LMFDB - Embedded newform 2394.2.by.b.647.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(647,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("2394.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.by (of order $6$, degree $2$, 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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.18
Character	$\chi$	$=$	2394.647
Dual form			2394.2.by.b.2357.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.580202 + 1.00494i) q^{5} +(2.42321 + 1.06211i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.580202 + 1.00494i) q^{5} +(2.42321 + 1.06211i) q^{7} -1.00000i q^{8} +(1.00494 + 0.580202i) q^{10} +(-3.13786 - 1.81165i) q^{11} -5.90088i q^{13} +(2.62961 - 0.291793i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.898169 - 1.55567i) q^{17} +(-0.866025 + 0.500000i) q^{19} +1.16040 q^{20} -3.62329 q^{22} +(-2.98738 + 1.72476i) q^{23} +(1.82673 - 3.16399i) q^{25} +(-2.95044 - 5.11031i) q^{26} +(2.13141 - 1.56751i) q^{28} -9.18226i q^{29} +(5.52559 + 3.19020i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.79634i q^{34} +(0.338598 + 3.05141i) q^{35} +(-5.57502 - 9.65622i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(1.00494 - 0.580202i) q^{40} -4.58062 q^{41} +6.40504 q^{43} +(-3.13786 + 1.81165i) q^{44} +(-1.72476 + 2.98738i) q^{46} +(3.52675 + 6.10852i) q^{47} +(4.74386 + 5.14740i) q^{49} -3.65346i q^{50} +(-5.11031 - 2.95044i) q^{52} +(8.82222 + 5.09351i) q^{53} -4.20448i q^{55} +(1.06211 - 2.42321i) q^{56} +(-4.59113 - 7.95207i) q^{58} +(4.00871 - 6.94329i) q^{59} +(5.93503 - 3.42659i) q^{61} +6.38040 q^{62} -1.00000 q^{64} +(5.93003 - 3.42371i) q^{65} +(-3.46710 + 6.00519i) q^{67} +(-0.898169 - 1.55567i) q^{68} +(1.81894 + 2.47330i) q^{70} -2.84418i q^{71} +(-8.04299 - 4.64362i) q^{73} +(-9.65622 - 5.57502i) q^{74} +1.00000i q^{76} +(-5.67953 - 7.72273i) q^{77} +(6.10458 + 10.5734i) q^{79} +(0.580202 - 1.00494i) q^{80} +(-3.96693 + 2.29031i) q^{82} -9.96211 q^{83} +2.08448 q^{85} +(5.54693 - 3.20252i) q^{86} +(-1.81165 + 3.13786i) q^{88} +(7.36921 + 12.7638i) q^{89} +(6.26736 - 14.2991i) q^{91} +3.44952i q^{92} +(6.10852 + 3.52675i) q^{94} +(-1.00494 - 0.580202i) q^{95} -0.298027i q^{97} +(6.68201 + 2.08585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 4 q^{7}+O(q^{10}) $ 48 * q + 24 * q^4 - 4 * q^7	$ 48 q + 24 q^{4} - 4 q^{7} - 12 q^{10} + 4 q^{14} - 24 q^{16} + 16 q^{17} + 8 q^{22} - 28 q^{25} + 4 q^{28} + 12 q^{31} + 24 q^{35} - 24 q^{38} - 12 q^{40} - 16 q^{41} + 8 q^{43} + 8 q^{46} - 32 q^{49} + 48 q^{53} - 4 q^{56} - 4 q^{58} - 16 q^{59} - 32 q^{62} - 48 q^{64} - 24 q^{67} - 16 q^{68} + 28 q^{70} + 12 q^{73} - 8 q^{77} - 20 q^{79} - 48 q^{82} - 128 q^{83} - 40 q^{85} + 4 q^{88} - 32 q^{89} + 40 q^{91} + 12 q^{95} + 16 q^{98}+O(q^{100}) $ 48 * q + 24 * q^4 - 4 * q^7 - 12 * q^10 + 4 * q^14 - 24 * q^16 + 16 * q^17 + 8 * q^22 - 28 * q^25 + 4 * q^28 + 12 * q^31 + 24 * q^35 - 24 * q^38 - 12 * q^40 - 16 * q^41 + 8 * q^43 + 8 * q^46 - 32 * q^49 + 48 * q^53 - 4 * q^56 - 4 * q^58 - 16 * q^59 - 32 * q^62 - 48 * q^64 - 24 * q^67 - 16 * q^68 + 28 * q^70 + 12 * q^73 - 8 * q^77 - 20 * q^79 - 48 * q^82 - 128 * q^83 - 40 * q^85 + 4 * q^88 - 32 * q^89 + 40 * q^91 + 12 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.580202	+	1.00494i	0.259474	+	0.449423i	0.966101	−	0.258164i	$-0.0831173\pi$
$5$	0.580202	+	1.00494i	0.259474	+	0.449423i	−0.706627	+	0.707586i	$0.749784\pi$
$6$		0			0
$7$	2.42321	+	1.06211i	0.915886	+	0.401438i
$7$	2.42321	+	1.06211i	0.915886	+	0.401438i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.00494	+	0.580202i	0.317790	+	0.183476i
$11$	−3.13786	−	1.81165i	−0.946101	−	0.546232i	−0.0542334	−	0.998528i	$-0.517271\pi$
$11$	−3.13786	−	1.81165i	−0.946101	−	0.546232i	−0.891868	+	0.452297i	$0.850605\pi$
$12$		0			0
$13$		−	5.90088i		−	1.63661i	−0.574784	−	0.818305i	$-0.694914\pi$
$13$		−	5.90088i		−	1.63661i	0.574784	−	0.818305i	$-0.305086\pi$
$14$	2.62961	−	0.291793i	0.702793	−	0.0779850i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.898169	−	1.55567i	0.217838	−	0.377307i	−0.736309	−	0.676646i	$-0.763433\pi$
$17$	0.898169	−	1.55567i	0.217838	−	0.377307i	0.954147	+	0.299339i	$0.0967662\pi$
$18$		0			0
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	1.16040			0.259474
$21$		0			0
$22$	−3.62329			−0.772488
$23$	−2.98738	+	1.72476i	−0.622911	+	0.359638i	−0.778001	−	0.628262i	$-0.783766\pi$
$23$	−2.98738	+	1.72476i	−0.622911	+	0.359638i	0.155090	+	0.987900i	$0.450433\pi$
$24$		0			0
$25$	1.82673	−	3.16399i	0.365346	−	0.632798i
$26$	−2.95044	−	5.11031i	−0.578629	−	1.00222i
$27$		0			0
$28$	2.13141	−	1.56751i	0.402799	−	0.296231i
$29$		−	9.18226i		−	1.70510i	−0.522643	−	0.852551i	$-0.675054\pi$
$29$		−	9.18226i		−	1.70510i	0.522643	−	0.852551i	$-0.324946\pi$
$30$		0			0
$31$	5.52559	+	3.19020i	0.992426	+	0.572977i	0.905998	−	0.423281i	$-0.139122\pi$
$31$	5.52559	+	3.19020i	0.992426	+	0.572977i	0.0864271	+	0.996258i	$0.472455\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	1.79634i		−	0.308069i
$35$	0.338598	+	3.05141i	0.0572336	+	0.515783i
$36$		0			0
$37$	−5.57502	−	9.65622i	−0.916528	−	1.58747i	−0.804649	−	0.593751i	$-0.797646\pi$
$37$	−5.57502	−	9.65622i	−0.916528	−	1.58747i	−0.111879	−	0.993722i	$-0.535687\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$		0			0
$40$	1.00494	−	0.580202i	0.158895	−	0.0917381i
$41$	−4.58062			−0.715373			−0.357686	−	0.933842i	$-0.616434\pi$
$41$	−4.58062			−0.715373			−0.357686	+	0.933842i	$0.616434\pi$
$42$		0			0
$43$	6.40504			0.976760			0.488380	−	0.872631i	$-0.337588\pi$
$43$	6.40504			0.976760			0.488380	+	0.872631i	$0.337588\pi$
$44$	−3.13786	+	1.81165i	−0.473050	+	0.273116i
$45$		0			0
$46$	−1.72476	+	2.98738i	−0.254302	+	0.440465i
$47$	3.52675	+	6.10852i	0.514430	+	0.891019i	0.999860	+	0.0167433i	$0.00532981\pi$
$47$	3.52675	+	6.10852i	0.514430	+	0.891019i	−0.485430	+	0.874276i	$0.661337\pi$
$48$		0			0
$49$	4.74386	+	5.14740i	0.677695	+	0.735343i
$50$		−	3.65346i		−	0.516677i
$51$		0			0
$52$	−5.11031	−	2.95044i	−0.708673	−	0.409153i
$53$	8.82222	+	5.09351i	1.21183	+	0.699648i	0.963157	−	0.268941i	$-0.0866737\pi$
$53$	8.82222	+	5.09351i	1.21183	+	0.699648i	0.248668	+	0.968589i	$0.420007\pi$
$54$		0			0
$55$		−	4.20448i		−	0.566933i
$56$	1.06211	−	2.42321i	0.141930	−	0.323815i
$57$		0			0
$58$	−4.59113	−	7.95207i	−0.602845	−	1.04416i
$59$	4.00871	−	6.94329i	0.521890	−	0.903940i	−0.477786	−	0.878476i	$-0.658561\pi$
$59$	4.00871	−	6.94329i	0.521890	−	0.903940i	0.999676	−	0.0254635i	$-0.00810616\pi$
$60$		0			0
$61$	5.93503	−	3.42659i	0.759903	−	0.438730i	−0.0693579	−	0.997592i	$-0.522095\pi$
$61$	5.93503	−	3.42659i	0.759903	−	0.438730i	0.829261	+	0.558862i	$0.188762\pi$
$62$	6.38040			0.810312
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.93003	−	3.42371i	0.735530	−	0.424659i
$66$		0			0
$67$	−3.46710	+	6.00519i	−0.423574	+	0.733651i	−0.996286	−	0.0861053i	$-0.972558\pi$
$67$	−3.46710	+	6.00519i	−0.423574	+	0.733651i	0.572712	+	0.819756i	$0.305891\pi$
$68$	−0.898169	−	1.55567i	−0.108919	−	0.188653i
$69$		0			0
$70$	1.81894	+	2.47330i	0.217405	+	0.295616i
$71$		−	2.84418i		−	0.337542i	−0.985655	−	0.168771i	$-0.946020\pi$
$71$		−	2.84418i		−	0.337542i	0.985655	−	0.168771i	$-0.0539799\pi$
$72$		0			0
$73$	−8.04299	−	4.64362i	−0.941360	−	0.543495i	−0.0509739	−	0.998700i	$-0.516233\pi$
$73$	−8.04299	−	4.64362i	−0.941360	−	0.543495i	−0.890386	+	0.455205i	$0.849566\pi$
$74$	−9.65622	−	5.57502i	−1.12251	−	0.648083i
$75$		0			0
$76$			1.00000i			0.114708i
$77$	−5.67953	−	7.72273i	−0.647243	−	0.880087i
$78$		0			0
$79$	6.10458	+	10.5734i	0.686818	+	1.18960i	0.972862	+	0.231388i	$0.0743266\pi$
$79$	6.10458	+	10.5734i	0.686818	+	1.18960i	−0.286043	+	0.958217i	$0.592340\pi$
$80$	0.580202	−	1.00494i	0.0648686	−	0.112356i
$81$		0			0
$82$	−3.96693	+	2.29031i	−0.438075	+	0.252922i
$83$	−9.96211			−1.09348			−0.546742	−	0.837301i	$-0.684132\pi$
$83$	−9.96211			−1.09348			−0.546742	+	0.837301i	$0.684132\pi$
$84$		0			0
$85$	2.08448			0.226094
$86$	5.54693	−	3.20252i	0.598141	−	0.345337i
$87$		0			0
$88$	−1.81165	+	3.13786i	−0.193122	+	0.334497i
$89$	7.36921	+	12.7638i	0.781135	+	1.35296i	0.931281	+	0.364301i	$0.118692\pi$
$89$	7.36921	+	12.7638i	0.781135	+	1.35296i	−0.150147	+	0.988664i	$0.547975\pi$
$90$		0			0
$91$	6.26736	−	14.2991i	0.656998	−	1.49895i
$92$			3.44952i			0.359638i
$93$		0			0
$94$	6.10852	+	3.52675i	0.630046	+	0.363757i
$95$	−1.00494	−	0.580202i	−0.103105	−	0.0595275i
$96$		0			0
$97$		−	0.298027i		−	0.0302601i	−0.999886	−	0.0151300i	$-0.995184\pi$
$97$		−	0.298027i		−	0.0302601i	0.999886	−	0.0151300i	$-0.00481622\pi$
$98$	6.68201	+	2.08585i	0.674985	+	0.210703i
$99$		0			0
$100$	−1.82673	−	3.16399i	−0.182673	−	0.316399i
$101$	−2.99872	+	5.19394i	−0.298384	+	0.516817i	−0.975766	−	0.218815i	$-0.929781\pi$
$101$	−2.99872	+	5.19394i	−0.298384	+	0.516817i	0.677382	+	0.735631i	$0.263114\pi$
$102$		0			0
$103$	17.3639	−	10.0251i	1.71092	−	0.987798i	0.777586	−	0.628777i	$-0.216444\pi$
$103$	17.3639	−	10.0251i	1.71092	−	0.987798i	0.933330	−	0.359021i	$-0.116889\pi$
$104$	−5.90088			−0.578629
$105$		0			0
$106$	10.1870			0.989451
$107$	8.87578	−	5.12444i	0.858054	−	0.495398i	−0.00530589	−	0.999986i	$-0.501689\pi$
$107$	8.87578	−	5.12444i	0.858054	−	0.495398i	0.863360	+	0.504588i	$0.168356\pi$
$108$		0			0
$109$	−4.28306	+	7.41848i	−0.410243	+	0.710562i	−0.994916	−	0.100707i	$-0.967889\pi$
$109$	−4.28306	+	7.41848i	−0.410243	+	0.710562i	0.584673	+	0.811269i	$0.301223\pi$
$110$	−2.10224	−	3.64119i	−0.200441	−	0.347174i
$111$		0			0
$112$	−0.291793	−	2.62961i	−0.0275719	−	0.248475i
$113$			11.1815i			1.05186i	0.850527	+	0.525932i	$0.176283\pi$
$113$			11.1815i			1.05186i	−0.850527	+	0.525932i	$0.823717\pi$
$114$		0			0
$115$	−3.46657	−	2.00142i	−0.323259	−	0.186634i
$116$	−7.95207	−	4.59113i	−0.738331	−	0.426276i
$117$		0			0
$118$		−	8.01742i		−	0.738064i
$119$	3.82874	−	2.81577i	0.350980	−	0.258121i
$120$		0			0
$121$	1.06412	+	1.84311i	0.0967380	+	0.167555i
$122$	3.42659	−	5.93503i	0.310229	−	0.537333i
$123$		0			0
$124$	5.52559	−	3.19020i	0.496213	−	0.286489i
$125$	10.0415			0.898141
$126$		0			0
$127$	18.4932			1.64101			0.820505	−	0.571639i	$-0.193692\pi$
$127$	18.4932			1.64101			0.820505	+	0.571639i	$0.193692\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	3.42371	−	5.93003i	0.300279	−	0.520098i
$131$	−2.81894	−	4.88254i	−0.246292	−	0.426590i	0.716202	−	0.697893i	$-0.245879\pi$
$131$	−2.81894	−	4.88254i	−0.246292	−	0.426590i	−0.962494	+	0.271303i	$0.912545\pi$
$132$		0			0
$133$	−2.62961	+	0.291793i	−0.228016	+	0.0253017i
$134$			6.93420i			0.599024i
$135$		0			0
$136$	−1.55567	−	0.898169i	−0.133398	−	0.0770174i
$137$	−14.6280	−	8.44551i	−1.24976	−	0.721548i	−0.278697	−	0.960379i	$-0.589903\pi$
$137$	−14.6280	−	8.44551i	−1.24976	−	0.721548i	−0.971061	+	0.238831i	$0.923236\pi$
$138$		0			0
$139$		−	17.9137i		−	1.51942i	−0.650262	−	0.759710i	$-0.725341\pi$
$139$		−	17.9137i		−	1.51942i	0.650262	−	0.759710i	$-0.274659\pi$
$140$	2.81190	+	1.23247i	0.237649	+	0.104163i
$141$		0			0
$142$	−1.42209	−	2.46313i	−0.119339	−	0.206702i
$143$	−10.6903	+	18.5162i	−0.893968	+	1.54840i
$144$		0			0
$145$	9.22762	−	5.32757i	0.766312	−	0.442431i
$146$	−9.28724			−0.768618
$147$		0			0
$148$	−11.1500			−0.916528
$149$	−16.9206	+	9.76912i	−1.38619	+	0.800318i	−0.992884	−	0.119089i	$-0.962003\pi$
$149$	−16.9206	+	9.76912i	−1.38619	+	0.800318i	−0.393307	+	0.919407i	$0.628669\pi$
$150$		0			0
$151$	0.294935	−	0.510843i	0.0240015	−	0.0415718i	−0.853775	−	0.520642i	$-0.825693\pi$
$151$	0.294935	−	0.510843i	0.0240015	−	0.0415718i	0.877777	+	0.479070i	$0.159026\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$		0			0
$154$	−8.77998	−	3.84832i	−0.707511	−	0.310106i
$155$			7.40385i			0.594692i
$156$		0			0
$157$	0.892192	+	0.515107i	0.0712047	+	0.0411100i	0.535180	−	0.844738i	$-0.320244\pi$
$157$	0.892192	+	0.515107i	0.0712047	+	0.0411100i	−0.463975	+	0.885848i	$0.653577\pi$
$158$	10.5734	+	6.10458i	0.841177	+	0.485654i
$159$		0			0
$160$		−	1.16040i		−	0.0917381i
$161$	−9.07091	+	1.00655i	−0.714888	+	0.0793271i
$162$		0			0
$163$	7.04188	+	12.1969i	0.551562	+	0.955334i	0.998162	+	0.0606001i	$0.0193014\pi$
$163$	7.04188	+	12.1969i	0.551562	+	0.955334i	−0.446600	+	0.894734i	$0.647365\pi$
$164$	−2.29031	+	3.96693i	−0.178843	+	0.309766i
$165$		0			0
$166$	−8.62744	+	4.98106i	−0.669619	+	0.386605i
$167$	−19.7974			−1.53197			−0.765984	−	0.642859i	$-0.777748\pi$
$167$	−19.7974			−1.53197			−0.765984	+	0.642859i	$0.777748\pi$
$168$		0			0
$169$	−21.8204			−1.67849
$170$	1.80521	−	1.04224i	0.138453	−	0.0799362i
$171$		0			0
$172$	3.20252	−	5.54693i	0.244190	−	0.422949i
$173$	−4.00762	−	6.94141i	−0.304694	−	0.527745i	0.672499	−	0.740098i	$-0.265221\pi$
$173$	−4.00762	−	6.94141i	−0.304694	−	0.527745i	−0.977193	+	0.212352i	$0.931888\pi$
$174$		0			0
$175$	7.78704	−	5.72682i	0.588645	−	0.432907i
$176$			3.62329i			0.273116i
$177$		0			0
$178$	12.7638	+	7.36921i	0.956691	+	0.552346i
$179$	−13.5721	−	7.83584i	−1.01442	−	0.585678i	−0.101940	−	0.994791i	$-0.532505\pi$
$179$	−13.5721	−	7.83584i	−1.01442	−	0.585678i	−0.912484	+	0.409113i	$0.865838\pi$
$180$		0			0
$181$		−	9.01734i		−	0.670254i	−0.942173	−	0.335127i	$-0.891221\pi$
$181$		−	9.01734i		−	0.670254i	0.942173	−	0.335127i	$-0.108779\pi$
$182$	−1.72184	−	15.5170i	−0.127631	−	1.15020i
$183$		0			0
$184$	1.72476	+	2.98738i	0.127151	+	0.220232i
$185$	6.46928	−	11.2051i	0.475631	−	0.823817i
$186$		0			0
$187$	−5.63666	+	3.25433i	−0.412194	+	0.237980i
$188$	7.05351			0.514430
$189$		0			0
$190$	−1.16040			−0.0841846
$191$	−1.91259	+	1.10423i	−0.138390	+	0.0798996i	−0.567597	−	0.823307i	$-0.692127\pi$
$191$	−1.91259	+	1.10423i	−0.138390	+	0.0798996i	0.429206	+	0.903206i	$0.358793\pi$
$192$		0			0
$193$	−5.85797	+	10.1463i	−0.421666	+	0.730347i	−0.996103	−	0.0882020i	$-0.971888\pi$
$193$	−5.85797	+	10.1463i	−0.421666	+	0.730347i	0.574436	+	0.818549i	$0.305221\pi$
$194$	−0.149014	−	0.258099i	−0.0106985	−	0.0185304i
$195$		0			0
$196$	6.82971	−	1.53461i	0.487837	−	0.109615i
$197$			9.10590i			0.648769i	0.945925	+	0.324384i	$0.105157\pi$
$197$			9.10590i			0.648769i	−0.945925	+	0.324384i	$0.894843\pi$
$198$		0			0
$199$	−13.4122	−	7.74352i	−0.950764	−	0.548924i	−0.0574456	−	0.998349i	$-0.518296\pi$
$199$	−13.4122	−	7.74352i	−0.950764	−	0.548924i	−0.893318	+	0.449425i	$0.851629\pi$
$200$	−3.16399	−	1.82673i	−0.223728	−	0.129169i
$201$		0			0
$202$			5.99745i			0.421979i
$203$	9.75253	−	22.2505i	0.684493	−	1.56168i
$204$		0			0
$205$	−2.65769	−	4.60325i	−0.185621	−	0.321505i
$206$	10.0251	−	17.3639i	0.698478	−	1.20980i
$207$		0			0
$208$	−5.11031	+	2.95044i	−0.354337	+	0.204576i
$209$	3.62329			0.250628
$210$		0			0
$211$	−18.7630			−1.29170			−0.645849	−	0.763466i	$-0.723496\pi$
$211$	−18.7630			−1.29170			−0.645849	+	0.763466i	$0.723496\pi$
$212$	8.82222	−	5.09351i	0.605913	−	0.349824i
$213$		0			0
$214$	5.12444	−	8.87578i	0.350299	−	0.606736i
$215$	3.71622	+	6.43668i	0.253444	+	0.438978i
$216$		0			0
$217$	10.0013	+	13.5993i	0.678934	+	0.923179i
$218$			8.56613i			0.580171i
$219$		0			0
$220$	−3.64119	−	2.10224i	−0.245489	−	0.141733i
$221$	−9.17985	−	5.29999i	−0.617504	−	0.356516i
$222$		0			0
$223$		−	18.2526i		−	1.22228i	−0.791522	−	0.611141i	$-0.790711\pi$
$223$		−	18.2526i		−	1.22228i	0.791522	−	0.611141i	$-0.209289\pi$
$224$	−1.56751	−	2.13141i	−0.104733	−	0.142411i
$225$		0			0
$226$	5.59073	+	9.68343i	0.371890	+	0.644132i
$227$	−1.14563	+	1.98429i	−0.0760381	+	0.131702i	−0.901537	−	0.432702i	$-0.857560\pi$
$227$	−1.14563	+	1.98429i	−0.0760381	+	0.131702i	0.825499	+	0.564403i	$0.190894\pi$
$228$		0			0
$229$	6.35395	−	3.66845i	0.419881	−	0.242418i	−0.275146	−	0.961403i	$-0.588726\pi$
$229$	6.35395	−	3.66845i	0.419881	−	0.242418i	0.695026	+	0.718984i	$0.255393\pi$
$230$	−4.00285			−0.263940
$231$		0			0
$232$	−9.18226			−0.602845
$233$	−20.2864	+	11.7123i	−1.32900	+	0.767301i	−0.985146	−	0.171720i	$-0.945068\pi$
$233$	−20.2864	+	11.7123i	−1.32900	+	0.767301i	−0.343859	+	0.939021i	$0.611734\pi$
$234$		0			0
$235$	−4.09246	+	7.08835i	−0.266963	+	0.462393i
$236$	−4.00871	−	6.94329i	−0.260945	−	0.451970i
$237$		0			0
$238$	1.90790	−	4.35290i	0.123671	−	0.282157i
$239$			13.4914i			0.872685i	0.899781	+	0.436343i	$0.143726\pi$
$239$			13.4914i			0.872685i	−0.899781	+	0.436343i	$0.856274\pi$
$240$		0			0
$241$	21.7250	+	12.5430i	1.39943	+	0.807962i	0.994333	−	0.106310i	$-0.0339037\pi$
$241$	21.7250	+	12.5430i	1.39943	+	0.807962i	0.405099	+	0.914273i	$0.367237\pi$
$242$	1.84311	+	1.06412i	0.118479	+	0.0684041i
$243$		0			0
$244$		−	6.85318i		−	0.438730i
$245$	−2.42043	+	7.75383i	−0.154636	+	0.495374i
$246$		0			0
$247$	2.95044	+	5.11031i	0.187732	+	0.325161i
$248$	3.19020	−	5.52559i	0.202578	−	0.350875i
$249$		0			0
$250$	8.69621	−	5.02076i	0.549997	−	0.317541i
$251$	8.11472			0.512196			0.256098	−	0.966651i	$-0.417563\pi$
$251$	8.11472			0.512196			0.256098	+	0.966651i	$0.417563\pi$
$252$		0			0
$253$	12.4986			0.785782
$254$	16.0156	−	9.24662i	1.00491	−	0.580185i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.38719	−	7.59884i	−0.273666	−	0.474003i	0.696132	−	0.717914i	$-0.254903\pi$
$257$	−4.38719	−	7.59884i	−0.273666	−	0.474003i	−0.969798	+	0.243911i	$0.921570\pi$
$258$		0			0
$259$	−3.25351	−	29.3203i	−0.202163	−	1.82187i
$260$		−	6.84741i		−	0.424659i
$261$		0			0
$262$	−4.88254	−	2.81894i	−0.301644	−	0.174154i
$263$	−3.19969	−	1.84734i	−0.197301	−	0.113912i	0.398095	−	0.917344i	$-0.369672\pi$
$263$	−3.19969	−	1.84734i	−0.197301	−	0.113912i	−0.595396	+	0.803432i	$0.703005\pi$
$264$		0			0
$265$			11.8211i			0.726163i
$266$	−2.13141	+	1.56751i	−0.130685	+	0.0961100i
$267$		0			0
$268$	3.46710	+	6.00519i	0.211787	+	0.366826i
$269$	5.28148	−	9.14779i	0.322017	−	0.557751i	−0.658887	−	0.752242i	$-0.728972\pi$
$269$	5.28148	−	9.14779i	0.322017	−	0.557751i	0.980904	+	0.194492i	$0.0623057\pi$
$270$		0			0
$271$	−3.74635	+	2.16296i	−0.227575	+	0.131390i	−0.609453	−	0.792822i	$-0.708611\pi$
$271$	−3.74635	+	2.16296i	−0.227575	+	0.131390i	0.381878	+	0.924213i	$0.375277\pi$
$272$	−1.79634			−0.108919
$273$		0			0
$274$	−16.8910			−1.02042
$275$	−11.4641	+	6.61877i	−0.691308	+	0.399127i
$276$		0			0
$277$	−6.74397	+	11.6809i	−0.405206	+	0.701837i	−0.994345	−	0.106194i	$-0.966133\pi$
$277$	−6.74397	+	11.6809i	−0.405206	+	0.701837i	0.589140	+	0.808031i	$0.299467\pi$
$278$	−8.95685	−	15.5137i	−0.537196	−	0.930451i
$279$		0			0
$280$	3.05141	−	0.338598i	0.182357	−	0.0202351i
$281$			20.0159i			1.19405i	0.802222	+	0.597025i	$0.203651\pi$
$281$			20.0159i			1.19405i	−0.802222	+	0.597025i	$0.796349\pi$
$282$		0			0
$283$	28.0503	+	16.1948i	1.66741	+	0.962682i	0.969024	+	0.246966i	$0.0794335\pi$
$283$	28.0503	+	16.1948i	1.66741	+	0.962682i	0.698391	+	0.715717i	$0.253900\pi$
$284$	−2.46313	−	1.42209i	−0.146160	−	0.0843856i
$285$		0			0
$286$			21.3806i			1.26426i
$287$	−11.0998	−	4.86510i	−0.655200	−	0.287178i
$288$		0			0
$289$	6.88658	+	11.9279i	0.405093	+	0.701642i
$290$	5.32757	−	9.22762i	0.312846	−	0.541865i
$291$		0			0
$292$	−8.04299	+	4.64362i	−0.470680	+	0.271747i
$293$	27.5365			1.60870			0.804348	−	0.594158i	$-0.202515\pi$
$293$	27.5365			1.60870			0.804348	+	0.594158i	$0.202515\pi$
$294$		0			0
$295$	9.30346			0.541668
$296$	−9.65622	+	5.57502i	−0.561256	+	0.324042i
$297$		0			0
$298$	−9.76912	+	16.9206i	−0.565910	+	0.980185i
$299$	10.1776	+	17.6282i	0.588587	+	1.01946i
$300$		0			0
$301$	15.5207	+	6.80283i	0.894601	+	0.392109i
$302$		−	0.589871i		−	0.0339433i
$303$		0			0
$304$	0.866025	+	0.500000i	0.0496700	+	0.0286770i
$305$	6.88704	+	3.97623i	0.394351	+	0.227679i
$306$		0			0
$307$			23.1632i			1.32199i	0.750388	+	0.660997i	$0.229866\pi$
$307$			23.1632i			1.32199i	−0.750388	+	0.660997i	$0.770134\pi$
$308$	−9.52785	+	1.05725i	−0.542899	+	0.0602425i
$309$		0			0
$310$	3.70193	+	6.41192i	0.210255	+	0.364173i
$311$	8.10958	−	14.0462i	0.459852	−	0.796488i	−0.539100	−	0.842241i	$-0.681236\pi$
$311$	8.10958	−	14.0462i	0.459852	−	0.796488i	0.998953	+	0.0457539i	$0.0145690\pi$
$312$		0			0
$313$	20.6578	−	11.9268i	1.16765	−	0.674143i	0.214524	−	0.976719i	$-0.431180\pi$
$313$	20.6578	−	11.9268i	1.16765	−	0.674143i	0.953125	+	0.302576i	$0.0978467\pi$
$314$	1.03021			0.0581384
$315$		0			0
$316$	12.2092			0.686818
$317$	−4.22493	+	2.43927i	−0.237296	+	0.137003i	−0.613933	−	0.789358i	$-0.710414\pi$
$317$	−4.22493	+	2.43927i	−0.237296	+	0.137003i	0.376637	+	0.926361i	$0.377080\pi$
$318$		0			0
$319$	−16.6350	+	28.8127i	−0.931381	+	1.61320i
$320$	−0.580202	−	1.00494i	−0.0324343	−	0.0561779i
$321$		0			0
$322$	−7.35236	+	5.40715i	−0.409731	+	0.301329i
$323$			1.79634i			0.0999509i
$324$		0			0
$325$	−18.6703	−	10.7793i	−1.03564	−	0.597929i
$326$	12.1969	+	7.04188i	0.675523	+	0.390013i
$327$		0			0
$328$			4.58062i			0.252922i
$329$	2.05817	+	18.5480i	0.113470	+	1.02258i
$330$		0			0
$331$	3.89686	+	6.74956i	0.214191	+	0.370989i	0.953022	−	0.302901i	$-0.0979553\pi$
$331$	3.89686	+	6.74956i	0.214191	+	0.370989i	−0.738831	+	0.673891i	$0.764622\pi$
$332$	−4.98106	+	8.62744i	−0.273371	+	0.473492i
$333$		0			0
$334$	−17.1450	+	9.89870i	−0.938135	+	0.541633i
$335$	−8.04648			−0.439626
$336$		0			0
$337$	−12.3848			−0.674643			−0.337321	−	0.941390i	$-0.609521\pi$
$337$	−12.3848			−0.674643			−0.337321	+	0.941390i	$0.609521\pi$
$338$	−18.8970	+	10.9102i	−1.02786	+	0.593437i
$339$		0			0
$340$	1.04224	−	1.80521i	0.0565234	−	0.0979014i
$341$	−11.5590	−	20.0208i	−0.625957	−	1.08419i
$342$		0			0
$343$	6.02828	+	17.5117i	0.325497	+	0.945543i
$344$		−	6.40504i		−	0.345337i
$345$		0			0
$346$	−6.94141	−	4.00762i	−0.373172	−	0.215451i
$347$	20.0169	+	11.5568i	1.07456	+	0.620400i	0.929425	−	0.369011i	$-0.120304\pi$
$347$	20.0169	+	11.5568i	1.07456	+	0.620400i	0.145140	+	0.989411i	$0.453637\pi$
$348$		0			0
$349$			6.96383i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$349$			6.96383i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$350$	3.88036	−	8.85309i	0.207414	−	0.473218i
$351$		0			0
$352$	1.81165	+	3.13786i	0.0965610	+	0.167249i
$353$	−3.72535	+	6.45249i	−0.198280	+	0.343432i	−0.947971	−	0.318357i	$-0.896869\pi$
$353$	−3.72535	+	6.45249i	−0.198280	+	0.343432i	0.749691	+	0.661788i	$0.230202\pi$
$354$		0			0
$355$	2.85823	−	1.65020i	0.151699	−	0.0875836i
$356$	14.7384			0.781135
$357$		0			0
$358$	−15.6717			−0.828274
$359$	1.22323	−	0.706231i	0.0645595	−	0.0372734i	−0.467373	−	0.884060i	$-0.654799\pi$
$359$	1.22323	−	0.706231i	0.0645595	−	0.0372734i	0.531932	+	0.846787i	$0.321466\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	−4.50867	−	7.80925i	−0.236970	−	0.410445i
$363$		0			0
$364$	−9.24967	−	12.5772i	−0.484814	−	0.659226i
$365$		−	10.7770i		−	0.564092i
$366$		0			0
$367$	−17.3050	−	9.99104i	−0.903313	−	0.521528i	−0.0250393	−	0.999686i	$-0.507971\pi$
$367$	−17.3050	−	9.99104i	−0.903313	−	0.521528i	−0.878274	+	0.478159i	$0.841304\pi$
$368$	2.98738	+	1.72476i	0.155728	+	0.0899095i
$369$		0			0
$370$		−	12.9386i		−	0.672644i
$371$	15.9682	+	21.7128i	0.829029	+	1.12727i
$372$		0			0
$373$	−1.23647	−	2.14163i	−0.0640220	−	0.110889i	0.832238	−	0.554419i	$-0.187059\pi$
$373$	−1.23647	−	2.14163i	−0.0640220	−	0.110889i	−0.896260	+	0.443530i	$0.853726\pi$
$374$	−3.25433	+	5.63666i	−0.168277	+	0.291465i
$375$		0			0
$376$	6.10852	−	3.52675i	0.315023	−	0.181878i
$377$	−54.1834			−2.79059
$378$		0			0
$379$	−33.3989			−1.71558			−0.857792	−	0.513996i	$-0.828164\pi$
$379$	−33.3989			−1.71558			−0.857792	+	0.513996i	$0.828164\pi$
$380$	−1.00494	+	0.580202i	−0.0515523	+	0.0297638i
$381$		0			0
$382$	−1.10423	+	1.91259i	−0.0564975	+	0.0978566i
$383$	14.7488	+	25.5456i	0.753626	+	1.30532i	0.946054	+	0.324008i	$0.105031\pi$
$383$	14.7488	+	25.5456i	0.753626	+	1.30532i	−0.192428	+	0.981311i	$0.561636\pi$
$384$		0			0
$385$	4.46561	−	10.1883i	0.227588	−	0.519246i
$386$			11.7159i			0.596326i
$387$		0			0
$388$	−0.258099	−	0.149014i	−0.0131030	−	0.00756501i
$389$	−4.44776	−	2.56792i	−0.225510	−	0.130198i	0.382989	−	0.923753i	$-0.374895\pi$
$389$	−4.44776	−	2.56792i	−0.225510	−	0.130198i	−0.608499	+	0.793555i	$0.708228\pi$
$390$		0			0
$391$			6.19651i			0.313371i
$392$	5.14740	−	4.74386i	0.259983	−	0.239601i
$393$		0			0
$394$	4.55295	+	7.88594i	0.229374	+	0.397288i
$395$	−7.08378	+	12.2695i	−0.356424	+	0.617344i
$396$		0			0
$397$	−0.811939	+	0.468773i	−0.0407500	+	0.0235270i	−0.520237	−	0.854022i	$-0.674156\pi$
$397$	−0.811939	+	0.468773i	−0.0407500	+	0.0235270i	0.479487	+	0.877549i	$0.340823\pi$
$398$	−15.4870			−0.776295
$399$		0			0
$400$	−3.65346			−0.182673
$401$	33.0425	−	19.0771i	1.65006	−	0.952665i	0.673021	−	0.739624i	$-0.264996\pi$
$401$	33.0425	−	19.0771i	1.65006	−	0.952665i	0.977043	−	0.213041i	$-0.0683369\pi$
$402$		0			0
$403$	18.8250	−	32.6059i	0.937740	−	1.62421i
$404$	2.99872	+	5.19394i	0.149192	+	0.258408i
$405$		0			0
$406$	−2.67932	−	24.1458i	−0.132973	−	1.19833i
$407$			40.3998i			2.00255i
$408$		0			0
$409$	−12.1739	−	7.02862i	−0.601962	−	0.347543i	0.167851	−	0.985812i	$-0.446317\pi$
$409$	−12.1739	−	7.02862i	−0.601962	−	0.347543i	−0.769813	+	0.638269i	$0.779651\pi$
$410$	−4.60325	−	2.65769i	−0.227338	−	0.131254i
$411$		0			0
$412$		−	20.0501i		−	0.987798i
$413$	17.0884	−	12.5674i	0.840868	−	0.618399i
$414$		0			0
$415$	−5.78004	−	10.0113i	−0.283731	−	0.491437i
$416$	−2.95044	+	5.11031i	−0.144657	+	0.250554i
$417$		0			0
$418$	3.13786	−	1.81165i	0.153478	−	0.0886105i
$419$	−8.60615			−0.420438			−0.210219	−	0.977654i	$-0.567418\pi$
$419$	−8.60615			−0.420438			−0.210219	+	0.977654i	$0.567418\pi$
$420$		0			0
$421$	18.0506			0.879732			0.439866	−	0.898063i	$-0.355026\pi$
$421$	18.0506			0.879732			0.439866	+	0.898063i	$0.355026\pi$
$422$	−16.2492	+	9.38149i	−0.791000	+	0.456684i
$423$		0			0
$424$	5.09351	−	8.82222i	0.247363	−	0.428445i
$425$	−3.28143	−	5.68360i	−0.159173	−	0.275695i
$426$		0			0
$427$	18.0212	−	1.99971i	0.872108	−	0.0967729i
$428$		−	10.2489i		−	0.495398i
$429$		0			0
$430$	6.43668	+	3.71622i	0.310404	+	0.179212i
$431$	33.4924	+	19.3368i	1.61327	+	0.931422i	0.988606	+	0.150529i	$0.0480977\pi$
$431$	33.4924	+	19.3368i	1.61327	+	0.931422i	0.624665	+	0.780893i	$0.285236\pi$
$432$		0			0
$433$			18.2000i			0.874636i	0.899307	+	0.437318i	$0.144072\pi$
$433$			18.2000i			0.874636i	−0.899307	+	0.437318i	$0.855928\pi$
$434$	15.4610	+	6.77666i	0.742154	+	0.325290i
$435$		0			0
$436$	4.28306	+	7.41848i	0.205122	+	0.355281i
$437$	1.72476	−	2.98738i	0.0825066	−	0.142906i
$438$		0			0
$439$	10.4038	−	6.00666i	0.496548	−	0.286682i	−0.230739	−	0.973016i	$-0.574114\pi$
$439$	10.4038	−	6.00666i	0.496548	−	0.286682i	0.727287	+	0.686333i	$0.240781\pi$
$440$	−4.20448			−0.200441
$441$		0			0
$442$	−10.6000			−0.504190
$443$	33.0761	−	19.0965i	1.57150	−	0.907303i	0.575509	−	0.817795i	$-0.304804\pi$
$443$	33.0761	−	19.0965i	1.57150	−	0.907303i	0.995986	−	0.0895078i	$-0.0285294\pi$
$444$		0			0
$445$	−8.55127	+	14.8112i	−0.405369	+	0.702120i
$446$	−9.12628	−	15.8072i	−0.432142	−	0.748491i
$447$		0			0
$448$	−2.42321	−	1.06211i	−0.114486	−	0.0501798i
$449$			35.3967i			1.67047i	0.549890	+	0.835237i	$0.314670\pi$
$449$			35.3967i			1.67047i	−0.549890	+	0.835237i	$0.685330\pi$
$450$		0			0
$451$	14.3734	+	8.29846i	0.676815	+	0.390759i
$452$	9.68343	+	5.59073i	0.455470	+	0.262966i
$453$		0			0
$454$			2.29126i			0.107534i
$455$	18.0060	−	1.99803i	0.844136	−	0.0936690i
$456$		0			0
$457$	10.5719	+	18.3110i	0.494530	+	0.856552i	0.999980	−	0.00630433i	$-0.00200674\pi$
$457$	10.5719	+	18.3110i	0.494530	+	0.856552i	−0.505450	+	0.862856i	$0.668673\pi$
$458$	3.66845	−	6.35395i	0.171416	−	0.296901i
$459$		0			0
$460$	−3.46657	+	2.00142i	−0.161629	+	0.0933168i
$461$	−2.18325			−0.101684			−0.0508421	−	0.998707i	$-0.516191\pi$
$461$	−2.18325			−0.101684			−0.0508421	+	0.998707i	$0.516191\pi$
$462$		0			0
$463$	3.72275			0.173011			0.0865055	−	0.996251i	$-0.472430\pi$
$463$	3.72275			0.173011			0.0865055	+	0.996251i	$0.472430\pi$
$464$	−7.95207	+	4.59113i	−0.369166	+	0.213138i
$465$		0			0
$466$	−11.7123	+	20.2864i	−0.542564	+	0.939748i
$467$	16.7638	+	29.0357i	0.775734	+	1.34361i	0.934381	+	0.356276i	$0.115954\pi$
$467$	16.7638	+	29.0357i	0.775734	+	1.34361i	−0.158647	+	0.987335i	$0.550713\pi$
$468$		0			0
$469$	−14.7796	+	10.8694i	−0.682461	+	0.501902i
$470$			8.18493i			0.377543i
$471$		0			0
$472$	−6.94329	−	4.00871i	−0.319591	−	0.184516i
$473$	−20.0981	−	11.6037i	−0.924113	−	0.533537i
$474$		0			0
$475$			3.65346i			0.167632i
$476$	−0.524159	−	4.72367i	−0.0240248	−	0.216509i
$477$		0			0
$478$	6.74569	+	11.6839i	0.308541	+	0.534408i
$479$	12.8997	−	22.3430i	0.589404	−	1.02088i	−0.404906	−	0.914358i	$-0.632696\pi$
$479$	12.8997	−	22.3430i	0.589404	−	1.02088i	0.994311	−	0.106520i	$-0.0339708\pi$
$480$		0			0
$481$	−56.9802	+	32.8975i	−2.59807	+	1.50000i
$482$	25.0859			1.14263
$483$		0			0
$484$	2.12824			0.0967380
$485$	0.299499	−	0.172916i	0.0135996	−	0.00785171i
$486$		0			0
$487$	−1.43278	+	2.48165i	−0.0649254	+	0.112454i	−0.896661	−	0.442718i	$-0.854014\pi$
$487$	−1.43278	+	2.48165i	−0.0649254	+	0.112454i	0.831735	+	0.555172i	$0.187348\pi$
$488$	−3.42659	−	5.93503i	−0.155115	−	0.268666i
$489$		0			0
$490$	1.78076	+	7.92523i	0.0804467	+	0.358026i
$491$		−	15.2107i		−	0.686448i	−0.939254	−	0.343224i	$-0.888481\pi$
$491$		−	15.2107i		−	0.686448i	0.939254	−	0.343224i	$-0.111519\pi$
$492$		0			0
$493$	−14.2846	−	8.24722i	−0.643346	−	0.371436i
$494$	5.11031	+	2.95044i	0.229924	+	0.132747i
$495$		0			0
$496$		−	6.38040i		−	0.286489i
$497$	3.02082	−	6.89204i	0.135502	−	0.309150i
$498$		0			0
$499$	−3.87566	−	6.71283i	−0.173498	−	0.300508i	0.766142	−	0.642671i	$-0.222174\pi$
$499$	−3.87566	−	6.71283i	−0.173498	−	0.300508i	−0.939641	+	0.342163i	$0.888840\pi$
$500$	5.02076	−	8.69621i	0.224535	−	0.388906i
$501$		0			0
$502$	7.02755	−	4.05736i	0.313655	−	0.181089i
$503$	1.55128			0.0691682			0.0345841	−	0.999402i	$-0.488989\pi$
$503$	1.55128			0.0691682			0.0345841	+	0.999402i	$0.488989\pi$
$504$		0			0
$505$	−6.95947			−0.309692
$506$	10.8241	−	6.24932i	0.481191	−	0.277816i
$507$		0			0
$508$	9.24662	−	16.0156i	0.410252	−	0.710578i
$509$	−13.6830	−	23.6996i	−0.606488	−	1.05047i	−0.991814	−	0.127688i	$-0.959244\pi$
$509$	−13.6830	−	23.6996i	−0.606488	−	1.05047i	0.385326	−	0.922780i	$-0.374089\pi$
$510$		0			0
$511$	−14.5578	−	19.7950i	−0.643999	−	0.875677i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−7.59884	−	4.38719i	−0.335171	−	0.193511i
$515$	20.1491	+	11.6331i	0.887878	+	0.512616i
$516$		0			0
$517$		−	25.5569i		−	1.12399i
$518$	−17.4778	−	23.7654i	−0.767929	−	1.04419i
$519$		0			0
$520$	−3.42371	−	5.93003i	−0.150139	−	0.260049i
$521$	−10.0943	+	17.4838i	−0.442239	+	0.765981i	−0.997855	−	0.0654582i	$-0.979149\pi$
$521$	−10.0943	+	17.4838i	−0.442239	+	0.765981i	0.555616	+	0.831439i	$0.312482\pi$
$522$		0			0
$523$	−24.4049	+	14.0902i	−1.06715	+	0.616120i	−0.927402	−	0.374067i	$-0.877963\pi$
$523$	−24.4049	+	14.0902i	−1.06715	+	0.616120i	−0.139749	+	0.990187i	$0.544630\pi$
$524$	−5.63787			−0.246292
$525$		0			0
$526$	−3.69468			−0.161096
$527$	9.92583	−	5.73068i	0.432376	−	0.249632i
$528$		0			0
$529$	−5.55039	+	9.61356i	−0.241321	+	0.417981i
$530$	5.91053	+	10.2373i	0.256737	+	0.444682i
$531$		0			0
$532$	−1.06211	+	2.42321i	−0.0460481	+	0.105059i
$533$			27.0297i			1.17079i
$534$		0			0
$535$	10.2995	+	5.94642i	0.445286	+	0.257086i
$536$	6.00519	+	3.46710i	0.259385	+	0.149756i
$537$		0			0
$538$		−	10.5630i		−	0.455401i
$539$	−5.56032	−	24.7460i	−0.239500	−	1.06589i
$540$		0			0
$541$	15.3147	+	26.5258i	0.658429	+	1.14043i	0.981022	+	0.193895i	$0.0621121\pi$
$541$	15.3147	+	26.5258i	0.658429	+	1.14043i	−0.322593	+	0.946538i	$0.604555\pi$
$542$	−2.16296	+	3.74635i	−0.0929069	+	0.160920i
$543$		0			0
$544$	−1.55567	+	0.898169i	−0.0666990	+	0.0385087i
$545$	−9.94017			−0.425790
$546$		0			0
$547$	12.2722			0.524723			0.262362	−	0.964970i	$-0.415499\pi$
$547$	12.2722			0.524723			0.262362	+	0.964970i	$0.415499\pi$
$548$	−14.6280	+	8.44551i	−0.624879	+	0.360774i
$549$		0			0
$550$	−6.61877	+	11.4641i	−0.282226	+	0.488829i
$551$	4.59113	+	7.95207i	0.195589	+	0.338770i
$552$		0			0
$553$	3.56255	+	32.1053i	0.151495	+	1.36526i
$554$			13.4879i			0.573047i
$555$		0			0
$556$	−15.5137	−	8.95685i	−0.657928	−	0.379855i
$557$	−21.2428	−	12.2645i	−0.900086	−	0.519665i	−0.0228580	−	0.999739i	$-0.507277\pi$
$557$	−21.2428	−	12.2645i	−0.900086	−	0.519665i	−0.877228	+	0.480074i	$0.840610\pi$
$558$		0			0
$559$		−	37.7954i		−	1.59858i
$560$	2.47330	−	1.81894i	0.104516	−	0.0768643i
$561$		0			0
$562$	10.0080	+	17.3343i	0.422161	+	0.731204i
$563$	5.79912	−	10.0444i	0.244404	−	0.423320i	−0.717560	−	0.696497i	$-0.754741\pi$
$563$	5.79912	−	10.0444i	0.244404	−	0.423320i	0.961964	+	0.273177i	$0.0880744\pi$
$564$		0			0
$565$	−11.2367	+	6.48751i	−0.472731	+	0.272932i
$566$	32.3896			1.36144
$567$		0			0
$568$	−2.84418			−0.119339
$569$	25.0645	−	14.4710i	1.05076	−	0.606655i	0.127896	−	0.991788i	$-0.459178\pi$
$569$	25.0645	−	14.4710i	1.05076	−	0.606655i	0.922861	+	0.385133i	$0.125844\pi$
$570$		0			0
$571$	−5.38458	+	9.32636i	−0.225337	+	0.390296i	−0.956421	−	0.291992i	$-0.905682\pi$
$571$	−5.38458	+	9.32636i	−0.225337	+	0.390296i	0.731083	+	0.682288i	$0.239015\pi$
$572$	10.6903	+	18.5162i	0.446984	+	0.774199i
$573$		0			0
$574$	−12.0453	+	1.33659i	−0.502759	+	0.0557884i
$575$			12.6027i			0.525569i
$576$		0			0
$577$	0.128205	+	0.0740195i	0.00533726	+	0.00308147i	0.502666	−	0.864481i	$-0.332352\pi$
$577$	0.128205	+	0.0740195i	0.00533726	+	0.00308147i	−0.497329	+	0.867562i	$0.665686\pi$
$578$	11.9279	+	6.88658i	0.496136	+	0.286444i
$579$		0			0
$580$		−	10.6551i		−	0.442431i
$581$	−24.1403	−	10.5808i	−1.00151	−	0.438966i
$582$		0			0
$583$	−18.4553	−	31.9655i	−0.764339	−	1.32387i
$584$	−4.64362	+	8.04299i	−0.192154	+	0.332821i
$585$		0			0
$586$	23.8473	−	13.7682i	0.985121	−	0.568760i
$587$	−33.0601			−1.36453			−0.682267	−	0.731103i	$-0.739006\pi$
$587$	−33.0601			−1.36453			−0.682267	+	0.731103i	$0.739006\pi$
$588$		0			0
$589$	−6.38040			−0.262900
$590$	8.05703	−	4.65173i	0.331703	−	0.191509i
$591$		0			0
$592$	−5.57502	+	9.65622i	−0.229132	+	0.396868i
$593$	9.39808	+	16.2780i	0.385933	+	0.668456i	0.991898	−	0.127036i	$-0.0405463\pi$
$593$	9.39808	+	16.2780i	0.385933	+	0.668456i	−0.605965	+	0.795491i	$0.707213\pi$
$594$		0			0
$595$	5.05113	+	2.21394i	0.207076	+	0.0907626i
$596$			19.5382i			0.800318i
$597$		0			0
$598$	17.6282	+	10.1776i	0.720869	+	0.416194i
$599$	−7.05303	−	4.07207i	−0.288179	−	0.166380i	0.348941	−	0.937145i	$-0.386541\pi$
$599$	−7.05303	−	4.07207i	−0.288179	−	0.166380i	−0.637120	+	0.770764i	$0.719875\pi$
$600$		0			0
$601$		−	7.23311i		−	0.295045i	−0.989059	−	0.147522i	$-0.952870\pi$
$601$		−	7.23311i		−	0.295045i	0.989059	−	0.147522i	$-0.0471298\pi$
$602$	16.8428	−	1.86895i	0.686460	−	0.0761726i
$603$		0			0
$604$	−0.294935	−	0.510843i	−0.0120008	−	0.0207859i
$605$	−1.23481	+	2.13875i	−0.0502021	+	0.0869525i
$606$		0			0
$607$	8.49622	−	4.90530i	0.344851	−	0.199100i	−0.317564	−	0.948237i	$-0.602865\pi$
$607$	8.49622	−	4.90530i	0.344851	−	0.199100i	0.662415	+	0.749137i	$0.269532\pi$
$608$	1.00000			0.0405554
$609$		0			0
$610$	7.95247			0.321986
$611$	36.0456	−	20.8110i	1.45825	−	0.841922i
$612$		0			0
$613$	−18.6268	+	32.2626i	−0.752331	+	1.30307i	0.194360	+	0.980930i	$0.437737\pi$
$613$	−18.6268	+	32.2626i	−0.752331	+	1.30307i	−0.946691	+	0.322144i	$0.895596\pi$
$614$	11.5816	+	20.0599i	0.467396	+	0.809553i
$615$		0			0
$616$	−7.72273	+	5.67953i	−0.311158	+	0.228835i
$617$		−	30.2276i		−	1.21692i	−0.793585	−	0.608459i	$-0.791788\pi$
$617$		−	30.2276i		−	1.21692i	0.793585	−	0.608459i	$-0.208212\pi$
$618$		0			0
$619$	10.0215	+	5.78591i	0.402798	+	0.232556i	0.687691	−	0.726004i	$-0.258625\pi$
$619$	10.0215	+	5.78591i	0.402798	+	0.232556i	−0.284893	+	0.958559i	$0.591958\pi$
$620$	6.41192	+	3.70193i	0.257509	+	0.148673i
$621$		0			0
$622$		−	16.2192i		−	0.650329i
$623$	4.30057	+	38.7563i	0.172299	+	1.55274i
$624$		0			0
$625$	−3.30754	−	5.72882i	−0.132302	−	0.229153i
$626$	11.9268	−	20.6578i	0.476691	−	0.825653i
$627$		0			0
$628$	0.892192	−	0.515107i	0.0356023	−	0.0205550i
$629$	−20.0292			−0.798618
$630$		0			0
$631$	−35.8171			−1.42586			−0.712928	−	0.701237i	$-0.752632\pi$
$631$	−35.8171			−1.42586			−0.712928	+	0.701237i	$0.752632\pi$
$632$	10.5734	−	6.10458i	0.420589	−	0.242827i
$633$		0			0
$634$	−2.43927	+	4.22493i	−0.0968757	+	0.167794i
$635$	10.7298	+	18.5846i	0.425800	+	0.737507i
$636$		0			0
$637$	30.3742	−	27.9930i	1.20347	−	1.10912i
$638$			33.2700i			1.31717i
$639$		0			0
$640$	−1.00494	−	0.580202i	−0.0397237	−	0.0229345i
$641$	−23.9666	−	13.8371i	−0.946625	−	0.546534i	−0.0545944	−	0.998509i	$-0.517387\pi$
$641$	−23.9666	−	13.8371i	−0.946625	−	0.546534i	−0.892031	+	0.451974i	$0.850720\pi$
$642$		0			0
$643$		−	23.3697i		−	0.921613i	−0.887501	−	0.460806i	$-0.847560\pi$
$643$		−	23.3697i		−	0.921613i	0.887501	−	0.460806i	$-0.152440\pi$
$644$	−3.66376	+	8.35891i	−0.144372	+	0.329387i
$645$		0			0
$646$	0.898169	+	1.55567i	0.0353380	+	0.0612072i
$647$	6.20432	−	10.7462i	0.243917	−	0.422476i	−0.717910	−	0.696136i	$-0.754901\pi$
$647$	6.20432	−	10.7462i	0.243917	−	0.422476i	0.961827	+	0.273660i	$0.0882343\pi$
$648$		0			0
$649$	−25.1576	+	14.5247i	−0.987521	+	0.570146i
$650$	−21.5586			−0.845599
$651$		0			0
$652$	14.0838			0.551562
$653$	20.7272	−	11.9669i	0.811119	−	0.468300i	−0.0362253	−	0.999344i	$-0.511533\pi$
$653$	20.7272	−	11.9669i	0.811119	−	0.468300i	0.847344	+	0.531044i	$0.178200\pi$
$654$		0			0
$655$	3.27111	−	5.66572i	0.127813	−	0.221378i
$656$	2.29031	+	3.96693i	0.0894216	+	0.154883i
$657$		0			0
$658$	11.0564	+	15.0339i	0.431024	+	0.586084i
$659$		−	1.03803i		−	0.0404359i	−0.999796	−	0.0202179i	$-0.993564\pi$
$659$		−	1.03803i		−	0.0404359i	0.999796	−	0.0202179i	$-0.00643601\pi$
$660$		0			0
$661$	−14.7680	−	8.52632i	−0.574409	−	0.331635i	0.184499	−	0.982833i	$-0.440934\pi$
$661$	−14.7680	−	8.52632i	−0.574409	−	0.331635i	−0.758908	+	0.651197i	$0.774267\pi$
$662$	6.74956	+	3.89686i	0.262329	+	0.151456i
$663$		0			0
$664$			9.96211i			0.386605i
$665$	−1.81894	−	2.47330i	−0.0705355	−	0.0959106i
$666$		0			0
$667$	15.8372	+	27.4309i	0.613220	+	1.06213i
$668$	−9.89870	+	17.1450i	−0.382992	+	0.663362i
$669$		0			0
$670$	−6.96846	+	4.02324i	−0.269215	+	0.155431i
$671$	−24.8311			−0.958593
$672$		0			0
$673$	−39.0749			−1.50623			−0.753113	−	0.657891i	$-0.771449\pi$
$673$	−39.0749			−1.50623			−0.753113	+	0.657891i	$0.771449\pi$
$674$	−10.7255	+	6.19240i	−0.413132	+	0.238522i
$675$		0			0
$676$	−10.9102	+	18.8970i	−0.419623	+	0.726809i
$677$	17.3697	+	30.0853i	0.667573	+	1.15627i	0.978581	+	0.205863i	$0.0660001\pi$
$677$	17.3697	+	30.0853i	0.667573	+	1.15627i	−0.311008	+	0.950407i	$0.600667\pi$
$678$		0			0
$679$	0.316536	−	0.722181i	0.0121475	−	0.0277148i
$680$		−	2.08448i		−	0.0799362i
$681$		0			0
$682$	−20.0208	−	11.5590i	−0.766637	−	0.442618i
$683$	35.8343	+	20.6889i	1.37116	+	0.791640i	0.991074	−	0.133310i	$-0.0425607\pi$
$683$	35.8343	+	20.6889i	1.37116	+	0.791640i	0.380087	+	0.924951i	$0.375894\pi$
$684$		0			0
$685$		−	19.6004i		−	0.748893i
$686$	13.9765	+	12.1514i	0.533625	+	0.463944i
$687$		0			0
$688$	−3.20252	−	5.54693i	−0.122095	−	0.211475i
$689$	30.0562	−	52.0589i	1.14505	−	1.98329i
$690$		0			0
$691$	−14.6532	+	8.46002i	−0.557433	+	0.321834i	−0.752115	−	0.659032i	$-0.770966\pi$
$691$	−14.6532	+	8.46002i	−0.557433	+	0.321834i	0.194681	+	0.980867i	$0.437633\pi$
$692$	−8.01525			−0.304694
$693$		0			0
$694$	23.1136			0.877378
$695$	18.0022	−	10.3936i	0.682862	−	0.394251i
$696$		0			0
$697$	−4.11417	+	7.12596i	−0.155835	+	0.269915i
$698$	3.48192	+	6.03085i	0.131792	+	0.228271i
$699$		0			0
$700$	−1.06606	−	9.60718i	−0.0402931	−	0.363117i
$701$		−	2.58430i		−	0.0976078i	−0.998808	−	0.0488039i	$-0.984459\pi$
$701$		−	2.58430i		−	0.0976078i	0.998808	−	0.0488039i	$-0.0155409\pi$
$702$		0			0
$703$	9.65622	+	5.57502i	0.364191	+	0.210266i
$704$	3.13786	+	1.81165i	0.118263	+	0.0682790i
$705$		0			0
$706$			7.45070i			0.280411i
$707$	−12.7830	+	9.40104i	−0.480756	+	0.353562i
$708$		0			0
$709$	10.2038	+	17.6735i	0.383212	+	0.663742i	0.991519	−	0.129959i	$-0.0414846\pi$
$709$	10.2038	+	17.6735i	0.383212	+	0.663742i	−0.608308	+	0.793701i	$0.708151\pi$
$710$	1.65020	−	2.85823i	0.0619310	−	0.107268i
$711$		0			0
$712$	12.7638	−	7.36921i	0.478345	−	0.276173i
$713$	−22.0094			−0.824257
$714$		0			0
$715$	−24.8102			−0.927848
$716$	−13.5721	+	7.83584i	−0.507212	+	0.292839i
$717$		0			0
$718$	0.706231	−	1.22323i	0.0263563	−	0.0456504i
$719$	4.93128	+	8.54123i	0.183906	+	0.318534i	0.943207	−	0.332205i	$-0.107793\pi$
$719$	4.93128	+	8.54123i	0.183906	+	0.318534i	−0.759301	+	0.650739i	$0.774459\pi$
$720$		0			0
$721$	52.7240	−	5.85048i	1.96354	−	0.217883i
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	−7.80925	−	4.50867i	−0.290228	−	0.167563i
$725$	−29.0526	−	16.7735i	−1.07899	−	0.622953i
$726$		0			0
$727$			14.1196i			0.523667i	0.965113	+	0.261833i	$0.0843271\pi$
$727$			14.1196i			0.523667i	−0.965113	+	0.261833i	$0.915673\pi$
$728$	−14.2991	−	6.26736i	−0.529958	−	0.232284i
$729$		0			0
$730$	−5.38848	−	9.33312i	−0.199437	−	0.345434i
$731$	5.75281	−	9.96416i	0.212775	−	0.368538i
$732$		0			0
$733$	−31.3246	+	18.0852i	−1.15700	+	0.667994i	−0.950583	−	0.310470i	$-0.899513\pi$
$733$	−31.3246	+	18.0852i	−1.15700	+	0.667994i	−0.206416	+	0.978464i	$0.566180\pi$
$734$	−19.9821			−0.737552
$735$		0			0
$736$	3.44952			0.127151
$737$	21.7586	−	12.5623i	0.801487	−	0.462739i
$738$		0			0
$739$	0.493559	−	0.854869i	0.0181559	−	0.0314469i	−0.856805	−	0.515641i	$-0.827554\pi$
$739$	0.493559	−	0.854869i	0.0181559	−	0.0314469i	0.874961	+	0.484194i	$0.160887\pi$
$740$	−6.46928	−	11.2051i	−0.237816	−	0.411909i
$741$		0			0
$742$	24.6853	+	10.8197i	0.906224	+	0.397203i
$743$		−	6.72577i		−	0.246745i	−0.992360	−	0.123372i	$-0.960629\pi$
$743$		−	6.72577i		−	0.246745i	0.992360	−	0.123372i	$-0.0393709\pi$
$744$		0			0
$745$	−19.6348	−	11.3361i	−0.719362	−	0.415324i
$746$	−2.14163	−	1.23647i	−0.0784107	−	0.0452704i
$747$		0			0
$748$			6.50866i			0.237980i
$749$	26.9506	−	2.99055i	0.984752	−	0.109272i
$750$		0			0
$751$	0.715008	+	1.23843i	0.0260910	+	0.0451909i	0.878776	−	0.477234i	$-0.158361\pi$
$751$	0.715008	+	1.23843i	0.0260910	+	0.0451909i	−0.852685	+	0.522425i	$0.825027\pi$
$752$	3.52675	−	6.10852i	0.128608	−	0.222755i
$753$		0			0
$754$	−46.9242	+	27.0917i	−1.70888	+	0.986622i
$755$	0.684489			0.0249111
$756$		0			0
$757$	−8.44547			−0.306956			−0.153478	−	0.988152i	$-0.549047\pi$
$757$	−8.44547			−0.306956			−0.153478	+	0.988152i	$0.549047\pi$
$758$	−28.9243	+	16.6994i	−1.05058	+	0.606551i
$759$		0			0
$760$	−0.580202	+	1.00494i	−0.0210462	+	0.0364530i
$761$	11.7619	+	20.3722i	0.426368	+	0.738492i	0.996547	−	0.0830288i	$-0.0264594\pi$
$761$	11.7619	+	20.3722i	0.426368	+	0.738492i	−0.570179	+	0.821521i	$0.693126\pi$
$762$		0			0
$763$	−18.2580	+	13.4275i	−0.660983	+	0.486107i
$764$			2.20847i			0.0798996i
$765$		0			0
$766$	25.5456	+	14.7488i	0.923000	+	0.532894i
$767$	−40.9716	−	23.6549i	−1.47940	−	0.854130i
$768$		0			0
$769$		−	45.5151i		−	1.64132i	−0.571419	−	0.820659i	$-0.693607\pi$
$769$		−	45.5151i		−	1.64132i	0.571419	−	0.820659i	$-0.306393\pi$
$770$	−1.22684	−	11.0562i	−0.0442123	−	0.398436i
$771$		0			0
$772$	5.85797	+	10.1463i	0.210833	+	0.365174i
$773$	12.2391	−	21.1987i	0.440208	−	0.762463i	−0.557496	−	0.830179i	$-0.688238\pi$
$773$	12.2391	−	21.1987i	0.440208	−	0.762463i	0.997705	+	0.0677162i	$0.0215712\pi$
$774$		0			0
$775$	20.1875	−	11.6553i	0.725158	−	0.418670i
$776$	−0.298027			−0.0106985
$777$		0			0
$778$	−5.13583			−0.184128
$779$	3.96693	−	2.29031i	0.142130	−	0.0820589i
$780$		0			0
$781$	−5.15265	+	8.92465i	−0.184376	+	0.319349i
$782$	3.09826	+	5.36634i	0.110793	+	0.191900i
$783$		0			0
$784$	2.08585	−	6.68201i	0.0744946	−	0.238643i
$785$			1.19547i			0.0426680i
$786$		0			0
$787$	−23.9956	−	13.8539i	−0.855351	−	0.493837i	0.00710167	−	0.999975i	$-0.497739\pi$
$787$	−23.9956	−	13.8539i	−0.855351	−	0.493837i	−0.862453	+	0.506138i	$0.831073\pi$
$788$	7.88594	+	4.55295i	0.280925	+	0.162192i
$789$		0			0
$790$			14.1676i			0.504059i
$791$	−11.8759	+	27.0950i	−0.422258	+	0.963387i
$792$		0			0
$793$	−20.2199	−	35.0219i	−0.718030	−	1.24367i
$794$	−0.468773	+	0.811939i	−0.0166361	+	0.0288146i
$795$		0			0
$796$	−13.4122	+	7.74352i	−0.475382	+	0.274462i
$797$	53.2859			1.88748			0.943741	−	0.330684i	$-0.107279\pi$
$797$	53.2859			1.88748			0.943741	+	0.330684i	$0.107279\pi$
$798$		0			0
$799$	12.6705			0.448250
$800$	−3.16399	+	1.82673i	−0.111864	+	0.0645847i
$801$		0			0
$802$	19.0771	−	33.0425i	0.673636	−	1.16677i
$803$	16.8252	+	29.1421i	0.593748	+	1.02840i
$804$		0			0
$805$	−6.27448	−	8.53172i	−0.221147	−	0.300704i
$806$		−	37.6500i		−	1.32617i
$807$		0			0
$808$	5.19394	+	2.99872i	0.182722	+	0.105495i
$809$	−0.504952	−	0.291534i	−0.0177532	−	0.0102498i	0.491097	−	0.871105i	$-0.336596\pi$
$809$	−0.504952	−	0.291534i	−0.0177532	−	0.0102498i	−0.508850	+	0.860855i	$0.669929\pi$
$810$		0			0
$811$			43.8214i			1.53878i	0.638780	+	0.769390i	$0.279439\pi$
$811$			43.8214i			1.53878i	−0.638780	+	0.769390i	$0.720561\pi$
$812$	−14.3932	−	19.5712i	−0.505104	−	0.686814i
$813$		0			0
$814$	20.1999	+	34.9873i	0.708007	+	1.22630i
$815$	−8.17143	+	14.1533i	−0.286233	+	0.495769i
$816$		0			0
$817$	−5.54693	+	3.20252i	−0.194063	+	0.112042i
$818$	−14.0572			−0.491500
$819$		0			0
$820$	−5.31538			−0.185621
$821$	−12.6261	+	7.28970i	−0.440655	+	0.254412i	−0.703875	−	0.710323i	$-0.748549\pi$
$821$	−12.6261	+	7.28970i	−0.440655	+	0.254412i	0.263220	+	0.964736i	$0.415215\pi$
$822$		0			0
$823$	14.0800	−	24.3873i	0.490798	−	0.850087i	−0.509146	−	0.860680i	$-0.670039\pi$
$823$	14.0800	−	24.3873i	0.490798	−	0.850087i	0.999944	+	0.0105930i	$0.00337192\pi$
$824$	−10.0251	−	17.3639i	−0.349239	−	0.604900i
$825$		0			0
$826$	8.51535	−	19.4279i	0.296287	−	0.675982i
$827$			10.8069i			0.375792i	0.982189	+	0.187896i	$0.0601668\pi$
$827$			10.8069i			0.375792i	−0.982189	+	0.187896i	$0.939833\pi$
$828$		0			0
$829$	−7.06515	−	4.07906i	−0.245383	−	0.141672i	0.372265	−	0.928126i	$-0.378581\pi$
$829$	−7.06515	−	4.07906i	−0.245383	−	0.141672i	−0.617648	+	0.786455i	$0.711914\pi$
$830$	−10.0113	−	5.78004i	−0.347498	−	0.200628i
$831$		0			0
$832$			5.90088i			0.204576i
$833$	12.2685	−	2.75667i	0.425078	−	0.0955130i
$834$		0			0
$835$	−11.4865	−	19.8952i	−0.397507	−	0.688502i
$836$	1.81165	−	3.13786i	0.0626571	−	0.108525i
$837$		0			0
$838$	−7.45314	+	4.30307i	−0.257464	+	0.148647i
$839$	−23.3544			−0.806285			−0.403142	−	0.915137i	$-0.632082\pi$
$839$	−23.3544			−0.806285			−0.403142	+	0.915137i	$0.632082\pi$
$840$		0			0
$841$	−55.3139			−1.90738
$842$	15.6323	−	9.02529i	0.538723	−	0.311032i
$843$		0			0
$844$	−9.38149	+	16.2492i	−0.322924	+	0.559321i
$845$	−12.6603	−	21.9282i	−0.435526	−	0.754353i
$846$		0			0
$847$	0.621005	+	5.59643i	0.0213380	+	0.192296i
$848$		−	10.1870i		−	0.349824i
$849$		0			0
$850$	−5.68360	−	3.28143i	−0.194946	−	0.112552i
$851$	33.3094	+	19.2312i	1.14183	+	0.659236i
$852$		0			0
$853$		−	43.9258i		−	1.50399i	−0.659169	−	0.751995i	$-0.729092\pi$
$853$		−	43.9258i		−	1.50399i	0.659169	−	0.751995i	$-0.270908\pi$
$854$	14.6070	−	10.7424i	0.499840	−	0.367598i
$855$		0			0
$856$	−5.12444	−	8.87578i	−0.175150	−	0.303368i
$857$	12.8342	−	22.2296i	0.438409	−	0.759347i	−0.559158	−	0.829061i	$-0.688875\pi$
$857$	12.8342	−	22.2296i	0.438409	−	0.759347i	0.997567	+	0.0697139i	$0.0222086\pi$
$858$		0			0
$859$	1.36077	−	0.785641i	0.0464289	−	0.0268057i	−0.476606	−	0.879117i	$-0.658133\pi$
$859$	1.36077	−	0.785641i	0.0464289	−	0.0268057i	0.523035	+	0.852311i	$0.324800\pi$
$860$	7.43244			0.253444
$861$		0			0
$862$	38.6736			1.31723
$863$	−25.2425	+	14.5738i	−0.859266	+	0.496098i	−0.863766	−	0.503892i	$-0.831901\pi$
$863$	−25.2425	+	14.5738i	−0.859266	+	0.496098i	0.00450027	+	0.999990i	$0.498568\pi$
$864$		0			0
$865$	4.65047	−	8.05484i	0.158121	−	0.273873i
$866$	9.10000	+	15.7617i	0.309230	+	0.535603i
$867$		0			0
$868$	16.7780	−	1.86176i	0.569482	−	0.0631922i
$869$		−	44.2373i		−	1.50065i
$870$		0			0
$871$	35.4359	+	20.4589i	1.20070	+	0.693225i
$872$	7.41848	+	4.28306i	0.251222	+	0.145043i
$873$		0			0
$874$		−	3.44952i		−	0.116682i
$875$	24.3327	+	10.6651i	0.822595	+	0.360548i
$876$		0			0
$877$	13.5921	+	23.5422i	0.458972	+	0.794962i	0.998907	−	0.0467445i	$-0.0148847\pi$
$877$	13.5921	+	23.5422i	0.458972	+	0.794962i	−0.539935	+	0.841706i	$0.681551\pi$
$878$	6.00666	−	10.4038i	0.202715	−	0.351113i
$879$		0			0
$880$	−3.64119	+	2.10224i	−0.122744	+	0.0708666i
$881$	29.5409			0.995259			0.497630	−	0.867390i	$-0.334204\pi$
$881$	29.5409			0.995259			0.497630	+	0.867390i	$0.334204\pi$
$882$		0			0
$883$	−5.38320			−0.181159			−0.0905796	−	0.995889i	$-0.528872\pi$
$883$	−5.38320			−0.181159			−0.0905796	+	0.995889i	$0.528872\pi$
$884$	−9.17985	+	5.29999i	−0.308752	+	0.178258i
$885$		0			0
$886$	19.0965	−	33.0761i	0.641560	−	1.11121i
$887$	−0.680743	−	1.17908i	−0.0228571	−	0.0395897i	0.854371	−	0.519664i	$-0.173943\pi$
$887$	−0.680743	−	1.17908i	−0.0228571	−	0.0395897i	−0.877228	+	0.480075i	$0.840610\pi$
$888$		0			0
$889$	44.8130	+	19.6418i	1.50298	+	0.658764i
$890$			17.1025i			0.573278i
$891$		0			0
$892$	−15.8072	−	9.12628i	−0.529263	−	0.305570i
$893$	−6.10852	−	3.52675i	−0.204414	−	0.118018i
$894$		0			0
$895$		−	18.1855i		−	0.607874i
$896$	−2.62961	+	0.291793i	−0.0878492	+	0.00974813i
$897$		0			0
$898$	17.6984	+	30.6545i	0.590602	+	1.02295i
$899$	29.2933	−	50.7374i	0.976985	−	1.69219i
$900$		0			0
$901$	15.8477	−	9.14967i	0.527963	−	0.304820i
$902$	16.5969			0.552617
$903$		0			0
$904$	11.1815			0.371890
$905$	9.06189	−	5.23188i	0.301227	−	0.173914i
$906$		0			0
$907$	−3.34018	+	5.78537i	−0.110909	+	0.192100i	−0.916137	−	0.400865i	$-0.868710\pi$
$907$	−3.34018	+	5.78537i	−0.110909	+	0.192100i	0.805228	+	0.592965i	$0.202043\pi$
$908$	1.14563	+	1.98429i	0.0380190	+	0.0658509i
$909$		0			0
$910$	14.5947	−	10.7334i	0.483809	−	0.355807i
$911$		−	24.4919i		−	0.811454i	−0.913994	−	0.405727i	$-0.867018\pi$
$911$		−	24.4919i		−	0.811454i	0.913994	−	0.405727i	$-0.132982\pi$
$912$		0			0
$913$	31.2597	+	18.0478i	1.03455	+	0.597295i
$914$	18.3110	+	10.5719i	0.605674	+	0.349686i
$915$		0			0
$916$		−	7.33691i		−	0.242418i
$917$	−1.64509	−	14.8254i	−0.0543258	−	0.489578i
$918$		0			0
$919$	7.65081	+	13.2516i	0.252377	+	0.437130i	0.964180	−	0.265250i	$-0.0854543\pi$
$919$	7.65081	+	13.2516i	0.252377	+	0.437130i	−0.711803	+	0.702379i	$0.752121\pi$
$920$	−2.00142	+	3.46657i	−0.0659850	+	0.114289i
$921$		0			0
$922$	−1.89075	+	1.09163i	−0.0622686	+	0.0359508i
$923$	−16.7832			−0.552425
$924$		0			0
$925$	−40.7362			−1.33940
$926$	3.22400	−	1.86138i	0.105947	−	0.0611686i
$927$		0			0
$928$	−4.59113	+	7.95207i	−0.150711	+	0.261040i
$929$	−17.9028	−	31.0086i	−0.587373	−	1.01736i	−0.994575	−	0.104022i	$-0.966829\pi$
$929$	−17.9028	−	31.0086i	−0.587373	−	1.01736i	0.407202	−	0.913338i	$-0.366505\pi$
$930$		0			0
$931$	−6.68201	−	2.08585i	−0.218994	−	0.0683609i
$932$			23.4247i			0.767301i
$933$		0			0
$934$	29.0357	+	16.7638i	0.950077	+	0.548527i
$935$	−6.54081	−	3.77634i	−0.213907	−	0.123499i
$936$		0			0
$937$			51.5347i			1.68356i	0.539818	+	0.841782i	$0.318493\pi$
$937$			51.5347i			1.68356i	−0.539818	+	0.841782i	$0.681507\pi$
$938$	−7.36485	+	16.8030i	−0.240471	+	0.548637i
$939$		0			0
$940$	4.09246	+	7.08835i	0.133481	+	0.231197i
$941$	−19.6847	+	34.0949i	−0.641702	+	1.11146i	0.343350	+	0.939207i	$0.388438\pi$
$941$	−19.6847	+	34.0949i	−0.641702	+	1.11146i	−0.985053	+	0.172254i	$0.944895\pi$
$942$		0			0
$943$	13.6840	−	7.90048i	0.445614	−	0.257275i
$944$	−8.01742			−0.260945
$945$		0			0
$946$	−23.2073			−0.754535
$947$	20.3436	−	11.7454i	0.661078	−	0.381673i	−0.131610	−	0.991302i	$-0.542015\pi$
$947$	20.3436	−	11.7454i	0.661078	−	0.381673i	0.792687	+	0.609628i	$0.208681\pi$
$948$		0			0
$949$	−27.4015	+	47.4607i	−0.889489	+	1.54064i
$950$	1.82673	+	3.16399i	0.0592670	+	0.102653i
$951$		0			0
$952$	−2.81577	−	3.82874i	−0.0912597	−	0.124090i
$953$		−	18.0892i		−	0.585967i	−0.956118	−	0.292983i	$-0.905352\pi$
$953$		−	18.0892i		−	0.585967i	0.956118	−	0.292983i	$-0.0946481\pi$
$954$		0			0
$955$	−2.21938	−	1.28136i	−0.0718174	−	0.0414638i
$956$	11.6839	+	6.74569i	0.377884	+	0.218171i
$957$		0			0
$958$		−	25.7995i		−	0.833544i
$959$	−26.4768	−	36.0017i	−0.854979	−	1.16256i
$960$		0			0
$961$	4.85478	+	8.40872i	0.156606	+	0.271249i
$962$	−32.8975	+	56.9802i	−1.06066	+	1.83712i
$963$		0			0
$964$	21.7250	−	12.5430i	0.699716	−	0.403981i
$965$	−13.5952			−0.437646
$966$		0			0
$967$	48.9057			1.57270			0.786351	−	0.617780i	$-0.211968\pi$
$967$	48.9057			1.57270			0.786351	+	0.617780i	$0.211968\pi$
$968$	1.84311	−	1.06412i	0.0592397	−	0.0342020i
$969$		0			0
$970$	0.172916	−	0.299499i	0.00555200	−	0.00961634i
$971$	10.4199	+	18.0477i	0.334390	+	0.579180i	0.983367	−	0.181628i	$-0.0581365\pi$
$971$	10.4199	+	18.0477i	0.334390	+	0.579180i	−0.648978	+	0.760807i	$0.724803\pi$
$972$		0			0
$973$	19.0262	−	43.4086i	0.609953	−	1.39162i
$974$			2.86556i			0.0918184i
$975$		0			0
$976$	−5.93503	−	3.42659i	−0.189976	−	0.109683i
$977$	−24.7701	−	14.3010i	−0.792464	−	0.457530i	0.0483650	−	0.998830i	$-0.484599\pi$
$977$	−24.7701	−	14.3010i	−0.792464	−	0.457530i	−0.840829	+	0.541300i	$0.817932\pi$
$978$		0			0
$979$		−	53.4016i		−	1.70672i
$980$	5.50480	+	5.97307i	0.175844	+	0.190803i
$981$		0			0
$982$	−7.60533	−	13.1728i	−0.242696	−	0.420362i
$983$	−1.40404	+	2.43187i	−0.0447820	+	0.0775647i	−0.887548	−	0.460716i	$-0.847593\pi$
$983$	−1.40404	+	2.43187i	−0.0447820	+	0.0775647i	0.842766	+	0.538281i	$0.180926\pi$
$984$		0			0
$985$	−9.15089	+	5.28327i	−0.291571	+	0.168339i
$986$	−16.4944			−0.525290
$987$		0			0
$988$	5.90088			0.187732
$989$	−19.1343	+	11.0472i	−0.608434	+	0.351280i
$990$		0			0
$991$	−12.9570	+	22.4422i	−0.411593	+	0.712899i	−0.995064	−	0.0992344i	$-0.968361\pi$
$991$	−12.9570	+	22.4422i	−0.411593	+	0.712899i	0.583472	+	0.812134i	$0.301694\pi$
$992$	−3.19020	−	5.52559i	−0.101289	−	0.175438i
$993$		0			0
$994$	−0.829914	−	7.47910i	−0.0263233	−	0.237223i
$995$		−	17.9712i		−	0.569727i
$996$		0			0
$997$	33.2419	+	19.1922i	1.05278	+	0.607824i	0.923427	−	0.383774i	$-0.125376\pi$
$997$	33.2419	+	19.1922i	1.05278	+	0.607824i	0.129356	+	0.991598i	$0.458709\pi$
$998$	−6.71283	−	3.87566i	−0.212491	−	0.122682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.by.b.647.18	yes	48
3.2	odd	2		2394.2.by.a.647.7	✓	48
7.5	odd	6		2394.2.by.a.2357.7	yes	48
21.5	even	6	inner	2394.2.by.b.2357.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.by.a.647.7	✓	48	3.2	odd	2
2394.2.by.a.2357.7	yes	48	7.5	odd	6
2394.2.by.b.647.18	yes	48	1.1	even	1	trivial
2394.2.by.b.2357.18	yes	48	21.5	even	6	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.580202 + 1.00494i) q^{5} +(2.42321 + 1.06211i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.580202 + 1.00494i) q^{5} +(2.42321 + 1.06211i) q^{7} -1.00000i q^{8} +(1.00494 + 0.580202i) q^{10} +(-3.13786 - 1.81165i) q^{11} -5.90088i q^{13} +(2.62961 - 0.291793i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.898169 - 1.55567i) q^{17} +(-0.866025 + 0.500000i) q^{19} +1.16040 q^{20} -3.62329 q^{22} +(-2.98738 + 1.72476i) q^{23} +(1.82673 - 3.16399i) q^{25} +(-2.95044 - 5.11031i) q^{26} +(2.13141 - 1.56751i) q^{28} -9.18226i q^{29} +(5.52559 + 3.19020i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.79634i q^{34} +(0.338598 + 3.05141i) q^{35} +(-5.57502 - 9.65622i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(1.00494 - 0.580202i) q^{40} -4.58062 q^{41} +6.40504 q^{43} +(-3.13786 + 1.81165i) q^{44} +(-1.72476 + 2.98738i) q^{46} +(3.52675 + 6.10852i) q^{47} +(4.74386 + 5.14740i) q^{49} -3.65346i q^{50} +(-5.11031 - 2.95044i) q^{52} +(8.82222 + 5.09351i) q^{53} -4.20448i q^{55} +(1.06211 - 2.42321i) q^{56} +(-4.59113 - 7.95207i) q^{58} +(4.00871 - 6.94329i) q^{59} +(5.93503 - 3.42659i) q^{61} +6.38040 q^{62} -1.00000 q^{64} +(5.93003 - 3.42371i) q^{65} +(-3.46710 + 6.00519i) q^{67} +(-0.898169 - 1.55567i) q^{68} +(1.81894 + 2.47330i) q^{70} -2.84418i q^{71} +(-8.04299 - 4.64362i) q^{73} +(-9.65622 - 5.57502i) q^{74} +1.00000i q^{76} +(-5.67953 - 7.72273i) q^{77} +(6.10458 + 10.5734i) q^{79} +(0.580202 - 1.00494i) q^{80} +(-3.96693 + 2.29031i) q^{82} -9.96211 q^{83} +2.08448 q^{85} +(5.54693 - 3.20252i) q^{86} +(-1.81165 + 3.13786i) q^{88} +(7.36921 + 12.7638i) q^{89} +(6.26736 - 14.2991i) q^{91} +3.44952i q^{92} +(6.10852 + 3.52675i) q^{94} +(-1.00494 - 0.580202i) q^{95} -0.298027i q^{97} +(6.68201 + 2.08585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 4 q^{7}+O(q^{10}) \) 48 * q + 24 * q^4 - 4 * q^7	\( 48 q + 24 q^{4} - 4 q^{7} - 12 q^{10} + 4 q^{14} - 24 q^{16} + 16 q^{17} + 8 q^{22} - 28 q^{25} + 4 q^{28} + 12 q^{31} + 24 q^{35} - 24 q^{38} - 12 q^{40} - 16 q^{41} + 8 q^{43} + 8 q^{46} - 32 q^{49} + 48 q^{53} - 4 q^{56} - 4 q^{58} - 16 q^{59} - 32 q^{62} - 48 q^{64} - 24 q^{67} - 16 q^{68} + 28 q^{70} + 12 q^{73} - 8 q^{77} - 20 q^{79} - 48 q^{82} - 128 q^{83} - 40 q^{85} + 4 q^{88} - 32 q^{89} + 40 q^{91} + 12 q^{95} + 16 q^{98}+O(q^{100}) \) 48 * q + 24 * q^4 - 4 * q^7 - 12 * q^10 + 4 * q^14 - 24 * q^16 + 16 * q^17 + 8 * q^22 - 28 * q^25 + 4 * q^28 + 12 * q^31 + 24 * q^35 - 24 * q^38 - 12 * q^40 - 16 * q^41 + 8 * q^43 + 8 * q^46 - 32 * q^49 + 48 * q^53 - 4 * q^56 - 4 * q^58 - 16 * q^59 - 32 * q^62 - 48 * q^64 - 24 * q^67 - 16 * q^68 + 28 * q^70 + 12 * q^73 - 8 * q^77 - 20 * q^79 - 48 * q^82 - 128 * q^83 - 40 * q^85 + 4 * q^88 - 32 * q^89 + 40 * q^91 + 12 * q^95 + 16 * q^98

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