LMFDB - Embedded newform 2340.2.fo.a.1961.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(1241,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2340.1241"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.fo (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1961.5
Character	$\chi$	$=$	2340.1961
Dual form			2340.2.fo.a.1241.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{5} +(1.29465 + 4.83171i) q^{7} +(1.26507 - 4.72131i) q^{11} +(3.20513 + 1.65141i) q^{13} +(1.47595 - 2.55642i) q^{17} +(3.97808 - 1.06592i) q^{19} +(0.451533 + 0.782079i) q^{23} -1.00000i q^{25} +(4.66272 - 2.69202i) q^{29} +(-4.05259 - 4.05259i) q^{31} +(-4.33199 - 2.50108i) q^{35} +(-4.50710 - 1.20767i) q^{37} +(6.53030 + 1.74979i) q^{41} +(5.10306 + 2.94625i) q^{43} +(3.65247 + 3.65247i) q^{47} +(-15.6071 + 9.01078i) q^{49} +9.56102i q^{53} +(2.44393 + 4.23301i) q^{55} +(8.99069 - 2.40905i) q^{59} +(2.81119 - 4.86913i) q^{61} +(-3.43409 + 1.09864i) q^{65} +(-1.99493 + 7.44517i) q^{67} +(-2.55892 - 9.55001i) q^{71} +(-3.73823 + 3.73823i) q^{73} +24.4498 q^{77} +9.42258 q^{79} +(-10.7770 + 10.7770i) q^{83} +(0.764007 + 2.85131i) q^{85} +(-2.43121 + 9.07341i) q^{89} +(-3.82963 + 17.6243i) q^{91} +(-2.05921 + 3.56665i) q^{95} +(-3.38946 + 0.908204i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{13} - 20 q^{19} - 28 q^{31} + 12 q^{49} + 16 q^{55} + 48 q^{61} + 16 q^{67} - 20 q^{73} + 80 q^{79} + 20 q^{85} + 4 q^{91} - 40 q^{97}+O(q^{100}) $ 40 * q - 12 * q^13 - 20 * q^19 - 28 * q^31 + 12 * q^49 + 16 * q^55 + 48 * q^61 + 16 * q^67 - 20 * q^73 + 80 * q^79 + 20 * q^85 + 4 * q^91 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	1.29465	+	4.83171i	0.489333	+	1.82622i	0.559702	+	0.828694i	$0.310916\pi$
$7$	1.29465	+	4.83171i	0.489333	+	1.82622i	−0.0703687	+	0.997521i	$0.522418\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.26507	−	4.72131i	0.381433	−	1.42353i	−0.462280	−	0.886734i	$-0.652969\pi$
$11$	1.26507	−	4.72131i	0.381433	−	1.42353i	0.843713	−	0.536794i	$-0.180365\pi$
$12$		0			0
$13$	3.20513	+	1.65141i	0.888942	+	0.458020i
$13$	3.20513	+	1.65141i	0.888942	+	0.458020i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.47595	−	2.55642i	0.357970	−	0.620022i	−0.629652	−	0.776878i	$-0.716802\pi$
$17$	1.47595	−	2.55642i	0.357970	−	0.620022i	0.987622	+	0.156856i	$0.0501357\pi$
$18$		0			0
$19$	3.97808	−	1.06592i	0.912635	−	0.244540i	0.228200	−	0.973614i	$-0.426716\pi$
$19$	3.97808	−	1.06592i	0.912635	−	0.244540i	0.684434	+	0.729075i	$0.260049\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.451533	+	0.782079i	0.0941512	+	0.163075i	0.909254	−	0.416242i	$-0.136653\pi$
$23$	0.451533	+	0.782079i	0.0941512	+	0.163075i	−0.815103	+	0.579316i	$0.803320\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.66272	−	2.69202i	0.865845	−	0.499896i	−0.000120517	−	1.00000i	$-0.500038\pi$
$29$	4.66272	−	2.69202i	0.865845	−	0.499896i	0.865965	+	0.500104i	$0.166705\pi$
$30$		0			0
$31$	−4.05259	−	4.05259i	−0.727866	−	0.727866i	0.242328	−	0.970194i	$-0.422089\pi$
$31$	−4.05259	−	4.05259i	−0.727866	−	0.727866i	−0.970194	+	0.242328i	$0.922089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.33199	−	2.50108i	−0.732241	−	0.422759i
$36$		0			0
$37$	−4.50710	−	1.20767i	−0.740963	−	0.198540i	−0.131457	−	0.991322i	$-0.541966\pi$
$37$	−4.50710	−	1.20767i	−0.740963	−	0.198540i	−0.609506	+	0.792781i	$0.708632\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.53030	+	1.74979i	1.01986	+	0.273271i	0.729744	−	0.683720i	$-0.239639\pi$
$41$	6.53030	+	1.74979i	1.01986	+	0.273271i	0.290117	+	0.956991i	$0.406306\pi$
$42$		0			0
$43$	5.10306	+	2.94625i	0.778209	+	0.449299i	0.835795	−	0.549041i	$-0.185007\pi$
$43$	5.10306	+	2.94625i	0.778209	+	0.449299i	−0.0575863	+	0.998341i	$0.518340\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.65247	+	3.65247i	0.532767	+	0.532767i	0.921395	−	0.388628i	$-0.127051\pi$
$47$	3.65247	+	3.65247i	0.532767	+	0.532767i	−0.388628	+	0.921395i	$0.627051\pi$
$48$		0			0
$49$	−15.6071	+	9.01078i	−2.22959	+	1.28725i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			9.56102i			1.31331i	0.754192	+	0.656654i	$0.228029\pi$
$53$			9.56102i			1.31331i	−0.754192	+	0.656654i	$0.771971\pi$
$54$		0			0
$55$	2.44393	+	4.23301i	0.329539	+	0.570779i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.99069	−	2.40905i	1.17049	−	0.313631i	0.379341	−	0.925257i	$-0.376151\pi$
$59$	8.99069	−	2.40905i	1.17049	−	0.313631i	0.791148	+	0.611625i	$0.209484\pi$
$60$		0			0
$61$	2.81119	−	4.86913i	0.359936	−	0.623428i	−0.628013	−	0.778203i	$-0.716132\pi$
$61$	2.81119	−	4.86913i	0.359936	−	0.623428i	0.987950	+	0.154774i	$0.0494650\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.43409	+	1.09864i	−0.425947	+	0.136270i
$66$		0			0
$67$	−1.99493	+	7.44517i	−0.243719	+	0.909573i	0.730303	+	0.683123i	$0.239379\pi$
$67$	−1.99493	+	7.44517i	−0.243719	+	0.909573i	−0.974023	+	0.226450i	$0.927288\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.55892	−	9.55001i	−0.303687	−	1.13338i	−0.934069	−	0.357092i	$-0.883768\pi$
$71$	−2.55892	−	9.55001i	−0.303687	−	1.13338i	0.630382	−	0.776285i	$-0.282898\pi$
$72$		0			0
$73$	−3.73823	+	3.73823i	−0.437527	+	0.437527i	−0.891179	−	0.453652i	$-0.850121\pi$
$73$	−3.73823	+	3.73823i	−0.437527	+	0.437527i	0.453652	+	0.891179i	$0.350121\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	24.4498			2.78632
$78$		0			0
$79$	9.42258			1.06012			0.530061	−	0.847959i	$-0.322169\pi$
$79$	9.42258			1.06012			0.530061	+	0.847959i	$0.322169\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.7770	+	10.7770i	−1.18293	+	1.18293i	−0.203943	+	0.978983i	$0.565376\pi$
$83$	−10.7770	+	10.7770i	−1.18293	+	1.18293i	−0.978983	+	0.203943i	$0.934624\pi$
$84$		0			0
$85$	0.764007	+	2.85131i	0.0828682	+	0.309268i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.43121	+	9.07341i	−0.257708	+	0.961780i	0.708856	+	0.705353i	$0.249212\pi$
$89$	−2.43121	+	9.07341i	−0.257708	+	0.961780i	−0.966564	+	0.256426i	$0.917455\pi$
$90$		0			0
$91$	−3.82963	+	17.6243i	−0.401454	+	1.84752i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.05921	+	3.56665i	−0.211270	+	0.365931i
$96$		0			0
$97$	−3.38946	+	0.908204i	−0.344148	+	0.0922142i	−0.426753	−	0.904368i	$-0.640343\pi$
$97$	−3.38946	+	0.908204i	−0.344148	+	0.0922142i	0.0826051	+	0.996582i	$0.473676\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.61150	−	7.98736i	−0.458862	−	0.794772i	0.540039	−	0.841640i	$-0.318409\pi$
$101$	−4.61150	−	7.98736i	−0.458862	−	0.794772i	−0.998901	+	0.0468678i	$0.985076\pi$
$102$		0			0
$103$			13.7230i			1.35217i	0.736824	+	0.676084i	$0.236324\pi$
$103$			13.7230i			1.35217i	−0.736824	+	0.676084i	$0.763676\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.43001	+	4.86707i	−0.814960	+	0.470517i	−0.848675	−	0.528914i	$-0.822599\pi$
$107$	−8.43001	+	4.86707i	−0.814960	+	0.470517i	0.0337157	+	0.999431i	$0.489266\pi$
$108$		0			0
$109$	6.71837	+	6.71837i	0.643503	+	0.643503i	0.951415	−	0.307912i	$-0.0996301\pi$
$109$	6.71837	+	6.71837i	0.643503	+	0.643503i	−0.307912	+	0.951415i	$0.599630\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.17334	−	4.14153i	−0.674811	−	0.389602i	0.123086	−	0.992396i	$-0.460721\pi$
$113$	−7.17334	−	4.14153i	−0.674811	−	0.389602i	−0.797897	+	0.602794i	$0.794054\pi$
$114$		0			0
$115$	−0.872295	−	0.233731i	−0.0813420	−	0.0217955i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.2627	+	3.82168i	1.30746	+	0.350333i
$120$		0			0
$121$	−11.1641	−	6.44557i	−1.01491	−	0.585961i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	12.3999	−	7.15909i	1.10031	−	0.635267i	0.164011	−	0.986459i	$-0.447557\pi$
$127$	12.3999	−	7.15909i	1.10031	−	0.635267i	0.936304	+	0.351192i	$0.114223\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		−	7.82649i		−	0.683804i	−0.939736	−	0.341902i	$-0.888929\pi$
$131$		−	7.82649i		−	0.683804i	0.939736	−	0.341902i	$-0.111071\pi$
$132$		0			0
$133$	10.3005	+	17.8409i	0.893164	+	1.54701i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.705335	−	0.188994i	0.0602609	−	0.0161469i	−0.228563	−	0.973529i	$-0.573403\pi$
$137$	0.705335	−	0.188994i	0.0602609	−	0.0161469i	0.288824	+	0.957382i	$0.406736\pi$
$138$		0			0
$139$	9.88757	−	17.1258i	0.838653	−	1.45259i	−0.0523682	−	0.998628i	$-0.516677\pi$
$139$	9.88757	−	17.1258i	0.838653	−	1.45259i	0.891021	−	0.453962i	$-0.149990\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.8515	−	13.0432i	0.991076	−	1.09073i
$144$		0			0
$145$	−1.39349	+	5.20058i	−0.115723	+	0.431885i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.31873	+	12.3857i	0.271881	+	1.01467i	0.957903	+	0.287093i	$0.0926888\pi$
$149$	3.31873	+	12.3857i	0.271881	+	1.01467i	−0.686022	+	0.727581i	$0.740645\pi$
$150$		0			0
$151$	−3.03916	+	3.03916i	−0.247323	+	0.247323i	−0.819871	−	0.572548i	$-0.805955\pi$
$151$	−3.03916	+	3.03916i	−0.247323	+	0.247323i	0.572548	+	0.819871i	$0.305955\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.73123			0.460343
$156$		0			0
$157$	15.0409			1.20040			0.600198	−	0.799852i	$-0.295089\pi$
$157$	15.0409			1.20040			0.600198	+	0.799852i	$0.295089\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.19420	+	3.19420i	−0.251738	+	0.251738i
$162$		0			0
$163$	−1.16112	−	4.33335i	−0.0909459	−	0.339415i	0.905428	−	0.424500i	$-0.139550\pi$
$163$	−1.16112	−	4.33335i	−0.0909459	−	0.339415i	−0.996374	+	0.0850858i	$0.972884\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.51731	−	13.1268i	0.272178	−	1.01578i	−0.685532	−	0.728043i	$-0.740430\pi$
$167$	3.51731	−	13.1268i	0.272178	−	1.01578i	0.957709	−	0.287738i	$-0.0929032\pi$
$168$		0			0
$169$	7.54567	+	10.5860i	0.580436	+	0.814306i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.29537	−	10.9039i	0.478628	−	0.829008i	−0.521072	−	0.853513i	$-0.674468\pi$
$173$	6.29537	−	10.9039i	0.478628	−	0.829008i	0.999700	+	0.0245050i	$0.00780097\pi$
$174$		0			0
$175$	4.83171	−	1.29465i	0.365243	−	0.0978666i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.46186	−	16.3884i	−0.707213	−	1.22493i	−0.965887	−	0.258964i	$-0.916619\pi$
$179$	−9.46186	−	16.3884i	−0.707213	−	1.22493i	0.258674	−	0.965965i	$-0.416714\pi$
$180$		0			0
$181$			23.5898i			1.75342i	0.481020	+	0.876710i	$0.340267\pi$
$181$			23.5898i			1.75342i	−0.481020	+	0.876710i	$0.659733\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.04096	−	2.33305i	0.297097	−	0.171529i
$186$		0			0
$187$	−10.2024	−	10.2024i	−0.746077	−	0.746077i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.55681	−	2.63088i	−0.329720	−	0.190364i	0.325997	−	0.945371i	$-0.394300\pi$
$191$	−4.55681	−	2.63088i	−0.329720	−	0.190364i	−0.655717	+	0.755007i	$0.727633\pi$
$192$		0			0
$193$	−4.47820	−	1.19993i	−0.322348	−	0.0863728i	0.0940167	−	0.995571i	$-0.470029\pi$
$193$	−4.47820	−	1.19993i	−0.322348	−	0.0863728i	−0.416364	+	0.909198i	$0.636696\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.0510	+	4.56880i	1.21483	+	0.325514i	0.808657	−	0.588281i	$-0.200195\pi$
$197$	17.0510	+	4.56880i	1.21483	+	0.325514i	0.406177	+	0.913795i	$0.366862\pi$
$198$		0			0
$199$	−5.93886	−	3.42880i	−0.420994	−	0.243061i	0.274508	−	0.961585i	$-0.411485\pi$
$199$	−5.93886	−	3.42880i	−0.420994	−	0.243061i	−0.695503	+	0.718524i	$0.744818\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	19.0437	+	19.0437i	1.33660	+	1.33660i
$204$		0			0
$205$	−5.85491	+	3.38033i	−0.408924	+	0.236093i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	20.1302i		−	1.39244i
$210$		0			0
$211$	3.20762	+	5.55576i	0.220821	+	0.382474i	0.955058	−	0.296420i	$-0.0957929\pi$
$211$	3.20762	+	5.55576i	0.220821	+	0.382474i	−0.734236	+	0.678894i	$0.762460\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.69172	+	1.52509i	−0.388172	+	0.104010i
$216$		0			0
$217$	14.3342	−	24.8276i	0.973072	−	1.68541i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.95230	−	5.75624i	0.602197	−	0.387206i
$222$		0			0
$223$	6.02636	−	22.4907i	0.403555	−	1.50609i	−0.403150	−	0.915134i	$-0.632085\pi$
$223$	6.02636	−	22.4907i	0.403555	−	1.50609i	0.806705	−	0.590954i	$-0.201249\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.142226	+	0.530796i	0.00943989	+	0.0352301i	0.970485	−	0.241161i	$-0.0775282\pi$
$227$	0.142226	+	0.530796i	0.00943989	+	0.0352301i	−0.961045	+	0.276391i	$0.910861\pi$
$228$		0			0
$229$	−15.8318	+	15.8318i	−1.04619	+	1.04619i	−0.0473117	+	0.998880i	$0.515065\pi$
$229$	−15.8318	+	15.8318i	−1.04619	+	1.04619i	−0.998880	+	0.0473117i	$0.984935\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−23.7509			−1.55598			−0.777988	−	0.628279i	$-0.783760\pi$
$233$	−23.7509			−1.55598			−0.777988	+	0.628279i	$0.783760\pi$
$234$		0			0
$235$	−5.16537			−0.336952
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.3671	+	14.3671i	−0.929331	+	0.929331i	−0.997663	−	0.0683319i	$-0.978232\pi$
$239$	−14.3671	+	14.3671i	−0.929331	+	0.929331i	0.0683319	+	0.997663i	$0.478232\pi$
$240$		0			0
$241$	4.89235	+	18.2585i	0.315144	+	1.17613i	0.923855	+	0.382742i	$0.125020\pi$
$241$	4.89235	+	18.2585i	0.315144	+	1.17613i	−0.608711	+	0.793392i	$0.708313\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.66432	−	17.4075i	0.297993	−	1.11212i
$246$		0			0
$247$	14.5105	+	3.15304i	0.923283	+	0.200623i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.19836	+	3.80766i	−0.138759	+	0.240338i	−0.927027	−	0.374994i	$-0.877645\pi$
$251$	−2.19836	+	3.80766i	−0.138759	+	0.240338i	0.788268	+	0.615332i	$0.210978\pi$
$252$		0			0
$253$	4.26365	−	1.14244i	0.268054	−	0.0718248i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.32092	+	14.4123i	0.519045	+	0.899012i	0.999755	+	0.0221323i	$0.00704551\pi$
$257$	8.32092	+	14.4123i	0.519045	+	0.899012i	−0.480710	+	0.876879i	$0.659621\pi$
$258$		0			0
$259$		−	23.3405i		−	1.45031i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.1731	−	5.87345i	0.627301	−	0.362172i	−0.152405	−	0.988318i	$-0.548702\pi$
$263$	10.1731	−	5.87345i	0.627301	−	0.362172i	0.779706	+	0.626146i	$0.215369\pi$
$264$		0			0
$265$	−6.76066	−	6.76066i	−0.415304	−	0.415304i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.43790	−	1.40752i	−0.148641	−	0.0858182i	0.423835	−	0.905740i	$-0.360684\pi$
$269$	−2.43790	−	1.40752i	−0.148641	−	0.0858182i	−0.572476	+	0.819921i	$0.694017\pi$
$270$		0			0
$271$	−4.96693	−	1.33088i	−0.301719	−	0.0808454i	0.104783	−	0.994495i	$-0.466585\pi$
$271$	−4.96693	−	1.33088i	−0.301719	−	0.0808454i	−0.406503	+	0.913650i	$0.633252\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.72131	−	1.26507i	−0.284706	−	0.0762866i
$276$		0			0
$277$	−15.4692	−	8.93115i	−0.929454	−	0.536621i	−0.0428152	−	0.999083i	$-0.513633\pi$
$277$	−15.4692	−	8.93115i	−0.929454	−	0.536621i	−0.886639	+	0.462462i	$0.846966\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.78331	−	6.78331i	−0.404658	−	0.404658i	0.475213	−	0.879871i	$-0.342371\pi$
$281$	−6.78331	−	6.78331i	−0.404658	−	0.404658i	−0.879871	+	0.475213i	$0.842371\pi$
$282$		0			0
$283$	−15.6599	+	9.04122i	−0.930882	+	0.537445i	−0.887090	−	0.461596i	$-0.847277\pi$
$283$	−15.6599	+	9.04122i	−0.930882	+	0.537445i	−0.0437914	+	0.999041i	$0.513944\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			33.8179i			1.99621i
$288$		0			0
$289$	4.14316	+	7.17616i	0.243715	+	0.422127i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.0243	−	6.97320i	1.52036	−	0.407379i	0.600498	−	0.799626i	$-0.294969\pi$
$293$	26.0243	−	6.97320i	1.52036	−	0.407379i	0.919860	+	0.392248i	$0.128302\pi$
$294$		0			0
$295$	−4.65393	+	8.06084i	−0.270962	+	0.469320i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.155686	+	3.25233i	0.00900355	+	0.188087i
$300$		0			0
$301$	−7.62875	+	28.4709i	−0.439714	+	1.64103i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.45518	+	5.43081i	0.0833234	+	0.310967i
$306$		0			0
$307$	−0.588995	+	0.588995i	−0.0336157	+	0.0336157i	−0.723715	−	0.690099i	$-0.757567\pi$
$307$	−0.588995	+	0.588995i	−0.0336157	+	0.0336157i	0.690099	+	0.723715i	$0.257567\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−23.6333			−1.34012			−0.670062	−	0.742305i	$-0.733732\pi$
$311$	−23.6333			−1.34012			−0.670062	+	0.742305i	$0.733732\pi$
$312$		0			0
$313$	9.65826			0.545917			0.272959	−	0.962026i	$-0.411998\pi$
$313$	9.65826			0.545917			0.272959	+	0.962026i	$0.411998\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.33201	+	5.33201i	−0.299475	+	0.299475i	−0.840808	−	0.541333i	$-0.817920\pi$
$317$	−5.33201	+	5.33201i	−0.299475	+	0.299475i	0.541333	+	0.840808i	$0.317920\pi$
$318$		0			0
$319$	−6.81119	−	25.4197i	−0.381353	−	1.42323i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.14650	−	11.7429i	0.175076	−	0.653391i
$324$		0			0
$325$	1.65141	−	3.20513i	0.0916039	−	0.177788i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.9190	+	22.3764i	−0.712247	+	1.23365i
$330$		0			0
$331$	−22.6503	+	6.06914i	−1.24497	+	0.333590i	−0.820393	−	0.571800i	$-0.806245\pi$
$331$	−22.6503	+	6.06914i	−1.24497	+	0.333590i	−0.424581	+	0.905390i	$0.639579\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.85391	−	6.67516i	−0.210561	−	0.364703i
$336$		0			0
$337$		−	17.2728i		−	0.940912i	−0.882423	−	0.470456i	$-0.844089\pi$
$337$		−	17.2728i		−	0.940912i	0.882423	−	0.470456i	$-0.155911\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−24.2603	+	14.0067i	−1.31377	+	0.758506i
$342$		0			0
$343$	−38.9839	−	38.9839i	−2.10493	−	2.10493i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.4321	−	7.17768i	−0.667390	−	0.385318i	0.127697	−	0.991813i	$-0.459242\pi$
$347$	−12.4321	−	7.17768i	−0.667390	−	0.385318i	−0.795087	+	0.606495i	$0.792575\pi$
$348$		0			0
$349$	13.9002	+	3.72455i	0.744062	+	0.199371i	0.610883	−	0.791721i	$-0.290815\pi$
$349$	13.9002	+	3.72455i	0.744062	+	0.199371i	0.133179	+	0.991092i	$0.457481\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−19.5034	−	5.22593i	−1.03806	−	0.278148i	−0.300753	−	0.953702i	$-0.597238\pi$
$353$	−19.5034	−	5.22593i	−1.03806	−	0.278148i	−0.737311	+	0.675554i	$0.763905\pi$
$354$		0			0
$355$	8.56230	+	4.94345i	0.454440	+	0.262371i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.9111	+	11.9111i	0.628646	+	0.628646i	0.947727	−	0.319081i	$-0.103374\pi$
$359$	11.9111	+	11.9111i	0.628646	+	0.628646i	−0.319081	+	0.947727i	$0.603374\pi$
$360$		0			0
$361$	−1.76554	+	1.01934i	−0.0929232	+	0.0536492i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	5.28666i		−	0.276716i
$366$		0			0
$367$	−7.90259	−	13.6877i	−0.412512	−	0.714491i	0.582652	−	0.812722i	$-0.302015\pi$
$367$	−7.90259	−	13.6877i	−0.412512	−	0.714491i	−0.995164	+	0.0982307i	$0.968682\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−46.1961	+	12.3782i	−2.39838	+	0.642645i
$372$		0			0
$373$	9.56288	−	16.5634i	0.495147	−	0.857620i	−0.504837	−	0.863215i	$-0.668447\pi$
$373$	9.56288	−	16.5634i	0.495147	−	0.857620i	0.999984	+	0.00559453i	$0.00178081\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.3902	−	0.928192i	0.998648	−	0.0478043i
$378$		0			0
$379$	0.0157597	−	0.0588159i	0.000809520	−	0.00302117i	−0.965520	−	0.260329i	$-0.916169\pi$
$379$	0.0157597	−	0.0588159i	0.000809520	−	0.00302117i	0.966329	+	0.257308i	$0.0828355\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.24921	−	23.3224i	−0.319320	−	1.19172i	−0.919900	−	0.392153i	$-0.871730\pi$
$383$	−6.24921	−	23.3224i	−0.319320	−	1.19172i	0.600580	−	0.799565i	$-0.294936\pi$
$384$		0			0
$385$	−17.2886	+	17.2886i	−0.881110	+	0.881110i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	33.1856			1.68258			0.841288	−	0.540587i	$-0.181798\pi$
$389$	33.1856			1.68258			0.841288	+	0.540587i	$0.181798\pi$
$390$		0			0
$391$	2.66576			0.134813
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.66277	+	6.66277i	−0.335240	+	0.335240i
$396$		0			0
$397$	7.20190	+	26.8779i	0.361453	+	1.34896i	0.872166	+	0.489210i	$0.162715\pi$
$397$	7.20190	+	26.8779i	0.361453	+	1.34896i	−0.510713	+	0.859751i	$0.670618\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.57520	+	20.8069i	−0.278412	+	1.03905i	0.675108	+	0.737719i	$0.264097\pi$
$401$	−5.57520	+	20.8069i	−0.278412	+	1.03905i	−0.953520	+	0.301329i	$0.902570\pi$
$402$		0			0
$403$	−6.29656	−	19.6816i	−0.313654	−	0.980408i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.4036	+	19.7516i	−0.565256	+	0.979051i
$408$		0			0
$409$	9.14530	−	2.45048i	0.452206	−	0.121168i	−0.0255253	−	0.999674i	$-0.508126\pi$
$409$	9.14530	−	2.45048i	0.452206	−	0.121168i	0.477732	+	0.878506i	$0.341459\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	23.2797	+	40.3216i	1.14552	+	1.98409i
$414$		0			0
$415$		−	15.2409i		−	0.748148i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.03957	−	4.64165i	0.392759	−	0.226759i	−0.290596	−	0.956846i	$-0.593854\pi$
$419$	8.03957	−	4.64165i	0.392759	−	0.226759i	0.683355	+	0.730086i	$0.260520\pi$
$420$		0			0
$421$	22.9212	+	22.9212i	1.11711	+	1.11711i	0.992163	+	0.124947i	$0.0398762\pi$
$421$	22.9212	+	22.9212i	1.11711	+	1.11711i	0.124947	+	0.992163i	$0.460124\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.55642	−	1.47595i	−0.124004	−	0.0715940i
$426$		0			0
$427$	27.1658	+	7.27904i	1.31464	+	0.352258i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.4567	−	6.55316i	−1.17804	−	0.315655i	−0.383891	−	0.923378i	$-0.625416\pi$
$431$	−24.4567	−	6.55316i	−1.17804	−	0.315655i	−0.794149	+	0.607724i	$0.792083\pi$
$432$		0			0
$433$	−30.7193	−	17.7358i	−1.47628	−	0.852329i	−0.476636	−	0.879101i	$-0.658144\pi$
$433$	−30.7193	−	17.7358i	−1.47628	−	0.852329i	−0.999642	+	0.0267717i	$0.991477\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.62987	+	2.62987i	0.125804	+	0.125804i
$438$		0			0
$439$	29.2884	−	16.9097i	1.39786	−	0.807055i	0.403691	−	0.914895i	$-0.367727\pi$
$439$	29.2884	−	16.9097i	1.39786	−	0.807055i	0.994168	+	0.107840i	$0.0343936\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			6.29148i			0.298917i	0.988768	+	0.149459i	$0.0477531\pi$
$443$			6.29148i			0.298917i	−0.988768	+	0.149459i	$0.952247\pi$
$444$		0			0
$445$	−4.69674	−	8.13500i	−0.222647	−	0.385636i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.46974	+	0.661766i	−0.116554	+	0.0312307i	−0.316625	−	0.948551i	$-0.602550\pi$
$449$	−2.46974	+	0.661766i	−0.116554	+	0.0312307i	0.200070	+	0.979782i	$0.435883\pi$
$450$		0			0
$451$	16.5226	−	28.6179i	0.778018	−	1.34757i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.75427	−	15.1702i	−0.457287	−	0.711189i
$456$		0			0
$457$	1.96538	−	7.33489i	0.0919365	−	0.343112i	−0.904601	−	0.426260i	$-0.859831\pi$
$457$	1.96538	−	7.33489i	0.0919365	−	0.343112i	0.996537	+	0.0831483i	$0.0264975\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.27469	−	34.6136i	−0.431966	−	1.61212i	−0.748225	−	0.663445i	$-0.769094\pi$
$461$	−9.27469	−	34.6136i	−0.431966	−	1.61212i	0.316260	−	0.948673i	$-0.397573\pi$
$462$		0			0
$463$	25.7771	−	25.7771i	1.19796	−	1.19796i	0.223189	−	0.974775i	$-0.428353\pi$
$463$	25.7771	−	25.7771i	1.19796	−	1.19796i	0.974775	−	0.223189i	$-0.0716467\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.9467			−1.24694			−0.623472	−	0.781846i	$-0.714278\pi$
$467$	−26.9467			−1.24694			−0.623472	+	0.781846i	$0.714278\pi$
$468$		0			0
$469$	−38.5557			−1.78034
$470$		0			0
$471$		0			0
$472$		0			0
$473$	20.3659	−	20.3659i	0.936424	−	0.936424i
$474$		0			0
$475$	−1.06592	−	3.97808i	−0.0489079	−	0.182527i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.59843	−	35.8218i	0.438564	−	1.63674i	−0.293828	−	0.955858i	$-0.594929\pi$
$479$	9.59843	−	35.8218i	0.438564	−	1.63674i	0.732392	−	0.680883i	$-0.238404\pi$
$480$		0			0
$481$	−12.4515	−	11.3138i	−0.567738	−	0.515867i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.75452	−	3.03891i	0.0796685	−	0.137990i
$486$		0			0
$487$	15.6125	−	4.18335i	0.707468	−	0.189565i	0.112895	−	0.993607i	$-0.463988\pi$
$487$	15.6125	−	4.18335i	0.707468	−	0.189565i	0.594573	+	0.804041i	$0.297321\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.0669	−	27.8287i	−0.725088	−	1.25589i	−0.958938	−	0.283617i	$-0.908466\pi$
$491$	−16.0669	−	27.8287i	−0.725088	−	1.25589i	0.233849	−	0.972273i	$-0.424868\pi$
$492$		0			0
$493$		−	15.8931i		−	0.715790i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	42.8300	−	24.7279i	1.92119	−	1.10920i
$498$		0			0
$499$	0.793611	+	0.793611i	0.0355269	+	0.0355269i	0.724647	−	0.689120i	$-0.242003\pi$
$499$	0.793611	+	0.793611i	0.0355269	+	0.0355269i	−0.689120	+	0.724647i	$0.742003\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−16.5556	−	9.55838i	−0.738178	−	0.426187i	0.0832285	−	0.996530i	$-0.473477\pi$
$503$	−16.5556	−	9.55838i	−0.738178	−	0.426187i	−0.821406	+	0.570343i	$0.806810\pi$
$504$		0			0
$505$	8.90874	+	2.38709i	0.396434	+	0.106224i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.9305	−	7.48394i	−1.23800	−	0.331720i	−0.420308	−	0.907382i	$-0.638078\pi$
$509$	−27.9305	−	7.48394i	−1.23800	−	0.331720i	−0.817688	+	0.575662i	$0.804745\pi$
$510$		0			0
$511$	−22.9018	−	13.2223i	−1.01311	−	0.584922i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.70363	−	9.70363i	−0.427593	−	0.427593i
$516$		0			0
$517$	21.8651	−	12.6238i	0.961624	−	0.555194i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			7.45705i			0.326699i	0.986568	+	0.163350i	$0.0522299\pi$
$521$			7.45705i			0.326699i	−0.986568	+	0.163350i	$0.947770\pi$
$522$		0			0
$523$	10.0343	+	17.3799i	0.438770	+	0.759972i	0.997595	−	0.0693137i	$-0.0220809\pi$
$523$	10.0343	+	17.3799i	0.438770	+	0.759972i	−0.558825	+	0.829286i	$0.688748\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−16.3415	+	4.37870i	−0.711847	+	0.190739i
$528$		0			0
$529$	11.0922	−	19.2123i	0.482271	−	0.835318i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.0408	+	16.3925i	0.781434	+	0.710039i
$534$		0			0
$535$	2.51938	−	9.40245i	0.108922	−	0.406503i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	22.7985	+	85.0853i	0.982003	+	3.66488i
$540$		0			0
$541$	13.1755	−	13.1755i	0.566459	−	0.566459i	−0.364676	−	0.931135i	$-0.618820\pi$
$541$	13.1755	−	13.1755i	0.566459	−	0.566459i	0.931135	+	0.364676i	$0.118820\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.50121			−0.406987
$546$		0			0
$547$	−32.6348			−1.39536			−0.697681	−	0.716409i	$-0.745785\pi$
$547$	−32.6348			−1.39536			−0.697681	+	0.716409i	$0.745785\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.6792	−	15.6792i	0.667955	−	0.667955i
$552$		0			0
$553$	12.1990	+	45.5272i	0.518753	+	1.93601i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.0217	+	44.8657i	−0.509377	+	1.90102i	−0.0828113	+	0.996565i	$0.526390\pi$
$557$	−12.0217	+	44.8657i	−0.509377	+	1.90102i	−0.426566	+	0.904456i	$0.640277\pi$
$558$		0			0
$559$	11.4905	+	17.8704i	0.485995	+	0.755836i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.5049	−	30.3194i	0.737743	−	1.27781i	−0.215766	−	0.976445i	$-0.569225\pi$
$563$	17.5049	−	30.3194i	0.737743	−	1.27781i	0.953509	−	0.301364i	$-0.0974419\pi$
$564$		0			0
$565$	8.00082	−	2.14381i	0.336597	−	0.0901909i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.75159	−	11.6941i	−0.283041	−	0.490242i	0.689091	−	0.724675i	$-0.258010\pi$
$569$	−6.75159	−	11.6941i	−0.283041	−	0.490242i	−0.972132	+	0.234433i	$0.924677\pi$
$570$		0			0
$571$			15.6642i			0.655526i	0.944760	+	0.327763i	$0.106295\pi$
$571$			15.6642i			0.655526i	−0.944760	+	0.327763i	$0.893705\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.782079	−	0.451533i	0.0326149	−	0.0188302i
$576$		0			0
$577$	8.34957	+	8.34957i	0.347597	+	0.347597i	0.859214	−	0.511617i	$-0.170953\pi$
$577$	8.34957	+	8.34957i	0.347597	+	0.347597i	−0.511617	+	0.859214i	$0.670953\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−66.0236	−	38.1187i	−2.73912	−	1.58143i
$582$		0			0
$583$	45.1405	+	12.0954i	1.86953	+	0.500939i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.9618	+	7.76028i	1.19538	+	0.320301i	0.801010	−	0.598651i	$-0.204296\pi$
$587$	28.9618	+	7.76028i	1.19538	+	0.320301i	0.394370	+	0.918952i	$0.370963\pi$
$588$		0			0
$589$	−20.4413	−	11.8018i	−0.842268	−	0.486284i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.64256	+	9.64256i	0.395973	+	0.395973i	0.876810	−	0.480837i	$-0.159667\pi$
$593$	9.64256	+	9.64256i	0.395973	+	0.395973i	−0.480837	+	0.876810i	$0.659667\pi$
$594$		0			0
$595$	−12.7876	+	7.38292i	−0.524240	+	0.302670i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	35.6265i		−	1.45566i	−0.685758	−	0.727829i	$-0.740529\pi$
$599$		−	35.6265i		−	1.45566i	0.685758	−	0.727829i	$-0.259471\pi$
$600$		0			0
$601$	−14.2791	−	24.7322i	−0.582459	−	1.00885i	−0.995187	−	0.0979937i	$-0.968757\pi$
$601$	−14.2791	−	24.7322i	−0.582459	−	1.00885i	0.412728	−	0.910854i	$-0.364576\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.4519	−	3.33647i	0.506241	−	0.135647i
$606$		0			0
$607$	13.9940	−	24.2383i	0.567999	−	0.983803i	−0.428765	−	0.903416i	$-0.641051\pi$
$607$	13.9940	−	24.2383i	0.567999	−	0.983803i	0.996764	−	0.0803867i	$-0.0256155\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.67489	+	17.7384i	0.229581	+	0.717617i
$612$		0			0
$613$	−1.21419	+	4.53143i	−0.0490408	+	0.183023i	−0.986102	−	0.166143i	$-0.946869\pi$
$613$	−1.21419	+	4.53143i	−0.0490408	+	0.183023i	0.937061	+	0.349166i	$0.113535\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.72124	+	21.3520i	0.230329	+	0.859598i	0.980199	+	0.198013i	$0.0634490\pi$
$617$	5.72124	+	21.3520i	0.230329	+	0.859598i	−0.749871	+	0.661584i	$0.769884\pi$
$618$		0			0
$619$	9.30361	−	9.30361i	0.373944	−	0.373944i	−0.494968	−	0.868911i	$-0.664820\pi$
$619$	9.30361	−	9.30361i	0.373944	−	0.373944i	0.868911	+	0.494968i	$0.164820\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−46.9877			−1.88252
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.73957	+	9.73957i	−0.388342	+	0.388342i
$630$		0			0
$631$	3.18322	+	11.8799i	0.126722	+	0.472933i	0.999895	−	0.0144773i	$-0.00460844\pi$
$631$	3.18322	+	11.8799i	0.126722	+	0.472933i	−0.873173	+	0.487410i	$0.837942\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.70582	+	13.8303i	−0.147061	+	0.548839i
$636$		0			0
$637$	−64.9033	+	3.10686i	−2.57156	+	0.123098i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.35676	+	14.4743i	−0.330072	+	0.571702i	−0.982526	−	0.186127i	$-0.940406\pi$
$641$	−8.35676	+	14.4743i	−0.330072	+	0.571702i	0.652453	+	0.757829i	$0.273740\pi$
$642$		0			0
$643$	−39.5404	+	10.5948i	−1.55932	+	0.417818i	−0.932448	−	0.361304i	$-0.882332\pi$
$643$	−39.5404	+	10.5948i	−1.55932	+	0.417818i	−0.626872	+	0.779123i	$0.715665\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.59770	−	13.1596i	−0.298697	−	0.517358i	0.677141	−	0.735853i	$-0.263219\pi$
$647$	−7.59770	−	13.1596i	−0.298697	−	0.517358i	−0.975838	+	0.218495i	$0.929885\pi$
$648$		0			0
$649$		−	45.4954i		−	1.78585i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−35.7721	+	20.6530i	−1.39987	+	0.808215i	−0.994379	−	0.105883i	$-0.966233\pi$
$653$	−35.7721	+	20.6530i	−1.39987	+	0.808215i	−0.405492	+	0.914099i	$0.632900\pi$
$654$		0			0
$655$	5.53416	+	5.53416i	0.216238	+	0.216238i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.9981	+	19.6288i	1.32438	+	0.764630i	0.984424	−	0.175812i	$-0.0562550\pi$
$659$	33.9981	+	19.6288i	1.32438	+	0.764630i	0.339954	+	0.940442i	$0.389588\pi$
$660$		0			0
$661$	−2.22310	−	0.595679i	−0.0864687	−	0.0231692i	0.215325	−	0.976542i	$-0.430919\pi$
$661$	−2.22310	−	0.595679i	−0.0864687	−	0.0231692i	−0.301794	+	0.953373i	$0.597585\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−19.8990	−	5.33192i	−0.771650	−	0.206763i
$666$		0			0
$667$	4.21074	+	2.43107i	0.163041	+	0.0941315i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.4323	−	19.4323i	−0.750176	−	0.750176i
$672$		0			0
$673$	−1.38701	+	0.800790i	−0.0534653	+	0.0308682i	−0.526494	−	0.850179i	$-0.676494\pi$
$673$	−1.38701	+	0.800790i	−0.0534653	+	0.0308682i	0.473029	+	0.881047i	$0.343161\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			6.78167i			0.260641i	0.991472	+	0.130320i	$0.0416006\pi$
$677$			6.78167i			0.260641i	−0.991472	+	0.130320i	$0.958399\pi$
$678$		0			0
$679$	−8.77636	−	15.2011i	−0.336806	−	0.583365i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.49948	+	1.74153i	−0.248696	+	0.0666378i	−0.381013	−	0.924570i	$-0.624425\pi$
$683$	−6.49948	+	1.74153i	−0.248696	+	0.0666378i	0.132318	+	0.991207i	$0.457758\pi$
$684$		0			0
$685$	−0.365108	+	0.632386i	−0.0139501	+	0.0241622i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.7892	+	30.6443i	−0.601521	+	1.16745i
$690$		0			0
$691$	5.49544	−	20.5093i	0.209057	−	0.780210i	−0.779118	−	0.626877i	$-0.784333\pi$
$691$	5.49544	−	20.5093i	0.209057	−	0.780210i	0.988175	−	0.153333i	$-0.0490006\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.11818	+	19.1013i	0.194144	+	0.724555i
$696$		0			0
$697$	14.1116	−	14.1116i	0.534514	−	0.534514i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−16.7276			−0.631791			−0.315896	−	0.948794i	$-0.602305\pi$
$701$	−16.7276			−0.631791			−0.315896	+	0.948794i	$0.602305\pi$
$702$		0			0
$703$	−19.2169			−0.724779
$704$		0			0
$705$		0			0
$706$		0			0
$707$	32.6223	−	32.6223i	1.22689	−	1.22689i
$708$		0			0
$709$	4.54094	+	16.9470i	0.170538	+	0.636458i	0.997269	+	0.0738596i	$0.0235317\pi$
$709$	4.54094	+	16.9470i	0.170538	+	0.636458i	−0.826730	+	0.562599i	$0.809802\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.33956	−	4.99932i	0.0501671	−	0.187226i
$714$		0			0
$715$	0.842651	+	17.6033i	0.0315134	+	0.658325i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.4389	+	44.0614i	−0.948710	+	1.64321i	−0.200564	+	0.979681i	$0.564277\pi$
$719$	−25.4389	+	44.0614i	−0.948710	+	1.64321i	−0.748146	+	0.663534i	$0.769056\pi$
$720$		0			0
$721$	−66.3056	+	17.7665i	−2.46935	+	0.661661i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.69202	−	4.66272i	−0.0999791	−	0.173169i
$726$		0			0
$727$		−	1.07231i		−	0.0397698i	−0.999802	−	0.0198849i	$-0.993670\pi$
$727$		−	1.07231i		−	0.0397698i	0.999802	−	0.0198849i	$-0.00632998\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.0637	−	8.69703i	0.557151	−	0.321671i
$732$		0			0
$733$	−37.9128	−	37.9128i	−1.40034	−	1.40034i	−0.798969	−	0.601372i	$-0.794621\pi$
$733$	−37.9128	−	37.9128i	−1.40034	−	1.40034i	−0.601372	−	0.798969i	$-0.705379\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	32.6272	+	18.8373i	1.20184	+	0.693882i
$738$		0			0
$739$	4.04046	+	1.08264i	0.148631	+	0.0398254i	0.332367	−	0.943150i	$-0.392153\pi$
$739$	4.04046	+	1.08264i	0.148631	+	0.0398254i	−0.183737	+	0.982976i	$0.558819\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−46.3917	−	12.4306i	−1.70195	−	0.456035i	−0.728518	−	0.685027i	$-0.759791\pi$
$743$	−46.3917	−	12.4306i	−1.70195	−	0.456035i	−0.973428	+	0.228991i	$0.926457\pi$
$744$		0			0
$745$	−11.1047	−	6.41130i	−0.406844	−	0.234892i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−34.4302	−	34.4302i	−1.25805	−	1.25805i
$750$		0			0
$751$	37.7380	−	21.7881i	1.37708	−	0.795058i	0.385274	−	0.922802i	$-0.374107\pi$
$751$	37.7380	−	21.7881i	1.37708	−	0.795058i	0.991807	+	0.127744i	$0.0407737\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	4.29802i		−	0.156421i
$756$		0			0
$757$	−5.14830	−	8.91712i	−0.187118	−	0.324098i	0.757170	−	0.653218i	$-0.226581\pi$
$757$	−5.14830	−	8.91712i	−0.187118	−	0.324098i	−0.944288	+	0.329120i	$0.893248\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	46.5535	−	12.4740i	1.68756	−	0.452181i	0.717803	−	0.696246i	$-0.245148\pi$
$761$	46.5535	−	12.4740i	1.68756	−	0.452181i	0.969759	+	0.244065i	$0.0784811\pi$
$762$		0			0
$763$	−23.7633	+	41.1592i	−0.860288	+	1.49006i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	32.7946	+	7.12605i	1.18415	+	0.257307i
$768$		0			0
$769$	−1.36511	+	5.09467i	−0.0492272	+	0.183718i	−0.986162	−	0.165787i	$-0.946984\pi$
$769$	−1.36511	+	5.09467i	−0.0492272	+	0.183718i	0.936934	+	0.349505i	$0.113650\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.79553	+	32.8254i	0.316353	+	1.18065i	0.922723	+	0.385464i	$0.125958\pi$
$773$	8.79553	+	32.8254i	0.316353	+	1.18065i	−0.606370	+	0.795183i	$0.707375\pi$
$774$		0			0
$775$	−4.05259	+	4.05259i	−0.145573	+	0.145573i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	27.8432			0.997587
$780$		0			0
$781$	−48.3257			−1.72923
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−10.6355	+	10.6355i	−0.379598	+	0.379598i
$786$		0			0
$787$	−12.8105	−	47.8093i	−0.456643	−	1.70422i	−0.683211	−	0.730221i	$-0.739417\pi$
$787$	−12.8105	−	47.8093i	−0.456643	−	1.70422i	0.226568	−	0.973995i	$-0.427249\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.7237	−	40.0213i	0.381290	−	1.42299i
$792$		0			0
$793$	17.0512	−	10.9637i	0.605505	−	0.389334i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.119917	−	0.207702i	0.00424766	−	0.00735717i	−0.863894	−	0.503674i	$-0.831981\pi$
$797$	0.119917	−	0.207702i	0.00424766	−	0.00735717i	0.868141	+	0.496317i	$0.165315\pi$
$798$		0			0
$799$	14.7281	−	3.94638i	0.521042	−	0.139613i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.9202	+	22.3785i	0.455944	+	0.789719i
$804$		0			0
$805$		−	4.51728i		−	0.159213i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	40.8499	−	23.5847i	1.43621	−	0.829194i	0.438623	−	0.898671i	$-0.355466\pi$
$809$	40.8499	−	23.5847i	1.43621	−	0.829194i	0.997584	+	0.0694772i	$0.0221331\pi$
$810$		0			0
$811$	−4.27615	−	4.27615i	−0.150156	−	0.150156i	0.628032	−	0.778188i	$-0.283861\pi$
$811$	−4.27615	−	4.27615i	−0.150156	−	0.150156i	−0.778188	+	0.628032i	$0.783861\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.88518	+	2.24311i	0.136092	+	0.0785727i
$816$		0			0
$817$	23.4409	+	6.28096i	0.820092	+	0.219743i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.6013	−	4.71625i	−0.614289	−	0.164598i	−0.0617587	−	0.998091i	$-0.519671\pi$
$821$	−17.6013	−	4.71625i	−0.614289	−	0.164598i	−0.552530	+	0.833493i	$0.686338\pi$
$822$		0			0
$823$	43.9961	+	25.4012i	1.53361	+	0.885429i	0.999191	+	0.0402071i	$0.0128018\pi$
$823$	43.9961	+	25.4012i	1.53361	+	0.885429i	0.534416	+	0.845222i	$0.320532\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.68880	+	5.68880i	0.197819	+	0.197819i	0.799064	−	0.601245i	$-0.205329\pi$
$827$	5.68880	+	5.68880i	0.197819	+	0.197819i	−0.601245	+	0.799064i	$0.705329\pi$
$828$		0			0
$829$	−19.7314	+	11.3919i	−0.685301	+	0.395658i	−0.801849	−	0.597527i	$-0.796150\pi$
$829$	−19.7314	+	11.3919i	−0.685301	+	0.395658i	0.116549	+	0.993185i	$0.462817\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			53.1978i			1.84319i
$834$		0			0
$835$	6.79492	+	11.7691i	0.235148	+	0.407288i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	40.9704	−	10.9780i	1.41445	−	0.379002i	0.530941	−	0.847409i	$-0.321838\pi$
$839$	40.9704	−	10.9780i	1.41445	−	0.379002i	0.883513	+	0.468407i	$0.155172\pi$
$840$		0			0
$841$	−0.00605310	+	0.0104843i	−0.000208727	+	0.000361526i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−12.8210	−	2.14982i	−0.441056	−	0.0739562i
$846$		0			0
$847$	16.6896	−	62.2863i	0.573460	−	2.14018i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.09061	−	4.07021i	−0.0373856	−	0.139525i
$852$		0			0
$853$	26.7767	−	26.7767i	0.916817	−	0.916817i	−0.0799792	−	0.996797i	$-0.525485\pi$
$853$	26.7767	−	26.7767i	0.916817	−	0.916817i	0.996797	+	0.0799792i	$0.0254854\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.8178			−0.813600			−0.406800	−	0.913517i	$-0.633355\pi$
$857$	−23.8178			−0.813600			−0.406800	+	0.913517i	$0.633355\pi$
$858$		0			0
$859$	−44.7622			−1.52727			−0.763633	−	0.645650i	$-0.776586\pi$
$859$	−44.7622			−1.52727			−0.763633	+	0.645650i	$0.776586\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.4545	+	11.4545i	−0.389917	+	0.389917i	−0.874658	−	0.484741i	$-0.838914\pi$
$863$	−11.4545	+	11.4545i	−0.389917	+	0.389917i	0.484741	+	0.874658i	$0.338914\pi$
$864$		0			0
$865$	3.25872	+	12.1617i	0.110800	+	0.413511i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.9202	−	44.4869i	0.404366	−	1.50911i
$870$		0			0
$871$	−18.6891	+	20.5683i	−0.633255	+	0.696929i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.50108	+	4.33199i	−0.0845519	+	0.146448i
$876$		0			0
$877$	−2.97974	+	0.798420i	−0.100619	+	0.0269607i	−0.308777	−	0.951134i	$-0.599920\pi$
$877$	−2.97974	+	0.798420i	−0.100619	+	0.0269607i	0.208158	+	0.978095i	$0.433253\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.884341	−	1.53172i	−0.0297942	−	0.0516051i	0.850744	−	0.525581i	$-0.176152\pi$
$881$	−0.884341	−	1.53172i	−0.0297942	−	0.0516051i	−0.880538	+	0.473975i	$0.842819\pi$
$882$		0			0
$883$		−	20.1220i		−	0.677158i	−0.940938	−	0.338579i	$-0.890054\pi$
$883$		−	20.1220i		−	0.677158i	0.940938	−	0.338579i	$-0.109946\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.8952	−	9.75447i	0.567287	−	0.327523i	−0.188778	−	0.982020i	$-0.560453\pi$
$887$	16.8952	−	9.75447i	0.567287	−	0.327523i	0.756065	+	0.654497i	$0.227119\pi$
$888$		0			0
$889$	50.6443	+	50.6443i	1.69855	+	1.69855i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.4231	+	10.6366i	0.616505	+	0.355939i
$894$		0			0
$895$	18.2789	+	4.89782i	0.610997	+	0.163716i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.8057	−	7.98642i	−0.994076	−	0.266362i
$900$		0			0
$901$	24.4420	+	14.1116i	0.814280	+	0.470125i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.6805	−	16.6805i	−0.554480	−	0.554480i
$906$		0			0
$907$	−5.37878	+	3.10544i	−0.178600	+	0.103115i	−0.586635	−	0.809852i	$-0.699547\pi$
$907$	−5.37878	+	3.10544i	−0.178600	+	0.103115i	0.408035	+	0.912966i	$0.366214\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			17.4945i			0.579618i	0.957085	+	0.289809i	$0.0935917\pi$
$911$			17.4945i			0.579618i	−0.957085	+	0.289809i	$0.906408\pi$
$912$		0			0
$913$	37.2477	+	64.5150i	1.23272	+	2.13513i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	37.8153	−	10.1326i	1.24877	−	0.334608i
$918$		0			0
$919$	−6.50509	+	11.2671i	−0.214583	+	0.371669i	−0.953144	−	0.302518i	$-0.902173\pi$
$919$	−6.50509	+	11.2671i	−0.214583	+	0.371669i	0.738560	+	0.674187i	$0.235506\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.56936	−	34.8348i	0.249149	−	1.14660i
$924$		0			0
$925$	−1.20767	+	4.50710i	−0.0397081	+	0.148193i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.52510	−	35.5481i	−0.312508	−	1.16630i	−0.926287	−	0.376819i	$-0.877018\pi$
$929$	−9.52510	−	35.5481i	−0.312508	−	1.16630i	0.613779	−	0.789478i	$-0.289649\pi$
$930$		0			0
$931$	−52.4816	+	52.4816i	−1.72002	+	1.72002i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	14.4284			0.471861
$936$		0			0
$937$	13.5562			0.442862			0.221431	−	0.975176i	$-0.428927\pi$
$937$	13.5562			0.442862			0.221431	+	0.975176i	$0.428927\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.1111	−	20.1111i	0.655603	−	0.655603i	−0.298733	−	0.954337i	$-0.596564\pi$
$941$	20.1111	−	20.1111i	0.655603	−	0.655603i	0.954337	+	0.298733i	$0.0965641\pi$
$942$		0			0
$943$	1.58018	+	5.89730i	0.0514576	+	0.192042i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.4238	−	46.3663i	0.403719	−	1.50670i	−0.402686	−	0.915338i	$-0.631923\pi$
$947$	12.4238	−	46.3663i	0.403719	−	1.50670i	0.806406	−	0.591363i	$-0.201410\pi$
$948$		0			0
$949$	−18.1549	+	5.80814i	−0.589332	+	0.188540i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4.01265	−	6.95011i	0.129982	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$953$	4.01265	−	6.95011i	0.129982	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$954$		0			0
$955$	5.08247	−	1.36184i	0.164465	−	0.0440682i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.82633	+	3.16330i	0.0589753	+	0.102148i
$960$		0			0
$961$			1.84695i			0.0595790i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.01504	−	2.31809i	0.129249	−	0.0746218i
$966$		0			0
$967$	22.9644	+	22.9644i	0.738484	+	0.738484i	0.972285	−	0.233800i	$-0.0751162\pi$
$967$	22.9644	+	22.9644i	0.738484	+	0.738484i	−0.233800	+	0.972285i	$0.575116\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.4507	+	8.34311i	0.463745	+	0.267743i	0.713618	−	0.700535i	$-0.247055\pi$
$971$	14.4507	+	8.34311i	0.463745	+	0.267743i	−0.249873	+	0.968279i	$0.580389\pi$
$972$		0			0
$973$	95.5478	+	25.6020i	3.06312	+	0.820761i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.7156	−	4.21099i	−0.502788	−	0.134722i	−0.00149424	−	0.999999i	$-0.500476\pi$
$977$	−15.7156	−	4.21099i	−0.502788	−	0.134722i	−0.501293	+	0.865277i	$0.667142\pi$
$978$		0			0
$979$	39.7627	+	22.9570i	1.27082	+	0.733709i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.23542	+	1.23542i	0.0394037	+	0.0394037i	0.726534	−	0.687130i	$-0.241130\pi$
$983$	1.23542	+	1.23542i	0.0394037	+	0.0394037i	−0.687130	+	0.726534i	$0.741130\pi$
$984$		0			0
$985$	−15.2875	+	8.82624i	−0.487100	+	0.281228i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			5.32132i			0.169208i
$990$		0			0
$991$	10.3071	+	17.8524i	0.327415	+	0.567100i	0.981998	−	0.188890i	$-0.0604890\pi$
$991$	10.3071	+	17.8524i	0.327415	+	0.567100i	−0.654583	+	0.755990i	$0.727156\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.62393	−	1.77488i	0.209993	−	0.0562674i
$996$		0			0
$997$	1.31531	−	2.27818i	0.0416561	−	0.0721506i	−0.844446	−	0.535641i	$-0.820070\pi$
$997$	1.31531	−	2.27818i	0.0416561	−	0.0721506i	0.886102	+	0.463491i	$0.153403\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.fo.a.1961.5	yes	40
3.2	odd	2	inner	2340.2.fo.a.1961.6	yes	40
13.6	odd	12	inner	2340.2.fo.a.1241.6	yes	40
39.32	even	12	inner	2340.2.fo.a.1241.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2340.2.fo.a.1241.5	✓	40	39.32	even	12	inner
2340.2.fo.a.1241.6	yes	40	13.6	odd	12	inner
2340.2.fo.a.1961.5	yes	40	1.1	even	1	trivial
2340.2.fo.a.1961.6	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.fo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{5} +(1.29465 + 4.83171i) q^{7} +(1.26507 - 4.72131i) q^{11} +(3.20513 + 1.65141i) q^{13} +(1.47595 - 2.55642i) q^{17} +(3.97808 - 1.06592i) q^{19} +(0.451533 + 0.782079i) q^{23} -1.00000i q^{25} +(4.66272 - 2.69202i) q^{29} +(-4.05259 - 4.05259i) q^{31} +(-4.33199 - 2.50108i) q^{35} +(-4.50710 - 1.20767i) q^{37} +(6.53030 + 1.74979i) q^{41} +(5.10306 + 2.94625i) q^{43} +(3.65247 + 3.65247i) q^{47} +(-15.6071 + 9.01078i) q^{49} +9.56102i q^{53} +(2.44393 + 4.23301i) q^{55} +(8.99069 - 2.40905i) q^{59} +(2.81119 - 4.86913i) q^{61} +(-3.43409 + 1.09864i) q^{65} +(-1.99493 + 7.44517i) q^{67} +(-2.55892 - 9.55001i) q^{71} +(-3.73823 + 3.73823i) q^{73} +24.4498 q^{77} +9.42258 q^{79} +(-10.7770 + 10.7770i) q^{83} +(0.764007 + 2.85131i) q^{85} +(-2.43121 + 9.07341i) q^{89} +(-3.82963 + 17.6243i) q^{91} +(-2.05921 + 3.56665i) q^{95} +(-3.38946 + 0.908204i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{13} - 20 q^{19} - 28 q^{31} + 12 q^{49} + 16 q^{55} + 48 q^{61} + 16 q^{67} - 20 q^{73} + 80 q^{79} + 20 q^{85} + 4 q^{91} - 40 q^{97}+O(q^{100}) \) 40 * q - 12 * q^13 - 20 * q^19 - 28 * q^31 + 12 * q^49 + 16 * q^55 + 48 * q^61 + 16 * q^67 - 20 * q^73 + 80 * q^79 + 20 * q^85 + 4 * q^91 - 40 * q^97

Introduction

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