LMFDB - Embedded newform 945.2.g.a.944.9

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			944.9
Character	$\chi$	$=$	945.944
Dual form			945.2.g.a.944.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29594 q^{2} -0.320531 q^{4} +(-1.01211 - 1.99390i) q^{5} +(-2.26270 + 1.37120i) q^{7} +3.00728 q^{8} +O(q^{10})$	\(q-1.29594 q^{2} -0.320531 q^{4} +(-1.01211 - 1.99390i) q^{5} +(-2.26270 + 1.37120i) q^{7} +3.00728 q^{8} +(1.31163 + 2.58398i) q^{10} +3.12266i q^{11} -2.45732 q^{13} +(2.93233 - 1.77699i) q^{14} -3.25620 q^{16} -4.43263i q^{17} +4.17348i q^{19} +(0.324411 + 0.639107i) q^{20} -4.04678i q^{22} +5.77131 q^{23} +(-2.95128 + 4.03608i) q^{25} +3.18454 q^{26} +(0.725266 - 0.439511i) q^{28} +0.339143i q^{29} +4.40671i q^{31} -1.79471 q^{32} +5.74444i q^{34} +(5.02412 + 3.12381i) q^{35} -11.2541i q^{37} -5.40860i q^{38} +(-3.04368 - 5.99621i) q^{40} +5.43627 q^{41} +0.439511i q^{43} -1.00091i q^{44} -7.47929 q^{46} -10.2861i q^{47} +(3.23965 - 6.20521i) q^{49} +(3.82469 - 5.23053i) q^{50} +0.787646 q^{52} +2.76404 q^{53} +(6.22627 - 3.16046i) q^{55} +(-6.80457 + 4.12356i) q^{56} -0.439511i q^{58} +5.00079 q^{59} -9.34145i q^{61} -5.71085i q^{62} +8.83823 q^{64} +(2.48707 + 4.89965i) q^{65} +15.7404i q^{67} +1.42080i q^{68} +(-6.51098 - 4.04828i) q^{70} -10.1219i q^{71} +9.26995 q^{73} +14.5846i q^{74} -1.33773i q^{76} +(-4.28177 - 7.06564i) q^{77} +15.6381 q^{79} +(3.29562 + 6.49254i) q^{80} -7.04510 q^{82} -4.13038i q^{83} +(-8.83823 + 4.48630i) q^{85} -0.569581i q^{86} +9.39069i q^{88} -5.20876 q^{89} +(5.56018 - 3.36946i) q^{91} -1.84988 q^{92} +13.3302i q^{94} +(8.32151 - 4.22401i) q^{95} +6.09151 q^{97} +(-4.19840 + 8.04161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.651500\pi$
$2$	−1.29594			−0.916370			−0.458185	+	0.888857i	$0.651500\pi$
$3$		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	$-0.610687\pi$
$13$	−2.45732			−0.681537			−0.340769	+	0.940147i	$0.610687\pi$
$14$	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	$-0.819355\pi$
$17$		−	4.43263i		−	1.07507i	0.843241	−	0.537536i	$-0.180645\pi$
$18$		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	$-0.294490\pi$
$23$	5.77131			1.20340			0.601701	+	0.798721i	$0.294490\pi$
$24$		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
$35$	5.02412	+	3.12381i	0.849232	+	0.528020i
$36$		0			0
$37$		−	11.2541i		−	1.85016i	−0.379777	−	0.925078i	$-0.623999\pi$
$37$		−	11.2541i		−	1.85016i	0.379777	−	0.925078i	$-0.376001\pi$
$38$		−	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	$0.0106693\pi$
$43$			0.439511i			0.0670247i	−0.999438	+	0.0335124i	$0.989331\pi$
$44$		−	1.00091i		−	0.150893i
$45$		0			0
$46$	−7.47929			−1.10276
$47$		−	10.2861i		−	1.50038i	−0.661224	−	0.750188i	$-0.729963\pi$
$47$		−	10.2861i		−	1.50038i	0.661224	−	0.750188i	$-0.270037\pi$
$48$		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	$-0.439205\pi$
$53$	2.76404			0.379670			0.189835	+	0.981816i	$0.439205\pi$
$54$		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	$0.411381\pi$
$67$			15.7404i			1.92299i	−0.274822	+	0.961495i	$0.588619\pi$
$68$			1.42080i			0.172297i
$69$		0			0
$70$	−6.51098	−	4.04828i	−0.778211	−	0.483862i
$71$		−	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	$-0.317484\pi$
$73$	9.26995			1.08497			0.542483	+	0.840067i	$0.317484\pi$
$74$			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	$-0.927211\pi$
$83$		−	4.13038i		−	0.453369i	0.973968	−	0.226684i	$-0.0727886\pi$
$84$		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	$-0.399922\pi$
$97$	6.09151			0.618499			0.309250	+	0.950981i	$0.399922\pi$
$98$	−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	$-0.470985\pi$
$103$	1.84762			0.182052			0.0910258	+	0.995849i	$0.470985\pi$
$104$	−7.38983			−0.724633
$105$		0			0
$106$	−3.58203			−0.347918
$107$	−5.68254			−0.549351			−0.274676	−	0.961537i	$-0.588570\pi$
$107$	−5.68254			−0.549351			−0.274676	+	0.961537i	$0.588570\pi$
$108$		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	$-0.273031\pi$
$113$	13.9072			1.30828			0.654139	+	0.756374i	$0.273031\pi$
$114$		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	$0.0951009\pi$
$127$			6.63416i			0.588687i	−0.955700	+	0.294343i	$0.904899\pi$
$128$	−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	$-0.796003\pi$
$137$	−18.7643			−1.60315			−0.801573	+	0.597897i	$0.796003\pi$
$138$		0			0
$139$		−	4.82472i		−	0.409227i	−0.978843	−	0.204614i	$-0.934406\pi$
$139$		−	4.82472i		−	0.409227i	0.978843	−	0.204614i	$-0.0655938\pi$
$140$	−1.61039	−	1.00128i	−0.136103	−	0.0846234i
$141$		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	$-0.509784\pi$
$157$	−0.770171			−0.0614663			−0.0307332	+	0.999528i	$0.509784\pi$
$158$	−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	$-0.811076\pi$
$163$		−	14.2809i		−	1.11857i	0.828975	−	0.559285i	$-0.188924\pi$
$164$	−1.74249			−0.136066
$165$		0			0
$166$			5.35274i			0.415453i
$167$			0.531134i			0.0411004i	0.999789	+	0.0205502i	$0.00654178\pi$
$167$			0.531134i			0.0411004i	−0.999789	+	0.0205502i	$0.993458\pi$
$168$		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	$0.266500\pi$
$173$			19.5399i			1.48559i	−0.669519	+	0.742795i	$0.733500\pi$
$174$		0			0
$175$	1.14362	−	13.1792i	0.0864498	−	0.996256i
$176$		−	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	$0.0147034\pi$
$193$			1.28298i			0.0923511i	−0.998933	+	0.0461755i	$0.985297\pi$
$194$	−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	$-0.471196\pi$
$197$	2.53671			0.180733			0.0903665	+	0.995909i	$0.471196\pi$
$198$		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	$-0.761947\pi$
$223$	−21.8963			−1.46628			−0.733142	+	0.680076i	$0.761947\pi$
$224$	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	$-0.895692\pi$
$227$		−	9.69865i		−	0.643722i	0.946787	−	0.321861i	$-0.104308\pi$
$228$		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	$-0.469523\pi$
$233$	2.91850			0.191197			0.0955986	+	0.995420i	$0.469523\pi$
$234$		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
$245$	−15.6515	−	0.179200i	−0.999934	−	0.0114487i
$246$		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	$-0.915990\pi$
$257$		−	8.36416i		−	0.521742i	0.965374	−	0.260871i	$-0.0840097\pi$
$258$		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	$-0.289824\pi$
$263$	19.8935			1.22669			0.613344	+	0.789816i	$0.289824\pi$
$264$		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	$0.0137554\pi$
$277$			1.43800i			0.0864008i	−0.999066	+	0.0432004i	$0.986245\pi$
$278$			6.25256i			0.375004i
$279$		0			0
$280$	15.1089	+	9.39416i	0.902931	+	0.561408i
$281$		−	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	$-0.675828\pi$
$283$	−17.6542			−1.04943			−0.524715	+	0.851278i	$0.675828\pi$
$284$			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	$0.135442\pi$
$293$			14.1313i			0.825558i	−0.910831	+	0.412779i	$0.864558\pi$
$294$		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	$-0.628808\pi$
$307$	−13.7967			−0.787418			−0.393709	+	0.919235i	$0.628808\pi$
$308$	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	$-0.100939\pi$
$313$	33.6194			1.90028			0.950141	+	0.311821i	$0.100939\pi$
$314$	0.998098			0.0563259
$315$		0			0
$316$	−5.01248			−0.281974
$317$	9.31484			0.523174			0.261587	−	0.965180i	$-0.415754\pi$
$317$	9.31484			0.523174			0.261587	+	0.965180i	$0.415754\pi$
$318$		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	$0.0478542\pi$
$337$			5.49892i			0.299545i	−0.988720	+	0.149773i	$0.952146\pi$
$338$	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	$-0.444680\pi$
$347$	6.44222			0.345837			0.172918	+	0.984936i	$0.444680\pi$
$348$		0			0
$349$			21.5187i			1.15187i	0.817497	+	0.575933i	$0.195361\pi$
$349$			21.5187i			1.15187i	−0.817497	+	0.575933i	$0.804639\pi$
$350$	−1.48207	+	17.0795i	−0.0792200	+	0.912940i
$351$		0			0
$352$		−	5.60425i		−	0.298707i
$353$		−	3.40039i		−	0.180984i	−0.995897	−	0.0904922i	$-0.971156\pi$
$353$		−	3.40039i		−	0.180984i	0.995897	−	0.0904922i	$-0.0288440\pi$
$354$		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	$-0.372121\pi$
$367$	14.9818			0.782046			0.391023	+	0.920381i	$0.372121\pi$
$368$	−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	$0.00712787\pi$
$373$			0.864884i			0.0447820i	−0.999749	+	0.0223910i	$0.992872\pi$
$374$	−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	$-0.661453\pi$
$383$		−	34.2129i		−	1.74820i	0.485749	−	0.874098i	$-0.338547\pi$
$384$		0			0
$385$	−9.75458	+	15.6886i	−0.497140	+	0.799565i
$386$		−	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	$-0.878498\pi$
$397$	−36.9817			−1.85606			−0.928029	+	0.372508i	$0.878498\pi$
$398$		−	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	$-0.508544\pi$
$433$	−1.11688			−0.0536740			−0.0268370	+	0.999640i	$0.508544\pi$
$434$	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	$-0.478034\pi$
$443$	2.90259			0.137906			0.0689530	+	0.997620i	$0.478034\pi$
$444$		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
$455$	−12.3459	−	7.67619i	−0.578783	−	0.359865i
$456$		0			0
$457$		−	6.61275i		−	0.309331i	−0.987967	−	0.154666i	$-0.950570\pi$
$457$		−	6.61275i		−	0.309331i	0.987967	−	0.154666i	$-0.0494300\pi$
$458$		−	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	$-0.846928\pi$
$463$		−	19.9066i		−	0.925138i	0.886583	−	0.462569i	$-0.153072\pi$
$464$		−	1.10432i		−	0.0512667i
$465$		0			0
$466$	−3.78221			−0.175207
$467$		−	3.12676i		−	0.144689i	−0.997380	−	0.0723445i	$-0.976952\pi$
$467$		−	3.12676i		−	0.144689i	0.997380	−	0.0723445i	$-0.0230481\pi$
$468$		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	$-0.670166\pi$
$487$		−	37.9781i		−	1.72095i	0.509491	−	0.860476i	$-0.329834\pi$
$488$		−	28.0923i		−	1.27168i
$489$		0			0
$490$	20.2834	+	0.232233i	0.916310	+	0.0104912i
$491$		−	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	$-0.783177\pi$
$503$		−	28.2455i		−	1.25940i	0.776837	−	0.629702i	$-0.216823\pi$
$504$		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	$-0.215013\pi$
$523$	35.6945			1.56081			0.780405	+	0.625275i	$0.215013\pi$
$524$	−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	$0.232195\pi$
$547$			31.1748i			1.33294i	−0.745533	+	0.666469i	$0.767805\pi$
$548$	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	$-0.0823473\pi$
$557$	45.6310			1.93345			0.966723	+	0.255826i	$0.0823473\pi$
$558$		0			0
$559$		−	1.08002i		−	0.0456798i
$560$	−16.3595	−	10.1717i	−0.691317	−	0.429835i
$561$		0			0
$562$			35.9456i			1.51627i
$563$			40.8434i			1.72134i	0.509159	+	0.860672i	$0.329956\pi$
$563$			40.8434i			1.72134i	−0.509159	+	0.860672i	$0.670044\pi$
$564$		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	$-0.718906\pi$
$577$	−30.4955			−1.26954			−0.634772	+	0.772700i	$0.718906\pi$
$578$	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	$-0.970089\pi$
$587$		−	4.54660i		−	0.187658i	0.995588	−	0.0938291i	$-0.0299107\pi$
$588$		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	$0.170106\pi$
$593$			24.8059i			1.01866i	−0.860572	+	0.509328i	$0.829894\pi$
$594$		0			0
$595$	13.8467	−	22.2701i	0.567660	−	0.912985i
$596$			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	$-0.571287\pi$
$607$	−10.9433			−0.444176			−0.222088	+	0.975027i	$0.571287\pi$
$608$		−	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	$-0.835086\pi$
$613$		−	24.5224i		−	0.990450i	0.868765	−	0.495225i	$-0.164914\pi$
$614$	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	$-0.645427\pi$
$617$	−21.9156			−0.882288			−0.441144	+	0.897436i	$0.645427\pi$
$618$		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	$-0.628278\pi$
$643$	−19.8893			−0.784356			−0.392178	+	0.919889i	$0.628278\pi$
$644$	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	$-0.790279\pi$
$647$		−	31.1448i		−	1.22443i	0.790693	−	0.612213i	$-0.209721\pi$
$648$		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	$-0.656839\pi$
$653$	−24.1754			−0.946058			−0.473029	+	0.881047i	$0.656839\pi$
$654$		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
$665$	−13.0372	+	20.9681i	−0.505560	+	0.813108i
$666$		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	$0.130071\pi$
$673$			20.6165i			0.794707i	−0.917666	+	0.397353i	$0.869929\pi$
$674$		−	7.12629i		−	0.274494i
$675$		0			0
$676$	2.23141			0.0858233
$677$			32.9347i			1.26578i	0.774241	+	0.632891i	$0.218132\pi$
$677$			32.9347i			1.26578i	−0.774241	+	0.632891i	$0.781868\pi$
$678$		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	$-0.749358\pi$
$683$	−36.8848			−1.41136			−0.705678	+	0.708533i	$0.749358\pi$
$684$		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
$700$	−0.366566	+	4.22435i	−0.0138549	+	0.159665i
$701$		−	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	$-0.265301\pi$
$727$	36.2551			1.34463			0.672314	+	0.740266i	$0.265301\pi$
$728$	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	$-0.484276\pi$
$733$	2.67380			0.0987590			0.0493795	+	0.998780i	$0.484276\pi$
$734$	−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	$-0.260365\pi$
$743$	37.2732			1.36742			0.683710	+	0.729754i	$0.260365\pi$
$744$		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	$-0.730954\pi$
$757$		−	41.1673i		−	1.49625i	0.663558	−	0.748125i	$-0.269046\pi$
$758$	−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	$-0.284175\pi$
$770$	12.6414	−	20.3315i	0.455564	−	0.732698i
$771$		0			0
$772$		−	0.411236i		−	0.0148007i
$773$			17.9294i			0.644876i	0.946591	+	0.322438i	$0.104502\pi$
$773$			17.9294i			0.644876i	−0.946591	+	0.322438i	$0.895498\pi$
$774$		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	$-0.518058\pi$
$787$	−3.18126			−0.113400			−0.0566998	+	0.998391i	$0.518058\pi$
$788$	−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	$0.338158\pi$
$797$			49.3201i			1.74701i	−0.486817	+	0.873504i	$0.661842\pi$
$798$		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
$805$	28.9958	+	18.0285i	1.02197	+	0.635421i
$806$			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	$-0.867958\pi$
$823$		−	23.1241i		−	0.806054i	0.915188	−	0.403027i	$-0.132042\pi$
$824$	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	$-0.589110\pi$
$827$	−15.8917			−0.552609			−0.276305	+	0.961070i	$0.589110\pi$
$828$		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	$-0.566799\pi$
$853$	−12.1684			−0.416637			−0.208318	+	0.978061i	$0.566799\pi$
$854$	−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	$0.146349\pi$
$857$			25.9807i			0.887485i	−0.896154	+	0.443742i	$0.853651\pi$
$858$		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	$-0.423970\pi$
$863$	13.9006			0.473181			0.236590	+	0.971609i	$0.423970\pi$
$864$		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
$875$	−27.4355	+	11.0585i	−0.927491	+	0.373846i
$876$		0			0
$877$			22.2450i			0.751161i	0.926790	+	0.375581i	$0.122557\pi$
$877$			22.2450i			0.751161i	−0.926790	+	0.375581i	$0.877443\pi$
$878$			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	$0.132340\pi$
$883$			24.0031i			0.807768i	−0.914810	+	0.403884i	$0.867660\pi$
$884$		−	3.49135i		−	0.117427i
$885$		0			0
$886$	−3.76159			−0.126373
$887$		−	52.1894i		−	1.75235i	−0.481995	−	0.876174i	$-0.660088\pi$
$887$		−	52.1894i		−	1.75235i	0.481995	−	0.876174i	$-0.339912\pi$
$888$		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	$-0.943561\pi$
$907$		−	10.6240i		−	0.352764i	0.984322	−	0.176382i	$-0.0564393\pi$
$908$			3.10872i			0.103166i
$909$		0			0
$910$	15.9995	+	9.94791i	0.530380	+	0.329770i
$911$		−	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	$-0.468811\pi$
$937$	5.98900			0.195652			0.0978261	+	0.995204i	$0.468811\pi$
$938$	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	$-0.622266\pi$
$947$	−23.0637			−0.749469			−0.374734	+	0.927132i	$0.622266\pi$
$948$		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	$-0.651065\pi$
$953$	−28.2138			−0.913936			−0.456968	+	0.889483i	$0.651065\pi$
$954$		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	$-0.988430\pi$
$967$		−	2.26006i		−	0.0726785i	0.999340	−	0.0363393i	$-0.0115697\pi$
$968$	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	$-0.672111\pi$
$977$	−32.1784			−1.02948			−0.514740	+	0.857347i	$0.672111\pi$
$978$		0			0
$979$		−	16.2652i		−	0.519836i
$980$	5.01677	+	0.0574391i	0.160255	+	0.00183483i
$981$		0			0
$982$			0.716732i			0.0228719i
$983$		−	6.61109i		−	0.210861i	−0.994427	−	0.105430i	$-0.966378\pi$
$983$		−	6.61109i		−	0.210861i	0.994427	−	0.105430i	$-0.0336220\pi$
$984$		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	$-0.561520\pi$
$997$	−12.1294			−0.384142			−0.192071	+	0.981381i	$0.561520\pi$
$998$	−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.944.9	✓	32
3.2	odd	2	inner	945.2.g.a.944.24	yes	32
5.4	even	2	inner	945.2.g.a.944.22	yes	32
7.6	odd	2	inner	945.2.g.a.944.12	yes	32
15.14	odd	2	inner	945.2.g.a.944.11	yes	32
21.20	even	2	inner	945.2.g.a.944.21	yes	32
35.34	odd	2	inner	945.2.g.a.944.23	yes	32
105.104	even	2	inner	945.2.g.a.944.10	yes	32

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

\(f(q)\)	\(=\)	\(q-1.29594 q^{2} -0.320531 q^{4} +(-1.01211 - 1.99390i) q^{5} +(-2.26270 + 1.37120i) q^{7} +3.00728 q^{8} +O(q^{10})\)	\(q-1.29594 q^{2} -0.320531 q^{4} +(-1.01211 - 1.99390i) q^{5} +(-2.26270 + 1.37120i) q^{7} +3.00728 q^{8} +(1.31163 + 2.58398i) q^{10} +3.12266i q^{11} -2.45732 q^{13} +(2.93233 - 1.77699i) q^{14} -3.25620 q^{16} -4.43263i q^{17} +4.17348i q^{19} +(0.324411 + 0.639107i) q^{20} -4.04678i q^{22} +5.77131 q^{23} +(-2.95128 + 4.03608i) q^{25} +3.18454 q^{26} +(0.725266 - 0.439511i) q^{28} +0.339143i q^{29} +4.40671i q^{31} -1.79471 q^{32} +5.74444i q^{34} +(5.02412 + 3.12381i) q^{35} -11.2541i q^{37} -5.40860i q^{38} +(-3.04368 - 5.99621i) q^{40} +5.43627 q^{41} +0.439511i q^{43} -1.00091i q^{44} -7.47929 q^{46} -10.2861i q^{47} +(3.23965 - 6.20521i) q^{49} +(3.82469 - 5.23053i) q^{50} +0.787646 q^{52} +2.76404 q^{53} +(6.22627 - 3.16046i) q^{55} +(-6.80457 + 4.12356i) q^{56} -0.439511i q^{58} +5.00079 q^{59} -9.34145i q^{61} -5.71085i q^{62} +8.83823 q^{64} +(2.48707 + 4.89965i) q^{65} +15.7404i q^{67} +1.42080i q^{68} +(-6.51098 - 4.04828i) q^{70} -10.1219i q^{71} +9.26995 q^{73} +14.5846i q^{74} -1.33773i q^{76} +(-4.28177 - 7.06564i) q^{77} +15.6381 q^{79} +(3.29562 + 6.49254i) q^{80} -7.04510 q^{82} -4.13038i q^{83} +(-8.83823 + 4.48630i) q^{85} -0.569581i q^{86} +9.39069i q^{88} -5.20876 q^{89} +(5.56018 - 3.36946i) q^{91} -1.84988 q^{92} +13.3302i q^{94} +(8.32151 - 4.22401i) q^{95} +6.09151 q^{97} +(-4.19840 + 8.04161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4}+O(q^{10}) \) 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

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