LMFDB - Embedded newform 2100.2.s.a.1793.7

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{12} + 424x^{8} - 159x^{4} + 16 $ x^16 + 24x^12 + 424x^8 - 159*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1793.7
Root			$0.0465948 + 0.660512i$ of defining polynomial
Character	$\chi$	$=$	2100.1793
Dual form			2100.2.s.a.1457.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64534 - 0.541157i) q^{3} +(0.707107 - 0.707107i) q^{7} +(2.41430 - 1.78078i) q^{9} +O(q^{10})$	$q+(1.64534 - 0.541157i) q^{3} +(0.707107 - 0.707107i) q^{7} +(2.41430 - 1.78078i) q^{9} -3.09218i q^{11} +(0.310029 + 0.310029i) q^{13} +(-3.41433 - 3.41433i) q^{17} -1.12311i q^{19} +(0.780776 - 1.54609i) q^{21} +(1.22783 - 1.22783i) q^{23} +(3.00867 - 4.23650i) q^{27} +1.35576 q^{29} -8.24621 q^{31} +(-1.67335 - 5.08769i) q^{33} +(2.20837 - 2.20837i) q^{37} +(0.677878 + 0.342329i) q^{39} -6.18435i q^{41} +(7.24517 + 7.24517i) q^{43} +(-2.18650 - 2.18650i) q^{47} -1.00000i q^{49} +(-7.46543 - 3.77005i) q^{51} +(-1.22783 + 1.22783i) q^{53} +(-0.607777 - 1.84789i) q^{57} +9.65719 q^{59} -5.12311 q^{61} +(0.447967 - 2.96637i) q^{63} +(-7.86522 + 7.86522i) q^{67} +(1.35576 - 2.68466i) q^{69} -14.1051i q^{71} +(4.24264 + 4.24264i) q^{73} +(-2.18650 - 2.18650i) q^{77} +5.56155i q^{79} +(2.65767 - 8.59865i) q^{81} +(1.22783 - 1.22783i) q^{83} +(2.23068 - 0.733677i) q^{87} +12.3687 q^{89} +0.438447 q^{91} +(-13.5678 + 4.46250i) q^{93} +(2.51840 - 2.51840i) q^{97} +(-5.50647 - 7.46543i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{21} - 4 q^{51} - 16 q^{61} + 92 q^{81} + 40 q^{91}+O(q^{100}) $ 16 * q - 4 * q^21 - 4 * q^51 - 16 * q^61 + 92 * q^81 + 40 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.64534	−	0.541157i	0.949938	−	0.312437i
$3$	1.64534	−	0.541157i	0.949938	−	0.312437i
$4$		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
$9$	2.41430	−	1.78078i	0.804766	−	0.593592i
$10$		0			0
$11$		−	3.09218i		−	0.932326i	−0.884699	−	0.466163i	$-0.845636\pi$
$11$		−	3.09218i		−	0.932326i	0.884699	−	0.466163i	$-0.154364\pi$
$12$		0			0
$13$	0.310029	+	0.310029i	0.0859866	+	0.0859866i	0.748792	−	0.662805i	$-0.230634\pi$
$13$	0.310029	+	0.310029i	0.0859866	+	0.0859866i	−0.662805	+	0.748792i	$0.730634\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.41433	−	3.41433i	−0.828097	−	0.828097i	0.159156	−	0.987253i	$-0.449123\pi$
$17$	−3.41433	−	3.41433i	−0.828097	−	0.828097i	−0.987253	+	0.159156i	$0.949123\pi$
$18$		0			0
$19$		−	1.12311i		−	0.257658i	−0.991667	−	0.128829i	$-0.958878\pi$
$19$		−	1.12311i		−	0.257658i	0.991667	−	0.128829i	$-0.0411218\pi$
$20$		0			0
$21$	0.780776	−	1.54609i	0.170379	−	0.337384i
$22$		0			0
$23$	1.22783	−	1.22783i	0.256021	−	0.256021i	−0.567413	−	0.823434i	$-0.692055\pi$
$23$	1.22783	−	1.22783i	0.256021	−	0.256021i	0.823434	+	0.567413i	$0.192055\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.00867	−	4.23650i	0.579018	−	0.815315i
$28$		0			0
$29$	1.35576			0.251758			0.125879	−	0.992046i	$-0.459825\pi$
$29$	1.35576			0.251758			0.125879	+	0.992046i	$0.459825\pi$
$30$		0			0
$31$	−8.24621			−1.48106			−0.740532	−	0.672022i	$-0.765426\pi$
$31$	−8.24621			−1.48106			−0.740532	+	0.672022i	$0.765426\pi$
$32$		0			0
$33$	−1.67335	−	5.08769i	−0.291293	−	0.885652i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.20837	−	2.20837i	0.363054	−	0.363054i	−0.501882	−	0.864936i	$-0.667359\pi$
$37$	2.20837	−	2.20837i	0.363054	−	0.363054i	0.864936	+	0.501882i	$0.167359\pi$
$38$		0			0
$39$	0.677878	+	0.342329i	0.108547	+	0.0548165i
$40$		0			0
$41$		−	6.18435i		−	0.965834i	−0.875666	−	0.482917i	$-0.839577\pi$
$41$		−	6.18435i		−	0.965834i	0.875666	−	0.482917i	$-0.160423\pi$
$42$		0			0
$43$	7.24517	+	7.24517i	1.10488	+	1.10488i	0.993813	+	0.111064i	$0.0354259\pi$
$43$	7.24517	+	7.24517i	1.10488	+	1.10488i	0.111064	+	0.993813i	$0.464574\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.18650	−	2.18650i	−0.318934	−	0.318934i	0.529424	−	0.848357i	$-0.322408\pi$
$47$	−2.18650	−	2.18650i	−0.318934	−	0.318934i	−0.848357	+	0.529424i	$0.822408\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−7.46543	−	3.77005i	−1.04537	−	0.527913i
$52$		0			0
$53$	−1.22783	+	1.22783i	−0.168656	+	0.168656i	−0.786388	−	0.617732i	$-0.788052\pi$
$53$	−1.22783	+	1.22783i	−0.168656	+	0.168656i	0.617732	+	0.786388i	$0.288052\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.607777	−	1.84789i	−0.0805020	−	0.244759i
$58$		0			0
$59$	9.65719			1.25726			0.628630	−	0.777705i	$-0.283616\pi$
$59$	9.65719			1.25726			0.628630	+	0.777705i	$0.283616\pi$
$60$		0			0
$61$	−5.12311			−0.655946			−0.327973	−	0.944687i	$-0.606366\pi$
$61$	−5.12311			−0.655946			−0.327973	+	0.944687i	$0.606366\pi$
$62$		0			0
$63$	0.447967	−	2.96637i	0.0564386	−	0.373727i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.86522	+	7.86522i	−0.960890	+	0.960890i	−0.999263	−	0.0383735i	$-0.987782\pi$
$67$	−7.86522	+	7.86522i	−0.960890	+	0.960890i	0.0383735	+	0.999263i	$0.487782\pi$
$68$		0			0
$69$	1.35576	−	2.68466i	0.163214	−	0.323195i
$70$		0			0
$71$		−	14.1051i		−	1.67397i	−0.547226	−	0.836985i	$-0.684316\pi$
$71$		−	14.1051i		−	1.67397i	0.547226	−	0.836985i	$-0.315684\pi$
$72$		0			0
$73$	4.24264	+	4.24264i	0.496564	+	0.496564i	0.910366	−	0.413803i	$-0.135800\pi$
$73$	4.24264	+	4.24264i	0.496564	+	0.496564i	−0.413803	+	0.910366i	$0.635800\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.18650	−	2.18650i	−0.249175	−	0.249175i
$78$		0			0
$79$			5.56155i			0.625724i	0.949799	+	0.312862i	$0.101288\pi$
$79$			5.56155i			0.625724i	−0.949799	+	0.312862i	$0.898712\pi$
$80$		0			0
$81$	2.65767	−	8.59865i	0.295297	−	0.955406i
$82$		0			0
$83$	1.22783	−	1.22783i	0.134772	−	0.134772i	−0.636502	−	0.771275i	$-0.719619\pi$
$83$	1.22783	−	1.22783i	0.134772	−	0.134772i	0.771275	+	0.636502i	$0.219619\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.23068	−	0.733677i	0.239154	−	0.0786584i
$88$		0			0
$89$	12.3687			1.31108			0.655540	−	0.755160i	$-0.272441\pi$
$89$	12.3687			1.31108			0.655540	+	0.755160i	$0.272441\pi$
$90$		0			0
$91$	0.438447			0.0459618
$92$		0			0
$93$	−13.5678	+	4.46250i	−1.40692	+	0.462739i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.51840	−	2.51840i	0.255705	−	0.255705i	−0.567600	−	0.823305i	$-0.692128\pi$
$97$	2.51840	−	2.51840i	0.255705	−	0.255705i	0.823305	+	0.567600i	$0.192128\pi$
$98$		0			0
$99$	−5.50647	−	7.46543i	−0.553421	−	0.750304i
$100$		0			0
$101$			3.47284i			0.345561i	0.984960	+	0.172780i	$0.0552751\pi$
$101$			3.47284i			0.345561i	−0.984960	+	0.172780i	$0.944725\pi$
$102$		0			0
$103$	−2.69250	−	2.69250i	−0.265299	−	0.265299i	0.561903	−	0.827203i	$-0.310069\pi$
$103$	−2.69250	−	2.69250i	−0.265299	−	0.265299i	−0.827203	+	0.561903i	$0.810069\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.3468	+	14.3468i	1.38696	+	1.38696i	0.831630	+	0.555330i	$0.187408\pi$
$107$	14.3468	+	14.3468i	1.38696	+	1.38696i	0.555330	+	0.831630i	$0.312592\pi$
$108$		0			0
$109$		−	12.9309i		−	1.23855i	−0.785173	−	0.619276i	$-0.787426\pi$
$109$		−	12.9309i		−	1.23855i	0.785173	−	0.619276i	$-0.212574\pi$
$110$		0			0
$111$	2.43845	−	4.82860i	0.231447	−	0.458310i
$112$		0			0
$113$	−1.22783	+	1.22783i	−0.115505	+	0.115505i	−0.762497	−	0.646992i	$-0.776027\pi$
$113$	−1.22783	+	1.22783i	−0.115505	+	0.115505i	0.646992	+	0.762497i	$0.276027\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.30059	+	0.196410i	0.120240	+	0.0181581i
$118$		0			0
$119$	−4.82860			−0.442637
$120$		0			0
$121$	1.43845			0.130768
$122$		0			0
$123$	−3.34671	−	10.1754i	−0.301762	−	0.917482i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.27691	+	6.27691i	−0.556986	+	0.556986i	−0.928448	−	0.371462i	$-0.878857\pi$
$127$	−6.27691	+	6.27691i	−0.556986	+	0.556986i	0.371462	+	0.928448i	$0.378857\pi$
$128$		0			0
$129$	15.8415	+	8.00000i	1.39477	+	0.704361i
$130$		0			0
$131$		−	18.5531i		−	1.62099i	−0.585747	−	0.810494i	$-0.699199\pi$
$131$		−	18.5531i		−	1.62099i	0.585747	−	0.810494i	$-0.300801\pi$
$132$		0			0
$133$	−0.794156	−	0.794156i	−0.0688620	−	0.0688620i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.14516	−	3.14516i	−0.268709	−	0.268709i	0.559871	−	0.828580i	$-0.310851\pi$
$137$	−3.14516	−	3.14516i	−0.268709	−	0.268709i	−0.828580	+	0.559871i	$0.810851\pi$
$138$		0			0
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$		0			0
$141$	−4.78078	−	2.41430i	−0.402614	−	0.203321i
$142$		0			0
$143$	0.958664	−	0.958664i	0.0801675	−	0.0801675i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.541157	−	1.64534i	−0.0446339	−	0.135705i
$148$		0			0
$149$	15.8415			1.29779			0.648895	−	0.760878i	$-0.275231\pi$
$149$	15.8415			1.29779			0.648895	+	0.760878i	$0.275231\pi$
$150$		0			0
$151$	−5.56155			−0.452593			−0.226296	−	0.974058i	$-0.572662\pi$
$151$	−5.56155			−0.452593			−0.226296	+	0.974058i	$0.572662\pi$
$152$		0			0
$153$	−14.3234	−	2.16305i	−1.15798	−	0.174873i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.4878	+	11.4878i	−0.916827	+	0.916827i	−0.996797	−	0.0799705i	$-0.974517\pi$
$157$	−11.4878	+	11.4878i	−0.916827	+	0.916827i	0.0799705	+	0.996797i	$0.474517\pi$
$158$		0			0
$159$	−1.35576	+	2.68466i	−0.107518	+	0.212907i
$160$		0			0
$161$		−	1.73642i		−	0.136849i
$162$		0			0
$163$	10.6937	+	10.6937i	0.837591	+	0.837591i	0.988541	−	0.150950i	$-0.0482333\pi$
$163$	10.6937	+	10.6937i	0.837591	+	0.837591i	−0.150950	+	0.988541i	$0.548233\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.3882	+	13.3882i	1.03601	+	1.03601i	0.999327	+	0.0366800i	$0.0116782\pi$
$167$	13.3882	+	13.3882i	1.03601	+	1.03601i	0.0366800	+	0.999327i	$0.488322\pi$
$168$		0			0
$169$		−	12.8078i		−	0.985213i
$170$		0			0
$171$	−2.00000	−	2.71151i	−0.152944	−	0.207354i
$172$		0			0
$173$	0.958664	−	0.958664i	0.0728859	−	0.0728859i	−0.669724	−	0.742610i	$-0.733588\pi$
$173$	0.958664	−	0.958664i	0.0728859	−	0.0728859i	0.742610	+	0.669724i	$0.233588\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	15.8894	−	5.22606i	1.19432	−	0.392815i
$178$		0			0
$179$	−17.5780			−1.31384			−0.656919	−	0.753961i	$-0.728141\pi$
$179$	−17.5780			−1.31384			−0.656919	+	0.753961i	$0.728141\pi$
$180$		0			0
$181$	−12.2462			−0.910254			−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462			−0.910254			−0.455127	+	0.890427i	$0.650406\pi$
$182$		0			0
$183$	−8.42926	+	2.77240i	−0.623109	+	0.204942i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.5577	+	10.5577i	−0.772057	+	0.772057i
$188$		0			0
$189$	−0.868210	−	5.12311i	−0.0631530	−	0.372651i
$190$		0			0
$191$			6.56502i			0.475028i	0.971384	+	0.237514i	$0.0763325\pi$
$191$			6.56502i			0.475028i	−0.971384	+	0.237514i	$0.923667\pi$
$192$		0			0
$193$	8.48528	+	8.48528i	0.610784	+	0.610784i	0.943150	−	0.332366i	$-0.107847\pi$
$193$	8.48528	+	8.48528i	0.610784	+	0.610784i	−0.332366	+	0.943150i	$0.607847\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.97383	+	9.97383i	0.710606	+	0.710606i	0.966662	−	0.256056i	$-0.0824232\pi$
$197$	9.97383	+	9.97383i	0.710606	+	0.710606i	−0.256056	+	0.966662i	$0.582423\pi$
$198$		0			0
$199$			22.4924i			1.59445i	0.603685	+	0.797223i	$0.293698\pi$
$199$			22.4924i			1.59445i	−0.603685	+	0.797223i	$0.706302\pi$
$200$		0			0
$201$	−8.68466	+	17.1973i	−0.612569	+	1.21300i
$202$		0			0
$203$	0.958664	−	0.958664i	0.0672850	−	0.0672850i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.777860	−	5.15086i	0.0540650	−	0.358009i
$208$		0			0
$209$	−3.47284			−0.240221
$210$		0			0
$211$	7.31534			0.503609			0.251804	−	0.967778i	$-0.418976\pi$
$211$	7.31534			0.503609			0.251804	+	0.967778i	$0.418976\pi$
$212$		0			0
$213$	−7.63309	−	23.2077i	−0.523011	−	1.59017i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.83095	+	5.83095i	−0.395831	+	0.395831i
$218$		0			0
$219$	9.27653	+	4.68466i	0.626850	+	0.316560i
$220$		0			0
$221$		−	2.11708i		−	0.142411i
$222$		0			0
$223$	14.0062	+	14.0062i	0.937925	+	0.937925i	0.998183	−	0.0602580i	$-0.0191924\pi$
$223$	14.0062	+	14.0062i	0.937925	+	0.937925i	−0.0602580	+	0.998183i	$0.519192\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.3055	−	15.3055i	−1.01586	−	1.01586i	−0.999872	−	0.0159889i	$-0.994910\pi$
$227$	−15.3055	−	15.3055i	−1.01586	−	1.01586i	−0.0159889	−	0.999872i	$-0.505090\pi$
$228$		0			0
$229$			8.24621i			0.544925i	0.962166	+	0.272462i	$0.0878381\pi$
$229$			8.24621i			0.544925i	−0.962166	+	0.272462i	$0.912162\pi$
$230$		0			0
$231$	−4.78078	−	2.41430i	−0.314552	−	0.158849i
$232$		0			0
$233$	−11.8912	+	11.8912i	−0.779016	+	0.779016i	−0.979663	−	0.200648i	$-0.935695\pi$
$233$	−11.8912	+	11.8912i	−0.779016	+	0.779016i	0.200648	+	0.979663i	$0.435695\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.00967	+	9.15065i	0.195499	+	0.594399i
$238$		0			0
$239$	−18.9337			−1.22472			−0.612360	−	0.790579i	$-0.709780\pi$
$239$	−18.9337			−1.22472			−0.612360	+	0.790579i	$0.709780\pi$
$240$		0			0
$241$	0.246211			0.0158599			0.00792993	−	0.999969i	$-0.497476\pi$
$241$	0.246211			0.0158599			0.00792993	+	0.999969i	$0.497476\pi$
$242$		0			0
$243$	−0.280444	−	15.5859i	−0.0179905	−	0.999838i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.348195	−	0.348195i	0.0221551	−	0.0221551i
$248$		0			0
$249$	1.35576	−	2.68466i	0.0859175	−	0.170133i
$250$		0			0
$251$		−	9.65719i		−	0.609557i	−0.952423	−	0.304778i	$-0.901418\pi$
$251$		−	9.65719i		−	0.609557i	0.952423	−	0.304778i	$-0.0985824\pi$
$252$		0			0
$253$	−3.79668	−	3.79668i	−0.238695	−	0.238695i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.9477	−	19.9477i	−1.24430	−	1.24430i	−0.958199	−	0.286101i	$-0.907641\pi$
$257$	−19.9477	−	19.9477i	−1.24430	−	1.24430i	−0.286101	−	0.958199i	$-0.592359\pi$
$258$		0			0
$259$		−	3.12311i		−	0.194060i
$260$		0			0
$261$	3.27320	−	2.41430i	0.202606	−	0.149441i
$262$		0			0
$263$	5.60083	−	5.60083i	0.345362	−	0.345362i	−0.513017	−	0.858379i	$-0.671472\pi$
$263$	5.60083	−	5.60083i	0.345362	−	0.345362i	0.858379	+	0.513017i	$0.171472\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	20.3507	−	6.69341i	1.24545	−	0.409630i
$268$		0			0
$269$	25.4987			1.55469			0.777343	−	0.629077i	$-0.216567\pi$
$269$	25.4987			1.55469			0.777343	+	0.629077i	$0.216567\pi$
$270$		0			0
$271$	17.1231			1.04015			0.520077	−	0.854119i	$-0.325903\pi$
$271$	17.1231			1.04015			0.520077	+	0.854119i	$0.325903\pi$
$272$		0			0
$273$	0.721395	−	0.237269i	0.0436608	−	0.0143602i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.6937	−	10.6937i	0.642519	−	0.642519i	−0.308655	−	0.951174i	$-0.599879\pi$
$277$	10.6937	−	10.6937i	0.642519	−	0.642519i	0.951174	+	0.308655i	$0.0998788\pi$
$278$		0			0
$279$	−19.9088	+	14.6847i	−1.19191	+	0.879148i
$280$		0			0
$281$			7.54011i			0.449805i	0.974381	+	0.224903i	$0.0722064\pi$
$281$			7.54011i			0.449805i	−0.974381	+	0.224903i	$0.927794\pi$
$282$		0			0
$283$	−3.31255	−	3.31255i	−0.196911	−	0.196911i	0.601763	−	0.798674i	$-0.294465\pi$
$283$	−3.31255	−	3.31255i	−0.196911	−	0.196911i	−0.798674	+	0.601763i	$0.794465\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.37300	−	4.37300i	−0.258130	−	0.258130i
$288$		0			0
$289$			6.31534i			0.371491i
$290$		0			0
$291$	2.78078	−	5.50647i	0.163012	−	0.322795i
$292$		0			0
$293$	−12.1603	+	12.1603i	−0.710414	+	0.710414i	−0.966622	−	0.256208i	$-0.917527\pi$
$293$	−12.1603	+	12.1603i	−0.710414	+	0.710414i	0.256208	+	0.966622i	$0.417527\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−13.1000	−	9.30332i	−0.760139	−	0.539834i
$298$		0			0
$299$	0.761329			0.0440288
$300$		0			0
$301$	10.2462			0.590582
$302$		0			0
$303$	1.87935	+	5.71401i	0.107966	+	0.328261i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−3.58442	+	3.58442i	−0.204573	+	0.204573i	−0.801956	−	0.597383i	$-0.796207\pi$
$307$	−3.58442	+	3.58442i	−0.204573	+	0.204573i	0.597383	+	0.801956i	$0.296207\pi$
$308$		0			0
$309$	−5.88714	−	2.97301i	−0.334908	−	0.169129i
$310$		0			0
$311$			28.2102i			1.59966i	0.600229	+	0.799828i	$0.295076\pi$
$311$			28.2102i			1.59966i	−0.600229	+	0.799828i	$0.704924\pi$
$312$		0			0
$313$	23.9057	+	23.9057i	1.35123	+	1.35123i	0.884288	+	0.466942i	$0.154644\pi$
$313$	23.9057	+	23.9057i	1.35123	+	1.35123i	0.466942	+	0.884288i	$0.345356\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.6372	+	20.6372i	1.15910	+	1.15910i	0.984670	+	0.174428i	$0.0558076\pi$
$317$	20.6372	+	20.6372i	1.15910	+	1.15910i	0.174428	+	0.984670i	$0.444192\pi$
$318$		0			0
$319$		−	4.19224i		−	0.234720i
$320$		0			0
$321$	31.3693	+	15.8415i	1.75086	+	0.884189i
$322$		0			0
$323$	−3.83466	+	3.83466i	−0.213366	+	0.213366i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.99763	−	21.2757i	−0.386970	−	1.17655i
$328$		0			0
$329$	−3.09218			−0.170477
$330$		0			0
$331$	−6.24621			−0.343323			−0.171661	−	0.985156i	$-0.554914\pi$
$331$	−6.24621			−0.343323			−0.171661	+	0.985156i	$0.554914\pi$
$332$		0			0
$333$	1.39905	−	9.26427i	0.0766675	−	0.507679i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.21342	−	8.21342i	0.447413	−	0.447413i	−0.447080	−	0.894494i	$-0.647536\pi$
$337$	8.21342	−	8.21342i	0.447413	−	0.447413i	0.894494	+	0.447080i	$0.147536\pi$
$338$		0			0
$339$	−1.35576	+	2.68466i	−0.0736346	+	0.145811i
$340$		0			0
$341$			25.4987i			1.38083i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−23.6312	−	23.6312i	−1.26859	−	1.26859i	−0.946818	−	0.321769i	$-0.895723\pi$
$347$	−23.6312	−	23.6312i	−1.26859	−	1.26859i	−0.321769	−	0.946818i	$-0.604277\pi$
$348$		0			0
$349$		−	19.3693i		−	1.03682i	−0.855133	−	0.518408i	$-0.826525\pi$
$349$		−	19.3693i		−	1.03682i	0.855133	−	0.518408i	$-0.173475\pi$
$350$		0			0
$351$	2.24621	−	0.380664i	0.119894	−	0.0203184i
$352$		0			0
$353$	16.5333	−	16.5333i	0.879980	−	0.879980i	−0.113552	−	0.993532i	$-0.536223\pi$
$353$	16.5333	−	16.5333i	0.879980	−	0.879980i	0.993532	+	0.113552i	$0.0362228\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.94469	+	2.61303i	−0.420478	+	0.138296i
$358$		0			0
$359$	−23.0010			−1.21395			−0.606973	−	0.794723i	$-0.707616\pi$
$359$	−23.0010			−1.21395			−0.606973	+	0.794723i	$0.707616\pi$
$360$		0			0
$361$	17.7386			0.933612
$362$		0			0
$363$	2.36674	−	0.778426i	0.124221	−	0.0408568i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.34935	+	8.34935i	−0.435833	+	0.435833i	−0.890607	−	0.454774i	$-0.849720\pi$
$367$	−8.34935	+	8.34935i	−0.435833	+	0.435833i	0.454774	+	0.890607i	$0.349720\pi$
$368$		0			0
$369$	−11.0129	−	14.9309i	−0.573311	−	0.777270i
$370$		0			0
$371$			1.73642i			0.0901504i
$372$		0			0
$373$	23.3238	+	23.3238i	1.20766	+	1.20766i	0.971783	+	0.235878i	$0.0757967\pi$
$373$	23.3238	+	23.3238i	1.20766	+	1.20766i	0.235878	+	0.971783i	$0.424203\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.420324	+	0.420324i	0.0216478	+	0.0216478i
$378$		0			0
$379$			16.4924i			0.847159i	0.905859	+	0.423579i	$0.139227\pi$
$379$			16.4924i			0.847159i	−0.905859	+	0.423579i	$0.860773\pi$
$380$		0			0
$381$	−6.93087	+	13.7245i	−0.355079	+	0.703125i
$382$		0			0
$383$	18.7198	−	18.7198i	0.956538	−	0.956538i	−0.0425558	−	0.999094i	$-0.513550\pi$
$383$	18.7198	−	18.7198i	0.956538	−	0.956538i	0.999094	+	0.0425558i	$0.0135500\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	30.3940	+	4.58997i	1.54501	+	0.233321i
$388$		0			0
$389$	1.35576			0.0687396			0.0343698	−	0.999409i	$-0.489058\pi$
$389$	1.35576			0.0687396			0.0343698	+	0.999409i	$0.489058\pi$
$390$		0			0
$391$	−8.38447			−0.424021
$392$		0			0
$393$	−10.0401	−	30.5261i	−0.506457	−	1.53984i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.52345	+	8.52345i	−0.427780	+	0.427780i	−0.887871	−	0.460092i	$-0.847816\pi$
$397$	−8.52345	+	8.52345i	−0.427780	+	0.427780i	0.460092	+	0.887871i	$0.347816\pi$
$398$		0			0
$399$	−1.73642	−	0.876894i	−0.0869297	−	0.0438996i
$400$		0			0
$401$			19.9088i			0.994199i	0.867694	+	0.497099i	$0.165602\pi$
$401$			19.9088i			0.994199i	−0.867694	+	0.497099i	$0.834398\pi$
$402$		0			0
$403$	−2.55656	−	2.55656i	−0.127352	−	0.127352i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.82867	−	6.82867i	−0.338484	−	0.338484i
$408$		0			0
$409$		−	5.12311i		−	0.253321i	−0.991946	−	0.126661i	$-0.959574\pi$
$409$		−	5.12311i		−	0.253321i	0.991946	−	0.126661i	$-0.0404259\pi$
$410$		0			0
$411$	−6.87689	−	3.47284i	−0.339212	−	0.171303i
$412$		0			0
$413$	6.82867	−	6.82867i	0.336017	−	0.336017i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.41157	−	16.4534i	−0.265006	−	0.805727i
$418$		0			0
$419$	−9.65719			−0.471785			−0.235892	−	0.971779i	$-0.575801\pi$
$419$	−9.65719			−0.471785			−0.235892	+	0.971779i	$0.575801\pi$
$420$		0			0
$421$	23.1771			1.12958			0.564791	−	0.825234i	$-0.308957\pi$
$421$	23.1771			1.12958			0.564791	+	0.825234i	$0.308957\pi$
$422$		0			0
$423$	−9.17252	−	1.38519i	−0.445983	−	0.0673505i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.62258	+	3.62258i	−0.175309	+	0.175309i
$428$		0			0
$429$	1.05854	−	2.09612i	0.0511069	−	0.101202i
$430$		0			0
$431$			18.9337i			0.912005i	0.889978	+	0.456003i	$0.150719\pi$
$431$			18.9337i			0.912005i	−0.889978	+	0.456003i	$0.849281\pi$
$432$		0			0
$433$	14.3162	+	14.3162i	0.687994	+	0.687994i	0.961788	−	0.273794i	$-0.0882787\pi$
$433$	14.3162	+	14.3162i	0.687994	+	0.687994i	−0.273794	+	0.961788i	$0.588279\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.37899	−	1.37899i	−0.0659659	−	0.0659659i
$438$		0			0
$439$			22.4924i			1.07350i	0.843740	+	0.536752i	$0.180349\pi$
$439$			22.4924i			1.07350i	−0.843740	+	0.536752i	$0.819651\pi$
$440$		0			0
$441$	−1.78078	−	2.41430i	−0.0847989	−	0.114967i
$442$		0			0
$443$	−28.0042	+	28.0042i	−1.33052	+	1.33052i	−0.425612	+	0.904906i	$0.639941\pi$
$443$	−28.0042	+	28.0042i	−1.33052	+	1.33052i	−0.904906	+	0.425612i	$0.860059\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	26.0648	−	8.57276i	1.23282	−	0.405478i
$448$		0			0
$449$	−4.82860			−0.227876			−0.113938	−	0.993488i	$-0.536346\pi$
$449$	−4.82860			−0.227876			−0.113938	+	0.993488i	$0.536346\pi$
$450$		0			0
$451$	−19.1231			−0.900472
$452$		0			0
$453$	−9.15065	+	3.00967i	−0.429935	+	0.141407i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	26.7723	−	26.7723i	1.25236	−	1.25236i	0.297694	−	0.954661i	$-0.403783\pi$
$457$	26.7723	−	26.7723i	1.25236	−	1.25236i	0.954661	−	0.297694i	$-0.0962174\pi$
$458$		0			0
$459$	−24.7374	+	4.19224i	−1.15464	+	0.195677i
$460$		0			0
$461$			24.7374i			1.15214i	0.817402	+	0.576068i	$0.195414\pi$
$461$			24.7374i			1.15214i	−0.817402	+	0.576068i	$0.804586\pi$
$462$		0			0
$463$	1.58831	+	1.58831i	0.0738151	+	0.0738151i	0.743050	−	0.669235i	$-0.233378\pi$
$463$	1.58831	+	1.58831i	0.0738151	+	0.0738151i	−0.669235	+	0.743050i	$0.733378\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.64816	−	1.64816i	−0.0762677	−	0.0762677i	0.667944	−	0.744212i	$-0.267175\pi$
$467$	−1.64816	−	1.64816i	−0.0762677	−	0.0762677i	−0.744212	+	0.667944i	$0.767175\pi$
$468$		0			0
$469$			11.1231i			0.513617i
$470$		0			0
$471$	−12.6847	+	25.1181i	−0.584478	+	1.15738i
$472$		0			0
$473$	22.4033	−	22.4033i	1.03011	−	1.03011i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.777860	+	5.15086i	−0.0356158	+	0.235842i
$478$		0			0
$479$	−30.9218			−1.41285			−0.706426	−	0.707787i	$-0.749694\pi$
$479$	−30.9218			−1.41285			−0.706426	+	0.707787i	$0.749694\pi$
$480$		0			0
$481$	1.36932			0.0624355
$482$		0			0
$483$	−0.939676	−	2.85700i	−0.0427567	−	0.129998i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−25.1840	+	25.1840i	−1.14120	+	1.14120i	−0.152963	+	0.988232i	$0.548882\pi$
$487$	−25.1840	+	25.1840i	−1.14120	+	1.14120i	−0.988232	+	0.152963i	$0.951118\pi$
$488$		0			0
$489$	23.3817	+	11.8078i	1.05735	+	0.533966i
$490$		0			0
$491$		−	9.27653i		−	0.418644i	−0.977847	−	0.209322i	$-0.932874\pi$
$491$		−	9.27653i		−	0.418644i	0.977847	−	0.209322i	$-0.0671257\pi$
$492$		0			0
$493$	−4.62900	−	4.62900i	−0.208480	−	0.208480i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.97383	−	9.97383i	−0.447387	−	0.447387i
$498$		0			0
$499$			14.0540i			0.629142i	0.949234	+	0.314571i	$0.101861\pi$
$499$			14.0540i			0.629142i	−0.949234	+	0.314571i	$0.898139\pi$
$500$		0			0
$501$	29.2732	+	14.7830i	1.30783	+	0.660456i
$502$		0			0
$503$	−11.4708	+	11.4708i	−0.511459	+	0.511459i	−0.914973	−	0.403514i	$-0.867789\pi$
$503$	−11.4708	+	11.4708i	−0.511459	+	0.511459i	0.403514	+	0.914973i	$0.367789\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.93101	−	21.0731i	−0.307817	−	0.935891i
$508$		0			0
$509$	−13.1300			−0.581978			−0.290989	−	0.956726i	$-0.593984\pi$
$509$	−13.1300			−0.581978			−0.290989	+	0.956726i	$0.593984\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$	−4.75804	−	3.37905i	−0.210072	−	0.149189i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−6.76104	+	6.76104i	−0.297350	+	0.297350i
$518$		0			0
$519$	1.05854	−	2.09612i	0.0464648	−	0.0920094i
$520$		0			0
$521$			8.89586i			0.389735i	0.980830	+	0.194867i	$0.0624277\pi$
$521$			8.89586i			0.389735i	−0.980830	+	0.194867i	$0.937572\pi$
$522$		0			0
$523$	−17.3188	−	17.3188i	−0.757296	−	0.757296i	0.218533	−	0.975830i	$-0.429873\pi$
$523$	−17.3188	−	17.3188i	−0.757296	−	0.757296i	−0.975830	+	0.218533i	$0.929873\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	28.1553	+	28.1553i	1.22646	+	1.22646i
$528$		0			0
$529$			19.9848i			0.868906i
$530$		0			0
$531$	23.3153	−	17.1973i	1.01180	−	0.746299i
$532$		0			0
$533$	1.91733	−	1.91733i	0.0830487	−	0.0830487i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−28.9218	+	9.51244i	−1.24807	+	0.410492i
$538$		0			0
$539$	−3.09218			−0.133189
$540$		0			0
$541$	34.6847			1.49121			0.745605	−	0.666388i	$-0.232161\pi$
$541$	34.6847			1.49121			0.745605	+	0.666388i	$0.232161\pi$
$542$		0			0
$543$	−20.1492	+	6.62712i	−0.864685	+	0.284397i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.89697	−	6.89697i	0.294893	−	0.294893i	−0.544117	−	0.839010i	$-0.683135\pi$
$547$	6.89697	−	6.89697i	0.294893	−	0.294893i	0.839010	+	0.544117i	$0.183135\pi$
$548$		0			0
$549$	−12.3687	+	9.12311i	−0.527883	+	0.389365i
$550$		0			0
$551$		−	1.52266i		−	0.0648674i
$552$		0			0
$553$	3.93261	+	3.93261i	0.167232	+	0.167232i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.5122	+	10.5122i	0.445415	+	0.445415i	0.893827	−	0.448412i	$-0.148010\pi$
$557$	10.5122	+	10.5122i	0.445415	+	0.445415i	−0.448412	+	0.893827i	$0.648010\pi$
$558$		0			0
$559$			4.49242i			0.190009i
$560$		0			0
$561$	−11.6577	+	23.0844i	−0.492187	+	0.974626i
$562$		0			0
$563$	9.97383	−	9.97383i	0.420347	−	0.420347i	−0.464976	−	0.885323i	$-0.653937\pi$
$563$	9.97383	−	9.97383i	0.420347	−	0.420347i	0.885323	+	0.464976i	$0.153937\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.20091	−	7.95942i	−0.176422	−	0.334264i
$568$		0			0
$569$	12.3687			0.518523			0.259262	−	0.965807i	$-0.416521\pi$
$569$	12.3687			0.518523			0.259262	+	0.965807i	$0.416521\pi$
$570$		0			0
$571$	−26.7386			−1.11898			−0.559488	−	0.828838i	$-0.689002\pi$
$571$	−26.7386			−1.11898			−0.559488	+	0.828838i	$0.689002\pi$
$572$		0			0
$573$	3.55270	+	10.8017i	0.148416	+	0.451247i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5.07496	+	5.07496i	−0.211273	+	0.211273i	−0.804808	−	0.593535i	$-0.797732\pi$
$577$	−5.07496	+	5.07496i	−0.211273	+	0.211273i	0.593535	+	0.804808i	$0.297732\pi$
$578$		0			0
$579$	18.5531	+	9.36932i	0.771039	+	0.389376i
$580$		0			0
$581$		−	1.73642i		−	0.0720388i
$582$		0			0
$583$	3.79668	+	3.79668i	0.157242	+	0.157242i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.7198	+	18.7198i	0.772650	+	0.772650i	0.978569	−	0.205919i	$-0.0660184\pi$
$587$	18.7198	+	18.7198i	0.772650	+	0.772650i	−0.205919	+	0.978569i	$0.566018\pi$
$588$		0			0
$589$			9.26137i			0.381608i
$590$		0			0
$591$	21.8078	+	11.0129i	0.897052	+	0.453012i
$592$		0			0
$593$	7.78733	−	7.78733i	0.319787	−	0.319787i	−0.528898	−	0.848685i	$-0.677395\pi$
$593$	7.78733	−	7.78733i	0.319787	−	0.319787i	0.848685	+	0.528898i	$0.177395\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	12.1719	+	37.0077i	0.498164	+	1.51463i
$598$		0			0
$599$	−11.9880			−0.489818			−0.244909	−	0.969546i	$-0.578758\pi$
$599$	−11.9880			−0.489818			−0.244909	+	0.969546i	$0.578758\pi$
$600$		0			0
$601$	−20.6307			−0.841543			−0.420772	−	0.907167i	$-0.638241\pi$
$601$	−20.6307			−0.841543			−0.420772	+	0.907167i	$0.638241\pi$
$602$		0			0
$603$	−4.98279	+	32.9952i	−0.202915	+	1.34367i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−16.4864	+	16.4864i	−0.669164	+	0.669164i	−0.957522	−	0.288359i	$-0.906890\pi$
$607$	−16.4864	+	16.4864i	−0.669164	+	0.669164i	0.288359	+	0.957522i	$0.406890\pi$
$608$		0			0
$609$	1.05854	−	2.09612i	0.0428943	−	0.0849390i
$610$		0			0
$611$		−	1.35576i		−	0.0548480i
$612$		0			0
$613$	−4.06854	−	4.06854i	−0.164327	−	0.164327i	0.620154	−	0.784480i	$-0.287070\pi$
$613$	−4.06854	−	4.06854i	−0.164327	−	0.164327i	−0.784480	+	0.620154i	$0.787070\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.4658	+	27.4658i	1.10573	+	1.10573i	0.993705	+	0.112027i	$0.0357343\pi$
$617$	27.4658	+	27.4658i	1.10573	+	1.10573i	0.112027	+	0.993705i	$0.464266\pi$
$618$		0			0
$619$		−	18.4924i		−	0.743273i	−0.928378	−	0.371637i	$-0.878797\pi$
$619$		−	18.4924i		−	0.743273i	0.928378	−	0.371637i	$-0.121203\pi$
$620$		0			0
$621$	−1.50758	−	8.89586i	−0.0604970	−	0.356979i
$622$		0			0
$623$	8.74599	−	8.74599i	0.350401	−	0.350401i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.71401	+	1.87935i	−0.228196	+	0.0750541i
$628$		0			0
$629$	−15.0802			−0.601288
$630$		0			0
$631$	26.0540			1.03719			0.518596	−	0.855019i	$-0.326455\pi$
$631$	26.0540			1.03719			0.518596	+	0.855019i	$0.326455\pi$
$632$		0			0
$633$	12.0362	−	3.95875i	0.478397	−	0.157346i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.310029	−	0.310029i	0.0122838	−	0.0122838i
$638$		0			0
$639$	−25.1181	−	34.0540i	−0.993656	−	1.34715i
$640$		0			0
$641$		−	12.3687i		−	0.488534i	−0.969708	−	0.244267i	$-0.921453\pi$
$641$		−	12.3687i		−	0.488534i	0.969708	−	0.244267i	$-0.0785474\pi$
$642$		0			0
$643$	−15.8664	−	15.8664i	−0.625709	−	0.625709i	0.321277	−	0.946985i	$-0.395888\pi$
$643$	−15.8664	−	15.8664i	−0.625709	−	0.625709i	−0.946985	+	0.321277i	$0.895888\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−29.9215	−	29.9215i	−1.17634	−	1.17634i	−0.980671	−	0.195664i	$-0.937314\pi$
$647$	−29.9215	−	29.9215i	−1.17634	−	1.17634i	−0.195664	−	0.980671i	$-0.562686\pi$
$648$		0			0
$649$		−	29.8617i		−	1.17218i
$650$		0			0
$651$	−6.43845	+	12.7494i	−0.252343	+	0.499687i
$652$		0			0
$653$	−34.2945	+	34.2945i	−1.34205	+	1.34205i	−0.448027	+	0.894020i	$0.647873\pi$
$653$	−34.2945	+	34.2945i	−1.34205	+	1.34205i	−0.894020	+	0.448027i	$0.852127\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	17.7982	+	2.68780i	0.694374	+	0.104861i
$658$		0			0
$659$	16.2222			0.631928			0.315964	−	0.948771i	$-0.397672\pi$
$659$	16.2222			0.631928			0.315964	+	0.948771i	$0.397672\pi$
$660$		0			0
$661$	19.3693			0.753379			0.376690	−	0.926340i	$-0.377062\pi$
$661$	19.3693			0.753379			0.376690	+	0.926340i	$0.377062\pi$
$662$		0			0
$663$	−1.14568	−	3.48333i	−0.0444943	−	0.135281i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.66464	−	1.66464i	0.0644553	−	0.0644553i
$668$		0			0
$669$	30.6245	+	15.4654i	1.18401	+	0.597928i
$670$		0			0
$671$			15.8415i			0.611556i
$672$		0			0
$673$	22.6274	+	22.6274i	0.872223	+	0.872223i	0.992714	−	0.120492i	$-0.0384471\pi$
$673$	22.6274	+	22.6274i	0.872223	+	0.872223i	−0.120492	+	0.992714i	$0.538447\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.0777	−	14.0777i	−0.541048	−	0.541048i	0.382788	−	0.923836i	$-0.374964\pi$
$677$	−14.0777	−	14.0777i	−0.541048	−	0.541048i	−0.923836	+	0.382788i	$0.874964\pi$
$678$		0			0
$679$		−	3.56155i		−	0.136680i
$680$		0			0
$681$	−33.4654	−	16.9001i	−1.28240	−	0.647613i
$682$		0			0
$683$	−10.5122	+	10.5122i	−0.402237	+	0.402237i	−0.879021	−	0.476784i	$-0.841803\pi$
$683$	−10.5122	+	10.5122i	−0.402237	+	0.402237i	0.476784	+	0.879021i	$0.341803\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.46250	+	13.5678i	0.170255	+	0.517645i
$688$		0			0
$689$	−0.761329			−0.0290043
$690$		0			0
$691$	12.6307			0.480494			0.240247	−	0.970712i	$-0.422772\pi$
$691$	12.6307			0.480494			0.240247	+	0.970712i	$0.422772\pi$
$692$		0			0
$693$	−9.17252	−	1.38519i	−0.348435	−	0.0526192i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−21.1154	+	21.1154i	−0.799804	+	0.799804i
$698$		0			0
$699$	−13.1300	+	26.0000i	−0.496623	+	0.983410i
$700$		0			0
$701$			33.0388i			1.24786i	0.781480	+	0.623930i	$0.214465\pi$
$701$			33.0388i			1.24786i	−0.781480	+	0.623930i	$0.785535\pi$
$702$		0			0
$703$	−2.48023	−	2.48023i	−0.0935437	−	0.0935437i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.45567	+	2.45567i	0.0923549	+	0.0923549i
$708$		0			0
$709$			17.8078i			0.668785i	0.942434	+	0.334392i	$0.108531\pi$
$709$			17.8078i			0.668785i	−0.942434	+	0.334392i	$0.891469\pi$
$710$		0			0
$711$	9.90388	+	13.4272i	0.371425	+	0.503561i
$712$		0			0
$713$	−10.1250	+	10.1250i	−0.379184	+	0.379184i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−31.1524	+	10.2461i	−1.16341	+	0.382648i
$718$		0			0
$719$	−9.65719			−0.360153			−0.180076	−	0.983653i	$-0.557634\pi$
$719$	−9.65719			−0.360153			−0.180076	+	0.983653i	$0.557634\pi$
$720$		0			0
$721$	−3.80776			−0.141809
$722$		0			0
$723$	0.405102	−	0.133239i	0.0150659	−	0.00495521i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	30.2208	−	30.2208i	1.12083	−	1.12083i	0.129209	−	0.991617i	$-0.458756\pi$
$727$	30.2208	−	30.2208i	1.12083	−	1.12083i	0.991617	−	0.129209i	$-0.0412439\pi$
$728$		0			0
$729$	−8.89586	−	25.4924i	−0.329476	−	0.944164i
$730$		0			0
$731$		−	49.4748i		−	1.82989i
$732$		0			0
$733$	−26.1141	−	26.1141i	−0.964545	−	0.964545i	0.0348475	−	0.999393i	$-0.488905\pi$
$733$	−26.1141	−	26.1141i	−0.964545	−	0.964545i	−0.999393	+	0.0348475i	$0.988905\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.3207	+	24.3207i	0.895863	+	0.895863i
$738$		0			0
$739$		−	37.1771i		−	1.36758i	−0.729678	−	0.683791i	$-0.760330\pi$
$739$		−	37.1771i		−	1.36758i	0.729678	−	0.683791i	$-0.239670\pi$
$740$		0			0
$741$	0.384472	−	0.761329i	0.0141239	−	0.0279681i
$742$		0			0
$743$	−32.3772	+	32.3772i	−1.18780	+	1.18780i	−0.210129	+	0.977674i	$0.567388\pi$
$743$	−32.3772	+	32.3772i	−1.18780	+	1.18780i	−0.977674	+	0.210129i	$0.932612\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.777860	−	5.15086i	0.0284604	−	0.188460i
$748$		0			0
$749$	20.2895			0.741361
$750$		0			0
$751$	39.4233			1.43858			0.719288	−	0.694712i	$-0.244468\pi$
$751$	39.4233			1.43858			0.719288	+	0.694712i	$0.244468\pi$
$752$		0			0
$753$	−5.22606	−	15.8894i	−0.190448	−	0.579041i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	4.06854	−	4.06854i	0.147874	−	0.147874i	−0.629294	−	0.777168i	$-0.716656\pi$
$757$	4.06854	−	4.06854i	0.147874	−	0.147874i	0.777168	+	0.629294i	$0.216656\pi$
$758$		0			0
$759$	−8.30144	−	4.19224i	−0.301323	−	0.152169i
$760$		0			0
$761$			41.3403i			1.49858i	0.662240	+	0.749292i	$0.269606\pi$
$761$			41.3403i			1.49858i	−0.662240	+	0.749292i	$0.730394\pi$
$762$		0			0
$763$	−9.14351	−	9.14351i	−0.331017	−	0.331017i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.99401	+	2.99401i	0.108107	+	0.108107i
$768$		0			0
$769$		−	17.1231i		−	0.617475i	−0.951147	−	0.308737i	$-0.900094\pi$
$769$		−	17.1231i		−	0.617475i	0.951147	−	0.308737i	$-0.0999065\pi$
$770$		0			0
$771$	−43.6155	−	22.0259i	−1.57077	−	0.793243i
$772$		0			0
$773$	25.2793	−	25.2793i	0.909234	−	0.909234i	−0.0869764	−	0.996210i	$-0.527720\pi$
$773$	25.2793	−	25.2793i	0.909234	−	0.909234i	0.996210	+	0.0869764i	$0.0277205\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.69009	−	5.13858i	−0.0606317	−	0.184345i
$778$		0			0
$779$	−6.94568			−0.248855
$780$		0			0
$781$	−43.6155			−1.56069
$782$		0			0
$783$	4.07902	−	5.74366i	0.145772	−	0.205262i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.2196	+	22.2196i	−0.792044	+	0.792044i	−0.981826	−	0.189782i	$-0.939222\pi$
$787$	−22.2196	+	22.2196i	−0.792044	+	0.792044i	0.189782	+	0.981826i	$0.439222\pi$
$788$		0			0
$789$	6.18435	−	12.2462i	0.220169	−	0.435977i
$790$		0			0
$791$			1.73642i			0.0617400i
$792$		0			0
$793$	−1.58831	−	1.58831i	−0.0564026	−	0.0564026i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.6987	+	12.6987i	0.449810	+	0.449810i	0.895291	−	0.445481i	$-0.146967\pi$
$797$	12.6987	+	12.6987i	0.449810	+	0.449810i	−0.445481	+	0.895291i	$0.646967\pi$
$798$		0			0
$799$			14.9309i			0.528216i
$800$		0			0
$801$	29.8617	−	22.0259i	1.05511	−	0.778247i
$802$		0			0
$803$	13.1190	−	13.1190i	0.462959	−	0.462959i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	41.9541	−	13.7988i	1.47686	−	0.485742i
$808$		0			0
$809$	33.8002			1.18835			0.594175	−	0.804335i	$-0.297478\pi$
$809$	33.8002			1.18835			0.594175	+	0.804335i	$0.297478\pi$
$810$		0			0
$811$	−40.7386			−1.43053			−0.715263	−	0.698855i	$-0.753693\pi$
$811$	−40.7386			−1.43053			−0.715263	+	0.698855i	$0.753693\pi$
$812$		0			0
$813$	28.1734	−	9.26629i	0.988083	−	0.324983i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.13709	−	8.13709i	0.284681	−	0.284681i
$818$		0			0
$819$	1.05854	−	0.780776i	0.0369885	−	0.0272825i
$820$		0			0
$821$		−	45.4075i		−	1.58473i	−0.610044	−	0.792367i	$-0.708848\pi$
$821$		−	45.4075i		−	1.58473i	0.610044	−	0.792367i	$-0.291152\pi$
$822$		0			0
$823$	−16.3505	−	16.3505i	−0.569943	−	0.569943i	0.362169	−	0.932112i	$-0.382036\pi$
$823$	−16.3505	−	16.3505i	−0.569943	−	0.569943i	−0.932112	+	0.362169i	$0.882036\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.1755	−	21.1755i	−0.736344	−	0.736344i	0.235524	−	0.971868i	$-0.424319\pi$
$827$	−21.1755	−	21.1755i	−0.736344	−	0.736344i	−0.971868	+	0.235524i	$0.924319\pi$
$828$		0			0
$829$		−	19.7538i		−	0.686077i	−0.939321	−	0.343039i	$-0.888544\pi$
$829$		−	19.7538i		−	0.686077i	0.939321	−	0.343039i	$-0.111456\pi$
$830$		0			0
$831$	11.8078	−	23.3817i	0.409607	−	0.811101i
$832$		0			0
$833$	−3.41433	+	3.41433i	−0.118300	+	0.118300i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−24.8101	+	34.9351i	−0.857562	+	1.20753i
$838$		0			0
$839$	44.8131			1.54712			0.773560	−	0.633723i	$-0.218474\pi$
$839$	44.8131			1.54712			0.773560	+	0.633723i	$0.218474\pi$
$840$		0			0
$841$	−27.1619			−0.936618
$842$		0			0
$843$	4.08038	+	12.4061i	0.140536	+	0.427287i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.01714	−	1.01714i	0.0349492	−	0.0349492i
$848$		0			0
$849$	−7.24289	−	3.65767i	−0.248575	−	0.125531i
$850$		0			0
$851$		−	5.42302i		−	0.185899i
$852$		0			0
$853$	14.6644	+	14.6644i	0.502100	+	0.502100i	0.912090	−	0.409990i	$-0.134468\pi$
$853$	14.6644	+	14.6644i	0.502100	+	0.502100i	−0.409990	+	0.912090i	$0.634468\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.6573	−	13.6573i	−0.466526	−	0.466526i	0.434261	−	0.900787i	$-0.357009\pi$
$857$	−13.6573	−	13.6573i	−0.466526	−	0.466526i	−0.900787	+	0.434261i	$0.857009\pi$
$858$		0			0
$859$			35.3693i			1.20679i	0.797444	+	0.603393i	$0.206185\pi$
$859$			35.3693i			1.20679i	−0.797444	+	0.603393i	$0.793815\pi$
$860$		0			0
$861$	−9.56155	−	4.82860i	−0.325857	−	0.164558i
$862$		0			0
$863$	−5.06249	+	5.06249i	−0.172329	+	0.172329i	−0.788002	−	0.615673i	$-0.788884\pi$
$863$	−5.06249	+	5.06249i	−0.172329	+	0.172329i	0.615673	+	0.788002i	$0.288884\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.41759	+	10.3909i	0.116067	+	0.352893i
$868$		0			0
$869$	17.1973			0.583378
$870$		0			0
$871$	−4.87689			−0.165247
$872$		0			0
$873$	1.59546	−	10.5649i	0.0539981	−	0.357567i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.6619	−	11.6619i	0.393795	−	0.393795i	−0.482243	−	0.876037i	$-0.660178\pi$
$877$	11.6619	−	11.6619i	0.393795	−	0.393795i	0.876037	+	0.482243i	$0.160178\pi$
$878$		0			0
$879$	−13.4272	+	26.5885i	−0.452890	+	0.896809i
$880$		0			0
$881$		−	17.7917i		−	0.599419i	−0.954031	−	0.299709i	$-0.903110\pi$
$881$		−	17.7917i		−	0.599419i	0.954031	−	0.299709i	$-0.0968897\pi$
$882$		0			0
$883$	12.0101	+	12.0101i	0.404172	+	0.404172i	0.879700	−	0.475528i	$-0.157743\pi$
$883$	12.0101	+	12.0101i	0.404172	+	0.404172i	−0.475528	+	0.879700i	$0.657743\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.4295	−	12.4295i	−0.417342	−	0.417342i	0.466945	−	0.884286i	$-0.345355\pi$
$887$	−12.4295	−	12.4295i	−0.417342	−	0.417342i	−0.884286	+	0.466945i	$0.845355\pi$
$888$		0			0
$889$			8.87689i			0.297721i
$890$		0			0
$891$	−26.5885	−	8.21799i	−0.890750	−	0.275313i
$892$		0			0
$893$	−2.45567	+	2.45567i	−0.0821758	+	0.0821758i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.25265	−	0.411998i	0.0418246	−	0.0137562i
$898$		0			0
$899$	−11.1798			−0.372869
$900$		0			0
$901$	8.38447			0.279327
$902$		0			0
$903$	16.8585	−	5.54481i	0.561016	−	0.184520i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	13.5221	−	13.5221i	0.448993	−	0.448993i	−0.446027	−	0.895020i	$-0.647161\pi$
$907$	13.5221	−	13.5221i	0.448993	−	0.448993i	0.895020	+	0.446027i	$0.147161\pi$
$908$		0			0
$909$	6.18435	+	8.38447i	0.205122	+	0.278095i
$910$		0			0
$911$			19.5281i			0.646996i	0.946229	+	0.323498i	$0.104859\pi$
$911$			19.5281i			0.646996i	−0.946229	+	0.323498i	$0.895141\pi$
$912$		0			0
$913$	−3.79668	−	3.79668i	−0.125652	−	0.125652i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.1190	−	13.1190i	−0.433227	−	0.433227i
$918$		0			0
$919$		−	1.17708i		−	0.0388283i	−0.999812	−	0.0194142i	$-0.993820\pi$
$919$		−	1.17708i		−	0.0388283i	0.999812	−	0.0194142i	$-0.00618011\pi$
$920$		0			0
$921$	−3.95786	+	7.83732i	−0.130416	+	0.258249i
$922$		0			0
$923$	4.37300	−	4.37300i	0.143939	−	0.143939i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.2952	−	1.70575i	−0.370984	−	0.0560243i
$928$		0			0
$929$	−34.3946			−1.12845			−0.564225	−	0.825621i	$-0.690825\pi$
$929$	−34.3946			−1.12845			−0.564225	+	0.825621i	$0.690825\pi$
$930$		0			0
$931$	−1.12311			−0.0368083
$932$		0			0
$933$	15.2662	+	46.4155i	0.499792	+	1.51958i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.2589	−	30.2589i	0.988517	−	0.988517i	−0.0114182	−	0.999935i	$-0.503635\pi$
$937$	30.2589	−	30.2589i	0.988517	−	0.988517i	0.999935	+	0.0114182i	$0.00363460\pi$
$938$		0			0
$939$	52.2698	+	26.3963i	1.70576	+	0.861411i
$940$		0			0
$941$		−	50.9975i		−	1.66247i	−0.555921	−	0.831235i	$-0.687634\pi$
$941$		−	50.9975i		−	1.66247i	0.555921	−	0.831235i	$-0.312366\pi$
$942$		0			0
$943$	−7.59336	−	7.59336i	−0.247274	−	0.247274i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.0101	+	25.0101i	0.812721	+	0.812721i	0.985041	−	0.172320i	$-0.0551264\pi$
$947$	25.0101	+	25.0101i	0.812721	+	0.812721i	−0.172320	+	0.985041i	$0.555126\pi$
$948$		0			0
$949$			2.63068i			0.0853956i
$950$		0			0
$951$	45.1231	+	22.7872i	1.46322	+	0.738926i
$952$		0			0
$953$	27.4658	−	27.4658i	0.889705	−	0.889705i	−0.104789	−	0.994494i	$-0.533417\pi$
$953$	27.4658	−	27.4658i	0.889705	−	0.889705i	0.994494	+	0.104789i	$0.0334168\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.26866	−	6.89766i	−0.0733353	−	0.222970i
$958$		0			0
$959$	−4.44793			−0.143631
$960$		0			0
$961$	37.0000			1.19355
$962$		0			0
$963$	60.1860	+	9.08903i	1.93947	+	0.292890i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−30.2208	+	30.2208i	−0.971835	+	0.971835i	−0.999614	−	0.0277794i	$-0.991156\pi$
$967$	−30.2208	+	30.2208i	−0.971835	+	0.971835i	0.0277794	+	0.999614i	$0.491156\pi$
$968$		0			0
$969$	−4.23417	+	8.38447i	−0.136021	+	0.269348i
$970$		0			0
$971$		−	50.2361i		−	1.61215i	−0.591810	−	0.806077i	$-0.701587\pi$
$971$		−	50.2361i		−	1.61215i	0.591810	−	0.806077i	$-0.298413\pi$
$972$		0			0
$973$	−7.07107	−	7.07107i	−0.226688	−	0.226688i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−41.6615	−	41.6615i	−1.33287	−	1.33287i	−0.902792	−	0.430077i	$-0.858486\pi$
$977$	−41.6615	−	41.6615i	−1.33287	−	1.33287i	−0.430077	−	0.902792i	$-0.641514\pi$
$978$		0			0
$979$		−	38.2462i		−	1.22235i
$980$		0			0
$981$	−23.0270	−	31.2190i	−0.735195	−	0.996745i
$982$		0			0
$983$	−4.10383	+	4.10383i	−0.130892	+	0.130892i	−0.769517	−	0.638626i	$-0.779503\pi$
$983$	−4.10383	+	4.10383i	−0.130892	+	0.130892i	0.638626	+	0.769517i	$0.279503\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.08769	+	1.67335i	−0.161943	+	0.0532634i
$988$		0			0
$989$	17.7917			0.565744
$990$		0			0
$991$	−21.7538			−0.691032			−0.345516	−	0.938413i	$-0.612296\pi$
$991$	−21.7538			−0.691032			−0.345516	+	0.938413i	$0.612296\pi$
$992$		0			0
$993$	−10.2772	+	3.38018i	−0.326136	+	0.107267i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	43.7047	−	43.7047i	1.38414	−	1.38414i	0.547025	−	0.837116i	$-0.315760\pi$
$997$	43.7047	−	43.7047i	1.38414	−	1.38414i	0.837116	−	0.547025i	$-0.184240\pi$
$998$		0			0
$999$	−2.71151	−	16.0000i	−0.0857884	−	0.506218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.a.1793.7	yes	16
3.2	odd	2	inner	2100.2.s.a.1793.3	yes	16
5.2	odd	4	inner	2100.2.s.a.1457.3	yes	16
5.3	odd	4	inner	2100.2.s.a.1457.6	yes	16
5.4	even	2	inner	2100.2.s.a.1793.2	yes	16
15.2	even	4	inner	2100.2.s.a.1457.7	yes	16
15.8	even	4	inner	2100.2.s.a.1457.2	✓	16
15.14	odd	2	inner	2100.2.s.a.1793.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.a.1457.2	✓	16	15.8	even	4	inner
2100.2.s.a.1457.3	yes	16	5.2	odd	4	inner
2100.2.s.a.1457.6	yes	16	5.3	odd	4	inner
2100.2.s.a.1457.7	yes	16	15.2	even	4	inner
2100.2.s.a.1793.2	yes	16	5.4	even	2	inner
2100.2.s.a.1793.3	yes	16	3.2	odd	2	inner
2100.2.s.a.1793.6	yes	16	15.14	odd	2	inner
2100.2.s.a.1793.7	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.64534 - 0.541157i) q^{3} +(0.707107 - 0.707107i) q^{7} +(2.41430 - 1.78078i) q^{9} +O(q^{10})\)	\(q+(1.64534 - 0.541157i) q^{3} +(0.707107 - 0.707107i) q^{7} +(2.41430 - 1.78078i) q^{9} -3.09218i q^{11} +(0.310029 + 0.310029i) q^{13} +(-3.41433 - 3.41433i) q^{17} -1.12311i q^{19} +(0.780776 - 1.54609i) q^{21} +(1.22783 - 1.22783i) q^{23} +(3.00867 - 4.23650i) q^{27} +1.35576 q^{29} -8.24621 q^{31} +(-1.67335 - 5.08769i) q^{33} +(2.20837 - 2.20837i) q^{37} +(0.677878 + 0.342329i) q^{39} -6.18435i q^{41} +(7.24517 + 7.24517i) q^{43} +(-2.18650 - 2.18650i) q^{47} -1.00000i q^{49} +(-7.46543 - 3.77005i) q^{51} +(-1.22783 + 1.22783i) q^{53} +(-0.607777 - 1.84789i) q^{57} +9.65719 q^{59} -5.12311 q^{61} +(0.447967 - 2.96637i) q^{63} +(-7.86522 + 7.86522i) q^{67} +(1.35576 - 2.68466i) q^{69} -14.1051i q^{71} +(4.24264 + 4.24264i) q^{73} +(-2.18650 - 2.18650i) q^{77} +5.56155i q^{79} +(2.65767 - 8.59865i) q^{81} +(1.22783 - 1.22783i) q^{83} +(2.23068 - 0.733677i) q^{87} +12.3687 q^{89} +0.438447 q^{91} +(-13.5678 + 4.46250i) q^{93} +(2.51840 - 2.51840i) q^{97} +(-5.50647 - 7.46543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{21} - 4 q^{51} - 16 q^{61} + 92 q^{81} + 40 q^{91}+O(q^{100}) \) 16 * q - 4 * q^21 - 4 * q^51 - 16 * q^61 + 92 * q^81 + 40 * q^91

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