LMFDB - Embedded newform 684.2.c.b.647.15

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			647.15
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528104 - 1.31191i) q^{2} +(-1.44221 + 1.38565i) q^{4} -3.80926i q^{5} +3.88443i q^{7} +(2.57948 + 1.16029i) q^{8} +O(q^{10})$	\(q+(-0.528104 - 1.31191i) q^{2} +(-1.44221 + 1.38565i) q^{4} -3.80926i q^{5} +3.88443i q^{7} +(2.57948 + 1.16029i) q^{8} +(-4.99741 + 2.01168i) q^{10} -4.83872 q^{11} -2.15700 q^{13} +(5.09602 - 2.05138i) q^{14} +(0.159958 - 3.99680i) q^{16} +5.74233i q^{17} -1.00000i q^{19} +(5.27830 + 5.49377i) q^{20} +(2.55535 + 6.34797i) q^{22} -5.47240 q^{23} -9.51048 q^{25} +(1.13912 + 2.82978i) q^{26} +(-5.38245 - 5.60217i) q^{28} +2.51769i q^{29} +3.04735i q^{31} +(-5.32792 + 1.90087i) q^{32} +(7.53342 - 3.03255i) q^{34} +14.7968 q^{35} +0.634791 q^{37} +(-1.31191 + 0.528104i) q^{38} +(4.41984 - 9.82593i) q^{40} -7.36005i q^{41} +5.91860i q^{43} +(6.97847 - 6.70477i) q^{44} +(2.88999 + 7.17929i) q^{46} -1.98384 q^{47} -8.08877 q^{49} +(5.02252 + 12.4769i) q^{50} +(3.11085 - 2.98884i) q^{52} +9.67744i q^{53} +18.4320i q^{55} +(-4.50705 + 10.0198i) q^{56} +(3.30298 - 1.32960i) q^{58} +10.1362 q^{59} +5.04621 q^{61} +(3.99784 - 1.60931i) q^{62} +(5.30747 + 5.98588i) q^{64} +8.21656i q^{65} -0.977067i q^{67} +(-7.95685 - 8.28167i) q^{68} +(-7.81424 - 19.4121i) q^{70} -15.0367 q^{71} -8.86251 q^{73} +(-0.335235 - 0.832788i) q^{74} +(1.38565 + 1.44221i) q^{76} -18.7957i q^{77} +9.39969i q^{79} +(-15.2249 - 0.609323i) q^{80} +(-9.65572 + 3.88687i) q^{82} +1.11846 q^{83} +21.8741 q^{85} +(7.76467 - 3.12563i) q^{86} +(-12.4814 - 5.61431i) q^{88} -8.19627i q^{89} -8.37869i q^{91} +(7.89237 - 7.58282i) q^{92} +(1.04767 + 2.60262i) q^{94} -3.80926 q^{95} +2.67818 q^{97} +(4.27171 + 10.6117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.528104	−	1.31191i	−0.373426	−	0.927660i
$2$	−0.528104	−	1.31191i	−0.373426	−	0.927660i
$3$		0			0
$3$		0			0
$4$	−1.44221	+	1.38565i	−0.721107	+	0.692824i
$5$		−	3.80926i		−	1.70355i	−0.523905	−	0.851777i	$-0.675525\pi$
$5$		−	3.80926i		−	1.70355i	0.523905	−	0.851777i	$-0.324475\pi$
$6$		0			0
$7$			3.88443i			1.46818i	0.679055	+	0.734088i	$0.262390\pi$
$7$			3.88443i			1.46818i	−0.679055	+	0.734088i	$0.737610\pi$
$8$	2.57948	+	1.16029i	0.911985	+	0.410224i
$9$		0			0
$10$	−4.99741	+	2.01168i	−1.58032	+	0.636151i
$11$	−4.83872			−1.45893			−0.729465	−	0.684018i	$-0.760231\pi$
$11$	−4.83872			−1.45893			−0.729465	+	0.684018i	$0.760231\pi$
$12$		0			0
$13$	−2.15700			−0.598243			−0.299122	−	0.954215i	$-0.596694\pi$
$13$	−2.15700			−0.598243			−0.299122	+	0.954215i	$0.596694\pi$
$14$	5.09602	−	2.05138i	1.36197	−	0.548254i
$15$		0			0
$16$	0.159958	−	3.99680i	0.0399896	−	0.999200i
$17$			5.74233i			1.39272i	0.717692	+	0.696360i	$0.245198\pi$
$17$			5.74233i			1.39272i	−0.717692	+	0.696360i	$0.754802\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	5.27830	+	5.49377i	1.18026	+	1.22844i
$21$		0			0
$22$	2.55535	+	6.34797i	0.544802	+	1.35339i
$23$	−5.47240			−1.14107			−0.570537	−	0.821272i	$-0.693265\pi$
$23$	−5.47240			−1.14107			−0.570537	+	0.821272i	$0.693265\pi$
$24$		0			0
$25$	−9.51048			−1.90210
$26$	1.13912	+	2.82978i	0.223399	+	0.554966i
$27$		0			0
$28$	−5.38245	−	5.60217i	−1.01719	−	1.05871i
$29$			2.51769i			0.467524i	0.972294	+	0.233762i	$0.0751036\pi$
$29$			2.51769i			0.467524i	−0.972294	+	0.233762i	$0.924896\pi$
$30$		0			0
$31$			3.04735i			0.547320i	0.961827	+	0.273660i	$0.0882343\pi$
$31$			3.04735i			0.547320i	−0.961827	+	0.273660i	$0.911766\pi$
$32$	−5.32792	+	1.90087i	−0.941851	+	0.336030i
$33$		0			0
$34$	7.53342	−	3.03255i	1.29197	−	0.520078i
$35$	14.7968			2.50112
$36$		0			0
$37$	0.634791			0.104359			0.0521795	−	0.998638i	$-0.483383\pi$
$37$	0.634791			0.104359			0.0521795	+	0.998638i	$0.483383\pi$
$38$	−1.31191	+	0.528104i	−0.212820	+	0.0856697i
$39$		0			0
$40$	4.41984	−	9.82593i	0.698838	−	1.55362i
$41$		−	7.36005i		−	1.14945i	−0.818348	−	0.574724i	$-0.805110\pi$
$41$		−	7.36005i		−	1.14945i	0.818348	−	0.574724i	$-0.194890\pi$
$42$		0			0
$43$			5.91860i			0.902578i	0.892378	+	0.451289i	$0.149036\pi$
$43$			5.91860i			0.902578i	−0.892378	+	0.451289i	$0.850964\pi$
$44$	6.97847	−	6.70477i	1.05204	−	1.01078i
$45$		0			0
$46$	2.88999	+	7.17929i	0.426106	+	1.05853i
$47$	−1.98384			−0.289372			−0.144686	−	0.989478i	$-0.546217\pi$
$47$	−1.98384			−0.289372			−0.144686	+	0.989478i	$0.546217\pi$
$48$		0			0
$49$	−8.08877			−1.15554
$50$	5.02252	+	12.4769i	0.710291	+	1.76450i
$51$		0			0
$52$	3.11085	−	2.98884i	0.431397	−	0.414477i
$53$			9.67744i			1.32930i	0.747155	+	0.664650i	$0.231419\pi$
$53$			9.67744i			1.32930i	−0.747155	+	0.664650i	$0.768581\pi$
$54$		0			0
$55$			18.4320i			2.48537i
$56$	−4.50705	+	10.0198i	−0.602280	+	1.33895i
$57$		0			0
$58$	3.30298	−	1.32960i	0.433703	−	0.174585i
$59$	10.1362			1.31962			0.659811	−	0.751431i	$-0.270636\pi$
$59$	10.1362			1.31962			0.659811	+	0.751431i	$0.270636\pi$
$60$		0			0
$61$	5.04621			0.646101			0.323050	−	0.946382i	$-0.395292\pi$
$61$	5.04621			0.646101			0.323050	+	0.946382i	$0.395292\pi$
$62$	3.99784	−	1.60931i	0.507727	−	0.204383i
$63$		0			0
$64$	5.30747	+	5.98588i	0.663433	+	0.748236i
$65$			8.21656i			1.01914i
$66$		0			0
$67$		−	0.977067i		−	0.119368i	−0.998217	−	0.0596838i	$-0.980991\pi$
$67$		−	0.977067i		−	0.119368i	0.998217	−	0.0596838i	$-0.0190093\pi$
$68$	−7.95685	−	8.28167i	−0.964910	−	1.00430i
$69$		0			0
$70$	−7.81424	−	19.4121i	−0.933980	−	2.32018i
$71$	−15.0367			−1.78453			−0.892267	−	0.451508i	$-0.850886\pi$
$71$	−15.0367			−1.78453			−0.892267	+	0.451508i	$0.850886\pi$
$72$		0			0
$73$	−8.86251			−1.03728			−0.518639	−	0.854993i	$-0.673561\pi$
$73$	−8.86251			−1.03728			−0.518639	+	0.854993i	$0.673561\pi$
$74$	−0.335235	−	0.832788i	−0.0389703	−	0.0968096i
$75$		0			0
$76$	1.38565	+	1.44221i	0.158945	+	0.165433i
$77$		−	18.7957i		−	2.14196i
$78$		0			0
$79$			9.39969i			1.05755i	0.848763	+	0.528774i	$0.177348\pi$
$79$			9.39969i			1.05755i	−0.848763	+	0.528774i	$0.822652\pi$
$80$	−15.2249	−	0.609323i	−1.70219	−	0.0681243i
$81$		0			0
$82$	−9.65572	+	3.88687i	−1.06630	+	0.429233i
$83$	1.11846			0.122767			0.0613835	−	0.998114i	$-0.480449\pi$
$83$	1.11846			0.122767			0.0613835	+	0.998114i	$0.480449\pi$
$84$		0			0
$85$	21.8741			2.37257
$86$	7.76467	−	3.12563i	0.837285	−	0.337046i
$87$		0			0
$88$	−12.4814	−	5.61431i	−1.33052	−	0.598487i
$89$		−	8.19627i		−	0.868803i	−0.900719	−	0.434402i	$-0.856960\pi$
$89$		−	8.19627i		−	0.868803i	0.900719	−	0.434402i	$-0.143040\pi$
$90$		0			0
$91$		−	8.37869i		−	0.878326i
$92$	7.89237	−	7.58282i	0.822836	−	0.790564i
$93$		0			0
$94$	1.04767	+	2.60262i	0.108059	+	0.268439i
$95$	−3.80926			−0.390822
$96$		0			0
$97$	2.67818			0.271928			0.135964	−	0.990714i	$-0.456587\pi$
$97$	2.67818			0.271928			0.135964	+	0.990714i	$0.456587\pi$
$98$	4.27171	+	10.6117i	0.431508	+	1.07195i
$99$		0			0
$100$	13.7161	−	13.1782i	1.37161	−	1.31782i
$101$		−	2.87704i		−	0.286277i	−0.989703	−	0.143138i	$-0.954281\pi$
$101$		−	2.87704i		−	0.286277i	0.989703	−	0.143138i	$-0.0457194\pi$
$102$		0			0
$103$		−	14.5720i		−	1.43582i	−0.696136	−	0.717910i	$-0.745099\pi$
$103$		−	14.5720i		−	1.43582i	0.696136	−	0.717910i	$-0.254901\pi$
$104$	−5.56393	−	2.50274i	−0.545589	−	0.245413i
$105$		0			0
$106$	12.6959	−	5.11069i	1.23314	−	0.496394i
$107$	−8.87827			−0.858294			−0.429147	−	0.903235i	$-0.641186\pi$
$107$	−8.87827			−0.858294			−0.429147	+	0.903235i	$0.641186\pi$
$108$		0			0
$109$	−9.62696			−0.922096			−0.461048	−	0.887375i	$-0.652526\pi$
$109$	−9.62696			−0.922096			−0.461048	+	0.887375i	$0.652526\pi$
$110$	24.1811	−	9.73398i	2.30557	−	0.928099i
$111$		0			0
$112$	15.5253	+	0.621346i	1.46700	+	0.0587117i
$113$			18.8918i			1.77720i	0.458687	+	0.888598i	$0.348320\pi$
$113$			18.8918i			1.77720i	−0.458687	+	0.888598i	$0.651680\pi$
$114$		0			0
$115$			20.8458i			1.94388i
$116$	−3.48864	−	3.63105i	−0.323912	−	0.337134i
$117$		0			0
$118$	−5.35297	−	13.2978i	−0.492781	−	1.22416i
$119$	−22.3057			−2.04476
$120$		0			0
$121$	12.4132			1.12848
$122$	−2.66492	−	6.62017i	−0.241271	−	0.599362i
$123$		0			0
$124$	−4.22255	−	4.39492i	−0.379196	−	0.394676i
$125$			17.1816i			1.53677i
$126$		0			0
$127$		−	17.8726i		−	1.58594i	−0.609262	−	0.792969i	$-0.708534\pi$
$127$		−	17.8726i		−	1.58594i	0.609262	−	0.792969i	$-0.291466\pi$
$128$	5.05005	−	10.1241i	0.446365	−	0.894851i
$129$		0			0
$130$	10.7794	−	4.33920i	0.945415	−	0.380573i
$131$	−6.16749			−0.538856			−0.269428	−	0.963020i	$-0.586835\pi$
$131$	−6.16749			−0.538856			−0.269428	+	0.963020i	$0.586835\pi$
$132$		0			0
$133$	3.88443			0.336822
$134$	−1.28182	+	0.515992i	−0.110733	+	0.0445750i
$135$		0			0
$136$	−6.66276	+	14.8123i	−0.571327	+	1.27014i
$137$		−	9.29816i		−	0.794395i	−0.917733	−	0.397198i	$-0.869983\pi$
$137$		−	9.29816i		−	0.794395i	0.917733	−	0.397198i	$-0.130017\pi$
$138$		0			0
$139$		−	13.6674i		−	1.15925i	−0.814883	−	0.579626i	$-0.803199\pi$
$139$		−	13.6674i		−	1.15925i	0.814883	−	0.579626i	$-0.196801\pi$
$140$	−21.3401	+	20.5032i	−1.80357	+	1.73283i
$141$		0			0
$142$	7.94096	+	19.7269i	0.666391	+	1.65544i
$143$	10.4371			0.872795
$144$		0			0
$145$	9.59055			0.796452
$146$	4.68032	+	11.6268i	0.387346	+	0.962242i
$147$		0			0
$148$	−0.915503	+	0.879596i	−0.0752539	+	0.0723024i
$149$		−	19.2132i		−	1.57401i	−0.616950	−	0.787003i	$-0.711632\pi$
$149$		−	19.2132i		−	1.57401i	0.616950	−	0.787003i	$-0.288368\pi$
$150$		0			0
$151$			8.88354i			0.722933i	0.932385	+	0.361466i	$0.117724\pi$
$151$			8.88354i			0.722933i	−0.932385	+	0.361466i	$0.882276\pi$
$152$	1.16029	−	2.57948i	0.0941118	−	0.209224i
$153$		0			0
$154$	−24.6582	+	9.92606i	−1.98702	+	0.799864i
$155$	11.6081			0.932388
$156$		0			0
$157$	−5.46895			−0.436470			−0.218235	−	0.975896i	$-0.570030\pi$
$157$	−5.46895			−0.436470			−0.218235	+	0.975896i	$0.570030\pi$
$158$	12.3315	−	4.96401i	0.981045	−	0.394915i
$159$		0			0
$160$	7.24093	+	20.2954i	0.572445	+	1.60449i
$161$		−	21.2571i		−	1.67530i
$162$		0			0
$163$			8.54025i			0.668924i	0.942409	+	0.334462i	$0.108555\pi$
$163$			8.54025i			0.668924i	−0.942409	+	0.334462i	$0.891445\pi$
$164$	10.1984	+	10.6148i	0.796365	+	0.828874i
$165$		0			0
$166$	−0.590663	−	1.46732i	−0.0458444	−	0.113886i
$167$	−20.1137			−1.55645			−0.778223	−	0.627988i	$-0.783879\pi$
$167$	−20.1137			−1.55645			−0.778223	+	0.627988i	$0.783879\pi$
$168$		0			0
$169$	−8.34737			−0.642105
$170$	−11.5518	−	28.6968i	−0.885980	−	2.20094i
$171$		0			0
$172$	−8.20109	−	8.53588i	−0.625328	−	0.650855i
$173$		−	6.54222i		−	0.497396i	−0.968581	−	0.248698i	$-0.919997\pi$
$173$		−	6.54222i		−	0.497396i	0.968581	−	0.248698i	$-0.0800026\pi$
$174$		0			0
$175$		−	36.9427i		−	2.79261i
$176$	−0.773993	+	19.3394i	−0.0583419	+	1.45776i
$177$		0			0
$178$	−10.7528	+	4.32848i	−0.805954	+	0.324433i
$179$	−5.78172			−0.432146			−0.216073	−	0.976377i	$-0.569325\pi$
$179$	−5.78172			−0.432146			−0.216073	+	0.976377i	$0.569325\pi$
$180$		0			0
$181$	−19.5164			−1.45064			−0.725321	−	0.688411i	$-0.758309\pi$
$181$	−19.5164			−1.45064			−0.725321	+	0.688411i	$0.758309\pi$
$182$	−10.9921	+	4.42482i	−0.814788	+	0.327989i
$183$		0			0
$184$	−14.1160	−	6.34956i	−1.04064	−	0.468096i
$185$		−	2.41808i		−	0.177781i
$186$		0			0
$187$		−	27.7856i		−	2.03188i
$188$	2.86112	−	2.74890i	0.208668	−	0.200484i
$189$		0			0
$190$	2.01168	+	4.99741i	0.145943	+	0.362550i
$191$	4.81685			0.348535			0.174268	−	0.984698i	$-0.444244\pi$
$191$	4.81685			0.348535			0.174268	+	0.984698i	$0.444244\pi$
$192$		0			0
$193$	13.9033			1.00078			0.500392	−	0.865799i	$-0.333189\pi$
$193$	13.9033			1.00078			0.500392	+	0.865799i	$0.333189\pi$
$194$	−1.41436	−	3.51353i	−0.101545	−	0.252257i
$195$		0			0
$196$	11.6657	−	11.2082i	0.833266	−	0.800585i
$197$		−	22.2186i		−	1.58301i	−0.611161	−	0.791506i	$-0.709297\pi$
$197$		−	22.2186i		−	1.58301i	0.611161	−	0.791506i	$-0.290703\pi$
$198$		0			0
$199$			22.4138i			1.58887i	0.607348	+	0.794436i	$0.292233\pi$
$199$			22.4138i			1.58887i	−0.607348	+	0.794436i	$0.707767\pi$
$200$	−24.5321	−	11.0349i	−1.73468	−	0.780284i
$201$		0			0
$202$	−3.77442	+	1.51938i	−0.265567	+	0.106903i
$203$	−9.77979			−0.686407
$204$		0			0
$205$	−28.0364			−1.95814
$206$	−19.1171	+	7.69551i	−1.33195	+	0.536172i
$207$		0			0
$208$	−0.345029	+	8.62108i	−0.0239235	+	0.597764i
$209$			4.83872i			0.334701i
$210$		0			0
$211$			1.75335i			0.120706i	0.998177	+	0.0603529i	$0.0192226\pi$
$211$			1.75335i			0.120706i	−0.998177	+	0.0603529i	$0.980777\pi$
$212$	−13.4095	−	13.9569i	−0.920971	−	0.958567i
$213$		0			0
$214$	4.68864	+	11.6475i	0.320509	+	0.796206i
$215$	22.5455			1.53759
$216$		0			0
$217$	−11.8372			−0.803561
$218$	5.08403	+	12.6297i	0.344334	+	0.855392i
$219$		0			0
$220$	−25.5402	−	26.5828i	−1.72192	−	1.79221i
$221$		−	12.3862i		−	0.833185i
$222$		0			0
$223$			21.2124i			1.42049i	0.703955	+	0.710245i	$0.251416\pi$
$223$			21.2124i			1.42049i	−0.703955	+	0.710245i	$0.748584\pi$
$224$	−7.38380	−	20.6959i	−0.493351	−	1.38280i
$225$		0			0
$226$	24.7844	−	9.97685i	1.64863	−	0.663650i
$227$	12.9384			0.858753			0.429377	−	0.903126i	$-0.358733\pi$
$227$	12.9384			0.858753			0.429377	+	0.903126i	$0.358733\pi$
$228$		0			0
$229$	−0.573288			−0.0378839			−0.0189420	−	0.999821i	$-0.506030\pi$
$229$	−0.573288			−0.0378839			−0.0189420	+	0.999821i	$0.506030\pi$
$230$	27.3478	−	11.0087i	1.80326	−	0.725895i
$231$		0			0
$232$	−2.92125	+	6.49434i	−0.191789	+	0.426375i
$233$			16.7679i			1.09850i	0.835659	+	0.549249i	$0.185086\pi$
$233$			16.7679i			1.09850i	−0.835659	+	0.549249i	$0.814914\pi$
$234$		0			0
$235$			7.55696i			0.492962i
$236$	−14.6186	+	14.0452i	−0.951589	+	0.914267i
$237$		0			0
$238$	11.7797	+	29.2630i	0.763565	+	1.89684i
$239$	−16.3015			−1.05446			−0.527229	−	0.849723i	$-0.676769\pi$
$239$	−16.3015			−1.05446			−0.527229	+	0.849723i	$0.676769\pi$
$240$		0			0
$241$	12.2004			0.785896			0.392948	−	0.919561i	$-0.371455\pi$
$241$	12.2004			0.785896			0.392948	+	0.919561i	$0.371455\pi$
$242$	−6.55547	−	16.2850i	−0.421402	−	1.04684i
$243$		0			0
$244$	−7.27771	+	6.99227i	−0.465908	+	0.447634i
$245$			30.8122i			1.96852i
$246$		0			0
$247$			2.15700i			0.137246i
$248$	−3.53580	+	7.86058i	−0.224523	+	0.499147i
$249$		0			0
$250$	22.5407	−	9.07365i	1.42560	−	0.573868i
$251$	18.4341			1.16355			0.581774	−	0.813350i	$-0.302359\pi$
$251$	18.4341			1.16355			0.581774	+	0.813350i	$0.302359\pi$
$252$		0			0
$253$	26.4794			1.66475
$254$	−23.4472	+	9.43859i	−1.47121	+	0.592230i
$255$		0			0
$256$	−15.9488	−	1.27864i	−0.996802	−	0.0799151i
$257$			25.2069i			1.57237i	0.617994	+	0.786183i	$0.287945\pi$
$257$			25.2069i			1.57237i	−0.617994	+	0.786183i	$0.712055\pi$
$258$		0			0
$259$			2.46580i			0.153217i
$260$	−11.3853	−	11.8500i	−0.706084	−	0.734908i
$261$		0			0
$262$	3.25708	+	8.09119i	0.201223	+	0.499876i
$263$	4.53707			0.279767			0.139884	−	0.990168i	$-0.455327\pi$
$263$	4.53707			0.279767			0.139884	+	0.990168i	$0.455327\pi$
$264$		0			0
$265$	36.8639			2.26453
$266$	−2.05138	−	5.09602i	−0.125778	−	0.312457i
$267$		0			0
$268$	1.35387	+	1.40914i	0.0827008	+	0.0860768i
$269$			16.9154i			1.03135i	0.856783	+	0.515676i	$0.172459\pi$
$269$			16.9154i			1.03135i	−0.856783	+	0.515676i	$0.827541\pi$
$270$		0			0
$271$		−	15.7923i		−	0.959317i	−0.877455	−	0.479658i	$-0.840761\pi$
$271$		−	15.7923i		−	0.959317i	0.877455	−	0.479658i	$-0.159239\pi$
$272$	22.9510	+	0.918533i	1.39161	+	0.0556943i
$273$		0			0
$274$	−12.1983	+	4.91039i	−0.736929	+	0.296647i
$275$	46.0186			2.77502
$276$		0			0
$277$	9.36248			0.562537			0.281268	−	0.959629i	$-0.409245\pi$
$277$	9.36248			0.562537			0.281268	+	0.959629i	$0.409245\pi$
$278$	−17.9304	+	7.21779i	−1.07539	+	0.432894i
$279$		0			0
$280$	38.1681	+	17.1685i	2.28098	+	1.02602i
$281$			4.10253i			0.244736i	0.992485	+	0.122368i	$0.0390489\pi$
$281$			4.10253i			0.244736i	−0.992485	+	0.122368i	$0.960951\pi$
$282$		0			0
$283$			1.53341i			0.0911517i	0.998961	+	0.0455758i	$0.0145123\pi$
$283$			1.53341i			0.0911517i	−0.998961	+	0.0455758i	$0.985488\pi$
$284$	21.6862	−	20.8356i	1.28684	−	1.23637i
$285$		0			0
$286$	−5.51187	−	13.6925i	−0.325924	−	0.809657i
$287$	28.5896			1.68759
$288$		0			0
$289$	−15.9744			−0.939671
$290$	−5.06480	−	12.5819i	−0.297415	−	0.738836i
$291$		0			0
$292$	12.7816	−	12.2803i	0.747988	−	0.718651i
$293$			18.9479i			1.10695i	0.832867	+	0.553473i	$0.186698\pi$
$293$			18.9479i			1.10695i	−0.832867	+	0.553473i	$0.813302\pi$
$294$		0			0
$295$		−	38.6115i		−	2.24805i
$296$	1.63743	+	0.736540i	0.0951738	+	0.0428105i
$297$		0			0
$298$	−25.2060	+	10.1466i	−1.46014	+	0.587774i
$299$	11.8039			0.682640
$300$		0			0
$301$	−22.9904			−1.32514
$302$	11.6544	−	4.69143i	0.670636	−	0.269962i
$303$		0			0
$304$	−3.99680	−	0.159958i	−0.229232	−	0.00917423i
$305$		−	19.2223i		−	1.10067i
$306$		0			0
$307$		−	19.0509i		−	1.08729i	−0.839314	−	0.543647i	$-0.817043\pi$
$307$		−	19.0509i		−	1.08729i	0.839314	−	0.543647i	$-0.182957\pi$
$308$	26.0442	+	27.1074i	1.48400	+	1.54458i
$309$		0			0
$310$	−6.13030	−	15.2288i	−0.348178	−	0.864940i
$311$	−3.23302			−0.183328			−0.0916639	−	0.995790i	$-0.529219\pi$
$311$	−3.23302			−0.183328			−0.0916639	+	0.995790i	$0.529219\pi$
$312$		0			0
$313$	26.1727			1.47937			0.739683	−	0.672956i	$-0.234976\pi$
$313$	26.1727			1.47937			0.739683	+	0.672956i	$0.234976\pi$
$314$	2.88817	+	7.17477i	0.162989	+	0.404896i
$315$		0			0
$316$	−13.0247	−	13.5564i	−0.732694	−	0.762605i
$317$			29.3554i			1.64876i	0.566034	+	0.824382i	$0.308477\pi$
$317$			29.3554i			1.64876i	−0.566034	+	0.824382i	$0.691523\pi$
$318$		0			0
$319$		−	12.1824i		−	0.682084i
$320$	22.8018	−	20.2175i	1.27466	−	1.13019i
$321$		0			0
$322$	−27.8874	+	11.2260i	−1.55411	+	0.625599i
$323$	5.74233			0.319512
$324$		0			0
$325$	20.5141			1.13792
$326$	11.2040	−	4.51014i	0.620534	−	0.249793i
$327$		0			0
$328$	8.53978	−	18.9851i	0.471530	−	1.04828i
$329$		−	7.70607i		−	0.424850i
$330$		0			0
$331$			6.73712i			0.370306i	0.982710	+	0.185153i	$0.0592780\pi$
$331$			6.73712i			0.370306i	−0.982710	+	0.185153i	$0.940722\pi$
$332$	−1.61306	+	1.54979i	−0.0885281	+	0.0850560i
$333$		0			0
$334$	10.6221	+	26.3874i	0.581217	+	1.44385i
$335$	−3.72190			−0.203349
$336$		0			0
$337$	10.5511			0.574753			0.287377	−	0.957818i	$-0.407217\pi$
$337$	10.5511			0.574753			0.287377	+	0.957818i	$0.407217\pi$
$338$	4.40828	+	10.9510i	0.239779	+	0.595655i
$339$		0			0
$340$	−31.5471	+	30.3097i	−1.71088	+	1.64378i
$341$		−	14.7453i		−	0.798501i
$342$		0			0
$343$		−	4.22925i		−	0.228358i
$344$	−6.86728	+	15.2669i	−0.370259	+	0.823137i
$345$		0			0
$346$	−8.58280	+	3.45497i	−0.461414	+	0.185740i
$347$	7.98591			0.428706			0.214353	−	0.976756i	$-0.431236\pi$
$347$	7.98591			0.428706			0.214353	+	0.976756i	$0.431236\pi$
$348$		0			0
$349$	7.31870			0.391761			0.195881	−	0.980628i	$-0.437244\pi$
$349$	7.31870			0.391761			0.195881	+	0.980628i	$0.437244\pi$
$350$	−48.4655	+	19.5096i	−2.59059	+	1.04283i
$351$		0			0
$352$	25.7803	−	9.19780i	1.37409	−	0.490244i
$353$			9.62552i			0.512315i	0.966635	+	0.256157i	$0.0824565\pi$
$353$			9.62552i			0.512315i	−0.966635	+	0.256157i	$0.917543\pi$
$354$		0			0
$355$			57.2789i			3.04005i
$356$	11.3572	+	11.8208i	0.601928	+	0.626500i
$357$		0			0
$358$	3.05335	+	7.58510i	0.161374	+	0.400885i
$359$	−7.22406			−0.381271			−0.190636	−	0.981661i	$-0.561055\pi$
$359$	−7.22406			−0.381271			−0.190636	+	0.981661i	$0.561055\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	10.3067	+	25.6037i	0.541707	+	1.34570i
$363$		0			0
$364$	11.6099	+	12.0839i	0.608525	+	0.633366i
$365$			33.7596i			1.76706i
$366$		0			0
$367$		−	11.2003i		−	0.584650i	−0.956319	−	0.292325i	$-0.905571\pi$
$367$		−	11.2003i		−	0.584650i	0.956319	−	0.292325i	$-0.0944290\pi$
$368$	−0.875355	+	21.8721i	−0.0456311	+	1.14016i
$369$		0			0
$370$	−3.17231	+	1.27700i	−0.164920	+	0.0663880i
$371$	−37.5913			−1.95164
$372$		0			0
$373$	4.79379			0.248213			0.124107	−	0.992269i	$-0.460394\pi$
$373$	4.79379			0.248213			0.124107	+	0.992269i	$0.460394\pi$
$374$	−36.4521	+	14.6737i	−1.88490	+	0.758757i
$375$		0			0
$376$	−5.11728	−	2.30182i	−0.263903	−	0.118707i
$377$		−	5.43065i		−	0.279693i
$378$		0			0
$379$		−	19.4337i		−	0.998241i	−0.866533	−	0.499120i	$-0.833657\pi$
$379$		−	19.4337i		−	0.998241i	0.866533	−	0.499120i	$-0.166343\pi$
$380$	5.49377	−	5.27830i	0.281824	−	0.270771i
$381$		0			0
$382$	−2.54380	−	6.31928i	−0.130152	−	0.323322i
$383$	−2.44219			−0.124790			−0.0623949	−	0.998052i	$-0.519874\pi$
$383$	−2.44219			−0.124790			−0.0623949	+	0.998052i	$0.519874\pi$
$384$		0			0
$385$	−71.5976			−3.64895
$386$	−7.34239	−	18.2399i	−0.373718	−	0.928387i
$387$		0			0
$388$	−3.86251	+	3.71102i	−0.196089	+	0.188398i
$389$		−	24.0453i		−	1.21914i	−0.792730	−	0.609572i	$-0.791341\pi$
$389$		−	24.0453i		−	1.21914i	0.792730	−	0.609572i	$-0.208659\pi$
$390$		0			0
$391$		−	31.4244i		−	1.58920i
$392$	−20.8648	−	9.38530i	−1.05383	−	0.474029i
$393$		0			0
$394$	−29.1488	+	11.7337i	−1.46850	+	0.591137i
$395$	35.8059			1.80159
$396$		0			0
$397$	3.85511			0.193482			0.0967412	−	0.995310i	$-0.469158\pi$
$397$	3.85511			0.193482			0.0967412	+	0.995310i	$0.469158\pi$
$398$	29.4049	−	11.8368i	1.47393	−	0.593326i
$399$		0			0
$400$	−1.52128	+	38.0115i	−0.0760639	+	1.90057i
$401$			3.19697i			0.159649i	0.996809	+	0.0798246i	$0.0254360\pi$
$401$			3.19697i			0.159649i	−0.996809	+	0.0798246i	$0.974564\pi$
$402$		0			0
$403$		−	6.57312i		−	0.327430i
$404$	3.98657	+	4.14931i	0.198339	+	0.206436i
$405$		0			0
$406$	5.16474	+	12.8302i	0.256322	+	0.636752i
$407$	−3.07158			−0.152252
$408$		0			0
$409$	3.75639			0.185742			0.0928708	−	0.995678i	$-0.470396\pi$
$409$	3.75639			0.185742			0.0928708	+	0.995678i	$0.470396\pi$
$410$	14.8061	+	36.7812i	0.731221	+	1.81649i
$411$		0			0
$412$	20.1916	+	21.0159i	0.994770	+	1.03538i
$413$			39.3734i			1.93744i
$414$		0			0
$415$		−	4.26051i		−	0.209140i
$416$	11.4923	−	4.10018i	0.563456	−	0.201028i
$417$		0			0
$418$	6.34797	−	2.55535i	0.310489	−	0.124986i
$419$	12.0633			0.589329			0.294664	−	0.955601i	$-0.404792\pi$
$419$	12.0633			0.589329			0.294664	+	0.955601i	$0.404792\pi$
$420$		0			0
$421$	−33.1868			−1.61742			−0.808712	−	0.588205i	$-0.799835\pi$
$421$	−33.1868			−1.61742			−0.808712	+	0.588205i	$0.799835\pi$
$422$	2.30024	−	0.925952i	0.111974	−	0.0450746i
$423$		0			0
$424$	−11.2286	+	24.9628i	−0.545310	+	1.21230i
$425$		−	54.6123i		−	2.64909i
$426$		0			0
$427$			19.6016i			0.948589i
$428$	12.8044	−	12.3022i	0.618922	−	0.594647i
$429$		0			0
$430$	−11.9064	−	29.5776i	−0.574175	−	1.42636i
$431$	−24.3680			−1.17376			−0.586882	−	0.809673i	$-0.699645\pi$
$431$	−24.3680			−1.17376			−0.586882	+	0.809673i	$0.699645\pi$
$432$		0			0
$433$	11.0624			0.531623			0.265812	−	0.964025i	$-0.414360\pi$
$433$	11.0624			0.531623			0.265812	+	0.964025i	$0.414360\pi$
$434$	6.25127	+	15.5293i	0.300070	+	0.745432i
$435$		0			0
$436$	13.8841	−	13.3396i	0.664929	−	0.638850i
$437$			5.47240i			0.261780i
$438$		0			0
$439$		−	4.39384i		−	0.209707i	−0.994488	−	0.104853i	$-0.966563\pi$
$439$		−	4.39384i		−	0.209707i	0.994488	−	0.104853i	$-0.0334373\pi$
$440$	−21.3864	+	47.5449i	−1.01956	+	2.26662i
$441$		0			0
$442$	−16.2496	+	6.54119i	−0.772913	+	0.311133i
$443$	8.51362			0.404495			0.202247	−	0.979334i	$-0.435176\pi$
$443$	8.51362			0.404495			0.202247	+	0.979334i	$0.435176\pi$
$444$		0			0
$445$	−31.2217			−1.48005
$446$	27.8288	−	11.2024i	1.31773	−	0.530447i
$447$		0			0
$448$	−23.2517	+	20.6165i	−1.09854	+	0.974036i
$449$			30.8460i			1.45571i	0.685730	+	0.727856i	$0.259483\pi$
$449$			30.8460i			1.45571i	−0.685730	+	0.727856i	$0.740517\pi$
$450$		0			0
$451$			35.6133i			1.67696i
$452$	−26.1775	−	27.2461i	−1.23128	−	1.28155i
$453$		0			0
$454$	−6.83283	−	16.9740i	−0.320680	−	0.796631i
$455$	−31.9166			−1.49627
$456$		0			0
$457$	36.5268			1.70865			0.854325	−	0.519739i	$-0.173971\pi$
$457$	36.5268			1.70865			0.854325	+	0.519739i	$0.173971\pi$
$458$	0.302755	+	0.752101i	0.0141468	+	0.0351434i
$459$		0			0
$460$	−28.8850	−	30.0641i	−1.34677	−	1.40175i
$461$		−	24.4172i		−	1.13722i	−0.822606	−	0.568611i	$-0.807481\pi$
$461$		−	24.4172i		−	1.13722i	0.822606	−	0.568611i	$-0.192519\pi$
$462$		0			0
$463$		−	23.0891i		−	1.07304i	−0.843887	−	0.536521i	$-0.819738\pi$
$463$		−	23.0891i		−	1.07304i	0.843887	−	0.536521i	$-0.180262\pi$
$464$	10.0627	+	0.402726i	0.467150	+	0.0186961i
$465$		0			0
$466$	21.9979	−	8.85516i	1.01903	−	0.410208i
$467$	−1.69030			−0.0782176			−0.0391088	−	0.999235i	$-0.512452\pi$
$467$	−1.69030			−0.0782176			−0.0391088	+	0.999235i	$0.512452\pi$
$468$		0			0
$469$	3.79534			0.175253
$470$	9.91404	−	3.99086i	0.457301	−	0.184084i
$471$		0			0
$472$	26.1462	+	11.7609i	1.20348	+	0.541340i
$473$		−	28.6385i		−	1.31680i
$474$		0			0
$475$			9.51048i			0.436371i
$476$	32.1695	−	30.9078i	1.47449	−	1.41666i
$477$		0			0
$478$	8.60889	+	21.3861i	0.393762	+	0.978179i
$479$	7.28304			0.332770			0.166385	−	0.986061i	$-0.446790\pi$
$479$	7.28304			0.332770			0.166385	+	0.986061i	$0.446790\pi$
$480$		0			0
$481$	−1.36924			−0.0624320
$482$	−6.44307	−	16.0058i	−0.293474	−	0.729044i
$483$		0			0
$484$	−17.9025	+	17.2004i	−0.813751	+	0.781835i
$485$		−	10.2019i		−	0.463244i
$486$		0			0
$487$		−	7.35823i		−	0.333433i	−0.986005	−	0.166717i	$-0.946684\pi$
$487$		−	7.35823i		−	0.333433i	0.986005	−	0.166717i	$-0.0533165\pi$
$488$	13.0166	+	5.85505i	0.589234	+	0.265046i
$489$		0			0
$490$	40.4229	−	16.2721i	1.82612	−	0.735096i
$491$	22.0612			0.995610			0.497805	−	0.867289i	$-0.334140\pi$
$491$	22.0612			0.995610			0.497805	+	0.867289i	$0.334140\pi$
$492$		0			0
$493$	−14.4574			−0.651130
$494$	2.82978	−	1.13912i	0.127318	−	0.0512513i
$495$		0			0
$496$	12.1796	+	0.487448i	0.546882	+	0.0218871i
$497$		−	58.4091i		−	2.62001i
$498$		0			0
$499$		−	10.7754i		−	0.482375i	−0.970479	−	0.241187i	$-0.922463\pi$
$499$		−	10.7754i		−	0.482375i	0.970479	−	0.241187i	$-0.0775369\pi$
$500$	−23.8076	−	24.7795i	−1.06471	−	1.10817i
$501$		0			0
$502$	−9.73510	−	24.1838i	−0.434499	−	1.07938i
$503$	−14.1448			−0.630686			−0.315343	−	0.948978i	$-0.602120\pi$
$503$	−14.1448			−0.630686			−0.315343	+	0.948978i	$0.602120\pi$
$504$		0			0
$505$	−10.9594			−0.487687
$506$	−13.9839	−	34.7386i	−0.621659	−	1.54432i
$507$		0			0
$508$	24.7651	+	25.7761i	1.09878	+	1.14363i
$509$		−	15.6772i		−	0.694878i	−0.937703	−	0.347439i	$-0.887051\pi$
$509$		−	15.6772i		−	0.694878i	0.937703	−	0.347439i	$-0.112949\pi$
$510$		0			0
$511$		−	34.4258i		−	1.52291i
$512$	6.74517	+	21.5987i	0.298097	+	0.954536i
$513$		0			0
$514$	33.0692	−	13.3119i	1.45862	−	0.587161i
$515$	−55.5085			−2.44600
$516$		0			0
$517$	9.59924			0.422174
$518$	3.23490	−	1.30220i	0.142133	−	0.0572152i
$519$		0			0
$520$	−9.53358	+	21.1945i	−0.418075	+	0.929440i
$521$			24.2701i			1.06329i	0.846966	+	0.531647i	$0.178427\pi$
$521$			24.2701i			1.06329i	−0.846966	+	0.531647i	$0.821573\pi$
$522$		0			0
$523$			40.1105i			1.75391i	0.480573	+	0.876954i	$0.340429\pi$
$523$			40.1105i			1.75391i	−0.480573	+	0.876954i	$0.659571\pi$
$524$	8.89484	−	8.54598i	0.388573	−	0.373333i
$525$		0			0
$526$	−2.39604	−	5.95222i	−0.104472	−	0.259529i
$527$	−17.4989			−0.762263
$528$		0			0
$529$	6.94717			0.302051
$530$	−19.4680	−	48.3621i	−0.845634	−	2.10072i
$531$		0			0
$532$	−5.60217	+	5.38245i	−0.242885	+	0.233359i
$533$			15.8756i			0.687649i
$534$		0			0
$535$			33.8196i			1.46215i
$536$	1.13368	−	2.52033i	0.0489674	−	0.108862i
$537$		0			0
$538$	22.1915	−	8.93311i	0.956745	−	0.385134i
$539$	39.1393			1.68585
$540$		0			0
$541$	22.2139			0.955051			0.477525	−	0.878618i	$-0.341534\pi$
$541$	22.2139			0.955051			0.477525	+	0.878618i	$0.341534\pi$
$542$	−20.7181	+	8.34000i	−0.889920	+	0.358234i
$543$		0			0
$544$	−10.9155	−	30.5947i	−0.467996	−	1.31174i
$545$			36.6716i			1.57084i
$546$		0			0
$547$			12.0647i			0.515849i	0.966165	+	0.257925i	$0.0830386\pi$
$547$			12.0647i			0.515849i	−0.966165	+	0.257925i	$0.916961\pi$
$548$	12.8840	+	13.4099i	0.550376	+	0.572844i
$549$		0			0
$550$	−24.3026	−	60.3722i	−1.03626	−	2.57428i
$551$	2.51769			0.107257
$552$		0			0
$553$	−36.5124			−1.55267
$554$	−4.94436	−	12.2827i	−0.210066	−	0.521843i
$555$		0			0
$556$	18.9382	+	19.7113i	0.803157	+	0.835944i
$557$		−	1.10882i		−	0.0469822i	−0.999724	−	0.0234911i	$-0.992522\pi$
$557$		−	1.10882i		−	0.0469822i	0.999724	−	0.0234911i	$-0.00747813\pi$
$558$		0			0
$559$		−	12.7664i		−	0.539961i
$560$	2.36687	−	59.1398i	0.100018	−	2.49911i
$561$		0			0
$562$	5.38215	−	2.16656i	0.227032	−	0.0913908i
$563$	16.5149			0.696019			0.348009	−	0.937491i	$-0.386858\pi$
$563$	16.5149			0.696019			0.348009	+	0.937491i	$0.386858\pi$
$564$		0			0
$565$	71.9640			3.02755
$566$	2.01169	−	0.809799i	0.0845578	−	0.0340384i
$567$		0			0
$568$	−38.7870	−	17.4470i	−1.62747	−	0.732058i
$569$			28.4274i			1.19174i	0.803081	+	0.595870i	$0.203193\pi$
$569$			28.4274i			1.19174i	−0.803081	+	0.595870i	$0.796807\pi$
$570$		0			0
$571$		−	8.65230i		−	0.362088i	−0.983475	−	0.181044i	$-0.942052\pi$
$571$		−	8.65230i		−	0.362088i	0.983475	−	0.181044i	$-0.0579476\pi$
$572$	−15.0525	+	14.4622i	−0.629378	+	0.604693i
$573$		0			0
$574$	−15.0983	−	37.5069i	−0.630189	−	1.56551i
$575$	52.0451			2.17043
$576$		0			0
$577$	−38.5864			−1.60637			−0.803186	−	0.595728i	$-0.796864\pi$
$577$	−38.5864			−1.60637			−0.803186	+	0.595728i	$0.796864\pi$
$578$	8.43614	+	20.9570i	0.350897	+	0.871695i
$579$		0			0
$580$	−13.8316	+	13.2891i	−0.574327	+	0.551801i
$581$			4.34458i			0.180244i
$582$		0			0
$583$		−	46.8265i		−	1.93935i
$584$	−22.8607	−	10.2831i	−0.945982	−	0.425516i
$585$		0			0
$586$	24.8579	−	10.0064i	1.02687	−	0.413362i
$587$	−44.8509			−1.85119			−0.925597	−	0.378511i	$-0.876436\pi$
$587$	−44.8509			−1.85119			−0.925597	+	0.378511i	$0.876436\pi$
$588$		0			0
$589$	3.04735			0.125564
$590$	−50.6548	+	20.3909i	−2.08542	+	0.839479i
$591$		0			0
$592$	0.101540	−	2.53713i	0.00417327	−	0.104275i
$593$		−	9.78085i		−	0.401651i	−0.979627	−	0.200826i	$-0.935638\pi$
$593$		−	9.78085i		−	0.401651i	0.979627	−	0.200826i	$-0.0643625\pi$
$594$		0			0
$595$			84.9682i			3.48335i
$596$	26.6227	+	27.7095i	1.09051	+	1.13503i
$597$		0			0
$598$	−6.23371	−	15.4857i	−0.254915	−	0.633258i
$599$	−24.7488			−1.01121			−0.505604	−	0.862766i	$-0.668730\pi$
$599$	−24.7488			−1.01121			−0.505604	+	0.862766i	$0.668730\pi$
$600$		0			0
$601$	6.41515			0.261679			0.130840	−	0.991404i	$-0.458233\pi$
$601$	6.41515			0.261679			0.130840	+	0.991404i	$0.458233\pi$
$602$	12.1413	+	30.1613i	0.494842	+	1.22928i
$603$		0			0
$604$	−12.3095	−	12.8120i	−0.500865	−	0.521311i
$605$		−	47.2853i		−	1.92242i
$606$		0			0
$607$			3.43035i			0.139234i	0.997574	+	0.0696168i	$0.0221776\pi$
$607$			3.43035i			0.139234i	−0.997574	+	0.0696168i	$0.977822\pi$
$608$	1.90087	+	5.32792i	0.0770906	+	0.216075i
$609$		0			0
$610$	−25.2180	+	10.1514i	−1.02105	+	0.411017i
$611$	4.27913			0.173115
$612$		0			0
$613$	11.0450			0.446103			0.223052	−	0.974807i	$-0.428398\pi$
$613$	11.0450			0.446103			0.223052	+	0.974807i	$0.428398\pi$
$614$	−24.9931	+	10.0609i	−1.00864	+	0.406024i
$615$		0			0
$616$	21.8084	−	48.4831i	0.878684	−	1.95344i
$617$			25.4332i			1.02390i	0.859015	+	0.511950i	$0.171077\pi$
$617$			25.4332i			1.02390i	−0.859015	+	0.511950i	$0.828923\pi$
$618$		0			0
$619$			1.08825i			0.0437403i	0.999761	+	0.0218701i	$0.00696204\pi$
$619$			1.08825i			0.0437403i	−0.999761	+	0.0218701i	$0.993038\pi$
$620$	−16.7414	+	16.0848i	−0.672352	+	0.645981i
$621$		0			0
$622$	1.70737	+	4.24143i	0.0684593	+	0.170066i
$623$	31.8378			1.27556
$624$		0			0
$625$	17.8968			0.715871
$626$	−13.8219	−	34.3362i	−0.552433	−	1.37235i
$627$		0			0
$628$	7.88740	−	7.57804i	0.314741	−	0.302397i
$629$			3.64518i			0.145343i
$630$		0			0
$631$			42.4081i			1.68824i	0.536155	+	0.844119i	$0.319876\pi$
$631$			42.4081i			1.68824i	−0.536155	+	0.844119i	$0.680124\pi$
$632$	−10.9063	+	24.2463i	−0.433831	+	0.964467i
$633$		0			0
$634$	38.5116	−	15.5027i	1.52949	−	0.615691i
$635$	−68.0814			−2.70173
$636$		0			0
$637$	17.4474			0.691293
$638$	−15.9822	+	6.43358i	−0.632742	+	0.254708i
$639$		0			0
$640$	−38.5653	−	19.2370i	−1.52443	−	0.760407i
$641$		−	20.2310i		−	0.799076i	−0.916717	−	0.399538i	$-0.869171\pi$
$641$		−	20.2310i		−	0.799076i	0.916717	−	0.399538i	$-0.130829\pi$
$642$		0			0
$643$			33.5252i			1.32211i	0.750339	+	0.661053i	$0.229890\pi$
$643$			33.5252i			1.32211i	−0.750339	+	0.661053i	$0.770110\pi$
$644$	29.4549	+	30.6573i	1.16069	+	1.20807i
$645$		0			0
$646$	−3.03255	−	7.53342i	−0.119314	−	0.296399i
$647$	40.4240			1.58923			0.794616	−	0.607112i	$-0.207672\pi$
$647$	40.4240			1.58923			0.794616	+	0.607112i	$0.207672\pi$
$648$		0			0
$649$	−49.0463			−1.92524
$650$	−10.8335	−	26.9126i	−0.424927	−	1.05560i
$651$		0			0
$652$	−11.8338	−	12.3169i	−0.463447	−	0.482366i
$653$		−	5.81291i		−	0.227477i	−0.993511	−	0.113738i	$-0.963717\pi$
$653$		−	5.81291i		−	0.227477i	0.993511	−	0.113738i	$-0.0362826\pi$
$654$		0			0
$655$			23.4936i			0.917971i
$656$	−29.4167	−	1.17730i	−1.14853	−	0.0459659i
$657$		0			0
$658$	−10.1097	+	4.06960i	−0.394116	+	0.158650i
$659$	−39.6932			−1.54623			−0.773115	−	0.634266i	$-0.781302\pi$
$659$	−39.6932			−1.54623			−0.773115	+	0.634266i	$0.781302\pi$
$660$		0			0
$661$	−36.8314			−1.43257			−0.716287	−	0.697805i	$-0.754160\pi$
$661$	−36.8314			−1.43257			−0.716287	+	0.697805i	$0.754160\pi$
$662$	8.83850	−	3.55790i	0.343518	−	0.138282i
$663$		0			0
$664$	2.88505	+	1.29774i	0.111962	+	0.0503619i
$665$		−	14.7968i		−	0.573795i
$666$		0			0
$667$		−	13.7778i		−	0.533479i
$668$	29.0083	−	27.8705i	1.12236	−	1.07834i
$669$		0			0
$670$	1.96555	+	4.88280i	0.0759358	+	0.188639i
$671$	−24.4172			−0.942616
$672$		0			0
$673$	−15.6444			−0.603047			−0.301524	−	0.953459i	$-0.597495\pi$
$673$	−15.6444			−0.603047			−0.301524	+	0.953459i	$0.597495\pi$
$674$	−5.57206	−	13.8420i	−0.214628	−	0.533176i
$675$		0			0
$676$	12.0387	−	11.5665i	0.463026	−	0.444866i
$677$			20.4343i			0.785353i	0.919677	+	0.392676i	$0.128451\pi$
$677$			20.4343i			0.785353i	−0.919677	+	0.392676i	$0.871549\pi$
$678$		0			0
$679$			10.4032i			0.399238i
$680$	56.4238	+	25.3802i	2.16375	+	0.973286i
$681$		0			0
$682$	−19.3445	+	7.78703i	−0.740738	+	0.298181i
$683$	13.2947			0.508708			0.254354	−	0.967111i	$-0.418137\pi$
$683$	13.2947			0.508708			0.254354	+	0.967111i	$0.418137\pi$
$684$		0			0
$685$	−35.4191			−1.35329
$686$	−5.54839	+	2.23348i	−0.211838	+	0.0852746i
$687$		0			0
$688$	23.6555	+	0.946728i	0.901856	+	0.0360937i
$689$		−	20.8742i		−	0.795244i
$690$		0			0
$691$			37.8325i			1.43922i	0.694381	+	0.719608i	$0.255678\pi$
$691$			37.8325i			1.43922i	−0.694381	+	0.719608i	$0.744322\pi$
$692$	9.06522	+	9.43528i	0.344608	+	0.358675i
$693$		0			0
$694$	−4.21739	−	10.4768i	−0.160090	−	0.397693i
$695$	−52.0626			−1.97485
$696$		0			0
$697$	42.2639			1.60086
$698$	−3.86503	−	9.60147i	−0.146294	−	0.363421i
$699$		0			0
$700$	51.1896	+	53.2793i	1.93479	+	2.01377i
$701$		−	0.665808i		−	0.0251472i	−0.999921	−	0.0125736i	$-0.995998\pi$
$701$		−	0.665808i		−	0.0251472i	0.999921	−	0.0125736i	$-0.00400241\pi$
$702$		0			0
$703$		−	0.634791i		−	0.0239416i
$704$	−25.6814	−	28.9640i	−0.967902	−	1.09162i
$705$		0			0
$706$	12.6278	−	5.08327i	0.475254	−	0.191311i
$707$	11.1757			0.420304
$708$		0			0
$709$	8.88117			0.333539			0.166770	−	0.985996i	$-0.446666\pi$
$709$	8.88117			0.333539			0.166770	+	0.985996i	$0.446666\pi$
$710$	75.1447	−	30.2492i	2.82013	−	1.13523i
$711$		0			0
$712$	9.51003	−	21.1421i	0.356404	−	0.792335i
$713$		−	16.6763i		−	0.624533i
$714$		0			0
$715$		−	39.7577i		−	1.48685i
$716$	8.33848	−	8.01143i	0.311623	−	0.299401i
$717$		0			0
$718$	3.81505	+	9.47731i	0.142376	+	0.353690i
$719$	−8.33469			−0.310832			−0.155416	−	0.987849i	$-0.549672\pi$
$719$	−8.33469			−0.310832			−0.155416	+	0.987849i	$0.549672\pi$
$720$		0			0
$721$	56.6038			2.10803
$722$	0.528104	+	1.31191i	0.0196540	+	0.0488242i
$723$		0			0
$724$	28.1468	−	27.0429i	1.04607	−	1.00504i
$725$		−	23.9444i		−	0.889274i
$726$		0			0
$727$		−	31.3415i		−	1.16239i	−0.813763	−	0.581196i	$-0.802585\pi$
$727$		−	31.3415i		−	1.16239i	0.813763	−	0.581196i	$-0.197415\pi$
$728$	9.72169	−	21.6127i	0.360310	−	0.801020i
$729$		0			0
$730$	44.2896	−	17.8286i	1.63923	−	0.659865i
$731$	−33.9866			−1.25704
$732$		0			0
$733$	−7.28636			−0.269128			−0.134564	−	0.990905i	$-0.542963\pi$
$733$	−7.28636			−0.269128			−0.134564	+	0.990905i	$0.542963\pi$
$734$	−14.6938	+	5.91491i	−0.542357	+	0.218323i
$735$		0			0
$736$	29.1565	−	10.4023i	1.07472	−	0.383435i
$737$			4.72775i			0.174149i
$738$		0			0
$739$		−	46.1509i		−	1.69769i	−0.528643	−	0.848844i	$-0.677299\pi$
$739$		−	46.1509i		−	1.69769i	0.528643	−	0.848844i	$-0.322701\pi$
$740$	3.35061	+	3.48739i	0.123171	+	0.128199i
$741$		0			0
$742$	19.8521	+	49.3164i	0.728794	+	1.81046i
$743$	−17.8805			−0.655973			−0.327987	−	0.944682i	$-0.606370\pi$
$743$	−17.8805			−0.655973			−0.327987	+	0.944682i	$0.606370\pi$
$744$		0			0
$745$	−73.1881			−2.68140
$746$	−2.53162	−	6.28902i	−0.0926891	−	0.230257i
$747$		0			0
$748$	38.5010	+	40.0727i	1.40774	+	1.46520i
$749$		−	34.4870i		−	1.26013i
$750$		0			0
$751$			34.5628i			1.26121i	0.776102	+	0.630607i	$0.217194\pi$
$751$			34.5628i			1.26121i	−0.776102	+	0.630607i	$0.782806\pi$
$752$	−0.317331	+	7.92900i	−0.0115719	+	0.289141i
$753$		0			0
$754$	−7.12452	+	2.86795i	−0.259460	+	0.104444i
$755$	33.8397			1.23155
$756$		0			0
$757$	8.06139			0.292996			0.146498	−	0.989211i	$-0.453200\pi$
$757$	8.06139			0.292996			0.146498	+	0.989211i	$0.453200\pi$
$758$	−25.4952	+	10.2630i	−0.926028	+	0.372769i
$759$		0			0
$760$	−9.82593	−	4.41984i	−0.356424	−	0.160324i
$761$			4.95166i			0.179497i	0.995964	+	0.0897487i	$0.0286064\pi$
$761$			4.95166i			0.179497i	−0.995964	+	0.0897487i	$0.971394\pi$
$762$		0			0
$763$		−	37.3952i		−	1.35380i
$764$	−6.94693	+	6.67447i	−0.251331	+	0.241474i
$765$		0			0
$766$	1.28973	+	3.20393i	0.0465997	+	0.115763i
$767$	−21.8638			−0.789455
$768$		0			0
$769$	26.3194			0.949100			0.474550	−	0.880228i	$-0.342611\pi$
$769$	26.3194			0.949100			0.474550	+	0.880228i	$0.342611\pi$
$770$	37.8109	+	93.9296i	1.36261	+	3.38499i
$771$		0			0
$772$	−20.0516	+	19.2651i	−0.721671	+	0.693367i
$773$			23.3945i			0.841442i	0.907190	+	0.420721i	$0.138223\pi$
$773$			23.3945i			0.841442i	−0.907190	+	0.420721i	$0.861777\pi$
$774$		0			0
$775$		−	28.9817i		−	1.04105i
$776$	6.90832	+	3.10746i	0.247994	+	0.111551i
$777$		0			0
$778$	−31.5453	+	12.6984i	−1.13095	+	0.455260i
$779$	−7.36005			−0.263701
$780$		0			0
$781$	72.7586			2.60351
$782$	−41.2259	+	16.5953i	−1.47424	+	0.593447i
$783$		0			0
$784$	−1.29387	+	32.3292i	−0.0462095	+	1.15461i
$785$			20.8327i			0.743550i
$786$		0			0
$787$		−	19.3231i		−	0.688794i	−0.938824	−	0.344397i	$-0.888083\pi$
$787$		−	19.3231i		−	0.688794i	0.938824	−	0.344397i	$-0.111917\pi$
$788$	30.7872	+	32.0440i	1.09675	+	1.14152i
$789$		0			0
$790$	−18.9092	−	46.9741i	−0.672759	−	1.67126i
$791$	−73.3840			−2.60923
$792$		0			0
$793$	−10.8847			−0.386525
$794$	−2.03590	−	5.05756i	−0.0722513	−	0.179486i
$795$		0			0
$796$	−31.0576	−	32.3255i	−1.10081	−	1.14575i
$797$		−	27.9590i		−	0.990358i	−0.868791	−	0.495179i	$-0.835102\pi$
$797$		−	27.9590i		−	0.990358i	0.868791	−	0.495179i	$-0.164898\pi$
$798$		0			0
$799$		−	11.3919i		−	0.403015i
$800$	50.6710	−	18.0782i	1.79149	−	0.639161i
$801$		0			0
$802$	4.19414	−	1.68833i	0.148100	−	0.0596171i
$803$	42.8832			1.51332
$804$		0			0
$805$	−80.9740			−2.85396
$806$	−8.62333	+	3.47129i	−0.303744	+	0.122271i
$807$		0			0
$808$	3.33820	−	7.42128i	0.117437	−	0.261080i
$809$			31.9284i			1.12254i	0.827631	+	0.561272i	$0.189688\pi$
$809$			31.9284i			1.12254i	−0.827631	+	0.561272i	$0.810312\pi$
$810$		0			0
$811$		−	8.93415i		−	0.313720i	−0.987621	−	0.156860i	$-0.949863\pi$
$811$		−	8.93415i		−	0.313720i	0.987621	−	0.156860i	$-0.0501372\pi$
$812$	14.1045	−	13.5513i	0.494972	−	0.475559i
$813$		0			0
$814$	1.62211	+	4.02963i	0.0568549	+	0.141238i
$815$	32.5321			1.13955
$816$		0			0
$817$	5.91860			0.207066
$818$	−1.98376	−	4.92804i	−0.0693606	−	0.172305i
$819$		0			0
$820$	40.4344	−	38.8485i	1.41203	−	1.35665i
$821$		−	3.80048i		−	0.132638i	−0.997798	−	0.0663188i	$-0.978875\pi$
$821$		−	3.80048i		−	0.132638i	0.997798	−	0.0663188i	$-0.0211254\pi$
$822$		0			0
$823$		−	17.7332i		−	0.618141i	−0.951039	−	0.309071i	$-0.899982\pi$
$823$		−	17.7332i		−	0.618141i	0.951039	−	0.309071i	$-0.100018\pi$
$824$	16.9077	−	37.5882i	0.589007	−	1.30945i
$825$		0			0
$826$	51.6543	−	20.7932i	1.79728	−	0.723489i
$827$	52.0576			1.81022			0.905110	−	0.425177i	$-0.139788\pi$
$827$	52.0576			1.81022			0.905110	+	0.425177i	$0.139788\pi$
$828$		0			0
$829$	−15.9163			−0.552794			−0.276397	−	0.961043i	$-0.589141\pi$
$829$	−15.9163			−0.552794			−0.276397	+	0.961043i	$0.589141\pi$
$830$	−5.58940	+	2.24999i	−0.194011	+	0.0780983i
$831$		0			0
$832$	−11.4482	−	12.9115i	−0.396894	−	0.447627i
$833$		−	46.4484i		−	1.60934i
$834$		0			0
$835$			76.6184i			2.65149i
$836$	−6.70477	−	6.97847i	−0.231889	−	0.241355i
$837$		0			0
$838$	−6.37065	−	15.8259i	−0.220071	−	0.546697i
$839$	6.44970			0.222668			0.111334	−	0.993783i	$-0.464488\pi$
$839$	6.44970			0.222668			0.111334	+	0.993783i	$0.464488\pi$
$840$		0			0
$841$	22.6612			0.781422
$842$	17.5260	+	43.5380i	0.603987	+	1.50042i
$843$		0			0
$844$	−2.42953	−	2.52871i	−0.0836279	−	0.0870417i
$845$			31.7973i			1.09386i
$846$		0			0
$847$			48.2183i			1.65680i
$848$	38.6788	+	1.54799i	1.32824	+	0.0531581i
$849$		0			0
$850$	−71.6464	+	28.8410i	−2.45745	+	0.989237i
$851$	−3.47383			−0.119081
$852$		0			0
$853$	−0.591890			−0.0202659			−0.0101330	−	0.999949i	$-0.503225\pi$
$853$	−0.591890			−0.0202659			−0.0101330	+	0.999949i	$0.503225\pi$
$854$	25.7156	−	10.3517i	0.879968	−	0.354227i
$855$		0			0
$856$	−22.9013	−	10.3013i	−0.782752	−	0.352093i
$857$			10.6502i			0.363806i	0.983317	+	0.181903i	$0.0582256\pi$
$857$			10.6502i			0.363806i	−0.983317	+	0.181903i	$0.941774\pi$
$858$		0			0
$859$			19.5766i			0.667944i	0.942583	+	0.333972i	$0.108389\pi$
$859$			19.5766i			0.667944i	−0.942583	+	0.333972i	$0.891611\pi$
$860$	−32.5154	+	31.2401i	−1.10877	+	1.06528i
$861$		0			0
$862$	12.8688	+	31.9686i	0.438313	+	1.08885i
$863$	9.89818			0.336938			0.168469	−	0.985707i	$-0.446118\pi$
$863$	9.89818			0.336938			0.168469	+	0.985707i	$0.446118\pi$
$864$		0			0
$865$	−24.9210			−0.847341
$866$	−5.84207	−	14.5128i	−0.198522	−	0.493166i
$867$		0			0
$868$	17.0718	−	16.4022i	0.579453	−	0.556727i
$869$		−	45.4825i		−	1.54289i
$870$		0			0
$871$			2.10753i			0.0714109i
$872$	−24.8326	−	11.1700i	−0.840938	−	0.378266i
$873$		0			0
$874$	7.17929	−	2.88999i	0.242843	−	0.0977555i
$875$	−66.7406			−2.25624
$876$		0			0
$877$	44.8997			1.51616			0.758078	−	0.652164i	$-0.226139\pi$
$877$	44.8997			1.51616			0.758078	+	0.652164i	$0.226139\pi$
$878$	−5.76433	+	2.32040i	−0.194537	+	0.0783099i
$879$		0			0
$880$	73.6689	+	2.94834i	2.48338	+	0.0993886i
$881$			28.7068i			0.967158i	0.875301	+	0.483579i	$0.160663\pi$
$881$			28.7068i			0.967158i	−0.875301	+	0.483579i	$0.839337\pi$
$882$		0			0
$883$		−	23.6077i		−	0.794461i	−0.917719	−	0.397230i	$-0.869971\pi$
$883$		−	23.6077i		−	0.794461i	0.917719	−	0.397230i	$-0.130029\pi$
$884$	17.1629	+	17.8635i	0.577251	+	0.600816i
$885$		0			0
$886$	−4.49608	−	11.1691i	−0.151049	−	0.375233i
$887$	−7.46039			−0.250495			−0.125248	−	0.992126i	$-0.539973\pi$
$887$	−7.46039			−0.250495			−0.125248	+	0.992126i	$0.539973\pi$
$888$		0			0
$889$	69.4248			2.32843
$890$	16.4883	+	40.9601i	0.552690	+	1.37299i
$891$		0			0
$892$	−29.3930	−	30.5928i	−0.984149	−	1.02432i
$893$			1.98384i			0.0663866i
$894$		0			0
$895$			22.0241i			0.736184i
$896$	39.3262	+	19.6165i	1.31380	+	0.655343i
$897$		0			0
$898$	40.4672	−	16.2899i	1.35041	−	0.543600i
$899$	−7.67228			−0.255885
$900$		0			0
$901$	−55.5711			−1.85134
$902$	46.7214	−	18.8075i	1.55565	−	0.626221i
$903$		0			0
$904$	−21.9200	+	48.7312i	−0.729048	+	1.62078i
$905$			74.3431i			2.47125i
$906$		0			0
$907$		−	38.9781i		−	1.29425i	−0.762385	−	0.647124i	$-0.775972\pi$
$907$		−	38.9781i		−	1.29425i	0.762385	−	0.647124i	$-0.224028\pi$
$908$	−18.6600	+	17.9281i	−0.619253	+	0.594965i
$909$		0			0
$910$	16.8553	+	41.8717i	0.558747	+	1.38803i
$911$	−18.3917			−0.609344			−0.304672	−	0.952457i	$-0.598547\pi$
$911$	−18.3917			−0.609344			−0.304672	+	0.952457i	$0.598547\pi$
$912$		0			0
$913$	−5.41192			−0.179108
$914$	−19.2899	−	47.9198i	−0.638054	−	1.58505i
$915$		0			0
$916$	0.826803	−	0.794375i	0.0273183	−	0.0262469i
$917$		−	23.9572i		−	0.791136i
$918$		0			0
$919$		−	44.5710i		−	1.47026i	−0.677926	−	0.735130i	$-0.737121\pi$
$919$		−	44.5710i		−	1.47026i	0.677926	−	0.735130i	$-0.262879\pi$
$920$	−24.1871	+	53.7714i	−0.797426	+	1.77279i
$921$		0			0
$922$	−32.0332	+	12.8948i	−1.05496	+	0.424668i
$923$	32.4342			1.06758
$924$		0			0
$925$	−6.03716			−0.198501
$926$	−30.2908	+	12.1934i	−0.995418	+	0.400701i
$927$		0			0
$928$	−4.78581	−	13.4140i	−0.157102	−	0.440338i
$929$			12.1231i			0.397745i	0.980025	+	0.198872i	$0.0637279\pi$
$929$			12.1231i			0.397745i	−0.980025	+	0.198872i	$0.936272\pi$
$930$		0			0
$931$			8.08877i			0.265099i
$932$	−23.2343	−	24.1828i	−0.761066	−	0.792135i
$933$		0			0
$934$	0.892651	+	2.21752i	0.0292084	+	0.0725593i
$935$	−105.842			−3.46142
$936$		0			0
$937$	31.6966			1.03548			0.517741	−	0.855537i	$-0.326773\pi$
$937$	31.6966			1.03548			0.517741	+	0.855537i	$0.326773\pi$
$938$	−2.00433	−	4.97915i	−0.0654438	−	0.162575i
$939$		0			0
$940$	−10.4713	−	10.8987i	−0.341536	−	0.355478i
$941$		−	16.4221i		−	0.535345i	−0.963510	−	0.267672i	$-0.913746\pi$
$941$		−	16.4221i		−	0.535345i	0.963510	−	0.267672i	$-0.0862544\pi$
$942$		0			0
$943$			40.2772i			1.31160i
$944$	1.62137	−	40.5124i	0.0527711	−	1.31857i
$945$		0			0
$946$	−37.5711	+	15.1241i	−1.22154	+	0.491726i
$947$	44.7282			1.45347			0.726736	−	0.686917i	$-0.241036\pi$
$947$	44.7282			1.45347			0.726736	+	0.686917i	$0.241036\pi$
$948$		0			0
$949$	19.1164			0.620544
$950$	12.4769	−	5.02252i	0.404804	−	0.162952i
$951$		0			0
$952$	−57.5371	−	25.8810i	−1.86479	−	0.838808i
$953$		−	7.36361i		−	0.238531i	−0.992862	−	0.119265i	$-0.961946\pi$
$953$		−	7.36361i		−	0.238531i	0.992862	−	0.119265i	$-0.0380539\pi$
$954$		0			0
$955$		−	18.3487i		−	0.593749i
$956$	23.5103	−	22.5882i	0.760377	−	0.730554i
$957$		0			0
$958$	−3.84620	−	9.55469i	−0.124265	−	0.308698i
$959$	36.1180			1.16631
$960$		0			0
$961$	21.7137			0.700441
$962$	0.723101	+	1.79632i	0.0233137	+	0.0579157i
$963$		0			0
$964$	−17.5956	+	16.9054i	−0.566715	+	0.544488i
$965$		−	52.9614i		−	1.70489i
$966$		0			0
$967$			12.7812i			0.411016i	0.978655	+	0.205508i	$0.0658847\pi$
$967$			12.7812i			0.411016i	−0.978655	+	0.205508i	$0.934115\pi$
$968$	32.0197	+	14.4029i	1.02915	+	0.462927i
$969$		0			0
$970$	−13.3840	+	5.38766i	−0.429733	+	0.172987i
$971$	−33.5268			−1.07593			−0.537963	−	0.842968i	$-0.680806\pi$
$971$	−33.5268			−1.07593			−0.537963	+	0.842968i	$0.680806\pi$
$972$		0			0
$973$	53.0899			1.70198
$974$	−9.65333	+	3.88591i	−0.309313	+	0.124512i
$975$		0			0
$976$	0.807182	−	20.1687i	0.0258373	−	0.645584i
$977$		−	20.8439i		−	0.666855i	−0.942776	−	0.333427i	$-0.891795\pi$
$977$		−	20.8439i		−	0.666855i	0.942776	−	0.333427i	$-0.108205\pi$
$978$		0			0
$979$			39.6595i			1.26752i
$980$	−42.6949	−	44.4378i	−1.36384	−	1.41951i
$981$		0			0
$982$	−11.6506	−	28.9424i	−0.371786	−	0.923588i
$983$	54.5300			1.73924			0.869619	−	0.493724i	$-0.164365\pi$
$983$	54.5300			1.73924			0.869619	+	0.493724i	$0.164365\pi$
$984$		0			0
$985$	−84.6366			−2.69675
$986$	7.63502	+	18.9668i	0.243149	+	0.604027i
$987$		0			0
$988$	−2.98884	−	3.11085i	−0.0950876	−	0.0989693i
$989$		−	32.3889i		−	1.02991i
$990$		0			0
$991$			26.1670i			0.831223i	0.909542	+	0.415612i	$0.136432\pi$
$991$			26.1670i			0.831223i	−0.909542	+	0.415612i	$0.863568\pi$
$992$	−5.79262	−	16.2360i	−0.183916	−	0.515494i
$993$		0			0
$994$	−76.6275	+	30.8461i	−2.43048	+	0.978378i
$995$	85.3800			2.70673
$996$		0			0
$997$	−59.0242			−1.86932			−0.934658	−	0.355547i	$-0.884295\pi$
$997$	−59.0242			−1.86932			−0.934658	+	0.355547i	$0.884295\pi$
$998$	−14.1364	+	5.69055i	−0.447480	+	0.180131i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.15	✓	32
3.2	odd	2	inner	684.2.c.b.647.18	yes	32
4.3	odd	2	inner	684.2.c.b.647.17	yes	32
12.11	even	2	inner	684.2.c.b.647.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.15	✓	32	1.1	even	1	trivial
684.2.c.b.647.16	yes	32	12.11	even	2	inner
684.2.c.b.647.17	yes	32	4.3	odd	2	inner
684.2.c.b.647.18	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.528104 - 1.31191i) q^{2} +(-1.44221 + 1.38565i) q^{4} -3.80926i q^{5} +3.88443i q^{7} +(2.57948 + 1.16029i) q^{8} +O(q^{10})\)	\(q+(-0.528104 - 1.31191i) q^{2} +(-1.44221 + 1.38565i) q^{4} -3.80926i q^{5} +3.88443i q^{7} +(2.57948 + 1.16029i) q^{8} +(-4.99741 + 2.01168i) q^{10} -4.83872 q^{11} -2.15700 q^{13} +(5.09602 - 2.05138i) q^{14} +(0.159958 - 3.99680i) q^{16} +5.74233i q^{17} -1.00000i q^{19} +(5.27830 + 5.49377i) q^{20} +(2.55535 + 6.34797i) q^{22} -5.47240 q^{23} -9.51048 q^{25} +(1.13912 + 2.82978i) q^{26} +(-5.38245 - 5.60217i) q^{28} +2.51769i q^{29} +3.04735i q^{31} +(-5.32792 + 1.90087i) q^{32} +(7.53342 - 3.03255i) q^{34} +14.7968 q^{35} +0.634791 q^{37} +(-1.31191 + 0.528104i) q^{38} +(4.41984 - 9.82593i) q^{40} -7.36005i q^{41} +5.91860i q^{43} +(6.97847 - 6.70477i) q^{44} +(2.88999 + 7.17929i) q^{46} -1.98384 q^{47} -8.08877 q^{49} +(5.02252 + 12.4769i) q^{50} +(3.11085 - 2.98884i) q^{52} +9.67744i q^{53} +18.4320i q^{55} +(-4.50705 + 10.0198i) q^{56} +(3.30298 - 1.32960i) q^{58} +10.1362 q^{59} +5.04621 q^{61} +(3.99784 - 1.60931i) q^{62} +(5.30747 + 5.98588i) q^{64} +8.21656i q^{65} -0.977067i q^{67} +(-7.95685 - 8.28167i) q^{68} +(-7.81424 - 19.4121i) q^{70} -15.0367 q^{71} -8.86251 q^{73} +(-0.335235 - 0.832788i) q^{74} +(1.38565 + 1.44221i) q^{76} -18.7957i q^{77} +9.39969i q^{79} +(-15.2249 - 0.609323i) q^{80} +(-9.65572 + 3.88687i) q^{82} +1.11846 q^{83} +21.8741 q^{85} +(7.76467 - 3.12563i) q^{86} +(-12.4814 - 5.61431i) q^{88} -8.19627i q^{89} -8.37869i q^{91} +(7.89237 - 7.58282i) q^{92} +(1.04767 + 2.60262i) q^{94} -3.80926 q^{95} +2.67818 q^{97} +(4.27171 + 10.6117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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