.514344	+	0.890869i
$552$		0			0
$553$	−34.4834	+	26.2064i	−1.46638	+	1.11441i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.0085	+	17.3353i	−0.424075	+	0.734520i	−0.996334	−	0.0855533i	$-0.972734\pi$
$557$	−10.0085	+	17.3353i	−0.424075	+	0.734520i	0.572258	+	0.820074i	$0.306068\pi$
$558$		0			0
$559$	2.78687			0.117872
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.4664	+	21.5924i	0.525396	+	0.910013i	0.999562	+	0.0295776i	$0.00941620\pi$
$563$	12.4664	+	21.5924i	0.525396	+	0.910013i	−0.474166	+	0.880435i	$0.657250\pi$
$564$		0			0
$565$	2.88597	−	4.99864i	0.121414	−	0.210294i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.90013	+	8.48727i	−0.205424	+	0.355805i	−0.950268	−	0.311434i	$-0.899191\pi$
$569$	−4.90013	+	8.48727i	−0.205424	+	0.355805i	0.744844	+	0.667239i	$0.232524\pi$
$570$		0			0
$571$	20.3948	+	35.3247i	0.853494	+	1.47829i	0.878035	+	0.478596i	$0.158854\pi$
$571$	20.3948	+	35.3247i	0.853494	+	1.47829i	−0.0245416	+	0.999699i	$0.507813\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.254841			−0.0106276
$576$		0			0
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	−0.996581	−	0.0826259i	$-0.973669\pi$
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	0.569846	+	0.821751i	$0.307003\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.99336	−	23.5829i	−0.124185	−	0.978385i
$582$		0			0
$583$	−20.1543	+	34.9083i	−0.834707	+	1.44575i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.2916	+	33.4141i	0.796251	+	1.37915i	0.922042	+	0.387090i	$0.126520\pi$
$587$	19.2916	+	33.4141i	0.796251	+	1.37915i	−0.125791	+	0.992057i	$0.540147\pi$
$588$		0			0
$589$	11.1673	−	19.3423i	0.460141	−	0.796987i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.26539	+	2.19172i	0.0519634	+	0.0900032i	0.890837	−	0.454323i	$-0.150119\pi$
$593$	1.26539	+	2.19172i	0.0519634	+	0.0900032i	−0.838874	+	0.544326i	$0.816785\pi$
$594$		0			0
$595$	6.10693	−	4.64109i	0.250360	−	0.190266i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.01092	−	13.8753i	−0.327317	−	0.566930i	0.654661	−	0.755922i	$-0.272811\pi$
$599$	−8.01092	−	13.8753i	−0.327317	−	0.566930i	−0.981979	+	0.188992i	$0.939478\pi$
$600$		0			0
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.822349	−	0.568983i	$-0.807337\pi$
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.0815796	−	0.996667i	$-0.525996\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.39517			−0.219345
$606$		0			0
$607$	−9.59214			−0.389333			−0.194666	−	0.980870i	$-0.562362\pi$
$607$	−9.59214			−0.389333			−0.194666	+	0.980870i	$0.562362\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.24897	+	3.89533i	0.0909835	+	0.157588i
$612$		0			0
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	−0.544761	−	0.838591i	$-0.683380\pi$
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	0.998622	+	0.0524815i	$0.0167131\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.7056	+	20.2746i	−0.471248	+	0.816226i	−0.999459	−	0.0328875i	$-0.989530\pi$
$617$	−11.7056	+	20.2746i	−0.471248	+	0.816226i	0.528211	+	0.849113i	$0.322863\pi$
$618$		0			0
$619$	15.9769			0.642164			0.321082	−	0.947051i	$-0.395953\pi$
$619$	15.9769			0.642164			0.321082	+	0.947051i	$0.395953\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.69838	+	37.0158i	0.188236	+	1.48301i
$624$		0			0
$625$	20.9263			0.837054
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.46622			−0.0983348
$630$		0			0
$631$	−0.882517			−0.0351324			−0.0175662	−	0.999846i	$-0.505592\pi$
$631$	−0.882517			−0.0351324			−0.0175662	+	0.999846i	$0.505592\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.73728			0.346729
$636$		0			0
$637$	3.31518	−	0.855367i	0.131352	−	0.0338909i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−40.4282			−1.59682			−0.798408	−	0.602116i	$-0.794324\pi$
$641$	−40.4282			−1.59682			−0.798408	+	0.602116i	$0.794324\pi$
$642$		0			0
$643$	2.99047	−	5.17964i	0.117932	−	0.204265i	−0.801016	−	0.598643i	$-0.795707\pi$
$643$	2.99047	−	5.17964i	0.117932	−	0.204265i	0.918948	+	0.394378i	$0.129040\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.4743	−	28.5343i	0.647672	−	1.12180i	−0.336005	−	0.941860i	$-0.609076\pi$
$647$	16.4743	−	28.5343i	0.647672	−	1.12180i	0.983677	−	0.179941i	$-0.0575906\pi$
$648$		0			0
$649$	15.2856	+	26.4755i	0.600014	+	1.03925i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−26.0333			−1.01876			−0.509380	−	0.860542i	$-0.670125\pi$
$653$	−26.0333			−1.01876			−0.509380	+	0.860542i	$0.670125\pi$
$654$		0			0
$655$	3.05974			0.119554
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.91651	−	8.51565i	−0.191520	−	0.331722i	0.754234	−	0.656606i	$-0.228008\pi$
$659$	−4.91651	−	8.51565i	−0.191520	−	0.331722i	−0.945754	+	0.324883i	$0.894675\pi$
$660$		0			0
$661$	2.75760	+	4.77630i	0.107258	+	0.185777i	0.914659	−	0.404227i	$-0.132460\pi$
$661$	2.75760	+	4.77630i	0.107258	+	0.185777i	−0.807400	+	0.590004i	$0.799126\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.644111	−	5.07458i	−0.0249776	−	0.196784i
$666$		0			0
$667$	0.177222	+	0.306958i	0.00686208	+	0.0118855i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.07339	+	1.85916i	−0.0414376	+	0.0717720i
$672$		0			0
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	0.944773	+	0.327725i	$0.106282\pi$
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	−0.188569	+	0.982060i	$0.560385\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.5816	+	32.1843i	−0.714149	+	1.23694i	0.249138	+	0.968468i	$0.419853\pi$
$677$	−18.5816	+	32.1843i	−0.714149	+	1.23694i	−0.963287	+	0.268474i	$0.913481\pi$
$678$		0			0
$679$	3.48084	+	27.4235i	0.133582	+	1.05242i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.10586	−	8.84360i	0.195370	−	0.338391i	−0.751652	−	0.659560i	$-0.770743\pi$
$683$	5.10586	−	8.84360i	0.195370	−	0.338391i	0.947022	+	0.321169i	$0.104076\pi$
$684$		0			0
$685$	−4.85305			−0.185426
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.13807	−	3.70325i	−0.0814542	−	0.141083i
$690$		0			0
$691$	17.5381	−	30.3768i	0.667179	−	1.15559i	−0.311510	−	0.950243i	$-0.600835\pi$
$691$	17.5381	−	30.3768i	0.667179	−	1.15559i	0.978690	−	0.205346i	$-0.0658318\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.62142	+	6.27248i	−0.137368	+	0.237929i
$696$		0			0
$697$	−13.9048	−	24.0839i	−0.526683	−	0.912242i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17.2500			−0.651522			−0.325761	−	0.945452i	$-0.605621\pi$
$701$	−17.2500			−0.651522			−0.325761	+	0.945452i	$0.605621\pi$
$702$		0			0
$703$	−0.822352	+	1.42436i	−0.0310156	+	0.0537206i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.3111	+	10.2025i	0.914311	+	0.383706i
$708$		0			0
$709$	7.25734	−	12.5701i	0.272555	−	0.472079i	−0.696960	−	0.717110i	$-0.745465\pi$
$709$	7.25734	−	12.5701i	0.272555	−	0.472079i	0.969515	+	0.245030i	$0.0787980\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.163922	−	0.283921i	−0.00613893	−	0.0106329i
$714$		0			0
$715$	0.593081	−	1.02725i	0.0221800	−	0.0384168i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.4295	+	38.8491i	0.836480	+	1.44883i	0.892820	+	0.450414i	$0.148723\pi$
$719$	22.4295	+	38.8491i	0.836480	+	1.44883i	−0.0563403	+	0.998412i	$0.517943\pi$
$720$		0			0
$721$	28.4242	+	11.9287i	1.05857	+	0.444248i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.5147	−	26.8723i	−0.576203	−	0.998013i
$726$		0			0
$727$	−2.22039	−	3.84582i	−0.0823496	−	0.142634i	0.821909	−	0.569619i	$-0.192909\pi$
$727$	−2.22039	−	3.84582i	−0.0823496	−	0.142634i	−0.904259	+	0.426985i	$0.859576\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31.4043			−1.16153
$732$		0			0
$733$	−38.2720			−1.41361			−0.706803	−	0.707410i	$-0.749863\pi$
$733$	−38.2720			−1.41361			−0.706803	+	0.707410i	$0.749863\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.9725	+	20.7370i	0.441014	+	0.763859i
$738$		0			0
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	−0.909782	−	0.415087i	$-0.863751\pi$
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	0.814367	+	0.580350i	$0.197084\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.3351	+	28.2932i	−0.599276	+	1.03798i	0.393653	+	0.919259i	$0.371211\pi$
$743$	−16.3351	+	28.2932i	−0.599276	+	1.03798i	−0.992928	+	0.118716i	$0.962122\pi$
$744$		0			0
$745$	−4.36629			−0.159968
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.63614	−	12.8902i	−0.0597832	−	0.470997i
$750$		0			0
$751$	−16.1221			−0.588304			−0.294152	−	0.955759i	$-0.595037\pi$
$751$	−16.1221			−0.588304			−0.294152	+	0.955759i	$0.595037\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.62595			0.277537
$756$		0			0
$757$	45.6421			1.65889			0.829444	−	0.558589i	$-0.188657\pi$
$757$	45.6421			1.65889			0.829444	+	0.558589i	$0.188657\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.2300			−0.443338			−0.221669	−	0.975122i	$-0.571150\pi$
$761$	−12.2300			−0.443338			−0.221669	+	0.975122i	$0.571150\pi$
$762$		0			0
$763$	−41.1333	+	31.2601i	−1.48912	+	1.13169i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.24316			−0.117104
$768$		0			0
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	−0.803117	−	0.595821i	$-0.796827\pi$
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	0.917555	+	0.397610i	$0.130160\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−24.4515	+	42.3512i	−0.879459	+	1.52327i	−0.0275225	+	0.999621i	$0.508762\pi$
$773$	−24.4515	+	42.3512i	−0.879459	+	1.52327i	−0.851936	+	0.523646i	$0.824572\pi$
$774$		0			0
$775$	14.3504	+	24.8556i	0.515481	+	0.892839i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−18.5460			−0.664481
$780$		0			0
$781$	8.12965			0.290902
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.28455	−	5.68900i	−0.117231	−	0.203049i
$786$		0			0
$787$	11.5749	+	20.0483i	0.412600	+	0.714645i	0.995173	−	0.0981337i	$-0.0312873\pi$
$787$	11.5749	+	20.0483i	0.412600	+	0.714645i	−0.582573	+	0.812778i	$0.697954\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.1147	+	17.5665i	−0.821864	+	0.624594i
$792$		0			0
$793$	−0.113870	−	0.197229i	−0.00404365	−	0.00700381i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.2284	+	41.9648i	−0.858214	+	1.48647i	0.0154170	+	0.999881i	$0.495092\pi$
$797$	−24.2284	+	41.9648i	−0.858214	+	1.48647i	−0.873631	+	0.486589i	$0.838241\pi$
$798$		0			0
$799$	−25.3429	−	43.8951i	−0.896566	−	1.55290i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	24.1488	−	41.8270i	0.852193	−	1.47604i
$804$		0			0
$805$	−0.0692363	−	0.0290562i	−0.00244026	−	0.00102410i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.2647	−	17.7791i	0.360889	−	0.625078i	−0.627218	−	0.778844i	$-0.715807\pi$
$809$	10.2647	−	17.7791i	0.360889	−	0.625078i	0.988107	+	0.153765i	$0.0491399\pi$
$810$		0			0
$811$	27.7882			0.975776			0.487888	−	0.872906i	$-0.337767\pi$
$811$	27.7882			0.975776			0.487888	+	0.872906i	$0.337767\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.30685	+	2.26353i	0.0457769	+	0.0792880i
$816$		0			0
$817$	−10.4716	+	18.1374i	−0.366356	+	0.634546i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.27932	+	14.3402i	−0.288950	+	0.500477i	−0.973559	−	0.228434i	$-0.926640\pi$
$821$	−8.27932	+	14.3402i	−0.288950	+	0.500477i	0.684609	+	0.728910i	$0.259973\pi$
$822$		0			0
$823$	−12.7352	−	22.0580i	−0.443922	−	0.768895i	0.554055	−	0.832480i	$-0.313080\pi$
$823$	−12.7352	−	22.0580i	−0.443922	−	0.768895i	−0.997976	+	0.0635853i	$0.979746\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.0798			−1.25462			−0.627309	−	0.778771i	$-0.715844\pi$
$827$	−36.0798			−1.25462			−0.627309	+	0.778771i	$0.715844\pi$
$828$		0			0
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	−0.157633	−	0.987498i	$-0.550386\pi$
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	0.934015	−	0.357234i	$-0.116280\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−37.3577	+	9.63884i	−1.29437	+	0.333966i
$834$		0			0
$835$	−5.26467	+	9.11868i	−0.182191	+	0.315565i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.86805	+	13.6279i	0.271635	+	0.470486i	0.969281	−	0.245957i	$-0.0791022\pi$
$839$	7.86805	+	13.6279i	0.271635	+	0.470486i	−0.697645	+	0.716443i	$0.745769\pi$
$840$		0			0
$841$	−7.07866	+	12.2606i	−0.244092	+	0.422779i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.35611	−	5.81296i	−0.115454	−	0.199972i
$846$		0			0
$847$	25.0230	+	10.5013i	0.859799	+	0.360829i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.0120711	+	0.0209078i	0.000413792	+	0.000716709i
$852$		0			0
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	0.999875	−	0.0158264i	$-0.00503792\pi$
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	−0.513643	+	0.858004i	$0.671705\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.97734			0.306660			0.153330	−	0.988175i	$-0.451000\pi$
$857$	8.97734			0.306660			0.153330	+	0.988175i	$0.451000\pi$
$858$		0			0
$859$	−0.942900			−0.0321713			−0.0160857	−	0.999871i	$-0.505120\pi$
$859$	−0.942900			−0.0321713			−0.0160857	+	0.999871i	$0.505120\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.0488	+	22.6011i	0.444185	+	0.769351i	0.997995	−	0.0632920i	$-0.0201600\pi$
$863$	13.0488	+	22.6011i	0.444185	+	0.769351i	−0.553810	+	0.832643i	$0.686827\pi$
$864$		0			0
$865$	−2.38145	+	4.12478i	−0.0809716	+	0.140247i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	37.7375	−	65.3633i	1.28016	−	2.21730i
$870$		0			0
$871$	−2.54022			−0.0860720
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.4775	+	5.23639i	0.421816	+	0.177022i
$876$		0			0
$877$	−26.3589			−0.890077			−0.445038	−	0.895512i	$-0.646810\pi$
$877$	−26.3589			−0.890077			−0.445038	+	0.895512i	$0.646810\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	45.6077			1.53656			0.768281	−	0.640113i	$-0.221112\pi$
$881$	45.6077			1.53656			0.768281	+	0.640113i	$0.221112\pi$
$882$		0			0
$883$	−26.1575			−0.880271			−0.440136	−	0.897931i	$-0.645070\pi$
$883$	−26.1575			−0.880271			−0.440136	+	0.897931i	$0.645070\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−37.1925			−1.24880			−0.624401	−	0.781104i	$-0.714657\pi$
$887$	−37.1925			−1.24880			−0.624401	+	0.781104i	$0.714657\pi$
$888$		0			0
$889$	−40.5238	−	17.0065i	−1.35912	−	0.570380i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.8019			−1.13114
$894$		0			0
$895$	−4.04589	+	7.00769i	−0.135239	+	0.234241i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	19.9592	−	34.5704i	0.665677	−	1.15299i
$900$		0			0
$901$	24.0932	+	41.7307i	0.802662	+	1.39025i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.02320			0.166977
$906$		0			0
$907$	25.8461			0.858206			0.429103	−	0.903255i	$-0.358830\pi$
$907$	25.8461			0.858206			0.429103	+	0.903255i	$0.358830\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.41211	+	4.17790i	0.0799169	+	0.138420i	0.903214	−	0.429191i	$-0.141201\pi$
$911$	2.41211	+	4.17790i	0.0799169	+	0.138420i	−0.823297	+	0.567611i	$0.807868\pi$
$912$		0			0
$913$	20.7128	+	35.8756i	0.685494	+	1.18731i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.1912	−	5.95558i	−0.468635	−	0.196670i
$918$		0			0
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	0.979666	−	0.200638i	$-0.0643014\pi$
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	−0.663590	+	0.748096i	$0.730968\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.431218	+	0.746891i	−0.0141937	+	0.0245842i
$924$		0			0
$925$	−1.05675	−	1.83035i	−0.0347458	−	0.0601815i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.0457	−	46.8445i	0.887340	−	1.53692i	0.0443327	−	0.999017i	$-0.485884\pi$
$929$	27.0457	−	46.8445i	0.887340	−	1.53692i	0.843008	−	0.537902i	$-0.180783\pi$
$930$		0			0
$931$	−6.88990	+	24.7898i	−0.225807	+	0.812452i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.68322	+	11.5757i	−0.218565	+	0.378565i
$936$		0			0
$937$	−16.6345			−0.543426			−0.271713	−	0.962378i	$-0.587590\pi$
$937$	−16.6345			−0.543426			−0.271713	+	0.962378i	$0.587590\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.44956	−	2.51071i	−0.0472543	−	0.0818468i	0.841431	−	0.540365i	$-0.181714\pi$
$941$	−1.44956	−	2.51071i	−0.0472543	−	0.0818468i	−0.888685	+	0.458518i	$0.848380\pi$
$942$		0			0
$943$	−0.136116	+	0.235760i	−0.00443256	+	0.00767742i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.8655	+	49.9966i	−0.938004	+	1.62467i	−0.168816	+	0.985648i	$0.553994\pi$
$947$	−28.8655	+	49.9966i	−0.938004	+	1.62467i	−0.769188	+	0.639023i	$0.779339\pi$
$948$		0			0
$949$	2.56183	+	4.43722i	0.0831605	+	0.144038i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.4070			−0.661046			−0.330523	−	0.943798i	$-0.607225\pi$
$953$	−20.4070			−0.661046			−0.330523	+	0.943798i	$0.607225\pi$
$954$		0			0
$955$	2.90440	−	5.03057i	0.0939843	−	0.162786i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.5086	+	9.44612i	0.726841	+	0.305031i
$960$		0			0
$961$	−2.96129	+	5.12911i	−0.0955256	+	0.165455i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.02193	+	12.1623i	0.226044	+	0.391519i
$966$		0			0
$967$	4.26365	−	7.38486i	0.137110	−	0.237481i	−0.789292	−	0.614019i	$-0.789552\pi$
$967$	4.26365	−	7.38486i	0.137110	−	0.237481i	0.926401	+	0.376537i	$0.122885\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.42651	−	16.3272i	−0.302511	−	0.523965i	0.674193	−	0.738555i	$-0.264492\pi$
$971$	−9.42651	−	16.3272i	−0.302511	−	0.523965i	−0.976704	+	0.214590i	$0.931158\pi$
$972$		0			0
$973$	29.0052	−	22.0431i	0.929864	−	0.706671i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.305649	+	0.529400i	0.00977859	+	0.0169370i	0.870873	−	0.491508i	$-0.163554\pi$
$977$	0.305649	+	0.529400i	0.00977859	+	0.0169370i	−0.861095	+	0.508445i	$0.830221\pi$
$978$		0			0
$979$	−32.5108	−	56.3104i	−1.03905	−	1.79969i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.25167			0.231292			0.115646	−	0.993290i	$-0.463106\pi$
$983$	7.25167			0.231292			0.115646	+	0.993290i	$0.463106\pi$
$984$		0			0
$985$	6.75318			0.215174
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.153710	+	0.266234i	0.00488770	+	0.00846575i
$990$		0			0
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	−0.902897	−	0.429857i	$-0.858564\pi$
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	0.823715	+	0.567004i	$0.191897\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.33412	+	9.23896i	−0.169103	+	0.292895i
$996$		0			0
$997$	−3.18344			−0.100821			−0.0504104	−	0.998729i	$-0.516053\pi$
$997$	−3.18344			−0.100821			−0.0504104	+	0.998729i	$0.516053\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.361.5		22
3.2	odd	2		504.2.t.c.193.6	yes	22
4.3	odd	2		3024.2.t.k.1873.5		22
7.2	even	3		1512.2.q.d.793.7		22
9.2	odd	6		504.2.q.c.25.10	✓	22
9.7	even	3		1512.2.q.d.1369.7		22
12.11	even	2		1008.2.t.l.193.6		22
21.2	odd	6		504.2.q.c.121.10	yes	22
28.23	odd	6		3024.2.q.l.2305.7		22
36.7	odd	6		3024.2.q.l.2881.7		22
36.11	even	6		1008.2.q.l.529.2		22
63.2	odd	6		504.2.t.c.457.6	yes	22
63.16	even	3	inner	1512.2.t.c.289.5		22
84.23	even	6		1008.2.q.l.625.2		22
252.79	odd	6		3024.2.t.k.289.5		22
252.191	even	6		1008.2.t.l.961.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.10	✓	22	9.2	odd	6
504.2.q.c.121.10	yes	22	21.2	odd	6
504.2.t.c.193.6	yes	22	3.2	odd	2
504.2.t.c.457.6	yes	22	63.2	odd	6
1008.2.q.l.529.2		22	36.11	even	6
1008.2.q.l.625.2		22	84.23	even	6
1008.2.t.l.193.6		22	12.11	even	2
1008.2.t.l.961.6		22	252.191	even	6
1512.2.q.d.793.7		22	7.2	even	3
1512.2.q.d.1369.7		22	9.7	even	3
1512.2.t.c.289.5		22	63.16	even	3	inner
1512.2.t.c.361.5		22	1.1	even	1	trivial
3024.2.q.l.2305.7		22	28.23	odd	6
3024.2.q.l.2881.7		22	36.7	odd	6
3024.2.t.k.289.5		22	252.79	odd	6
3024.2.t.k.1873.5		22	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +O(q^{10})\)	\(q-0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} -4.61052 q^{11} +(0.244554 - 0.423580i) q^{13} +(-2.75579 + 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +0.0539537 q^{23} -4.72332 q^{25} +(3.28471 + 5.68929i) q^{29} +(-3.03820 - 5.26231i) q^{31} +(-1.28325 - 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-2.52284 + 4.36968i) q^{41} +(2.84893 + 4.93449i) q^{43} +(-4.59810 + 7.96415i) q^{47} +(4.90354 + 4.99552i) q^{49} +(4.37138 - 7.57145i) q^{53} +2.42515 q^{55} +(-3.31538 - 5.74241i) q^{59} +(0.232812 - 0.403243i) q^{61} +(-0.128636 + 0.222805i) q^{65} +(-2.59679 - 4.49777i) q^{67} -1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(-11.2479 - 4.72039i) q^{77} +(-8.18509 + 14.1770i) q^{79} +(-4.49251 - 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(7.05145 + 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +(-0.966699 - 1.67437i) q^{95} +(5.22413 + 9.04847i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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