LMFDB - Embedded newform 684.2.c.b.647.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(647,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			647.2
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39577 + 0.227661i) q^{2} +(1.89634 - 0.635524i) q^{4} -2.96037i q^{5} +2.79268i q^{7} +(-2.50217 + 1.31877i) q^{8} +O(q^{10})$	\(q+(-1.39577 + 0.227661i) q^{2} +(1.89634 - 0.635524i) q^{4} -2.96037i q^{5} +2.79268i q^{7} +(-2.50217 + 1.31877i) q^{8} +(0.673961 + 4.13199i) q^{10} -1.59280 q^{11} -6.51231 q^{13} +(-0.635785 - 3.89794i) q^{14} +(3.19222 - 2.41034i) q^{16} -2.52959i q^{17} +1.00000i q^{19} +(-1.88139 - 5.61387i) q^{20} +(2.22318 - 0.362619i) q^{22} -4.93288 q^{23} -3.76379 q^{25} +(9.08968 - 1.48260i) q^{26} +(1.77482 + 5.29588i) q^{28} +7.17104i q^{29} +1.92056i q^{31} +(-3.90686 + 4.09102i) q^{32} +(0.575890 + 3.53072i) q^{34} +8.26737 q^{35} +0.232255 q^{37} +(-0.227661 - 1.39577i) q^{38} +(3.90404 + 7.40734i) q^{40} +6.49372i q^{41} -2.68176i q^{43} +(-3.02049 + 1.01226i) q^{44} +(6.88517 - 1.12303i) q^{46} -12.6975 q^{47} -0.799071 q^{49} +(5.25338 - 0.856868i) q^{50} +(-12.3496 + 4.13873i) q^{52} -3.18560i q^{53} +4.71528i q^{55} +(-3.68290 - 6.98776i) q^{56} +(-1.63257 - 10.0091i) q^{58} -13.0918 q^{59} +0.431148 q^{61} +(-0.437237 - 2.68066i) q^{62} +(4.52170 - 6.59956i) q^{64} +19.2789i q^{65} -16.3299i q^{67} +(-1.60762 - 4.79697i) q^{68} +(-11.5393 + 1.88216i) q^{70} +7.97855 q^{71} -11.9265 q^{73} +(-0.324174 + 0.0528754i) q^{74} +(0.635524 + 1.89634i) q^{76} -4.44819i q^{77} +5.31738i q^{79} +(-7.13550 - 9.45014i) q^{80} +(-1.47837 - 9.06373i) q^{82} +5.22797 q^{83} -7.48853 q^{85} +(0.610532 + 3.74311i) q^{86} +(3.98546 - 2.10054i) q^{88} +8.73011i q^{89} -18.1868i q^{91} +(-9.35443 + 3.13497i) q^{92} +(17.7228 - 2.89073i) q^{94} +2.96037 q^{95} -3.65258 q^{97} +(1.11532 - 0.181917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.39577	+	0.227661i	−0.986958	+	0.160981i
$2$	−1.39577	+	0.227661i	−0.986958	+	0.160981i
$3$		0			0
$3$		0			0
$4$	1.89634	−	0.635524i	0.948170	−	0.317762i
$5$		−	2.96037i		−	1.32392i	−0.749540	−	0.661959i	$-0.769725\pi$
$5$		−	2.96037i		−	1.32392i	0.749540	−	0.661959i	$-0.230275\pi$
$6$		0			0
$7$			2.79268i			1.05553i	0.849389	+	0.527767i	$0.176971\pi$
$7$			2.79268i			1.05553i	−0.849389	+	0.527767i	$0.823029\pi$
$8$	−2.50217	+	1.31877i	−0.884650	+	0.466255i
$9$		0			0
$10$	0.673961	+	4.13199i	0.213125	+	1.30665i
$11$	−1.59280			−0.480248			−0.240124	−	0.970742i	$-0.577188\pi$
$11$	−1.59280			−0.480248			−0.240124	+	0.970742i	$0.577188\pi$
$12$		0			0
$13$	−6.51231			−1.80619			−0.903096	−	0.429440i	$-0.858711\pi$
$13$	−6.51231			−1.80619			−0.903096	+	0.429440i	$0.858711\pi$
$14$	−0.635785	−	3.89794i	−0.169921	−	1.04177i
$15$		0			0
$16$	3.19222	−	2.41034i	0.798054	−	0.602585i
$17$		−	2.52959i		−	0.613516i	−0.951788	−	0.306758i	$-0.900756\pi$
$17$		−	2.52959i		−	0.613516i	0.951788	−	0.306758i	$-0.0992442\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.88139	−	5.61387i	−0.420691	−	1.25530i
$21$		0			0
$22$	2.22318	−	0.362619i	0.473984	−	0.0773106i
$23$	−4.93288			−1.02858			−0.514289	−	0.857617i	$-0.671944\pi$
$23$	−4.93288			−1.02858			−0.514289	+	0.857617i	$0.671944\pi$
$24$		0			0
$25$	−3.76379			−0.752757
$26$	9.08968	−	1.48260i	1.78263	−	0.290762i
$27$		0			0
$28$	1.77482	+	5.29588i	0.335409	+	1.00083i
$29$			7.17104i			1.33163i	0.746117	+	0.665815i	$0.231916\pi$
$29$			7.17104i			1.33163i	−0.746117	+	0.665815i	$0.768084\pi$
$30$		0			0
$31$			1.92056i			0.344943i	0.985015	+	0.172471i	$0.0551753\pi$
$31$			1.92056i			0.344943i	−0.985015	+	0.172471i	$0.944825\pi$
$32$	−3.90686	+	4.09102i	−0.690641	+	0.723198i
$33$		0			0
$34$	0.575890	+	3.53072i	0.0987642	+	0.605514i
$35$	8.26737			1.39744
$36$		0			0
$37$	0.232255			0.0381825			0.0190912	−	0.999818i	$-0.493923\pi$
$37$	0.232255			0.0381825			0.0190912	+	0.999818i	$0.493923\pi$
$38$	−0.227661	−	1.39577i	−0.0369315	−	0.226424i
$39$		0			0
$40$	3.90404	+	7.40734i	0.617283	+	1.17120i
$41$			6.49372i			1.01415i	0.861902	+	0.507074i	$0.169273\pi$
$41$			6.49372i			1.01415i	−0.861902	+	0.507074i	$0.830727\pi$
$42$		0			0
$43$		−	2.68176i		−	0.408964i	−0.978870	−	0.204482i	$-0.934449\pi$
$43$		−	2.68176i		−	0.408964i	0.978870	−	0.204482i	$-0.0655510\pi$
$44$	−3.02049	+	1.01226i	−0.455357	+	0.152605i
$45$		0			0
$46$	6.88517	−	1.12303i	1.01516	−	0.165581i
$47$	−12.6975			−1.85212			−0.926060	−	0.377376i	$-0.876826\pi$
$47$	−12.6975			−1.85212			−0.926060	+	0.377376i	$0.876826\pi$
$48$		0			0
$49$	−0.799071			−0.114153
$50$	5.25338	−	0.856868i	0.742939	−	0.121179i
$51$		0			0
$52$	−12.3496	+	4.13873i	−1.71258	+	0.573939i
$53$		−	3.18560i		−	0.437576i	−0.975772	−	0.218788i	$-0.929790\pi$
$53$		−	3.18560i		−	0.437576i	0.975772	−	0.218788i	$-0.0702103\pi$
$54$		0			0
$55$			4.71528i			0.635808i
$56$	−3.68290	−	6.98776i	−0.492148	−	0.933779i
$57$		0			0
$58$	−1.63257	−	10.0091i	−0.214367	−	1.31426i
$59$	−13.0918			−1.70440			−0.852202	−	0.523212i	$-0.824734\pi$
$59$	−13.0918			−1.70440			−0.852202	+	0.523212i	$0.824734\pi$
$60$		0			0
$61$	0.431148			0.0552028			0.0276014	−	0.999619i	$-0.491213\pi$
$61$	0.431148			0.0552028			0.0276014	+	0.999619i	$0.491213\pi$
$62$	−0.437237	−	2.68066i	−0.0555292	−	0.340444i
$63$		0			0
$64$	4.52170	−	6.59956i	0.565213	−	0.824945i
$65$			19.2789i			2.39125i
$66$		0			0
$67$		−	16.3299i		−	1.99502i	−0.0705335	−	0.997509i	$-0.522470\pi$
$67$		−	16.3299i		−	1.99502i	0.0705335	−	0.997509i	$-0.477530\pi$
$68$	−1.60762	−	4.79697i	−0.194952	−	0.581718i
$69$		0			0
$70$	−11.5393	+	1.88216i	−1.37921	+	0.224961i
$71$	7.97855			0.946880			0.473440	−	0.880826i	$-0.343012\pi$
$71$	7.97855			0.946880			0.473440	+	0.880826i	$0.343012\pi$
$72$		0			0
$73$	−11.9265			−1.39590			−0.697948	−	0.716149i	$-0.745903\pi$
$73$	−11.9265			−1.39590			−0.697948	+	0.716149i	$0.745903\pi$
$74$	−0.324174	+	0.0528754i	−0.0376845	+	0.00614664i
$75$		0			0
$76$	0.635524	+	1.89634i	0.0728997	+	0.217525i
$77$		−	4.44819i		−	0.506918i
$78$		0			0
$79$			5.31738i			0.598252i	0.954214	+	0.299126i	$0.0966951\pi$
$79$			5.31738i			0.598252i	−0.954214	+	0.299126i	$0.903305\pi$
$80$	−7.13550	−	9.45014i	−0.797773	−	1.05656i
$81$		0			0
$82$	−1.47837	−	9.06373i	−0.163258	−	1.00092i
$83$	5.22797			0.573844			0.286922	−	0.957954i	$-0.407368\pi$
$83$	5.22797			0.573844			0.286922	+	0.957954i	$0.407368\pi$
$84$		0			0
$85$	−7.48853			−0.812245
$86$	0.610532	+	3.74311i	0.0658354	+	0.403630i
$87$		0			0
$88$	3.98546	−	2.10054i	0.424851	−	0.223918i
$89$			8.73011i			0.925390i	0.886518	+	0.462695i	$0.153118\pi$
$89$			8.73011i			0.925390i	−0.886518	+	0.462695i	$0.846882\pi$
$90$		0			0
$91$		−	18.1868i		−	1.90650i
$92$	−9.35443	+	3.13497i	−0.975267	+	0.326843i
$93$		0			0
$94$	17.7228	−	2.89073i	1.82796	−	0.298156i
$95$	2.96037			0.303727
$96$		0			0
$97$	−3.65258			−0.370863			−0.185432	−	0.982657i	$-0.559368\pi$
$97$	−3.65258			−0.370863			−0.185432	+	0.982657i	$0.559368\pi$
$98$	1.11532	−	0.181917i	0.112664	−	0.0183764i
$99$		0			0
$100$	−7.13742	+	2.39198i	−0.713742	+	0.239198i
$101$			4.79873i			0.477491i	0.971082	+	0.238746i	$0.0767362\pi$
$101$			4.79873i			0.477491i	−0.971082	+	0.238746i	$0.923264\pi$
$102$		0			0
$103$			17.3050i			1.70511i	0.522634	+	0.852557i	$0.324949\pi$
$103$			17.3050i			1.70511i	−0.522634	+	0.852557i	$0.675051\pi$
$104$	16.2949	−	8.58823i	1.59785	−	0.842146i
$105$		0			0
$106$	0.725238	+	4.44636i	0.0704413	+	0.431869i
$107$	−8.61213			−0.832566			−0.416283	−	0.909235i	$-0.636667\pi$
$107$	−8.61213			−0.832566			−0.416283	+	0.909235i	$0.636667\pi$
$108$		0			0
$109$	−11.6043			−1.11149			−0.555745	−	0.831353i	$-0.687567\pi$
$109$	−11.6043			−1.11149			−0.555745	+	0.831353i	$0.687567\pi$
$110$	−1.07349	−	6.58144i	−0.102353	−	0.627516i
$111$		0			0
$112$	6.73132	+	8.91485i	0.636050	+	0.842374i
$113$		−	6.68847i		−	0.629199i	−0.949225	−	0.314599i	$-0.898130\pi$
$113$		−	6.68847i		−	0.629199i	0.949225	−	0.314599i	$-0.101870\pi$
$114$		0			0
$115$			14.6032i			1.36175i
$116$	4.55737	+	13.5987i	0.423142	+	1.26261i
$117$		0			0
$118$	18.2731	−	2.98049i	1.68218	−	0.274376i
$119$	7.06434			0.647587
$120$		0			0
$121$	−8.46299			−0.769362
$122$	−0.601783	+	0.0981556i	−0.0544829	+	0.00888659i
$123$		0			0
$124$	1.22056	+	3.64204i	0.109610	+	0.327065i
$125$		−	3.65965i		−	0.327329i
$126$		0			0
$127$			7.42275i			0.658662i	0.944214	+	0.329331i	$0.106823\pi$
$127$			7.42275i			0.658662i	−0.944214	+	0.329331i	$0.893177\pi$
$128$	−4.80879	+	10.2409i	−0.425041	+	0.905174i
$129$		0			0
$130$	−4.38904	−	26.9088i	−0.384945	−	2.36006i
$131$	17.2451			1.50671			0.753356	−	0.657612i	$-0.228434\pi$
$131$	17.2451			1.50671			0.753356	+	0.657612i	$0.228434\pi$
$132$		0			0
$133$	−2.79268			−0.242156
$134$	3.71769	+	22.7928i	0.321160	+	1.96900i
$135$		0			0
$136$	3.33594	+	6.32947i	0.286055	+	0.542747i
$137$		−	6.76538i		−	0.578005i	−0.957328	−	0.289003i	$-0.906676\pi$
$137$		−	6.76538i		−	0.578005i	0.957328	−	0.289003i	$-0.0933236\pi$
$138$		0			0
$139$		−	13.7252i		−	1.16416i	−0.813133	−	0.582079i	$-0.802240\pi$
$139$		−	13.7252i		−	1.16416i	0.813133	−	0.582079i	$-0.197760\pi$
$140$	15.6778	−	5.25412i	1.32501	−	0.444054i
$141$		0			0
$142$	−11.1362	+	1.81641i	−0.934530	+	0.152429i
$143$	10.3728			0.867419
$144$		0			0
$145$	21.2289			1.76297
$146$	16.6467	−	2.71521i	1.37769	−	0.224712i
$147$		0			0
$148$	0.440435	−	0.147604i	0.0362035	−	0.0121330i
$149$		−	1.02994i		−	0.0843762i	−0.999110	−	0.0421881i	$-0.986567\pi$
$149$		−	1.02994i		−	0.0843762i	0.999110	−	0.0421881i	$-0.0134329\pi$
$150$		0			0
$151$		−	17.3841i		−	1.41470i	−0.706863	−	0.707350i	$-0.749890\pi$
$151$		−	17.3841i		−	1.41470i	0.706863	−	0.707350i	$-0.250110\pi$
$152$	−1.31877	−	2.50217i	−0.106966	−	0.202953i
$153$		0			0
$154$	1.01268	+	6.20864i	0.0816040	+	0.500306i
$155$	5.68557			0.456676
$156$		0			0
$157$	23.9572			1.91199			0.955995	−	0.293384i	$-0.0947816\pi$
$157$	23.9572			1.91199			0.955995	+	0.293384i	$0.0947816\pi$
$158$	−1.21056	−	7.42183i	−0.0963070	−	0.590449i
$159$		0			0
$160$	12.1109	+	11.5657i	0.957454	+	0.914352i
$161$		−	13.7760i		−	1.08570i
$162$		0			0
$163$		−	6.89717i		−	0.540228i	−0.962828	−	0.270114i	$-0.912939\pi$
$163$		−	6.89717i		−	0.540228i	0.962828	−	0.270114i	$-0.0870614\pi$
$164$	4.12692	+	12.3143i	0.322258	+	0.961586i
$165$		0			0
$166$	−7.29703	+	1.19020i	−0.566360	+	0.0923778i
$167$	13.8381			1.07083			0.535413	−	0.844591i	$-0.320156\pi$
$167$	13.8381			1.07083			0.535413	+	0.844591i	$0.320156\pi$
$168$		0			0
$169$	29.4102			2.26233
$170$	10.4522	−	1.70485i	0.801651	−	0.130756i
$171$		0			0
$172$	−1.70432	−	5.08553i	−0.129953	−	0.387768i
$173$			7.85803i			0.597435i	0.954342	+	0.298718i	$0.0965589\pi$
$173$			7.85803i			0.597435i	−0.954342	+	0.298718i	$0.903441\pi$
$174$		0			0
$175$		−	10.5111i		−	0.794561i
$176$	−5.08457	+	3.83919i	−0.383264	+	0.289390i
$177$		0			0
$178$	−1.98751	−	12.1852i	−0.148970	−	0.913321i
$179$	11.1237			0.831424			0.415712	−	0.909496i	$-0.363532\pi$
$179$	11.1237			0.831424			0.415712	+	0.909496i	$0.363532\pi$
$180$		0			0
$181$	−22.1559			−1.64683			−0.823417	−	0.567436i	$-0.807935\pi$
$181$	−22.1559			−1.64683			−0.823417	+	0.567436i	$0.807935\pi$
$182$	4.14043	+	25.3846i	0.306909	+	1.88163i
$183$		0			0
$184$	12.3429	−	6.50533i	0.909931	−	0.479579i
$185$		−	0.687561i		−	0.0505505i
$186$		0			0
$187$			4.02914i			0.294640i
$188$	−24.0788	+	8.06957i	−1.75613	+	0.588534i
$189$		0			0
$190$	−4.13199	+	0.673961i	−0.299766	+	0.0488943i
$191$	−17.2539			−1.24845			−0.624225	−	0.781245i	$-0.714585\pi$
$191$	−17.2539			−1.24845			−0.624225	+	0.781245i	$0.714585\pi$
$192$		0			0
$193$	−4.96124			−0.357118			−0.178559	−	0.983929i	$-0.557143\pi$
$193$	−4.96124			−0.357118			−0.178559	+	0.983929i	$0.557143\pi$
$194$	5.09815	−	0.831550i	0.366026	−	0.0597018i
$195$		0			0
$196$	−1.51531	+	0.507829i	−0.108237	+	0.0362735i
$197$		−	18.4474i		−	1.31432i	−0.753749	−	0.657162i	$-0.771757\pi$
$197$		−	18.4474i		−	1.31432i	0.753749	−	0.657162i	$-0.228243\pi$
$198$		0			0
$199$			2.19745i			0.155773i	0.996962	+	0.0778866i	$0.0248172\pi$
$199$			2.19745i			0.155773i	−0.996962	+	0.0778866i	$0.975183\pi$
$200$	9.41763	−	4.96356i	0.665927	−	0.350977i
$201$		0			0
$202$	−1.09248	−	6.69792i	−0.0768669	−	0.471264i
$203$	−20.0264			−1.40558
$204$		0			0
$205$	19.2238			1.34265
$206$	−3.93968	−	24.1538i	−0.274491	−	1.68288i
$207$		0			0
$208$	−20.7887	+	15.6969i	−1.44144	+	1.08838i
$209$		−	1.59280i		−	0.110176i
$210$		0			0
$211$		−	19.8654i		−	1.36759i	−0.729673	−	0.683796i	$-0.760328\pi$
$211$		−	19.8654i		−	1.36759i	0.729673	−	0.683796i	$-0.239672\pi$
$212$	−2.02453	−	6.04099i	−0.139045	−	0.414897i
$213$		0			0
$214$	12.0205	−	1.96065i	0.821708	−	0.134027i
$215$	−7.93899			−0.541435
$216$		0			0
$217$	−5.36352			−0.364099
$218$	16.1969	−	2.64185i	1.09699	−	0.178929i
$219$		0			0
$220$	2.99667	+	8.94178i	0.202036	+	0.602854i
$221$			16.4735i			1.10813i
$222$		0			0
$223$			1.04524i			0.0699943i	0.999387	+	0.0349972i	$0.0111422\pi$
$223$			1.04524i			0.0699943i	−0.999387	+	0.0349972i	$0.988858\pi$
$224$	−11.4249	−	10.9106i	−0.763360	−	0.728996i
$225$		0			0
$226$	1.52271	+	9.33556i	0.101289	+	0.620992i
$227$	9.79419			0.650063			0.325032	−	0.945703i	$-0.394625\pi$
$227$	9.79419			0.650063			0.325032	+	0.945703i	$0.394625\pi$
$228$		0			0
$229$	8.30898			0.549073			0.274536	−	0.961577i	$-0.411476\pi$
$229$	8.30898			0.549073			0.274536	+	0.961577i	$0.411476\pi$
$230$	−3.32457	−	20.3826i	−0.219216	−	1.34399i
$231$		0			0
$232$	−9.45694	−	17.9432i	−0.620879	−	1.17803i
$233$		−	9.13932i		−	0.598737i	−0.954138	−	0.299368i	$-0.903224\pi$
$233$		−	9.13932i		−	0.598737i	0.954138	−	0.299368i	$-0.0967759\pi$
$234$		0			0
$235$			37.5893i			2.45205i
$236$	−24.8265	+	8.32015i	−1.61607	+	0.541596i
$237$		0			0
$238$	−9.86019	+	1.60828i	−0.639141	+	0.104249i
$239$	12.1947			0.788812			0.394406	−	0.918936i	$-0.370950\pi$
$239$	12.1947			0.788812			0.394406	+	0.918936i	$0.370950\pi$
$240$		0			0
$241$	10.6275			0.684576			0.342288	−	0.939595i	$-0.388798\pi$
$241$	10.6275			0.684576			0.342288	+	0.939595i	$0.388798\pi$
$242$	11.8124	−	1.92669i	0.759328	−	0.123852i
$243$		0			0
$244$	0.817604	−	0.274005i	0.0523417	−	0.0175414i
$245$			2.36555i			0.151129i
$246$		0			0
$247$		−	6.51231i		−	0.414369i
$248$	−2.53278	−	4.80557i	−0.160831	−	0.305154i
$249$		0			0
$250$	0.833160	+	5.10802i	0.0526936	+	0.323060i
$251$	−12.9935			−0.820141			−0.410070	−	0.912054i	$-0.634496\pi$
$251$	−12.9935			−0.820141			−0.410070	+	0.912054i	$0.634496\pi$
$252$		0			0
$253$	7.85710			0.493972
$254$	−1.68987	−	10.3604i	−0.106032	−	0.650072i
$255$		0			0
$256$	4.38050	−	15.3887i	0.273781	−	0.961792i
$257$			4.73511i			0.295368i	0.989035	+	0.147684i	$0.0471818\pi$
$257$			4.73511i			0.295368i	−0.989035	+	0.147684i	$0.952818\pi$
$258$		0			0
$259$			0.648614i			0.0403029i
$260$	12.2522	+	36.5593i	0.759848	+	2.26731i
$261$		0			0
$262$	−24.0702	+	3.92604i	−1.48706	+	0.242552i
$263$	−9.75716			−0.601652			−0.300826	−	0.953679i	$-0.597262\pi$
$263$	−9.75716			−0.601652			−0.300826	+	0.953679i	$0.597262\pi$
$264$		0			0
$265$	−9.43056			−0.579315
$266$	3.89794	−	0.635785i	0.238998	−	0.0389825i
$267$		0			0
$268$	−10.3781	−	30.9671i	−0.633942	−	1.89162i
$269$		−	14.9609i		−	0.912179i	−0.889934	−	0.456090i	$-0.849250\pi$
$269$		−	14.9609i		−	0.912179i	0.889934	−	0.456090i	$-0.150750\pi$
$270$		0			0
$271$			16.0101i			0.972545i	0.873807	+	0.486272i	$0.161644\pi$
$271$			16.0101i			0.972545i	−0.873807	+	0.486272i	$0.838356\pi$
$272$	−6.09718	−	8.07501i	−0.369696	−	0.489619i
$273$		0			0
$274$	1.54021	+	9.44290i	0.0930477	+	0.570467i
$275$	5.99496			0.361510
$276$		0			0
$277$	12.7524			0.766215			0.383107	−	0.923704i	$-0.374854\pi$
$277$	12.7524			0.766215			0.383107	+	0.923704i	$0.374854\pi$
$278$	3.12470	+	19.1572i	0.187407	+	1.14897i
$279$		0			0
$280$	−20.6864	+	10.9027i	−1.23625	+	0.651564i
$281$		−	5.93967i		−	0.354331i	−0.984181	−	0.177166i	$-0.943307\pi$
$281$		−	5.93967i		−	0.354331i	0.984181	−	0.177166i	$-0.0566928\pi$
$282$		0			0
$283$		−	13.0937i		−	0.778341i	−0.921166	−	0.389170i	$-0.872762\pi$
$283$		−	13.0937i		−	0.778341i	0.921166	−	0.389170i	$-0.127238\pi$
$284$	15.1301	−	5.07056i	0.897803	−	0.300883i
$285$		0			0
$286$	−14.4781	+	2.36149i	−0.856106	+	0.139638i
$287$	−18.1349			−1.07047
$288$		0			0
$289$	10.6012			0.623598
$290$	−29.6307	+	4.83300i	−1.73997	+	0.283804i
$291$		0			0
$292$	−22.6168	+	7.57960i	−1.32355	+	0.443563i
$293$			15.4720i			0.903881i	0.892048	+	0.451941i	$0.149268\pi$
$293$			15.4720i			0.903881i	−0.892048	+	0.451941i	$0.850732\pi$
$294$		0			0
$295$			38.7565i			2.25649i
$296$	−0.581141	+	0.306291i	−0.0337782	+	0.0178028i
$297$		0			0
$298$	0.234478	+	1.43756i	0.0135829	+	0.0832758i
$299$	32.1245			1.85781
$300$		0			0
$301$	7.48930			0.431676
$302$	3.95769	+	24.2642i	0.227739	+	1.39625i
$303$		0			0
$304$	2.41034	+	3.19222i	0.138243	+	0.183086i
$305$		−	1.27636i		−	0.0730840i
$306$		0			0
$307$			32.8979i			1.87758i	0.344487	+	0.938791i	$0.388053\pi$
$307$			32.8979i			1.87758i	−0.344487	+	0.938791i	$0.611947\pi$
$308$	−2.82693	−	8.43528i	−0.161079	−	0.480645i
$309$		0			0
$310$	−7.93574	+	1.29438i	−0.450720	+	0.0735160i
$311$	−5.33532			−0.302538			−0.151269	−	0.988493i	$-0.548336\pi$
$311$	−5.33532			−0.302538			−0.151269	+	0.988493i	$0.548336\pi$
$312$		0			0
$313$	−12.1147			−0.684762			−0.342381	−	0.939561i	$-0.611233\pi$
$313$	−12.1147			−0.684762			−0.342381	+	0.939561i	$0.611233\pi$
$314$	−33.4386	+	5.45411i	−1.88705	+	0.307793i
$315$		0			0
$316$	3.37932	+	10.0836i	0.190102	+	0.567245i
$317$		−	0.940229i		−	0.0528085i	−0.999651	−	0.0264042i	$-0.991594\pi$
$317$		−	0.940229i		−	0.0528085i	0.999651	−	0.0264042i	$-0.00840571\pi$
$318$		0			0
$319$		−	11.4220i		−	0.639512i
$320$	−19.5371	−	13.3859i	−1.09216	−	0.748295i
$321$		0			0
$322$	3.13625	+	19.2281i	0.174777	+	1.07154i
$323$	2.52959			0.140750
$324$		0			0
$325$	24.5110			1.35962
$326$	1.57022	+	9.62685i	0.0869663	+	0.533182i
$327$		0			0
$328$	−8.56371	−	16.2484i	−0.472852	−	0.897167i
$329$		−	35.4601i		−	1.95498i
$330$		0			0
$331$		−	0.610977i		−	0.0335824i	−0.999859	−	0.0167912i	$-0.994655\pi$
$331$		−	0.610977i		−	0.0335824i	0.999859	−	0.0167912i	$-0.00534505\pi$
$332$	9.91401	−	3.32250i	0.544102	−	0.182346i
$333$		0			0
$334$	−19.3148	+	3.15040i	−1.05686	+	0.172382i
$335$	−48.3426			−2.64124
$336$		0			0
$337$	5.73617			0.312469			0.156235	−	0.987720i	$-0.450064\pi$
$337$	5.73617			0.312469			0.156235	+	0.987720i	$0.450064\pi$
$338$	−41.0499	+	6.69557i	−2.23282	+	0.364191i
$339$		0			0
$340$	−14.2008	+	4.75914i	−0.770146	+	0.258101i
$341$		−	3.05907i		−	0.165658i
$342$		0			0
$343$			17.3172i			0.935042i
$344$	3.53662	+	6.71021i	0.190682	+	0.361790i
$345$		0			0
$346$	−1.78897	−	10.9680i	−0.0961755	−	0.589643i
$347$	11.8946			0.638536			0.319268	−	0.947665i	$-0.396563\pi$
$347$	11.8946			0.638536			0.319268	+	0.947665i	$0.396563\pi$
$348$		0			0
$349$	−25.8304			−1.38267			−0.691334	−	0.722535i	$-0.742977\pi$
$349$	−25.8304			−1.38267			−0.691334	+	0.722535i	$0.742977\pi$
$350$	2.39296	+	14.6710i	0.127909	+	0.784198i
$351$		0			0
$352$	6.22284	−	6.51619i	0.331679	−	0.347314i
$353$			37.1794i			1.97886i	0.145020	+	0.989429i	$0.453675\pi$
$353$			37.1794i			1.97886i	−0.145020	+	0.989429i	$0.546325\pi$
$354$		0			0
$355$		−	23.6195i		−	1.25359i
$356$	5.54820	+	16.5553i	0.294054	+	0.877428i
$357$		0			0
$358$	−15.5261	+	2.53243i	−0.820580	+	0.133843i
$359$	−22.8495			−1.20595			−0.602976	−	0.797759i	$-0.706019\pi$
$359$	−22.8495			−1.20595			−0.602976	+	0.797759i	$0.706019\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	30.9245	−	5.04403i	1.62536	−	0.265109i
$363$		0			0
$364$	−11.5582	−	34.4884i	−0.605813	−	1.80768i
$365$			35.3069i			1.84805i
$366$		0			0
$367$		−	27.4061i		−	1.43059i	−0.698824	−	0.715294i	$-0.746293\pi$
$367$		−	27.4061i		−	1.43059i	0.698824	−	0.715294i	$-0.253707\pi$
$368$	−15.7468	+	11.8899i	−0.820861	+	0.619806i
$369$		0			0
$370$	0.156531	+	0.959676i	0.00813765	+	0.0498912i
$371$	8.89637			0.461877
$372$		0			0
$373$	10.3325			0.534994			0.267497	−	0.963559i	$-0.413803\pi$
$373$	10.3325			0.534994			0.267497	+	0.963559i	$0.413803\pi$
$374$	−0.917277	−	5.62374i	−0.0474313	−	0.290797i
$375$		0			0
$376$	31.7713	−	16.7451i	1.63848	−	0.863560i
$377$		−	46.7001i		−	2.40518i
$378$		0			0
$379$		−	22.1448i		−	1.13750i	−0.822509	−	0.568752i	$-0.807426\pi$
$379$		−	22.1448i		−	1.13750i	0.822509	−	0.568752i	$-0.192574\pi$
$380$	5.61387	−	1.88139i	0.287985	−	0.0965131i
$381$		0			0
$382$	24.0825	−	3.92805i	1.23217	−	0.200976i
$383$	0.867347			0.0443193			0.0221597	−	0.999754i	$-0.492946\pi$
$383$	0.867347			0.0443193			0.0221597	+	0.999754i	$0.492946\pi$
$384$		0			0
$385$	−13.1683			−0.671117
$386$	6.92474	−	1.12948i	0.352460	−	0.0574891i
$387$		0			0
$388$	−6.92653	+	2.32130i	−0.351641	+	0.117846i
$389$		−	27.5438i		−	1.39652i	−0.715842	−	0.698262i	$-0.753957\pi$
$389$		−	27.5438i		−	1.39652i	0.715842	−	0.698262i	$-0.246043\pi$
$390$		0			0
$391$			12.4782i			0.631049i
$392$	1.99941	−	1.05379i	0.100986	−	0.0532244i
$393$		0			0
$394$	4.19976	+	25.7483i	0.211581	+	1.29718i
$395$	15.7414			0.792036
$396$		0			0
$397$	−24.0324			−1.20615			−0.603076	−	0.797684i	$-0.706058\pi$
$397$	−24.0324			−1.20615			−0.603076	+	0.797684i	$0.706058\pi$
$398$	−0.500274	−	3.06713i	−0.0250765	−	0.153742i
$399$		0			0
$400$	−12.0148	+	9.07201i	−0.600741	+	0.453601i
$401$		−	21.8949i		−	1.09338i	−0.837336	−	0.546689i	$-0.815888\pi$
$401$		−	21.8949i		−	1.09338i	0.837336	−	0.546689i	$-0.184112\pi$
$402$		0			0
$403$		−	12.5073i		−	0.623033i
$404$	3.04971	+	9.10003i	0.151729	+	0.452743i
$405$		0			0
$406$	27.9523	−	4.55924i	1.38725	−	0.226271i
$407$	−0.369936			−0.0183370
$408$		0			0
$409$	32.8142			1.62256			0.811278	−	0.584661i	$-0.198772\pi$
$409$	32.8142			1.62256			0.811278	+	0.584661i	$0.198772\pi$
$410$	−26.8320	+	4.37651i	−1.32514	+	0.216141i
$411$		0			0
$412$	10.9978	+	32.8162i	0.541821	+	1.61674i
$413$		−	36.5612i		−	1.79906i
$414$		0			0
$415$		−	15.4767i		−	0.759722i
$416$	25.4427	−	26.6420i	1.24743	−	1.30623i
$417$		0			0
$418$	0.362619	+	2.22318i	0.0177363	+	0.108739i
$419$	15.0937			0.737377			0.368689	−	0.929553i	$-0.379807\pi$
$419$	15.0937			0.737377			0.368689	+	0.929553i	$0.379807\pi$
$420$		0			0
$421$	−31.8754			−1.55351			−0.776755	−	0.629803i	$-0.783136\pi$
$421$	−31.8754			−1.55351			−0.776755	+	0.629803i	$0.783136\pi$
$422$	4.52258	+	27.7275i	0.220156	+	1.34976i
$423$		0			0
$424$	4.20107	+	7.97091i	0.204022	+	0.387102i
$425$			9.52084i			0.461829i
$426$		0			0
$427$			1.20406i			0.0582685i
$428$	−16.3315	+	5.47322i	−0.789415	+	0.264558i
$429$		0			0
$430$	11.0810	−	1.80740i	0.534373	−	0.0871606i
$431$	−12.8437			−0.618657			−0.309329	−	0.950955i	$-0.600104\pi$
$431$	−12.8437			−0.618657			−0.309329	+	0.950955i	$0.600104\pi$
$432$		0			0
$433$	−22.8564			−1.09841			−0.549204	−	0.835688i	$-0.685069\pi$
$433$	−22.8564			−1.09841			−0.549204	+	0.835688i	$0.685069\pi$
$434$	7.48623	−	1.22106i	0.359350	−	0.0586129i
$435$		0			0
$436$	−22.0057	+	7.37482i	−1.05388	+	0.353190i
$437$		−	4.93288i		−	0.235972i
$438$		0			0
$439$			20.8570i			0.995452i	0.867334	+	0.497726i	$0.165831\pi$
$439$			20.8570i			0.995452i	−0.867334	+	0.497726i	$0.834169\pi$
$440$	−6.21836	−	11.7984i	−0.296449	−	0.562468i
$441$		0			0
$442$	−3.75037	−	22.9932i	−0.178387	−	1.09367i
$443$	−1.48091			−0.0703599			−0.0351800	−	0.999381i	$-0.511200\pi$
$443$	−1.48091			−0.0703599			−0.0351800	+	0.999381i	$0.511200\pi$
$444$		0			0
$445$	25.8444			1.22514
$446$	−0.237960	−	1.45891i	−0.0112677	−	0.0690814i
$447$		0			0
$448$	18.4305	+	12.6277i	0.870758	+	0.596601i
$449$		−	23.7798i		−	1.12224i	−0.827735	−	0.561119i	$-0.810371\pi$
$449$		−	23.7798i		−	1.12224i	0.827735	−	0.561119i	$-0.189629\pi$
$450$		0			0
$451$		−	10.3432i		−	0.487042i
$452$	−4.25069	−	12.6836i	−0.199936	−	0.596588i
$453$		0			0
$454$	−13.6704	+	2.22976i	−0.641585	+	0.104648i
$455$	−53.8397			−2.52404
$456$		0			0
$457$	−27.2816			−1.27618			−0.638090	−	0.769962i	$-0.720275\pi$
$457$	−27.2816			−1.27618			−0.638090	+	0.769962i	$0.720275\pi$
$458$	−11.5974	+	1.89163i	−0.541912	+	0.0883901i
$459$		0			0
$460$	9.28066	+	27.6926i	0.432713	+	1.29117i
$461$			28.8557i			1.34394i	0.740576	+	0.671972i	$0.234553\pi$
$461$			28.8557i			1.34394i	−0.740576	+	0.671972i	$0.765447\pi$
$462$		0			0
$463$			34.9248i			1.62309i	0.584289	+	0.811546i	$0.301373\pi$
$463$			34.9248i			1.62309i	−0.584289	+	0.811546i	$0.698627\pi$
$464$	17.2847	+	22.8915i	0.802421	+	1.06271i
$465$		0			0
$466$	2.08067	+	12.7564i	0.0963850	+	0.590928i
$467$	3.65656			0.169205			0.0846027	−	0.996415i	$-0.473038\pi$
$467$	3.65656			0.169205			0.0846027	+	0.996415i	$0.473038\pi$
$468$		0			0
$469$	45.6043			2.10581
$470$	−8.55762	−	52.4659i	−0.394733	−	2.42007i
$471$		0			0
$472$	32.7579	−	17.2650i	1.50780	−	0.794687i
$473$			4.27151i			0.196404i
$474$		0			0
$475$		−	3.76379i		−	0.172694i
$476$	13.3964	−	4.48956i	0.614023	−	0.205779i
$477$		0			0
$478$	−17.0210	+	2.77627i	−0.778524	+	0.126984i
$479$	−10.7806			−0.492580			−0.246290	−	0.969196i	$-0.579212\pi$
$479$	−10.7806			−0.492580			−0.246290	+	0.969196i	$0.579212\pi$
$480$		0			0
$481$	−1.51252			−0.0689649
$482$	−14.8335	+	2.41946i	−0.675648	+	0.110204i
$483$		0			0
$484$	−16.0487	+	5.37843i	−0.729487	+	0.244474i
$485$			10.8130i			0.490992i
$486$		0			0
$487$		−	10.2294i		−	0.463537i	−0.972771	−	0.231768i	$-0.925549\pi$
$487$		−	10.2294i		−	0.463537i	0.972771	−	0.231768i	$-0.0744511\pi$
$488$	−1.07881	+	0.568584i	−0.0488352	+	0.0257386i
$489$		0			0
$490$	−0.538543	−	3.30176i	−0.0243289	−	0.149158i
$491$	14.1486			0.638519			0.319260	−	0.947667i	$-0.396566\pi$
$491$	14.1486			0.638519			0.319260	+	0.947667i	$0.396566\pi$
$492$		0			0
$493$	18.1398			0.816976
$494$	1.48260	+	9.08968i	0.0667053	+	0.408964i
$495$		0			0
$496$	4.62921	+	6.13085i	0.207858	+	0.275283i
$497$			22.2816i			0.999464i
$498$		0			0
$499$			28.0736i			1.25675i	0.777912	+	0.628373i	$0.216279\pi$
$499$			28.0736i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$500$	−2.32580	−	6.93994i	−0.104013	−	0.310364i
$501$		0			0
$502$	18.1359	−	2.95811i	0.809444	−	0.132027i
$503$	−9.00219			−0.401388			−0.200694	−	0.979654i	$-0.564320\pi$
$503$	−9.00219			−0.401388			−0.200694	+	0.979654i	$0.564320\pi$
$504$		0			0
$505$	14.2060			0.632159
$506$	−10.9667	+	1.78876i	−0.487529	+	0.0795199i
$507$		0			0
$508$	4.71734	+	14.0761i	0.209298	+	0.624524i
$509$		−	16.5791i		−	0.734854i	−0.930052	−	0.367427i	$-0.880239\pi$
$509$		−	16.5791i		−	0.734854i	0.930052	−	0.367427i	$-0.119761\pi$
$510$		0			0
$511$		−	33.3070i		−	1.47342i
$512$	−2.61077	+	22.4763i	−0.115381	+	0.993321i
$513$		0			0
$514$	−1.07800	−	6.60911i	−0.0475485	−	0.291515i
$515$	51.2293			2.25743
$516$		0			0
$517$	20.2246			0.889476
$518$	−0.147664	−	0.905316i	−0.00648800	−	0.0397773i
$519$		0			0
$520$	−25.4243	−	48.2390i	−1.11493	−	2.11542i
$521$			34.2990i			1.50267i	0.659922	+	0.751334i	$0.270589\pi$
$521$			34.2990i			1.50267i	−0.659922	+	0.751334i	$0.729411\pi$
$522$		0			0
$523$			28.5966i			1.25044i	0.780448	+	0.625220i	$0.214991\pi$
$523$			28.5966i			1.25044i	−0.780448	+	0.625220i	$0.785009\pi$
$524$	32.7026	−	10.9597i	1.42862	−	0.478776i
$525$		0			0
$526$	13.6187	−	2.22133i	0.593805	−	0.0968544i
$527$	4.85824			0.211628
$528$		0			0
$529$	1.33335			0.0579716
$530$	13.1629	−	2.14697i	0.571759	−	0.0932585i
$531$		0			0
$532$	−5.29588	+	1.77482i	−0.229605	+	0.0769481i
$533$		−	42.2891i		−	1.83175i
$534$		0			0
$535$			25.4951i			1.10225i
$536$	21.5354	+	40.8603i	0.930187	+	1.76489i
$537$		0			0
$538$	3.40600	+	20.8819i	0.146843	+	0.900282i
$539$	1.27276			0.0548217
$540$		0			0
$541$	−21.4761			−0.923332			−0.461666	−	0.887054i	$-0.652748\pi$
$541$	−21.4761			−0.923332			−0.461666	+	0.887054i	$0.652748\pi$
$542$	−3.64488	−	22.3464i	−0.156561	−	0.959860i
$543$		0			0
$544$	10.3486	+	9.88275i	0.443693	+	0.423719i
$545$			34.3530i			1.47152i
$546$		0			0
$547$			23.2114i			0.992450i	0.868194	+	0.496225i	$0.165281\pi$
$547$			23.2114i			0.992450i	−0.868194	+	0.496225i	$0.834719\pi$
$548$	−4.29956	−	12.8295i	−0.183668	−	0.548047i
$549$		0			0
$550$	−8.36758	+	1.36482i	−0.356795	+	0.0581961i
$551$	−7.17104			−0.305497
$552$		0			0
$553$	−14.8497			−0.631476
$554$	−17.7993	+	2.90322i	−0.756222	+	0.123346i
$555$		0			0
$556$	−8.72271	−	26.0277i	−0.369925	−	1.10382i
$557$		−	0.120205i		−	0.00509324i	−0.999997	−	0.00254662i	$-0.999189\pi$
$557$		−	0.120205i		−	0.00509324i	0.999997	−	0.00254662i	$-0.000810616\pi$
$558$		0			0
$559$			17.4645i			0.738668i
$560$	26.3912	−	19.9272i	1.11523	−	0.842077i
$561$		0			0
$562$	1.35223	+	8.29041i	0.0570405	+	0.349710i
$563$	−2.96182			−0.124826			−0.0624129	−	0.998050i	$-0.519880\pi$
$563$	−2.96182			−0.124826			−0.0624129	+	0.998050i	$0.519880\pi$
$564$		0			0
$565$	−19.8004			−0.833007
$566$	2.98093	+	18.2758i	0.125298	+	0.768189i
$567$		0			0
$568$	−19.9637	+	10.5219i	−0.837658	+	0.441487i
$569$			9.95504i			0.417337i	0.977986	+	0.208669i	$0.0669130\pi$
$569$			9.95504i			0.417337i	−0.977986	+	0.208669i	$0.933087\pi$
$570$		0			0
$571$		−	44.8390i		−	1.87646i	−0.346018	−	0.938228i	$-0.612467\pi$
$571$		−	44.8390i		−	1.87646i	0.346018	−	0.938228i	$-0.387533\pi$
$572$	19.6704	−	6.59218i	0.822461	−	0.275633i
$573$		0			0
$574$	25.3121	−	4.12861i	1.05651	−	0.172325i
$575$	18.5663			0.774269
$576$		0			0
$577$	26.3997			1.09903			0.549516	−	0.835483i	$-0.314812\pi$
$577$	26.3997			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$578$	−14.7968	+	2.41347i	−0.615465	+	0.100387i
$579$		0			0
$580$	40.2573	−	13.4915i	1.67159	−	0.560204i
$581$			14.6001i			0.605712i
$582$		0			0
$583$			5.07403i			0.210145i
$584$	29.8422	−	15.7283i	1.23488	−	0.650843i
$585$		0			0
$586$	−3.52236	−	21.5953i	−0.145507	−	0.892092i
$587$	0.268830			0.0110958			0.00554791	−	0.999985i	$-0.498234\pi$
$587$	0.268830			0.0110958			0.00554791	+	0.999985i	$0.498234\pi$
$588$		0			0
$589$	−1.92056			−0.0791353
$590$	−8.82335	−	54.0951i	−0.363252	−	2.22706i
$591$		0			0
$592$	0.741409	−	0.559814i	0.0304717	−	0.0230082i
$593$		−	22.5690i		−	0.926796i	−0.886150	−	0.463398i	$-0.846630\pi$
$593$		−	22.5690i		−	0.926796i	0.886150	−	0.463398i	$-0.153370\pi$
$594$		0			0
$595$		−	20.9131i		−	0.857352i
$596$	−0.654554	−	1.95312i	−0.0268116	−	0.0800031i
$597$		0			0
$598$	−44.8384	+	7.31350i	−1.83358	+	0.299071i
$599$	19.9928			0.816885			0.408443	−	0.912784i	$-0.366072\pi$
$599$	19.9928			0.816885			0.408443	+	0.912784i	$0.366072\pi$
$600$		0			0
$601$	−20.7269			−0.845468			−0.422734	−	0.906254i	$-0.638929\pi$
$601$	−20.7269			−0.845468			−0.422734	+	0.906254i	$0.638929\pi$
$602$	−10.4533	+	1.70502i	−0.426046	+	0.0694915i
$603$		0			0
$604$	−11.0480	−	32.9662i	−0.449538	−	1.34138i
$605$			25.0536i			1.01857i
$606$		0			0
$607$		−	25.2875i		−	1.02639i	−0.858273	−	0.513194i	$-0.828462\pi$
$607$		−	25.2875i		−	1.02639i	0.858273	−	0.513194i	$-0.171538\pi$
$608$	−4.09102	−	3.90686i	−0.165913	−	0.158444i
$609$		0			0
$610$	0.290577	+	1.78150i	0.0117651	+	0.0721308i
$611$	82.6901			3.34528
$612$		0			0
$613$	−32.7837			−1.32412			−0.662060	−	0.749451i	$-0.730317\pi$
$613$	−32.7837			−1.32412			−0.662060	+	0.749451i	$0.730317\pi$
$614$	−7.48957	−	45.9179i	−0.302255	−	1.85309i
$615$		0			0
$616$	5.86613	+	11.1301i	0.236353	+	0.448445i
$617$			17.3406i			0.698107i	0.937103	+	0.349053i	$0.113497\pi$
$617$			17.3406i			0.698107i	−0.937103	+	0.349053i	$0.886503\pi$
$618$		0			0
$619$			8.87831i			0.356849i	0.983954	+	0.178425i	$0.0571001\pi$
$619$			8.87831i			0.356849i	−0.983954	+	0.178425i	$0.942900\pi$
$620$	10.7818	−	3.61332i	0.433007	−	0.145114i
$621$		0			0
$622$	7.44687	−	1.21464i	0.298592	−	0.0487028i
$623$	−24.3804			−0.976781
$624$		0			0
$625$	−29.6528			−1.18611
$626$	16.9093	−	2.75804i	0.675831	−	0.110234i
$627$		0			0
$628$	45.4309	−	15.2254i	1.81289	−	0.607558i
$629$		−	0.587510i		−	0.0234256i
$630$		0			0
$631$		−	7.92683i		−	0.315562i	−0.987474	−	0.157781i	$-0.949566\pi$
$631$		−	7.92683i		−	0.315562i	0.987474	−	0.157781i	$-0.0504340\pi$
$632$	−7.01239	−	13.3050i	−0.278938	−	0.529244i
$633$		0			0
$634$	0.214053	+	1.31234i	0.00850115	+	0.0521197i
$635$	21.9741			0.872015
$636$		0			0
$637$	5.20380			0.206182
$638$	2.60036	+	15.9425i	0.102949	+	0.631171i
$639$		0			0
$640$	30.3168	+	14.2358i	1.19838	+	0.562719i
$641$			16.1509i			0.637923i	0.947768	+	0.318961i	$0.103334\pi$
$641$			16.1509i			0.637923i	−0.947768	+	0.318961i	$0.896666\pi$
$642$		0			0
$643$			19.2221i			0.758047i	0.925387	+	0.379024i	$0.123740\pi$
$643$			19.2221i			0.758047i	−0.925387	+	0.379024i	$0.876260\pi$
$644$	−8.75497	−	26.1239i	−0.344994	−	1.02943i
$645$		0			0
$646$	−3.53072	+	0.575890i	−0.138915	+	0.0226581i
$647$	17.4550			0.686229			0.343114	−	0.939294i	$-0.388518\pi$
$647$	17.4550			0.686229			0.343114	+	0.939294i	$0.388518\pi$
$648$		0			0
$649$	20.8526			0.818536
$650$	−34.2116	+	5.58019i	−1.34189	+	0.218873i
$651$		0			0
$652$	−4.38332	−	13.0794i	−0.171664	−	0.512228i
$653$			47.5883i			1.86227i	0.364670	+	0.931137i	$0.381182\pi$
$653$			47.5883i			1.86227i	−0.364670	+	0.931137i	$0.618818\pi$
$654$		0			0
$655$		−	51.0519i		−	1.99476i
$656$	15.6521	+	20.7294i	0.611111	+	0.809346i
$657$		0			0
$658$	8.07288	+	49.4941i	0.314713	+	1.92948i
$659$	−30.2024			−1.17652			−0.588260	−	0.808672i	$-0.700187\pi$
$659$	−30.2024			−1.17652			−0.588260	+	0.808672i	$0.700187\pi$
$660$		0			0
$661$	−11.1151			−0.432326			−0.216163	−	0.976357i	$-0.569354\pi$
$661$	−11.1151			−0.432326			−0.216163	+	0.976357i	$0.569354\pi$
$662$	0.139096	+	0.852783i	0.00540611	+	0.0331444i
$663$		0			0
$664$	−13.0813	+	6.89448i	−0.507651	+	0.267558i
$665$			8.26737i			0.320595i
$666$		0			0
$667$		−	35.3739i		−	1.36968i
$668$	26.2418	−	8.79446i	1.01533	−	0.340268i
$669$		0			0
$670$	67.4751	−	11.0057i	2.60679	−	0.425189i
$671$	−0.686733			−0.0265110
$672$		0			0
$673$	22.6433			0.872835			0.436417	−	0.899744i	$-0.356247\pi$
$673$	22.6433			0.872835			0.436417	+	0.899744i	$0.356247\pi$
$674$	−8.00637	+	1.30590i	−0.308394	+	0.0503015i
$675$		0			0
$676$	55.7718	−	18.6909i	2.14507	−	0.718882i
$677$			43.6173i			1.67635i	0.545401	+	0.838175i	$0.316377\pi$
$677$			43.6173i			1.67635i	−0.545401	+	0.838175i	$0.683623\pi$
$678$		0			0
$679$		−	10.2005i		−	0.391459i
$680$	18.7376	−	9.87563i	0.718553	−	0.378713i
$681$		0			0
$682$	0.696432	+	4.26976i	0.0266677	+	0.163497i
$683$	−29.7385			−1.13791			−0.568956	−	0.822368i	$-0.692653\pi$
$683$	−29.7385			−1.13791			−0.568956	+	0.822368i	$0.692653\pi$
$684$		0			0
$685$	−20.0280			−0.765231
$686$	−3.94246	−	24.1708i	−0.150524	−	0.922847i
$687$		0			0
$688$	−6.46395	−	8.56076i	−0.246436	−	0.326376i
$689$			20.7456i			0.790346i
$690$		0			0
$691$			8.79762i			0.334677i	0.985899	+	0.167339i	$0.0535173\pi$
$691$			8.79762i			0.334677i	−0.985899	+	0.167339i	$0.946483\pi$
$692$	4.99397	+	14.9015i	0.189842	+	0.566470i
$693$		0			0
$694$	−16.6021	+	2.70794i	−0.630208	+	0.102792i
$695$	−40.6317			−1.54125
$696$		0			0
$697$	16.4265			0.622196
$698$	36.0532	−	5.88057i	1.36463	−	0.222583i
$699$		0			0
$700$	−6.68003	−	19.9325i	−0.252482	−	0.753379i
$701$			28.2381i			1.06654i	0.845946	+	0.533269i	$0.179037\pi$
$701$			28.2381i			1.06654i	−0.845946	+	0.533269i	$0.820963\pi$
$702$		0			0
$703$			0.232255i			0.00875967i
$704$	−7.20217	+	10.5118i	−0.271442	+	0.396178i
$705$		0			0
$706$	−8.46429	−	51.8938i	−0.318558	−	1.95305i
$707$	−13.4013			−0.504009
$708$		0			0
$709$	−30.5503			−1.14734			−0.573669	−	0.819087i	$-0.694481\pi$
$709$	−30.5503			−1.14734			−0.573669	+	0.819087i	$0.694481\pi$
$710$	5.37723	+	32.9673i	0.201804	+	1.23724i
$711$		0			0
$712$	−11.5130	−	21.8442i	−0.431468	−	0.818647i
$713$		−	9.47391i		−	0.354801i
$714$		0			0
$715$		−	30.7074i		−	1.14839i
$716$	21.0943	−	7.06938i	0.788332	−	0.264195i
$717$		0			0
$718$	31.8927	−	5.20195i	1.19022	−	0.194135i
$719$	50.0999			1.86841			0.934205	−	0.356737i	$-0.116111\pi$
$719$	50.0999			1.86841			0.934205	+	0.356737i	$0.116111\pi$
$720$		0			0
$721$	−48.3274			−1.79981
$722$	1.39577	−	0.227661i	0.0519451	−	0.00847267i
$723$		0			0
$724$	−42.0151	+	14.0806i	−1.56148	+	0.523302i
$725$		−	26.9903i		−	1.00239i
$726$		0			0
$727$		−	10.4157i		−	0.386296i	−0.981170	−	0.193148i	$-0.938130\pi$
$727$		−	10.4157i		−	0.386296i	0.981170	−	0.193148i	$-0.0618697\pi$
$728$	23.9842	+	45.5065i	0.888914	+	1.68658i
$729$		0			0
$730$	−8.03802	−	49.2803i	−0.297500	−	1.82395i
$731$	−6.78375			−0.250906
$732$		0			0
$733$	5.74852			0.212327			0.106163	−	0.994349i	$-0.466143\pi$
$733$	5.74852			0.212327			0.106163	+	0.994349i	$0.466143\pi$
$734$	6.23931	+	38.2526i	0.230297	+	1.41193i
$735$		0			0
$736$	19.2721	−	20.1805i	0.710378	−	0.743865i
$737$			26.0103i			0.958103i
$738$		0			0
$739$			0.584322i			0.0214946i	0.999942	+	0.0107473i	$0.00342104\pi$
$739$			0.584322i			0.0214946i	−0.999942	+	0.0107473i	$0.996579\pi$
$740$	−0.436962	−	1.30385i	−0.0160630	−	0.0479305i
$741$		0			0
$742$	−12.4173	+	2.02536i	−0.455853	+	0.0743532i
$743$	−47.9287			−1.75833			−0.879167	−	0.476514i	$-0.841900\pi$
$743$	−47.9287			−1.75833			−0.879167	+	0.476514i	$0.841900\pi$
$744$		0			0
$745$	−3.04901			−0.111707
$746$	−14.4217	+	2.35230i	−0.528016	+	0.0861237i
$747$		0			0
$748$	2.56061	+	7.64061i	0.0936253	+	0.279369i
$749$		−	24.0509i		−	0.878802i
$750$		0			0
$751$		−	21.0910i		−	0.769620i	−0.922996	−	0.384810i	$-0.874267\pi$
$751$		−	21.0910i		−	0.769620i	0.922996	−	0.384810i	$-0.125733\pi$
$752$	−40.5332	+	30.6053i	−1.47809	+	1.11606i
$753$		0			0
$754$	10.6318	+	65.1825i	0.387187	+	2.37381i
$755$	−51.4634			−1.87295
$756$		0			0
$757$	−2.92802			−0.106421			−0.0532104	−	0.998583i	$-0.516945\pi$
$757$	−2.92802			−0.106421			−0.0532104	+	0.998583i	$0.516945\pi$
$758$	5.04152	+	30.9091i	0.183116	+	1.12267i
$759$		0			0
$760$	−7.40734	+	3.90404i	−0.268693	+	0.141614i
$761$			35.6476i			1.29223i	0.763242	+	0.646113i	$0.223606\pi$
$761$			35.6476i			1.29223i	−0.763242	+	0.646113i	$0.776394\pi$
$762$		0			0
$763$		−	32.4071i		−	1.17322i
$764$	−32.7193	+	10.9653i	−1.18374	+	0.396710i
$765$		0			0
$766$	−1.21062	+	0.197461i	−0.0437413	+	0.00713456i
$767$	85.2578			3.07848
$768$		0			0
$769$	−12.7963			−0.461446			−0.230723	−	0.973019i	$-0.574109\pi$
$769$	−12.7963			−0.461446			−0.230723	+	0.973019i	$0.574109\pi$
$770$	18.3799	−	2.99790i	0.662364	−	0.108037i
$771$		0			0
$772$	−9.40820	+	3.15299i	−0.338608	+	0.113479i
$773$			9.65634i			0.347314i	0.984806	+	0.173657i	$0.0555585\pi$
$773$			9.65634i			0.347314i	−0.984806	+	0.173657i	$0.944442\pi$
$774$		0			0
$775$		−	7.22858i		−	0.259658i
$776$	9.13937	−	4.81690i	0.328084	−	0.172917i
$777$		0			0
$778$	6.27065	+	38.4447i	0.224814	+	1.37831i
$779$	−6.49372			−0.232662
$780$		0			0
$781$	−12.7082			−0.454737
$782$	−2.84080	−	17.4167i	−0.101587	−	0.622818i
$783$		0			0
$784$	−2.55081	+	1.92603i	−0.0911003	+	0.0687870i
$785$		−	70.9220i		−	2.53132i
$786$		0			0
$787$			21.8326i			0.778248i	0.921185	+	0.389124i	$0.127222\pi$
$787$			21.8326i			0.778248i	−0.921185	+	0.389124i	$0.872778\pi$
$788$	−11.7238	−	34.9826i	−0.417643	−	1.24620i
$789$		0			0
$790$	−21.9714	+	3.58371i	−0.781706	+	0.127503i
$791$	18.6788			0.664141
$792$		0			0
$793$	−2.80777			−0.0997069
$794$	33.5437	−	5.47124i	1.19042	−	0.194167i
$795$		0			0
$796$	1.39653	+	4.16712i	0.0494988	+	0.147700i
$797$		−	39.7428i		−	1.40776i	−0.710317	−	0.703882i	$-0.751448\pi$
$797$		−	39.7428i		−	1.40776i	0.710317	−	0.703882i	$-0.248552\pi$
$798$		0			0
$799$			32.1195i			1.13631i
$800$	14.7046	−	15.3977i	0.519885	−	0.544392i
$801$		0			0
$802$	4.98461	+	30.5602i	0.176013	+	1.07912i
$803$	18.9966			0.670375
$804$		0			0
$805$	−40.7820			−1.43738
$806$	2.84743	+	17.4573i	0.100296	+	0.614907i
$807$		0			0
$808$	−6.32841	−	12.0072i	−0.222633	−	0.422413i
$809$			14.1754i			0.498382i	0.968454	+	0.249191i	$0.0801647\pi$
$809$			14.1754i			0.498382i	−0.968454	+	0.249191i	$0.919835\pi$
$810$		0			0
$811$			4.34499i			0.152573i	0.997086	+	0.0762867i	$0.0243064\pi$
$811$			4.34499i			0.152573i	−0.997086	+	0.0762867i	$0.975694\pi$
$812$	−37.9770	+	12.7273i	−1.33273	+	0.446640i
$813$		0			0
$814$	0.516345	−	0.0842200i	0.0180979	−	0.00295191i
$815$	−20.4182			−0.715217
$816$		0			0
$817$	2.68176			0.0938228
$818$	−45.8010	+	7.47051i	−1.60139	+	0.261200i
$819$		0			0
$820$	36.4549	−	12.2172i	1.27306	−	0.426643i
$821$			34.0312i			1.18770i	0.804577	+	0.593848i	$0.202392\pi$
$821$			34.0312i			1.18770i	−0.804577	+	0.593848i	$0.797608\pi$
$822$		0			0
$823$			54.0922i			1.88553i	0.333452	+	0.942767i	$0.391786\pi$
$823$			54.0922i			1.88553i	−0.333452	+	0.942767i	$0.608214\pi$
$824$	−22.8213	−	43.3001i	−0.795018	−	1.50843i
$825$		0			0
$826$	8.32356	+	51.0310i	0.289614	+	1.77559i
$827$	−7.38185			−0.256692			−0.128346	−	0.991729i	$-0.540967\pi$
$827$	−7.38185			−0.256692			−0.128346	+	0.991729i	$0.540967\pi$
$828$		0			0
$829$	−6.55168			−0.227549			−0.113775	−	0.993507i	$-0.536294\pi$
$829$	−6.55168			−0.227549			−0.113775	+	0.993507i	$0.536294\pi$
$830$	3.52345	+	21.6019i	0.122301	+	0.749813i
$831$		0			0
$832$	−29.4467	+	42.9784i	−1.02088	+	1.49001i
$833$			2.02132i			0.0700347i
$834$		0			0
$835$		−	40.9659i		−	1.41768i
$836$	−1.01226	−	3.02049i	−0.0350099	−	0.104466i
$837$		0			0
$838$	−21.0674	+	3.43626i	−0.727760	+	0.118704i
$839$	−23.5892			−0.814391			−0.407196	−	0.913341i	$-0.633493\pi$
$839$	−23.5892			−0.814391			−0.407196	+	0.913341i	$0.633493\pi$
$840$		0			0
$841$	−22.4239			−0.773237
$842$	44.4906	−	7.25678i	1.53325	−	0.250085i
$843$		0			0
$844$	−12.6250	−	37.6716i	−0.434569	−	1.29671i
$845$		−	87.0652i		−	2.99513i
$846$		0			0
$847$		−	23.6344i		−	0.812088i
$848$	−7.67839	−	10.1691i	−0.263677	−	0.349209i
$849$		0			0
$850$	−2.16753	−	13.2889i	−0.0743455	−	0.455805i
$851$	−1.14569			−0.0392737
$852$		0			0
$853$	−30.8150			−1.05509			−0.527543	−	0.849528i	$-0.676887\pi$
$853$	−30.8150			−1.05509			−0.527543	+	0.849528i	$0.676887\pi$
$854$	−0.274117	−	1.68059i	−0.00938010	−	0.0575085i
$855$		0			0
$856$	21.5490	−	11.3574i	0.736530	−	0.388188i
$857$		−	23.4576i		−	0.801295i	−0.916232	−	0.400647i	$-0.868785\pi$
$857$		−	23.4576i		−	0.801295i	0.916232	−	0.400647i	$-0.131215\pi$
$858$		0			0
$859$			22.9148i			0.781843i	0.920424	+	0.390921i	$0.127844\pi$
$859$			22.9148i			0.781843i	−0.920424	+	0.390921i	$0.872156\pi$
$860$	−15.0550	+	5.04543i	−0.513373	+	0.172048i
$861$		0			0
$862$	17.9268	−	2.92400i	0.610589	−	0.0995919i
$863$	−22.2718			−0.758141			−0.379071	−	0.925368i	$-0.623756\pi$
$863$	−22.2718			−0.758141			−0.379071	+	0.925368i	$0.623756\pi$
$864$		0			0
$865$	23.2627			0.790955
$866$	31.9022	−	5.20351i	1.08408	−	0.176822i
$867$		0			0
$868$	−10.1711	+	3.40865i	−0.345228	+	0.115697i
$869$		−	8.46953i		−	0.287309i
$870$		0			0
$871$			106.346i			3.60339i
$872$	29.0359	−	15.3034i	0.983281	−	0.518238i
$873$		0			0
$874$	1.12303	+	6.88517i	0.0379869	+	0.232894i
$875$	10.2202			0.345507
$876$		0			0
$877$	−42.2668			−1.42725			−0.713624	−	0.700529i	$-0.752947\pi$
$877$	−42.2668			−1.42725			−0.713624	+	0.700529i	$0.752947\pi$
$878$	−4.74833	−	29.1116i	−0.160249	−	0.982469i
$879$		0			0
$880$	11.3654	+	15.0522i	0.383129	+	0.507409i
$881$			0.198847i			0.00669931i	0.999994	+	0.00334966i	$0.00106623\pi$
$881$			0.198847i			0.00669931i	−0.999994	+	0.00334966i	$0.998934\pi$
$882$		0			0
$883$		−	46.1728i		−	1.55384i	−0.629600	−	0.776919i	$-0.716781\pi$
$883$		−	46.1728i		−	1.55384i	0.629600	−	0.776919i	$-0.283219\pi$
$884$	10.4693	+	31.2394i	0.352121	+	1.05069i
$885$		0			0
$886$	2.06700	−	0.337145i	0.0694423	−	0.0113266i
$887$	−0.538116			−0.0180682			−0.00903408	−	0.999959i	$-0.502876\pi$
$887$	−0.538116			−0.0180682			−0.00903408	+	0.999959i	$0.502876\pi$
$888$		0			0
$889$	−20.7294			−0.695241
$890$	−36.0727	+	5.88375i	−1.20916	+	0.197224i
$891$		0			0
$892$	0.664274	+	1.98213i	0.0222415	+	0.0663665i
$893$		−	12.6975i		−	0.424905i
$894$		0			0
$895$		−	32.9303i		−	1.10074i
$896$	−28.5995	−	13.4294i	−0.955443	−	0.448645i
$897$		0			0
$898$	5.41373	+	33.1911i	0.180659	+	1.10760i
$899$	−13.7724			−0.459336
$900$		0			0
$901$	−8.05827			−0.268460
$902$	2.35474	+	14.4367i	0.0784044	+	0.480690i
$903$		0			0
$904$	8.82055	+	16.7357i	0.293367	+	0.556621i
$905$			65.5896i			2.18027i
$906$		0			0
$907$			34.1782i			1.13487i	0.823419	+	0.567434i	$0.192064\pi$
$907$			34.1782i			1.13487i	−0.823419	+	0.567434i	$0.807936\pi$
$908$	18.5731	−	6.22445i	0.616371	−	0.206566i
$909$		0			0
$910$	75.1478	−	12.2572i	2.49112	−	0.406322i
$911$	33.6676			1.11546			0.557728	−	0.830024i	$-0.311673\pi$
$911$	33.6676			1.11546			0.557728	+	0.830024i	$0.311673\pi$
$912$		0			0
$913$	−8.32711			−0.275587
$914$	38.0788	−	6.21096i	1.25954	−	0.205440i
$915$		0			0
$916$	15.7567	−	5.28056i	0.520615	−	0.174475i
$917$			48.1601i			1.59039i
$918$		0			0
$919$		−	10.5231i		−	0.347124i	−0.984823	−	0.173562i	$-0.944472\pi$
$919$		−	10.5231i		−	0.347124i	0.984823	−	0.173562i	$-0.0555277\pi$
$920$	−19.2582	−	36.5396i	−0.634923	−	1.20467i
$921$		0			0
$922$	−6.56932	−	40.2759i	−0.216349	−	1.32642i
$923$	−51.9588			−1.71025
$924$		0			0
$925$	−0.874158			−0.0287422
$926$	−7.95101	−	48.7469i	−0.261286	−	1.60192i
$927$		0			0
$928$	−29.3369	−	28.0162i	−0.963031	−	0.919678i
$929$			9.92696i			0.325693i	0.986651	+	0.162846i	$0.0520675\pi$
$929$			9.92696i			0.325693i	−0.986651	+	0.162846i	$0.947932\pi$
$930$		0			0
$931$		−	0.799071i		−	0.0261885i
$932$	−5.80826	−	17.3313i	−0.190256	−	0.567704i
$933$		0			0
$934$	−5.10371	+	0.832457i	−0.166999	+	0.0272388i
$935$	11.9277			0.390078
$936$		0			0
$937$	32.9042			1.07493			0.537467	−	0.843285i	$-0.319381\pi$
$937$	32.9042			1.07493			0.537467	+	0.843285i	$0.319381\pi$
$938$	−63.6531	+	10.3823i	−2.07835	+	0.338995i
$939$		0			0
$940$	23.8889	+	71.2821i	0.779170	+	2.32497i
$941$		−	34.8706i		−	1.13675i	−0.822770	−	0.568375i	$-0.807572\pi$
$941$		−	34.8706i		−	1.13675i	0.822770	−	0.568375i	$-0.192428\pi$
$942$		0			0
$943$		−	32.0328i		−	1.04313i
$944$	−41.7918	+	31.5557i	−1.36021	+	1.02705i
$945$		0			0
$946$	−0.972456	−	5.96204i	−0.0316173	−	0.193843i
$947$	42.4401			1.37912			0.689558	−	0.724230i	$-0.257805\pi$
$947$	42.4401			1.37912			0.689558	+	0.724230i	$0.257805\pi$
$948$		0			0
$949$	77.6693			2.52125
$950$	0.856868	+	5.25338i	0.0278005	+	0.170442i
$951$		0			0
$952$	−17.6762	+	9.31623i	−0.572888	+	0.301941i
$953$		−	55.2982i		−	1.79128i	−0.444775	−	0.895642i	$-0.646716\pi$
$953$		−	55.2982i		−	1.79128i	0.444775	−	0.895642i	$-0.353284\pi$
$954$		0			0
$955$			51.0780i			1.65284i
$956$	23.1254	−	7.75005i	0.747928	−	0.250655i
$957$		0			0
$958$	15.0473	−	2.45433i	0.486156	−	0.0792959i
$959$	18.8935			0.610104
$960$		0			0
$961$	27.3114			0.881014
$962$	2.11113	−	0.344341i	0.0680654	−	0.0111020i
$963$		0			0
$964$	20.1533	−	6.75402i	0.649095	−	0.217532i
$965$			14.6871i			0.472794i
$966$		0			0
$967$			41.3253i			1.32893i	0.747318	+	0.664466i	$0.231341\pi$
$967$			41.3253i			1.32893i	−0.747318	+	0.664466i	$0.768659\pi$
$968$	21.1758	−	11.1607i	0.680617	−	0.358719i
$969$		0			0
$970$	−2.46169	−	15.0924i	−0.0790402	−	0.484588i
$971$	−11.0359			−0.354158			−0.177079	−	0.984197i	$-0.556665\pi$
$971$	−11.0359			−0.354158			−0.177079	+	0.984197i	$0.556665\pi$
$972$		0			0
$973$	38.3301			1.22881
$974$	2.32883	+	14.2778i	0.0746204	+	0.457491i
$975$		0			0
$976$	1.37632	−	1.03921i	0.0440549	−	0.0332644i
$977$		−	1.86563i		−	0.0596867i	−0.999555	−	0.0298433i	$-0.990499\pi$
$977$		−	1.86563i		−	0.0596867i	0.999555	−	0.0298433i	$-0.00950084\pi$
$978$		0			0
$979$		−	13.9053i		−	0.444416i
$980$	1.50336	+	4.48588i	0.0480231	+	0.143296i
$981$		0			0
$982$	−19.7482	+	3.22110i	−0.630192	+	0.102789i
$983$	−36.5993			−1.16734			−0.583668	−	0.811993i	$-0.698383\pi$
$983$	−36.5993			−1.16734			−0.583668	+	0.811993i	$0.698383\pi$
$984$		0			0
$985$	−54.6112			−1.74006
$986$	−25.3190	+	4.12973i	−0.806321	+	0.131517i
$987$		0			0
$988$	−4.13873	−	12.3496i	−0.131671	−	0.392892i
$989$			13.2288i			0.420651i
$990$		0			0
$991$			29.0900i			0.924075i	0.886860	+	0.462038i	$0.152882\pi$
$991$			29.0900i			0.924075i	−0.886860	+	0.462038i	$0.847118\pi$
$992$	−7.85706	−	7.50336i	−0.249462	−	0.238232i
$993$		0			0
$994$	−5.07264	−	31.0999i	−0.160894	−	0.986429i
$995$	6.50527			0.206231
$996$		0			0
$997$	30.1753			0.955663			0.477831	−	0.878452i	$-0.341423\pi$
$997$	30.1753			0.955663			0.477831	+	0.878452i	$0.341423\pi$
$998$	−6.39126	−	39.1842i	−0.202312	−	1.24036i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.2	yes	32
3.2	odd	2	inner	684.2.c.b.647.31	yes	32
4.3	odd	2	inner	684.2.c.b.647.32	yes	32
12.11	even	2	inner	684.2.c.b.647.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.1	✓	32	12.11	even	2	inner
684.2.c.b.647.2	yes	32	1.1	even	1	trivial
684.2.c.b.647.31	yes	32	3.2	odd	2	inner
684.2.c.b.647.32	yes	32	4.3	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39577 + 0.227661i) q^{2} +(1.89634 - 0.635524i) q^{4} -2.96037i q^{5} +2.79268i q^{7} +(-2.50217 + 1.31877i) q^{8} +O(q^{10})\)	\(q+(-1.39577 + 0.227661i) q^{2} +(1.89634 - 0.635524i) q^{4} -2.96037i q^{5} +2.79268i q^{7} +(-2.50217 + 1.31877i) q^{8} +(0.673961 + 4.13199i) q^{10} -1.59280 q^{11} -6.51231 q^{13} +(-0.635785 - 3.89794i) q^{14} +(3.19222 - 2.41034i) q^{16} -2.52959i q^{17} +1.00000i q^{19} +(-1.88139 - 5.61387i) q^{20} +(2.22318 - 0.362619i) q^{22} -4.93288 q^{23} -3.76379 q^{25} +(9.08968 - 1.48260i) q^{26} +(1.77482 + 5.29588i) q^{28} +7.17104i q^{29} +1.92056i q^{31} +(-3.90686 + 4.09102i) q^{32} +(0.575890 + 3.53072i) q^{34} +8.26737 q^{35} +0.232255 q^{37} +(-0.227661 - 1.39577i) q^{38} +(3.90404 + 7.40734i) q^{40} +6.49372i q^{41} -2.68176i q^{43} +(-3.02049 + 1.01226i) q^{44} +(6.88517 - 1.12303i) q^{46} -12.6975 q^{47} -0.799071 q^{49} +(5.25338 - 0.856868i) q^{50} +(-12.3496 + 4.13873i) q^{52} -3.18560i q^{53} +4.71528i q^{55} +(-3.68290 - 6.98776i) q^{56} +(-1.63257 - 10.0091i) q^{58} -13.0918 q^{59} +0.431148 q^{61} +(-0.437237 - 2.68066i) q^{62} +(4.52170 - 6.59956i) q^{64} +19.2789i q^{65} -16.3299i q^{67} +(-1.60762 - 4.79697i) q^{68} +(-11.5393 + 1.88216i) q^{70} +7.97855 q^{71} -11.9265 q^{73} +(-0.324174 + 0.0528754i) q^{74} +(0.635524 + 1.89634i) q^{76} -4.44819i q^{77} +5.31738i q^{79} +(-7.13550 - 9.45014i) q^{80} +(-1.47837 - 9.06373i) q^{82} +5.22797 q^{83} -7.48853 q^{85} +(0.610532 + 3.74311i) q^{86} +(3.98546 - 2.10054i) q^{88} +8.73011i q^{89} -18.1868i q^{91} +(-9.35443 + 3.13497i) q^{92} +(17.7228 - 2.89073i) q^{94} +2.96037 q^{95} -3.65258 q^{97} +(1.11532 - 0.181917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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