LMFDB - Embedded newform 945.2.g.a.944.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(944,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("945.944");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.g (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			944.22
Character	$\chi$	$=$	945.944
Dual form			945.2.g.a.944.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.29594 q^{2} -0.320531 q^{4} +(-1.01211 + 1.99390i) q^{5} +(2.26270 - 1.37120i) q^{7} -3.00728 q^{8} +O(q^{10})$	\(q+1.29594 q^{2} -0.320531 q^{4} +(-1.01211 + 1.99390i) q^{5} +(2.26270 - 1.37120i) q^{7} -3.00728 q^{8} +(-1.31163 + 2.58398i) q^{10} +3.12266i q^{11} +2.45732 q^{13} +(2.93233 - 1.77699i) q^{14} -3.25620 q^{16} +4.43263i q^{17} +4.17348i q^{19} +(0.324411 - 0.639107i) q^{20} +4.04678i q^{22} -5.77131 q^{23} +(-2.95128 - 4.03608i) q^{25} +3.18454 q^{26} +(-0.725266 + 0.439511i) q^{28} +0.339143i q^{29} +4.40671i q^{31} +1.79471 q^{32} +5.74444i q^{34} +(0.443932 + 5.89940i) q^{35} +11.2541i q^{37} +5.40860i q^{38} +(3.04368 - 5.99621i) q^{40} +5.43627 q^{41} -0.439511i q^{43} -1.00091i q^{44} -7.47929 q^{46} +10.2861i q^{47} +(3.23965 - 6.20521i) q^{49} +(-3.82469 - 5.23053i) q^{50} -0.787646 q^{52} -2.76404 q^{53} +(-6.22627 - 3.16046i) q^{55} +(-6.80457 + 4.12356i) q^{56} +0.439511i q^{58} +5.00079 q^{59} -9.34145i q^{61} +5.71085i q^{62} +8.83823 q^{64} +(-2.48707 + 4.89965i) q^{65} -15.7404i q^{67} -1.42080i q^{68} +(0.575311 + 7.64529i) q^{70} -10.1219i q^{71} -9.26995 q^{73} +14.5846i q^{74} -1.33773i q^{76} +(4.28177 + 7.06564i) q^{77} +15.6381 q^{79} +(3.29562 - 6.49254i) q^{80} +7.04510 q^{82} +4.13038i q^{83} +(-8.83823 - 4.48630i) q^{85} -0.569581i q^{86} -9.39069i q^{88} -5.20876 q^{89} +(5.56018 - 3.36946i) q^{91} +1.84988 q^{92} +13.3302i q^{94} +(-8.32151 - 4.22401i) q^{95} -6.09151 q^{97} +(4.19840 - 8.04161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4}+O(q^{10}) $ 32 * q + 32 * q^4	$ 32 q + 32 q^{4} + 32 q^{16} - 28 q^{25} + 72 q^{46} - 52 q^{49} + 56 q^{64} - 48 q^{70} - 80 q^{79} - 56 q^{85} - 20 q^{91}+O(q^{100}) $ 32 * q + 32 * q^4 + 32 * q^16 - 28 * q^25 + 72 * q^46 - 52 * q^49 + 56 * q^64 - 48 * q^70 - 80 * q^79 - 56 * q^85 - 20 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.29594			0.916370			0.458185	−	0.888857i	$-0.348500\pi$
$2$	1.29594			0.916370			0.458185	+	0.888857i	$0.348500\pi$
$3$		0			0
$3$		0			0
$4$	−0.320531			−0.160265
$5$	−1.01211	+	1.99390i	−0.452628	+	0.891700i
$5$	−1.01211	+	1.99390i	−0.452628	+	0.891700i
$6$		0			0
$7$	2.26270	−	1.37120i	0.855221	−	0.518263i
$7$	2.26270	−	1.37120i	0.855221	−	0.518263i
$8$	−3.00728			−1.06323
$9$		0			0
$10$	−1.31163	+	2.58398i	−0.414774	+	0.817127i
$11$			3.12266i			0.941516i	0.882262	+	0.470758i	$0.156020\pi$
$11$			3.12266i			0.941516i	−0.882262	+	0.470758i	$0.843980\pi$
$12$		0			0
$13$	2.45732			0.681537			0.340769	−	0.940147i	$-0.389313\pi$
$13$	2.45732			0.681537			0.340769	+	0.940147i	$0.389313\pi$
$14$	2.93233	−	1.77699i	0.783699	−	0.474921i
$15$		0			0
$16$	−3.25620			−0.814050
$17$			4.43263i			1.07507i	0.843241	+	0.537536i	$0.180645\pi$
$17$			4.43263i			1.07507i	−0.843241	+	0.537536i	$0.819355\pi$
$18$		0			0
$19$			4.17348i			0.957463i	0.877961	+	0.478731i	$0.158903\pi$
$19$			4.17348i			0.957463i	−0.877961	+	0.478731i	$0.841097\pi$
$20$	0.324411	−	0.639107i	0.0725406	−	0.142909i
$21$		0			0
$22$			4.04678i			0.862777i
$23$	−5.77131			−1.20340			−0.601701	−	0.798721i	$-0.705510\pi$
$23$	−5.77131			−1.20340			−0.601701	+	0.798721i	$0.705510\pi$
$24$		0			0
$25$	−2.95128	−	4.03608i	−0.590257	−	0.807216i
$26$	3.18454			0.624540
$27$		0			0
$28$	−0.725266	+	0.439511i	−0.137062	+	0.0830597i
$29$			0.339143i			0.0629773i	0.999504	+	0.0314887i	$0.0100248\pi$
$29$			0.339143i			0.0629773i	−0.999504	+	0.0314887i	$0.989975\pi$
$30$		0			0
$31$			4.40671i			0.791469i	0.918365	+	0.395734i	$0.129510\pi$
$31$			4.40671i			0.791469i	−0.918365	+	0.395734i	$0.870490\pi$
$32$	1.79471			0.317262
$33$		0			0
$34$			5.74444i			0.985164i
$35$	0.443932	+	5.89940i	0.0750383	+	0.997181i
$36$		0			0
$37$			11.2541i			1.85016i	0.379777	+	0.925078i	$0.376001\pi$
$37$			11.2541i			1.85016i	−0.379777	+	0.925078i	$0.623999\pi$
$38$			5.40860i			0.877390i
$39$		0			0
$40$	3.04368	−	5.99621i	0.481249	−	0.948084i
$41$	5.43627			0.849003			0.424502	−	0.905427i	$-0.360449\pi$
$41$	5.43627			0.849003			0.424502	+	0.905427i	$0.360449\pi$
$42$		0			0
$43$		−	0.439511i		−	0.0670247i	−0.999438	−	0.0335124i	$-0.989331\pi$
$43$		−	0.439511i		−	0.0670247i	0.999438	−	0.0335124i	$-0.0106693\pi$
$44$		−	1.00091i		−	0.150893i
$45$		0			0
$46$	−7.47929			−1.10276
$47$			10.2861i			1.50038i	0.661224	+	0.750188i	$0.270037\pi$
$47$			10.2861i			1.50038i	−0.661224	+	0.750188i	$0.729963\pi$
$48$		0			0
$49$	3.23965	−	6.20521i	0.462807	−	0.886459i
$50$	−3.82469	−	5.23053i	−0.540894	−	0.739709i
$51$		0			0
$52$	−0.787646			−0.109227
$53$	−2.76404			−0.379670			−0.189835	−	0.981816i	$-0.560795\pi$
$53$	−2.76404			−0.379670			−0.189835	+	0.981816i	$0.560795\pi$
$54$		0			0
$55$	−6.22627	−	3.16046i	−0.839550	−	0.426156i
$56$	−6.80457	+	4.12356i	−0.909299	+	0.551034i
$57$		0			0
$58$			0.439511i			0.0577106i
$59$	5.00079			0.651047			0.325524	−	0.945534i	$-0.394459\pi$
$59$	5.00079			0.651047			0.325524	+	0.945534i	$0.394459\pi$
$60$		0			0
$61$		−	9.34145i		−	1.19605i	−0.801477	−	0.598025i	$-0.795952\pi$
$61$		−	9.34145i		−	1.19605i	0.801477	−	0.598025i	$-0.204048\pi$
$62$			5.71085i			0.725278i
$63$		0			0
$64$	8.83823			1.10478
$65$	−2.48707	+	4.89965i	−0.308483	+	0.607726i
$66$		0			0
$67$		−	15.7404i		−	1.92299i	−0.274822	−	0.961495i	$-0.588619\pi$
$67$		−	15.7404i		−	1.92299i	0.274822	−	0.961495i	$-0.411381\pi$
$68$		−	1.42080i		−	0.172297i
$69$		0			0
$70$	0.575311	+	7.64529i	0.0687629	+	0.913787i
$71$		−	10.1219i		−	1.20125i	−0.799531	−	0.600625i	$-0.794918\pi$
$71$		−	10.1219i		−	1.20125i	0.799531	−	0.600625i	$-0.205082\pi$
$72$		0			0
$73$	−9.26995			−1.08497			−0.542483	−	0.840067i	$-0.682516\pi$
$73$	−9.26995			−1.08497			−0.542483	+	0.840067i	$0.682516\pi$
$74$			14.5846i			1.69543i
$75$		0			0
$76$		−	1.33773i		−	0.153448i
$77$	4.28177	+	7.06564i	0.487953	+	0.805205i
$78$		0			0
$79$	15.6381			1.75942			0.879709	−	0.475512i	$-0.157737\pi$
$79$	15.6381			1.75942			0.879709	+	0.475512i	$0.157737\pi$
$80$	3.29562	−	6.49254i	0.368461	−	0.725888i
$81$		0			0
$82$	7.04510			0.778001
$83$			4.13038i			0.453369i	0.973968	+	0.226684i	$0.0727886\pi$
$83$			4.13038i			0.453369i	−0.973968	+	0.226684i	$0.927211\pi$
$84$		0			0
$85$	−8.83823	−	4.48630i	−0.958641	−	0.486607i
$86$		−	0.569581i		−	0.0614195i
$87$		0			0
$88$		−	9.39069i		−	1.00105i
$89$	−5.20876			−0.552127			−0.276064	−	0.961139i	$-0.589030\pi$
$89$	−5.20876			−0.552127			−0.276064	+	0.961139i	$0.589030\pi$
$90$		0			0
$91$	5.56018	−	3.36946i	0.582865	−	0.353216i
$92$	1.84988			0.192864
$93$		0			0
$94$			13.3302i			1.37490i
$95$	−8.32151	−	4.22401i	−0.853769	−	0.433374i
$96$		0			0
$97$	−6.09151			−0.618499			−0.309250	−	0.950981i	$-0.600078\pi$
$97$	−6.09151			−0.618499			−0.309250	+	0.950981i	$0.600078\pi$
$98$	4.19840	−	8.04161i	0.424102	−	0.812325i
$99$		0			0
$100$	0.945977	+	1.29369i	0.0945977	+	0.129369i
$101$	−3.19163			−0.317579			−0.158790	−	0.987312i	$-0.550759\pi$
$101$	−3.19163			−0.317579			−0.158790	+	0.987312i	$0.550759\pi$
$102$		0			0
$103$	−1.84762			−0.182052			−0.0910258	−	0.995849i	$-0.529015\pi$
$103$	−1.84762			−0.182052			−0.0910258	+	0.995849i	$0.529015\pi$
$104$	−7.38983			−0.724633
$105$		0			0
$106$	−3.58203			−0.347918
$107$	5.68254			0.549351			0.274676	−	0.961537i	$-0.411430\pi$
$107$	5.68254			0.549351			0.274676	+	0.961537i	$0.411430\pi$
$108$		0			0
$109$	9.12753			0.874259			0.437130	−	0.899399i	$-0.355995\pi$
$109$	9.12753			0.874259			0.437130	+	0.899399i	$0.355995\pi$
$110$	−8.06889	−	4.09578i	−0.769338	−	0.390517i
$111$		0			0
$112$	−7.36781	+	4.46488i	−0.696192	+	0.421892i
$113$	−13.9072			−1.30828			−0.654139	−	0.756374i	$-0.726969\pi$
$113$	−13.9072			−1.30828			−0.654139	+	0.756374i	$0.726969\pi$
$114$		0			0
$115$	5.84118	−	11.5074i	0.544693	−	1.07307i
$116$		−	0.108706i		−	0.0100931i
$117$		0			0
$118$	6.48074			0.596600
$119$	6.07801	+	10.0297i	0.557170	+	0.919424i
$120$		0			0
$121$	1.24902			0.113547
$122$		−	12.1060i		−	1.09602i
$123$		0			0
$124$		−	1.41249i		−	0.126845i
$125$	11.0346	−	1.79963i	0.986960	−	0.160963i
$126$		0			0
$127$		−	6.63416i		−	0.588687i	−0.955700	−	0.294343i	$-0.904899\pi$
$127$		−	6.63416i		−	0.588687i	0.955700	−	0.294343i	$-0.0951009\pi$
$128$	7.86444			0.695125
$129$		0			0
$130$	−3.22310	+	6.34966i	−0.282684	+	0.556902i
$131$	21.9264			1.91572			0.957860	−	0.287235i	$-0.0927360\pi$
$131$	21.9264			1.91572			0.957860	+	0.287235i	$0.0927360\pi$
$132$		0			0
$133$	5.72266	+	9.44335i	0.496218	+	0.818843i
$134$		−	20.3986i		−	1.76217i
$135$		0			0
$136$		−	13.3302i		−	1.14305i
$137$	18.7643			1.60315			0.801573	−	0.597897i	$-0.203997\pi$
$137$	18.7643			1.60315			0.801573	+	0.597897i	$0.203997\pi$
$138$		0			0
$139$		−	4.82472i		−	0.409227i	−0.978843	−	0.204614i	$-0.934406\pi$
$139$		−	4.82472i		−	0.409227i	0.978843	−	0.204614i	$-0.0655938\pi$
$140$	−0.142294	−	1.89094i	−0.0120260	−	0.159814i
$141$		0			0
$142$		−	13.1174i		−	1.10079i
$143$			7.67335i			0.641678i
$144$		0			0
$145$	−0.676218	−	0.343249i	−0.0561569	−	0.0285053i
$146$	−12.0133			−0.994230
$147$		0			0
$148$		−	3.60727i		−	0.296516i
$149$		−	13.9229i		−	1.14060i	−0.821435	−	0.570302i	$-0.806826\pi$
$149$		−	13.9229i		−	1.14060i	0.821435	−	0.570302i	$-0.193174\pi$
$150$		0			0
$151$	−5.54363			−0.451134			−0.225567	−	0.974228i	$-0.572423\pi$
$151$	−5.54363			−0.451134			−0.225567	+	0.974228i	$0.572423\pi$
$152$		−	12.5508i		−	1.01801i
$153$		0			0
$154$	5.54893	+	9.15667i	0.447146	+	0.737866i
$155$	−8.78655	−	4.46006i	−0.705752	−	0.358241i
$156$		0			0
$157$	0.770171			0.0614663			0.0307332	−	0.999528i	$-0.490216\pi$
$157$	0.770171			0.0614663			0.0307332	+	0.999528i	$0.490216\pi$
$158$	20.2660			1.61228
$159$		0			0
$160$	−1.81643	+	3.57846i	−0.143602	+	0.282902i
$161$	−13.0588	+	7.91360i	−1.02917	+	0.623679i
$162$		0			0
$163$			14.2809i			1.11857i	0.828975	+	0.559285i	$0.188924\pi$
$163$			14.2809i			1.11857i	−0.828975	+	0.559285i	$0.811076\pi$
$164$	−1.74249			−0.136066
$165$		0			0
$166$			5.35274i			0.415453i
$167$		−	0.531134i		−	0.0411004i	−0.999789	−	0.0205502i	$-0.993458\pi$
$167$		−	0.531134i		−	0.0411004i	0.999789	−	0.0205502i	$-0.00654178\pi$
$168$		0			0
$169$	−6.96159			−0.535507
$170$	−11.4538	−	5.81398i	−0.878470	−	0.445912i
$171$		0			0
$172$			0.140877i			0.0107417i
$173$		−	19.5399i		−	1.48559i	−0.669519	−	0.742795i	$-0.733500\pi$
$173$		−	19.5399i		−	1.48559i	0.669519	−	0.742795i	$-0.266500\pi$
$174$		0			0
$175$	−12.2121	−	5.08566i	−0.923150	−	0.384440i
$176$		−	10.1680i		−	0.766441i
$177$		0			0
$178$	−6.75025			−0.505953
$179$			13.5837i			1.01529i	0.861565	+	0.507647i	$0.169485\pi$
$179$			13.5837i			1.01529i	−0.861565	+	0.507647i	$0.830515\pi$
$180$		0			0
$181$		−	2.83575i		−	0.210780i	−0.994431	−	0.105390i	$-0.966391\pi$
$181$		−	2.83575i		−	0.210780i	0.994431	−	0.105390i	$-0.0336091\pi$
$182$	7.20568	−	4.36663i	0.534120	−	0.323676i
$183$		0			0
$184$	17.3559			1.27950
$185$	−22.4395	−	11.3903i	−1.64978	−	0.837432i
$186$		0			0
$187$	−13.8416			−1.01220
$188$		−	3.29700i		−	0.240459i
$189$		0			0
$190$	−10.7842	−	5.47408i	−0.782369	−	0.397131i
$191$			7.24622i			0.524318i	0.965025	+	0.262159i	$0.0844345\pi$
$191$			7.24622i			0.524318i	−0.965025	+	0.262159i	$0.915566\pi$
$192$		0			0
$193$		−	1.28298i		−	0.0923511i	−0.998933	−	0.0461755i	$-0.985297\pi$
$193$		−	1.28298i		−	0.0923511i	0.998933	−	0.0461755i	$-0.0147034\pi$
$194$	−7.89425			−0.566774
$195$		0			0
$196$	−1.03841	+	1.98896i	−0.0741719	+	0.142069i
$197$	−2.53671			−0.180733			−0.0903665	−	0.995909i	$-0.528804\pi$
$197$	−2.53671			−0.180733			−0.0903665	+	0.995909i	$0.528804\pi$
$198$		0			0
$199$			6.08769i			0.431545i	0.976444	+	0.215772i	$0.0692269\pi$
$199$			6.08769i			0.431545i	−0.976444	+	0.215772i	$0.930773\pi$
$200$	8.87532	+	12.1376i	0.627580	+	0.858258i
$201$		0			0
$202$	−4.13618			−0.291020
$203$	0.465032	+	0.767381i	0.0326388	+	0.0538596i
$204$		0			0
$205$	−5.50209	+	10.8394i	−0.384282	+	0.757056i
$206$	−2.39441			−0.166827
$207$		0			0
$208$	−8.00151			−0.554805
$209$	−13.0324			−0.901467
$210$		0			0
$211$	−5.24902			−0.361358			−0.180679	−	0.983542i	$-0.557829\pi$
$211$	−5.24902			−0.361358			−0.180679	+	0.983542i	$0.557829\pi$
$212$	0.885959			0.0608479
$213$		0			0
$214$	7.36424			0.503409
$215$	0.876340	+	0.444831i	0.0597659	+	0.0303372i
$216$		0			0
$217$	6.04246	+	9.97108i	0.410189	+	0.676881i
$218$	11.8288			0.801145
$219$		0			0
$220$	1.99571	+	1.01302i	0.134551	+	0.0682981i
$221$			10.8924i			0.732701i
$222$		0			0
$223$	21.8963			1.46628			0.733142	−	0.680076i	$-0.238053\pi$
$223$	21.8963			1.46628			0.733142	+	0.680076i	$0.238053\pi$
$224$	4.06088	−	2.46089i	0.271329	−	0.164425i
$225$		0			0
$226$	−18.0229			−1.19887
$227$			9.69865i			0.643722i	0.946787	+	0.321861i	$0.104308\pi$
$227$			9.69865i			0.643722i	−0.946787	+	0.321861i	$0.895692\pi$
$228$		0			0
$229$			21.0636i			1.39192i	0.718081	+	0.695960i	$0.245021\pi$
$229$			21.0636i			1.39192i	−0.718081	+	0.695960i	$0.754979\pi$
$230$	7.56984	−	14.9130i	0.499140	−	0.983332i
$231$		0			0
$232$		−	1.01990i		−	0.0669596i
$233$	−2.91850			−0.191197			−0.0955986	−	0.995420i	$-0.530477\pi$
$233$	−2.91850			−0.191197			−0.0955986	+	0.995420i	$0.530477\pi$
$234$		0			0
$235$	−20.5094	−	10.4106i	−1.33789	−	0.679112i
$236$	−1.60291			−0.104340
$237$		0			0
$238$	7.87675	+	12.9980i	0.510574	+	0.842533i
$239$		−	21.1526i		−	1.36824i	−0.729367	−	0.684122i	$-0.760185\pi$
$239$		−	21.1526i		−	1.36824i	0.729367	−	0.684122i	$-0.239815\pi$
$240$		0			0
$241$			8.11374i			0.522652i	0.965251	+	0.261326i	$0.0841598\pi$
$241$			8.11374i			0.522652i	−0.965251	+	0.261326i	$0.915840\pi$
$242$	1.61866			0.104051
$243$		0			0
$244$			2.99422i			0.191686i
$245$	9.09372	+	12.7399i	0.580976	+	0.813920i
$246$		0			0
$247$			10.2556i			0.652546i
$248$		−	13.2522i		−	0.841515i
$249$		0			0
$250$	14.3002	−	2.33221i	0.904421	−	0.147502i
$251$	−13.6869			−0.863909			−0.431954	−	0.901895i	$-0.642176\pi$
$251$	−13.6869			−0.863909			−0.431954	+	0.901895i	$0.642176\pi$
$252$		0			0
$253$		−	18.0218i		−	1.13302i
$254$		−	8.59750i		−	0.539455i
$255$		0			0
$256$	−7.48460			−0.467787
$257$			8.36416i			0.521742i	0.965374	+	0.260871i	$0.0840097\pi$
$257$			8.36416i			0.521742i	−0.965374	+	0.260871i	$0.915990\pi$
$258$		0			0
$259$	15.4315	+	25.4646i	0.958868	+	1.58229i
$260$	0.797181	−	1.57049i	0.0494391	−	0.0973976i
$261$		0			0
$262$	28.4154			1.75551
$263$	−19.8935			−1.22669			−0.613344	−	0.789816i	$-0.710176\pi$
$263$	−19.8935			−1.22669			−0.613344	+	0.789816i	$0.710176\pi$
$264$		0			0
$265$	2.79750	−	5.51121i	0.171849	−	0.338551i
$266$	7.41624	+	12.2380i	0.454719	+	0.750363i
$267$		0			0
$268$			5.04527i			0.308189i
$269$	25.4758			1.55329			0.776643	−	0.629941i	$-0.216921\pi$
$269$	25.4758			1.55329			0.776643	+	0.629941i	$0.216921\pi$
$270$		0			0
$271$			18.9161i			1.14907i	0.818479	+	0.574536i	$0.194818\pi$
$271$			18.9161i			1.14907i	−0.818479	+	0.574536i	$0.805182\pi$
$272$		−	14.4335i		−	0.875161i
$273$		0			0
$274$	24.3175			1.46908
$275$	12.6033	−	9.21584i	0.760007	−	0.555736i
$276$		0			0
$277$		−	1.43800i		−	0.0864008i	−0.999066	−	0.0432004i	$-0.986245\pi$
$277$		−	1.43800i		−	0.0864008i	0.999066	−	0.0432004i	$-0.0137554\pi$
$278$		−	6.25256i		−	0.375004i
$279$		0			0
$280$	−1.33503	−	17.7411i	−0.0797832	−	1.06024i
$281$		−	27.7370i		−	1.65465i	−0.561723	−	0.827326i	$-0.689861\pi$
$281$		−	27.7370i		−	1.65465i	0.561723	−	0.827326i	$-0.310139\pi$
$282$		0			0
$283$	17.6542			1.04943			0.524715	−	0.851278i	$-0.324172\pi$
$283$	17.6542			1.04943			0.524715	+	0.851278i	$0.324172\pi$
$284$			3.24439i			0.192519i
$285$		0			0
$286$			9.94423i			0.588015i
$287$	12.3007	−	7.45419i	0.726086	−	0.440007i
$288$		0			0
$289$	−2.64824			−0.155779
$290$	−0.876340	−	0.444831i	−0.0514605	−	0.0261214i
$291$		0			0
$292$	2.97131			0.173883
$293$		−	14.1313i		−	0.825558i	−0.910831	−	0.412779i	$-0.864558\pi$
$293$		−	14.1313i		−	0.825558i	0.910831	−	0.412779i	$-0.135442\pi$
$294$		0			0
$295$	−5.06133	+	9.97108i	−0.294682	+	0.580539i
$296$		−	33.8441i		−	1.96715i
$297$		0			0
$298$		−	18.0432i		−	1.04522i
$299$	−14.1819			−0.820163
$300$		0			0
$301$	−0.602655	−	0.994482i	−0.0347364	−	0.0573210i
$302$	−7.18423			−0.413406
$303$		0			0
$304$		−	13.5897i		−	0.779422i
$305$	18.6259	+	9.45454i	1.06652	+	0.541365i
$306$		0			0
$307$	13.7967			0.787418			0.393709	−	0.919235i	$-0.371192\pi$
$307$	13.7967			0.787418			0.393709	+	0.919235i	$0.371192\pi$
$308$	−1.37244	−	2.26476i	−0.0782020	−	0.129046i
$309$		0			0
$310$	−11.3869	−	5.77998i	−0.646730	−	0.328281i
$311$	11.6045			0.658030			0.329015	−	0.944325i	$-0.393283\pi$
$311$	11.6045			0.658030			0.329015	+	0.944325i	$0.393283\pi$
$312$		0			0
$313$	−33.6194			−1.90028			−0.950141	−	0.311821i	$-0.899061\pi$
$313$	−33.6194			−1.90028			−0.950141	+	0.311821i	$0.899061\pi$
$314$	0.998098			0.0563259
$315$		0			0
$316$	−5.01248			−0.281974
$317$	−9.31484			−0.523174			−0.261587	−	0.965180i	$-0.584246\pi$
$317$	−9.31484			−0.523174			−0.261587	+	0.965180i	$0.584246\pi$
$318$		0			0
$319$	−1.05903			−0.0592942
$320$	−8.94523	+	17.6226i	−0.500053	+	0.985131i
$321$		0			0
$322$	−16.9234	+	10.2556i	−0.943105	+	0.571521i
$323$	−18.4995			−1.02934
$324$		0			0
$325$	−7.25224	−	9.91793i	−0.402282	−	0.550148i
$326$			18.5073i			1.02502i
$327$		0			0
$328$	−16.3484			−0.902688
$329$	14.1042	+	23.2743i	0.777590	+	1.28315i
$330$		0			0
$331$	13.4203			0.737645			0.368822	−	0.929500i	$-0.379761\pi$
$331$	13.4203			0.737645			0.368822	+	0.929500i	$0.379761\pi$
$332$		−	1.32392i		−	0.0726593i
$333$		0			0
$334$		−	0.688319i		−	0.0376631i
$335$	31.3847	+	15.9309i	1.71473	+	0.870398i
$336$		0			0
$337$		−	5.49892i		−	0.299545i	−0.988720	−	0.149773i	$-0.952146\pi$
$337$		−	5.49892i		−	0.299545i	0.988720	−	0.149773i	$-0.0478542\pi$
$338$	−9.02183			−0.490723
$339$		0			0
$340$	2.83293	+	1.43800i	0.153637	+	0.0779863i
$341$	−13.7606			−0.745180
$342$		0			0
$343$	−1.17820	−	18.4827i	−0.0636170	−	0.997974i
$344$			1.32173i			0.0712629i
$345$		0			0
$346$		−	25.3226i		−	1.36135i
$347$	−6.44222			−0.345837			−0.172918	−	0.984936i	$-0.555320\pi$
$347$	−6.44222			−0.345837			−0.172918	+	0.984936i	$0.555320\pi$
$348$		0			0
$349$			21.5187i			1.15187i	0.817497	+	0.575933i	$0.195361\pi$
$349$			21.5187i			1.15187i	−0.817497	+	0.575933i	$0.804639\pi$
$350$	−15.8262	−	6.59073i	−0.845947	−	0.352289i
$351$		0			0
$352$			5.60425i			0.298707i
$353$			3.40039i			0.180984i	0.995897	+	0.0904922i	$0.0288440\pi$
$353$			3.40039i			0.180984i	−0.995897	+	0.0904922i	$0.971156\pi$
$354$		0			0
$355$	20.1821	+	10.2445i	1.07115	+	0.543719i
$356$	1.66957			0.0884869
$357$		0			0
$358$			17.6037i			0.930386i
$359$			34.9998i			1.84722i	0.383338	+	0.923608i	$0.374774\pi$
$359$			34.9998i			1.84722i	−0.383338	+	0.923608i	$0.625226\pi$
$360$		0			0
$361$	1.58203			0.0832650
$362$		−	3.67498i		−	0.193152i
$363$		0			0
$364$	−1.78221	+	1.08002i	−0.0934131	+	0.0566083i
$365$	9.38217	−	18.4834i	0.491085	−	0.967463i
$366$		0			0
$367$	−14.9818			−0.782046			−0.391023	−	0.920381i	$-0.627879\pi$
$367$	−14.9818			−0.782046			−0.391023	+	0.920381i	$0.627879\pi$
$368$	18.7925			0.979629
$369$		0			0
$370$	−29.0803	−	14.7612i	−1.51181	−	0.767397i
$371$	−6.25419	+	3.79003i	−0.324701	+	0.196769i
$372$		0			0
$373$		−	0.864884i		−	0.0447820i	−0.999749	−	0.0223910i	$-0.992872\pi$
$373$		−	0.864884i		−	0.0447820i	0.999749	−	0.0223910i	$-0.00712787\pi$
$374$	−17.9379			−0.927547
$375$		0			0
$376$		−	30.9330i		−	1.59525i
$377$			0.833383i			0.0429214i
$378$		0			0
$379$	13.1972			0.677893			0.338947	−	0.940806i	$-0.389929\pi$
$379$	13.1972			0.677893			0.338947	+	0.940806i	$0.389929\pi$
$380$	2.66730	+	1.35393i	0.136830	+	0.0694549i
$381$		0			0
$382$			9.39069i			0.480469i
$383$			34.2129i			1.74820i	0.485749	+	0.874098i	$0.338547\pi$
$383$			34.2129i			1.74820i	−0.485749	+	0.874098i	$0.661453\pi$
$384$		0			0
$385$	−18.4218	+	1.38625i	−0.938862	+	0.0706498i
$386$		−	1.66267i		−	0.0846278i
$387$		0			0
$388$	1.95252			0.0991240
$389$		−	29.2779i		−	1.48445i	−0.670150	−	0.742225i	$-0.733770\pi$
$389$		−	29.2779i		−	1.48445i	0.670150	−	0.742225i	$-0.266230\pi$
$390$		0			0
$391$		−	25.5821i		−	1.29374i
$392$	−9.74251	+	18.6608i	−0.492071	+	0.942513i
$393$		0			0
$394$	−3.28743			−0.165618
$395$	−15.8274	+	31.1807i	−0.796362	+	1.56887i
$396$		0			0
$397$	36.9817			1.85606			0.928029	−	0.372508i	$-0.121502\pi$
$397$	36.9817			1.85606			0.928029	+	0.372508i	$0.121502\pi$
$398$			7.88930i			0.395455i
$399$		0			0
$400$	9.60996	+	13.1423i	0.480498	+	0.657114i
$401$			15.6942i			0.783733i	0.920022	+	0.391866i	$0.128170\pi$
$401$			15.6942i			0.783733i	−0.920022	+	0.391866i	$0.871830\pi$
$402$		0			0
$403$			10.8287i			0.539415i
$404$	1.02302			0.0508970
$405$		0			0
$406$	0.602655	+	0.994482i	0.0299093	+	0.0493553i
$407$	−35.1425			−1.74195
$408$		0			0
$409$		−	13.5634i		−	0.670666i	−0.942100	−	0.335333i	$-0.891151\pi$
$409$		−	13.5634i		−	0.670666i	0.942100	−	0.335333i	$-0.108849\pi$
$410$	−7.13039	+	14.0472i	−0.352145	+	0.693744i
$411$		0			0
$412$	0.592220			0.0291766
$413$	11.3153	−	6.85706i	0.556789	−	0.337414i
$414$		0			0
$415$	−8.23558	−	4.18039i	−0.404269	−	0.205207i
$416$	4.41016			0.216226
$417$		0			0
$418$	−16.8892			−0.826077
$419$	−28.7199			−1.40306			−0.701530	−	0.712640i	$-0.747499\pi$
$419$	−28.7199			−1.40306			−0.701530	+	0.712640i	$0.747499\pi$
$420$		0			0
$421$	16.7998			0.818773			0.409387	−	0.912361i	$-0.365743\pi$
$421$	16.7998			0.818773			0.409387	+	0.912361i	$0.365743\pi$
$422$	−6.80243			−0.331137
$423$		0			0
$424$	8.31222			0.403677
$425$	17.8905	−	13.0820i	0.867815	−	0.634568i
$426$		0			0
$427$	−12.8090	−	21.1369i	−0.619869	−	1.02289i
$428$	−1.82143			−0.0880421
$429$		0			0
$430$	1.13569	+	0.576476i	0.0547677	+	0.0278001i
$431$			6.15313i			0.296386i	0.988958	+	0.148193i	$0.0473456\pi$
$431$			6.15313i			0.296386i	−0.988958	+	0.148193i	$0.952654\pi$
$432$		0			0
$433$	1.11688			0.0536740			0.0268370	−	0.999640i	$-0.491456\pi$
$433$	1.11688			0.0536740			0.0268370	+	0.999640i	$0.491456\pi$
$434$	7.83069	+	12.9219i	0.375885	+	0.620273i
$435$		0			0
$436$	−2.92566			−0.140114
$437$		−	24.0865i		−	1.15221i
$438$		0			0
$439$		−	28.2576i		−	1.34866i	−0.738430	−	0.674330i	$-0.764432\pi$
$439$		−	28.2576i		−	1.34866i	0.738430	−	0.674330i	$-0.235568\pi$
$440$	18.7241	+	9.50437i	0.892637	+	0.453103i
$441$		0			0
$442$			14.1159i			0.671426i
$443$	−2.90259			−0.137906			−0.0689530	−	0.997620i	$-0.521966\pi$
$443$	−2.90259			−0.137906			−0.0689530	+	0.997620i	$0.521966\pi$
$444$		0			0
$445$	5.27181	−	10.3857i	0.249908	−	0.492331i
$446$	28.3763			1.34366
$447$		0			0
$448$	19.9983	−	12.1189i	0.944830	−	0.572566i
$449$		−	4.70437i		−	0.222013i	−0.993820	−	0.111006i	$-0.964593\pi$
$449$		−	4.70437i		−	0.222013i	0.993820	−	0.111006i	$-0.0354074\pi$
$450$		0			0
$451$			16.9756i			0.799350i
$452$	4.45768			0.209672
$453$		0			0
$454$			12.5689i			0.589888i
$455$	1.09088	+	14.4967i	0.0511414	+	0.679616i
$456$		0			0
$457$			6.61275i			0.309331i	0.987967	+	0.154666i	$0.0494300\pi$
$457$			6.61275i			0.309331i	−0.987967	+	0.154666i	$0.950570\pi$
$458$			27.2972i			1.27551i
$459$		0			0
$460$	−1.87228	+	3.68849i	−0.0872955	+	0.171977i
$461$	23.5276			1.09579			0.547895	−	0.836547i	$-0.315429\pi$
$461$	23.5276			1.09579			0.547895	+	0.836547i	$0.315429\pi$
$462$		0			0
$463$			19.9066i			0.925138i	0.886583	+	0.462569i	$0.153072\pi$
$463$			19.9066i			0.925138i	−0.886583	+	0.462569i	$0.846928\pi$
$464$		−	1.10432i		−	0.0512667i
$465$		0			0
$466$	−3.78221			−0.175207
$467$			3.12676i			0.144689i	0.997380	+	0.0723445i	$0.0230481\pi$
$467$			3.12676i			0.144689i	−0.997380	+	0.0723445i	$0.976952\pi$
$468$		0			0
$469$	−21.5831	−	35.6157i	−0.996615	−	1.64458i
$470$	−26.5790	−	13.4915i	−1.22600	−	0.622318i
$471$		0			0
$472$	−15.0388			−0.692215
$473$	1.37244			0.0631049
$474$		0			0
$475$	16.8445	−	12.3171i	0.772879	−	0.565149i
$476$	−1.94819	−	3.21484i	−0.0892951	−	0.147352i
$477$		0			0
$478$		−	27.4125i		−	1.25382i
$479$	35.0419			1.60110			0.800552	−	0.599263i	$-0.204540\pi$
$479$	35.0419			1.60110			0.800552	+	0.599263i	$0.204540\pi$
$480$		0			0
$481$			27.6548i			1.26095i
$482$			10.5149i			0.478943i
$483$		0			0
$484$	−0.400350			−0.0181977
$485$	6.16525	−	12.1459i	0.279950	−	0.551515i
$486$		0			0
$487$			37.9781i			1.72095i	0.509491	+	0.860476i	$0.329834\pi$
$487$			37.9781i			1.72095i	−0.509491	+	0.860476i	$0.670166\pi$
$488$			28.0923i			1.27168i
$489$		0			0
$490$	11.7849	+	16.5102i	0.532389	+	0.745853i
$491$		−	0.553059i		−	0.0249592i	−0.999922	−	0.0124796i	$-0.996028\pi$
$491$		−	0.553059i		−	0.0249592i	0.999922	−	0.0124796i	$-0.00397248\pi$
$492$		0			0
$493$	−1.50330			−0.0677051
$494$			13.2906i			0.597974i
$495$		0			0
$496$		−	14.3491i		−	0.644295i
$497$	−13.8791	−	22.9029i	−0.622564	−	1.02733i
$498$		0			0
$499$	2.29461			0.102721			0.0513603	−	0.998680i	$-0.483644\pi$
$499$	2.29461			0.102721			0.0513603	+	0.998680i	$0.483644\pi$
$500$	−3.53692	+	0.576836i	−0.158176	+	0.0257969i
$501$		0			0
$502$	−17.7374			−0.791660
$503$			28.2455i			1.25940i	0.776837	+	0.629702i	$0.216823\pi$
$503$			28.2455i			1.25940i	−0.776837	+	0.629702i	$0.783177\pi$
$504$		0			0
$505$	3.23027	−	6.36380i	0.143745	−	0.283185i
$506$		−	23.3553i		−	1.03827i
$507$		0			0
$508$			2.12645i			0.0943461i
$509$	5.76910			0.255711			0.127855	−	0.991793i	$-0.459191\pi$
$509$	5.76910			0.255711			0.127855	+	0.991793i	$0.459191\pi$
$510$		0			0
$511$	−20.9751	+	12.7109i	−0.927886	+	0.562298i
$512$	−25.4285			−1.12379
$513$		0			0
$514$			10.8395i			0.478109i
$515$	1.86999	−	3.68398i	0.0824016	−	0.162335i
$516$		0			0
$517$	−32.1198			−1.41263
$518$	19.9984	+	33.0007i	0.878678	+	1.44997i
$519$		0			0
$520$	7.47929	−	14.7346i	0.327989	−	0.646155i
$521$	−11.2397			−0.492418			−0.246209	−	0.969217i	$-0.579185\pi$
$521$	−11.2397			−0.492418			−0.246209	+	0.969217i	$0.579185\pi$
$522$		0			0
$523$	−35.6945			−1.56081			−0.780405	−	0.625275i	$-0.784987\pi$
$523$	−35.6945			−1.56081			−0.780405	+	0.625275i	$0.784987\pi$
$524$	−7.02810			−0.307024
$525$		0			0
$526$	−25.7809			−1.12410
$527$	−19.5333			−0.850885
$528$		0			0
$529$	10.3080			0.448176
$530$	3.62540	−	7.14222i	0.157477	−	0.310238i
$531$		0			0
$532$	−1.83429	−	3.02689i	−0.0795266	−	0.131232i
$533$	13.3586			0.578627
$534$		0			0
$535$	−5.75133	+	11.3304i	−0.248652	+	0.489856i
$536$			47.3356i			2.04459i
$537$		0			0
$538$	33.0152			1.42339
$539$	19.3767	+	10.1163i	0.834616	+	0.435740i
$540$		0			0
$541$	36.7190			1.57867			0.789337	−	0.613960i	$-0.210424\pi$
$541$	36.7190			1.57867			0.789337	+	0.613960i	$0.210424\pi$
$542$			24.5142i			1.05298i
$543$		0			0
$544$			7.95527i			0.341079i
$545$	−9.23803	+	18.1994i	−0.395714	+	0.779576i
$546$		0			0
$547$		−	31.1748i		−	1.33294i	−0.745533	−	0.666469i	$-0.767805\pi$
$547$		−	31.1748i		−	1.33294i	0.745533	−	0.666469i	$-0.232195\pi$
$548$	−6.01455			−0.256929
$549$		0			0
$550$	16.3331	−	11.9432i	0.696447	−	0.509260i
$551$	−1.41541			−0.0602985
$552$		0			0
$553$	35.3843	−	21.4428i	1.50469	−	0.911842i
$554$		−	1.86356i		−	0.0791752i
$555$		0			0
$556$			1.54647i			0.0655850i
$557$	−45.6310			−1.93345			−0.966723	−	0.255826i	$-0.917653\pi$
$557$	−45.6310			−1.93345			−0.966723	+	0.255826i	$0.917653\pi$
$558$		0			0
$559$		−	1.08002i		−	0.0456798i
$560$	−1.44553	−	19.2096i	−0.0610849	−	0.811754i
$561$		0			0
$562$		−	35.9456i		−	1.51627i
$563$		−	40.8434i		−	1.72134i	−0.509159	−	0.860672i	$-0.670044\pi$
$563$		−	40.8434i		−	1.72134i	0.509159	−	0.860672i	$-0.329956\pi$
$564$		0			0
$565$	14.0755	−	27.7295i	0.592163	−	1.16659i
$566$	22.8788			0.961667
$567$		0			0
$568$			30.4394i			1.27721i
$569$		−	24.0613i		−	1.00870i	−0.863499	−	0.504351i	$-0.831732\pi$
$569$		−	24.0613i		−	1.00870i	0.863499	−	0.504351i	$-0.168268\pi$
$570$		0			0
$571$	28.2129			1.18067			0.590337	−	0.807157i	$-0.298995\pi$
$571$	28.2129			1.18067			0.590337	+	0.807157i	$0.298995\pi$
$572$		−	2.45955i		−	0.102839i
$573$		0			0
$574$	15.9410	−	9.66021i	0.665363	−	0.403209i
$575$	17.0328	+	23.2935i	0.710316	+	0.971405i
$576$		0			0
$577$	30.4955			1.26954			0.634772	−	0.772700i	$-0.281094\pi$
$577$	30.4955			1.26954			0.634772	+	0.772700i	$0.281094\pi$
$578$	−3.43197			−0.142751
$579$		0			0
$580$	0.216749	+	0.110022i	0.00900001	+	0.00456841i
$581$	5.66356	+	9.34583i	0.234964	+	0.387730i
$582$		0			0
$583$		−	8.63113i		−	0.357465i
$584$	27.8773			1.15357
$585$		0			0
$586$		−	18.3133i		−	0.756517i
$587$			4.54660i			0.187658i	0.995588	+	0.0938291i	$0.0299107\pi$
$587$			4.54660i			0.187658i	−0.995588	+	0.0938291i	$0.970089\pi$
$588$		0			0
$589$	−18.3913			−0.757802
$590$	−6.55919	+	12.9219i	−0.270038	+	0.531988i
$591$		0			0
$592$		−	36.6454i		−	1.50612i
$593$		−	24.8059i		−	1.01866i	−0.860572	−	0.509328i	$-0.829894\pi$
$593$		−	24.8059i		−	1.01866i	0.860572	−	0.509328i	$-0.170106\pi$
$594$		0			0
$595$	−26.1499	+	1.96779i	−1.07204	+	0.0806715i
$596$			4.46271i			0.182800i
$597$		0			0
$598$	−18.3790			−0.751573
$599$			7.12449i			0.291099i	0.989351	+	0.145549i	$0.0464950\pi$
$599$			7.12449i			0.291099i	−0.989351	+	0.145549i	$0.953505\pi$
$600$		0			0
$601$			32.8712i			1.34084i	0.741980	+	0.670422i	$0.233887\pi$
$601$			32.8712i			1.34084i	−0.741980	+	0.670422i	$0.766113\pi$
$602$	−0.781006	−	1.28879i	−0.0318314	−	0.0525272i
$603$		0			0
$604$	1.77690			0.0723012
$605$	−1.26414	+	2.49043i	−0.0513947	+	0.101250i
$606$		0			0
$607$	10.9433			0.444176			0.222088	−	0.975027i	$-0.428713\pi$
$607$	10.9433			0.444176			0.222088	+	0.975027i	$0.428713\pi$
$608$			7.49017i			0.303767i
$609$		0			0
$610$	24.1381	+	12.2525i	0.977325	+	0.496091i
$611$			25.2761i			1.02256i
$612$		0			0
$613$			24.5224i			0.990450i	0.868765	+	0.495225i	$0.164914\pi$
$613$			24.5224i			0.990450i	−0.868765	+	0.495225i	$0.835086\pi$
$614$	17.8797			0.721567
$615$		0			0
$616$	−12.8765	−	21.2483i	−0.518808	−	0.856120i
$617$	21.9156			0.882288			0.441144	−	0.897436i	$-0.354573\pi$
$617$	21.9156			0.882288			0.441144	+	0.897436i	$0.354573\pi$
$618$		0			0
$619$			18.8061i			0.755881i	0.925830	+	0.377941i	$0.123368\pi$
$619$			18.8061i			0.755881i	−0.925830	+	0.377941i	$0.876632\pi$
$620$	2.81636	+	1.42959i	0.113108	+	0.0574136i
$621$		0			0
$622$	15.0388			0.602999
$623$	−11.7859	+	7.14222i	−0.472191	+	0.286147i
$624$		0			0
$625$	−7.57986	+	23.8232i	−0.303195	+	0.952929i
$626$	−43.5689			−1.74136
$627$		0			0
$628$	−0.246864			−0.00985093
$629$	−49.8851			−1.98905
$630$		0			0
$631$	0.607960			0.0242025			0.0121013	−	0.999927i	$-0.496148\pi$
$631$	0.607960			0.0242025			0.0121013	+	0.999927i	$0.496148\pi$
$632$	−47.0280			−1.87067
$633$		0			0
$634$	−12.0715			−0.479421
$635$	13.2279	+	6.71447i	0.524932	+	0.266456i
$636$		0			0
$637$	7.96084	−	15.2482i	0.315420	−	0.604155i
$638$	−1.37244			−0.0543354
$639$		0			0
$640$	−7.95965	+	15.6809i	−0.314633	+	0.619842i
$641$		−	38.4450i		−	1.51849i	−0.650807	−	0.759244i	$-0.725569\pi$
$641$		−	38.4450i		−	1.51849i	0.650807	−	0.759244i	$-0.274431\pi$
$642$		0			0
$643$	19.8893			0.784356			0.392178	−	0.919889i	$-0.371722\pi$
$643$	19.8893			0.784356			0.392178	+	0.919889i	$0.371722\pi$
$644$	4.18574	−	2.53655i	0.164941	−	0.0999542i
$645$		0			0
$646$	−23.9743			−0.943258
$647$			31.1448i			1.22443i	0.790693	+	0.612213i	$0.209721\pi$
$647$			31.1448i			1.22443i	−0.790693	+	0.612213i	$0.790279\pi$
$648$		0			0
$649$			15.6157i			0.612971i
$650$	−9.39849	−	12.8531i	−0.368639	−	0.504139i
$651$		0			0
$652$		−	4.57749i		−	0.179268i
$653$	24.1754			0.946058			0.473029	−	0.881047i	$-0.343161\pi$
$653$	24.1754			0.946058			0.473029	+	0.881047i	$0.343161\pi$
$654$		0			0
$655$	−22.1919	+	43.7191i	−0.867108	+	1.70825i
$656$	−17.7016			−0.691131
$657$		0			0
$658$	18.2782	+	30.1622i	0.712560	+	1.17584i
$659$		−	39.1694i		−	1.52582i	−0.646502	−	0.762912i	$-0.723769\pi$
$659$		−	39.1694i		−	1.52582i	0.646502	−	0.762912i	$-0.276231\pi$
$660$		0			0
$661$			10.4944i			0.408185i	0.978952	+	0.204092i	$0.0654243\pi$
$661$			10.4944i			0.408185i	−0.978952	+	0.204092i	$0.934576\pi$
$662$	17.3919			0.675956
$663$		0			0
$664$		−	12.4212i		−	0.482036i
$665$	−24.6211	+	1.85274i	−0.954763	+	0.0718464i
$666$		0			0
$667$		−	1.95730i		−	0.0757870i
$668$			0.170245i			0.00658697i
$669$		0			0
$670$	40.6728	+	20.6456i	1.57133	+	0.797607i
$671$	29.1701			1.12610
$672$		0			0
$673$		−	20.6165i		−	0.794707i	−0.917666	−	0.397353i	$-0.869929\pi$
$673$		−	20.6165i		−	0.794707i	0.917666	−	0.397353i	$-0.130071\pi$
$674$		−	7.12629i		−	0.274494i
$675$		0			0
$676$	2.23141			0.0858233
$677$		−	32.9347i		−	1.26578i	−0.774241	−	0.632891i	$-0.781868\pi$
$677$		−	32.9347i		−	1.26578i	0.774241	−	0.632891i	$-0.218132\pi$
$678$		0			0
$679$	−13.7833	+	8.35265i	−0.528954	+	0.320545i
$680$	26.5790	+	13.4915i	1.01926	+	0.517377i
$681$		0			0
$682$	−17.8330			−0.682861
$683$	36.8848			1.41136			0.705678	−	0.708533i	$-0.250642\pi$
$683$	36.8848			1.41136			0.705678	+	0.708533i	$0.250642\pi$
$684$		0			0
$685$	−18.9915	+	37.4142i	−0.725628	+	1.42952i
$686$	−1.52688	−	23.9526i	−0.0582967	−	0.914514i
$687$		0			0
$688$			1.43113i			0.0545614i
$689$	−6.79211			−0.258759
$690$		0			0
$691$		−	7.73523i		−	0.294262i	−0.989117	−	0.147131i	$-0.952996\pi$
$691$		−	7.73523i		−	0.294262i	0.989117	−	0.147131i	$-0.0470039\pi$
$692$			6.26314i			0.238089i
$693$		0			0
$694$	−8.34876			−0.316914
$695$	9.62001	+	4.88312i	0.364908	+	0.185227i
$696$		0			0
$697$			24.0970i			0.912739i
$698$			27.8870i			1.05554i
$699$		0			0
$700$	3.91436	+	1.63011i	0.147949	+	0.0616124i
$701$		−	6.69316i		−	0.252797i	−0.991980	−	0.126399i	$-0.959658\pi$
$701$		−	6.69316i		−	0.252797i	0.991980	−	0.126399i	$-0.0403418\pi$
$702$		0			0
$703$	−46.9686			−1.77146
$704$			27.5988i			1.04017i
$705$		0			0
$706$			4.40671i			0.165849i
$707$	−7.22172	+	4.37635i	−0.271601	+	0.164590i
$708$		0			0
$709$	−43.9297			−1.64981			−0.824906	−	0.565269i	$-0.808772\pi$
$709$	−43.9297			−1.64981			−0.824906	+	0.565269i	$0.808772\pi$
$710$	26.1549	+	13.2762i	0.981574	+	0.498248i
$711$		0			0
$712$	15.6642			0.587040
$713$		−	25.4325i		−	0.952455i
$714$		0			0
$715$	−15.2999	−	7.76625i	−0.572184	−	0.290441i
$716$		−	4.35400i		−	0.162717i
$717$		0			0
$718$			45.3577i			1.69273i
$719$	−15.2050			−0.567049			−0.283525	−	0.958965i	$-0.591504\pi$
$719$	−15.2050			−0.567049			−0.283525	+	0.958965i	$0.591504\pi$
$720$		0			0
$721$	−4.18062	+	2.53345i	−0.155694	+	0.0943506i
$722$	2.05023			0.0763015
$723$		0			0
$724$			0.908947i			0.0337807i
$725$	1.36881	−	1.00091i	0.0508363	−	0.0371728i
$726$		0			0
$727$	−36.2551			−1.34463			−0.672314	−	0.740266i	$-0.734699\pi$
$727$	−36.2551			−1.34463			−0.672314	+	0.740266i	$0.734699\pi$
$728$	−16.7210	+	10.1329i	−0.619721	+	0.375550i
$729$		0			0
$730$	12.1588	−	23.9534i	0.450016	−	0.886555i
$731$	1.94819			0.0720564
$732$		0			0
$733$	−2.67380			−0.0987590			−0.0493795	−	0.998780i	$-0.515724\pi$
$733$	−2.67380			−0.0987590			−0.0493795	+	0.998780i	$0.515724\pi$
$734$	−19.4156			−0.716644
$735$		0			0
$736$	−10.3578			−0.381794
$737$	49.1517			1.81053
$738$		0			0
$739$	−13.1016			−0.481950			−0.240975	−	0.970531i	$-0.577467\pi$
$739$	−13.1016			−0.481950			−0.240975	+	0.970531i	$0.577467\pi$
$740$	7.19255	+	3.65094i	0.264403	+	0.134211i
$741$		0			0
$742$	−8.10508	+	4.91167i	−0.297547	+	0.180313i
$743$	−37.2732			−1.36742			−0.683710	−	0.729754i	$-0.739635\pi$
$743$	−37.2732			−1.36742			−0.683710	+	0.729754i	$0.739635\pi$
$744$		0			0
$745$	27.7608	+	14.0914i	1.01708	+	0.516269i
$746$		−	1.12084i		−	0.0410369i
$747$		0			0
$748$	4.43666			0.162220
$749$	12.8579	−	7.79187i	0.469817	−	0.284709i
$750$		0			0
$751$	1.81327			0.0661671			0.0330836	−	0.999453i	$-0.489467\pi$
$751$	1.81327			0.0661671			0.0330836	+	0.999453i	$0.489467\pi$
$752$		−	33.4935i		−	1.22138i
$753$		0			0
$754$			1.08002i			0.0393319i
$755$	5.61074	−	11.0534i	0.204196	−	0.402276i
$756$		0			0
$757$			41.1673i			1.49625i	0.663558	+	0.748125i	$0.269046\pi$
$757$			41.1673i			1.49625i	−0.663558	+	0.748125i	$0.730954\pi$
$758$	17.1028			0.621201
$759$		0			0
$760$	25.0251	+	12.7028i	0.907755	+	0.460778i
$761$	−40.2089			−1.45757			−0.728786	−	0.684742i	$-0.759915\pi$
$761$	−40.2089			−1.45757			−0.728786	+	0.684742i	$0.759915\pi$
$762$		0			0
$763$	20.6529	−	12.5156i	0.747685	−	0.453096i
$764$		−	2.32264i		−	0.0840301i
$765$		0			0
$766$			44.3379i			1.60200i
$767$	12.2885			0.443713
$768$		0			0
$769$		−	43.1940i		−	1.55761i	−0.627264	−	0.778807i	$-0.715825\pi$
$769$		−	43.1940i		−	1.55761i	0.627264	−	0.778807i	$-0.284175\pi$
$770$	−23.8736	+	1.79650i	−0.860345	+	0.0647413i
$771$		0			0
$772$			0.411236i			0.0148007i
$773$		−	17.9294i		−	0.644876i	−0.946591	−	0.322438i	$-0.895498\pi$
$773$		−	17.9294i		−	0.644876i	0.946591	−	0.322438i	$-0.104502\pi$
$774$		0			0
$775$	17.7858	−	13.0054i	0.638886	−	0.467169i
$776$	18.3189			0.657608
$777$		0			0
$778$		−	37.9426i		−	1.36031i
$779$			22.6882i			0.812889i
$780$		0			0
$781$	31.6073			1.13100
$782$		−	33.1530i		−	1.18555i
$783$		0			0
$784$	−10.5489	+	20.2054i	−0.376748	+	0.721622i
$785$	−0.779495	+	1.53564i	−0.0278214	+	0.0548095i
$786$		0			0
$787$	3.18126			0.113400			0.0566998	−	0.998391i	$-0.481942\pi$
$787$	3.18126			0.113400			0.0566998	+	0.998391i	$0.481942\pi$
$788$	0.813093			0.0289652
$789$		0			0
$790$	−20.5114	+	40.4085i	−0.729762	+	1.43767i
$791$	−31.4678	+	19.0695i	−1.11887	+	0.678032i
$792$		0			0
$793$		−	22.9549i		−	0.815152i
$794$	47.9262			1.70084
$795$		0			0
$796$		−	1.95129i		−	0.0691618i
$797$		−	49.3201i		−	1.74701i	−0.486817	−	0.873504i	$-0.661842\pi$
$797$		−	49.3201i		−	1.74701i	0.486817	−	0.873504i	$-0.338158\pi$
$798$		0			0
$799$	−45.5943			−1.61301
$800$	−5.29668	−	7.24357i	−0.187266	−	0.256099i
$801$		0			0
$802$			20.3388i			0.718189i
$803$		−	28.9469i		−	1.02151i
$804$		0			0
$805$	−2.56207	−	34.0473i	−0.0903012	−	1.20001i
$806$			14.0334i			0.494304i
$807$		0			0
$808$	9.59813			0.337661
$809$		−	23.6595i		−	0.831824i	−0.909405	−	0.415912i	$-0.863462\pi$
$809$		−	23.6595i		−	0.831824i	0.909405	−	0.415912i	$-0.136538\pi$
$810$		0			0
$811$			24.4644i			0.859062i	0.903052	+	0.429531i	$0.141321\pi$
$811$			24.4644i			0.859062i	−0.903052	+	0.429531i	$0.858679\pi$
$812$	−0.149057	−	0.245969i	−0.00523088	−	0.00863183i
$813$		0			0
$814$	−45.5428			−1.59627
$815$	−28.4748	−	14.4538i	−0.997428	−	0.506296i
$816$		0			0
$817$	1.83429			0.0641737
$818$		−	17.5774i		−	0.614578i
$819$		0			0
$820$	1.76359	−	3.47436i	0.0615872	−	0.121330i
$821$		−	4.27834i		−	0.149315i	−0.997209	−	0.0746575i	$-0.976214\pi$
$821$		−	4.27834i		−	0.149315i	0.997209	−	0.0746575i	$-0.0237864\pi$
$822$		0			0
$823$			23.1241i			0.806054i	0.915188	+	0.403027i	$0.132042\pi$
$823$			23.1241i			0.806054i	−0.915188	+	0.403027i	$0.867958\pi$
$824$	5.55631			0.193563
$825$		0			0
$826$	14.6640	−	8.88636i	0.510225	−	0.309196i
$827$	15.8917			0.552609			0.276305	−	0.961070i	$-0.410890\pi$
$827$	15.8917			0.552609			0.276305	+	0.961070i	$0.410890\pi$
$828$		0			0
$829$		−	16.5336i		−	0.574237i	−0.957895	−	0.287119i	$-0.907303\pi$
$829$		−	16.5336i		−	0.574237i	0.957895	−	0.287119i	$-0.0926974\pi$
$830$	−10.6728	−	5.41754i	−0.370460	−	0.188046i
$831$		0			0
$832$	21.7183			0.752948
$833$	27.5054	+	14.3602i	0.953007	+	0.497550i
$834$		0			0
$835$	1.05903	+	0.537564i	0.0366492	+	0.0186032i
$836$	4.17727			0.144474
$837$		0			0
$838$	−37.2194			−1.28572
$839$	−43.5160			−1.50234			−0.751170	−	0.660109i	$-0.770510\pi$
$839$	−43.5160			−1.50234			−0.751170	+	0.660109i	$0.770510\pi$
$840$		0			0
$841$	28.8850			0.996034
$842$	21.7716			0.750300
$843$		0			0
$844$	1.68247			0.0579131
$845$	7.04587	−	13.8807i	0.242385	−	0.477512i
$846$		0			0
$847$	2.82616	−	1.71265i	0.0971082	−	0.0588474i
$848$	9.00025			0.309070
$849$		0			0
$850$	23.1850	−	16.9535i	0.795240	−	0.581499i
$851$		−	64.9507i		−	2.22648i
$852$		0			0
$853$	12.1684			0.416637			0.208318	−	0.978061i	$-0.433201\pi$
$853$	12.1684			0.416637			0.208318	+	0.978061i	$0.433201\pi$
$854$	−16.5997	−	27.3923i	−0.568029	−	0.937344i
$855$		0			0
$856$	−17.0890			−0.584088
$857$		−	25.9807i		−	0.887485i	−0.896154	−	0.443742i	$-0.853651\pi$
$857$		−	25.9807i		−	0.887485i	0.896154	−	0.443742i	$-0.146349\pi$
$858$		0			0
$859$		−	30.2202i		−	1.03110i	−0.856859	−	0.515550i	$-0.827587\pi$
$859$		−	30.2202i		−	1.03110i	0.856859	−	0.515550i	$-0.172413\pi$
$860$	−0.280894	−	0.142582i	−0.00957841	−	0.00486201i
$861$		0			0
$862$			7.97410i			0.271599i
$863$	−13.9006			−0.473181			−0.236590	−	0.971609i	$-0.576030\pi$
$863$	−13.9006			−0.473181			−0.236590	+	0.971609i	$0.576030\pi$
$864$		0			0
$865$	38.9606	+	19.7764i	1.32470	+	0.672419i
$866$	1.44742			0.0491853
$867$		0			0
$868$	−1.93680	−	3.19604i	−0.0657391	−	0.108481i
$869$			48.8323i			1.65652i
$870$		0			0
$871$		−	38.6790i		−	1.31059i
$872$	−27.4490			−0.929541
$873$		0			0
$874$		−	31.2147i		−	1.05585i
$875$	22.5003	−	19.2025i	0.760648	−	0.649164i
$876$		0			0
$877$		−	22.2450i		−	0.751161i	−0.926790	−	0.375581i	$-0.877443\pi$
$877$		−	22.2450i		−	0.751161i	0.926790	−	0.375581i	$-0.122557\pi$
$878$		−	36.6202i		−	1.23587i
$879$		0			0
$880$	20.2740	+	10.2911i	0.683435	+	0.346912i
$881$	32.2821			1.08761			0.543806	−	0.839211i	$-0.316983\pi$
$881$	32.2821			1.08761			0.543806	+	0.839211i	$0.316983\pi$
$882$		0			0
$883$		−	24.0031i		−	0.807768i	−0.914810	−	0.403884i	$-0.867660\pi$
$883$		−	24.0031i		−	0.807768i	0.914810	−	0.403884i	$-0.132340\pi$
$884$		−	3.49135i		−	0.117427i
$885$		0			0
$886$	−3.76159			−0.126373
$887$			52.1894i			1.75235i	0.481995	+	0.876174i	$0.339912\pi$
$887$			52.1894i			1.75235i	−0.481995	+	0.876174i	$0.660088\pi$
$888$		0			0
$889$	−9.09673	−	15.0111i	−0.305095	−	0.503457i
$890$	6.83197	−	13.4593i	0.229008	−	0.451158i
$891$		0			0
$892$	−7.01844			−0.234995
$893$	−42.9287			−1.43655
$894$		0			0
$895$	−27.0846	−	13.7482i	−0.905338	−	0.459550i
$896$	17.7949	−	10.7837i	0.594485	−	0.360257i
$897$		0			0
$898$		−	6.09660i		−	0.203446i
$899$	−1.49451			−0.0498446
$900$		0			0
$901$		−	12.2520i		−	0.408172i
$902$			21.9994i			0.732501i
$903$		0			0
$904$	41.8227			1.39100
$905$	5.65421	+	2.87008i	0.187952	+	0.0954048i
$906$		0			0
$907$			10.6240i			0.352764i	0.984322	+	0.176382i	$0.0564393\pi$
$907$			10.6240i			0.352764i	−0.984322	+	0.176382i	$0.943561\pi$
$908$		−	3.10872i		−	0.103166i
$909$		0			0
$910$	1.41372	+	18.7869i	0.0468644	+	0.622780i
$911$		−	6.24531i		−	0.206916i	−0.994634	−	0.103458i	$-0.967009\pi$
$911$		−	6.24531i		−	0.206916i	0.994634	−	0.103458i	$-0.0329908\pi$
$912$		0			0
$913$	−12.8978			−0.426854
$914$			8.56975i			0.283462i
$915$		0			0
$916$		−	6.75152i		−	0.223077i
$917$	49.6130	−	30.0654i	1.63836	−	0.992847i
$918$		0			0
$919$	0.0465465			0.00153543			0.000767714	−	1.00000i	$-0.499756\pi$
$919$	0.0465465			0.00153543			0.000767714		1.00000i	$0.499756\pi$
$920$	−17.5660	+	34.6060i	−0.579135	+	1.14093i
$921$		0			0
$922$	30.4904			1.00415
$923$		−	24.8728i		−	0.818697i
$924$		0			0
$925$	45.4223	−	33.2139i	1.49347	−	1.09207i
$926$			25.7978i			0.847769i
$927$		0			0
$928$			0.608662i			0.0199803i
$929$	−29.3775			−0.963846			−0.481923	−	0.876214i	$-0.660062\pi$
$929$	−29.3775			−0.963846			−0.481923	+	0.876214i	$0.660062\pi$
$930$		0			0
$931$	25.8974	+	13.5206i	0.848752	+	0.443120i
$932$	0.935469			0.0306423
$933$		0			0
$934$			4.05210i			0.132589i
$935$	14.0092	−	27.5988i	0.458148	−	0.902576i
$936$		0			0
$937$	−5.98900			−0.195652			−0.0978261	−	0.995204i	$-0.531189\pi$
$937$	−5.98900			−0.195652			−0.0978261	+	0.995204i	$0.531189\pi$
$938$	−27.9705	−	46.1560i	−0.913268	−	1.50705i
$939$		0			0
$940$	6.57389	+	3.33692i	0.214417	+	0.108838i
$941$	−37.6846			−1.22848			−0.614242	−	0.789118i	$-0.710538\pi$
$941$	−37.6846			−1.22848			−0.614242	+	0.789118i	$0.710538\pi$
$942$		0			0
$943$	−31.3744			−1.02169
$944$	−16.2836			−0.529985
$945$		0			0
$946$	1.77860			0.0578274
$947$	23.0637			0.749469			0.374734	−	0.927132i	$-0.377734\pi$
$947$	23.0637			0.749469			0.374734	+	0.927132i	$0.377734\pi$
$948$		0			0
$949$	−22.7792			−0.739444
$950$	21.8295	−	15.9623i	0.708243	−	0.517885i
$951$		0			0
$952$	−18.2782	−	30.1622i	−0.592401	−	0.977562i
$953$	28.2138			0.913936			0.456968	−	0.889483i	$-0.348935\pi$
$953$	28.2138			0.913936			0.456968	+	0.889483i	$0.348935\pi$
$954$		0			0
$955$	−14.4482	−	7.33394i	−0.467534	−	0.237321i
$956$			6.78005i			0.219282i
$957$		0			0
$958$	45.4123			1.46720
$959$	42.4581	−	25.7296i	1.37104	−	0.830851i
$960$		0			0
$961$	11.5809			0.373577
$962$			35.8390i			1.15550i
$963$		0			0
$964$		−	2.60070i		−	0.0837631i
$965$	2.55814	+	1.29851i	0.0823494	+	0.0418006i
$966$		0			0
$967$			2.26006i			0.0726785i	0.999340	+	0.0363393i	$0.0115697\pi$
$967$			2.26006i			0.0726785i	−0.999340	+	0.0363393i	$0.988430\pi$
$968$	−3.75615			−0.120727
$969$		0			0
$970$	7.98982	−	15.7404i	0.256538	−	0.505392i
$971$	−15.1814			−0.487195			−0.243597	−	0.969876i	$-0.578328\pi$
$971$	−15.1814			−0.487195			−0.243597	+	0.969876i	$0.578328\pi$
$972$		0			0
$973$	−6.61563	−	10.9169i	−0.212087	−	0.349980i
$974$			49.2175i			1.57703i
$975$		0			0
$976$			30.4176i			0.973644i
$977$	32.1784			1.02948			0.514740	−	0.857347i	$-0.327889\pi$
$977$	32.1784			1.02948			0.514740	+	0.857347i	$0.327889\pi$
$978$		0			0
$979$		−	16.2652i		−	0.519836i
$980$	−2.91482	−	4.08352i	−0.0931104	−	0.130443i
$981$		0			0
$982$		−	0.716732i		−	0.0228719i
$983$			6.61109i			0.210861i	0.994427	+	0.105430i	$0.0336220\pi$
$983$			6.61109i			0.210861i	−0.994427	+	0.105430i	$0.966378\pi$
$984$		0			0
$985$	2.56742	−	5.05794i	0.0818047	−	0.161159i
$986$	−1.94819			−0.0620430
$987$		0			0
$988$		−	3.28723i		−	0.104581i
$989$			2.53655i			0.0806577i
$990$		0			0
$991$	30.1162			0.956673			0.478337	−	0.878177i	$-0.341240\pi$
$991$	30.1162			0.956673			0.478337	+	0.878177i	$0.341240\pi$
$992$			7.90875i			0.251103i
$993$		0			0
$994$	−17.9866	−	29.6808i	−0.570499	−	0.941419i
$995$	−12.1383	−	6.16139i	−0.384808	−	0.195329i
$996$		0			0
$997$	12.1294			0.384142			0.192071	−	0.981381i	$-0.438480\pi$
$997$	12.1294			0.384142			0.192071	+	0.981381i	$0.438480\pi$
$998$	2.97368			0.0941301
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.g.a.944.22	yes	32
3.2	odd	2	inner	945.2.g.a.944.11	yes	32
5.4	even	2	inner	945.2.g.a.944.9	✓	32
7.6	odd	2	inner	945.2.g.a.944.23	yes	32
15.14	odd	2	inner	945.2.g.a.944.24	yes	32
21.20	even	2	inner	945.2.g.a.944.10	yes	32
35.34	odd	2	inner	945.2.g.a.944.12	yes	32
105.104	even	2	inner	945.2.g.a.944.21	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.g.a.944.9	✓	32	5.4	even	2	inner
945.2.g.a.944.10	yes	32	21.20	even	2	inner
945.2.g.a.944.11	yes	32	3.2	odd	2	inner
945.2.g.a.944.12	yes	32	35.34	odd	2	inner
945.2.g.a.944.21	yes	32	105.104	even	2	inner
945.2.g.a.944.22	yes	32	1.1	even	1	trivial
945.2.g.a.944.23	yes	32	7.6	odd	2	inner
945.2.g.a.944.24	yes	32	15.14	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.29594 q^{2} -0.320531 q^{4} +(-1.01211 + 1.99390i) q^{5} +(2.26270 - 1.37120i) q^{7} -3.00728 q^{8} +O(q^{10})\)	\(q+1.29594 q^{2} -0.320531 q^{4} +(-1.01211 + 1.99390i) q^{5} +(2.26270 - 1.37120i) q^{7} -3.00728 q^{8} +(-1.31163 + 2.58398i) q^{10} +3.12266i q^{11} +2.45732 q^{13} +(2.93233 - 1.77699i) q^{14} -3.25620 q^{16} +4.43263i q^{17} +4.17348i q^{19} +(0.324411 - 0.639107i) q^{20} +4.04678i q^{22} -5.77131 q^{23} +(-2.95128 - 4.03608i) q^{25} +3.18454 q^{26} +(-0.725266 + 0.439511i) q^{28} +0.339143i q^{29} +4.40671i q^{31} +1.79471 q^{32} +5.74444i q^{34} +(0.443932 + 5.89940i) q^{35} +11.2541i q^{37} +5.40860i q^{38} +(3.04368 - 5.99621i) q^{40} +5.43627 q^{41} -0.439511i q^{43} -1.00091i q^{44} -7.47929 q^{46} +10.2861i q^{47} +(3.23965 - 6.20521i) q^{49} +(-3.82469 - 5.23053i) q^{50} -0.787646 q^{52} -2.76404 q^{53} +(-6.22627 - 3.16046i) q^{55} +(-6.80457 + 4.12356i) q^{56} +0.439511i q^{58} +5.00079 q^{59} -9.34145i q^{61} +5.71085i q^{62} +8.83823 q^{64} +(-2.48707 + 4.89965i) q^{65} -15.7404i q^{67} -1.42080i q^{68} +(0.575311 + 7.64529i) q^{70} -10.1219i q^{71} -9.26995 q^{73} +14.5846i q^{74} -1.33773i q^{76} +(4.28177 + 7.06564i) q^{77} +15.6381 q^{79} +(3.29562 - 6.49254i) q^{80} +7.04510 q^{82} +4.13038i q^{83} +(-8.83823 - 4.48630i) q^{85} -0.569581i q^{86} -9.39069i q^{88} -5.20876 q^{89} +(5.56018 - 3.36946i) q^{91} +1.84988 q^{92} +13.3302i q^{94} +(-8.32151 - 4.22401i) q^{95} -6.09151 q^{97} +(4.19840 - 8.04161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4}+O(q^{10}) \) 32 * q + 32 * q^4	\( 32 q + 32 q^{4} + 32 q^{16} - 28 q^{25} + 72 q^{46} - 52 q^{49} + 56 q^{64} - 48 q^{70} - 80 q^{79} - 56 q^{85} - 20 q^{91}+O(q^{100}) \) 32 * q + 32 * q^4 + 32 * q^16 - 28 * q^25 + 72 * q^46 - 52 * q^49 + 56 * q^64 - 48 * q^70 - 80 * q^79 - 56 * q^85 - 20 * q^91

Introduction

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