LMFDB - Embedded newform 931.2.c.f.930.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(930,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("931.930");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.c (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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			930.10
Character	$\chi$	$=$	931.930
Dual form			931.2.c.f.930.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82908i q^{2} +0.702444 q^{3} -1.34552 q^{4} -2.40246i q^{5} -1.28482i q^{6} -1.19710i q^{8} -2.50657 q^{9} +O(q^{10})$	\(q-1.82908i q^{2} +0.702444 q^{3} -1.34552 q^{4} -2.40246i q^{5} -1.28482i q^{6} -1.19710i q^{8} -2.50657 q^{9} -4.39428 q^{10} +6.30517 q^{11} -0.945152 q^{12} +4.93162 q^{13} -1.68759i q^{15} -4.88062 q^{16} -4.48479i q^{17} +4.58471i q^{18} +(-4.24827 - 0.975794i) q^{19} +3.23255i q^{20} -11.5326i q^{22} +3.11584 q^{23} -0.840894i q^{24} -0.771805 q^{25} -9.02031i q^{26} -3.86806 q^{27} +9.51567i q^{29} -3.08674 q^{30} -7.76385 q^{31} +6.53282i q^{32} +4.42903 q^{33} -8.20303 q^{34} +3.37264 q^{36} -5.58124i q^{37} +(-1.78480 + 7.77041i) q^{38} +3.46419 q^{39} -2.87598 q^{40} -5.58388 q^{41} +4.27059 q^{43} -8.48371 q^{44} +6.02193i q^{45} -5.69911i q^{46} +5.67213i q^{47} -3.42836 q^{48} +1.41169i q^{50} -3.15032i q^{51} -6.63558 q^{52} -1.58695i q^{53} +7.07498i q^{54} -15.1479i q^{55} +(-2.98418 - 0.685441i) q^{57} +17.4049 q^{58} -2.93924 q^{59} +2.27069i q^{60} -6.15831i q^{61} +14.2007i q^{62} +2.18780 q^{64} -11.8480i q^{65} -8.10103i q^{66} +10.0170i q^{67} +6.03437i q^{68} +2.18871 q^{69} -4.82771i q^{71} +3.00061i q^{72} -8.50626i q^{73} -10.2085 q^{74} -0.542150 q^{75} +(5.71613 + 1.31295i) q^{76} -6.33626i q^{78} +7.30664i q^{79} +11.7255i q^{80} +4.80262 q^{81} +10.2133i q^{82} +3.15450i q^{83} -10.7745 q^{85} -7.81124i q^{86} +6.68423i q^{87} -7.54789i q^{88} +14.5937 q^{89} +11.0146 q^{90} -4.19242 q^{92} -5.45367 q^{93} +10.3748 q^{94} +(-2.34430 + 10.2063i) q^{95} +4.58895i q^{96} +5.33945 q^{97} -15.8043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 40 * q^4 + 40 * q^9	$ 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.82908i		−	1.29335i	−0.762765	−	0.646676i	$-0.776159\pi$
$2$		−	1.82908i		−	1.29335i	0.762765	−	0.646676i	$-0.223841\pi$
$3$	0.702444			0.405557			0.202778	−	0.979225i	$-0.435003\pi$
$3$	0.702444			0.405557			0.202778	+	0.979225i	$0.435003\pi$
$4$	−1.34552			−0.672759
$5$		−	2.40246i		−	1.07441i	−0.843451	−	0.537206i	$-0.819480\pi$
$5$		−	2.40246i		−	1.07441i	0.843451	−	0.537206i	$-0.180520\pi$
$6$		−	1.28482i		−	0.524527i
$7$		0			0
$7$		0			0
$8$		−	1.19710i		−	0.423238i
$9$	−2.50657			−0.835524
$10$	−4.39428			−1.38959
$11$	6.30517			1.90108			0.950539	−	0.310604i	$-0.100531\pi$
$11$	6.30517			1.90108			0.950539	+	0.310604i	$0.100531\pi$
$12$	−0.945152			−0.272842
$13$	4.93162			1.36779			0.683893	−	0.729583i	$-0.260286\pi$
$13$	4.93162			1.36779			0.683893	+	0.729583i	$0.260286\pi$
$14$		0			0
$15$		−	1.68759i		−	0.435735i
$16$	−4.88062			−1.22015
$17$		−	4.48479i		−	1.08772i	−0.839175	−	0.543861i	$-0.816962\pi$
$17$		−	4.48479i		−	1.08772i	0.839175	−	0.543861i	$-0.183038\pi$
$18$			4.58471i			1.08063i
$19$	−4.24827	−	0.975794i	−0.974621	−	0.223862i
$19$	−4.24827	−	0.975794i	−0.974621	−	0.223862i
$20$			3.23255i			0.722820i
$21$		0			0
$22$		−	11.5326i		−	2.45876i
$23$	3.11584			0.649698			0.324849	−	0.945766i	$-0.394687\pi$
$23$	3.11584			0.649698			0.324849	+	0.945766i	$0.394687\pi$
$24$		−	0.840894i		−	0.171647i
$25$	−0.771805			−0.154361
$26$		−	9.02031i		−	1.76903i
$27$	−3.86806			−0.744409
$28$		0			0
$29$			9.51567i			1.76702i	0.468416	+	0.883508i	$0.344825\pi$
$29$			9.51567i			1.76702i	−0.468416	+	0.883508i	$0.655175\pi$
$30$	−3.08674			−0.563558
$31$	−7.76385			−1.39443			−0.697214	−	0.716863i	$-0.745577\pi$
$31$	−7.76385			−1.39443			−0.697214	+	0.716863i	$0.745577\pi$
$32$			6.53282i			1.15485i
$33$	4.42903			0.770995
$34$	−8.20303			−1.40681
$35$		0			0
$36$	3.37264			0.562106
$37$		−	5.58124i		−	0.917550i	−0.888552	−	0.458775i	$-0.848288\pi$
$37$		−	5.58124i		−	0.917550i	0.888552	−	0.458775i	$-0.151712\pi$
$38$	−1.78480	+	7.77041i	−0.289533	+	1.26053i
$39$	3.46419			0.554714
$40$	−2.87598			−0.454732
$41$	−5.58388			−0.872056			−0.436028	−	0.899933i	$-0.643615\pi$
$41$	−5.58388			−0.872056			−0.436028	+	0.899933i	$0.643615\pi$
$42$		0			0
$43$	4.27059			0.651259			0.325630	−	0.945497i	$-0.394424\pi$
$43$	4.27059			0.651259			0.325630	+	0.945497i	$0.394424\pi$
$44$	−8.48371			−1.27897
$45$			6.02193i			0.897697i
$46$		−	5.69911i		−	0.840288i
$47$			5.67213i			0.827365i	0.910421	+	0.413683i	$0.135758\pi$
$47$			5.67213i			0.827365i	−0.910421	+	0.413683i	$0.864242\pi$
$48$	−3.42836			−0.494842
$49$		0			0
$50$			1.41169i			0.199643i
$51$		−	3.15032i		−	0.441133i
$52$	−6.63558			−0.920190
$53$		−	1.58695i		−	0.217985i	−0.994043	−	0.108992i	$-0.965238\pi$
$53$		−	1.58695i		−	0.217985i	0.994043	−	0.108992i	$-0.0347624\pi$
$54$			7.07498i			0.962782i
$55$		−	15.1479i		−	2.04254i
$56$		0			0
$57$	−2.98418	−	0.685441i	−0.395264	−	0.0907889i
$58$	17.4049			2.28537
$59$	−2.93924			−0.382657			−0.191328	−	0.981526i	$-0.561280\pi$
$59$	−2.93924			−0.382657			−0.191328	+	0.981526i	$0.561280\pi$
$60$			2.27069i			0.293145i
$61$		−	6.15831i		−	0.788490i	−0.919005	−	0.394245i	$-0.871006\pi$
$61$		−	6.15831i		−	0.788490i	0.919005	−	0.394245i	$-0.128994\pi$
$62$			14.2007i			1.80349i
$63$		0			0
$64$	2.18780			0.273475
$65$		−	11.8480i		−	1.46956i
$66$		−	8.10103i		−	0.997168i
$67$			10.0170i			1.22377i	0.790945	+	0.611887i	$0.209589\pi$
$67$			10.0170i			1.22377i	−0.790945	+	0.611887i	$0.790411\pi$
$68$			6.03437i			0.731775i
$69$	2.18871			0.263489
$70$		0			0
$71$		−	4.82771i		−	0.572943i	−0.958089	−	0.286472i	$-0.907518\pi$
$71$		−	4.82771i		−	0.572943i	0.958089	−	0.286472i	$-0.0924824\pi$
$72$			3.00061i			0.353625i
$73$		−	8.50626i		−	0.995583i	−0.867297	−	0.497791i	$-0.834144\pi$
$73$		−	8.50626i		−	0.995583i	0.867297	−	0.497791i	$-0.165856\pi$
$74$	−10.2085			−1.18672
$75$	−0.542150			−0.0626021
$76$	5.71613	+	1.31295i	0.655685	+	0.150605i
$77$		0			0
$78$		−	6.33626i		−	0.717441i
$79$			7.30664i			0.822061i	0.911622	+	0.411030i	$0.134831\pi$
$79$			7.30664i			0.822061i	−0.911622	+	0.411030i	$0.865169\pi$
$80$			11.7255i			1.31095i
$81$	4.80262			0.533624
$82$			10.2133i			1.12788i
$83$			3.15450i			0.346251i	0.984900	+	0.173126i	$0.0553867\pi$
$83$			3.15450i			0.346251i	−0.984900	+	0.173126i	$0.944613\pi$
$84$		0			0
$85$	−10.7745			−1.16866
$86$		−	7.81124i		−	0.842307i
$87$			6.68423i			0.716625i
$88$		−	7.54789i		−	0.804608i
$89$	14.5937			1.54693			0.773465	−	0.633839i	$-0.218522\pi$
$89$	14.5937			1.54693			0.773465	+	0.633839i	$0.218522\pi$
$90$	11.0146			1.16104
$91$		0			0
$92$	−4.19242			−0.437090
$93$	−5.45367			−0.565519
$94$	10.3748			1.07007
$95$	−2.34430	+	10.2063i	−0.240520	+	1.04714i
$96$			4.58895i			0.468357i
$97$	5.33945			0.542139			0.271069	−	0.962560i	$-0.412623\pi$
$97$	5.33945			0.542139			0.271069	+	0.962560i	$0.412623\pi$
$98$		0			0
$99$	−15.8043			−1.58840
$100$	1.03848			0.103848
$101$			5.96768i			0.593806i	0.954908	+	0.296903i	$0.0959538\pi$
$101$			5.96768i			0.593806i	−0.954908	+	0.296903i	$0.904046\pi$
$102$	−5.76217			−0.570540
$103$	5.35313			0.527459			0.263730	−	0.964597i	$-0.415047\pi$
$103$	5.35313			0.527459			0.263730	+	0.964597i	$0.415047\pi$
$104$		−	5.90363i		−	0.578898i
$105$		0			0
$106$	−2.90265			−0.281931
$107$		−	9.16077i		−	0.885605i	−0.896619	−	0.442803i	$-0.853984\pi$
$107$		−	9.16077i		−	0.885605i	0.896619	−	0.442803i	$-0.146016\pi$
$108$	5.20455			0.500808
$109$		−	4.03186i		−	0.386182i	−0.981181	−	0.193091i	$-0.938149\pi$
$109$		−	4.03186i		−	0.386182i	0.981181	−	0.193091i	$-0.0618513\pi$
$110$	−27.7067			−2.64173
$111$		−	3.92051i		−	0.372119i
$112$		0			0
$113$			10.3750i			0.976002i	0.872843	+	0.488001i	$0.162274\pi$
$113$			10.3750i			0.976002i	−0.872843	+	0.488001i	$0.837726\pi$
$114$	−1.25372	+	5.45828i	−0.117422	+	0.511215i
$115$		−	7.48568i		−	0.698043i
$116$		−	12.8035i		−	1.18878i
$117$	−12.3615			−1.14282
$118$			5.37610i			0.494910i
$119$		0			0
$120$	−2.02021			−0.184419
$121$	28.7551			2.61410
$122$	−11.2640			−1.01980
$123$	−3.92237			−0.353668
$124$	10.4464			0.938114
$125$		−	10.1581i		−	0.908565i
$126$		0			0
$127$		−	4.67466i		−	0.414809i	−0.978255	−	0.207404i	$-0.933498\pi$
$127$		−	4.67466i		−	0.414809i	0.978255	−	0.207404i	$-0.0665016\pi$
$128$			9.06400i			0.801152i
$129$	2.99985			0.264122
$130$	−21.6709			−1.90066
$131$			14.2128i			1.24178i	0.783897	+	0.620891i	$0.213229\pi$
$131$			14.2128i			1.24178i	−0.783897	+	0.620891i	$0.786771\pi$
$132$	−5.95934			−0.518694
$133$		0			0
$134$	18.3219			1.58277
$135$			9.29285i			0.799802i
$136$	−5.36873			−0.460365
$137$	9.75993			0.833847			0.416924	−	0.908942i	$-0.363108\pi$
$137$	9.75993			0.833847			0.416924	+	0.908942i	$0.363108\pi$
$138$		−	4.00331i		−	0.340784i
$139$			10.6947i			0.907112i	0.891228	+	0.453556i	$0.149845\pi$
$139$			10.6947i			0.907112i	−0.891228	+	0.453556i	$0.850155\pi$
$140$		0			0
$141$			3.98436i			0.335543i
$142$	−8.83024			−0.741017
$143$	31.0947			2.60027
$144$	12.2336			1.01947
$145$	22.8610			1.89850
$146$	−15.5586			−1.28764
$147$		0			0
$148$			7.50966i			0.617290i
$149$	2.39202			0.195962			0.0979809	−	0.995188i	$-0.468762\pi$
$149$	2.39202			0.195962			0.0979809	+	0.995188i	$0.468762\pi$
$150$			0.991634i			0.0809666i
$151$			17.9334i			1.45940i	0.683770	+	0.729698i	$0.260339\pi$
$151$			17.9334i			1.45940i	−0.683770	+	0.729698i	$0.739661\pi$
$152$	−1.16812	+	5.08560i	−0.0947470	+	0.412496i
$153$			11.2415i			0.908818i
$154$		0			0
$155$			18.6523i			1.49819i
$156$	−4.66113			−0.373189
$157$			5.83904i			0.466006i	0.972476	+	0.233003i	$0.0748552\pi$
$157$			5.83904i			0.466006i	−0.972476	+	0.233003i	$0.925145\pi$
$158$	13.3644			1.06321
$159$		−	1.11475i		−	0.0884050i
$160$	15.6948			1.24079
$161$		0			0
$162$		−	8.78435i		−	0.690164i
$163$	−1.72212			−0.134887			−0.0674434	−	0.997723i	$-0.521484\pi$
$163$	−1.72212			−0.134887			−0.0674434	+	0.997723i	$0.521484\pi$
$164$	7.51322			0.586684
$165$		−	10.6406i		−	0.828366i
$166$	5.76982			0.447825
$167$	3.62838			0.280773			0.140386	−	0.990097i	$-0.455166\pi$
$167$	3.62838			0.280773			0.140386	+	0.990097i	$0.455166\pi$
$168$		0			0
$169$	11.3209			0.870837
$170$			19.7074i			1.51149i
$171$	10.6486	+	2.44590i	0.814319	+	0.187042i
$172$	−5.74616			−0.438141
$173$	12.3904			0.942028			0.471014	−	0.882126i	$-0.343888\pi$
$173$	12.3904			0.942028			0.471014	+	0.882126i	$0.343888\pi$
$174$	12.2260			0.926848
$175$		0			0
$176$	−30.7731			−2.31961
$177$	−2.06465			−0.155189
$178$		−	26.6930i		−	2.00073i
$179$		−	14.5869i		−	1.09028i	−0.838345	−	0.545139i	$-0.816477\pi$
$179$		−	14.5869i		−	1.09028i	0.838345	−	0.545139i	$-0.183523\pi$
$180$		−	8.10262i		−	0.603934i
$181$	−7.73309			−0.574796			−0.287398	−	0.957811i	$-0.592790\pi$
$181$	−7.73309			−0.574796			−0.287398	+	0.957811i	$0.592790\pi$
$182$		0			0
$183$		−	4.32587i		−	0.319777i
$184$		−	3.72996i		−	0.274977i
$185$	−13.4087			−0.985827
$186$			9.97518i			0.731416i
$187$		−	28.2774i		−	2.06785i
$188$		−	7.63195i		−	0.556617i
$189$		0			0
$190$	18.6681	+	4.28791i	1.35433	+	0.311078i
$191$	−2.01018			−0.145452			−0.0727259	−	0.997352i	$-0.523170\pi$
$191$	−2.01018			−0.145452			−0.0727259	+	0.997352i	$0.523170\pi$
$192$	1.53681			0.110909
$193$		−	8.19687i		−	0.590024i	−0.955494	−	0.295012i	$-0.904676\pi$
$193$		−	8.19687i		−	0.590024i	0.955494	−	0.295012i	$-0.0953236\pi$
$194$		−	9.76626i		−	0.701176i
$195$		−	8.32257i		−	0.595992i
$196$		0			0
$197$	7.89898			0.562779			0.281390	−	0.959594i	$-0.409205\pi$
$197$	7.89898			0.562779			0.281390	+	0.959594i	$0.409205\pi$
$198$			28.9074i			2.05436i
$199$		−	27.0789i		−	1.91957i	−0.280731	−	0.959787i	$-0.590577\pi$
$199$		−	27.0789i		−	1.91957i	0.280731	−	0.959787i	$-0.409423\pi$
$200$			0.923926i			0.0653314i
$201$			7.03640i			0.496310i
$202$	10.9153			0.768000
$203$		0			0
$204$			4.23881i			0.296776i
$205$			13.4150i			0.936948i
$206$		−	9.79127i		−	0.682190i
$207$	−7.81008			−0.542838
$208$	−24.0693			−1.66891
$209$	−26.7861	−	6.15254i	−1.85283	−	0.425580i
$210$		0			0
$211$			6.00909i			0.413683i	0.978374	+	0.206842i	$0.0663185\pi$
$211$			6.00909i			0.413683i	−0.978374	+	0.206842i	$0.933682\pi$
$212$			2.13527i			0.146651i
$213$		−	3.39120i		−	0.232361i
$214$	−16.7557			−1.14540
$215$		−	10.2599i		−	0.699721i
$216$			4.63044i			0.315062i
$217$		0			0
$218$	−7.37458			−0.499469
$219$		−	5.97518i		−	0.403765i
$220$			20.3818i			1.37414i
$221$		−	22.1173i		−	1.48777i
$222$	−7.17091			−0.481280
$223$	15.9480			1.06796			0.533979	−	0.845498i	$-0.320696\pi$
$223$	15.9480			1.06796			0.533979	+	0.845498i	$0.320696\pi$
$224$		0			0
$225$	1.93459			0.128972
$226$	18.9767			1.26231
$227$	2.85570			0.189539			0.0947696	−	0.995499i	$-0.469789\pi$
$227$	2.85570			0.189539			0.0947696	+	0.995499i	$0.469789\pi$
$228$	4.01526	+	0.922273i	0.265917	+	0.0610790i
$229$		−	16.3245i		−	1.07876i	−0.842064	−	0.539378i	$-0.818659\pi$
$229$		−	16.3245i		−	1.07876i	0.842064	−	0.539378i	$-0.181341\pi$
$230$	−13.6919			−0.902816
$231$		0			0
$232$	11.3912			0.747868
$233$	−26.2953			−1.72266			−0.861332	−	0.508043i	$-0.830369\pi$
$233$	−26.2953			−1.72266			−0.861332	+	0.508043i	$0.830369\pi$
$234$			22.6100i			1.47806i
$235$	13.6271			0.888931
$236$	3.95480			0.257436
$237$			5.13251i			0.333392i
$238$		0			0
$239$	9.33390			0.603760			0.301880	−	0.953346i	$-0.402386\pi$
$239$	9.33390			0.603760			0.301880	+	0.953346i	$0.402386\pi$
$240$			8.23650i			0.531664i
$241$	12.4870			0.804357			0.402178	−	0.915561i	$-0.368253\pi$
$241$	12.4870			0.804357			0.402178	+	0.915561i	$0.368253\pi$
$242$		−	52.5953i		−	3.38095i
$243$	14.9778			0.960823
$244$			8.28611i			0.530464i
$245$		0			0
$246$			7.17431i			0.457417i
$247$	−20.9509	−	4.81224i	−1.33307	−	0.306196i
$248$			9.29408i			0.590175i
$249$			2.21586i			0.140425i
$250$	−18.5799			−1.17509
$251$			1.31712i			0.0831356i	0.999136	+	0.0415678i	$0.0132353\pi$
$251$			1.31712i			0.0831356i	−0.999136	+	0.0415678i	$0.986765\pi$
$252$		0			0
$253$	19.6459			1.23513
$254$	−8.55030			−0.536494
$255$	−7.56851			−0.473958
$256$	20.9543			1.30965
$257$	−23.6155			−1.47309			−0.736546	−	0.676387i	$-0.763545\pi$
$257$	−23.6155			−1.47309			−0.736546	+	0.676387i	$0.763545\pi$
$258$		−	5.48696i		−	0.341603i
$259$		0			0
$260$			15.9417i			0.988663i
$261$		−	23.8517i		−	1.47638i
$262$	25.9964			1.60606
$263$	12.3695			0.762739			0.381369	−	0.924423i	$-0.375453\pi$
$263$	12.3695			0.762739			0.381369	+	0.924423i	$0.375453\pi$
$264$		−	5.30198i		−	0.326314i
$265$	−3.81258			−0.234205
$266$		0			0
$267$	10.2513			0.627368
$268$		−	13.4781i		−	0.823305i
$269$	15.8002			0.963355			0.481677	−	0.876349i	$-0.340028\pi$
$269$	15.8002			0.963355			0.481677	+	0.876349i	$0.340028\pi$
$270$	16.9973			1.03442
$271$			11.2306i			0.682209i	0.940025	+	0.341105i	$0.110801\pi$
$271$			11.2306i			0.682209i	−0.940025	+	0.341105i	$0.889199\pi$
$272$			21.8886i			1.32719i
$273$		0			0
$274$		−	17.8517i		−	1.07846i
$275$	−4.86636			−0.293453
$276$	−2.94494			−0.177265
$277$	−20.9827			−1.26073			−0.630365	−	0.776299i	$-0.717095\pi$
$277$	−20.9827			−1.26073			−0.630365	+	0.776299i	$0.717095\pi$
$278$	19.5614			1.17322
$279$	19.4606			1.16508
$280$		0			0
$281$		−	1.15404i		−	0.0688442i	−0.999407	−	0.0344221i	$-0.989041\pi$
$281$		−	1.15404i		−	0.0688442i	0.999407	−	0.0344221i	$-0.0109591\pi$
$282$	7.28769			0.433976
$283$		−	3.59035i		−	0.213424i	−0.994290	−	0.106712i	$-0.965968\pi$
$283$		−	3.59035i		−	0.213424i	0.994290	−	0.106712i	$-0.0340323\pi$
$284$			6.49577i			0.385453i
$285$	−1.64674	+	7.16936i	−0.0975446	+	0.424676i
$286$		−	56.8745i		−	3.36306i
$287$		0			0
$288$		−	16.3750i		−	0.964906i
$289$	−3.11336			−0.183139
$290$		−	41.8145i		−	2.45543i
$291$	3.75067			0.219868
$292$			11.4453i			0.669787i
$293$	10.8120			0.631644			0.315822	−	0.948818i	$-0.397720\pi$
$293$	10.8120			0.631644			0.315822	+	0.948818i	$0.397720\pi$
$294$		0			0
$295$			7.06141i			0.411131i
$296$	−6.68129			−0.388342
$297$	−24.3888			−1.41518
$298$		−	4.37519i		−	0.253448i
$299$	15.3661			0.888647
$300$	0.729473			0.0421162
$301$		0			0
$302$	32.8015			1.88751
$303$			4.19196i			0.240822i
$304$	20.7342	+	4.76248i	1.18919	+	0.273147i
$305$	−14.7951			−0.847163
$306$	20.5615			1.17542
$307$	−17.7811			−1.01482			−0.507411	−	0.861704i	$-0.669397\pi$
$307$	−17.7811			−1.01482			−0.507411	+	0.861704i	$0.669397\pi$
$308$		0			0
$309$	3.76027			0.213914
$310$	34.1165			1.93769
$311$			18.5198i			1.05016i	0.851052	+	0.525082i	$0.175965\pi$
$311$			18.5198i			1.05016i	−0.851052	+	0.525082i	$0.824035\pi$
$312$		−	4.14697i		−	0.234776i
$313$		−	6.41136i		−	0.362391i	−0.983447	−	0.181196i	$-0.942003\pi$
$313$		−	6.41136i		−	0.362391i	0.983447	−	0.181196i	$-0.0579967\pi$
$314$	10.6800			0.602709
$315$		0			0
$316$		−	9.83121i		−	0.553049i
$317$			7.64115i			0.429170i	0.976705	+	0.214585i	$0.0688399\pi$
$317$			7.64115i			0.429170i	−0.976705	+	0.214585i	$0.931160\pi$
$318$	−2.03895			−0.114339
$319$			59.9979i			3.35924i
$320$		−	5.25609i		−	0.293824i
$321$		−	6.43493i		−	0.359163i
$322$		0			0
$323$	−4.37623	+	19.0526i	−0.243500	+	1.06012i
$324$	−6.46201			−0.359000
$325$	−3.80625			−0.211133
$326$			3.14989i			0.174456i
$327$		−	2.83216i		−	0.156619i
$328$			6.68445i			0.369087i
$329$		0			0
$330$	−19.4624			−1.07137
$331$			13.0625i			0.717978i	0.933342	+	0.358989i	$0.116878\pi$
$331$			13.0625i			0.717978i	−0.933342	+	0.358989i	$0.883122\pi$
$332$		−	4.24444i		−	0.232944i
$333$			13.9898i			0.766635i
$334$		−	6.63659i		−	0.363138i
$335$	24.0655			1.31484
$336$		0			0
$337$		−	11.9819i		−	0.652698i	−0.945249	−	0.326349i	$-0.894182\pi$
$337$		−	11.9819i		−	0.652698i	0.945249	−	0.326349i	$-0.105818\pi$
$338$		−	20.7067i		−	1.12630i
$339$			7.28789i			0.395824i
$340$	14.4973			0.786228
$341$	−48.9523			−2.65092
$342$	4.47373	−	19.4771i	0.241912	−	1.05320i
$343$		0			0
$344$		−	5.11231i		−	0.275637i
$345$		−	5.25827i		−	0.283096i
$346$		−	22.6631i		−	1.21837i
$347$	−13.6416			−0.732318			−0.366159	−	0.930552i	$-0.619327\pi$
$347$	−13.6416			−0.732318			−0.366159	+	0.930552i	$0.619327\pi$
$348$		−	8.99376i		−	0.482116i
$349$			5.93607i			0.317750i	0.987299	+	0.158875i	$0.0507868\pi$
$349$			5.93607i			0.317750i	−0.987299	+	0.158875i	$0.949213\pi$
$350$		0			0
$351$	−19.0758			−1.01819
$352$			41.1905i			2.19546i
$353$			33.5050i			1.78329i	0.452735	+	0.891645i	$0.350448\pi$
$353$			33.5050i			1.78329i	−0.452735	+	0.891645i	$0.649552\pi$
$354$			3.77641i			0.200714i
$355$	−11.5984			−0.615577
$356$	−19.6361			−1.04071
$357$		0			0
$358$	−26.6806			−1.41011
$359$	18.7224			0.988133			0.494066	−	0.869424i	$-0.335510\pi$
$359$	18.7224			0.988133			0.494066	+	0.869424i	$0.335510\pi$
$360$	7.20884			0.379939
$361$	17.0957	+	8.29088i	0.899771	+	0.436362i
$362$			14.1444i			0.743413i
$363$	20.1989			1.06017
$364$		0			0
$365$	−20.4359			−1.06967
$366$	−7.91234			−0.413585
$367$			1.97130i			0.102901i	0.998676	+	0.0514506i	$0.0163845\pi$
$367$			1.97130i			0.102901i	−0.998676	+	0.0514506i	$0.983616\pi$
$368$	−15.2072			−0.792732
$369$	13.9964			0.728624
$370$			24.5255i			1.27502i
$371$		0			0
$372$	7.33801			0.380458
$373$		−	6.35335i		−	0.328964i	−0.986380	−	0.164482i	$-0.947405\pi$
$373$		−	6.35335i		−	0.328964i	0.986380	−	0.164482i	$-0.0525952\pi$
$374$	−51.7214			−2.67445
$375$		−	7.13547i		−	0.368474i
$376$	6.79009			0.350172
$377$			46.9277i			2.41690i
$378$		0			0
$379$		−	21.4992i		−	1.10434i	−0.833731	−	0.552171i	$-0.813800\pi$
$379$		−	21.4992i		−	1.10434i	0.833731	−	0.552171i	$-0.186200\pi$
$380$	3.15430	−	13.7328i	0.161812	−	0.704476i
$381$		−	3.28369i		−	0.168228i
$382$			3.67678i			0.188120i
$383$	31.5247			1.61084			0.805419	−	0.592706i	$-0.201940\pi$
$383$	31.5247			1.61084			0.805419	+	0.592706i	$0.201940\pi$
$384$			6.36696i			0.324913i
$385$		0			0
$386$	−14.9927			−0.763108
$387$	−10.7045			−0.544143
$388$	−7.18432			−0.364729
$389$	−31.9049			−1.61764			−0.808822	−	0.588053i	$-0.799895\pi$
$389$	−31.9049			−1.61764			−0.808822	+	0.588053i	$0.799895\pi$
$390$	−15.2226			−0.770827
$391$		−	13.9739i		−	0.706691i
$392$		0			0
$393$			9.98373i			0.503613i
$394$		−	14.4478i		−	0.727872i
$395$	17.5539			0.883232
$396$	21.2650			1.06861
$397$			27.1380i			1.36202i	0.732276	+	0.681008i	$0.238458\pi$
$397$			27.1380i			1.36202i	−0.732276	+	0.681008i	$0.761542\pi$
$398$	−49.5294			−2.48268
$399$		0			0
$400$	3.76689			0.188344
$401$		−	7.81064i		−	0.390045i	−0.980799	−	0.195022i	$-0.937522\pi$
$401$		−	7.81064i		−	0.390045i	0.980799	−	0.195022i	$-0.0624780\pi$
$402$	12.8701			0.641903
$403$	−38.2883			−1.90728
$404$		−	8.02962i		−	0.399488i
$405$		−	11.5381i		−	0.573332i
$406$		0			0
$407$		−	35.1906i		−	1.74434i
$408$	−3.77124			−0.186704
$409$	−23.2161			−1.14796			−0.573982	−	0.818868i	$-0.694602\pi$
$409$	−23.2161			−1.14796			−0.573982	+	0.818868i	$0.694602\pi$
$410$	24.5371			1.21180
$411$	6.85581			0.338172
$412$	−7.20273			−0.354853
$413$		0			0
$414$			14.2852i			0.702081i
$415$	7.57856			0.372017
$416$			32.2174i			1.57959i
$417$			7.51243i			0.367885i
$418$	−11.2535	+	48.9937i	−0.550425	+	2.39636i
$419$			12.8935i			0.629888i	0.949110	+	0.314944i	$0.101986\pi$
$419$			12.8935i			0.629888i	−0.949110	+	0.314944i	$0.898014\pi$
$420$		0			0
$421$		−	1.02878i		−	0.0501395i	−0.999686	−	0.0250698i	$-0.992019\pi$
$421$		−	1.02878i		−	0.0501395i	0.999686	−	0.0250698i	$-0.00798079\pi$
$422$	10.9911			0.535038
$423$		−	14.2176i		−	0.691283i
$424$	−1.89973			−0.0922593
$425$			3.46139i			0.167902i
$426$	−6.20275			−0.300524
$427$		0			0
$428$			12.3260i			0.595799i
$429$	21.8423			1.05456
$430$	−18.7662			−0.904985
$431$			2.17363i			0.104700i	0.998629	+	0.0523499i	$0.0166711\pi$
$431$			2.17363i			0.104700i	−0.998629	+	0.0523499i	$0.983329\pi$
$432$	18.8785			0.908293
$433$	−25.2490			−1.21339			−0.606694	−	0.794935i	$-0.707505\pi$
$433$	−25.2490			−1.21339			−0.606694	+	0.794935i	$0.707505\pi$
$434$		0			0
$435$	16.0586			0.769950
$436$			5.42494i			0.259807i
$437$	−13.2369	−	3.04042i	−0.633209	−	0.145443i
$438$	−10.9291			−0.522210
$439$	13.4247			0.640728			0.320364	−	0.947295i	$-0.396195\pi$
$439$	13.4247			0.640728			0.320364	+	0.947295i	$0.396195\pi$
$440$	−18.1335			−0.864481
$441$		0			0
$442$	−40.4542			−1.92421
$443$	13.8776			0.659345			0.329672	−	0.944095i	$-0.393062\pi$
$443$	13.8776			0.659345			0.329672	+	0.944095i	$0.393062\pi$
$444$			5.27512i			0.250346i
$445$		−	35.0608i		−	1.66204i
$446$		−	29.1701i		−	1.38124i
$447$	1.68026			0.0794736
$448$		0			0
$449$			31.9326i			1.50699i	0.657453	+	0.753495i	$0.271634\pi$
$449$			31.9326i			1.50699i	−0.657453	+	0.753495i	$0.728366\pi$
$450$		−	3.53850i		−	0.166807i
$451$	−35.2073			−1.65785
$452$		−	13.9598i		−	0.656614i
$453$			12.5972i			0.591867i
$454$		−	5.22328i		−	0.245141i
$455$		0			0
$456$	−0.820539	+	3.57235i	−0.0384253	+	0.167291i
$457$	−10.7551			−0.503102			−0.251551	−	0.967844i	$-0.580941\pi$
$457$	−10.7551			−0.503102			−0.251551	+	0.967844i	$0.580941\pi$
$458$	−29.8588			−1.39521
$459$			17.3475i			0.809710i
$460$			10.0721i			0.469615i
$461$		−	11.1460i		−	0.519119i	−0.965727	−	0.259559i	$-0.916423\pi$
$461$		−	11.1460i		−	0.519119i	0.965727	−	0.259559i	$-0.0835773\pi$
$462$		0			0
$463$	12.3281			0.572934			0.286467	−	0.958090i	$-0.407519\pi$
$463$	12.3281			0.572934			0.286467	+	0.958090i	$0.407519\pi$
$464$		−	46.4424i		−	2.15603i
$465$			13.1022i			0.607601i
$466$			48.0961i			2.22801i
$467$			32.5245i			1.50506i	0.658561	+	0.752528i	$0.271166\pi$
$467$			32.5245i			1.50506i	−0.658561	+	0.752528i	$0.728834\pi$
$468$	16.6326			0.768841
$469$		0			0
$470$		−	24.9249i		−	1.14970i
$471$			4.10160i			0.188992i
$472$			3.51856i			0.161955i
$473$	26.9268			1.23810
$474$	9.38774			0.431193
$475$	3.27884	+	0.753123i	0.150443	+	0.0345556i
$476$		0			0
$477$			3.97781i			0.182131i
$478$		−	17.0724i		−	0.780874i
$479$		−	4.74230i		−	0.216681i	−0.994114	−	0.108341i	$-0.965446\pi$
$479$		−	4.74230i		−	0.216681i	0.994114	−	0.108341i	$-0.0345537\pi$
$480$	11.0248			0.503209
$481$		−	27.5246i		−	1.25501i
$482$		−	22.8396i		−	1.04032i
$483$		0			0
$484$	−38.6905			−1.75866
$485$		−	12.8278i		−	0.582480i
$486$		−	27.3954i		−	1.24268i
$487$		−	18.9805i		−	0.860091i	−0.902807	−	0.430045i	$-0.858498\pi$
$487$		−	18.9805i		−	0.860091i	0.902807	−	0.430045i	$-0.141502\pi$
$488$	−7.37209			−0.333719
$489$	−1.20969			−0.0547043
$490$		0			0
$491$	−9.12580			−0.411842			−0.205921	−	0.978569i	$-0.566019\pi$
$491$	−9.12580			−0.411842			−0.205921	+	0.978569i	$0.566019\pi$
$492$	5.27762			0.237933
$493$	42.6758			1.92202
$494$	−8.80196	+	38.3207i	−0.396019	+	1.72413i
$495$			37.9693i			1.70659i
$496$	37.8924			1.70142
$497$		0			0
$498$	4.05298			0.181618
$499$	−17.3598			−0.777130			−0.388565	−	0.921421i	$-0.627029\pi$
$499$	−17.3598			−0.777130			−0.388565	+	0.921421i	$0.627029\pi$
$500$			13.6679i			0.611245i
$501$	2.54874			0.113869
$502$	2.40910			0.107524
$503$			33.3606i			1.48748i	0.668471	+	0.743739i	$0.266949\pi$
$503$			33.3606i			1.48748i	−0.668471	+	0.743739i	$0.733051\pi$
$504$		0			0
$505$	14.3371			0.637992
$506$		−	35.9338i		−	1.59745i
$507$	7.95229			0.353173
$508$			6.28984i			0.279066i
$509$	−40.2860			−1.78565			−0.892823	−	0.450407i	$-0.851279\pi$
$509$	−40.2860			−1.78565			−0.892823	+	0.450407i	$0.851279\pi$
$510$			13.8434i			0.612995i
$511$		0			0
$512$		−	20.1991i		−	0.892681i
$513$	16.4326	+	3.77443i	0.725516	+	0.166645i
$514$			43.1945i			1.90523i
$515$		−	12.8607i		−	0.566708i
$516$	−4.03636			−0.177691
$517$			35.7637i			1.57289i
$518$		0			0
$519$	8.70360			0.382046
$520$	−14.1832			−0.621975
$521$	−11.0512			−0.484162			−0.242081	−	0.970256i	$-0.577830\pi$
$521$	−11.0512			−0.484162			−0.242081	+	0.970256i	$0.577830\pi$
$522$	−43.6266			−1.90948
$523$	−22.6837			−0.991888			−0.495944	−	0.868355i	$-0.665178\pi$
$523$	−22.6837			−0.991888			−0.495944	+	0.868355i	$0.665178\pi$
$524$		−	19.1236i		−	0.835420i
$525$		0			0
$526$		−	22.6248i		−	0.986490i
$527$			34.8192i			1.51675i
$528$	−21.6164			−0.940733
$529$	−13.2915			−0.577893
$530$			6.97351i			0.302910i
$531$	7.36742			0.319719
$532$		0			0
$533$	−27.5376			−1.19279
$534$		−	18.7504i		−	0.811407i
$535$	−22.0084			−0.951505
$536$	11.9913			0.517947
$537$		−	10.2465i		−	0.442170i
$538$		−	28.8998i		−	1.24596i
$539$		0			0
$540$		−	12.5037i		−	0.538074i
$541$	−5.59979			−0.240754			−0.120377	−	0.992728i	$-0.538410\pi$
$541$	−5.59979			−0.240754			−0.120377	+	0.992728i	$0.538410\pi$
$542$	20.5416			0.882337
$543$	−5.43207			−0.233112
$544$	29.2984			1.25616
$545$	−9.68637			−0.414919
$546$		0			0
$547$			1.64738i			0.0704370i	0.999380	+	0.0352185i	$0.0112127\pi$
$547$			1.64738i			0.0704370i	−0.999380	+	0.0352185i	$0.988787\pi$
$548$	−13.1322			−0.560978
$549$			15.4362i			0.658802i
$550$			8.90094i			0.379537i
$551$	9.28533	−	40.4252i	0.395569	−	1.72217i
$552$		−	2.62009i		−	0.111519i
$553$		0			0
$554$			38.3790i			1.63057i
$555$	−9.41887			−0.399809
$556$		−	14.3899i		−	0.610268i
$557$	−24.6982			−1.04650			−0.523249	−	0.852180i	$-0.675280\pi$
$557$	−24.6982			−1.04650			−0.523249	+	0.852180i	$0.675280\pi$
$558$		−	35.5950i		−	1.50686i
$559$	21.0609			0.890783
$560$		0			0
$561$		−	19.8633i		−	0.838628i
$562$	−2.11082			−0.0890397
$563$	−11.7684			−0.495980			−0.247990	−	0.968763i	$-0.579770\pi$
$563$	−11.7684			−0.495980			−0.247990	+	0.968763i	$0.579770\pi$
$564$		−	5.36102i		−	0.225740i
$565$	24.9256			1.04863
$566$	−6.56701			−0.276032
$567$		0			0
$568$	−5.77923			−0.242491
$569$		−	23.5483i		−	0.987197i	−0.869690	−	0.493598i	$-0.835681\pi$
$569$		−	23.5483i		−	0.987197i	0.869690	−	0.493598i	$-0.164319\pi$
$570$	13.1133	+	3.01202i	0.549256	+	0.126160i
$571$	41.0220			1.71672			0.858358	−	0.513051i	$-0.171485\pi$
$571$	41.0220			1.71672			0.858358	+	0.513051i	$0.171485\pi$
$572$	−41.8385			−1.74935
$573$	−1.41204			−0.0589889
$574$		0			0
$575$	−2.40482			−0.100288
$576$	−5.48387			−0.228495
$577$		−	16.4682i		−	0.685579i	−0.939412	−	0.342790i	$-0.888628\pi$
$577$		−	16.4682i		−	0.685579i	0.939412	−	0.342790i	$-0.111372\pi$
$578$			5.69458i			0.236863i
$579$		−	5.75785i		−	0.239288i
$580$	−30.7599			−1.27724
$581$		0			0
$582$		−	6.86025i		−	0.284367i
$583$		−	10.0060i		−	0.414406i
$584$	−10.1828			−0.421368
$585$			29.6979i			1.22786i
$586$		−	19.7760i		−	0.816938i
$587$		−	16.9877i		−	0.701158i	−0.936533	−	0.350579i	$-0.885985\pi$
$587$		−	16.9877i		−	0.701158i	0.936533	−	0.350579i	$-0.114015\pi$
$588$		0			0
$589$	32.9829	+	7.57591i	1.35904	+	0.312160i
$590$	12.9159			0.531737
$591$	5.54860			0.228239
$592$			27.2399i			1.11955i
$593$			34.9474i			1.43512i	0.696499	+	0.717558i	$0.254740\pi$
$593$			34.9474i			1.43512i	−0.696499	+	0.717558i	$0.745260\pi$
$594$			44.6089i			1.83033i
$595$		0			0
$596$	−3.21851			−0.131835
$597$		−	19.0214i		−	0.778495i
$598$		−	28.1058i		−	1.14933i
$599$		−	39.4402i		−	1.61148i	−0.592268	−	0.805741i	$-0.701767\pi$
$599$		−	39.4402i		−	1.61148i	0.592268	−	0.805741i	$-0.298233\pi$
$600$			0.649007i			0.0264956i
$601$	−32.9205			−1.34285			−0.671427	−	0.741071i	$-0.734318\pi$
$601$	−32.9205			−1.34285			−0.671427	+	0.741071i	$0.734318\pi$
$602$		0			0
$603$		−	25.1084i		−	1.02249i
$604$		−	24.1297i		−	0.981822i
$605$		−	69.0830i		−	2.80862i
$606$	7.66741			0.311467
$607$	−18.4483			−0.748795			−0.374397	−	0.927268i	$-0.622150\pi$
$607$	−18.4483			−0.748795			−0.374397	+	0.927268i	$0.622150\pi$
$608$	6.37469	−	27.7532i	0.258528	−	1.12554i
$609$		0			0
$610$			27.0613i			1.09568i
$611$			27.9728i			1.13166i
$612$		−	15.1256i		−	0.611415i
$613$	26.5550			1.07255			0.536273	−	0.844044i	$-0.319832\pi$
$613$	26.5550			1.07255			0.536273	+	0.844044i	$0.319832\pi$
$614$			32.5230i			1.31252i
$615$			9.42333i			0.379985i
$616$		0			0
$617$	−8.16815			−0.328838			−0.164419	−	0.986391i	$-0.552575\pi$
$617$	−8.16815			−0.328838			−0.164419	+	0.986391i	$0.552575\pi$
$618$		−	6.87782i		−	0.276667i
$619$			16.9750i			0.682282i	0.940012	+	0.341141i	$0.110813\pi$
$619$			16.9750i			0.682282i	−0.940012	+	0.341141i	$0.889187\pi$
$620$		−	25.0970i		−	1.00792i
$621$	−12.0523			−0.483641
$622$	33.8742			1.35823
$623$		0			0
$624$	−16.9074			−0.676837
$625$	−28.2633			−1.13053
$626$	−11.7269			−0.468699
$627$	−18.8157	−	4.32182i	−0.751428	−	0.172597i
$628$		−	7.85653i		−	0.313510i
$629$	−25.0307			−0.998040
$630$		0			0
$631$	−12.3946			−0.493419			−0.246710	−	0.969089i	$-0.579349\pi$
$631$	−12.3946			−0.493419			−0.246710	+	0.969089i	$0.579349\pi$
$632$	8.74675			0.347927
$633$			4.22106i			0.167772i
$634$	13.9762			0.555068
$635$	−11.2307			−0.445675
$636$			1.49991i			0.0594753i
$637$		0			0
$638$	109.741			4.34468
$639$			12.1010i			0.478708i
$640$	21.7759			0.860768
$641$		−	24.9391i		−	0.985035i	−0.870303	−	0.492517i	$-0.836077\pi$
$641$		−	24.9391i		−	0.985035i	0.870303	−	0.492517i	$-0.163923\pi$
$642$	−11.7700			−0.464524
$643$		−	23.1610i		−	0.913382i	−0.889625	−	0.456691i	$-0.849035\pi$
$643$		−	23.1610i		−	0.913382i	0.889625	−	0.456691i	$-0.150965\pi$
$644$		0			0
$645$		−	7.20702i		−	0.283776i
$646$	34.8487	+	8.00446i	1.37110	+	0.314931i
$647$			20.3472i			0.799933i	0.916530	+	0.399966i	$0.130978\pi$
$647$			20.3472i			0.799933i	−0.916530	+	0.399966i	$0.869022\pi$
$648$		−	5.74920i		−	0.225850i
$649$	−18.5324			−0.727461
$650$			6.96192i			0.273069i
$651$		0			0
$652$	2.31714			0.0907464
$653$	−25.9506			−1.01552			−0.507762	−	0.861497i	$-0.669527\pi$
$653$	−25.9506			−1.01552			−0.507762	+	0.861497i	$0.669527\pi$
$654$	−5.18023			−0.202563
$655$	34.1458			1.33419
$656$	27.2528			1.06404
$657$			21.3216i			0.831833i
$658$		0			0
$659$		−	25.6459i		−	0.999022i	−0.866307	−	0.499511i	$-0.833513\pi$
$659$		−	25.6459i		−	0.999022i	0.866307	−	0.499511i	$-0.166487\pi$
$660$			14.3171i			0.557291i
$661$	0.0365007			0.00141971			0.000709857	−	1.00000i	$-0.499774\pi$
$661$	0.0365007			0.00141971			0.000709857		1.00000i	$0.499774\pi$
$662$	23.8922			0.928598
$663$		−	15.5362i		−	0.603375i
$664$	3.77624			0.146547
$665$		0			0
$666$	25.5884			0.991529
$667$			29.6493i			1.14803i
$668$	−4.88206			−0.188892
$669$	11.2026			0.433117
$670$		−	44.0176i		−	1.70055i
$671$		−	38.8291i		−	1.49898i
$672$		0			0
$673$			41.9773i			1.61811i	0.587736	+	0.809053i	$0.300019\pi$
$673$			41.9773i			1.61811i	−0.587736	+	0.809053i	$0.699981\pi$
$674$	−21.9159			−0.844168
$675$	2.98539			0.114908
$676$	−15.2324			−0.585863
$677$	11.4988			0.441936			0.220968	−	0.975281i	$-0.429078\pi$
$677$	11.4988			0.441936			0.220968	+	0.975281i	$0.429078\pi$
$678$	13.3301			0.511940
$679$		0			0
$680$			12.8982i			0.494622i
$681$	2.00597			0.0768689
$682$			89.5376i			3.42857i
$683$			46.7975i			1.79066i	0.445406	+	0.895329i	$0.353059\pi$
$683$			46.7975i			1.79066i	−0.445406	+	0.895329i	$0.646941\pi$
$684$	−14.3279	−	3.29100i	−0.547840	−	0.125834i
$685$		−	23.4478i		−	0.895896i
$686$		0			0
$687$		−	11.4671i		−	0.437497i
$688$	−20.8431			−0.794637
$689$		−	7.82624i		−	0.298156i
$690$	−9.61778			−0.366143
$691$			20.4411i			0.777618i	0.921318	+	0.388809i	$0.127113\pi$
$691$			20.4411i			0.777618i	−0.921318	+	0.388809i	$0.872887\pi$
$692$	−16.6716			−0.633758
$693$		0			0
$694$			24.9515i			0.947145i
$695$	25.6936			0.974612
$696$	8.00167			0.303303
$697$			25.0426i			0.948555i
$698$	10.8575			0.410963
$699$	−18.4710			−0.698637
$700$		0			0
$701$	25.2576			0.953967			0.476984	−	0.878912i	$-0.341730\pi$
$701$	25.2576			0.953967			0.476984	+	0.878912i	$0.341730\pi$
$702$			34.8911i			1.31688i
$703$	−5.44614	+	23.7106i	−0.205405	+	0.894264i
$704$	13.7944			0.519897
$705$	9.57225			0.360512
$706$	61.2832			2.30642
$707$		0			0
$708$	2.77803			0.104405
$709$	−33.9722			−1.27585			−0.637927	−	0.770097i	$-0.720208\pi$
$709$	−33.9722			−1.27585			−0.637927	+	0.770097i	$0.720208\pi$
$710$			21.2143i			0.796158i
$711$		−	18.3146i		−	0.686851i
$712$		−	17.4701i		−	0.654719i
$713$	−24.1909			−0.905957
$714$		0			0
$715$		−	74.7037i		−	2.79376i
$716$			19.6270i			0.733495i
$717$	6.55655			0.244859
$718$		−	34.2448i		−	1.27800i
$719$			13.4443i			0.501389i	0.968066	+	0.250694i	$0.0806589\pi$
$719$			13.4443i			0.501389i	−0.968066	+	0.250694i	$0.919341\pi$
$720$		−	29.3908i		−	1.09533i
$721$		0			0
$722$	15.1646	−	31.2692i	0.564369	−	1.16372i
$723$	8.77140			0.326212
$724$	10.4050			0.386699
$725$		−	7.34425i		−	0.272759i
$726$		−	36.9453i		−	1.37117i
$727$			28.5133i			1.05750i	0.848778	+	0.528750i	$0.177339\pi$
$727$			28.5133i			1.05750i	−0.848778	+	0.528750i	$0.822661\pi$
$728$		0			0
$729$	−3.88681			−0.143956
$730$			37.3789i			1.38345i
$731$		−	19.1527i		−	0.708389i
$732$			5.82053i			0.215133i
$733$		−	22.3016i		−	0.823728i	−0.911245	−	0.411864i	$-0.864878\pi$
$733$		−	22.3016i		−	0.823728i	0.911245	−	0.411864i	$-0.135122\pi$
$734$	3.60566			0.133088
$735$		0			0
$736$			20.3552i			0.750304i
$737$			63.1590i			2.32649i
$738$		−	25.6005i		−	0.942367i
$739$	4.67321			0.171907			0.0859534	−	0.996299i	$-0.472606\pi$
$739$	4.67321			0.171907			0.0859534	+	0.996299i	$0.472606\pi$
$740$	18.0416			0.663224
$741$	−14.7168	−	3.38033i	−0.540636	−	0.124180i
$742$		0			0
$743$		−	43.2175i		−	1.58550i	−0.609550	−	0.792748i	$-0.708650\pi$
$743$		−	43.2175i		−	1.58550i	0.609550	−	0.792748i	$-0.291350\pi$
$744$			6.52857i			0.239349i
$745$		−	5.74673i		−	0.210544i
$746$	−11.6208			−0.425466
$747$		−	7.90698i		−	0.289301i
$748$			38.0477i			1.39116i
$749$		0			0
$750$	−13.0513			−0.476567
$751$		−	32.7905i		−	1.19654i	−0.801294	−	0.598271i	$-0.795855\pi$
$751$		−	32.7905i		−	1.19654i	0.801294	−	0.598271i	$-0.204145\pi$
$752$		−	27.6835i		−	1.00951i
$753$			0.925201i			0.0337162i
$754$	85.8343			3.12590
$755$	43.0841			1.56799
$756$		0			0
$757$	−4.90256			−0.178187			−0.0890933	−	0.996023i	$-0.528397\pi$
$757$	−4.90256			−0.178187			−0.0890933	+	0.996023i	$0.528397\pi$
$758$	−39.3237			−1.42830
$759$	13.8002			0.500914
$760$	12.2179	+	2.80636i	0.443191	+	0.101797i
$761$		−	4.60193i		−	0.166820i	−0.996515	−	0.0834098i	$-0.973419\pi$
$761$		−	4.60193i		−	0.166820i	0.996515	−	0.0834098i	$-0.0265811\pi$
$762$	−6.00611			−0.217578
$763$		0			0
$764$	2.70474			0.0978540
$765$	27.0071			0.976445
$766$		−	57.6611i		−	2.08338i
$767$	−14.4952			−0.523392
$768$	14.7193			0.531136
$769$		−	6.56319i		−	0.236675i	−0.992973	−	0.118337i	$-0.962244\pi$
$769$		−	6.56319i		−	0.236675i	0.992973	−	0.118337i	$-0.0377564\pi$
$770$		0			0
$771$	−16.5886			−0.597422
$772$			11.0290i			0.396944i
$773$	19.3250			0.695071			0.347536	−	0.937667i	$-0.387019\pi$
$773$	19.3250			0.695071			0.347536	+	0.937667i	$0.387019\pi$
$774$			19.5794i			0.703768i
$775$	5.99218			0.215245
$776$		−	6.39184i		−	0.229454i
$777$		0			0
$778$			58.3565i			2.09218i
$779$	23.7219	+	5.44872i	0.849924	+	0.195221i
$780$			11.1982i			0.400959i
$781$		−	30.4395i		−	1.08921i
$782$	−25.5593			−0.914000
$783$		−	36.8072i		−	1.31538i
$784$		0			0
$785$	14.0280			0.500682
$786$	18.2610			0.651349
$787$	−16.8326			−0.600016			−0.300008	−	0.953937i	$-0.596989\pi$
$787$	−16.8326			−0.600016			−0.300008	+	0.953937i	$0.596989\pi$
$788$	−10.6282			−0.378615
$789$	8.68892			0.309334
$790$		−	32.1074i		−	1.14233i
$791$		0			0
$792$			18.9193i			0.672269i
$793$		−	30.3704i		−	1.07849i
$794$	49.6374			1.76157
$795$	−2.67813			−0.0949834
$796$			36.4352i			1.29141i
$797$	16.7541			0.593459			0.296730	−	0.954962i	$-0.404104\pi$
$797$	16.7541			0.593459			0.296730	+	0.954962i	$0.404104\pi$
$798$		0			0
$799$	25.4383			0.899943
$800$		−	5.04207i		−	0.178264i
$801$	−36.5802			−1.29250
$802$	−14.2863			−0.504465
$803$		−	53.6334i		−	1.89268i
$804$		−	9.46761i		−	0.333897i
$805$		0			0
$806$			70.0323i			2.46678i
$807$	11.0988			0.390695
$808$	7.14389			0.251321
$809$	−36.3987			−1.27971			−0.639855	−	0.768496i	$-0.721006\pi$
$809$	−36.3987			−1.27971			−0.639855	+	0.768496i	$0.721006\pi$
$810$	−21.1040			−0.741520
$811$	23.8958			0.839095			0.419548	−	0.907733i	$-0.362189\pi$
$811$	23.8958			0.839095			0.419548	+	0.907733i	$0.362189\pi$
$812$		0			0
$813$			7.88886i			0.276674i
$814$	−64.3664			−2.25604
$815$			4.13732i			0.144924i
$816$			15.3755i			0.538250i
$817$	−18.1426	−	4.16722i	−0.634731	−	0.145792i
$818$			42.4641i			1.48472i
$819$		0			0
$820$		−	18.0502i		−	0.630340i
$821$	11.2363			0.392148			0.196074	−	0.980589i	$-0.437181\pi$
$821$	11.2363			0.392148			0.196074	+	0.980589i	$0.437181\pi$
$822$		−	12.5398i		−	0.437376i
$823$	36.9881			1.28933			0.644663	−	0.764467i	$-0.276998\pi$
$823$	36.9881			1.28933			0.644663	+	0.764467i	$0.276998\pi$
$824$		−	6.40821i		−	0.223241i
$825$	−3.41835			−0.119012
$826$		0			0
$827$			13.4192i			0.466633i	0.972401	+	0.233316i	$0.0749578\pi$
$827$			13.4192i			0.466633i	−0.972401	+	0.233316i	$0.925042\pi$
$828$	10.5086			0.365199
$829$	47.6804			1.65601			0.828005	−	0.560721i	$-0.189476\pi$
$829$	47.6804			1.65601			0.828005	+	0.560721i	$0.189476\pi$
$830$		−	13.8618i		−	0.481148i
$831$	−14.7392			−0.511297
$832$	10.7894			0.374055
$833$		0			0
$834$	13.7408			0.475805
$835$		−	8.71704i		−	0.301666i
$836$	36.0411	+	8.27835i	1.24651	+	0.286313i
$837$	30.0310			1.03802
$838$	23.5832			0.814667
$839$	−4.54352			−0.156860			−0.0784299	−	0.996920i	$-0.524991\pi$
$839$	−4.54352			−0.156860			−0.0784299	+	0.996920i	$0.524991\pi$
$840$		0			0
$841$	−61.5481			−2.12235
$842$	−1.88171			−0.0648480
$843$		−	0.810648i		−	0.0279202i
$844$		−	8.08535i		−	0.278309i
$845$		−	27.1979i		−	0.935637i
$846$	−26.0051			−0.894073
$847$		0			0
$848$			7.74530i			0.265975i
$849$		−	2.52202i		−	0.0865554i
$850$	6.33114			0.217156
$851$		−	17.3903i		−	0.596131i
$852$			4.56292i			0.156323i
$853$			48.4579i			1.65917i	0.558383	+	0.829584i	$0.311422\pi$
$853$			48.4579i			1.65917i	−0.558383	+	0.829584i	$0.688578\pi$
$854$		0			0
$855$	5.87616	−	25.5828i	0.200961	−	0.874914i
$856$	−10.9663			−0.374821
$857$	−22.2813			−0.761113			−0.380557	−	0.924758i	$-0.624268\pi$
$857$	−22.2813			−0.761113			−0.380557	+	0.924758i	$0.624268\pi$
$858$		−	39.9512i		−	1.36391i
$859$		−	20.2621i		−	0.691335i	−0.938357	−	0.345667i	$-0.887653\pi$
$859$		−	20.2621i		−	0.691335i	0.938357	−	0.345667i	$-0.112347\pi$
$860$			13.8049i			0.470743i
$861$		0			0
$862$	3.97573			0.135414
$863$			9.48731i			0.322952i	0.986877	+	0.161476i	$0.0516254\pi$
$863$			9.48731i			0.322952i	−0.986877	+	0.161476i	$0.948375\pi$
$864$		−	25.2694i		−	0.859681i
$865$		−	29.7675i		−	1.01213i
$866$			46.1823i			1.56934i
$867$	−2.18697			−0.0742732
$868$		0			0
$869$			46.0696i			1.56280i
$870$		−	29.3724i		−	0.995817i
$871$			49.4001i			1.67386i
$872$	−4.82653			−0.163447
$873$	−13.3837			−0.452970
$874$	−5.56116	+	24.2114i	−0.188109	+	0.818962i
$875$		0			0
$876$			8.03971i			0.271637i
$877$			15.7552i			0.532016i	0.963971	+	0.266008i	$0.0857047\pi$
$877$			15.7552i			0.532016i	−0.963971	+	0.266008i	$0.914295\pi$
$878$		−	24.5549i		−	0.828686i
$879$	7.59483			0.256167
$880$			73.9311i			2.49222i
$881$		−	23.3192i		−	0.785642i	−0.919615	−	0.392821i	$-0.871499\pi$
$881$		−	23.3192i		−	0.785642i	0.919615	−	0.392821i	$-0.128501\pi$
$882$		0			0
$883$	−38.5540			−1.29745			−0.648723	−	0.761025i	$-0.724696\pi$
$883$	−38.5540			−1.29745			−0.648723	+	0.761025i	$0.724696\pi$
$884$			29.7592i			1.00091i
$885$			4.96025i			0.166737i
$886$		−	25.3832i		−	0.852765i
$887$	−39.4303			−1.32394			−0.661970	−	0.749530i	$-0.730279\pi$
$887$	−39.4303			−1.32394			−0.661970	+	0.749530i	$0.730279\pi$
$888$	−4.69323			−0.157495
$889$		0			0
$890$	−64.1288			−2.14960
$891$	30.2813			1.01446
$892$	−21.4583			−0.718478
$893$	5.53483	−	24.0968i	0.185216	−	0.806367i
$894$		−	3.07332i		−	0.102787i
$895$	−35.0445			−1.17141
$896$		0			0
$897$	10.7939			0.360397
$898$	58.4071			1.94907
$899$		−	73.8782i		−	2.46398i
$900$	−2.60302			−0.0867673
$901$	−7.11715			−0.237107
$902$			64.3969i			2.14418i
$903$		0			0
$904$	12.4199			0.413081
$905$			18.5784i			0.617568i
$906$	23.0412			0.765493
$907$		−	45.3990i		−	1.50745i	−0.657191	−	0.753724i	$-0.728255\pi$
$907$		−	45.3990i		−	1.50745i	0.657191	−	0.753724i	$-0.271745\pi$
$908$	−3.84239			−0.127514
$909$		−	14.9584i		−	0.496139i
$910$		0			0
$911$			53.4354i			1.77039i	0.465218	+	0.885196i	$0.345976\pi$
$911$			53.4354i			1.77039i	−0.465218	+	0.885196i	$0.654024\pi$
$912$	14.5646	+	3.34537i	0.482283	+	0.110776i
$913$			19.8896i			0.658251i
$914$			19.6719i			0.650688i
$915$	−10.3927			−0.343573
$916$			21.9650i			0.725743i
$917$		0			0
$918$	31.7298			1.04724
$919$	−7.46516			−0.246253			−0.123126	−	0.992391i	$-0.539292\pi$
$919$	−7.46516			−0.246253			−0.123126	+	0.992391i	$0.539292\pi$
$920$	−8.96108			−0.295438
$921$	−12.4902			−0.411568
$922$	−20.3868			−0.671403
$923$		−	23.8084i		−	0.783663i
$924$		0			0
$925$			4.30763i			0.141634i
$926$		−	22.5490i		−	0.741005i
$927$	−13.4180			−0.440705
$928$	−62.1642			−2.04064
$929$			49.9239i			1.63795i	0.573828	+	0.818976i	$0.305458\pi$
$929$			49.9239i			1.63795i	−0.573828	+	0.818976i	$0.694542\pi$
$930$	23.9650			0.785842
$931$		0			0
$932$	35.3808			1.15894
$933$			13.0092i			0.425901i
$934$	59.4898			1.94657
$935$	−67.9352			−2.22172
$936$			14.7979i			0.483683i
$937$		−	53.2907i		−	1.74093i	−0.492230	−	0.870465i	$-0.663818\pi$
$937$		−	53.2907i		−	1.74093i	0.492230	−	0.870465i	$-0.336182\pi$
$938$		0			0
$939$		−	4.50362i		−	0.146970i
$940$	−18.3354			−0.598036
$941$	39.2705			1.28018			0.640091	−	0.768299i	$-0.278897\pi$
$941$	39.2705			1.28018			0.640091	+	0.768299i	$0.278897\pi$
$942$	7.50213			0.244433
$943$	−17.3985			−0.566573
$944$	14.3453			0.466900
$945$		0			0
$946$		−	49.2511i		−	1.60129i
$947$	−17.9281			−0.582586			−0.291293	−	0.956634i	$-0.594085\pi$
$947$	−17.9281			−0.582586			−0.291293	+	0.956634i	$0.594085\pi$
$948$		−	6.90588i		−	0.224293i
$949$		−	41.9497i		−	1.36174i
$950$	1.37752	−	5.99725i	0.0446926	−	0.194576i
$951$			5.36749i			0.174053i
$952$		0			0
$953$		−	24.1119i		−	0.781063i	−0.920590	−	0.390531i	$-0.872291\pi$
$953$		−	24.1119i		−	0.781063i	0.920590	−	0.390531i	$-0.127709\pi$
$954$	7.27571			0.235560
$955$			4.82938i			0.156275i
$956$	−12.5589			−0.406185
$957$			42.1452i			1.36236i
$958$	−8.67403			−0.280245
$959$		0			0
$960$		−	3.69211i		−	0.119162i
$961$	29.2773			0.944430
$962$	−50.3445			−1.62317
$963$			22.9621i			0.739944i
$964$	−16.8014			−0.541138
$965$	−19.6926			−0.633928
$966$		0			0
$967$	29.8531			0.960011			0.480006	−	0.877265i	$-0.340635\pi$
$967$	29.8531			0.960011			0.480006	+	0.877265i	$0.340635\pi$
$968$		−	34.4227i		−	1.10639i
$969$	−3.07406	+	13.3834i	−0.0987530	+	0.429937i
$970$	−23.4630			−0.753352
$971$	11.3291			0.363569			0.181784	−	0.983338i	$-0.441813\pi$
$971$	11.3291			0.363569			0.181784	+	0.983338i	$0.441813\pi$
$972$	−20.1528			−0.646403
$973$		0			0
$974$	−34.7169			−1.11240
$975$	−2.67368			−0.0856263
$976$			30.0563i			0.962080i
$977$			20.0499i			0.641452i	0.947172	+	0.320726i	$0.103927\pi$
$977$			20.0499i			0.641452i	−0.947172	+	0.320726i	$0.896073\pi$
$978$			2.21262i			0.0707519i
$979$	92.0158			2.94084
$980$		0			0
$981$			10.1061i			0.322664i
$982$			16.6918i			0.532656i
$983$	51.2312			1.63402			0.817011	−	0.576622i	$-0.195630\pi$
$983$	51.2312			1.63402			0.817011	+	0.576622i	$0.195630\pi$
$984$			4.69546i			0.149686i
$985$		−	18.9770i		−	0.604657i
$986$		−	78.0573i		−	2.48585i
$987$		0			0
$988$	28.1898	+	6.47496i	0.896836	+	0.205996i
$989$	13.3065			0.423122
$990$	69.4487			2.20722
$991$			11.5205i			0.365961i	0.983117	+	0.182981i	$0.0585746\pi$
$991$			11.5205i			0.365961i	−0.983117	+	0.182981i	$0.941425\pi$
$992$		−	50.7199i		−	1.61036i
$993$			9.17565i			0.291181i
$994$		0			0
$995$	−65.0560			−2.06241
$996$		−	2.98148i		−	0.0944719i
$997$		−	13.2279i		−	0.418933i	−0.977816	−	0.209467i	$-0.932827\pi$
$997$		−	13.2279i		−	0.418933i	0.977816	−	0.209467i	$-0.0671728\pi$
$998$			31.7523i			1.00510i
$999$			21.5886i			0.683032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.c.f.930.10	yes	40
7.2	even	3		931.2.o.i.227.9		80
7.3	odd	6		931.2.o.i.607.32		80
7.4	even	3		931.2.o.i.607.31		80
7.5	odd	6		931.2.o.i.227.10		80
7.6	odd	2	inner	931.2.c.f.930.9	✓	40
19.18	odd	2	inner	931.2.c.f.930.31	yes	40
133.18	odd	6		931.2.o.i.607.10		80
133.37	odd	6		931.2.o.i.227.32		80
133.75	even	6		931.2.o.i.227.31		80
133.94	even	6		931.2.o.i.607.9		80
133.132	even	2	inner	931.2.c.f.930.32	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.c.f.930.9	✓	40	7.6	odd	2	inner
931.2.c.f.930.10	yes	40	1.1	even	1	trivial
931.2.c.f.930.31	yes	40	19.18	odd	2	inner
931.2.c.f.930.32	yes	40	133.132	even	2	inner
931.2.o.i.227.9		80	7.2	even	3
931.2.o.i.227.10		80	7.5	odd	6
931.2.o.i.227.31		80	133.75	even	6
931.2.o.i.227.32		80	133.37	odd	6
931.2.o.i.607.9		80	133.94	even	6
931.2.o.i.607.10		80	133.18	odd	6
931.2.o.i.607.31		80	7.4	even	3
931.2.o.i.607.32		80	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.82908i q^{2} +0.702444 q^{3} -1.34552 q^{4} -2.40246i q^{5} -1.28482i q^{6} -1.19710i q^{8} -2.50657 q^{9} +O(q^{10})\)	\(q-1.82908i q^{2} +0.702444 q^{3} -1.34552 q^{4} -2.40246i q^{5} -1.28482i q^{6} -1.19710i q^{8} -2.50657 q^{9} -4.39428 q^{10} +6.30517 q^{11} -0.945152 q^{12} +4.93162 q^{13} -1.68759i q^{15} -4.88062 q^{16} -4.48479i q^{17} +4.58471i q^{18} +(-4.24827 - 0.975794i) q^{19} +3.23255i q^{20} -11.5326i q^{22} +3.11584 q^{23} -0.840894i q^{24} -0.771805 q^{25} -9.02031i q^{26} -3.86806 q^{27} +9.51567i q^{29} -3.08674 q^{30} -7.76385 q^{31} +6.53282i q^{32} +4.42903 q^{33} -8.20303 q^{34} +3.37264 q^{36} -5.58124i q^{37} +(-1.78480 + 7.77041i) q^{38} +3.46419 q^{39} -2.87598 q^{40} -5.58388 q^{41} +4.27059 q^{43} -8.48371 q^{44} +6.02193i q^{45} -5.69911i q^{46} +5.67213i q^{47} -3.42836 q^{48} +1.41169i q^{50} -3.15032i q^{51} -6.63558 q^{52} -1.58695i q^{53} +7.07498i q^{54} -15.1479i q^{55} +(-2.98418 - 0.685441i) q^{57} +17.4049 q^{58} -2.93924 q^{59} +2.27069i q^{60} -6.15831i q^{61} +14.2007i q^{62} +2.18780 q^{64} -11.8480i q^{65} -8.10103i q^{66} +10.0170i q^{67} +6.03437i q^{68} +2.18871 q^{69} -4.82771i q^{71} +3.00061i q^{72} -8.50626i q^{73} -10.2085 q^{74} -0.542150 q^{75} +(5.71613 + 1.31295i) q^{76} -6.33626i q^{78} +7.30664i q^{79} +11.7255i q^{80} +4.80262 q^{81} +10.2133i q^{82} +3.15450i q^{83} -10.7745 q^{85} -7.81124i q^{86} +6.68423i q^{87} -7.54789i q^{88} +14.5937 q^{89} +11.0146 q^{90} -4.19242 q^{92} -5.45367 q^{93} +10.3748 q^{94} +(-2.34430 + 10.2063i) q^{95} +4.58895i q^{96} +5.33945 q^{97} -15.8043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 40 * q^4 + 40 * q^9	\( 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Introduction

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