LMFDB - Embedded newform 2520.2.bi.q.1801.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, 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:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.2
Root			$3.17656i$ of defining polynomial
Character	$\chi$	$=$	2520.1801
Dual form			2520.2.bi.q.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +(-2.25098 - 3.89881i) q^{11} +5.09052 q^{13} +(1.00000 + 1.73205i) q^{17} +(1.54526 - 2.67647i) q^{19} +(2.89812 - 5.01969i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.50196 q^{29} +(-2.70572 - 4.68644i) q^{31} +(2.54526 + 0.722254i) q^{35} +(-3.54526 + 6.14057i) q^{37} +6.59248 q^{41} +4.70572 q^{43} +(5.04722 - 8.74204i) q^{47} +(-6.16242 + 3.32033i) q^{49} +(4.95670 + 8.58526i) q^{53} -4.50196 q^{55} +(4.00000 + 6.92820i) q^{59} +(4.45670 - 7.71923i) q^{61} +(2.54526 - 4.40852i) q^{65} +(0.0585795 + 0.101463i) q^{67} +(-4.09052 - 7.08499i) q^{73} +(8.54526 - 8.29771i) q^{77} +(7.09052 - 12.2811i) q^{79} +10.7057 q^{83} +2.00000 q^{85} +(2.04526 - 3.54249i) q^{89} +(3.29428 + 13.0592i) q^{91} +(-1.54526 - 2.67647i) q^{95} -2.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 6 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 6 * q^7	$ 6 q + 3 q^{5} + 6 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} - 3 q^{25} - 24 q^{29} - 12 q^{31} + 3 q^{35} - 9 q^{37} - 18 q^{41} + 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} + 6 q^{55} + 24 q^{59} + 6 q^{61} + 3 q^{65} - 6 q^{67} + 39 q^{77} + 18 q^{79} + 60 q^{83} + 12 q^{85} + 24 q^{91} + 3 q^{95} - 12 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 6 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 - 3 * q^25 - 24 * q^29 - 12 * q^31 + 3 * q^35 - 9 * q^37 - 18 * q^41 + 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 + 6 * q^55 + 24 * q^59 + 6 * q^61 + 3 * q^65 - 6 * q^67 + 39 * q^77 + 18 * q^79 + 60 * q^83 + 12 * q^85 + 24 * q^91 + 3 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.647140	+	2.56539i	0.244596	+	0.969625i
$7$	0.647140	+	2.56539i	0.244596	+	0.969625i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.25098	−	3.89881i	−0.678696	−	1.17554i	−0.975374	−	0.220558i	$-0.929212\pi$
$11$	−2.25098	−	3.89881i	−0.678696	−	1.17554i	0.296678	−	0.954978i	$-0.404121\pi$
$12$		0			0
$13$	5.09052			1.41186			0.705928	−	0.708283i	$-0.250530\pi$
$13$	5.09052			1.41186			0.705928	+	0.708283i	$0.250530\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	1.54526	−	2.67647i	0.354507	−	0.614024i	−0.632526	−	0.774539i	$-0.717982\pi$
$19$	1.54526	−	2.67647i	0.354507	−	0.614024i	0.987033	+	0.160515i	$0.0513154\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.89812	−	5.01969i	0.604300	−	1.04668i	−0.387862	−	0.921717i	$-0.626786\pi$
$23$	2.89812	−	5.01969i	0.604300	−	1.04668i	0.992162	−	0.124960i	$-0.0398804\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.50196			−1.76447			−0.882235	−	0.470810i	$-0.843962\pi$
$29$	−9.50196			−1.76447			−0.882235	+	0.470810i	$0.843962\pi$
$30$		0			0
$31$	−2.70572	−	4.68644i	−0.485962	−	0.841710i	0.513908	−	0.857845i	$-0.328197\pi$
$31$	−2.70572	−	4.68644i	−0.485962	−	0.841710i	−0.999870	+	0.0161350i	$0.994864\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.54526	+	0.722254i	0.430228	+	0.122083i
$36$		0			0
$37$	−3.54526	+	6.14057i	−0.582837	+	1.00950i	0.412304	+	0.911046i	$0.364724\pi$
$37$	−3.54526	+	6.14057i	−0.582837	+	1.00950i	−0.995141	+	0.0984573i	$0.968609\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.59248			1.02957			0.514786	−	0.857319i	$-0.327871\pi$
$41$	6.59248			1.02957			0.514786	+	0.857319i	$0.327871\pi$
$42$		0			0
$43$	4.70572			0.717616			0.358808	−	0.933411i	$-0.383183\pi$
$43$	4.70572			0.717616			0.358808	+	0.933411i	$0.383183\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.04722	−	8.74204i	0.736213	−	1.27516i	−0.217977	−	0.975954i	$-0.569946\pi$
$47$	5.04722	−	8.74204i	0.736213	−	1.27516i	0.954189	−	0.299204i	$-0.0967210\pi$
$48$		0			0
$49$	−6.16242	+	3.32033i	−0.880346	+	0.474333i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.95670	+	8.58526i	0.680855	+	1.17928i	0.974720	+	0.223429i	$0.0717250\pi$
$53$	4.95670	+	8.58526i	0.680855	+	1.17928i	−0.293865	+	0.955847i	$0.594942\pi$
$54$		0			0
$55$	−4.50196			−0.607044
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	4.45670	−	7.71923i	0.570622	−	0.988346i	−0.425880	−	0.904780i	$-0.640036\pi$
$61$	4.45670	−	7.71923i	0.570622	−	0.988346i	0.996502	−	0.0835666i	$-0.0266311\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.54526	−	4.40852i	0.315701	−	0.546810i
$66$		0			0
$67$	0.0585795	+	0.101463i	0.00715662	+	0.0123956i	0.869582	−	0.493789i	$-0.164389\pi$
$67$	0.0585795	+	0.101463i	0.00715662	+	0.0123956i	−0.862425	+	0.506185i	$0.831055\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−4.09052	−	7.08499i	−0.478759	−	0.829235i	0.520944	−	0.853591i	$-0.325580\pi$
$73$	−4.09052	−	7.08499i	−0.478759	−	0.829235i	−0.999703	+	0.0243555i	$0.992247\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.54526	−	8.29771i	0.973823	−	0.945612i
$78$		0			0
$79$	7.09052	−	12.2811i	0.797746	−	1.38174i	−0.123335	−	0.992365i	$-0.539359\pi$
$79$	7.09052	−	12.2811i	0.797746	−	1.38174i	0.921081	−	0.389371i	$-0.127308\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.7057			1.17511			0.587553	−	0.809186i	$-0.300091\pi$
$83$	10.7057			1.17511			0.587553	+	0.809186i	$0.300091\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.04526	−	3.54249i	0.216797	−	0.375504i	−0.737030	−	0.675860i	$-0.763772\pi$
$89$	2.04526	−	3.54249i	0.216797	−	0.375504i	0.953827	+	0.300356i	$0.0971056\pi$
$90$		0			0
$91$	3.29428	+	13.0592i	0.345334	+	1.36897i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.54526	−	2.67647i	−0.158540	−	0.274600i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.66046	−	2.87600i	−0.165222	−	0.286173i	0.771512	−	0.636215i	$-0.219501\pi$
$101$	−1.66046	−	2.87600i	−0.165222	−	0.286173i	−0.936734	+	0.350042i	$0.886167\pi$
$102$		0			0
$103$	5.44338	−	9.42821i	0.536352	−	0.928989i	−0.462744	−	0.886492i	$-0.653135\pi$
$103$	5.44338	−	9.42821i	0.536352	−	0.928989i	0.999097	−	0.0424975i	$-0.0135314\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.94142	−	3.36264i	0.187684	−	0.325079i	−0.756794	−	0.653654i	$-0.773235\pi$
$107$	1.94142	−	3.36264i	0.187684	−	0.325079i	0.944478	+	0.328575i	$0.106569\pi$
$108$		0			0
$109$	5.13578	+	8.89543i	0.491919	+	0.852028i	0.999957	−	0.00930661i	$-0.00296243\pi$
$109$	5.13578	+	8.89543i	0.491919	+	0.852028i	−0.508038	+	0.861335i	$0.669629\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.82288			−0.265554			−0.132777	−	0.991146i	$-0.542389\pi$
$113$	−2.82288			−0.265554			−0.132777	+	0.991146i	$0.542389\pi$
$114$		0			0
$115$	−2.89812	−	5.01969i	−0.270251	−	0.468089i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.79624	+	3.68627i	−0.348001	+	0.337919i
$120$		0			0
$121$	−4.63382	+	8.02601i	−0.421256	+	0.729638i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.73236			−0.153722			−0.0768610	−	0.997042i	$-0.524490\pi$
$127$	−1.73236			−0.153722			−0.0768610	+	0.997042i	$0.524490\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.36814	+	11.0299i	−0.556387	+	0.963690i	0.441407	+	0.897307i	$0.354479\pi$
$131$	−6.36814	+	11.0299i	−0.556387	+	0.963690i	−0.997794	+	0.0663835i	$0.978854\pi$
$132$		0			0
$133$	7.86618	+	2.23214i	0.682084	+	0.193551i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−1.41144			−0.119717			−0.0598584	−	0.998207i	$-0.519065\pi$
$139$	−1.41144			−0.119717			−0.0598584	+	0.998207i	$0.519065\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.4587	−	19.8470i	−0.958221	−	1.65969i
$144$		0			0
$145$	−4.75098	+	8.22894i	−0.394547	+	0.683376i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.5472	−	20.0004i	0.945985	−	1.63849i	0.192218	−	0.981352i	$-0.438432\pi$
$149$	11.5472	−	20.0004i	0.945985	−	1.63849i	0.753767	−	0.657142i	$-0.228235\pi$
$150$		0			0
$151$	0.203760	+	0.352922i	0.0165817	+	0.0287204i	0.874197	−	0.485571i	$-0.161388\pi$
$151$	0.203760	+	0.352922i	0.0165817	+	0.0287204i	−0.857615	+	0.514291i	$0.828055\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.41144			−0.434657
$156$		0			0
$157$	7.04722	+	12.2061i	0.562429	+	0.974156i	0.997284	+	0.0736555i	$0.0234665\pi$
$157$	7.04722	+	12.2061i	0.562429	+	0.974156i	−0.434854	+	0.900501i	$0.643200\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.7529	+	4.18636i	1.16269	+	0.329931i
$162$		0			0
$163$	8.09052	−	14.0132i	0.633698	−	1.09760i	−0.353091	−	0.935589i	$-0.614869\pi$
$163$	8.09052	−	14.0132i	0.633698	−	1.09760i	0.986789	−	0.162009i	$-0.0517973\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.79624			−0.603291			−0.301646	−	0.953420i	$-0.597536\pi$
$167$	−7.79624			−0.603291			−0.301646	+	0.953420i	$0.597536\pi$
$168$		0			0
$169$	12.9134			0.993338
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.45474	+	7.71584i	−0.338688	+	0.586624i	−0.984186	−	0.177137i	$-0.943316\pi$
$173$	−4.45474	+	7.71584i	−0.338688	+	0.586624i	0.645499	+	0.763762i	$0.276650\pi$
$174$		0			0
$175$	1.89812	−	1.84313i	0.143484	−	0.139328i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.839541	+	1.45413i	0.0627502	+	0.108687i	0.895694	−	0.444671i	$-0.146680\pi$
$179$	0.839541	+	1.45413i	0.0627502	+	0.108687i	−0.832944	+	0.553358i	$0.813346\pi$
$180$		0			0
$181$	12.5059			0.929555			0.464777	−	0.885428i	$-0.346134\pi$
$181$	12.5059			0.929555			0.464777	+	0.885428i	$0.346134\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.54526	+	6.14057i	0.260653	+	0.451464i
$186$		0			0
$187$	4.50196	−	7.79762i	0.329216	−	0.570219i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.29428	−	5.70586i	0.238366	−	0.412862i	−0.721880	−	0.692019i	$-0.756722\pi$
$191$	3.29428	−	5.70586i	0.238366	−	0.412862i	0.960245	+	0.279157i	$0.0900550\pi$
$192$		0			0
$193$	−8.91340	−	15.4385i	−0.641601	−	1.11128i	−0.985075	−	0.172123i	$-0.944937\pi$
$193$	−8.91340	−	15.4385i	−0.641601	−	1.11128i	0.343475	−	0.939162i	$-0.388396\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.09052			−0.362685			−0.181342	−	0.983420i	$-0.558044\pi$
$197$	−5.09052			−0.362685			−0.181342	+	0.983420i	$0.558044\pi$
$198$		0			0
$199$	−12.1810	−	21.0982i	−0.863491	−	1.49561i	−0.868538	−	0.495623i	$-0.834940\pi$
$199$	−12.1810	−	21.0982i	−0.863491	−	1.49561i	0.00504654	−	0.999987i	$-0.498394\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.14910	−	24.3762i	−0.431582	−	1.71087i
$204$		0			0
$205$	3.29624	−	5.70926i	0.230219	−	0.398752i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.9134			−0.962410
$210$		0			0
$211$	−8.26764			−0.569168			−0.284584	−	0.958651i	$-0.591855\pi$
$211$	−8.26764			−0.569168			−0.284584	+	0.958651i	$0.591855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.35286	−	4.07527i	0.160464	−	0.277931i
$216$		0			0
$217$	10.2716	−	9.97400i	0.697279	−	0.677079i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.09052	+	8.81704i	0.342425	+	0.593098i
$222$		0			0
$223$	−17.8268			−1.19377			−0.596885	−	0.802327i	$-0.703595\pi$
$223$	−17.8268			−1.19377			−0.596885	+	0.802327i	$0.703595\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.67908	+	4.64030i	0.177817	+	0.307988i	0.941133	−	0.338038i	$-0.109763\pi$
$227$	2.67908	+	4.64030i	0.177817	+	0.307988i	−0.763316	+	0.646026i	$0.776430\pi$
$228$		0			0
$229$	−12.0905	+	20.9414i	−0.798964	+	1.38385i	0.121327	+	0.992613i	$0.461285\pi$
$229$	−12.0905	+	20.9414i	−0.798964	+	1.38385i	−0.920291	+	0.391234i	$0.872048\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$	−5.04722	−	8.74204i	−0.329244	−	0.570268i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.7696			0.825997			0.412998	−	0.910732i	$-0.364481\pi$
$239$	12.7696			0.825997			0.412998	+	0.910732i	$0.364481\pi$
$240$		0			0
$241$	11.0472	+	19.1343i	0.711614	+	1.23255i	0.964251	+	0.264990i	$0.0853688\pi$
$241$	11.0472	+	19.1343i	0.711614	+	1.23255i	−0.252637	+	0.967561i	$0.581298\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.205720	+	6.99698i	−0.0131429	+	0.447020i
$246$		0			0
$247$	7.86618	−	13.6246i	0.500513	−	0.866914i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.5059			0.852484			0.426242	−	0.904609i	$-0.359837\pi$
$251$	13.5059			0.852484			0.426242	+	0.904609i	$0.359837\pi$
$252$		0			0
$253$	−26.0944			−1.64054
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.18104	+	14.1700i	−0.510319	+	0.883899i	0.489609	+	0.871942i	$0.337139\pi$
$257$	−8.18104	+	14.1700i	−0.510319	+	0.883899i	−0.999929	+	0.0119570i	$0.996194\pi$
$258$		0			0
$259$	−18.0472	−	5.12115i	−1.12140	−	0.318213i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.55662	+	7.89230i	0.280973	+	0.486660i	0.971625	−	0.236528i	$-0.0760095\pi$
$263$	4.55662	+	7.89230i	0.280973	+	0.486660i	−0.690651	+	0.723188i	$0.742676\pi$
$264$		0			0
$265$	9.91340			0.608975
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.45670	+	7.71923i	0.271730	+	0.470650i	0.969305	−	0.245862i	$-0.0790710\pi$
$269$	4.45670	+	7.71923i	0.271730	+	0.470650i	−0.697575	+	0.716512i	$0.745738\pi$
$270$		0			0
$271$	−8.18104	+	14.1700i	−0.496963	+	0.860765i	−0.999994	−	0.00350346i	$-0.998885\pi$
$271$	−8.18104	+	14.1700i	−0.496963	+	0.860765i	0.503031	+	0.864268i	$0.332218\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.25098	+	3.89881i	−0.135739	+	0.235107i
$276$		0			0
$277$	−5.58856	−	9.67967i	−0.335784	−	0.581595i	0.647851	−	0.761767i	$-0.275668\pi$
$277$	−5.58856	−	9.67967i	−0.335784	−	0.581595i	−0.983635	+	0.180172i	$0.942335\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	28.2755			1.68677			0.843387	−	0.537307i	$-0.180558\pi$
$281$	28.2755			1.68677			0.843387	+	0.537307i	$0.180558\pi$
$282$		0			0
$283$	6.41144	+	11.1049i	0.381121	+	0.660120i	0.991223	−	0.132203i	$-0.0422050\pi$
$283$	6.41144	+	11.1049i	0.381121	+	0.660120i	−0.610102	+	0.792323i	$0.708872\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.26626	+	16.9123i	0.251829	+	0.998299i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.90948			−0.520497			−0.260249	−	0.965542i	$-0.583805\pi$
$293$	−8.90948			−0.520497			−0.260249	+	0.965542i	$0.583805\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$		0			0
$298$		0			0
$299$	14.7529	−	25.5528i	0.853185	−	1.47776i
$300$		0			0
$301$	3.04526	+	12.0720i	0.175526	+	0.695818i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.45670	−	7.71923i	−0.255190	−	0.442002i
$306$		0			0
$307$	−9.12108			−0.520567			−0.260284	−	0.965532i	$-0.583816\pi$
$307$	−9.12108			−0.520567			−0.260284	+	0.965532i	$0.583816\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.58856	−	11.4117i	−0.373603	−	0.647099i	0.616514	−	0.787344i	$-0.288544\pi$
$311$	−6.58856	−	11.4117i	−0.373603	−	0.647099i	−0.990117	+	0.140245i	$0.955211\pi$
$312$		0			0
$313$	8.76960	−	15.1894i	0.495687	−	0.858555i	−0.504300	−	0.863528i	$-0.668250\pi$
$313$	8.76960	−	15.1894i	0.495687	−	0.858555i	0.999988	+	0.00497286i	$0.00158292\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.59248	+	11.4185i	−0.370271	+	0.641327i	−0.989607	−	0.143798i	$-0.954068\pi$
$317$	−6.59248	+	11.4185i	−0.370271	+	0.641327i	0.619336	+	0.785126i	$0.287402\pi$
$318$		0			0
$319$	21.3887	+	37.0464i	1.19754	+	2.07420i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.18104			0.343922
$324$		0			0
$325$	−2.54526	−	4.40852i	−0.141186	−	0.244541i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	25.6930	+	7.29075i	1.41650	+	0.401952i
$330$		0			0
$331$	−4.25098	+	7.36291i	−0.233655	+	0.404702i	−0.958881	−	0.283809i	$-0.908402\pi$
$331$	−4.25098	+	7.36291i	−0.233655	+	0.404702i	0.725226	+	0.688511i	$0.241735\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.117159			0.00640108
$336$		0			0
$337$	28.1889			1.53555			0.767773	−	0.640722i	$-0.221365\pi$
$337$	28.1889			1.53555			0.767773	+	0.640722i	$0.221365\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.1810	+	21.0982i	−0.659640	+	1.14253i
$342$		0			0
$343$	−12.5059	−	13.6603i	−0.675254	−	0.737585i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.35286	+	2.34322i	0.0726253	+	0.125791i	0.900051	−	0.435784i	$-0.143529\pi$
$347$	1.35286	+	2.34322i	0.0726253	+	0.125791i	−0.827426	+	0.561575i	$0.810196\pi$
$348$		0			0
$349$	−13.6830			−0.732434			−0.366217	−	0.930529i	$-0.619347\pi$
$349$	−13.6830			−0.732434			−0.366217	+	0.930529i	$0.619347\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.1810	−	17.6341i	−0.541882	−	0.938567i	−0.998796	−	0.0490565i	$-0.984379\pi$
$353$	−10.1810	−	17.6341i	−0.541882	−	0.938567i	0.456914	−	0.889511i	$-0.348955\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.20768	+	15.9482i	−0.485963	+	0.841712i	−0.999870	−	0.0161337i	$-0.994864\pi$
$359$	−9.20768	+	15.9482i	−0.485963	+	0.841712i	0.513907	+	0.857846i	$0.328198\pi$
$360$		0			0
$361$	4.72434	+	8.18280i	0.248650	+	0.430674i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.18104			−0.428215
$366$		0			0
$367$	12.8115	+	22.1902i	0.668756	+	1.15832i	0.978252	+	0.207419i	$0.0665062\pi$
$367$	12.8115	+	22.1902i	0.668756	+	1.15832i	−0.309496	+	0.950901i	$0.600160\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.8168	+	18.2717i	−0.976921	+	0.948620i
$372$		0			0
$373$	−14.0944	+	24.4123i	−0.729782	+	1.26402i	0.227193	+	0.973850i	$0.427045\pi$
$373$	−14.0944	+	24.4123i	−0.729782	+	1.26402i	−0.956975	+	0.290170i	$0.906288\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−48.3699			−2.49118
$378$		0			0
$379$	21.7402			1.11672			0.558359	−	0.829599i	$-0.311431\pi$
$379$	21.7402			1.11672			0.558359	+	0.829599i	$0.311431\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.1058	+	17.5038i	−0.516382	+	0.894400i	0.483437	+	0.875379i	$0.339388\pi$
$383$	−10.1058	+	17.5038i	−0.516382	+	0.894400i	−0.999819	+	0.0190210i	$0.993945\pi$
$384$		0			0
$385$	−2.91340	−	11.5493i	−0.148481	−	0.588605i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.91340	+	11.9744i	0.350523	+	0.607124i	0.986341	−	0.164715i	$-0.0526704\pi$
$389$	6.91340	+	11.9744i	0.350523	+	0.607124i	−0.635818	+	0.771839i	$0.719337\pi$
$390$		0			0
$391$	11.5925			0.586257
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.09052	−	12.2811i	−0.356763	−	0.617931i
$396$		0			0
$397$	−18.1850	+	31.4973i	−0.912677	+	1.58080i	−0.102410	+	0.994742i	$0.532655\pi$
$397$	−18.1850	+	31.4973i	−0.912677	+	1.58080i	−0.810267	+	0.586061i	$0.800678\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.40948	+	5.90539i	−0.170261	+	0.294901i	−0.938511	−	0.345249i	$-0.887795\pi$
$401$	−3.40948	+	5.90539i	−0.170261	+	0.294901i	0.768250	+	0.640150i	$0.221128\pi$
$402$		0			0
$403$	−13.7735	−	23.8564i	−0.686108	−	1.18837i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	31.9212			1.58228
$408$		0			0
$409$	8.93202	+	15.4707i	0.441660	+	0.764978i	0.997813	−	0.0661025i	$-0.0210564\pi$
$409$	8.93202	+	15.4707i	0.441660	+	0.764978i	−0.556153	+	0.831080i	$0.687723\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.1850	+	14.7451i	−0.747203	+	0.725557i
$414$		0			0
$415$	5.35286	−	9.27143i	0.262762	−	0.455116i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−18.4487			−0.901277			−0.450639	−	0.892706i	$-0.648804\pi$
$419$	−18.4487			−0.901277			−0.450639	+	0.892706i	$0.648804\pi$
$420$		0			0
$421$	−10.7324			−0.523063			−0.261532	−	0.965195i	$-0.584228\pi$
$421$	−10.7324			−0.523063			−0.261532	+	0.965195i	$0.584228\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	22.6869	+	6.43773i	1.09790	+	0.311544i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.29428	+	5.70586i	0.158680	+	0.274842i	0.934393	−	0.356244i	$-0.115943\pi$
$431$	3.29428	+	5.70586i	0.158680	+	0.274842i	−0.775713	+	0.631086i	$0.782610\pi$
$432$		0			0
$433$	5.17712			0.248797			0.124398	−	0.992232i	$-0.460300\pi$
$433$	5.17712			0.248797			0.124398	+	0.992232i	$0.460300\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.95670	−	15.5135i	−0.428457	−	0.742109i
$438$		0			0
$439$	−15.5059	+	26.8570i	−0.740055	+	1.28181i	0.212414	+	0.977180i	$0.431867\pi$
$439$	−15.5059	+	26.8570i	−0.740055	+	1.28181i	−0.952470	+	0.304634i	$0.901466\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.43946	−	4.22527i	0.115902	−	0.200749i	−0.802238	−	0.597005i	$-0.796357\pi$
$443$	2.43946	−	4.22527i	0.115902	−	0.200749i	0.918140	+	0.396256i	$0.129691\pi$
$444$		0			0
$445$	−2.04526	−	3.54249i	−0.0969546	−	0.167930i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.7696			−1.31053			−0.655264	−	0.755400i	$-0.727443\pi$
$449$	−27.7696			−1.31053			−0.655264	+	0.755400i	$0.727443\pi$
$450$		0			0
$451$	−14.8395	−	25.7028i	−0.698767	−	1.21030i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.9567	+	3.67665i	0.607419	+	0.172364i
$456$		0			0
$457$	12.5020	−	21.6540i	0.584817	−	1.01293i	−0.410081	−	0.912049i	$-0.634500\pi$
$457$	12.5020	−	21.6540i	0.584817	−	1.01293i	0.994898	−	0.100884i	$-0.0321670\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.00784			0.186664			0.0933318	−	0.995635i	$-0.470248\pi$
$461$	4.00784			0.186664			0.0933318	+	0.995635i	$0.470248\pi$
$462$		0			0
$463$	−36.8002			−1.71025			−0.855124	−	0.518423i	$-0.826519\pi$
$463$	−36.8002			−1.71025			−0.855124	+	0.518423i	$0.826519\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.7377	+	20.3302i	−0.543154	+	0.940771i	0.455566	+	0.890202i	$0.349437\pi$
$467$	−11.7377	+	20.3302i	−0.543154	+	0.940771i	−0.998721	+	0.0505688i	$0.983897\pi$
$468$		0			0
$469$	−0.222382	+	0.215939i	−0.0102686	+	0.00997116i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.5925	−	18.3467i	−0.487043	−	0.843583i
$474$		0			0
$475$	−3.09052			−0.141803
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.8868	−	32.7128i	−0.862958	−	1.49469i	−0.869060	−	0.494706i	$-0.835276\pi$
$479$	−18.8868	−	32.7128i	−0.862958	−	1.49469i	0.00610232	−	0.999981i	$-0.498058\pi$
$480$		0			0
$481$	−18.0472	+	31.2587i	−0.822882	+	1.42527i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	3.08660	+	5.34615i	0.139867	+	0.242257i	0.927446	−	0.373957i	$-0.121999\pi$
$487$	3.08660	+	5.34615i	0.139867	+	0.242257i	−0.787579	+	0.616214i	$0.788666\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−39.7814			−1.79531			−0.897654	−	0.440701i	$-0.854730\pi$
$491$	−39.7814			−1.79531			−0.897654	+	0.440701i	$0.854730\pi$
$492$		0			0
$493$	−9.50196	−	16.4579i	−0.427947	−	0.741226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.88284	+	3.26118i	−0.0842875	+	0.145990i	−0.905087	−	0.425226i	$-0.860195\pi$
$499$	−1.88284	+	3.26118i	−0.0842875	+	0.145990i	0.820800	+	0.571216i	$0.193528\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.7057			−0.834047			−0.417023	−	0.908896i	$-0.636927\pi$
$503$	−18.7057			−0.834047			−0.417023	+	0.908896i	$0.636927\pi$
$504$		0			0
$505$	−3.32092			−0.147779
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.16242	−	10.6736i	0.273144	−	0.473100i	−0.696521	−	0.717537i	$-0.745270\pi$
$509$	6.16242	−	10.6736i	0.273144	−	0.473100i	0.969665	+	0.244437i	$0.0786030\pi$
$510$		0			0
$511$	15.5286	−	15.0787i	0.686945	−	0.667045i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.44338	−	9.42821i	−0.239864	−	0.415457i
$516$		0			0
$517$	−45.4448			−1.99866
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−14.7796	−	25.5990i	−0.647505	−	1.12151i	−0.983717	−	0.179725i	$-0.942479\pi$
$521$	−14.7796	−	25.5990i	−0.647505	−	1.12151i	0.336212	−	0.941786i	$-0.390854\pi$
$522$		0			0
$523$	21.5020	−	37.2425i	0.940215	−	1.62850i	0.175155	−	0.984541i	$-0.443957\pi$
$523$	21.5020	−	37.2425i	0.940215	−	1.62850i	0.765060	−	0.643959i	$-0.222709\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.41144	−	9.37289i	0.235726	−	0.408289i
$528$		0			0
$529$	−5.29820	−	9.17675i	−0.230357	−	0.398989i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	33.5592			1.45361
$534$		0			0
$535$	−1.94142	−	3.36264i	−0.0839349	−	0.145380i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	26.8168	+	16.5521i	1.15508	+	0.712950i
$540$		0			0
$541$	2.48334	−	4.30127i	0.106767	−	0.184926i	−0.807692	−	0.589605i	$-0.799283\pi$
$541$	2.48334	−	4.30127i	0.106767	−	0.184926i	0.914459	+	0.404679i	$0.132617\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.2716			0.439985
$546$		0			0
$547$	−22.1250			−0.945997			−0.472998	−	0.881063i	$-0.656828\pi$
$547$	−22.1250			−0.945997			−0.472998	+	0.881063i	$0.656828\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.6830	+	25.4317i	−0.625517	+	1.08343i
$552$		0			0
$553$	36.0944	+	10.2423i	1.53489	+	0.435547i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.77958	+	4.81437i	0.117775	+	0.203991i	0.918885	−	0.394524i	$-0.129091\pi$
$557$	2.77958	+	4.81437i	0.117775	+	0.203991i	−0.801111	+	0.598516i	$0.795757\pi$
$558$		0			0
$559$	23.9546			1.01317
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.74158	+	8.21266i	0.199834	+	0.346122i	0.948474	−	0.316854i	$-0.102626\pi$
$563$	4.74158	+	8.21266i	0.199834	+	0.346122i	−0.748641	+	0.662976i	$0.769293\pi$
$564$		0			0
$565$	−1.41144	+	2.44468i	−0.0593797	+	0.102849i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.1417	+	29.6902i	−0.718616	+	1.24468i	0.242933	+	0.970043i	$0.421891\pi$
$569$	−17.1417	+	29.6902i	−0.718616	+	1.24468i	−0.961548	+	0.274636i	$0.911443\pi$
$570$		0			0
$571$	15.7735	+	27.3205i	0.660101	+	1.14333i	0.980589	+	0.196076i	$0.0628200\pi$
$571$	15.7735	+	27.3205i	0.660101	+	1.14333i	−0.320487	+	0.947253i	$0.603847\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.79624			−0.241720
$576$		0			0
$577$	5.32092	+	9.21610i	0.221513	+	0.383671i	0.955268	−	0.295743i	$-0.0955672\pi$
$577$	5.32092	+	9.21610i	0.221513	+	0.383671i	−0.733755	+	0.679414i	$0.762234\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.92810	+	27.4643i	0.287426	+	1.13941i
$582$		0			0
$583$	22.3149	−	38.6505i	0.924187	−	1.60074i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.64184			−0.274138			−0.137069	−	0.990562i	$-0.543768\pi$
$587$	−6.64184			−0.274138			−0.137069	+	0.990562i	$0.543768\pi$
$588$		0			0
$589$	−16.7242			−0.689107
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.76960	−	11.7253i	0.277994	−	0.481500i	−0.692892	−	0.721041i	$-0.743664\pi$
$593$	6.76960	−	11.7253i	0.277994	−	0.481500i	0.970886	+	0.239541i	$0.0769971\pi$
$594$		0			0
$595$	1.29428	+	5.13077i	0.0530603	+	0.210341i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.0905	+	22.6734i	0.534864	+	0.926412i	0.999170	+	0.0407369i	$0.0129706\pi$
$599$	13.0905	+	22.6734i	0.534864	+	0.926412i	−0.464306	+	0.885675i	$0.653696\pi$
$600$		0			0
$601$	−36.0078			−1.46879			−0.734395	−	0.678722i	$-0.762534\pi$
$601$	−36.0078			−1.46879			−0.734395	+	0.678722i	$0.762534\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.63382	+	8.02601i	0.188392	+	0.326304i
$606$		0			0
$607$	−11.8715	+	20.5620i	−0.481849	+	0.834586i	−0.999783	−	0.0208341i	$-0.993368\pi$
$607$	−11.8715	+	20.5620i	−0.481849	+	0.834586i	0.517934	+	0.855420i	$0.326701\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	25.6930	−	44.5015i	1.03943	−	1.80034i
$612$		0			0
$613$	4.77958	+	8.27847i	0.193045	+	0.334364i	0.946258	−	0.323413i	$-0.104830\pi$
$613$	4.77958	+	8.27847i	0.193045	+	0.334364i	−0.753213	+	0.657777i	$0.771497\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.8268			0.798197			0.399098	−	0.916908i	$-0.369323\pi$
$617$	19.8268			0.798197			0.399098	+	0.916908i	$0.369323\pi$
$618$		0			0
$619$	−13.5758	−	23.5140i	−0.545658	−	0.945108i	−0.998565	−	0.0535500i	$-0.982946\pi$
$619$	−13.5758	−	23.5140i	−0.545658	−	0.945108i	0.452907	−	0.891558i	$-0.350387\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.4114	+	2.95439i	0.417126	+	0.118365i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.1810			−0.565435
$630$		0			0
$631$	−49.7735			−1.98145			−0.990726	−	0.135873i	$-0.956616\pi$
$631$	−49.7735			−1.98145			−0.990726	+	0.135873i	$0.956616\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.866179	+	1.50027i	−0.0343733	+	0.0595362i
$636$		0			0
$637$	−31.3699	+	16.9022i	−1.24292	+	0.669690i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.1152	+	17.5200i	0.399526	+	0.692000i	0.993667	−	0.112361i	$-0.0358413\pi$
$641$	10.1152	+	17.5200i	0.399526	+	0.692000i	−0.594141	+	0.804361i	$0.702508\pi$
$642$		0			0
$643$	−25.1850			−0.993198			−0.496599	−	0.867980i	$-0.665418\pi$
$643$	−25.1850			−0.993198			−0.496599	+	0.867980i	$0.665418\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.78488	+	16.9479i	0.384683	+	0.666291i	0.991725	−	0.128379i	$-0.0409773\pi$
$647$	9.78488	+	16.9479i	0.384683	+	0.666291i	−0.607042	+	0.794670i	$0.707644\pi$
$648$		0			0
$649$	18.0078	−	31.1905i	0.706870	−	1.22433i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.13382	−	15.8202i	0.357434	−	0.619094i	−0.630097	−	0.776516i	$-0.716985\pi$
$653$	9.13382	−	15.8202i	0.357434	−	0.619094i	0.987531	+	0.157422i	$0.0503184\pi$
$654$		0			0
$655$	6.36814	+	11.0299i	0.248824	+	0.430975i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−46.0078			−1.79221			−0.896105	−	0.443841i	$-0.853615\pi$
$659$	−46.0078			−1.79221			−0.896105	+	0.443841i	$0.853615\pi$
$660$		0			0
$661$	24.2302	+	41.9680i	0.942446	+	1.63236i	0.760785	+	0.649004i	$0.224814\pi$
$661$	24.2302	+	41.9680i	0.942446	+	1.63236i	0.181661	+	0.983361i	$0.441853\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.86618	−	5.69624i	0.227481	−	0.220891i
$666$		0			0
$667$	−27.5378	+	47.6969i	−1.06627	+	1.84683i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−40.1278			−1.54912
$672$		0			0
$673$	−15.0118			−0.578661			−0.289330	−	0.957229i	$-0.593433\pi$
$673$	−15.0118			−0.578661			−0.289330	+	0.957229i	$0.593433\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.95670	−	6.85320i	0.152068	−	0.263390i	−0.779919	−	0.625880i	$-0.784740\pi$
$677$	3.95670	−	6.85320i	0.152068	−	0.263390i	0.931988	+	0.362490i	$0.118073\pi$
$678$		0			0
$679$	−1.29428	−	5.13077i	−0.0496699	−	0.196901i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.8548	+	25.7293i	0.568404	+	0.984504i	0.996724	+	0.0808774i	$0.0257722\pi$
$683$	14.8548	+	25.7293i	0.568404	+	0.984504i	−0.428320	+	0.903627i	$0.640894\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.2322	+	43.7034i	0.961270	+	1.66497i
$690$		0			0
$691$	10.8868	−	18.8564i	0.414152	−	0.717332i	−0.581187	−	0.813770i	$-0.697412\pi$
$691$	10.8868	−	18.8564i	0.414152	−	0.717332i	0.995339	+	0.0964378i	$0.0307449\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.705720	+	1.22234i	−0.0267695	+	0.0463661i
$696$		0			0
$697$	6.59248	+	11.4185i	0.249708	+	0.432507i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−24.0905			−0.909886			−0.454943	−	0.890520i	$-0.650340\pi$
$701$	−24.0905			−0.909886			−0.454943	+	0.890520i	$0.650340\pi$
$702$		0			0
$703$	10.9567	+	18.9776i	0.413240	+	0.715752i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.30350	−	6.12090i	0.237068	−	0.230200i
$708$		0			0
$709$	12.0186	−	20.8169i	0.451369	−	0.781794i	−0.547103	−	0.837066i	$-0.684269\pi$
$709$	12.0186	−	20.8169i	0.451369	−	0.781794i	0.998471	+	0.0552719i	$0.0176026\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−31.3660			−1.17467
$714$		0			0
$715$	−22.9173			−0.857059
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.117159	+	0.202925i	−0.00436929	+	0.00756783i	−0.868202	−	0.496211i	$-0.834724\pi$
$719$	−0.117159	+	0.202925i	−0.00436929	+	0.00756783i	0.863832	+	0.503779i	$0.168057\pi$
$720$		0			0
$721$	27.7096	+	7.86300i	1.03196	+	0.292833i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.75098	+	8.22894i	0.176447	+	0.305615i
$726$		0			0
$727$	9.44200			0.350184			0.175092	−	0.984552i	$-0.443978\pi$
$727$	9.44200			0.350184			0.175092	+	0.984552i	$0.443978\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.70572	+	8.15055i	0.174047	+	0.301459i
$732$		0			0
$733$	14.3721	−	24.8931i	0.530844	−	0.919449i	−0.468508	−	0.883459i	$-0.655208\pi$
$733$	14.3721	−	24.8931i	0.530844	−	0.919449i	0.999352	−	0.0359897i	$-0.0114584\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.263722	−	0.456781i	0.00971434	−	0.0168257i
$738$		0			0
$739$	13.0739	+	22.6446i	0.480930	+	0.832995i	0.999761	−	0.0218823i	$-0.00696591\pi$
$739$	13.0739	+	22.6446i	0.480930	+	0.832995i	−0.518831	+	0.854877i	$0.673633\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.7547			−1.20165			−0.600827	−	0.799379i	$-0.705162\pi$
$743$	−32.7547			−1.20165			−0.600827	+	0.799379i	$0.705162\pi$
$744$		0			0
$745$	−11.5472	−	20.0004i	−0.423057	−	0.732757i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.88284	+	2.80440i	0.361111	+	0.102470i
$750$		0			0
$751$	−13.0905	+	22.6734i	−0.477680	+	0.827366i	−0.999673	−	0.0255841i	$-0.991855\pi$
$751$	−13.0905	+	22.6734i	−0.477680	+	0.827366i	0.521993	+	0.852950i	$0.325189\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.407520			0.0148312
$756$		0			0
$757$	16.8229			0.611438			0.305719	−	0.952122i	$-0.401103\pi$
$757$	16.8229			0.611438			0.305719	+	0.952122i	$0.401103\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.95278	+	5.11436i	−0.107038	+	0.185396i	−0.914569	−	0.404430i	$-0.867470\pi$
$761$	−2.95278	+	5.11436i	−0.107038	+	0.185396i	0.807531	+	0.589825i	$0.200803\pi$
$762$		0			0
$763$	−19.4967	+	18.9319i	−0.705826	+	0.685379i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.3621	+	35.2682i	0.735232	+	1.27346i
$768$		0			0
$769$	0.275481			0.00993410			0.00496705	−	0.999988i	$-0.498419\pi$
$769$	0.275481			0.00993410			0.00496705	+	0.999988i	$0.498419\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.68906	+	6.38964i	0.132686	+	0.229819i	0.924711	−	0.380669i	$-0.124306\pi$
$773$	3.68906	+	6.38964i	0.132686	+	0.229819i	−0.792025	+	0.610489i	$0.790973\pi$
$774$		0			0
$775$	−2.70572	+	4.68644i	−0.0971923	+	0.168342i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.1871	−	17.6446i	0.364991	−	0.632182i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.0944			0.503052
$786$		0			0
$787$	9.33014	+	16.1603i	0.332584	+	0.576052i	0.983018	−	0.183511i	$-0.0587463\pi$
$787$	9.33014	+	16.1603i	0.332584	+	0.576052i	−0.650434	+	0.759563i	$0.725413\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.82680	−	7.24178i	−0.0649535	−	0.257488i
$792$		0			0
$793$	22.6869	−	39.2949i	0.805636	−	1.39540i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.81896			−0.347805			−0.173903	−	0.984763i	$-0.555638\pi$
$797$	−9.81896			−0.347805			−0.173903	+	0.984763i	$0.555638\pi$
$798$		0			0
$799$	20.1889			0.714231
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−18.4154	+	31.8963i	−0.649864	+	1.12560i
$804$		0			0
$805$	11.0020	−	10.6832i	0.387768	−	0.376535i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.0020	−	27.7162i	−0.562599	−	0.974450i	−0.997269	−	0.0738600i	$-0.976468\pi$
$809$	−16.0020	−	27.7162i	−0.562599	−	0.974450i	0.434670	−	0.900590i	$-0.356865\pi$
$810$		0			0
$811$	43.5137			1.52797			0.763987	−	0.645232i	$-0.223239\pi$
$811$	43.5137			1.52797			0.763987	+	0.645232i	$0.223239\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.09052	−	14.0132i	−0.283399	−	0.490861i
$816$		0			0
$817$	7.27156	−	12.5947i	0.254400	−	0.440633i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.3621	+	30.0720i	−0.605941	+	1.04952i	0.385961	+	0.922515i	$0.373870\pi$
$821$	−17.3621	+	30.0720i	−0.605941	+	1.04952i	−0.991902	+	0.127005i	$0.959463\pi$
$822$		0			0
$823$	11.6511	+	20.1802i	0.406130	+	0.703439i	0.994452	−	0.105188i	$-0.0335445\pi$
$823$	11.6511	+	20.1802i	0.406130	+	0.703439i	−0.588322	+	0.808627i	$0.700211\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.2943			−0.392741			−0.196370	−	0.980530i	$-0.562915\pi$
$827$	−11.2943			−0.392741			−0.196370	+	0.980530i	$0.562915\pi$
$828$		0			0
$829$	−10.0039	−	17.3273i	−0.347450	−	0.601802i	0.638345	−	0.769750i	$-0.279619\pi$
$829$	−10.0039	−	17.3273i	−0.347450	−	0.601802i	−0.985796	+	0.167948i	$0.946286\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.9134	−	7.35329i	−0.412775	−	0.254777i
$834$		0			0
$835$	−3.89812	+	6.75174i	−0.134900	+	0.233654i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.5846			−0.468994			−0.234497	−	0.972117i	$-0.575344\pi$
$839$	−13.5846			−0.468994			−0.234497	+	0.972117i	$0.575344\pi$
$840$		0			0
$841$	61.2872			2.11335
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.45670	−	11.1833i	0.222117	−	0.384718i
$846$		0			0
$847$	−23.5886	−	6.69359i	−0.810513	−	0.229994i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	20.5492	+	35.5922i	0.704417	+	1.22009i
$852$		0			0
$853$	−29.6336			−1.01464			−0.507318	−	0.861759i	$-0.669363\pi$
$853$	−29.6336			−1.01464			−0.507318	+	0.861759i	$0.669363\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.41536	−	16.3079i	−0.321623	−	0.557067i	0.659200	−	0.751967i	$-0.270895\pi$
$857$	−9.41536	−	16.3079i	−0.321623	−	0.557067i	−0.980823	+	0.194901i	$0.937562\pi$
$858$		0			0
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.92868	−	17.1970i	0.337976	−	0.585392i	−0.646076	−	0.763273i	$-0.723591\pi$
$863$	9.92868	−	17.1970i	0.337976	−	0.585392i	0.984052	+	0.177881i	$0.0569244\pi$
$864$		0			0
$865$	4.45474	+	7.71584i	0.151466	+	0.262346i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−63.8425			−2.16571
$870$		0			0
$871$	0.298200	+	0.516497i	0.0101041	+	0.0175008i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.647140	−	2.56539i	−0.0218773	−	0.0867259i
$876$		0			0
$877$	6.77566	−	11.7358i	0.228798	−	0.396289i	−0.728654	−	0.684882i	$-0.759854\pi$
$877$	6.77566	−	11.7358i	0.228798	−	0.396289i	0.957452	+	0.288592i	$0.0931872\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	47.5964			1.60356			0.801782	−	0.597617i	$-0.203886\pi$
$881$	47.5964			1.60356			0.801782	+	0.597617i	$0.203886\pi$
$882$		0			0
$883$	36.6497			1.23336			0.616680	−	0.787214i	$-0.288477\pi$
$883$	36.6497			1.23336			0.616680	+	0.787214i	$0.288477\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.0625	−	39.9454i	0.774363	−	1.34124i	−0.160789	−	0.986989i	$-0.551404\pi$
$887$	23.0625	−	39.9454i	0.774363	−	1.34124i	0.935152	−	0.354247i	$-0.115263\pi$
$888$		0			0
$889$	−1.12108	−	4.44417i	−0.0375998	−	0.149053i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.5985	−	27.0175i	−0.521985	−	0.904105i
$894$		0			0
$895$	1.67908			0.0561255
$896$		0			0
$897$		0			0
$898$		0			0
$899$	25.7096	+	44.5304i	0.857464	+	1.48517i
$900$		0			0
$901$	−9.91340	+	17.1705i	−0.330263	+	0.572033i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.25294	−	10.8304i	0.207855	−	0.360015i
$906$		0			0
$907$	2.53390	+	4.38884i	0.0841368	+	0.145729i	0.905023	−	0.425363i	$-0.139853\pi$
$907$	2.53390	+	4.38884i	0.0841368	+	0.145729i	−0.820886	+	0.571092i	$0.806520\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.41536			0.0800244			0.0400122	−	0.999199i	$-0.487260\pi$
$911$	2.41536			0.0800244			0.0400122	+	0.999199i	$0.487260\pi$
$912$		0			0
$913$	−24.0984	−	41.7396i	−0.797539	−	1.38138i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−32.4171	−	9.19882i	−1.07051	−	0.303772i
$918$		0			0
$919$	−18.2755	+	31.6541i	−0.602852	+	1.04417i	0.389534	+	0.921012i	$0.372636\pi$
$919$	−18.2755	+	31.6541i	−0.602852	+	1.04417i	−0.992387	+	0.123159i	$0.960697\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	7.09052			0.233135
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8.11520	+	14.0559i	−0.266251	+	0.461160i	−0.967891	−	0.251372i	$-0.919118\pi$
$929$	−8.11520	+	14.0559i	−0.266251	+	0.461160i	0.701640	+	0.712532i	$0.252452\pi$
$930$		0			0
$931$	−0.635781	+	21.6243i	−0.0208369	+	0.708708i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.50196	−	7.79762i	−0.147230	−	0.255010i
$936$		0			0
$937$	−44.1889			−1.44359			−0.721794	−	0.692108i	$-0.756682\pi$
$937$	−44.1889			−1.44359			−0.721794	+	0.692108i	$0.756682\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.7363	+	20.3278i	0.382592	+	0.662668i	0.991432	−	0.130625i	$-0.0416983\pi$
$941$	11.7363	+	20.3278i	0.382592	+	0.662668i	−0.608840	+	0.793293i	$0.708365\pi$
$942$		0			0
$943$	19.1058	−	33.0922i	0.622170	−	1.07763i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.0359	−	48.5595i	0.911043	−	1.57797i	0.0984495	−	0.995142i	$-0.468612\pi$
$947$	28.0359	−	48.5595i	0.911043	−	1.57797i	0.812594	−	0.582831i	$-0.198055\pi$
$948$		0			0
$949$	−20.8229	−	36.0663i	−0.675939	−	1.17076i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.7163			0.735854			0.367927	−	0.929855i	$-0.380068\pi$
$953$	22.7163			0.735854			0.367927	+	0.929855i	$0.380068\pi$
$954$		0			0
$955$	−3.29428	−	5.70586i	−0.106600	−	0.184637i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.59248	+	7.37253i	−0.245174	+	0.238072i
$960$		0			0
$961$	0.858162	−	1.48638i	0.0276827	−	0.0479478i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.8268			−0.573865
$966$		0			0
$967$	10.9400			0.351808			0.175904	−	0.984407i	$-0.443715\pi$
$967$	10.9400			0.351808			0.175904	+	0.984407i	$0.443715\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.8701	−	22.2917i	0.413021	−	0.715374i	−0.582197	−	0.813048i	$-0.697807\pi$
$971$	12.8701	−	22.2917i	0.413021	−	0.715374i	0.995218	+	0.0976739i	$0.0311402\pi$
$972$		0			0
$973$	−0.913399	−	3.62089i	−0.0292822	−	0.116080i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.41144	+	14.5690i	0.269106	+	0.466105i	0.968631	−	0.248503i	$-0.0799385\pi$
$977$	8.41144	+	14.5690i	0.269106	+	0.466105i	−0.699525	+	0.714608i	$0.746605\pi$
$978$		0			0
$979$	−18.4154			−0.588557
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.9926	−	38.0922i	−0.701454	−	1.21495i	−0.967956	−	0.251119i	$-0.919201\pi$
$983$	−21.9926	−	38.0922i	−0.701454	−	1.21495i	0.266502	−	0.963834i	$-0.414132\pi$
$984$		0			0
$985$	−2.54526	+	4.40852i	−0.0810987	+	0.140467i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.6377	−	23.6213i	0.433655	−	0.751112i
$990$		0			0
$991$	22.1172	+	38.3080i	0.702575	+	1.21690i	0.967560	+	0.252643i	$0.0812997\pi$
$991$	22.1172	+	38.3080i	0.702575	+	1.21690i	−0.264985	+	0.964253i	$0.585367\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−24.3621			−0.772330
$996$		0			0
$997$	−17.0984	−	29.6152i	−0.541510	−	0.937924i	−0.998818	−	0.0486148i	$-0.984519\pi$
$997$	−17.0984	−	29.6152i	−0.541510	−	0.937924i	0.457307	−	0.889309i	$-0.348814\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.q.1801.2		6
3.2	odd	2		280.2.q.e.121.2	yes	6
7.4	even	3	inner	2520.2.bi.q.361.2		6
12.11	even	2		560.2.q.l.401.2		6
15.2	even	4		1400.2.bh.i.849.3		12
15.8	even	4		1400.2.bh.i.849.4		12
15.14	odd	2		1400.2.q.j.401.2		6
21.2	odd	6		1960.2.a.w.1.2		3
21.5	even	6		1960.2.a.v.1.2		3
21.11	odd	6		280.2.q.e.81.2	✓	6
21.17	even	6		1960.2.q.w.361.2		6
21.20	even	2		1960.2.q.w.961.2		6
84.11	even	6		560.2.q.l.81.2		6
84.23	even	6		3920.2.a.cc.1.2		3
84.47	odd	6		3920.2.a.cb.1.2		3
105.32	even	12		1400.2.bh.i.249.4		12
105.44	odd	6		9800.2.a.ce.1.2		3
105.53	even	12		1400.2.bh.i.249.3		12
105.74	odd	6		1400.2.q.j.1201.2		6
105.89	even	6		9800.2.a.cf.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.2	✓	6	21.11	odd	6
280.2.q.e.121.2	yes	6	3.2	odd	2
560.2.q.l.81.2		6	84.11	even	6
560.2.q.l.401.2		6	12.11	even	2
1400.2.q.j.401.2		6	15.14	odd	2
1400.2.q.j.1201.2		6	105.74	odd	6
1400.2.bh.i.249.3		12	105.53	even	12
1400.2.bh.i.249.4		12	105.32	even	12
1400.2.bh.i.849.3		12	15.2	even	4
1400.2.bh.i.849.4		12	15.8	even	4
1960.2.a.v.1.2		3	21.5	even	6
1960.2.a.w.1.2		3	21.2	odd	6
1960.2.q.w.361.2		6	21.17	even	6
1960.2.q.w.961.2		6	21.20	even	2
2520.2.bi.q.361.2		6	7.4	even	3	inner
2520.2.bi.q.1801.2		6	1.1	even	1	trivial
3920.2.a.cb.1.2		3	84.47	odd	6
3920.2.a.cc.1.2		3	84.23	even	6
9800.2.a.ce.1.2		3	105.44	odd	6
9800.2.a.cf.1.2		3	105.89	even	6

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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +(-2.25098 - 3.89881i) q^{11} +5.09052 q^{13} +(1.00000 + 1.73205i) q^{17} +(1.54526 - 2.67647i) q^{19} +(2.89812 - 5.01969i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.50196 q^{29} +(-2.70572 - 4.68644i) q^{31} +(2.54526 + 0.722254i) q^{35} +(-3.54526 + 6.14057i) q^{37} +6.59248 q^{41} +4.70572 q^{43} +(5.04722 - 8.74204i) q^{47} +(-6.16242 + 3.32033i) q^{49} +(4.95670 + 8.58526i) q^{53} -4.50196 q^{55} +(4.00000 + 6.92820i) q^{59} +(4.45670 - 7.71923i) q^{61} +(2.54526 - 4.40852i) q^{65} +(0.0585795 + 0.101463i) q^{67} +(-4.09052 - 7.08499i) q^{73} +(8.54526 - 8.29771i) q^{77} +(7.09052 - 12.2811i) q^{79} +10.7057 q^{83} +2.00000 q^{85} +(2.04526 - 3.54249i) q^{89} +(3.29428 + 13.0592i) q^{91} +(-1.54526 - 2.67647i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 6 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 6 * q^7	\( 6 q + 3 q^{5} + 6 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} - 3 q^{25} - 24 q^{29} - 12 q^{31} + 3 q^{35} - 9 q^{37} - 18 q^{41} + 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} + 6 q^{55} + 24 q^{59} + 6 q^{61} + 3 q^{65} - 6 q^{67} + 39 q^{77} + 18 q^{79} + 60 q^{83} + 12 q^{85} + 24 q^{91} + 3 q^{95} - 12 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 6 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 - 3 * q^25 - 24 * q^29 - 12 * q^31 + 3 * q^35 - 9 * q^37 - 18 * q^41 + 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 + 6 * q^55 + 24 * q^59 + 6 * q^61 + 3 * q^65 - 6 * q^67 + 39 * q^77 + 18 * q^79 + 60 * q^83 + 12 * q^85 + 24 * q^91 + 3 * q^95 - 12 * q^97

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