LMFDB - Embedded newform 798.2.cc.a.317.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			317.20
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.a.725.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(1.19003 + 1.25850i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.890265 + 2.44598i) q^{5} +(-1.03273 + 1.39049i) q^{6} +(-2.59902 - 0.495088i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.167638 + 2.99531i) q^{9} +(-2.56342 - 0.452000i) q^{10} +(0.968132 + 0.558951i) q^{11} +(-1.54870 - 0.775586i) q^{12} +(-0.376322 - 1.03393i) q^{13} +(0.0362518 - 2.64550i) q^{14} +(-4.13771 + 1.79041i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.469922 - 1.29110i) q^{17} +(-2.97892 + 0.355040i) q^{18} +(-1.32697 + 4.15200i) q^{19} -2.60296i q^{20} +(-2.46985 - 3.86003i) q^{21} +(-0.382345 + 1.05049i) q^{22} +(-1.94234 + 2.31479i) q^{23} +(0.494875 - 1.65985i) q^{24} +(-1.36004 - 1.14121i) q^{25} +(0.952880 - 0.550145i) q^{26} +(-3.96909 + 3.35355i) q^{27} +(2.61161 - 0.423686i) q^{28} +(-3.58761 - 3.01036i) q^{29} +(-2.48171 - 3.76395i) q^{30} -7.98280i q^{31} +(0.766044 + 0.642788i) q^{32} +(0.448671 + 1.88356i) q^{33} +(1.35309 + 0.238586i) q^{34} +(3.52479 - 5.91639i) q^{35} +(-0.866929 - 2.87201i) q^{36} +(-4.01120 - 2.31587i) q^{37} +(-4.31935 - 0.585824i) q^{38} +(0.853370 - 1.70402i) q^{39} +(2.56342 - 0.452000i) q^{40} +(2.98936 + 1.08804i) q^{41} +(3.37250 - 3.10262i) q^{42} +(0.593141 + 3.36387i) q^{43} +(-1.10092 - 0.194122i) q^{44} +(-7.17725 - 3.07666i) q^{45} +(-2.61691 - 1.51087i) q^{46} +(3.38692 + 9.30550i) q^{47} +(1.72057 + 0.199127i) q^{48} +(6.50978 + 2.57348i) q^{49} +(0.887706 - 1.53755i) q^{50} +(2.18407 - 0.945057i) q^{51} +(0.707253 + 0.842871i) q^{52} +(-5.40713 + 1.96804i) q^{53} +(-3.99183 - 3.32645i) q^{54} +(-2.22908 + 1.87042i) q^{55} +(0.870750 + 2.49836i) q^{56} +(-6.80443 + 3.27103i) q^{57} +(2.34165 - 4.05585i) q^{58} +(1.60078 + 0.582635i) q^{59} +(3.27582 - 3.09761i) q^{60} +(3.23637 + 2.71564i) q^{61} +(7.86152 - 1.38620i) q^{62} +(1.91864 - 7.70187i) q^{63} +(-0.500000 + 0.866025i) q^{64} +2.86401 q^{65} +(-1.77704 + 0.768932i) q^{66} +(1.15342 + 0.203379i) q^{67} +1.37396i q^{68} +(-5.22461 + 0.310247i) q^{69} +(6.43858 + 2.44387i) q^{70} +(0.436878 + 2.47766i) q^{71} +(2.67784 - 1.35248i) q^{72} +(0.846397 + 4.80015i) q^{73} +(1.58415 - 4.35241i) q^{74} +(-0.182285 - 3.06970i) q^{75} +(-0.173123 - 4.35546i) q^{76} +(-2.23946 - 1.93203i) q^{77} +(1.82632 + 0.544506i) q^{78} +(-1.88575 - 2.24736i) q^{79} +(0.890265 + 2.44598i) q^{80} +(-8.94380 - 1.00425i) q^{81} +(-0.552412 + 3.13288i) q^{82} +(15.0823 + 8.70774i) q^{83} +(3.64111 + 2.78250i) q^{84} +(2.73966 + 2.29884i) q^{85} +(-3.20977 + 1.16826i) q^{86} +(-0.480842 - 8.09744i) q^{87} -1.11790i q^{88} +(-2.27005 + 12.8741i) q^{89} +(1.78361 - 7.60246i) q^{90} +(0.466177 + 2.87353i) q^{91} +(1.03350 - 2.83951i) q^{92} +(10.0463 - 9.49981i) q^{93} +(-8.57599 + 4.95135i) q^{94} +(-8.97438 - 6.94214i) q^{95} +(0.102672 + 1.72901i) q^{96} +(-8.80844 - 10.4975i) q^{97} +(-1.40398 + 6.85776i) q^{98} +(-1.83653 + 2.80616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 q^{15} + 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} - 9 q^{27} - 12 q^{28} + 6 q^{29} + 12 q^{33} + 6 q^{34} - 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * q^15 + 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 - 9 * q^27 - 12 * q^28 + 6 * q^29 + 12 * q^33 + 6 * q^34 - 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 + 6 * q^44 + 18 * q^45 - 18 * q^46 + 12 * q^47 + 24 * q^49 + 87 * q^50 - 24 * q^51 + 12 * q^52 - 36 * q^53 - 18 * q^54 - 18 * q^57 + 24 * q^59 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * q^63 - 81 * q^64 - 72 * q^65 + 12 * q^66 - 63 * q^67 + 9 * q^69 + 12 * q^70 + 12 * q^71 - 51 * q^73 - 42 * q^74 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.19003	+	1.25850i	0.687067	+	0.726595i
$3$	1.19003	+	1.25850i	0.687067	+	0.726595i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.890265	+	2.44598i	−0.398139	+	1.09388i	0.565051	+	0.825056i	$0.308856\pi$
$5$	−0.890265	+	2.44598i	−0.398139	+	1.09388i	−0.963190	+	0.268822i	$0.913366\pi$
$6$	−1.03273	+	1.39049i	−0.421611	+	0.567665i
$7$	−2.59902	−	0.495088i	−0.982336	−	0.187126i
$7$	−2.59902	−	0.495088i	−0.982336	−	0.187126i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.167638	+	2.99531i	−0.0558792	+	0.998438i
$10$	−2.56342	−	0.452000i	−0.810624	−	0.142935i
$11$	0.968132	+	0.558951i	0.291903	+	0.168530i	0.638800	−	0.769373i	$-0.279431\pi$
$11$	0.968132	+	0.558951i	0.291903	+	0.168530i	−0.346897	+	0.937903i	$0.612765\pi$
$12$	−1.54870	−	0.775586i	−0.447071	−	0.223892i
$13$	−0.376322	−	1.03393i	−0.104373	−	0.286762i	0.876503	−	0.481396i	$-0.159870\pi$
$13$	−0.376322	−	1.03393i	−0.104373	−	0.286762i	−0.980876	+	0.194634i	$0.937648\pi$
$14$	0.0362518	−	2.64550i	0.00968871	−	0.707040i
$15$	−4.13771	+	1.79041i	−1.06835	+	0.462281i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.469922	−	1.29110i	0.113973	−	0.313138i	−0.869571	−	0.493808i	$-0.835604\pi$
$17$	0.469922	−	1.29110i	0.113973	−	0.313138i	0.983544	+	0.180670i	$0.0578267\pi$
$18$	−2.97892	+	0.355040i	−0.702137	+	0.0836837i
$19$	−1.32697	+	4.15200i	−0.304428	+	0.952535i
$19$	−1.32697	+	4.15200i	−0.304428	+	0.952535i
$20$		−	2.60296i		−	0.582040i
$21$	−2.46985	−	3.86003i	−0.538966	−	0.842328i
$22$	−0.382345	+	1.05049i	−0.0815163	+	0.223964i
$23$	−1.94234	+	2.31479i	−0.405006	+	0.482667i	−0.929539	−	0.368723i	$-0.879795\pi$
$23$	−1.94234	+	2.31479i	−0.405006	+	0.482667i	0.524534	+	0.851390i	$0.324240\pi$
$24$	0.494875	−	1.65985i	0.101016	−	0.338815i
$25$	−1.36004	−	1.14121i	−0.272009	−	0.228243i
$26$	0.952880	−	0.550145i	0.186875	−	0.107892i
$27$	−3.96909	+	3.35355i	−0.763852	+	0.645391i
$28$	2.61161	−	0.423686i	0.493547	−	0.0800691i
$29$	−3.58761	−	3.01036i	−0.666203	−	0.559011i	0.245736	−	0.969337i	$-0.420970\pi$
$29$	−3.58761	−	3.01036i	−0.666203	−	0.559011i	−0.911939	+	0.410326i	$0.865415\pi$
$30$	−2.48171	−	3.76395i	−0.453097	−	0.687200i
$31$		−	7.98280i		−	1.43375i	−0.697200	−	0.716877i	$-0.745571\pi$
$31$		−	7.98280i		−	1.43375i	0.697200	−	0.716877i	$-0.254429\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	0.448671	+	1.88356i	0.0781036	+	0.327886i
$34$	1.35309	+	0.238586i	0.232052	+	0.0409171i
$35$	3.52479	−	5.91639i	0.595799	−	1.00005i
$36$	−0.866929	−	2.87201i	−0.144488	−	0.478668i
$37$	−4.01120	−	2.31587i	−0.659438	−	0.380726i	0.132625	−	0.991166i	$-0.457659\pi$
$37$	−4.01120	−	2.31587i	−0.659438	−	0.380726i	−0.792063	+	0.610440i	$0.790993\pi$
$38$	−4.31935	−	0.585824i	−0.700692	−	0.0950333i
$39$	0.853370	−	1.70402i	0.136649	−	0.272861i
$40$	2.56342	−	0.452000i	0.405312	−	0.0714674i
$41$	2.98936	+	1.08804i	0.466860	+	0.169923i	0.564729	−	0.825276i	$-0.308981\pi$
$41$	2.98936	+	1.08804i	0.466860	+	0.169923i	−0.0978694	+	0.995199i	$0.531203\pi$
$42$	3.37250	−	3.10262i	0.520388	−	0.478744i
$43$	0.593141	+	3.36387i	0.0904532	+	0.512985i	0.996046	+	0.0888376i	$0.0283152\pi$
$43$	0.593141	+	3.36387i	0.0904532	+	0.512985i	−0.905593	+	0.424148i	$0.860574\pi$
$44$	−1.10092	−	0.194122i	−0.165970	−	0.0292650i
$45$	−7.17725	−	3.07666i	−1.06992	−	0.458642i
$46$	−2.61691	−	1.51087i	−0.385842	−	0.222766i
$47$	3.38692	+	9.30550i	0.494034	+	1.35735i	0.896959	+	0.442113i	$0.145771\pi$
$47$	3.38692	+	9.30550i	0.494034	+	1.35735i	−0.402926	+	0.915233i	$0.632007\pi$
$48$	1.72057	+	0.199127i	0.248342	+	0.0287415i
$49$	6.50978	+	2.57348i	0.929968	+	0.367640i
$50$	0.887706	−	1.53755i	0.125541	−	0.217443i
$51$	2.18407	−	0.945057i	0.305831	−	0.132334i
$52$	0.707253	+	0.842871i	0.0980784	+	0.116885i
$53$	−5.40713	+	1.96804i	−0.742727	+	0.270331i	−0.685542	−	0.728033i	$-0.740435\pi$
$53$	−5.40713	+	1.96804i	−0.742727	+	0.270331i	−0.0571850	+	0.998364i	$0.518212\pi$
$54$	−3.99183	−	3.32645i	−0.543219	−	0.452673i
$55$	−2.22908	+	1.87042i	−0.300569	+	0.252208i
$56$	0.870750	+	2.49836i	0.116359	+	0.333857i
$57$	−6.80443	+	3.27103i	−0.901269	+	0.433259i
$58$	2.34165	−	4.05585i	0.307473	−	0.532559i
$59$	1.60078	+	0.582635i	0.208403	+	0.0758526i	0.444112	−	0.895971i	$-0.353519\pi$
$59$	1.60078	+	0.582635i	0.208403	+	0.0758526i	−0.235709	+	0.971824i	$0.575741\pi$
$60$	3.27582	−	3.09761i	0.422907	−	0.399900i
$61$	3.23637	+	2.71564i	0.414375	+	0.347702i	0.826018	−	0.563643i	$-0.190601\pi$
$61$	3.23637	+	2.71564i	0.414375	+	0.347702i	−0.411643	+	0.911345i	$0.635045\pi$
$62$	7.86152	−	1.38620i	0.998415	−	0.176047i
$63$	1.91864	−	7.70187i	0.241725	−	0.970345i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.86401			0.355237
$66$	−1.77704	+	0.768932i	−0.218738	+	0.0946490i
$67$	1.15342	+	0.203379i	0.140913	+	0.0248467i	0.243660	−	0.969861i	$-0.421652\pi$
$67$	1.15342	+	0.203379i	0.140913	+	0.0248467i	−0.102747	+	0.994708i	$0.532763\pi$
$68$			1.37396i			0.166617i
$69$	−5.22461	+	0.310247i	−0.628969	+	0.0373494i
$70$	6.43858	+	2.44387i	0.769558	+	0.292098i
$71$	0.436878	+	2.47766i	0.0518478	+	0.294044i	0.999695	−	0.0246804i	$-0.00785681\pi$
$71$	0.436878	+	2.47766i	0.0518478	+	0.294044i	−0.947848	+	0.318724i	$0.896746\pi$
$72$	2.67784	−	1.35248i	0.315586	−	0.159391i
$73$	0.846397	+	4.80015i	0.0990632	+	0.561816i	0.993426	+	0.114474i	$0.0365182\pi$
$73$	0.846397	+	4.80015i	0.0990632	+	0.561816i	−0.894363	+	0.447342i	$0.852371\pi$
$74$	1.58415	−	4.35241i	0.184153	−	0.505957i
$75$	−0.182285	−	3.06970i	−0.0210484	−	0.354458i
$76$	−0.173123	−	4.35546i	−0.0198586	−	0.499605i
$77$	−2.23946	−	1.93203i	−0.255210	−	0.220176i
$78$	1.82632	+	0.544506i	0.206790	+	0.0616532i
$79$	−1.88575	−	2.24736i	−0.212164	−	0.252847i	0.649458	−	0.760397i	$-0.274996\pi$
$79$	−1.88575	−	2.24736i	−0.212164	−	0.252847i	−0.861622	+	0.507550i	$0.830551\pi$
$80$	0.890265	+	2.44598i	0.0995347	+	0.273469i
$81$	−8.94380	−	1.00425i	−0.993755	−	0.111584i
$82$	−0.552412	+	3.13288i	−0.0610037	+	0.345969i
$83$	15.0823	+	8.70774i	1.65549	+	0.955799i	0.974757	+	0.223270i	$0.0716733\pi$
$83$	15.0823	+	8.70774i	1.65549	+	0.955799i	0.680736	+	0.732529i	$0.261660\pi$
$84$	3.64111	+	2.78250i	0.397278	+	0.303596i
$85$	2.73966	+	2.29884i	0.297157	+	0.249345i
$86$	−3.20977	+	1.16826i	−0.346118	+	0.125977i
$87$	−0.480842	−	8.09744i	−0.0515516	−	0.868137i
$88$		−	1.11790i		−	0.119169i
$89$	−2.27005	+	12.8741i	−0.240625	+	1.36465i	0.589812	+	0.807540i	$0.299202\pi$
$89$	−2.27005	+	12.8741i	−0.240625	+	1.36465i	−0.830437	+	0.557112i	$0.811909\pi$
$90$	1.78361	−	7.60246i	0.188009	−	0.801370i
$91$	0.466177	+	2.87353i	0.0488687	+	0.301227i
$92$	1.03350	−	2.83951i	0.107749	−	0.296039i
$93$	10.0463	−	9.49981i	1.04176	−	0.985084i
$94$	−8.57599	+	4.95135i	−0.884546	+	0.510693i
$95$	−8.97438	−	6.94214i	−0.920752	−	0.712249i
$96$	0.102672	+	1.72901i	0.0104789	+	0.176466i
$97$	−8.80844	−	10.4975i	−0.894362	−	1.06586i	−0.997463	−	0.0711883i	$-0.977321\pi$
$97$	−8.80844	−	10.4975i	−0.894362	−	1.06586i	0.103101	−	0.994671i	$-0.467124\pi$
$98$	−1.40398	+	6.85776i	−0.141823	+	0.692738i
$99$	−1.83653	+	2.80616i	−0.184578	+	0.282029i
$100$	1.66834	+	0.607227i	0.166834	+	0.0607227i
$101$	2.14541	−	2.55680i	0.213476	−	0.254411i	−0.648671	−	0.761069i	$-0.724675\pi$
$101$	2.14541	−	2.55680i	0.213476	−	0.254411i	0.862147	+	0.506658i	$0.169119\pi$
$102$	1.30996	+	1.98678i	0.129705	+	0.196721i
$103$			12.9217i			1.27321i	0.771188	+	0.636607i	$0.219663\pi$
$103$			12.9217i			1.27321i	−0.771188	+	0.636607i	$0.780337\pi$
$104$	−0.707253	+	0.842871i	−0.0693519	+	0.0826503i
$105$	11.6404	−	2.60477i	1.13599	−	0.254199i
$106$	−2.87708	−	4.98324i	−0.279446	−	0.484015i
$107$	3.00269	+	5.20081i	0.290281	+	0.502781i	0.973876	−	0.227080i	$-0.0729179\pi$
$107$	3.00269	+	5.20081i	0.290281	+	0.502781i	−0.683595	+	0.729861i	$0.739585\pi$
$108$	2.58274	−	4.50882i	0.248525	−	0.433861i
$109$	10.8134	+	12.8869i	1.03574	+	1.23434i	0.971656	+	0.236398i	$0.0759668\pi$
$109$	10.8134	+	12.8869i	1.03574	+	1.23434i	0.0640799	+	0.997945i	$0.479589\pi$
$110$	−2.22908	−	1.87042i	−0.212535	−	0.178338i
$111$	−1.85895	−	7.80405i	−0.176444	−	0.740728i
$112$	−2.30920	+	1.29136i	−0.218199	+	0.122022i
$113$	−6.36375			−0.598651			−0.299325	−	0.954151i	$-0.596762\pi$
$113$	−6.36375			−0.598651			−0.299325	+	0.954151i	$0.596762\pi$
$114$	−4.40292	−	6.13305i	−0.412371	−	0.574413i
$115$	−3.93274	−	6.81171i	−0.366730	−	0.635195i
$116$	4.40086	+	1.60178i	0.408609	+	0.148722i
$117$	3.16004	−	0.953874i	0.292146	−	0.0881857i
$118$	−0.295811	+	1.67763i	−0.0272317	+	0.154438i
$119$	−1.86054	+	3.12294i	−0.170556	+	0.286279i
$120$	3.61939	+	2.68816i	0.330404	+	0.245395i
$121$	−4.87515	−	8.44400i	−0.443195	−	0.767637i
$122$	−2.11239	+	3.65877i	−0.191247	+	0.331249i
$123$	2.18815	+	5.05691i	0.197299	+	0.455966i
$124$	2.73028	+	7.50138i	0.245186	+	0.673644i
$125$	−7.26897	+	4.19674i	−0.650156	+	0.375368i
$126$	7.91803	+	0.552072i	0.705394	+	0.0491824i
$127$	−0.844346	−	2.31982i	−0.0749236	−	0.205851i	0.896577	−	0.442888i	$-0.146046\pi$
$127$	−0.844346	−	2.31982i	−0.0749236	−	0.205851i	−0.971501	+	0.237037i	$0.923824\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−3.52757	+	4.74959i	−0.310585	+	0.418178i
$130$	0.497331	+	2.82050i	0.0436188	+	0.247375i
$131$	−5.94250	+	1.04782i	−0.519199	+	0.0915488i	−0.427106	−	0.904202i	$-0.640467\pi$
$131$	−5.94250	+	1.04782i	−0.519199	+	0.0915488i	−0.0920931	+	0.995750i	$0.529356\pi$
$132$	−1.06583	−	1.61652i	−0.0927686	−	0.140700i
$133$	5.50443	−	10.1342i	0.477295	−	0.878743i
$134$			1.17121i			0.101177i
$135$	−4.66919	−	12.6939i	−0.401860	−	1.09252i
$136$	−1.35309	+	0.238586i	−0.116026	+	0.0204586i
$137$	−0.0979446	−	0.269101i	−0.00836798	−	0.0229908i	0.935438	−	0.353490i	$-0.115005\pi$
$137$	−0.0979446	−	0.269101i	−0.00836798	−	0.0229908i	−0.943806	+	0.330499i	$0.892783\pi$
$138$	−1.21278	−	5.09136i	−0.103238	−	0.433405i
$139$	9.06026	−	3.29766i	0.768481	−	0.279704i	0.0721202	−	0.997396i	$-0.477023\pi$
$139$	9.06026	−	3.29766i	0.768481	−	0.279704i	0.696361	+	0.717692i	$0.254801\pi$
$140$	−1.28869	+	6.76514i	−0.108915	+	0.571759i
$141$	−7.68040	+	15.3363i	−0.646806	+	1.29155i
$142$	−2.36415	+	0.860481i	−0.198395	+	0.0722099i
$143$	0.213590	−	1.21133i	0.0178613	−	0.101297i
$144$	1.79693	+	2.40230i	0.149744	+	0.200191i
$145$	10.5572	−	6.09522i	0.876730	−	0.506180i
$146$	−4.58025	+	1.66708i	−0.379064	+	0.137968i
$147$	4.50813	+	11.2551i	0.371824	+	0.928303i
$148$	4.56137	+	0.804293i	0.374942	+	0.0661125i
$149$	3.23877	+	3.85982i	0.265330	+	0.316208i	0.882216	−	0.470844i	$-0.156051\pi$
$149$	3.23877	+	3.85982i	0.265330	+	0.316208i	−0.616886	+	0.787052i	$0.711606\pi$
$150$	2.99141	−	0.712562i	0.244247	−	0.0581805i
$151$	−12.2792	+	7.08940i	−0.999268	+	0.576927i	−0.908032	−	0.418902i	$-0.862415\pi$
$151$	−12.2792	+	7.08940i	−0.999268	+	0.576927i	−0.0912362	+	0.995829i	$0.529082\pi$
$152$	4.25923	−	0.926811i	0.345469	−	0.0751743i
$153$	3.78847	+	1.62400i	0.306280	+	0.131293i
$154$	1.51380	−	2.54093i	0.121986	−	0.204754i
$155$	19.5258	+	7.10681i	1.56835	+	0.570833i
$156$	−0.219097	+	1.89312i	−0.0175418	+	0.151571i
$157$	15.9911	−	13.4182i	1.27623	−	1.07089i	0.282480	−	0.959273i	$-0.408843\pi$
$157$	15.9911	−	13.4182i	1.27623	−	1.07089i	0.993752	−	0.111612i	$-0.0356014\pi$
$158$	1.88575	−	2.24736i	0.150023	−	0.178790i
$159$	−8.91144	−	4.46284i	−0.706724	−	0.353926i
$160$	−2.25423	+	1.30148i	−0.178213	+	0.102891i
$161$	6.19419	−	5.05455i	0.488171	−	0.398354i
$162$	−0.564076	−	8.98231i	−0.0443180	−	0.705717i
$163$	−16.3604			−1.28144			−0.640722	−	0.767773i	$-0.721365\pi$
$163$	−16.3604			−1.28144			−0.640722	+	0.767773i	$0.721365\pi$
$164$	−3.18121			−0.248411
$165$	−5.00660	−	0.579431i	−0.389764	−	0.0451086i
$166$	−5.95645	+	16.3652i	−0.462310	+	1.27019i
$167$	0.438514	−	2.48693i	0.0339332	−	0.192445i	−0.963129	−	0.269040i	$-0.913294\pi$
$167$	0.438514	−	2.48693i	0.0339332	−	0.192445i	0.997062	+	0.0765950i	$0.0244048\pi$
$168$	−2.10796	+	4.06897i	−0.162633	+	0.313928i
$169$	9.03117	−	7.57805i	0.694706	−	0.582927i
$170$	−1.78818	+	3.09722i	−0.137147	+	0.237546i
$171$	−12.2141	−	4.67073i	−0.934036	−	0.357180i
$172$	−1.70788	−	2.95814i	−0.130225	−	0.225556i
$173$	1.29503	+	7.34445i	0.0984589	+	0.558388i	0.993632	+	0.112670i	$0.0359404\pi$
$173$	1.29503	+	7.34445i	0.0984589	+	0.558388i	−0.895173	+	0.445718i	$0.852948\pi$
$174$	7.89092	−	1.87964i	0.598209	−	0.142495i
$175$	2.96978	+	3.63937i	0.224494	+	0.275111i
$176$	1.10092	−	0.194122i	0.0829849	−	0.0146325i
$177$	1.17173	+	2.70793i	0.0880728	+	0.203540i
$178$	−13.0727			−0.979841
$179$	−8.57267	+	14.8483i	−0.640752	+	1.10981i	0.344514	+	0.938781i	$0.388044\pi$
$179$	−8.57267	+	14.8483i	−0.640752	+	1.10981i	−0.985265	+	0.171033i	$0.945290\pi$
$180$	7.79669	+	0.436355i	0.581131	+	0.0325239i
$181$	13.7700	−	16.4104i	1.02351	−	1.21978i	0.0482256	−	0.998836i	$-0.484643\pi$
$181$	13.7700	−	16.4104i	1.02351	−	1.21978i	0.975288	−	0.220939i	$-0.0709122\pi$
$182$	−2.74892	+	0.958078i	−0.203764	+	0.0710174i
$183$	0.433766	+	7.30467i	0.0320649	+	0.539977i
$184$	2.97584	+	0.524720i	0.219382	+	0.0386829i
$185$	9.23561	−	7.74960i	0.679016	−	0.569762i
$186$	11.1000	+	8.24409i	0.813892	+	0.604486i
$187$	1.17661	−	0.987292i	0.0860422	−	0.0721980i
$188$	−6.36533	−	7.58591i	−0.464240	−	0.553259i
$189$	11.9760	−	6.75089i	0.871129	−	0.491055i
$190$	5.27829	−	10.0435i	0.382927	−	0.728634i
$191$	−6.54766	−	3.78029i	−0.473772	−	0.273532i	0.244045	−	0.969764i	$-0.421525\pi$
$191$	−6.54766	−	3.78029i	−0.473772	−	0.273532i	−0.717817	+	0.696231i	$0.754859\pi$
$192$	−1.68491	+	0.401350i	−0.121598	+	0.0289650i
$193$	10.2727	−	1.81135i	0.739442	−	0.130384i	0.208775	−	0.977964i	$-0.433052\pi$
$193$	10.2727	−	1.81135i	0.739442	−	0.130384i	0.530667	+	0.847580i	$0.321941\pi$
$194$	8.80844	−	10.4975i	0.632409	−	0.753676i
$195$	3.40828	+	3.60436i	0.244072	+	0.258113i
$196$	−6.99737	−	0.191809i	−0.499812	−	0.0137006i
$197$	12.7071	+	7.33645i	0.905343	+	0.522700i	0.878930	−	0.476951i	$-0.158258\pi$
$197$	12.7071	+	7.33645i	0.905343	+	0.522700i	0.0264133	+	0.999651i	$0.491591\pi$
$198$	−3.08244	−	1.32134i	−0.219059	−	0.0939039i
$199$	−3.45999	+	19.6226i	−0.245272	+	1.39101i	0.574587	+	0.818444i	$0.305163\pi$
$199$	−3.45999	+	19.6226i	−0.245272	+	1.39101i	−0.819859	+	0.572565i	$0.805948\pi$
$200$	−0.308297	+	1.74844i	−0.0217999	+	0.123633i
$201$	1.11666	+	1.69360i	0.0787629	+	0.119458i
$202$	2.89051	+	1.66883i	0.203375	+	0.117419i
$203$	7.83387	+	9.60017i	0.549830	+	0.673800i
$204$	−1.72913	+	1.63506i	−0.121063	+	0.114477i
$205$	−5.32265	+	6.34329i	−0.371750	+	0.443035i
$206$	−12.7254	+	2.24383i	−0.886621	+	0.156335i
$207$	−6.60791	−	6.20596i	−0.459281	−	0.431344i
$208$	−0.952880	−	0.550145i	−0.0660703	−	0.0381457i
$209$	−3.60545	+	3.27798i	−0.249394	+	0.226742i
$210$	4.58653	+	11.0112i	0.316500	+	0.759848i
$211$	−0.799909	−	0.953295i	−0.0550680	−	0.0656275i	0.737807	−	0.675011i	$-0.235861\pi$
$211$	−0.799909	−	0.953295i	−0.0550680	−	0.0656275i	−0.792875	+	0.609384i	$0.791417\pi$
$212$	4.40794	−	3.69870i	0.302738	−	0.254028i
$213$	−2.59823	+	3.49830i	−0.178028	+	0.239700i
$214$	−4.60039	+	3.86018i	−0.314476	+	0.263877i
$215$	−8.75603	−	1.54392i	−0.597156	−	0.105295i
$216$	4.88881	+	1.76056i	0.332641	+	0.119791i
$217$	−3.95219	+	20.7474i	−0.268292	+	1.40843i
$218$	−10.8134	+	12.8869i	−0.732376	+	0.872812i
$219$	−5.03375	+	6.77754i	−0.340149	+	0.457983i
$220$	1.45493	−	2.52001i	0.0980913	−	0.169899i
$221$	−1.51176			−0.101692
$222$	7.36269	−	3.18587i	0.494151	−	0.213821i
$223$	17.1463	−	3.02336i	1.14820	−	0.202459i	0.433011	−	0.901389i	$-0.357451\pi$
$223$	17.1463	−	3.02336i	1.14820	−	0.202459i	0.715190	+	0.698930i	$0.246340\pi$
$224$	−1.67273	−	2.04988i	−0.111764	−	0.136963i
$225$	3.64628	−	3.88245i	0.243086	−	0.258830i
$226$	−1.10505	−	6.26707i	−0.0735070	−	0.416879i
$227$	10.8527	+	18.7975i	0.720322	+	1.24763i	0.960871	+	0.276997i	$0.0893392\pi$
$227$	10.8527	+	18.7975i	0.720322	+	1.24763i	−0.240549	+	0.970637i	$0.577328\pi$
$228$	5.27532	−	5.40102i	0.349366	−	0.357691i
$229$	14.5288	−	25.1647i	0.960092	−	1.66293i	0.237832	−	0.971306i	$-0.423563\pi$
$229$	14.5288	−	25.1647i	0.960092	−	1.66293i	0.722260	−	0.691621i	$-0.243103\pi$
$230$	6.02531	−	5.05583i	0.397297	−	0.333372i
$231$	−0.233573	−	5.11755i	−0.0153680	−	0.336710i
$232$	−0.813246	+	4.61214i	−0.0533922	+	0.302802i
$233$	−8.18791	+	22.4961i	−0.536408	+	1.47377i	0.314911	+	0.949121i	$0.398025\pi$
$233$	−8.18791	+	22.4961i	−0.536408	+	1.47377i	−0.851319	+	0.524648i	$0.824197\pi$
$234$	1.48812	+	2.94640i	0.0972814	+	0.192612i
$235$	−25.7764			−1.68146
$236$	−1.70351			−0.110889
$237$	0.584181	−	5.04765i	0.0379466	−	0.327880i
$238$	−3.39857	−	1.28999i	−0.220297	−	0.0836173i
$239$	−7.85952	+	4.53770i	−0.508390	+	0.293519i	−0.732172	−	0.681120i	$-0.761493\pi$
$239$	−7.85952	+	4.53770i	−0.508390	+	0.293519i	0.223782	+	0.974639i	$0.428160\pi$
$240$	−2.01882	+	4.03120i	−0.130314	+	0.260213i
$241$	−4.82535	+	5.75063i	−0.310828	+	0.370431i	−0.898731	−	0.438501i	$-0.855510\pi$
$241$	−4.82535	+	5.75063i	−0.310828	+	0.370431i	0.587902	+	0.808932i	$0.299954\pi$
$242$	7.46916	−	6.26737i	0.480136	−	0.402882i
$243$	−9.37957	−	12.4509i	−0.601700	−	0.798722i
$244$	−3.97000	−	1.44496i	−0.254153	−	0.0925042i
$245$	−12.0901	+	13.6317i	−0.772410	+	0.870899i
$246$	−4.60012	+	3.03303i	−0.293293	+	0.193379i
$247$	4.79227	−	0.190486i	0.304925	−	0.0121203i
$248$	−6.91331	+	3.99140i	−0.438996	+	0.253454i
$249$	6.98971	+	29.3435i	0.442955	+	1.85957i
$250$	−5.39523	−	6.42978i	−0.341224	−	0.406655i
$251$	29.5757	+	5.21499i	1.86680	+	0.329167i	0.988771	−	0.149441i	$-0.0477475\pi$
$251$	29.5757	+	5.21499i	1.86680	+	0.329167i	0.878028	+	0.478608i	$0.158859\pi$
$252$	0.831267	+	7.89360i	0.0523649	+	0.497250i
$253$	−3.17430	+	1.15535i	−0.199566	+	0.0726362i
$254$	2.13796	−	1.23435i	0.134148	−	0.0774501i
$255$	0.367192	+	6.18356i	0.0229944	+	0.387229i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−6.18569	+	2.25141i	−0.385853	+	0.140439i	−0.527661	−	0.849455i	$-0.676931\pi$
$257$	−6.18569	+	2.25141i	−0.385853	+	0.140439i	0.141808	+	0.989894i	$0.454708\pi$
$258$	−5.28999	−	2.64922i	−0.329340	−	0.164933i
$259$	9.27862	+	8.00488i	0.576546	+	0.497399i
$260$	−2.69129	+	0.979551i	−0.166907	+	0.0607492i
$261$	9.61840	−	10.2414i	0.595364	−	0.633925i
$262$	−2.06381	−	5.67027i	−0.127503	−	0.350311i
$263$	3.85842	−	0.680343i	0.237920	−	0.0419518i	−0.0534165	−	0.998572i	$-0.517011\pi$
$263$	3.85842	−	0.680343i	0.237920	−	0.0419518i	0.291337	+	0.956621i	$0.405900\pi$
$264$	1.40688	−	1.33034i	0.0865874	−	0.0818769i
$265$		−	14.9778i		−	0.920081i
$266$	10.9360	+	3.66103i	0.670531	+	0.224472i
$267$	−18.9035	+	12.4638i	−1.15687	+	0.762770i
$268$	−1.15342	+	0.203379i	−0.0704563	+	0.0124233i
$269$	−4.24238	−	24.0597i	−0.258662	−	1.46695i	−0.786494	−	0.617598i	$-0.788106\pi$
$269$	−4.24238	−	24.0597i	−0.258662	−	1.46695i	0.527831	−	0.849349i	$-0.323005\pi$
$270$	11.6902	−	6.80253i	0.711445	−	0.413989i
$271$	13.2628	+	4.82727i	0.805658	+	0.293236i	0.711829	−	0.702353i	$-0.247867\pi$
$271$	13.2628	+	4.82727i	0.805658	+	0.293236i	0.0938290	+	0.995588i	$0.470089\pi$
$272$	−0.469922	−	1.29110i	−0.0284932	−	0.0782845i
$273$	−3.06156	+	4.00628i	−0.185294	+	0.242471i
$274$	0.248005	−	0.143185i	0.0149825	−	0.00865015i
$275$	−0.678820	−	1.86504i	−0.0409344	−	0.112466i
$276$	4.80341	−	2.07846i	0.289132	−	0.125108i
$277$	−1.75593	+	3.04137i	−0.105504	+	0.182738i	−0.913944	−	0.405840i	$-0.866979\pi$
$277$	−1.75593	+	3.04137i	−0.105504	+	0.182738i	0.808440	+	0.588578i	$0.200312\pi$
$278$	4.82086	+	8.34998i	0.289136	+	0.500799i
$279$	23.9110	+	1.33822i	1.43151	+	0.0801170i
$280$	−6.88614	−	0.0943621i	−0.411526	−	0.00563922i
$281$	4.63222	−	26.2706i	0.276335	−	1.56717i	−0.458354	−	0.888770i	$-0.651561\pi$
$281$	4.63222	−	26.2706i	0.276335	−	1.56717i	0.734689	−	0.678404i	$-0.237328\pi$
$282$	−16.4370	−	4.90060i	−0.978809	−	0.291826i
$283$	19.2872	+	7.01997i	1.14651	+	0.417294i	0.844259	−	0.535936i	$-0.180041\pi$
$283$	19.2872	+	7.01997i	1.14651	+	0.417294i	0.302247	+	0.953230i	$0.402263\pi$
$284$	−1.25794	−	2.17881i	−0.0746449	−	0.129289i
$285$	−1.94315	−	19.5556i	−0.115102	−	1.15838i
$286$	1.23002			0.0727325
$287$	−7.23073	−	4.30783i	−0.426816	−	0.254283i
$288$	−2.05377	+	2.18679i	−0.121019	+	0.128858i
$289$	11.5766	+	9.71396i	0.680979	+	0.571409i
$290$	7.83586	+	9.33842i	0.460138	+	0.548371i
$291$	2.72873	−	23.5778i	0.159961	−	1.38215i
$292$	−2.43710	−	4.22118i	−0.142621	−	0.247026i
$293$	−13.4257	−	23.2540i	−0.784339	−	1.35851i	−0.929393	−	0.369091i	$-0.879669\pi$
$293$	−13.4257	−	23.2540i	−0.784339	−	1.35851i	0.145055	−	0.989424i	$-0.453664\pi$
$294$	−10.3013	+	6.39407i	−0.600782	+	0.372909i
$295$	−2.85023	+	3.39677i	−0.165947	+	0.197768i
$296$			4.63174i			0.269214i
$297$	−5.71708	+	1.02815i	−0.331739	+	0.0596595i
$298$	−3.23877	+	3.85982i	−0.187617	+	0.223593i
$299$	3.12429	+	1.13715i	0.180682	+	0.0657629i
$300$	1.22119	+	2.82223i	0.0705054	+	0.162941i
$301$	0.123828	−	9.03641i	0.00713731	−	0.520850i
$302$	−9.11396	−	10.8616i	−0.524450	−	0.625015i
$303$	5.77084	−	0.342684i	0.331526	−	0.0196867i
$304$	1.65234	+	4.03358i	0.0947681	+	0.231342i
$305$	−9.52364	+	5.49848i	−0.545322	+	0.314842i
$306$	−0.941467	+	4.01292i	−0.0538201	+	0.229403i
$307$	5.95890	−	16.3719i	0.340092	−	0.934396i	−0.645275	−	0.763951i	$-0.723257\pi$
$307$	5.95890	−	16.3719i	0.340092	−	0.934396i	0.985367	−	0.170446i	$-0.0545207\pi$
$308$	2.76520	+	1.04958i	0.157562	+	0.0598052i
$309$	−16.2620	+	15.3773i	−0.925111	+	0.874783i
$310$	−3.60822	+	20.4633i	−0.204933	+	1.16223i
$311$		−	20.5119i		−	1.16312i	−0.813502	−	0.581562i	$-0.802442\pi$
$311$		−	20.5119i		−	1.16312i	0.813502	−	0.581562i	$-0.197558\pi$
$312$	−1.90241	+	0.112969i	−0.107703	+	0.00639559i
$313$	13.5601	−	4.93546i	0.766460	−	0.278968i	0.0709448	−	0.997480i	$-0.477399\pi$
$313$	13.5601	−	4.93546i	0.766460	−	0.278968i	0.695515	+	0.718512i	$0.255176\pi$
$314$	15.9911	+	13.4182i	0.902432	+	0.757230i
$315$	17.1306	+	11.5497i	0.965198	+	0.650750i
$316$	2.54067	+	1.46686i	0.142924	+	0.0825171i
$317$	3.52070	−	19.9669i	0.197742	−	1.12145i	−0.710717	−	0.703478i	$-0.751630\pi$
$317$	3.52070	−	19.9669i	0.197742	−	1.12145i	0.908459	−	0.417973i	$-0.137259\pi$
$318$	2.84758	−	9.55102i	0.159685	−	0.535595i
$319$	−1.79064	−	4.91973i	−0.100256	−	0.275452i
$320$	−1.67315	−	1.99398i	−0.0935320	−	0.111467i
$321$	−2.97191	+	9.96802i	−0.165876	+	0.556361i
$322$	6.05337	+	5.22238i	0.337341	+	0.291032i
$323$	4.73708	+	3.66437i	0.263578	+	0.203891i
$324$	8.74789	−	2.11527i	0.485994	−	0.117515i
$325$	−0.668126	+	1.83566i	−0.0370609	+	0.101824i
$326$	−2.84095	−	16.1118i	−0.157346	−	0.892351i
$327$	−3.34984	+	28.9445i	−0.185247	+	1.60064i
$328$	−0.552412	−	3.13288i	−0.0305018	−	0.172985i
$329$	−4.19563	−	25.8620i	−0.231313	−	1.42582i
$330$	−0.298760	−	5.03116i	−0.0164462	−	0.276956i
$331$			14.9539i			0.821938i	0.911649	+	0.410969i	$0.134810\pi$
$331$			14.9539i			0.821938i	−0.911649	+	0.410969i	$0.865190\pi$
$332$	−17.1509	−	3.02417i	−0.941278	−	0.165973i
$333$	7.60918	−	11.6266i	0.416980	−	0.637132i
$334$	2.52530			0.138178
$335$	−1.52431	+	2.64018i	−0.0832820	+	0.144249i
$336$	−4.37320	−	1.36937i	−0.238577	−	0.0747050i
$337$	−18.7841	+	3.31215i	−1.02324	+	0.180424i	−0.659994	−	0.751270i	$-0.729441\pi$
$337$	−18.7841	+	3.31215i	−1.02324	+	0.180424i	−0.363242	+	0.931695i	$0.618330\pi$
$338$	9.03117	+	7.57805i	0.491231	+	0.412192i
$339$	−7.57308	−	8.00877i	−0.411313	−	0.434976i
$340$	−3.36069	−	1.22319i	−0.182259	−	0.0663368i
$341$	4.46200	−	7.72841i	0.241631	−	0.418517i
$342$	2.47881	−	12.8396i	0.134039	−	0.694286i
$343$	−15.6449	−	9.91144i	−0.844746	−	0.535167i
$344$	2.61663	−	2.19561i	0.141079	−	0.118379i
$345$	3.89243	−	13.0555i	0.209561	−	0.702885i
$346$	−7.00800	+	2.55070i	−0.376752	+	0.137127i
$347$	−20.9171	−	24.9280i	−1.12289	−	1.33821i	−0.934439	−	0.356124i	$-0.884098\pi$
$347$	−20.9171	−	24.9280i	−1.12289	−	1.33821i	−0.188450	−	0.982083i	$-0.560346\pi$
$348$	3.22133	+	7.44465i	0.172681	+	0.399075i
$349$	7.51533	−	13.0169i	0.402286	−	0.696781i	−0.591715	−	0.806147i	$-0.701549\pi$
$349$	7.51533	−	13.0169i	0.402286	−	0.696781i	0.994001	+	0.109367i	$0.0348823\pi$
$350$	−3.06839	+	3.55663i	−0.164012	+	0.190110i
$351$	4.96101	+	2.84177i	0.264799	+	0.151682i
$352$	0.382345	+	1.05049i	0.0203791	+	0.0559910i
$353$	−12.7233	−	7.34583i	−0.677195	−	0.390979i	0.121602	−	0.992579i	$-0.461197\pi$
$353$	−12.7233	−	7.34583i	−0.677195	−	0.390979i	−0.798798	+	0.601600i	$0.794530\pi$
$354$	−2.46332	+	1.62416i	−0.130924	+	0.0863231i
$355$	−6.44924	−	1.13718i	−0.342290	−	0.0603550i
$356$	−2.27005	−	12.8741i	−0.120313	−	0.682326i
$357$	−6.14432	+	1.37491i	−0.325192	+	0.0727681i
$358$	−16.1114	−	5.86405i	−0.851511	−	0.309925i
$359$	18.9603	−	3.34321i	1.00069	−	0.176448i	0.350776	−	0.936459i	$-0.385918\pi$
$359$	18.9603	−	3.34321i	1.00069	−	0.176448i	0.649909	+	0.760012i	$0.274807\pi$
$360$	0.924155	+	7.75401i	0.0487072	+	0.408672i
$361$	−15.4783	−	11.0192i	−0.814647	−	0.579957i
$362$	18.5522	+	10.7111i	0.975083	+	0.562964i
$363$	4.82517	−	16.1840i	0.253256	−	0.849441i
$364$	−1.42087	−	2.54079i	−0.0744737	−	0.133174i
$365$	−12.4946	−	2.20314i	−0.653998	−	0.115318i
$366$	−7.11838	+	1.69562i	−0.372083	+	0.0886314i
$367$	−9.19799	−	7.71803i	−0.480131	−	0.402878i	0.370343	−	0.928895i	$-0.379240\pi$
$367$	−9.19799	−	7.71803i	−0.480131	−	0.402878i	−0.850474	+	0.526017i	$0.823685\pi$
$368$			3.02174i			0.157519i
$369$	−3.76015	+	8.77168i	−0.195745	+	0.456635i
$370$	9.23561	+	7.74960i	0.480137	+	0.402882i
$371$	15.0276	−	2.43795i	0.780193	−	0.126572i
$372$	−6.19135	+	12.3629i	−0.321007	+	0.640989i
$373$	−6.16796	+	3.56107i	−0.319365	+	0.184385i	−0.651109	−	0.758984i	$-0.725696\pi$
$373$	−6.16796	+	3.56107i	−0.319365	+	0.184385i	0.331745	+	0.943369i	$0.392363\pi$
$374$	1.17661	+	0.987292i	0.0608410	+	0.0510517i
$375$	−13.9319	−	4.15372i	−0.719441	−	0.214497i
$376$	6.36533	−	7.58591i	0.328267	−	0.391213i
$377$	−1.76242	+	4.84222i	−0.0907695	+	0.249387i
$378$	8.72795	+	10.6218i	0.448917	+	0.546327i
$379$			11.7593i			0.604033i	0.953303	+	0.302016i	$0.0976597\pi$
$379$			11.7593i			0.604033i	−0.953303	+	0.302016i	$0.902340\pi$
$380$	10.8075	+	3.45406i	0.554414	+	0.177189i
$381$	1.91469	−	3.82328i	0.0980927	−	0.195872i
$382$	2.58587	−	7.10463i	0.132305	−	0.363504i
$383$	1.70812	−	1.43329i	0.0872810	−	0.0732375i	−0.598103	−	0.801419i	$-0.704079\pi$
$383$	1.70812	−	1.43329i	0.0872810	−	0.0732375i	0.685384	+	0.728182i	$0.259634\pi$
$384$	−0.687834	−	1.58962i	−0.0351009	−	0.0811198i
$385$	6.71944	−	3.75766i	0.342454	−	0.191508i
$386$	3.56766	+	9.80206i	0.181589	+	0.498912i
$387$	−10.1753	+	1.21273i	−0.517238	+	0.0616466i
$388$	11.8676	+	6.85175i	0.602485	+	0.347845i
$389$	1.31460	+	0.231800i	0.0666531	+	0.0117527i	0.206875	−	0.978367i	$-0.433671\pi$
$389$	1.31460	+	0.231800i	0.0666531	+	0.0117527i	−0.140222	+	0.990120i	$0.544782\pi$
$390$	−2.95776	+	3.98239i	−0.149772	+	0.201656i
$391$	2.07588	+	3.59552i	0.104982	+	0.181834i
$392$	−1.02619	−	6.92437i	−0.0518302	−	0.349734i
$393$	−8.39047	−	6.23169i	−0.423243	−	0.314347i
$394$	−5.01843	+	13.7880i	−0.252825	+	0.694630i
$395$	7.17582	−	2.61178i	0.361055	−	0.131413i
$396$	0.766011	−	3.26506i	0.0384935	−	0.164075i
$397$	0.930554	+	5.27743i	0.0467032	+	0.264867i	0.999214	−	0.0396375i	$-0.0126203\pi$
$397$	0.930554	+	5.27743i	0.0467032	+	0.264867i	−0.952511	+	0.304504i	$0.901509\pi$
$398$	−19.9253			−0.998765
$399$	19.3043	−	5.13268i	0.966423	−	0.256955i
$400$	−1.77541			−0.0887706
$401$	−2.73821	−	15.5292i	−0.136740	−	0.775489i	−0.973632	−	0.228122i	$-0.926741\pi$
$401$	−2.73821	−	15.5292i	−0.136740	−	0.775489i	0.836893	−	0.547367i	$-0.184370\pi$
$402$	−1.47397	+	1.39378i	−0.0735149	+	0.0695156i
$403$	−8.25370	+	3.00410i	−0.411146	+	0.149645i
$404$	−1.14155	+	3.13638i	−0.0567942	+	0.156041i
$405$	10.4187	−	20.9823i	0.517711	−	1.04262i
$406$	−8.09398	+	9.38191i	−0.401698	+	0.465616i
$407$	−2.58892	−	4.48413i	−0.128328	−	0.222270i
$408$	−1.91048	−	1.41893i	−0.0945828	−	0.0702476i
$409$	13.4280	+	2.36771i	0.663970	+	0.117076i	0.495469	−	0.868626i	$-0.334996\pi$
$409$	13.4280	+	2.36771i	0.663970	+	0.117076i	0.168501	+	0.985701i	$0.446107\pi$
$410$	−7.17119	−	4.14029i	−0.354160	−	0.204474i
$411$	0.222105	−	0.443502i	0.0109557	−	0.0218764i
$412$	−4.41949	−	12.1424i	−0.217733	−	0.598215i
$413$	−3.87199	−	2.30680i	−0.190528	−	0.113510i
$414$	4.96422	−	7.58517i	0.243978	−	0.372791i
$415$	−34.7262	+	29.1388i	−1.70464	+	1.43037i
$416$	0.376322	−	1.03393i	0.0184507	−	0.0506928i
$417$	14.9321	+	7.47799i	0.731229	+	0.366199i
$418$	−3.85426	−	2.98146i	−0.188518	−	0.145828i
$419$			9.43950i			0.461150i	0.973055	+	0.230575i	$0.0740607\pi$
$419$			9.43950i			0.461150i	−0.973055	+	0.230575i	$0.925939\pi$
$420$	−10.0475	+	6.42893i	−0.490268	+	0.313700i
$421$	−3.02079	+	8.29954i	−0.147224	+	0.404495i	−0.991282	−	0.131757i	$-0.957938\pi$
$421$	−3.02079	+	8.29954i	−0.147224	+	0.404495i	0.844058	+	0.536252i	$0.180160\pi$
$422$	0.799909	−	0.953295i	0.0389390	−	0.0464057i
$423$	−28.4406	+	8.58494i	−1.38283	+	0.417414i
$424$	4.40794	+	3.69870i	0.214068	+	0.179625i
$425$	−2.11254	+	1.21967i	−0.102473	+	0.0591628i
$426$	−3.89633	−	1.95128i	−0.188778	−	0.0945398i
$427$	−7.06691	−	8.66028i	−0.341992	−	0.419100i
$428$	−4.60039	−	3.86018i	−0.222368	−	0.186589i
$429$	1.77864	−	1.17272i	0.0858735	−	0.0566196i
$430$		−	8.89110i		−	0.428767i
$431$	−12.9380	−	10.8563i	−0.623202	−	0.522929i	0.275606	−	0.961271i	$-0.411122\pi$
$431$	−12.9380	−	10.8563i	−0.623202	−	0.522929i	−0.898808	+	0.438342i	$0.855566\pi$
$432$	−0.884878	+	5.12025i	−0.0425737	+	0.246348i
$433$	−27.0498	−	4.76961i	−1.29993	−	0.229213i	−0.519508	−	0.854466i	$-0.673885\pi$
$433$	−27.0498	−	4.76961i	−1.29993	−	0.229213i	−0.780422	+	0.625253i	$0.784996\pi$
$434$	−21.1185	−	0.289391i	−1.01372	−	0.0138912i
$435$	20.2343	+	6.03274i	0.970160	+	0.289248i
$436$	−14.5689	−	8.41134i	−0.697722	−	0.402830i
$437$	−7.03359	−	11.1363i	−0.336462	−	0.532720i
$438$	−7.54867	−	3.78037i	−0.360689	−	0.180633i
$439$	−21.3932	+	3.77220i	−1.02104	+	0.180037i	−0.659015	−	0.752130i	$-0.729027\pi$
$439$	−21.3932	+	3.77220i	−1.02104	+	0.180037i	−0.362028	+	0.932167i	$0.617915\pi$
$440$	2.73437	+	0.995230i	0.130356	+	0.0474457i
$441$	−8.79967	+	19.0674i	−0.419032	+	0.907972i
$442$	−0.262514	−	1.48879i	−0.0124865	−	0.0708145i
$443$	−23.4539	−	4.13556i	−1.11433	−	0.196486i	−0.413980	−	0.910286i	$-0.635862\pi$
$443$	−23.4539	−	4.13556i	−1.11433	−	0.196486i	−0.700350	+	0.713800i	$0.746973\pi$
$444$	4.41599	+	6.69761i	0.209573	+	0.317855i
$445$	−29.4689	−	17.0139i	−1.39696	−	0.806535i
$446$	5.95485	+	16.3608i	0.281970	+	0.774707i
$447$	−1.00333	+	8.66930i	−0.0474557	+	0.410044i
$448$	1.72827	−	2.00327i	0.0816529	−	0.0946456i
$449$	18.6884	−	32.3693i	0.881961	−	1.52760i	0.0328044	−	0.999462i	$-0.489556\pi$
$449$	18.6884	−	32.3693i	0.881961	−	1.52760i	0.849157	−	0.528140i	$-0.177110\pi$
$450$	4.45664	+	2.91671i	0.210088	+	0.137495i
$451$	2.28594	+	2.72427i	0.107641	+	0.128281i
$452$	5.97997	−	2.17653i	0.281274	−	0.102375i
$453$	−23.5347	−	7.01673i	−1.10576	−	0.329675i
$454$	−16.6274	+	13.9520i	−0.780361	+	0.654801i
$455$	−7.44362	−	1.41794i	−0.348962	−	0.0664740i
$456$	6.23502	+	4.25730i	0.291981	+	0.199366i
$457$	−1.00123	+	1.73418i	−0.0468355	+	0.0811215i	−0.888493	−	0.458891i	$-0.848247\pi$
$457$	−1.00123	+	1.73418i	−0.0468355	+	0.0811215i	0.841657	+	0.540012i	$0.181580\pi$
$458$	27.3053	+	9.93830i	1.27589	+	0.464386i
$459$	2.46461	+	6.70040i	0.115038	+	0.312748i
$460$	6.02531	+	5.05583i	0.280931	+	0.235729i
$461$	12.1682	−	2.14559i	0.566730	−	0.0999299i	0.117061	−	0.993125i	$-0.462653\pi$
$461$	12.1682	−	2.14559i	0.566730	−	0.0999299i	0.449670	+	0.893195i	$0.351542\pi$
$462$	4.99924	−	1.11868i	0.232586	−	0.0520456i
$463$	4.35338	−	7.54027i	0.202319	−	0.350426i	−0.746956	−	0.664873i	$-0.768486\pi$
$463$	4.35338	−	7.54027i	0.202319	−	0.350426i	0.949275	+	0.314447i	$0.101819\pi$
$464$	−4.68329			−0.217416
$465$	14.2925	+	33.0306i	0.662797	+	1.53176i
$466$	−23.5762	−	4.15711i	−1.09214	−	0.192575i
$467$			22.1727i			1.02603i	0.858379	+	0.513016i	$0.171472\pi$
$467$			22.1727i			1.02603i	−0.858379	+	0.513016i	$0.828528\pi$
$468$	−2.64323	+	1.97715i	−0.122183	+	0.0913937i
$469$	−2.89707	−	1.09963i	−0.133774	−	0.0507762i
$470$	−4.47602	−	25.3848i	−0.206463	−	1.17091i
$471$	35.9167	+	4.15676i	1.65496	+	0.191533i
$472$	−0.295811	−	1.67763i	−0.0136158	−	0.0772192i
$473$	−1.30600	+	3.58821i	−0.0600500	+	0.164986i
$474$	5.07241	−	0.301209i	0.232983	−	0.0138350i
$475$	6.54306	−	4.13255i	0.300216	−	0.189615i
$476$	0.680231	−	3.57095i	0.0311783	−	0.163674i
$477$	−4.98844	−	16.5260i	−0.228405	−	0.756672i
$478$	−5.83355	−	6.95215i	−0.266820	−	0.317984i
$479$	6.10663	+	16.7778i	0.279019	+	0.766599i	0.997474	+	0.0710256i	$0.0226272\pi$
$479$	6.10663	+	16.7778i	0.279019	+	0.766599i	−0.718455	+	0.695573i	$0.755151\pi$
$480$	−4.32052	−	1.28814i	−0.197204	−	0.0587953i
$481$	−0.884956	+	5.01883i	−0.0403505	+	0.228839i
$482$	−6.50118	−	3.75346i	−0.296121	−	0.170965i
$483$	13.7324	+	1.78030i	0.624848	+	0.0810065i
$484$	7.46916	+	6.26737i	0.339507	+	0.284880i
$485$	33.5186	−	12.1998i	1.52200	−	0.553963i
$486$	10.6329	−	11.3991i	0.482320	−	0.517075i
$487$			15.2673i			0.691829i	0.938266	+	0.345914i	$0.112431\pi$
$487$			15.2673i			0.691829i	−0.938266	+	0.345914i	$0.887569\pi$
$488$	0.733626	−	4.16060i	0.0332097	−	0.188342i
$489$	−19.4694	−	20.5895i	−0.880437	−	0.931090i
$490$	−15.5241	−	9.53933i	−0.701305	−	0.430943i
$491$	9.16347	−	25.1764i	0.413541	−	1.13620i	−0.541752	−	0.840538i	$-0.682239\pi$
$491$	9.16347	−	25.1764i	0.413541	−	1.13620i	0.955294	−	0.295658i	$-0.0955388\pi$
$492$	−3.78575	−	4.00355i	−0.170675	−	0.180494i
$493$	−5.57258	+	3.21733i	−0.250976	+	0.144901i
$494$	1.01976	+	4.68639i	0.0458812	+	0.210851i
$495$	−5.22882	−	6.99035i	−0.235018	−	0.314193i
$496$	−5.13125	−	6.11518i	−0.230400	−	0.274580i
$497$	0.0912052	−	6.65576i	0.00409111	−	0.298552i
$498$	−27.6840	+	11.9790i	−1.24055	+	0.536791i
$499$	37.6516	+	13.7041i	1.68552	+	0.613478i	0.994049	−	0.108929i	$-0.0347422\pi$
$499$	37.6516	+	13.7041i	1.68552	+	0.613478i	0.691468	+	0.722407i	$0.256964\pi$
$500$	5.39523	−	6.42978i	0.241282	−	0.287548i
$501$	3.65165	−	2.40767i	0.163144	−	0.107567i
$502$			30.0319i			1.34039i
$503$	−18.4283	+	21.9620i	−0.821676	+	0.979235i	−0.999989	−	0.00473862i	$-0.998492\pi$
$503$	−18.4283	+	21.9620i	−0.821676	+	0.979235i	0.178313	+	0.983974i	$0.442936\pi$
$504$	−7.62934	+	2.18935i	−0.339838	+	0.0975213i
$505$	4.34391	+	7.52388i	0.193302	+	0.334808i
$506$	−1.68901	−	2.92545i	−0.0750855	−	0.130052i
$507$	20.2844	+	2.34758i	0.900861	+	0.104260i
$508$	1.58685	+	1.89114i	0.0704052	+	0.0839056i
$509$	−19.3383	−	16.2267i	−0.857153	−	0.719237i	0.104200	−	0.994556i	$-0.466772\pi$
$509$	−19.3383	−	16.2267i	−0.857153	−	0.719237i	−0.961353	+	0.275320i	$0.911216\pi$
$510$	−6.02585	+	1.43538i	−0.266829	+	0.0635595i
$511$	0.176699	−	12.8947i	0.00781670	−	0.570429i
$512$	1.00000			0.0441942
$513$	−8.65709	−	20.9298i	−0.382220	−	0.924071i
$514$	−3.29134	−	5.70076i	−0.145175	−	0.251450i
$515$	−31.6063	−	11.5038i	−1.39274	−	0.506916i
$516$	1.69038	−	5.66965i	0.0744146	−	0.249593i
$517$	−1.92233	+	10.9021i	−0.0845440	+	0.479473i
$518$	−6.27205	+	10.5277i	−0.275578	+	0.462560i
$519$	−7.70186	+	10.3699i	−0.338074	+	0.455190i
$520$	−1.43201	−	2.48031i	−0.0627977	−	0.108769i
$521$	17.5600	−	30.4148i	0.769318	−	1.33250i	−0.168614	−	0.985682i	$-0.553929\pi$
$521$	17.5600	−	30.4148i	0.769318	−	1.33250i	0.937933	−	0.346817i	$-0.112737\pi$
$522$	11.7560	+	7.69388i	0.514546	+	0.336752i
$523$	−9.43305	−	25.9171i	−0.412479	−	1.13328i	−0.955868	−	0.293795i	$-0.905082\pi$
$523$	−9.43305	−	25.9171i	−0.412479	−	1.13328i	0.543390	−	0.839480i	$-0.317141\pi$
$524$	5.22575	−	3.01709i	0.228288	−	0.131802i
$525$	−1.04601	+	8.06844i	−0.0456516	+	0.352136i
$526$	1.34001	+	3.68166i	0.0584274	+	0.160528i
$527$	−10.3066	−	3.75130i	−0.448962	−	0.163409i
$528$	1.55443	+	1.15449i	0.0676480	+	0.0502429i
$529$	2.40834	+	13.6584i	0.104710	+	0.593842i
$530$	14.7503	−	2.60087i	0.640712	−	0.112975i
$531$	−2.01352	+	4.69715i	−0.0873795	+	0.203839i
$532$	−1.70638	+	11.4056i	−0.0739812	+	0.494496i
$533$		−	3.50026i		−	0.151613i
$534$	−15.5570	−	16.4520i	−0.673216	−	0.711947i
$535$	−15.3943	+	2.71443i	−0.665553	+	0.117355i
$536$	−0.400578	−	1.10058i	−0.0173024	−	0.0475378i
$537$	−28.8883	+	6.88129i	−1.24662	+	0.296950i
$538$	22.9575	−	8.35586i	0.989769	−	0.360247i
$539$	4.86387	+	6.13012i	0.209502	+	0.264043i
$540$	8.72917	+	10.3314i	0.375644	+	0.444592i
$541$	27.8091	−	10.1217i	1.19561	−	0.435165i	0.333918	−	0.942602i	$-0.391629\pi$
$541$	27.8091	−	10.1217i	1.19561	−	0.435165i	0.861689	+	0.507437i	$0.169407\pi$
$542$	−2.45087	+	13.8996i	−0.105274	+	0.597037i
$543$	37.0392	−	2.19946i	1.58950	−	0.0943878i
$544$	1.18988	−	0.686980i	0.0510159	−	0.0294540i
$545$	−41.1480	+	14.9766i	−1.76259	+	0.641529i
$546$	−4.47705	−	2.31937i	−0.191600	−	0.0992598i
$547$	18.3825	+	3.24133i	0.785978	+	0.138589i	0.552212	−	0.833704i	$-0.313784\pi$
$547$	18.3825	+	3.24133i	0.785978	+	0.138589i	0.233766	+	0.972293i	$0.424895\pi$
$548$	0.184076	+	0.219373i	0.00786333	+	0.00937115i
$549$	−8.67672	+	9.23870i	−0.370314	+	0.394298i
$550$	1.71883	−	0.992369i	0.0732913	−	0.0423148i
$551$	17.2597	−	10.9011i	0.735288	−	0.464403i
$552$	2.88099	+	4.36952i	0.122623	+	0.185979i
$553$	3.78847	+	6.77453i	0.161102	+	0.288082i
$554$	−3.30007	−	1.20113i	−0.140207	−	0.0510311i
$555$	20.7436	+	2.40072i	0.880515	+	0.101905i
$556$	−7.38599	+	6.19758i	−0.313236	+	0.262836i
$557$	−28.2090	+	33.6182i	−1.19526	+	1.42445i	−0.315564	+	0.948904i	$0.602194\pi$
$557$	−28.2090	+	33.6182i	−1.19526	+	1.42445i	−0.879691	+	0.475546i	$0.842251\pi$
$558$	2.83421	+	23.7801i	0.119982	+	1.00669i
$559$	3.25481	−	1.87917i	0.137664	−	0.0794803i
$560$	−1.10284	−	6.79791i	−0.0466034	−	0.287264i
$561$	2.64271	+	0.305850i	0.111575	+	0.0129130i
$562$	26.6759			1.12525
$563$	31.9871			1.34809			0.674047	−	0.738688i	$-0.264554\pi$
$563$	31.9871			1.34809			0.674047	+	0.738688i	$0.264554\pi$
$564$	1.97189	−	17.0383i	0.0830317	−	0.717440i
$565$	5.66542	−	15.5656i	0.238346	−	0.654851i
$566$	−3.56413	+	20.2132i	−0.149812	+	0.849624i
$567$	22.7479	+	7.03804i	0.955321	+	0.295570i
$568$	1.92727	−	1.61717i	0.0808666	−	0.0678551i
$569$	11.2287	−	19.4486i	0.470730	−	0.815329i	−0.528709	−	0.848803i	$-0.677324\pi$
$569$	11.2287	−	19.4486i	0.470730	−	0.815329i	0.999440	+	0.0334743i	$0.0106572\pi$
$570$	18.9211	−	5.30942i	0.792518	−	0.222387i
$571$	−15.1765	−	26.2864i	−0.635115	−	1.10005i	−0.986491	−	0.163817i	$-0.947619\pi$
$571$	−15.1765	−	26.2864i	−0.635115	−	1.10005i	0.351375	−	0.936235i	$-0.385714\pi$
$572$	0.213590	+	1.21133i	0.00893066	+	0.0506483i
$573$	−3.03444	−	12.7389i	−0.126766	−	0.532175i
$574$	2.98678	−	7.86893i	0.124666	−	0.328443i
$575$	5.28333	−	0.931594i	0.220330	−	0.0388502i
$576$	−2.51020	−	1.64283i	−0.104592	−	0.0684514i
$577$	34.7259			1.44566			0.722829	−	0.691027i	$-0.242841\pi$
$577$	34.7259			1.44566			0.722829	+	0.691027i	$0.242841\pi$
$578$	−7.55612	+	13.0876i	−0.314293	+	0.544371i
$579$	14.5044	+	10.7726i	0.602782	+	0.447693i
$580$	−7.83586	+	9.33842i	−0.325366	+	0.387757i
$581$	−34.8879	−	30.0986i	−1.44740	−	1.24870i
$582$	23.6934	−	1.40696i	0.982124	−	0.0583205i
$583$	−6.33486	−	1.11701i	−0.262363	−	0.0462617i
$584$	3.73386	−	3.13308i	0.154508	−	0.129648i
$585$	−0.480117	+	8.57862i	−0.0198504	+	0.354682i
$586$	20.5694	−	17.2598i	0.849714	−	0.712994i
$587$	23.3883	+	27.8731i	0.965339	+	1.15045i	0.988577	+	0.150716i	$0.0481578\pi$
$587$	23.3883	+	27.8731i	0.965339	+	1.15045i	−0.0232386	+	0.999730i	$0.507398\pi$
$588$	−8.08572	−	9.03444i	−0.333449	−	0.372574i
$589$	33.1446	+	10.5930i	1.36570	+	0.436475i
$590$	−3.84011	−	2.21709i	−0.158095	−	0.0912760i
$591$	5.88897	+	24.7225i	0.242240	+	1.01695i
$592$	−4.56137	+	0.804293i	−0.187471	+	0.0330562i
$593$	−16.1782	+	19.2805i	−0.664360	+	0.791754i	−0.988004	−	0.154425i	$-0.950647\pi$
$593$	−16.1782	+	19.2805i	−0.664360	+	0.791754i	0.323644	+	0.946179i	$0.395092\pi$
$594$	−2.00529	−	5.45169i	−0.0822782	−	0.223685i
$595$	−5.98228	−	7.33111i	−0.245250	−	0.300546i
$596$	−4.36358	−	2.51932i	−0.178739	−	0.103195i
$597$	−28.8125	+	18.9972i	−1.17922	+	0.777502i
$598$	−0.577345	+	3.27428i	−0.0236094	+	0.133895i
$599$	1.51603	−	8.59786i	0.0619435	−	0.351299i	−0.938045	−	0.346513i	$-0.887366\pi$
$599$	1.51603	−	8.59786i	0.0619435	−	0.351299i	0.999989	−	0.00478565i	$-0.00152333\pi$
$600$	−2.56729	+	1.69271i	−0.104809	+	0.0691046i
$601$	28.4413	+	16.4206i	1.16014	+	0.669809i	0.951338	−	0.308148i	$-0.0997091\pi$
$601$	28.4413	+	16.4206i	1.16014	+	0.669809i	0.208805	+	0.977957i	$0.433042\pi$
$602$	8.92063	−	1.44721i	0.363578	−	0.0589839i
$603$	−0.802540	+	3.42076i	−0.0326820	+	0.139304i
$604$	9.11396	−	10.8616i	0.370842	−	0.441952i
$605$	24.9941	−	4.40713i	1.01615	−	0.179175i
$606$	1.33957	+	5.62367i	0.0544165	+	0.228446i
$607$	20.1429	+	11.6295i	0.817573	+	0.472026i	0.849579	−	0.527461i	$-0.176856\pi$
$607$	20.1429	+	11.6295i	0.817573	+	0.472026i	−0.0320055	+	0.999488i	$0.510189\pi$
$608$	−3.68538	+	2.32766i	−0.149462	+	0.0943990i
$609$	−2.75923	+	21.2834i	−0.111810	+	0.862449i
$610$	−7.06870	−	8.42415i	−0.286203	−	0.341084i
$611$	8.34670	−	7.00372i	0.337672	−	0.283340i
$612$	−4.11544	−	0.230328i	−0.166357	−	0.00931044i
$613$	23.0602	−	19.3498i	0.931393	−	0.781532i	−0.0446736	−	0.999002i	$-0.514225\pi$
$613$	23.0602	−	19.3498i	0.931393	−	0.781532i	0.976067	+	0.217470i	$0.0697803\pi$
$614$	17.1580	+	3.02541i	0.692439	+	0.122096i
$615$	−14.3172	+	0.850181i	−0.577324	+	0.0342826i
$616$	−0.553460	+	2.90545i	−0.0222995	+	0.117064i
$617$	3.19642	−	3.80934i	0.128683	−	0.153358i	−0.697856	−	0.716239i	$-0.745862\pi$
$617$	3.19642	−	3.80934i	0.128683	−	0.153358i	0.826539	+	0.562880i	$0.190307\pi$
$618$	−17.9675	−	13.3447i	−0.722760	−	0.536801i
$619$	−7.29465	+	12.6347i	−0.293197	+	0.507832i	−0.974564	−	0.224110i	$-0.928052\pi$
$619$	−7.29465	+	12.6347i	−0.293197	+	0.507832i	0.681367	+	0.731942i	$0.261386\pi$
$620$	−20.7789			−0.834502
$621$	−0.0534467	−	15.7013i	−0.00214474	−	0.630073i
$622$	20.2003	−	3.56186i	0.809958	−	0.142818i
$623$	12.2737	−	32.3361i	0.491736	−	1.29552i
$624$	−0.441602	−	1.85389i	−0.0176782	−	0.0742150i
$625$	−5.33534	−	30.2582i	−0.213413	−	1.21033i
$626$	7.21515	+	12.4970i	0.288376	+	0.499481i
$627$	−8.41594	−	0.636554i	−0.336100	−	0.0254215i
$628$	−10.4375	+	18.0782i	−0.416500	+	0.721400i
$629$	−4.87497	+	4.09059i	−0.194378	+	0.163102i
$630$	−8.39951	+	18.8759i	−0.334644	+	0.752033i
$631$	−5.69425	+	32.2937i	−0.226685	+	1.28559i	0.632754	+	0.774353i	$0.281925\pi$
$631$	−5.69425	+	32.2937i	−0.226685	+	1.28559i	−0.859438	+	0.511239i	$0.829187\pi$
$632$	−1.00339	+	2.75679i	−0.0399127	+	0.109659i
$633$	0.247801	−	2.14114i	0.00984920	−	0.0851026i
$634$	20.2749			0.805219
$635$	6.42594			0.255006
$636$	9.90040	+	1.14581i	0.392576	+	0.0454341i
$637$	0.211045	−	7.69914i	0.00836192	−	0.305051i
$638$	4.53405	−	2.61773i	0.179505	−	0.103637i
$639$	−7.49459	+	0.893236i	−0.296481	+	0.0353359i
$640$	1.67315	−	1.99398i	0.0661371	−	0.0788192i
$641$	−25.2637	+	21.1988i	−0.997856	+	0.837301i	−0.986686	−	0.162637i	$-0.948000\pi$
$641$	−25.2637	+	21.1988i	−0.997856	+	0.837301i	−0.0111701	+	0.999938i	$0.503556\pi$
$642$	−10.3326	−	1.19583i	−0.407797	−	0.0471957i
$643$	−21.1348	−	7.69244i	−0.833475	−	0.303360i	−0.110191	−	0.993910i	$-0.535146\pi$
$643$	−21.1348	−	7.69244i	−0.833475	−	0.303360i	−0.723284	+	0.690550i	$0.757368\pi$
$644$	−4.09188	+	6.86826i	−0.161243	+	0.270647i
$645$	−8.47694	−	12.8568i	−0.333779	−	0.506235i
$646$	−2.78612	+	5.30143i	−0.109618	+	0.208582i
$647$	−42.4581	+	24.5132i	−1.66920	+	0.963713i	−0.701130	+	0.713033i	$0.747321\pi$
$647$	−42.4581	+	24.5132i	−1.66920	+	0.963713i	−0.968070	+	0.250680i	$0.919346\pi$
$648$	3.60219	+	8.24768i	0.141507	+	0.324000i
$649$	1.22410	+	1.45882i	0.0480501	+	0.0572638i
$650$	−1.92379	−	0.339216i	−0.0754573	−	0.0133052i
$651$	−30.8139	+	19.7163i	−1.20769	+	0.772744i
$652$	15.3737	−	5.59558i	0.602081	−	0.219140i
$653$	15.3263	−	8.84864i	0.599764	−	0.346274i	−0.169185	−	0.985584i	$-0.554113\pi$
$653$	15.3263	−	8.84864i	0.599764	−	0.346274i	0.768949	+	0.639310i	$0.220780\pi$
$654$	−29.0865	+	1.72721i	−1.13737	+	0.0675393i
$655$	2.72745	−	15.4681i	0.106570	−	0.604389i
$656$	2.98936	−	1.08804i	0.116715	−	0.0424808i
$657$	−14.5198	+	1.73054i	−0.566473	+	0.0675146i
$658$	24.7405	−	8.62277i	0.964485	−	0.336151i
$659$	−16.7387	+	6.09237i	−0.652045	+	0.237325i	−0.646798	−	0.762661i	$-0.723892\pi$
$659$	−16.7387	+	6.09237i	−0.652045	+	0.237325i	−0.00524703	+	0.999986i	$0.501670\pi$
$660$	4.90285	−	1.16787i	0.190843	−	0.0454594i
$661$	6.93087	+	19.0424i	0.269580	+	0.740664i	0.998431	+	0.0559923i	$0.0178322\pi$
$661$	6.93087	+	19.0424i	0.269580	+	0.740664i	−0.728851	+	0.684672i	$0.759946\pi$
$662$	−14.7267	+	2.59671i	−0.572368	+	0.100924i
$663$	−1.79904	−	1.90254i	−0.0698690	−	0.0738886i
$664$		−	17.4155i		−	0.675852i
$665$	19.8876	+	22.4858i	0.771208	+	0.871964i
$666$	12.7713	+	5.47464i	0.494876	+	0.212138i
$667$	13.9367	−	2.45742i	0.539632	−	0.0951516i
$668$	0.438514	+	2.48693i	0.0169666	+	0.0962224i
$669$	24.2096	+	17.9807i	0.935996	+	0.695174i
$670$	−2.86477	−	1.04269i	−0.110676	−	0.0402826i
$671$	1.61533	+	4.43807i	0.0623590	+	0.171330i
$672$	0.589164	−	4.54454i	0.0227275	−	0.175310i
$673$	−31.8301	+	18.3771i	−1.22696	+	0.708386i	−0.966393	−	0.257069i	$-0.917243\pi$
$673$	−31.8301	+	18.3771i	−1.22696	+	0.708386i	−0.260568	+	0.965455i	$0.583910\pi$
$674$	−6.52366	−	17.9236i	−0.251282	−	0.690392i
$675$	9.22526	−	0.0314024i	0.355080	−	0.00120868i
$676$	−5.89468	+	10.2099i	−0.226718	+	0.392688i
$677$	−12.3761	−	21.4360i	−0.475652	−	0.823854i	0.523959	−	0.851744i	$-0.324455\pi$
$677$	−12.3761	−	21.4360i	−0.475652	−	0.823854i	−0.999611	+	0.0278897i	$0.991121\pi$
$678$	6.57204	−	8.84873i	0.252398	−	0.339833i
$679$	17.6961	+	31.6441i	0.679114	+	1.21439i
$680$	0.621030	−	3.52203i	0.0238154	−	0.135064i
$681$	−10.7415	+	36.0278i	−0.411615	+	1.38059i
$682$	8.38581	+	3.05219i	0.321109	+	0.116874i
$683$	4.19218	+	7.26107i	0.160409	+	0.277837i	0.935016	−	0.354607i	$-0.115385\pi$
$683$	4.19218	+	7.26107i	0.160409	+	0.277837i	−0.774606	+	0.632444i	$0.782052\pi$
$684$	13.0750	+	0.211581i	0.499935	+	0.00808999i
$685$	0.745413			0.0284808
$686$	7.04415	−	17.1283i	0.268947	−	0.653963i
$687$	48.9595	−	11.6623i	1.86792	−	0.444945i
$688$	2.61663	+	2.19561i	0.0997580	+	0.0837069i
$689$	4.06964	+	4.85001i	0.155041	+	0.184771i
$690$	13.5331	+	1.56623i	0.515196	+	0.0596253i
$691$	−24.5656	−	42.5489i	−0.934520	−	1.61864i	−0.775487	−	0.631364i	$-0.782496\pi$
$691$	−24.5656	−	42.5489i	−0.934520	−	1.61864i	−0.159034	−	0.987273i	$-0.550838\pi$
$692$	−3.72888	−	6.45860i	−0.141751	−	0.245519i
$693$	6.16247	−	6.38401i	0.234093	−	0.242508i
$694$	20.9171	−	24.9280i	0.794002	−	0.946255i
$695$			25.0970i			0.951985i
$696$	−6.77217	+	4.46514i	−0.256698	+	0.169251i
$697$	2.80954	−	3.34827i	0.106419	−	0.126825i
$698$	14.1242	+	5.14079i	0.534609	+	0.194582i
$699$	−38.0552	+	16.4667i	−1.43938	+	0.622826i
$700$	−4.03542	−	2.40417i	−0.152524	−	0.0908690i
$701$	11.0867	+	13.2126i	0.418739	+	0.499034i	0.933638	−	0.358217i	$-0.116615\pi$
$701$	11.0867	+	13.2126i	0.418739	+	0.499034i	−0.514899	+	0.857251i	$0.672171\pi$
$702$	−1.93713	+	5.37911i	−0.0731121	+	0.203021i
$703$	14.9383	−	13.5814i	0.563407	−	0.512234i
$704$	−0.968132	+	0.558951i	−0.0364879	+	0.0210663i
$705$	−30.6747	−	32.4395i	−1.15528	−	1.22174i
$706$	5.02484	−	13.8056i	0.189112	−	0.519582i
$707$	−6.84180	+	5.58300i	−0.257312	+	0.209970i
$708$	−2.02724	−	2.14387i	−0.0761882	−	0.0805714i
$709$	−6.26475	+	35.5291i	−0.235278	+	1.33433i	0.606751	+	0.794892i	$0.292473\pi$
$709$	−6.26475	+	35.5291i	−0.235278	+	1.33433i	−0.842028	+	0.539433i	$0.818639\pi$
$710$		−	6.54873i		−	0.245770i
$711$	7.04765	−	5.27168i	0.264308	−	0.197704i
$712$	12.2843	−	4.47113i	0.460375	−	0.167563i
$713$	18.4785	+	15.5053i	0.692025	+	0.580678i
$714$	−2.42098	−	5.81223i	−0.0906027	−	0.217517i
$715$	2.77274	+	1.60085i	0.103695	+	0.0598682i
$716$	2.97726	−	16.8849i	0.111265	−	0.631017i
$717$	−15.0638	−	4.49118i	−0.562567	−	0.167726i
$718$	6.58484	+	18.0917i	0.245744	+	0.675176i
$719$	−3.38711	−	4.03660i	−0.126318	−	0.150540i	0.699179	−	0.714947i	$-0.253549\pi$
$719$	−3.38711	−	4.03660i	−0.126318	−	0.150540i	−0.825496	+	0.564407i	$0.809105\pi$
$720$	−7.47573	+	2.25658i	−0.278604	+	0.0840979i
$721$	6.39738	−	33.5838i	0.238251	−	1.25072i
$722$	8.16401	−	17.1566i	0.303833	−	0.638503i
$723$	−12.9795	+	0.770748i	−0.482713	+	0.0286644i
$724$	−7.32684	+	20.1303i	−0.272300	+	0.748138i
$725$	1.44385	+	8.18846i	0.0536231	+	0.304112i
$726$	16.7760	+	1.94154i	0.622617	+	0.0720575i
$727$	5.53183	+	31.3726i	0.205164	+	1.16354i	0.897181	+	0.441663i	$0.145611\pi$
$727$	5.53183	+	31.3726i	0.205164	+	1.16354i	−0.692017	+	0.721882i	$0.743278\pi$
$728$	2.25546	−	1.84048i	0.0835928	−	0.0682129i
$729$	4.50737	−	26.6211i	0.166940	−	0.985967i
$730$		−	12.6874i		−	0.469581i
$731$	4.62182	+	0.814952i	0.170944	+	0.0301421i
$732$	−2.90595	−	6.71579i	−0.107407	−	0.248223i
$733$	9.13036			0.337238			0.168619	−	0.985681i	$-0.446069\pi$
$733$	9.13036			0.337238			0.168619	+	0.985681i	$0.446069\pi$
$734$	6.00356	−	10.3985i	0.221596	−	0.383815i
$735$	−31.5432	+	1.00681i	−1.16349	+	0.0371367i
$736$	−2.97584	+	0.524720i	−0.109691	+	0.0193414i
$737$	1.00298	+	0.841603i	0.0369454	+	0.0310009i
$738$	−9.29136	−	2.17984i	−0.342020	−	0.0802409i
$739$	21.5744	+	7.85244i	0.793627	+	0.288857i	0.706843	−	0.707370i	$-0.250119\pi$
$739$	21.5744	+	7.85244i	0.793627	+	0.288857i	0.0867842	+	0.996227i	$0.472341\pi$
$740$	−6.02812	+	10.4410i	−0.221598	+	0.383819i
$741$	5.94269	+	5.80438i	0.218310	+	0.213229i
$742$	5.01043	+	14.3759i	0.183939	+	0.527757i
$743$	−25.4125	+	21.3236i	−0.932294	+	0.782287i	−0.976228	−	0.216747i	$-0.930455\pi$
$743$	−25.4125	+	21.3236i	−0.932294	+	0.782287i	0.0439340	+	0.999034i	$0.486011\pi$
$744$	−13.2502	−	3.95049i	−0.485778	−	0.144832i
$745$	−12.3244	+	4.48572i	−0.451532	+	0.164344i
$746$	−4.57802	−	5.45588i	−0.167613	−	0.199754i
$747$	−28.6108	+	43.7163i	−1.04681	+	1.59950i
$748$	−0.767977	+	1.33018i	−0.0280800	+	0.0486360i
$749$	−5.22918	−	15.0036i	−0.191070	−	0.548219i
$750$	1.67137	−	14.4415i	0.0610297	−	0.527331i
$751$	−11.6792	−	32.0885i	−0.426182	−	1.17092i	−0.948112	−	0.317936i	$-0.897010\pi$
$751$	−11.6792	−	32.0885i	−0.426182	−	1.17092i	0.521930	−	0.852988i	$-0.325212\pi$
$752$	8.57599	+	4.95135i	0.312734	+	0.180557i
$753$	28.6330	+	43.4269i	1.04344	+	1.58257i
$754$	−5.07470	−	0.894806i	−0.184810	−	0.0325869i
$755$	−6.40882	−	36.3462i	−0.233241	−	1.32277i
$756$	−8.94485	+	10.4398i	−0.325321	+	0.379692i
$757$	−23.1563	−	8.42819i	−0.841629	−	0.306328i	−0.115006	−	0.993365i	$-0.536689\pi$
$757$	−23.1563	−	8.42819i	−0.841629	−	0.306328i	−0.726622	+	0.687037i	$0.758911\pi$
$758$	−11.5806	+	2.04197i	−0.420627	+	0.0741679i
$759$	−5.23152	−	2.61994i	−0.189892	−	0.0950979i
$760$	−1.52488	+	11.2431i	−0.0553132	+	0.407831i
$761$	36.5720	+	21.1148i	1.32573	+	0.765412i	0.984637	−	0.174616i	$-0.0558684\pi$
$761$	36.5720	+	21.1148i	1.32573	+	0.765412i	0.341097	+	0.940028i	$0.389202\pi$
$762$	4.09767	+	1.22170i	0.148443	+	0.0442575i
$763$	−21.7241	−	38.8469i	−0.786464	−	1.40635i
$764$	7.44572	+	1.31288i	0.269377	+	0.0474984i
$765$	−7.34503	+	7.82075i	−0.265560	+	0.282760i
$766$	1.70812	+	1.43329i	0.0617170	+	0.0517867i
$767$		−	1.87436i		−	0.0676791i
$768$	1.44603	−	0.953419i	0.0521790	−	0.0344035i
$769$	14.3737	+	12.0610i	0.518329	+	0.434930i	0.864049	−	0.503408i	$-0.167921\pi$
$769$	14.3737	+	12.0610i	0.518329	+	0.434930i	−0.345720	+	0.938338i	$0.612365\pi$
$770$	4.86740	+	5.96485i	0.175409	+	0.214958i
$771$	−10.1946	−	5.10543i	−0.367149	−	0.183868i
$772$	−9.03363	+	5.21557i	−0.325127	+	0.187712i
$773$	−1.19382	−	1.00174i	−0.0429388	−	0.0360299i	0.621066	−	0.783758i	$-0.286700\pi$
$773$	−1.19382	−	1.00174i	−0.0429388	−	0.0360299i	−0.664005	+	0.747729i	$0.731144\pi$
$774$	−2.96123	−	9.81010i	−0.106439	−	0.352617i
$775$	−9.11007	+	10.8570i	−0.327244	+	0.389994i
$776$	−4.68688	+	12.8771i	−0.168249	+	0.462260i
$777$	0.967749	+	21.2032i	0.0347178	+	0.760661i
$778$			1.33488i			0.0478579i
$779$	−8.48435	+	10.9681i	−0.303983	+	0.392971i
$780$	−4.43549	−	2.22129i	−0.158816	−	0.0795350i
$781$	−0.961934	+	2.64289i	−0.0344207	+	0.0945701i
$782$	−3.18043	+	2.66870i	−0.113732	+	0.0954324i
$783$	24.3350	−	0.0828353i	0.869661	−	0.00296029i
$784$	6.64098	−	2.21300i	0.237178	−	0.0790357i
$785$	18.5842	+	51.0598i	0.663300	+	1.82240i
$786$	4.68002	−	9.34512i	0.166931	−	0.333329i
$787$	44.8445	+	25.8910i	1.59853	+	0.922913i	0.991770	+	0.128029i	$0.0408652\pi$
$787$	44.8445	+	25.8910i	1.59853	+	0.922913i	0.606762	+	0.794884i	$0.292468\pi$
$788$	−14.4500	−	2.54792i	−0.514759	−	0.0907659i
$789$	5.44786	+	4.04618i	0.193949	+	0.144048i
$790$	3.81817	+	6.61327i	0.135845	+	0.235290i
$791$	16.5395	+	3.15061i	0.588076	+	0.112023i
$792$	3.34847	+	0.187403i	0.118983	+	0.00665906i
$793$	1.58988	−	4.36815i	0.0564582	−	0.155118i
$794$	−5.03567	+	1.83283i	−0.178709	+	0.0650448i
$795$	18.8496	−	17.8241i	0.668526	−	0.632157i
$796$	−3.45999	−	19.6226i	−0.122636	−	0.695504i
$797$	−26.3598			−0.933713			−0.466856	−	0.884333i	$-0.654614\pi$
$797$	−26.3598			−0.933713			−0.466856	+	0.884333i	$0.654614\pi$
$798$	8.40686	+	18.1197i	0.297600	+	0.641432i
$799$	13.6059			0.481343
$800$	−0.308297	−	1.74844i	−0.0108999	−	0.0618167i
$801$	−38.1814	−	8.95770i	−1.34907	−	0.316505i
$802$	14.8178	−	5.39322i	0.523233	−	0.190441i
$803$	−1.86363	+	5.12028i	−0.0657660	+	0.180691i
$804$	−1.62856	−	1.20955i	−0.0574349	−	0.0426575i
$805$	6.84887	+	19.6508i	0.241391	+	0.692599i
$806$	−4.39170	−	7.60665i	−0.154691	−	0.267933i
$807$	25.2306	−	33.9709i	0.888158	−	1.19583i
$808$	−3.28696	−	0.579580i	−0.115635	−	0.0203896i
$809$	17.1172	+	9.88263i	0.601809	+	0.347455i	0.769753	−	0.638342i	$-0.220379\pi$
$809$	17.1172	+	9.88263i	0.601809	+	0.347455i	−0.167944	+	0.985797i	$0.553713\pi$
$810$	22.4728	+	6.61692i	0.789612	+	0.232495i
$811$	−2.08632	−	5.73213i	−0.0732607	−	0.201282i	0.897657	−	0.440694i	$-0.145268\pi$
$811$	−2.08632	−	5.73213i	−0.0732607	−	0.201282i	−0.970918	+	0.239412i	$0.923045\pi$
$812$	−10.6449	−	6.34187i	−0.373562	−	0.222556i
$813$	9.70808	+	22.4358i	0.340477	+	0.786859i
$814$	3.96645	−	3.32825i	0.139024	−	0.116655i
$815$	14.5651	−	40.0172i	0.510192	−	1.40174i
$816$	1.06562	−	2.12785i	0.0373043	−	0.0744896i
$817$	−14.7539	−	2.00104i	−0.516173	−	0.0700074i
$818$			13.6351i			0.476741i
$819$	−8.68526	+	0.914636i	−0.303488	+	0.0319600i
$820$	2.83212	−	7.78120i	0.0989021	−	0.271731i
$821$	−10.8270	+	12.9031i	−0.377866	+	0.450323i	−0.921139	−	0.389233i	$-0.872740\pi$
$821$	−10.8270	+	12.9031i	−0.377866	+	0.450323i	0.543274	+	0.839556i	$0.317185\pi$
$822$	0.475333	+	0.141718i	0.0165791	+	0.00494297i
$823$	−17.0972	−	14.3462i	−0.595970	−	0.500078i	0.294178	−	0.955751i	$-0.404954\pi$
$823$	−17.0972	−	14.3462i	−0.595970	−	0.500078i	−0.890147	+	0.455673i	$0.849399\pi$
$824$	11.1905	−	6.46086i	0.389841	−	0.225075i
$825$	1.53934	−	3.07376i	0.0535928	−	0.107015i
$826$	1.59939	−	4.21374i	0.0556500	−	0.146615i
$827$	27.4862	+	23.0637i	0.955789	+	0.802002i	0.980263	−	0.197698i	$-0.0633466\pi$
$827$	27.4862	+	23.0637i	0.955789	+	0.802002i	−0.0244738	+	0.999700i	$0.507791\pi$
$828$	8.33196	+	3.57165i	0.289556	+	0.124124i
$829$		−	50.6545i		−	1.75930i	−0.475618	−	0.879652i	$-0.657775\pi$
$829$		−	50.6545i		−	1.75930i	0.475618	−	0.879652i	$-0.342225\pi$
$830$	−34.7262	−	29.1388i	−1.20536	−	1.01142i
$831$	−5.91717	+	1.40949i	−0.205264	+	0.0488946i
$832$	1.08357	+	0.191063i	0.0375662	+	0.00662393i
$833$	6.38171	−	7.19544i	0.221113	−	0.249307i
$834$	−4.77145	+	16.0038i	−0.165222	+	0.554167i
$835$	5.69261	+	3.28663i	0.197001	+	0.113738i
$836$	2.26688	−	4.31343i	0.0784018	−	0.149183i
$837$	26.7707	+	31.6845i	0.925332	+	1.09518i
$838$	−9.29610	+	1.63915i	−0.321128	+	0.0566236i
$839$	3.57967	+	1.30289i	0.123584	+	0.0449809i	0.403072	−	0.915168i	$-0.367942\pi$
$839$	3.57967	+	1.30289i	0.123584	+	0.0449809i	−0.279488	+	0.960149i	$0.590165\pi$
$840$	−8.07599	−	8.77850i	−0.278648	−	0.302887i
$841$	−1.22713	−	6.95939i	−0.0423148	−	0.239979i
$842$	−8.69801	−	1.53369i	−0.299753	−	0.0528546i
$843$	38.5740	−	25.4333i	1.32856	−	0.875969i
$844$	1.07772	+	0.622219i	0.0370965	+	0.0214177i
$845$	10.4957	+	28.8366i	0.361062	+	0.992009i
$846$	−13.3932	−	26.5178i	−0.460467	−	0.911701i
$847$	8.49007	+	24.3597i	0.291722	+	0.837010i
$848$	−2.87708	+	4.98324i	−0.0987992	+	0.171125i
$849$	14.1178	+	32.6269i	0.484522	+	1.11975i
$850$	−1.56798	−	1.86865i	−0.0537813	−	0.0640941i
$851$	13.1519	−	4.78689i	0.450840	−	0.164092i
$852$	1.24504	−	4.17598i	0.0426545	−	0.143067i
$853$	−20.6495	+	17.3270i	−0.707026	+	0.593265i	−0.923763	−	0.382965i	$-0.874903\pi$
$853$	−20.6495	+	17.3270i	−0.707026	+	0.593265i	0.216737	+	0.976230i	$0.430459\pi$
$854$	7.30155	−	8.46339i	0.249854	−	0.289611i
$855$	22.2983	−	25.7173i	0.762587	−	0.879514i
$856$	3.00269	−	5.20081i	0.102630	−	0.177760i
$857$	31.9415	+	11.6257i	1.09110	+	0.397128i	0.824028	−	0.566549i	$-0.191722\pi$
$857$	31.9415	+	11.6257i	1.09110	+	0.397128i	0.267072	+	0.963677i	$0.413944\pi$
$858$	1.46376	+	1.54798i	0.0499721	+	0.0528470i
$859$	−26.0121	−	21.8267i	−0.887521	−	0.744719i	0.0801902	−	0.996780i	$-0.474447\pi$
$859$	−26.0121	−	21.8267i	−0.887521	−	0.744719i	−0.967711	+	0.252061i	$0.918892\pi$
$860$	8.75603	−	1.54392i	0.298578	−	0.0526474i
$861$	−3.18342	−	14.2263i	−0.108491	−	0.484832i
$862$	8.44469	−	14.6266i	0.287627	−	0.498185i
$863$	−35.4482			−1.20667			−0.603335	−	0.797488i	$-0.706162\pi$
$863$	−35.4482			−1.20667			−0.603335	+	0.797488i	$0.706162\pi$
$864$	−5.19612	+	0.0176874i	−0.176776	+	0.000601737i
$865$	−19.1173	−	3.37090i	−0.650009	−	0.114614i
$866$		−	27.4671i		−	0.933369i
$867$	1.55160	+	26.1291i	0.0526950	+	0.887392i
$868$	−3.38220	−	20.8479i	−0.114799	−	0.707625i
$869$	−0.569498	−	3.22978i	−0.0193189	−	0.109563i
$870$	−2.42744	+	20.9745i	−0.0822980	+	0.711101i
$871$	−0.223776	−	1.26910i	−0.00758236	−	0.0430017i
$872$	5.75369	−	15.8081i	0.194845	−	0.535331i
$873$	32.9199	−	24.6243i	1.11417	−	0.833405i
$874$	9.74571	−	8.86052i	0.329653	−	0.299712i
$875$	20.9699	−	7.30862i	0.708913	−	0.247076i
$876$	2.41212	−	8.09044i	0.0814980	−	0.273351i
$877$	2.61470	+	3.11608i	0.0882921	+	0.105222i	0.808382	−	0.588659i	$-0.200344\pi$
$877$	2.61470	+	3.11608i	0.0882921	+	0.105222i	−0.720090	+	0.693881i	$0.755899\pi$
$878$	−7.42978	−	20.4132i	−0.250743	−	0.688911i
$879$	13.2881	−	44.5693i	0.448196	−	1.50329i
$880$	−0.505292	+	2.86565i	−0.0170334	+	0.0966011i
$881$	38.2535	+	22.0857i	1.28879	+	0.744086i	0.978439	−	0.206535i	$-0.0662187\pi$
$881$	38.2535	+	22.0857i	1.28879	+	0.744086i	0.310355	+	0.950621i	$0.399552\pi$
$882$	−20.3058	−	5.35496i	−0.683731	−	0.180311i
$883$	3.70911	+	3.11232i	0.124822	+	0.104738i	0.703062	−	0.711129i	$-0.251816\pi$
$883$	3.70911	+	3.11232i	0.124822	+	0.104738i	−0.578240	+	0.815867i	$0.696260\pi$
$884$	1.42059	−	0.517051i	0.0477795	−	0.0173903i
$885$	−7.66671	+	0.455264i	−0.257714	+	0.0153035i
$886$		−	23.8157i		−	0.800105i
$887$	−3.43582	+	19.4855i	−0.115364	+	0.654260i	0.871206	+	0.490918i	$0.163339\pi$
$887$	−3.43582	+	19.4855i	−0.115364	+	0.654260i	−0.986569	+	0.163342i	$0.947773\pi$
$888$	−5.82903	+	5.51192i	−0.195610	+	0.184968i
$889$	1.04595	+	6.44728i	0.0350802	+	0.216235i
$890$	11.6382	−	31.9756i	0.390113	−	1.07183i
$891$	−8.09745	−	5.97140i	−0.271275	−	0.200049i
$892$	−15.0782	+	8.70541i	−0.504856	+	0.291479i
$893$	−43.1308	+	1.71439i	−1.44332	+	0.0573698i
$894$	−8.71182	+	0.517325i	−0.291367	+	0.0173019i
$895$	−28.6868	−	34.1876i	−0.958893	−	1.14276i
$896$	2.27295	+	1.35415i	0.0759338	+	0.0452389i
$897$	2.28691	+	5.28515i	0.0763576	+	0.176466i
$898$	35.1228	+	12.7836i	1.17206	+	0.426596i
$899$	−24.0311	+	28.6392i	−0.801483	+	0.955171i
$900$	−2.09851	+	4.89541i	−0.0699503	+	0.163180i
$901$			7.90598i			0.263386i
$902$	−2.28594	+	2.72427i	−0.0761134	+	0.0907084i
$903$	11.5197	−	10.5978i	0.383351	−	0.352673i
$904$	3.18187	+	5.51117i	0.105828	+	0.183299i
$905$	27.8807	+	48.2907i	0.926785	+	1.60524i
$906$	2.82338	−	24.3956i	0.0938005	−	0.810489i
$907$	28.3274	+	33.7593i	0.940596	+	1.12096i	0.992492	+	0.122307i	$0.0390292\pi$
$907$	28.3274	+	33.7593i	0.940596	+	1.12096i	−0.0518959	+	0.998653i	$0.516526\pi$
$908$	−16.6274	−	13.9520i	−0.551798	−	0.463014i
$909$	7.29877	+	6.85479i	0.242085	+	0.227359i
$910$	0.103826	−	7.57676i	0.00344179	−	0.251167i
$911$	−13.6933			−0.453679			−0.226840	−	0.973932i	$-0.572839\pi$
$911$	−13.6933			−0.453679			−0.226840	+	0.973932i	$0.572839\pi$
$912$	−3.10992	+	6.87956i	−0.102980	+	0.227805i
$913$	9.73441	+	16.8605i	0.322162	+	0.558001i
$914$	−1.88170	−	0.684881i	−0.0622410	−	0.0226539i
$915$	−18.2533	−	5.44211i	−0.603435	−	0.179911i
$916$	−5.04581	+	28.6162i	−0.166718	+	0.945506i
$917$	15.9634	+	0.218750i	0.527159	+	0.00722376i
$918$	−6.17064	+	3.59068i	−0.203661	+	0.118510i
$919$	11.8445	+	20.5152i	0.390713	+	0.676735i	0.992544	−	0.121889i	$-0.0388951\pi$
$919$	11.8445	+	20.5152i	0.390713	+	0.676735i	−0.601831	+	0.798624i	$0.705562\pi$
$920$	−3.93274	+	6.81171i	−0.129659	+	0.224575i
$921$	27.6954	−	11.9839i	0.912593	−	0.394883i
$922$	4.22598	+	11.6108i	0.139175	+	0.382381i
$923$	2.39733	−	1.38410i	0.0789090	−	0.0455581i
$924$	1.96979	+	4.72903i	0.0648014	+	0.155574i
$925$	2.81251	+	7.72732i	0.0924749	+	0.254073i
$926$	8.18167	+	2.97789i	0.268867	+	0.0978594i
$927$	−38.7046	−	2.16617i	−1.27123	−	0.0711462i
$928$	−0.813246	−	4.61214i	−0.0266961	−	0.151401i
$929$	−18.5812	+	3.27637i	−0.609630	+	0.107494i	−0.469936	−	0.882701i	$-0.655723\pi$
$929$	−18.5812	+	3.27637i	−0.609630	+	0.107494i	−0.139694	+	0.990195i	$0.544612\pi$
$930$	−30.0469	+	19.8110i	−0.985276	+	0.649629i
$931$	−19.3234	+	23.6137i	−0.633299	+	0.773907i
$932$		−	23.9399i		−	0.784176i
$933$	25.8142	−	24.4099i	0.845120	−	0.799144i
$934$	−21.8359	+	3.85025i	−0.714492	+	0.125984i
$935$	1.36741	+	3.75692i	0.0447190	+	0.122864i
$936$	−2.40610	−	2.25974i	−0.0786459	−	0.0738620i
$937$	−20.8403	+	7.58525i	−0.680823	+	0.247799i	−0.659201	−	0.751967i	$-0.729105\pi$
$937$	−20.8403	+	7.58525i	−0.680823	+	0.247799i	−0.0216219	+	0.999766i	$0.506883\pi$
$938$	0.579853	−	3.04400i	0.0189329	−	0.0993902i
$939$	22.3482	+	11.1919i	0.729306	+	0.365235i
$940$	24.2219	−	8.81603i	0.790030	−	0.287547i
$941$	−1.74075	+	9.87230i	−0.0567469	+	0.321828i	−0.999946	−	0.0104005i	$-0.996689\pi$
$941$	−1.74075	+	9.87230i	−0.0567469	+	0.321828i	0.943199	+	0.332228i	$0.107800\pi$
$942$	2.14327	+	36.0929i	0.0698314	+	1.17597i
$943$	−8.32494	+	4.80640i	−0.271097	+	0.156518i
$944$	1.60078	−	0.582635i	0.0521008	−	0.0189631i
$945$	5.85072	+	35.3033i	0.190324	+	1.14842i
$946$	−3.76048	−	0.663074i	−0.122264	−	0.0215584i
$947$	−16.3357	−	19.4681i	−0.530839	−	0.632630i	0.432269	−	0.901745i	$-0.357713\pi$
$947$	−16.3357	−	19.4681i	−0.530839	−	0.632630i	−0.963108	+	0.269115i	$0.913269\pi$
$948$	1.17745	+	4.94304i	0.0382417	+	0.160542i
$949$	4.64453	−	2.68152i	0.150768	−	0.0870458i
$950$	5.20596	+	5.72605i	0.168904	+	0.185778i
$951$	29.3180	−	19.3305i	0.950702	−	0.626833i
$952$	3.63482	+	0.0498086i	0.117805	+	0.00161431i
$953$	40.3622	+	14.6906i	1.30746	+	0.475877i	0.899419	−	0.437087i	$-0.143990\pi$
$953$	40.3622	+	14.6906i	1.30746	+	0.475877i	0.408041	+	0.912964i	$0.366212\pi$
$954$	15.4087	−	7.78236i	0.498874	−	0.251963i
$955$	15.0757	−	12.6500i	0.487838	−	0.409345i
$956$	5.83355	−	6.95215i	0.188670	−	0.224849i
$957$	4.06056	−	8.10816i	0.131259	−	0.262100i
$958$	−15.4625	+	8.92730i	−0.499572	+	0.288428i
$959$	0.121331	+	0.747888i	0.00391799	+	0.0241506i
$960$	0.518319	−	4.47857i	0.0167287	−	0.144545i
$961$	−32.7251			−1.05565
$962$	−5.09626			−0.164310
$963$	−16.0814	+	8.12214i	−0.518216	+	0.261732i
$964$	2.56752	−	7.05419i	0.0826941	−	0.227200i
$965$	−4.71487	+	26.7393i	−0.151777	+	0.860770i
$966$	0.631359	+	13.8330i	0.0203136	+	0.445068i
$967$	−1.38160	+	1.15930i	−0.0444293	+	0.0372806i	−0.664732	−	0.747082i	$-0.731454\pi$
$967$	−1.38160	+	1.15930i	−0.0444293	+	0.0372806i	0.620303	+	0.784363i	$0.287010\pi$
$968$	−4.87515	+	8.44400i	−0.156693	+	0.271400i
$969$	1.02568	+	10.3223i	0.0329496	+	0.331601i
$970$	17.8349	+	30.8909i	0.572643	+	0.991846i
$971$	−6.66208	−	37.7826i	−0.213796	−	1.21250i	−0.882983	−	0.469405i	$-0.844468\pi$
$971$	−6.66208	−	37.7826i	−0.213796	−	1.21250i	0.669186	−	0.743095i	$-0.266643\pi$
$972$	13.0724	+	8.49197i	0.419296	+	0.272380i
$973$	−25.1804	+	4.08506i	−0.807247	+	0.130961i
$974$	−15.0354	+	2.65114i	−0.481765	+	0.0849481i
$975$	−3.10527	+	1.34366i	−0.0994482	+	0.0430317i
$976$	4.22478			0.135232
$977$	16.4482	−	28.4892i	0.526225	−	0.911449i	−0.473308	−	0.880897i	$-0.656940\pi$
$977$	16.4482	−	28.4892i	0.526225	−	0.911449i	0.999533	−	0.0305521i	$-0.00972654\pi$
$978$	16.8959	−	22.7489i	0.540271	−	0.727431i
$979$	−9.39371	+	11.1950i	−0.300224	+	0.357793i
$980$	6.69868	−	16.9447i	0.213981	−	0.541279i
$981$	−40.4131	+	30.2292i	−1.29029	+	0.965144i
$982$	26.3852	+	4.65241i	0.841984	+	0.148464i
$983$	−13.5510	+	11.3706i	−0.432210	+	0.362667i	−0.832785	−	0.553597i	$-0.813255\pi$
$983$	−13.5510	+	11.3706i	−0.432210	+	0.362667i	0.400575	+	0.916264i	$0.368810\pi$
$984$	3.28534	−	4.42345i	0.104733	−	0.141014i
$985$	−29.2575	+	24.5500i	−0.932222	+	0.782227i
$986$	−4.13612	−	4.92924i	−0.131721	−	0.156979i
$987$	27.5543	−	36.0568i	0.877063	−	1.14770i
$988$	−4.43811	+	1.81805i	−0.141195	+	0.0578399i
$989$	−8.93873	−	5.16078i	−0.284235	−	0.164103i
$990$	5.97617	−	6.36324i	0.189935	−	0.202237i
$991$	49.7346	−	8.76955i	1.57987	−	0.278574i	0.686239	−	0.727376i	$-0.259260\pi$
$991$	49.7346	−	8.76955i	1.57987	−	0.278574i	0.893631	+	0.448802i	$0.148149\pi$
$992$	5.13125	−	6.11518i	0.162917	−	0.194157i
$993$	−18.8194	+	17.7956i	−0.597216	+	0.564726i
$994$	6.57048	−	1.06594i	0.208403	−	0.0338096i
$995$	−44.9162	−	25.9324i	−1.42394	−	0.822112i
$996$	−16.6043	−	25.1833i	−0.526126	−	0.797962i
$997$	7.94071	−	45.0340i	0.251485	−	1.42624i	−0.553452	−	0.832881i	$-0.686690\pi$
$997$	7.94071	−	45.0340i	0.251485	−	1.42624i	0.804937	−	0.593361i	$-0.202199\pi$
$998$	−6.95773	+	39.4593i	−0.220243	+	1.24906i
$999$	23.6872	−	4.25988i	0.749430	−	0.134777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.a.317.20	yes	162
3.2	odd	2		798.2.cc.b.317.17	yes	162
7.4	even	3		798.2.bu.a.431.16	✓	162
19.3	odd	18		798.2.bu.b.611.2	yes	162
21.11	odd	6		798.2.bu.b.431.2	yes	162
57.41	even	18		798.2.bu.a.611.16	yes	162
133.60	odd	18		798.2.cc.b.725.17	yes	162
399.326	even	18	inner	798.2.cc.a.725.20	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.16	✓	162	7.4	even	3
798.2.bu.a.611.16	yes	162	57.41	even	18
798.2.bu.b.431.2	yes	162	21.11	odd	6
798.2.bu.b.611.2	yes	162	19.3	odd	18
798.2.cc.a.317.20	yes	162	1.1	even	1	trivial
798.2.cc.a.725.20	yes	162	399.326	even	18	inner
798.2.cc.b.317.17	yes	162	3.2	odd	2
798.2.cc.b.725.17	yes	162	133.60	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.19003 + 1.25850i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.890265 + 2.44598i) q^{5} +(-1.03273 + 1.39049i) q^{6} +(-2.59902 - 0.495088i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.167638 + 2.99531i) q^{9} +(-2.56342 - 0.452000i) q^{10} +(0.968132 + 0.558951i) q^{11} +(-1.54870 - 0.775586i) q^{12} +(-0.376322 - 1.03393i) q^{13} +(0.0362518 - 2.64550i) q^{14} +(-4.13771 + 1.79041i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.469922 - 1.29110i) q^{17} +(-2.97892 + 0.355040i) q^{18} +(-1.32697 + 4.15200i) q^{19} -2.60296i q^{20} +(-2.46985 - 3.86003i) q^{21} +(-0.382345 + 1.05049i) q^{22} +(-1.94234 + 2.31479i) q^{23} +(0.494875 - 1.65985i) q^{24} +(-1.36004 - 1.14121i) q^{25} +(0.952880 - 0.550145i) q^{26} +(-3.96909 + 3.35355i) q^{27} +(2.61161 - 0.423686i) q^{28} +(-3.58761 - 3.01036i) q^{29} +(-2.48171 - 3.76395i) q^{30} -7.98280i q^{31} +(0.766044 + 0.642788i) q^{32} +(0.448671 + 1.88356i) q^{33} +(1.35309 + 0.238586i) q^{34} +(3.52479 - 5.91639i) q^{35} +(-0.866929 - 2.87201i) q^{36} +(-4.01120 - 2.31587i) q^{37} +(-4.31935 - 0.585824i) q^{38} +(0.853370 - 1.70402i) q^{39} +(2.56342 - 0.452000i) q^{40} +(2.98936 + 1.08804i) q^{41} +(3.37250 - 3.10262i) q^{42} +(0.593141 + 3.36387i) q^{43} +(-1.10092 - 0.194122i) q^{44} +(-7.17725 - 3.07666i) q^{45} +(-2.61691 - 1.51087i) q^{46} +(3.38692 + 9.30550i) q^{47} +(1.72057 + 0.199127i) q^{48} +(6.50978 + 2.57348i) q^{49} +(0.887706 - 1.53755i) q^{50} +(2.18407 - 0.945057i) q^{51} +(0.707253 + 0.842871i) q^{52} +(-5.40713 + 1.96804i) q^{53} +(-3.99183 - 3.32645i) q^{54} +(-2.22908 + 1.87042i) q^{55} +(0.870750 + 2.49836i) q^{56} +(-6.80443 + 3.27103i) q^{57} +(2.34165 - 4.05585i) q^{58} +(1.60078 + 0.582635i) q^{59} +(3.27582 - 3.09761i) q^{60} +(3.23637 + 2.71564i) q^{61} +(7.86152 - 1.38620i) q^{62} +(1.91864 - 7.70187i) q^{63} +(-0.500000 + 0.866025i) q^{64} +2.86401 q^{65} +(-1.77704 + 0.768932i) q^{66} +(1.15342 + 0.203379i) q^{67} +1.37396i q^{68} +(-5.22461 + 0.310247i) q^{69} +(6.43858 + 2.44387i) q^{70} +(0.436878 + 2.47766i) q^{71} +(2.67784 - 1.35248i) q^{72} +(0.846397 + 4.80015i) q^{73} +(1.58415 - 4.35241i) q^{74} +(-0.182285 - 3.06970i) q^{75} +(-0.173123 - 4.35546i) q^{76} +(-2.23946 - 1.93203i) q^{77} +(1.82632 + 0.544506i) q^{78} +(-1.88575 - 2.24736i) q^{79} +(0.890265 + 2.44598i) q^{80} +(-8.94380 - 1.00425i) q^{81} +(-0.552412 + 3.13288i) q^{82} +(15.0823 + 8.70774i) q^{83} +(3.64111 + 2.78250i) q^{84} +(2.73966 + 2.29884i) q^{85} +(-3.20977 + 1.16826i) q^{86} +(-0.480842 - 8.09744i) q^{87} -1.11790i q^{88} +(-2.27005 + 12.8741i) q^{89} +(1.78361 - 7.60246i) q^{90} +(0.466177 + 2.87353i) q^{91} +(1.03350 - 2.83951i) q^{92} +(10.0463 - 9.49981i) q^{93} +(-8.57599 + 4.95135i) q^{94} +(-8.97438 - 6.94214i) q^{95} +(0.102672 + 1.72901i) q^{96} +(-8.80844 - 10.4975i) q^{97} +(-1.40398 + 6.85776i) q^{98} +(-1.83653 + 2.80616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 q^{15} + 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} - 9 q^{27} - 12 q^{28} + 6 q^{29} + 12 q^{33} + 6 q^{34} - 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * q^15 + 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 - 9 * q^27 - 12 * q^28 + 6 * q^29 + 12 * q^33 + 6 * q^34 - 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 + 6 * q^44 + 18 * q^45 - 18 * q^46 + 12 * q^47 + 24 * q^49 + 87 * q^50 - 24 * q^51 + 12 * q^52 - 36 * q^53 - 18 * q^54 - 18 * q^57 + 24 * q^59 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * q^63 - 81 * q^64 - 72 * q^65 + 12 * q^66 - 63 * q^67 + 9 * q^69 + 12 * q^70 + 12 * q^71 - 51 * q^73 - 42 * q^74 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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