LMFDB - Embedded newform 2100.2.s.c.1457.16

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			1457.16
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.c.1793.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73156 + 0.0412661i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.99659 + 0.142909i) q^{9} +O(q^{10})$	$q+(1.73156 + 0.0412661i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.99659 + 0.142909i) q^{9} -1.76542i q^{11} +(0.719742 - 0.719742i) q^{13} +(1.55115 - 1.55115i) q^{17} +5.12249i q^{19} +(-1.19522 - 1.25358i) q^{21} +(1.47001 + 1.47001i) q^{23} +(5.18288 + 0.371114i) q^{27} +7.63621 q^{29} -0.104617 q^{31} +(0.0728519 - 3.05693i) q^{33} +(0.0126355 + 0.0126355i) q^{37} +(1.27598 - 1.21658i) q^{39} -9.35682i q^{41} +(2.66423 - 2.66423i) q^{43} +(3.98447 - 3.98447i) q^{47} +1.00000i q^{49} +(2.74992 - 2.62190i) q^{51} +(-5.44907 - 5.44907i) q^{53} +(-0.211385 + 8.86989i) q^{57} +5.32780 q^{59} -4.82359 q^{61} +(-2.01786 - 2.21996i) q^{63} +(3.01428 + 3.01428i) q^{67} +(2.48475 + 2.60608i) q^{69} -5.20665i q^{71} +(7.10198 - 7.10198i) q^{73} +(-1.24834 + 1.24834i) q^{77} +15.4899i q^{79} +(8.95915 + 0.856482i) q^{81} +(-3.76280 - 3.76280i) q^{83} +(13.2225 + 0.315116i) q^{87} +2.98785 q^{89} -1.01787 q^{91} +(-0.181150 - 0.00431713i) q^{93} +(-6.41605 - 6.41605i) q^{97} +(0.252295 - 5.29024i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.73156	+	0.0412661i	0.999716	+	0.0238250i
$3$	1.73156	+	0.0412661i	0.999716	+	0.0238250i
$4$		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	$-0.914249\pi$
$11$		−	1.76542i		−	0.532294i	0.963933	−	0.266147i	$-0.0857506\pi$
$12$		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	−0.493523	−	0.869733i	$-0.664291\pi$
$17$	1.55115	−	1.55115i	0.376209	−	0.376209i	0.869733	+	0.493523i	$0.164291\pi$
$18$		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	0.843558	−	0.537039i	$-0.180457\pi$
$23$	1.47001	+	1.47001i	0.306519	+	0.306519i	−0.537039	+	0.843558i	$0.680457\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.18288	+	0.371114i	0.997446	+	0.0714208i
$28$		0			0
$29$	7.63621			1.41801			0.709004	−	0.705204i	$-0.249145\pi$
$29$	7.63621			1.41801			0.709004	+	0.705204i	$0.249145\pi$
$30$		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
$33$	0.0728519	−	3.05693i	0.0126819	−	0.532142i
$34$		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	$-0.739219\pi$
$41$		−	9.35682i		−	1.46129i	0.682757	−	0.730645i	$-0.260781\pi$
$42$		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	−0.354037	−	0.935232i	$-0.615191\pi$
$47$	3.98447	−	3.98447i	0.581195	−	0.581195i	0.935232	+	0.354037i	$0.115191\pi$
$48$		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	0.225707	−	0.974195i	$-0.427531\pi$
$53$	−5.44907	−	5.44907i	−0.748488	−	0.748488i	−0.974195	+	0.225707i	$0.927531\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.211385	+	8.86989i	−0.0279986	+	1.17485i
$58$		0			0
$59$	5.32780			0.693621			0.346810	−	0.937935i	$-0.387265\pi$
$59$	5.32780			0.693621			0.346810	+	0.937935i	$0.387265\pi$
$60$		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
$63$	−2.01786	−	2.21996i	−0.254226	−	0.279689i
$64$		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	$-0.900020\pi$
$71$		−	5.20665i		−	0.617916i	0.951076	−	0.308958i	$-0.0999802\pi$
$72$		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	0.469769	−	0.882789i	$-0.344337\pi$
$83$	−3.76280	−	3.76280i	−0.413021	−	0.413021i	−0.882789	+	0.469769i	$0.844337\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	13.2225	+	0.315116i	1.41761	+	0.0337840i
$88$		0			0
$89$	2.98785			0.316711			0.158356	−	0.987382i	$-0.449381\pi$
$89$	2.98785			0.316711			0.158356	+	0.987382i	$0.449381\pi$
$90$		0			0
$91$	−1.01787			−0.106702
$92$		0			0
$93$	−0.181150	−	0.00431713i	−0.0187844	−	0.000447665i
$94$		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	$0.422139\pi$
$101$			19.5014i			1.94047i	−0.242175	+	0.970233i	$0.577861\pi$
$102$		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	$-0.411353\pi$
$107$	12.7892	−	12.7892i	1.23638	−	1.23638i	0.961471	−	0.274908i	$-0.0886474\pi$
$108$		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	0.327517	−	0.944845i	$-0.393788\pi$
$113$	−6.56229	−	6.56229i	−0.617328	−	0.617328i	−0.944845	+	0.327517i	$0.893788\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.25963	−	2.05392i	0.208903	−	0.189885i
$118$		0			0
$119$	−2.19366			−0.201092
$120$		0			0
$121$	7.88330			0.716664
$122$		0			0
$123$	0.386119	−	16.2019i	0.0348152	−	1.46088i
$124$		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	$0.183619\pi$
$131$			12.4846i			1.09078i	−0.838182	+	0.545391i	$0.816381\pi$
$132$		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	−0.999942	−	0.0107709i	$-0.996571\pi$
$137$	−11.5780	+	11.5780i	−0.989171	+	0.989171i	0.0107709	+	0.999942i	$0.496571\pi$
$138$		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
$147$	−0.0412661	+	1.73156i	−0.00340357	+	0.142817i
$148$		0			0
$149$	5.94073			0.486684			0.243342	−	0.969941i	$-0.421756\pi$
$149$	5.94073			0.486684			0.243342	+	0.969941i	$0.421756\pi$
$150$		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
$153$	4.86984	−	4.42650i	0.393704	−	0.357861i
$154$		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	−0.804417	−	0.594065i	$-0.797522\pi$
$167$	−2.71835	+	2.71835i	−0.210352	+	0.210352i	0.594065	+	0.804417i	$0.297522\pi$
$168$		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	$-0.920167\pi$
$173$	−16.0058	−	16.0058i	−1.21690	−	1.21690i	−0.248183	−	0.968713i	$-0.579833\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.22540	+	0.219857i	0.693424	+	0.0165255i
$178$		0			0
$179$	−0.351893			−0.0263017			−0.0131509	−	0.999914i	$-0.504186\pi$
$179$	−0.351893			−0.0263017			−0.0131509	+	0.999914i	$0.504186\pi$
$180$		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
$183$	−8.35233	−	0.199050i	−0.617422	−	0.0147142i
$184$		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	$-0.908385\pi$
$191$		−	7.84604i		−	0.567720i	0.958866	−	0.283860i	$-0.0916151\pi$
$192$		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	−0.957911	−	0.287066i	$-0.907320\pi$
$197$	−9.41576	+	9.41576i	−0.670845	+	0.670845i	0.287066	+	0.957911i	$0.407320\pi$
$198$		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
$207$	4.19495	+	4.61511i	0.291569	+	0.320772i
$208$		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
$213$	0.214858	−	9.01563i	0.0147218	−	0.617740i
$214$		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	$-0.410216\pi$
$227$	18.6647	−	18.6647i	1.23882	−	1.23882i	0.960483	−	0.278338i	$-0.0897836\pi$
$228$		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	$0.107070\pi$
$233$	19.4471	+	19.4471i	1.27402	+	1.27402i	0.330062	+	0.943959i	$0.392930\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.639209	+	26.8218i	−0.0415211	+	1.74226i
$238$		0			0
$239$	−17.7348			−1.14717			−0.573583	−	0.819147i	$-0.694447\pi$
$239$	−17.7348			−1.14717			−0.573583	+	0.819147i	$0.694447\pi$
$240$		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
$243$	15.4780	+	1.85276i	0.992912	+	0.118855i
$244$		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	$-0.948234\pi$
$251$		−	5.13030i		−	0.323822i	0.986805	−	0.161911i	$-0.0517657\pi$
$252$		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	−0.667684	−	0.744445i	$-0.732714\pi$
$257$	1.23056	−	1.23056i	0.0767602	−	0.0767602i	0.744445	+	0.667684i	$0.232714\pi$
$258$		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	0.718424	−	0.695606i	$-0.244864\pi$
$263$	0.370051	+	0.370051i	0.0228183	+	0.0228183i	−0.695606	+	0.718424i	$0.744864\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.17364	+	0.123297i	0.316621	+	0.00754564i
$268$		0			0
$269$	−15.2276			−0.928444			−0.464222	−	0.885719i	$-0.653666\pi$
$269$	−15.2276			−0.928444			−0.464222	+	0.885719i	$0.653666\pi$
$270$		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
$273$	−1.76250	−	0.0420035i	−0.106671	−	0.00254217i
$274$		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	$-0.708897\pi$
$281$		−	26.5619i		−	1.58455i	0.610166	−	0.792274i	$-0.291103\pi$
$282$		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	0.864639	−	0.502394i	$-0.167547\pi$
$293$	6.20064	+	6.20064i	0.362245	+	0.362245i	−0.502394	+	0.864639i	$0.667547\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.655171	−	9.14996i	0.0380169	−	0.530934i
$298$		0			0
$299$	2.11606			0.122375
$300$		0			0
$301$	−3.76779			−0.217172
$302$		0			0
$303$	−0.804748	+	33.7679i	−0.0462315	+	1.93991i
$304$		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	$0.358138\pi$
$311$			31.8252i			1.80464i	−0.431065	+	0.902321i	$0.641862\pi$
$312$		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	−0.889663	−	0.456617i	$-0.849061\pi$
$317$	−7.71018	+	7.71018i	−0.433047	+	0.433047i	0.456617	+	0.889663i	$0.349061\pi$
$318$		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
$327$	−0.298972	+	12.5451i	−0.0165332	+	0.693746i
$328$		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
$333$	0.0360579	+	0.0396693i	0.00197596	+	0.00217387i
$334$		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	−0.556370	−	0.830935i	$-0.687806\pi$
$347$	5.11458	−	5.11458i	0.274565	−	0.274565i	0.830935	+	0.556370i	$0.187806\pi$
$348$		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	0.969633	−	0.244565i	$-0.0786451\pi$
$353$	13.6228	+	13.6228i	0.725068	+	0.725068i	−0.244565	+	0.969633i	$0.578645\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.79845	−	0.0905237i	−0.201035	−	0.00479102i
$358$		0			0
$359$	26.9640			1.42311			0.711554	−	0.702632i	$-0.247992\pi$
$359$	26.9640			1.42311			0.711554	+	0.702632i	$0.247992\pi$
$360$		0			0
$361$	−7.23987			−0.381046
$362$		0			0
$363$	13.6504	+	0.325313i	0.716460	+	0.0170745i
$364$		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	0.995360	−	0.0962236i	$-0.0306764\pi$
$383$	17.5964	+	17.5964i	0.899136	+	0.899136i	−0.0962236	+	0.995360i	$0.530676\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.36436	−	7.60287i	0.425184	−	0.386476i
$388$		0			0
$389$	−29.6512			−1.50338			−0.751688	−	0.659519i	$-0.770760\pi$
$389$	−29.6512			−1.50338			−0.751688	+	0.659519i	$0.770760\pi$
$390$		0			0
$391$	4.56043			0.230631
$392$		0			0
$393$	−0.515189	+	21.6178i	−0.0259878	+	1.09047i
$394$		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	$-0.702599\pi$
$401$		−	32.2078i		−	1.60838i	0.594370	−	0.804191i	$-0.297401\pi$
$402$		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
$417$	−0.617832	+	25.9248i	−0.0302554	+	1.26954i
$418$		0			0
$419$	−0.442296			−0.0216076			−0.0108038	−	0.999942i	$-0.503439\pi$
$419$	−0.442296			−0.0216076			−0.0108038	+	0.999942i	$0.503439\pi$
$420$		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
$423$	12.5093	−	11.3704i	0.608221	−	0.552849i
$424$		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	$0.0330064\pi$
$431$			4.29772i			0.207014i	−0.994629	+	0.103507i	$0.966994\pi$
$432$		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	$0.0674804\pi$
$443$	25.0050	+	25.0050i	1.18802	+	1.18802i	0.210411	+	0.977613i	$0.432520\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	10.2867	+	0.245151i	0.486546	+	0.0115952i
$448$		0			0
$449$	10.7127			0.505566			0.252783	−	0.967523i	$-0.418654\pi$
$449$	10.7127			0.505566			0.252783	+	0.967523i	$0.418654\pi$
$450$		0			0
$451$	−16.5187			−0.777836
$452$		0			0
$453$	−29.4895	−	0.702787i	−1.38554	−	0.0330198i
$454$		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	$-0.899793\pi$
$461$		−	13.2962i		−	0.619268i	0.950856	−	0.309634i	$-0.100207\pi$
$462$		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	−0.996465	−	0.0840140i	$-0.973226\pi$
$467$	−19.7182	+	19.7182i	−0.912451	+	0.912451i	0.0840140	+	0.996465i	$0.473226\pi$
$468$		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
$477$	−15.5499	−	17.1074i	−0.711983	−	0.783293i
$478$		0			0
$479$	−15.7258			−0.718530			−0.359265	−	0.933236i	$-0.616973\pi$
$479$	−15.7258			−0.718530			−0.359265	+	0.933236i	$0.616973\pi$
$480$		0			0
$481$	0.0181887			0.000829332
$482$		0			0
$483$	0.0857885	−	3.59976i	0.00390351	−	0.163795i
$484$		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	$-0.987835\pi$
$491$		−	1.69331i		−	0.0764179i	0.999270	−	0.0382090i	$-0.0121652\pi$
$492$		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	$0.0671617\pi$
$503$	26.6274	+	26.6274i	1.18726	+	1.18726i	0.209433	+	0.977823i	$0.432838\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.493705	+	20.7163i	−0.0219262	+	0.920042i
$508$		0			0
$509$	−24.5004			−1.08596			−0.542981	−	0.839745i	$-0.682705\pi$
$509$	−24.5004			−1.08596			−0.542981	+	0.839745i	$0.682705\pi$
$510$		0			0
$511$	−10.0437			−0.444308
$512$		0			0
$513$	−1.90102	+	26.5492i	−0.0839323	+	1.17218i
$514$		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	$-0.996604\pi$
$521$		−	0.487097i		−	0.0213401i	0.999943	−	0.0106701i	$-0.00339645\pi$
$522$		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
$537$	−0.609324	−	0.0145212i	−0.0262943	−	0.000626638i
$538$		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
$543$	9.22011	+	0.219731i	0.395673	+	0.00942957i
$544$		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	−0.858054	−	0.513560i	$-0.828326\pi$
$557$	−8.13033	+	8.13033i	−0.344493	+	0.344493i	0.513560	+	0.858054i	$0.328326\pi$
$558$		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	$-0.959614\pi$
$563$	−26.5393	−	26.5393i	−1.11850	−	1.11850i	−0.126535	−	0.991962i	$-0.540386\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.72945	−	6.94070i	−0.240614	−	0.291482i
$568$		0			0
$569$	−12.3882			−0.519341			−0.259671	−	0.965697i	$-0.583614\pi$
$569$	−12.3882			−0.519341			−0.259671	+	0.965697i	$0.583614\pi$
$570$		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
$573$	0.323775	−	13.5859i	0.0135259	−	0.567559i
$574$		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	−0.980978	−	0.194121i	$-0.937815\pi$
$587$	−19.0640	+	19.0640i	−0.786857	+	0.786857i	0.194121	+	0.980978i	$0.437815\pi$
$588$		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	0.214562	−	0.976710i	$-0.431167\pi$
$593$	−18.5595	−	18.5595i	−0.762148	−	0.762148i	−0.976710	+	0.214562i	$0.931167\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0914543	+	3.83750i	−0.00374298	+	0.157058i
$598$		0			0
$599$	3.58329			0.146409			0.0732046	−	0.997317i	$-0.476677\pi$
$599$	3.58329			0.146409			0.0732046	+	0.997317i	$0.476677\pi$
$600$		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
$603$	8.60182	+	9.46336i	0.350293	+	0.385378i
$604$		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	−0.698581	−	0.715531i	$-0.746185\pi$
$617$	0.421041	−	0.421041i	0.0169505	−	0.0169505i	0.715531	+	0.698581i	$0.246185\pi$
$618$		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
$627$	15.6591	+	0.373183i	0.625363	+	0.0149035i
$628$		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
$633$	0.750027	+	0.0178744i	0.0298109	+	0.000710445i
$634$		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	$0.229046\pi$
$641$			33.3722i			1.31812i	−0.752089	+	0.659062i	$0.770954\pi$
$642$		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	−0.882242	−	0.470796i	$-0.843967\pi$
$647$	−10.4656	+	10.4656i	−0.411446	+	0.411446i	0.470796	+	0.882242i	$0.343967\pi$
$648$		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	0.940711	−	0.339210i	$-0.110160\pi$
$653$	15.3707	+	15.3707i	0.601500	+	0.601500i	−0.339210	+	0.940711i	$0.610160\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	22.2967	−	20.2668i	0.869876	−	0.790683i
$658$		0			0
$659$	2.70465			0.105358			0.0526791	−	0.998611i	$-0.483224\pi$
$659$	2.70465			0.105358			0.0526791	+	0.998611i	$0.483224\pi$
$660$		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
$663$	0.0921413	−	3.86633i	0.00357847	−	0.150156i
$664$		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	−0.118344	−	0.992973i	$-0.537758\pi$
$677$	22.7572	−	22.7572i	0.874629	−	0.874629i	0.992973	+	0.118344i	$0.0377584\pi$
$678$		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	0.0371629	−	0.999309i	$-0.488168\pi$
$683$	−25.1450	−	25.1450i	−0.962146	−	0.962146i	−0.999309	+	0.0371629i	$0.988168\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.200418	+	8.40971i	−0.00764642	+	0.320850i
$688$		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
$693$	−3.91917	+	3.56237i	−0.148877	+	0.135323i
$694$		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	$0.211294\pi$
$701$			32.6250i			1.23223i	−0.787657	+	0.616114i	$0.788706\pi$
$702$		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
$717$	−30.7088	−	0.731844i	−1.14684	−	0.0273312i
$718$		0			0
$719$	−51.0469			−1.90373			−0.951863	−	0.306523i	$-0.900834\pi$
$719$	−51.0469			−1.90373			−0.951863	+	0.306523i	$0.900834\pi$
$720$		0			0
$721$	−3.61754			−0.134724
$722$		0			0
$723$	−37.9334	−	0.904020i	−1.41076	−	0.0336209i
$724$		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	$0.0316215\pi$
$743$	29.8270	+	29.8270i	1.09425	+	1.09425i	0.0991785	+	0.995070i	$0.468379\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−10.7378	−	11.8133i	−0.392877	−	0.432227i
$748$		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
$753$	0.211707	−	8.88342i	0.00771505	−	0.323730i
$754$		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	$-0.950411\pi$
$761$		−	8.56045i		−	0.310316i	0.987890	−	0.155158i	$-0.0495887\pi$
$762$		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	$-0.971976\pi$
$773$	−30.1398	−	30.1398i	−1.08405	−	1.08405i	−0.0879261	−	0.996127i	$-0.528024\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.000737398	−	0.0309419i	2.64540e−5	−	0.00111003i
$778$		0			0
$779$	47.9302			1.71728
$780$		0			0
$781$	−9.19192			−0.328913
$782$		0			0
$783$	39.5776	+	2.83390i	1.41439	+	0.101275i
$784$		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	−0.463792	−	0.885944i	$-0.653512\pi$
$797$	11.9179	−	11.9179i	0.422152	−	0.422152i	0.885944	+	0.463792i	$0.153512\pi$
$798$		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
$807$	−26.3675	−	0.628384i	−0.928180	−	0.0221202i
$808$		0			0
$809$	2.44921			0.0861097			0.0430549	−	0.999073i	$-0.486291\pi$
$809$	2.44921			0.0861097			0.0430549	+	0.999073i	$0.486291\pi$
$810$		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
$813$	−28.2048	−	0.672170i	−0.989186	−	0.0235740i
$814$		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	$-0.750140\pi$
$821$		−	40.5038i		−	1.41359i	0.707417	−	0.706797i	$-0.249860\pi$
$822$		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	−0.0948428	−	0.995492i	$-0.530235\pi$
$827$	25.9005	−	25.9005i	0.900649	−	0.900649i	0.995492	+	0.0948428i	$0.0302349\pi$
$828$		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
$837$	−0.542217	−	0.0388247i	−0.0187418	−	0.00134198i
$838$		0			0
$839$	20.4082			0.704570			0.352285	−	0.935893i	$-0.385405\pi$
$839$	20.4082			0.704570			0.352285	+	0.935893i	$0.385405\pi$
$840$		0			0
$841$	29.3117			1.01075
$842$		0			0
$843$	1.09610	−	45.9934i	0.0377518	−	1.58410i
$844$		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	$0.522048\pi$
$857$	−31.2305	+	31.2305i	−1.06681	+	1.06681i	−0.997602	+	0.0692109i	$0.977952\pi$
$858$		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	0.516116	−	0.856519i	$-0.327377\pi$
$863$	−9.99997	−	9.99997i	−0.340403	−	0.340403i	−0.856519	+	0.516116i	$0.827377\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.502945	+	21.1040i	−0.0170809	+	0.716729i
$868$		0			0
$869$	27.3462			0.927657
$870$		0			0
$871$	4.33902			0.147022
$872$		0			0
$873$	−18.3094	−	20.1432i	−0.619679	−	0.681745i
$874$		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	$-0.799703\pi$
$881$		−	34.9376i		−	1.17708i	0.808469	−	0.588539i	$-0.200297\pi$
$882$		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	−0.985137	−	0.171769i	$-0.945052\pi$
$887$	−24.2242	+	24.2242i	−0.813369	+	0.813369i	0.171769	+	0.985137i	$0.445052\pi$
$888$		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
$897$	3.66409	+	0.0873215i	0.122340	+	0.00291558i
$898$		0			0
$899$	−0.798876			−0.0266440
$900$		0			0
$901$	−16.9047			−0.563176
$902$		0			0
$903$	−6.52415	−	0.155482i	−0.217110	−	0.00517411i
$904$		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	$-0.977283\pi$
$911$		−	4.30457i		−	0.142617i	0.997454	−	0.0713083i	$-0.0227174\pi$
$912$		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
$927$	8.03081	−	7.29969i	0.263766	−	0.239753i
$928$		0			0
$929$	30.1698			0.989840			0.494920	−	0.868938i	$-0.335197\pi$
$929$	30.1698			0.989840			0.494920	+	0.868938i	$0.335197\pi$
$930$		0			0
$931$	−5.12249			−0.167883
$932$		0			0
$933$	−1.31330	+	55.1072i	−0.0429955	+	1.80413i
$934$		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	$-0.919867\pi$
$941$		−	15.2822i		−	0.498187i	0.968480	−	0.249093i	$-0.0801326\pi$
$942$		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	−0.474923	−	0.880027i	$-0.657524\pi$
$947$	12.4664	−	12.4664i	0.405104	−	0.405104i	0.880027	+	0.474923i	$0.157524\pi$
$948$		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	0.950323	−	0.311265i	$-0.100753\pi$
$953$	19.7282	+	19.7282i	0.639058	+	0.639058i	−0.311265	+	0.950323i	$0.600753\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.556312	−	23.3433i	0.0179830	−	0.754582i
$958$		0			0
$959$	16.3737			0.528734
$960$		0			0
$961$	−30.9891			−0.999647
$962$		0			0
$963$	40.1517	−	36.4963i	1.29387	−	1.17608i
$964$		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	$0.0662064\pi$
$971$			12.8693i			0.412994i	−0.978447	+	0.206497i	$0.933794\pi$
$972$		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	−0.417048	−	0.908884i	$-0.636935\pi$
$977$	15.3733	−	15.3733i	0.491836	−	0.491836i	0.908884	+	0.417048i	$0.136935\pi$
$978$		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	0.400292	−	0.916388i	$-0.368909\pi$
$983$	−16.1811	−	16.1811i	−0.516096	−	0.516096i	−0.916388	+	0.400292i	$0.868909\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−9.75715	−	0.232530i	−0.310574	−	0.00740151i
$988$		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
$993$	27.0781	+	0.645319i	0.859299	+	0.0204786i
$994$		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.1457.16	yes	32
3.2	odd	2	inner	2100.2.s.c.1457.8	yes	32
5.2	odd	4	inner	2100.2.s.c.1793.9	yes	32
5.3	odd	4	inner	2100.2.s.c.1793.8	yes	32
5.4	even	2	inner	2100.2.s.c.1457.1	✓	32
15.2	even	4	inner	2100.2.s.c.1793.1	yes	32
15.8	even	4	inner	2100.2.s.c.1793.16	yes	32
15.14	odd	2	inner	2100.2.s.c.1457.9	yes	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more