LMFDB - Embedded newform 1476.2.bb.a.865.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1476,2,Mod(433,1476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1476, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("1476.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1476 = 2^{2} \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1476.bb (of order $10$, degree $4$, 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:	$11.7859193383$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			865.2
Root			$-0.0272949 + 1.41395i$ of defining polynomial
Character	$\chi$	$=$	1476.865
Dual form			1476.2.bb.a.1261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36361 - 4.19675i) q^{5} +(1.38197 - 1.90211i) q^{7} +O(q^{10})$	$q+(1.36361 - 4.19675i) q^{5} +(1.38197 - 1.90211i) q^{7} +(-5.77633 + 1.87684i) q^{11} +(-1.38197 - 1.90211i) q^{13} +(-4.41272 + 1.43378i) q^{17} +(3.88197 - 5.34307i) q^{19} +(1.36361 - 0.990718i) q^{23} +(-11.7082 - 8.50651i) q^{25} +(2.20636 + 0.716891i) q^{29} +(1.73607 + 5.34307i) q^{31} +(-6.09824 - 8.39350i) q^{35} +(-2.45492 + 7.55545i) q^{37} +(-3.04912 + 5.63053i) q^{41} +(6.47214 - 4.70228i) q^{43} +(-1.88446 - 2.59373i) q^{47} +(0.454915 + 1.40008i) q^{49} +(-10.1891 - 3.31062i) q^{53} +26.8011i q^{55} +(0.842755 - 0.612298i) q^{59} +(2.54508 + 1.84911i) q^{61} +(-9.86715 + 3.20603i) q^{65} +(10.5902 + 3.44095i) q^{67} +(1.36361 - 0.443063i) q^{71} -6.14590 q^{73} +(-4.41272 + 13.5810i) q^{77} -13.0373i q^{79} +8.18164 q^{83} +20.4742i q^{85} +(5.45443 - 7.50738i) q^{89} -5.52786 q^{91} +(-17.1300 - 23.5775i) q^{95} +(-6.97214 - 2.26538i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 20 q^{7}+O(q^{10}) $ 8 * q + 20 * q^7	$ 8 q + 20 q^{7} - 20 q^{13} + 40 q^{19} - 40 q^{25} - 4 q^{31} - 42 q^{37} + 16 q^{43} + 26 q^{49} - 2 q^{61} + 40 q^{67} - 76 q^{73} - 80 q^{91} - 20 q^{97}+O(q^{100}) $ 8 * q + 20 * q^7 - 20 * q^13 + 40 * q^19 - 40 * q^25 - 4 * q^31 - 42 * q^37 + 16 * q^43 + 26 * q^49 - 2 * q^61 + 40 * q^67 - 76 * q^73 - 80 * q^91 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1476\mathbb{Z}\right)^\times$.

$n$	$739$	$821$	$1441$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.36361	−	4.19675i	0.609824	−	1.87684i	0.150403	−	0.988625i	$-0.451943\pi$
$5$	1.36361	−	4.19675i	0.609824	−	1.87684i	0.459420	−	0.888219i	$-0.348057\pi$
$6$		0			0
$7$	1.38197	−	1.90211i	0.522334	−	0.718931i	−0.463604	−	0.886043i	$-0.653444\pi$
$7$	1.38197	−	1.90211i	0.522334	−	0.718931i	0.985938	+	0.167111i	$0.0534439\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.77633	+	1.87684i	−1.74163	+	0.565890i	−0.995047	−	0.0994035i	$-0.968307\pi$
$11$	−5.77633	+	1.87684i	−1.74163	+	0.565890i	−0.746582	+	0.665293i	$0.768307\pi$
$12$		0			0
$13$	−1.38197	−	1.90211i	−0.383288	−	0.527551i	0.573164	−	0.819441i	$-0.305716\pi$
$13$	−1.38197	−	1.90211i	−0.383288	−	0.527551i	−0.956452	+	0.291890i	$0.905716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.41272	+	1.43378i	−1.07024	+	0.347743i	−0.790582	−	0.612356i	$-0.790222\pi$
$17$	−4.41272	+	1.43378i	−1.07024	+	0.347743i	−0.279661	+	0.960099i	$0.590222\pi$
$18$		0			0
$19$	3.88197	−	5.34307i	0.890584	−	1.22578i	−0.0827913	−	0.996567i	$-0.526383\pi$
$19$	3.88197	−	5.34307i	0.890584	−	1.22578i	0.973375	−	0.229217i	$-0.0736165\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.36361	−	0.990718i	0.284332	−	0.206579i	−0.436473	−	0.899717i	$-0.643773\pi$
$23$	1.36361	−	0.990718i	0.284332	−	0.206579i	0.720805	+	0.693138i	$0.243773\pi$
$24$		0			0
$25$	−11.7082	−	8.50651i	−2.34164	−	1.70130i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.20636	+	0.716891i	0.409711	+	0.133123i	0.506619	−	0.862170i	$-0.330895\pi$
$29$	2.20636	+	0.716891i	0.409711	+	0.133123i	−0.0969077	+	0.995293i	$0.530895\pi$
$30$		0			0
$31$	1.73607	+	5.34307i	0.311807	+	0.959643i	0.977049	+	0.213015i	$0.0683284\pi$
$31$	1.73607	+	5.34307i	0.311807	+	0.959643i	−0.665242	+	0.746628i	$0.731672\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.09824	−	8.39350i	−1.03079	−	1.41876i
$36$		0			0
$37$	−2.45492	+	7.55545i	−0.403586	+	1.24211i	0.518485	+	0.855087i	$0.326496\pi$
$37$	−2.45492	+	7.55545i	−0.403586	+	1.24211i	−0.922071	+	0.387022i	$0.873504\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.04912	+	5.63053i	−0.476192	+	0.879341i
$41$	−3.04912	+	5.63053i	−0.476192	+	0.879341i
$42$		0			0
$43$	6.47214	−	4.70228i	0.986991	−	0.717091i	0.0277313	−	0.999615i	$-0.491172\pi$
$43$	6.47214	−	4.70228i	0.986991	−	0.717091i	0.959260	+	0.282524i	$0.0911717\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.88446	−	2.59373i	−0.274876	−	0.378335i	0.649152	−	0.760659i	$-0.275124\pi$
$47$	−1.88446	−	2.59373i	−0.274876	−	0.378335i	−0.924028	+	0.382324i	$0.875124\pi$
$48$		0			0
$49$	0.454915	+	1.40008i	0.0649879	+	0.200012i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.1891	−	3.31062i	−1.39957	−	0.454749i	−0.490521	−	0.871429i	$-0.663194\pi$
$53$	−10.1891	−	3.31062i	−1.39957	−	0.454749i	−0.909053	+	0.416680i	$0.863194\pi$
$54$		0			0
$55$			26.8011i			3.61386i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.842755	−	0.612298i	0.109717	−	0.0797144i	−0.531574	−	0.847012i	$-0.678399\pi$
$59$	0.842755	−	0.612298i	0.109717	−	0.0797144i	0.641291	+	0.767298i	$0.278399\pi$
$60$		0			0
$61$	2.54508	+	1.84911i	0.325865	+	0.236755i	0.738674	−	0.674063i	$-0.235452\pi$
$61$	2.54508	+	1.84911i	0.325865	+	0.236755i	−0.412809	+	0.910818i	$0.635452\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.86715	+	3.20603i	−1.22387	+	0.397659i
$66$		0			0
$67$	10.5902	+	3.44095i	1.29380	+	0.420380i	0.873419	−	0.486970i	$-0.161898\pi$
$67$	10.5902	+	3.44095i	1.29380	+	0.420380i	0.420377	+	0.907350i	$0.361898\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.36361	−	0.443063i	0.161830	−	0.0525819i	−0.226981	−	0.973899i	$-0.572886\pi$
$71$	1.36361	−	0.443063i	0.161830	−	0.0525819i	0.388812	+	0.921317i	$0.372886\pi$
$72$		0			0
$73$	−6.14590			−0.719323			−0.359661	−	0.933083i	$-0.617108\pi$
$73$	−6.14590			−0.719323			−0.359661	+	0.933083i	$0.617108\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.41272	+	13.5810i	−0.502877	+	1.54770i
$78$		0			0
$79$		−	13.0373i		−	1.46681i	−0.679793	−	0.733404i	$-0.737930\pi$
$79$		−	13.0373i		−	1.46681i	0.679793	−	0.733404i	$-0.262070\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.18164			0.898052			0.449026	−	0.893519i	$-0.351771\pi$
$83$	8.18164			0.898052			0.449026	+	0.893519i	$0.351771\pi$
$84$		0			0
$85$			20.4742i			2.22074i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.45443	−	7.50738i	0.578168	−	0.795780i	−0.415325	−	0.909673i	$-0.636332\pi$
$89$	5.45443	−	7.50738i	0.578168	−	0.795780i	0.993493	+	0.113893i	$0.0363321\pi$
$90$		0			0
$91$	−5.52786			−0.579478
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−17.1300	−	23.5775i	−1.75751	−	2.41900i
$96$		0			0
$97$	−6.97214	−	2.26538i	−0.707913	−	0.230015i	−0.0671382	−	0.997744i	$-0.521387\pi$
$97$	−6.97214	−	2.26538i	−0.707913	−	0.230015i	−0.640775	+	0.767729i	$0.721387\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.13994	−	9.82728i	0.710450	−	0.977851i	−0.289337	−	0.957227i	$-0.593435\pi$
$101$	7.13994	−	9.82728i	0.710450	−	0.977851i	0.999787	−	0.0206237i	$-0.00656520\pi$
$102$		0			0
$103$	−1.80902	−	1.31433i	−0.178248	−	0.129505i	0.495084	−	0.868845i	$-0.335137\pi$
$103$	−1.80902	−	1.31433i	−0.178248	−	0.129505i	−0.673332	+	0.739341i	$0.735137\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.41272	−	3.20603i	−0.426594	−	0.309939i	0.353691	−	0.935362i	$-0.384926\pi$
$107$	−4.41272	−	3.20603i	−0.426594	−	0.309939i	−0.780286	+	0.625423i	$0.784926\pi$
$108$		0			0
$109$		−	10.5801i		−	1.01339i	−0.862124	−	0.506697i	$-0.830866\pi$
$109$		−	10.5801i		−	1.01339i	0.862124	−	0.506697i	$-0.169134\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.09082	−	12.5903i	−0.384832	−	1.18439i	−0.936602	−	0.350395i	$-0.886047\pi$
$113$	−4.09082	−	12.5903i	−0.384832	−	1.18439i	0.551770	−	0.833996i	$-0.313953\pi$
$114$		0			0
$115$	−2.29837	−	7.07367i	−0.214324	−	0.659623i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.37102	+	10.3749i	−0.309021	+	0.951069i
$120$		0			0
$121$	20.9443	−	15.2169i	1.90402	−	1.38335i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−33.8152	+	24.5682i	−3.02453	+	2.19745i
$126$		0			0
$127$	−3.63525	+	11.1882i	−0.322577	+	0.992789i	0.649946	+	0.759980i	$0.274792\pi$
$127$	−3.63525	+	11.1882i	−0.322577	+	0.992789i	−0.972523	+	0.232809i	$0.925208\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$131$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$132$		0			0
$133$	−4.79837	−	14.7679i	−0.416072	−	1.28054i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	13.5810i		−	1.16030i	−0.814509	−	0.580150i	$-0.802994\pi$
$137$		−	13.5810i		−	1.16030i	0.814509	−	0.580150i	$-0.197006\pi$
$138$		0			0
$139$	−16.8992	−	12.2780i	−1.43337	−	1.04140i	−0.989377	−	0.145375i	$-0.953561\pi$
$139$	−16.8992	−	12.2780i	−1.43337	−	1.04140i	−0.443994	−	0.896030i	$-0.646439\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.5527	+	8.39350i	0.966082	+	0.701900i
$144$		0			0
$145$	6.01722	−	8.28199i	0.499703	−	0.687782i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.842755	+	0.273828i	0.0690412	+	0.0224328i	0.343334	−	0.939213i	$-0.388444\pi$
$149$	0.842755	+	0.273828i	0.0690412	+	0.0224328i	−0.274293	+	0.961646i	$0.588444\pi$
$150$		0			0
$151$	−0.690983	−	0.951057i	−0.0562314	−	0.0773959i	0.779975	−	0.625810i	$-0.215232\pi$
$151$	−0.690983	−	0.951057i	−0.0562314	−	0.0773959i	−0.836207	+	0.548414i	$0.815232\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	24.7908			1.99125
$156$		0			0
$157$	4.04508	−	5.56758i	0.322833	−	0.444341i	−0.616497	−	0.787358i	$-0.711449\pi$
$157$	4.04508	−	5.56758i	0.322833	−	0.444341i	0.939329	+	0.343016i	$0.111449\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.96287i		−	0.312318i
$162$		0			0
$163$	13.9443			1.09220			0.546100	−	0.837720i	$-0.316112\pi$
$163$	13.9443			1.09220			0.546100	+	0.837720i	$0.316112\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	12.1472i		−	0.939978i	−0.882672	−	0.469989i	$-0.844258\pi$
$167$		−	12.1472i		−	0.939978i	0.882672	−	0.469989i	$-0.155742\pi$
$168$		0			0
$169$	2.30902	−	7.10642i	0.177617	−	0.546648i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.49613			−0.493892			−0.246946	−	0.969029i	$-0.579427\pi$
$173$	−6.49613			−0.493892			−0.246946	+	0.969029i	$0.579427\pi$
$174$		0			0
$175$	−32.3607	+	10.5146i	−2.44624	+	0.794831i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.1717	+	5.90436i	1.35822	+	0.441313i	0.895449	−	0.445165i	$-0.146855\pi$
$179$	18.1717	+	5.90436i	1.35822	+	0.441313i	0.462772	+	0.886477i	$0.346855\pi$
$180$		0			0
$181$	−10.4271	+	3.38795i	−0.775037	+	0.251825i	−0.669720	−	0.742614i	$-0.733586\pi$
$181$	−10.4271	+	3.38795i	−0.775037	+	0.251825i	−0.105317	+	0.994439i	$0.533586\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	28.3608	+	20.6053i	2.08513	+	1.51493i
$186$		0			0
$187$	22.7984	−	16.5640i	1.66718	−	1.21128i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	0.547656i		−	0.0396270i	−0.999804	−	0.0198135i	$-0.993693\pi$
$191$		−	0.547656i		−	0.0396270i	0.999804	−	0.0198135i	$-0.00630724\pi$
$192$		0			0
$193$	10.8541	+	3.52671i	0.781295	+	0.253858i	0.672393	−	0.740194i	$-0.265266\pi$
$193$	10.8541	+	3.52671i	0.781295	+	0.253858i	0.108902	+	0.994052i	$0.465266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.73463	+	14.5717i	0.337328	+	1.03819i	0.965564	+	0.260166i	$0.0837774\pi$
$197$	4.73463	+	14.5717i	0.337328	+	1.03819i	−0.628235	+	0.778023i	$0.716223\pi$
$198$		0			0
$199$	−4.37132	−	6.01661i	−0.309875	−	0.426506i	0.625467	−	0.780250i	$-0.284908\pi$
$199$	−4.37132	−	6.01661i	−0.309875	−	0.426506i	−0.935342	+	0.353744i	$0.884908\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.41272	−	3.20603i	0.309713	−	0.225019i
$204$		0			0
$205$	19.4721	+	20.4742i	1.35999	+	1.42998i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.3954	+	38.1492i	−0.857409	+	2.63883i
$210$		0			0
$211$	−0.527864	−	0.726543i	−0.0363397	−	0.0500173i	0.790461	−	0.612513i	$-0.209841\pi$
$211$	−0.527864	−	0.726543i	−0.0363397	−	0.0500173i	−0.826800	+	0.562496i	$0.809841\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.9089	−	33.5740i	−0.743978	−	2.28973i
$216$		0			0
$217$	12.5623	+	4.08174i	0.852785	+	0.277087i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.82545	+	6.41206i	0.593664	+	0.431322i
$222$		0			0
$223$	−1.80902	+	1.31433i	−0.121141	+	0.0880139i	−0.646706	−	0.762739i	$-0.723854\pi$
$223$	−1.80902	+	1.31433i	−0.121141	+	0.0880139i	0.525565	+	0.850753i	$0.323854\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.1891	+	14.0240i	−0.676271	+	0.930808i	−0.999882	−	0.0153828i	$-0.995103\pi$
$227$	−10.1891	+	14.0240i	−0.676271	+	0.930808i	0.323610	+	0.946190i	$0.395103\pi$
$228$		0			0
$229$	15.4894	−	5.03280i	1.02357	−	0.332577i	0.251322	−	0.967903i	$-0.419135\pi$
$229$	15.4894	−	5.03280i	1.02357	−	0.332577i	0.772243	+	0.635327i	$0.219135\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.66820	−	13.3071i	−0.633385	−	0.871780i	0.364856	−	0.931064i	$-0.381118\pi$
$233$	−9.66820	−	13.3071i	−0.633385	−	0.871780i	−0.998241	+	0.0592841i	$0.981118\pi$
$234$		0			0
$235$	−13.4549	+	4.37177i	−0.877702	+	0.285183i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.842755	−	1.15995i	0.0545133	−	0.0750311i	−0.780890	−	0.624669i	$-0.785234\pi$
$239$	0.842755	−	1.15995i	0.0545133	−	0.0750311i	0.835403	+	0.549637i	$0.185234\pi$
$240$		0			0
$241$	−7.44427	+	22.9111i	−0.479528	+	1.47583i	0.360225	+	0.932865i	$0.382700\pi$
$241$	−7.44427	+	22.9111i	−0.479528	+	1.47583i	−0.839753	+	0.542969i	$0.817300\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.49613			0.415023
$246$		0			0
$247$	−15.5279			−0.988014
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.13994	−	21.9745i	0.450669	−	1.38702i	−0.425477	−	0.904969i	$-0.639894\pi$
$251$	7.13994	−	21.9745i	0.450669	−	1.38702i	0.876145	−	0.482047i	$-0.160106\pi$
$252$		0			0
$253$	−6.01722	+	8.28199i	−0.378299	+	0.520685i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.2308	+	3.64909i	−0.700555	+	0.227624i	−0.637573	−	0.770390i	$-0.720061\pi$
$257$	−11.2308	+	3.64909i	−0.700555	+	0.227624i	−0.0629829	+	0.998015i	$0.520061\pi$
$258$		0			0
$259$	10.9787	+	15.1109i	0.682184	+	0.938946i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.61167	+	1.49842i	−0.284368	+	0.0923967i	−0.447728	−	0.894170i	$-0.647767\pi$
$263$	−4.61167	+	1.49842i	−0.284368	+	0.0923967i	0.163360	+	0.986566i	$0.447767\pi$
$264$		0			0
$265$	−27.7877	+	38.2465i	−1.70699	+	2.34947i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.72721	+	1.98144i	−0.166281	+	0.120810i	−0.667814	−	0.744328i	$-0.732770\pi$
$269$	−2.72721	+	1.98144i	−0.166281	+	0.120810i	0.501533	+	0.865139i	$0.332770\pi$
$270$		0			0
$271$	0.809017	+	0.587785i	0.0491443	+	0.0357054i	0.612086	−	0.790791i	$-0.290331\pi$
$271$	0.809017	+	0.587785i	0.0491443	+	0.0357054i	−0.562942	+	0.826496i	$0.690331\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	83.5958	+	27.1619i	5.04102	+	1.63793i
$276$		0			0
$277$	3.43769	+	10.5801i	0.206551	+	0.635699i	0.999646	+	0.0266009i	$0.00846832\pi$
$277$	3.43769	+	10.5801i	0.206551	+	0.635699i	−0.793095	+	0.609098i	$0.791532\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.3880	−	14.2979i	−0.619696	−	0.852939i	0.377634	−	0.925955i	$-0.376738\pi$
$281$	−10.3880	−	14.2979i	−0.619696	−	0.852939i	−0.997331	+	0.0730160i	$0.976738\pi$
$282$		0			0
$283$	7.00000	−	21.5438i	0.416107	−	1.28065i	−0.495150	−	0.868807i	$-0.664887\pi$
$283$	7.00000	−	21.5438i	0.416107	−	1.28065i	0.911257	−	0.411838i	$-0.135113\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.49613	+	13.5810i	0.383454	+	0.801659i
$288$		0			0
$289$	3.66312	−	2.66141i	0.215478	−	0.156554i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.8820	+	19.1069i	0.810994	+	1.11624i	0.991169	+	0.132603i	$0.0423335\pi$
$293$	13.8820	+	19.1069i	0.810994	+	1.11624i	−0.180175	+	0.983635i	$0.557666\pi$
$294$		0			0
$295$	−1.42047	−	4.37177i	−0.0827031	−	0.254534i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.76892	−	1.22460i	−0.217962	−	0.0708202i
$300$		0			0
$301$		−	18.8091i		−	1.08414i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.2308	−	8.15962i	0.643071	−	0.467219i
$306$		0			0
$307$	6.54508	+	4.75528i	0.373548	+	0.271398i	0.758681	−	0.651463i	$-0.225844\pi$
$307$	6.54508	+	4.75528i	0.373548	+	0.271398i	−0.385133	+	0.922861i	$0.625844\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	24.4689	−	7.95044i	1.38751	−	0.450828i	0.482376	−	0.875964i	$-0.339774\pi$
$311$	24.4689	−	7.95044i	1.38751	−	0.450828i	0.905129	+	0.425136i	$0.139774\pi$
$312$		0			0
$313$	−22.2361	−	7.22494i	−1.25686	−	0.408378i	−0.396484	−	0.918042i	$-0.629770\pi$
$313$	−22.2361	−	7.22494i	−1.25686	−	0.408378i	−0.860373	+	0.509664i	$0.829770\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.41272	−	1.43378i	0.247843	−	0.0805292i	−0.182461	−	0.983213i	$-0.558406\pi$
$317$	4.41272	−	1.43378i	0.247843	−	0.0805292i	0.430304	+	0.902684i	$0.358406\pi$
$318$		0			0
$319$	−14.0902			−0.788898
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.46926	+	29.1434i	−0.526884	+	1.62158i
$324$		0			0
$325$			34.0260i			1.88742i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.53783			−0.415574
$330$		0			0
$331$		−	20.6457i		−	1.13479i	−0.823445	−	0.567396i	$-0.807951\pi$
$331$		−	20.6457i		−	1.13479i	0.823445	−	0.567396i	$-0.192049\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	28.8817	−	39.7522i	1.57797	−	2.17189i
$336$		0			0
$337$	12.4164			0.676365			0.338182	−	0.941081i	$-0.390188\pi$
$337$	12.4164			0.676365			0.338182	+	0.941081i	$0.390188\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−20.0562	−	27.6050i	−1.08610	−	1.49489i
$342$		0			0
$343$	18.9443	+	6.15537i	1.02289	+	0.332359i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.53568	−	6.24283i	0.243488	−	0.335133i	−0.669729	−	0.742605i	$-0.733590\pi$
$347$	4.53568	−	6.24283i	0.243488	−	0.335133i	0.913217	+	0.407473i	$0.133590\pi$
$348$		0			0
$349$	−17.2533	−	12.5352i	−0.923547	−	0.670996i	0.0208571	−	0.999782i	$-0.493361\pi$
$349$	−17.2533	−	12.5352i	−0.923547	−	0.670996i	−0.944404	+	0.328786i	$0.893361\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.09082	+	2.97216i	0.217732	+	0.158192i	0.691305	−	0.722563i	$-0.257036\pi$
$353$	4.09082	+	2.97216i	0.217732	+	0.158192i	−0.473573	+	0.880755i	$0.657036\pi$
$354$		0			0
$355$		−	6.32688i		−	0.335796i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.198948	+	0.612298i	0.0105001	+	0.0323158i	0.956169	−	0.292814i	$-0.0945918\pi$
$359$	0.198948	+	0.612298i	0.0105001	+	0.0323158i	−0.945669	+	0.325130i	$0.894592\pi$
$360$		0			0
$361$	−7.60739	−	23.4131i	−0.400389	−	1.23227i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.38059	+	25.7928i	−0.438660	+	1.35006i
$366$		0			0
$367$	−29.3156	+	21.2990i	−1.53026	+	1.11180i	−0.574168	+	0.818737i	$0.694675\pi$
$367$	−29.3156	+	21.2990i	−1.53026	+	1.11180i	−0.956093	+	0.293063i	$0.905325\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−20.3781	+	14.8056i	−1.05798	+	0.768667i
$372$		0			0
$373$	6.60739	−	20.3355i	0.342118	−	1.05293i	−0.620991	−	0.783818i	$-0.713270\pi$
$373$	6.60739	−	20.3355i	0.342118	−	1.05293i	0.963109	−	0.269112i	$-0.0867303\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.68551	−	5.18747i	−0.0868082	−	0.267168i
$378$		0			0
$379$	8.28115	+	25.4868i	0.425374	+	1.30917i	0.902635	+	0.430406i	$0.141630\pi$
$379$	8.28115	+	25.4868i	0.425374	+	1.30917i	−0.477261	+	0.878761i	$0.658370\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			32.6879i			1.67027i	0.550043	+	0.835136i	$0.314611\pi$
$383$			32.6879i			1.67027i	−0.550043	+	0.835136i	$0.685389\pi$
$384$		0			0
$385$	50.9787	+	37.0382i	2.59812	+	1.88764i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	27.1961	+	19.7592i	1.37890	+	1.00183i	0.996982	+	0.0776324i	$0.0247361\pi$
$389$	27.1961	+	19.7592i	1.37890	+	1.00183i	0.381917	+	0.924197i	$0.375264\pi$
$390$		0			0
$391$	−4.59675	+	6.32688i	−0.232468	+	0.319964i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−54.7142	−	17.7777i	−2.75297	−	0.894494i
$396$		0			0
$397$	−13.3541	−	18.3803i	−0.670223	−	0.922483i	0.329542	−	0.944141i	$-0.393106\pi$
$397$	−13.3541	−	18.3803i	−0.670223	−	0.922483i	−0.999765	+	0.0216578i	$0.993106\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	31.9308			1.59455			0.797273	−	0.603618i	$-0.206275\pi$
$401$	31.9308			1.59455			0.797273	+	0.603618i	$0.206275\pi$
$402$		0			0
$403$	7.76393	−	10.6861i	0.386749	−	0.532314i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	48.2503i		−	2.39168i
$408$		0			0
$409$	5.70820			0.282253			0.141126	−	0.989992i	$-0.454928\pi$
$409$	5.70820			0.282253			0.141126	+	0.989992i	$0.454928\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	2.44919i		−	0.120517i
$414$		0			0
$415$	11.1565	−	34.3363i	0.547653	−	1.68550i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	20.3781			0.995536			0.497768	−	0.867310i	$-0.334153\pi$
$419$	20.3781			0.995536			0.497768	+	0.867310i	$0.334153\pi$
$420$		0			0
$421$	34.2705	−	11.1352i	1.67024	−	0.542695i	0.687263	−	0.726409i	$-0.258812\pi$
$421$	34.2705	−	11.1352i	1.67024	−	0.542695i	0.982980	+	0.183714i	$0.0588121\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	63.8615	+	20.7499i	3.09774	+	1.00652i
$426$		0			0
$427$	7.03444	−	2.28563i	0.340421	−	0.110609i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.0562	+	14.5717i	0.966073	+	0.701893i	0.954553	−	0.298040i	$-0.0963329\pi$
$431$	20.0562	+	14.5717i	0.966073	+	0.701893i	0.0115202	+	0.999934i	$0.496333\pi$
$432$		0			0
$433$	−13.6074	+	9.88635i	−0.653929	+	0.475108i	−0.864607	−	0.502448i	$-0.832433\pi$
$433$	−13.6074	+	9.88635i	−0.653929	+	0.475108i	0.210678	+	0.977556i	$0.432433\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	11.1318i		−	0.532505i
$438$		0			0
$439$	32.5623	+	10.5801i	1.55411	+	0.504962i	0.955228	−	0.295872i	$-0.0956101\pi$
$439$	32.5623	+	10.5801i	1.55411	+	0.504962i	0.598886	+	0.800834i	$0.295610\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.20636	+	6.79048i	0.104827	+	0.322626i	0.989690	−	0.143227i	$-0.0457478\pi$
$443$	2.20636	+	6.79048i	0.104827	+	0.322626i	−0.884862	+	0.465852i	$0.845748\pi$
$444$		0			0
$445$	−24.0689	−	33.1280i	−1.14097	−	1.57042i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5.45443	−	3.96287i	0.257410	−	0.187020i	−0.451594	−	0.892223i	$-0.649145\pi$
$449$	5.45443	−	3.96287i	0.257410	−	0.187020i	0.709005	+	0.705204i	$0.249145\pi$
$450$		0			0
$451$	7.04508	−	38.2465i	0.331740	−	1.80096i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.53783	+	23.1991i	−0.353379	+	1.08759i
$456$		0			0
$457$	−0.954915	−	1.31433i	−0.0446690	−	0.0614817i	0.786098	−	0.618102i	$-0.212098\pi$
$457$	−0.954915	−	1.31433i	−0.0446690	−	0.0614817i	−0.830767	+	0.556620i	$0.812098\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.54525	+	29.3773i	0.444567	+	1.36824i	0.882958	+	0.469451i	$0.155548\pi$
$461$	9.54525	+	29.3773i	0.444567	+	1.36824i	−0.438392	+	0.898784i	$0.644452\pi$
$462$		0			0
$463$	2.92705	+	0.951057i	0.136032	+	0.0441993i	0.376242	−	0.926522i	$-0.377216\pi$
$463$	2.92705	+	0.951057i	0.136032	+	0.0441993i	−0.240210	+	0.970721i	$0.577216\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.2135	−	13.9594i	−0.889093	−	0.645964i	0.0465487	−	0.998916i	$-0.485178\pi$
$467$	−19.2135	−	13.9594i	−0.889093	−	0.645964i	−0.935641	+	0.352953i	$0.885178\pi$
$468$		0			0
$469$	21.1803	−	15.3884i	0.978017	−	0.710571i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−28.5598	+	39.3091i	−1.31318	+	1.80744i
$474$		0			0
$475$	−90.9017	+	29.5358i	−4.17086	+	1.35519i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.9506	−	16.4485i	−0.546035	−	0.751553i	0.443433	−	0.896308i	$-0.353761\pi$
$479$	−11.9506	−	16.4485i	−0.546035	−	0.751553i	−0.989468	+	0.144755i	$0.953761\pi$
$480$		0			0
$481$	17.7639	−	5.77185i	0.809966	−	0.263174i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.0145	+	26.1712i	−0.863404	+	1.18837i
$486$		0			0
$487$	7.92705	−	24.3970i	0.359209	−	1.10553i	−0.594320	−	0.804229i	$-0.702579\pi$
$487$	7.92705	−	24.3970i	0.359209	−	1.10553i	0.953529	−	0.301303i	$-0.0974214\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.05653			−0.228198			−0.114099	−	0.993469i	$-0.536398\pi$
$491$	−5.05653			−0.228198			−0.114099	+	0.993469i	$0.536398\pi$
$492$		0			0
$493$	−10.7639			−0.484783
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.04170	−	3.20603i	0.0467268	−	0.143810i
$498$		0			0
$499$	9.53444	−	13.1230i	0.426820	−	0.587468i	−0.540399	−	0.841409i	$-0.681727\pi$
$499$	9.53444	−	13.1230i	0.426820	−	0.587468i	0.967220	+	0.253941i	$0.0817269\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.9407	−	7.12895i	0.978286	−	0.317864i	0.224130	−	0.974559i	$-0.428046\pi$
$503$	21.9407	−	7.12895i	0.978286	−	0.317864i	0.754156	+	0.656695i	$0.228046\pi$
$504$		0			0
$505$	−31.5066	−	43.3651i	−1.40202	−	1.92972i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.20636	+	0.716891i	−0.0977953	+	0.0317756i	−0.357506	−	0.933911i	$-0.616373\pi$
$509$	−2.20636	+	0.716891i	−0.0977953	+	0.0317756i	0.259711	+	0.965686i	$0.416373\pi$
$510$		0			0
$511$	−8.49342	+	11.6902i	−0.375727	+	0.517144i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.98269	+	5.79977i	−0.351759	+	0.255568i
$516$		0			0
$517$	15.7533	+	11.4454i	0.692829	+	0.503370i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.2552	−	6.58130i	−0.887394	−	0.288332i	−0.170370	−	0.985380i	$-0.554496\pi$
$521$	−20.2552	−	6.58130i	−0.887394	−	0.288332i	−0.717024	+	0.697048i	$0.754496\pi$
$522$		0			0
$523$	9.93769	+	30.5851i	0.434545	+	1.33739i	0.893552	+	0.448959i	$0.148205\pi$
$523$	9.93769	+	30.5851i	0.434545	+	1.33739i	−0.459007	+	0.888433i	$0.651795\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.3216	−	21.0883i	−0.667418	−	0.918623i
$528$		0			0
$529$	−6.22949	+	19.1724i	−0.270847	+	0.833583i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	14.9237	−	1.98144i	0.646416	−	0.0858255i
$534$		0			0
$535$	−19.4721	+	14.1473i	−0.841854	+	0.611643i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.25548	−	7.23355i	−0.226370	−	0.311571i
$540$		0			0
$541$	−6.52786	−	20.0907i	−0.280655	−	0.863767i	−0.987668	−	0.156566i	$-0.949958\pi$
$541$	−6.52786	−	20.0907i	−0.280655	−	0.863767i	0.707013	−	0.707201i	$-0.250042\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−44.4022	−	14.4271i	−1.90198	−	0.617991i
$546$		0			0
$547$		−	6.15537i		−	0.263184i	−0.991304	−	0.131592i	$-0.957991\pi$
$547$		−	6.15537i		−	0.263184i	0.991304	−	0.131592i	$-0.0420090\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.3954	−	9.00580i	0.528063	−	0.383660i
$552$		0			0
$553$	−24.7984	−	18.0171i	−1.05453	−	0.766164i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.7343	−	6.41206i	0.836169	−	0.271688i	0.140528	−	0.990077i	$-0.455120\pi$
$557$	19.7343	−	6.41206i	0.836169	−	0.271688i	0.695642	+	0.718389i	$0.255120\pi$
$558$		0			0
$559$	−17.8885	−	5.81234i	−0.756605	−	0.245836i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	30.7661	−	9.99652i	1.29664	−	0.421303i	0.422227	−	0.906490i	$-0.361249\pi$
$563$	30.7661	−	9.99652i	1.29664	−	0.421303i	0.874410	+	0.485187i	$0.161249\pi$
$564$		0			0
$565$	−58.4164			−2.45760
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.62650	+	26.5496i	−0.361642	+	1.11302i	0.590416	+	0.807099i	$0.298964\pi$
$569$	−8.62650	+	26.5496i	−0.361642	+	1.11302i	−0.952057	+	0.305919i	$0.901036\pi$
$570$		0			0
$571$			7.11894i			0.297918i	0.988843	+	0.148959i	$0.0475923\pi$
$571$			7.11894i			0.297918i	−0.988843	+	0.148959i	$0.952408\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.3929			−1.01726
$576$		0			0
$577$		−	37.1442i		−	1.54633i	−0.634203	−	0.773167i	$-0.718672\pi$
$577$		−	37.1442i		−	1.54633i	0.634203	−	0.773167i	$-0.281328\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.3067	−	15.5624i	0.469083	−	0.645637i
$582$		0			0
$583$	65.0689			2.69488
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.61167	−	6.34742i	−0.190344	−	0.261986i	0.703170	−	0.711022i	$-0.251767\pi$
$587$	−4.61167	−	6.34742i	−0.190344	−	0.261986i	−0.893514	+	0.449036i	$0.851767\pi$
$588$		0			0
$589$	35.2877	+	11.4657i	1.45401	+	0.472435i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.88446	+	2.59373i	−0.0773854	+	0.106512i	−0.845955	−	0.533254i	$-0.820969\pi$
$593$	−1.88446	+	2.59373i	−0.0773854	+	0.106512i	0.768570	+	0.639766i	$0.220969\pi$
$594$		0			0
$595$	38.9443	+	28.2947i	1.59656	+	1.15997i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.50354	+	6.17819i	0.347445	+	0.252434i	0.747797	−	0.663928i	$-0.231112\pi$
$599$	8.50354	+	6.17819i	0.347445	+	0.252434i	−0.400351	+	0.916362i	$0.631112\pi$
$600$		0			0
$601$			21.7153i			0.885785i	0.896575	+	0.442893i	$0.146048\pi$
$601$			21.7153i			0.885785i	−0.896575	+	0.442893i	$0.853952\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−35.3018	−	108.648i	−1.43522	−	4.41716i
$606$		0			0
$607$	7.51722	+	23.1356i	0.305115	+	0.939046i	0.979634	+	0.200789i	$0.0643507\pi$
$607$	7.51722	+	23.1356i	0.305115	+	0.939046i	−0.674520	+	0.738257i	$0.735649\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.32932	+	7.16891i	−0.0942341	+	0.290023i
$612$		0			0
$613$	−4.76393	+	3.46120i	−0.192413	+	0.139797i	−0.679821	−	0.733378i	$-0.737943\pi$
$613$	−4.76393	+	3.46120i	−0.192413	+	0.139797i	0.487408	+	0.873175i	$0.337943\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.6018	+	10.6088i	−0.587846	+	0.427095i	−0.841544	−	0.540189i	$-0.818353\pi$
$617$	−14.6018	+	10.6088i	−0.587846	+	0.427095i	0.253698	+	0.967283i	$0.418353\pi$
$618$		0			0
$619$	−10.1074	+	31.1074i	−0.406250	+	1.25031i	0.513596	+	0.858032i	$0.328313\pi$
$619$	−10.1074	+	31.1074i	−0.406250	+	1.25031i	−0.919847	+	0.392278i	$0.871687\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.74204	−	20.7499i	−0.270114	−	0.831326i
$624$		0			0
$625$	34.6353	+	106.596i	1.38541	+	4.26385i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	36.8599i		−	1.46970i
$630$		0			0
$631$	4.61803	+	3.35520i	0.183841	+	0.133568i	0.675899	−	0.736994i	$-0.263755\pi$
$631$	4.61803	+	3.35520i	0.183841	+	0.133568i	−0.492058	+	0.870562i	$0.663755\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	41.9969	+	30.5125i	1.66660	+	1.21085i
$636$		0			0
$637$	2.03444	−	2.80017i	0.0806075	−	0.110947i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.7000	+	6.72584i	0.817601	+	0.265655i	0.687814	−	0.725887i	$-0.258570\pi$
$641$	20.7000	+	6.72584i	0.817601	+	0.265655i	0.129787	+	0.991542i	$0.458570\pi$
$642$		0			0
$643$	0.163119	+	0.224514i	0.00643278	+	0.00885397i	0.812221	−	0.583349i	$-0.198258\pi$
$643$	0.163119	+	0.224514i	0.00643278	+	0.00885397i	−0.805788	+	0.592203i	$0.798258\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.1470			−0.949318			−0.474659	−	0.880170i	$-0.657429\pi$
$647$	−24.1470			−0.949318			−0.474659	+	0.880170i	$0.657429\pi$
$648$		0			0
$649$	−3.71885	+	5.11855i	−0.145978	+	0.200921i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	17.1255i		−	0.670171i	−0.942188	−	0.335086i	$-0.891235\pi$
$653$		−	17.1255i		−	0.670171i	0.942188	−	0.335086i	$-0.108765\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$			3.07675i			0.119853i	0.998203	+	0.0599265i	$0.0190866\pi$
$659$			3.07675i			0.119853i	−0.998203	+	0.0599265i	$0.980913\pi$
$660$		0			0
$661$	−9.95492	+	30.6381i	−0.387201	+	1.19168i	0.547669	+	0.836695i	$0.315515\pi$
$661$	−9.95492	+	30.6381i	−0.387201	+	1.19168i	−0.934871	+	0.354988i	$0.884485\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−68.5202			−2.65710
$666$		0			0
$667$	3.71885	−	1.20833i	0.143994	−	0.0467866i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.1717	−	5.90436i	−0.701513	−	0.227935i
$672$		0			0
$673$	−0.364745	+	0.118513i	−0.0140599	+	0.00456834i	−0.316038	−	0.948746i	$-0.602353\pi$
$673$	−0.364745	+	0.118513i	−0.0140599	+	0.00456834i	0.301979	+	0.953315i	$0.402353\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.82545	+	6.41206i	0.339190	+	0.246436i	0.744320	−	0.667823i	$-0.232774\pi$
$677$	8.82545	+	6.41206i	0.339190	+	0.246436i	−0.405130	+	0.914259i	$0.632774\pi$
$678$		0			0
$679$	−13.9443	+	10.1311i	−0.535132	+	0.388796i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			25.0512i			0.958558i	0.877663	+	0.479279i	$0.159102\pi$
$683$			25.0512i			0.958558i	−0.877663	+	0.479279i	$0.840898\pi$
$684$		0			0
$685$	−56.9959	−	18.5191i	−2.17770	−	0.707579i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.78375	+	23.9559i	0.296537	+	0.912647i
$690$		0			0
$691$	25.2254	+	34.7198i	0.959620	+	1.32080i	0.947119	+	0.320882i	$0.103979\pi$
$691$	25.2254	+	34.7198i	0.959620	+	1.32080i	0.0125013	+	0.999922i	$0.496021\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−74.5715	+	54.1793i	−2.82866	+	2.05514i
$696$		0			0
$697$	5.38197	−	29.2177i	0.203856	−	1.10670i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.77633	+	17.7777i	−0.218169	+	0.671455i	0.780744	+	0.624851i	$0.214840\pi$
$701$	−5.77633	+	17.7777i	−0.218169	+	0.671455i	−0.998913	+	0.0466047i	$0.985160\pi$
$702$		0			0
$703$	30.8394	+	42.4468i	1.16313	+	1.60091i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.82545	−	27.1619i	−0.331915	−	1.02153i
$708$		0			0
$709$	−16.7082	−	5.42882i	−0.627490	−	0.203884i	−0.0220270	−	0.999757i	$-0.507012\pi$
$709$	−16.7082	−	5.42882i	−0.627490	−	0.203884i	−0.605463	+	0.795874i	$0.707012\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.66079	+	5.56589i	0.286899	+	0.208444i
$714$		0			0
$715$	50.9787	−	37.0382i	1.90650	−	1.38515i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.08341	−	2.86756i	0.0776979	−	0.106942i	−0.768399	−	0.639971i	$-0.778946\pi$
$719$	2.08341	−	2.86756i	0.0776979	−	0.106942i	0.846097	+	0.533029i	$0.178946\pi$
$720$		0			0
$721$	−5.00000	+	1.62460i	−0.186210	+	0.0605032i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.7343	−	27.1619i	−0.732914	−	1.00877i
$726$		0			0
$727$	1.80902	−	0.587785i	0.0670927	−	0.0217997i	−0.275278	−	0.961365i	$-0.588770\pi$
$727$	1.80902	−	0.587785i	0.0670927	−	0.0217997i	0.342371	+	0.939565i	$0.388770\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.8177	+	30.0295i	−0.806957	+	1.11068i
$732$		0			0
$733$	−0.135255	+	0.416272i	−0.00499575	+	0.0153754i	−0.953523	−	0.301319i	$-0.902573\pi$
$733$	−0.135255	+	0.416272i	−0.00499575	+	0.0153754i	0.948528	+	0.316695i	$0.102573\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−67.6305			−2.49120
$738$		0			0
$739$	−14.1246			−0.519582			−0.259791	−	0.965665i	$-0.583654\pi$
$739$	−14.1246			−0.519582			−0.259791	+	0.965665i	$0.583654\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.2799	−	43.9489i	0.523878	−	1.61233i	−0.242646	−	0.970115i	$-0.578015\pi$
$743$	14.2799	−	43.9489i	0.523878	−	1.61233i	0.766524	−	0.642215i	$-0.221985\pi$
$744$		0			0
$745$	2.29837	−	3.16344i	0.0842059	−	0.115899i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.1965	+	3.96287i	−0.445649	+	0.144800i
$750$		0			0
$751$	−8.88197	−	12.2250i	−0.324108	−	0.446096i	0.615608	−	0.788052i	$-0.288910\pi$
$751$	−8.88197	−	12.2250i	−0.324108	−	0.446096i	−0.939716	+	0.341957i	$0.888910\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.93358	+	1.60302i	−0.179551	+	0.0583397i
$756$		0			0
$757$	−14.2082	+	19.5559i	−0.516406	+	0.710772i	−0.984983	−	0.172651i	$-0.944767\pi$
$757$	−14.2082	+	19.5559i	−0.516406	+	0.710772i	0.468577	+	0.883423i	$0.344767\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	27.1961	−	19.7592i	0.985859	−	0.716269i	0.0268490	−	0.999640i	$-0.491453\pi$
$761$	27.1961	−	19.7592i	0.985859	−	0.716269i	0.959010	+	0.283371i	$0.0914527\pi$
$762$		0			0
$763$	−20.1246	−	14.6214i	−0.728560	−	0.529330i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.32932	−	0.756841i	−0.0841068	−	0.0273280i
$768$		0			0
$769$	−3.34346	−	10.2901i	−0.120568	−	0.371071i	0.872499	−	0.488615i	$-0.162498\pi$
$769$	−3.34346	−	10.2901i	−0.120568	−	0.371071i	−0.993068	+	0.117544i	$0.962498\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.24807	+	4.47058i	0.116825	+	0.160796i	0.863425	−	0.504478i	$-0.168315\pi$
$773$	3.24807	+	4.47058i	0.116825	+	0.160796i	−0.746600	+	0.665273i	$0.768315\pi$
$774$		0			0
$775$	25.1246	−	77.3256i	0.902503	−	2.77762i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.2477	+	38.1492i	0.653793	+	1.36684i
$780$		0			0
$781$	−7.04508	+	5.11855i	−0.252093	+	0.183156i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−17.8498	−	24.5682i	−0.637088	−	0.876877i
$786$		0			0
$787$	−4.75329	−	14.6291i	−0.169436	−	0.521472i	0.829899	−	0.557913i	$-0.188398\pi$
$787$	−4.75329	−	14.6291i	−0.169436	−	0.521472i	−0.999336	+	0.0364414i	$0.988398\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−29.6015	−	9.61810i	−1.05251	−	0.341980i
$792$		0			0
$793$		−	7.39645i		−	0.262656i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	37.9061	−	27.5404i	1.34270	−	0.975530i	0.343361	−	0.939203i	$-0.388434\pi$
$797$	37.9061	−	27.5404i	1.34270	−	0.975530i	0.999340	−	0.0363261i	$-0.0115655\pi$
$798$		0			0
$799$	12.0344	+	8.74353i	0.425748	+	0.309324i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	35.5007	−	11.5349i	1.25279	−	0.407057i
$804$		0			0
$805$	−16.6312	−	5.40380i	−0.586172	−	0.190459i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	36.0216	−	11.7041i	1.26645	−	0.411495i	0.402663	−	0.915348i	$-0.368085\pi$
$809$	36.0216	−	11.7041i	1.26645	−	0.411495i	0.863789	+	0.503853i	$0.168085\pi$
$810$		0			0
$811$	−21.6525			−0.760321			−0.380161	−	0.924920i	$-0.624131\pi$
$811$	−21.6525			−0.760321			−0.380161	+	0.924920i	$0.624131\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	19.0145	−	58.5206i	0.666049	−	2.04989i
$816$		0			0
$817$		−	52.8352i		−	1.84847i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−45.1689			−1.57641			−0.788204	−	0.615415i	$-0.788989\pi$
$821$	−45.1689			−1.57641			−0.788204	+	0.615415i	$0.788989\pi$
$822$		0			0
$823$			14.1068i			0.491734i	0.969304	+	0.245867i	$0.0790726\pi$
$823$			14.1068i			0.491734i	−0.969304	+	0.245867i	$0.920927\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.7516	−	16.1747i	0.408644	−	0.562450i	−0.554243	−	0.832355i	$-0.686992\pi$
$827$	11.7516	−	16.1747i	0.408644	−	0.562450i	0.962887	+	0.269905i	$0.0869923\pi$
$828$		0			0
$829$	−5.03444			−0.174853			−0.0874267	−	0.996171i	$-0.527864\pi$
$829$	−5.03444			−0.174853			−0.0874267	+	0.996171i	$0.527864\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.01483	−	5.52594i	−0.139106	−	0.191462i
$834$		0			0
$835$	−50.9787	−	16.5640i	−1.76419	−	0.573220i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.7760	+	28.5957i	−0.717267	+	0.987234i	0.282343	+	0.959314i	$0.408888\pi$
$839$	−20.7760	+	28.5957i	−0.717267	+	0.987234i	−0.999610	+	0.0279203i	$0.991112\pi$
$840$		0			0
$841$	−19.1074	−	13.8823i	−0.658876	−	0.478701i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.6753	−	19.3807i	−0.917658	−	0.666718i
$846$		0			0
$847$		−	60.8676i		−	2.09144i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.13779	+	12.7348i	0.141841	+	0.436543i
$852$		0			0
$853$	5.56231	+	17.1190i	0.190450	+	0.586144i	1.00000		0.000907135i	$-0.000288750\pi$
$853$	5.56231	+	17.1190i	0.190450	+	0.586144i	−0.809550	+	0.587051i	$0.800289\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.3880	−	31.9710i	0.354847	−	1.09211i	−0.601250	−	0.799061i	$-0.705331\pi$
$857$	10.3880	−	31.9710i	0.354847	−	1.09211i	0.956098	−	0.293047i	$-0.0946694\pi$
$858$		0			0
$859$	12.9164	−	9.38432i	0.440702	−	0.320189i	−0.345212	−	0.938525i	$-0.612193\pi$
$859$	12.9164	−	9.38432i	0.440702	−	0.320189i	0.785914	+	0.618336i	$0.212193\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.52827	+	1.83689i	−0.0860632	+	0.0625286i	−0.629985	−	0.776607i	$-0.716939\pi$
$863$	−2.52827	+	1.83689i	−0.0860632	+	0.0625286i	0.543922	+	0.839136i	$0.316939\pi$
$864$		0			0
$865$	−8.85817	+	27.2626i	−0.301187	+	0.926957i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	24.4689	+	75.3076i	0.830052	+	2.55464i
$870$		0			0
$871$	−8.09017	−	24.8990i	−0.274125	−	0.843670i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			98.2728i			3.32223i
$876$		0			0
$877$	−11.8713	−	8.62502i	−0.400866	−	0.291246i	0.369028	−	0.929418i	$-0.379691\pi$
$877$	−11.8713	−	8.62502i	−0.400866	−	0.291246i	−0.769894	+	0.638172i	$0.779691\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.56997	−	2.59373i	−0.120275	−	0.0873851i	0.526021	−	0.850471i	$-0.323683\pi$
$881$	−3.56997	−	2.59373i	−0.120275	−	0.0873851i	−0.646297	+	0.763086i	$0.723683\pi$
$882$		0			0
$883$	−3.98278	+	5.48183i	−0.134031	+	0.184478i	−0.870757	−	0.491713i	$-0.836371\pi$
$883$	−3.98278	+	5.48183i	−0.134031	+	0.184478i	0.736726	+	0.676191i	$0.236371\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−55.3580	−	17.9869i	−1.85874	−	0.603941i	−0.994984	−	0.100030i	$-0.968106\pi$
$887$	−55.3580	−	17.9869i	−1.85874	−	0.603941i	−0.863755	−	0.503911i	$-0.831894\pi$
$888$		0			0
$889$	16.2574	+	22.3763i	0.545254	+	0.750478i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−21.1739			−0.708558
$894$		0			0
$895$	49.5582	−	68.2111i	1.65655	−	2.28004i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			13.0333i			0.434685i
$900$		0			0
$901$	49.7082			1.65602
$902$		0			0
$903$		0			0
$904$		0			0
$905$			48.3796i			1.60819i
$906$		0			0
$907$	−11.7877	+	36.2789i	−0.391405	+	1.20462i	0.540321	+	0.841459i	$0.318303\pi$
$907$	−11.7877	+	36.2789i	−0.391405	+	1.20462i	−0.931726	+	0.363162i	$0.881697\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.5527			−0.382757			−0.191378	−	0.981516i	$-0.561296\pi$
$911$	−11.5527			−0.382757			−0.191378	+	0.981516i	$0.561296\pi$
$912$		0			0
$913$	−47.2599	+	15.3557i	−1.56407	+	0.508198i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12.2361	−	3.97574i	0.403631	−	0.131148i	−0.100164	−	0.994971i	$-0.531937\pi$
$919$	12.2361	−	3.97574i	0.403631	−	0.131148i	0.503795	+	0.863823i	$0.331937\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.72721	−	1.98144i	−0.0897673	−	0.0652198i
$924$		0			0
$925$	93.0132	−	67.5780i	3.05825	−	2.22195i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			19.8637i			0.651708i	0.945420	+	0.325854i	$0.105652\pi$
$929$			19.8637i			0.651708i	−0.945420	+	0.325854i	$0.894348\pi$
$930$		0			0
$931$	9.24671	+	3.00444i	0.303049	+	0.0984665i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−38.4269	−	118.266i	−1.25669	−	3.86771i
$936$		0			0
$937$	−27.8500	−	38.3323i	−0.909821	−	1.25226i	−0.967228	−	0.253910i	$-0.918283\pi$
$937$	−27.8500	−	38.3323i	−0.909821	−	1.25226i	0.0574067	−	0.998351i	$-0.481717\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.6435	+	11.3657i	−0.509963	+	0.370510i	−0.812810	−	0.582530i	$-0.802063\pi$
$941$	−15.6435	+	11.3657i	−0.509963	+	0.370510i	0.302847	+	0.953039i	$0.402063\pi$
$942$		0			0
$943$	1.42047	+	10.6986i	0.0462570	+	0.348396i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.85974	−	24.1898i	0.255407	−	0.786062i	−0.738342	−	0.674426i	$-0.764391\pi$
$947$	7.85974	−	24.1898i	0.255407	−	0.786062i	0.993749	−	0.111636i	$-0.0356090\pi$
$948$		0			0
$949$	8.49342	+	11.6902i	0.275708	+	0.379480i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	9.46926	+	29.1434i	0.306739	+	0.944047i	0.979022	+	0.203752i	$0.0653138\pi$
$953$	9.46926	+	29.1434i	0.306739	+	0.944047i	−0.672283	+	0.740294i	$0.734686\pi$
$954$		0			0
$955$	−2.29837	−	0.746787i	−0.0743736	−	0.0241655i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−25.8325	−	18.7684i	−0.834176	−	0.606064i
$960$		0			0
$961$	−0.454915	+	0.330515i	−0.0146747	+	0.0106618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	29.6015	−	40.7429i	0.952905	−	1.31156i
$966$		0			0
$967$	16.5451	−	5.37582i	0.532054	−	0.172875i	−0.0306547	−	0.999530i	$-0.509759\pi$
$967$	16.5451	−	5.37582i	0.532054	−	0.172875i	0.562709	+	0.826655i	$0.309759\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.81062	+	6.62125i	0.154380	+	0.212486i	0.879201	−	0.476452i	$-0.158077\pi$
$971$	4.81062	+	6.62125i	0.154380	+	0.212486i	−0.724820	+	0.688938i	$0.758077\pi$
$972$		0			0
$973$	−46.7082	+	15.1764i	−1.49740	+	0.486534i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.9580	−	19.2115i	0.446555	−	0.614630i	−0.525098	−	0.851042i	$-0.675971\pi$
$977$	13.9580	−	19.2115i	0.446555	−	0.614630i	0.971653	+	0.236411i	$0.0759713\pi$
$978$		0			0
$979$	−17.4164	+	53.6022i	−0.556631	+	1.71313i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.32932			−0.0742937			−0.0371469	−	0.999310i	$-0.511827\pi$
$983$	−2.32932			−0.0742937			−0.0371469	+	0.999310i	$0.511827\pi$
$984$		0			0
$985$	67.6099			2.15423
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.16681	−	12.8241i	0.132497	−	0.407784i
$990$		0			0
$991$	−26.6074	+	36.6219i	−0.845212	+	1.16333i	0.139686	+	0.990196i	$0.455391\pi$
$991$	−26.6074	+	36.6219i	−0.845212	+	1.16333i	−0.984898	+	0.173138i	$0.944609\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−31.2110	+	10.1411i	−0.989454	+	0.321493i
$996$		0			0
$997$	25.7533	+	35.4464i	0.815615	+	1.12260i	0.990433	+	0.137997i	$0.0440663\pi$
$997$	25.7533	+	35.4464i	0.815615	+	1.12260i	−0.174818	+	0.984601i	$0.555934\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1476.2.bb.a.865.2	yes	8
3.2	odd	2	inner	1476.2.bb.a.865.1	✓	8
41.31	even	10	inner	1476.2.bb.a.1261.2	yes	8
123.113	odd	10	inner	1476.2.bb.a.1261.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1476.2.bb.a.865.1	✓	8	3.2	odd	2	inner
1476.2.bb.a.865.2	yes	8	1.1	even	1	trivial
1476.2.bb.a.1261.1	yes	8	123.113	odd	10	inner
1476.2.bb.a.1261.2	yes	8	41.31	even	10	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:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1476.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36361 - 4.19675i) q^{5} +(1.38197 - 1.90211i) q^{7} +O(q^{10})\)	\(q+(1.36361 - 4.19675i) q^{5} +(1.38197 - 1.90211i) q^{7} +(-5.77633 + 1.87684i) q^{11} +(-1.38197 - 1.90211i) q^{13} +(-4.41272 + 1.43378i) q^{17} +(3.88197 - 5.34307i) q^{19} +(1.36361 - 0.990718i) q^{23} +(-11.7082 - 8.50651i) q^{25} +(2.20636 + 0.716891i) q^{29} +(1.73607 + 5.34307i) q^{31} +(-6.09824 - 8.39350i) q^{35} +(-2.45492 + 7.55545i) q^{37} +(-3.04912 + 5.63053i) q^{41} +(6.47214 - 4.70228i) q^{43} +(-1.88446 - 2.59373i) q^{47} +(0.454915 + 1.40008i) q^{49} +(-10.1891 - 3.31062i) q^{53} +26.8011i q^{55} +(0.842755 - 0.612298i) q^{59} +(2.54508 + 1.84911i) q^{61} +(-9.86715 + 3.20603i) q^{65} +(10.5902 + 3.44095i) q^{67} +(1.36361 - 0.443063i) q^{71} -6.14590 q^{73} +(-4.41272 + 13.5810i) q^{77} -13.0373i q^{79} +8.18164 q^{83} +20.4742i q^{85} +(5.45443 - 7.50738i) q^{89} -5.52786 q^{91} +(-17.1300 - 23.5775i) q^{95} +(-6.97214 - 2.26538i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 20 q^{7}+O(q^{10}) \) 8 * q + 20 * q^7	\( 8 q + 20 q^{7} - 20 q^{13} + 40 q^{19} - 40 q^{25} - 4 q^{31} - 42 q^{37} + 16 q^{43} + 26 q^{49} - 2 q^{61} + 40 q^{67} - 76 q^{73} - 80 q^{91} - 20 q^{97}+O(q^{100}) \) 8 * q + 20 * q^7 - 20 * q^13 + 40 * q^19 - 40 * q^25 - 4 * q^31 - 42 * q^37 + 16 * q^43 + 26 * q^49 - 2 * q^61 + 40 * q^67 - 76 * q^73 - 80 * q^91 - 20 * q^97

Introduction

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