LMFDB - Embedded newform 2100.2.s.c.1457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.8
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.c.1793.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0412661 - 1.73156i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +O(q^{10})$	\(q+(-0.0412661 - 1.73156i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +1.76542i q^{11} +(0.719742 - 0.719742i) q^{13} +(-1.55115 + 1.55115i) q^{17} +5.12249i q^{19} +(-1.19522 + 1.25358i) q^{21} +(-1.47001 - 1.47001i) q^{23} +(0.371114 + 5.18288i) q^{27} -7.63621 q^{29} -0.104617 q^{31} +(3.05693 - 0.0728519i) q^{33} +(0.0126355 + 0.0126355i) q^{37} +(-1.27598 - 1.21658i) q^{39} +9.35682i q^{41} +(2.66423 - 2.66423i) q^{43} +(-3.98447 + 3.98447i) q^{47} +1.00000i q^{49} +(2.74992 + 2.62190i) q^{51} +(5.44907 + 5.44907i) q^{53} +(8.86989 - 0.211385i) q^{57} -5.32780 q^{59} -4.82359 q^{61} +(2.21996 + 2.01786i) q^{63} +(3.01428 + 3.01428i) q^{67} +(-2.48475 + 2.60608i) q^{69} +5.20665i q^{71} +(7.10198 - 7.10198i) q^{73} +(1.24834 - 1.24834i) q^{77} +15.4899i q^{79} +(8.95915 - 0.856482i) q^{81} +(3.76280 + 3.76280i) q^{83} +(0.315116 + 13.2225i) q^{87} -2.98785 q^{89} -1.01787 q^{91} +(0.00431713 + 0.181150i) q^{93} +(-6.41605 - 6.41605i) q^{97} +(-0.252295 - 5.29024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) $ 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0412661	−	1.73156i	−0.0238250	−	0.999716i
$3$	−0.0412661	−	1.73156i	−0.0238250	−	0.999716i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$	−2.99659	+	0.142909i	−0.998865	+	0.0476364i
$10$		0			0
$11$			1.76542i			0.532294i	0.963933	+	0.266147i	$0.0857506\pi$
$11$			1.76542i			0.532294i	−0.963933	+	0.266147i	$0.914249\pi$
$12$		0			0
$13$	0.719742	−	0.719742i	0.199621	−	0.199621i	−0.600217	−	0.799837i	$-0.704919\pi$
$13$	0.719742	−	0.719742i	0.199621	−	0.199621i	0.799837	+	0.600217i	$0.204919\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.55115	+	1.55115i	−0.376209	+	0.376209i	−0.869733	−	0.493523i	$-0.835709\pi$
$17$	−1.55115	+	1.55115i	−0.376209	+	0.376209i	0.493523	+	0.869733i	$0.335709\pi$
$18$		0			0
$19$			5.12249i			1.17518i	0.809159	+	0.587589i	$0.199923\pi$
$19$			5.12249i			1.17518i	−0.809159	+	0.587589i	$0.800077\pi$
$20$		0			0
$21$	−1.19522	+	1.25358i	−0.260818	+	0.273553i
$22$		0			0
$23$	−1.47001	−	1.47001i	−0.306519	−	0.306519i	0.537039	−	0.843558i	$-0.319543\pi$
$23$	−1.47001	−	1.47001i	−0.306519	−	0.306519i	−0.843558	+	0.537039i	$0.819543\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.371114	+	5.18288i	0.0714208	+	0.997446i
$28$		0			0
$29$	−7.63621			−1.41801			−0.709004	−	0.705204i	$-0.750855\pi$
$29$	−7.63621			−1.41801			−0.709004	+	0.705204i	$0.750855\pi$
$30$		0			0
$31$	−0.104617			−0.0187897			−0.00939487	−	0.999956i	$-0.502991\pi$
$31$	−0.104617			−0.0187897			−0.00939487	+	0.999956i	$0.502991\pi$
$32$		0			0
$33$	3.05693	−	0.0728519i	0.532142	−	0.0126819i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.0126355	+	0.0126355i	0.00207727	+	0.00207727i	0.708145	−	0.706067i	$-0.249532\pi$
$37$	0.0126355	+	0.0126355i	0.00207727	+	0.00207727i	−0.706067	+	0.708145i	$0.749532\pi$
$38$		0			0
$39$	−1.27598	−	1.21658i	−0.204320	−	0.194808i
$40$		0			0
$41$			9.35682i			1.46129i	0.682757	+	0.730645i	$0.260781\pi$
$41$			9.35682i			1.46129i	−0.682757	+	0.730645i	$0.739219\pi$
$42$		0			0
$43$	2.66423	−	2.66423i	0.406291	−	0.406291i	−0.474152	−	0.880443i	$-0.657245\pi$
$43$	2.66423	−	2.66423i	0.406291	−	0.406291i	0.880443	+	0.474152i	$0.157245\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.98447	+	3.98447i	−0.581195	+	0.581195i	−0.935232	−	0.354037i	$-0.884809\pi$
$47$	−3.98447	+	3.98447i	−0.581195	+	0.581195i	0.354037	+	0.935232i	$0.384809\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	2.74992	+	2.62190i	0.385066	+	0.367139i
$52$		0			0
$53$	5.44907	+	5.44907i	0.748488	+	0.748488i	0.974195	−	0.225707i	$-0.0724693\pi$
$53$	5.44907	+	5.44907i	0.748488	+	0.748488i	−0.225707	+	0.974195i	$0.572469\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.86989	−	0.211385i	1.17485	−	0.0279986i
$58$		0			0
$59$	−5.32780			−0.693621			−0.346810	−	0.937935i	$-0.612735\pi$
$59$	−5.32780			−0.693621			−0.346810	+	0.937935i	$0.612735\pi$
$60$		0			0
$61$	−4.82359			−0.617597			−0.308798	−	0.951127i	$-0.599927\pi$
$61$	−4.82359			−0.617597			−0.308798	+	0.951127i	$0.599927\pi$
$62$		0			0
$63$	2.21996	+	2.01786i	0.279689	+	0.254226i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.01428	+	3.01428i	0.368253	+	0.368253i	0.866840	−	0.498587i	$-0.166147\pi$
$67$	3.01428	+	3.01428i	0.368253	+	0.368253i	−0.498587	+	0.866840i	$0.666147\pi$
$68$		0			0
$69$	−2.48475	+	2.60608i	−0.299129	+	0.313735i
$70$		0			0
$71$			5.20665i			0.617916i	0.951076	+	0.308958i	$0.0999802\pi$
$71$			5.20665i			0.617916i	−0.951076	+	0.308958i	$0.900020\pi$
$72$		0			0
$73$	7.10198	−	7.10198i	0.831224	−	0.831224i	−0.156461	−	0.987684i	$-0.550008\pi$
$73$	7.10198	−	7.10198i	0.831224	−	0.831224i	0.987684	+	0.156461i	$0.0500084\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.24834	−	1.24834i	0.142261	−	0.142261i
$78$		0			0
$79$			15.4899i			1.74275i	0.490613	+	0.871377i	$0.336773\pi$
$79$			15.4899i			1.74275i	−0.490613	+	0.871377i	$0.663227\pi$
$80$		0			0
$81$	8.95915	−	0.856482i	0.995462	−	0.0951647i
$82$		0			0
$83$	3.76280	+	3.76280i	0.413021	+	0.413021i	0.882789	−	0.469769i	$-0.155663\pi$
$83$	3.76280	+	3.76280i	0.413021	+	0.413021i	−0.469769	+	0.882789i	$0.655663\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.315116	+	13.2225i	0.0337840	+	1.41761i
$88$		0			0
$89$	−2.98785			−0.316711			−0.158356	−	0.987382i	$-0.550619\pi$
$89$	−2.98785			−0.316711			−0.158356	+	0.987382i	$0.550619\pi$
$90$		0			0
$91$	−1.01787			−0.106702
$92$		0			0
$93$	0.00431713	+	0.181150i	0.000447665	+	0.0187844i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.41605	−	6.41605i	−0.651451	−	0.651451i	0.301891	−	0.953342i	$-0.402382\pi$
$97$	−6.41605	−	6.41605i	−0.651451	−	0.651451i	−0.953342	+	0.301891i	$0.902382\pi$
$98$		0			0
$99$	−0.252295	−	5.29024i	−0.0253566	−	0.531689i
$100$		0			0
$101$		−	19.5014i		−	1.94047i	−0.242175	−	0.970233i	$-0.577861\pi$
$101$		−	19.5014i		−	1.94047i	0.242175	−	0.970233i	$-0.422139\pi$
$102$		0			0
$103$	2.55799	−	2.55799i	0.252046	−	0.252046i	−0.569763	−	0.821809i	$-0.692965\pi$
$103$	2.55799	−	2.55799i	0.252046	−	0.252046i	0.821809	+	0.569763i	$0.192965\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.7892	+	12.7892i	−1.23638	+	1.23638i	−0.274908	+	0.961471i	$0.588647\pi$
$107$	−12.7892	+	12.7892i	−1.23638	+	1.23638i	−0.961471	+	0.274908i	$0.911353\pi$
$108$		0			0
$109$			7.24497i			0.693943i	0.937876	+	0.346971i	$0.112790\pi$
$109$			7.24497i			0.693943i	−0.937876	+	0.346971i	$0.887210\pi$
$110$		0			0
$111$	0.0213578	−	0.0224006i	0.00202719	−	0.00212617i
$112$		0			0
$113$	6.56229	+	6.56229i	0.617328	+	0.617328i	0.944845	−	0.327517i	$-0.106212\pi$
$113$	6.56229	+	6.56229i	0.617328	+	0.617328i	−0.327517	+	0.944845i	$0.606212\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.05392	+	2.25963i	−0.189885	+	0.208903i
$118$		0			0
$119$	2.19366			0.201092
$120$		0			0
$121$	7.88330			0.716664
$122$		0			0
$123$	16.2019	−	0.386119i	1.46088	−	0.0348152i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.16223	+	3.16223i	0.280603	+	0.280603i	0.833349	−	0.552746i	$-0.186420\pi$
$127$	3.16223	+	3.16223i	0.280603	+	0.280603i	−0.552746	+	0.833349i	$0.686420\pi$
$128$		0			0
$129$	−4.72321	−	4.50333i	−0.415856	−	0.396496i
$130$		0			0
$131$		−	12.4846i		−	1.09078i	−0.838182	−	0.545391i	$-0.816381\pi$
$131$		−	12.4846i		−	1.09078i	0.838182	−	0.545391i	$-0.183619\pi$
$132$		0			0
$133$	3.62214	−	3.62214i	0.314080	−	0.314080i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.5780	−	11.5780i	0.989171	−	0.989171i	−0.0107709	−	0.999942i	$-0.503429\pi$
$137$	11.5780	−	11.5780i	0.989171	−	0.989171i	0.999942	+	0.0107709i	$0.00342854\pi$
$138$		0			0
$139$			14.9719i			1.26990i	0.772553	+	0.634951i	$0.218980\pi$
$139$			14.9719i			1.26990i	−0.772553	+	0.634951i	$0.781020\pi$
$140$		0			0
$141$	7.06377	+	6.73492i	0.594877	+	0.567183i
$142$		0			0
$143$	1.27065	+	1.27065i	0.106257	+	0.106257i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.73156	−	0.0412661i	0.142817	−	0.00340357i
$148$		0			0
$149$	−5.94073			−0.486684			−0.243342	−	0.969941i	$-0.578244\pi$
$149$	−5.94073			−0.486684			−0.243342	+	0.969941i	$0.578244\pi$
$150$		0			0
$151$	−17.0306			−1.38593			−0.692967	−	0.720970i	$-0.743697\pi$
$151$	−17.0306			−1.38593			−0.692967	+	0.720970i	$0.743697\pi$
$152$		0			0
$153$	4.42650	−	4.86984i	0.357861	−	0.393704i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.04726	−	8.04726i	−0.642241	−	0.642241i	0.308865	−	0.951106i	$-0.400051\pi$
$157$	−8.04726	−	8.04726i	−0.642241	−	0.642241i	−0.951106	+	0.308865i	$0.900051\pi$
$158$		0			0
$159$	9.21053	−	9.66025i	0.730443	−	0.766108i
$160$		0			0
$161$			2.07891i			0.163841i
$162$		0			0
$163$	−6.10483	+	6.10483i	−0.478167	+	0.478167i	−0.904545	−	0.426378i	$-0.859789\pi$
$163$	−6.10483	+	6.10483i	−0.478167	+	0.478167i	0.426378	+	0.904545i	$0.359789\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.71835	−	2.71835i	0.210352	−	0.210352i	−0.594065	−	0.804417i	$-0.702478\pi$
$167$	2.71835	−	2.71835i	0.210352	−	0.210352i	0.804417	+	0.594065i	$0.202478\pi$
$168$		0			0
$169$			11.9639i			0.920303i
$170$		0			0
$171$	−0.732051	−	15.3500i	−0.0559813	−	1.17384i
$172$		0			0
$173$	16.0058	+	16.0058i	1.21690	+	1.21690i	0.968713	+	0.248183i	$0.0798334\pi$
$173$	16.0058	+	16.0058i	1.21690	+	1.21690i	0.248183	+	0.968713i	$0.420167\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.219857	+	9.22540i	0.0165255	+	0.693424i
$178$		0			0
$179$	0.351893			0.0263017			0.0131509	−	0.999914i	$-0.495814\pi$
$179$	0.351893			0.0263017			0.0131509	+	0.999914i	$0.495814\pi$
$180$		0			0
$181$	5.32474			0.395785			0.197893	−	0.980224i	$-0.436590\pi$
$181$	5.32474			0.395785			0.197893	+	0.980224i	$0.436590\pi$
$182$		0			0
$183$	0.199050	+	8.35233i	0.0147142	+	0.617422i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.73843	−	2.73843i	−0.200254	−	0.200254i
$188$		0			0
$189$	3.40243	−	3.92727i	0.247491	−	0.285667i
$190$		0			0
$191$			7.84604i			0.567720i	0.958866	+	0.283860i	$0.0916151\pi$
$191$			7.84604i			0.567720i	−0.958866	+	0.283860i	$0.908385\pi$
$192$		0			0
$193$	−0.268377	+	0.268377i	−0.0193182	+	0.0193182i	−0.716700	−	0.697382i	$-0.754348\pi$
$193$	−0.268377	+	0.268377i	−0.0193182	+	0.0193182i	0.697382	+	0.716700i	$0.254348\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.41576	−	9.41576i	0.670845	−	0.670845i	−0.287066	−	0.957911i	$-0.592680\pi$
$197$	9.41576	−	9.41576i	0.670845	−	0.670845i	0.957911	+	0.287066i	$0.0926797\pi$
$198$		0			0
$199$			2.21621i			0.157103i	0.996910	+	0.0785515i	$0.0250295\pi$
$199$			2.21621i			0.157103i	−0.996910	+	0.0785515i	$0.974970\pi$
$200$		0			0
$201$	5.09502	−	5.34380i	0.359375	−	0.376923i
$202$		0			0
$203$	5.39961	+	5.39961i	0.378979	+	0.378979i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.61511	+	4.19495i	0.320772	+	0.291569i
$208$		0			0
$209$	−9.04333			−0.625540
$210$		0			0
$211$	0.433151			0.0298193			0.0149097	−	0.999889i	$-0.495254\pi$
$211$	0.433151			0.0298193			0.0149097	+	0.999889i	$0.495254\pi$
$212$		0			0
$213$	9.01563	−	0.214858i	0.617740	−	0.0147218i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.0739753	+	0.0739753i	0.00502177	+	0.00502177i
$218$		0			0
$219$	−12.5906	−	12.0044i	−0.850792	−	0.811184i
$220$		0			0
$221$			2.23286i			0.150198i
$222$		0			0
$223$	−16.2689	+	16.2689i	−1.08944	+	1.08944i	−0.0938585	+	0.995586i	$0.529920\pi$
$223$	−16.2689	+	16.2689i	−1.08944	+	1.08944i	−0.995586	+	0.0938585i	$0.970080\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.6647	+	18.6647i	−1.23882	+	1.23882i	−0.278338	+	0.960483i	$0.589784\pi$
$227$	−18.6647	+	18.6647i	−1.23882	+	1.23882i	−0.960483	+	0.278338i	$0.910216\pi$
$228$		0			0
$229$			4.85673i			0.320941i	0.987041	+	0.160471i	$0.0513012\pi$
$229$			4.85673i			0.320941i	−0.987041	+	0.160471i	$0.948699\pi$
$230$		0			0
$231$	−2.21309	−	2.11006i	−0.145610	−	0.138832i
$232$		0			0
$233$	−19.4471	−	19.4471i	−1.27402	−	1.27402i	−0.943959	−	0.330062i	$-0.892930\pi$
$233$	−19.4471	−	19.4471i	−1.27402	−	1.27402i	−0.330062	−	0.943959i	$-0.607070\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	26.8218	−	0.639209i	1.74226	−	0.0415211i
$238$		0			0
$239$	17.7348			1.14717			0.573583	−	0.819147i	$-0.305553\pi$
$239$	17.7348			1.14717			0.573583	+	0.819147i	$0.305553\pi$
$240$		0			0
$241$	−21.9071			−1.41116			−0.705580	−	0.708630i	$-0.749313\pi$
$241$	−21.9071			−1.41116			−0.705580	+	0.708630i	$0.749313\pi$
$242$		0			0
$243$	−1.85276	−	15.4780i	−0.118855	−	0.992912i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.68687	+	3.68687i	0.234590	+	0.234590i
$248$		0			0
$249$	6.36023	−	6.67078i	0.403063	−	0.422744i
$250$		0			0
$251$			5.13030i			0.323822i	0.986805	+	0.161911i	$0.0517657\pi$
$251$			5.13030i			0.323822i	−0.986805	+	0.161911i	$0.948234\pi$
$252$		0			0
$253$	2.59519	−	2.59519i	0.163158	−	0.163158i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.23056	+	1.23056i	−0.0767602	+	0.0767602i	−0.744445	−	0.667684i	$-0.767286\pi$
$257$	−1.23056	+	1.23056i	−0.0767602	+	0.0767602i	0.667684	+	0.744445i	$0.267286\pi$
$258$		0			0
$259$		−	0.0178694i		−	0.00111035i
$260$		0			0
$261$	22.8826	−	1.09128i	1.41640	−	0.0675488i
$262$		0			0
$263$	−0.370051	−	0.370051i	−0.0228183	−	0.0228183i	0.695606	−	0.718424i	$-0.255136\pi$
$263$	−0.370051	−	0.370051i	−0.0228183	−	0.0228183i	−0.718424	+	0.695606i	$0.755136\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.123297	+	5.17364i	0.00754564	+	0.316621i
$268$		0			0
$269$	15.2276			0.928444			0.464222	−	0.885719i	$-0.346334\pi$
$269$	15.2276			0.928444			0.464222	+	0.885719i	$0.346334\pi$
$270$		0			0
$271$	−16.2887			−0.989467			−0.494734	−	0.869045i	$-0.664734\pi$
$271$	−16.2887			−0.989467			−0.494734	+	0.869045i	$0.664734\pi$
$272$		0			0
$273$	0.0420035	+	1.76250i	0.00254217	+	0.106671i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.4653	−	16.4653i	−0.989306	−	0.989306i	0.0106374	−	0.999943i	$-0.496614\pi$
$277$	−16.4653	−	16.4653i	−0.989306	−	0.989306i	−0.999943	+	0.0106374i	$0.996614\pi$
$278$		0			0
$279$	0.313494	−	0.0149507i	0.0187684	−	0.000895076i
$280$		0			0
$281$			26.5619i			1.58455i	0.610166	+	0.792274i	$0.291103\pi$
$281$			26.5619i			1.58455i	−0.610166	+	0.792274i	$0.708897\pi$
$282$		0			0
$283$	−6.64836	+	6.64836i	−0.395204	+	0.395204i	−0.876538	−	0.481334i	$-0.840153\pi$
$283$	−6.64836	+	6.64836i	−0.395204	+	0.395204i	0.481334	+	0.876538i	$0.340153\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.61627	−	6.61627i	0.390546	−	0.390546i
$288$		0			0
$289$			12.1879i			0.716933i
$290$		0			0
$291$	−10.8450	+	11.3745i	−0.635746	+	0.666787i
$292$		0			0
$293$	−6.20064	−	6.20064i	−0.362245	−	0.362245i	0.502394	−	0.864639i	$-0.332453\pi$
$293$	−6.20064	−	6.20064i	−0.362245	−	0.362245i	−0.864639	+	0.502394i	$0.832453\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−9.14996	+	0.655171i	−0.530934	+	0.0380169i
$298$		0			0
$299$	−2.11606			−0.122375
$300$		0			0
$301$	−3.76779			−0.217172
$302$		0			0
$303$	−33.7679	+	0.804748i	−1.93991	+	0.0462315i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.71993	−	2.71993i	−0.155235	−	0.155235i	0.625217	−	0.780451i	$-0.285011\pi$
$307$	−2.71993	−	2.71993i	−0.155235	−	0.155235i	−0.780451	+	0.625217i	$0.785011\pi$
$308$		0			0
$309$	−4.53486	−	4.32375i	−0.257979	−	0.245969i
$310$		0			0
$311$		−	31.8252i		−	1.80464i	−0.431065	−	0.902321i	$-0.641862\pi$
$311$		−	31.8252i		−	1.80464i	0.431065	−	0.902321i	$-0.358138\pi$
$312$		0			0
$313$	14.2759	−	14.2759i	0.806922	−	0.806922i	−0.177245	−	0.984167i	$-0.556719\pi$
$313$	14.2759	−	14.2759i	0.806922	−	0.806922i	0.984167	+	0.177245i	$0.0567185\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.71018	−	7.71018i	0.433047	−	0.433047i	−0.456617	−	0.889663i	$-0.650939\pi$
$317$	7.71018	−	7.71018i	0.433047	−	0.433047i	0.889663	+	0.456617i	$0.150939\pi$
$318$		0			0
$319$		−	13.4811i		−	0.754797i
$320$		0			0
$321$	22.6730	+	21.6175i	1.26548	+	1.20657i
$322$		0			0
$323$	−7.94575	−	7.94575i	−0.442113	−	0.442113i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.5451	−	0.298972i	0.693746	−	0.0165332i
$328$		0			0
$329$	5.63489			0.310662
$330$		0			0
$331$	15.6380			0.859543			0.429771	−	0.902938i	$-0.358594\pi$
$331$	15.6380			0.859543			0.429771	+	0.902938i	$0.358594\pi$
$332$		0			0
$333$	−0.0396693	−	0.0360579i	−0.00217387	−	0.00197596i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−21.5849	−	21.5849i	−1.17581	−	1.17581i	−0.980803	−	0.195003i	$-0.937528\pi$
$337$	−21.5849	−	21.5849i	−1.17581	−	1.17581i	−0.195003	−	0.980803i	$-0.562472\pi$
$338$		0			0
$339$	11.0922	−	11.6338i	0.602445	−	0.631861i
$340$		0			0
$341$		−	0.184692i		−	0.0100017i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.11458	+	5.11458i	−0.274565	+	0.274565i	−0.830935	−	0.556370i	$-0.812194\pi$
$347$	−5.11458	+	5.11458i	−0.274565	+	0.274565i	0.556370	+	0.830935i	$0.312194\pi$
$348$		0			0
$349$		−	25.9034i		−	1.38657i	−0.720661	−	0.693287i	$-0.756162\pi$
$349$		−	25.9034i		−	1.38657i	0.720661	−	0.693287i	$-0.243838\pi$
$350$		0			0
$351$	3.99745	+	3.46323i	0.213368	+	0.184854i
$352$		0			0
$353$	−13.6228	−	13.6228i	−0.725068	−	0.725068i	0.244565	−	0.969633i	$-0.421355\pi$
$353$	−13.6228	−	13.6228i	−0.725068	−	0.725068i	−0.969633	+	0.244565i	$0.921355\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.0905237	−	3.79845i	−0.00479102	−	0.201035i
$358$		0			0
$359$	−26.9640			−1.42311			−0.711554	−	0.702632i	$-0.752008\pi$
$359$	−26.9640			−1.42311			−0.711554	+	0.702632i	$0.752008\pi$
$360$		0			0
$361$	−7.23987			−0.381046
$362$		0			0
$363$	−0.325313	−	13.6504i	−0.0170745	−	0.716460i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.56565	−	9.56565i	−0.499323	−	0.499323i	0.411904	−	0.911227i	$-0.364864\pi$
$367$	−9.56565	−	9.56565i	−0.499323	−	0.499323i	−0.911227	+	0.411904i	$0.864864\pi$
$368$		0			0
$369$	−1.33718	−	28.0386i	−0.0696107	−	1.45963i
$370$		0			0
$371$		−	7.70615i		−	0.400084i
$372$		0			0
$373$	−14.3181	+	14.3181i	−0.741364	+	0.741364i	−0.972841	−	0.231476i	$-0.925644\pi$
$373$	−14.3181	+	14.3181i	−0.741364	+	0.741364i	0.231476	+	0.972841i	$0.425644\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.49610	+	5.49610i	−0.283064	+	0.283064i
$378$		0			0
$379$			29.1422i			1.49694i	0.663171	+	0.748468i	$0.269210\pi$
$379$			29.1422i			1.49694i	−0.663171	+	0.748468i	$0.730790\pi$
$380$		0			0
$381$	5.34510	−	5.60609i	0.273838	−	0.287209i
$382$		0			0
$383$	−17.5964	−	17.5964i	−0.899136	−	0.899136i	0.0962236	−	0.995360i	$-0.469324\pi$
$383$	−17.5964	−	17.5964i	−0.899136	−	0.899136i	−0.995360	+	0.0962236i	$0.969324\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.60287	+	8.36436i	−0.386476	+	0.425184i
$388$		0			0
$389$	29.6512			1.50338			0.751688	−	0.659519i	$-0.229240\pi$
$389$	29.6512			1.50338			0.751688	+	0.659519i	$0.229240\pi$
$390$		0			0
$391$	4.56043			0.230631
$392$		0			0
$393$	−21.6178	+	0.515189i	−1.09047	+	0.0259878i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.22593	−	8.22593i	−0.412847	−	0.412847i	0.469882	−	0.882729i	$-0.344297\pi$
$397$	−8.22593	−	8.22593i	−0.412847	−	0.412847i	−0.882729	+	0.469882i	$0.844297\pi$
$398$		0			0
$399$	−6.42143	−	6.12249i	−0.321474	−	0.306508i
$400$		0			0
$401$			32.2078i			1.60838i	0.594370	+	0.804191i	$0.297401\pi$
$401$			32.2078i			1.60838i	−0.594370	+	0.804191i	$0.702599\pi$
$402$		0			0
$403$	−0.0752972	+	0.0752972i	−0.00375082	+	0.00375082i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.0223070	+	0.0223070i	−0.00110572	+	0.00110572i
$408$		0			0
$409$		−	7.75602i		−	0.383511i	−0.981443	−	0.191755i	$-0.938582\pi$
$409$		−	7.75602i		−	0.383511i	0.981443	−	0.191755i	$-0.0614180\pi$
$410$		0			0
$411$	−20.5257	−	19.5701i	−1.01246	−	0.965323i
$412$		0			0
$413$	3.76732	+	3.76732i	0.185378	+	0.185378i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	25.9248	−	0.617832i	1.26954	−	0.0302554i
$418$		0			0
$419$	0.442296			0.0216076			0.0108038	−	0.999942i	$-0.496561\pi$
$419$	0.442296			0.0216076			0.0108038	+	0.999942i	$0.496561\pi$
$420$		0			0
$421$	−15.5754			−0.759097			−0.379549	−	0.925172i	$-0.623921\pi$
$421$	−15.5754			−0.759097			−0.379549	+	0.925172i	$0.623921\pi$
$422$		0			0
$423$	11.3704	−	12.5093i	0.552849	−	0.608221i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.41079	+	3.41079i	0.165060	+	0.165060i
$428$		0			0
$429$	2.14776	−	2.25263i	0.103695	−	0.108758i
$430$		0			0
$431$		−	4.29772i		−	0.207014i	−0.994629	−	0.103507i	$-0.966994\pi$
$431$		−	4.29772i		−	0.207014i	0.994629	−	0.103507i	$-0.0330064\pi$
$432$		0			0
$433$	−25.3909	+	25.3909i	−1.22021	+	1.22021i	−0.252649	+	0.967558i	$0.581302\pi$
$433$	−25.3909	+	25.3909i	−1.22021	+	1.22021i	−0.967558	+	0.252649i	$0.918698\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.53012	−	7.53012i	0.360215	−	0.360215i
$438$		0			0
$439$		−	16.3148i		−	0.778665i	−0.921097	−	0.389333i	$-0.872706\pi$
$439$		−	16.3148i		−	0.778665i	0.921097	−	0.389333i	$-0.127294\pi$
$440$		0			0
$441$	−0.142909	−	2.99659i	−0.00680520	−	0.142695i
$442$		0			0
$443$	−25.0050	−	25.0050i	−1.18802	−	1.18802i	−0.977613	−	0.210411i	$-0.932520\pi$
$443$	−25.0050	−	25.0050i	−1.18802	−	1.18802i	−0.210411	−	0.977613i	$-0.567480\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.245151	+	10.2867i	0.0115952	+	0.486546i
$448$		0			0
$449$	−10.7127			−0.505566			−0.252783	−	0.967523i	$-0.581346\pi$
$449$	−10.7127			−0.505566			−0.252783	+	0.967523i	$0.581346\pi$
$450$		0			0
$451$	−16.5187			−0.777836
$452$		0			0
$453$	0.702787	+	29.4895i	0.0330198	+	1.38554i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.78419	−	6.78419i	−0.317351	−	0.317351i	0.530398	−	0.847749i	$-0.322043\pi$
$457$	−6.78419	−	6.78419i	−0.317351	−	0.317351i	−0.847749	+	0.530398i	$0.822043\pi$
$458$		0			0
$459$	−8.61509	−	7.46378i	−0.402118	−	0.348380i
$460$		0			0
$461$			13.2962i			0.619268i	0.950856	+	0.309634i	$0.100207\pi$
$461$			13.2962i			0.619268i	−0.950856	+	0.309634i	$0.899793\pi$
$462$		0			0
$463$	−25.5971	+	25.5971i	−1.18960	+	1.18960i	−0.212419	+	0.977179i	$0.568134\pi$
$463$	−25.5971	+	25.5971i	−1.18960	+	1.18960i	−0.977179	+	0.212419i	$0.931866\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.7182	−	19.7182i	0.912451	−	0.912451i	−0.0840140	−	0.996465i	$-0.526774\pi$
$467$	19.7182	−	19.7182i	0.912451	−	0.912451i	0.996465	+	0.0840140i	$0.0267740\pi$
$468$		0			0
$469$		−	4.26284i		−	0.196840i
$470$		0			0
$471$	−13.6022	+	14.2664i	−0.626757	+	0.657360i
$472$		0			0
$473$	4.70348	+	4.70348i	0.216266	+	0.216266i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.1074	−	15.5499i	−0.783293	−	0.711983i
$478$		0			0
$479$	15.7258			0.718530			0.359265	−	0.933236i	$-0.383027\pi$
$479$	15.7258			0.718530			0.359265	+	0.933236i	$0.383027\pi$
$480$		0			0
$481$	0.0181887			0.000829332
$482$		0			0
$483$	3.59976	−	0.0857885i	0.163795	−	0.00390351i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−15.1070	−	15.1070i	−0.684564	−	0.684564i	0.276461	−	0.961025i	$-0.410838\pi$
$487$	−15.1070	−	15.1070i	−0.684564	−	0.684564i	−0.961025	+	0.276461i	$0.910838\pi$
$488$		0			0
$489$	10.8228	+	10.3190i	0.489424	+	0.466639i
$490$		0			0
$491$			1.69331i			0.0764179i	0.999270	+	0.0382090i	$0.0121652\pi$
$491$			1.69331i			0.0764179i	−0.999270	+	0.0382090i	$0.987835\pi$
$492$		0			0
$493$	11.8449	−	11.8449i	0.533468	−	0.533468i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.68166	−	3.68166i	0.165145	−	0.165145i
$498$		0			0
$499$			42.9129i			1.92104i	0.278203	+	0.960522i	$0.410261\pi$
$499$			42.9129i			1.92104i	−0.278203	+	0.960522i	$0.589739\pi$
$500$		0			0
$501$	−4.81916	−	4.59481i	−0.215304	−	0.205281i
$502$		0			0
$503$	−26.6274	−	26.6274i	−1.18726	−	1.18726i	−0.977823	−	0.209433i	$-0.932838\pi$
$503$	−26.6274	−	26.6274i	−1.18726	−	1.18726i	−0.209433	−	0.977823i	$-0.567162\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.7163	−	0.493705i	0.920042	−	0.0219262i
$508$		0			0
$509$	24.5004			1.08596			0.542981	−	0.839745i	$-0.317295\pi$
$509$	24.5004			1.08596			0.542981	+	0.839745i	$0.317295\pi$
$510$		0			0
$511$	−10.0437			−0.444308
$512$		0			0
$513$	−26.5492	+	1.90102i	−1.17218	+	0.0839323i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.03426	−	7.03426i	−0.309366	−	0.309366i
$518$		0			0
$519$	27.0544	−	28.3754i	1.18756	−	1.24554i
$520$		0			0
$521$			0.487097i			0.0213401i	0.999943	+	0.0106701i	$0.00339645\pi$
$521$			0.487097i			0.0213401i	−0.999943	+	0.0106701i	$0.996604\pi$
$522$		0			0
$523$	−1.98037	+	1.98037i	−0.0865954	+	0.0865954i	−0.749078	−	0.662482i	$-0.769503\pi$
$523$	−1.98037	+	1.98037i	−0.0865954	+	0.0865954i	0.662482	+	0.749078i	$0.269503\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.162277	−	0.162277i	0.00706888	−	0.00706888i
$528$		0			0
$529$		−	18.6781i		−	0.812092i
$530$		0			0
$531$	15.9653	−	0.761392i	0.692833	−	0.0330416i
$532$		0			0
$533$	6.73450	+	6.73450i	0.291704	+	0.291704i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.0145212	−	0.609324i	−0.000626638	−	0.0262943i
$538$		0			0
$539$	−1.76542			−0.0760419
$540$		0			0
$541$	39.1538			1.68335			0.841677	−	0.539982i	$-0.181569\pi$
$541$	39.1538			1.68335			0.841677	+	0.539982i	$0.181569\pi$
$542$		0			0
$543$	−0.219731	−	9.22011i	−0.00942957	−	0.395673i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	21.3666	+	21.3666i	0.913568	+	0.913568i	0.996551	−	0.0829826i	$-0.0264446\pi$
$547$	21.3666	+	21.3666i	0.913568	+	0.913568i	−0.0829826	+	0.996551i	$0.526445\pi$
$548$		0			0
$549$	14.4543	−	0.689335i	0.616896	−	0.0294201i
$550$		0			0
$551$		−	39.1164i		−	1.66641i
$552$		0			0
$553$	10.9530	−	10.9530i	0.465771	−	0.465771i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.13033	−	8.13033i	0.344493	−	0.344493i	−0.513560	−	0.858054i	$-0.671674\pi$
$557$	8.13033	−	8.13033i	0.344493	−	0.344493i	0.858054	+	0.513560i	$0.171674\pi$
$558$		0			0
$559$		−	3.83512i		−	0.162208i
$560$		0			0
$561$	−4.62875	+	4.85476i	−0.195426	+	0.204968i
$562$		0			0
$563$	26.5393	+	26.5393i	1.11850	+	1.11850i	0.991962	+	0.126535i	$0.0403856\pi$
$563$	26.5393	+	26.5393i	1.11850	+	1.11850i	0.126535	+	0.991962i	$0.459614\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.94070	−	5.72945i	−0.291482	−	0.240614i
$568$		0			0
$569$	12.3882			0.519341			0.259671	−	0.965697i	$-0.416386\pi$
$569$	12.3882			0.519341			0.259671	+	0.965697i	$0.416386\pi$
$570$		0			0
$571$	1.56580			0.0655267			0.0327633	−	0.999463i	$-0.489569\pi$
$571$	1.56580			0.0655267			0.0327633	+	0.999463i	$0.489569\pi$
$572$		0			0
$573$	13.5859	−	0.323775i	0.567559	−	0.0135259i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.04688	−	6.04688i	−0.251735	−	0.251735i	0.569947	−	0.821682i	$-0.306964\pi$
$577$	−6.04688	−	6.04688i	−0.251735	−	0.251735i	−0.821682	+	0.569947i	$0.806964\pi$
$578$		0			0
$579$	0.475786	+	0.453636i	0.0197730	+	0.0188525i
$580$		0			0
$581$		−	5.32140i		−	0.220769i
$582$		0			0
$583$	−9.61989	+	9.61989i	−0.398415	+	0.398415i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.0640	−	19.0640i	0.786857	−	0.786857i	−0.194121	−	0.980978i	$-0.562185\pi$
$587$	19.0640	−	19.0640i	0.786857	−	0.786857i	0.980978	+	0.194121i	$0.0621855\pi$
$588$		0			0
$589$		−	0.535898i		−	0.0220813i
$590$		0			0
$591$	−16.6925	−	15.9154i	−0.686638	−	0.654672i
$592$		0			0
$593$	18.5595	+	18.5595i	0.762148	+	0.762148i	0.976710	−	0.214562i	$-0.0688326\pi$
$593$	18.5595	+	18.5595i	0.762148	+	0.762148i	−0.214562	+	0.976710i	$0.568833\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.83750	−	0.0914543i	0.157058	−	0.00374298i
$598$		0			0
$599$	−3.58329			−0.146409			−0.0732046	−	0.997317i	$-0.523323\pi$
$599$	−3.58329			−0.146409			−0.0732046	+	0.997317i	$0.523323\pi$
$600$		0			0
$601$	−17.2133			−0.702145			−0.351072	−	0.936348i	$-0.614183\pi$
$601$	−17.2133			−0.702145			−0.351072	+	0.936348i	$0.614183\pi$
$602$		0			0
$603$	−9.46336	−	8.60182i	−0.385378	−	0.350293i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.02293	−	6.02293i	−0.244463	−	0.244463i	0.574230	−	0.818694i	$-0.305301\pi$
$607$	−6.02293	−	6.02293i	−0.244463	−	0.244463i	−0.818694	+	0.574230i	$0.805301\pi$
$608$		0			0
$609$	9.12693	−	9.57257i	0.369842	−	0.387900i
$610$		0			0
$611$			5.73558i			0.232037i
$612$		0			0
$613$	4.01752	−	4.01752i	0.162266	−	0.162266i	−0.621304	−	0.783570i	$-0.713397\pi$
$613$	4.01752	−	4.01752i	0.162266	−	0.162266i	0.783570	+	0.621304i	$0.213397\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.421041	+	0.421041i	−0.0169505	+	0.0169505i	−0.715531	−	0.698581i	$-0.753815\pi$
$617$	−0.421041	+	0.421041i	−0.0169505	+	0.0169505i	0.698581	+	0.715531i	$0.253815\pi$
$618$		0			0
$619$		−	29.0434i		−	1.16735i	−0.811986	−	0.583676i	$-0.801614\pi$
$619$		−	29.0434i		−	1.16735i	0.811986	−	0.583676i	$-0.198386\pi$
$620$		0			0
$621$	7.07336	−	8.16445i	0.283844	−	0.327628i
$622$		0			0
$623$	2.11273	+	2.11273i	0.0846446	+	0.0846446i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.373183	+	15.6591i	0.0149035	+	0.625363i
$628$		0			0
$629$	−0.0391993			−0.00156298
$630$		0			0
$631$	27.4797			1.09395			0.546975	−	0.837149i	$-0.315779\pi$
$631$	27.4797			1.09395			0.546975	+	0.837149i	$0.315779\pi$
$632$		0			0
$633$	−0.0178744	−	0.750027i	−0.000710445	−	0.0298109i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.719742	+	0.719742i	0.0285172	+	0.0285172i
$638$		0			0
$639$	−0.744079	−	15.6022i	−0.0294353	−	0.617214i
$640$		0			0
$641$		−	33.3722i		−	1.31812i	−0.752089	−	0.659062i	$-0.770954\pi$
$641$		−	33.3722i		−	1.31812i	0.752089	−	0.659062i	$-0.229046\pi$
$642$		0			0
$643$	−29.8928	+	29.8928i	−1.17886	+	1.17886i	−0.198824	+	0.980035i	$0.563712\pi$
$643$	−29.8928	+	29.8928i	−1.17886	+	1.17886i	−0.980035	+	0.198824i	$0.936288\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.4656	−	10.4656i	0.411446	−	0.411446i	−0.470796	−	0.882242i	$-0.656033\pi$
$647$	10.4656	−	10.4656i	0.411446	−	0.411446i	0.882242	+	0.470796i	$0.156033\pi$
$648$		0			0
$649$		−	9.40580i		−	0.369210i
$650$		0			0
$651$	0.125040	−	0.131145i	0.00490070	−	0.00513999i
$652$		0			0
$653$	−15.3707	−	15.3707i	−0.601500	−	0.601500i	0.339210	−	0.940711i	$-0.389840\pi$
$653$	−15.3707	−	15.3707i	−0.601500	−	0.601500i	−0.940711	+	0.339210i	$0.889840\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−20.2668	+	22.2967i	−0.790683	+	0.869876i
$658$		0			0
$659$	−2.70465			−0.105358			−0.0526791	−	0.998611i	$-0.516776\pi$
$659$	−2.70465			−0.105358			−0.0526791	+	0.998611i	$0.516776\pi$
$660$		0			0
$661$	−30.8272			−1.19904			−0.599519	−	0.800360i	$-0.704642\pi$
$661$	−30.8272			−1.19904			−0.599519	+	0.800360i	$0.704642\pi$
$662$		0			0
$663$	3.86633	−	0.0921413i	0.150156	−	0.00357847i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.2253	+	11.2253i	0.434646	+	0.434646i
$668$		0			0
$669$	28.8419	+	27.4992i	1.11509	+	1.06318i
$670$		0			0
$671$		−	8.51565i		−	0.328743i
$672$		0			0
$673$	20.1553	−	20.1553i	0.776930	−	0.776930i	−0.202378	−	0.979308i	$-0.564867\pi$
$673$	20.1553	−	20.1553i	0.776930	−	0.776930i	0.979308	+	0.202378i	$0.0648669\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.7572	+	22.7572i	−0.874629	+	0.874629i	−0.992973	−	0.118344i	$-0.962242\pi$
$677$	−22.7572	+	22.7572i	−0.874629	+	0.874629i	0.118344	+	0.992973i	$0.462242\pi$
$678$		0			0
$679$			9.07367i			0.348215i
$680$		0			0
$681$	33.0893	+	31.5489i	1.26798	+	1.20895i
$682$		0			0
$683$	25.1450	+	25.1450i	0.962146	+	0.962146i	0.999309	−	0.0371629i	$-0.0118320\pi$
$683$	25.1450	+	25.1450i	0.962146	+	0.962146i	−0.0371629	+	0.999309i	$0.511832\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.40971	−	0.200418i	0.320850	−	0.00764642i
$688$		0			0
$689$	7.84386			0.298827
$690$		0			0
$691$	−22.6399			−0.861261			−0.430631	−	0.902528i	$-0.641709\pi$
$691$	−22.6399			−0.861261			−0.430631	+	0.902528i	$0.641709\pi$
$692$		0			0
$693$	−3.56237	+	3.91917i	−0.135323	+	0.148877i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−14.5139	−	14.5139i	−0.549751	−	0.549751i
$698$		0			0
$699$	−32.8713	+	34.4763i	−1.24331	+	1.30401i
$700$		0			0
$701$		−	32.6250i		−	1.23223i	−0.787657	−	0.616114i	$-0.788706\pi$
$701$		−	32.6250i		−	1.23223i	0.787657	−	0.616114i	$-0.211294\pi$
$702$		0			0
$703$	−0.0647254	+	0.0647254i	−0.00244117	+	0.00244117i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.7896	+	13.7896i	−0.518611	+	0.518611i
$708$		0			0
$709$			0.338874i			0.0127267i	0.999980	+	0.00636333i	$0.00202553\pi$
$709$			0.338874i			0.0127267i	−0.999980	+	0.00636333i	$0.997974\pi$
$710$		0			0
$711$	−2.21366	−	46.4171i	−0.0830186	−	1.74078i
$712$		0			0
$713$	0.153788	+	0.153788i	0.00575941	+	0.00575941i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.731844	−	30.7088i	−0.0273312	−	1.14684i
$718$		0			0
$719$	51.0469			1.90373			0.951863	−	0.306523i	$-0.0991657\pi$
$719$	51.0469			1.90373			0.951863	+	0.306523i	$0.0991657\pi$
$720$		0			0
$721$	−3.61754			−0.134724
$722$		0			0
$723$	0.904020	+	37.9334i	0.0336209	+	1.41076i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−14.3223	−	14.3223i	−0.531185	−	0.531185i	0.389740	−	0.920925i	$-0.372565\pi$
$727$	−14.3223	−	14.3223i	−0.531185	−	0.531185i	−0.920925	+	0.389740i	$0.872565\pi$
$728$		0			0
$729$	−26.7245	+	3.84688i	−0.989798	+	0.142477i
$730$		0			0
$731$			8.26525i			0.305701i
$732$		0			0
$733$	29.8460	−	29.8460i	1.10239	−	1.10239i	0.108264	−	0.994122i	$-0.465471\pi$
$733$	29.8460	−	29.8460i	1.10239	−	1.10239i	0.994122	−	0.108264i	$-0.0345293\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.32147	+	5.32147i	−0.196019	+	0.196019i
$738$		0			0
$739$		−	12.5764i		−	0.462631i	−0.972879	−	0.231316i	$-0.925697\pi$
$739$		−	12.5764i		−	0.462631i	0.972879	−	0.231316i	$-0.0743030\pi$
$740$		0			0
$741$	6.23189	−	6.53618i	0.228934	−	0.240112i
$742$		0			0
$743$	−29.8270	−	29.8270i	−1.09425	−	1.09425i	−0.995070	−	0.0991785i	$-0.968379\pi$
$743$	−29.8270	−	29.8270i	−1.09425	−	1.09425i	−0.0991785	−	0.995070i	$-0.531621\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.8133	−	10.7378i	−0.432227	−	0.392877i
$748$		0			0
$749$	18.0867			0.660872
$750$		0			0
$751$	37.9527			1.38491			0.692456	−	0.721460i	$-0.256528\pi$
$751$	37.9527			1.38491			0.692456	+	0.721460i	$0.256528\pi$
$752$		0			0
$753$	8.88342	−	0.211707i	0.323730	−	0.00771505i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.5520	+	17.5520i	0.637938	+	0.637938i	0.950047	−	0.312108i	$-0.101035\pi$
$757$	17.5520	+	17.5520i	0.637938	+	0.637938i	−0.312108	+	0.950047i	$0.601035\pi$
$758$		0			0
$759$	−4.60081	−	4.38663i	−0.166999	−	0.159224i
$760$		0			0
$761$			8.56045i			0.310316i	0.987890	+	0.155158i	$0.0495887\pi$
$761$			8.56045i			0.310316i	−0.987890	+	0.155158i	$0.950411\pi$
$762$		0			0
$763$	5.12297	−	5.12297i	0.185464	−	0.185464i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.83464	+	3.83464i	−0.138461	+	0.138461i
$768$		0			0
$769$		−	9.71231i		−	0.350235i	−0.984548	−	0.175117i	$-0.943969\pi$
$769$		−	9.71231i		−	0.350235i	0.984548	−	0.175117i	$-0.0560305\pi$
$770$		0			0
$771$	2.18157	+	2.08001i	0.0785672	+	0.0749096i
$772$		0			0
$773$	30.1398	+	30.1398i	1.08405	+	1.08405i	0.996127	+	0.0879261i	$0.0280239\pi$
$773$	30.1398	+	30.1398i	1.08405	+	1.08405i	0.0879261	+	0.996127i	$0.471976\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.0309419		0.000737398i	−0.00111003		2.64540e-5i
$778$		0			0
$779$	−47.9302			−1.71728
$780$		0			0
$781$	−9.19192			−0.328913
$782$		0			0
$783$	−2.83390	−	39.5776i	−0.101275	−	1.41439i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	8.55996	+	8.55996i	0.305130	+	0.305130i	0.843017	−	0.537887i	$-0.180777\pi$
$787$	8.55996	+	8.55996i	0.305130	+	0.305130i	−0.537887	+	0.843017i	$0.680777\pi$
$788$		0			0
$789$	−0.625495	+	0.656036i	−0.0222682	+	0.0233555i
$790$		0			0
$791$		−	9.28048i		−	0.329976i
$792$		0			0
$793$	−3.47174	+	3.47174i	−0.123285	+	0.123285i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.9179	+	11.9179i	−0.422152	+	0.422152i	−0.885944	−	0.463792i	$-0.846488\pi$
$797$	−11.9179	+	11.9179i	−0.422152	+	0.422152i	0.463792	+	0.885944i	$0.346488\pi$
$798$		0			0
$799$		−	12.3610i		−	0.437302i
$800$		0			0
$801$	8.95337	−	0.426991i	0.316352	−	0.0150870i
$802$		0			0
$803$	12.5380	+	12.5380i	0.442455	+	0.442455i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.628384	−	26.3675i	−0.0221202	−	0.928180i
$808$		0			0
$809$	−2.44921			−0.0861097			−0.0430549	−	0.999073i	$-0.513709\pi$
$809$	−2.44921			−0.0861097			−0.0430549	+	0.999073i	$0.513709\pi$
$810$		0			0
$811$	1.32051			0.0463693			0.0231847	−	0.999731i	$-0.492619\pi$
$811$	1.32051			0.0463693			0.0231847	+	0.999731i	$0.492619\pi$
$812$		0			0
$813$	0.672170	+	28.2048i	0.0235740	+	0.989186i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.6475	+	13.6475i	0.477465	+	0.477465i
$818$		0			0
$819$	3.05014	−	0.145463i	0.106581	−	0.00508289i
$820$		0			0
$821$			40.5038i			1.41359i	0.707417	+	0.706797i	$0.249860\pi$
$821$			40.5038i			1.41359i	−0.707417	+	0.706797i	$0.750140\pi$
$822$		0			0
$823$	−28.1227	+	28.1227i	−0.980296	+	0.980296i	−0.999810	−	0.0195133i	$-0.993788\pi$
$823$	−28.1227	+	28.1227i	−0.980296	+	0.980296i	0.0195133	+	0.999810i	$0.493788\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.9005	+	25.9005i	−0.900649	+	0.900649i	−0.995492	−	0.0948428i	$-0.969765\pi$
$827$	−25.9005	+	25.9005i	−0.900649	+	0.900649i	0.0948428	+	0.995492i	$0.469765\pi$
$828$		0			0
$829$		−	3.31951i		−	0.115291i	−0.998337	−	0.0576457i	$-0.981641\pi$
$829$		−	3.31951i		−	0.115291i	0.998337	−	0.0576457i	$-0.0183594\pi$
$830$		0			0
$831$	−27.8312	+	29.1902i	−0.965455	+	1.01260i
$832$		0			0
$833$	−1.55115	−	1.55115i	−0.0537442	−	0.0537442i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.0388247	−	0.542217i	−0.00134198	−	0.0187418i
$838$		0			0
$839$	−20.4082			−0.704570			−0.352285	−	0.935893i	$-0.614595\pi$
$839$	−20.4082			−0.704570			−0.352285	+	0.935893i	$0.614595\pi$
$840$		0			0
$841$	29.3117			1.01075
$842$		0			0
$843$	45.9934	−	1.09610i	1.58410	−	0.0377518i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.57433	−	5.57433i	−0.191536	−	0.191536i
$848$		0			0
$849$	11.7864	+	11.2377i	0.404508	+	0.385676i
$850$		0			0
$851$		−	0.0371488i		−	0.00127345i
$852$		0			0
$853$	6.05842	−	6.05842i	0.207436	−	0.207436i	−0.595741	−	0.803177i	$-0.703141\pi$
$853$	6.05842	−	6.05842i	0.207436	−	0.207436i	0.803177	+	0.595741i	$0.203141\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	31.2305	−	31.2305i	1.06681	−	1.06681i	0.0692109	−	0.997602i	$-0.477952\pi$
$857$	31.2305	−	31.2305i	1.06681	−	1.06681i	0.997602	−	0.0692109i	$-0.0220481\pi$
$858$		0			0
$859$			50.7305i			1.73090i	0.500992	+	0.865452i	$0.332969\pi$
$859$			50.7305i			1.73090i	−0.500992	+	0.865452i	$0.667031\pi$
$860$		0			0
$861$	−11.7295	−	11.1834i	−0.399740	−	0.381131i
$862$		0			0
$863$	9.99997	+	9.99997i	0.340403	+	0.340403i	0.856519	−	0.516116i	$-0.172623\pi$
$863$	9.99997	+	9.99997i	0.340403	+	0.340403i	−0.516116	+	0.856519i	$0.672623\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	21.1040	−	0.502945i	0.716729	−	0.0170809i
$868$		0			0
$869$	−27.3462			−0.927657
$870$		0			0
$871$	4.33902			0.147022
$872$		0			0
$873$	20.1432	+	18.3094i	0.681745	+	0.619679i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	33.6199	+	33.6199i	1.13526	+	1.13526i	0.989288	+	0.145974i	$0.0466317\pi$
$877$	33.6199	+	33.6199i	1.13526	+	1.13526i	0.145974	+	0.989288i	$0.453368\pi$
$878$		0			0
$879$	−10.4809	+	10.9927i	−0.353512	+	0.370773i
$880$		0			0
$881$			34.9376i			1.17708i	0.808469	+	0.588539i	$0.200297\pi$
$881$			34.9376i			1.17708i	−0.808469	+	0.588539i	$0.799703\pi$
$882$		0			0
$883$	27.3663	−	27.3663i	0.920948	−	0.920948i	−0.0761487	−	0.997096i	$-0.524262\pi$
$883$	27.3663	−	27.3663i	0.920948	−	0.920948i	0.997096	+	0.0761487i	$0.0242624\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.2242	−	24.2242i	0.813369	−	0.813369i	−0.171769	−	0.985137i	$-0.554948\pi$
$887$	24.2242	−	24.2242i	0.813369	−	0.813369i	0.985137	+	0.171769i	$0.0549482\pi$
$888$		0			0
$889$		−	4.47208i		−	0.149989i
$890$		0			0
$891$	1.51205	+	15.8167i	0.0506556	+	0.529878i
$892$		0			0
$893$	−20.4104	−	20.4104i	−0.683008	−	0.683008i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.0873215	+	3.66409i	0.00291558	+	0.122340i
$898$		0			0
$899$	0.798876			0.0266440
$900$		0			0
$901$	−16.9047			−0.563176
$902$		0			0
$903$	0.155482	+	6.52415i	0.00517411	+	0.217110i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.2907	+	24.2907i	0.806558	+	0.806558i	0.984111	−	0.177553i	$-0.0568181\pi$
$907$	24.2907	+	24.2907i	0.806558	+	0.806558i	−0.177553	+	0.984111i	$0.556818\pi$
$908$		0			0
$909$	2.78694	+	58.4379i	0.0924368	+	1.93826i
$910$		0			0
$911$			4.30457i			0.142617i	0.997454	+	0.0713083i	$0.0227174\pi$
$911$			4.30457i			0.142617i	−0.997454	+	0.0713083i	$0.977283\pi$
$912$		0			0
$913$	−6.64291	+	6.64291i	−0.219848	+	0.219848i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.82792	+	8.82792i	−0.291524	+	0.291524i
$918$		0			0
$919$			28.6567i			0.945299i	0.881251	+	0.472649i	$0.156702\pi$
$919$			28.6567i			0.945299i	−0.881251	+	0.472649i	$0.843298\pi$
$920$		0			0
$921$	−4.59748	+	4.82196i	−0.151492	+	0.158889i
$922$		0			0
$923$	3.74745	+	3.74745i	0.123349	+	0.123349i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−7.29969	+	8.03081i	−0.239753	+	0.263766i
$928$		0			0
$929$	−30.1698			−0.989840			−0.494920	−	0.868938i	$-0.664803\pi$
$929$	−30.1698			−0.989840			−0.494920	+	0.868938i	$0.664803\pi$
$930$		0			0
$931$	−5.12249			−0.167883
$932$		0			0
$933$	−55.1072	+	1.31330i	−1.80413	+	0.0429955i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−7.29925	−	7.29925i	−0.238456	−	0.238456i	0.577755	−	0.816211i	$-0.303929\pi$
$937$	−7.29925	−	7.29925i	−0.238456	−	0.238456i	−0.816211	+	0.577755i	$0.803929\pi$
$938$		0			0
$939$	−25.3087	−	24.1305i	−0.825918	−	0.787468i
$940$		0			0
$941$			15.2822i			0.498187i	0.968480	+	0.249093i	$0.0801326\pi$
$941$			15.2822i			0.498187i	−0.968480	+	0.249093i	$0.919867\pi$
$942$		0			0
$943$	13.7547	−	13.7547i	0.447913	−	0.447913i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.4664	+	12.4664i	−0.405104	+	0.405104i	−0.880027	−	0.474923i	$-0.842476\pi$
$947$	−12.4664	+	12.4664i	−0.405104	+	0.405104i	0.474923	+	0.880027i	$0.342476\pi$
$948$		0			0
$949$		−	10.2232i		−	0.331859i
$950$		0			0
$951$	−13.6688	−	13.0325i	−0.443241	−	0.422606i
$952$		0			0
$953$	−19.7282	−	19.7282i	−0.639058	−	0.639058i	0.311265	−	0.950323i	$-0.399247\pi$
$953$	−19.7282	−	19.7282i	−0.639058	−	0.639058i	−0.950323	+	0.311265i	$0.899247\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−23.3433	+	0.556312i	−0.754582	+	0.0179830i
$958$		0			0
$959$	−16.3737			−0.528734
$960$		0			0
$961$	−30.9891			−0.999647
$962$		0			0
$963$	36.4963	−	40.1517i	1.17608	−	1.29387i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	27.4624	+	27.4624i	0.883130	+	0.883130i	0.993852	−	0.110721i	$-0.0353160\pi$
$967$	27.4624	+	27.4624i	0.883130	+	0.883130i	−0.110721	+	0.993852i	$0.535316\pi$
$968$		0			0
$969$	−13.4306	+	14.0864i	−0.431455	+	0.452521i
$970$		0			0
$971$		−	12.8693i		−	0.412994i	−0.978447	−	0.206497i	$-0.933794\pi$
$971$		−	12.8693i		−	0.412994i	0.978447	−	0.206497i	$-0.0662064\pi$
$972$		0			0
$973$	10.5867	−	10.5867i	0.339395	−	0.339395i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.3733	+	15.3733i	−0.491836	+	0.491836i	−0.908884	−	0.417048i	$-0.863065\pi$
$977$	−15.3733	+	15.3733i	−0.491836	+	0.491836i	0.417048	+	0.908884i	$0.363065\pi$
$978$		0			0
$979$		−	5.27480i		−	0.168583i
$980$		0			0
$981$	−1.03537	−	21.7102i	−0.0330569	−	0.693155i
$982$		0			0
$983$	16.1811	+	16.1811i	0.516096	+	0.516096i	0.916388	−	0.400292i	$-0.131091\pi$
$983$	16.1811	+	16.1811i	0.516096	+	0.516096i	−0.400292	+	0.916388i	$0.631091\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.232530	−	9.75715i	−0.00740151	−	0.310574i
$988$		0			0
$989$	−7.83290			−0.249072
$990$		0			0
$991$	14.4737			0.459772			0.229886	−	0.973218i	$-0.426165\pi$
$991$	14.4737			0.459772			0.229886	+	0.973218i	$0.426165\pi$
$992$		0			0
$993$	−0.645319	−	27.0781i	−0.0204786	−	0.859299i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	11.9234	+	11.9234i	0.377617	+	0.377617i	0.870242	−	0.492625i	$-0.163963\pi$
$997$	11.9234	+	11.9234i	0.377617	+	0.377617i	−0.492625	+	0.870242i	$0.663963\pi$
$998$		0			0
$999$	−0.0607993	+	0.0701778i	−0.00192361	+	0.00222033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.c.1457.8	yes	32
3.2	odd	2	inner	2100.2.s.c.1457.16	yes	32
5.2	odd	4	inner	2100.2.s.c.1793.1	yes	32
5.3	odd	4	inner	2100.2.s.c.1793.16	yes	32
5.4	even	2	inner	2100.2.s.c.1457.9	yes	32
15.2	even	4	inner	2100.2.s.c.1793.9	yes	32
15.8	even	4	inner	2100.2.s.c.1793.8	yes	32
15.14	odd	2	inner	2100.2.s.c.1457.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.c.1457.1	✓	32	15.14	odd	2	inner
2100.2.s.c.1457.8	yes	32	1.1	even	1	trivial
2100.2.s.c.1457.9	yes	32	5.4	even	2	inner
2100.2.s.c.1457.16	yes	32	3.2	odd	2	inner
2100.2.s.c.1793.1	yes	32	5.2	odd	4	inner
2100.2.s.c.1793.8	yes	32	15.8	even	4	inner
2100.2.s.c.1793.9	yes	32	15.2	even	4	inner
2100.2.s.c.1793.16	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0412661 - 1.73156i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +O(q^{10})\)	\(q+(-0.0412661 - 1.73156i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +1.76542i q^{11} +(0.719742 - 0.719742i) q^{13} +(-1.55115 + 1.55115i) q^{17} +5.12249i q^{19} +(-1.19522 + 1.25358i) q^{21} +(-1.47001 - 1.47001i) q^{23} +(0.371114 + 5.18288i) q^{27} -7.63621 q^{29} -0.104617 q^{31} +(3.05693 - 0.0728519i) q^{33} +(0.0126355 + 0.0126355i) q^{37} +(-1.27598 - 1.21658i) q^{39} +9.35682i q^{41} +(2.66423 - 2.66423i) q^{43} +(-3.98447 + 3.98447i) q^{47} +1.00000i q^{49} +(2.74992 + 2.62190i) q^{51} +(5.44907 + 5.44907i) q^{53} +(8.86989 - 0.211385i) q^{57} -5.32780 q^{59} -4.82359 q^{61} +(2.21996 + 2.01786i) q^{63} +(3.01428 + 3.01428i) q^{67} +(-2.48475 + 2.60608i) q^{69} +5.20665i q^{71} +(7.10198 - 7.10198i) q^{73} +(1.24834 - 1.24834i) q^{77} +15.4899i q^{79} +(8.95915 - 0.856482i) q^{81} +(3.76280 + 3.76280i) q^{83} +(0.315116 + 13.2225i) q^{87} -2.98785 q^{89} -1.01787 q^{91} +(0.00431713 + 0.181150i) q^{93} +(-6.41605 - 6.41605i) q^{97} +(-0.252295 - 5.29024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) \) 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

Introduction

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