LMFDB - Embedded newform 684.2.l.a.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(121,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("684.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.6
Character	$\chi$	$=$	684.277
Dual form			684.2.l.a.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04626 + 1.38034i) q^{3} -2.40565 q^{5} +(-1.53172 + 2.65301i) q^{7} +(-0.810664 - 2.88839i) q^{9} +(-2.96810 + 5.14089i) q^{11} +(2.81967 - 4.88381i) q^{13} +(2.51694 - 3.32060i) q^{15} +(1.15507 - 2.00063i) q^{17} +(1.16718 - 4.19973i) q^{19} +(-2.05947 - 4.89004i) q^{21} +(-0.654760 + 1.13408i) q^{23} +0.787132 q^{25} +(4.83513 + 1.90303i) q^{27} +6.77137 q^{29} +(-4.86166 - 8.42064i) q^{31} +(-3.99076 - 9.47571i) q^{33} +(3.68477 - 6.38221i) q^{35} -2.91406 q^{37} +(3.79119 + 9.00185i) q^{39} -3.91785 q^{41} +(-0.0602912 - 0.104427i) q^{43} +(1.95017 + 6.94845i) q^{45} -10.0218 q^{47} +(-1.19232 - 2.06516i) q^{49} +(1.55305 + 3.68757i) q^{51} +(-4.85905 - 8.41612i) q^{53} +(7.14019 - 12.3672i) q^{55} +(4.57586 + 6.00512i) q^{57} +8.36293 q^{59} +9.94221 q^{61} +(8.90466 + 2.27350i) q^{63} +(-6.78312 + 11.7487i) q^{65} +(5.03862 - 8.72714i) q^{67} +(-0.880358 - 2.09033i) q^{69} +(-1.00262 + 1.73659i) q^{71} +(-4.09931 + 7.10022i) q^{73} +(-0.823547 + 1.08651i) q^{75} +(-9.09258 - 15.7488i) q^{77} +(-5.70591 - 9.88293i) q^{79} +(-7.68565 + 4.68303i) q^{81} +(-2.77092 + 4.79938i) q^{83} +(-2.77868 + 4.81282i) q^{85} +(-7.08464 + 9.34678i) q^{87} +(-4.48313 - 7.76501i) q^{89} +(8.63788 + 14.9612i) q^{91} +(16.7099 + 2.09948i) q^{93} +(-2.80781 + 10.1031i) q^{95} +(-3.43051 - 5.94182i) q^{97} +(17.2551 + 4.40550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) $ 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.04626	+	1.38034i	−0.604061	+	0.796938i
$3$	−1.04626	+	1.38034i	−0.604061	+	0.796938i
$4$		0			0
$5$	−2.40565			−1.07584			−0.537919	−	0.842997i	$-0.680789\pi$
$5$	−2.40565			−1.07584			−0.537919	+	0.842997i	$0.680789\pi$
$6$		0			0
$7$	−1.53172	+	2.65301i	−0.578935	+	1.00275i	0.416667	+	0.909059i	$0.363198\pi$
$7$	−1.53172	+	2.65301i	−0.578935	+	1.00275i	−0.995602	+	0.0936857i	$0.970135\pi$
$8$		0			0
$9$	−0.810664	−	2.88839i	−0.270221	−	0.962798i
$10$		0			0
$11$	−2.96810	+	5.14089i	−0.894915	+	1.55004i	−0.0610046	+	0.998137i	$0.519430\pi$
$11$	−2.96810	+	5.14089i	−0.894915	+	1.55004i	−0.833910	+	0.551900i	$0.813903\pi$
$12$		0			0
$13$	2.81967	−	4.88381i	0.782035	−	1.35453i	−0.148719	−	0.988880i	$-0.547515\pi$
$13$	2.81967	−	4.88381i	0.782035	−	1.35453i	0.930754	−	0.365646i	$-0.119152\pi$
$14$		0			0
$15$	2.51694	−	3.32060i	0.649871	−	0.857376i
$16$		0			0
$17$	1.15507	−	2.00063i	0.280145	−	0.485225i	−0.691275	−	0.722591i	$-0.742951\pi$
$17$	1.15507	−	2.00063i	0.280145	−	0.485225i	0.971420	+	0.237366i	$0.0762841\pi$
$18$		0			0
$19$	1.16718	−	4.19973i	0.267769	−	0.963483i
$19$	1.16718	−	4.19973i	0.267769	−	0.963483i
$20$		0			0
$21$	−2.05947	−	4.89004i	−0.449414	−	1.06709i
$22$		0			0
$23$	−0.654760	+	1.13408i	−0.136527	+	0.236472i	−0.926180	−	0.377082i	$-0.876927\pi$
$23$	−0.654760	+	1.13408i	−0.136527	+	0.236472i	0.789653	+	0.613554i	$0.210261\pi$
$24$		0			0
$25$	0.787132			0.157426
$26$		0			0
$27$	4.83513	+	1.90303i	0.930521	+	0.366239i
$28$		0			0
$29$	6.77137			1.25741			0.628706	−	0.777643i	$-0.283585\pi$
$29$	6.77137			1.25741			0.628706	+	0.777643i	$0.283585\pi$
$30$		0			0
$31$	−4.86166	−	8.42064i	−0.873179	−	1.51239i	−0.858690	−	0.512496i	$-0.828721\pi$
$31$	−4.86166	−	8.42064i	−0.873179	−	1.51239i	−0.0144895	−	0.999895i	$-0.504612\pi$
$32$		0			0
$33$	−3.99076	−	9.47571i	−0.694702	−	1.64951i
$34$		0			0
$35$	3.68477	−	6.38221i	0.622840	−	1.07879i
$36$		0			0
$37$	−2.91406			−0.479068			−0.239534	−	0.970888i	$-0.576995\pi$
$37$	−2.91406			−0.479068			−0.239534	+	0.970888i	$0.576995\pi$
$38$		0			0
$39$	3.79119	+	9.00185i	0.607076	+	1.44145i
$40$		0			0
$41$	−3.91785			−0.611866			−0.305933	−	0.952053i	$-0.598968\pi$
$41$	−3.91785			−0.611866			−0.305933	+	0.952053i	$0.598968\pi$
$42$		0			0
$43$	−0.0602912	−	0.104427i	−0.00919432	−	0.0159250i	0.861392	−	0.507941i	$-0.169593\pi$
$43$	−0.0602912	−	0.104427i	−0.00919432	−	0.0159250i	−0.870586	+	0.492016i	$0.836260\pi$
$44$		0			0
$45$	1.95017	+	6.94845i	0.290714	+	1.03581i
$46$		0			0
$47$	−10.0218			−1.46184			−0.730918	−	0.682466i	$-0.760908\pi$
$47$	−10.0218			−1.46184			−0.730918	+	0.682466i	$0.760908\pi$
$48$		0			0
$49$	−1.19232	−	2.06516i	−0.170332	−	0.295023i
$50$		0			0
$51$	1.55305	+	3.68757i	0.217470	+	0.516364i
$52$		0			0
$53$	−4.85905	−	8.41612i	−0.667442	−	1.15604i	−0.978617	−	0.205690i	$-0.934056\pi$
$53$	−4.85905	−	8.41612i	−0.667442	−	1.15604i	0.311176	−	0.950352i	$-0.399277\pi$
$54$		0			0
$55$	7.14019	−	12.3672i	0.962783	−	1.66759i
$56$		0			0
$57$	4.57586	+	6.00512i	0.606088	+	0.795398i
$58$		0			0
$59$	8.36293			1.08876			0.544381	−	0.838838i	$-0.316765\pi$
$59$	8.36293			1.08876			0.544381	+	0.838838i	$0.316765\pi$
$60$		0			0
$61$	9.94221			1.27297			0.636485	−	0.771289i	$-0.280388\pi$
$61$	9.94221			1.27297			0.636485	+	0.771289i	$0.280388\pi$
$62$		0			0
$63$	8.90466	+	2.27350i	1.12188	+	0.286435i
$64$		0			0
$65$	−6.78312	+	11.7487i	−0.841343	+	1.45725i
$66$		0			0
$67$	5.03862	−	8.72714i	0.615565	−	1.06619i	−0.374720	−	0.927138i	$-0.622261\pi$
$67$	5.03862	−	8.72714i	0.615565	−	1.06619i	0.990285	−	0.139052i	$-0.0444055\pi$
$68$		0			0
$69$	−0.880358	−	2.09033i	−0.105983	−	0.251647i
$70$		0			0
$71$	−1.00262	+	1.73659i	−0.118989	+	0.206095i	−0.919367	−	0.393400i	$-0.871299\pi$
$71$	−1.00262	+	1.73659i	−0.118989	+	0.206095i	0.800378	+	0.599495i	$0.204632\pi$
$72$		0			0
$73$	−4.09931	+	7.10022i	−0.479788	+	0.831018i	−0.999731	−	0.0231832i	$-0.992620\pi$
$73$	−4.09931	+	7.10022i	−0.479788	+	0.831018i	0.519943	+	0.854201i	$0.325953\pi$
$74$		0			0
$75$	−0.823547	+	1.08651i	−0.0950951	+	0.125459i
$76$		0			0
$77$	−9.09258	−	15.7488i	−1.03620	−	1.79474i
$78$		0			0
$79$	−5.70591	−	9.88293i	−0.641965	−	1.11192i	−0.984994	−	0.172591i	$-0.944786\pi$
$79$	−5.70591	−	9.88293i	−0.641965	−	1.11192i	0.343028	−	0.939325i	$-0.388547\pi$
$80$		0			0
$81$	−7.68565	+	4.68303i	−0.853961	+	0.520337i
$82$		0			0
$83$	−2.77092	+	4.79938i	−0.304148	+	0.526800i	−0.977071	−	0.212912i	$-0.931705\pi$
$83$	−2.77092	+	4.79938i	−0.304148	+	0.526800i	0.672923	+	0.739712i	$0.265038\pi$
$84$		0			0
$85$	−2.77868	+	4.81282i	−0.301390	+	0.522023i
$86$		0			0
$87$	−7.08464	+	9.34678i	−0.759553	+	1.00208i
$88$		0			0
$89$	−4.48313	−	7.76501i	−0.475211	−	0.823089i	0.524386	−	0.851481i	$-0.324295\pi$
$89$	−4.48313	−	7.76501i	−0.475211	−	0.823089i	−0.999597	+	0.0283913i	$0.990962\pi$
$90$		0			0
$91$	8.63788	+	14.9612i	0.905496	+	1.56836i
$92$		0			0
$93$	16.7099	+	2.09948i	1.73274	+	0.217706i
$94$		0			0
$95$	−2.80781	+	10.1031i	−0.288076	+	1.03655i
$96$		0			0
$97$	−3.43051	−	5.94182i	−0.348316	−	0.603301i	0.637635	−	0.770339i	$-0.279913\pi$
$97$	−3.43051	−	5.94182i	−0.348316	−	0.603301i	−0.985950	+	0.167038i	$0.946580\pi$
$98$		0			0
$99$	17.2551	+	4.40550i	1.73420	+	0.442769i
$100$		0			0
$101$	−6.49379			−0.646157			−0.323078	−	0.946372i	$-0.604718\pi$
$101$	−6.49379			−0.646157			−0.323078	+	0.946372i	$0.604718\pi$
$102$		0			0
$103$	4.46179	+	7.72805i	0.439634	+	0.761468i	0.997661	−	0.0683548i	$-0.0217750\pi$
$103$	4.46179	+	7.72805i	0.439634	+	0.761468i	−0.558028	+	0.829822i	$0.688442\pi$
$104$		0			0
$105$	4.95436	+	11.7637i	0.483496	+	1.14802i
$106$		0			0
$107$	−13.2084			−1.27690			−0.638451	−	0.769662i	$-0.720425\pi$
$107$	−13.2084			−1.27690			−0.638451	+	0.769662i	$0.720425\pi$
$108$		0			0
$109$	−6.42890	+	11.1352i	−0.615777	+	1.06656i	0.374471	+	0.927239i	$0.377824\pi$
$109$	−6.42890	+	11.1352i	−0.615777	+	1.06656i	−0.990248	+	0.139318i	$0.955509\pi$
$110$		0			0
$111$	3.04887	−	4.02238i	0.289386	−	0.381788i
$112$		0			0
$113$	2.97088	+	5.14571i	0.279477	+	0.484068i	0.971255	−	0.238042i	$-0.0765057\pi$
$113$	2.97088	+	5.14571i	0.279477	+	0.484068i	−0.691778	+	0.722110i	$0.743172\pi$
$114$		0			0
$115$	1.57512	−	2.72819i	0.146881	−	0.254405i
$116$		0			0
$117$	−16.3922	−	4.18519i	−1.51546	−	0.386921i
$118$		0			0
$119$	3.53847	+	6.12882i	0.324371	+	0.561828i
$120$		0			0
$121$	−12.1192	−	20.9911i	−1.10174	−	1.90828i
$122$		0			0
$123$	4.09911	−	5.40796i	0.369604	−	0.487619i
$124$		0			0
$125$	10.1347			0.906472
$126$		0			0
$127$	−1.27031	−	2.20024i	−0.112722	−	0.195240i	0.804145	−	0.594433i	$-0.202624\pi$
$127$	−1.27031	−	2.20024i	−0.112722	−	0.195240i	−0.916867	+	0.399193i	$0.869290\pi$
$128$		0			0
$129$	0.207226	+	0.0260364i	0.0182452	+	0.00229238i
$130$		0			0
$131$	−5.23943			−0.457771			−0.228886	−	0.973453i	$-0.573508\pi$
$131$	−5.23943			−0.457771			−0.228886	+	0.973453i	$0.573508\pi$
$132$		0			0
$133$	9.35415	+	9.52933i	0.811107	+	0.826298i
$134$		0			0
$135$	−11.6316	−	4.57802i	−1.00109	−	0.394014i
$136$		0			0
$137$	−15.7623			−1.34667			−0.673333	−	0.739339i	$-0.735138\pi$
$137$	−15.7623			−1.34667			−0.673333	+	0.739339i	$0.735138\pi$
$138$		0			0
$139$	−4.62283	+	8.00698i	−0.392104	+	0.679144i	−0.992727	−	0.120389i	$-0.961586\pi$
$139$	−4.62283	+	8.00698i	−0.392104	+	0.679144i	0.600623	+	0.799532i	$0.294919\pi$
$140$		0			0
$141$	10.4855	−	13.8335i	0.883037	−	1.16499i
$142$		0			0
$143$	16.7381	+	28.9912i	1.39971	+	2.42437i
$144$		0			0
$145$	−16.2895			−1.35277
$146$		0			0
$147$	4.09811	+	0.514898i	0.338006	+	0.0424681i
$148$		0			0
$149$	−4.19966			−0.344049			−0.172025	−	0.985093i	$-0.555031\pi$
$149$	−4.19966			−0.344049			−0.172025	+	0.985093i	$0.555031\pi$
$150$		0			0
$151$	0.904477	−	1.56660i	0.0736053	−	0.127488i	−0.826874	−	0.562388i	$-0.809883\pi$
$151$	0.904477	−	1.56660i	0.0736053	−	0.127488i	0.900479	+	0.434900i	$0.143216\pi$
$152$		0			0
$153$	−6.71499	−	1.71445i	−0.542875	−	0.138605i
$154$		0			0
$155$	11.6954	+	20.2571i	0.939399	+	1.62709i
$156$		0			0
$157$	16.9966			1.35648			0.678240	−	0.734840i	$-0.262743\pi$
$157$	16.9966			1.35648			0.678240	+	0.734840i	$0.262743\pi$
$158$		0			0
$159$	16.7009	+	2.09835i	1.32447	+	0.166410i
$160$		0			0
$161$	−2.00582	−	3.47417i	−0.158080	−	0.273803i
$162$		0			0
$163$	−21.5075			−1.68459			−0.842297	−	0.539013i	$-0.818797\pi$
$163$	−21.5075			−1.68459			−0.842297	+	0.539013i	$0.818797\pi$
$164$		0			0
$165$	9.60035	+	22.7952i	0.747386	+	1.77460i
$166$		0			0
$167$	1.64867	−	2.85559i	0.127578	−	0.220972i	−0.795160	−	0.606400i	$-0.792613\pi$
$167$	1.64867	−	2.85559i	0.127578	−	0.220972i	0.922738	+	0.385428i	$0.125946\pi$
$168$		0			0
$169$	−9.40106	−	16.2831i	−0.723159	−	1.25255i
$170$		0			0
$171$	−13.0767	+	0.0332986i	−0.999997	+	0.00254641i
$172$		0			0
$173$	−6.99902	−	12.1227i	−0.532126	−	0.921669i	−0.999297	−	0.0375018i	$-0.988060\pi$
$173$	−6.99902	−	12.1227i	−0.532126	−	0.921669i	0.467171	−	0.884167i	$-0.345273\pi$
$174$		0			0
$175$	−1.20566	+	2.08827i	−0.0911396	+	0.157858i
$176$		0			0
$177$	−8.74984	+	11.5437i	−0.657678	+	0.867676i
$178$		0			0
$179$	8.09027			0.604695			0.302348	−	0.953198i	$-0.402230\pi$
$179$	8.09027			0.604695			0.302348	+	0.953198i	$0.402230\pi$
$180$		0			0
$181$	3.30463	+	5.72378i	0.245631	+	0.425446i	0.962309	−	0.271959i	$-0.0876715\pi$
$181$	3.30463	+	5.72378i	0.245631	+	0.425446i	−0.716678	+	0.697404i	$0.754338\pi$
$182$		0			0
$183$	−10.4022	+	13.7236i	−0.768951	+	1.01448i
$184$		0			0
$185$	7.01019			0.515399
$186$		0			0
$187$	6.85670	+	11.8762i	0.501412	+	0.868470i
$188$		0			0
$189$	−12.4548	+	9.91275i	−0.905955	+	0.721047i
$190$		0			0
$191$	9.09541	−	15.7537i	0.658121	−	1.13990i	−0.322981	−	0.946406i	$-0.604685\pi$
$191$	9.09541	−	15.7537i	0.658121	−	1.13990i	0.981102	−	0.193493i	$-0.0619818\pi$
$192$		0			0
$193$	−8.59739			−0.618853			−0.309427	−	0.950923i	$-0.600137\pi$
$193$	−8.59739			−0.618853			−0.309427	+	0.950923i	$0.600137\pi$
$194$		0			0
$195$	−9.12026	−	21.6553i	−0.653115	−	1.55077i
$196$		0			0
$197$	2.67567			0.190634			0.0953169	−	0.995447i	$-0.469614\pi$
$197$	2.67567			0.190634			0.0953169	+	0.995447i	$0.469614\pi$
$198$		0			0
$199$	−12.4456	−	21.5564i	−0.882245	−	1.52809i	−0.848839	−	0.528652i	$-0.822698\pi$
$199$	−12.4456	−	21.5564i	−0.882245	−	1.52809i	−0.0334064	−	0.999442i	$-0.510636\pi$
$200$		0			0
$201$	6.77468	+	16.0859i	0.477849	+	1.13461i
$202$		0			0
$203$	−10.3718	+	17.9645i	−0.727960	+	1.26086i
$204$		0			0
$205$	9.42496			0.658268
$206$		0			0
$207$	3.80645	+	0.971849i	0.264567	+	0.0675482i
$208$		0			0
$209$	18.1261	+	18.4655i	1.25381	+	1.27729i
$210$		0			0
$211$	12.9210			0.889517			0.444758	−	0.895651i	$-0.353290\pi$
$211$	12.9210			0.889517			0.444758	+	0.895651i	$0.353290\pi$
$212$		0			0
$213$	−1.34807	−	3.20088i	−0.0923684	−	0.219321i
$214$		0			0
$215$	0.145039	+	0.251215i	0.00989160	+	0.0171327i
$216$		0			0
$217$	29.7868			2.02206
$218$		0			0
$219$	−5.51174	−	13.0871i	−0.372449	−	0.884347i
$220$		0			0
$221$	−6.51381	−	11.2823i	−0.438166	−	0.758927i
$222$		0			0
$223$	9.89723	+	17.1425i	0.662768	+	1.14795i	0.979885	+	0.199561i	$0.0639516\pi$
$223$	9.89723	+	17.1425i	0.662768	+	1.14795i	−0.317118	+	0.948386i	$0.602715\pi$
$224$		0			0
$225$	−0.638099	−	2.27355i	−0.0425400	−	0.151570i
$226$		0			0
$227$	1.14847	−	1.98921i	0.0762267	−	0.132029i	−0.825392	−	0.564560i	$-0.809046\pi$
$227$	1.14847	−	1.98921i	0.0762267	−	0.132029i	0.901619	+	0.432531i	$0.142379\pi$
$228$		0			0
$229$	3.81796	+	6.61291i	0.252298	+	0.436993i	0.964158	−	0.265328i	$-0.0854803\pi$
$229$	3.81796	+	6.61291i	0.252298	+	0.436993i	−0.711860	+	0.702321i	$0.752147\pi$
$230$		0			0
$231$	31.2519	+	3.92658i	2.05622	+	0.258350i
$232$		0			0
$233$	−6.62451	+	11.4740i	−0.433986	+	0.751686i	−0.997212	−	0.0746170i	$-0.976227\pi$
$233$	−6.62451	+	11.4740i	−0.433986	+	0.751686i	0.563226	+	0.826303i	$0.309560\pi$
$234$		0			0
$235$	24.1090			1.57270
$236$		0			0
$237$	19.6117	+	2.46407i	1.27391	+	0.160058i
$238$		0			0
$239$	−10.3828	−	17.9835i	−0.671606	−	1.16326i	−0.977449	−	0.211174i	$-0.932271\pi$
$239$	−10.3828	−	17.9835i	−0.671606	−	1.16326i	0.305843	−	0.952082i	$-0.401062\pi$
$240$		0			0
$241$	7.53358			0.485281			0.242640	−	0.970116i	$-0.421987\pi$
$241$	7.53358			0.485281			0.242640	+	0.970116i	$0.421987\pi$
$242$		0			0
$243$	1.57705	−	15.5085i	0.101168	−	0.994869i
$244$		0			0
$245$	2.86830	+	4.96805i	0.183249	+	0.317397i
$246$		0			0
$247$	−17.2196	−	17.5421i	−1.09566	−	1.11618i
$248$		0			0
$249$	−3.72565	−	8.84622i	−0.236103	−	0.560607i
$250$		0			0
$251$	−11.4643	−	19.8567i	−0.723620	−	1.25335i	−0.959540	−	0.281574i	$-0.909144\pi$
$251$	−11.4643	−	19.8567i	−0.723620	−	1.25335i	0.235920	−	0.971773i	$-0.424190\pi$
$252$		0			0
$253$	−3.88678	−	6.73210i	−0.244360	−	0.423244i
$254$		0			0
$255$	−3.73608	−	8.87100i	−0.233962	−	0.555523i
$256$		0			0
$257$	−14.6036	+	25.2941i	−0.910945	+	1.57780i	−0.0982122	+	0.995165i	$0.531312\pi$
$257$	−14.6036	+	25.2941i	−0.910945	+	1.57780i	−0.812732	+	0.582637i	$0.802021\pi$
$258$		0			0
$259$	4.46351	−	7.73103i	0.277349	−	0.480383i
$260$		0			0
$261$	−5.48931	−	19.5584i	−0.339780	−	1.21063i
$262$		0			0
$263$	1.39551	+	2.41710i	0.0860510	+	0.149045i	0.905839	−	0.423623i	$-0.139242\pi$
$263$	1.39551	+	2.41710i	0.0860510	+	0.149045i	−0.819788	+	0.572668i	$0.805909\pi$
$264$		0			0
$265$	11.6891	+	20.2462i	0.718059	+	1.24371i
$266$		0			0
$267$	15.4089	+	1.93602i	0.943008	+	0.118482i
$268$		0			0
$269$	14.0669	−	24.3646i	0.857674	−	1.48553i	−0.0164688	−	0.999864i	$-0.505242\pi$
$269$	14.0669	−	24.3646i	0.857674	−	1.48553i	0.874142	−	0.485670i	$-0.161424\pi$
$270$		0			0
$271$	10.5055	−	18.1960i	0.638161	−	1.10533i	−0.347675	−	0.937615i	$-0.613029\pi$
$271$	10.5055	−	18.1960i	0.638161	−	1.10533i	0.985836	−	0.167712i	$-0.0536380\pi$
$272$		0			0
$273$	−29.6891	−	3.73022i	−1.79686	−	0.225763i
$274$		0			0
$275$	−2.33628	+	4.04656i	−0.140883	+	0.244017i
$276$		0			0
$277$	3.31964	−	5.74979i	0.199458	−	0.345471i	−0.748895	−	0.662689i	$-0.769415\pi$
$277$	3.31964	−	5.74979i	0.199458	−	0.345471i	0.948353	+	0.317217i	$0.102749\pi$
$278$		0			0
$279$	−20.3809	+	20.8687i	−1.22018	+	1.24938i
$280$		0			0
$281$	−4.37245			−0.260839			−0.130419	−	0.991459i	$-0.541632\pi$
$281$	−4.37245			−0.260839			−0.130419	+	0.991459i	$0.541632\pi$
$282$		0			0
$283$	−1.08030			−0.0642169			−0.0321085	−	0.999484i	$-0.510222\pi$
$283$	−1.08030			−0.0642169			−0.0321085	+	0.999484i	$0.510222\pi$
$284$		0			0
$285$	−11.0079	−	14.4462i	−0.652052	−	0.855718i
$286$		0			0
$287$	6.00105	−	10.3941i	0.354231	−	0.613545i
$288$		0			0
$289$	5.83164	+	10.1007i	0.343038	+	0.594159i
$290$		0			0
$291$	11.7909	+	1.48145i	0.691197	+	0.0868440i
$292$		0			0
$293$	−1.97495	−	3.42072i	−0.115378	−	0.199840i	0.802553	−	0.596581i	$-0.203475\pi$
$293$	−1.97495	−	3.42072i	−0.115378	−	0.199840i	−0.917931	+	0.396741i	$0.870141\pi$
$294$		0			0
$295$	−20.1183			−1.17133
$296$		0			0
$297$	−24.1344	+	19.2085i	−1.40042	+	1.11459i
$298$		0			0
$299$	3.69241	+	6.39545i	0.213538	+	0.369858i
$300$		0			0
$301$	0.369397			0.0212917
$302$		0			0
$303$	6.79422	−	8.96363i	0.390318	−	0.514947i
$304$		0			0
$305$	−23.9174			−1.36951
$306$		0			0
$307$	−9.58836	+	16.6075i	−0.547237	+	0.947842i	0.451226	+	0.892410i	$0.350987\pi$
$307$	−9.58836	+	16.6075i	−0.547237	+	0.947842i	−0.998462	+	0.0554320i	$0.982346\pi$
$308$		0			0
$309$	−15.3355	−	1.92680i	−0.872408	−	0.109612i
$310$		0			0
$311$	−12.1904	−	21.1144i	−0.691255	−	1.19729i	−0.971427	−	0.237338i	$-0.923725\pi$
$311$	−12.1904	−	21.1144i	−0.691255	−	1.19729i	0.280173	−	0.959950i	$-0.409608\pi$
$312$		0			0
$313$	−12.6505			−0.715051			−0.357526	−	0.933903i	$-0.616380\pi$
$313$	−12.6505			−0.715051			−0.357526	+	0.933903i	$0.616380\pi$
$314$		0			0
$315$	−21.4215	−	5.46925i	−1.20696	−	0.308157i
$316$		0			0
$317$	−11.6315			−0.653288			−0.326644	−	0.945147i	$-0.605918\pi$
$317$	−11.6315			−0.653288			−0.326644	+	0.945147i	$0.605918\pi$
$318$		0			0
$319$	−20.0981	+	34.8109i	−1.12528	+	1.94904i
$320$		0			0
$321$	13.8195	−	18.2320i	0.771327	−	1.01761i
$322$		0			0
$323$	−7.05395	−	7.18606i	−0.392492	−	0.399843i
$324$		0			0
$325$	2.21945	−	3.84420i	0.123113	−	0.213238i
$326$		0			0
$327$	−8.64398	−	20.5244i	−0.478013	−	1.13500i
$328$		0			0
$329$	15.3506	−	26.5881i	0.846308	−	1.46585i
$330$		0			0
$331$	6.72638	−	11.6504i	0.369715	−	0.640366i	−0.619805	−	0.784755i	$-0.712789\pi$
$331$	6.72638	−	11.6504i	0.369715	−	0.640366i	0.989521	+	0.144390i	$0.0461218\pi$
$332$		0			0
$333$	2.36232	+	8.41694i	0.129454	+	0.461246i
$334$		0			0
$335$	−12.1211	+	20.9944i	−0.662248	+	1.14705i
$336$		0			0
$337$	8.29518			0.451867			0.225934	−	0.974143i	$-0.427457\pi$
$337$	8.29518			0.451867			0.225934	+	0.974143i	$0.427457\pi$
$338$		0			0
$339$	−10.2111	−	1.28296i	−0.554593	−	0.0696807i
$340$		0			0
$341$	57.7195			3.12568
$342$		0			0
$343$	−14.1388			−0.763426
$344$		0			0
$345$	2.11783	+	5.02860i	0.114020	+	0.270731i
$346$		0			0
$347$	−4.99351			−0.268066			−0.134033	−	0.990977i	$-0.542793\pi$
$347$	−4.99351			−0.268066			−0.134033	+	0.990977i	$0.542793\pi$
$348$		0			0
$349$	−5.53573	+	9.58817i	−0.296321	+	0.513243i	−0.975291	−	0.220923i	$-0.929093\pi$
$349$	−5.53573	+	9.58817i	−0.296321	+	0.513243i	0.678970	+	0.734166i	$0.262426\pi$
$350$		0			0
$351$	22.9275	−	18.2479i	1.22378	−	0.974002i
$352$		0			0
$353$	3.35029	−	5.80288i	0.178318	−	0.308856i	−0.762986	−	0.646414i	$-0.776268\pi$
$353$	3.35029	−	5.80288i	0.178318	−	0.308856i	0.941305	+	0.337558i	$0.109601\pi$
$354$		0			0
$355$	2.41195	−	4.17761i	0.128013	−	0.221725i
$356$		0			0
$357$	−12.1620	−	1.52807i	−0.643682	−	0.0808741i
$358$		0			0
$359$	7.16145	−	12.4040i	0.377967	−	0.654658i	−0.612799	−	0.790238i	$-0.709957\pi$
$359$	7.16145	−	12.4040i	0.377967	−	0.654658i	0.990766	+	0.135581i	$0.0432900\pi$
$360$		0			0
$361$	−16.2754	−	9.80365i	−0.856600	−	0.515981i
$362$		0			0
$363$	41.6546	+	5.23361i	2.18630	+	0.274693i
$364$		0			0
$365$	9.86150	−	17.0806i	0.516174	−	0.894040i
$366$		0			0
$367$	−1.07940			−0.0563442			−0.0281721	−	0.999603i	$-0.508969\pi$
$367$	−1.07940			−0.0563442			−0.0281721	+	0.999603i	$0.508969\pi$
$368$		0			0
$369$	3.17606	+	11.3163i	0.165339	+	0.589103i
$370$		0			0
$371$	29.7708			1.54562
$372$		0			0
$373$	−4.47156	−	7.74497i	−0.231529	−	0.401019i	0.726730	−	0.686924i	$-0.241039\pi$
$373$	−4.47156	−	7.74497i	−0.231529	−	0.401019i	−0.958258	+	0.285904i	$0.907706\pi$
$374$		0			0
$375$	−10.6035	+	13.9893i	−0.547564	+	0.722403i
$376$		0			0
$377$	19.0930	−	33.0701i	0.983341	−	1.70320i
$378$		0			0
$379$	−20.9577			−1.07653			−0.538263	−	0.842777i	$-0.680919\pi$
$379$	−20.9577			−1.07653			−0.538263	+	0.842777i	$0.680919\pi$
$380$		0			0
$381$	4.36616	+	0.548576i	0.223685	+	0.0281044i
$382$		0			0
$383$	−5.92505			−0.302756			−0.151378	−	0.988476i	$-0.548371\pi$
$383$	−5.92505			−0.302756			−0.151378	+	0.988476i	$0.548371\pi$
$384$		0			0
$385$	21.8735	+	37.8860i	1.11478	+	1.93085i
$386$		0			0
$387$	−0.252752	+	0.258800i	−0.0128481	+	0.0131556i
$388$		0			0
$389$	24.6128			1.24792			0.623959	−	0.781457i	$-0.285523\pi$
$389$	24.6128			1.24792			0.623959	+	0.781457i	$0.285523\pi$
$390$		0			0
$391$	1.51258	+	2.61987i	0.0764946	+	0.132493i
$392$		0			0
$393$	5.48183	−	7.23218i	0.276522	−	0.364815i
$394$		0			0
$395$	13.7264	+	23.7748i	0.690650	+	1.19624i
$396$		0			0
$397$	4.02356	−	6.96901i	0.201937	−	0.349765i	−0.747216	−	0.664582i	$-0.768610\pi$
$397$	4.02356	−	6.96901i	0.201937	−	0.349765i	0.949152	+	0.314817i	$0.101943\pi$
$398$		0			0
$399$	−22.9406	+	2.94168i	−1.14847	+	0.147268i
$400$		0			0
$401$	23.5206			1.17456			0.587281	−	0.809383i	$-0.300198\pi$
$401$	23.5206			1.17456			0.587281	+	0.809383i	$0.300198\pi$
$402$		0			0
$403$	−54.8330			−2.73143
$404$		0			0
$405$	18.4889	−	11.2657i	0.918723	−	0.559798i
$406$		0			0
$407$	8.64920	−	14.9809i	0.428725	−	0.742573i
$408$		0			0
$409$	1.19951	−	2.07762i	0.0593121	−	0.102731i	−0.834845	−	0.550485i	$-0.814443\pi$
$409$	1.19951	−	2.07762i	0.0593121	−	0.102731i	0.894157	+	0.447754i	$0.147776\pi$
$410$		0			0
$411$	16.4915	−	21.7573i	0.813468	−	1.07321i
$412$		0			0
$413$	−12.8097	+	22.1870i	−0.630322	+	1.09175i
$414$		0			0
$415$	6.66586	−	11.5456i	0.327214	−	0.566751i
$416$		0			0
$417$	−6.21564	−	14.7585i	−0.304381	−	0.722726i
$418$		0			0
$419$	9.37939	+	16.2456i	0.458213	+	0.793648i	0.998867	−	0.0475971i	$-0.0151564\pi$
$419$	9.37939	+	16.2456i	0.458213	+	0.793648i	−0.540654	+	0.841245i	$0.681823\pi$
$420$		0			0
$421$	−13.6967	−	23.7233i	−0.667535	−	1.15620i	−0.978591	−	0.205813i	$-0.934016\pi$
$421$	−13.6967	−	23.7233i	−0.667535	−	1.15620i	0.311056	−	0.950392i	$-0.399317\pi$
$422$		0			0
$423$	8.12434	+	28.9470i	0.395019	+	1.40745i
$424$		0			0
$425$	0.909190	−	1.57476i	0.0441022	−	0.0763872i
$426$		0			0
$427$	−15.2287	+	26.3768i	−0.736967	+	1.27646i
$428$		0			0
$429$	−57.5302	−	7.22826i	−2.77758	−	0.348983i
$430$		0			0
$431$	0.510575	+	0.884342i	0.0245935	+	0.0425972i	0.878060	−	0.478550i	$-0.158838\pi$
$431$	0.510575	+	0.884342i	0.0245935	+	0.0425972i	−0.853467	+	0.521147i	$0.825504\pi$
$432$		0			0
$433$	−7.79908	−	13.5084i	−0.374800	−	0.649172i	0.615497	−	0.788139i	$-0.288955\pi$
$433$	−7.79908	−	13.5084i	−0.374800	−	0.649172i	−0.990297	+	0.138967i	$0.955622\pi$
$434$		0			0
$435$	17.0431	−	22.4850i	0.817156	−	1.07808i
$436$		0			0
$437$	3.99859	+	4.07348i	0.191279	+	0.194861i
$438$		0			0
$439$	−0.771383	−	1.33608i	−0.0368161	−	0.0637674i	0.847030	−	0.531545i	$-0.178388\pi$
$439$	−0.771383	−	1.33608i	−0.0368161	−	0.0637674i	−0.883846	+	0.467777i	$0.845055\pi$
$440$		0			0
$441$	−4.99843	+	5.11805i	−0.238021	+	0.243717i
$442$		0			0
$443$	−8.72562			−0.414567			−0.207283	−	0.978281i	$-0.566462\pi$
$443$	−8.72562			−0.414567			−0.207283	+	0.978281i	$0.566462\pi$
$444$		0			0
$445$	10.7848	+	18.6799i	0.511250	+	0.885510i
$446$		0			0
$447$	4.39395	−	5.79694i	0.207827	−	0.274186i
$448$		0			0
$449$	−7.45439			−0.351794			−0.175897	−	0.984409i	$-0.556283\pi$
$449$	−7.45439			−0.351794			−0.175897	+	0.984409i	$0.556283\pi$
$450$		0			0
$451$	11.6286	−	20.1413i	0.547568	−	0.948415i
$452$		0			0
$453$	1.21612	+	2.88756i	0.0571381	+	0.135669i
$454$		0			0
$455$	−20.7797	−	35.9914i	−0.974166	−	1.68731i
$456$		0			0
$457$	−14.9187	+	25.8399i	−0.697867	+	1.20874i	0.271338	+	0.962484i	$0.412534\pi$
$457$	−14.9187	+	25.8399i	−0.697867	+	1.20874i	−0.969205	+	0.246257i	$0.920799\pi$
$458$		0			0
$459$	9.39217	−	7.47520i	0.438389	−	0.348912i
$460$		0			0
$461$	−8.48128	−	14.6900i	−0.395013	−	0.684182i	0.598090	−	0.801429i	$-0.295926\pi$
$461$	−8.48128	−	14.6900i	−0.395013	−	0.684182i	−0.993103	+	0.117247i	$0.962593\pi$
$462$		0			0
$463$	18.9367	+	32.7993i	0.880063	+	1.52431i	0.851270	+	0.524728i	$0.175833\pi$
$463$	18.9367	+	32.7993i	0.880063	+	1.52431i	0.0287929	+	0.999585i	$0.490834\pi$
$464$		0			0
$465$	−40.1981	−	5.05060i	−1.86414	−	0.234216i
$466$		0			0
$467$	36.8780			1.70651			0.853255	−	0.521494i	$-0.174625\pi$
$467$	36.8780			1.70651			0.853255	+	0.521494i	$0.174625\pi$
$468$		0			0
$469$	15.4355	+	26.7350i	0.712744	+	1.23451i
$470$		0			0
$471$	−17.7830	+	23.4611i	−0.819396	+	1.08103i
$472$		0			0
$473$	0.715800			0.0329125
$474$		0			0
$475$	0.918722	−	3.30574i	0.0421539	−	0.151678i
$476$		0			0
$477$	−20.3700	+	20.8575i	−0.932679	+	0.954999i
$478$		0			0
$479$	4.33345			0.198000			0.0990001	−	0.995087i	$-0.468436\pi$
$479$	4.33345			0.198000			0.0990001	+	0.995087i	$0.468436\pi$
$480$		0			0
$481$	−8.21667	+	14.2317i	−0.374648	+	0.648909i
$482$		0			0
$483$	6.89415	+	0.866200i	0.313695	+	0.0394135i
$484$		0			0
$485$	8.25260	+	14.2939i	0.374731	+	0.649053i
$486$		0			0
$487$	−9.69069			−0.439127			−0.219563	−	0.975598i	$-0.570463\pi$
$487$	−9.69069			−0.439127			−0.219563	+	0.975598i	$0.570463\pi$
$488$		0			0
$489$	22.5025	−	29.6876i	1.01760	−	1.34252i
$490$		0			0
$491$	−37.9721			−1.71365			−0.856827	−	0.515603i	$-0.827568\pi$
$491$	−37.9721			−1.71365			−0.856827	+	0.515603i	$0.827568\pi$
$492$		0			0
$493$	7.82139	−	13.5470i	0.352258	−	0.610128i
$494$		0			0
$495$	−41.5096	−	10.5981i	−1.86572	−	0.476348i
$496$		0			0
$497$	−3.07146	−	5.31993i	−0.137774	−	0.238631i
$498$		0			0
$499$	−28.5012			−1.27589			−0.637944	−	0.770083i	$-0.720215\pi$
$499$	−28.5012			−1.27589			−0.637944	+	0.770083i	$0.720215\pi$
$500$		0			0
$501$	2.21673	+	5.26342i	0.0990360	+	0.235152i
$502$		0			0
$503$	2.47407	+	4.28522i	0.110314	+	0.191069i	0.915897	−	0.401414i	$-0.131481\pi$
$503$	2.47407	+	4.28522i	0.110314	+	0.191069i	−0.805583	+	0.592483i	$0.798148\pi$
$504$		0			0
$505$	15.6218			0.695159
$506$		0			0
$507$	32.3122	+	4.05980i	1.43503	+	0.180302i
$508$		0			0
$509$	2.82795	−	4.89816i	0.125347	−	0.217107i	−0.796522	−	0.604610i	$-0.793329\pi$
$509$	2.82795	−	4.89816i	0.125347	−	0.217107i	0.921868	+	0.387503i	$0.126662\pi$
$510$		0			0
$511$	−12.5580	−	21.7511i	−0.555533	−	0.962211i
$512$		0			0
$513$	13.6357	−	18.0850i	0.602029	−	0.798474i
$514$		0			0
$515$	−10.7335	−	18.5910i	−0.472974	−	0.819215i
$516$		0			0
$517$	29.7458	−	51.5212i	1.30822	−	2.26590i
$518$		0			0
$519$	24.0562	+	3.02249i	1.05595	+	0.132673i
$520$		0			0
$521$	35.3278			1.54774			0.773869	−	0.633345i	$-0.218319\pi$
$521$	35.3278			1.54774			0.773869	+	0.633345i	$0.218319\pi$
$522$		0			0
$523$	21.1307	+	36.5994i	0.923980	+	1.60038i	0.793193	+	0.608970i	$0.208417\pi$
$523$	21.1307	+	36.5994i	0.923980	+	1.60038i	0.130787	+	0.991410i	$0.458250\pi$
$524$		0			0
$525$	−1.62108	−	3.84911i	−0.0707496	−	0.167989i
$526$		0			0
$527$	−22.4622			−0.978467
$528$		0			0
$529$	10.6426	+	18.4335i	0.462721	+	0.801456i
$530$		0			0
$531$	−6.77953	−	24.1555i	−0.294207	−	1.04826i
$532$		0			0
$533$	−11.0470	+	19.1340i	−0.478501	+	0.828787i
$534$		0			0
$535$	31.7747			1.37374
$536$		0			0
$537$	−8.46456	+	11.1673i	−0.365273	+	0.481905i
$538$		0			0
$539$	14.1557			0.609730
$540$		0			0
$541$	21.6732	+	37.5391i	0.931804	+	1.61393i	0.780237	+	0.625484i	$0.215099\pi$
$541$	21.6732	+	37.5391i	0.931804	+	1.61393i	0.151567	+	0.988447i	$0.451568\pi$
$542$		0			0
$543$	−11.3583	−	1.42709i	−0.487430	−	0.0612421i
$544$		0			0
$545$	15.4656	−	26.7873i	0.662476	−	1.14744i
$546$		0			0
$547$	−27.6688			−1.18303			−0.591516	−	0.806293i	$-0.701470\pi$
$547$	−27.6688			−1.18303			−0.591516	+	0.806293i	$0.701470\pi$
$548$		0			0
$549$	−8.05979	−	28.7170i	−0.343984	−	1.22561i
$550$		0			0
$551$	7.90339	−	28.4379i	0.336696	−	1.21150i
$552$		0			0
$553$	34.9594			1.48662
$554$		0			0
$555$	−7.33450	+	9.67642i	−0.311332	+	0.410741i
$556$		0			0
$557$	−4.91182	−	8.50752i	−0.208120	−	0.360475i	0.743002	−	0.669289i	$-0.233401\pi$
$557$	−4.91182	−	8.50752i	−0.208120	−	0.360475i	−0.951122	+	0.308814i	$0.900068\pi$
$558$		0			0
$559$	−0.680005			−0.0287611
$560$		0			0
$561$	−23.5670	−	2.96103i	−0.995000	−	0.125015i
$562$		0			0
$563$	17.6935	+	30.6460i	0.745692	+	1.29158i	0.949871	+	0.312643i	$0.101214\pi$
$563$	17.6935	+	30.6460i	0.745692	+	1.29158i	−0.204178	+	0.978934i	$0.565452\pi$
$564$		0			0
$565$	−7.14688	−	12.3788i	−0.300671	−	0.520778i
$566$		0			0
$567$	−0.651909	−	27.5632i	−0.0273776	−	1.15755i
$568$		0			0
$569$	−13.8420	+	23.9751i	−0.580287	+	1.00509i	0.415158	+	0.909749i	$0.363726\pi$
$569$	−13.8420	+	23.9751i	−0.580287	+	1.00509i	−0.995445	+	0.0953373i	$0.969607\pi$
$570$		0			0
$571$	13.5265	+	23.4286i	0.566068	+	0.980458i	0.996949	+	0.0780495i	$0.0248692\pi$
$571$	13.5265	+	23.4286i	0.566068	+	0.980458i	−0.430882	+	0.902408i	$0.641797\pi$
$572$		0			0
$573$	12.2292	+	29.0373i	0.510884	+	1.21305i
$574$		0			0
$575$	−0.515382	+	0.892668i	−0.0214929	+	0.0372268i
$576$		0			0
$577$	8.38351			0.349010			0.174505	−	0.984656i	$-0.444167\pi$
$577$	8.38351			0.349010			0.174505	+	0.984656i	$0.444167\pi$
$578$		0			0
$579$	8.99513	−	11.8673i	0.373825	−	0.493188i
$580$		0			0
$581$	−8.48854	−	14.7026i	−0.352164	−	0.609966i
$582$		0			0
$583$	57.6885			2.38921
$584$		0			0
$585$	39.4338	+	10.0681i	1.63039	+	0.416264i
$586$		0			0
$587$	19.0111	+	32.9282i	0.784672	+	1.35909i	0.929195	+	0.369591i	$0.120502\pi$
$587$	19.0111	+	32.9282i	0.784672	+	1.35909i	−0.144522	+	0.989502i	$0.546165\pi$
$588$		0			0
$589$	−41.0388	+	10.5893i	−1.69097	+	0.436323i
$590$		0			0
$591$	−2.79946	+	3.69333i	−0.115154	+	0.151923i
$592$		0			0
$593$	−3.60681	−	6.24718i	−0.148114	−	0.256541i	0.782416	−	0.622756i	$-0.213987\pi$
$593$	−3.60681	−	6.24718i	−0.148114	−	0.256541i	−0.930530	+	0.366215i	$0.880654\pi$
$594$		0			0
$595$	−8.51232	−	14.7438i	−0.348971	−	0.604435i
$596$		0			0
$597$	42.7765	+	5.37456i	1.75073	+	0.219966i
$598$		0			0
$599$	−15.8137	+	27.3901i	−0.646131	+	1.11913i	0.337909	+	0.941179i	$0.390281\pi$
$599$	−15.8137	+	27.3901i	−0.646131	+	1.11913i	−0.984039	+	0.177952i	$0.943053\pi$
$600$		0			0
$601$	−3.66763	+	6.35252i	−0.149606	+	0.259125i	−0.931082	−	0.364811i	$-0.881134\pi$
$601$	−3.66763	+	6.35252i	−0.149606	+	0.259125i	0.781476	+	0.623935i	$0.214467\pi$
$602$		0			0
$603$	−29.2921	−	7.47874i	−1.19286	−	0.304558i
$604$		0			0
$605$	29.1545	+	50.4970i	1.18530	+	2.05300i
$606$		0			0
$607$	−12.9317	−	22.3983i	−0.524881	−	0.909120i	−0.999580	−	0.0289720i	$-0.990777\pi$
$607$	−12.9317	−	22.3983i	−0.524881	−	0.909120i	0.474700	−	0.880148i	$-0.342557\pi$
$608$		0			0
$609$	−13.9455	−	33.1123i	−0.565099	−	1.34178i
$610$		0			0
$611$	−28.2583	+	48.9447i	−1.14321	+	1.98009i
$612$		0			0
$613$	−7.10430	+	12.3050i	−0.286940	+	0.496995i	−0.973078	−	0.230477i	$-0.925971\pi$
$613$	−7.10430	+	12.3050i	−0.286940	+	0.496995i	0.686138	+	0.727472i	$0.259305\pi$
$614$		0			0
$615$	−9.86100	+	13.0096i	−0.397634	+	0.524599i
$616$		0			0
$617$	9.42220	−	16.3197i	0.379324	−	0.657008i	−0.611640	−	0.791136i	$-0.709490\pi$
$617$	9.42220	−	16.3197i	0.379324	−	0.657008i	0.990964	+	0.134128i	$0.0428234\pi$
$618$		0			0
$619$	−3.70769	+	6.42190i	−0.149025	+	0.258118i	−0.930867	−	0.365358i	$-0.880947\pi$
$619$	−3.70769	+	6.42190i	−0.149025	+	0.258118i	0.781843	+	0.623476i	$0.214280\pi$
$620$		0			0
$621$	−5.32404	+	4.23738i	−0.213646	+	0.170040i
$622$		0			0
$623$	27.4676			1.10047
$624$		0			0
$625$	−28.3161			−1.13264
$626$		0			0
$627$	−44.4533	+	5.70026i	−1.77529	+	0.227646i
$628$		0			0
$629$	−3.36593	+	5.82996i	−0.134208	+	0.232456i
$630$		0			0
$631$	−5.19989	−	9.00648i	−0.207004	−	0.358542i	0.743765	−	0.668441i	$-0.233038\pi$
$631$	−5.19989	−	9.00648i	−0.207004	−	0.358542i	−0.950770	+	0.309899i	$0.899705\pi$
$632$		0			0
$633$	−13.5188	+	17.8353i	−0.537322	+	0.708890i
$634$		0			0
$635$	3.05592	+	5.29300i	0.121270	+	0.210046i
$636$		0			0
$637$	−13.4478			−0.532822
$638$		0			0
$639$	5.82874	+	1.48817i	0.230581	+	0.0588711i
$640$		0			0
$641$	−9.68760	−	16.7794i	−0.382637	−	0.662747i	0.608801	−	0.793323i	$-0.291651\pi$
$641$	−9.68760	−	16.7794i	−0.382637	−	0.662747i	−0.991438	+	0.130576i	$0.958317\pi$
$642$		0			0
$643$	8.41115			0.331704			0.165852	−	0.986151i	$-0.446963\pi$
$643$	8.41115			0.331704			0.165852	+	0.986151i	$0.446963\pi$
$644$		0			0
$645$	−0.498511	−	0.0626344i	−0.0196289	−	0.00246623i
$646$		0			0
$647$	−18.2120			−0.715987			−0.357993	−	0.933724i	$-0.616539\pi$
$647$	−18.2120			−0.715987			−0.357993	+	0.933724i	$0.616539\pi$
$648$		0			0
$649$	−24.8220	+	42.9930i	−0.974349	+	1.68762i
$650$		0			0
$651$	−31.1648	+	41.1158i	−1.22144	+	1.61145i
$652$		0			0
$653$	0.205260	+	0.355522i	0.00803246	+	0.0139126i	0.870014	−	0.493028i	$-0.164110\pi$
$653$	0.205260	+	0.355522i	0.00803246	+	0.0139126i	−0.861981	+	0.506940i	$0.830776\pi$
$654$		0			0
$655$	12.6042			0.492487
$656$		0			0
$657$	23.8314	+	6.08454i	0.929752	+	0.237381i
$658$		0			0
$659$	22.5408			0.878065			0.439033	−	0.898471i	$-0.355321\pi$
$659$	22.5408			0.878065			0.439033	+	0.898471i	$0.355321\pi$
$660$		0			0
$661$	6.74334	−	11.6798i	0.262286	−	0.454292i	−0.704563	−	0.709641i	$-0.748857\pi$
$661$	6.74334	−	11.6798i	0.262286	−	0.454292i	0.966849	+	0.255349i	$0.0821904\pi$
$662$		0			0
$663$	22.3885	+	2.81295i	0.869497	+	0.109246i
$664$		0			0
$665$	−22.5028	−	22.9242i	−0.872620	−	0.888962i
$666$		0			0
$667$	−4.43362	+	7.67926i	−0.171671	+	0.297342i
$668$		0			0
$669$	−34.0176	−	4.27406i	−1.31519	−	0.165245i
$670$		0			0
$671$	−29.5094	+	51.1118i	−1.13920	+	1.97315i
$672$		0			0
$673$	−16.2484	+	28.1431i	−0.626331	+	1.08484i	0.361950	+	0.932197i	$0.382111\pi$
$673$	−16.2484	+	28.1431i	−0.626331	+	1.08484i	−0.988282	+	0.152640i	$0.951222\pi$
$674$		0			0
$675$	3.80588	+	1.49794i	0.146488	+	0.0576556i
$676$		0			0
$677$	−8.95815	+	15.5160i	−0.344290	+	0.596327i	−0.985224	−	0.171268i	$-0.945214\pi$
$677$	−8.95815	+	15.5160i	−0.344290	+	0.596327i	0.640935	+	0.767595i	$0.278547\pi$
$678$		0			0
$679$	21.0183			0.806609
$680$		0			0
$681$	1.54418	+	3.66652i	0.0591730	+	0.140501i
$682$		0			0
$683$	−21.3782			−0.818013			−0.409007	−	0.912531i	$-0.634125\pi$
$683$	−21.3782			−0.818013			−0.409007	+	0.912531i	$0.634125\pi$
$684$		0			0
$685$	37.9186			1.44879
$686$		0			0
$687$	−13.1226	−	1.64877i	−0.500660	−	0.0629044i
$688$		0			0
$689$	−54.8036			−2.08785
$690$		0			0
$691$	−6.55424	+	11.3523i	−0.249335	+	0.431861i	−0.963342	−	0.268278i	$-0.913545\pi$
$691$	−6.55424	+	11.3523i	−0.249335	+	0.431861i	0.714006	+	0.700139i	$0.246879\pi$
$692$		0			0
$693$	−38.1177	+	39.0299i	−1.44797	+	1.48262i
$694$		0			0
$695$	11.1209	−	19.2620i	0.421840	−	0.730648i
$696$		0			0
$697$	−4.52538	+	7.83819i	−0.171411	+	0.296893i
$698$		0			0
$699$	−8.90699	−	21.1489i	−0.336893	−	0.799924i
$700$		0			0
$701$	14.6527	−	25.3792i	0.553423	−	0.958557i	−0.444601	−	0.895729i	$-0.646654\pi$
$701$	14.6527	−	25.3792i	0.553423	−	0.958557i	0.998024	−	0.0628287i	$-0.0200122\pi$
$702$		0			0
$703$	−3.40122	+	12.2382i	−0.128279	+	0.461574i
$704$		0			0
$705$	−25.2244	+	33.2785i	−0.950005	+	1.25334i
$706$		0			0
$707$	9.94666	−	17.2281i	0.374083	−	0.647930i
$708$		0			0
$709$	35.4120			1.32993			0.664963	−	0.746876i	$-0.268447\pi$
$709$	35.4120			1.32993			0.664963	+	0.746876i	$0.268447\pi$
$710$		0			0
$711$	−23.9202	+	24.4927i	−0.897078	+	0.918546i
$712$		0			0
$713$	12.7329			0.476850
$714$		0			0
$715$	−40.2659	−	69.7426i	−1.50586	−	2.60823i
$716$		0			0
$717$	35.6864	+	4.48375i	1.33273	+	0.167449i
$718$		0			0
$719$	−22.1802	+	38.4172i	−0.827181	+	1.43272i	0.0730598	+	0.997328i	$0.476724\pi$
$719$	−22.1802	+	38.4172i	−0.827181	+	1.43272i	−0.900241	+	0.435392i	$0.856610\pi$
$720$		0			0
$721$	−27.3368			−1.01808
$722$		0			0
$723$	−7.88211	+	10.3989i	−0.293139	+	0.386739i
$724$		0			0
$725$	5.32996			0.197950
$726$		0			0
$727$	15.2280	+	26.3757i	0.564776	+	0.978221i	0.997070	+	0.0764886i	$0.0243709\pi$
$727$	15.2280	+	26.3757i	0.564776	+	0.978221i	−0.432294	+	0.901733i	$0.642296\pi$
$728$		0			0
$729$	19.7569	+	18.4028i	0.731738	+	0.681586i
$730$		0			0
$731$	−0.278562			−0.0103030
$732$		0			0
$733$	9.44532	+	16.3598i	0.348871	+	0.604262i	0.986049	−	0.166454i	$-0.0532318\pi$
$733$	9.44532	+	16.3598i	0.348871	+	0.604262i	−0.637178	+	0.770716i	$0.719898\pi$
$734$		0			0
$735$	−9.85859	−	1.23866i	−0.363640	−	0.0456887i
$736$		0			0
$737$	29.9102	+	51.8060i	1.10176	+	1.90830i
$738$		0			0
$739$	−1.35127	+	2.34047i	−0.0497073	+	0.0860955i	−0.889808	−	0.456334i	$-0.849162\pi$
$739$	−1.35127	+	2.34047i	−0.0497073	+	0.0860955i	0.840101	+	0.542430i	$0.182496\pi$
$740$		0			0
$741$	42.2303	−	5.41520i	1.55137	−	0.198932i
$742$		0			0
$743$	35.8953			1.31687			0.658436	−	0.752637i	$-0.271218\pi$
$743$	35.8953			1.31687			0.658436	+	0.752637i	$0.271218\pi$
$744$		0			0
$745$	10.1029			0.370141
$746$		0			0
$747$	16.1088	+	4.11283i	0.589390	+	0.150481i
$748$		0			0
$749$	20.2315	−	35.0420i	0.739244	−	1.28041i
$750$		0			0
$751$	−8.02604	+	13.9015i	−0.292874	+	0.507273i	−0.974488	−	0.224439i	$-0.927945\pi$
$751$	−8.02604	+	13.9015i	−0.292874	+	0.507273i	0.681614	+	0.731712i	$0.261278\pi$
$752$		0			0
$753$	39.4037	+	4.95079i	1.43595	+	0.180417i
$754$		0			0
$755$	−2.17585	+	3.76868i	−0.0791873	+	0.137156i
$756$		0			0
$757$	7.03341	−	12.1822i	0.255634	−	0.442771i	−0.709434	−	0.704772i	$-0.751049\pi$
$757$	7.03341	−	12.1822i	0.255634	−	0.442771i	0.965067	+	0.262001i	$0.0843825\pi$
$758$		0			0
$759$	13.3592	+	1.67849i	0.484907	+	0.0609252i
$760$		0			0
$761$	−1.57990	−	2.73647i	−0.0572714	−	0.0991969i	0.835968	−	0.548778i	$-0.184907\pi$
$761$	−1.57990	−	2.73647i	−0.0572714	−	0.0991969i	−0.893240	+	0.449581i	$0.851573\pi$
$762$		0			0
$763$	−19.6945	−	34.1119i	−0.712989	−	1.23493i
$764$		0			0
$765$	16.1539	+	4.12435i	0.584045	+	0.149116i
$766$		0			0
$767$	23.5807	−	40.8430i	0.851450	−	1.47475i
$768$		0			0
$769$	−6.19324	+	10.7270i	−0.223334	+	0.386826i	−0.955818	−	0.293958i	$-0.905027\pi$
$769$	−6.19324	+	10.7270i	−0.223334	+	0.386826i	0.732484	+	0.680784i	$0.238361\pi$
$770$		0			0
$771$	−19.6352	−	46.6221i	−0.707145	−	1.67906i
$772$		0			0
$773$	−15.2111	−	26.3464i	−0.547105	−	0.947614i	−0.998471	−	0.0552754i	$-0.982396\pi$
$773$	−15.2111	−	26.3464i	−0.547105	−	0.947614i	0.451366	−	0.892339i	$-0.350937\pi$
$774$		0			0
$775$	−3.82676	−	6.62815i	−0.137461	−	0.238090i
$776$		0			0
$777$	6.00142	+	14.2499i	0.215300	+	0.511211i
$778$		0			0
$779$	−4.57283	+	16.4539i	−0.163839	+	0.589522i
$780$		0			0
$781$	−5.95174	−	10.3087i	−0.212970	−	0.368875i
$782$		0			0
$783$	32.7405	+	12.8861i	1.17005	+	0.460513i
$784$		0			0
$785$	−40.8879			−1.45935
$786$		0			0
$787$	−13.5315	−	23.4372i	−0.482346	−	0.835447i	0.517449	−	0.855714i	$-0.326882\pi$
$787$	−13.5315	−	23.4372i	−0.482346	−	0.835447i	−0.999795	+	0.0202669i	$0.993548\pi$
$788$		0			0
$789$	−4.79649	−	0.602644i	−0.170759	−	0.0214547i
$790$		0			0
$791$	−18.2022			−0.647195
$792$		0			0
$793$	28.0337	−	48.5559i	0.995507	−	1.72427i
$794$		0			0
$795$	−40.1765	−	5.04789i	−1.42491	−	0.179030i
$796$		0			0
$797$	13.0870	+	22.6674i	0.463566	+	0.802919i	0.999136	−	0.0415716i	$-0.0132365\pi$
$797$	13.0870	+	22.6674i	0.463566	+	0.802919i	−0.535570	+	0.844491i	$0.679903\pi$
$798$		0			0
$799$	−11.5759	+	20.0500i	−0.409526	+	0.709319i
$800$		0			0
$801$	−18.7941	+	19.2439i	−0.664057	+	0.679948i
$802$		0			0
$803$	−24.3343	−	42.1483i	−0.858739	−	1.48738i
$804$		0			0
$805$	4.82528	+	8.35763i	0.170069	+	0.294568i
$806$		0			0
$807$	18.9137	+	44.9088i	0.665792	+	1.58087i
$808$		0			0
$809$	0.390777			0.0137390			0.00686949	−	0.999976i	$-0.497813\pi$
$809$	0.390777			0.0137390			0.00686949	+	0.999976i	$0.497813\pi$
$810$		0			0
$811$	−16.5905	−	28.7355i	−0.582570	−	1.00904i	−0.995174	−	0.0981302i	$-0.968714\pi$
$811$	−16.5905	−	28.7355i	−0.582570	−	1.00904i	0.412604	−	0.910911i	$-0.364620\pi$
$812$		0			0
$813$	14.1251	+	33.5389i	0.495390	+	1.17626i
$814$		0			0
$815$	51.7393			1.81235
$816$		0			0
$817$	−0.508937	+	0.131321i	−0.0178055	+	0.00459435i
$818$		0			0
$819$	36.2116	−	37.0781i	1.26533	−	1.29561i
$820$		0			0
$821$	−33.4789			−1.16842			−0.584211	−	0.811602i	$-0.698596\pi$
$821$	−33.4789			−1.16842			−0.584211	+	0.811602i	$0.698596\pi$
$822$		0			0
$823$	5.66143	−	9.80589i	0.197345	−	0.341812i	−0.750322	−	0.661073i	$-0.770101\pi$
$823$	5.66143	−	9.80589i	0.197345	−	0.341812i	0.947667	+	0.319261i	$0.103435\pi$
$824$		0			0
$825$	−3.14125	−	7.45863i	−0.109364	−	0.259676i
$826$		0			0
$827$	−26.3316	−	45.6077i	−0.915640	−	1.58593i	−0.805962	−	0.591967i	$-0.798351\pi$
$827$	−26.3316	−	45.6077i	−0.915640	−	1.58593i	−0.109678	−	0.993967i	$-0.534982\pi$
$828$		0			0
$829$	−20.5958			−0.715320			−0.357660	−	0.933852i	$-0.616425\pi$
$829$	−20.5958			−0.715320			−0.357660	+	0.933852i	$0.616425\pi$
$830$		0			0
$831$	4.46343	+	10.5980i	0.154835	+	0.367641i
$832$		0			0
$833$	−5.50885			−0.190870
$834$		0			0
$835$	−3.96613	+	6.86953i	−0.137253	+	0.237730i
$836$		0			0
$837$	−7.48198	−	49.9667i	−0.258615	−	1.72710i
$838$		0			0
$839$	−6.57498	−	11.3882i	−0.226994	−	0.393164i	0.729922	−	0.683530i	$-0.239556\pi$
$839$	−6.57498	−	11.3882i	−0.226994	−	0.393164i	−0.956916	+	0.290366i	$0.906223\pi$
$840$		0			0
$841$	16.8515			0.581086
$842$		0			0
$843$	4.57474	−	6.03546i	0.157562	−	0.207872i
$844$		0			0
$845$	22.6156	+	39.1714i	0.778001	+	1.34754i
$846$		0			0
$847$	74.2528			2.55135
$848$		0			0
$849$	1.13027	−	1.49117i	0.0387909	−	0.0511769i
$850$		0			0
$851$	1.90801	−	3.30477i	0.0654056	−	0.113286i
$852$		0			0
$853$	10.2958	+	17.8328i	0.352520	+	0.610583i	0.986690	−	0.162610i	$-0.0519914\pi$
$853$	10.2958	+	17.8328i	0.352520	+	0.610583i	−0.634170	+	0.773194i	$0.718658\pi$
$854$		0			0
$855$	31.4578	−	0.0801047i	1.07583	−	0.00273952i
$856$		0			0
$857$	−16.9467	−	29.3525i	−0.578887	−	1.00266i	−0.995607	−	0.0936271i	$-0.970154\pi$
$857$	−16.9467	−	29.3525i	−0.578887	−	1.00266i	0.416720	−	0.909035i	$-0.363179\pi$
$858$		0			0
$859$	8.09848	−	14.0270i	0.276316	−	0.478594i	−0.694150	−	0.719830i	$-0.744220\pi$
$859$	8.09848	−	14.0270i	0.276316	−	0.478594i	0.970466	+	0.241236i	$0.0775529\pi$
$860$		0			0
$861$	8.06871	+	19.1585i	0.274981	+	0.652919i
$862$		0			0
$863$	−18.4208			−0.627052			−0.313526	−	0.949580i	$-0.601510\pi$
$863$	−18.4208			−0.627052			−0.313526	+	0.949580i	$0.601510\pi$
$864$		0			0
$865$	16.8372	+	29.1628i	0.572481	+	0.991566i
$866$		0			0
$867$	−20.0438	−	2.51836i	−0.680723	−	0.0855280i
$868$		0			0
$869$	67.7428			2.29802
$870$		0			0
$871$	−28.4145	−	49.2153i	−0.962787	−	1.66760i
$872$		0			0
$873$	−14.3813	+	14.7255i	−0.486734	+	0.498382i
$874$		0			0
$875$	−15.5235	+	26.8874i	−0.524789	+	0.908961i
$876$		0			0
$877$	−24.5510			−0.829028			−0.414514	−	0.910043i	$-0.636048\pi$
$877$	−24.5510			−0.829028			−0.414514	+	0.910043i	$0.636048\pi$
$878$		0			0
$879$	6.78807	+	0.852872i	0.228956	+	0.0287667i
$880$		0			0
$881$	25.2988			0.852339			0.426169	−	0.904643i	$-0.359863\pi$
$881$	25.2988			0.852339			0.426169	+	0.904643i	$0.359863\pi$
$882$		0			0
$883$	−17.1678	−	29.7355i	−0.577743	−	1.00068i	−0.995738	−	0.0922306i	$-0.970600\pi$
$883$	−17.1678	−	29.7355i	−0.577743	−	1.00068i	0.417995	−	0.908449i	$-0.362733\pi$
$884$		0			0
$885$	21.0490	−	27.7700i	0.707555	−	0.933478i
$886$		0			0
$887$	−21.9212	+	37.9687i	−0.736043	+	1.27486i	0.218221	+	0.975899i	$0.429975\pi$
$887$	−21.9212	+	37.9687i	−0.736043	+	1.27486i	−0.954264	+	0.298964i	$0.903359\pi$
$888$		0			0
$889$	7.78303			0.261034
$890$		0			0
$891$	−1.26324	−	53.4108i	−0.0423202	−	1.78933i
$892$		0			0
$893$	−11.6973	+	42.0890i	−0.391434	+	1.40845i
$894$		0			0
$895$	−19.4623			−0.650554
$896$		0			0
$897$	−12.6911	−	1.59455i	−0.423744	−	0.0532404i
$898$		0			0
$899$	−32.9201	−	57.0193i	−1.09795	−	1.90170i
$900$		0			0
$901$	−22.4501			−0.747921
$902$		0			0
$903$	−0.386486	+	0.509892i	−0.0128615	+	0.0169681i
$904$		0			0
$905$	−7.94977	−	13.7694i	−0.264259	−	0.457710i
$906$		0			0
$907$	−12.4217	−	21.5151i	−0.412457	−	0.714396i	0.582701	−	0.812687i	$-0.301996\pi$
$907$	−12.4217	−	21.5151i	−0.412457	−	0.714396i	−0.995158	+	0.0982903i	$0.968663\pi$
$908$		0			0
$909$	5.26428	+	18.7566i	0.174605	+	0.622118i
$910$		0			0
$911$	−9.32820	+	16.1569i	−0.309057	+	0.535302i	−0.978156	−	0.207871i	$-0.933347\pi$
$911$	−9.32820	+	16.1569i	−0.309057	+	0.535302i	0.669099	+	0.743173i	$0.266680\pi$
$912$		0			0
$913$	−16.4487	−	28.4900i	−0.544373	−	0.942882i
$914$		0			0
$915$	25.0239	−	33.0141i	0.827266	−	1.09141i
$916$		0			0
$917$	8.02533	−	13.9003i	0.265020	−	0.459028i
$918$		0			0
$919$	38.4666			1.26890			0.634448	−	0.772966i	$-0.281228\pi$
$919$	38.4666			1.26890			0.634448	+	0.772966i	$0.281228\pi$
$920$		0			0
$921$	−12.8920	−	30.6110i	−0.424807	−	1.00867i
$922$		0			0
$923$	5.65411	+	9.79320i	0.186107	+	0.322347i
$924$		0			0
$925$	−2.29375			−0.0754179
$926$		0			0
$927$	18.7046	−	19.1523i	0.614341	−	0.629043i
$928$		0			0
$929$	11.7816	+	20.4063i	0.386540	+	0.669507i	0.991982	−	0.126383i	$-0.0403367\pi$
$929$	11.7816	+	20.4063i	0.386540	+	0.669507i	−0.605441	+	0.795890i	$0.707003\pi$
$930$		0			0
$931$	−10.0648	+	2.59702i	−0.329859	+	0.0851138i
$932$		0			0
$933$	41.8994	+	5.26436i	1.37172	+	0.172347i
$934$		0			0
$935$	−16.4948	−	28.5698i	−0.539437	−	0.934333i
$936$		0			0
$937$	−9.71354	−	16.8243i	−0.317328	−	0.549628i	0.662602	−	0.748972i	$-0.269452\pi$
$937$	−9.71354	−	16.8243i	−0.317328	−	0.549628i	−0.979930	+	0.199344i	$0.936119\pi$
$938$		0			0
$939$	13.2358	−	17.4620i	0.431934	−	0.569852i
$940$		0			0
$941$	12.5297	−	21.7022i	0.408458	−	0.707470i	−0.586259	−	0.810124i	$-0.699400\pi$
$941$	12.5297	−	21.7022i	0.408458	−	0.707470i	0.994717	+	0.102653i	$0.0327332\pi$
$942$		0			0
$943$	2.56525	−	4.44315i	0.0835361	−	0.144689i
$944$		0			0
$945$	29.9619	−	23.8466i	0.974661	−	0.775729i
$946$		0			0
$947$	−6.86239	−	11.8860i	−0.222998	−	0.386243i	0.732719	−	0.680531i	$-0.238251\pi$
$947$	−6.86239	−	11.8860i	−0.222998	−	0.386243i	−0.955717	+	0.294288i	$0.904918\pi$
$948$		0			0
$949$	23.1174	+	40.0405i	0.750423	+	1.29977i
$950$		0			0
$951$	12.1696	−	16.0553i	0.394625	−	0.520630i
$952$		0			0
$953$	−4.03543	+	6.98957i	−0.130720	+	0.226414i	−0.923955	−	0.382502i	$-0.875062\pi$
$953$	−4.03543	+	6.98957i	−0.130720	+	0.226414i	0.793234	+	0.608917i	$0.208396\pi$
$954$		0			0
$955$	−21.8803	+	37.8979i	−0.708031	+	1.22635i
$956$		0			0
$957$	−27.0229	−	64.1635i	−0.873526	−	2.07411i
$958$		0			0
$959$	24.1434	−	41.8177i	0.779632	−	1.35036i
$960$		0			0
$961$	−31.7714	+	55.0297i	−1.02488	+	1.77515i
$962$		0			0
$963$	10.7076	+	38.1510i	0.345046	+	1.22940i
$964$		0			0
$965$	20.6823			0.665786
$966$		0			0
$967$	−16.3246			−0.524965			−0.262483	−	0.964937i	$-0.584541\pi$
$967$	−16.3246			−0.524965			−0.262483	+	0.964937i	$0.584541\pi$
$968$		0			0
$969$	17.2995	−	2.21832i	0.555739	−	0.0712627i
$970$		0			0
$971$	−1.43687	+	2.48874i	−0.0461115	+	0.0798674i	−0.888160	−	0.459534i	$-0.848016\pi$
$971$	−1.43687	+	2.48874i	−0.0461115	+	0.0798674i	0.842048	+	0.539402i	$0.181350\pi$
$972$		0			0
$973$	−14.1618	−	24.5289i	−0.454005	−	0.786360i
$974$		0			0
$975$	2.98416	+	7.08564i	0.0955698	+	0.226922i
$976$		0			0
$977$	4.32031	+	7.48300i	0.138219	+	0.239402i	0.926823	−	0.375500i	$-0.122529\pi$
$977$	4.32031	+	7.48300i	0.138219	+	0.239402i	−0.788604	+	0.614902i	$0.789196\pi$
$978$		0			0
$979$	53.2255			1.70109
$980$		0			0
$981$	37.3745	+	9.54231i	1.19327	+	0.304662i
$982$		0			0
$983$	−7.94611	−	13.7631i	−0.253441	−	0.438974i	0.711030	−	0.703162i	$-0.248229\pi$
$983$	−7.94611	−	13.7631i	−0.253441	−	0.438974i	−0.964471	+	0.264189i	$0.914896\pi$
$984$		0			0
$985$	−6.43672			−0.205091
$986$		0			0
$987$	20.6397	+	49.0072i	0.656969	+	1.55992i
$988$		0			0
$989$	0.157905			0.00502109
$990$		0			0
$991$	−6.36050	+	11.0167i	−0.202048	+	0.349957i	−0.949188	−	0.314709i	$-0.898093\pi$
$991$	−6.36050	+	11.0167i	−0.202048	+	0.349957i	0.747140	+	0.664666i	$0.231426\pi$
$992$		0			0
$993$	9.04397	+	21.4741i	0.287002	+	0.681460i
$994$		0			0
$995$	29.9397	+	51.8571i	0.949153	+	1.64398i
$996$		0			0
$997$	26.2182			0.830339			0.415169	−	0.909744i	$-0.363722\pi$
$997$	26.2182			0.830339			0.415169	+	0.909744i	$0.363722\pi$
$998$		0			0
$999$	−14.0898	−	5.54554i	−0.445783	−	0.175453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.l.a.277.6	yes	40
3.2	odd	2		2052.2.l.a.505.15		40
9.4	even	3		684.2.j.a.49.9	✓	40
9.5	odd	6		2052.2.j.a.1873.6		40
19.7	even	3		684.2.j.a.349.9	yes	40
57.26	odd	6		2052.2.j.a.1261.6		40
171.121	even	3	inner	684.2.l.a.121.6	yes	40
171.140	odd	6		2052.2.l.a.577.15		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.j.a.49.9	✓	40	9.4	even	3
684.2.j.a.349.9	yes	40	19.7	even	3
684.2.l.a.121.6	yes	40	171.121	even	3	inner
684.2.l.a.277.6	yes	40	1.1	even	1	trivial
2052.2.j.a.1261.6		40	57.26	odd	6
2052.2.j.a.1873.6		40	9.5	odd	6
2052.2.l.a.505.15		40	3.2	odd	2
2052.2.l.a.577.15		40	171.140	odd	6

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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04626 + 1.38034i) q^{3} -2.40565 q^{5} +(-1.53172 + 2.65301i) q^{7} +(-0.810664 - 2.88839i) q^{9} +(-2.96810 + 5.14089i) q^{11} +(2.81967 - 4.88381i) q^{13} +(2.51694 - 3.32060i) q^{15} +(1.15507 - 2.00063i) q^{17} +(1.16718 - 4.19973i) q^{19} +(-2.05947 - 4.89004i) q^{21} +(-0.654760 + 1.13408i) q^{23} +0.787132 q^{25} +(4.83513 + 1.90303i) q^{27} +6.77137 q^{29} +(-4.86166 - 8.42064i) q^{31} +(-3.99076 - 9.47571i) q^{33} +(3.68477 - 6.38221i) q^{35} -2.91406 q^{37} +(3.79119 + 9.00185i) q^{39} -3.91785 q^{41} +(-0.0602912 - 0.104427i) q^{43} +(1.95017 + 6.94845i) q^{45} -10.0218 q^{47} +(-1.19232 - 2.06516i) q^{49} +(1.55305 + 3.68757i) q^{51} +(-4.85905 - 8.41612i) q^{53} +(7.14019 - 12.3672i) q^{55} +(4.57586 + 6.00512i) q^{57} +8.36293 q^{59} +9.94221 q^{61} +(8.90466 + 2.27350i) q^{63} +(-6.78312 + 11.7487i) q^{65} +(5.03862 - 8.72714i) q^{67} +(-0.880358 - 2.09033i) q^{69} +(-1.00262 + 1.73659i) q^{71} +(-4.09931 + 7.10022i) q^{73} +(-0.823547 + 1.08651i) q^{75} +(-9.09258 - 15.7488i) q^{77} +(-5.70591 - 9.88293i) q^{79} +(-7.68565 + 4.68303i) q^{81} +(-2.77092 + 4.79938i) q^{83} +(-2.77868 + 4.81282i) q^{85} +(-7.08464 + 9.34678i) q^{87} +(-4.48313 - 7.76501i) q^{89} +(8.63788 + 14.9612i) q^{91} +(16.7099 + 2.09948i) q^{93} +(-2.80781 + 10.1031i) q^{95} +(-3.43051 - 5.94182i) q^{97} +(17.2551 + 4.40550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) \) 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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