LMFDB - Embedded newform 3024.2.r.g.1009.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1009,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1009"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-5,0,-3,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.3
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.g.2017.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.590972 - 1.02359i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.85185 + 3.20750i) q^{11} +(-0.500000 + 0.866025i) q^{13} +6.94282 q^{17} -1.94282 q^{19} +(2.80150 - 4.85235i) q^{23} +(1.80150 + 3.12030i) q^{25} +(0.119562 + 0.207087i) q^{29} +(0.830095 - 1.43777i) q^{31} -1.18194 q^{35} -9.54583 q^{37} +(-5.09097 + 8.81782i) q^{41} +(1.11273 + 1.92730i) q^{43} +(-2.91423 - 5.04759i) q^{47} +(-0.500000 + 0.866025i) q^{49} +11.6030 q^{53} +4.37756 q^{55} +(-1.30150 + 2.25427i) q^{59} +(3.80150 + 6.58440i) q^{61} +(0.590972 + 1.02359i) q^{65} +(1.75404 - 3.03809i) q^{67} +8.60301 q^{71} +15.1488 q^{73} +(1.85185 - 3.20750i) q^{77} +(3.68878 + 6.38915i) q^{79} +(3.47141 + 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} -2.74720 q^{89} +1.00000 q^{91} +(-1.14815 + 1.98866i) q^{95} +(-3.58414 - 6.20790i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59}+ \cdots - 3 q^{97}+O(q^{100}) $ 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

Character values

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

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

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
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	−0.703087	−	0.711104i	$-0.748196\pi$
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	0.967378	+	0.253339i	$0.0815289\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	0.997634	+	0.0687465i	$0.0219000\pi$
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	−0.439281	+	0.898350i	$0.644767\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.94282			1.68388			0.841941	−	0.539570i	$-0.181413\pi$
$17$	6.94282			1.68388			0.841941	+	0.539570i	$0.181413\pi$
$18$		0			0
$19$	−1.94282			−0.445713			−0.222857	−	0.974851i	$-0.571538\pi$
$19$	−1.94282			−0.445713			−0.222857	+	0.974851i	$0.571538\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.80150	−	4.85235i	0.584154	−	1.01178i	−0.410826	−	0.911714i	$-0.634760\pi$
$23$	2.80150	−	4.85235i	0.584154	−	1.01178i	0.994980	−	0.100071i	$-0.0319070\pi$
$24$		0			0
$25$	1.80150	+	3.12030i	0.360301	+	0.624060i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.119562	+	0.207087i	0.0222020	+	0.0384551i	0.876913	−	0.480649i	$-0.159599\pi$
$29$	0.119562	+	0.207087i	0.0222020	+	0.0384551i	−0.854711	+	0.519104i	$0.826266\pi$
$30$		0			0
$31$	0.830095	−	1.43777i	0.149089	−	0.258231i	−0.781802	−	0.623527i	$-0.785699\pi$
$31$	0.830095	−	1.43777i	0.149089	−	0.258231i	0.930891	+	0.365297i	$0.119032\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.18194			−0.199785
$36$		0			0
$37$	−9.54583			−1.56932			−0.784662	−	0.619923i	$-0.787164\pi$
$37$	−9.54583			−1.56932			−0.784662	+	0.619923i	$0.787164\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.09097	+	8.81782i	−0.795076	+	1.37711i	0.127715	+	0.991811i	$0.459236\pi$
$41$	−5.09097	+	8.81782i	−0.795076	+	1.37711i	−0.922791	+	0.385301i	$0.874097\pi$
$42$		0			0
$43$	1.11273	+	1.92730i	0.169689	+	0.293910i	0.938311	−	0.345794i	$-0.112390\pi$
$43$	1.11273	+	1.92730i	0.169689	+	0.293910i	−0.768622	+	0.639704i	$0.779057\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.91423	−	5.04759i	−0.425084	−	0.736267i	0.571344	−	0.820711i	$-0.306422\pi$
$47$	−2.91423	−	5.04759i	−0.425084	−	0.736267i	−0.996428	+	0.0844432i	$0.973089\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	11.6030			1.59380			0.796898	−	0.604114i	$-0.206473\pi$
$53$	11.6030			1.59380			0.796898	+	0.604114i	$0.206473\pi$
$54$		0			0
$55$	4.37756			0.590270
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.30150	+	2.25427i	−0.169442	+	0.293481i	−0.938224	−	0.346029i	$-0.887530\pi$
$59$	−1.30150	+	2.25427i	−0.169442	+	0.293481i	0.768782	+	0.639511i	$0.220863\pi$
$60$		0			0
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	0.999884	−	0.0152524i	$-0.00485519\pi$
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	−0.513151	+	0.858298i	$0.671522\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.590972	+	1.02359i	0.0733010	+	0.126961i
$66$		0			0
$67$	1.75404	−	3.03809i	0.214290	−	0.371161i	−0.738763	−	0.673966i	$-0.764590\pi$
$67$	1.75404	−	3.03809i	0.214290	−	0.371161i	0.953053	+	0.302804i	$0.0979229\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.60301			1.02099			0.510495	−	0.859881i	$-0.329462\pi$
$71$	8.60301			1.02099			0.510495	+	0.859881i	$0.329462\pi$
$72$		0			0
$73$	15.1488			1.77304			0.886519	−	0.462693i	$-0.153117\pi$
$73$	15.1488			1.77304			0.886519	+	0.462693i	$0.153117\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.85185	−	3.20750i	0.211038	−	0.365528i
$78$		0			0
$79$	3.68878	+	6.38915i	0.415020	+	0.718836i	0.995431	−	0.0954881i	$-0.0304412\pi$
$79$	3.68878	+	6.38915i	0.415020	+	0.718836i	−0.580410	+	0.814324i	$0.697108\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.47141	+	6.01266i	0.381037	+	0.659975i	0.991211	−	0.132292i	$-0.0422338\pi$
$83$	3.47141	+	6.01266i	0.381037	+	0.659975i	−0.610174	+	0.792267i	$0.708900\pi$
$84$		0			0
$85$	4.10301	−	7.10662i	0.445034	−	0.770821i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.74720			−0.291203			−0.145602	−	0.989343i	$-0.546512\pi$
$89$	−2.74720			−0.291203			−0.145602	+	0.989343i	$0.546512\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.14815	+	1.98866i	−0.117798	+	0.204032i
$96$		0			0
$97$	−3.58414	−	6.20790i	−0.363914	−	0.630317i	0.624687	−	0.780875i	$-0.285226\pi$
$97$	−3.58414	−	6.20790i	−0.363914	−	0.630317i	−0.988601	+	0.150558i	$0.951893\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	−0.986286	−	0.165044i	$-0.947223\pi$
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	0.350211	−	0.936671i	$-0.386110\pi$
$102$		0			0
$103$	−2.19850	+	3.80791i	−0.216624	+	0.375204i	−0.953774	−	0.300526i	$-0.902838\pi$
$103$	−2.19850	+	3.80791i	−0.216624	+	0.375204i	0.737150	+	0.675730i	$0.236171\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.7278			1.32711			0.663557	−	0.748126i	$-0.269046\pi$
$107$	13.7278			1.32711			0.663557	+	0.748126i	$0.269046\pi$
$108$		0			0
$109$	1.26320			0.120993			0.0604963	−	0.998168i	$-0.480732\pi$
$109$	1.26320			0.120993			0.0604963	+	0.998168i	$0.480732\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.08126	−	10.5330i	0.572076	−	0.990866i	−0.424276	−	0.905533i	$-0.639471\pi$
$113$	6.08126	−	10.5330i	0.572076	−	0.990866i	0.996353	−	0.0853326i	$-0.0271953\pi$
$114$		0			0
$115$	−3.31122	−	5.73520i	−0.308773	−	0.534810i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.47141	−	6.01266i	−0.318224	−	0.551180i
$120$		0			0
$121$	−1.35868	+	2.35331i	−0.123517	+	0.213937i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.1683			0.909478
$126$		0			0
$127$	−1.33981			−0.118889			−0.0594445	−	0.998232i	$-0.518933\pi$
$127$	−1.33981			−0.118889			−0.0594445	+	0.998232i	$0.518933\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.48345	−	4.30146i	0.216980	−	0.375820i	−0.736903	−	0.675998i	$-0.763713\pi$
$131$	2.48345	−	4.30146i	0.216980	−	0.375820i	0.953883	+	0.300178i	$0.0970461\pi$
$132$		0			0
$133$	0.971410	+	1.68253i	0.0842319	+	0.145894i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.16991	−	3.75839i	−0.185387	−	0.321101i	0.758320	−	0.651883i	$-0.226021\pi$
$137$	−2.16991	−	3.75839i	−0.185387	−	0.321101i	−0.943707	+	0.330782i	$0.892687\pi$
$138$		0			0
$139$	1.97141	−	3.41458i	0.167213	−	0.289621i	−0.770226	−	0.637771i	$-0.779857\pi$
$139$	1.97141	−	3.41458i	0.167213	−	0.289621i	0.937439	+	0.348150i	$0.113190\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.70370			−0.309719
$144$		0			0
$145$	0.282630			0.0234712
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.55555	−	9.62249i	0.455128	−	0.788305i	−0.543568	−	0.839365i	$-0.682927\pi$
$149$	5.55555	−	9.62249i	0.455128	−	0.788305i	0.998696	+	0.0510606i	$0.0162602\pi$
$150$		0			0
$151$	6.96169	+	12.0580i	0.566535	+	0.981267i	0.996905	+	0.0786145i	$0.0250496\pi$
$151$	6.96169	+	12.0580i	0.566535	+	0.981267i	−0.430370	+	0.902652i	$0.641617\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.981125	−	1.69936i	−0.0788059	−	0.136496i
$156$		0			0
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	−0.867164	−	0.498023i	$-0.834060\pi$
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	0.864882	+	0.501975i	$0.167393\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.60301			−0.441579
$162$		0			0
$163$	1.50808			0.118122			0.0590610	−	0.998254i	$-0.481189\pi$
$163$	1.50808			0.118122			0.0590610	+	0.998254i	$0.481189\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.34213	−	12.7169i	0.568151	−	0.984067i	−0.428598	−	0.903496i	$-0.640992\pi$
$167$	7.34213	−	12.7169i	0.568151	−	0.984067i	0.996749	−	0.0805714i	$-0.0256745\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	0.870790	−	0.491655i	$-0.163608\pi$
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	−0.861180	+	0.508299i	$0.830274\pi$
$174$		0			0
$175$	1.80150	−	3.12030i	0.136181	−	0.235872i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.1923			1.06079			0.530393	−	0.847752i	$-0.322044\pi$
$179$	14.1923			1.06079			0.530393	+	0.847752i	$0.322044\pi$
$180$		0			0
$181$	−1.43147			−0.106400			−0.0532002	−	0.998584i	$-0.516942\pi$
$181$	−1.43147			−0.106400			−0.0532002	+	0.998584i	$0.516942\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.64132	+	9.77104i	−0.414758	+	0.718381i
$186$		0			0
$187$	12.8571	+	22.2691i	0.940201	+	1.62848i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.53379	−	13.0489i	−0.545126	−	0.944186i	−0.998599	−	0.0529159i	$-0.983148\pi$
$191$	−7.53379	−	13.0489i	−0.545126	−	0.944186i	0.453473	−	0.891270i	$-0.350185\pi$
$192$		0			0
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	−0.689536	−	0.724251i	$-0.742186\pi$
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	0.971988	+	0.235030i	$0.0755190\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.69002			−0.476644			−0.238322	−	0.971186i	$-0.576597\pi$
$197$	−6.69002			−0.476644			−0.238322	+	0.971186i	$0.576597\pi$
$198$		0			0
$199$	19.9396			1.41348			0.706739	−	0.707475i	$-0.250166\pi$
$199$	19.9396			1.41348			0.706739	+	0.707475i	$0.250166\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.119562	−	0.207087i	0.00839158	−	0.0145346i
$204$		0			0
$205$	6.01724	+	10.4222i	0.420262	+	0.727916i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.59781	−	6.23159i	−0.248866	−	0.431048i
$210$		0			0
$211$	−9.04583	+	15.6678i	−0.622741	+	1.07862i	0.366233	+	0.930523i	$0.380647\pi$
$211$	−9.04583	+	15.6678i	−0.622741	+	1.07862i	−0.988973	+	0.148095i	$0.952686\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.63036			0.179389
$216$		0			0
$217$	−1.66019			−0.112701
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.47141	+	6.01266i	−0.233512	+	0.404455i
$222$		0			0
$223$	−11.3285	−	19.6215i	−0.758610	−	1.31395i	−0.943560	−	0.331203i	$-0.892546\pi$
$223$	−11.3285	−	19.6215i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.64132	+	4.57489i	0.175310	+	0.303646i	0.940269	−	0.340433i	$-0.110574\pi$
$227$	2.64132	+	4.57489i	0.175310	+	0.303646i	−0.764958	+	0.644080i	$0.777240\pi$
$228$		0			0
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	0.346778	+	0.937947i	$0.387276\pi$
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	−0.985675	+	0.168655i	$0.946058\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.9806			1.11243			0.556217	−	0.831037i	$-0.312252\pi$
$233$	16.9806			1.11243			0.556217	+	0.831037i	$0.312252\pi$
$234$		0			0
$235$	−6.88891			−0.449383
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	0.452415	+	0.891808i	$0.350563\pi$
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	−0.998535	+	0.0541011i	$0.982771\pi$
$240$		0			0
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.857507	−	0.514473i	$-0.827988\pi$
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.0167933	−	0.999859i	$-0.505346\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.590972	+	1.02359i	0.0377558	+	0.0653950i
$246$		0			0
$247$	0.971410	−	1.68253i	0.0618093	−	0.107057i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.0780			−1.20419			−0.602096	−	0.798424i	$-0.705668\pi$
$251$	−19.0780			−1.20419			−0.602096	+	0.798424i	$0.705668\pi$
$252$		0			0
$253$	20.7518			1.30466
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	−0.999105	−	0.0423070i	$-0.986529\pi$
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	0.536191	+	0.844097i	$0.319863\pi$
$258$		0			0
$259$	4.77292	+	8.26693i	0.296575	+	0.513682i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	0.960335	−	0.278847i	$-0.0899523\pi$
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	−0.721656	+	0.692251i	$0.756619\pi$
$264$		0			0
$265$	6.85705	−	11.8768i	0.421225	−	0.729584i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.51135			0.0921486			0.0460743	−	0.998938i	$-0.485329\pi$
$269$	1.51135			0.0921486			0.0460743	+	0.998938i	$0.485329\pi$
$270$		0			0
$271$	21.9806			1.33522			0.667612	−	0.744509i	$-0.267316\pi$
$271$	21.9806			1.33522			0.667612	+	0.744509i	$0.267316\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.67223	+	11.5566i	−0.402350	+	0.696892i
$276$		0			0
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	0.981575	−	0.191077i	$-0.0611982\pi$
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	−0.656265	+	0.754530i	$0.727865\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.43831	−	14.6156i	−0.503387	−	0.871892i	−0.999992	−	0.00391559i	$-0.998754\pi$
$281$	−8.43831	−	14.6156i	−0.503387	−	0.871892i	0.496605	−	0.867977i	$-0.334580\pi$
$282$		0			0
$283$	−7.65856	+	13.2650i	−0.455254	+	0.788523i	−0.998703	−	0.0509194i	$-0.983785\pi$
$283$	−7.65856	+	13.2650i	−0.455254	+	0.788523i	0.543449	+	0.839442i	$0.317118\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.1819			0.601021
$288$		0			0
$289$	31.2028			1.83546
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.68482	+	8.11435i	−0.273690	+	0.474045i	−0.969804	−	0.243886i	$-0.921578\pi$
$293$	−4.68482	+	8.11435i	−0.273690	+	0.474045i	0.696114	+	0.717932i	$0.254911\pi$
$294$		0			0
$295$	1.53831	+	2.66442i	0.0895636	+	0.155129i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.80150	+	4.85235i	0.162015	+	0.280619i
$300$		0			0
$301$	1.11273	−	1.92730i	0.0641364	−	0.111088i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.98633			0.514556
$306$		0			0
$307$	−2.71410			−0.154902			−0.0774509	−	0.996996i	$-0.524678\pi$
$307$	−2.71410			−0.154902			−0.0774509	+	0.996996i	$0.524678\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.99028	−	12.1075i	0.396383	−	0.686555i	−0.596894	−	0.802320i	$-0.703599\pi$
$311$	6.99028	−	12.1075i	0.396383	−	0.686555i	0.993277	+	0.115765i	$0.0369320\pi$
$312$		0			0
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	0.998985	+	0.0450364i	$0.0143404\pi$
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	−0.460490	+	0.887665i	$0.652326\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.00972	−	3.48093i	−0.112877	−	0.195508i	0.804052	−	0.594559i	$-0.202673\pi$
$317$	−2.00972	−	3.48093i	−0.112877	−	0.195508i	−0.916929	+	0.399050i	$0.869340\pi$
$318$		0			0
$319$	−0.442820	+	0.766987i	−0.0247932	+	0.0429430i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.4887			−0.750529
$324$		0			0
$325$	−3.60301			−0.199859
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.91423	+	5.04759i	−0.160667	+	0.278283i
$330$		0			0
$331$	−6.18878	−	10.7193i	−0.340166	−	0.589185i	0.644297	−	0.764775i	$-0.277150\pi$
$331$	−6.18878	−	10.7193i	−0.340166	−	0.589185i	−0.984463	+	0.175590i	$0.943817\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.07318	−	3.59085i	−0.113270	−	0.196189i
$336$		0			0
$337$	−6.12997	+	10.6174i	−0.333920	+	0.578367i	−0.983277	−	0.182117i	$-0.941705\pi$
$337$	−6.12997	+	10.6174i	−0.333920	+	0.578367i	0.649356	+	0.760484i	$0.275038\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.14884			0.332978
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	−0.941363	−	0.337394i	$-0.890454\pi$
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	0.762874	+	0.646547i	$0.223788\pi$
$348$		0			0
$349$	−5.71737	−	9.90278i	−0.306044	−	0.530083i	0.671449	−	0.741050i	$-0.265672\pi$
$349$	−5.71737	−	9.90278i	−0.306044	−	0.530083i	−0.977493	+	0.210967i	$0.932339\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	−0.994141	−	0.108087i	$-0.965528\pi$
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	0.403465	−	0.914995i	$-0.367806\pi$
$354$		0			0
$355$	5.08414	−	8.80598i	0.269838	−	0.467373i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.55623			−0.398803			−0.199401	−	0.979918i	$-0.563900\pi$
$359$	−7.55623			−0.398803			−0.199401	+	0.979918i	$0.563900\pi$
$360$		0			0
$361$	−15.2255			−0.801339
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.95254	−	15.5062i	0.468597	−	0.811634i
$366$		0			0
$367$	−9.26157	−	16.0415i	−0.483450	−	0.837360i	0.516370	−	0.856366i	$-0.327283\pi$
$367$	−9.26157	−	16.0415i	−0.483450	−	0.837360i	−0.999819	+	0.0190063i	$0.993950\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.80150	−	10.0485i	−0.301199	−	0.521692i
$372$		0			0
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	−0.994371	−	0.105954i	$-0.966210\pi$
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	0.588944	+	0.808174i	$0.299544\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.239123			−0.0123155
$378$		0			0
$379$	−4.03775			−0.207405			−0.103703	−	0.994608i	$-0.533069\pi$
$379$	−4.03775			−0.207405			−0.103703	+	0.994608i	$0.533069\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.112725	+	0.195246i	−0.00575998	+	0.00997659i	−0.868891	−	0.495003i	$-0.835167\pi$
$383$	−0.112725	+	0.195246i	−0.00575998	+	0.00997659i	0.863131	+	0.504980i	$0.168500\pi$
$384$		0			0
$385$	−2.18878	−	3.79108i	−0.111551	−	0.193211i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.6316	+	21.8786i	0.640448	+	1.10929i	0.985333	+	0.170643i	$0.0545844\pi$
$389$	12.6316	+	21.8786i	0.640448	+	1.10929i	−0.344885	+	0.938645i	$0.612082\pi$
$390$		0			0
$391$	19.4503	−	33.6890i	0.983646	−	1.70373i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.71986			0.438744
$396$		0			0
$397$	−20.3009			−1.01888			−0.509438	−	0.860508i	$-0.670147\pi$
$397$	−20.3009			−1.01888			−0.509438	+	0.860508i	$0.670147\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.61273	+	13.1856i	−0.380161	+	0.658459i	−0.991085	−	0.133231i	$-0.957465\pi$
$401$	−7.61273	+	13.1856i	−0.380161	+	0.658459i	0.610924	+	0.791689i	$0.290798\pi$
$402$		0			0
$403$	0.830095	+	1.43777i	0.0413500	+	0.0716203i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.6774	−	30.6182i	−0.876238	−	1.51769i
$408$		0			0
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	−0.885781	−	0.464104i	$-0.846376\pi$
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	0.844816	+	0.535057i	$0.179710\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.60301			0.128086
$414$		0			0
$415$	8.20602			0.402818
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.6871	+	28.9030i	−0.815220	+	1.41200i	0.0939492	+	0.995577i	$0.470051\pi$
$419$	−16.6871	+	28.9030i	−0.815220	+	1.41200i	−0.909170	+	0.416426i	$0.863282\pi$
$420$		0			0
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	0.553523	−	0.832834i	$-0.313283\pi$
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	−0.998017	+	0.0629481i	$0.979950\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.5075	+	21.6637i	0.606704	+	1.05084i
$426$		0			0
$427$	3.80150	−	6.58440i	0.183968	−	0.318641i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	29.2826			1.41049			0.705247	−	0.708961i	$-0.250836\pi$
$431$	29.2826			1.41049			0.705247	+	0.708961i	$0.250836\pi$
$432$		0			0
$433$	−12.2449			−0.588451			−0.294226	−	0.955736i	$-0.595062\pi$
$433$	−12.2449			−0.588451			−0.294226	+	0.955736i	$0.595062\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.44282	+	9.42724i	−0.260365	+	0.450966i
$438$		0			0
$439$	−2.41586	−	4.18440i	−0.115303	−	0.199711i	0.802598	−	0.596520i	$-0.203451\pi$
$439$	−2.41586	−	4.18440i	−0.115303	−	0.199711i	−0.917901	+	0.396810i	$0.870117\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	0.850860	−	0.525392i	$-0.176081\pi$
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	−0.880433	+	0.474170i	$0.842748\pi$
$444$		0			0
$445$	−1.62352	+	2.81202i	−0.0769622	+	0.133302i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8.82846			−0.416641			−0.208320	−	0.978061i	$-0.566800\pi$
$449$	−8.82846			−0.416641			−0.208320	+	0.978061i	$0.566800\pi$
$450$		0			0
$451$	−37.7108			−1.77573
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.590972	−	1.02359i	0.0277052	−	0.0479868i
$456$		0			0
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	0.962349	−	0.271817i	$-0.0876247\pi$
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	−0.716575	+	0.697510i	$0.754291\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.2758	+	19.5302i	0.525166	+	0.909614i	0.999570	+	0.0293073i	$0.00933013\pi$
$461$	11.2758	+	19.5302i	0.525166	+	0.909614i	−0.474404	+	0.880307i	$0.657337\pi$
$462$		0			0
$463$	5.19850	−	9.00406i	0.241595	−	0.418454i	−0.719574	−	0.694416i	$-0.755663\pi$
$463$	5.19850	−	9.00406i	0.241595	−	0.418454i	0.961169	+	0.275962i	$0.0889963\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.3171			0.616242			0.308121	−	0.951347i	$-0.400300\pi$
$467$	13.3171			0.616242			0.308121	+	0.951347i	$0.400300\pi$
$468$		0			0
$469$	−3.50808			−0.161988
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.12120	+	7.13812i	−0.189493	+	0.328211i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.26771	−	12.5880i	−0.332070	−	0.575163i	0.650847	−	0.759209i	$-0.274414\pi$
$479$	−7.26771	−	12.5880i	−0.332070	−	0.575163i	−0.982918	+	0.184046i	$0.941080\pi$
$480$		0			0
$481$	4.77292	−	8.26693i	0.217626	−	0.376940i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.47249			−0.384716
$486$		0			0
$487$	−13.0539			−0.591529			−0.295765	−	0.955261i	$-0.595574\pi$
$487$	−13.0539			−0.591529			−0.295765	+	0.955261i	$0.595574\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	−0.997417	−	0.0718303i	$-0.977116\pi$
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	0.560915	+	0.827873i	$0.310449\pi$
$492$		0			0
$493$	0.830095	+	1.43777i	0.0373856	+	0.0647538i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.30150	−	7.45043i	−0.192949	−	0.334197i
$498$		0			0
$499$	−18.1111	+	31.3693i	−0.810764	+	1.40428i	0.101566	+	0.994829i	$0.467615\pi$
$499$	−18.1111	+	31.3693i	−0.810764	+	1.40428i	−0.912330	+	0.409455i	$0.865719\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	15.6764			0.698974			0.349487	−	0.936941i	$-0.386356\pi$
$503$	15.6764			0.698974			0.349487	+	0.936941i	$0.386356\pi$
$504$		0			0
$505$	−15.1111			−0.672435
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	−0.182492	−	0.983207i	$-0.558416\pi$
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	0.942729	−	0.333561i	$-0.108250\pi$
$510$		0			0
$511$	−7.57442	−	13.1193i	−0.335073	−	0.580363i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.59850	+	4.50073i	0.114503	+	0.198326i
$516$		0			0
$517$	10.7934	−	18.6948i	0.474694	−	0.822195i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.2449			0.448836			0.224418	−	0.974493i	$-0.427952\pi$
$521$	10.2449			0.448836			0.224418	+	0.974493i	$0.427952\pi$
$522$		0			0
$523$	−30.6030			−1.33818			−0.669088	−	0.743183i	$-0.733315\pi$
$523$	−30.6030			−1.33818			−0.669088	+	0.743183i	$0.733315\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.76320	−	9.98215i	0.251049	−	0.434829i
$528$		0			0
$529$	−4.19686	−	7.26918i	−0.182472	−	0.316051i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.09097	−	8.81782i	−0.220514	−	0.381942i
$534$		0			0
$535$	8.11273	−	14.0517i	0.350744	−	0.607506i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.70370			−0.159530
$540$		0			0
$541$	−26.0917			−1.12177			−0.560884	−	0.827894i	$-0.689539\pi$
$541$	−26.0917			−1.12177			−0.560884	+	0.827894i	$0.689539\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.746515	−	1.29300i	0.0319772	−	0.0553861i
$546$		0			0
$547$	−5.46169	−	9.45993i	−0.233525	−	0.404478i	0.725318	−	0.688414i	$-0.241693\pi$
$547$	−5.46169	−	9.45993i	−0.233525	−	0.404478i	−0.958843	+	0.283937i	$0.908359\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.232287	−	0.402332i	−0.00989575	−	0.0171399i
$552$		0			0
$553$	3.68878	−	6.38915i	0.156863	−	0.271694i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.9442			0.590835			0.295417	−	0.955368i	$-0.404541\pi$
$557$	13.9442			0.590835			0.295417	+	0.955368i	$0.404541\pi$
$558$		0			0
$559$	−2.22545			−0.0941265
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.1287	+	26.2037i	−0.637600	+	1.10435i	0.348358	+	0.937361i	$0.386739\pi$
$563$	−15.1287	+	26.2037i	−0.637600	+	1.10435i	−0.985958	+	0.166993i	$0.946594\pi$
$564$		0			0
$565$	−7.18770	−	12.4495i	−0.302389	−	0.523753i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.5676	−	18.3036i	−0.443016	−	0.767326i	0.554896	−	0.831920i	$-0.312758\pi$
$569$	−10.5676	−	18.3036i	−0.443016	−	0.767326i	−0.997912	+	0.0645936i	$0.979425\pi$
$570$		0			0
$571$	−16.3932	+	28.3938i	−0.686033	+	1.18824i	0.287078	+	0.957907i	$0.407316\pi$
$571$	−16.3932	+	28.3938i	−0.686033	+	1.18824i	−0.973111	+	0.230336i	$0.926017\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	20.1877			0.841885
$576$		0			0
$577$	−17.3743			−0.723301			−0.361651	−	0.932314i	$-0.617787\pi$
$577$	−17.3743			−0.723301			−0.361651	+	0.932314i	$0.617787\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.47141	−	6.01266i	0.144018	−	0.249447i
$582$		0			0
$583$	21.4870	+	37.2166i	0.889901	+	1.54135i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.48796	−	14.7016i	−0.350336	−	0.606799i	0.635973	−	0.771712i	$-0.280599\pi$
$587$	−8.48796	−	14.7016i	−0.350336	−	0.606799i	−0.986308	+	0.164913i	$0.947266\pi$
$588$		0			0
$589$	−1.61273	+	2.79332i	−0.0664512	+	0.115097i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.0733			0.536858			0.268429	−	0.963300i	$-0.413496\pi$
$593$	13.0733			0.536858			0.268429	+	0.963300i	$0.413496\pi$
$594$		0			0
$595$	−8.20602			−0.336414
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	0.396647	+	0.917971i	$0.370174\pi$
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	−0.993310	+	0.115479i	$0.963160\pi$
$600$		0			0
$601$	−3.89536	−	6.74695i	−0.158895	−	0.275214i	0.775576	−	0.631255i	$-0.217460\pi$
$601$	−3.89536	−	6.74695i	−0.158895	−	0.275214i	−0.934470	+	0.356041i	$0.884126\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.60589	+	2.78148i	0.0652887	+	0.113083i
$606$		0			0
$607$	−9.82038	+	17.0094i	−0.398597	+	0.690390i	−0.993553	−	0.113368i	$-0.963836\pi$
$607$	−9.82038	+	17.0094i	−0.398597	+	0.690390i	0.594956	+	0.803758i	$0.297169\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.82846			0.235794
$612$		0			0
$613$	23.5653			0.951792			0.475896	−	0.879502i	$-0.342124\pi$
$613$	23.5653			0.951792			0.475896	+	0.879502i	$0.342124\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.33009	+	9.23200i	−0.214582	+	0.371666i	−0.953143	−	0.302520i	$-0.902172\pi$
$617$	−5.33009	+	9.23200i	−0.214582	+	0.371666i	0.738562	+	0.674186i	$0.235505\pi$
$618$		0			0
$619$	−9.00752	−	15.6015i	−0.362043	−	0.627077i	0.626254	−	0.779619i	$-0.284587\pi$
$619$	−9.00752	−	15.6015i	−0.362043	−	0.627077i	−0.988297	+	0.152542i	$0.951254\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.37360	+	2.37915i	0.0550322	+	0.0953186i
$624$		0			0
$625$	−2.99837	+	5.19332i	−0.119935	+	0.207733i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−66.2750			−2.64256
$630$		0			0
$631$	−12.4703			−0.496436			−0.248218	−	0.968704i	$-0.579845\pi$
$631$	−12.4703			−0.496436			−0.248218	+	0.968704i	$0.579845\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.791790	+	1.37142i	−0.0314212	+	0.0544232i
$636$		0			0
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.57279	+	16.5806i	0.378102	+	0.654892i	0.990786	−	0.135436i	$-0.0432434\pi$
$641$	9.57279	+	16.5806i	0.378102	+	0.654892i	−0.612684	+	0.790328i	$0.709910\pi$
$642$		0			0
$643$	3.24433	−	5.61934i	0.127944	−	0.221605i	−0.794936	−	0.606693i	$-0.792496\pi$
$643$	3.24433	−	5.61934i	0.127944	−	0.221605i	0.922880	+	0.385088i	$0.125829\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.0988			−1.89096			−0.945479	−	0.325682i	$-0.894406\pi$
$647$	−48.0988			−1.89096			−0.945479	+	0.325682i	$0.894406\pi$
$648$		0			0
$649$	−9.64076			−0.378433
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.6202	+	37.4474i	−0.846066	+	1.46543i	0.0386267	+	0.999254i	$0.487702\pi$
$653$	−21.6202	+	37.4474i	−0.846066	+	1.46543i	−0.884692	+	0.466175i	$0.845632\pi$
$654$		0			0
$655$	−2.93530	−	5.08408i	−0.114691	−	0.198651i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	0.889417	−	0.457097i	$-0.151111\pi$
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	−0.840566	+	0.541709i	$0.817778\pi$
$660$		0			0
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	−0.0798613	−	0.996806i	$-0.525448\pi$
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	0.903190	−	0.429241i	$-0.141219\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.29630			0.0890468
$666$		0			0
$667$	1.33981			0.0518777
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.0796	+	24.3866i	−0.543538	+	0.941435i
$672$		0			0
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	0.707296	−	0.706918i	$-0.249915\pi$
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	−0.965857	+	0.259077i	$0.916582\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	0.884263	−	0.466989i	$-0.154661\pi$
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	−0.846556	+	0.532300i	$0.821328\pi$
$678$		0			0
$679$	−3.58414	+	6.20790i	−0.137546	+	0.238237i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	27.1672			1.03952			0.519761	−	0.854312i	$-0.326021\pi$
$683$	27.1672			1.03952			0.519761	+	0.854312i	$0.326021\pi$
$684$		0			0
$685$	−5.12941			−0.195985
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.80150	+	10.0485i	−0.221020	+	0.382817i
$690$		0			0
$691$	−25.1586	−	43.5759i	−0.957077	−	1.65771i	−0.729543	−	0.683935i	$-0.760267\pi$
$691$	−25.1586	−	43.5759i	−0.957077	−	1.65771i	−0.227534	−	0.973770i	$-0.573066\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.33009	−	4.03584i	−0.0883855	−	0.153088i
$696$		0			0
$697$	−35.3457	+	61.2205i	−1.33881	+	2.31889i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−45.1672			−1.70594			−0.852970	−	0.521960i	$-0.825201\pi$
$701$	−45.1672			−1.70594			−0.852970	+	0.521960i	$0.825201\pi$
$702$		0			0
$703$	18.5458			0.699469
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.39248	+	11.0721i	−0.240414	+	0.416409i
$708$		0			0
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	−0.950687	−	0.310153i	$-0.899620\pi$
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	0.206743	−	0.978395i	$-0.433714\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.65103	−	8.05582i	−0.174182	−	0.301693i
$714$		0			0
$715$	−2.18878	+	3.79108i	−0.0818557	+	0.141778i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−22.0377			−0.821869			−0.410935	−	0.911665i	$-0.634798\pi$
$719$	−22.0377			−0.821869			−0.410935	+	0.911665i	$0.634798\pi$
$720$		0			0
$721$	4.39699			0.163752
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.430782	+	0.746136i	−0.0159988	+	0.0277108i
$726$		0			0
$727$	14.0555	+	24.3449i	0.521291	+	0.902903i	0.999693	+	0.0247621i	$0.00788284\pi$
$727$	14.0555	+	24.3449i	0.521291	+	0.902903i	−0.478402	+	0.878141i	$0.658784\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.72545	+	13.3809i	0.285736	+	0.494909i
$732$		0			0
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	−0.954565	−	0.298003i	$-0.903680\pi$
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	0.735360	+	0.677676i	$0.237013\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.9929			0.478598
$738$		0			0
$739$	12.1844			0.448212			0.224106	−	0.974565i	$-0.428054\pi$
$739$	12.1844			0.448212			0.224106	+	0.974565i	$0.428054\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	−0.0925987	−	0.995704i	$-0.529517\pi$
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	0.908604	−	0.417659i	$-0.137149\pi$
$744$		0			0
$745$	−6.56634	−	11.3732i	−0.240572	−	0.416683i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.86389	−	11.8886i	−0.250801	−	0.434400i
$750$		0			0
$751$	21.4029	−	37.0709i	0.781002	−	1.35274i	−0.150356	−	0.988632i	$-0.548042\pi$
$751$	21.4029	−	37.0709i	0.781002	−	1.35274i	0.931358	−	0.364104i	$-0.118625\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.4567			0.598919
$756$		0			0
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	−0.966201	−	0.257788i	$-0.917006\pi$
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	0.706352	+	0.707861i	$0.250340\pi$
$762$		0			0
$763$	−0.631600	−	1.09396i	−0.0228655	−	0.0396041i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.30150	−	2.25427i	−0.0469946	−	0.0813971i
$768$		0			0
$769$	15.6105	−	27.0382i	0.562930	−	0.975024i	−0.434309	−	0.900764i	$-0.643007\pi$
$769$	15.6105	−	27.0382i	0.562930	−	0.975024i	0.997239	−	0.0742597i	$-0.0236594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.38005			−0.157539			−0.0787697	−	0.996893i	$-0.525099\pi$
$773$	−4.38005			−0.157539			−0.0787697	+	0.996893i	$0.525099\pi$
$774$		0			0
$775$	5.98168			0.214868
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.89084	−	17.1314i	0.354376	−	0.613798i
$780$		0			0
$781$	15.9315	+	27.5941i	0.570073	+	0.987395i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.0337917	+	0.0585290i	0.00120608	+	0.00208899i
$786$		0			0
$787$	13.8107	−	23.9208i	0.492297	−	0.852683i	−0.507664	−	0.861555i	$-0.669491\pi$
$787$	13.8107	−	23.9208i	0.492297	−	0.852683i	0.999961	+	0.00887191i	$0.00282405\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.1625			−0.432449
$792$		0			0
$793$	−7.60301			−0.269991
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.48181	+	2.56658i	−0.0524885	+	0.0909128i	−0.891076	−	0.453854i	$-0.850049\pi$
$797$	−1.48181	+	2.56658i	−0.0524885	+	0.0909128i	0.838587	+	0.544767i	$0.183382\pi$
$798$		0			0
$799$	−20.2330	−	35.0445i	−0.715791	−	1.23979i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	28.0534	+	48.5898i	0.989981	+	1.71470i
$804$		0			0
$805$	−3.31122	+	5.73520i	−0.116705	+	0.202139i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	24.7896			0.871556			0.435778	−	0.900054i	$-0.356473\pi$
$809$	24.7896			0.871556			0.435778	+	0.900054i	$0.356473\pi$
$810$		0			0
$811$	−8.24377			−0.289478			−0.144739	−	0.989470i	$-0.546234\pi$
$811$	−8.24377			−0.289478			−0.144739	+	0.989470i	$0.546234\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.891233	−	1.54366i	0.0312185	−	0.0540721i
$816$		0			0
$817$	−2.16182	−	3.74439i	−0.0756327	−	0.131000i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.4497	−	25.0275i	−0.504296	−	0.873467i	−0.999988	−	0.00496829i	$-0.998419\pi$
$821$	−14.4497	−	25.0275i	−0.504296	−	0.873467i	0.495691	−	0.868499i	$-0.334915\pi$
$822$		0			0
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	0.360623	+	0.932712i	$0.382564\pi$
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	−0.988063	+	0.154047i	$0.950769\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−50.7108			−1.76339			−0.881694	−	0.471821i	$-0.843597\pi$
$827$	−50.7108			−1.76339			−0.881694	+	0.471821i	$0.843597\pi$
$828$		0			0
$829$	14.8123			0.514452			0.257226	−	0.966351i	$-0.417191\pi$
$829$	14.8123			0.514452			0.257226	+	0.966351i	$0.417191\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.47141	+	6.01266i	−0.120277	+	0.208326i
$834$		0			0
$835$	−8.67799	−	15.0307i	−0.300314	−	0.520159i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−16.8606	−	29.2034i	−0.582093	−	1.00821i	−0.995231	−	0.0975464i	$-0.968901\pi$
$839$	−16.8606	−	29.2034i	−0.582093	−	1.00821i	0.413138	−	0.910669i	$-0.364433\pi$
$840$		0			0
$841$	14.4714	−	25.0652i	0.499014	−	0.864318i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.1833			0.487921
$846$		0			0
$847$	2.71737			0.0933699
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−26.7427	+	46.3197i	−0.916728	+	1.58782i
$852$		0			0
$853$	−5.89480	−	10.2101i	−0.201834	−	0.349587i	0.747285	−	0.664503i	$-0.231357\pi$
$853$	−5.89480	−	10.2101i	−0.201834	−	0.349587i	−0.949119	+	0.314916i	$0.898024\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	−0.999161	−	0.0409451i	$-0.986963\pi$
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	0.464121	−	0.885772i	$-0.346370\pi$
$858$		0			0
$859$	−25.1947	+	43.6384i	−0.859631	+	1.48892i	0.0126501	+	0.999920i	$0.495973\pi$
$859$	−25.1947	+	43.6384i	−0.859631	+	1.48892i	−0.872281	+	0.489005i	$0.837360\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.13268			0.0385568			0.0192784	−	0.999814i	$-0.493863\pi$
$863$	1.13268			0.0385568			0.0192784	+	0.999814i	$0.493863\pi$
$864$		0			0
$865$	0.298791			0.0101592
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−13.6621	+	23.6635i	−0.463456	+	0.802729i
$870$		0			0
$871$	1.75404	+	3.03809i	0.0594334	+	0.102942i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.08414	−	8.80598i	−0.171875	−	0.297696i
$876$		0			0
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	−0.536575	−	0.843853i	$-0.680282\pi$
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	0.999085	+	0.0427615i	$0.0136156\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.20929			−0.0407420			−0.0203710	−	0.999792i	$-0.506485\pi$
$881$	−1.20929			−0.0407420			−0.0203710	+	0.999792i	$0.506485\pi$
$882$		0			0
$883$	51.0884			1.71926			0.859631	−	0.510916i	$-0.170694\pi$
$883$	51.0884			1.71926			0.859631	+	0.510916i	$0.170694\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.7878	−	36.0056i	0.697987	−	1.20895i	−0.271176	−	0.962530i	$-0.587413\pi$
$887$	20.7878	−	36.0056i	0.697987	−	1.20895i	0.969163	−	0.246419i	$-0.0792541\pi$
$888$		0			0
$889$	0.669905	+	1.16031i	0.0224679	+	0.0389155i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.66182	+	9.80657i	0.189466	+	0.328164i
$894$		0			0
$895$	8.38727	−	14.5272i	0.280356	−	0.485590i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.396990			0.0132404
$900$		0			0
$901$	80.5576			2.68376
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.845958	+	1.46524i	−0.0281206	+	0.0487063i
$906$		0			0
$907$	17.7255	+	30.7014i	0.588564	+	1.01942i	0.994421	+	0.105486i	$0.0336398\pi$
$907$	17.7255	+	30.7014i	0.588564	+	1.01942i	−0.405857	+	0.913937i	$0.633027\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	0.985005	−	0.172526i	$-0.0551930\pi$
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	−0.641915	+	0.766776i	$0.721860\pi$
$912$		0			0
$913$	−12.8571	+	22.2691i	−0.425506	+	0.736998i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.96690			−0.164021
$918$		0			0
$919$	−14.3926			−0.474768			−0.237384	−	0.971416i	$-0.576290\pi$
$919$	−14.3926			−0.474768			−0.237384	+	0.971416i	$0.576290\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.30150	+	7.45043i	−0.141586	+	0.245234i
$924$		0			0
$925$	−17.1969	−	29.7858i	−0.565429	−	0.979352i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	−0.973509	−	0.228647i	$-0.926570\pi$
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	0.288741	−	0.957407i	$-0.406763\pi$
$930$		0			0
$931$	0.971410	−	1.68253i	0.0318367	−	0.0551427i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	30.3926			0.993945
$936$		0			0
$937$	3.17154			0.103610			0.0518048	−	0.998657i	$-0.483503\pi$
$937$	3.17154			0.103610			0.0518048	+	0.998657i	$0.483503\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	−0.891080	−	0.453846i	$-0.850052\pi$
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	0.838582	+	0.544775i	$0.183385\pi$
$942$		0			0
$943$	28.5248	+	49.4063i	0.928894	+	1.60889i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.6735	+	39.2716i	0.736789	+	1.27616i	0.953934	+	0.300016i	$0.0969922\pi$
$947$	22.6735	+	39.2716i	0.736789	+	1.27616i	−0.217145	+	0.976139i	$0.569675\pi$
$948$		0			0
$949$	−7.57442	+	13.1193i	−0.245876	+	0.425870i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	54.2703			1.75799			0.878994	−	0.476832i	$-0.158215\pi$
$953$	54.2703			1.75799			0.878994	+	0.476832i	$0.158215\pi$
$954$		0			0
$955$	−17.8090			−0.576287
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.16991	+	3.75839i	−0.0700699	+	0.121365i
$960$		0			0
$961$	14.1219	+	24.4598i	0.455545	+	0.789027i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.63788	−	8.03305i	−0.149299	−	0.258593i
$966$		0			0
$967$	12.8295	−	22.2214i	0.412570	−	0.714593i	−0.582600	−	0.812759i	$-0.697964\pi$
$967$	12.8295	−	22.2214i	0.412570	−	0.714593i	0.995170	+	0.0981667i	$0.0312978\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.0183			−0.674510			−0.337255	−	0.941413i	$-0.609498\pi$
$971$	−21.0183			−0.674510			−0.337255	+	0.941413i	$0.609498\pi$
$972$		0			0
$973$	−3.94282			−0.126401
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.04910	+	1.81709i	−0.0335637	+	0.0581340i	−0.882319	−	0.470651i	$-0.844019\pi$
$977$	−1.04910	+	1.81709i	−0.0335637	+	0.0581340i	0.848756	+	0.528785i	$0.177352\pi$
$978$		0			0
$979$	−5.08740	−	8.81164i	−0.162594	−	0.281621i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.4962	−	37.2325i	−0.685622	−	1.18753i	−0.973241	−	0.229787i	$-0.926197\pi$
$983$	−21.4962	−	37.2325i	−0.685622	−	1.18753i	0.287620	−	0.957745i	$-0.407136\pi$
$984$		0			0
$985$	−3.95361	+	6.84786i	−0.125973	+	0.218191i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.4692			0.396498
$990$		0			0
$991$	17.2632			0.548384			0.274192	−	0.961675i	$-0.411590\pi$
$991$	17.2632			0.548384			0.274192	+	0.961675i	$0.411590\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	11.7837	−	20.4100i	0.373569	−	0.647040i
$996$		0			0
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	0.990205	+	0.139619i	$0.0445878\pi$
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	−0.374189	+	0.927352i	$0.622079\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.g.1009.3		6
3.2	odd	2		1008.2.r.k.337.2		6
4.3	odd	2		189.2.f.a.64.2		6
9.2	odd	6		1008.2.r.k.673.2		6
9.4	even	3		9072.2.a.cd.1.1		3
9.5	odd	6		9072.2.a.bq.1.3		3
9.7	even	3	inner	3024.2.r.g.2017.3		6
12.11	even	2		63.2.f.b.22.2	✓	6
28.3	even	6		1323.2.h.e.226.2		6
28.11	odd	6		1323.2.h.d.226.2		6
28.19	even	6		1323.2.g.b.361.2		6
28.23	odd	6		1323.2.g.c.361.2		6
28.27	even	2		1323.2.f.c.442.2		6
36.7	odd	6		189.2.f.a.127.2		6
36.11	even	6		63.2.f.b.43.2	yes	6
36.23	even	6		567.2.a.d.1.2		3
36.31	odd	6		567.2.a.g.1.2		3
84.11	even	6		441.2.h.c.373.2		6
84.23	even	6		441.2.g.e.67.2		6
84.47	odd	6		441.2.g.d.67.2		6
84.59	odd	6		441.2.h.b.373.2		6
84.83	odd	2		441.2.f.d.148.2		6
252.11	even	6		441.2.g.e.79.2		6
252.47	odd	6		441.2.h.b.214.2		6
252.79	odd	6		1323.2.h.d.802.2		6
252.83	odd	6		441.2.f.d.295.2		6
252.115	even	6		1323.2.g.b.667.2		6
252.139	even	6		3969.2.a.p.1.2		3
252.151	odd	6		1323.2.g.c.667.2		6
252.167	odd	6		3969.2.a.m.1.2		3
252.187	even	6		1323.2.h.e.802.2		6
252.191	even	6		441.2.h.c.214.2		6
252.223	even	6		1323.2.f.c.883.2		6
252.227	odd	6		441.2.g.d.79.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	12.11	even	2
63.2.f.b.43.2	yes	6	36.11	even	6
189.2.f.a.64.2		6	4.3	odd	2
189.2.f.a.127.2		6	36.7	odd	6
441.2.f.d.148.2		6	84.83	odd	2
441.2.f.d.295.2		6	252.83	odd	6
441.2.g.d.67.2		6	84.47	odd	6
441.2.g.d.79.2		6	252.227	odd	6
441.2.g.e.67.2		6	84.23	even	6
441.2.g.e.79.2		6	252.11	even	6
441.2.h.b.214.2		6	252.47	odd	6
441.2.h.b.373.2		6	84.59	odd	6
441.2.h.c.214.2		6	252.191	even	6
441.2.h.c.373.2		6	84.11	even	6
567.2.a.d.1.2		3	36.23	even	6
567.2.a.g.1.2		3	36.31	odd	6
1008.2.r.k.337.2		6	3.2	odd	2
1008.2.r.k.673.2		6	9.2	odd	6
1323.2.f.c.442.2		6	28.27	even	2
1323.2.f.c.883.2		6	252.223	even	6
1323.2.g.b.361.2		6	28.19	even	6
1323.2.g.b.667.2		6	252.115	even	6
1323.2.g.c.361.2		6	28.23	odd	6
1323.2.g.c.667.2		6	252.151	odd	6
1323.2.h.d.226.2		6	28.11	odd	6
1323.2.h.d.802.2		6	252.79	odd	6
1323.2.h.e.226.2		6	28.3	even	6
1323.2.h.e.802.2		6	252.187	even	6
3024.2.r.g.1009.3		6	1.1	even	1	trivial
3024.2.r.g.2017.3		6	9.7	even	3	inner
3969.2.a.m.1.2		3	252.167	odd	6
3969.2.a.p.1.2		3	252.139	even	6
9072.2.a.bq.1.3		3	9.5	odd	6
9072.2.a.cd.1.1		3	9.4	even	3

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.590972 - 1.02359i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.85185 + 3.20750i) q^{11} +(-0.500000 + 0.866025i) q^{13} +6.94282 q^{17} -1.94282 q^{19} +(2.80150 - 4.85235i) q^{23} +(1.80150 + 3.12030i) q^{25} +(0.119562 + 0.207087i) q^{29} +(0.830095 - 1.43777i) q^{31} -1.18194 q^{35} -9.54583 q^{37} +(-5.09097 + 8.81782i) q^{41} +(1.11273 + 1.92730i) q^{43} +(-2.91423 - 5.04759i) q^{47} +(-0.500000 + 0.866025i) q^{49} +11.6030 q^{53} +4.37756 q^{55} +(-1.30150 + 2.25427i) q^{59} +(3.80150 + 6.58440i) q^{61} +(0.590972 + 1.02359i) q^{65} +(1.75404 - 3.03809i) q^{67} +8.60301 q^{71} +15.1488 q^{73} +(1.85185 - 3.20750i) q^{77} +(3.68878 + 6.38915i) q^{79} +(3.47141 + 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} -2.74720 q^{89} +1.00000 q^{91} +(-1.14815 + 1.98866i) q^{95} +(-3.58414 - 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59}+ \cdots - 3 q^{97}+O(q^{100}) \) 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

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