LMFDB - Embedded newform 968.2.k.c.475.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(403,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("968.403");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.k (of order $10$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			475.1
Root			$0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	968.475
Dual form			968.2.k.c.699.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 - 0.437016i) q^{2} +(-0.0359800 + 0.0261410i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.0598171 - 0.0194357i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(-0.926440 + 2.85129i) q^{9} -0.0889475 q^{12} +(1.23607 + 3.80423i) q^{16} +(-3.76454 + 1.22317i) q^{17} +(2.49212 - 3.43011i) q^{18} +(-2.65926 - 3.66016i) q^{19} +(0.119634 + 0.0388715i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-0.0824317 - 0.253699i) q^{27} -5.65685i q^{32} +5.59785 q^{34} +(-4.85090 + 3.52439i) q^{36} +(1.97715 + 6.08505i) q^{38} +(-7.45294 - 10.2581i) q^{41} +12.7426i q^{43} +(-0.143920 - 0.104564i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(6.72499 - 2.18508i) q^{50} +(0.103473 - 0.142419i) q^{51} +0.377248i q^{54} +(0.191361 + 0.0621769i) q^{57} +(-9.38125 - 6.81588i) q^{59} +(-2.47214 + 7.60845i) q^{64} +12.3962 q^{67} +(-7.52909 - 2.44635i) q^{68} +(8.06466 - 2.62037i) q^{72} +(-7.37900 + 10.1563i) q^{73} +(0.0687157 - 0.211485i) q^{75} -9.04842i q^{76} +(-7.26675 - 5.27961i) q^{81} +(5.54123 + 17.0542i) q^{82} +(-12.2386 + 3.97655i) q^{83} +(5.56872 - 17.1387i) q^{86} -17.8873 q^{89} +(0.147876 + 0.203534i) q^{96} +(-5.58246 + 17.1810i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 4 q^{4} - 12 q^{9} + 8 q^{12} - 8 q^{16} - 30 q^{17} - 10 q^{25} - 42 q^{27} + 16 q^{34} + 4 q^{36} + 36 q^{38} - 30 q^{41} + 24 q^{48} + 14 q^{49} + 10 q^{51} + 50 q^{57} + 12 q^{59} + 16 q^{64}+ \cdots - 20 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 + 4 * q^4 - 12 * q^9 + 8 * q^12 - 8 * q^16 - 30 * q^17 - 10 * q^25 - 42 * q^27 + 16 * q^34 + 4 * q^36 + 36 * q^38 - 30 * q^41 + 24 * q^48 + 14 * q^49 + 10 * q^51 + 50 * q^57 + 12 * q^59 + 16 * q^64 - 28 * q^67 - 60 * q^68 + 80 * q^72 + 10 * q^73 - 20 * q^75 - 48 * q^81 + 32 * q^82 + 24 * q^86 - 36 * q^89 + 80 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$3$	−0.0359800	+	0.0261410i	−0.0207731	+	0.0150925i	−0.598123	−	0.801404i	$-0.704087\pi$
$3$	−0.0359800	+	0.0261410i	−0.0207731	+	0.0150925i	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.61803	+	1.17557i	0.809017	+	0.587785i
$5$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$5$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$6$	0.0598171	−	0.0194357i	0.0244202	−	0.00793461i
$7$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$7$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$8$	−1.66251	−	2.28825i	−0.587785	−	0.809017i
$9$	−0.926440	+	2.85129i	−0.308813	+	0.950429i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−0.0889475			−0.0256769
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$		0			0
$15$		0			0
$16$	1.23607	+	3.80423i	0.309017	+	0.951057i
$17$	−3.76454	+	1.22317i	−0.913036	+	0.296663i	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−3.76454	+	1.22317i	−0.913036	+	0.296663i	−0.185429	+	0.982658i	$0.559367\pi$
$18$	2.49212	−	3.43011i	0.587398	−	0.808484i
$19$	−2.65926	−	3.66016i	−0.610077	−	0.839699i	0.386507	−	0.922287i	$-0.373682\pi$
$19$	−2.65926	−	3.66016i	−0.610077	−	0.839699i	−0.996584	+	0.0825877i	$0.973682\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	0.119634	+	0.0388715i	0.0244202	+	0.00793461i
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$		0			0
$27$	−0.0824317	−	0.253699i	−0.0158640	−	0.0488243i
$28$		0			0
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	5.59785			0.960023
$35$		0			0
$36$	−4.85090	+	3.52439i	−0.808484	+	0.587398i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$	1.97715	+	6.08505i	0.320736	+	0.987125i
$39$		0			0
$40$		0			0
$41$	−7.45294	−	10.2581i	−1.16395	−	1.60204i	−0.695432	−	0.718592i	$-0.744787\pi$
$41$	−7.45294	−	10.2581i	−1.16395	−	1.60204i	−0.468521	−	0.883452i	$-0.655213\pi$
$42$		0			0
$43$			12.7426i			1.94323i	0.236575	+	0.971613i	$0.423975\pi$
$43$			12.7426i			1.94323i	−0.236575	+	0.971613i	$0.576025\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	−0.143920	−	0.104564i	−0.0207731	−	0.0150925i
$49$	−2.16312	−	6.65740i	−0.309017	−	0.951057i
$50$	6.72499	−	2.18508i	0.951057	−	0.309017i
$51$	0.103473	−	0.142419i	0.0144892	−	0.0199426i
$52$		0			0
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$			0.377248i			0.0513369i
$55$		0			0
$56$		0			0
$57$	0.191361	+	0.0621769i	0.0253464	+	0.00823553i
$58$		0			0
$59$	−9.38125	−	6.81588i	−1.22134	−	0.887352i	−0.225125	−	0.974330i	$-0.572279\pi$
$59$	−9.38125	−	6.81588i	−1.22134	−	0.887352i	−0.996210	+	0.0869778i	$0.972279\pi$
$60$		0			0
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$		0			0
$63$		0			0
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$		0			0
$66$		0			0
$67$	12.3962			1.51444			0.757220	−	0.653160i	$-0.226557\pi$
$67$	12.3962			1.51444			0.757220	+	0.653160i	$0.226557\pi$
$68$	−7.52909	−	2.44635i	−0.913036	−	0.296663i
$69$		0			0
$70$		0			0
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$	8.06466	−	2.62037i	0.950429	−	0.308813i
$73$	−7.37900	+	10.1563i	−0.863647	+	1.18871i	0.117041	+	0.993127i	$0.462659\pi$
$73$	−7.37900	+	10.1563i	−0.863647	+	1.18871i	−0.980688	+	0.195580i	$0.937341\pi$
$74$		0			0
$75$	0.0687157	−	0.211485i	0.00793461	−	0.0244202i
$76$		−	9.04842i		−	1.03792i
$77$		0			0
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	−7.26675	−	5.27961i	−0.807417	−	0.586623i
$82$	5.54123	+	17.0542i	0.611926	+	1.88332i
$83$	−12.2386	+	3.97655i	−1.34336	+	0.436483i	−0.890452	−	0.455077i	$-0.849612\pi$
$83$	−12.2386	+	3.97655i	−1.34336	+	0.436483i	−0.452904	+	0.891559i	$0.649612\pi$
$84$		0			0
$85$		0			0
$86$	5.56872	−	17.1387i	0.600490	−	1.84812i
$87$		0			0
$88$		0			0
$89$	−17.8873			−1.89605			−0.948026	−	0.318192i	$-0.896924\pi$
$89$	−17.8873			−1.89605			−0.948026	+	0.318192i	$0.896924\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.147876	+	0.203534i	0.0150925	+	0.0207731i
$97$	−5.58246	+	17.1810i	−0.566813	+	1.74447i	0.0956901	+	0.995411i	$0.469494\pi$
$97$	−5.58246	+	17.1810i	−0.566813	+	1.74447i	−0.662503	+	0.749059i	$0.730506\pi$
$98$			9.89949i			1.00000i
$99$		0			0
$100$	−10.0000			−1.00000
$101$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$101$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$102$	−0.201411	+	0.146333i	−0.0199426	+	0.0144892i
$103$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$103$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.34203	+	10.1054i	0.709781	+	0.976930i	0.999802	+	0.0199092i	$0.00633772\pi$
$107$	7.34203	+	10.1054i	0.709781	+	0.976930i	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0.164863	−	0.507397i	0.0158640	−	0.0488243i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.20500	+	3.05511i	−0.395573	+	0.287401i	−0.767736	−	0.640767i	$-0.778617\pi$
$113$	−4.20500	+	3.05511i	−0.395573	+	0.287401i	0.372162	+	0.928168i	$0.378617\pi$
$114$	−0.230207	−	0.167255i	−0.0215609	−	0.0156649i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	9.63911	+	13.2671i	0.887352	+	1.22134i
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$	0.536314	+	0.174259i	0.0483578	+	0.0157124i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	6.65003	−	9.15298i	0.587785	−	0.809017i
$129$	−0.333104	−	0.458479i	−0.0293282	−	0.0403668i
$130$		0			0
$131$			21.4892i			1.87752i	0.344574	+	0.938759i	$0.388023\pi$
$131$			21.4892i			1.87752i	−0.344574	+	0.938759i	$0.611977\pi$
$132$		0			0
$133$		0			0
$134$	−16.6729	−	5.41735i	−1.44032	−	0.467987i
$135$		0			0
$136$	9.05751	+	6.58066i	0.776675	+	0.564287i
$137$	−5.60995	−	17.2656i	−0.479290	−	1.47510i	−0.840083	−	0.542457i	$-0.817494\pi$
$137$	−5.60995	−	17.2656i	−0.479290	−	1.47510i	0.360794	−	0.932646i	$-0.382506\pi$
$138$		0			0
$139$	−4.98752	+	6.86474i	−0.423036	+	0.582259i	−0.966337	−	0.257279i	$-0.917174\pi$
$139$	−4.98752	+	6.86474i	−0.423036	+	0.582259i	0.543301	+	0.839538i	$0.317174\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.9921			−0.999341
$145$		0			0
$146$	14.3632	−	10.4355i	1.18871	−	0.863647i
$147$	0.251860	+	0.182987i	0.0207731	+	0.0150925i
$148$		0			0
$149$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$149$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$150$	−0.184845	+	0.254417i	−0.0150925	+	0.0207731i
$151$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$151$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$152$	−3.95430	+	12.1701i	−0.320736	+	0.987125i
$153$		−	11.8670i		−	0.959390i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$157$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	7.46649	+	10.2767i	0.586623	+	0.807417i
$163$	7.29030	−	22.4372i	0.571021	−	1.75742i	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	7.29030	−	22.4372i	0.571021	−	1.75742i	0.649347	−	0.760493i	$-0.275042\pi$
$164$		−	25.3594i		−	1.98024i
$165$		0			0
$166$	18.1986			1.41249
$167$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$167$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$168$		0			0
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$	12.8998	−	4.19141i	0.986474	−	0.320525i
$172$	−14.9798	+	20.6179i	−1.14220	+	1.57210i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.515712			0.0387633
$178$	24.0584	+	7.81705i	1.80325	+	0.585912i
$179$	19.7338	−	14.3374i	1.47497	−	1.07163i	0.495835	−	0.868416i	$-0.334862\pi$
$179$	19.7338	−	14.3374i	1.47497	−	1.07163i	0.979135	−	0.203212i	$-0.0651381\pi$
$180$		0			0
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	−0.109945	−	0.338376i	−0.00793461	−	0.0244202i
$193$	−16.1400	+	5.24419i	−1.16178	+	0.377485i	−0.825569	−	0.564301i	$-0.809146\pi$
$193$	−16.1400	+	5.24419i	−1.16178	+	0.377485i	−0.336211	+	0.941787i	$0.609146\pi$
$194$	15.0168	−	20.6688i	1.07814	−	1.48394i
$195$		0			0
$196$	4.32624	−	13.3148i	0.309017	−	0.951057i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	13.4500	+	4.37016i	0.951057	+	0.309017i
$201$	−0.446016	+	0.324050i	−0.0314596	+	0.0228567i
$202$		0			0
$203$		0			0
$204$	0.334847	−	0.108798i	0.0234440	−	0.00761741i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	11.7600	+	3.82106i	0.809593	+	0.263053i	0.684425	−	0.729083i	$-0.260053\pi$
$211$	11.7600	+	3.82106i	0.809593	+	0.263053i	0.125168	+	0.992136i	$0.460053\pi$
$212$		0			0
$213$		0			0
$214$	−5.45877	−	16.8004i	−0.373154	−	1.14845i
$215$		0			0
$216$	−0.443482	+	0.610400i	−0.0301751	+	0.0415325i
$217$		0			0
$218$		0			0
$219$		−	0.558319i		−	0.0377277i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$223$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$224$		0			0
$225$	−4.63220	−	14.2564i	−0.308813	−	0.950429i
$226$	6.99085	−	2.27147i	0.465024	−	0.151096i
$227$	17.2843	−	23.7897i	1.14720	−	1.57898i	0.396923	−	0.917852i	$-0.370078\pi$
$227$	17.2843	−	23.7897i	1.14720	−	1.57898i	0.750273	−	0.661128i	$-0.229922\pi$
$228$	0.236535	+	0.325562i	0.0156649	+	0.0215609i
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.4180	+	4.03486i	0.813531	+	0.264332i	0.686092	−	0.727514i	$-0.259325\pi$
$233$	12.4180	+	4.03486i	0.813531	+	0.264332i	0.127438	+	0.991847i	$0.459325\pi$
$234$		0			0
$235$		0			0
$236$	−7.16664	−	22.0567i	−0.466509	−	1.43577i
$237$		0			0
$238$		0			0
$239$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$239$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$240$		0			0
$241$		−	29.9717i		−	1.93064i	−0.261061	−	0.965322i	$-0.584072\pi$
$241$		−	29.9717i		−	1.93064i	0.261061	−	0.965322i	$-0.415928\pi$
$242$		0			0
$243$	1.19974			0.0769631
$244$		0			0
$245$		0			0
$246$	−0.645187	−	0.468755i	−0.0411356	−	0.0298868i
$247$		0			0
$248$		0			0
$249$	0.336393	−	0.463005i	0.0213180	−	0.0293417i
$250$		0			0
$251$	1.85410	−	5.70634i	0.117030	−	0.360181i	−0.875335	−	0.483517i	$-0.839359\pi$
$251$	1.85410	−	5.70634i	0.117030	−	0.360181i	0.992365	+	0.123336i	$0.0393592\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	14.2553	+	10.3571i	0.889219	+	0.646056i	0.935674	−	0.352865i	$-0.114792\pi$
$257$	14.2553	+	10.3571i	0.889219	+	0.646056i	−0.0464552	+	0.998920i	$0.514792\pi$
$258$	0.247662	+	0.762224i	0.0154187	+	0.0474540i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	9.39111	−	28.9029i	0.580185	−	1.78563i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.643586	−	0.467593i	0.0393868	−	0.0286162i
$268$	20.0575	+	14.5726i	1.22521	+	0.890165i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$271$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$272$	−9.30646	−	12.8092i	−0.564287	−	0.776675i
$273$		0			0
$274$			25.6739i			1.55101i
$275$		0			0
$276$		0			0
$277$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$277$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$278$	9.70820	−	7.05342i	0.582259	−	0.423036i
$279$		0			0
$280$		0			0
$281$	11.7002	−	3.80163i	0.697976	−	0.226786i	0.0615273	−	0.998105i	$-0.480403\pi$
$281$	11.7002	−	3.80163i	0.697976	−	0.226786i	0.636448	+	0.771319i	$0.280403\pi$
$282$		0			0
$283$	14.9626	+	20.5942i	0.889432	+	1.22420i	0.973718	+	0.227757i	$0.0731392\pi$
$283$	14.9626	+	20.5942i	0.889432	+	1.22420i	−0.0842855	+	0.996442i	$0.526861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.1293	+	5.24073i	0.950429	+	0.308813i
$289$	−1.07766	+	0.782965i	−0.0633917	+	0.0460567i
$290$		0			0
$291$	−0.248273	−	0.764106i	−0.0145540	−	0.0447927i
$292$	−23.8789	+	7.75874i	−1.39741	+	0.454046i
$293$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$293$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$294$	−0.258783	−	0.356184i	−0.0150925	−	0.0207731i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.359800	−	0.261410i	0.0207731	−	0.0150925i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	10.6371	−	14.6406i	0.610077	−	0.839699i
$305$		0			0
$306$	−5.18607	+	15.9611i	−0.296468	+	0.912434i
$307$		−	13.1200i		−	0.748796i	−0.927268	−	0.374398i	$-0.877849\pi$
$307$		−	13.1200i		−	0.748796i	0.927268	−	0.374398i	$-0.122151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	9.02013	+	27.7611i	0.509848	+	1.56915i	0.792465	+	0.609918i	$0.208798\pi$
$313$	9.02013	+	27.7611i	0.509848	+	1.56915i	−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.528333	−	0.171666i	−0.0294887	−	0.00958145i
$322$		0			0
$323$	14.4879	+	10.5261i	0.806130	+	0.585688i
$324$	−5.55131	−	17.0852i	−0.308406	−	0.949176i
$325$		0			0
$326$	−19.6109	+	26.9920i	−1.08615	+	1.49495i
$327$		0			0
$328$	−11.0825	+	34.1083i	−0.611926	+	1.88332i
$329$		0			0
$330$		0			0
$331$	35.9970			1.97857			0.989287	−	0.145981i	$-0.0466339\pi$
$331$	35.9970			1.97857			0.989287	+	0.145981i	$0.0466339\pi$
$332$	−24.4771	−	7.95310i	−1.34336	−	0.436483i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.66132	+	2.28661i	−0.0904979	+	0.124560i	−0.851865	−	0.523761i	$-0.824528\pi$
$337$	−1.66132	+	2.28661i	−0.0904979	+	0.124560i	0.761367	+	0.648321i	$0.224528\pi$
$338$	−10.8063	−	14.8736i	−0.587785	−	0.809017i
$339$	0.0714324	−	0.219846i	0.00387967	−	0.0119404i
$340$		0			0
$341$		0			0
$342$	−19.1819			−1.03724
$343$		0			0
$344$	29.1582	−	21.1847i	1.57210	−	1.14220i
$345$		0			0
$346$		0			0
$347$	5.37925	−	1.74782i	0.288773	−	0.0938281i	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	5.37925	−	1.74782i	0.288773	−	0.0938281i	0.449822	+	0.893118i	$0.351488\pi$
$348$		0			0
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−30.7905			−1.63881			−0.819405	−	0.573214i	$-0.805696\pi$
$353$	−30.7905			−1.63881			−0.819405	+	0.573214i	$0.805696\pi$
$354$	−0.693631	−	0.225374i	−0.0368661	−	0.0119785i
$355$		0			0
$356$	−28.9423	−	21.0278i	−1.53394	−	1.11447i
$357$		0			0
$358$	−32.8075	+	10.6598i	−1.73393	+	0.563388i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$		0			0
$361$	−0.453782	+	1.39660i	−0.0238833	+	0.0735051i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$367$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$368$		0			0
$369$	36.1535	−	11.7470i	1.88207	−	0.611523i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	11.0412	+	33.9814i	0.567150	+	1.74551i	0.661476	+	0.749966i	$0.269930\pi$
$379$	11.0412	+	33.9814i	0.567150	+	1.74551i	−0.0943260	+	0.995541i	$0.530070\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$383$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$384$			0.503163i			0.0256769i
$385$		0			0
$386$	24.0000			1.22157
$387$	−36.3328	−	11.8052i	−1.84690	−	0.600094i
$388$	−29.2301	+	21.2369i	−1.48394	+	1.07814i
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	−11.6376	+	16.0177i	−0.587785	+	0.809017i
$393$	−0.561749	−	0.773181i	−0.0283365	−	0.0390018i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−16.1803	−	11.7557i	−0.809017	−	0.587785i
$401$	5.69240	+	17.5194i	0.284265	+	0.874878i	0.986618	+	0.163049i	$0.0521329\pi$
$401$	5.69240	+	17.5194i	0.284265	+	0.874878i	−0.702353	+	0.711829i	$0.747867\pi$
$402$	0.741506	−	0.240930i	0.0369829	−	0.0120165i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.497915			−0.0246504
$409$	−32.2799	−	10.4884i	−1.59614	−	0.518617i	−0.629991	−	0.776603i	$-0.716941\pi$
$409$	−32.2799	−	10.4884i	−1.59614	−	0.518617i	−0.966149	+	0.257985i	$0.916941\pi$
$410$		0			0
$411$	0.653187	+	0.474568i	0.0322194	+	0.0234087i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	0.377372i		−	0.0184800i
$418$		0			0
$419$	−36.1749			−1.76726			−0.883630	−	0.468186i	$-0.844908\pi$
$419$	−36.1749			−1.76726			−0.883630	+	0.468186i	$0.844908\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$	−14.1473	−	10.2786i	−0.688681	−	0.500356i
$423$		0			0
$424$		0			0
$425$	11.6331	−	16.0116i	0.564287	−	0.776675i
$426$		0			0
$427$		0			0
$428$			24.9820i			1.20755i
$429$		0			0
$430$		0			0
$431$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$431$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$432$	0.863236	−	0.627178i	0.0415325	−	0.0301751i
$433$	3.55751	+	2.58468i	0.170963	+	0.124212i	0.669976	−	0.742382i	$-0.266304\pi$
$433$	3.55751	+	2.58468i	0.170963	+	0.124212i	−0.499014	+	0.866594i	$0.666304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.243994	+	0.750938i	−0.0116585	+	0.0358812i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	20.9862			0.999341
$442$		0			0
$443$	−28.8344	+	20.9494i	−1.36996	+	0.995335i	−0.372221	+	0.928144i	$0.621404\pi$
$443$	−28.8344	+	20.9494i	−1.36996	+	0.995335i	−0.997740	+	0.0671913i	$0.978596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.34814	−	7.22682i	0.110815	−	0.341055i	−0.880236	−	0.474536i	$-0.842616\pi$
$449$	2.34814	−	7.22682i	0.110815	−	0.341055i	0.991051	+	0.133482i	$0.0426157\pi$
$450$			21.1992i			0.999341i
$451$		0			0
$452$	−10.3953			−0.488956
$453$		0			0
$454$	−33.6438	+	24.4436i	−1.57898	+	1.14720i
$455$		0			0
$456$	−0.175863	−	0.541250i	−0.00823553	−	0.0253464i
$457$	−11.5806	+	3.76275i	−0.541716	+	0.176014i	−0.567078	−	0.823664i	$-0.691926\pi$
$457$	−11.5806	+	3.76275i	−0.541716	+	0.176014i	0.0253618	+	0.999678i	$0.491926\pi$
$458$		0			0
$459$	0.620635	+	0.854231i	0.0289688	+	0.0398721i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	−14.9389	−	10.8537i	−0.692031	−	0.502790i
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	0.899123	+	0.437695i	$0.144205\pi$
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	−0.470135	+	0.882594i	$0.655795\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$			32.7981i			1.50965i
$473$		0			0
$474$		0			0
$475$	21.5139	+	6.99029i	0.987125	+	0.320736i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$479$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$480$		0			0
$481$		0			0
$482$	−13.0981	+	40.3118i	−0.596602	+	1.83615i
$483$		0			0
$484$		0			0
$485$		0			0
$486$	−1.61364	−	0.524304i	−0.0731963	−	0.0237829i
$487$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$487$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$488$		0			0
$489$	0.324227	+	0.997869i	0.0146621	+	0.0451252i
$490$		0			0
$491$	−7.78566	+	10.7160i	−0.351362	+	0.483608i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−7.78566	+	10.7160i	−0.351362	+	0.483608i	0.596355	+	0.802721i	$0.296615\pi$
$492$	0.662920	+	0.912432i	0.0298868	+	0.0411356i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.654788	+	0.475731i	−0.0293417	+	0.0213180i
$499$	−29.3381	−	21.3154i	−1.31335	−	0.954207i	−0.999990	−	0.00457310i	$-0.998544\pi$
$499$	−29.3381	−	21.3154i	−1.31335	−	0.954207i	−0.313363	−	0.949633i	$-0.601456\pi$
$500$		0			0
$501$		0			0
$502$	−4.98752	+	6.86474i	−0.222604	+	0.306388i
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.578159			−0.0256769
$508$		0			0
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	21.5200	−	6.99226i	0.951057	−	0.309017i
$513$	−0.709371	+	0.976365i	−0.0313195	+	0.0431076i
$514$	−14.6471	−	20.1600i	−0.646056	−	0.889219i
$515$		0			0
$516$		−	1.13342i		−	0.0498961i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−33.3200	−	24.2084i	−1.45978	−	1.06059i	−0.983421	−	0.181337i	$-0.941958\pi$
$521$	−33.3200	−	24.2084i	−1.45978	−	1.06059i	−0.476355	−	0.879253i	$-0.658042\pi$
$522$		0			0
$523$	26.8900	−	8.73710i	1.17582	−	0.382047i	0.345007	−	0.938600i	$-0.387876\pi$
$523$	26.8900	−	8.73710i	1.17582	−	0.382047i	0.830812	+	0.556553i	$0.187876\pi$
$524$	−25.2620	+	34.7702i	−1.10358	+	1.51894i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	28.1252	−	20.4342i	1.22053	−	0.886767i
$532$		0			0
$533$		0			0
$534$	−1.06997	+	0.347653i	−0.0463020	+	0.0150444i
$535$		0			0
$536$	−20.6088	−	28.3656i	−0.890165	−	1.22521i
$537$	−0.335227	+	1.03172i	−0.0144661	+	0.0445221i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$		0			0
$543$		0			0
$544$	6.91932	+	21.2955i	0.296663	+	0.913036i
$545$		0			0
$546$		0			0
$547$	−27.2560	−	37.5147i	−1.16538	−	1.60401i	−0.688969	−	0.724791i	$-0.741936\pi$
$547$	−27.2560	−	37.5147i	−1.16538	−	1.60401i	−0.476414	−	0.879221i	$-0.658064\pi$
$548$	11.2199	−	34.5313i	0.479290	−	1.47510i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−16.1400	+	5.24419i	−0.684487	+	0.222403i
$557$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$557$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−17.3981			−0.733895
$563$	−11.5208	−	3.74332i	−0.485542	−	0.157762i	0.0560088	−	0.998430i	$-0.482163\pi$
$563$	−11.5208	−	3.74332i	−0.485542	−	0.157762i	−0.541551	+	0.840668i	$0.682163\pi$
$564$		0			0
$565$		0			0
$566$	−11.1246	−	34.2380i	−0.467602	−	1.43913i
$567$		0			0
$568$		0			0
$569$	27.5887	+	37.9725i	1.15658	+	1.59189i	0.723130	+	0.690712i	$0.242703\pi$
$569$	27.5887	+	37.9725i	1.15658	+	1.59189i	0.433447	+	0.901179i	$0.357297\pi$
$570$		0			0
$571$		−	42.4264i		−	1.77549i	−0.460336	−	0.887745i	$-0.652271\pi$
$571$		−	42.4264i		−	1.77549i	0.460336	−	0.887745i	$-0.347729\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−19.4036	−	14.0975i	−0.808484	−	0.587398i
$577$	13.2218	+	40.6924i	0.550429	+	1.69405i	0.707719	+	0.706494i	$0.249724\pi$
$577$	13.2218	+	40.6924i	0.550429	+	1.69405i	−0.157290	+	0.987552i	$0.550276\pi$
$578$	1.79162	−	0.582131i	0.0745214	−	0.0242135i
$579$	0.443628	−	0.610601i	0.0184365	−	0.0253757i
$580$		0			0
$581$		0			0
$582$			1.13622i			0.0470978i
$583$		0			0
$584$	35.5078			1.46932
$585$		0			0
$586$		0			0
$587$	38.4963	+	27.9692i	1.58891	+	1.15441i	0.905474	+	0.424402i	$0.139516\pi$
$587$	38.4963	+	27.9692i	1.58891	+	1.15441i	0.683437	+	0.730010i	$0.260484\pi$
$588$	0.192404	+	0.592159i	0.00793461	+	0.0244202i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			31.1035i			1.27727i	0.769510	+	0.638634i	$0.220500\pi$
$593$			31.1035i			1.27727i	−0.769510	+	0.638634i	$0.779500\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$	−0.598171	+	0.194357i	−0.0244202	+	0.00793461i
$601$	7.82263	−	10.7669i	0.319092	−	0.439192i	−0.619098	−	0.785314i	$-0.712502\pi$
$601$	7.82263	−	10.7669i	0.319092	−	0.439192i	0.938190	+	0.346122i	$0.112502\pi$
$602$		0			0
$603$	−11.4844	+	35.3452i	−0.467679	+	1.43937i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$607$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$608$	−20.7050	+	15.0431i	−0.839699	+	0.610077i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	13.9505	−	19.2012i	0.563915	−	0.776163i
$613$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$613$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$614$	−5.73363	+	17.6463i	−0.231391	+	0.712147i
$615$		0			0
$616$		0			0
$617$	28.3894			1.14291			0.571457	−	0.820632i	$-0.306378\pi$
$617$	28.3894			1.14291			0.571457	+	0.820632i	$0.306378\pi$
$618$		0			0
$619$	−39.1438	+	28.4396i	−1.57332	+	1.14308i	−0.649434	+	0.760418i	$0.724994\pi$
$619$	−39.1438	+	28.4396i	−1.57332	+	1.14308i	−0.923887	+	0.382667i	$0.875006\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$		−	41.2806i		−	1.64990i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		0			0
$633$	−0.523012	+	0.169937i	−0.0207879	+	0.00675439i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.0394	+	10.2002i	−0.554522	+	0.402884i	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−14.0394	+	10.2002i	−0.554522	+	0.402884i	0.274928	+	0.961465i	$0.411346\pi$
$642$	0.635586	+	0.461780i	0.0250846	+	0.0182250i
$643$	−10.9588	−	33.7276i	−0.432172	−	1.33009i	−0.895957	−	0.444140i	$-0.853509\pi$
$643$	−10.9588	−	33.7276i	−0.432172	−	1.33009i	0.463786	−	0.885948i	$-0.346491\pi$
$644$		0			0
$645$		0			0
$646$	−14.8861	−	20.4890i	−0.585688	−	0.806130i
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$			25.4055i			0.998023i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	38.1725	−	27.7340i	1.49495	−	1.08615i
$653$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$653$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$654$		0			0
$655$		0			0
$656$	29.8117	−	41.0324i	1.16395	−	1.60204i
$657$	−22.1224	−	30.4489i	−0.863077	−	1.18792i
$658$		0			0
$659$			2.26047i			0.0880555i	0.999030	+	0.0440278i	$0.0140190\pi$
$659$			2.26047i			0.0880555i	−0.999030	+	0.0440278i	$0.985981\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	−48.4159	−	15.7313i	−1.88174	−	0.611413i
$663$		0			0
$664$	29.4460	+	21.3938i	1.14273	+	0.830240i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−5.91748	−	1.92271i	−0.228102	−	0.0741149i	0.192736	−	0.981251i	$-0.438264\pi$
$673$	−5.91748	−	1.92271i	−0.228102	−	0.0741149i	−0.420838	+	0.907136i	$0.638264\pi$
$674$	3.23376	−	2.34946i	0.124560	−	0.0904979i
$675$	1.07905	+	0.783972i	0.0415325	+	0.0301751i
$676$	8.03444	+	24.7275i	0.309017	+	0.951057i
$677$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$677$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$678$	−0.192153	+	0.264475i	−0.00737958	+	0.0101571i
$679$		0			0
$680$		0			0
$681$			1.30778i			0.0501144i
$682$		0			0
$683$	−42.0000			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$684$	25.7997	+	8.38281i	0.986474	+	0.320525i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−48.4757	+	15.7507i	−1.84812	+	0.600490i
$689$		0			0
$690$		0			0
$691$	3.08868	−	9.50597i	0.117499	−	0.361624i	−0.874961	−	0.484193i	$-0.839113\pi$
$691$	3.08868	−	9.50597i	0.117499	−	0.361624i	0.992460	+	0.122569i	$0.0391133\pi$
$692$		0			0
$693$		0			0
$694$	−7.99890			−0.303634
$695$		0			0
$696$		0			0
$697$	40.6043	+	29.5008i	1.53800	+	1.11742i
$698$		0			0
$699$	−0.552276	+	0.179445i	−0.0208890	+	0.00678724i
$700$		0			0
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	41.4131	+	13.4559i	1.55860	+	0.506420i
$707$		0			0
$708$	0.834439	+	0.606256i	0.0313602	+	0.0227845i
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$		0			0
$712$	29.7378	+	40.9306i	1.11447	+	1.53394i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	48.7845			1.82316
$717$		0			0
$718$		0			0
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$		0			0
$722$	1.22067	−	1.68011i	0.0454286	−	0.0625272i
$723$	0.783490	+	1.07838i	0.0291383	+	0.0401054i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	21.7571	−	15.8075i	0.805818	−	0.585461i
$730$		0			0
$731$	−15.5864	−	47.9700i	−0.576484	−	1.77424i
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−53.7599			−1.97893
$739$	−18.2845	−	5.94099i	−0.672605	−	0.218543i	−0.0472504	−	0.998883i	$-0.515046\pi$
$739$	−18.2845	−	5.94099i	−0.672605	−	0.218543i	−0.625355	+	0.780340i	$0.715046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$743$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	38.5797i		−	1.41156i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$	0.0824589	+	0.253782i	0.00300497	+	0.00924834i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$757$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$758$		−	50.5301i		−	1.83534i
$759$		0			0
$760$		0			0
$761$	52.1685	+	16.9506i	1.89111	+	0.614457i	0.978749	+	0.205061i	$0.0657392\pi$
$761$	52.1685	+	16.9506i	1.89111	+	0.614457i	0.912356	+	0.409397i	$0.134261\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.219890	−	0.676753i	0.00793461	−	0.0244202i
$769$			50.9117i			1.83592i	0.396670	+	0.917961i	$0.370166\pi$
$769$			50.9117i			1.83592i	−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	−0.783649			−0.0282224
$772$	−32.2799	−	10.4884i	−1.16178	−	0.377485i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	43.7084	+	31.7560i	1.57107	+	1.14145i
$775$		0			0
$776$	48.5953	−	15.7896i	1.74447	−	0.566813i
$777$		0			0
$778$		0			0
$779$	−17.7269	+	54.5579i	−0.635134	+	1.95474i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	22.6525	−	16.4580i	0.809017	−	0.587785i
$785$		0			0
$786$	0.417658	+	1.28542i	0.0148974	+	0.0458494i
$787$	−52.7067	+	17.1254i	−1.87879	+	0.610456i	−0.891154	+	0.453701i	$0.850103\pi$
$787$	−52.7067	+	17.1254i	−1.87879	+	0.610456i	−0.987638	+	0.156755i	$0.949897\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	16.6251	+	22.8825i	0.587785	+	0.809017i
$801$	16.5715	−	51.0019i	0.585526	−	1.80206i
$802$		−	26.0512i		−	0.919901i
$803$		0			0
$804$	−1.10261			−0.0388862
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.0521	+	7.16517i	−0.775312	+	0.251914i	−0.669837	−	0.742508i	$-0.733636\pi$
$809$	−22.0521	+	7.16517i	−0.775312	+	0.251914i	−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	−7.04628	−	9.69837i	−0.247428	−	0.340556i	0.667180	−	0.744896i	$-0.267501\pi$
$811$	−7.04628	−	9.69837i	−0.247428	−	0.340556i	−0.914609	+	0.404340i	$0.867501\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.669694	+	0.217597i	0.0234440	+	0.00761741i
$817$	46.6399	−	33.8859i	1.63173	−	1.18552i
$818$	38.8328	+	28.2137i	1.35776	+	0.986469i
$819$		0			0
$820$		0			0
$821$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$821$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$822$	−0.671141	−	0.923746i	−0.0234087	−	0.0322194i
$823$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$823$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	43.0247	+	13.9796i	1.49611	+	0.486117i	0.938882	−	0.344239i	$-0.111863\pi$
$827$	43.0247	+	13.9796i	1.49611	+	0.486117i	0.557233	+	0.830356i	$0.311863\pi$
$828$		0			0
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.2863	+	22.4162i	0.564287	+	0.776675i
$834$	−0.164918	+	0.507565i	−0.00571064	+	0.0175755i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	48.6551	+	15.8090i	1.68076	+	0.546113i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$		0			0
$843$	−0.321595	+	0.442638i	−0.0110763	+	0.0152453i
$844$	14.5362	+	20.0073i	0.500356	+	0.688681i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.07671	−	0.349843i	−0.0369525	−	0.0120066i
$850$	−22.6438	+	16.4517i	−0.776675	+	0.564287i
$851$		0			0
$852$		0			0
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$	10.9175	−	33.6007i	0.373154	−	1.14845i
$857$			13.4344i			0.458912i	0.973319	+	0.229456i	$0.0736947\pi$
$857$			13.4344i			0.458912i	−0.973319	+	0.229456i	$0.926305\pi$
$858$		0			0
$859$	25.9930			0.886869			0.443434	−	0.896307i	$-0.353760\pi$
$859$	25.9930			0.886869			0.443434	+	0.896307i	$0.353760\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$863$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$864$	−1.43514	+	0.466304i	−0.0488243	+	0.0158640i
$865$		0			0
$866$	−3.65529	−	5.03107i	−0.124212	−	0.170963i
$867$	0.0183067	−	0.0563422i	0.000621728	−	0.00191348i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−43.8163	−	31.8344i	−1.48296	−	1.07743i
$874$		0			0
$875$		0			0
$876$	0.656344	−	0.903380i	0.0221758	−	0.0305224i
$877$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.6878			0.629610			0.314805	−	0.949156i	$-0.398061\pi$
$881$	18.6878			0.629610			0.314805	+	0.949156i	$0.398061\pi$
$882$	−28.2263	−	9.17129i	−0.950429	−	0.308813i
$883$	29.5540	−	21.4722i	0.994570	−	0.722597i	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	29.5540	−	21.4722i	0.994570	−	0.722597i	0.960917	+	0.276836i	$0.0892860\pi$
$884$		0			0
$885$		0			0
$886$	47.9373	−	15.5758i	1.61049	−	0.523279i
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−6.31647	+	8.69388i	−0.210783	+	0.290118i
$899$		0			0
$900$	9.26440	−	28.5129i	0.308813	−	0.950429i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	13.9817	+	4.54293i	0.465024	+	0.151096i
$905$		0			0
$906$		0			0
$907$	−18.4112	−	56.6640i	−0.611335	−	1.88150i	−0.445313	−	0.895375i	$-0.646908\pi$
$907$	−18.4112	−	56.6640i	−0.611335	−	1.88150i	−0.166022	−	0.986122i	$-0.553092\pi$
$908$	55.9330	−	18.1737i	1.85620	−	0.603117i
$909$		0			0
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$			0.804834i			0.0266507i
$913$		0			0
$914$	17.2202			0.569594
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.461440	−	1.42017i	−0.0152298	−	0.0468725i
$919$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$919$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$920$		0			0
$921$	0.342969	+	0.472057i	0.0113012	+	0.0155548i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.4691	−	41.4536i	−0.441906	−	1.36005i	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−13.4691	−	41.4536i	−0.441906	−	1.36005i	0.443935	−	0.896059i	$-0.353582\pi$
$930$		0			0
$931$	−18.6148	+	25.6211i	−0.610077	+	0.839699i
$932$	15.3495	+	21.1268i	0.502790	+	0.692031i
$933$		0			0
$934$		−	42.4264i		−	1.38823i
$935$		0			0
$936$		0			0
$937$	−45.7159	−	14.8540i	−1.49347	−	0.485258i	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−45.7159	−	14.8540i	−1.49347	−	0.485258i	−0.938106	+	0.346348i	$0.887422\pi$
$938$		0			0
$939$	−1.05025	−	0.763050i	−0.0342736	−	0.0249012i
$940$		0			0
$941$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$941$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$		0			0
$944$	14.3333	−	44.1133i	0.466509	−	1.43577i
$945$		0			0
$946$		0			0
$947$	−60.3804			−1.96210			−0.981050	−	0.193757i	$-0.937933\pi$
$947$	−60.3804			−1.96210			−0.981050	+	0.193757i	$0.937933\pi$
$948$		0			0
$949$		0			0
$950$	−25.8813	−	18.8038i	−0.839699	−	0.610077i
$951$		0			0
$952$		0			0
$953$	7.00931	−	9.64749i	0.227054	−	0.312513i	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	7.00931	−	9.64749i	0.227054	−	0.312513i	0.907311	+	0.420461i	$0.138132\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−25.0795	−	18.2213i	−0.809017	−	0.587785i
$962$		0			0
$963$	−35.6155	+	11.5722i	−1.14769	+	0.372908i
$964$	35.2338	−	48.4952i	1.13480	−	1.56192i
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		0			0
$969$	−0.796439			−0.0255853
$970$		0			0
$971$	−43.6869	+	31.7404i	−1.40198	+	1.01860i	−0.407552	+	0.913182i	$0.633617\pi$
$971$	−43.6869	+	31.7404i	−1.40198	+	1.01860i	−0.994428	+	0.105416i	$0.966383\pi$
$972$	1.94121	+	1.41037i	0.0622645	+	0.0452378i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.85410	−	5.70634i	0.0593180	−	0.182562i	−0.917007	−	0.398871i	$-0.869402\pi$
$977$	1.85410	−	5.70634i	0.0593180	−	0.182562i	0.976325	+	0.216309i	$0.0694020\pi$
$978$		−	1.48382i		−	0.0474474i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	15.1548	−	11.0106i	0.483608	−	0.351362i
$983$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$983$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$984$	−0.492879	−	1.51692i	−0.0157124	−	0.0483578i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	−1.29517	+	0.940999i	−0.0411011	+	0.0298617i
$994$		0			0
$995$		0			0
$996$	1.08859	−	0.353704i	0.0344933	−	0.0112075i
$997$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$997$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$998$	30.1445	+	41.4903i	0.954207	+	1.31335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.k.c.475.1		8
8.3	odd	2	CM	968.2.k.c.475.1		8
11.2	odd	10		968.2.k.b.723.1		8
11.3	even	5		968.2.k.b.403.1		8
11.4	even	5		968.2.g.a.483.3		8
11.5	even	5		968.2.k.d.699.2		8
11.6	odd	10	inner	968.2.k.c.699.1		8
11.7	odd	10		968.2.g.a.483.7		8
11.8	odd	10		88.2.k.a.51.2	yes	8
11.9	even	5		88.2.k.a.19.2	✓	8
11.10	odd	2		968.2.k.d.475.2		8
33.8	even	10		792.2.bp.a.667.1		8
33.20	odd	10		792.2.bp.a.19.1		8
44.7	even	10		3872.2.g.b.1935.3		8
44.15	odd	10		3872.2.g.b.1935.4		8
44.19	even	10		352.2.s.a.271.1		8
44.31	odd	10		352.2.s.a.239.1		8
88.3	odd	10		968.2.k.b.403.1		8
88.19	even	10		88.2.k.a.51.2	yes	8
88.27	odd	10		968.2.k.d.699.2		8
88.29	odd	10		3872.2.g.b.1935.3		8
88.35	even	10		968.2.k.b.723.1		8
88.37	even	10		3872.2.g.b.1935.4		8
88.43	even	2		968.2.k.d.475.2		8
88.51	even	10		968.2.g.a.483.7		8
88.53	even	10		352.2.s.a.239.1		8
88.59	odd	10		968.2.g.a.483.3		8
88.75	odd	10		88.2.k.a.19.2	✓	8
88.83	even	10	inner	968.2.k.c.699.1		8
88.85	odd	10		352.2.s.a.271.1		8
264.107	odd	10		792.2.bp.a.667.1		8
264.251	even	10		792.2.bp.a.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.a.19.2	✓	8	11.9	even	5
88.2.k.a.19.2	✓	8	88.75	odd	10
88.2.k.a.51.2	yes	8	11.8	odd	10
88.2.k.a.51.2	yes	8	88.19	even	10
352.2.s.a.239.1		8	44.31	odd	10
352.2.s.a.239.1		8	88.53	even	10
352.2.s.a.271.1		8	44.19	even	10
352.2.s.a.271.1		8	88.85	odd	10
792.2.bp.a.19.1		8	33.20	odd	10
792.2.bp.a.19.1		8	264.251	even	10
792.2.bp.a.667.1		8	33.8	even	10
792.2.bp.a.667.1		8	264.107	odd	10
968.2.g.a.483.3		8	11.4	even	5
968.2.g.a.483.3		8	88.59	odd	10
968.2.g.a.483.7		8	11.7	odd	10
968.2.g.a.483.7		8	88.51	even	10
968.2.k.b.403.1		8	11.3	even	5
968.2.k.b.403.1		8	88.3	odd	10
968.2.k.b.723.1		8	11.2	odd	10
968.2.k.b.723.1		8	88.35	even	10
968.2.k.c.475.1		8	1.1	even	1	trivial
968.2.k.c.475.1		8	8.3	odd	2	CM
968.2.k.c.699.1		8	11.6	odd	10	inner
968.2.k.c.699.1		8	88.83	even	10	inner
968.2.k.d.475.2		8	11.10	odd	2
968.2.k.d.475.2		8	88.43	even	2
968.2.k.d.699.2		8	11.5	even	5
968.2.k.d.699.2		8	88.27	odd	10
3872.2.g.b.1935.3		8	44.7	even	10
3872.2.g.b.1935.3		8	88.29	odd	10
3872.2.g.b.1935.4		8	44.15	odd	10
3872.2.g.b.1935.4		8	88.37	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.k (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(-0.0359800 + 0.0261410i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.0598171 - 0.0194357i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(-0.926440 + 2.85129i) q^{9} -0.0889475 q^{12} +(1.23607 + 3.80423i) q^{16} +(-3.76454 + 1.22317i) q^{17} +(2.49212 - 3.43011i) q^{18} +(-2.65926 - 3.66016i) q^{19} +(0.119634 + 0.0388715i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-0.0824317 - 0.253699i) q^{27} -5.65685i q^{32} +5.59785 q^{34} +(-4.85090 + 3.52439i) q^{36} +(1.97715 + 6.08505i) q^{38} +(-7.45294 - 10.2581i) q^{41} +12.7426i q^{43} +(-0.143920 - 0.104564i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(6.72499 - 2.18508i) q^{50} +(0.103473 - 0.142419i) q^{51} +0.377248i q^{54} +(0.191361 + 0.0621769i) q^{57} +(-9.38125 - 6.81588i) q^{59} +(-2.47214 + 7.60845i) q^{64} +12.3962 q^{67} +(-7.52909 - 2.44635i) q^{68} +(8.06466 - 2.62037i) q^{72} +(-7.37900 + 10.1563i) q^{73} +(0.0687157 - 0.211485i) q^{75} -9.04842i q^{76} +(-7.26675 - 5.27961i) q^{81} +(5.54123 + 17.0542i) q^{82} +(-12.2386 + 3.97655i) q^{83} +(5.56872 - 17.1387i) q^{86} -17.8873 q^{89} +(0.147876 + 0.203534i) q^{96} +(-5.58246 + 17.1810i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 4 q^{4} - 12 q^{9} + 8 q^{12} - 8 q^{16} - 30 q^{17} - 10 q^{25} - 42 q^{27} + 16 q^{34} + 4 q^{36} + 36 q^{38} - 30 q^{41} + 24 q^{48} + 14 q^{49} + 10 q^{51} + 50 q^{57} + 12 q^{59} + 16 q^{64}+ \cdots - 20 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 + 4 * q^4 - 12 * q^9 + 8 * q^12 - 8 * q^16 - 30 * q^17 - 10 * q^25 - 42 * q^27 + 16 * q^34 + 4 * q^36 + 36 * q^38 - 30 * q^41 + 24 * q^48 + 14 * q^49 + 10 * q^51 + 50 * q^57 + 12 * q^59 + 16 * q^64 - 28 * q^67 - 60 * q^68 + 80 * q^72 + 10 * q^73 - 20 * q^75 - 48 * q^81 + 32 * q^82 + 24 * q^86 - 36 * q^89 + 80 * q^96 - 20 * q^97

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