LMFDB - Embedded newform 2100.2.s.b.1457.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.4
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.b.1793.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.625101 + 1.61532i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.21850 - 2.01947i) q^{9} +O(q^{10})$	\(q+(-0.625101 + 1.61532i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.21850 - 2.01947i) q^{9} -1.94476i q^{11} +(-0.405496 + 0.405496i) q^{13} +(-0.0645540 + 0.0645540i) q^{17} -0.513741i q^{19} +(1.58421 - 0.700188i) q^{21} +(2.07221 + 2.07221i) q^{23} +(4.64887 - 2.32120i) q^{27} +1.78624 q^{29} +4.83761 q^{31} +(3.14140 + 1.21567i) q^{33} +(5.59183 + 5.59183i) q^{37} +(-0.401529 - 0.908482i) q^{39} +12.4425i q^{41} +(-4.95241 + 4.95241i) q^{43} +(-6.03030 + 6.03030i) q^{47} +1.00000i q^{49} +(-0.0639223 - 0.144628i) q^{51} +(-2.74748 - 2.74748i) q^{53} +(0.829855 + 0.321140i) q^{57} +12.3481 q^{59} +12.0067 q^{61} +(0.140731 + 2.99670i) q^{63} +(0.645504 + 0.645504i) q^{67} +(-4.64262 + 2.05194i) q^{69} -10.2091i q^{71} +(6.71462 - 6.71462i) q^{73} +(-1.37515 + 1.37515i) q^{77} +9.75115i q^{79} +(0.843455 + 8.96039i) q^{81} +(-11.7264 - 11.7264i) q^{83} +(-1.11658 + 2.88535i) q^{87} -2.42006 q^{89} +0.573459 q^{91} +(-3.02400 + 7.81428i) q^{93} +(12.0332 + 12.0332i) q^{97} +(-3.92739 + 4.31445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.625101	+	1.61532i	−0.360902	+	0.932604i
$3$	−0.625101	+	1.61532i	−0.360902	+	0.932604i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$	−2.21850	−	2.01947i	−0.739499	−	0.673158i
$10$		0			0
$11$		−	1.94476i		−	0.586367i	−0.956056	−	0.293184i	$-0.905285\pi$
$11$		−	1.94476i		−	0.586367i	0.956056	−	0.293184i	$-0.0947148\pi$
$12$		0			0
$13$	−0.405496	+	0.405496i	−0.112464	+	0.112464i	−0.761100	−	0.648635i	$-0.775340\pi$
$13$	−0.405496	+	0.405496i	−0.112464	+	0.112464i	0.648635	+	0.761100i	$0.275340\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.0645540	+	0.0645540i	−0.0156566	+	0.0156566i	−0.714892	−	0.699235i	$-0.753524\pi$
$17$	−0.0645540	+	0.0645540i	−0.0156566	+	0.0156566i	0.699235	+	0.714892i	$0.253524\pi$
$18$		0			0
$19$		−	0.513741i		−	0.117860i	−0.998262	−	0.0589302i	$-0.981231\pi$
$19$		−	0.513741i		−	0.117860i	0.998262	−	0.0589302i	$-0.0187689\pi$
$20$		0			0
$21$	1.58421	−	0.700188i	0.345704	−	0.152794i
$22$		0			0
$23$	2.07221	+	2.07221i	0.432086	+	0.432086i	0.889337	−	0.457252i	$-0.151166\pi$
$23$	2.07221	+	2.07221i	0.432086	+	0.432086i	−0.457252	+	0.889337i	$0.651166\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.64887	−	2.32120i	0.894676	−	0.446715i
$28$		0			0
$29$	1.78624			0.331697			0.165849	−	0.986151i	$-0.446964\pi$
$29$	1.78624			0.331697			0.165849	+	0.986151i	$0.446964\pi$
$30$		0			0
$31$	4.83761			0.868861			0.434430	−	0.900705i	$-0.356950\pi$
$31$	4.83761			0.868861			0.434430	+	0.900705i	$0.356950\pi$
$32$		0			0
$33$	3.14140	+	1.21567i	0.546848	+	0.211621i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.59183	+	5.59183i	0.919291	+	0.919291i	0.996978	−	0.0776870i	$-0.0247535\pi$
$37$	5.59183	+	5.59183i	0.919291	+	0.919291i	−0.0776870	+	0.996978i	$0.524753\pi$
$38$		0			0
$39$	−0.401529	−	0.908482i	−0.0642961	−	0.145473i
$40$		0			0
$41$			12.4425i			1.94319i	0.236655	+	0.971594i	$0.423949\pi$
$41$			12.4425i			1.94319i	−0.236655	+	0.971594i	$0.576051\pi$
$42$		0			0
$43$	−4.95241	+	4.95241i	−0.755235	+	0.755235i	−0.975451	−	0.220216i	$-0.929324\pi$
$43$	−4.95241	+	4.95241i	−0.755235	+	0.755235i	0.220216	+	0.975451i	$0.429324\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.03030	+	6.03030i	−0.879610	+	0.879610i	−0.993494	−	0.113884i	$-0.963671\pi$
$47$	−6.03030	+	6.03030i	−0.879610	+	0.879610i	0.113884	+	0.993494i	$0.463671\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−0.0639223	−	0.144628i	−0.00895092	−	0.0202520i
$52$		0			0
$53$	−2.74748	−	2.74748i	−0.377395	−	0.377395i	0.492767	−	0.870161i	$-0.335986\pi$
$53$	−2.74748	−	2.74748i	−0.377395	−	0.377395i	−0.870161	+	0.492767i	$0.835986\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.829855	+	0.321140i	0.109917	+	0.0425361i
$58$		0			0
$59$	12.3481			1.60758			0.803792	−	0.594910i	$-0.202812\pi$
$59$	12.3481			1.60758			0.803792	+	0.594910i	$0.202812\pi$
$60$		0			0
$61$	12.0067			1.53730			0.768650	−	0.639669i	$-0.220929\pi$
$61$	12.0067			1.53730			0.768650	+	0.639669i	$0.220929\pi$
$62$		0			0
$63$	0.140731	+	2.99670i	0.0177304	+	0.377548i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.645504	+	0.645504i	0.0788608	+	0.0788608i	0.745437	−	0.666576i	$-0.232241\pi$
$67$	0.645504	+	0.645504i	0.0788608	+	0.0788608i	−0.666576	+	0.745437i	$0.732241\pi$
$68$		0			0
$69$	−4.64262	+	2.05194i	−0.558906	+	0.247024i
$70$		0			0
$71$		−	10.2091i		−	1.21160i	−0.795616	−	0.605801i	$-0.792853\pi$
$71$		−	10.2091i		−	1.21160i	0.795616	−	0.605801i	$-0.207147\pi$
$72$		0			0
$73$	6.71462	−	6.71462i	0.785887	−	0.785887i	−0.194930	−	0.980817i	$-0.562448\pi$
$73$	6.71462	−	6.71462i	0.785887	−	0.785887i	0.980817	+	0.194930i	$0.0624480\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.37515	+	1.37515i	−0.156713	+	0.156713i
$78$		0			0
$79$			9.75115i			1.09709i	0.836121	+	0.548545i	$0.184818\pi$
$79$			9.75115i			1.09709i	−0.836121	+	0.548545i	$0.815182\pi$
$80$		0			0
$81$	0.843455	+	8.96039i	0.0937173	+	0.995599i
$82$		0			0
$83$	−11.7264	−	11.7264i	−1.28714	−	1.28714i	−0.936519	−	0.350616i	$-0.885972\pi$
$83$	−11.7264	−	11.7264i	−1.28714	−	1.28714i	−0.350616	−	0.936519i	$-0.614028\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.11658	+	2.88535i	−0.119710	+	0.309342i
$88$		0			0
$89$	−2.42006			−0.256526			−0.128263	−	0.991740i	$-0.540940\pi$
$89$	−2.42006			−0.256526			−0.128263	+	0.991740i	$0.540940\pi$
$90$		0			0
$91$	0.573459			0.0601148
$92$		0			0
$93$	−3.02400	+	7.81428i	−0.313574	+	0.810303i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.0332	+	12.0332i	1.22179	+	1.22179i	0.966995	+	0.254797i	$0.0820086\pi$
$97$	12.0332	+	12.0332i	1.22179	+	1.22179i	0.254797	+	0.966995i	$0.417991\pi$
$98$		0			0
$99$	−3.92739	+	4.31445i	−0.394718	+	0.433618i
$100$		0			0
$101$			10.9795i			1.09250i	0.837621	+	0.546252i	$0.183946\pi$
$101$			10.9795i			1.09250i	−0.837621	+	0.546252i	$0.816054\pi$
$102$		0			0
$103$	−1.78176	+	1.78176i	−0.175562	+	0.175562i	−0.789418	−	0.613856i	$-0.789617\pi$
$103$	−1.78176	+	1.78176i	−0.175562	+	0.175562i	0.613856	+	0.789418i	$0.289617\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.76716	+	9.76716i	−0.944227	+	0.944227i	−0.998525	−	0.0542973i	$-0.982708\pi$
$107$	−9.76716	+	9.76716i	−0.944227	+	0.944227i	0.0542973	+	0.998525i	$0.482708\pi$
$108$		0			0
$109$			6.09847i			0.584128i	0.956399	+	0.292064i	$0.0943420\pi$
$109$			6.09847i			0.584128i	−0.956399	+	0.292064i	$0.905658\pi$
$110$		0			0
$111$	−12.5280	+	5.53711i	−1.18911	+	0.525560i
$112$		0			0
$113$	−7.91276	−	7.91276i	−0.744369	−	0.744369i	0.229046	−	0.973416i	$-0.426439\pi$
$113$	−7.91276	−	7.91276i	−0.744369	−	0.744369i	−0.973416	+	0.229046i	$0.926439\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.71848	−	0.0807033i	0.158874	−	0.00746102i
$118$		0			0
$119$	0.0912931			0.00836882
$120$		0			0
$121$	7.21790			0.656173
$122$		0			0
$123$	−20.0985	−	7.77780i	−1.81222	−	0.701301i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.09638	+	1.09638i	0.0972884	+	0.0972884i	0.754076	−	0.656787i	$-0.228085\pi$
$127$	1.09638	+	1.09638i	0.0972884	+	0.0972884i	−0.656787	+	0.754076i	$0.728085\pi$
$128$		0			0
$129$	−4.90395	−	11.0955i	−0.431769	−	0.976901i
$130$		0			0
$131$			0.801286i			0.0700087i	0.999387	+	0.0350043i	$0.0111445\pi$
$131$			0.801286i			0.0700087i	−0.999387	+	0.0350043i	$0.988855\pi$
$132$		0			0
$133$	−0.363270	+	0.363270i	−0.0314995	+	0.0314995i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.18908	−	6.18908i	0.528769	−	0.528769i	−0.391436	−	0.920205i	$-0.628022\pi$
$137$	6.18908	−	6.18908i	0.528769	−	0.528769i	0.920205	+	0.391436i	$0.128022\pi$
$138$		0			0
$139$			18.0763i			1.53322i	0.642116	+	0.766608i	$0.278057\pi$
$139$			18.0763i			1.53322i	−0.642116	+	0.766608i	$0.721943\pi$
$140$		0			0
$141$	−5.97130	−	13.5104i	−0.502874	−	1.13778i
$142$		0			0
$143$	0.788594	+	0.788594i	0.0659455	+	0.0659455i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.61532	−	0.625101i	−0.133229	−	0.0515575i
$148$		0			0
$149$	−7.12044			−0.583329			−0.291665	−	0.956521i	$-0.594209\pi$
$149$	−7.12044			−0.583329			−0.291665	+	0.956521i	$0.594209\pi$
$150$		0			0
$151$	4.06832			0.331075			0.165538	−	0.986203i	$-0.447064\pi$
$151$	4.06832			0.331075			0.165538	+	0.986203i	$0.447064\pi$
$152$		0			0
$153$	0.273578	−	0.0128478i	0.0221175	−	0.00103868i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.7597	+	11.7597i	0.938523	+	0.938523i	0.998217	−	0.0596942i	$-0.0190126\pi$
$157$	11.7597	+	11.7597i	0.938523	+	0.938523i	−0.0596942	+	0.998217i	$0.519013\pi$
$158$		0			0
$159$	6.15549	−	2.72059i	0.488162	−	0.215757i
$160$		0			0
$161$		−	2.93055i		−	0.230960i
$162$		0			0
$163$	−0.565870	+	0.565870i	−0.0443224	+	0.0443224i	−0.728921	−	0.684598i	$-0.759978\pi$
$163$	−0.565870	+	0.565870i	−0.0443224	+	0.0443224i	0.684598	+	0.728921i	$0.259978\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.05176	−	7.05176i	0.545682	−	0.545682i	−0.379507	−	0.925189i	$-0.623906\pi$
$167$	7.05176	−	7.05176i	0.545682	−	0.545682i	0.925189	+	0.379507i	$0.123906\pi$
$168$		0			0
$169$			12.6711i			0.974703i
$170$		0			0
$171$	−1.03749	+	1.13973i	−0.0793386	+	0.0871576i
$172$		0			0
$173$	13.7209	+	13.7209i	1.04318	+	1.04318i	0.999025	+	0.0441559i	$0.0140598\pi$
$173$	13.7209	+	13.7209i	1.04318	+	1.04318i	0.0441559	+	0.999025i	$0.485940\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.71881	+	19.9461i	−0.580181	+	1.49924i
$178$		0			0
$179$	−20.7620			−1.55183			−0.775913	−	0.630840i	$-0.782710\pi$
$179$	−20.7620			−1.55183			−0.775913	+	0.630840i	$0.782710\pi$
$180$		0			0
$181$	0.798004			0.0593152			0.0296576	−	0.999560i	$-0.490558\pi$
$181$	0.798004			0.0593152			0.0296576	+	0.999560i	$0.490558\pi$
$182$		0			0
$183$	−7.50541	+	19.3946i	−0.554816	+	1.43369i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.125542	+	0.125542i	0.00918054	+	0.00918054i
$188$		0			0
$189$	−4.92859	−	1.64591i	−0.358502	−	0.119723i
$190$		0			0
$191$		−	24.8581i		−	1.79867i	−0.437259	−	0.899335i	$-0.644051\pi$
$191$		−	24.8581i		−	1.79867i	0.437259	−	0.899335i	$-0.355949\pi$
$192$		0			0
$193$	1.53137	−	1.53137i	0.110230	−	0.110230i	−0.649840	−	0.760071i	$-0.725164\pi$
$193$	1.53137	−	1.53137i	0.110230	−	0.110230i	0.760071	+	0.649840i	$0.225164\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.89771	+	8.89771i	−0.633936	+	0.633936i	−0.949053	−	0.315117i	$-0.897956\pi$
$197$	−8.89771	+	8.89771i	−0.633936	+	0.633936i	0.315117	+	0.949053i	$0.397956\pi$
$198$		0			0
$199$		−	15.1753i		−	1.07575i	−0.843025	−	0.537874i	$-0.819228\pi$
$199$		−	15.1753i		−	1.07575i	0.843025	−	0.537874i	$-0.180772\pi$
$200$		0			0
$201$	−1.44620	+	0.639188i	−0.102007	+	0.0450848i
$202$		0			0
$203$	−1.26307	−	1.26307i	−0.0886498	−	0.0886498i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.412419	−	8.78197i	−0.0286651	−	0.610389i
$208$		0			0
$209$	−0.999104			−0.0691095
$210$		0			0
$211$	11.6116			0.799377			0.399688	−	0.916651i	$-0.369118\pi$
$211$	11.6116			0.799377			0.399688	+	0.916651i	$0.369118\pi$
$212$		0			0
$213$	16.4910	+	6.38175i	1.12994	+	0.437270i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.42071	−	3.42071i	−0.232213	−	0.232213i
$218$		0			0
$219$	6.64892	+	15.0436i	0.449293	+	1.01655i
$220$		0			0
$221$		−	0.0523528i		−	0.00352163i
$222$		0			0
$223$	−5.05141	+	5.05141i	−0.338268	+	0.338268i	−0.855715	−	0.517447i	$-0.826882\pi$
$223$	−5.05141	+	5.05141i	−0.338268	+	0.338268i	0.517447	+	0.855715i	$0.326882\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.08743	+	1.08743i	−0.0721752	+	0.0721752i	−0.742273	−	0.670098i	$-0.766252\pi$
$227$	−1.08743	+	1.08743i	−0.0721752	+	0.0721752i	0.670098	+	0.742273i	$0.266252\pi$
$228$		0			0
$229$		−	13.8811i		−	0.917289i	−0.888620	−	0.458644i	$-0.848335\pi$
$229$		−	13.8811i		−	0.917289i	0.888620	−	0.458644i	$-0.151665\pi$
$230$		0			0
$231$	−1.36170	−	3.08092i	−0.0895932	−	0.202710i
$232$		0			0
$233$	15.5689	+	15.5689i	1.01995	+	1.01995i	0.999797	+	0.0201533i	$0.00641543\pi$
$233$	15.5689	+	15.5689i	1.01995	+	1.01995i	0.0201533	+	0.999797i	$0.493585\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−15.7512	−	6.09546i	−1.02315	−	0.395943i
$238$		0			0
$239$	−19.2184			−1.24313			−0.621567	−	0.783361i	$-0.713504\pi$
$239$	−19.2184			−1.24313			−0.621567	+	0.783361i	$0.713504\pi$
$240$		0			0
$241$	17.9762			1.15795			0.578973	−	0.815346i	$-0.303454\pi$
$241$	17.9762			1.15795			0.578973	+	0.815346i	$0.303454\pi$
$242$		0			0
$243$	−15.0011	−	4.23870i	−0.962322	−	0.271913i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.208320	+	0.208320i	0.0132551	+	0.0132551i
$248$		0			0
$249$	26.2719	−	11.6116i	1.66492	−	0.735857i
$250$		0			0
$251$			4.35587i			0.274940i	0.990506	+	0.137470i	$0.0438971\pi$
$251$			4.35587i			0.274940i	−0.990506	+	0.137470i	$0.956103\pi$
$252$		0			0
$253$	4.02996	−	4.02996i	0.253361	−	0.253361i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.93850	−	7.93850i	0.495190	−	0.495190i	−0.414747	−	0.909937i	$-0.636130\pi$
$257$	7.93850	−	7.93850i	0.495190	−	0.495190i	0.909937	+	0.414747i	$0.136130\pi$
$258$		0			0
$259$		−	7.90804i		−	0.491382i
$260$		0			0
$261$	−3.96278	−	3.60727i	−0.245290	−	0.223285i
$262$		0			0
$263$	19.9654	+	19.9654i	1.23112	+	1.23112i	0.963533	+	0.267589i	$0.0862268\pi$
$263$	19.9654	+	19.9654i	1.23112	+	1.23112i	0.267589	+	0.963533i	$0.413773\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.51278	−	3.90917i	0.0925809	−	0.239237i
$268$		0			0
$269$	6.00391			0.366065			0.183032	−	0.983107i	$-0.441409\pi$
$269$	6.00391			0.366065			0.183032	+	0.983107i	$0.441409\pi$
$270$		0			0
$271$	1.33362			0.0810119			0.0405060	−	0.999179i	$-0.487103\pi$
$271$	1.33362			0.0810119			0.0405060	+	0.999179i	$0.487103\pi$
$272$		0			0
$273$	−0.358470	+	0.926317i	−0.0216956	+	0.0560633i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.58795	+	6.58795i	0.395832	+	0.395832i	0.876760	−	0.480928i	$-0.159700\pi$
$277$	6.58795	+	6.58795i	0.395832	+	0.395832i	−0.480928	+	0.876760i	$0.659700\pi$
$278$		0			0
$279$	−10.7322	−	9.76943i	−0.642522	−	0.584880i
$280$		0			0
$281$			12.0096i			0.716431i	0.933639	+	0.358215i	$0.116615\pi$
$281$			12.0096i			0.716431i	−0.933639	+	0.358215i	$0.883385\pi$
$282$		0			0
$283$	14.4376	−	14.4376i	0.858228	−	0.858228i	−0.132901	−	0.991129i	$-0.542429\pi$
$283$	14.4376	−	14.4376i	0.858228	−	0.858228i	0.991129	+	0.132901i	$0.0424293\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.79816	−	8.79816i	0.519339	−	0.519339i
$288$		0			0
$289$			16.9917i			0.999510i
$290$		0			0
$291$	−26.9595	+	11.9155i	−1.58039	+	0.698500i
$292$		0			0
$293$	−18.0519	−	18.0519i	−1.05460	−	1.05460i	−0.998420	−	0.0561834i	$-0.982107\pi$
$293$	−18.0519	−	18.0519i	−1.05460	−	1.05460i	−0.0561834	−	0.998420i	$-0.517893\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.51418	−	9.04095i	−0.261939	−	0.524609i
$298$		0			0
$299$	−1.68055			−0.0971886
$300$		0			0
$301$	7.00376			0.403690
$302$		0			0
$303$	−17.7354	−	6.86331i	−1.01887	−	0.394287i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.38982	+	1.38982i	0.0793211	+	0.0793211i	0.745654	−	0.666333i	$-0.232137\pi$
$307$	1.38982	+	1.38982i	0.0793211	+	0.0793211i	−0.666333	+	0.745654i	$0.732137\pi$
$308$		0			0
$309$	−1.76432	−	3.99188i	−0.100369	−	0.227090i
$310$		0			0
$311$			22.2043i			1.25909i	0.776964	+	0.629545i	$0.216759\pi$
$311$			22.2043i			1.25909i	−0.776964	+	0.629545i	$0.783241\pi$
$312$		0			0
$313$	24.1425	−	24.1425i	1.36461	−	1.36461i	0.496683	−	0.867932i	$-0.334551\pi$
$313$	24.1425	−	24.1425i	1.36461	−	1.36461i	0.867932	−	0.496683i	$-0.165449\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.95642	−	2.95642i	0.166049	−	0.166049i	−0.619191	−	0.785240i	$-0.712539\pi$
$317$	2.95642	−	2.95642i	0.166049	−	0.166049i	0.785240	+	0.619191i	$0.212539\pi$
$318$		0			0
$319$		−	3.47382i		−	0.194496i
$320$		0			0
$321$	−9.67160	−	21.8825i	−0.539816	−	1.22136i
$322$		0			0
$323$	0.0331640	+	0.0331640i	0.00184530	+	0.00184530i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.85096	−	3.81216i	−0.544759	−	0.210813i
$328$		0			0
$329$	8.52814			0.470171
$330$		0			0
$331$	−24.4043			−1.34138			−0.670691	−	0.741737i	$-0.734002\pi$
$331$	−24.4043			−1.34138			−0.670691	+	0.741737i	$0.734002\pi$
$332$		0			0
$333$	−1.11290	−	23.6980i	−0.0609868	−	1.29864i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−14.4454	−	14.4454i	−0.786890	−	0.786890i	0.194093	−	0.980983i	$-0.437824\pi$
$337$	−14.4454	−	14.4454i	−0.786890	−	0.786890i	−0.980983	+	0.194093i	$0.937824\pi$
$338$		0			0
$339$	17.7279	−	7.83533i	0.962846	−	0.425557i
$340$		0			0
$341$		−	9.40800i		−	0.509472i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.5004	−	16.5004i	0.885790	−	0.885790i	−0.108326	−	0.994115i	$-0.534549\pi$
$347$	16.5004	−	16.5004i	0.885790	−	0.885790i	0.994115	+	0.108326i	$0.0345490\pi$
$348$		0			0
$349$			18.3880i			0.984287i	0.870514	+	0.492144i	$0.163786\pi$
$349$			18.3880i			0.984287i	−0.870514	+	0.492144i	$0.836214\pi$
$350$		0			0
$351$	−0.943864	+	2.82634i	−0.0503797	+	0.150859i
$352$		0			0
$353$	8.02018	+	8.02018i	0.426871	+	0.426871i	0.887561	−	0.460690i	$-0.152398\pi$
$353$	8.02018	+	8.02018i	0.426871	+	0.426871i	−0.460690	+	0.887561i	$0.652398\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.0570674	+	0.147467i	−0.00302033	+	0.00780480i
$358$		0			0
$359$	2.09751			0.110702			0.0553512	−	0.998467i	$-0.482372\pi$
$359$	2.09751			0.110702			0.0553512	+	0.998467i	$0.482372\pi$
$360$		0			0
$361$	18.7361			0.986109
$362$		0			0
$363$	−4.51192	+	11.6592i	−0.236814	+	0.611949i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−22.2915	−	22.2915i	−1.16361	−	1.16361i	−0.983680	−	0.179925i	$-0.942415\pi$
$367$	−22.2915	−	22.2915i	−1.16361	−	1.16361i	−0.179925	−	0.983680i	$-0.557585\pi$
$368$		0			0
$369$	25.1272	−	27.6036i	1.30807	−	1.43698i
$370$		0			0
$371$			3.88552i			0.201726i
$372$		0			0
$373$	5.24256	−	5.24256i	0.271449	−	0.271449i	−0.558234	−	0.829684i	$-0.688521\pi$
$373$	5.24256	−	5.24256i	0.271449	−	0.271449i	0.829684	+	0.558234i	$0.188521\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.724316	+	0.724316i	−0.0373042	+	0.0373042i
$378$		0			0
$379$			7.17910i			0.368765i	0.982855	+	0.184383i	$0.0590286\pi$
$379$			7.17910i			0.368765i	−0.982855	+	0.184383i	$0.940971\pi$
$380$		0			0
$381$	−2.45636	+	1.08566i	−0.125843	+	0.0556199i
$382$		0			0
$383$	−2.44262	−	2.44262i	−0.124812	−	0.124812i	0.641942	−	0.766754i	$-0.278129\pi$
$383$	−2.44262	−	2.44262i	−0.124812	−	0.124812i	−0.766754	+	0.641942i	$0.778129\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	20.9882	−	0.985645i	1.06689	−	0.0501032i
$388$		0			0
$389$	7.12387			0.361195			0.180597	−	0.983557i	$-0.442197\pi$
$389$	7.12387			0.361195			0.180597	+	0.983557i	$0.442197\pi$
$390$		0			0
$391$	−0.267539			−0.0135300
$392$		0			0
$393$	−1.29433	−	0.500885i	−0.0652903	−	0.0252663i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.0937	−	14.0937i	−0.707343	−	0.707343i	0.258633	−	0.965976i	$-0.416728\pi$
$397$	−14.0937	−	14.0937i	−0.707343	−	0.707343i	−0.965976	+	0.258633i	$0.916728\pi$
$398$		0			0
$399$	−0.359716	−	0.813877i	−0.0180083	−	0.0407448i
$400$		0			0
$401$			14.6745i			0.732809i	0.930456	+	0.366405i	$0.119411\pi$
$401$			14.6745i			0.732809i	−0.930456	+	0.366405i	$0.880589\pi$
$402$		0			0
$403$	−1.96163	+	1.96163i	−0.0977160	+	0.0977160i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.8748	−	10.8748i	0.539042	−	0.539042i
$408$		0			0
$409$		−	32.2017i		−	1.59227i	−0.605117	−	0.796137i	$-0.706874\pi$
$409$		−	32.2017i		−	1.59227i	0.605117	−	0.796137i	$-0.293126\pi$
$410$		0			0
$411$	6.12853	+	13.8661i	0.302298	+	0.683966i
$412$		0			0
$413$	−8.73142	−	8.73142i	−0.429645	−	0.429645i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−29.1990	−	11.2995i	−1.42988	−	0.553341i
$418$		0			0
$419$	5.62472			0.274786			0.137393	−	0.990517i	$-0.456128\pi$
$419$	5.62472			0.274786			0.137393	+	0.990517i	$0.456128\pi$
$420$		0			0
$421$	−34.7907			−1.69560			−0.847798	−	0.530319i	$-0.822072\pi$
$421$	−34.7907			−1.69560			−0.847798	+	0.530319i	$0.822072\pi$
$422$		0			0
$423$	25.5562	−	1.20017i	1.24259	−	0.0583543i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−8.49002	−	8.49002i	−0.410861	−	0.410861i
$428$		0			0
$429$	−1.76678	+	0.780878i	−0.0853009	+	0.0377011i
$430$		0			0
$431$		−	27.8845i		−	1.34315i	−0.740937	−	0.671575i	$-0.765618\pi$
$431$		−	27.8845i		−	1.34315i	0.740937	−	0.671575i	$-0.234382\pi$
$432$		0			0
$433$	2.60002	−	2.60002i	0.124949	−	0.124949i	−0.641867	−	0.766816i	$-0.721840\pi$
$433$	2.60002	−	2.60002i	0.124949	−	0.124949i	0.766816	+	0.641867i	$0.221840\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.06458	−	1.06458i	0.0509258	−	0.0509258i
$438$		0			0
$439$			0.518026i			0.0247241i	0.999924	+	0.0123620i	$0.00393506\pi$
$439$			0.518026i			0.0247241i	−0.999924	+	0.0123620i	$0.996065\pi$
$440$		0			0
$441$	2.01947	−	2.21850i	0.0961654	−	0.105643i
$442$		0			0
$443$	−13.3408	−	13.3408i	−0.633843	−	0.633843i	0.315187	−	0.949030i	$-0.397933\pi$
$443$	−13.3408	−	13.3408i	−0.633843	−	0.633843i	−0.949030	+	0.315187i	$0.897933\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.45100	−	11.5018i	0.210525	−	0.544015i
$448$		0			0
$449$	22.1040			1.04315			0.521575	−	0.853205i	$-0.325345\pi$
$449$	22.1040			1.04315			0.521575	+	0.853205i	$0.325345\pi$
$450$		0			0
$451$	24.1976			1.13942
$452$		0			0
$453$	−2.54311	+	6.57163i	−0.119486	+	0.308762i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.7883	+	16.7883i	0.785322	+	0.785322i	0.980723	−	0.195402i	$-0.0626011\pi$
$457$	16.7883	+	16.7883i	0.785322	+	0.785322i	−0.195402	+	0.980723i	$0.562601\pi$
$458$		0			0
$459$	−0.150261	+	0.449946i	−0.00701357	+	0.0210017i
$460$		0			0
$461$		−	23.9614i		−	1.11599i	−0.829843	−	0.557996i	$-0.811570\pi$
$461$		−	23.9614i		−	1.11599i	0.829843	−	0.557996i	$-0.188430\pi$
$462$		0			0
$463$	13.9347	−	13.9347i	0.647598	−	0.647598i	−0.304814	−	0.952412i	$-0.598594\pi$
$463$	13.9347	−	13.9347i	0.647598	−	0.647598i	0.952412	+	0.304814i	$0.0985942\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.29814	−	7.29814i	0.337718	−	0.337718i	−0.517790	−	0.855508i	$-0.673245\pi$
$467$	7.29814	−	7.29814i	0.337718	−	0.337718i	0.855508	+	0.517790i	$0.173245\pi$
$468$		0			0
$469$		−	0.912880i		−	0.0421529i
$470$		0			0
$471$	−26.3465	+	11.6446i	−1.21398	+	0.536554i
$472$		0			0
$473$	9.63125	+	9.63125i	0.442845	+	0.442845i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.546812	+	11.6437i	0.0250368	+	0.533129i
$478$		0			0
$479$	25.9862			1.18734			0.593671	−	0.804708i	$-0.297678\pi$
$479$	25.9862			1.18734			0.593671	+	0.804708i	$0.297678\pi$
$480$		0			0
$481$	−4.53493			−0.206775
$482$		0			0
$483$	4.73377	+	1.83189i	0.215394	+	0.0833539i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−24.2348	−	24.2348i	−1.09818	−	1.09818i	−0.994623	−	0.103561i	$-0.966976\pi$
$487$	−24.2348	−	24.2348i	−1.09818	−	1.09818i	−0.103561	−	0.994623i	$-0.533024\pi$
$488$		0			0
$489$	−0.560333	−	1.26779i	−0.0253392	−	0.0573313i
$490$		0			0
$491$			26.6797i			1.20404i	0.798482	+	0.602019i	$0.205637\pi$
$491$			26.6797i			1.20404i	−0.798482	+	0.602019i	$0.794363\pi$
$492$		0			0
$493$	−0.115309	+	0.115309i	−0.00519326	+	0.00519326i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.21895	+	7.21895i	−0.323814	+	0.323814i
$498$		0			0
$499$			7.96990i			0.356782i	0.983960	+	0.178391i	$0.0570891\pi$
$499$			7.96990i			0.356782i	−0.983960	+	0.178391i	$0.942911\pi$
$500$		0			0
$501$	6.98276	+	15.7989i	0.311967	+	0.705843i
$502$		0			0
$503$	16.1093	+	16.1093i	0.718279	+	0.718279i	0.968253	−	0.249974i	$-0.0804221\pi$
$503$	16.1093	+	16.1093i	0.718279	+	0.718279i	−0.249974	+	0.968253i	$0.580422\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−20.4679	−	7.92075i	−0.909012	−	0.351773i
$508$		0			0
$509$	19.4728			0.863117			0.431559	−	0.902085i	$-0.357964\pi$
$509$	19.4728			0.863117			0.431559	+	0.902085i	$0.357964\pi$
$510$		0			0
$511$	−9.49591			−0.420074
$512$		0			0
$513$	−1.19250	−	2.38832i	−0.0526500	−	0.105447i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	11.7275	+	11.7275i	0.515775	+	0.515775i
$518$		0			0
$519$	−30.7405	+	13.5866i	−1.34936	+	0.596388i
$520$		0			0
$521$		−	19.7755i		−	0.866380i	−0.901303	−	0.433190i	$-0.857388\pi$
$521$		−	19.7755i		−	0.866380i	0.901303	−	0.433190i	$-0.142612\pi$
$522$		0			0
$523$	7.48995	−	7.48995i	0.327513	−	0.327513i	−0.524127	−	0.851640i	$-0.675608\pi$
$523$	7.48995	−	7.48995i	0.327513	−	0.327513i	0.851640	+	0.524127i	$0.175608\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.312287	+	0.312287i	−0.0136034	+	0.0136034i
$528$		0			0
$529$		−	14.4119i		−	0.626604i
$530$		0			0
$531$	−27.3942	−	24.9366i	−1.18881	−	1.08216i
$532$		0			0
$533$	−5.04538	−	5.04538i	−0.218540	−	0.218540i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	12.9784	−	33.5372i	0.560058	−	1.44724i
$538$		0			0
$539$	1.94476			0.0837668
$540$		0			0
$541$	−35.3737			−1.52083			−0.760416	−	0.649436i	$-0.775005\pi$
$541$	−35.3737			−1.52083			−0.760416	+	0.649436i	$0.775005\pi$
$542$		0			0
$543$	−0.498833	+	1.28903i	−0.0214070	+	0.0553175i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	18.3855	+	18.3855i	0.786109	+	0.786109i	0.980854	−	0.194745i	$-0.0623879\pi$
$547$	18.3855	+	18.3855i	0.786109	+	0.786109i	−0.194745	+	0.980854i	$0.562388\pi$
$548$		0			0
$549$	−26.6368	−	24.2472i	−1.13683	−	1.03485i
$550$		0			0
$551$		−	0.917667i		−	0.0390939i
$552$		0			0
$553$	6.89511	−	6.89511i	0.293210	−	0.293210i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.8228	+	21.8228i	−0.924663	+	0.924663i	−0.997354	−	0.0726917i	$-0.976841\pi$
$557$	−21.8228	+	21.8228i	−0.924663	+	0.924663i	0.0726917	+	0.997354i	$0.476841\pi$
$558$		0			0
$559$		−	4.01637i		−	0.169874i
$560$		0			0
$561$	−0.281267	+	0.124314i	−0.0118751	+	0.00524853i
$562$		0			0
$563$	−9.07525	−	9.07525i	−0.382476	−	0.382476i	0.489517	−	0.871994i	$-0.337173\pi$
$563$	−9.07525	−	9.07525i	−0.382476	−	0.382476i	−0.871994	+	0.489517i	$0.837173\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	5.73954	−	6.93237i	0.241038	−	0.291132i
$568$		0			0
$569$	−45.0923			−1.89037			−0.945183	−	0.326541i	$-0.894117\pi$
$569$	−45.0923			−1.89037			−0.945183	+	0.326541i	$0.894117\pi$
$570$		0			0
$571$	26.3965			1.10466			0.552330	−	0.833625i	$-0.313739\pi$
$571$	26.3965			1.10466			0.552330	+	0.833625i	$0.313739\pi$
$572$		0			0
$573$	40.1537	+	15.5388i	1.67745	+	0.649145i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.0392630	+	0.0392630i	0.00163454	+	0.00163454i	0.707924	−	0.706289i	$-0.249632\pi$
$577$	0.0392630	+	0.0392630i	0.00163454	+	0.00163454i	−0.706289	+	0.707924i	$0.749632\pi$
$578$		0			0
$579$	1.51639	+	3.43091i	0.0630188	+	0.142584i
$580$		0			0
$581$			16.5836i			0.688003i
$582$		0			0
$583$	−5.34318	+	5.34318i	−0.221292	+	0.221292i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−27.5472	+	27.5472i	−1.13700	+	1.13700i	−0.148009	+	0.988986i	$0.547287\pi$
$587$	−27.5472	+	27.5472i	−1.13700	+	1.13700i	−0.988986	+	0.148009i	$0.952713\pi$
$588$		0			0
$589$		−	2.48528i		−	0.102404i
$590$		0			0
$591$	−8.81065	−	19.9346i	−0.362422	−	0.820000i
$592$		0			0
$593$	7.66004	+	7.66004i	0.314560	+	0.314560i	0.846673	−	0.532113i	$-0.178602\pi$
$593$	7.66004	+	7.66004i	0.314560	+	0.314560i	−0.532113	+	0.846673i	$0.678602\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	24.5129	+	9.48610i	1.00325	+	0.388240i
$598$		0			0
$599$	−15.6187			−0.638162			−0.319081	−	0.947727i	$-0.603374\pi$
$599$	−15.6187			−0.638162			−0.319081	+	0.947727i	$0.603374\pi$
$600$		0			0
$601$	8.53521			0.348158			0.174079	−	0.984732i	$-0.444305\pi$
$601$	8.53521			0.348158			0.174079	+	0.984732i	$0.444305\pi$
$602$		0			0
$603$	−0.128470	−	2.73563i	−0.00523172	−	0.111403i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−22.1509	−	22.1509i	−0.899077	−	0.899077i	0.0962777	−	0.995355i	$-0.469306\pi$
$607$	−22.1509	−	22.1509i	−0.899077	−	0.899077i	−0.995355	+	0.0962777i	$0.969306\pi$
$608$		0			0
$609$	2.82979	−	1.25071i	0.114669	−	0.0506812i
$610$		0			0
$611$		−	4.89053i		−	0.197850i
$612$		0			0
$613$	−4.66852	+	4.66852i	−0.188560	+	0.188560i	−0.795073	−	0.606513i	$-0.792568\pi$
$613$	−4.66852	+	4.66852i	−0.188560	+	0.188560i	0.606513	+	0.795073i	$0.292568\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.3531	−	20.3531i	0.819384	−	0.819384i	−0.166635	−	0.986019i	$-0.553290\pi$
$617$	20.3531	−	20.3531i	0.819384	−	0.819384i	0.986019	+	0.166635i	$0.0532900\pi$
$618$		0			0
$619$			34.7975i			1.39863i	0.714814	+	0.699315i	$0.246511\pi$
$619$			34.7975i			1.39863i	−0.714814	+	0.699315i	$0.753489\pi$
$620$		0			0
$621$	14.4435	+	4.82343i	0.579596	+	0.193558i
$622$		0			0
$623$	1.71124	+	1.71124i	0.0685595	+	0.0685595i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.624541	−	1.61387i	0.0249418	−	0.0644517i
$628$		0			0
$629$	−0.721949			−0.0287860
$630$		0			0
$631$	−8.89358			−0.354048			−0.177024	−	0.984207i	$-0.556647\pi$
$631$	−8.89358			−0.354048			−0.177024	+	0.984207i	$0.556647\pi$
$632$		0			0
$633$	−7.25844	+	18.7564i	−0.288497	+	0.745502i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.405496	−	0.405496i	−0.0160664	−	0.0160664i
$638$		0			0
$639$	−20.6171	+	22.6489i	−0.815600	+	0.895979i
$640$		0			0
$641$		−	28.4863i		−	1.12514i	−0.826749	−	0.562570i	$-0.809812\pi$
$641$		−	28.4863i		−	1.12514i	0.826749	−	0.562570i	$-0.190188\pi$
$642$		0			0
$643$	−31.6802	+	31.6802i	−1.24934	+	1.24934i	−0.293334	+	0.956010i	$0.594765\pi$
$643$	−31.6802	+	31.6802i	−1.24934	+	1.24934i	−0.956010	+	0.293334i	$0.905235\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.35421	+	6.35421i	−0.249810	+	0.249810i	−0.820892	−	0.571083i	$-0.806524\pi$
$647$	−6.35421	+	6.35421i	−0.249810	+	0.249810i	0.571083	+	0.820892i	$0.306524\pi$
$648$		0			0
$649$		−	24.0141i		−	0.942635i
$650$		0			0
$651$	7.66382	−	3.38724i	0.300369	−	0.132756i
$652$		0			0
$653$	−25.5038	−	25.5038i	−0.998042	−	0.998042i	0.00195560	−	0.999998i	$-0.499378\pi$
$653$	−25.5038	−	25.5038i	−0.998042	−	0.998042i	−0.999998	+	0.00195560i	$0.999378\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−28.4564	+	1.33637i	−1.11019	+	0.0521367i
$658$		0			0
$659$	1.12056			0.0436508			0.0218254	−	0.999762i	$-0.493052\pi$
$659$	1.12056			0.0436508			0.0218254	+	0.999762i	$0.493052\pi$
$660$		0			0
$661$	1.15897			0.0450787			0.0225394	−	0.999746i	$-0.492825\pi$
$661$	1.15897			0.0450787			0.0225394	+	0.999746i	$0.492825\pi$
$662$		0			0
$663$	0.0845664	+	0.0327258i	0.00328429	+	0.00127097i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.70147	+	3.70147i	0.143322	+	0.143322i
$668$		0			0
$669$	−5.00199	−	11.3173i	−0.193388	−	0.437551i
$670$		0			0
$671$		−	23.3502i		−	0.901423i
$672$		0			0
$673$	−5.07000	+	5.07000i	−0.195434	+	0.195434i	−0.798039	−	0.602605i	$-0.794129\pi$
$673$	−5.07000	+	5.07000i	−0.195434	+	0.195434i	0.602605	+	0.798039i	$0.294129\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.38278	+	5.38278i	−0.206877	+	0.206877i	−0.802939	−	0.596062i	$-0.796731\pi$
$677$	−5.38278	+	5.38278i	−0.206877	+	0.206877i	0.596062	+	0.802939i	$0.296731\pi$
$678$		0			0
$679$		−	17.0176i		−	0.653075i
$680$		0			0
$681$	−1.07679	−	2.43630i	−0.0412626	−	0.0933591i
$682$		0			0
$683$	19.4903	+	19.4903i	0.745775	+	0.745775i	0.973683	−	0.227908i	$-0.0731885\pi$
$683$	19.4903	+	19.4903i	0.745775	+	0.745775i	−0.227908	+	0.973683i	$0.573188\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	22.4224	+	8.67709i	0.855467	+	0.331052i
$688$		0			0
$689$	2.22818			0.0848870
$690$		0			0
$691$	8.44415			0.321231			0.160615	−	0.987017i	$-0.448652\pi$
$691$	8.44415			0.321231			0.160615	+	0.987017i	$0.448652\pi$
$692$		0			0
$693$	5.82786	−	0.273688i	0.221382	−	0.0103965i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.803211	−	0.803211i	−0.0304238	−	0.0304238i
$698$		0			0
$699$	−34.8808	+	15.4165i	−1.31931	+	0.583107i
$700$		0			0
$701$		−	37.1005i		−	1.40127i	−0.713522	−	0.700633i	$-0.752901\pi$
$701$		−	37.1005i		−	1.40127i	0.713522	−	0.700633i	$-0.247099\pi$
$702$		0			0
$703$	2.87275	−	2.87275i	0.108348	−	0.108348i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.76369	−	7.76369i	0.291984	−	0.291984i
$708$		0			0
$709$			50.0763i			1.88065i	0.340271	+	0.940327i	$0.389481\pi$
$709$			50.0763i			1.88065i	−0.340271	+	0.940327i	$0.610519\pi$
$710$		0			0
$711$	19.6922	−	21.6329i	0.738515	−	0.811297i
$712$		0			0
$713$	10.0246	+	10.0246i	0.375422	+	0.375422i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.0134	−	31.0438i	0.448650	−	1.15935i
$718$		0			0
$719$	−16.7001			−0.622808			−0.311404	−	0.950278i	$-0.600799\pi$
$719$	−16.7001			−0.622808			−0.311404	+	0.950278i	$0.600799\pi$
$720$		0			0
$721$	2.51978			0.0938416
$722$		0			0
$723$	−11.2369	+	29.0372i	−0.417906	+	1.07991i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	21.4751	+	21.4751i	0.796469	+	0.796469i	0.982537	−	0.186068i	$-0.0595745\pi$
$727$	21.4751	+	21.4751i	0.796469	+	0.796469i	−0.186068	+	0.982537i	$0.559574\pi$
$728$		0			0
$729$	16.2241	−	21.5819i	0.600891	−	0.799331i
$730$		0			0
$731$		−	0.639395i		−	0.0236489i
$732$		0			0
$733$	9.69104	−	9.69104i	0.357947	−	0.357947i	−0.505109	−	0.863056i	$-0.668548\pi$
$733$	9.69104	−	9.69104i	0.357947	−	0.357947i	0.863056	+	0.505109i	$0.168548\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.25535	−	1.25535i	0.0462414	−	0.0462414i
$738$		0			0
$739$		−	16.7765i		−	0.617134i	−0.951203	−	0.308567i	$-0.900151\pi$
$739$		−	16.7765i		−	0.617134i	0.951203	−	0.308567i	$-0.0998495\pi$
$740$		0			0
$741$	−0.466725	+	0.206282i	−0.0171456	+	0.00757796i
$742$		0			0
$743$	−21.3036	−	21.3036i	−0.781552	−	0.781552i	0.198540	−	0.980093i	$-0.436380\pi$
$743$	−21.3036	−	21.3036i	−0.781552	−	0.781552i	−0.980093	+	0.198540i	$0.936380\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.33382	+	49.6960i	0.0853900	+	1.81828i
$748$		0			0
$749$	13.8129			0.504711
$750$		0			0
$751$	−30.0835			−1.09776			−0.548880	−	0.835901i	$-0.684946\pi$
$751$	−30.0835			−1.09776			−0.548880	+	0.835901i	$0.684946\pi$
$752$		0			0
$753$	−7.03611	−	2.72286i	−0.256410	−	0.0992266i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.57404	−	7.57404i	−0.275283	−	0.275283i	0.555940	−	0.831223i	$-0.312359\pi$
$757$	−7.57404	−	7.57404i	−0.275283	−	0.275283i	−0.831223	+	0.555940i	$0.812359\pi$
$758$		0			0
$759$	3.99052	+	9.02878i	0.144847	+	0.327724i
$760$		0			0
$761$			23.9175i			0.867008i	0.901152	+	0.433504i	$0.142723\pi$
$761$			23.9175i			0.867008i	−0.901152	+	0.433504i	$0.857277\pi$
$762$		0			0
$763$	4.31227	−	4.31227i	0.156115	−	0.156115i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.00711	+	5.00711i	−0.180796	+	0.180796i
$768$		0			0
$769$			44.6698i			1.61084i	0.592707	+	0.805418i	$0.298059\pi$
$769$			44.6698i			1.61084i	−0.592707	+	0.805418i	$0.701941\pi$
$770$		0			0
$771$	7.86082	+	17.7856i	0.283101	+	0.640531i
$772$		0			0
$773$	−6.10439	−	6.10439i	−0.219560	−	0.219560i	0.588753	−	0.808313i	$-0.299619\pi$
$773$	−6.10439	−	6.10439i	−0.219560	−	0.219560i	−0.808313	+	0.588753i	$0.799619\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.7740	+	4.94333i	0.458264	+	0.177341i
$778$		0			0
$779$	6.39221			0.229025
$780$		0			0
$781$	−19.8543			−0.710444
$782$		0			0
$783$	8.30402	−	4.14623i	0.296762	−	0.148174i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−11.0024	−	11.0024i	−0.392192	−	0.392192i	0.483276	−	0.875468i	$-0.339447\pi$
$787$	−11.0024	−	11.0024i	−0.392192	−	0.392192i	−0.875468	+	0.483276i	$0.839447\pi$
$788$		0			0
$789$	−44.7309	+	19.7701i	−1.59246	+	0.703834i
$790$		0			0
$791$			11.1903i			0.397882i
$792$		0			0
$793$	−4.86868	+	4.86868i	−0.172892	+	0.172892i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5330	+	13.5330i	−0.479362	+	0.479362i	−0.904928	−	0.425565i	$-0.860075\pi$
$797$	−13.5330	+	13.5330i	−0.479362	+	0.479362i	0.425565	+	0.904928i	$0.360075\pi$
$798$		0			0
$799$		−	0.778560i		−	0.0275435i
$800$		0			0
$801$	5.36890	+	4.88725i	0.189701	+	0.172683i
$802$		0			0
$803$	−13.0583	−	13.0583i	−0.460819	−	0.460819i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.75305	+	9.69822i	−0.132114	+	0.341393i
$808$		0			0
$809$	13.3438			0.469143			0.234571	−	0.972099i	$-0.424631\pi$
$809$	13.3438			0.469143			0.234571	+	0.972099i	$0.424631\pi$
$810$		0			0
$811$	42.3994			1.48884			0.744422	−	0.667709i	$-0.232725\pi$
$811$	42.3994			1.48884			0.744422	+	0.667709i	$0.232725\pi$
$812$		0			0
$813$	−0.833651	+	2.15423i	−0.0292374	+	0.0755520i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.54426	+	2.54426i	0.0890123	+	0.0890123i
$818$		0			0
$819$	−1.27222	−	1.15808i	−0.0444548	−	0.0404667i
$820$		0			0
$821$			15.5259i			0.541858i	0.962599	+	0.270929i	$0.0873308\pi$
$821$			15.5259i			0.541858i	−0.962599	+	0.270929i	$0.912669\pi$
$822$		0			0
$823$	23.8421	−	23.8421i	0.831084	−	0.831084i	−0.156581	−	0.987665i	$-0.550047\pi$
$823$	23.8421	−	23.8421i	0.831084	−	0.831084i	0.987665	+	0.156581i	$0.0500473\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−27.1537	+	27.1537i	−0.944228	+	0.944228i	−0.998525	−	0.0542972i	$-0.982708\pi$
$827$	−27.1537	+	27.1537i	−0.944228	+	0.944228i	0.0542972	+	0.998525i	$0.482708\pi$
$828$		0			0
$829$		−	31.9479i		−	1.10960i	−0.831985	−	0.554798i	$-0.812796\pi$
$829$		−	31.9479i		−	1.10960i	0.831985	−	0.554798i	$-0.187204\pi$
$830$		0			0
$831$	−14.7598	+	6.52349i	−0.512011	+	0.226297i
$832$		0			0
$833$	−0.0645540	−	0.0645540i	−0.00223666	−	0.00223666i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	22.4894	−	11.2291i	0.777349	−	0.388133i
$838$		0			0
$839$	13.2631			0.457894			0.228947	−	0.973439i	$-0.426472\pi$
$839$	13.2631			0.457894			0.228947	+	0.973439i	$0.426472\pi$
$840$		0			0
$841$	−25.8093			−0.889977
$842$		0			0
$843$	−19.3992	−	7.50719i	−0.668146	−	0.258561i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.10383	−	5.10383i	−0.175370	−	0.175370i
$848$		0			0
$849$	14.2964	+	32.3463i	0.490650	+	1.11012i
$850$		0			0
$851$			23.1749i			0.794425i
$852$		0			0
$853$	−19.6625	+	19.6625i	−0.673231	+	0.673231i	−0.958459	−	0.285229i	$-0.907930\pi$
$853$	−19.6625	+	19.6625i	−0.673231	+	0.673231i	0.285229	+	0.958459i	$0.407930\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.7822	−	23.7822i	0.812385	−	0.812385i	−0.172606	−	0.984991i	$-0.555219\pi$
$857$	23.7822	−	23.7822i	0.812385	−	0.812385i	0.984991	+	0.172606i	$0.0552188\pi$
$858$		0			0
$859$		−	49.5637i		−	1.69109i	−0.533903	−	0.845546i	$-0.679275\pi$
$859$		−	49.5637i		−	1.69109i	0.533903	−	0.845546i	$-0.320725\pi$
$860$		0			0
$861$	8.71207	+	19.7115i	0.296907	+	0.671768i
$862$		0			0
$863$	−6.89758	−	6.89758i	−0.234796	−	0.234796i	0.579895	−	0.814691i	$-0.303094\pi$
$863$	−6.89758	−	6.89758i	−0.234796	−	0.234796i	−0.814691	+	0.579895i	$0.803094\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−27.4469	−	10.6215i	−0.932146	−	0.360725i
$868$		0			0
$869$	18.9637			0.643298
$870$		0			0
$871$	−0.523499			−0.0177381
$872$		0			0
$873$	−2.39490	−	50.9966i	−0.0810550	−	1.72597i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.8291	+	12.8291i	0.433207	+	0.433207i	0.889718	−	0.456511i	$-0.150901\pi$
$877$	12.8291	+	12.8291i	0.433207	+	0.433207i	−0.456511	+	0.889718i	$0.650901\pi$
$878$		0			0
$879$	40.4438	−	17.8753i	1.36414	−	0.602918i
$880$		0			0
$881$			16.7935i			0.565786i	0.959151	+	0.282893i	$0.0912942\pi$
$881$			16.7935i			0.565786i	−0.959151	+	0.282893i	$0.908706\pi$
$882$		0			0
$883$	11.2235	−	11.2235i	0.377700	−	0.377700i	−0.492572	−	0.870272i	$-0.663943\pi$
$883$	11.2235	−	11.2235i	0.377700	−	0.377700i	0.870272	+	0.492572i	$0.163943\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.0458	−	15.0458i	0.505189	−	0.505189i	−0.407857	−	0.913046i	$-0.633724\pi$
$887$	15.0458	−	15.0458i	0.505189	−	0.505189i	0.913046	+	0.407857i	$0.133724\pi$
$888$		0			0
$889$		−	1.55052i		−	0.0520028i
$890$		0			0
$891$	17.4258	−	1.64032i	0.583787	−	0.0549527i
$892$		0			0
$893$	3.09802	+	3.09802i	0.103671	+	0.103671i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.05051	−	2.71462i	0.0350756	−	0.0906385i
$898$		0			0
$899$	8.64116			0.288199
$900$		0			0
$901$	0.354721			0.0118175
$902$		0			0
$903$	−4.37806	+	11.3133i	−0.145693	+	0.376483i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	35.1729	+	35.1729i	1.16790	+	1.16790i	0.982702	+	0.185196i	$0.0592921\pi$
$907$	35.1729	+	35.1729i	1.16790	+	1.16790i	0.185196	+	0.982702i	$0.440708\pi$
$908$		0			0
$909$	22.1729	−	24.3580i	0.735427	−	0.807905i
$910$		0			0
$911$			32.7744i			1.08586i	0.839777	+	0.542931i	$0.182686\pi$
$911$			32.7744i			1.08586i	−0.839777	+	0.542931i	$0.817314\pi$
$912$		0			0
$913$	−22.8050	+	22.8050i	−0.754734	+	0.754734i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.566595	−	0.566595i	0.0187106	−	0.0187106i
$918$		0			0
$919$			26.0194i			0.858299i	0.903233	+	0.429150i	$0.141187\pi$
$919$			26.0194i			0.858299i	−0.903233	+	0.429150i	$0.858813\pi$
$920$		0			0
$921$	−3.11377	+	1.37622i	−0.102602	+	0.0453479i
$922$		0			0
$923$	4.13977	+	4.13977i	0.136262	+	0.136262i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.55103	−	0.354611i	0.248008	−	0.0116470i
$928$		0			0
$929$	9.53028			0.312678			0.156339	−	0.987703i	$-0.450031\pi$
$929$	9.53028			0.312678			0.156339	+	0.987703i	$0.450031\pi$
$930$		0			0
$931$	0.513741			0.0168372
$932$		0			0
$933$	−35.8670	−	13.8799i	−1.17423	−	0.454409i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	25.8481	+	25.8481i	0.844421	+	0.844421i	0.989430	−	0.145009i	$-0.0463211\pi$
$937$	25.8481	+	25.8481i	0.844421	+	0.844421i	−0.145009	+	0.989430i	$0.546321\pi$
$938$		0			0
$939$	23.9063	+	54.0893i	0.780152	+	1.76514i
$940$		0			0
$941$			12.5997i			0.410738i	0.978685	+	0.205369i	$0.0658394\pi$
$941$			12.5997i			0.410738i	−0.978685	+	0.205369i	$0.934161\pi$
$942$		0			0
$943$	−25.7834	+	25.7834i	−0.839624	+	0.839624i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22.7418	+	22.7418i	−0.739009	+	0.739009i	−0.972386	−	0.233378i	$-0.925022\pi$
$947$	−22.7418	+	22.7418i	−0.739009	+	0.739009i	0.233378	+	0.972386i	$0.425022\pi$
$948$		0			0
$949$			5.44551i			0.176769i
$950$		0			0
$951$	2.92749	+	6.62362i	0.0949305	+	0.214786i
$952$		0			0
$953$	−0.732678	−	0.732678i	−0.0237338	−	0.0237338i	0.695140	−	0.718874i	$-0.255342\pi$
$953$	−0.732678	−	0.732678i	−0.0237338	−	0.0237338i	−0.718874	+	0.695140i	$0.755342\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	5.61132	+	2.17149i	0.181388	+	0.0701942i
$958$		0			0
$959$	−8.75269			−0.282639
$960$		0			0
$961$	−7.59751			−0.245081
$962$		0			0
$963$	41.3930	−	1.94389i	1.33387	−	0.0626411i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−14.8198	−	14.8198i	−0.476572	−	0.476572i	0.427461	−	0.904034i	$-0.359408\pi$
$967$	−14.8198	−	14.8198i	−0.476572	−	0.476572i	−0.904034	+	0.427461i	$0.859408\pi$
$968$		0			0
$969$	−0.0743013	+	0.0328395i	−0.00238690	+	0.00105496i
$970$		0			0
$971$			27.9976i			0.898487i	0.893409	+	0.449244i	$0.148306\pi$
$971$			27.9976i			0.898487i	−0.893409	+	0.449244i	$0.851694\pi$
$972$		0			0
$973$	12.7819	−	12.7819i	0.409769	−	0.409769i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.7544	+	21.7544i	−0.695986	+	0.695986i	−0.963542	−	0.267556i	$-0.913784\pi$
$977$	−21.7544	+	21.7544i	−0.695986	+	0.695986i	0.267556	+	0.963542i	$0.413784\pi$
$978$		0			0
$979$			4.70644i			0.150419i
$980$		0			0
$981$	12.3157	−	13.5294i	0.393210	−	0.431962i
$982$		0			0
$983$	−28.8057	−	28.8057i	−0.918759	−	0.918759i	0.0781807	−	0.996939i	$-0.475089\pi$
$983$	−28.8057	−	28.8057i	−0.918759	−	0.918759i	−0.996939	+	0.0781807i	$0.975089\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.33095	+	13.7756i	−0.169686	+	0.438484i
$988$		0			0
$989$	−20.5249			−0.652653
$990$		0			0
$991$	8.20377			0.260601			0.130301	−	0.991475i	$-0.458406\pi$
$991$	8.20377			0.260601			0.130301	+	0.991475i	$0.458406\pi$
$992$		0			0
$993$	15.2552	−	39.4207i	0.484108	−	1.25098i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.14423	−	4.14423i	−0.131249	−	0.131249i	0.638430	−	0.769680i	$-0.279584\pi$
$997$	−4.14423	−	4.14423i	−0.131249	−	0.131249i	−0.769680	+	0.638430i	$0.779584\pi$
$998$		0			0
$999$	38.9755	+	13.0160i	1.23313	+	0.411807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.b.1457.4		24
3.2	odd	2	inner	2100.2.s.b.1457.2		24
5.2	odd	4		420.2.s.a.113.11	yes	24
5.3	odd	4	inner	2100.2.s.b.1793.2		24
5.4	even	2		420.2.s.a.197.9	yes	24
15.2	even	4		420.2.s.a.113.9	✓	24
15.8	even	4	inner	2100.2.s.b.1793.4		24
15.14	odd	2		420.2.s.a.197.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.s.a.113.9	✓	24	15.2	even	4
420.2.s.a.113.11	yes	24	5.2	odd	4
420.2.s.a.197.9	yes	24	5.4	even	2
420.2.s.a.197.11	yes	24	15.14	odd	2
2100.2.s.b.1457.2		24	3.2	odd	2	inner
2100.2.s.b.1457.4		24	1.1	even	1	trivial
2100.2.s.b.1793.2		24	5.3	odd	4	inner
2100.2.s.b.1793.4		24	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.625101 + 1.61532i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.21850 - 2.01947i) q^{9} +O(q^{10})\)	\(q+(-0.625101 + 1.61532i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.21850 - 2.01947i) q^{9} -1.94476i q^{11} +(-0.405496 + 0.405496i) q^{13} +(-0.0645540 + 0.0645540i) q^{17} -0.513741i q^{19} +(1.58421 - 0.700188i) q^{21} +(2.07221 + 2.07221i) q^{23} +(4.64887 - 2.32120i) q^{27} +1.78624 q^{29} +4.83761 q^{31} +(3.14140 + 1.21567i) q^{33} +(5.59183 + 5.59183i) q^{37} +(-0.401529 - 0.908482i) q^{39} +12.4425i q^{41} +(-4.95241 + 4.95241i) q^{43} +(-6.03030 + 6.03030i) q^{47} +1.00000i q^{49} +(-0.0639223 - 0.144628i) q^{51} +(-2.74748 - 2.74748i) q^{53} +(0.829855 + 0.321140i) q^{57} +12.3481 q^{59} +12.0067 q^{61} +(0.140731 + 2.99670i) q^{63} +(0.645504 + 0.645504i) q^{67} +(-4.64262 + 2.05194i) q^{69} -10.2091i q^{71} +(6.71462 - 6.71462i) q^{73} +(-1.37515 + 1.37515i) q^{77} +9.75115i q^{79} +(0.843455 + 8.96039i) q^{81} +(-11.7264 - 11.7264i) q^{83} +(-1.11658 + 2.88535i) q^{87} -2.42006 q^{89} +0.573459 q^{91} +(-3.02400 + 7.81428i) q^{93} +(12.0332 + 12.0332i) q^{97} +(-3.92739 + 4.31445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

Introduction

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