LMFDB - Embedded newform 2940.2.x.b.97.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(97,2940)] 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("2940.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.11
Character	$\chi$	$=$	2940.97
Dual form			2940.2.x.b.1273.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(2.07369 - 0.836546i) q^{5} +1.00000i q^{9} +2.28881 q^{11} +(0.277290 + 0.277290i) q^{13} +(2.05785 + 0.874793i) q^{15} +(0.0556418 - 0.0556418i) q^{17} +3.08243 q^{19} +(-0.206886 + 0.206886i) q^{23} +(3.60038 - 3.46947i) q^{25} +(-0.707107 + 0.707107i) q^{27} +3.92904i q^{29} +1.24185i q^{31} +(1.61844 + 1.61844i) q^{33} +(1.47548 + 1.47548i) q^{37} +0.392148i q^{39} +0.184951i q^{41} +(-0.541181 + 0.541181i) q^{43} +(0.836546 + 2.07369i) q^{45} +(5.46908 - 5.46908i) q^{47} +0.0786894 q^{51} +(7.91828 - 7.91828i) q^{53} +(4.74629 - 1.91470i) q^{55} +(2.17961 + 2.17961i) q^{57} -5.78405 q^{59} +6.85231i q^{61} +(0.806980 + 0.343048i) q^{65} +(-7.59248 - 7.59248i) q^{67} -0.292581 q^{69} -3.95718 q^{71} +(5.30939 + 5.30939i) q^{73} +(4.99914 + 0.0925647i) q^{75} +13.0447i q^{79} -1.00000 q^{81} +(7.50874 + 7.50874i) q^{83} +(0.0688370 - 0.161931i) q^{85} +(-2.77825 + 2.77825i) q^{87} +11.0670 q^{89} +(-0.878121 + 0.878121i) q^{93} +(6.39201 - 2.57860i) q^{95} +(6.10165 - 6.10165i) q^{97} +2.28881i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	2.07369	−	0.836546i	0.927382	−	0.374115i
$5$	2.07369	−	0.836546i	0.927382	−	0.374115i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	2.28881			0.690103			0.345052	−	0.938584i	$-0.387861\pi$
$11$	2.28881			0.690103			0.345052	+	0.938584i	$0.387861\pi$
$12$		0			0
$13$	0.277290	+	0.277290i	0.0769065	+	0.0769065i	0.744514	−	0.667607i	$-0.232681\pi$
$13$	0.277290	+	0.277290i	0.0769065	+	0.0769065i	−0.667607	+	0.744514i	$0.732681\pi$
$14$		0			0
$15$	2.05785	+	0.874793i	0.531334	+	0.225871i
$16$		0			0
$17$	0.0556418	−	0.0556418i	0.0134951	−	0.0134951i	−0.700327	−	0.713822i	$-0.746962\pi$
$17$	0.0556418	−	0.0556418i	0.0134951	−	0.0134951i	0.713822	+	0.700327i	$0.246962\pi$
$18$		0			0
$19$	3.08243			0.707159			0.353579	−	0.935405i	$-0.384964\pi$
$19$	3.08243			0.707159			0.353579	+	0.935405i	$0.384964\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.206886	+	0.206886i	−0.0431388	+	0.0431388i	−0.728347	−	0.685208i	$-0.759711\pi$
$23$	−0.206886	+	0.206886i	−0.0431388	+	0.0431388i	0.685208	+	0.728347i	$0.259711\pi$
$24$		0			0
$25$	3.60038	−	3.46947i	0.720076	−	0.693895i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			3.92904i			0.729604i	0.931085	+	0.364802i	$0.118863\pi$
$29$			3.92904i			0.729604i	−0.931085	+	0.364802i	$0.881137\pi$
$30$		0			0
$31$			1.24185i			0.223043i	0.993762	+	0.111521i	$0.0355724\pi$
$31$			1.24185i			0.223043i	−0.993762	+	0.111521i	$0.964428\pi$
$32$		0			0
$33$	1.61844	+	1.61844i	0.281733	+	0.281733i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.47548	+	1.47548i	0.242567	+	0.242567i	0.817911	−	0.575344i	$-0.195132\pi$
$37$	1.47548	+	1.47548i	0.242567	+	0.242567i	−0.575344	+	0.817911i	$0.695132\pi$
$38$		0			0
$39$			0.392148i			0.0627939i
$40$		0			0
$41$			0.184951i			0.0288846i	0.999896	+	0.0144423i	$0.00459728\pi$
$41$			0.184951i			0.0288846i	−0.999896	+	0.0144423i	$0.995403\pi$
$42$		0			0
$43$	−0.541181	+	0.541181i	−0.0825293	+	0.0825293i	−0.747166	−	0.664637i	$-0.768586\pi$
$43$	−0.541181	+	0.541181i	−0.0825293	+	0.0825293i	0.664637	+	0.747166i	$0.268586\pi$
$44$		0			0
$45$	0.836546	+	2.07369i	0.124705	+	0.309127i
$46$		0			0
$47$	5.46908	−	5.46908i	0.797747	−	0.797747i	−0.184993	−	0.982740i	$-0.559226\pi$
$47$	5.46908	−	5.46908i	0.797747	−	0.797747i	0.982740	+	0.184993i	$0.0592263\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.0786894			0.0110187
$52$		0			0
$53$	7.91828	−	7.91828i	1.08766	−	1.08766i	0.0918904	−	0.995769i	$-0.470709\pi$
$53$	7.91828	−	7.91828i	1.08766	−	1.08766i	0.995769	−	0.0918904i	$-0.0292910\pi$
$54$		0			0
$55$	4.74629	−	1.91470i	0.639989	−	0.258178i
$56$		0			0
$57$	2.17961	+	2.17961i	0.288696	+	0.288696i
$58$		0			0
$59$	−5.78405			−0.753019			−0.376510	−	0.926413i	$-0.622876\pi$
$59$	−5.78405			−0.753019			−0.376510	+	0.926413i	$0.622876\pi$
$60$		0			0
$61$			6.85231i			0.877349i	0.898646	+	0.438674i	$0.144552\pi$
$61$			6.85231i			0.877349i	−0.898646	+	0.438674i	$0.855448\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.806980	+	0.343048i	0.100094	+	0.0425499i
$66$		0			0
$67$	−7.59248	−	7.59248i	−0.927570	−	0.927570i	0.0699789	−	0.997548i	$-0.477707\pi$
$67$	−7.59248	−	7.59248i	−0.927570	−	0.927570i	−0.997548	+	0.0699789i	$0.977707\pi$
$68$		0			0
$69$	−0.292581			−0.0352227
$70$		0			0
$71$	−3.95718			−0.469631			−0.234816	−	0.972040i	$-0.575449\pi$
$71$	−3.95718			−0.469631			−0.234816	+	0.972040i	$0.575449\pi$
$72$		0			0
$73$	5.30939	+	5.30939i	0.621418	+	0.621418i	0.945894	−	0.324476i	$-0.105188\pi$
$73$	5.30939	+	5.30939i	0.621418	+	0.621418i	−0.324476	+	0.945894i	$0.605188\pi$
$74$		0			0
$75$	4.99914	+	0.0925647i	0.577251	+	0.0106885i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			13.0447i			1.46764i	0.679344	+	0.733820i	$0.262265\pi$
$79$			13.0447i			1.46764i	−0.679344	+	0.733820i	$0.737735\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	7.50874	+	7.50874i	0.824192	+	0.824192i	0.986706	−	0.162514i	$-0.0519604\pi$
$83$	7.50874	+	7.50874i	0.824192	+	0.824192i	−0.162514	+	0.986706i	$0.551960\pi$
$84$		0			0
$85$	0.0688370	−	0.161931i	0.00746642	−	0.0175639i
$86$		0			0
$87$	−2.77825	+	2.77825i	−0.297860	+	0.297860i
$88$		0			0
$89$	11.0670			1.17310			0.586550	−	0.809913i	$-0.300486\pi$
$89$	11.0670			1.17310			0.586550	+	0.809913i	$0.300486\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.878121	+	0.878121i	−0.0910569	+	0.0910569i
$94$		0			0
$95$	6.39201	−	2.57860i	0.655807	−	0.264559i
$96$		0			0
$97$	6.10165	−	6.10165i	0.619528	−	0.619528i	−0.325882	−	0.945410i	$-0.605661\pi$
$97$	6.10165	−	6.10165i	0.619528	−	0.619528i	0.945410	+	0.325882i	$0.105661\pi$
$98$		0			0
$99$			2.28881i			0.230034i
$100$		0			0
$101$		−	13.9593i		−	1.38900i	−0.719492	−	0.694500i	$-0.755626\pi$
$101$		−	13.9593i		−	1.38900i	0.719492	−	0.694500i	$-0.244374\pi$
$102$		0			0
$103$	6.97996	+	6.97996i	0.687756	+	0.687756i	0.961735	−	0.273980i	$-0.0883402\pi$
$103$	6.97996	+	6.97996i	0.687756	+	0.687756i	−0.273980	+	0.961735i	$0.588340\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.05242	+	4.05242i	0.391762	+	0.391762i	0.875315	−	0.483553i	$-0.160654\pi$
$107$	4.05242	+	4.05242i	0.391762	+	0.391762i	−0.483553	+	0.875315i	$0.660654\pi$
$108$		0			0
$109$		−	12.1720i		−	1.16586i	−0.812521	−	0.582932i	$-0.801905\pi$
$109$		−	12.1720i		−	1.16586i	0.812521	−	0.582932i	$-0.198095\pi$
$110$		0			0
$111$			2.08664i			0.198055i
$112$		0			0
$113$	−7.20875	+	7.20875i	−0.678142	+	0.678142i	−0.959580	−	0.281438i	$-0.909189\pi$
$113$	−7.20875	+	7.20875i	−0.678142	+	0.678142i	0.281438	+	0.959580i	$0.409189\pi$
$114$		0			0
$115$	−0.255948	+	0.602088i	−0.0238673	+	0.0561450i
$116$		0			0
$117$	−0.277290	+	0.277290i	−0.0256355	+	0.0256355i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.76133			−0.523758
$122$		0			0
$123$	−0.130780	+	0.130780i	−0.0117921	+	0.0117921i
$124$		0			0
$125$	4.56370	−	10.2065i	0.408190	−	0.912897i
$126$		0			0
$127$	−14.5425	−	14.5425i	−1.29044	−	1.29044i	−0.934514	−	0.355927i	$-0.884165\pi$
$127$	−14.5425	−	14.5425i	−1.29044	−	1.29044i	−0.355927	−	0.934514i	$-0.615835\pi$
$128$		0			0
$129$	−0.765345			−0.0673849
$130$		0			0
$131$		−	1.38446i		−	0.120961i	−0.998169	−	0.0604805i	$-0.980737\pi$
$131$		−	1.38446i		−	0.120961i	0.998169	−	0.0604805i	$-0.0192633\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.874793	+	2.05785i	−0.0752902	+	0.177111i
$136$		0			0
$137$	−8.73424	−	8.73424i	−0.746217	−	0.746217i	0.227550	−	0.973766i	$-0.426929\pi$
$137$	−8.73424	−	8.73424i	−0.746217	−	0.746217i	−0.973766	+	0.227550i	$0.926929\pi$
$138$		0			0
$139$	22.9305			1.94494			0.972471	−	0.233024i	$-0.0748620\pi$
$139$	22.9305			1.94494			0.972471	+	0.233024i	$0.0748620\pi$
$140$		0			0
$141$	7.73444			0.651357
$142$		0			0
$143$	0.634665	+	0.634665i	0.0530734	+	0.0530734i
$144$		0			0
$145$	3.28682	+	8.14761i	0.272956	+	0.676622i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			19.8569i			1.62674i	0.581746	+	0.813371i	$0.302370\pi$
$149$			19.8569i			1.62674i	−0.581746	+	0.813371i	$0.697630\pi$
$150$		0			0
$151$	−19.0423			−1.54964			−0.774819	−	0.632183i	$-0.782159\pi$
$151$	−19.0423			−1.54964			−0.774819	+	0.632183i	$0.782159\pi$
$152$		0			0
$153$	0.0556418	+	0.0556418i	0.00449838	+	0.00449838i
$154$		0			0
$155$	1.03887	+	2.57521i	0.0834437	+	0.206846i
$156$		0			0
$157$	8.69946	−	8.69946i	0.694293	−	0.694293i	−0.268881	−	0.963173i	$-0.586654\pi$
$157$	8.69946	−	8.69946i	0.694293	−	0.694293i	0.963173	+	0.268881i	$0.0866538\pi$
$158$		0			0
$159$	11.1981			0.888070
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.26684	+	1.26684i	−0.0992265	+	0.0992265i	−0.754977	−	0.655751i	$-0.772352\pi$
$163$	−1.26684	+	1.26684i	−0.0992265	+	0.0992265i	0.655751	+	0.754977i	$0.272352\pi$
$164$		0			0
$165$	4.71003	+	2.00224i	0.366675	+	0.155874i
$166$		0			0
$167$	−7.33988	+	7.33988i	−0.567977	+	0.567977i	−0.931561	−	0.363584i	$-0.881553\pi$
$167$	−7.33988	+	7.33988i	−0.567977	+	0.567977i	0.363584	+	0.931561i	$0.381553\pi$
$168$		0			0
$169$		−	12.8462i		−	0.988171i
$170$		0			0
$171$			3.08243i			0.235720i
$172$		0			0
$173$	8.83046	+	8.83046i	0.671368	+	0.671368i	0.958031	−	0.286664i	$-0.0925462\pi$
$173$	8.83046	+	8.83046i	0.671368	+	0.671368i	−0.286664	+	0.958031i	$0.592546\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.08994	−	4.08994i	−0.307419	−	0.307419i
$178$		0			0
$179$			11.1505i			0.833430i	0.909037	+	0.416715i	$0.136819\pi$
$179$			11.1505i			0.833430i	−0.909037	+	0.416715i	$0.863181\pi$
$180$		0			0
$181$		−	7.88851i		−	0.586349i	−0.956059	−	0.293174i	$-0.905288\pi$
$181$		−	7.88851i		−	0.586349i	0.956059	−	0.293174i	$-0.0947116\pi$
$182$		0			0
$183$	−4.84532	+	4.84532i	−0.358176	+	0.358176i
$184$		0			0
$185$	4.29398	+	1.82538i	0.315700	+	0.134204i
$186$		0			0
$187$	0.127354	−	0.127354i	0.00931303	−	0.00931303i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.30401			−0.673214			−0.336607	−	0.941645i	$-0.609279\pi$
$191$	−9.30401			−0.673214			−0.336607	+	0.941645i	$0.609279\pi$
$192$		0			0
$193$	6.04956	−	6.04956i	0.435457	−	0.435457i	−0.455023	−	0.890480i	$-0.650369\pi$
$193$	6.04956	−	6.04956i	0.435457	−	0.435457i	0.890480	+	0.455023i	$0.150369\pi$
$194$		0			0
$195$	0.328050	+	0.813192i	0.0234921	+	0.0582339i
$196$		0			0
$197$	15.0910	+	15.0910i	1.07519	+	1.07519i	0.996933	+	0.0782575i	$0.0249356\pi$
$197$	15.0910	+	15.0910i	1.07519	+	1.07519i	0.0782575	+	0.996933i	$0.475064\pi$
$198$		0			0
$199$	−19.1567			−1.35799			−0.678993	−	0.734145i	$-0.737583\pi$
$199$	−19.1567			−1.35799			−0.678993	+	0.734145i	$0.737583\pi$
$200$		0			0
$201$		−	10.7374i		−	0.757357i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.154720	+	0.383532i	0.0108061	+	0.0267870i
$206$		0			0
$207$	−0.206886	−	0.206886i	−0.0143796	−	0.0143796i
$208$		0			0
$209$	7.05511			0.488012
$210$		0			0
$211$	−9.33914			−0.642933			−0.321467	−	0.946921i	$-0.604176\pi$
$211$	−9.33914			−0.642933			−0.321467	+	0.946921i	$0.604176\pi$
$212$		0			0
$213$	−2.79815	−	2.79815i	−0.191726	−	0.191726i
$214$		0			0
$215$	−0.669519	+	1.57496i	−0.0456608	+	0.107412i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			7.50862i			0.507385i
$220$		0			0
$221$	0.0308579			0.00207572
$222$		0			0
$223$	13.6421	+	13.6421i	0.913545	+	0.913545i	0.996549	−	0.0830041i	$-0.0264515\pi$
$223$	13.6421	+	13.6421i	0.913545	+	0.913545i	−0.0830041	+	0.996549i	$0.526451\pi$
$224$		0			0
$225$	3.46947	+	3.60038i	0.231298	+	0.240025i
$226$		0			0
$227$	−2.69977	+	2.69977i	−0.179190	+	0.179190i	−0.791003	−	0.611813i	$-0.790441\pi$
$227$	−2.69977	+	2.69977i	−0.179190	+	0.179190i	0.611813	+	0.791003i	$0.290441\pi$
$228$		0			0
$229$	−12.9320			−0.854572			−0.427286	−	0.904116i	$-0.640530\pi$
$229$	−12.9320			−0.854572			−0.427286	+	0.904116i	$0.640530\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.09761	+	5.09761i	−0.333956	+	0.333956i	−0.854087	−	0.520131i	$-0.825883\pi$
$233$	−5.09761	+	5.09761i	−0.333956	+	0.333956i	0.520131	+	0.854087i	$0.325883\pi$
$234$		0			0
$235$	6.76603	−	15.9163i	0.441367	−	1.03826i
$236$		0			0
$237$	−9.22398	+	9.22398i	−0.599162	+	0.599162i
$238$		0			0
$239$			1.43608i			0.0928925i	0.998921	+	0.0464462i	$0.0147896\pi$
$239$			1.43608i			0.0928925i	−0.998921	+	0.0464462i	$0.985210\pi$
$240$		0			0
$241$		−	15.6295i		−	1.00678i	−0.864059	−	0.503391i	$-0.832085\pi$
$241$		−	15.6295i		−	1.00678i	0.864059	−	0.503391i	$-0.167915\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.854729	+	0.854729i	0.0543851	+	0.0543851i
$248$		0			0
$249$			10.6190i			0.672950i
$250$		0			0
$251$			24.7587i			1.56275i	0.624060	+	0.781376i	$0.285482\pi$
$251$			24.7587i			1.56275i	−0.624060	+	0.781376i	$0.714518\pi$
$252$		0			0
$253$	−0.473524	+	0.473524i	−0.0297702	+	0.0297702i
$254$		0			0
$255$	0.163177	−	0.0658273i	0.0102186	−	0.00412227i
$256$		0			0
$257$	18.3037	−	18.3037i	1.14175	−	1.14175i	0.153623	−	0.988130i	$-0.450906\pi$
$257$	18.3037	−	18.3037i	1.14175	−	1.14175i	0.988130	−	0.153623i	$-0.0490941\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.92904			−0.243201
$262$		0			0
$263$	0.988117	−	0.988117i	0.0609299	−	0.0609299i	−0.675985	−	0.736915i	$-0.736282\pi$
$263$	0.988117	−	0.988117i	0.0609299	−	0.0609299i	0.736915	+	0.675985i	$0.236282\pi$
$264$		0			0
$265$	9.79605	−	23.0441i	0.601767	−	1.41559i
$266$		0			0
$267$	7.82555	+	7.82555i	0.478916	+	0.478916i
$268$		0			0
$269$	−13.6242			−0.830683			−0.415342	−	0.909665i	$-0.636338\pi$
$269$	−13.6242			−0.830683			−0.415342	+	0.909665i	$0.636338\pi$
$270$		0			0
$271$		−	3.66031i		−	0.222348i	−0.993801	−	0.111174i	$-0.964539\pi$
$271$		−	3.66031i		−	0.222348i	0.993801	−	0.111174i	$-0.0354611\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.24060	−	7.94098i	0.496927	−	0.478859i
$276$		0			0
$277$	−9.72500	−	9.72500i	−0.584318	−	0.584318i	0.351769	−	0.936087i	$-0.385580\pi$
$277$	−9.72500	−	9.72500i	−0.584318	−	0.584318i	−0.936087	+	0.351769i	$0.885580\pi$
$278$		0			0
$279$	−1.24185			−0.0743477
$280$		0			0
$281$	24.5150			1.46244			0.731222	−	0.682139i	$-0.238950\pi$
$281$	24.5150			1.46244			0.731222	+	0.682139i	$0.238950\pi$
$282$		0			0
$283$	5.15072	+	5.15072i	0.306178	+	0.306178i	0.843425	−	0.537247i	$-0.180536\pi$
$283$	5.15072	+	5.15072i	0.306178	+	0.306178i	−0.537247	+	0.843425i	$0.680536\pi$
$284$		0			0
$285$	6.34318	+	2.69649i	0.375738	+	0.159726i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			16.9938i			0.999636i
$290$		0			0
$291$	8.62903			0.505843
$292$		0			0
$293$	0.799164	+	0.799164i	0.0466876	+	0.0466876i	0.730065	−	0.683378i	$-0.239490\pi$
$293$	0.799164	+	0.799164i	0.0466876	+	0.0466876i	−0.683378	+	0.730065i	$0.739490\pi$
$294$		0			0
$295$	−11.9943	+	4.83863i	−0.698337	+	0.281716i
$296$		0			0
$297$	−1.61844	+	1.61844i	−0.0939111	+	0.0939111i
$298$		0			0
$299$	−0.114735			−0.00663530
$300$		0			0
$301$		0			0
$302$		0			0
$303$	9.87070	−	9.87070i	0.567057	−	0.567057i
$304$		0			0
$305$	5.73227	+	14.2096i	0.328229	+	0.813638i
$306$		0			0
$307$	−14.8183	+	14.8183i	−0.845724	+	0.845724i	−0.989596	−	0.143872i	$-0.954045\pi$
$307$	−14.8183	+	14.8183i	−0.845724	+	0.845724i	0.143872	+	0.989596i	$0.454045\pi$
$308$		0			0
$309$			9.87115i			0.561550i
$310$		0			0
$311$			18.1846i			1.03115i	0.856844	+	0.515576i	$0.172422\pi$
$311$			18.1846i			1.03115i	−0.856844	+	0.515576i	$0.827578\pi$
$312$		0			0
$313$	−5.14246	−	5.14246i	−0.290669	−	0.290669i	0.546676	−	0.837345i	$-0.315893\pi$
$313$	−5.14246	−	5.14246i	−0.290669	−	0.290669i	−0.837345	+	0.546676i	$0.815893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.64730	−	1.64730i	−0.0925216	−	0.0925216i	0.659331	−	0.751853i	$-0.270840\pi$
$317$	−1.64730	−	1.64730i	−0.0925216	−	0.0925216i	−0.751853	+	0.659331i	$0.770840\pi$
$318$		0			0
$319$			8.99283i			0.503502i
$320$		0			0
$321$			5.73099i			0.319872i
$322$		0			0
$323$	0.171512	−	0.171512i	0.00954320	−	0.00954320i
$324$		0			0
$325$	1.96040	+	0.0362990i	0.108744	+	0.00201351i
$326$		0			0
$327$	8.60689	−	8.60689i	0.475962	−	0.475962i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.58179			−0.306803			−0.153401	−	0.988164i	$-0.549023\pi$
$331$	−5.58179			−0.306803			−0.153401	+	0.988164i	$0.549023\pi$
$332$		0			0
$333$	−1.47548	+	1.47548i	−0.0808556	+	0.0808556i
$334$		0			0
$335$	−22.0959	−	9.39300i	−1.20723	−	0.513194i
$336$		0			0
$337$	−10.0749	−	10.0749i	−0.548817	−	0.548817i	0.377282	−	0.926098i	$-0.376859\pi$
$337$	−10.0749	−	10.0749i	−0.548817	−	0.548817i	−0.926098	+	0.377282i	$0.876859\pi$
$338$		0			0
$339$	−10.1947			−0.553701
$340$		0			0
$341$			2.84236i			0.153923i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.606723	+	0.244758i	−0.0326649	+	0.0131773i
$346$		0			0
$347$	−7.06843	−	7.06843i	−0.379453	−	0.379453i	0.491452	−	0.870905i	$-0.336466\pi$
$347$	−7.06843	−	7.06843i	−0.379453	−	0.379453i	−0.870905	+	0.491452i	$0.836466\pi$
$348$		0			0
$349$	17.5907			0.941607			0.470803	−	0.882238i	$-0.343964\pi$
$349$	17.5907			0.941607			0.470803	+	0.882238i	$0.343964\pi$
$350$		0			0
$351$	−0.392148			−0.0209313
$352$		0			0
$353$	6.59733	+	6.59733i	0.351140	+	0.351140i	0.860534	−	0.509393i	$-0.170130\pi$
$353$	6.59733	+	6.59733i	0.351140	+	0.351140i	−0.509393	+	0.860534i	$0.670130\pi$
$354$		0			0
$355$	−8.20597	+	3.31037i	−0.435528	+	0.175696i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	6.73381i		−	0.355397i	−0.984085	−	0.177698i	$-0.943135\pi$
$359$		−	6.73381i		−	0.355397i	0.984085	−	0.177698i	$-0.0568651\pi$
$360$		0			0
$361$	−9.49860			−0.499926
$362$		0			0
$363$	−4.07388	−	4.07388i	−0.213823	−	0.213823i
$364$		0			0
$365$	15.4516	+	6.56848i	0.808773	+	0.343810i
$366$		0			0
$367$	13.5974	−	13.5974i	0.709777	−	0.709777i	−0.256711	−	0.966488i	$-0.582639\pi$
$367$	13.5974	−	13.5974i	0.709777	−	0.709777i	0.966488	+	0.256711i	$0.0826389\pi$
$368$		0			0
$369$	−0.184951			−0.00962819
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.3537	−	14.3537i	0.743205	−	0.743205i	−0.229988	−	0.973193i	$-0.573869\pi$
$373$	14.3537	−	14.3537i	0.743205	−	0.743205i	0.973193	+	0.229988i	$0.0738688\pi$
$374$		0			0
$375$	10.4441	−	3.99006i	0.539331	−	0.206046i
$376$		0			0
$377$	−1.08948	+	1.08948i	−0.0561113	+	0.0561113i
$378$		0			0
$379$		−	31.9414i		−	1.64072i	−0.571847	−	0.820361i	$-0.693773\pi$
$379$		−	31.9414i		−	1.64072i	0.571847	−	0.820361i	$-0.306227\pi$
$380$		0			0
$381$		−	20.5662i		−	1.05364i
$382$		0			0
$383$	7.29520	+	7.29520i	0.372768	+	0.372768i	0.868484	−	0.495717i	$-0.165095\pi$
$383$	7.29520	+	7.29520i	0.372768	+	0.372768i	−0.495717	+	0.868484i	$0.665095\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.541181	−	0.541181i	−0.0275098	−	0.0275098i
$388$		0			0
$389$			32.7735i			1.66168i	0.556508	+	0.830842i	$0.312141\pi$
$389$			32.7735i			1.66168i	−0.556508	+	0.830842i	$0.687859\pi$
$390$		0			0
$391$			0.0230231i			0.00116433i
$392$		0			0
$393$	0.978963	−	0.978963i	0.0493822	−	0.0493822i
$394$		0			0
$395$	10.9125	+	27.0506i	0.549066	+	1.36106i
$396$		0			0
$397$	−21.9796	+	21.9796i	−1.10312	+	1.10312i	−0.109093	+	0.994032i	$0.534795\pi$
$397$	−21.9796	+	21.9796i	−1.10312	+	1.10312i	−0.994032	+	0.109093i	$0.965205\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−33.4872			−1.67227			−0.836135	−	0.548523i	$-0.815190\pi$
$401$	−33.4872			−1.67227			−0.836135	+	0.548523i	$0.815190\pi$
$402$		0			0
$403$	−0.344353	+	0.344353i	−0.0171534	+	0.0171534i
$404$		0			0
$405$	−2.07369	+	0.836546i	−0.103042	+	0.0415683i
$406$		0			0
$407$	3.37709	+	3.37709i	0.167396	+	0.167396i
$408$		0			0
$409$	10.6526			0.526736			0.263368	−	0.964695i	$-0.415167\pi$
$409$	10.6526			0.526736			0.263368	+	0.964695i	$0.415167\pi$
$410$		0			0
$411$		−	12.3521i		−	0.609283i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	21.8522	+	9.28940i	1.07268	+	0.455999i
$416$		0			0
$417$	16.2143	+	16.2143i	0.794019	+	0.794019i
$418$		0			0
$419$	−10.2028			−0.498442			−0.249221	−	0.968447i	$-0.580175\pi$
$419$	−10.2028			−0.498442			−0.249221	+	0.968447i	$0.580175\pi$
$420$		0			0
$421$	−3.12064			−0.152091			−0.0760455	−	0.997104i	$-0.524229\pi$
$421$	−3.12064			−0.152091			−0.0760455	+	0.997104i	$0.524229\pi$
$422$		0			0
$423$	5.46908	+	5.46908i	0.265916	+	0.265916i
$424$		0			0
$425$	0.00728386	−	0.393380i	0.000353319	−	0.0190817i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			0.897552i			0.0433342i
$430$		0			0
$431$	−4.46700			−0.215168			−0.107584	−	0.994196i	$-0.534311\pi$
$431$	−4.46700			−0.215168			−0.107584	+	0.994196i	$0.534311\pi$
$432$		0			0
$433$	−26.7518	−	26.7518i	−1.28561	−	1.28561i	−0.937427	−	0.348181i	$-0.886800\pi$
$433$	−26.7518	−	26.7518i	−1.28561	−	1.28561i	−0.348181	−	0.937427i	$-0.613200\pi$
$434$		0			0
$435$	−3.43709	+	8.08536i	−0.164796	+	0.387663i
$436$		0			0
$437$	−0.637713	+	0.637713i	−0.0305060	+	0.0305060i
$438$		0			0
$439$	−28.2855			−1.34999			−0.674997	−	0.737820i	$-0.735855\pi$
$439$	−28.2855			−1.34999			−0.674997	+	0.737820i	$0.735855\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.3825	−	23.3825i	1.11094	−	1.11094i	0.117912	−	0.993024i	$-0.462380\pi$
$443$	23.3825	−	23.3825i	1.11094	−	1.11094i	0.993024	−	0.117912i	$-0.0376200\pi$
$444$		0			0
$445$	22.9495	−	9.25805i	1.08791	−	0.438874i
$446$		0			0
$447$	−14.0410	+	14.0410i	−0.664115	+	0.664115i
$448$		0			0
$449$		−	10.8305i		−	0.511125i	−0.966793	−	0.255563i	$-0.917739\pi$
$449$		−	10.8305i		−	0.511125i	0.966793	−	0.255563i	$-0.0822607\pi$
$450$		0			0
$451$			0.423319i			0.0199333i
$452$		0			0
$453$	−13.4649	−	13.4649i	−0.632637	−	0.632637i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−23.0525	−	23.0525i	−1.07835	−	1.07835i	−0.996657	−	0.0816940i	$-0.973967\pi$
$457$	−23.0525	−	23.0525i	−1.07835	−	1.07835i	−0.0816940	−	0.996657i	$-0.526033\pi$
$458$		0			0
$459$			0.0786894i			0.00367291i
$460$		0			0
$461$			5.31744i			0.247658i	0.992304	+	0.123829i	$0.0395174\pi$
$461$			5.31744i			0.247658i	−0.992304	+	0.123829i	$0.960483\pi$
$462$		0			0
$463$	−0.558334	+	0.558334i	−0.0259480	+	0.0259480i	−0.719962	−	0.694014i	$-0.755841\pi$
$463$	−0.558334	+	0.558334i	−0.0259480	+	0.0259480i	0.694014	+	0.719962i	$0.255841\pi$
$464$		0			0
$465$	−1.08636	+	2.55554i	−0.0503788	+	0.118510i
$466$		0			0
$467$	4.50072	−	4.50072i	0.208268	−	0.208268i	−0.595263	−	0.803531i	$-0.702952\pi$
$467$	4.50072	−	4.50072i	0.208268	−	0.208268i	0.803531	+	0.595263i	$0.202952\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.3029			0.566887
$472$		0			0
$473$	−1.23866	+	1.23866i	−0.0569537	+	0.0569537i
$474$		0			0
$475$	11.0979	−	10.6944i	0.509208	−	0.490694i
$476$		0			0
$477$	7.91828	+	7.91828i	0.362553	+	0.362553i
$478$		0			0
$479$	−17.9767			−0.821377			−0.410689	−	0.911776i	$-0.634712\pi$
$479$	−17.9767			−0.821377			−0.410689	+	0.911776i	$0.634712\pi$
$480$		0			0
$481$			0.818270i			0.0373099i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.54862	−	17.7572i	0.342765	−	0.806315i
$486$		0			0
$487$	−17.0083	−	17.0083i	−0.770719	−	0.770719i	0.207513	−	0.978232i	$-0.433463\pi$
$487$	−17.0083	−	17.0083i	−0.770719	−	0.770719i	−0.978232	+	0.207513i	$0.933463\pi$
$488$		0			0
$489$	−1.79158			−0.0810181
$490$		0			0
$491$	−11.2938			−0.509682			−0.254841	−	0.966983i	$-0.582023\pi$
$491$	−11.2938			−0.509682			−0.254841	+	0.966983i	$0.582023\pi$
$492$		0			0
$493$	0.218619	+	0.218619i	0.00984610	+	0.00984610i
$494$		0			0
$495$	1.91470	+	4.74629i	0.0860593	+	0.213330i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	4.59893i		−	0.205876i	−0.994688	−	0.102938i	$-0.967176\pi$
$499$		−	4.59893i		−	0.205876i	0.994688	−	0.102938i	$-0.0328244\pi$
$500$		0			0
$501$	−10.3802			−0.463751
$502$		0			0
$503$	−18.0393	−	18.0393i	−0.804331	−	0.804331i	0.179438	−	0.983769i	$-0.442572\pi$
$503$	−18.0393	−	18.0393i	−0.804331	−	0.804331i	−0.983769	+	0.179438i	$0.942572\pi$
$504$		0			0
$505$	−11.6776	−	28.9472i	−0.519646	−	1.28813i
$506$		0			0
$507$	9.08365	−	9.08365i	0.403419	−	0.403419i
$508$		0			0
$509$	−37.7997			−1.67544			−0.837720	−	0.546100i	$-0.816112\pi$
$509$	−37.7997			−1.67544			−0.837720	+	0.546100i	$0.816112\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.17961	+	2.17961i	−0.0962321	+	0.0962321i
$514$		0			0
$515$	20.3133	+	8.63521i	0.895112	+	0.380513i
$516$		0			0
$517$	12.5177	−	12.5177i	0.550527	−	0.550527i
$518$		0			0
$519$			12.4882i			0.548169i
$520$		0			0
$521$		−	22.8999i		−	1.00326i	−0.865082	−	0.501631i	$-0.832734\pi$
$521$		−	22.8999i		−	1.00326i	0.865082	−	0.501631i	$-0.167266\pi$
$522$		0			0
$523$	−13.5479	−	13.5479i	−0.592409	−	0.592409i	0.345873	−	0.938281i	$-0.387583\pi$
$523$	−13.5479	−	13.5479i	−0.592409	−	0.592409i	−0.938281	+	0.345873i	$0.887583\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.0690988	+	0.0690988i	0.00300999	+	0.00300999i
$528$		0			0
$529$			22.9144i			0.996278i
$530$		0			0
$531$		−	5.78405i		−	0.251006i
$532$		0			0
$533$	−0.0512852	+	0.0512852i	−0.00222141	+	0.00222141i
$534$		0			0
$535$	11.7935	+	5.01343i	0.509877	+	0.216749i
$536$		0			0
$537$	−7.88462	+	7.88462i	−0.340246	+	0.340246i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9.44937			0.406260			0.203130	−	0.979152i	$-0.434889\pi$
$541$	9.44937			0.406260			0.203130	+	0.979152i	$0.434889\pi$
$542$		0			0
$543$	5.57802	−	5.57802i	0.239376	−	0.239376i
$544$		0			0
$545$	−10.1824	−	25.2409i	−0.436167	−	1.08120i
$546$		0			0
$547$	−23.9768	−	23.9768i	−1.02518	−	1.02518i	−0.999675	−	0.0255007i	$-0.991882\pi$
$547$	−23.9768	−	23.9768i	−1.02518	−	1.02518i	−0.0255007	−	0.999675i	$-0.508118\pi$
$548$		0			0
$549$	−6.85231			−0.292450
$550$		0			0
$551$			12.1110i			0.515946i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.74557	+	4.32704i	0.0740953	+	0.183673i
$556$		0			0
$557$	−20.5250	−	20.5250i	−0.869671	−	0.869671i	0.122765	−	0.992436i	$-0.460824\pi$
$557$	−20.5250	−	20.5250i	−0.869671	−	0.869671i	−0.992436	+	0.122765i	$0.960824\pi$
$558$		0			0
$559$	−0.300128			−0.0126941
$560$		0			0
$561$	0.180105			0.00760406
$562$		0			0
$563$	23.4784	+	23.4784i	0.989498	+	0.989498i	0.999945	−	0.0104475i	$-0.00332560\pi$
$563$	23.4784	+	23.4784i	0.989498	+	0.989498i	−0.0104475	+	0.999945i	$0.503326\pi$
$564$		0			0
$565$	−8.91826	+	20.9792i	−0.375194	+	0.882600i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	5.14915i		−	0.215864i	−0.994158	−	0.107932i	$-0.965577\pi$
$569$		−	5.14915i		−	0.215864i	0.994158	−	0.107932i	$-0.0344228\pi$
$570$		0			0
$571$	−35.5714			−1.48862			−0.744309	−	0.667835i	$-0.767221\pi$
$571$	−35.5714			−1.48862			−0.744309	+	0.667835i	$0.767221\pi$
$572$		0			0
$573$	−6.57893	−	6.57893i	−0.274839	−	0.274839i
$574$		0			0
$575$	−0.0270827	+	1.46266i	−0.00112943	+	0.0609970i
$576$		0			0
$577$	1.78128	−	1.78128i	0.0741558	−	0.0741558i	−0.669056	−	0.743212i	$-0.733301\pi$
$577$	1.78128	−	1.78128i	0.0741558	−	0.0741558i	0.743212	+	0.669056i	$0.233301\pi$
$578$		0			0
$579$	8.55537			0.355549
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.1235	−	18.1235i	0.750597	−	0.750597i
$584$		0			0
$585$	−0.343048	+	0.806980i	−0.0141833	+	0.0333645i
$586$		0			0
$587$	−12.5600	+	12.5600i	−0.518405	+	0.518405i	−0.917089	−	0.398683i	$-0.869467\pi$
$587$	−12.5600	+	12.5600i	−0.518405	+	0.518405i	0.398683	+	0.917089i	$0.369467\pi$
$588$		0			0
$589$			3.82792i			0.157727i
$590$		0			0
$591$			21.3419i			0.877890i
$592$		0			0
$593$	2.79730	+	2.79730i	0.114871	+	0.114871i	0.762206	−	0.647335i	$-0.224116\pi$
$593$	2.79730	+	2.79730i	0.114871	+	0.114871i	−0.647335	+	0.762206i	$0.724116\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−13.5459	−	13.5459i	−0.554395	−	0.554395i
$598$		0			0
$599$			38.9034i			1.58955i	0.606905	+	0.794775i	$0.292411\pi$
$599$			38.9034i			1.58955i	−0.606905	+	0.794775i	$0.707589\pi$
$600$		0			0
$601$		−	16.6030i		−	0.677250i	−0.940921	−	0.338625i	$-0.890038\pi$
$601$		−	16.6030i		−	0.677250i	0.940921	−	0.338625i	$-0.109962\pi$
$602$		0			0
$603$	7.59248	−	7.59248i	0.309190	−	0.309190i
$604$		0			0
$605$	−11.9472	+	4.81962i	−0.485724	+	0.195946i
$606$		0			0
$607$	−27.9067	+	27.9067i	−1.13270	+	1.13270i	−0.142971	+	0.989727i	$0.545665\pi$
$607$	−27.9067	+	27.9067i	−1.13270	+	1.13270i	−0.989727	+	0.142971i	$0.954335\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.03304			0.122704
$612$		0			0
$613$	13.6844	−	13.6844i	0.552707	−	0.552707i	−0.374514	−	0.927221i	$-0.622190\pi$
$613$	13.6844	−	13.6844i	0.552707	−	0.552707i	0.927221	+	0.374514i	$0.122190\pi$
$614$		0			0
$615$	−0.161794	+	0.380602i	−0.00652417	+	0.0153474i
$616$		0			0
$617$	2.30085	+	2.30085i	0.0926289	+	0.0926289i	0.751903	−	0.659274i	$-0.229136\pi$
$617$	2.30085	+	2.30085i	0.0926289	+	0.0926289i	−0.659274	+	0.751903i	$0.729136\pi$
$618$		0			0
$619$	−20.0764			−0.806940			−0.403470	−	0.914993i	$-0.632196\pi$
$619$	−20.0764			−0.806940			−0.403470	+	0.914993i	$0.632196\pi$
$620$		0			0
$621$		−	0.292581i		−	0.0117409i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.925488	−	24.9829i	0.0370195	−	0.999315i
$626$		0			0
$627$	4.98872	+	4.98872i	0.199230	+	0.199230i
$628$		0			0
$629$	0.164196			0.00654694
$630$		0			0
$631$	−27.9800			−1.11387			−0.556934	−	0.830557i	$-0.688022\pi$
$631$	−27.9800			−1.11387			−0.556934	+	0.830557i	$0.688022\pi$
$632$		0			0
$633$	−6.60377	−	6.60377i	−0.262476	−	0.262476i
$634$		0			0
$635$	−42.3222	−	17.9912i	−1.67951	−	0.713959i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		−	3.95718i		−	0.156544i
$640$		0			0
$641$	−0.151003			−0.00596427			−0.00298213	−	0.999996i	$-0.500949\pi$
$641$	−0.151003			−0.00596427			−0.00298213	+	0.999996i	$0.500949\pi$
$642$		0			0
$643$	1.68210	+	1.68210i	0.0663354	+	0.0663354i	0.739496	−	0.673161i	$-0.235064\pi$
$643$	1.68210	+	1.68210i	0.0663354	+	0.0663354i	−0.673161	+	0.739496i	$0.735064\pi$
$644$		0			0
$645$	−1.58709	+	0.640247i	−0.0624916	+	0.0252097i
$646$		0			0
$647$	15.0622	−	15.0622i	0.592154	−	0.592154i	−0.346059	−	0.938213i	$-0.612480\pi$
$647$	15.0622	−	15.0622i	0.592154	−	0.592154i	0.938213	+	0.346059i	$0.112480\pi$
$648$		0			0
$649$	−13.2386			−0.519661
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.4040	+	16.4040i	−0.641939	+	0.641939i	−0.951032	−	0.309093i	$-0.899975\pi$
$653$	−16.4040	+	16.4040i	−0.641939	+	0.641939i	0.309093	+	0.951032i	$0.399975\pi$
$654$		0			0
$655$	−1.15817	−	2.87095i	−0.0452533	−	0.112177i
$656$		0			0
$657$	−5.30939	+	5.30939i	−0.207139	+	0.207139i
$658$		0			0
$659$			0.414351i			0.0161408i	0.999967	+	0.00807041i	$0.00256892\pi$
$659$			0.414351i			0.0161408i	−0.999967	+	0.00807041i	$0.997431\pi$
$660$		0			0
$661$		−	28.3629i		−	1.10319i	−0.834112	−	0.551595i	$-0.814019\pi$
$661$		−	28.3629i		−	1.10319i	0.834112	−	0.551595i	$-0.185981\pi$
$662$		0			0
$663$	0.0218198	+	0.0218198i	0.000847411	+	0.000847411i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.812864	−	0.812864i	−0.0314742	−	0.0314742i
$668$		0			0
$669$			19.2929i			0.745906i
$670$		0			0
$671$			15.6837i			0.605461i
$672$		0			0
$673$	12.2846	−	12.2846i	0.473538	−	0.473538i	−0.429520	−	0.903057i	$-0.641317\pi$
$673$	12.2846	−	12.2846i	0.473538	−	0.473538i	0.903057	+	0.429520i	$0.141317\pi$
$674$		0			0
$675$	−0.0925647	+	4.99914i	−0.00356282	+	0.192417i
$676$		0			0
$677$	9.32133	−	9.32133i	0.358248	−	0.358248i	−0.504919	−	0.863167i	$-0.668478\pi$
$677$	9.32133	−	9.32133i	0.358248	−	0.358248i	0.863167	+	0.504919i	$0.168478\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.81806			−0.146308
$682$		0			0
$683$	9.41791	−	9.41791i	0.360366	−	0.360366i	−0.503582	−	0.863948i	$-0.667985\pi$
$683$	9.41791	−	9.41791i	0.360366	−	0.360366i	0.863948	+	0.503582i	$0.167985\pi$
$684$		0			0
$685$	−25.4187	−	10.8055i	−0.971199	−	0.412858i
$686$		0			0
$687$	−9.14432	−	9.14432i	−0.348878	−	0.348878i
$688$		0			0
$689$	4.39132			0.167296
$690$		0			0
$691$		−	16.0959i		−	0.612317i	−0.951981	−	0.306158i	$-0.900956\pi$
$691$		−	16.0959i		−	0.612317i	0.951981	−	0.306158i	$-0.0990437\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	47.5508	−	19.1824i	1.80371	−	0.727632i
$696$		0			0
$697$	0.0102910	+	0.0102910i	0.000389801	+	0.000389801i
$698$		0			0
$699$	−7.20912			−0.272674
$700$		0			0
$701$	8.85208			0.334338			0.167169	−	0.985928i	$-0.446537\pi$
$701$	8.85208			0.334338			0.167169	+	0.985928i	$0.446537\pi$
$702$		0			0
$703$	4.54806	+	4.54806i	0.171533	+	0.171533i
$704$		0			0
$705$	16.0388	−	6.47022i	0.604057	−	0.243682i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			2.66733i			0.100174i	0.998745	+	0.0500868i	$0.0159498\pi$
$709$			2.66733i			0.100174i	−0.998745	+	0.0500868i	$0.984050\pi$
$710$		0			0
$711$	−13.0447			−0.489214
$712$		0			0
$713$	−0.256922	−	0.256922i	−0.00962180	−	0.00962180i
$714$		0			0
$715$	1.84703	+	0.785172i	0.0690749	+	0.0293638i
$716$		0			0
$717$	−1.01546	+	1.01546i	−0.0379232	+	0.0379232i
$718$		0			0
$719$	−29.2614			−1.09126			−0.545632	−	0.838025i	$-0.683711\pi$
$719$	−29.2614			−1.09126			−0.545632	+	0.838025i	$0.683711\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	11.0517	−	11.0517i	0.411017	−	0.411017i
$724$		0			0
$725$	13.6317	+	14.1460i	0.506269	+	0.525371i
$726$		0			0
$727$	−18.1764	+	18.1764i	−0.674124	+	0.674124i	−0.958664	−	0.284540i	$-0.908159\pi$
$727$	−18.1764	+	18.1764i	−0.674124	+	0.674124i	0.284540	+	0.958664i	$0.408159\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			0.0602246i			0.00222749i
$732$		0			0
$733$	−28.6104	−	28.6104i	−1.05675	−	1.05675i	−0.998290	−	0.0584586i	$-0.981381\pi$
$733$	−28.6104	−	28.6104i	−1.05675	−	1.05675i	−0.0584586	−	0.998290i	$-0.518619\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17.3778	−	17.3778i	−0.640119	−	0.640119i
$738$		0			0
$739$			31.3187i			1.15208i	0.817423	+	0.576038i	$0.195402\pi$
$739$			31.3187i			1.15208i	−0.817423	+	0.576038i	$0.804598\pi$
$740$		0			0
$741$			1.20877i			0.0444052i
$742$		0			0
$743$	−6.99076	+	6.99076i	−0.256466	+	0.256466i	−0.823615	−	0.567149i	$-0.808046\pi$
$743$	−6.99076	+	6.99076i	−0.256466	+	0.256466i	0.567149	+	0.823615i	$0.308046\pi$
$744$		0			0
$745$	16.6112	+	41.1771i	0.608588	+	1.50861i
$746$		0			0
$747$	−7.50874	+	7.50874i	−0.274731	+	0.274731i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.32435			−0.303760			−0.151880	−	0.988399i	$-0.548533\pi$
$751$	−8.32435			−0.303760			−0.151880	+	0.988399i	$0.548533\pi$
$752$		0			0
$753$	−17.5070	+	17.5070i	−0.637991	+	0.637991i
$754$		0			0
$755$	−39.4878	+	15.9297i	−1.43711	+	0.579742i
$756$		0			0
$757$	5.60454	+	5.60454i	0.203700	+	0.203700i	0.801583	−	0.597883i	$-0.203991\pi$
$757$	5.60454	+	5.60454i	0.203700	+	0.203700i	−0.597883	+	0.801583i	$0.703991\pi$
$758$		0			0
$759$	−0.669664			−0.0243073
$760$		0			0
$761$		−	4.68178i		−	0.169714i	−0.996393	−	0.0848572i	$-0.972957\pi$
$761$		−	4.68178i		−	0.169714i	0.996393	−	0.0848572i	$-0.0270434\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.161931	+	0.0688370i	0.00585462	+	0.00248881i
$766$		0			0
$767$	−1.60386	−	1.60386i	−0.0579121	−	0.0579121i
$768$		0			0
$769$	30.3007			1.09267			0.546335	−	0.837566i	$-0.316022\pi$
$769$	30.3007			1.09267			0.546335	+	0.837566i	$0.316022\pi$
$770$		0			0
$771$	25.8853			0.932237
$772$		0			0
$773$	−26.3086	−	26.3086i	−0.946256	−	0.946256i	0.0523721	−	0.998628i	$-0.483322\pi$
$773$	−26.3086	−	26.3086i	−0.946256	−	0.946256i	−0.998628	+	0.0523721i	$0.983322\pi$
$774$		0			0
$775$	4.30857	+	4.47114i	0.154768	+	0.160608i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			0.570101i			0.0204260i
$780$		0			0
$781$	−9.05725			−0.324094
$782$		0			0
$783$	−2.77825	−	2.77825i	−0.0992865	−	0.0992865i
$784$		0			0
$785$	10.7625	−	25.3175i	0.384130	−	0.903620i
$786$		0			0
$787$	12.6053	−	12.6053i	0.449332	−	0.449332i	−0.445800	−	0.895132i	$-0.647081\pi$
$787$	12.6053	−	12.6053i	0.449332	−	0.449332i	0.895132	+	0.445800i	$0.147081\pi$
$788$		0			0
$789$	1.39741			0.0497491
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.90008	+	1.90008i	−0.0674738	+	0.0674738i
$794$		0			0
$795$	23.2215	−	9.36776i	0.823581	−	0.332240i
$796$		0			0
$797$	3.21723	−	3.21723i	0.113960	−	0.113960i	−0.647827	−	0.761787i	$-0.724322\pi$
$797$	3.21723	−	3.21723i	0.113960	−	0.113960i	0.761787	+	0.647827i	$0.224322\pi$
$798$		0			0
$799$		−	0.608619i		−	0.0215314i
$800$		0			0
$801$			11.0670i			0.391033i
$802$		0			0
$803$	12.1522	+	12.1522i	0.428842	+	0.428842i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.63378	−	9.63378i	−0.339125	−	0.339125i
$808$		0			0
$809$			54.2441i			1.90712i	0.301200	+	0.953561i	$0.402613\pi$
$809$			54.2441i			1.90712i	−0.301200	+	0.953561i	$0.597387\pi$
$810$		0			0
$811$			27.9495i			0.981441i	0.871317	+	0.490720i	$0.163266\pi$
$811$			27.9495i			0.981441i	−0.871317	+	0.490720i	$0.836734\pi$
$812$		0			0
$813$	2.58823	−	2.58823i	0.0907733	−	0.0907733i
$814$		0			0
$815$	−1.56726	+	3.68680i	−0.0548988	+	0.129143i
$816$		0			0
$817$	−1.66815	+	1.66815i	−0.0583613	+	0.0583613i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.49188			0.261468			0.130734	−	0.991417i	$-0.458267\pi$
$821$	7.49188			0.261468			0.130734	+	0.991417i	$0.458267\pi$
$822$		0			0
$823$	−26.9353	+	26.9353i	−0.938907	+	0.938907i	−0.998238	−	0.0593316i	$-0.981103\pi$
$823$	−26.9353	+	26.9353i	−0.938907	+	0.938907i	0.0593316	+	0.998238i	$0.481103\pi$
$824$		0			0
$825$	11.4421	+	0.211863i	0.398363	+	0.00737613i
$826$		0			0
$827$	7.04766	+	7.04766i	0.245071	+	0.245071i	0.818944	−	0.573873i	$-0.194560\pi$
$827$	7.04766	+	7.04766i	0.245071	+	0.245071i	−0.573873	+	0.818944i	$0.694560\pi$
$828$		0			0
$829$	−16.8938			−0.586745			−0.293373	−	0.955998i	$-0.594778\pi$
$829$	−16.8938			−0.586745			−0.293373	+	0.955998i	$0.594778\pi$
$830$		0			0
$831$		−	13.7532i		−	0.477094i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−9.08049	+	21.3608i	−0.314243	+	0.739221i
$836$		0			0
$837$	−0.878121	−	0.878121i	−0.0303523	−	0.0303523i
$838$		0			0
$839$	3.25695			0.112442			0.0562212	−	0.998418i	$-0.482095\pi$
$839$	3.25695			0.112442			0.0562212	+	0.998418i	$0.482095\pi$
$840$		0			0
$841$	13.5627			0.467678
$842$		0			0
$843$	17.3347	+	17.3347i	0.597040	+	0.597040i
$844$		0			0
$845$	−10.7465	−	26.6391i	−0.369689	−	0.916412i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			7.28421i			0.249994i
$850$		0			0
$851$	−0.610512			−0.0209281
$852$		0			0
$853$	−34.0365	−	34.0365i	−1.16539	−	1.16539i	−0.983278	−	0.182111i	$-0.941707\pi$
$853$	−34.0365	−	34.0365i	−1.16539	−	1.16539i	−0.182111	−	0.983278i	$-0.558293\pi$
$854$		0			0
$855$	2.57860	+	6.39201i	0.0881862	+	0.218602i
$856$		0			0
$857$	16.9119	−	16.9119i	0.577698	−	0.577698i	−0.356570	−	0.934268i	$-0.616054\pi$
$857$	16.9119	−	16.9119i	0.577698	−	0.577698i	0.934268	+	0.356570i	$0.116054\pi$
$858$		0			0
$859$	−5.09659			−0.173893			−0.0869467	−	0.996213i	$-0.527711\pi$
$859$	−5.09659			−0.173893			−0.0869467	+	0.996213i	$0.527711\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.24451	+	4.24451i	−0.144485	+	0.144485i	−0.775649	−	0.631164i	$-0.782577\pi$
$863$	−4.24451	+	4.24451i	−0.144485	+	0.144485i	0.631164	+	0.775649i	$0.282577\pi$
$864$		0			0
$865$	25.6987	+	10.9246i	0.873783	+	0.371446i
$866$		0			0
$867$	−12.0164	+	12.0164i	−0.408100	+	0.408100i
$868$		0			0
$869$			29.8568i			1.01282i
$870$		0			0
$871$		−	4.21064i		−	0.142672i
$872$		0			0
$873$	6.10165	+	6.10165i	0.206509	+	0.206509i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.9219	−	39.9219i	−1.34807	−	1.34807i	−0.887758	−	0.460310i	$-0.847738\pi$
$877$	−39.9219	−	39.9219i	−1.34807	−	1.34807i	−0.460310	−	0.887758i	$-0.652262\pi$
$878$		0			0
$879$			1.13019i			0.0381203i
$880$		0			0
$881$			30.7955i			1.03753i	0.854918	+	0.518764i	$0.173608\pi$
$881$			30.7955i			1.03753i	−0.854918	+	0.518764i	$0.826392\pi$
$882$		0			0
$883$	20.5690	−	20.5690i	0.692202	−	0.692202i	−0.270514	−	0.962716i	$-0.587194\pi$
$883$	20.5690	−	20.5690i	0.692202	−	0.692202i	0.962716	+	0.270514i	$0.0871938\pi$
$884$		0			0
$885$	−11.9027	−	5.05985i	−0.400105	−	0.170085i
$886$		0			0
$887$	29.2386	−	29.2386i	0.981735	−	0.981735i	−0.0181014	−	0.999836i	$-0.505762\pi$
$887$	29.2386	−	29.2386i	0.981735	−	0.981735i	0.999836	+	0.0181014i	$0.00576215\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.28881			−0.0766781
$892$		0			0
$893$	16.8581	−	16.8581i	0.564134	−	0.564134i
$894$		0			0
$895$	9.32794	+	23.1228i	0.311799	+	0.772908i
$896$		0			0
$897$	−0.0811300	−	0.0811300i	−0.00270885	−	0.00270885i
$898$		0			0
$899$	−4.87928			−0.162733
$900$		0			0
$901$		−	0.881175i		−	0.0293562i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.59911	−	16.3583i	−0.219362	−	0.543769i
$906$		0			0
$907$	3.22270	+	3.22270i	0.107008	+	0.107008i	0.758584	−	0.651576i	$-0.225892\pi$
$907$	3.22270	+	3.22270i	0.107008	+	0.107008i	−0.651576	+	0.758584i	$0.725892\pi$
$908$		0			0
$909$	13.9593			0.463000
$910$		0			0
$911$	−13.6960			−0.453768			−0.226884	−	0.973922i	$-0.572854\pi$
$911$	−13.6960			−0.453768			−0.226884	+	0.973922i	$0.572854\pi$
$912$		0			0
$913$	17.1861	+	17.1861i	0.568777	+	0.568777i
$914$		0			0
$915$	−5.99435	+	14.1010i	−0.198167	+	0.466165i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			27.1493i			0.895574i	0.894140	+	0.447787i	$0.147788\pi$
$919$			27.1493i			0.895574i	−0.894140	+	0.447787i	$0.852212\pi$
$920$		0			0
$921$	−20.9562			−0.690531
$922$		0			0
$923$	−1.09729	−	1.09729i	−0.0361177	−	0.0361177i
$924$		0			0
$925$	10.4314	+	0.193149i	0.342982	+	0.00635070i
$926$		0			0
$927$	−6.97996	+	6.97996i	−0.229252	+	0.229252i
$928$		0			0
$929$	−16.1209			−0.528910			−0.264455	−	0.964398i	$-0.585192\pi$
$929$	−16.1209			−0.528910			−0.264455	+	0.964398i	$0.585192\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.8584	+	12.8584i	−0.420966	+	0.420966i
$934$		0			0
$935$	0.157555	−	0.370629i	0.00515260	−	0.0121209i
$936$		0			0
$937$	−16.0235	+	16.0235i	−0.523464	+	0.523464i	−0.918616	−	0.395152i	$-0.870692\pi$
$937$	−16.0235	+	16.0235i	−0.523464	+	0.523464i	0.395152	+	0.918616i	$0.370692\pi$
$938$		0			0
$939$		−	7.27254i		−	0.237330i
$940$		0			0
$941$		−	29.8631i		−	0.973508i	−0.873539	−	0.486754i	$-0.838181\pi$
$941$		−	29.8631i		−	0.973508i	0.873539	−	0.486754i	$-0.161819\pi$
$942$		0			0
$943$	−0.0382639	−	0.0382639i	−0.00124605	−	0.00124605i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.3617	+	27.3617i	0.889135	+	0.889135i	0.994440	−	0.105305i	$-0.0335818\pi$
$947$	27.3617	+	27.3617i	0.889135	+	0.889135i	−0.105305	+	0.994440i	$0.533582\pi$
$948$		0			0
$949$			2.94449i			0.0955821i
$950$		0			0
$951$		−	2.32964i		−	0.0755436i
$952$		0			0
$953$	−1.86257	+	1.86257i	−0.0603345	+	0.0603345i	−0.736630	−	0.676296i	$-0.763584\pi$
$953$	−1.86257	+	1.86257i	−0.0603345	+	0.0603345i	0.676296	+	0.736630i	$0.263584\pi$
$954$		0			0
$955$	−19.2936	+	7.78323i	−0.624327	+	0.251859i
$956$		0			0
$957$	−6.35889	+	6.35889i	−0.205554	+	0.205554i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	29.4578			0.950252
$962$		0			0
$963$	−4.05242	+	4.05242i	−0.130587	+	0.130587i
$964$		0			0
$965$	7.48417	−	17.6056i	0.240924	−	0.566746i
$966$		0			0
$967$	25.3352	+	25.3352i	0.814726	+	0.814726i	0.985338	−	0.170612i	$-0.0545745\pi$
$967$	25.3352	+	25.3352i	0.814726	+	0.814726i	−0.170612	+	0.985338i	$0.554575\pi$
$968$		0			0
$969$	0.242555			0.00779199
$970$		0			0
$971$			5.86779i			0.188306i	0.995558	+	0.0941532i	$0.0300144\pi$
$971$			5.86779i			0.188306i	−0.995558	+	0.0941532i	$0.969986\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.36055	+	1.41188i	0.0435723	+	0.0452164i
$976$		0			0
$977$	−9.41583	−	9.41583i	−0.301239	−	0.301239i	0.540259	−	0.841498i	$-0.318326\pi$
$977$	−9.41583	−	9.41583i	−0.301239	−	0.301239i	−0.841498	+	0.540259i	$0.818326\pi$
$978$		0			0
$979$	25.3303			0.809559
$980$		0			0
$981$	12.1720			0.388621
$982$		0			0
$983$	−28.3348	−	28.3348i	−0.903740	−	0.903740i	0.0920171	−	0.995757i	$-0.470669\pi$
$983$	−28.3348	−	28.3348i	−0.903740	−	0.903740i	−0.995757	+	0.0920171i	$0.970669\pi$
$984$		0			0
$985$	43.9184	+	18.6698i	1.39936	+	0.594868i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	0.223926i		−	0.00712043i
$990$		0			0
$991$	−35.9561			−1.14218			−0.571091	−	0.820887i	$-0.693480\pi$
$991$	−35.9561			−1.14218			−0.571091	+	0.820887i	$0.693480\pi$
$992$		0			0
$993$	−3.94692	−	3.94692i	−0.125252	−	0.125252i
$994$		0			0
$995$	−39.7252	+	16.0255i	−1.25937	+	0.508043i
$996$		0			0
$997$	−12.1867	+	12.1867i	−0.385958	+	0.385958i	−0.873243	−	0.487285i	$-0.837987\pi$
$997$	−12.1867	+	12.1867i	−0.385958	+	0.385958i	0.487285	+	0.873243i	$0.337987\pi$
$998$		0			0
$999$	−2.08664			−0.0660183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.x.b.97.11	yes	24
5.3	odd	4		2940.2.x.a.1273.2	yes	24
7.6	odd	2		2940.2.x.a.97.2	✓	24
35.13	even	4	inner	2940.2.x.b.1273.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.x.a.97.2	✓	24	7.6	odd	2
2940.2.x.a.1273.2	yes	24	5.3	odd	4
2940.2.x.b.97.11	yes	24	1.1	even	1	trivial
2940.2.x.b.1273.11	yes	24	35.13	even	4	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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(2.07369 - 0.836546i) q^{5} +1.00000i q^{9} +2.28881 q^{11} +(0.277290 + 0.277290i) q^{13} +(2.05785 + 0.874793i) q^{15} +(0.0556418 - 0.0556418i) q^{17} +3.08243 q^{19} +(-0.206886 + 0.206886i) q^{23} +(3.60038 - 3.46947i) q^{25} +(-0.707107 + 0.707107i) q^{27} +3.92904i q^{29} +1.24185i q^{31} +(1.61844 + 1.61844i) q^{33} +(1.47548 + 1.47548i) q^{37} +0.392148i q^{39} +0.184951i q^{41} +(-0.541181 + 0.541181i) q^{43} +(0.836546 + 2.07369i) q^{45} +(5.46908 - 5.46908i) q^{47} +0.0786894 q^{51} +(7.91828 - 7.91828i) q^{53} +(4.74629 - 1.91470i) q^{55} +(2.17961 + 2.17961i) q^{57} -5.78405 q^{59} +6.85231i q^{61} +(0.806980 + 0.343048i) q^{65} +(-7.59248 - 7.59248i) q^{67} -0.292581 q^{69} -3.95718 q^{71} +(5.30939 + 5.30939i) q^{73} +(4.99914 + 0.0925647i) q^{75} +13.0447i q^{79} -1.00000 q^{81} +(7.50874 + 7.50874i) q^{83} +(0.0688370 - 0.161931i) q^{85} +(-2.77825 + 2.77825i) q^{87} +11.0670 q^{89} +(-0.878121 + 0.878121i) q^{93} +(6.39201 - 2.57860i) q^{95} +(6.10165 - 6.10165i) q^{97} +2.28881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Introduction

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Database

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