LMFDB - Embedded newform 2394.2.e.c.1063.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1063,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2394.1063");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.e (of order $2$, degree $1$, 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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 44x^{14} + 708x^{12} + 5378x^{10} + 20592x^{8} + 38856x^{6} + 33265x^{4} + 10216x^{2} + 900 $ x^16 + 44x^14 + 708x^12 + 5378x^10 + 20592x^8 + 38856x^6 + 33265x^4 + 10216*x^2 + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 266)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1063.16
Root			$-1.23100i$ of defining polynomial
Character	$\chi$	$=$	2394.1063
Dual form			2394.2.e.c.1063.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +3.34318i q^{5} +(2.62955 + 0.292339i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +3.34318i q^{5} +(2.62955 + 0.292339i) q^{7} -1.00000i q^{8} -3.34318 q^{10} +5.17687 q^{11} -4.32908 q^{13} +(-0.292339 + 2.62955i) q^{14} +1.00000 q^{16} -0.584678i q^{17} +(-1.47098 + 4.10319i) q^{19} -3.34318i q^{20} +5.17687i q^{22} +3.25910 q^{23} -6.17687 q^{25} -4.32908i q^{26} +(-2.62955 - 0.292339i) q^{28} +9.37639i q^{29} +4.46199 q^{31} +1.00000i q^{32} +0.584678 q^{34} +(-0.977343 + 8.79107i) q^{35} -4.23645i q^{37} +(-4.10319 - 1.47098i) q^{38} +3.34318 q^{40} +6.03256 q^{41} -4.28176 q^{43} -5.17687 q^{44} +3.25910i q^{46} +5.75764i q^{47} +(6.82908 + 1.53744i) q^{49} -6.17687i q^{50} +4.32908 q^{52} -4.08223i q^{53} +17.3072i q^{55} +(0.292339 - 2.62955i) q^{56} -9.37639 q^{58} -2.75850 q^{59} -12.7947i q^{61} +4.46199i q^{62} -1.00000 q^{64} -14.4729i q^{65} +13.6128i q^{67} +0.584678i q^{68} +(-8.79107 - 0.977343i) q^{70} +11.6951i q^{71} -3.07488i q^{73} +4.23645 q^{74} +(1.47098 - 4.10319i) q^{76} +(13.6128 + 1.51340i) q^{77} -10.2364i q^{79} +3.34318i q^{80} +6.03256i q^{82} +2.68938i q^{83} +1.95469 q^{85} -4.28176i q^{86} -5.17687i q^{88} -7.61509 q^{89} +(-11.3835 - 1.26556i) q^{91} -3.25910 q^{92} -5.75764 q^{94} +(-13.7177 - 4.91777i) q^{95} -12.0771 q^{97} +(-1.53744 + 6.82908i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 6 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 6 * q^7	$ 16 q - 16 q^{4} + 6 q^{7} + 12 q^{11} + 16 q^{16} - 20 q^{23} - 28 q^{25} - 6 q^{28} - 8 q^{35} - 4 q^{43} - 12 q^{44} + 10 q^{49} - 16 q^{58} - 16 q^{64} - 12 q^{74} + 4 q^{77} + 16 q^{85} + 20 q^{92} - 12 q^{95}+O(q^{100}) $ 16 * q - 16 * q^4 + 6 * q^7 + 12 * q^11 + 16 * q^16 - 20 * q^23 - 28 * q^25 - 6 * q^28 - 8 * q^35 - 4 * q^43 - 12 * q^44 + 10 * q^49 - 16 * q^58 - 16 * q^64 - 12 * q^74 + 4 * q^77 + 16 * q^85 + 20 * q^92 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$			3.34318i			1.49512i	0.664196	+	0.747558i	$0.268774\pi$
$5$			3.34318i			1.49512i	−0.664196	+	0.747558i	$0.731226\pi$
$6$		0			0
$7$	2.62955	+	0.292339i	0.993877	+	0.110494i
$7$	2.62955	+	0.292339i	0.993877	+	0.110494i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−3.34318			−1.05721
$11$	5.17687			1.56088			0.780442	−	0.625228i	$-0.214994\pi$
$11$	5.17687			1.56088			0.780442	+	0.625228i	$0.214994\pi$
$12$		0			0
$13$	−4.32908			−1.20067			−0.600335	−	0.799749i	$-0.704966\pi$
$13$	−4.32908			−1.20067			−0.600335	+	0.799749i	$0.704966\pi$
$14$	−0.292339	+	2.62955i	−0.0781309	+	0.702777i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.584678i		−	0.141805i	−0.997483	−	0.0709027i	$-0.977412\pi$
$17$		−	0.584678i		−	0.141805i	0.997483	−	0.0709027i	$-0.0225880\pi$
$18$		0			0
$19$	−1.47098	+	4.10319i	−0.337467	+	0.941337i
$19$	−1.47098	+	4.10319i	−0.337467	+	0.941337i
$20$		−	3.34318i		−	0.747558i
$21$		0			0
$22$			5.17687i			1.10371i
$23$	3.25910			0.679570			0.339785	−	0.940503i	$-0.389646\pi$
$23$	3.25910			0.679570			0.339785	+	0.940503i	$0.389646\pi$
$24$		0			0
$25$	−6.17687			−1.23537
$26$		−	4.32908i		−	0.849002i
$27$		0			0
$28$	−2.62955	−	0.292339i	−0.496938	−	0.0552469i
$29$			9.37639i			1.74115i	0.492034	+	0.870576i	$0.336254\pi$
$29$			9.37639i			1.74115i	−0.492034	+	0.870576i	$0.663746\pi$
$30$		0			0
$31$	4.46199			0.801397			0.400699	−	0.916210i	$-0.368767\pi$
$31$	4.46199			0.801397			0.400699	+	0.916210i	$0.368767\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.584678			0.100272
$35$	−0.977343	+	8.79107i	−0.165201	+	1.48596i
$36$		0			0
$37$		−	4.23645i		−	0.696467i	−0.937408	−	0.348234i	$-0.886782\pi$
$37$		−	4.23645i		−	0.696467i	0.937408	−	0.348234i	$-0.113218\pi$
$38$	−4.10319	−	1.47098i	−0.665626	−	0.238625i
$39$		0			0
$40$	3.34318			0.528604
$41$	6.03256			0.942128			0.471064	−	0.882099i	$-0.343870\pi$
$41$	6.03256			0.942128			0.471064	+	0.882099i	$0.343870\pi$
$42$		0			0
$43$	−4.28176			−0.652962			−0.326481	−	0.945204i	$-0.605863\pi$
$43$	−4.28176			−0.652962			−0.326481	+	0.945204i	$0.605863\pi$
$44$	−5.17687			−0.780442
$45$		0			0
$46$			3.25910i			0.480528i
$47$			5.75764i			0.839838i	0.907562	+	0.419919i	$0.137942\pi$
$47$			5.75764i			0.839838i	−0.907562	+	0.419919i	$0.862058\pi$
$48$		0			0
$49$	6.82908	+	1.53744i	0.975582	+	0.219635i
$50$		−	6.17687i		−	0.873541i
$51$		0			0
$52$	4.32908			0.600335
$53$		−	4.08223i		−	0.560738i	−0.959892	−	0.280369i	$-0.909543\pi$
$53$		−	4.08223i		−	0.560738i	0.959892	−	0.280369i	$-0.0904568\pi$
$54$		0			0
$55$			17.3072i			2.33370i
$56$	0.292339	−	2.62955i	0.0390655	−	0.351389i
$57$		0			0
$58$	−9.37639			−1.23118
$59$	−2.75850			−0.359127			−0.179563	−	0.983746i	$-0.557468\pi$
$59$	−2.75850			−0.359127			−0.179563	+	0.983746i	$0.557468\pi$
$60$		0			0
$61$		−	12.7947i		−	1.63819i	−0.573658	−	0.819095i	$-0.694476\pi$
$61$		−	12.7947i		−	1.63819i	0.573658	−	0.819095i	$-0.305524\pi$
$62$			4.46199i			0.566674i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	14.4729i		−	1.79514i
$66$		0			0
$67$			13.6128i			1.66307i	0.555470	+	0.831536i	$0.312538\pi$
$67$			13.6128i			1.66307i	−0.555470	+	0.831536i	$0.687462\pi$
$68$			0.584678i			0.0709027i
$69$		0			0
$70$	−8.79107	−	0.977343i	−1.05073	−	0.116815i
$71$			11.6951i			1.38795i	0.719999	+	0.693975i	$0.244142\pi$
$71$			11.6951i			1.38795i	−0.719999	+	0.693975i	$0.755858\pi$
$72$		0			0
$73$		−	3.07488i		−	0.359888i	−0.983677	−	0.179944i	$-0.942408\pi$
$73$		−	3.07488i		−	0.359888i	0.983677	−	0.179944i	$-0.0575916\pi$
$74$	4.23645			0.492477
$75$		0			0
$76$	1.47098	−	4.10319i	0.168733	−	0.470669i
$77$	13.6128	+	1.51340i	1.55133	+	0.172468i
$78$		0			0
$79$		−	10.2364i		−	1.15169i	−0.817559	−	0.575845i	$-0.804673\pi$
$79$		−	10.2364i		−	1.15169i	0.817559	−	0.575845i	$-0.195327\pi$
$80$			3.34318i			0.373779i
$81$		0			0
$82$			6.03256i			0.666185i
$83$			2.68938i			0.295198i	0.989047	+	0.147599i	$0.0471545\pi$
$83$			2.68938i			0.295198i	−0.989047	+	0.147599i	$0.952845\pi$
$84$		0			0
$85$	1.95469			0.212016
$86$		−	4.28176i		−	0.461714i
$87$		0			0
$88$		−	5.17687i		−	0.551856i
$89$	−7.61509			−0.807198			−0.403599	−	0.914936i	$-0.632241\pi$
$89$	−7.61509			−0.807198			−0.403599	+	0.914936i	$0.632241\pi$
$90$		0			0
$91$	−11.3835	−	1.26556i	−1.19332	−	0.132667i
$92$	−3.25910			−0.339785
$93$		0			0
$94$	−5.75764			−0.593855
$95$	−13.7177	−	4.91777i	−1.40741	−	0.504552i
$96$		0			0
$97$	−12.0771			−1.22624			−0.613121	−	0.789989i	$-0.710086\pi$
$97$	−12.0771			−1.22624			−0.613121	+	0.789989i	$0.710086\pi$
$98$	−1.53744	+	6.82908i	−0.155305	+	0.689841i
$99$		0			0
$100$	6.17687			0.617687
$101$			9.37575i			0.932922i	0.884542	+	0.466461i	$0.154471\pi$
$101$			9.37575i			0.932922i	−0.884542	+	0.466461i	$0.845529\pi$
$102$		0			0
$103$	3.40698			0.335699			0.167850	−	0.985813i	$-0.446318\pi$
$103$	3.40698			0.335699			0.167850	+	0.985813i	$0.446318\pi$
$104$			4.32908i			0.424501i
$105$		0			0
$106$	4.08223			0.396502
$107$		−	1.30442i		−	0.126103i	−0.998010	−	0.0630513i	$-0.979917\pi$
$107$		−	1.30442i		−	0.126103i	0.998010	−	0.0630513i	$-0.0200832\pi$
$108$		0			0
$109$		−	4.08223i		−	0.391007i	−0.980703	−	0.195504i	$-0.937366\pi$
$109$		−	4.08223i		−	0.391007i	0.980703	−	0.195504i	$-0.0626341\pi$
$110$	−17.3072			−1.65018
$111$		0			0
$112$	2.62955	+	0.292339i	0.248469	+	0.0276235i
$113$		−	6.30842i		−	0.593446i	−0.954964	−	0.296723i	$-0.904106\pi$
$113$		−	6.30842i		−	0.593446i	0.954964	−	0.296723i	$-0.0958939\pi$
$114$		0			0
$115$			10.8958i			1.01604i
$116$		−	9.37639i		−	0.870576i
$117$		0			0
$118$		−	2.75850i		−	0.253941i
$119$	0.170924	−	1.53744i	0.0156686	−	0.140937i
$120$		0			0
$121$	15.8000			1.43636
$122$	12.7947			1.15838
$123$		0			0
$124$	−4.46199			−0.400699
$125$		−	3.93448i		−	0.351911i
$126$		0			0
$127$			1.05771i			0.0938569i	0.998898	+	0.0469285i	$0.0149433\pi$
$127$			1.05771i			0.0938569i	−0.998898	+	0.0469285i	$0.985057\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	14.4729			1.26936
$131$		−	9.37575i		−	0.819163i	−0.912274	−	0.409581i	$-0.865675\pi$
$131$		−	9.37575i		−	0.819163i	0.912274	−	0.409581i	$-0.134325\pi$
$132$		0			0
$133$	−5.06755	+	10.3595i	−0.439412	+	0.898285i
$134$	−13.6128			−1.17597
$135$		0			0
$136$	−0.584678			−0.0501358
$137$	−11.3311			−0.968079			−0.484040	−	0.875046i	$-0.660831\pi$
$137$	−11.3311			−0.968079			−0.484040	+	0.875046i	$0.660831\pi$
$138$		0			0
$139$		−	1.50678i		−	0.127803i	−0.997956	−	0.0639016i	$-0.979646\pi$
$139$		−	1.50678i		−	0.127803i	0.997956	−	0.0639016i	$-0.0203544\pi$
$140$	0.977343	−	8.79107i	0.0826006	−	0.742981i
$141$		0			0
$142$	−11.6951			−0.981429
$143$	−22.4111			−1.87411
$144$		0			0
$145$	−31.3470			−2.60323
$146$	3.07488			0.254479
$147$		0			0
$148$			4.23645i			0.348234i
$149$	−7.95469			−0.651673			−0.325837	−	0.945426i	$-0.605646\pi$
$149$	−7.95469			−0.651673			−0.325837	+	0.945426i	$0.605646\pi$
$150$		0			0
$151$		−	20.9173i		−	1.70222i	−0.524986	−	0.851111i	$-0.675929\pi$
$151$		−	20.9173i		−	1.70222i	0.524986	−	0.851111i	$-0.324071\pi$
$152$	4.10319	+	1.47098i	0.332813	+	0.119313i
$153$		0			0
$154$	−1.51340	+	13.6128i	−0.121953	+	1.09695i
$155$			14.9173i			1.19818i
$156$		0			0
$157$			18.1734i			1.45040i	0.688539	+	0.725199i	$0.258252\pi$
$157$			18.1734i			1.45040i	−0.688539	+	0.725199i	$0.741748\pi$
$158$	10.2364			0.814368
$159$		0			0
$160$	−3.34318			−0.264302
$161$	8.56997	+	0.952763i	0.675409	+	0.0750883i
$162$		0			0
$163$	−13.1769			−1.03209			−0.516046	−	0.856561i	$-0.672597\pi$
$163$	−13.1769			−1.03209			−0.516046	+	0.856561i	$0.672597\pi$
$164$	−6.03256			−0.471064
$165$		0			0
$166$	−2.68938			−0.208737
$167$	20.0591			1.55222			0.776110	−	0.630598i	$-0.217190\pi$
$167$	20.0591			1.55222			0.776110	+	0.630598i	$0.217190\pi$
$168$		0			0
$169$	5.74090			0.441608
$170$			1.95469i			0.149918i
$171$		0			0
$172$	4.28176			0.326481
$173$	−21.5791			−1.64063			−0.820315	−	0.571912i	$-0.806202\pi$
$173$	−21.5791			−1.64063			−0.820315	+	0.571912i	$0.806202\pi$
$174$		0			0
$175$	−16.2424	−	1.80574i	−1.22781	−	0.136501i
$176$	5.17687			0.390221
$177$		0			0
$178$		−	7.61509i		−	0.570775i
$179$		−	8.47289i		−	0.633294i	−0.948544	−	0.316647i	$-0.897443\pi$
$179$		−	8.47289i		−	0.633294i	0.948544	−	0.316647i	$-0.102557\pi$
$180$		0			0
$181$	7.40396			0.550332			0.275166	−	0.961397i	$-0.411267\pi$
$181$	7.40396			0.550332			0.275166	+	0.961397i	$0.411267\pi$
$182$	1.26556	−	11.3835i	0.0938094	−	0.843803i
$183$		0			0
$184$		−	3.25910i		−	0.240264i
$185$	14.1632			1.04130
$186$		0			0
$187$		−	3.02680i		−	0.221342i
$188$		−	5.75764i		−	0.419919i
$189$		0			0
$190$	4.91777	−	13.7177i	0.356772	−	0.995189i
$191$	5.42357			0.392436			0.196218	−	0.980560i	$-0.437134\pi$
$191$	5.42357			0.392436			0.196218	+	0.980560i	$0.437134\pi$
$192$		0			0
$193$			12.4444i			0.895765i	0.894092	+	0.447882i	$0.147822\pi$
$193$			12.4444i			0.895765i	−0.894092	+	0.447882i	$0.852178\pi$
$194$		−	12.0771i		−	0.867084i
$195$		0			0
$196$	−6.82908	−	1.53744i	−0.487791	−	0.109817i
$197$	−12.5182			−0.891885			−0.445943	−	0.895062i	$-0.647131\pi$
$197$	−12.5182			−0.891885			−0.445943	+	0.895062i	$0.647131\pi$
$198$		0			0
$199$		−	7.78660i		−	0.551977i	−0.961161	−	0.275989i	$-0.910995\pi$
$199$		−	7.78660i		−	0.551977i	0.961161	−	0.275989i	$-0.0890052\pi$
$200$			6.17687i			0.436771i
$201$		0			0
$202$	−9.37575			−0.659675
$203$	−2.74109	+	24.6557i	−0.192387	+	1.73049i
$204$		0			0
$205$			20.1680i			1.40859i
$206$			3.40698i			0.237375i
$207$		0			0
$208$	−4.32908			−0.300167
$209$	−7.61509	+	21.2417i	−0.526747	+	1.46932i
$210$		0			0
$211$			21.7773i			1.49921i	0.661885	+	0.749606i	$0.269757\pi$
$211$			21.7773i			1.49921i	−0.661885	+	0.749606i	$0.730243\pi$
$212$			4.08223i			0.280369i
$213$		0			0
$214$	1.30442			0.0891680
$215$		−	14.3147i		−	0.976254i
$216$		0			0
$217$	11.7330	+	1.30442i	0.796490	+	0.0885495i
$218$	4.08223			0.276484
$219$		0			0
$220$		−	17.3072i		−	1.16685i
$221$			2.53112i			0.170261i
$222$		0			0
$223$	−19.2699			−1.29041			−0.645204	−	0.764010i	$-0.723228\pi$
$223$	−19.2699			−1.29041			−0.645204	+	0.764010i	$0.723228\pi$
$224$	−0.292339	+	2.62955i	−0.0195327	+	0.175694i
$225$		0			0
$226$	6.30842			0.419630
$227$	11.8311			0.785259			0.392629	−	0.919697i	$-0.371566\pi$
$227$	11.8311			0.785259			0.392629	+	0.919697i	$0.371566\pi$
$228$		0			0
$229$		−	14.2390i		−	0.940937i	−0.882417	−	0.470468i	$-0.844085\pi$
$229$		−	14.2390i		−	0.940937i	0.882417	−	0.470468i	$-0.155915\pi$
$230$	−10.8958			−0.718446
$231$		0			0
$232$	9.37639			0.615590
$233$	1.13155			0.0741306			0.0370653	−	0.999313i	$-0.488199\pi$
$233$	1.13155			0.0741306			0.0370653	+	0.999313i	$0.488199\pi$
$234$		0			0
$235$	−19.2488			−1.25566
$236$	2.75850			0.179563
$237$		0			0
$238$	1.53744	+	0.170924i	0.0996575	+	0.0110794i
$239$	−7.09463			−0.458914			−0.229457	−	0.973319i	$-0.573695\pi$
$239$	−7.09463			−0.458914			−0.229457	+	0.973319i	$0.573695\pi$
$240$		0			0
$241$	25.9906			1.67420			0.837100	−	0.547050i	$-0.184249\pi$
$241$	25.9906			1.67420			0.837100	+	0.547050i	$0.184249\pi$
$242$			15.8000i			1.01566i
$243$		0			0
$244$			12.7947i			0.819095i
$245$	−5.13995	+	22.8308i	−0.328379	+	1.45861i
$246$		0			0
$247$	6.36800	−	17.7630i	0.405186	−	1.13024i
$248$		−	4.46199i		−	0.283337i
$249$		0			0
$250$	3.93448			0.248839
$251$			14.8928i			0.940022i	0.882660	+	0.470011i	$0.155750\pi$
$251$			14.8928i			0.940022i	−0.882660	+	0.470011i	$0.844250\pi$
$252$		0			0
$253$	16.8719			1.06073
$254$	−1.05771			−0.0663669
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.515556			−0.0321595			−0.0160798	−	0.999871i	$-0.505119\pi$
$257$	−0.515556			−0.0321595			−0.0160798	+	0.999871i	$0.505119\pi$
$258$		0			0
$259$	1.23848	−	11.1399i	0.0769553	−	0.692203i
$260$			14.4729i			0.897571i
$261$		0			0
$262$	9.37575			0.579236
$263$	16.4276			1.01297			0.506484	−	0.862249i	$-0.330945\pi$
$263$	16.4276			1.01297			0.506484	+	0.862249i	$0.330945\pi$
$264$		0			0
$265$	13.6477			0.838369
$266$	−10.3595	−	5.06755i	−0.635184	−	0.310711i
$267$		0			0
$268$		−	13.6128i		−	0.831536i
$269$	25.2519			1.53964			0.769819	−	0.638263i	$-0.220347\pi$
$269$	25.2519			1.53964			0.769819	+	0.638263i	$0.220347\pi$
$270$		0			0
$271$			15.7806i			0.958601i	0.877651	+	0.479301i	$0.159110\pi$
$271$			15.7806i			0.958601i	−0.877651	+	0.479301i	$0.840890\pi$
$272$		−	0.584678i		−	0.0354513i
$273$		0			0
$274$		−	11.3311i		−	0.684536i
$275$	−31.9768			−1.92828
$276$		0			0
$277$	−0.119154			−0.00715927			−0.00357964	−	0.999994i	$-0.501139\pi$
$277$	−0.119154			−0.00715927			−0.00357964	+	0.999994i	$0.501139\pi$
$278$	1.50678			0.0903705
$279$		0			0
$280$	8.79107	+	0.977343i	0.525367	+	0.0584074i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$		−	20.8910i		−	1.24184i	−0.783873	−	0.620921i	$-0.786759\pi$
$283$		−	20.8910i		−	1.24184i	0.783873	−	0.620921i	$-0.213241\pi$
$284$		−	11.6951i		−	0.693975i
$285$		0			0
$286$		−	22.4111i		−	1.32519i
$287$	15.8629	+	1.76355i	0.936359	+	0.104099i
$288$		0			0
$289$	16.6582			0.979891
$290$		−	31.3470i		−	1.84076i
$291$		0			0
$292$			3.07488i			0.179944i
$293$	−5.75102			−0.335978			−0.167989	−	0.985789i	$-0.553727\pi$
$293$	−5.75102			−0.335978			−0.167989	+	0.985789i	$0.553727\pi$
$294$		0			0
$295$		−	9.22218i		−	0.536936i
$296$	−4.23645			−0.246238
$297$		0			0
$298$		−	7.95469i		−	0.460803i
$299$	−14.1089			−0.815939
$300$		0			0
$301$	−11.2591	−	1.25173i	−0.648964	−	0.0721483i
$302$	20.9173			1.20365
$303$		0			0
$304$	−1.47098	+	4.10319i	−0.0843667	+	0.235334i
$305$	42.7749			2.44929
$306$		0			0
$307$	20.0085			1.14195			0.570974	−	0.820968i	$-0.306566\pi$
$307$	20.0085			1.14195			0.570974	+	0.820968i	$0.306566\pi$
$308$	−13.6128	−	1.51340i	−0.775663	−	0.0862341i
$309$		0			0
$310$	−14.9173			−0.847243
$311$		−	30.6108i		−	1.73578i	−0.496756	−	0.867890i	$-0.665476\pi$
$311$		−	30.6108i		−	1.73578i	0.496756	−	0.867890i	$-0.334524\pi$
$312$		0			0
$313$			10.9306i			0.617834i	0.951089	+	0.308917i	$0.0999666\pi$
$313$			10.9306i			0.617834i	−0.951089	+	0.308917i	$0.900033\pi$
$314$	−18.1734			−1.02559
$315$		0			0
$316$			10.2364i			0.575845i
$317$		−	11.7533i		−	0.660131i	−0.943958	−	0.330066i	$-0.892929\pi$
$317$		−	11.7533i		−	0.660131i	0.943958	−	0.330066i	$-0.107071\pi$
$318$		0			0
$319$			48.5403i			2.71774i
$320$		−	3.34318i		−	0.186890i
$321$		0			0
$322$	−0.952763	+	8.56997i	−0.0530954	+	0.477586i
$323$	2.39905	+	0.860052i	0.133487	+	0.0478546i
$324$		0			0
$325$	26.7401			1.48328
$326$		−	13.1769i		−	0.729799i
$327$		0			0
$328$		−	6.03256i		−	0.333093i
$329$	−1.68318	+	15.1400i	−0.0927970	+	0.834696i
$330$		0			0
$331$			10.6956i			0.587883i	0.955823	+	0.293941i	$0.0949670\pi$
$331$			10.6956i			0.587883i	−0.955823	+	0.293941i	$0.905033\pi$
$332$		−	2.68938i		−	0.147599i
$333$		0			0
$334$			20.0591i			1.09758i
$335$	−45.5102			−2.48649
$336$		0			0
$337$		−	8.91725i		−	0.485754i	−0.970057	−	0.242877i	$-0.921909\pi$
$337$		−	8.91725i		−	0.485754i	0.970057	−	0.242877i	$-0.0780911\pi$
$338$			5.74090i			0.312264i
$339$		0			0
$340$	−1.95469			−0.106008
$341$	23.0991			1.25089
$342$		0			0
$343$	17.5079	+	6.03919i	0.945340	+	0.326085i
$344$			4.28176i			0.230857i
$345$		0			0
$346$		−	21.5791i		−	1.16010i
$347$	−21.1270			−1.13416			−0.567079	−	0.823663i	$-0.691927\pi$
$347$	−21.1270			−1.13416			−0.567079	+	0.823663i	$0.691927\pi$
$348$		0			0
$349$		−	2.15278i		−	0.115236i	−0.998339	−	0.0576179i	$-0.981649\pi$
$349$		−	2.15278i		−	0.115236i	0.998339	−	0.0576179i	$-0.0183505\pi$
$350$	1.80574	−	16.2424i	0.0965209	−	0.868192i
$351$		0			0
$352$			5.17687i			0.275928i
$353$			3.62473i			0.192925i	0.995337	+	0.0964624i	$0.0307528\pi$
$353$			3.62473i			0.192925i	−0.995337	+	0.0964624i	$0.969247\pi$
$354$		0			0
$355$	−39.0988			−2.07515
$356$	7.61509			0.403599
$357$		0			0
$358$	8.47289			0.447806
$359$	23.6582			1.24863			0.624315	−	0.781173i	$-0.285378\pi$
$359$	23.6582			1.24863			0.624315	+	0.781173i	$0.285378\pi$
$360$		0			0
$361$	−14.6724	−	12.0715i	−0.772232	−	0.635340i
$362$			7.40396i			0.389143i
$363$		0			0
$364$	11.3835	+	1.26556i	0.596659	+	0.0663333i
$365$	10.2799			0.538074
$366$		0			0
$367$		−	27.1508i		−	1.41726i	−0.705579	−	0.708631i	$-0.749313\pi$
$367$		−	27.1508i		−	1.41726i	0.705579	−	0.708631i	$-0.250687\pi$
$368$	3.25910			0.169892
$369$		0			0
$370$			14.1632i			0.736310i
$371$	1.19340	−	10.7344i	0.0619581	−	0.557304i
$372$		0			0
$373$			9.37639i			0.485491i	0.970090	+	0.242746i	$0.0780480\pi$
$373$			9.37639i			0.485491i	−0.970090	+	0.242746i	$0.921952\pi$
$374$	3.02680			0.156512
$375$		0			0
$376$	5.75764			0.296928
$377$		−	40.5911i		−	2.09055i
$378$		0			0
$379$		−	25.6128i		−	1.31564i	−0.753174	−	0.657822i	$-0.771478\pi$
$379$		−	25.6128i		−	1.31564i	0.753174	−	0.657822i	$-0.228522\pi$
$380$	13.7177	+	4.91777i	0.703705	+	0.252276i
$381$		0			0
$382$			5.42357i			0.277494i
$383$	32.8123			1.67663			0.838315	−	0.545186i	$-0.183541\pi$
$383$	32.8123			1.67663			0.838315	+	0.545186i	$0.183541\pi$
$384$		0			0
$385$	−5.05958	+	45.5102i	−0.257860	+	2.31941i
$386$	−12.4444			−0.633401
$387$		0			0
$388$	12.0771			0.613121
$389$	4.35374			0.220743			0.110372	−	0.993890i	$-0.464796\pi$
$389$	4.35374			0.220743			0.110372	+	0.993890i	$0.464796\pi$
$390$		0			0
$391$		−	1.90553i		−	0.0963666i
$392$	1.53744	−	6.82908i	0.0776525	−	0.344920i
$393$		0			0
$394$		−	12.5182i		−	0.630658i
$395$	34.2223			1.72191
$396$		0			0
$397$		−	21.2002i		−	1.06401i	−0.846741	−	0.532005i	$-0.821439\pi$
$397$		−	21.2002i		−	1.06401i	0.846741	−	0.532005i	$-0.178561\pi$
$398$	7.78660			0.390307
$399$		0			0
$400$	−6.17687			−0.308843
$401$			8.60883i			0.429904i	0.976625	+	0.214952i	$0.0689596\pi$
$401$			8.60883i			0.429904i	−0.976625	+	0.214952i	$0.931040\pi$
$402$		0			0
$403$	−19.3163			−0.962214
$404$		−	9.37575i		−	0.466461i
$405$		0			0
$406$	−24.6557	−	2.74109i	−1.22364	−	0.136038i
$407$		−	21.9315i		−	1.08710i
$408$		0			0
$409$	−2.46501			−0.121887			−0.0609434	−	0.998141i	$-0.519411\pi$
$409$	−2.46501			−0.121887			−0.0609434	+	0.998141i	$0.519411\pi$
$410$	−20.1680			−0.996025
$411$		0			0
$412$	−3.40698			−0.167850
$413$	−7.25363	−	0.806419i	−0.356928	−	0.0396813i
$414$		0			0
$415$	−8.99109			−0.441355
$416$		−	4.32908i		−	0.212250i
$417$		0			0
$418$	−21.2417	−	7.61509i	−1.03897	−	0.372466i
$419$			37.4553i			1.82981i	0.403668	+	0.914906i	$0.367735\pi$
$419$			37.4553i			1.82981i	−0.403668	+	0.914906i	$0.632265\pi$
$420$		0			0
$421$		−	0.860052i		−	0.0419164i	−0.999780	−	0.0209582i	$-0.993328\pi$
$421$		−	0.860052i		−	0.0419164i	0.999780	−	0.0209582i	$-0.00667169\pi$
$422$	−21.7773			−1.06010
$423$		0			0
$424$	−4.08223			−0.198251
$425$			3.61148i			0.175183i
$426$		0			0
$427$	3.74038	−	33.6442i	0.181010	−	1.62816i
$428$			1.30442i			0.0630513i
$429$		0			0
$430$	14.3147			0.690316
$431$		−	12.4479i		−	0.599592i	−0.954003	−	0.299796i	$-0.903081\pi$
$431$		−	12.4479i		−	0.599592i	0.954003	−	0.299796i	$-0.0969186\pi$
$432$		0			0
$433$	18.4646			0.887353			0.443676	−	0.896187i	$-0.353674\pi$
$433$	18.4646			0.887353			0.443676	+	0.896187i	$0.353674\pi$
$434$	−1.30442	+	11.7330i	−0.0626139	+	0.563204i
$435$		0			0
$436$			4.08223i			0.195504i
$437$	−4.79409	+	13.3727i	−0.229332	+	0.639704i
$438$		0			0
$439$	11.7679			0.561650			0.280825	−	0.959759i	$-0.409392\pi$
$439$	11.7679			0.561650			0.280825	+	0.959759i	$0.409392\pi$
$440$	17.3072			0.825089
$441$		0			0
$442$	−2.53112			−0.120393
$443$	−4.75465			−0.225900			−0.112950	−	0.993601i	$-0.536030\pi$
$443$	−4.75465			−0.225900			−0.112950	+	0.993601i	$0.536030\pi$
$444$		0			0
$445$		−	25.4586i		−	1.20685i
$446$		−	19.2699i		−	0.912457i
$447$		0			0
$448$	−2.62955	−	0.292339i	−0.124235	−	0.0138117i
$449$		−	14.6088i		−	0.689433i	−0.938707	−	0.344717i	$-0.887975\pi$
$449$		−	14.6088i		−	0.689433i	0.938707	−	0.344717i	$-0.112025\pi$
$450$		0			0
$451$	31.2298			1.47055
$452$			6.30842i			0.296723i
$453$		0			0
$454$			11.8311i			0.555262i
$455$	4.23099	−	38.0572i	0.198352	−	1.78415i
$456$		0			0
$457$	19.2626			0.901066			0.450533	−	0.892760i	$-0.351234\pi$
$457$	19.2626			0.901066			0.450533	+	0.892760i	$0.351234\pi$
$458$	14.2390			0.665343
$459$		0			0
$460$		−	10.8958i		−	0.508018i
$461$		−	2.43550i		−	0.113433i	−0.998390	−	0.0567163i	$-0.981937\pi$
$461$		−	2.43550i		−	0.113433i	0.998390	−	0.0567163i	$-0.0180631\pi$
$462$		0			0
$463$	35.6700			1.65773			0.828864	−	0.559451i	$-0.188988\pi$
$463$	35.6700			1.65773			0.828864	+	0.559451i	$0.188988\pi$
$464$			9.37639i			0.435288i
$465$		0			0
$466$			1.13155i			0.0524182i
$467$		−	20.2715i		−	0.938054i	−0.883184	−	0.469027i	$-0.844605\pi$
$467$		−	20.2715i		−	0.938054i	0.883184	−	0.469027i	$-0.155395\pi$
$468$		0			0
$469$	−3.97957	+	35.7956i	−0.183759	+	1.65289i
$470$		−	19.2488i		−	0.887883i
$471$		0			0
$472$			2.75850i			0.126970i
$473$	−22.1661			−1.01920
$474$		0			0
$475$	9.08607	−	25.3449i	0.416898	−	1.16290i
$476$	−0.170924	+	1.53744i	−0.00783431	+	0.0704685i
$477$		0			0
$478$		−	7.09463i		−	0.324501i
$479$		−	20.7261i		−	0.947002i	−0.880793	−	0.473501i	$-0.842990\pi$
$479$		−	20.7261i		−	0.947002i	0.880793	−	0.473501i	$-0.157010\pi$
$480$		0			0
$481$			18.3399i			0.836227i
$482$			25.9906i			1.18384i
$483$		0			0
$484$	−15.8000			−0.718180
$485$		−	40.3759i		−	1.83337i
$486$		0			0
$487$		−	3.00974i		−	0.136384i	−0.997672	−	0.0681922i	$-0.978277\pi$
$487$		−	3.00974i		−	0.136384i	0.997672	−	0.0681922i	$-0.0217231\pi$
$488$	−12.7947			−0.579188
$489$		0			0
$490$	−22.8308	−	5.13995i	−1.03139	−	0.232199i
$491$	21.1270			0.953450			0.476725	−	0.879053i	$-0.341824\pi$
$491$	21.1270			0.953450			0.476725	+	0.879053i	$0.341824\pi$
$492$		0			0
$493$	5.48217			0.246905
$494$	17.7630	+	6.36800i	0.799197	+	0.286510i
$495$		0			0
$496$	4.46199			0.200349
$497$	−3.41893	+	30.7528i	−0.153360	+	1.37945i
$498$		0			0
$499$	−12.8986			−0.577421			−0.288710	−	0.957416i	$-0.593226\pi$
$499$	−12.8986			−0.577421			−0.288710	+	0.957416i	$0.593226\pi$
$500$			3.93448i			0.175955i
$501$		0			0
$502$	−14.8928			−0.664696
$503$		−	0.0691221i		−	0.00308200i	−0.999999	−	0.00154100i	$-0.999509\pi$
$503$		−	0.0691221i		−	0.00308200i	0.999999	−	0.00154100i	$-0.000490516\pi$
$504$		0			0
$505$	−31.3448			−1.39483
$506$			16.8719i			0.750049i
$507$		0			0
$508$		−	1.05771i		−	0.0469285i
$509$	−18.5391			−0.821730			−0.410865	−	0.911696i	$-0.634773\pi$
$509$	−18.5391			−0.821730			−0.410865	+	0.911696i	$0.634773\pi$
$510$		0			0
$511$	0.898909	−	8.08556i	0.0397654	−	0.357684i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	0.515556i		−	0.0227402i
$515$			11.3901i			0.501910i
$516$		0			0
$517$			29.8066i			1.31089i
$518$	11.1399	+	1.23848i	0.489461	+	0.0544156i
$519$		0			0
$520$	−14.4729			−0.634678
$521$	43.1582			1.89080			0.945398	−	0.325917i	$-0.105673\pi$
$521$	43.1582			1.89080			0.945398	+	0.325917i	$0.105673\pi$
$522$		0			0
$523$	−8.52524			−0.372783			−0.186391	−	0.982476i	$-0.559679\pi$
$523$	−8.52524			−0.372783			−0.186391	+	0.982476i	$0.559679\pi$
$524$			9.37575i			0.409581i
$525$		0			0
$526$			16.4276i			0.716276i
$527$		−	2.60883i		−	0.113642i
$528$		0			0
$529$	−12.3783			−0.538185
$530$			13.6477i			0.592816i
$531$		0			0
$532$	5.06755	−	10.3595i	0.219706	−	0.449143i
$533$	−26.1154			−1.13118
$534$		0			0
$535$	4.36090			0.188538
$536$	13.6128			0.587985
$537$		0			0
$538$			25.2519i			1.08869i
$539$	35.3532	+	7.95913i	1.52277	+	0.342824i
$540$		0			0
$541$	20.4444			0.878972			0.439486	−	0.898249i	$-0.355161\pi$
$541$	20.4444			0.878972			0.439486	+	0.898249i	$0.355161\pi$
$542$	−15.7806			−0.677833
$543$		0			0
$544$	0.584678			0.0250679
$545$	13.6477			0.584601
$546$		0			0
$547$		−	7.67106i		−	0.327991i	−0.986461	−	0.163996i	$-0.947562\pi$
$547$		−	7.67106i		−	0.327991i	0.986461	−	0.163996i	$-0.0524383\pi$
$548$	11.3311			0.484040
$549$		0			0
$550$		−	31.9768i		−	1.36350i
$551$	−38.4732	−	13.7925i	−1.63901	−	0.587581i
$552$		0			0
$553$	2.99251	−	26.9173i	0.127255	−	1.14464i
$554$		−	0.119154i		−	0.00506237i
$555$		0			0
$556$			1.50678i			0.0639016i
$557$	−14.2383			−0.603296			−0.301648	−	0.953419i	$-0.597537\pi$
$557$	−14.2383			−0.603296			−0.301648	+	0.953419i	$0.597537\pi$
$558$		0			0
$559$	18.5361			0.783992
$560$	−0.977343	+	8.79107i	−0.0413003	+	0.371490i
$561$		0			0
$562$		0			0
$563$	−22.3564			−0.942208			−0.471104	−	0.882078i	$-0.656144\pi$
$563$	−22.3564			−0.942208			−0.471104	+	0.882078i	$0.656144\pi$
$564$		0			0
$565$	21.0902			0.887272
$566$	20.8910			0.878115
$567$		0			0
$568$	11.6951			0.490714
$569$			15.6700i			0.656922i	0.944518	+	0.328461i	$0.106530\pi$
$569$			15.6700i			0.656922i	−0.944518	+	0.328461i	$0.893470\pi$
$570$		0			0
$571$	−4.11463			−0.172192			−0.0860960	−	0.996287i	$-0.527439\pi$
$571$	−4.11463			−0.172192			−0.0860960	+	0.996287i	$0.527439\pi$
$572$	22.4111			0.937053
$573$		0			0
$574$	−1.76355	+	15.8629i	−0.0736094	+	0.662106i
$575$	−20.1310			−0.839522
$576$		0			0
$577$			37.7579i			1.57188i	0.618302	+	0.785941i	$0.287821\pi$
$577$			37.7579i			1.57188i	−0.618302	+	0.785941i	$0.712179\pi$
$578$			16.6582i			0.692888i
$579$		0			0
$580$	31.3470			1.30161
$581$	−0.786212	+	7.07187i	−0.0326176	+	0.293390i
$582$		0			0
$583$		−	21.1332i		−	0.875247i
$584$	−3.07488			−0.127240
$585$		0			0
$586$		−	5.75102i		−	0.237572i
$587$		−	16.0754i		−	0.663501i	−0.943367	−	0.331751i	$-0.892361\pi$
$587$		−	16.0754i		−	0.663501i	0.943367	−	0.331751i	$-0.107639\pi$
$588$		0			0
$589$	−6.56352	+	18.3084i	−0.270445	+	0.754385i
$590$	9.22218			0.379671
$591$		0			0
$592$		−	4.23645i		−	0.174117i
$593$			15.7114i			0.645192i	0.946537	+	0.322596i	$0.104555\pi$
$593$			15.7114i			0.645192i	−0.946537	+	0.322596i	$0.895445\pi$
$594$		0			0
$595$	5.13995	+	0.571432i	0.210717	+	0.0234264i
$596$	7.95469			0.325837
$597$		0			0
$598$		−	14.1089i		−	0.576956i
$599$			35.6951i			1.45846i	0.684268	+	0.729231i	$0.260122\pi$
$599$			35.6951i			1.45846i	−0.684268	+	0.729231i	$0.739878\pi$
$600$		0			0
$601$	5.41591			0.220920			0.110460	−	0.993881i	$-0.464768\pi$
$601$	5.41591			0.220920			0.110460	+	0.993881i	$0.464768\pi$
$602$	1.25173	−	11.2591i	0.0510165	−	0.458887i
$603$		0			0
$604$			20.9173i			0.851111i
$605$			52.8222i			2.14753i
$606$		0			0
$607$	5.25118			0.213139			0.106569	−	0.994305i	$-0.466013\pi$
$607$	5.25118			0.213139			0.106569	+	0.994305i	$0.466013\pi$
$608$	−4.10319	−	1.47098i	−0.166407	−	0.0596563i
$609$		0			0
$610$			42.7749i			1.73191i
$611$		−	24.9253i		−	1.00837i
$612$		0			0
$613$	31.7439			1.28212			0.641062	−	0.767489i	$-0.278494\pi$
$613$	31.7439			1.28212			0.641062	+	0.767489i	$0.278494\pi$
$614$			20.0085i			0.807479i
$615$		0			0
$616$	1.51340	−	13.6128i	0.0609767	−	0.548477i
$617$	19.0551			0.767128			0.383564	−	0.923514i	$-0.374697\pi$
$617$	19.0551			0.767128			0.383564	+	0.923514i	$0.374697\pi$
$618$		0			0
$619$		−	7.57363i		−	0.304410i	−0.988349	−	0.152205i	$-0.951363\pi$
$619$		−	7.57363i		−	0.304410i	0.988349	−	0.152205i	$-0.0486374\pi$
$620$		−	14.9173i		−	0.599091i
$621$		0			0
$622$	30.6108			1.22738
$623$	−20.0243	−	2.22619i	−0.802255	−	0.0891904i
$624$		0			0
$625$	−17.7306			−0.709226
$626$	−10.9306			−0.436875
$627$		0			0
$628$		−	18.1734i		−	0.725199i
$629$	−2.47696			−0.0987628
$630$		0			0
$631$	8.66216			0.344835			0.172418	−	0.985024i	$-0.444842\pi$
$631$	8.66216			0.344835			0.172418	+	0.985024i	$0.444842\pi$
$632$	−10.2364			−0.407184
$633$		0			0
$634$	11.7533			0.466783
$635$	−3.53613			−0.140327
$636$		0			0
$637$	−29.5636	−	6.65570i	−1.17135	−	0.263708i
$638$	−48.5403			−1.92173
$639$		0			0
$640$	3.34318			0.132151
$641$			20.9173i			0.826182i	0.910690	+	0.413091i	$0.135551\pi$
$641$			20.9173i			0.826182i	−0.910690	+	0.413091i	$0.864449\pi$
$642$		0			0
$643$		−	2.04338i		−	0.0805829i	−0.999188	−	0.0402914i	$-0.987171\pi$
$643$		−	2.04338i		−	0.0805829i	0.999188	−	0.0402914i	$-0.0128286\pi$
$644$	−8.56997	−	0.952763i	−0.337704	−	0.0375441i
$645$		0			0
$646$	−0.860052	+	2.39905i	−0.0338383	+	0.0943893i
$647$		−	12.7670i		−	0.501923i	−0.967997	−	0.250961i	$-0.919253\pi$
$647$		−	12.7670i		−	0.501923i	0.967997	−	0.250961i	$-0.0807467\pi$
$648$		0			0
$649$	−14.2804			−0.560555
$650$			26.7401i			1.04883i
$651$		0			0
$652$	13.1769			0.516046
$653$	32.4977			1.27173			0.635866	−	0.771799i	$-0.280643\pi$
$653$	32.4977			1.27173			0.635866	+	0.771799i	$0.280643\pi$
$654$		0			0
$655$	31.3448			1.22474
$656$	6.03256			0.235532
$657$		0			0
$658$	−15.1400	−	1.68318i	−0.590219	−	0.0656174i
$659$			25.1194i			0.978514i	0.872140	+	0.489257i	$0.162732\pi$
$659$			25.1194i			0.978514i	−0.872140	+	0.489257i	$0.837268\pi$
$660$		0			0
$661$	36.1875			1.40753			0.703765	−	0.710433i	$-0.251501\pi$
$661$	36.1875			1.40753			0.703765	+	0.710433i	$0.251501\pi$
$662$	−10.6956			−0.415696
$663$		0			0
$664$	2.68938			0.104368
$665$	−34.6338	−	16.9417i	−1.34304	−	0.656973i
$666$		0			0
$667$			30.5586i			1.18323i
$668$	−20.0591			−0.776110
$669$		0			0
$670$		−	45.5102i		−	1.75821i
$671$		−	66.2363i		−	2.55703i
$672$		0			0
$673$		−	7.24619i		−	0.279320i	−0.990200	−	0.139660i	$-0.955399\pi$
$673$		−	7.24619i		−	0.279320i	0.990200	−	0.139660i	$-0.0446010\pi$
$674$	8.91725			0.343480
$675$		0			0
$676$	−5.74090			−0.220804
$677$	23.9659			0.921085			0.460542	−	0.887638i	$-0.347655\pi$
$677$	23.9659			0.921085			0.460542	+	0.887638i	$0.347655\pi$
$678$		0			0
$679$	−31.7573	−	3.53060i	−1.21873	−	0.135492i
$680$		−	1.95469i		−	0.0749588i
$681$		0			0
$682$			23.0991i			0.884512i
$683$			45.3616i			1.73571i	0.496814	+	0.867857i	$0.334503\pi$
$683$			45.3616i			1.73571i	−0.496814	+	0.867857i	$0.665497\pi$
$684$		0			0
$685$		−	37.8819i		−	1.44739i
$686$	−6.03919	+	17.5079i	−0.230577	+	0.668457i
$687$		0			0
$688$	−4.28176			−0.163241
$689$			17.6723i			0.673261i
$690$		0			0
$691$			25.2519i			0.960629i	0.877096	+	0.480314i	$0.159477\pi$
$691$			25.2519i			0.960629i	−0.877096	+	0.480314i	$0.840523\pi$
$692$	21.5791			0.820315
$693$		0			0
$694$		−	21.1270i		−	0.801971i
$695$	5.03743			0.191081
$696$		0			0
$697$		−	3.52711i		−	0.133599i
$698$	2.15278			0.0814841
$699$		0			0
$700$	16.2424	+	1.80574i	0.613905	+	0.0682506i
$701$	28.0523			1.05952			0.529760	−	0.848147i	$-0.322282\pi$
$701$	28.0523			1.05952			0.529760	+	0.848147i	$0.322282\pi$
$702$		0			0
$703$	17.3830	+	6.23174i	0.655611	+	0.235035i
$704$	−5.17687			−0.195111
$705$		0			0
$706$	−3.62473			−0.136418
$707$	−2.74090	+	24.6540i	−0.103082	+	0.927209i
$708$		0			0
$709$	31.6700			1.18939			0.594697	−	0.803950i	$-0.297272\pi$
$709$	31.6700			1.18939			0.594697	+	0.803950i	$0.297272\pi$
$710$		−	39.0988i		−	1.46735i
$711$		0			0
$712$			7.61509i			0.285387i
$713$	14.5421			0.544605
$714$		0			0
$715$		−	74.9242i		−	2.80201i
$716$			8.47289i			0.316647i
$717$		0			0
$718$			23.6582i			0.882914i
$719$		−	12.0170i		−	0.448160i	−0.974571	−	0.224080i	$-0.928062\pi$
$719$		−	12.0170i		−	0.448160i	0.974571	−	0.224080i	$-0.0719377\pi$
$720$		0			0
$721$	8.95882	+	0.995993i	0.333644	+	0.0370927i
$722$	12.0715	−	14.6724i	0.449253	−	0.546051i
$723$		0			0
$724$	−7.40396			−0.275166
$725$		−	57.9167i		−	2.15097i
$726$		0			0
$727$		−	50.0504i		−	1.85627i	−0.372248	−	0.928133i	$-0.621413\pi$
$727$		−	50.0504i		−	1.85627i	0.372248	−	0.928133i	$-0.378587\pi$
$728$	−1.26556	+	11.3835i	−0.0469047	+	0.421902i
$729$		0			0
$730$			10.2799i			0.380476i
$731$			2.50345i			0.0925935i
$732$		0			0
$733$			31.1198i			1.14943i	0.818352	+	0.574717i	$0.194888\pi$
$733$			31.1198i			1.14943i	−0.818352	+	0.574717i	$0.805112\pi$
$734$	27.1508			1.00216
$735$		0			0
$736$			3.25910i			0.120132i
$737$			70.4719i			2.59586i
$738$		0			0
$739$	−0.636521			−0.0234148			−0.0117074	−	0.999931i	$-0.503727\pi$
$739$	−0.636521			−0.0234148			−0.0117074	+	0.999931i	$0.503727\pi$
$740$	−14.1632			−0.520650
$741$		0			0
$742$	10.7344	+	1.19340i	0.394074	+	0.0438110i
$743$			48.0995i			1.76460i	0.470689	+	0.882299i	$0.344005\pi$
$743$			48.0995i			1.76460i	−0.470689	+	0.882299i	$0.655995\pi$
$744$		0			0
$745$		−	26.5940i		−	0.974328i
$746$	−9.37639			−0.343294
$747$		0			0
$748$			3.02680i			0.110671i
$749$	0.381332	−	3.43003i	0.0139336	−	0.125330i
$750$		0			0
$751$		−	8.87380i		−	0.323810i	−0.986806	−	0.161905i	$-0.948236\pi$
$751$		−	8.87380i		−	0.323810i	0.986806	−	0.161905i	$-0.0517638\pi$
$752$			5.75764i			0.209960i
$753$		0			0
$754$	40.5911			1.47824
$755$	69.9302			2.54502
$756$		0			0
$757$	−41.1350			−1.49508			−0.747539	−	0.664217i	$-0.768765\pi$
$757$	−41.1350			−1.49508			−0.747539	+	0.664217i	$0.768765\pi$
$758$	25.6128			0.930300
$759$		0			0
$760$	−4.91777	+	13.7177i	−0.178386	+	0.497594i
$761$			40.8676i			1.48145i	0.671809	+	0.740725i	$0.265518\pi$
$761$			40.8676i			1.48145i	−0.671809	+	0.740725i	$0.734482\pi$
$762$		0			0
$763$	1.19340	−	10.7344i	0.0432039	−	0.388613i
$764$	−5.42357			−0.196218
$765$		0			0
$766$			32.8123i			1.18556i
$767$	11.9418			0.431192
$768$		0			0
$769$		−	17.7685i		−	0.640747i	−0.947291	−	0.320374i	$-0.896192\pi$
$769$		−	17.7685i		−	0.640747i	0.947291	−	0.320374i	$-0.103808\pi$
$770$	−45.5102	−	5.05958i	−1.64007	−	0.182335i
$771$		0			0
$772$		−	12.4444i		−	0.447882i
$773$	31.3271			1.12676			0.563379	−	0.826199i	$-0.309501\pi$
$773$	31.3271			1.12676			0.563379	+	0.826199i	$0.309501\pi$
$774$		0			0
$775$	−27.5611			−0.990025
$776$			12.0771i			0.433542i
$777$		0			0
$778$			4.35374i			0.156089i
$779$	−8.87380	+	24.7528i	−0.317937	+	0.886861i
$780$		0			0
$781$			60.5438i			2.16643i
$782$	1.90553			0.0681415
$783$		0			0
$784$	6.82908	+	1.53744i	0.243896	+	0.0549086i
$785$	−60.7571			−2.16851
$786$		0			0
$787$	40.0328			1.42702			0.713508	−	0.700647i	$-0.247105\pi$
$787$	40.0328			1.42702			0.713508	+	0.700647i	$0.247105\pi$
$788$	12.5182			0.445943
$789$		0			0
$790$			34.2223i			1.21757i
$791$	1.84420	−	16.5883i	0.0655722	−	0.589813i
$792$		0			0
$793$			55.3891i			1.96693i
$794$	21.2002			0.752368
$795$		0			0
$796$			7.78660i			0.275989i
$797$	11.8311			0.419080			0.209540	−	0.977800i	$-0.432803\pi$
$797$	11.8311			0.419080			0.209540	+	0.977800i	$0.432803\pi$
$798$		0			0
$799$	3.36637			0.119094
$800$		−	6.17687i		−	0.218385i
$801$		0			0
$802$	−8.60883			−0.303988
$803$		−	15.9183i		−	0.561743i
$804$		0			0
$805$	−3.18526	+	28.6510i	−0.112266	+	1.00981i
$806$		−	19.3163i		−	0.680388i
$807$		0			0
$808$	9.37575			0.329838
$809$	5.63950			0.198274			0.0991372	−	0.995074i	$-0.468392\pi$
$809$	5.63950			0.198274			0.0991372	+	0.995074i	$0.468392\pi$
$810$		0			0
$811$	12.9753			0.455624			0.227812	−	0.973705i	$-0.426843\pi$
$811$	12.9753			0.455624			0.227812	+	0.973705i	$0.426843\pi$
$812$	2.74109	−	24.6557i	0.0961933	−	0.865246i
$813$		0			0
$814$	21.9315			0.768699
$815$		−	44.0527i		−	1.54310i
$816$		0			0
$817$	6.29840	−	17.5689i	0.220353	−	0.614658i
$818$		−	2.46501i		−	0.0861869i
$819$		0			0
$820$		−	20.1680i		−	0.704296i
$821$	10.7981			0.376856			0.188428	−	0.982087i	$-0.439661\pi$
$821$	10.7981			0.376856			0.188428	+	0.982087i	$0.439661\pi$
$822$		0			0
$823$	−28.9577			−1.00940			−0.504700	−	0.863295i	$-0.668397\pi$
$823$	−28.9577			−1.00940			−0.504700	+	0.863295i	$0.668397\pi$
$824$		−	3.40698i		−	0.118688i
$825$		0			0
$826$	0.806419	−	7.25363i	0.0280589	−	0.252386i
$827$		−	22.9745i		−	0.798900i	−0.916755	−	0.399450i	$-0.869201\pi$
$827$		−	22.9745i		−	0.798900i	0.916755	−	0.399450i	$-0.130799\pi$
$828$		0			0
$829$	−50.2062			−1.74373			−0.871867	−	0.489743i	$-0.837091\pi$
$829$	−50.2062			−1.74373			−0.871867	+	0.489743i	$0.837091\pi$
$830$		−	8.99109i		−	0.312085i
$831$		0			0
$832$	4.32908			0.150084
$833$	0.898909	−	3.99281i	0.0311453	−	0.138343i
$834$		0			0
$835$			67.0612i			2.32075i
$836$	7.61509	−	21.2417i	0.263373	−	0.734659i
$837$		0			0
$838$	−37.4553			−1.29387
$839$	−2.87531			−0.0992668			−0.0496334	−	0.998768i	$-0.515805\pi$
$839$	−2.87531			−0.0992668			−0.0496334	+	0.998768i	$0.515805\pi$
$840$		0			0
$841$	−58.9167			−2.03161
$842$	0.860052			0.0296394
$843$		0			0
$844$		−	21.7773i		−	0.749606i
$845$			19.1929i			0.660255i
$846$		0			0
$847$	41.5468	+	4.61895i	1.42757	+	0.158709i
$848$		−	4.08223i		−	0.140184i
$849$		0			0
$850$	−3.61148			−0.123873
$851$		−	13.8070i		−	0.473298i
$852$		0			0
$853$			22.7274i			0.778173i	0.921201	+	0.389086i	$0.127209\pi$
$853$			22.7274i			0.778173i	−0.921201	+	0.389086i	$0.872791\pi$
$854$	33.6442	+	3.74038i	1.15128	+	0.127993i
$855$		0			0
$856$	−1.30442			−0.0445840
$857$	−34.7659			−1.18758			−0.593791	−	0.804620i	$-0.702369\pi$
$857$	−34.7659			−1.18758			−0.593791	+	0.804620i	$0.702369\pi$
$858$		0			0
$859$		−	11.3161i		−	0.386101i	−0.981189	−	0.193050i	$-0.938162\pi$
$859$		−	11.3161i		−	0.386101i	0.981189	−	0.193050i	$-0.0618380\pi$
$860$			14.3147i			0.488127i
$861$		0			0
$862$	12.4479			0.423976
$863$			27.1822i			0.925294i	0.886543	+	0.462647i	$0.153100\pi$
$863$			27.1822i			0.925294i	−0.886543	+	0.462647i	$0.846900\pi$
$864$		0			0
$865$		−	72.1429i		−	2.45293i
$866$			18.4646i			0.627453i
$867$		0			0
$868$	−11.7330	−	1.30442i	−0.398245	−	0.0442747i
$869$		−	52.9927i		−	1.79766i
$870$		0			0
$871$		−	58.9310i		−	1.99680i
$872$	−4.08223			−0.138242
$873$		0			0
$874$	−13.3727	−	4.79409i	−0.452339	−	0.162162i
$875$	1.15020	−	10.3459i	0.0388840	−	0.349756i
$876$		0			0
$877$		−	49.7523i		−	1.68001i	−0.542575	−	0.840007i	$-0.682551\pi$
$877$		−	49.7523i		−	1.68001i	0.542575	−	0.840007i	$-0.317449\pi$
$878$			11.7679i			0.397146i
$879$		0			0
$880$			17.3072i			0.583426i
$881$		−	3.64631i		−	0.122847i	−0.998112	−	0.0614237i	$-0.980436\pi$
$881$		−	3.64631i		−	0.122847i	0.998112	−	0.0614237i	$-0.0195641\pi$
$882$		0			0
$883$	−15.5474			−0.523211			−0.261606	−	0.965175i	$-0.584252\pi$
$883$	−15.5474			−0.523211			−0.261606	+	0.965175i	$0.584252\pi$
$884$		−	2.53112i		−	0.0851307i
$885$		0			0
$886$		−	4.75465i		−	0.159736i
$887$	−36.3204			−1.21952			−0.609760	−	0.792586i	$-0.708734\pi$
$887$	−36.3204			−1.21952			−0.609760	+	0.792586i	$0.708734\pi$
$888$		0			0
$889$	−0.309211	+	2.78131i	−0.0103706	+	0.0932822i
$890$	25.4586			0.853375
$891$		0			0
$892$	19.2699			0.645204
$893$	−23.6247	−	8.46940i	−0.790571	−	0.283418i
$894$		0			0
$895$	28.3264			0.946848
$896$	0.292339	−	2.62955i	0.00976637	−	0.0878471i
$897$		0			0
$898$	14.6088			0.487503
$899$			41.8374i			1.39536i
$900$		0			0
$901$	−2.38679			−0.0795156
$902$			31.2298i			1.03984i
$903$		0			0
$904$	−6.30842			−0.209815
$905$			24.7528i			0.822810i
$906$		0			0
$907$			14.1062i			0.468390i	0.972190	+	0.234195i	$0.0752454\pi$
$907$			14.1062i			0.468390i	−0.972190	+	0.234195i	$0.924755\pi$
$908$	−11.8311			−0.392629
$909$		0			0
$910$	38.0572	+	4.23099i	1.26158	+	0.140256i
$911$		−	7.15370i		−	0.237013i	−0.992953	−	0.118506i	$-0.962189\pi$
$911$		−	7.15370i		−	0.237013i	0.992953	−	0.118506i	$-0.0378106\pi$
$912$		0			0
$913$			13.9226i			0.460770i
$914$			19.2626i			0.637150i
$915$		0			0
$916$			14.2390i			0.470468i
$917$	2.74090	−	24.6540i	0.0905124	−	0.814147i
$918$		0			0
$919$	40.1558			1.32462			0.662310	−	0.749230i	$-0.269576\pi$
$919$	40.1558			1.32462			0.662310	+	0.749230i	$0.269576\pi$
$920$	10.8958			0.359223
$921$		0			0
$922$	2.43550			0.0802090
$923$		−	50.6289i		−	1.66647i
$924$		0			0
$925$			26.1680i			0.860397i
$926$			35.6700i			1.17219i
$927$		0			0
$928$	−9.37639			−0.307795
$929$		−	50.2910i		−	1.65000i	−0.565136	−	0.824998i	$-0.691176\pi$
$929$		−	50.2910i		−	1.65000i	0.565136	−	0.824998i	$-0.308824\pi$
$930$		0			0
$931$	−16.3539	+	25.7595i	−0.535977	+	0.844233i
$932$	−1.13155			−0.0370653
$933$		0			0
$934$	20.2715			0.663304
$935$	10.1192			0.330932
$936$		0			0
$937$		−	50.8276i		−	1.66047i	−0.557416	−	0.830233i	$-0.688207\pi$
$937$		−	50.8276i		−	1.66047i	0.557416	−	0.830233i	$-0.311793\pi$
$938$	−35.7956	−	3.97957i	−1.16877	−	0.129937i
$939$		0			0
$940$	19.2488			0.627828
$941$	33.1557			1.08085			0.540423	−	0.841394i	$-0.318264\pi$
$941$	33.1557			1.08085			0.540423	+	0.841394i	$0.318264\pi$
$942$		0			0
$943$	19.6607			0.640242
$944$	−2.75850			−0.0897817
$945$		0			0
$946$		−	22.1661i		−	0.720682i
$947$	−7.71186			−0.250602			−0.125301	−	0.992119i	$-0.539990\pi$
$947$	−7.71186			−0.250602			−0.125301	+	0.992119i	$0.539990\pi$
$948$		0			0
$949$			13.3114i			0.432106i
$950$	25.3449	+	9.08607i	0.822297	+	0.294791i
$951$		0			0
$952$	−1.53744	−	0.170924i	−0.0498288	−	0.00553969i
$953$		−	33.8550i		−	1.09667i	−0.836258	−	0.548336i	$-0.815262\pi$
$953$		−	33.8550i		−	1.09667i	0.836258	−	0.548336i	$-0.184738\pi$
$954$		0			0
$955$			18.1320i			0.586737i
$956$	7.09463			0.229457
$957$		0			0
$958$	20.7261			0.669631
$959$	−29.7956	−	3.31252i	−0.962152	−	0.106967i
$960$		0			0
$961$	−11.0906			−0.357762
$962$	−18.3399			−0.591302
$963$		0			0
$964$	−25.9906			−0.837100
$965$	−41.6038			−1.33927
$966$		0			0
$967$	28.6541			0.921455			0.460728	−	0.887542i	$-0.347589\pi$
$967$	28.6541			0.921455			0.460728	+	0.887542i	$0.347589\pi$
$968$		−	15.8000i		−	0.507830i
$969$		0			0
$970$	40.3759			1.29639
$971$	−4.81396			−0.154487			−0.0772436	−	0.997012i	$-0.524612\pi$
$971$	−4.81396			−0.154487			−0.0772436	+	0.997012i	$0.524612\pi$
$972$		0			0
$973$	0.440490	−	3.96215i	0.0141215	−	0.127021i
$974$	3.00974			0.0964384
$975$		0			0
$976$		−	12.7947i		−	0.409548i
$977$			31.5546i			1.00952i	0.863259	+	0.504761i	$0.168419\pi$
$977$			31.5546i			1.00952i	−0.863259	+	0.504761i	$0.831581\pi$
$978$		0			0
$979$	−39.4223			−1.25994
$980$	5.13995	−	22.8308i	0.164190	−	0.729305i
$981$		0			0
$982$			21.1270i			0.674191i
$983$	3.79781			0.121131			0.0605656	−	0.998164i	$-0.480710\pi$
$983$	3.79781			0.121131			0.0605656	+	0.998164i	$0.480710\pi$
$984$		0			0
$985$		−	41.8506i		−	1.33347i
$986$			5.48217i			0.174588i
$987$		0			0
$988$	−6.36800	+	17.7630i	−0.202593	+	0.565118i
$989$	−13.9547			−0.443733
$990$		0			0
$991$		−	14.9207i		−	0.473973i	−0.971513	−	0.236987i	$-0.923840\pi$
$991$		−	14.9207i		−	0.473973i	0.971513	−	0.236987i	$-0.0761597\pi$
$992$			4.46199i			0.141668i
$993$		0			0
$994$	−30.7528	−	3.41893i	−0.975419	−	0.108442i
$995$	26.0320			0.825271
$996$		0			0
$997$		−	37.8061i		−	1.19733i	−0.800999	−	0.598666i	$-0.795698\pi$
$997$		−	37.8061i		−	1.19733i	0.800999	−	0.598666i	$-0.204302\pi$
$998$		−	12.8986i		−	0.408298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.e.c.1063.16		16
3.2	odd	2		266.2.d.a.265.2	✓	16
7.6	odd	2	inner	2394.2.e.c.1063.9		16
12.11	even	2		2128.2.m.f.1329.13		16
19.18	odd	2	inner	2394.2.e.c.1063.8		16
21.20	even	2		266.2.d.a.265.7	yes	16
57.56	even	2		266.2.d.a.265.15	yes	16
84.83	odd	2		2128.2.m.f.1329.4		16
133.132	even	2	inner	2394.2.e.c.1063.1		16
228.227	odd	2		2128.2.m.f.1329.3		16
399.398	odd	2		266.2.d.a.265.10	yes	16
1596.1595	even	2		2128.2.m.f.1329.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.d.a.265.2	✓	16	3.2	odd	2
266.2.d.a.265.7	yes	16	21.20	even	2
266.2.d.a.265.10	yes	16	399.398	odd	2
266.2.d.a.265.15	yes	16	57.56	even	2
2128.2.m.f.1329.3		16	228.227	odd	2
2128.2.m.f.1329.4		16	84.83	odd	2
2128.2.m.f.1329.13		16	12.11	even	2
2128.2.m.f.1329.14		16	1596.1595	even	2
2394.2.e.c.1063.1		16	133.132	even	2	inner
2394.2.e.c.1063.8		16	19.18	odd	2	inner
2394.2.e.c.1063.9		16	7.6	odd	2	inner
2394.2.e.c.1063.16		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +3.34318i q^{5} +(2.62955 + 0.292339i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +3.34318i q^{5} +(2.62955 + 0.292339i) q^{7} -1.00000i q^{8} -3.34318 q^{10} +5.17687 q^{11} -4.32908 q^{13} +(-0.292339 + 2.62955i) q^{14} +1.00000 q^{16} -0.584678i q^{17} +(-1.47098 + 4.10319i) q^{19} -3.34318i q^{20} +5.17687i q^{22} +3.25910 q^{23} -6.17687 q^{25} -4.32908i q^{26} +(-2.62955 - 0.292339i) q^{28} +9.37639i q^{29} +4.46199 q^{31} +1.00000i q^{32} +0.584678 q^{34} +(-0.977343 + 8.79107i) q^{35} -4.23645i q^{37} +(-4.10319 - 1.47098i) q^{38} +3.34318 q^{40} +6.03256 q^{41} -4.28176 q^{43} -5.17687 q^{44} +3.25910i q^{46} +5.75764i q^{47} +(6.82908 + 1.53744i) q^{49} -6.17687i q^{50} +4.32908 q^{52} -4.08223i q^{53} +17.3072i q^{55} +(0.292339 - 2.62955i) q^{56} -9.37639 q^{58} -2.75850 q^{59} -12.7947i q^{61} +4.46199i q^{62} -1.00000 q^{64} -14.4729i q^{65} +13.6128i q^{67} +0.584678i q^{68} +(-8.79107 - 0.977343i) q^{70} +11.6951i q^{71} -3.07488i q^{73} +4.23645 q^{74} +(1.47098 - 4.10319i) q^{76} +(13.6128 + 1.51340i) q^{77} -10.2364i q^{79} +3.34318i q^{80} +6.03256i q^{82} +2.68938i q^{83} +1.95469 q^{85} -4.28176i q^{86} -5.17687i q^{88} -7.61509 q^{89} +(-11.3835 - 1.26556i) q^{91} -3.25910 q^{92} -5.75764 q^{94} +(-13.7177 - 4.91777i) q^{95} -12.0771 q^{97} +(-1.53744 + 6.82908i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 6 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 6 * q^7	\( 16 q - 16 q^{4} + 6 q^{7} + 12 q^{11} + 16 q^{16} - 20 q^{23} - 28 q^{25} - 6 q^{28} - 8 q^{35} - 4 q^{43} - 12 q^{44} + 10 q^{49} - 16 q^{58} - 16 q^{64} - 12 q^{74} + 4 q^{77} + 16 q^{85} + 20 q^{92} - 12 q^{95}+O(q^{100}) \) 16 * q - 16 * q^4 + 6 * q^7 + 12 * q^11 + 16 * q^16 - 20 * q^23 - 28 * q^25 - 6 * q^28 - 8 * q^35 - 4 * q^43 - 12 * q^44 + 10 * q^49 - 16 * q^58 - 16 * q^64 - 12 * q^74 + 4 * q^77 + 16 * q^85 + 20 * q^92 - 12 * q^95

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