LMFDB - Embedded newform 684.2.c.b.647.7

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			647.7
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15329 - 0.818482i) q^{2} +(0.660175 + 1.88790i) q^{4} -3.65888i q^{5} -0.320351i q^{7} +(0.783836 - 2.71765i) q^{8} +O(q^{10})$	\(q+(-1.15329 - 0.818482i) q^{2} +(0.660175 + 1.88790i) q^{4} -3.65888i q^{5} -0.320351i q^{7} +(0.783836 - 2.71765i) q^{8} +(-2.99473 + 4.21977i) q^{10} +6.11983 q^{11} +4.17821 q^{13} +(-0.262201 + 0.369459i) q^{14} +(-3.12834 + 2.49269i) q^{16} +2.63976i q^{17} -1.00000i q^{19} +(6.90760 - 2.41550i) q^{20} +(-7.05797 - 5.00897i) q^{22} -4.43138 q^{23} -8.38741 q^{25} +(-4.81870 - 3.41979i) q^{26} +(0.604790 - 0.211488i) q^{28} -1.67404i q^{29} -1.39882i q^{31} +(5.64812 - 0.314319i) q^{32} +(2.16059 - 3.04442i) q^{34} -1.17213 q^{35} +7.03570 q^{37} +(-0.818482 + 1.15329i) q^{38} +(-9.94354 - 2.86796i) q^{40} -7.88710i q^{41} +0.224056i q^{43} +(4.04016 + 11.5536i) q^{44} +(5.11069 + 3.62700i) q^{46} -9.44950 q^{47} +6.89738 q^{49} +(9.67315 + 6.86494i) q^{50} +(2.75835 + 7.88804i) q^{52} -12.2397i q^{53} -22.3917i q^{55} +(-0.870600 - 0.251102i) q^{56} +(-1.37017 + 1.93066i) q^{58} +5.64373 q^{59} -5.73949 q^{61} +(-1.14491 + 1.61325i) q^{62} +(-6.77120 - 4.26038i) q^{64} -15.2876i q^{65} +7.49820i q^{67} +(-4.98360 + 1.74270i) q^{68} +(1.35181 + 0.959363i) q^{70} +3.81721 q^{71} -4.29493 q^{73} +(-8.11424 - 5.75859i) q^{74} +(1.88790 - 0.660175i) q^{76} -1.96049i q^{77} +3.82612i q^{79} +(9.12046 + 11.4462i) q^{80} +(-6.45545 + 9.09615i) q^{82} -16.7131 q^{83} +9.65856 q^{85} +(0.183386 - 0.258403i) q^{86} +(4.79694 - 16.6315i) q^{88} +17.0463i q^{89} -1.33849i q^{91} +(-2.92549 - 8.36600i) q^{92} +(10.8981 + 7.73424i) q^{94} -3.65888 q^{95} +1.06801 q^{97} +(-7.95470 - 5.64538i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.15329	−	0.818482i	−0.815502	−	0.578754i
$2$	−1.15329	−	0.818482i	−0.815502	−	0.578754i
$3$		0			0
$3$		0			0
$4$	0.660175	+	1.88790i	0.330088	+	0.943950i
$5$		−	3.65888i		−	1.63630i	−0.575004	−	0.818151i	$-0.695000\pi$
$5$		−	3.65888i		−	1.63630i	0.575004	−	0.818151i	$-0.305000\pi$
$6$		0			0
$7$		−	0.320351i		−	0.121081i	−0.998166	−	0.0605406i	$-0.980718\pi$
$7$		−	0.320351i		−	0.121081i	0.998166	−	0.0605406i	$-0.0192825\pi$
$8$	0.783836	−	2.71765i	0.277128	−	0.960833i
$9$		0			0
$10$	−2.99473	+	4.21977i	−0.947016	+	1.33441i
$11$	6.11983			1.84520			0.922600	−	0.385759i	$-0.126060\pi$
$11$	6.11983			1.84520			0.922600	+	0.385759i	$0.126060\pi$
$12$		0			0
$13$	4.17821			1.15883			0.579413	−	0.815034i	$-0.303282\pi$
$13$	4.17821			1.15883			0.579413	+	0.815034i	$0.303282\pi$
$14$	−0.262201	+	0.369459i	−0.0700762	+	0.0987420i
$15$		0			0
$16$	−3.12834	+	2.49269i	−0.782084	+	0.623173i
$17$			2.63976i			0.640235i	0.947378	+	0.320118i	$0.103722\pi$
$17$			2.63976i			0.640235i	−0.947378	+	0.320118i	$0.896278\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	6.90760	−	2.41550i	1.54459	−	0.540123i
$21$		0			0
$22$	−7.05797	−	5.00897i	−1.50476	−	1.06792i
$23$	−4.43138			−0.924007			−0.462003	−	0.886878i	$-0.652869\pi$
$23$	−4.43138			−0.924007			−0.462003	+	0.886878i	$0.652869\pi$
$24$		0			0
$25$	−8.38741			−1.67748
$26$	−4.81870	−	3.41979i	−0.945025	−	0.670675i
$27$		0			0
$28$	0.604790	−	0.211488i	0.114295	−	0.0399674i
$29$		−	1.67404i		−	0.310861i	−0.987847	−	0.155430i	$-0.950324\pi$
$29$		−	1.67404i		−	0.310861i	0.987847	−	0.155430i	$-0.0496764\pi$
$30$		0			0
$31$		−	1.39882i		−	0.251235i	−0.992079	−	0.125618i	$-0.959909\pi$
$31$		−	1.39882i		−	0.251235i	0.992079	−	0.125618i	$-0.0400912\pi$
$32$	5.64812	−	0.314319i	0.998455	−	0.0555644i
$33$		0			0
$34$	2.16059	−	3.04442i	0.370539	−	0.522113i
$35$	−1.17213			−0.198125
$36$		0			0
$37$	7.03570			1.15666			0.578331	−	0.815802i	$-0.303704\pi$
$37$	7.03570			1.15666			0.578331	+	0.815802i	$0.303704\pi$
$38$	−0.818482	+	1.15329i	−0.132775	+	0.187089i
$39$		0			0
$40$	−9.94354	−	2.86796i	−1.57221	−	0.453464i
$41$		−	7.88710i		−	1.23176i	−0.787840	−	0.615879i	$-0.788801\pi$
$41$		−	7.88710i		−	1.23176i	0.787840	−	0.615879i	$-0.211199\pi$
$42$		0			0
$43$			0.224056i			0.0341682i	0.999854	+	0.0170841i	$0.00543831\pi$
$43$			0.224056i			0.0341682i	−0.999854	+	0.0170841i	$0.994562\pi$
$44$	4.04016	+	11.5536i	0.609077	+	1.74178i
$45$		0			0
$46$	5.11069	+	3.62700i	0.753529	+	0.534772i
$47$	−9.44950			−1.37835			−0.689176	−	0.724594i	$-0.742027\pi$
$47$	−9.44950			−1.37835			−0.689176	+	0.724594i	$0.742027\pi$
$48$		0			0
$49$	6.89738			0.985339
$50$	9.67315	+	6.86494i	1.36799	+	0.970849i
$51$		0			0
$52$	2.75835	+	7.88804i	0.382514	+	1.09387i
$53$		−	12.2397i		−	1.68125i	−0.541620	−	0.840624i	$-0.682189\pi$
$53$		−	12.2397i		−	1.68125i	0.541620	−	0.840624i	$-0.317811\pi$
$54$		0			0
$55$		−	22.3917i		−	3.01930i
$56$	−0.870600	−	0.251102i	−0.116339	−	0.0335550i
$57$		0			0
$58$	−1.37017	+	1.93066i	−0.179912	+	0.253508i
$59$	5.64373			0.734750			0.367375	−	0.930073i	$-0.380256\pi$
$59$	5.64373			0.734750			0.367375	+	0.930073i	$0.380256\pi$
$60$		0			0
$61$	−5.73949			−0.734867			−0.367433	−	0.930050i	$-0.619763\pi$
$61$	−5.73949			−0.734867			−0.367433	+	0.930050i	$0.619763\pi$
$62$	−1.14491	+	1.61325i	−0.145403	+	0.204883i
$63$		0			0
$64$	−6.77120	−	4.26038i	−0.846400	−	0.532547i
$65$		−	15.2876i		−	1.89619i
$66$		0			0
$67$			7.49820i			0.916051i	0.888939	+	0.458025i	$0.151443\pi$
$67$			7.49820i			0.916051i	−0.888939	+	0.458025i	$0.848557\pi$
$68$	−4.98360	+	1.74270i	−0.604350	+	0.211334i
$69$		0			0
$70$	1.35181	+	0.959363i	0.161572	+	0.114666i
$71$	3.81721			0.453020			0.226510	−	0.974009i	$-0.427268\pi$
$71$	3.81721			0.453020			0.226510	+	0.974009i	$0.427268\pi$
$72$		0			0
$73$	−4.29493			−0.502683			−0.251342	−	0.967898i	$-0.580872\pi$
$73$	−4.29493			−0.502683			−0.251342	+	0.967898i	$0.580872\pi$
$74$	−8.11424	−	5.75859i	−0.943261	−	0.669423i
$75$		0			0
$76$	1.88790	−	0.660175i	0.216557	−	0.0757273i
$77$		−	1.96049i		−	0.223419i
$78$		0			0
$79$			3.82612i			0.430472i	0.976562	+	0.215236i	$0.0690521\pi$
$79$			3.82612i			0.430472i	−0.976562	+	0.215236i	$0.930948\pi$
$80$	9.12046	+	11.4462i	1.01970	+	1.27973i
$81$		0			0
$82$	−6.45545	+	9.09615i	−0.712885	+	1.00450i
$83$	−16.7131			−1.83450			−0.917251	−	0.398309i	$-0.869597\pi$
$83$	−16.7131			−1.83450			−0.917251	+	0.398309i	$0.869597\pi$
$84$		0			0
$85$	9.65856			1.04762
$86$	0.183386	−	0.258403i	0.0197750	−	0.0278643i
$87$		0			0
$88$	4.79694	−	16.6315i	0.511356	−	1.77293i
$89$			17.0463i			1.80691i	0.428687	+	0.903453i	$0.358976\pi$
$89$			17.0463i			1.80691i	−0.428687	+	0.903453i	$0.641024\pi$
$90$		0			0
$91$		−	1.33849i		−	0.140312i
$92$	−2.92549	−	8.36600i	−0.305003	−	0.872216i
$93$		0			0
$94$	10.8981	+	7.73424i	1.12405	+	0.797726i
$95$	−3.65888			−0.375393
$96$		0			0
$97$	1.06801			0.108440			0.0542198	−	0.998529i	$-0.482733\pi$
$97$	1.06801			0.108440			0.0542198	+	0.998529i	$0.482733\pi$
$98$	−7.95470	−	5.64538i	−0.803546	−	0.570269i
$99$		0			0
$100$	−5.53716	−	15.8346i	−0.553716	−	1.58346i
$101$		−	2.18738i		−	0.217653i	−0.994061	−	0.108826i	$-0.965291\pi$
$101$		−	2.18738i		−	0.217653i	0.994061	−	0.108826i	$-0.0347093\pi$
$102$		0			0
$103$		−	15.3369i		−	1.51119i	−0.655037	−	0.755597i	$-0.727347\pi$
$103$		−	15.3369i		−	1.51119i	0.655037	−	0.755597i	$-0.272653\pi$
$104$	3.27503	−	11.3549i	0.321143	−	1.11344i
$105$		0			0
$106$	−10.0179	+	14.1159i	−0.973029	+	1.37106i
$107$	−16.8452			−1.62849			−0.814246	−	0.580520i	$-0.802849\pi$
$107$	−16.8452			−1.62849			−0.814246	+	0.580520i	$0.802849\pi$
$108$		0			0
$109$	−1.74730			−0.167361			−0.0836803	−	0.996493i	$-0.526667\pi$
$109$	−1.74730			−0.167361			−0.0836803	+	0.996493i	$0.526667\pi$
$110$	−18.3272	+	25.8243i	−1.74743	+	2.46225i
$111$		0			0
$112$	0.798535	+	1.00217i	0.0754545	+	0.0946957i
$113$			7.95427i			0.748275i	0.927373	+	0.374137i	$0.122061\pi$
$113$			7.95427i			0.748275i	−0.927373	+	0.374137i	$0.877939\pi$
$114$		0			0
$115$			16.2139i			1.51195i
$116$	3.16041	−	1.10516i	0.293437	−	0.102611i
$117$		0			0
$118$	−6.50888	−	4.61929i	−0.599191	−	0.425240i
$119$	0.845648			0.0775204
$120$		0			0
$121$	26.4524			2.40476
$122$	6.61932	+	4.69767i	0.599285	+	0.425307i
$123$		0			0
$124$	2.64083	−	0.923465i	0.237153	−	0.0829296i
$125$			12.3941i			1.10856i
$126$		0			0
$127$			2.99954i			0.266166i	0.991105	+	0.133083i	$0.0424877\pi$
$127$			2.99954i			0.266166i	−0.991105	+	0.133083i	$0.957512\pi$
$128$	4.32215	+	10.4556i	0.382028	+	0.924151i
$129$		0			0
$130$	−12.5126	+	17.6311i	−1.09743	+	1.54635i
$131$	9.01301			0.787470			0.393735	−	0.919224i	$-0.371183\pi$
$131$	9.01301			0.787470			0.393735	+	0.919224i	$0.371183\pi$
$132$		0			0
$133$	−0.320351			−0.0277779
$134$	6.13714	−	8.64763i	0.530168	−	0.747041i
$135$		0			0
$136$	7.17393	+	2.06914i	0.615159	+	0.177427i
$137$			14.4820i			1.23728i	0.785673	+	0.618642i	$0.212317\pi$
$137$			14.4820i			1.23728i	−0.785673	+	0.618642i	$0.787683\pi$
$138$		0			0
$139$			12.8647i			1.09117i	0.838055	+	0.545586i	$0.183693\pi$
$139$			12.8647i			1.09117i	−0.838055	+	0.545586i	$0.816307\pi$
$140$	−0.773808	−	2.21286i	−0.0653987	−	0.187020i
$141$		0			0
$142$	−4.40237	−	3.12432i	−0.369439	−	0.262187i
$143$	25.5699			2.13827
$144$		0			0
$145$	−6.12510			−0.508662
$146$	4.95332	+	3.51532i	0.409939	+	0.290930i
$147$		0			0
$148$	4.64480	+	13.2827i	0.381800	+	1.09183i
$149$			13.2002i			1.08140i	0.841216	+	0.540700i	$0.181840\pi$
$149$			13.2002i			1.08140i	−0.841216	+	0.540700i	$0.818160\pi$
$150$		0			0
$151$		−	20.9691i		−	1.70644i	−0.521547	−	0.853222i	$-0.674645\pi$
$151$		−	20.9691i		−	1.70644i	0.521547	−	0.853222i	$-0.325355\pi$
$152$	−2.71765	−	0.783836i	−0.220430	−	0.0635775i
$153$		0			0
$154$	−1.60463	+	2.26103i	−0.129305	+	0.182199i
$155$	−5.11811			−0.411096
$156$		0			0
$157$	4.18797			0.334237			0.167118	−	0.985937i	$-0.446554\pi$
$157$	4.18797			0.334237			0.167118	+	0.985937i	$0.446554\pi$
$158$	3.13161	−	4.41265i	0.249138	−	0.351051i
$159$		0			0
$160$	−1.15006	−	20.6658i	−0.0909200	−	1.63377i
$161$			1.41960i			0.111880i
$162$		0			0
$163$		−	14.5487i		−	1.13954i	−0.821803	−	0.569772i	$-0.807032\pi$
$163$		−	14.5487i		−	1.13954i	0.821803	−	0.569772i	$-0.192968\pi$
$164$	14.8901	−	5.20687i	1.16272	−	0.406588i
$165$		0			0
$166$	19.2751	+	13.6794i	1.49604	+	1.06173i
$167$	11.8446			0.916565			0.458282	−	0.888807i	$-0.348465\pi$
$167$	11.8446			0.916565			0.458282	+	0.888807i	$0.348465\pi$
$168$		0			0
$169$	4.45742			0.342878
$170$	−11.1392	−	7.90535i	−0.854334	−	0.606313i
$171$		0			0
$172$	−0.422996	+	0.147916i	−0.0322531	+	0.0112785i
$173$			10.9004i			0.828743i	0.910108	+	0.414372i	$0.135999\pi$
$173$			10.9004i			0.828743i	−0.910108	+	0.414372i	$0.864001\pi$
$174$		0			0
$175$			2.68691i			0.203111i
$176$	−19.1449	+	15.2549i	−1.44310	+	1.14988i
$177$		0			0
$178$	13.9521	−	19.6594i	1.04575	−	1.47354i
$179$	23.7777			1.77723			0.888614	−	0.458656i	$-0.151669\pi$
$179$	23.7777			1.77723			0.888614	+	0.458656i	$0.151669\pi$
$180$		0			0
$181$	10.9440			0.813462			0.406731	−	0.913548i	$-0.366669\pi$
$181$	10.9440			0.813462			0.406731	+	0.913548i	$0.366669\pi$
$182$	−1.09553	+	1.54367i	−0.0812062	+	0.114425i
$183$		0			0
$184$	−3.47347	+	12.0429i	−0.256068	+	0.887816i
$185$		−	25.7428i		−	1.89265i
$186$		0			0
$187$			16.1549i			1.18136i
$188$	−6.23833	−	17.8397i	−0.454977	−	1.30109i
$189$		0			0
$190$	4.21977	+	2.99473i	0.306134	+	0.217260i
$191$	−20.9193			−1.51366			−0.756832	−	0.653609i	$-0.773254\pi$
$191$	−20.9193			−1.51366			−0.756832	+	0.653609i	$0.773254\pi$
$192$		0			0
$193$	12.0743			0.869124			0.434562	−	0.900642i	$-0.356903\pi$
$193$	12.0743			0.869124			0.434562	+	0.900642i	$0.356903\pi$
$194$	−1.23173	−	0.874144i	−0.0884328	−	0.0627599i
$195$		0			0
$196$	4.55348	+	13.0216i	0.325248	+	0.930111i
$197$			14.6394i			1.04301i	0.853248	+	0.521506i	$0.174630\pi$
$197$			14.6394i			1.04301i	−0.853248	+	0.521506i	$0.825370\pi$
$198$		0			0
$199$			19.4617i			1.37960i	0.724000	+	0.689800i	$0.242302\pi$
$199$			19.4617i			1.37960i	−0.724000	+	0.689800i	$0.757698\pi$
$200$	−6.57435	+	22.7940i	−0.464877	+	1.61178i
$201$		0			0
$202$	−1.79033	+	2.52270i	−0.125967	+	0.177496i
$203$	−0.536279			−0.0376394
$204$		0			0
$205$	−28.8580			−2.01553
$206$	−12.5530	+	17.6880i	−0.874609	+	1.23238i
$207$		0			0
$208$	−13.0708	+	10.4150i	−0.906300	+	0.722149i
$209$		−	6.11983i		−	0.423318i
$210$		0			0
$211$		−	2.57321i		−	0.177147i	−0.996070	−	0.0885735i	$-0.971769\pi$
$211$		−	2.57321i		−	0.177147i	0.996070	−	0.0885735i	$-0.0282308\pi$
$212$	23.1073	−	8.08033i	1.58701	−	0.554959i
$213$		0			0
$214$	19.4275	+	13.7875i	1.32804	+	0.942496i
$215$	0.819795			0.0559095
$216$		0			0
$217$	−0.448112			−0.0304198
$218$	2.01515	+	1.43013i	0.136483	+	0.0968606i
$219$		0			0
$220$	42.2734	−	14.7825i	2.85007	−	0.996634i
$221$			11.0295i			0.741921i
$222$		0			0
$223$			13.4584i			0.901243i	0.892715	+	0.450622i	$0.148798\pi$
$223$			13.4584i			0.901243i	−0.892715	+	0.450622i	$0.851202\pi$
$224$	−0.100692	−	1.80938i	−0.00672780	−	0.120894i
$225$		0			0
$226$	6.51042	−	9.17361i	0.433067	−	0.610220i
$227$	−19.3191			−1.28226			−0.641128	−	0.767434i	$-0.721533\pi$
$227$	−19.3191			−1.28226			−0.641128	+	0.767434i	$0.721533\pi$
$228$		0			0
$229$	−5.08617			−0.336103			−0.168052	−	0.985778i	$-0.553748\pi$
$229$	−5.08617			−0.336103			−0.168052	+	0.985778i	$0.553748\pi$
$230$	13.2708	−	18.6994i	0.875049	−	1.23300i
$231$		0			0
$232$	−4.54944	−	1.31217i	−0.298685	−	0.0861481i
$233$			0.396353i			0.0259659i	0.999916	+	0.0129830i	$0.00413272\pi$
$233$			0.396353i			0.0259659i	−0.999916	+	0.0129830i	$0.995867\pi$
$234$		0			0
$235$			34.5746i			2.25540i
$236$	3.72585	+	10.6548i	0.242532	+	0.693568i
$237$		0			0
$238$	−0.975281	−	0.692148i	−0.0632181	−	0.0448653i
$239$	15.6397			1.01165			0.505825	−	0.862636i	$-0.331188\pi$
$239$	15.6397			1.01165			0.505825	+	0.862636i	$0.331188\pi$
$240$		0			0
$241$	−2.14590			−0.138230			−0.0691149	−	0.997609i	$-0.522018\pi$
$241$	−2.14590			−0.138230			−0.0691149	+	0.997609i	$0.522018\pi$
$242$	−30.5074	−	21.6508i	−1.96109	−	1.39176i
$243$		0			0
$244$	−3.78907	−	10.8356i	−0.242570	−	0.693678i
$245$		−	25.2367i		−	1.61231i
$246$		0			0
$247$		−	4.17821i		−	0.265853i
$248$	−3.80149	−	1.09644i	−0.241395	−	0.0696242i
$249$		0			0
$250$	10.1444	−	14.2941i	0.641586	−	0.904036i
$251$	9.95517			0.628365			0.314182	−	0.949363i	$-0.398270\pi$
$251$	9.95517			0.628365			0.314182	+	0.949363i	$0.398270\pi$
$252$		0			0
$253$	−27.1193			−1.70498
$254$	2.45507	−	3.45935i	0.154045	−	0.217059i
$255$		0			0
$256$	3.57298	−	15.5960i	0.223312	−	0.974747i
$257$		−	14.4278i		−	0.899980i	−0.893034	−	0.449990i	$-0.851428\pi$
$257$		−	14.4278i		−	0.899980i	0.893034	−	0.449990i	$-0.148572\pi$
$258$		0			0
$259$		−	2.25389i		−	0.140050i
$260$	28.8614	−	10.0925i	1.78991	−	0.625909i
$261$		0			0
$262$	−10.3946	−	7.37698i	−0.642184	−	0.455751i
$263$	23.2348			1.43272			0.716359	−	0.697731i	$-0.245807\pi$
$263$	23.2348			1.43272			0.716359	+	0.697731i	$0.245807\pi$
$264$		0			0
$265$	−44.7835			−2.75103
$266$	0.369459	+	0.262201i	0.0226530	+	0.0160766i
$267$		0			0
$268$	−14.1559	+	4.95013i	−0.864706	+	0.302377i
$269$		−	12.9727i		−	0.790958i	−0.918475	−	0.395479i	$-0.870579\pi$
$269$		−	12.9727i		−	0.790958i	0.918475	−	0.395479i	$-0.129421\pi$
$270$		0			0
$271$			1.13320i			0.0688371i	0.999408	+	0.0344186i	$0.0109579\pi$
$271$			1.13320i			0.0688371i	−0.999408	+	0.0344186i	$0.989042\pi$
$272$	−6.58010	−	8.25805i	−0.398977	−	0.500718i
$273$		0			0
$274$	11.8533	−	16.7020i	0.716083	−	1.00901i
$275$	−51.3295			−3.09529
$276$		0			0
$277$	−1.41456			−0.0849925			−0.0424963	−	0.999097i	$-0.513531\pi$
$277$	−1.41456			−0.0849925			−0.0424963	+	0.999097i	$0.513531\pi$
$278$	10.5296	−	14.8368i	0.631521	−	0.889854i
$279$		0			0
$280$	−0.918753	+	3.18542i	−0.0549060	+	0.190365i
$281$			25.0119i			1.49208i	0.665900	+	0.746041i	$0.268048\pi$
$281$			25.0119i			1.49208i	−0.665900	+	0.746041i	$0.731952\pi$
$282$		0			0
$283$			8.88561i			0.528194i	0.964496	+	0.264097i	$0.0850740\pi$
$283$			8.88561i			0.528194i	−0.964496	+	0.264097i	$0.914926\pi$
$284$	2.52003	+	7.20652i	0.149536	+	0.427628i
$285$		0			0
$286$	−29.4897	−	20.9285i	−1.74376	−	1.23753i
$287$	−2.52664			−0.149143
$288$		0			0
$289$	10.0317			0.590099
$290$	7.06404	+	5.01328i	0.414815	+	0.294390i
$291$		0			0
$292$	−2.83541	−	8.10840i	−0.165930	−	0.474508i
$293$			4.76121i			0.278153i	0.990282	+	0.139077i	$0.0444134\pi$
$293$			4.76121i			0.278153i	−0.990282	+	0.139077i	$0.955587\pi$
$294$		0			0
$295$		−	20.6497i		−	1.20227i
$296$	5.51483	−	19.1206i	0.320543	−	1.11136i
$297$		0			0
$298$	10.8041	−	15.2237i	0.625864	−	0.881884i
$299$	−18.5152			−1.07076
$300$		0			0
$301$	0.0717765			0.00413713
$302$	−17.1629	+	24.1836i	−0.987612	+	1.39161i
$303$		0			0
$304$	2.49269	+	3.12834i	0.142966	+	0.179422i
$305$			21.0001i			1.20246i
$306$		0			0
$307$		−	2.28227i		−	0.130256i	−0.997877	−	0.0651281i	$-0.979254\pi$
$307$		−	2.28227i		−	0.130256i	0.997877	−	0.0651281i	$-0.0207456\pi$
$308$	3.70122	−	1.29427i	0.210896	−	0.0737478i
$309$		0			0
$310$	5.90268	+	4.18908i	0.335250	+	0.237924i
$311$	−16.7151			−0.947827			−0.473914	−	0.880571i	$-0.657159\pi$
$311$	−16.7151			−0.947827			−0.473914	+	0.880571i	$0.657159\pi$
$312$		0			0
$313$	−22.6278			−1.27900			−0.639498	−	0.768793i	$-0.720858\pi$
$313$	−22.6278			−1.27900			−0.639498	+	0.768793i	$0.720858\pi$
$314$	−4.82997	−	3.42778i	−0.272571	−	0.193441i
$315$		0			0
$316$	−7.22334	+	2.52591i	−0.406345	+	0.142094i
$317$		−	0.0161487i		−	0.000907002i	−1.00000		0.000453501i	$-0.999856\pi$
$317$		−	0.0161487i		−	0.000907002i	1.00000		0.000453501i	$-0.000144354\pi$
$318$		0			0
$319$		−	10.2448i		−	0.573600i
$320$	−15.5882	+	24.7750i	−0.871407	+	1.38497i
$321$		0			0
$322$	1.16191	−	1.63721i	0.0647509	−	0.0912382i
$323$	2.63976			0.146880
$324$		0			0
$325$	−35.0443			−1.94391
$326$	−11.9079	+	16.7790i	−0.659515	+	0.929300i
$327$		0			0
$328$	−21.4344	−	6.18219i	−1.18351	−	0.341355i
$329$			3.02715i			0.166892i
$330$		0			0
$331$			0.0472389i			0.00259648i	0.999999	+	0.00129824i	$0.000413243\pi$
$331$			0.0472389i			0.00259648i	−0.999999	+	0.00129824i	$0.999587\pi$
$332$	−11.0336	−	31.5527i	−0.605547	−	1.73168i
$333$		0			0
$334$	−13.6603	−	9.69461i	−0.747461	−	0.530466i
$335$	27.4350			1.49893
$336$		0			0
$337$	2.69866			0.147006			0.0735028	−	0.997295i	$-0.476582\pi$
$337$	2.69866			0.147006			0.0735028	+	0.997295i	$0.476582\pi$
$338$	−5.14071	−	3.64831i	−0.279618	−	0.198442i
$339$		0			0
$340$	6.37634	+	18.2344i	0.345806	+	0.988899i
$341$		−	8.56053i		−	0.463579i
$342$		0			0
$343$		−	4.45203i		−	0.240387i
$344$	0.608905	+	0.175623i	0.0328300	+	0.00946897i
$345$		0			0
$346$	8.92179	−	12.5714i	0.479638	−	0.675842i
$347$	35.3416			1.89723			0.948617	−	0.316425i	$-0.102483\pi$
$347$	35.3416			1.89723			0.948617	+	0.316425i	$0.102483\pi$
$348$		0			0
$349$	27.2991			1.46129			0.730643	−	0.682759i	$-0.239220\pi$
$349$	27.2991			1.46129			0.730643	+	0.682759i	$0.239220\pi$
$350$	2.19919	−	3.09880i	0.117552	−	0.165638i
$351$		0			0
$352$	34.5655	−	1.92358i	1.84235	−	0.102527i
$353$		−	23.1615i		−	1.23276i	−0.787448	−	0.616381i	$-0.788598\pi$
$353$		−	23.1615i		−	1.23276i	0.787448	−	0.616381i	$-0.211402\pi$
$354$		0			0
$355$		−	13.9667i		−	0.741277i
$356$	−32.1818	+	11.2536i	−1.70563	+	0.596438i
$357$		0			0
$358$	−27.4227	−	19.4616i	−1.44933	−	1.02858i
$359$	14.7385			0.777868			0.388934	−	0.921266i	$-0.372843\pi$
$359$	14.7385			0.777868			0.388934	+	0.921266i	$0.372843\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−12.6217	−	8.95747i	−0.663380	−	0.470794i
$363$		0			0
$364$	2.52694	−	0.883639i	0.132448	−	0.0463153i
$365$			15.7146i			0.822541i
$366$		0			0
$367$		−	13.2113i		−	0.689625i	−0.938672	−	0.344812i	$-0.887943\pi$
$367$		−	13.2113i		−	0.689625i	0.938672	−	0.344812i	$-0.112057\pi$
$368$	13.8629	−	11.0461i	0.722651	−	0.575816i
$369$		0			0
$370$	−21.0700	+	29.6890i	−1.09538	+	1.54346i
$371$	−3.92099			−0.203567
$372$		0			0
$373$	6.21026			0.321555			0.160777	−	0.986991i	$-0.448600\pi$
$373$	6.21026			0.321555			0.160777	+	0.986991i	$0.448600\pi$
$374$	13.2225	−	18.6313i	0.683718	−	0.963403i
$375$		0			0
$376$	−7.40685	+	25.6804i	−0.381979	+	1.32437i
$377$		−	6.99447i		−	0.360233i
$378$		0			0
$379$		−	0.447240i		−	0.0229732i	−0.999934	−	0.0114866i	$-0.996344\pi$
$379$		−	0.447240i		−	0.0229732i	0.999934	−	0.0114866i	$-0.00365638\pi$
$380$	−2.41550	−	6.90760i	−0.123913	−	0.354353i
$381$		0			0
$382$	24.1261	+	17.1220i	1.23440	+	0.876039i
$383$	21.4211			1.09457			0.547283	−	0.836947i	$-0.315662\pi$
$383$	21.4211			1.09457			0.547283	+	0.836947i	$0.315662\pi$
$384$		0			0
$385$	−7.17321			−0.365581
$386$	−13.9252	−	9.88255i	−0.708772	−	0.503009i
$387$		0			0
$388$	0.705072	+	2.01629i	0.0357946	+	0.102362i
$389$			11.0106i			0.558262i	0.960253	+	0.279131i	$0.0900464\pi$
$389$			11.0106i			0.558262i	−0.960253	+	0.279131i	$0.909954\pi$
$390$		0			0
$391$		−	11.6978i		−	0.591582i
$392$	5.40641	−	18.7446i	0.273065	−	0.946747i
$393$		0			0
$394$	11.9821	−	16.8835i	0.603647	−	0.850579i
$395$	13.9993			0.704383
$396$		0			0
$397$	−30.3371			−1.52258			−0.761288	−	0.648414i	$-0.775432\pi$
$397$	−30.3371			−1.52258			−0.761288	+	0.648414i	$0.775432\pi$
$398$	15.9290	−	22.4450i	0.798449	−	1.12507i
$399$		0			0
$400$	26.2386	−	20.9072i	1.31193	−	1.04536i
$401$		−	5.10087i		−	0.254725i	−0.991856	−	0.127363i	$-0.959349\pi$
$401$		−	5.10087i		−	0.254725i	0.991856	−	0.127363i	$-0.0406512\pi$
$402$		0			0
$403$		−	5.84455i		−	0.291138i
$404$	4.12956	−	1.44406i	0.205454	−	0.0718445i
$405$		0			0
$406$	0.618487	+	0.438934i	0.0306950	+	0.0217839i
$407$	43.0573			2.13427
$408$		0			0
$409$	−21.4750			−1.06187			−0.530936	−	0.847412i	$-0.678159\pi$
$409$	−21.4750			−1.06187			−0.530936	+	0.847412i	$0.678159\pi$
$410$	33.2817	+	23.6197i	1.64367	+	1.16649i
$411$		0			0
$412$	28.9546	−	10.1251i	1.42649	−	0.498826i
$413$		−	1.80797i		−	0.0889645i
$414$		0			0
$415$			61.1513i			3.00180i
$416$	23.5990	−	1.31329i	1.15704	−	0.0643894i
$417$		0			0
$418$	−5.00897	+	7.05797i	−0.244997	+	0.345217i
$419$	−7.85036			−0.383515			−0.191758	−	0.981442i	$-0.561419\pi$
$419$	−7.85036			−0.383515			−0.191758	+	0.981442i	$0.561419\pi$
$420$		0			0
$421$	13.1644			0.641594			0.320797	−	0.947148i	$-0.396049\pi$
$421$	13.1644			0.641594			0.320797	+	0.947148i	$0.396049\pi$
$422$	−2.10612	+	2.96767i	−0.102525	+	0.144464i
$423$		0			0
$424$	−33.2631	−	9.59389i	−1.61540	−	0.465920i
$425$		−	22.1407i		−	1.07398i
$426$		0			0
$427$			1.83865i			0.0889785i
$428$	−11.1208	−	31.8021i	−0.537545	−	1.53721i
$429$		0			0
$430$	−0.945464	−	0.670987i	−0.0455943	−	0.0323579i
$431$	10.0417			0.483693			0.241847	−	0.970315i	$-0.422247\pi$
$431$	10.0417			0.483693			0.241847	+	0.970315i	$0.422247\pi$
$432$		0			0
$433$	−8.40541			−0.403938			−0.201969	−	0.979392i	$-0.564734\pi$
$433$	−8.40541			−0.403938			−0.201969	+	0.979392i	$0.564734\pi$
$434$	0.516805	+	0.366772i	0.0248074	+	0.0176056i
$435$		0			0
$436$	−1.15352	−	3.29872i	−0.0552437	−	0.157980i
$437$			4.43138i			0.211982i
$438$		0			0
$439$			4.73890i			0.226175i	0.993585	+	0.113088i	$0.0360741\pi$
$439$			4.73890i			0.226175i	−0.993585	+	0.113088i	$0.963926\pi$
$440$	−60.8528	−	17.5514i	−2.90104	−	0.836732i
$441$		0			0
$442$	9.02741	−	12.7202i	0.429390	−	0.605038i
$443$	−21.0930			−1.00216			−0.501079	−	0.865401i	$-0.667064\pi$
$443$	−21.0930			−1.00216			−0.501079	+	0.865401i	$0.667064\pi$
$444$		0			0
$445$	62.3704			2.95664
$446$	11.0155	−	15.5215i	0.521598	−	0.734966i
$447$		0			0
$448$	−1.36481	+	2.16916i	−0.0644814	+	0.102483i
$449$			37.0945i			1.75060i	0.483584	+	0.875298i	$0.339335\pi$
$449$			37.0945i			1.75060i	−0.483584	+	0.875298i	$0.660665\pi$
$450$		0			0
$451$		−	48.2678i		−	2.27284i
$452$	−15.0169	+	5.25121i	−0.706334	+	0.246996i
$453$		0			0
$454$	22.2806	+	15.8123i	1.04568	+	0.742110i
$455$	−4.89738			−0.229593
$456$		0			0
$457$	23.7973			1.11319			0.556595	−	0.830784i	$-0.312108\pi$
$457$	23.7973			1.11319			0.556595	+	0.830784i	$0.312108\pi$
$458$	5.86585	+	4.16294i	0.274093	+	0.194521i
$459$		0			0
$460$	−30.6102	+	10.7040i	−1.42721	+	0.499077i
$461$			16.3647i			0.762182i	0.924537	+	0.381091i	$0.124452\pi$
$461$			16.3647i			0.762182i	−0.924537	+	0.381091i	$0.875548\pi$
$462$		0			0
$463$			18.3561i			0.853082i	0.904468	+	0.426541i	$0.140268\pi$
$463$			18.3561i			0.853082i	−0.904468	+	0.426541i	$0.859732\pi$
$464$	4.17285	+	5.23695i	0.193720	+	0.243119i
$465$		0			0
$466$	0.324407	−	0.457111i	0.0150279	−	0.0211753i
$467$	−24.8582			−1.15030			−0.575149	−	0.818048i	$-0.695056\pi$
$467$	−24.8582			−1.15030			−0.575149	+	0.818048i	$0.695056\pi$
$468$		0			0
$469$	2.40205			0.110917
$470$	28.2987	−	39.8747i	1.30532	−	1.83928i
$471$		0			0
$472$	4.42375	−	15.3376i	0.203620	−	0.705973i
$473$			1.37119i			0.0630472i
$474$		0			0
$475$			8.38741i			0.384841i
$476$	0.558276	+	1.59650i	0.0255885	+	0.0731754i
$477$		0			0
$478$	−18.0372	−	12.8008i	−0.825004	−	0.585497i
$479$	20.4756			0.935552			0.467776	−	0.883847i	$-0.345055\pi$
$479$	20.4756			0.935552			0.467776	+	0.883847i	$0.345055\pi$
$480$		0			0
$481$	29.3966			1.34037
$482$	2.47486	+	1.75638i	0.112727	+	0.0800011i
$483$		0			0
$484$	17.4632	+	49.9394i	0.793782	+	2.26997i
$485$		−	3.90771i		−	0.177440i
$486$		0			0
$487$		−	13.5028i		−	0.611869i	−0.952052	−	0.305935i	$-0.901031\pi$
$487$		−	13.5028i		−	0.611869i	0.952052	−	0.305935i	$-0.0989689\pi$
$488$	−4.49882	+	15.5979i	−0.203652	+	0.706084i
$489$		0			0
$490$	−20.6558	+	29.1053i	−0.933132	+	1.31484i
$491$	−29.5307			−1.33270			−0.666352	−	0.745637i	$-0.732145\pi$
$491$	−29.5307			−1.33270			−0.666352	+	0.745637i	$0.732145\pi$
$492$		0			0
$493$	4.41905			0.199024
$494$	−3.41979	+	4.81870i	−0.153863	+	0.216804i
$495$		0			0
$496$	3.48682	+	4.37597i	0.156563	+	0.196487i
$497$		−	1.22285i		−	0.0548522i
$498$		0			0
$499$			24.8889i			1.11418i	0.830452	+	0.557090i	$0.188082\pi$
$499$			24.8889i			1.11418i	−0.830452	+	0.557090i	$0.811918\pi$
$500$	−23.3989	+	8.18229i	−1.04643	+	0.365923i
$501$		0			0
$502$	−11.4812	−	8.14812i	−0.512433	−	0.363669i
$503$	−27.2666			−1.21576			−0.607878	−	0.794031i	$-0.707979\pi$
$503$	−27.2666			−1.21576			−0.607878	+	0.794031i	$0.707979\pi$
$504$		0			0
$505$	−8.00338			−0.356146
$506$	31.2765	+	22.1967i	1.39041	+	0.986762i
$507$		0			0
$508$	−5.66283	+	1.98022i	−0.251247	+	0.0878581i
$509$		−	34.7537i		−	1.54043i	−0.637784	−	0.770215i	$-0.720149\pi$
$509$		−	34.7537i		−	1.54043i	0.637784	−	0.770215i	$-0.279851\pi$
$510$		0			0
$511$			1.37588i			0.0608655i
$512$	−16.8857	+	15.0623i	−0.746250	+	0.665666i
$513$		0			0
$514$	−11.8089	+	16.6395i	−0.520867	+	0.733935i
$515$	−56.1160			−2.47277
$516$		0			0
$517$	−57.8294			−2.54333
$518$	−1.84477	+	2.59940i	−0.0810545	+	0.114211i
$519$		0			0
$520$	−41.5462	−	11.9829i	−1.82192	−	0.525486i
$521$			9.03218i			0.395707i	0.980232	+	0.197853i	$0.0633970\pi$
$521$			9.03218i			0.395707i	−0.980232	+	0.197853i	$0.936603\pi$
$522$		0			0
$523$		−	30.0596i		−	1.31442i	−0.753710	−	0.657208i	$-0.771737\pi$
$523$		−	30.0596i		−	1.31442i	0.753710	−	0.657208i	$-0.228263\pi$
$524$	5.95017	+	17.0157i	0.259934	+	0.743333i
$525$		0			0
$526$	−26.7966	−	19.0173i	−1.16839	−	0.829192i
$527$	3.69254			0.160850
$528$		0			0
$529$	−3.36287			−0.146212
$530$	51.6485	+	36.6545i	2.24347	+	1.59217i
$531$		0			0
$532$	−0.211488	−	0.604790i	−0.00916915	−	0.0262210i
$533$		−	32.9540i		−	1.42739i
$534$		0			0
$535$			61.6347i			2.66470i
$536$	20.3774	+	5.87735i	0.880172	+	0.253863i
$537$		0			0
$538$	−10.6179	+	14.9613i	−0.457770	+	0.645028i
$539$	42.2108			1.81815
$540$		0			0
$541$	−2.04586			−0.0879585			−0.0439792	−	0.999032i	$-0.514004\pi$
$541$	−2.04586			−0.0879585			−0.0439792	+	0.999032i	$0.514004\pi$
$542$	0.927505	−	1.30692i	0.0398398	−	0.0561368i
$543$		0			0
$544$	0.829727	+	14.9097i	0.0355743	+	0.639246i
$545$			6.39315i			0.273852i
$546$		0			0
$547$			17.6949i			0.756580i	0.925687	+	0.378290i	$0.123488\pi$
$547$			17.6949i			0.756580i	−0.925687	+	0.378290i	$0.876512\pi$
$548$	−27.3406	+	9.56068i	−1.16793	+	0.408412i
$549$		0			0
$550$	59.1981	+	42.0123i	2.52421	+	1.79141i
$551$	−1.67404			−0.0713163
$552$		0			0
$553$	1.22570			0.0521221
$554$	1.63140	+	1.15779i	0.0693116	+	0.0491898i
$555$		0			0
$556$	−24.2873	+	8.49298i	−1.03001	+	0.360183i
$557$			31.9084i			1.35200i	0.736900	+	0.676002i	$0.236289\pi$
$557$			31.9084i			1.35200i	−0.736900	+	0.676002i	$0.763711\pi$
$558$		0			0
$559$			0.936153i			0.0395950i
$560$	3.66680	−	2.92175i	0.154951	−	0.123466i
$561$		0			0
$562$	20.4718	−	28.8460i	0.863549	−	1.21680i
$563$	16.0136			0.674894			0.337447	−	0.941344i	$-0.390437\pi$
$563$	16.0136			0.674894			0.337447	+	0.941344i	$0.390437\pi$
$564$		0			0
$565$	29.1037			1.22440
$566$	7.27271	−	10.2477i	0.305695	−	0.430744i
$567$		0			0
$568$	2.99207	−	10.3738i	0.125544	−	0.435276i
$569$		−	0.274051i		−	0.0114888i	−0.999984	−	0.00574441i	$-0.998171\pi$
$569$		−	0.274051i		−	0.0114888i	0.999984	−	0.00574441i	$-0.00182851\pi$
$570$		0			0
$571$			38.8262i			1.62483i	0.583082	+	0.812414i	$0.301847\pi$
$571$			38.8262i			1.62483i	−0.583082	+	0.812414i	$0.698153\pi$
$572$	16.8806	+	48.2735i	0.705815	+	2.01842i
$573$		0			0
$574$	2.91396	+	2.06801i	0.121626	+	0.0863170i
$575$	37.1678			1.55000
$576$		0			0
$577$	−32.4775			−1.35206			−0.676029	−	0.736875i	$-0.736300\pi$
$577$	−32.4775			−1.35206			−0.676029	+	0.736875i	$0.736300\pi$
$578$	−11.5695	−	8.21075i	−0.481227	−	0.341522i
$579$		0			0
$580$	−4.04364	−	11.5636i	−0.167903	−	0.480151i
$581$			5.35406i			0.222124i
$582$		0			0
$583$		−	74.9047i		−	3.10224i
$584$	−3.36652	+	11.6721i	−0.139307	+	0.482995i
$585$		0			0
$586$	3.89697	−	5.49108i	0.160982	−	0.226834i
$587$	−13.6295			−0.562550			−0.281275	−	0.959627i	$-0.590757\pi$
$587$	−13.6295			−0.562550			−0.281275	+	0.959627i	$0.590757\pi$
$588$		0			0
$589$	−1.39882			−0.0576373
$590$	−16.9014	+	23.8152i	−0.695820	+	0.980456i
$591$		0			0
$592$	−22.0101	+	17.5378i	−0.904608	+	0.720801i
$593$			15.3254i			0.629341i	0.949201	+	0.314670i	$0.101894\pi$
$593$			15.3254i			0.629341i	−0.949201	+	0.314670i	$0.898106\pi$
$594$		0			0
$595$		−	3.09413i		−	0.126847i
$596$	−24.9206	+	8.71442i	−1.02079	+	0.356957i
$597$		0			0
$598$	21.3535	+	15.1544i	0.873210	+	0.619708i
$599$	−39.4952			−1.61373			−0.806865	−	0.590736i	$-0.798838\pi$
$599$	−39.4952			−1.61373			−0.806865	+	0.590736i	$0.798838\pi$
$600$		0			0
$601$	7.62210			0.310912			0.155456	−	0.987843i	$-0.450315\pi$
$601$	7.62210			0.310912			0.155456	+	0.987843i	$0.450315\pi$
$602$	−0.0827795	−	0.0587478i	−0.00337384	−	0.00239438i
$603$		0			0
$604$	39.5877	−	13.8433i	1.61080	−	0.563276i
$605$		−	96.7860i		−	3.93491i
$606$		0			0
$607$			20.8480i			0.846193i	0.906085	+	0.423097i	$0.139057\pi$
$607$			20.8480i			0.846193i	−0.906085	+	0.423097i	$0.860943\pi$
$608$	−0.314319	−	5.64812i	−0.0127473	−	0.229061i
$609$		0			0
$610$	17.1882	−	24.2193i	0.695930	−	0.980611i
$611$	−39.4820			−1.59727
$612$		0			0
$613$	26.8163			1.08310			0.541550	−	0.840669i	$-0.317838\pi$
$613$	26.8163			1.08310			0.541550	+	0.840669i	$0.317838\pi$
$614$	−1.86800	+	2.63213i	−0.0753863	+	0.106224i
$615$		0			0
$616$	−5.32793	−	1.53670i	−0.214668	−	0.0619156i
$617$			1.92026i			0.0773067i	0.999253	+	0.0386533i	$0.0123068\pi$
$617$			1.92026i			0.0773067i	−0.999253	+	0.0386533i	$0.987693\pi$
$618$		0			0
$619$		−	23.6584i		−	0.950911i	−0.879740	−	0.475455i	$-0.842283\pi$
$619$		−	23.6584i		−	0.950911i	0.879740	−	0.475455i	$-0.157717\pi$
$620$	−3.37885	−	9.66248i	−0.135698	−	0.388054i
$621$		0			0
$622$	19.2775	+	13.6810i	0.772955	+	0.548559i
$623$	5.46080			0.218782
$624$		0			0
$625$	3.41157			0.136463
$626$	26.0965	+	18.5204i	1.04302	+	0.740224i
$627$		0			0
$628$	2.76480	+	7.90648i	0.110327	+	0.315503i
$629$			18.5725i			0.740536i
$630$		0			0
$631$		−	27.2172i		−	1.08350i	−0.840540	−	0.541749i	$-0.817762\pi$
$631$		−	27.2172i		−	1.08350i	0.840540	−	0.541749i	$-0.182238\pi$
$632$	10.3980	+	2.99905i	0.413612	+	0.119296i
$633$		0			0
$634$	−0.0132174	+	0.0186242i	−0.000524931	+	0.000739662i
$635$	10.9749			0.435528
$636$		0			0
$637$	28.8187			1.14184
$638$	−8.38520	+	11.8153i	−0.331973	+	0.467772i
$639$		0			0
$640$	38.2557	−	15.8142i	1.51219	−	0.625112i
$641$			2.72771i			0.107738i	0.998548	+	0.0538691i	$0.0171554\pi$
$641$			2.72771i			0.107738i	−0.998548	+	0.0538691i	$0.982845\pi$
$642$		0			0
$643$		−	2.04383i		−	0.0806008i	−0.999188	−	0.0403004i	$-0.987169\pi$
$643$		−	2.04383i		−	0.0806008i	0.999188	−	0.0403004i	$-0.0128315\pi$
$644$	−2.68006	+	0.937182i	−0.105609	+	0.0369302i
$645$		0			0
$646$	−3.04442	−	2.16059i	−0.119781	−	0.0850074i
$647$	15.7675			0.619884			0.309942	−	0.950756i	$-0.399690\pi$
$647$	15.7675			0.619884			0.309942	+	0.950756i	$0.399690\pi$
$648$		0			0
$649$	34.5387			1.35576
$650$	40.4164	+	28.6831i	1.58526	+	1.12505i
$651$		0			0
$652$	27.4665	−	9.60471i	1.07567	−	0.376149i
$653$		−	40.4064i		−	1.58122i	−0.612318	−	0.790612i	$-0.709763\pi$
$653$		−	40.4064i		−	1.58122i	0.612318	−	0.790612i	$-0.290237\pi$
$654$		0			0
$655$		−	32.9775i		−	1.28854i
$656$	19.6601	+	24.6735i	0.767598	+	0.963339i
$657$		0			0
$658$	2.47767	−	3.49120i	0.0965896	−	0.136101i
$659$	−10.7737			−0.419683			−0.209842	−	0.977735i	$-0.567295\pi$
$659$	−10.7737			−0.419683			−0.209842	+	0.977735i	$0.567295\pi$
$660$		0			0
$661$	38.6347			1.50272			0.751359	−	0.659894i	$-0.229399\pi$
$661$	38.6347			1.50272			0.751359	+	0.659894i	$0.229399\pi$
$662$	0.0386642	−	0.0544803i	0.00150273	−	0.00211744i
$663$		0			0
$664$	−13.1003	+	45.4203i	−0.508392	+	1.76265i
$665$			1.17213i			0.0454531i
$666$		0			0
$667$			7.41829i			0.287237i
$668$	7.81953	+	22.3615i	0.302547	+	0.865192i
$669$		0			0
$670$	−31.6406	−	22.4551i	−1.22238	−	0.867514i
$671$	−35.1247			−1.35598
$672$		0			0
$673$	−7.38877			−0.284816			−0.142408	−	0.989808i	$-0.545485\pi$
$673$	−7.38877			−0.284816			−0.142408	+	0.989808i	$0.545485\pi$
$674$	−3.11235	−	2.20881i	−0.119883	−	0.0850800i
$675$		0			0
$676$	2.94268	+	8.41516i	0.113180	+	0.323660i
$677$			44.6064i			1.71436i	0.515013	+	0.857182i	$0.327787\pi$
$677$			44.6064i			1.71436i	−0.515013	+	0.857182i	$0.672213\pi$
$678$		0			0
$679$		−	0.342137i		−	0.0131300i
$680$	7.57072	−	26.2485i	0.290324	−	1.00659i
$681$		0			0
$682$	−7.00664	+	9.87281i	−0.268298	+	0.378049i
$683$	−17.9271			−0.685961			−0.342980	−	0.939343i	$-0.611436\pi$
$683$	−17.9271			−0.685961			−0.342980	+	0.939343i	$0.611436\pi$
$684$		0			0
$685$	52.9880			2.02457
$686$	−3.64391	+	5.13451i	−0.139125	+	0.196036i
$687$		0			0
$688$	−0.558503	−	0.700923i	−0.0212927	−	0.0267224i
$689$		−	51.1399i		−	1.94827i
$690$		0			0
$691$			43.8349i			1.66756i	0.552099	+	0.833779i	$0.313827\pi$
$691$			43.8349i			1.66756i	−0.552099	+	0.833779i	$0.686173\pi$
$692$	−20.5789	+	7.19619i	−0.782292	+	0.273558i
$693$		0			0
$694$	−40.7592	−	28.9264i	−1.54720	−	1.09803i
$695$	47.0705			1.78549
$696$		0			0
$697$	20.8200			0.788615
$698$	−31.4839	−	22.3438i	−1.19168	−	0.845726i
$699$		0			0
$700$	−5.07262	+	1.77383i	−0.191727	+	0.0670446i
$701$			50.7623i			1.91726i	0.284648	+	0.958632i	$0.408123\pi$
$701$			50.7623i			1.91726i	−0.284648	+	0.958632i	$0.591877\pi$
$702$		0			0
$703$		−	7.03570i		−	0.265357i
$704$	−41.4386	−	26.0728i	−1.56178	−	0.982655i
$705$		0			0
$706$	−18.9573	+	26.7120i	−0.713466	+	1.00532i
$707$	−0.700730			−0.0263537
$708$		0			0
$709$	−42.8669			−1.60990			−0.804950	−	0.593343i	$-0.797808\pi$
$709$	−42.8669			−1.60990			−0.804950	+	0.593343i	$0.797808\pi$
$710$	−11.4315	+	16.1077i	−0.429017	+	0.604513i
$711$		0			0
$712$	46.3259	+	13.3615i	1.73614	+	0.500744i
$713$			6.19869i			0.232143i
$714$		0			0
$715$		−	93.5573i		−	3.49885i
$716$	15.6974	+	44.8899i	0.586641	+	1.67761i
$717$		0			0
$718$	−16.9978	−	12.0632i	−0.634353	−	0.450194i
$719$	−10.8608			−0.405040			−0.202520	−	0.979278i	$-0.564913\pi$
$719$	−10.8608			−0.405040			−0.202520	+	0.979278i	$0.564913\pi$
$720$		0			0
$721$	−4.91320			−0.182977
$722$	1.15329	+	0.818482i	0.0429212	+	0.0304607i
$723$		0			0
$724$	7.22496	+	20.6612i	0.268514	+	0.767867i
$725$			14.0408i			0.521463i
$726$		0			0
$727$		−	4.93274i		−	0.182945i	−0.995808	−	0.0914726i	$-0.970843\pi$
$727$		−	4.93274i		−	0.182945i	0.995808	−	0.0914726i	$-0.0291574\pi$
$728$	−3.63755	−	1.04916i	−0.134816	−	0.0388844i
$729$		0			0
$730$	12.8621	−	18.1236i	0.476049	−	0.670784i
$731$	−0.591454			−0.0218757
$732$		0			0
$733$	−14.6668			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$733$	−14.6668			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$734$	−10.8132	+	15.2365i	−0.399123	+	0.562391i
$735$		0			0
$736$	−25.0289	+	1.39287i	−0.922579	+	0.0513418i
$737$			45.8877i			1.69030i
$738$		0			0
$739$			27.7975i			1.02255i	0.859418	+	0.511273i	$0.170826\pi$
$739$			27.7975i			1.02255i	−0.859418	+	0.511273i	$0.829174\pi$
$740$	48.5998	−	16.9948i	1.78657	−	0.624740i
$741$		0			0
$742$	4.52205	+	3.20926i	0.166010	+	0.117815i
$743$	−3.47030			−0.127313			−0.0636566	−	0.997972i	$-0.520276\pi$
$743$	−3.47030			−0.127313			−0.0636566	+	0.997972i	$0.520276\pi$
$744$		0			0
$745$	48.2978			1.76950
$746$	−7.16225	−	5.08298i	−0.262229	−	0.186101i
$747$		0			0
$748$	−30.4988	+	10.6650i	−1.11515	+	0.389953i
$749$			5.39639i			0.197180i
$750$		0			0
$751$			9.96665i			0.363688i	0.983327	+	0.181844i	$0.0582066\pi$
$751$			9.96665i			0.363688i	−0.983327	+	0.181844i	$0.941793\pi$
$752$	29.5612	−	23.5547i	1.07799	−	0.858951i
$753$		0			0
$754$	−5.72484	+	8.06668i	−0.208487	+	0.293771i
$755$	−76.7236			−2.79226
$756$		0			0
$757$	11.8945			0.432314			0.216157	−	0.976359i	$-0.430648\pi$
$757$	11.8945			0.432314			0.216157	+	0.976359i	$0.430648\pi$
$758$	−0.366058	+	0.515799i	−0.0132958	+	0.0187347i
$759$		0			0
$760$	−2.86796	+	9.94354i	−0.104032	+	0.360690i
$761$		−	5.81871i		−	0.210928i	−0.994423	−	0.105464i	$-0.966367\pi$
$761$		−	5.81871i		−	0.210928i	0.994423	−	0.105464i	$-0.0336328\pi$
$762$		0			0
$763$			0.559747i			0.0202642i
$764$	−13.8104	−	39.4935i	−0.499642	−	1.42882i
$765$		0			0
$766$	−24.7048	−	17.5328i	−0.892621	−	0.633485i
$767$	23.5807			0.851448
$768$		0			0
$769$	1.13881			0.0410667			0.0205333	−	0.999789i	$-0.493464\pi$
$769$	1.13881			0.0410667			0.0205333	+	0.999789i	$0.493464\pi$
$770$	8.27282	+	5.87114i	0.298132	+	0.211581i
$771$		0			0
$772$	7.97112	+	22.7950i	0.286887	+	0.820410i
$773$		−	1.09374i		−	0.0393389i	−0.999807	−	0.0196695i	$-0.993739\pi$
$773$		−	1.09374i		−	0.0393389i	0.999807	−	0.0196695i	$-0.00626139\pi$
$774$		0			0
$775$			11.7325i			0.421442i
$776$	0.837142	−	2.90246i	0.0300516	−	0.104192i
$777$		0			0
$778$	9.01201	−	12.6985i	0.323096	−	0.455264i
$779$	−7.88710			−0.282585
$780$		0			0
$781$	23.3607			0.835912
$782$	−9.57441	+	13.4910i	−0.342380	+	0.482436i
$783$		0			0
$784$	−21.5773	+	17.1930i	−0.770618	+	0.614037i
$785$		−	15.3233i		−	0.546912i
$786$		0			0
$787$			7.78108i			0.277366i	0.990337	+	0.138683i	$0.0442868\pi$
$787$			7.78108i			0.277366i	−0.990337	+	0.138683i	$0.955713\pi$
$788$	−27.6377	+	9.66455i	−0.984552	+	0.344286i
$789$		0			0
$790$	−16.1453	−	11.4582i	−0.574426	−	0.407664i
$791$	2.54816			0.0906020
$792$		0			0
$793$	−23.9808			−0.851583
$794$	34.9876	+	24.8304i	1.24166	+	0.881197i
$795$		0			0
$796$	−36.7417	+	12.8481i	−1.30227	+	0.455389i
$797$			19.6145i			0.694781i	0.937721	+	0.347390i	$0.112932\pi$
$797$			19.6145i			0.694781i	−0.937721	+	0.347390i	$0.887068\pi$
$798$		0			0
$799$		−	24.9444i		−	0.882469i
$800$	−47.3730	+	2.63633i	−1.67489	+	0.0932082i
$801$		0			0
$802$	−4.17497	+	5.88281i	−0.147423	+	0.207729i
$803$	−26.2842			−0.927551
$804$		0			0
$805$	5.19413			0.183069
$806$	−4.78366	+	6.74049i	−0.168497	+	0.237423i
$807$		0			0
$808$	−5.94454	−	1.71455i	−0.209128	−	0.0603177i
$809$			12.9082i			0.453829i	0.973915	+	0.226914i	$0.0728637\pi$
$809$			12.9082i			0.453829i	−0.973915	+	0.226914i	$0.927136\pi$
$810$		0			0
$811$		−	42.2798i		−	1.48465i	−0.670042	−	0.742323i	$-0.733724\pi$
$811$		−	42.2798i		−	1.48465i	0.670042	−	0.742323i	$-0.266276\pi$
$812$	−0.354038	−	1.01244i	−0.0124243	−	0.0355297i
$813$		0			0
$814$	−49.6578	−	35.2416i	−1.74050	−	1.23522i
$815$	−53.2320			−1.86464
$816$		0			0
$817$	0.224056			0.00783873
$818$	24.7670	+	17.5769i	0.865959	+	0.614562i
$819$		0			0
$820$	−19.0513	−	54.4810i	−0.665301	−	1.90256i
$821$		−	23.6258i		−	0.824545i	−0.911061	−	0.412272i	$-0.864735\pi$
$821$		−	23.6258i		−	0.824545i	0.911061	−	0.412272i	$-0.135265\pi$
$822$		0			0
$823$		−	17.8728i		−	0.623008i	−0.950245	−	0.311504i	$-0.899167\pi$
$823$		−	17.8728i		−	0.623008i	0.950245	−	0.311504i	$-0.100833\pi$
$824$	−41.6804	−	12.0216i	−1.45201	−	0.418794i
$825$		0			0
$826$	−1.47979	+	2.08512i	−0.0514885	+	0.0725507i
$827$	55.8298			1.94139			0.970696	−	0.240310i	$-0.0772491\pi$
$827$	55.8298			1.94139			0.970696	+	0.240310i	$0.0772491\pi$
$828$		0			0
$829$	−21.2326			−0.737438			−0.368719	−	0.929541i	$-0.620204\pi$
$829$	−21.2326			−0.737438			−0.368719	+	0.929541i	$0.620204\pi$
$830$	50.0512	−	70.5254i	1.73730	−	2.44797i
$831$		0			0
$832$	−28.2915	−	17.8007i	−0.980831	−	0.617129i
$833$			18.2074i			0.630849i
$834$		0			0
$835$		−	43.3381i		−	1.49978i
$836$	11.5536	−	4.04016i	0.399591	−	0.139732i
$837$		0			0
$838$	9.05377	+	6.42537i	0.312757	+	0.221961i
$839$	47.9139			1.65417			0.827086	−	0.562075i	$-0.189997\pi$
$839$	47.9139			1.65417			0.827086	+	0.562075i	$0.189997\pi$
$840$		0			0
$841$	26.1976			0.903366
$842$	−15.1824	−	10.7748i	−0.523221	−	0.371325i
$843$		0			0
$844$	4.85796	−	1.69877i	0.167218	−	0.0584741i
$845$		−	16.3092i		−	0.561052i
$846$		0			0
$847$		−	8.47403i		−	0.291171i
$848$	30.5097	+	38.2898i	1.04771	+	1.31488i
$849$		0			0
$850$	−18.1218	+	25.5348i	−0.621572	+	0.875835i
$851$	−31.1779			−1.06876
$852$		0			0
$853$	4.04321			0.138437			0.0692185	−	0.997602i	$-0.477949\pi$
$853$	4.04321			0.138437			0.0692185	+	0.997602i	$0.477949\pi$
$854$	1.50490	−	2.12050i	0.0514967	−	0.0725622i
$855$		0			0
$856$	−13.2039	+	45.7794i	−0.451300	+	1.56471i
$857$			0.834726i			0.0285137i	0.999898	+	0.0142569i	$0.00453825\pi$
$857$			0.834726i			0.0285137i	−0.999898	+	0.0142569i	$0.995462\pi$
$858$		0			0
$859$			24.0610i			0.820949i	0.911872	+	0.410475i	$0.134637\pi$
$859$			24.0610i			0.820949i	−0.911872	+	0.410475i	$0.865363\pi$
$860$	0.541208	+	1.54769i	0.0184550	+	0.0527758i
$861$		0			0
$862$	−11.5811	−	8.21897i	−0.394453	−	0.279939i
$863$	11.6872			0.397838			0.198919	−	0.980016i	$-0.436257\pi$
$863$	11.6872			0.397838			0.198919	+	0.980016i	$0.436257\pi$
$864$		0			0
$865$	39.8833			1.35607
$866$	9.69392	+	6.87968i	0.329413	+	0.233781i
$867$		0			0
$868$	−0.295833	−	0.845991i	−0.0100412	−	0.0287148i
$869$			23.4152i			0.794307i
$870$		0			0
$871$			31.3290i			1.06154i
$872$	−1.36959	+	4.74853i	−0.0463803	+	0.160806i
$873$		0			0
$874$	3.62700	−	5.11069i	0.122685	−	0.172872i
$875$	3.97047			0.134226
$876$		0			0
$877$	−41.2068			−1.39145			−0.695727	−	0.718306i	$-0.744918\pi$
$877$	−41.2068			−1.39145			−0.695727	+	0.718306i	$0.744918\pi$
$878$	3.87870	−	5.46535i	0.130900	−	0.184447i
$879$		0			0
$880$	55.8157	+	70.0489i	1.88155	+	2.36135i
$881$		−	52.0626i		−	1.75403i	−0.480461	−	0.877016i	$-0.659531\pi$
$881$		−	52.0626i		−	1.75403i	0.480461	−	0.877016i	$-0.340469\pi$
$882$		0			0
$883$			14.2067i			0.478094i	0.971008	+	0.239047i	$0.0768349\pi$
$883$			14.2067i			0.478094i	−0.971008	+	0.239047i	$0.923165\pi$
$884$	−20.8225	+	7.28137i	−0.700337	+	0.244899i
$885$		0			0
$886$	24.3264	+	17.2642i	0.817263	+	0.580003i
$887$	9.89973			0.332401			0.166200	−	0.986092i	$-0.446850\pi$
$887$	9.89973			0.332401			0.166200	+	0.986092i	$0.446850\pi$
$888$		0			0
$889$	0.960904			0.0322277
$890$	−71.9315	−	51.0491i	−2.41115	−	1.71117i
$891$		0			0
$892$	−25.4082	+	8.88493i	−0.850729	+	0.297489i
$893$			9.44950i			0.316215i
$894$		0			0
$895$		−	86.9997i		−	2.90808i
$896$	3.34945	−	1.38460i	0.111897	−	0.0462564i
$897$		0			0
$898$	30.3611	−	42.7808i	1.01316	−	1.42761i
$899$	−2.34167			−0.0780991
$900$		0			0
$901$	32.3097			1.07639
$902$	−39.5063	+	55.6669i	−1.31542	+	1.85351i
$903$		0			0
$904$	21.6169	+	6.23484i	0.718967	+	0.207368i
$905$		−	40.0428i		−	1.33107i
$906$		0			0
$907$			28.6983i			0.952910i	0.879199	+	0.476455i	$0.158079\pi$
$907$			28.6983i			0.952910i	−0.879199	+	0.476455i	$0.841921\pi$
$908$	−12.7540	−	36.4726i	−0.423257	−	1.21039i
$909$		0			0
$910$	5.64812	+	4.00842i	0.187233	+	0.132878i
$911$	−41.4871			−1.37453			−0.687264	−	0.726407i	$-0.741189\pi$
$911$	−41.4871			−1.37453			−0.687264	+	0.726407i	$0.741189\pi$
$912$		0			0
$913$	−102.281			−3.38502
$914$	−27.4453	−	19.4776i	−0.907809	−	0.644263i
$915$		0			0
$916$	−3.35776	−	9.60218i	−0.110944	−	0.317265i
$917$		−	2.88732i		−	0.0953478i
$918$		0			0
$919$		−	48.2208i		−	1.59066i	−0.606179	−	0.795328i	$-0.707298\pi$
$919$		−	48.2208i		−	1.59066i	0.606179	−	0.795328i	$-0.292702\pi$
$920$	44.0636	+	12.7090i	1.45273	+	0.419004i
$921$		0			0
$922$	13.3942	−	18.8734i	0.441116	−	0.621561i
$923$	15.9491			0.524971
$924$		0			0
$925$	−59.0113			−1.94028
$926$	15.0242	−	21.1700i	0.493725	−	0.695690i
$927$		0			0
$928$	−0.526182	−	9.45515i	−0.0172728	−	0.310380i
$929$		−	22.8789i		−	0.750632i	−0.926897	−	0.375316i	$-0.877534\pi$
$929$		−	22.8789i		−	0.750632i	0.926897	−	0.375316i	$-0.122466\pi$
$930$		0			0
$931$		−	6.89738i		−	0.226052i
$932$	−0.748275	+	0.261662i	−0.0245105	+	0.00857103i
$933$		0			0
$934$	28.6688	+	20.3460i	0.938071	+	0.665740i
$935$	59.1088			1.93306
$936$		0			0
$937$	32.0857			1.04819			0.524096	−	0.851659i	$-0.324403\pi$
$937$	32.0857			1.04819			0.524096	+	0.851659i	$0.324403\pi$
$938$	−2.77027	−	1.96604i	−0.0904527	−	0.0641934i
$939$		0			0
$940$	−65.2734	+	22.8253i	−2.12898	+	0.744479i
$941$			16.7654i			0.546536i	0.961938	+	0.273268i	$0.0881046\pi$
$941$			16.7654i			0.546536i	−0.961938	+	0.273268i	$0.911895\pi$
$942$		0			0
$943$			34.9508i			1.13815i
$944$	−17.6555	+	14.0681i	−0.574637	+	0.457876i
$945$		0			0
$946$	1.12229	−	1.58138i	0.0364888	−	0.0514151i
$947$	4.30581			0.139920			0.0699601	−	0.997550i	$-0.477713\pi$
$947$	4.30581			0.139920			0.0699601	+	0.997550i	$0.477713\pi$
$948$		0			0
$949$	−17.9451			−0.582523
$950$	6.86494	−	9.67315i	0.222728	−	0.313838i
$951$		0			0
$952$	0.662849	−	2.29817i	0.0214831	−	0.0744842i
$953$		−	42.6831i		−	1.38264i	−0.722548	−	0.691321i	$-0.757029\pi$
$953$		−	42.6831i		−	1.38264i	0.722548	−	0.691321i	$-0.242971\pi$
$954$		0			0
$955$			76.5411i			2.47681i
$956$	10.3250	+	29.5263i	0.333933	+	0.954948i
$957$		0			0
$958$	−23.6143	−	16.7589i	−0.762945	−	0.541454i
$959$	4.63933			0.149812
$960$		0			0
$961$	29.0433			0.936881
$962$	−33.9030	−	24.0606i	−1.09308	−	0.775745i
$963$		0			0
$964$	−1.41667	−	4.05125i	−0.0456280	−	0.130482i
$965$		−	44.1782i		−	1.42215i
$966$		0			0
$967$		−	11.6416i		−	0.374367i	−0.982325	−	0.187184i	$-0.940064\pi$
$967$		−	11.6416i		−	0.374367i	0.982325	−	0.187184i	$-0.0599359\pi$
$968$	20.7343	−	71.8882i	0.666426	−	2.31057i
$969$		0			0
$970$	−3.19839	+	4.50674i	−0.102694	+	0.144703i
$971$	38.1563			1.22449			0.612247	−	0.790667i	$-0.290266\pi$
$971$	38.1563			1.22449			0.612247	+	0.790667i	$0.290266\pi$
$972$		0			0
$973$	4.12123			0.132121
$974$	−11.0518	+	15.5727i	−0.354122	+	0.498981i
$975$		0			0
$976$	17.9551	−	14.3068i	0.574728	−	0.457949i
$977$			15.5483i			0.497433i	0.968576	+	0.248717i	$0.0800088\pi$
$977$			15.5483i			0.497433i	−0.968576	+	0.248717i	$0.919991\pi$
$978$		0			0
$979$			104.321i			3.33410i
$980$	47.6443	−	16.6606i	1.52194	−	0.532204i
$981$		0			0
$982$	34.0576	+	24.1704i	1.08682	+	0.771308i
$983$	5.80391			0.185116			0.0925580	−	0.995707i	$-0.470496\pi$
$983$	5.80391			0.185116			0.0925580	+	0.995707i	$0.470496\pi$
$984$		0			0
$985$	53.5637			1.70668
$986$	−5.09646	−	3.61691i	−0.162304	−	0.115186i
$987$		0			0
$988$	7.88804	−	2.75835i	0.250952	−	0.0877548i
$989$		−	0.992878i		−	0.0315717i
$990$		0			0
$991$			15.4048i			0.489351i	0.969605	+	0.244675i	$0.0786814\pi$
$991$			15.4048i			0.489351i	−0.969605	+	0.244675i	$0.921319\pi$
$992$	−0.439676	−	7.90068i	−0.0139597	−	0.250847i
$993$		0			0
$994$	−1.00088	+	1.41030i	−0.0317459	+	0.0447321i
$995$	71.2079			2.25744
$996$		0			0
$997$	−58.7741			−1.86139			−0.930697	−	0.365791i	$-0.880798\pi$
$997$	−58.7741			−1.86139			−0.930697	+	0.365791i	$0.880798\pi$
$998$	20.3711	−	28.7042i	0.644836	−	0.908615i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.7	✓	32
3.2	odd	2	inner	684.2.c.b.647.26	yes	32
4.3	odd	2	inner	684.2.c.b.647.25	yes	32
12.11	even	2	inner	684.2.c.b.647.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.7	✓	32	1.1	even	1	trivial
684.2.c.b.647.8	yes	32	12.11	even	2	inner
684.2.c.b.647.25	yes	32	4.3	odd	2	inner
684.2.c.b.647.26	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)

\(f(q)\)	\(=\)	\(q+(-1.15329 - 0.818482i) q^{2} +(0.660175 + 1.88790i) q^{4} -3.65888i q^{5} -0.320351i q^{7} +(0.783836 - 2.71765i) q^{8} +O(q^{10})\)	\(q+(-1.15329 - 0.818482i) q^{2} +(0.660175 + 1.88790i) q^{4} -3.65888i q^{5} -0.320351i q^{7} +(0.783836 - 2.71765i) q^{8} +(-2.99473 + 4.21977i) q^{10} +6.11983 q^{11} +4.17821 q^{13} +(-0.262201 + 0.369459i) q^{14} +(-3.12834 + 2.49269i) q^{16} +2.63976i q^{17} -1.00000i q^{19} +(6.90760 - 2.41550i) q^{20} +(-7.05797 - 5.00897i) q^{22} -4.43138 q^{23} -8.38741 q^{25} +(-4.81870 - 3.41979i) q^{26} +(0.604790 - 0.211488i) q^{28} -1.67404i q^{29} -1.39882i q^{31} +(5.64812 - 0.314319i) q^{32} +(2.16059 - 3.04442i) q^{34} -1.17213 q^{35} +7.03570 q^{37} +(-0.818482 + 1.15329i) q^{38} +(-9.94354 - 2.86796i) q^{40} -7.88710i q^{41} +0.224056i q^{43} +(4.04016 + 11.5536i) q^{44} +(5.11069 + 3.62700i) q^{46} -9.44950 q^{47} +6.89738 q^{49} +(9.67315 + 6.86494i) q^{50} +(2.75835 + 7.88804i) q^{52} -12.2397i q^{53} -22.3917i q^{55} +(-0.870600 - 0.251102i) q^{56} +(-1.37017 + 1.93066i) q^{58} +5.64373 q^{59} -5.73949 q^{61} +(-1.14491 + 1.61325i) q^{62} +(-6.77120 - 4.26038i) q^{64} -15.2876i q^{65} +7.49820i q^{67} +(-4.98360 + 1.74270i) q^{68} +(1.35181 + 0.959363i) q^{70} +3.81721 q^{71} -4.29493 q^{73} +(-8.11424 - 5.75859i) q^{74} +(1.88790 - 0.660175i) q^{76} -1.96049i q^{77} +3.82612i q^{79} +(9.12046 + 11.4462i) q^{80} +(-6.45545 + 9.09615i) q^{82} -16.7131 q^{83} +9.65856 q^{85} +(0.183386 - 0.258403i) q^{86} +(4.79694 - 16.6315i) q^{88} +17.0463i q^{89} -1.33849i q^{91} +(-2.92549 - 8.36600i) q^{92} +(10.8981 + 7.73424i) q^{94} -3.65888 q^{95} +1.06801 q^{97} +(-7.95470 - 5.64538i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 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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