LMFDB - Embedded newform 798.2.bu.b.611.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] 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, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (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			611.20
Character	$\chi$	$=$	798.611
Dual form			798.2.bu.b.431.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(1.33292 + 1.10604i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.29205 + 1.53980i) q^{5} +(1.63082 + 0.583453i) q^{6} +(2.56194 + 0.660635i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.553349 + 2.94853i) q^{9} +(-0.687483 + 1.88884i) q^{10} -2.67795i q^{11} +(1.73202 - 0.00950808i) q^{12} +(-1.33096 + 3.65679i) q^{13} +(2.63339 - 0.255442i) q^{14} +(-3.42527 + 0.623375i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.293478 - 0.0517481i) q^{17} +(1.52843 + 2.58145i) q^{18} +(1.41705 + 4.12213i) q^{19} +2.01007i q^{20} +(2.68418 + 3.71419i) q^{21} +(-0.915914 - 2.51645i) q^{22} +(2.13849 - 5.87546i) q^{23} +(1.62432 - 0.601322i) q^{24} +(0.166639 + 0.945059i) q^{25} +3.89147i q^{26} +(-2.52362 + 4.54217i) q^{27} +(2.38721 - 1.14071i) q^{28} +(3.13515 - 2.63071i) q^{29} +(-3.00550 + 1.75729i) q^{30} +(-8.01290 - 4.62625i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.96192 - 3.56949i) q^{33} +(-0.293478 + 0.0517481i) q^{34} +(-4.32739 + 3.09131i) q^{35} +(2.31917 + 1.90302i) q^{36} +(4.07083 + 2.35029i) q^{37} +(2.74145 + 3.38887i) q^{38} +(-5.81862 + 3.40210i) q^{39} +(0.687483 + 1.88884i) q^{40} +(-1.17992 + 0.429457i) q^{41} +(3.79263 + 2.57215i) q^{42} +(0.132594 - 0.751977i) q^{43} +(-1.72135 - 2.05143i) q^{44} +(-5.25509 - 2.95758i) q^{45} -6.25254i q^{46} +(0.0609376 - 0.0107449i) q^{47} +(1.32070 - 1.12061i) q^{48} +(6.12712 + 3.38502i) q^{49} +(0.479819 + 0.831071i) q^{50} +(-0.333947 - 0.393574i) q^{51} +(1.33096 + 3.65679i) q^{52} +(-1.86260 + 1.56291i) q^{53} +(-0.817911 + 5.13138i) q^{54} +(4.12351 + 3.46003i) q^{55} +(1.85310 - 1.88839i) q^{56} +(-2.67042 + 7.06179i) q^{57} +(2.04633 - 3.54434i) q^{58} +(1.95384 - 11.0808i) q^{59} +(-2.22321 + 2.67926i) q^{60} +(12.7879 + 4.65441i) q^{61} +(-9.11193 - 1.60668i) q^{62} +(-0.530251 + 7.91952i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.91105 - 6.77414i) q^{65} +(1.56246 - 4.36727i) q^{66} +(0.168251 - 0.462267i) q^{67} +(-0.258080 + 0.149003i) q^{68} +(9.34894 - 5.46626i) q^{69} +(-3.00913 + 4.38494i) q^{70} +(2.31924 - 13.1531i) q^{71} +(2.83017 + 0.995048i) q^{72} +(-10.0116 - 8.40077i) q^{73} +(4.62917 + 0.816248i) q^{74} +(-0.823156 + 1.44400i) q^{75} +(3.73518 + 2.24687i) q^{76} +(1.76915 - 6.86077i) q^{77} +(-4.30412 + 5.18702i) q^{78} +(-8.33498 - 1.46968i) q^{79} +(1.29205 + 1.53980i) q^{80} +(-8.38761 + 3.26313i) q^{81} +(-0.961883 + 0.807115i) q^{82} +(-7.99484 + 4.61582i) q^{83} +(4.44363 + 1.11988i) q^{84} +(0.458868 - 0.385036i) q^{85} +(-0.132594 - 0.751977i) q^{86} +(7.08858 - 0.0389133i) q^{87} +(-2.31917 - 1.33898i) q^{88} +(-10.5089 + 8.81798i) q^{89} +(-5.94972 - 0.981871i) q^{90} +(-5.82565 + 8.48920i) q^{91} +(-2.13849 - 5.87546i) q^{92} +(-5.56373 - 15.0290i) q^{93} +(0.0535876 - 0.0309388i) q^{94} +(-8.17815 - 3.14400i) q^{95} +(0.857778 - 1.50473i) q^{96} +(12.3055 - 14.6652i) q^{97} +(6.91536 + 1.08528i) q^{98} +(7.89601 - 1.48184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.33292	+	1.10604i	0.769561	+	0.638573i
$3$	1.33292	+	1.10604i	0.769561	+	0.638573i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.29205	+	1.53980i	−0.577820	+	0.688619i	−0.973216	−	0.229891i	$-0.926163\pi$
$5$	−1.29205	+	1.53980i	−0.577820	+	0.688619i	0.395396	+	0.918511i	$0.370607\pi$
$6$	1.63082	+	0.583453i	0.665781	+	0.238194i
$7$	2.56194	+	0.660635i	0.968324	+	0.249697i
$7$	2.56194	+	0.660635i	0.968324	+	0.249697i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.553349	+	2.94853i	0.184450	+	0.982842i
$10$	−0.687483	+	1.88884i	−0.217401	+	0.597305i
$11$		−	2.67795i		−	0.807433i	−0.914884	−	0.403716i	$-0.867718\pi$
$11$		−	2.67795i		−	0.807433i	0.914884	−	0.403716i	$-0.132282\pi$
$12$	1.73202	−	0.00950808i	0.499992	−	0.00274475i
$13$	−1.33096	+	3.65679i	−0.369142	+	1.01421i	0.606546	+	0.795048i	$0.292554\pi$
$13$	−1.33096	+	3.65679i	−0.369142	+	1.01421i	−0.975689	+	0.219162i	$0.929668\pi$
$14$	2.63339	−	0.255442i	0.703803	−	0.0682699i
$15$	−3.42527	+	0.623375i	−0.884402	+	0.160955i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.293478	−	0.0517481i	−0.0711789	−	0.0125508i	0.137945	−	0.990440i	$-0.455950\pi$
$17$	−0.293478	−	0.0517481i	−0.0711789	−	0.0125508i	−0.209124	+	0.977889i	$0.567061\pi$
$18$	1.52843	+	2.58145i	0.360255	+	0.608454i
$19$	1.41705	+	4.12213i	0.325094	+	0.945682i
$19$	1.41705	+	4.12213i	0.325094	+	0.945682i
$20$			2.01007i			0.449464i
$21$	2.68418	+	3.71419i	0.585735	+	0.810502i
$22$	−0.915914	−	2.51645i	−0.195273	−	0.536509i
$23$	2.13849	−	5.87546i	0.445907	−	1.22512i	−0.489643	−	0.871923i	$-0.662873\pi$
$23$	2.13849	−	5.87546i	0.445907	−	1.22512i	0.935550	−	0.353196i	$-0.114905\pi$
$24$	1.62432	−	0.601322i	0.331563	−	0.122744i
$25$	0.166639	+	0.945059i	0.0333279	+	0.189012i
$26$			3.89147i			0.763180i
$27$	−2.52362	+	4.54217i	−0.485671	+	0.874142i
$28$	2.38721	−	1.14071i	0.451141	−	0.215574i
$29$	3.13515	−	2.63071i	0.582184	−	0.488510i	−0.303480	−	0.952838i	$-0.598149\pi$
$29$	3.13515	−	2.63071i	0.582184	−	0.488510i	0.885663	+	0.464328i	$0.153704\pi$
$30$	−3.00550	+	1.75729i	−0.548726	+	0.320836i
$31$	−8.01290	−	4.62625i	−1.43916	−	0.830899i	−0.441368	−	0.897326i	$-0.645507\pi$
$31$	−8.01290	−	4.62625i	−1.43916	−	0.830899i	−0.997791	+	0.0664276i	$0.978840\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	2.96192	−	3.56949i	0.515605	−	0.621369i
$34$	−0.293478	+	0.0517481i	−0.0503310	+	0.00887472i
$35$	−4.32739	+	3.09131i	−0.731463	+	0.522527i
$36$	2.31917	+	1.90302i	0.386528	+	0.317169i
$37$	4.07083	+	2.35029i	0.669240	+	0.386386i	0.795788	−	0.605575i	$-0.207057\pi$
$37$	4.07083	+	2.35029i	0.669240	+	0.386386i	−0.126549	+	0.991960i	$0.540390\pi$
$38$	2.74145	+	3.38887i	0.444721	+	0.549748i
$39$	−5.81862	+	3.40210i	−0.931724	+	0.544773i
$40$	0.687483	+	1.88884i	0.108701	+	0.298652i
$41$	−1.17992	+	0.429457i	−0.184273	+	0.0670699i	−0.432509	−	0.901630i	$-0.642372\pi$
$41$	−1.17992	+	0.429457i	−0.184273	+	0.0670699i	0.248236	+	0.968700i	$0.420149\pi$
$42$	3.79263	+	2.57215i	0.585215	+	0.396892i
$43$	0.132594	−	0.751977i	0.0202204	−	0.114675i	−0.973027	−	0.230691i	$-0.925901\pi$
$43$	0.132594	−	0.751977i	0.0202204	−	0.114675i	0.993247	+	0.116016i	$0.0370124\pi$
$44$	−1.72135	−	2.05143i	−0.259504	−	0.309265i
$45$	−5.25509	−	2.95758i	−0.783383	−	0.440890i
$46$		−	6.25254i		−	0.921886i
$47$	0.0609376	−	0.0107449i	0.00888866	−	0.00156731i	−0.169202	−	0.985581i	$-0.554119\pi$
$47$	0.0609376	−	0.0107449i	0.00888866	−	0.00156731i	0.178091	+	0.984014i	$0.443008\pi$
$48$	1.32070	−	1.12061i	0.190626	−	0.161746i
$49$	6.12712	+	3.38502i	0.875303	+	0.483575i
$50$	0.479819	+	0.831071i	0.0678566	+	0.117531i
$51$	−0.333947	−	0.393574i	−0.0467619	−	0.0551115i
$52$	1.33096	+	3.65679i	0.184571	+	0.507105i
$53$	−1.86260	+	1.56291i	−0.255848	+	0.214682i	−0.761686	−	0.647947i	$-0.775628\pi$
$53$	−1.86260	+	1.56291i	−0.255848	+	0.214682i	0.505837	+	0.862629i	$0.331184\pi$
$54$	−0.817911	+	5.13138i	−0.111304	+	0.698292i
$55$	4.12351	+	3.46003i	0.556014	+	0.466551i
$56$	1.85310	−	1.88839i	0.247631	−	0.252347i
$57$	−2.67042	+	7.06179i	−0.353706	+	0.935357i
$58$	2.04633	−	3.54434i	0.268696	−	0.465395i
$59$	1.95384	−	11.0808i	0.254368	−	1.44259i	−0.543323	−	0.839524i	$-0.682834\pi$
$59$	1.95384	−	11.0808i	0.254368	−	1.44259i	0.797690	−	0.603067i	$-0.206055\pi$
$60$	−2.22321	+	2.67926i	−0.287016	+	0.345890i
$61$	12.7879	+	4.65441i	1.63732	+	0.595936i	0.986568	−	0.163353i	$-0.0522310\pi$
$61$	12.7879	+	4.65441i	1.63732	+	0.595936i	0.650753	+	0.759289i	$0.274453\pi$
$62$	−9.11193	−	1.60668i	−1.15722	−	0.204048i
$63$	−0.530251	+	7.91952i	−0.0668053	+	0.997766i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.91105	−	6.77414i	−0.485107	−	0.840229i
$66$	1.56246	−	4.36727i	0.192325	−	0.537573i
$67$	0.168251	−	0.462267i	0.0205552	−	0.0564749i	−0.928991	−	0.370103i	$-0.879322\pi$
$67$	0.168251	−	0.462267i	0.0205552	−	0.0564749i	0.949546	+	0.313628i	$0.101545\pi$
$68$	−0.258080	+	0.149003i	−0.0312968	+	0.0180692i
$69$	9.34894	−	5.46626i	1.12548	−	0.658060i
$70$	−3.00913	+	4.38494i	−0.359660	+	0.524100i
$71$	2.31924	−	13.1531i	0.275243	−	1.56098i	−0.462946	−	0.886387i	$-0.653208\pi$
$71$	2.31924	−	13.1531i	0.275243	−	1.56098i	0.738189	−	0.674594i	$-0.235681\pi$
$72$	2.83017	+	0.995048i	0.333539	+	0.117268i
$73$	−10.0116	−	8.40077i	−1.17177	−	0.983235i	−0.171776	−	0.985136i	$-0.554951\pi$
$73$	−10.0116	−	8.40077i	−1.17177	−	0.983235i	−0.999998	+	0.00190057i	$0.999395\pi$
$74$	4.62917	+	0.816248i	0.538130	+	0.0948869i
$75$	−0.823156	+	1.44400i	−0.0950499	+	0.166738i
$76$	3.73518	+	2.24687i	0.428455	+	0.257734i
$77$	1.76915	−	6.86077i	0.201613	−	0.781857i
$78$	−4.30412	+	5.18702i	−0.487346	+	0.587314i
$79$	−8.33498	−	1.46968i	−0.937758	−	0.165352i	−0.316176	−	0.948701i	$-0.602399\pi$
$79$	−8.33498	−	1.46968i	−0.937758	−	0.165352i	−0.621583	+	0.783349i	$0.713510\pi$
$80$	1.29205	+	1.53980i	0.144455	+	0.172155i
$81$	−8.38761	+	3.26313i	−0.931957	+	0.362570i
$82$	−0.961883	+	0.807115i	−0.106222	+	0.0891310i
$83$	−7.99484	+	4.61582i	−0.877547	+	0.506652i	−0.869849	−	0.493318i	$-0.835784\pi$
$83$	−7.99484	+	4.61582i	−0.877547	+	0.506652i	−0.00769833	+	0.999970i	$0.502450\pi$
$84$	4.44363	+	1.11988i	0.484840	+	0.122189i
$85$	0.458868	−	0.385036i	0.0497713	−	0.0417630i
$86$	−0.132594	−	0.751977i	−0.0142980	−	0.0810878i
$87$	7.08858	−	0.0389133i	0.759975	−	0.00417194i
$88$	−2.31917	−	1.33898i	−0.247225	−	0.142735i
$89$	−10.5089	+	8.81798i	−1.11394	+	0.934704i	−0.998282	−	0.0585858i	$-0.981341\pi$
$89$	−10.5089	+	8.81798i	−1.11394	+	0.934704i	−0.115654	+	0.993290i	$0.536896\pi$
$90$	−5.94972	−	0.981871i	−0.627156	−	0.103498i
$91$	−5.82565	+	8.48920i	−0.610694	+	0.889910i
$92$	−2.13849	−	5.87546i	−0.222953	−	0.612559i
$93$	−5.56373	−	15.0290i	−0.576932	−	1.55844i
$94$	0.0535876	−	0.0309388i	0.00552714	−	0.00319110i
$95$	−8.17815	−	3.14400i	−0.839061	−	0.322568i
$96$	0.857778	−	1.50473i	0.0875466	−	0.153576i
$97$	12.3055	−	14.6652i	1.24944	−	1.48902i	0.444362	−	0.895847i	$-0.353430\pi$
$97$	12.3055	−	14.6652i	1.24944	−	1.48902i	0.805075	−	0.593173i	$-0.202125\pi$
$98$	6.91536	+	1.08528i	0.698557	+	0.109630i
$99$	7.89601	−	1.48184i	0.793579	−	0.148931i
$100$	0.735125	+	0.616843i	0.0735125	+	0.0616843i
$101$	5.49310	−	0.968583i	0.546584	−	0.0963776i	0.106464	−	0.994317i	$-0.466047\pi$
$101$	5.49310	−	0.968583i	0.546584	−	0.0963776i	0.440120	+	0.897939i	$0.354936\pi$
$102$	−0.448418	−	0.255622i	−0.0444000	−	0.0253104i
$103$	2.67317	−	1.54335i	0.263395	−	0.152071i	−0.362487	−	0.931989i	$-0.618072\pi$
$103$	2.67317	−	1.54335i	0.263395	−	0.152071i	0.625882	+	0.779918i	$0.284739\pi$
$104$	2.50139	+	2.98104i	0.245281	+	0.292315i
$105$	−9.18718	−	0.665805i	−0.896577	−	0.0649759i
$106$	−1.21573	+	2.10570i	−0.118082	+	0.204524i
$107$	13.0976			1.26619			0.633095	−	0.774074i	$-0.281784\pi$
$107$	13.0976			1.26619			0.633095	+	0.774074i	$0.281784\pi$
$108$	0.986449	+	5.10166i	0.0949211	+	0.490907i
$109$	−4.96378	−	13.6379i	−0.475444	−	1.30627i	−0.913323	−	0.407237i	$-0.866492\pi$
$109$	−4.96378	−	13.6379i	−0.475444	−	1.30627i	0.437879	−	0.899034i	$-0.355730\pi$
$110$	5.05823	+	1.84105i	0.482284	+	0.175537i
$111$	2.82657	+	7.63525i	0.268286	+	0.724706i
$112$	1.09548	−	2.40830i	0.103513	−	0.227563i
$113$	−18.7624			−1.76502			−0.882509	−	0.470295i	$-0.844147\pi$
$113$	−18.7624			−1.76502			−0.882509	+	0.470295i	$0.844147\pi$
$114$	−0.0941050	+	7.54925i	−0.00881374	+	0.707052i
$115$	6.28400	+	10.8842i	0.585986	+	1.01496i
$116$	0.710682	−	4.03048i	0.0659851	−	0.374220i
$117$	−11.5186	−	1.90089i	−1.06490	−	0.175738i
$118$	−1.95384	−	11.0808i	−0.179865	−	1.02007i
$119$	−0.717688	−	0.326458i	−0.0657903	−	0.0299263i
$120$	−1.17278	+	3.27806i	−0.107059	+	0.299245i
$121$	3.82857			0.348052
$122$	13.6086			1.23206
$123$	−2.04774	−	0.732611i	−0.184639	−	0.0660573i
$124$	−9.11193	+	1.60668i	−0.818276	+	0.144284i
$125$	−10.3743	−	5.98963i	−0.927910	−	0.535729i
$126$	2.21036	+	7.62327i	0.196915	+	0.679135i
$127$	2.75904	−	7.58040i	0.244825	−	0.672652i	−0.755031	−	0.655689i	$-0.772378\pi$
$127$	2.75904	−	7.58040i	0.244825	−	0.672652i	0.999856	−	0.0169625i	$-0.00539960\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	1.00845	−	0.855671i	0.0887894	−	0.0753376i
$130$	−5.99208	−	5.02795i	−0.525540	−	0.440981i
$131$	−2.88823	−	7.93534i	−0.252346	−	0.693314i	−0.999586	−	0.0287603i	$-0.990844\pi$
$131$	−2.88823	−	7.93534i	−0.252346	−	0.693314i	0.747241	−	0.664553i	$-0.231378\pi$
$132$	−0.0254622	−	4.63828i	−0.00221620	−	0.403710i
$133$	0.907187	+	11.4968i	0.0786631	+	0.996901i
$134$		−	0.491934i		−	0.0424966i
$135$	−3.73341	−	9.75456i	−0.321321	−	0.839539i
$136$	−0.191554	+	0.228285i	−0.0164256	+	0.0195753i
$137$	8.06879	+	9.61601i	0.689363	+	0.821551i	0.991279	−	0.131783i	$-0.0420703\pi$
$137$	8.06879	+	9.61601i	0.689363	+	0.821551i	−0.301915	+	0.953335i	$0.597626\pi$
$138$	6.91556	−	8.33413i	0.588691	−	0.709448i
$139$	−4.89477	−	1.78155i	−0.415169	−	0.151109i	0.125986	−	0.992032i	$-0.459791\pi$
$139$	−4.89477	−	1.78155i	−0.415169	−	0.151109i	−0.541155	+	0.840923i	$0.682013\pi$
$140$	−1.32792	+	5.14968i	−0.112230	+	0.435227i
$141$	0.0931092	+	0.0530773i	0.00784121	+	0.00446991i
$142$	−2.31924	−	13.1531i	−0.194626	−	1.10378i
$143$	9.79270	+	3.56425i	0.818906	+	0.298058i
$144$	2.99982	−	0.0329365i	0.249985	−	0.00274471i
$145$			8.22650i			0.683174i
$146$	−12.2811	−	4.46995i	−1.01639	−	0.369936i
$147$	4.42299	+	11.2888i	0.364802	+	0.931085i
$148$	4.62917	−	0.816248i	0.380516	−	0.0670952i
$149$	−1.24633	−	0.219761i	−0.102103	−	0.0180035i	0.122363	−	0.992485i	$-0.460953\pi$
$149$	−1.24633	−	0.219761i	−0.102103	−	0.0180035i	−0.224466	+	0.974482i	$0.572064\pi$
$150$	−0.279638	+	1.63845i	−0.0228323	+	0.133779i
$151$	−0.0720732	+	0.0416115i	−0.00586523	+	0.00338629i	−0.502930	−	0.864327i	$-0.667745\pi$
$151$	−0.0720732	+	0.0416115i	−0.00586523	+	0.00338629i	0.497065	+	0.867714i	$0.334411\pi$
$152$	4.27840	+	0.833861i	0.347024	+	0.0676351i
$153$	−0.00981524	−	0.893962i	−0.000793515	−	0.0722725i
$154$	−0.684063	−	7.05210i	−0.0551233	−	0.568274i
$155$	17.4765	−	6.36093i	1.40375	−	0.510922i
$156$	−2.27049	+	6.34630i	−0.181785	+	0.508110i
$157$	10.7458	−	3.91115i	0.857608	−	0.312144i	0.124470	−	0.992223i	$-0.460277\pi$
$157$	10.7458	−	3.91115i	0.857608	−	0.312144i	0.733138	+	0.680080i	$0.238055\pi$
$158$	−8.33498	+	1.46968i	−0.663095	+	0.116922i
$159$	−4.21134	+	0.0231185i	−0.333981	+	0.00183342i
$160$	1.74077	+	1.00503i	0.137620	+	0.0794548i
$161$	9.36024	−	13.6398i	0.737690	−	1.07497i
$162$	−6.76572	+	5.93507i	−0.531565	+	0.466303i
$163$	−6.45080	−	11.1731i	−0.505266	−	0.875146i	−0.999981	−	0.00609080i	$-0.998061\pi$
$163$	−6.45080	−	11.1731i	−0.505266	−	0.875146i	0.494716	−	0.869055i	$-0.335272\pi$
$164$	−0.627824	+	1.08742i	−0.0490248	+	0.0849135i
$165$	1.66937	+	9.17272i	0.129960	+	0.714095i
$166$	−5.93398	+	7.07185i	−0.460567	+	0.548882i
$167$	3.38885	+	19.2191i	0.262237	+	1.48722i	0.776790	+	0.629760i	$0.216847\pi$
$167$	3.38885	+	19.2191i	0.262237	+	1.48722i	−0.514553	+	0.857459i	$0.672042\pi$
$168$	4.55867	−	0.467471i	0.351709	−	0.0360662i
$169$	−1.64204	−	1.37784i	−0.126311	−	0.105988i
$170$	0.299505	−	0.518758i	0.0229710	−	0.0397869i
$171$	−11.3701	+	6.45920i	−0.869492	+	0.493947i
$172$	−0.381789	−	0.661278i	−0.0291111	−	0.0504219i
$173$	−1.32076	+	0.480717i	−0.100415	+	0.0365482i	−0.391739	−	0.920076i	$-0.628126\pi$
$173$	−1.32076	+	0.480717i	−0.100415	+	0.0365482i	0.291324	+	0.956624i	$0.405904\pi$
$174$	6.64777	−	2.46100i	0.503966	−	0.186568i
$175$	−0.197418	+	2.53128i	−0.0149234	+	0.191346i
$176$	−2.63727	−	0.465022i	−0.198792	−	0.0350523i
$177$	14.8601	−	12.6087i	1.11695	−	0.947730i
$178$	−6.85917	+	11.8804i	−0.514116	+	0.890476i
$179$	−0.781429			−0.0584067			−0.0292034	−	0.999573i	$-0.509297\pi$
$179$	−0.781429			−0.0584067			−0.0292034	+	0.999573i	$0.509297\pi$
$180$	−5.92673	+	1.11227i	−0.441752	+	0.0829036i
$181$	−2.47749	−	2.95256i	−0.184150	−	0.219462i	0.666069	−	0.745890i	$-0.267975\pi$
$181$	−2.47749	−	2.95256i	−0.184150	−	0.219462i	−0.850220	+	0.526428i	$0.823531\pi$
$182$	−2.57084	+	9.96973i	−0.190564	+	0.739006i
$183$	11.8973	+	20.3479i	0.879471	+	1.50416i
$184$	−4.01905	−	4.78972i	−0.296289	−	0.353103i
$185$	−8.87867	+	3.23157i	−0.652773	+	0.237590i
$186$	−10.3684	−	12.2197i	−0.760249	−	0.895995i
$187$	−0.138579	+	0.785920i	−0.0101339	+	0.0574722i
$188$	0.0397742	−	0.0474010i	0.00290083	−	0.00345707i
$189$	−9.46609	+	9.96961i	−0.688557	+	0.725182i
$190$	−8.76026	−	0.157302i	−0.635536	−	0.0114119i
$191$	−7.63961	−	4.41073i	−0.552783	−	0.319149i	0.197461	−	0.980311i	$-0.436731\pi$
$191$	−7.63961	−	4.41073i	−0.552783	−	0.319149i	−0.750244	+	0.661161i	$0.770064\pi$
$192$	0.291399	−	1.70736i	0.0210299	−	0.123218i
$193$	−16.6242	+	19.8119i	−1.19663	+	1.42609i	−0.318337	+	0.947978i	$0.603124\pi$
$193$	−16.6242	+	19.8119i	−1.19663	+	1.42609i	−0.878297	+	0.478115i	$0.841320\pi$
$194$	6.54763	−	17.9895i	0.470093	−	1.29157i
$195$	2.27936	−	13.3552i	0.163228	−	0.956384i
$196$	6.86950	−	1.34536i	0.490678	−	0.0960971i
$197$	−4.18467	+	2.41602i	−0.298145	+	0.172134i	−0.641609	−	0.767032i	$-0.721733\pi$
$197$	−4.18467	+	2.41602i	−0.298145	+	0.172134i	0.343464	+	0.939166i	$0.388400\pi$
$198$	6.91300	−	4.09307i	0.491286	−	0.290882i
$199$	−2.00219	−	0.728739i	−0.141932	−	0.0516589i	0.270078	−	0.962839i	$-0.412951\pi$
$199$	−2.00219	−	0.728739i	−0.141932	−	0.0516589i	−0.412009	+	0.911180i	$0.635173\pi$
$200$	0.901764	+	0.328215i	0.0637644	+	0.0232083i
$201$	0.735552	−	0.430072i	0.0518818	−	0.0303349i
$202$	4.83055	−	2.78892i	0.339877	−	0.196228i
$203$	9.77003	−	4.66853i	0.685722	−	0.327667i
$204$	−0.508803	−	0.0868385i	−0.0356233	−	0.00607991i
$205$	0.863237	−	2.37172i	0.0602911	−	0.165648i
$206$	1.98410	−	2.36455i	0.138239	−	0.164746i
$207$	18.5073	+	3.05422i	1.28635	+	0.212283i
$208$	3.37011	+	1.94573i	0.233675	+	0.134912i
$209$	11.0389	−	3.79480i	0.763574	−	0.262492i
$210$	−8.86085	+	2.51655i	−0.611456	+	0.173658i
$211$	−8.33462	+	9.93281i	−0.573779	+	0.683803i	−0.972402	−	0.233312i	$-0.925044\pi$
$211$	−8.33462	+	9.93281i	−0.573779	+	0.683803i	0.398623	+	0.917115i	$0.369488\pi$
$212$	−0.422218	+	2.39452i	−0.0289981	+	0.164456i
$213$	17.6392	−	14.9668i	1.20862	−	1.02551i
$214$	12.3077	−	4.47963i	0.841336	−	0.306221i
$215$	0.986577	+	1.17576i	0.0672840	+	0.0801859i
$216$	2.67183	+	4.45661i	0.181795	+	0.303234i
$217$	−17.4723	−	17.1458i	−1.18610	−	1.16393i
$218$	−9.32885	−	11.1177i	−0.631830	−	0.752985i
$219$	−4.05313	−	22.2708i	−0.273885	−	1.50492i
$220$	5.38286			0.362912
$221$	0.579839	−	1.00431i	0.0390042	−	0.0675573i
$222$	5.26751	+	6.20805i	0.353532	+	0.416657i
$223$	19.1270	+	3.37261i	1.28084	+	0.225847i	0.772337	−	0.635213i	$-0.219088\pi$
$223$	19.1270	+	3.37261i	1.28084	+	0.225847i	0.508504	+	0.861060i	$0.330199\pi$
$224$	0.205722	−	2.63774i	0.0137454	−	0.176241i
$225$	−2.69432	+	1.01429i	−0.179621	+	0.0676192i
$226$	−17.6309	+	6.41712i	−1.17279	+	0.426860i
$227$	−8.87531	−	15.3725i	−0.589075	−	1.02031i	−0.994354	−	0.106115i	$-0.966159\pi$
$227$	−8.87531	−	15.3725i	−0.589075	−	1.02031i	0.405279	−	0.914193i	$-0.367174\pi$
$228$	2.49357	+	7.12616i	0.165140	+	0.471941i
$229$	−0.957176	+	1.65788i	−0.0632520	+	0.109556i	−0.895917	−	0.444221i	$-0.853481\pi$
$229$	−0.957176	+	1.65788i	−0.0632520	+	0.109556i	0.832665	+	0.553777i	$0.186814\pi$
$230$	9.62765	+	8.07856i	0.634829	+	0.532684i
$231$	9.94642	−	7.18810i	0.654426	−	0.472942i
$232$	−0.710682	−	4.03048i	−0.0466585	−	0.264614i
$233$	−14.9824	+	17.8554i	−0.981533	+	1.16975i	0.00395374	+	0.999992i	$0.498741\pi$
$233$	−14.9824	+	17.8554i	−0.981533	+	1.16975i	−0.985487	+	0.169753i	$0.945703\pi$
$234$	−11.4741	+	2.15334i	−0.750085	+	0.140768i
$235$	−0.0621890	+	0.107715i	−0.00405677	+	0.00702652i
$236$	−5.62585	−	9.74425i	−0.366211	−	0.634297i
$237$	−9.48433	−	11.1778i	−0.616073	−	0.726076i
$238$	−0.786061	−	0.0613062i	−0.0509528	−	0.00397389i
$239$	8.39001	+	4.84398i	0.542705	+	0.313331i	0.746174	−	0.665751i	$-0.231889\pi$
$239$	8.39001	+	4.84398i	0.542705	+	0.313331i	−0.203470	+	0.979081i	$0.565222\pi$
$240$	0.0191119	+	3.48148i	0.00123367	+	0.224729i
$241$	−16.9881	+	2.99547i	−1.09430	+	0.192955i	−0.691532	−	0.722346i	$-0.743064\pi$
$241$	−16.9881	+	2.99547i	−1.09430	+	0.192955i	−0.402771	+	0.915301i	$0.631953\pi$
$242$	3.59768	−	1.30945i	0.231268	−	0.0841746i
$243$	−14.7892	−	4.92755i	−0.948725	−	0.316102i
$244$	12.7879	−	4.65441i	0.818660	−	0.297968i
$245$	−13.1288	+	5.06094i	−0.838767	+	0.323331i
$246$	−2.17481	+	0.0119388i	−0.138661	+	0.000761191i
$247$	−16.9598	−	0.304535i	−1.07913	−	0.0193771i
$248$	−8.01290	+	4.62625i	−0.508820	+	0.293767i
$249$	−15.7618	−	2.69009i	−0.998861	−	0.170478i
$250$	−11.7973	−	2.08018i	−0.746125	−	0.131562i
$251$	13.2827	−	2.34209i	0.838393	−	0.147831i	0.262066	−	0.965050i	$-0.415596\pi$
$251$	13.2827	−	2.34209i	0.838393	−	0.147831i	0.576328	+	0.817219i	$0.304485\pi$
$252$	4.68438	+	6.40754i	0.295088	+	0.403637i
$253$	−15.7342	−	5.72678i	−0.989201	−	0.360040i
$254$		−	8.06689i		−	0.506162i
$255$	1.03750	−	0.00569544i	0.0649708	−	0.000356662i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	3.32646	+	18.8653i	0.207499	+	1.17679i	0.893458	+	0.449146i	$0.148272\pi$
$257$	3.32646	+	18.8653i	0.207499	+	1.17679i	−0.685959	+	0.727640i	$0.740617\pi$
$258$	0.654980	−	1.14898i	0.0407773	−	0.0715323i
$259$	8.87654	+	8.71065i	0.551562	+	0.541254i
$260$	−7.35038	−	2.67532i	−0.455851	−	0.165916i
$261$	9.49154	+	7.78838i	0.587512	+	0.482089i
$262$	−5.42809	−	6.46895i	−0.335349	−	0.399653i
$263$	−0.712627	+	0.849276i	−0.0439425	+	0.0523686i	−0.787568	−	0.616228i	$-0.788660\pi$
$263$	−0.712627	+	0.849276i	−0.0439425	+	0.0523686i	0.743626	+	0.668596i	$0.233105\pi$
$264$	−1.61031	−	4.34985i	−0.0991078	−	0.267715i
$265$		−	4.88739i		−	0.300230i
$266$	4.78462	+	10.4932i	0.293364	+	0.643380i
$267$	−23.7605	+	0.130435i	−1.45412	+	0.00798250i
$268$	−0.168251	−	0.462267i	−0.0102776	−	0.0282374i
$269$	−5.57885	−	4.68121i	−0.340148	−	0.285418i	0.456671	−	0.889635i	$-0.349042\pi$
$269$	−5.57885	−	4.68121i	−0.340148	−	0.285418i	−0.796820	+	0.604217i	$0.793486\pi$
$270$	−6.84451	−	7.88939i	−0.416544	−	0.480133i
$271$	2.54416	+	2.13481i	0.154547	+	0.129680i	0.716782	−	0.697297i	$-0.245614\pi$
$271$	2.54416	+	2.13481i	0.154547	+	0.129680i	−0.562235	+	0.826977i	$0.690059\pi$
$272$	−0.101924	+	0.280033i	−0.00618004	+	0.0169795i
$273$	−17.1545	+	4.87202i	−1.03824	+	0.294868i
$274$	10.8711	+	6.27641i	0.656744	+	0.379172i
$275$	2.53082	−	0.446252i	0.152614	−	0.0269100i
$276$	3.64806	−	10.1968i	0.219587	−	0.613774i
$277$	8.66421			0.520582			0.260291	−	0.965530i	$-0.416182\pi$
$277$	8.66421			0.520582			0.260291	+	0.965530i	$0.416182\pi$
$278$	−5.20891			−0.312409
$279$	9.20668	−	26.1862i	0.551190	−	1.56772i
$280$	0.513456	+	5.29329i	0.0306849	+	0.316334i
$281$	0.271101	+	1.53749i	0.0161725	+	0.0917189i	0.991826	−	0.127600i	$-0.0407275\pi$
$281$	0.271101	+	1.53749i	0.0161725	+	0.0917189i	−0.975653	+	0.219319i	$0.929616\pi$
$282$	0.105648	+	0.0180311i	0.00629122	+	0.00107374i
$283$	−0.977979	+	5.54640i	−0.0581348	+	0.329699i	−0.999980	−	0.00634855i	$-0.997979\pi$
$283$	−0.977979	+	5.54640i	−0.0581348	+	0.329699i	0.941845	+	0.336048i	$0.109090\pi$
$284$	−6.67798	−	11.5666i	−0.396265	−	0.686352i
$285$	−7.42343	−	13.2361i	−0.439726	−	0.784037i
$286$	10.4212			0.616217
$287$	−3.30661	+	0.320746i	−0.195183	+	0.0189330i
$288$	2.80764	−	1.05695i	0.165442	−	0.0622813i
$289$	−15.8913	−	5.78397i	−0.934784	−	0.340233i
$290$	2.81363	+	7.73038i	0.165222	+	0.453944i
$291$	32.6225	−	5.93706i	1.91237	−	0.348037i
$292$	−13.0693			−0.764821
$293$	13.5475	−	23.4650i	0.791454	−	1.37084i	−0.133613	−	0.991034i	$-0.542658\pi$
$293$	13.5475	−	23.4650i	0.791454	−	1.37084i	0.925067	−	0.379805i	$-0.124009\pi$
$294$	8.01725	+	9.09526i	0.467575	+	0.530446i
$295$	14.5377	+	17.3253i	0.846417	+	1.00872i
$296$	4.07083	−	2.35029i	0.236612	−	0.136608i
$297$	12.1637	+	6.75813i	0.705811	+	0.392146i
$298$	−1.24633	+	0.219761i	−0.0721978	+	0.0127304i
$299$	18.6391	+	15.6400i	1.07792	+	0.904486i
$300$	0.297609	+	1.63528i	0.0171825	+	0.0944130i
$301$	0.836481	−	1.83893i	0.0482140	−	0.105994i
$302$	−0.0534947	+	0.0637525i	−0.00307827	+	0.00366854i
$303$	8.39316	+	4.78455i	0.482174	+	0.274865i
$304$	4.30557	−	0.679725i	0.246942	−	0.0389849i
$305$	−23.6894	+	13.6771i	−1.35645	+	0.783147i
$306$	−0.314976	−	0.836693i	−0.0180060	−	0.0478305i
$307$	8.82093	+	24.2353i	0.503437	+	1.38318i	0.887898	+	0.460041i	$0.152165\pi$
$307$	8.82093	+	24.2353i	0.503437	+	1.38318i	−0.384461	+	0.923141i	$0.625613\pi$
$308$	−3.05477	−	6.39284i	−0.174062	−	0.364266i
$309$	5.27013	+	0.899464i	0.299807	+	0.0511687i
$310$	14.2470	−	11.9546i	0.809175	−	0.678978i
$311$	9.11019	+	5.25977i	0.516592	+	0.298254i	0.735539	−	0.677482i	$-0.236929\pi$
$311$	9.11019	+	5.25977i	0.516592	+	0.298254i	−0.218947	+	0.975737i	$0.570262\pi$
$312$	0.0370004	+	6.74012i	0.00209474	+	0.381584i
$313$	5.40642	+	30.6613i	0.305589	+	1.73308i	0.620720	+	0.784032i	$0.286840\pi$
$313$	5.40642	+	30.6613i	0.305589	+	1.73308i	−0.315131	+	0.949048i	$0.602048\pi$
$314$	8.76005	−	7.35056i	0.494358	−	0.414816i
$315$	−11.5094	−	11.0489i	−0.648479	−	0.622533i
$316$	−7.32966	+	4.23178i	−0.412325	+	0.238056i
$317$	−6.92923	+	5.81432i	−0.389184	+	0.326565i	−0.816295	−	0.577635i	$-0.803976\pi$
$317$	−6.92923	+	5.81432i	−0.389184	+	0.326565i	0.427111	+	0.904199i	$0.359531\pi$
$318$	−3.94946	+	1.46209i	−0.221475	+	0.0819899i
$319$	−7.04491	−	8.39579i	−0.394439	−	0.470074i
$320$	1.97953	+	0.349044i	0.110659	+	0.0195122i
$321$	17.4580	+	14.4864i	0.974411	+	0.808554i
$322$	4.13065	−	16.0187i	0.230192	−	0.892685i
$323$	−0.202562	−	1.28308i	−0.0112708	−	0.0713927i
$324$	−4.32778	+	7.89115i	−0.240432	+	0.438397i
$325$	−3.67767	−	0.648472i	−0.204000	−	0.0359707i
$326$	−9.88320	−	8.29299i	−0.547380	−	0.459306i
$327$	8.46772	−	23.6683i	0.468266	−	1.30886i
$328$	−0.218041	+	1.23657i	−0.0120393	+	0.0682783i
$329$	0.163217	+	0.0127296i	0.00899845	+	0.000701805i
$330$	4.70595	+	8.04858i	0.259054	+	0.443060i
$331$	17.9469	−	10.3616i	0.986449	−	0.569526i	0.0822377	−	0.996613i	$-0.473793\pi$
$331$	17.9469	−	10.3616i	0.986449	−	0.569526i	0.904211	+	0.427086i	$0.140460\pi$
$332$	−3.15741	+	8.67491i	−0.173285	+	0.476097i
$333$	−4.67731	+	13.3035i	−0.256315	+	0.729026i
$334$	9.75779	+	16.9010i	0.533923	+	0.924781i
$335$	0.494410	+	0.856343i	0.0270125	+	0.0467870i
$336$	4.12386	−	1.99844i	0.224975	−	0.109024i
$337$	−7.19199	−	1.26814i	−0.391773	−	0.0690801i	−0.0257080	−	0.999669i	$-0.508184\pi$
$337$	−7.19199	−	1.26814i	−0.391773	−	0.0690801i	−0.366065	+	0.930589i	$0.619295\pi$
$338$	−2.01427	−	0.733133i	−0.109562	−	0.0398772i
$339$	−25.0088	−	20.7520i	−1.35829	−	1.12709i
$340$	0.104017	−	0.589910i	0.00564111	−	0.0319924i
$341$	−12.3889	+	21.4582i	−0.670895	+	1.16202i
$342$	−8.47521	+	9.95846i	−0.458287	+	0.538492i
$343$	13.4611	+	12.7200i	0.726830	+	0.686817i
$344$	−0.584934	−	0.490818i	−0.0315375	−	0.0264631i
$345$	−3.66231	+	21.4581i	−0.197172	+	1.15527i
$346$	−1.07669	+	0.903452i	−0.0578833	+	0.0485699i
$347$	−1.22247	−	3.35872i	−0.0656258	−	0.180305i	0.902545	−	0.430595i	$-0.141696\pi$
$347$	−1.22247	−	3.35872i	−0.0656258	−	0.180305i	−0.968171	+	0.250290i	$0.919474\pi$
$348$	5.40515	−	4.58626i	0.289747	−	0.245849i
$349$	2.44139	+	4.22861i	0.130685	+	0.226352i	0.923941	−	0.382536i	$-0.124949\pi$
$349$	2.44139	+	4.22861i	0.130685	+	0.226352i	−0.793256	+	0.608888i	$0.791616\pi$
$350$	0.680235	+	2.44614i	0.0363601	+	0.130752i
$351$	−13.2509	−	15.2738i	−0.707282	−	0.815255i
$352$	−2.63727	+	0.465022i	−0.140567	+	0.0247857i
$353$			12.5718i			0.669131i	0.942372	+	0.334566i	$0.108590\pi$
$353$			12.5718i			0.669131i	−0.942372	+	0.334566i	$0.891410\pi$
$354$	9.65146	−	16.9308i	0.512969	−	0.899861i
$355$	17.2565	+	20.5655i	0.915880	+	1.09150i
$356$	−2.38216	+	13.5099i	−0.126254	+	0.716025i
$357$	−0.595545	−	1.22893i	−0.0315196	−	0.0650420i
$358$	−0.734303	+	0.267264i	−0.0388091	+	0.0141254i
$359$	3.27908	+	9.00921i	0.173063	+	0.475488i	0.995652	−	0.0931488i	$-0.0296932\pi$
$359$	3.27908	+	9.00921i	0.173063	+	0.475488i	−0.822589	+	0.568637i	$0.807471\pi$
$360$	−5.18889	+	3.07225i	−0.273478	+	0.161922i
$361$	−14.9839	+	11.6826i	−0.788627	+	0.614871i
$362$	−3.33791	−	1.92714i	−0.175437	−	0.101288i
$363$	5.10318	+	4.23456i	0.267847	+	0.222257i
$364$	0.994046	+	10.2478i	0.0521022	+	0.537129i
$365$	25.8710	−	4.56175i	1.35415	−	0.238773i
$366$	18.1391	+	15.0516i	0.948148	+	0.786762i
$367$	−1.73263	−	9.82622i	−0.0904424	−	0.512924i	−0.996049	−	0.0888056i	$-0.971695\pi$
$367$	−1.73263	−	9.82622i	−0.0904424	−	0.512924i	0.905607	−	0.424119i	$-0.139416\pi$
$368$	−5.41486	−	3.12627i	−0.282269	−	0.162968i
$369$	−1.91918	−	3.24140i	−0.0999083	−	0.168740i
$370$	−7.23796	+	6.07337i	−0.376284	+	0.315739i
$371$	−5.80440	+	2.77359i	−0.301350	+	0.143998i
$372$	−13.9225	−	7.93659i	−0.721849	−	0.411493i
$373$			16.4573i			0.852125i	0.904694	+	0.426063i	$0.140100\pi$
$373$			16.4573i			0.852125i	−0.904694	+	0.426063i	$0.859900\pi$
$374$	0.138579	+	0.785920i	0.00716574	+	0.0406389i
$375$	−7.20339	−	19.4581i	−0.371982	−	1.00481i
$376$	0.0211634	−	0.0581460i	0.00109142	−	0.00299865i
$377$	5.44716	+	14.9660i	0.280543	+	0.770786i
$378$	−5.48541	+	12.6060i	−0.282139	+	0.648381i
$379$			23.7387i			1.21937i	0.792642	+	0.609687i	$0.208705\pi$
$379$			23.7387i			1.21937i	−0.792642	+	0.609687i	$0.791295\pi$
$380$	−8.28575	+	2.84837i	−0.425050	+	0.146118i
$381$	12.0618	−	7.05245i	0.617945	−	0.361308i
$382$	−8.68745	−	1.53183i	−0.444489	−	0.0783753i
$383$	0.251956	−	1.42892i	0.0128744	−	0.0730142i	−0.977694	−	0.210036i	$-0.932642\pi$
$383$	0.251956	−	1.42892i	0.0128744	−	0.0730142i	0.990568	+	0.137022i	$0.0437530\pi$
$384$	−0.310127	−	1.70406i	−0.0158261	−	0.0869600i
$385$	8.27838	+	11.5886i	0.421905	+	0.590607i
$386$	−8.84554	+	24.3029i	−0.450226	+	1.23699i
$387$	2.29059	−	0.0251495i	0.116437	−	0.00127842i
$388$		−	19.1440i		−	0.971889i
$389$	2.50978	−	6.89556i	0.127251	−	0.349619i	−0.859664	−	0.510859i	$-0.829327\pi$
$389$	2.50978	−	6.89556i	0.127251	−	0.349619i	0.986915	+	0.161241i	$0.0515495\pi$
$390$	−2.42584	−	13.3293i	−0.122837	−	0.674958i
$391$	−0.931645	+	1.61366i	−0.0471153	+	0.0816061i
$392$	5.99508	−	3.61373i	0.302797	−	0.182521i
$393$	4.92703	−	13.7717i	0.248536	−	0.694689i
$394$	−3.10598	+	3.70156i	−0.156477	+	0.186482i
$395$	13.0322	−	10.9353i	0.655720	−	0.550215i
$396$	5.09619	−	6.21062i	0.256093	−	0.312095i
$397$	1.36145	−	0.495528i	0.0683293	−	0.0248698i	−0.307629	−	0.951506i	$-0.599536\pi$
$397$	1.36145	−	0.495528i	0.0683293	−	0.0248698i	0.375959	+	0.926636i	$0.377313\pi$
$398$	−2.13069			−0.106802
$399$	−11.5067	+	16.3277i	−0.576058	+	0.817409i
$400$	0.959638			0.0479819
$401$	19.7733	−	7.19688i	0.987429	−	0.359395i	0.202705	−	0.979240i	$-0.435027\pi$
$401$	19.7733	−	7.19688i	0.987429	−	0.359395i	0.784724	+	0.619845i	$0.212805\pi$
$402$	0.544099	−	0.655709i	0.0271372	−	0.0327038i
$403$	27.5821	−	23.1441i	1.37396	−	1.15289i
$404$	3.58537	−	4.27288i	0.178379	−	0.212584i
$405$	5.81261	−	17.1313i	0.288831	−	0.851263i
$406$	7.58409	−	7.72853i	0.376392	−	0.383561i
$407$	6.29397	−	10.9015i	0.311981	−	0.540366i
$408$	−0.507819	+	0.0924194i	−0.0251408	+	0.00457544i
$409$	7.62929	−	20.9613i	0.377244	−	1.03647i	−0.595250	−	0.803541i	$-0.702947\pi$
$409$	7.62929	−	20.9613i	0.377244	−	1.03647i	0.972494	−	0.232929i	$-0.0748309\pi$
$410$		−	2.52394i		−	0.124648i
$411$	0.119353	+	21.7418i	0.00588726	+	1.07244i
$412$	1.05572	−	2.90056i	0.0520114	−	0.142900i
$413$	12.3260	−	27.0975i	0.606521	−	1.33338i
$414$	18.4358	−	3.45984i	0.906069	−	0.170042i
$415$	3.22225	−	18.2743i	0.158174	−	0.897050i
$416$	3.83235	+	0.675747i	0.187896	+	0.0331312i
$417$	−4.55387	−	7.78848i	−0.223004	−	0.381403i
$418$	9.07524	−	7.34146i	0.443885	−	0.359083i
$419$		−	6.85190i		−	0.334737i	−0.985894	−	0.167369i	$-0.946473\pi$
$419$		−	6.85190i		−	0.334737i	0.985894	−	0.167369i	$-0.0535270\pi$
$420$	−7.46576	+	5.39537i	−0.364292	+	0.263267i
$421$	9.74119	+	26.7637i	0.474757	+	1.30438i	0.913890	+	0.405961i	$0.133063\pi$
$421$	9.74119	+	26.7637i	0.474757	+	1.30438i	−0.439134	+	0.898422i	$0.644714\pi$
$422$	−4.43476	+	12.1844i	−0.215881	+	0.593127i
$423$	0.0654015	+	0.173730i	0.00317993	+	0.00844706i
$424$	0.422218	+	2.39452i	0.0205047	+	0.116288i
$425$		−	0.285977i		−	0.0138719i
$426$	11.4565	−	20.0971i	0.555067	−	0.973710i
$427$	29.6870	+	20.3725i	1.43665	+	0.985893i
$428$	10.0333	−	8.41896i	0.484979	−	0.406946i
$429$	9.11067	+	15.5820i	0.439867	+	0.752305i
$430$	1.32921	+	0.767420i	0.0641002	+	0.0370083i
$431$	0.0856113	+	0.485526i	0.00412375	+	0.0233869i	0.986800	−	0.161942i	$-0.0517759\pi$
$431$	0.0856113	+	0.485526i	0.00412375	+	0.0233869i	−0.982676	+	0.185329i	$0.940665\pi$
$432$	4.03495	+	3.27402i	0.194131	+	0.157521i
$433$	19.0575	−	3.36035i	0.915845	−	0.161488i	0.304189	−	0.952612i	$-0.401615\pi$
$433$	19.0575	−	3.36035i	0.915845	−	0.161488i	0.611656	+	0.791124i	$0.290504\pi$
$434$	−22.2828	−	10.1359i	−1.06961	−	0.486538i
$435$	−9.09884	+	10.9653i	−0.436256	+	0.525744i
$436$	−12.5687	−	7.25656i	−0.601933	−	0.347526i
$437$	27.2498	+	0.489305i	1.30353	+	0.0234066i
$438$	−11.4258	−	19.5415i	−0.545944	−	0.933728i
$439$	−9.52665	−	26.1743i	−0.454682	−	1.24923i	−0.929395	−	0.369088i	$-0.879670\pi$
$439$	−9.52665	−	26.1743i	−0.454682	−	1.24923i	0.474712	−	0.880141i	$-0.342552\pi$
$440$	5.05823	−	1.84105i	0.241142	−	0.0877684i
$441$	−6.59039	+	19.9391i	−0.313828	+	0.949480i
$442$	0.201376	−	1.14206i	0.00957848	−	0.0543223i
$443$	17.5268	+	20.8877i	0.832725	+	0.992402i	0.999979	+	0.00648868i	$0.00206542\pi$
$443$	17.5268	+	20.8877i	0.832725	+	0.992402i	−0.167254	+	0.985914i	$0.553490\pi$
$444$	7.07312	+	4.03206i	0.335675	+	0.191353i
$445$		−	27.5748i		−	1.30717i
$446$	19.1270	−	3.37261i	0.905692	−	0.159698i
$447$	−1.41819	−	1.67141i	−0.0670781	−	0.0790551i
$448$	−0.708845	−	2.54903i	−0.0334898	−	0.120430i
$449$	−0.561837	−	0.973130i	−0.0265147	−	0.0459248i	0.852464	−	0.522787i	$-0.175108\pi$
$449$	−0.561837	−	0.973130i	−0.0265147	−	0.0459248i	−0.878978	+	0.476862i	$0.841774\pi$
$450$	−2.18493	+	1.87463i	−0.102998	+	0.0883709i
$451$	1.15007	+	3.15978i	0.0541545	+	0.148788i
$452$	−14.3728	+	12.0602i	−0.676041	+	0.567266i
$453$	−0.142092	−	0.0242511i	−0.00667605	−	0.00113942i
$454$	−13.5978	−	11.4099i	−0.638175	−	0.535492i
$455$	−5.54466	−	19.9388i	−0.259938	−	0.934744i
$456$	4.78047	+	5.84355i	0.223866	+	0.273649i
$457$	4.27104	−	7.39766i	0.199791	−	0.346048i	−0.748670	−	0.662943i	$-0.769307\pi$
$457$	4.27104	−	7.39766i	0.199791	−	0.346048i	0.948461	+	0.316895i	$0.102640\pi$
$458$	−0.332424	+	1.88527i	−0.0155331	+	0.0880928i
$459$	0.975675	−	1.20244i	0.0455406	−	0.0561249i
$460$	11.8101	+	4.29851i	0.550647	+	0.200419i
$461$	−25.5592	−	4.50677i	−1.19041	−	0.209901i	−0.456860	−	0.889538i	$-0.651026\pi$
$461$	−25.5592	−	4.50677i	−1.19041	−	0.209901i	−0.733548	+	0.679637i	$0.762137\pi$
$462$	6.88810	−	10.1565i	0.320464	−	0.472522i
$463$	−8.18339	−	14.1741i	−0.380314	−	0.658724i	0.610793	−	0.791791i	$-0.290851\pi$
$463$	−8.18339	−	14.1741i	−0.380314	−	0.658724i	−0.991107	+	0.133067i	$0.957518\pi$
$464$	−2.04633	−	3.54434i	−0.0949983	−	0.164542i
$465$	30.3302	+	10.8511i	1.40653	+	0.503209i
$466$	−7.97199	+	21.9029i	−0.369296	+	1.01463i
$467$	−19.6929	+	11.3697i	−0.911277	+	0.526126i	−0.880842	−	0.473411i	$-0.843023\pi$
$467$	−19.6929	+	11.3697i	−0.911277	+	0.526126i	−0.0304352	+	0.999537i	$0.509689\pi$
$468$	−10.0456	+	5.94785i	−0.464360	+	0.274940i
$469$	0.736441	−	1.07315i	0.0340057	−	0.0495534i
$470$	−0.0215980	+	0.122488i	−0.000996243	+	0.00564997i
$471$	18.6492	+	6.67204i	0.859309	+	0.307431i
$472$	−8.61930	−	7.23245i	−0.396735	−	0.332900i
$473$	−2.01376	−	0.355080i	−0.0925927	−	0.0163266i
$474$	−12.7354	−	7.25986i	−0.584956	−	0.333456i
$475$	−3.65952	+	2.02611i	−0.167910	+	0.0929642i
$476$	−0.759624	+	0.211240i	−0.0348173	+	0.00968215i
$477$	−5.63895	−	4.62710i	−0.258190	−	0.211860i
$478$	9.54077	+	1.68229i	0.436385	+	0.0769464i
$479$	−8.83547	−	10.5297i	−0.403703	−	0.481115i	0.525442	−	0.850829i	$-0.323900\pi$
$479$	−8.83547	−	10.5297i	−0.403703	−	0.481115i	−0.929145	+	0.369715i	$0.879455\pi$
$480$	1.20870	+	3.26499i	0.0551692	+	0.149026i
$481$	−14.0126	+	11.7580i	−0.638921	+	0.536118i
$482$	−14.9391	+	8.62511i	−0.680459	+	0.392863i
$483$	27.5627	−	7.82801i	1.25414	−	0.356187i
$484$	2.93286	−	2.46096i	0.133312	−	0.111862i
$485$	6.68210	+	37.8961i	0.303419	+	1.72077i
$486$	−15.5826	+	0.427812i	−0.706840	+	0.0194059i
$487$	3.38832	+	1.95625i	0.153539	+	0.0886461i	0.574801	−	0.818293i	$-0.305079\pi$
$487$	3.38832	+	1.95625i	0.153539	+	0.0886461i	−0.421262	+	0.906939i	$0.638413\pi$
$488$	10.4248	−	8.74743i	0.471908	−	0.395977i
$489$	3.75952	−	22.0277i	0.170011	−	0.996127i
$490$	−10.6061	+	9.24603i	−0.479133	+	0.417693i
$491$	9.38312	+	25.7799i	0.423454	+	1.16343i	0.949717	+	0.313109i	$0.101370\pi$
$491$	9.38312	+	25.7799i	0.423454	+	1.16343i	−0.526263	+	0.850322i	$0.676407\pi$
$492$	−2.03957	+	0.755049i	−0.0919511	+	0.0340402i
$493$	−1.05623	+	0.609816i	−0.0475703	+	0.0274647i
$494$	−16.0411	+	5.51442i	−0.721725	+	0.248106i
$495$	−7.92026	+	14.0729i	−0.355989	+	0.632529i
$496$	−5.94739	+	7.08782i	−0.267046	+	0.318253i
$497$	14.6311	−	32.1652i	0.656296	−	1.44281i
$498$	−15.7313	+	2.86298i	−0.704935	+	0.128293i
$499$	16.4765	+	13.8254i	0.737588	+	0.618910i	0.932189	−	0.361973i	$-0.117897\pi$
$499$	16.4765	+	13.8254i	0.737588	+	0.618910i	−0.194601	+	0.980883i	$0.562341\pi$
$500$	−11.7973	+	2.08018i	−0.527590	+	0.0930283i
$501$	−16.7400	+	29.3657i	−0.747890	+	1.31196i
$502$	11.6806	−	6.74378i	0.521329	−	0.300990i
$503$	12.4332	+	14.8173i	0.554368	+	0.660670i	0.968345	−	0.249617i	$-0.0803048\pi$
$503$	12.4332	+	14.8173i	0.554368	+	0.660670i	−0.413976	+	0.910288i	$0.635860\pi$
$504$	6.59338	+	4.41897i	0.293693	+	0.196837i
$505$	−5.60592	+	9.70973i	−0.249460	+	0.432077i
$506$	−16.7440			−0.744361
$507$	−0.664767	−	3.65271i	−0.0295234	−	0.162223i
$508$	−2.75904	−	7.58040i	−0.122413	−	0.336326i
$509$	4.78113	+	1.74019i	0.211920	+	0.0771325i	0.445799	−	0.895133i	$-0.352920\pi$
$509$	4.78113	+	1.74019i	0.211920	+	0.0771325i	−0.233879	+	0.972266i	$0.575142\pi$
$510$	0.972983	−	0.360198i	0.0430844	−	0.0159498i
$511$	−20.0994	−	28.1363i	−0.889147	−	1.24468i
$512$	−1.00000			−0.0441942
$513$	−22.2995	−	3.96618i	−0.984549	−	0.175111i
$514$	9.57817	+	16.5899i	0.422475	+	0.731748i
$515$	−1.07740	+	6.11022i	−0.0474758	+	0.269249i
$516$	0.222506	−	1.30370i	0.00979528	−	0.0573923i
$517$	−0.0287744	−	0.163188i	−0.00126550	−	0.00717700i
$518$	11.3204	+	5.14938i	0.497392	+	0.226251i
$519$	−2.29216	−	0.820055i	−0.100614	−	0.0359964i
$520$	−7.82211			−0.343022
$521$	−41.5470			−1.82021			−0.910103	−	0.414382i	$-0.863998\pi$
$521$	−41.5470			−1.82021			−0.910103	+	0.414382i	$0.863998\pi$
$522$	11.5829	+	4.07239i	0.506970	+	0.178244i
$523$	12.5794	−	2.21809i	0.550060	−	0.0969904i	0.108291	−	0.994119i	$-0.465462\pi$
$523$	12.5794	−	2.21809i	0.550060	−	0.0969904i	0.441769	+	0.897129i	$0.354351\pi$
$524$	−7.31325	−	4.22231i	−0.319481	−	0.184452i
$525$	−3.06284	+	3.15563i	−0.133673	+	0.137723i
$526$	−0.379181	+	1.04179i	−0.0165331	+	0.0454243i
$527$	2.11221	+	1.77235i	0.0920093	+	0.0772049i
$528$	−3.00093	−	3.53676i	−0.130599	−	0.153918i
$529$	−12.3289	−	10.3452i	−0.536039	−	0.449790i
$530$	−1.67159	−	4.59264i	−0.0726090	−	0.199492i
$531$	33.7530	−	0.370591i	1.46476	−	0.0160823i
$532$	8.08496	+	8.22395i	0.350528	+	0.356554i
$533$		−	4.88632i		−	0.211650i
$534$	−22.2830	+	8.24914i	−0.964278	+	0.356975i
$535$	−16.9226	+	20.1676i	−0.731630	+	0.871923i
$536$	−0.316209	−	0.376843i	−0.0136582	−	0.0162772i
$537$	−1.04158	−	0.864292i	−0.0449476	−	0.0372969i
$538$	−6.84347	−	2.49082i	−0.295043	−	0.107387i
$539$	9.06493	−	16.4081i	0.390454	−	0.706749i
$540$	−9.13007	−	5.07264i	−0.392896	−	0.218292i
$541$	4.24466	+	24.0727i	0.182492	+	1.03497i	0.929135	+	0.369740i	$0.120553\pi$
$541$	4.24466	+	24.0727i	0.182492	+	1.03497i	−0.746643	+	0.665225i	$0.768336\pi$
$542$	3.12088	+	1.13591i	0.134053	+	0.0487914i
$543$	−0.0366469	−	6.67572i	−0.00157267	−	0.286483i
$544$			0.298005i			0.0127769i
$545$	27.4130	+	9.97752i	1.17424	+	0.427390i
$546$	−14.4537	+	10.4454i	−0.618559	+	0.447022i
$547$	28.8866	−	5.09349i	1.23510	−	0.217782i	0.482286	−	0.876014i	$-0.339806\pi$
$547$	28.8866	−	5.09349i	1.23510	−	0.217782i	0.752815	+	0.658232i	$0.228695\pi$
$548$	12.3621	+	2.17977i	0.528083	+	0.0931153i
$549$	−6.64748	+	40.2809i	−0.283708	+	1.71915i
$550$	2.22557	−	1.28493i	0.0948985	−	0.0547897i
$551$	15.2868	+	9.19566i	0.651239	+	0.391748i
$552$	−0.0594496	−	10.8295i	−0.00253034	−	0.460936i
$553$	−20.3828	−	9.27163i	−0.866766	−	0.394270i
$554$	8.14169	−	2.96333i	0.345907	−	0.125900i
$555$	−15.4088	−	5.51274i	−0.654067	−	0.234003i
$556$	−4.89477	+	1.78155i	−0.207585	+	0.0755546i
$557$	−15.0866	+	2.66017i	−0.639239	+	0.112715i	−0.483868	−	0.875141i	$-0.660768\pi$
$557$	−15.0866	+	2.66017i	−0.639239	+	0.112715i	−0.155371	+	0.987856i	$0.549657\pi$
$558$	−0.304745	−	27.7558i	−0.0129009	−	1.17500i
$559$	2.57334	+	1.48572i	0.108841	+	0.0628392i
$560$	2.29290	+	4.79845i	0.0968928	+	0.202772i
$561$	−1.05397	+	0.894294i	−0.0444988	+	0.0377571i
$562$	0.780604	+	1.35205i	0.0329278	+	0.0570326i
$563$	−17.4708	+	30.2603i	−0.736305	+	1.27532i	0.217843	+	0.975984i	$0.430098\pi$
$563$	−17.4708	+	30.2603i	−0.736305	+	1.27532i	−0.954148	+	0.299334i	$0.903236\pi$
$564$	0.105443	−	0.0191899i	0.00443996	−	0.000808040i
$565$	24.2419	−	28.8903i	1.01986	−	1.21543i
$566$	0.977979	+	5.54640i	0.0411075	+	0.233132i
$567$	−23.6443	+	2.81880i	−0.992969	+	0.118379i
$568$	−10.2313	−	8.58505i	−0.429294	−	0.360221i
$569$	−4.17880	+	7.23789i	−0.175184	+	0.303428i	−0.940225	−	0.340554i	$-0.889385\pi$
$569$	−4.17880	+	7.23789i	−0.175184	+	0.303428i	0.765041	+	0.643982i	$0.222719\pi$
$570$	−11.5027	−	9.89887i	−0.481797	−	0.414618i
$571$	6.65930	+	11.5342i	0.278683	+	0.482693i	0.971058	−	0.238845i	$-0.0767687\pi$
$571$	6.65930	+	11.5342i	0.278683	+	0.482693i	−0.692375	+	0.721538i	$0.743435\pi$
$572$	9.79270	−	3.56425i	0.409453	−	0.149029i
$573$	−5.30454	−	14.3289i	−0.221600	−	0.598597i
$574$	−2.99750	+	1.43233i	−0.125113	+	0.0597843i
$575$	5.90901	+	1.04192i	0.246423	+	0.0434510i
$576$	2.27682	−	1.95348i	0.0948677	−	0.0813949i
$577$	−2.89158	+	5.00837i	−0.120378	+	0.208501i	−0.919917	−	0.392114i	$-0.871744\pi$
$577$	−2.89158	+	5.00837i	−0.120378	+	0.208501i	0.799539	+	0.600615i	$0.205077\pi$
$578$	−16.9112			−0.703413
$579$	−44.0715	+	8.02068i	−1.83155	+	0.333328i
$580$	5.28789	+	6.30186i	0.219568	+	0.261671i
$581$	−23.5317	+	6.54381i	−0.976260	+	0.271483i
$582$	28.6246	−	16.7366i	1.18653	−	0.693753i
$583$	4.18540	+	4.98797i	0.173342	+	0.206580i
$584$	−12.2811	+	4.46995i	−0.508196	+	0.184968i
$585$	17.8096	−	15.2803i	0.736335	−	0.631763i
$586$	4.70500	−	26.6834i	0.194362	−	1.10228i
$587$	−19.9057	+	23.7227i	−0.821595	+	0.979139i	−0.999988	−	0.00482049i	$-0.998466\pi$
$587$	−19.9057	+	23.7227i	−0.821595	+	0.979139i	0.178393	+	0.983959i	$0.442910\pi$
$588$	10.6445	+	5.80469i	0.438972	+	0.239381i
$589$	7.71530	−	39.5859i	0.317903	−	1.63111i
$590$	19.5866	+	11.3083i	0.806367	+	0.465556i
$591$	−8.25004	−	1.40805i	−0.339361	−	0.0579196i
$592$	3.02148	−	3.60086i	0.124182	−	0.147994i
$593$	−8.92808	+	24.5297i	−0.366632	+	1.00731i	0.610001	+	0.792401i	$0.291169\pi$
$593$	−8.92808	+	24.5297i	−0.366632	+	1.00731i	−0.976633	+	0.214913i	$0.931053\pi$
$594$	13.7416	+	2.19033i	0.563824	+	0.0898702i
$595$	1.42996	−	0.683297i	0.0586228	−	0.0280124i
$596$	−1.09600	+	0.632777i	−0.0448940	+	0.0259196i
$597$	−1.86275	−	3.18586i	−0.0762372	−	0.130388i
$598$	22.8642	+	8.32188i	0.934986	+	0.340307i
$599$	−35.2677	−	12.8364i	−1.44100	−	0.524480i	−0.500936	−	0.865484i	$-0.667011\pi$
$599$	−35.2677	−	12.8364i	−1.44100	−	0.524480i	−0.940062	+	0.341004i	$0.889233\pi$
$600$	0.838960	+	1.43487i	0.0342504	+	0.0585784i
$601$	4.35784	−	2.51600i	0.177760	−	0.102630i	−0.408480	−	0.912767i	$-0.633941\pi$
$601$	4.35784	−	2.51600i	0.177760	−	0.102630i	0.586240	+	0.810138i	$0.300608\pi$
$602$	0.157085	−	2.01412i	0.00640229	−	0.0820894i
$603$	1.45611	+	0.240299i	0.0592973	+	0.00978571i
$604$	−0.0284639	+	0.0782040i	−0.00115818	+	0.00318207i
$605$	−4.94669	+	5.89523i	−0.201111	+	0.239675i
$606$	9.52340	+	1.62538i	0.386862	+	0.0660265i
$607$	−5.49371	−	3.17180i	−0.222983	−	0.128739i	0.384348	−	0.923188i	$-0.374426\pi$
$607$	−5.49371	−	3.17180i	−0.222983	−	0.128739i	−0.607331	+	0.794449i	$0.707760\pi$
$608$	3.81344	−	2.11133i	0.154655	−	0.0856256i
$609$	18.1862	+	4.58327i	0.736944	+	0.185724i
$610$	−17.5829	+	20.9545i	−0.711911	+	0.848422i
$611$	−0.0418136	+	0.237137i	−0.00169160	+	0.00959352i
$612$	−0.582147	−	0.678506i	−0.0235319	−	0.0274270i
$613$	−4.55644	+	1.65841i	−0.184033	+	0.0669825i	−0.432393	−	0.901685i	$-0.642331\pi$
$613$	−4.55644	+	1.65841i	−0.184033	+	0.0669825i	0.248360	+	0.968668i	$0.420108\pi$
$614$	16.5779	+	19.7568i	0.669031	+	0.797320i
$615$	3.77385	−	2.20654i	0.152176	−	0.0889764i
$616$	−5.05702	−	4.96251i	−0.203753	−	0.199945i
$617$	21.2275	+	25.2979i	0.854586	+	1.01846i	0.999579	+	0.0290233i	$0.00923970\pi$
$617$	21.2275	+	25.2979i	0.854586	+	1.01846i	−0.144993	+	0.989433i	$0.546316\pi$
$618$	5.25994	−	0.957270i	0.211586	−	0.0385070i
$619$	18.0961			0.727346			0.363673	−	0.931527i	$-0.381523\pi$
$619$	18.0961			0.727346			0.363673	+	0.931527i	$0.381523\pi$
$620$	9.29906	−	16.1064i	0.373459	−	0.646850i
$621$	21.2906	+	24.5408i	0.854364	+	0.984790i
$622$	10.3597	+	1.82670i	0.415387	+	0.0732440i
$623$	−32.7486	+	15.6486i	−1.31204	+	0.626950i
$624$	2.34003	+	6.32099i	0.0936760	+	0.253042i
$625$	18.1181	−	6.59446i	0.724725	−	0.263778i
$626$	15.5672	+	26.9631i	0.622189	+	1.07766i
$627$	18.9111	+	7.15127i	0.755238	+	0.285594i
$628$	5.71772	−	9.90338i	0.228162	−	0.395188i
$629$	−1.07307	−	0.900416i	−0.0427863	−	0.0359020i
$630$	−14.5942	−	6.44610i	−0.581447	−	0.256819i
$631$	−1.33794	−	7.58782i	−0.0532625	−	0.302067i	0.946526	−	0.322627i	$-0.104566\pi$
$631$	−1.33794	−	7.58782i	−0.0532625	−	0.302067i	−0.999789	+	0.0205606i	$0.993455\pi$
$632$	−5.44027	+	6.48346i	−0.216402	+	0.257898i
$633$	−22.0955	+	4.02121i	−0.878216	+	0.159829i
$634$	−4.52274	+	7.83361i	−0.179621	+	0.311112i
$635$	8.10749	+	14.0426i	0.321736	+	0.557263i
$636$	−3.21122	+	2.72471i	−0.127333	+	0.108042i
$637$	−20.5333	+	17.9002i	−0.813557	+	0.709233i
$638$	−9.49158	−	5.47996i	−0.375775	−	0.216954i
$639$	40.0655	−	0.439898i	1.58497	−	0.0174021i
$640$	1.97953	−	0.349044i	0.0782477	−	0.0137972i
$641$	−34.6597	+	12.6151i	−1.36898	+	0.498267i	−0.918818	−	0.394682i	$-0.870855\pi$
$641$	−34.6597	+	12.6151i	−1.36898	+	0.498267i	−0.450158	+	0.892949i	$0.648632\pi$
$642$	21.3598	+	7.64181i	0.843005	+	0.301598i
$643$	−29.8824	+	10.8763i	−1.17845	+	0.428920i	−0.855653	−	0.517549i	$-0.826844\pi$
$643$	−29.8824	+	10.8763i	−1.17845	+	0.428920i	−0.322794	+	0.946469i	$0.604622\pi$
$644$	−1.59716	−	16.4654i	−0.0629371	−	0.648827i
$645$	0.0145934	+	2.65838i	0.000574614	+	0.104674i
$646$	−0.629186	−	1.13642i	−0.0247550	−	0.0447120i
$647$	−5.95626	+	3.43885i	−0.234165	+	0.135195i	−0.612492	−	0.790477i	$-0.709833\pi$
$647$	−5.95626	+	3.43885i	−0.234165	+	0.135195i	0.378327	+	0.925672i	$0.376499\pi$
$648$	−1.36785	+	8.89545i	−0.0537343	+	0.349446i
$649$	−29.6737	−	5.23228i	−1.16480	−	0.205385i
$650$	−3.67767	+	0.648472i	−0.144250	+	0.0254352i
$651$	−4.32528	−	42.1791i	−0.169521	−	1.65313i
$652$	−12.1235	−	4.41261i	−0.474794	−	0.172811i
$653$		−	48.9903i		−	1.91714i	−0.284862	−	0.958569i	$-0.591948\pi$
$653$		−	48.9903i		−	1.91714i	0.284862	−	0.958569i	$-0.408052\pi$
$654$	−0.137992	−	25.1371i	−0.00539591	−	0.982937i
$655$	15.9505	+	5.80552i	0.623240	+	0.226841i
$656$	0.218041	+	1.23657i	0.00851307	+	0.0482800i
$657$	19.2299	−	34.1682i	0.750232	−	1.33303i
$658$	0.157728	−	0.0438617i	0.00614887	−	0.00170991i
$659$	29.3153	+	10.6699i	1.14196	+	0.415641i	0.842622	−	0.538505i	$-0.181011\pi$
$659$	29.3153	+	10.6699i	1.14196	+	0.415641i	0.299342	+	0.954146i	$0.403233\pi$
$660$	7.17492	+	5.95366i	0.279283	+	0.231746i
$661$	−8.46707	−	10.0907i	−0.329331	−	0.392481i	0.575817	−	0.817579i	$-0.304684\pi$
$661$	−8.46707	−	10.0907i	−0.329331	−	0.392481i	−0.905147	+	0.425098i	$0.860240\pi$
$662$	13.3206	−	15.8749i	0.517722	−	0.616997i
$663$	1.88369	−	0.697340i	0.0731564	−	0.0270825i
$664$			9.23164i			0.358257i
$665$	−18.8749	−	13.4575i	−0.731938	−	0.521861i
$666$	0.154821	+	14.1009i	0.00599918	+	0.546399i
$667$	−8.75211	−	24.0462i	−0.338883	−	0.931074i
$668$	14.9498	+	12.5444i	0.578425	+	0.485357i
$669$	21.7646	+	25.6507i	0.841467	+	0.991714i
$670$	0.757480	+	0.635601i	0.0292640	+	0.0245554i
$671$	12.4643	−	34.2453i	0.481178	−	1.32203i
$672$	3.19166	−	3.28836i	0.123121	−	0.126851i
$673$	−25.9486	−	14.9815i	−1.00025	−	0.577493i	−0.0919256	−	0.995766i	$-0.529302\pi$
$673$	−25.9486	−	14.9815i	−1.00025	−	0.577493i	−0.908321	+	0.418273i	$0.862636\pi$
$674$	−7.19199	+	1.26814i	−0.277025	+	0.0488470i
$675$	−4.71316	−	1.62806i	−0.181409	−	0.0626642i
$676$	−2.14354			−0.0824437
$677$	−19.6200			−0.754059			−0.377029	−	0.926201i	$-0.623054\pi$
$677$	−19.6200			−0.754059			−0.377029	+	0.926201i	$0.623054\pi$
$678$	−30.5982	−	10.9470i	−1.17511	−	0.420416i
$679$	41.2144	−	29.4418i	1.58166	−	1.12987i
$680$	−0.104017	−	0.589910i	−0.00398887	−	0.0226220i
$681$	5.17252	−	30.3067i	0.198211	−	1.16136i
$682$	−4.30261	+	24.4013i	−0.164755	+	0.934375i
$683$	2.89110	+	5.00752i	0.110625	+	0.191608i	0.916022	−	0.401127i	$-0.131382\pi$
$683$	2.89110	+	5.00752i	0.110625	+	0.191608i	−0.805398	+	0.592735i	$0.798048\pi$
$684$	−4.55810	+	12.2566i	−0.174283	+	0.468642i
$685$	−25.2320			−0.964064
$686$	16.9998	+	7.34896i	0.649055	+	0.280585i
$687$	−3.10952	+	1.15114i	−0.118636	+	0.0439188i
$688$	−0.717528	−	0.261159i	−0.0273555	−	0.00995659i
$689$	−3.23618	−	8.89132i	−0.123288	−	0.338732i
$690$	3.89767	+	21.4166i	0.148382	+	0.815318i
$691$	−47.4775			−1.80613			−0.903065	−	0.429503i	$-0.858689\pi$
$691$	−47.4775			−1.80613			−0.903065	+	0.429503i	$0.858689\pi$
$692$	−0.702761	+	1.21722i	−0.0267149	+	0.0462716i
$693$	21.2081	+	1.41999i	0.805629	+	0.0539408i
$694$	−2.29750	−	2.73805i	−0.0872118	−	0.103935i
$695$	9.06750	−	5.23512i	0.343950	−	0.198579i
$696$	3.51059	−	6.15834i	0.133069	−	0.233431i
$697$	0.368505	−	0.0649774i	0.0139581	−	0.00246119i
$698$	3.74042	+	3.13859i	0.141577	+	0.118797i
$699$	−39.7192	+	7.22860i	−1.50232	+	0.273411i
$700$	1.47584	+	2.06597i	0.0557816	+	0.0780862i
$701$	32.8155	−	39.1080i	1.23942	−	1.47709i	0.416301	−	0.909227i	$-0.363326\pi$
$701$	32.8155	−	39.1080i	1.23942	−	1.47709i	0.823124	−	0.567862i	$-0.192229\pi$
$702$	−17.6757	−	9.82059i	−0.667128	−	0.370654i
$703$	−3.91963	+	20.1110i	−0.147832	+	0.758499i
$704$	−2.31917	+	1.33898i	−0.0874072	+	0.0504646i
$705$	−0.202030	+	0.0747913i	−0.00760888	+	0.00281680i
$706$	4.29982	+	11.8137i	0.161826	+	0.444613i
$707$	14.7129	+	1.14748i	0.553336	+	0.0431556i
$708$	3.27874	−	19.2107i	0.123222	−	0.721983i
$709$	9.01981	−	7.56852i	0.338746	−	0.284242i	−0.457506	−	0.889206i	$-0.651257\pi$
$709$	9.01981	−	7.56852i	0.338746	−	0.284242i	0.796252	+	0.604965i	$0.206813\pi$
$710$	23.2496	+	13.4232i	0.872543	+	0.503763i
$711$	−0.278760	−	25.3891i	−0.0104543	−	0.952167i
$712$	2.38216	+	13.5099i	0.0892754	+	0.506306i
$713$	−44.3169	+	37.1863i	−1.65968	+	1.39264i
$714$	−0.979949	−	0.951131i	−0.0366737	−	0.0355952i
$715$	−18.1408	+	10.4736i	−0.678429	+	0.391691i
$716$	−0.598609	+	0.502293i	−0.0223711	+	0.0187716i
$717$	5.82558	+	15.7363i	0.217560	+	0.587684i
$718$	6.16266	+	7.34438i	0.229989	+	0.274090i
$719$	2.46848	+	0.435259i	0.0920587	+	0.0162324i	0.219488	−	0.975615i	$-0.429561\pi$
$719$	2.46848	+	0.435259i	0.0920587	+	0.0162324i	−0.127429	+	0.991848i	$0.540673\pi$
$720$	−3.82519	+	4.66167i	−0.142556	+	0.173730i
$721$	7.86810	−	2.18800i	0.293023	−	0.0814853i
$722$	−10.0846	+	16.1028i	−0.375310	+	0.599285i
$723$	−25.9569	−	14.7969i	−0.965349	−	0.550301i
$724$	−3.79573	−	0.669290i	−0.141067	−	0.0248740i
$725$	3.00861	+	2.52453i	0.111737	+	0.0937585i
$726$	6.24372	+	2.23379i	0.231726	+	0.0829037i
$727$	5.94241	−	33.7011i	0.220392	−	1.24990i	−0.650909	−	0.759156i	$-0.725612\pi$
$727$	5.94241	−	33.7011i	0.220392	−	1.24990i	0.871301	−	0.490749i	$-0.163277\pi$
$728$	4.43904	+	9.28976i	0.164522	+	0.344301i
$729$	−14.2627	−	22.9254i	−0.528248	−	0.849090i
$730$	22.7506	−	13.1350i	0.842036	−	0.486150i
$731$	−0.0778267	+	0.213827i	−0.00287853	+	0.00790868i
$732$	22.1932	+	7.93996i	0.820284	+	0.293470i
$733$	−24.2543	−	42.0097i	−0.895854	−	1.55166i	−0.832744	−	0.553658i	$-0.813231\pi$
$733$	−24.2543	−	42.0097i	−0.895854	−	1.55166i	−0.0631100	−	0.998007i	$-0.520102\pi$
$734$	−4.98890	−	8.64103i	−0.184144	−	0.318946i
$735$	−23.0972	−	7.77513i	−0.851953	−	0.286790i
$736$	−6.15755	−	1.08574i	−0.226970	−	0.0400210i
$737$	−1.23793	−	0.450569i	−0.0455997	−	0.0165969i
$738$	−2.91206	−	2.38952i	−0.107194	−	0.0879594i
$739$	2.23706	−	12.6870i	0.0822916	−	0.466699i	−0.915617	−	0.402052i	$-0.868297\pi$
$739$	2.23706	−	12.6870i	0.0822916	−	0.466699i	0.997908	−	0.0646463i	$-0.0205919\pi$
$740$	−4.72424	+	8.18263i	−0.173667	+	0.300799i
$741$	−22.2692	−	19.1641i	−0.818080	−	0.704012i
$742$	−4.50573	+	4.59154i	−0.165411	+	0.168561i
$743$	−16.3878	−	13.7510i	−0.601211	−	0.504476i	0.290623	−	0.956838i	$-0.406137\pi$
$743$	−16.3878	−	13.7510i	−0.601211	−	0.504476i	−0.891835	+	0.452361i	$0.850582\pi$
$744$	−15.7974	−	2.69617i	−0.579160	−	0.0988464i
$745$	1.94870	−	1.63515i	0.0713948	−	0.0599074i
$746$	5.62872	+	15.4648i	0.206082	+	0.566206i
$747$	−18.0338	−	21.0188i	−0.659822	−	0.769038i
$748$	0.399022	+	0.691126i	0.0145897	+	0.0252701i
$749$	33.5552	+	8.65272i	1.22608	+	0.316163i
$750$	−13.4241	−	15.8210i	−0.490177	−	0.577700i
$751$	−43.0517	+	7.59118i	−1.57098	+	0.277006i	−0.890230	−	0.455511i	$-0.849457\pi$
$751$	−43.0517	+	7.59118i	−1.57098	+	0.277006i	−0.680749	+	0.732517i	$0.738346\pi$
$752$		−	0.0618776i		−	0.00225645i
$753$	20.2952	+	11.5693i	0.739596	+	0.421610i
$754$	10.2373	+	12.2004i	0.372821	+	0.444311i
$755$	0.0290485	−	0.164742i	0.00105718	−	0.00599558i
$756$	−0.843108	+	13.7219i	−0.0306635	+	0.499059i
$757$	37.0813	−	13.4965i	1.34774	−	0.490538i	0.435499	−	0.900189i	$-0.356572\pi$
$757$	37.0813	−	13.4965i	1.34774	−	0.490538i	0.912242	+	0.409651i	$0.134350\pi$
$758$	8.11911	+	22.3071i	0.294899	+	0.810229i
$759$	−14.6384	−	25.0360i	−0.531340	−	0.908750i
$760$	−6.81186	+	5.51049i	−0.247092	+	0.199886i
$761$	37.8134	+	21.8316i	1.37074	+	0.791394i	0.991021	−	0.133709i	$-0.0426888\pi$
$761$	37.8134	+	21.8316i	1.37074	+	0.791394i	0.379715	+	0.925104i	$0.376022\pi$
$762$	8.92231	−	10.7525i	0.323221	−	0.389523i
$763$	−3.70727	−	38.2187i	−0.134212	−	1.38361i
$764$	−8.68745	+	1.53183i	−0.314301	+	0.0554197i
$765$	1.38920	+	1.13993i	0.0502268	+	0.0412141i
$766$	−0.251956	−	1.42892i	−0.00910356	−	0.0516288i
$767$	37.9195	+	21.8928i	1.36919	+	0.790504i
$768$	−0.874247	−	1.49522i	−0.0315467	−	0.0539542i
$769$	−9.02223	+	7.57055i	−0.325350	+	0.273001i	−0.790802	−	0.612072i	$-0.790336\pi$
$769$	−9.02223	+	7.57055i	−0.325350	+	0.273001i	0.465452	+	0.885073i	$0.345892\pi$
$770$	11.7427	+	8.05831i	0.423176	+	0.290401i
$771$	−16.4319	+	28.8252i	−0.591780	+	1.03811i
$772$			25.8626i			0.930816i
$773$	−6.20925	−	35.2144i	−0.223331	−	1.26657i	−0.865850	−	0.500304i	$-0.833222\pi$
$773$	−6.20925	−	35.2144i	−0.223331	−	1.26657i	0.642519	−	0.766270i	$-0.277889\pi$
$774$	2.14385	−	0.807062i	0.0770592	−	0.0290093i
$775$	3.03681	−	8.34357i	0.109086	−	0.299710i
$776$	−6.54763	−	17.9895i	−0.235046	−	0.645784i
$777$	2.19739	+	21.4284i	0.0788308	+	0.768740i
$778$		−	7.33810i		−	0.263084i
$779$	−3.44229	−	4.25524i	−0.123333	−	0.152460i
$780$	−6.83845	−	11.6958i	−0.244856	−	0.418777i
$781$	−35.2233	−	6.21081i	−1.26039	−	0.222240i
$782$	−0.323557	+	1.83498i	−0.0115704	+	0.0656188i
$783$	4.03719	+	20.8793i	0.144278	+	0.746166i
$784$	4.39756	−	5.44623i	0.157056	−	0.194508i
$785$	−7.86167	+	21.5998i	−0.280595	+	0.770928i
$786$	−0.0802920	−	14.6263i	−0.00286392	−	0.521702i
$787$		−	27.6560i		−	0.985831i	−0.870077	−	0.492915i	$-0.835931\pi$
$787$		−	27.6560i		−	0.985831i	0.870077	−	0.492915i	$-0.164069\pi$
$788$	−1.65265	+	4.54063i	−0.0588734	+	0.161753i
$789$	−1.88921	+	0.343822i	−0.0672576	+	0.0122404i
$790$	8.50615	−	14.7331i	0.302635	−	0.524180i
$791$	−48.0682	−	12.3951i	−1.70911	−	0.440719i
$792$	2.66469	−	7.57907i	0.0946857	−	0.269310i
$793$	−34.0404	+	40.5677i	−1.20881	+	1.44060i
$794$	1.10987	−	0.931287i	0.0393876	−	0.0330502i
$795$	5.40565	−	6.51450i	0.191719	−	0.231045i
$796$	−2.00219	+	0.728739i	−0.0709658	+	0.0258295i
$797$	36.7936			1.30330			0.651648	−	0.758522i	$-0.274078\pi$
$797$	36.7936			1.30330			0.651648	+	0.758522i	$0.274078\pi$
$798$	−5.22839	+	19.2786i	−0.185083	+	0.682455i
$799$	−0.0184399			−0.000652355
$800$	0.901764	−	0.328215i	0.0318822	−	0.0116042i
$801$	−31.8151	−	26.1062i	−1.12413	−	0.922418i
$802$	16.1193	−	13.5257i	0.569192	−	0.477609i
$803$	−22.4969	+	26.8107i	−0.793897	+	0.946129i
$804$	0.287020	−	0.802258i	0.0101224	−	0.0282934i
$805$	8.90877	+	32.0362i	0.313993	+	1.12913i
$806$	18.0029	−	31.1819i	0.634125	−	1.09834i
$807$	−2.25855	−	12.4101i	−0.0795047	−	0.436856i
$808$	1.90774	−	5.24146i	0.0671139	−	0.184394i
$809$		−	16.7905i		−	0.590323i	−0.955447	−	0.295161i	$-0.904627\pi$
$809$		−	16.7905i		−	0.590323i	0.955447	−	0.295161i	$-0.0953734\pi$
$810$	−0.397203	−	18.0862i	−0.0139563	−	0.635485i
$811$	−6.17774	+	16.9732i	−0.216930	+	0.596009i	−0.999652	−	0.0263611i	$-0.991608\pi$
$811$	−6.17774	+	16.9732i	−0.216930	+	0.596009i	0.782723	+	0.622370i	$0.213830\pi$
$812$	4.48340	−	9.85636i	0.157337	−	0.345890i
$813$	1.02998	+	5.65947i	0.0361231	+	0.198486i
$814$	2.18587	−	12.3967i	0.0766148	−	0.434504i
$815$	25.5391	+	4.50323i	0.894595	+	0.157741i
$816$	−0.445584	+	0.260530i	−0.0155986	+	0.00912038i
$817$	3.28764	−	0.519023i	0.115020	−	0.0181583i
$818$		−	22.3066i		−	0.779930i
$819$	−28.2543	−	12.4796i	−0.987283	−	0.436072i
$820$	−0.863237	−	2.37172i	−0.0301455	−	0.0828242i
$821$	9.23294	−	25.3673i	0.322232	−	0.885325i	−0.667782	−	0.744357i	$-0.732756\pi$
$821$	9.23294	−	25.3673i	0.322232	−	0.885325i	0.990014	−	0.140968i	$-0.0450215\pi$
$822$	7.54828	+	20.3898i	0.263277	+	0.711175i
$823$	−1.99479	−	11.3130i	−0.0695339	−	0.394347i	−0.999634	−	0.0270411i	$-0.991391\pi$
$823$	−1.99479	−	11.3130i	−0.0695339	−	0.394347i	0.930100	−	0.367305i	$-0.119720\pi$
$824$		−	3.08671i		−	0.107531i
$825$	3.86695	+	2.20437i	0.134630	+	0.0767464i
$826$	2.31472	−	29.6791i	0.0805394	−	1.03267i
$827$	11.9477	−	10.0253i	0.415463	−	0.348615i	−0.410971	−	0.911648i	$-0.634810\pi$
$827$	11.9477	−	10.0253i	0.415463	−	0.348615i	0.826434	+	0.563033i	$0.190366\pi$
$828$	16.1406	−	9.55659i	0.560925	−	0.332114i
$829$	−20.8634	−	12.0455i	−0.724615	−	0.418357i	0.0918340	−	0.995774i	$-0.470727\pi$
$829$	−20.8634	−	12.0455i	−0.724615	−	0.418357i	−0.816449	+	0.577418i	$0.804060\pi$
$830$	−3.22225	−	18.2743i	−0.111846	−	0.634310i
$831$	11.5487	+	9.58297i	0.400620	+	0.332429i
$832$	3.83235	−	0.675747i	0.132863	−	0.0234273i
$833$	−1.62301	−	1.31050i	−0.0562338	−	0.0454060i
$834$	−6.94305	−	5.76126i	−0.240418	−	0.199496i
$835$	−33.9721	−	19.6138i	−1.17565	−	0.678764i
$836$	6.01701	−	10.0026i	0.208103	−	0.345948i
$837$	41.2347	−	24.7211i	1.42528	−	0.854486i
$838$	−2.34349	−	6.43868i	−0.0809545	−	0.222421i
$839$	−36.3834	+	13.2425i	−1.25609	+	0.457181i	−0.882457	−	0.470393i	$-0.844112\pi$
$839$	−36.3834	+	13.2425i	−1.25609	+	0.457181i	−0.373638	+	0.927575i	$0.621890\pi$
$840$	−5.17020	+	7.62343i	−0.178389	+	0.263033i
$841$	−2.12722	+	12.0641i	−0.0733525	+	0.416003i
$842$	18.3075	+	21.8180i	0.630917	+	0.751897i
$843$	−1.33917	+	2.34920i	−0.0461235	+	0.0809107i
$844$			12.9664i			0.446321i
$845$	4.24319	−	0.748189i	0.145970	−	0.0257385i
$846$	0.120877	+	0.140884i	0.00415582	+	0.00484371i
$847$	9.80859	+	2.52929i	0.337027	+	0.0869075i
$848$	1.21573	+	2.10570i	0.0417483	+	0.0723102i
$849$	−7.43811	+	6.31122i	−0.255275	+	0.216600i
$850$	−0.0978099	−	0.268731i	−0.00335485	−	0.00921738i
$851$	22.5145	−	18.8919i	0.771787	−	0.647606i
$852$	3.89192	−	22.8035i	0.133335	−	0.781234i
$853$	2.85982	+	2.39967i	0.0979182	+	0.0821632i	0.690433	−	0.723397i	$-0.257420\pi$
$853$	2.85982	+	2.39967i	0.0979182	+	0.0821632i	−0.592514	+	0.805560i	$0.701865\pi$
$854$	34.8644	+	8.99031i	1.19304	+	0.307642i
$855$	4.74479	−	25.8532i	0.162268	−	0.884161i
$856$	6.54878	−	11.3428i	0.223833	−	0.387690i
$857$	4.78244	−	27.1226i	0.163365	−	0.926489i	−0.787369	−	0.616482i	$-0.788557\pi$
$857$	4.78244	−	27.1226i	0.163365	−	0.926489i	0.950734	−	0.310007i	$-0.100332\pi$
$858$	13.8906	+	11.5262i	0.474217	+	0.393499i
$859$	22.4388	+	8.16705i	0.765601	+	0.278656i	0.695155	−	0.718860i	$-0.255336\pi$
$859$	22.4388	+	8.16705i	0.765601	+	0.278656i	0.0704458	+	0.997516i	$0.477558\pi$
$860$	1.51152	+	0.266522i	0.0515425	+	0.00908833i
$861$	−4.76221	−	3.22972i	−0.162296	−	0.110069i
$862$	0.246508	+	0.426964i	0.00839609	+	0.0145425i
$863$	−13.3143	−	23.0610i	−0.453223	−	0.785005i	0.545361	−	0.838201i	$-0.316393\pi$
$863$	−13.3143	−	23.0610i	−0.453223	−	0.785005i	−0.998584	+	0.0531960i	$0.983059\pi$
$864$	4.91139	+	1.69654i	0.167089	+	0.0577174i
$865$	0.966272	−	2.65481i	0.0328542	−	0.0902662i
$866$	16.7589	−	9.67575i	0.569490	−	0.328795i
$867$	−14.7846	−	25.2860i	−0.502110	−	0.858758i
$868$	−24.4057	−	1.90344i	−0.828383	−	0.0646070i
$869$	−3.93574	+	22.3207i	−0.133511	+	0.757177i
$870$	−4.79977	+	13.4160i	−0.162728	+	0.454844i
$871$	1.46647	+	1.23052i	0.0496896	+	0.0416945i
$872$	−14.2926	−	2.52018i	−0.484009	−	0.0853439i
$873$	50.0498	+	28.1682i	1.69393	+	0.953349i
$874$	25.7738	−	8.86018i	0.871811	−	0.299700i
$875$	−22.6215	−	22.1988i	−0.764747	−	0.750455i
$876$	−17.4203	−	14.4551i	−0.588577	−	0.488394i
$877$	−37.3809	−	6.59127i	−1.26226	−	0.222571i	−0.497831	−	0.867274i	$-0.665870\pi$
$877$	−37.3809	−	6.59127i	−1.26226	−	0.222571i	−0.764433	+	0.644703i	$0.776981\pi$
$878$	−17.9042	−	21.3374i	−0.604239	−	0.720104i
$879$	44.0109	−	16.2928i	1.48445	−	0.549543i
$880$	4.12351	−	3.46003i	0.139003	−	0.116638i
$881$	−16.7337	+	9.66119i	−0.563772	+	0.325494i	−0.754658	−	0.656119i	$-0.772197\pi$
$881$	−16.7337	+	9.66119i	−0.563772	+	0.325494i	0.190886	+	0.981612i	$0.438864\pi$
$882$	0.626625	+	20.9906i	0.0210996	+	0.706792i
$883$	38.1264	−	31.9919i	1.28306	−	1.07661i	0.290241	−	0.956954i	$-0.406265\pi$
$883$	38.1264	−	31.9919i	1.28306	−	1.07661i	0.992815	−	0.119658i	$-0.0381798\pi$
$884$	−0.201376	−	1.14206i	−0.00677301	−	0.0384116i
$885$	0.215041	+	39.1726i	0.00722852	+	1.31677i
$886$	23.6138	+	13.6334i	0.793322	+	0.458025i
$887$	32.8974	−	27.6042i	1.10459	−	0.926859i	0.106862	−	0.994274i	$-0.465920\pi$
$887$	32.8974	−	27.6042i	1.10459	−	0.926859i	0.997725	+	0.0674150i	$0.0214751\pi$
$888$	8.02560	+	1.36975i	0.269322	+	0.0459657i
$889$	12.0764	−	17.5978i	0.405029	−	0.590213i
$890$	−9.43112	−	25.9118i	−0.316132	−	0.868565i
$891$	8.73850	+	22.4616i	0.292751	+	0.752492i
$892$	16.8200	−	9.71105i	0.563177	−	0.325150i
$893$	0.130644	+	0.235966i	0.00437183	+	0.00789632i
$894$	−1.90432	−	1.08557i	−0.0636900	−	0.0363067i
$895$	1.00964	−	1.20324i	0.0337486	−	0.0402200i
$896$	−1.53792	−	2.15286i	−0.0513781	−	0.0719221i
$897$	7.54586	+	41.4624i	0.251949	+	1.38439i
$898$	−0.860784	−	0.722284i	−0.0287247	−	0.0241029i
$899$	−37.2920	+	6.57558i	−1.24376	+	0.219308i
$900$	−1.41200	+	2.50887i	−0.0470666	+	0.0836288i
$901$	0.627511	−	0.362294i	0.0209054	−	0.0120697i
$902$	2.16142	+	2.57588i	0.0719673	+	0.0857673i
$903$	3.14889	−	1.52596i	0.104788	−	0.0507808i
$904$	−9.38120	+	16.2487i	−0.312014	+	0.540424i
$905$	7.74737			0.257531
$906$	−0.141817	+	0.0258096i	−0.00471155	+	0.000857468i
$907$	1.62129	+	4.45447i	0.0538342	+	0.147908i	0.963695	−	0.267005i	$-0.0860341\pi$
$907$	1.62129	+	4.45447i	0.0538342	+	0.147908i	−0.909861	+	0.414913i	$0.863812\pi$
$908$	−16.6801	−	6.07107i	−0.553550	−	0.201476i
$909$	5.89550	+	15.6606i	0.195541	+	0.519429i
$910$	−12.0297	−	16.8399i	−0.398782	−	0.558238i
$911$	−59.3490			−1.96632			−0.983159	−	0.182751i	$-0.941500\pi$
$911$	−59.3490			−1.96632			−0.983159	+	0.182751i	$0.941500\pi$
$912$	6.49079	+	3.85612i	0.214931	+	0.127689i
$913$	12.3609	+	21.4098i	0.409088	+	0.708561i
$914$	1.48332	−	8.41231i	0.0490638	−	0.278254i
$915$	−46.7034	−	7.97098i	−1.54397	−	0.263512i
$916$	0.332424	+	1.88527i	0.0109836	+	0.0622910i
$917$	−2.15711	−	22.2380i	−0.0712341	−	0.734362i
$918$	0.505578	−	1.46362i	0.0166865	−	0.0483067i
$919$	−17.6140			−0.581033			−0.290517	−	0.956870i	$-0.593827\pi$
$919$	−17.6140			−0.581033			−0.290517	+	0.956870i	$0.593827\pi$
$920$	12.5680			0.414355
$921$	−15.0476	+	42.0600i	−0.495837	+	1.38592i
$922$	−25.5592	+	4.50677i	−0.841746	+	0.148423i
$923$	45.0111	+	25.9872i	1.48156	+	0.855378i
$924$	2.99898	−	11.8998i	0.0986592	−	0.391476i
$925$	−1.54280	+	4.23882i	−0.0507271	+	0.139372i
$926$	−12.5377	−	10.5204i	−0.412014	−	0.345721i
$927$	6.02981	+	7.02789i	0.198045	+	0.230826i
$928$	−3.13515	−	2.63071i	−0.102916	−	0.0863572i
$929$	−9.90667	−	27.2183i	−0.325027	−	0.893005i	−0.989350	−	0.145559i	$-0.953502\pi$
$929$	−9.90667	−	27.2183i	−0.325027	−	0.893005i	0.664322	−	0.747446i	$-0.268720\pi$
$930$	32.2124	−	0.176832i	1.05629	−	0.00579856i
$931$	−5.27105	+	30.0536i	−0.172752	+	0.984965i
$932$			23.3086i			0.763497i
$933$	6.32563	+	17.0871i	0.207092	+	0.559406i
$934$	−14.6166	+	17.4194i	−0.478269	+	0.569979i
$935$	−1.03111	−	1.22883i	−0.0337209	−	0.0401870i
$936$	−7.40553	+	9.02496i	−0.242057	+	0.294990i
$937$	−39.9908	−	14.5555i	−1.30644	−	0.475507i	−0.407354	−	0.913270i	$-0.633548\pi$
$937$	−39.9908	−	14.5555i	−1.30644	−	0.475507i	−0.899090	+	0.437764i	$0.855771\pi$
$938$	0.324989	−	1.26031i	0.0106113	−	0.0411505i
$939$	−26.7063	+	46.8488i	−0.871529	+	1.52885i
$940$	0.0215980	+	0.122488i	0.000704450	+	0.00399513i
$941$	−19.7126	−	7.17481i	−0.642613	−	0.233892i	9.89387e−5	−	1.00000i	$-0.499969\pi$
$941$	−19.7126	−	7.17481i	−0.642613	−	0.233892i	−0.642712	+	0.766108i	$0.722191\pi$
$942$	19.8065	−	0.108729i	0.645329	−	0.00354258i
$943$			7.85099i			0.255663i
$944$	−10.5731	−	3.84831i	−0.344126	−	0.125252i
$945$	−3.12058	−	27.4571i	−0.101512	−	0.893178i
$946$	−2.01376	+	0.355080i	−0.0654729	+	0.0115446i
$947$	4.56870	+	0.805584i	0.148463	+	0.0261780i	0.247386	−	0.968917i	$-0.420429\pi$
$947$	4.56870	+	0.805584i	0.148463	+	0.0261780i	−0.0989228	+	0.995095i	$0.531540\pi$
$948$	−14.4504	−	2.46628i	−0.469326	−	0.0801009i
$949$	44.0449	−	25.4293i	1.42976	−	0.825471i
$950$	−2.74585	+	3.15555i	−0.0890872	+	0.102379i
$951$	−15.6670	+	0.0860051i	−0.508037	+	0.00278891i
$952$	−0.641564	+	0.458307i	−0.0207932	+	0.0148538i
$953$	−8.75027	+	3.18484i	−0.283449	+	0.103167i	−0.479832	−	0.877360i	$-0.659303\pi$
$953$	−8.75027	+	3.18484i	−0.283449	+	0.103167i	0.196383	+	0.980527i	$0.437080\pi$
$954$	−6.88144	−	2.41942i	−0.222795	−	0.0783315i
$955$	16.6624	−	6.06461i	0.539182	−	0.196246i
$956$	9.54077	−	1.68229i	0.308571	−	0.0544093i
$957$	−0.104208	−	18.9829i	−0.00336856	−	0.613629i
$958$	−11.9040	−	6.87278i	−0.384601	−	0.222049i
$959$	14.3191	+	29.9662i	0.462389	+	0.967660i
$960$	2.25249	+	2.65469i	0.0726989	+	0.0856796i
$961$	27.3044	+	47.2925i	0.880786	+	1.52557i
$962$	−9.14609	+	15.8415i	−0.294882	+	0.510750i
$963$	7.24753	+	38.6185i	0.233548	+	1.24446i
$964$	−11.0882	+	13.2144i	−0.357128	+	0.425608i
$965$	−9.02720	−	51.1958i	−0.290596	−	1.64805i
$966$	23.2231	−	16.7829i	0.747191	−	0.539981i
$967$	19.1060	+	16.0318i	0.614406	+	0.515548i	0.896040	−	0.443974i	$-0.146432\pi$
$967$	19.1060	+	16.0318i	0.614406	+	0.515548i	−0.281634	+	0.959522i	$0.590876\pi$
$968$	1.91429	−	3.31564i	0.0615275	−	0.106569i
$969$	1.14914	−	1.93429i	0.0369158	−	0.0621383i
$970$	19.2403	+	33.3253i	0.617770	+	1.07001i
$971$	−30.4426	+	11.0802i	−0.976949	+	0.355580i	−0.780653	−	0.624965i	$-0.785113\pi$
$971$	−30.4426	+	11.0802i	−0.976949	+	0.355580i	−0.196295	+	0.980545i	$0.562891\pi$
$972$	−14.4965	+	5.73157i	−0.464976	+	0.183840i
$973$	−11.3632	−	7.79789i	−0.364287	−	0.249989i
$974$	3.85306	+	0.679398i	0.123460	+	0.0217693i
$975$	−4.18480	−	4.93201i	−0.134021	−	0.157951i
$976$	6.80429	−	11.7854i	0.217800	−	0.377241i
$977$	−60.3690			−1.93138			−0.965688	−	0.259704i	$-0.916375\pi$
$977$	−60.3690			−1.93138			−0.965688	+	0.259704i	$0.916375\pi$
$978$	−4.00113	−	21.9851i	−0.127942	−	0.703006i
$979$	23.6141	+	28.1422i	0.754711	+	0.899429i
$980$	−6.80412	+	12.3159i	−0.217350	+	0.393417i
$981$	37.4649	−	22.1823i	1.19616	−	0.708227i
$982$	17.6345	+	21.0160i	0.562739	+	0.670646i
$983$	25.0946	−	9.13370i	0.800394	−	0.291320i	0.0907445	−	0.995874i	$-0.471075\pi$
$983$	25.0946	−	9.13370i	0.800394	−	0.291320i	0.709650	+	0.704554i	$0.248853\pi$
$984$	−1.65833	+	1.40709i	−0.0528656	+	0.0448564i
$985$	1.68660	−	9.56516i	0.0537394	−	0.304771i
$986$	−0.783965	+	0.934293i	−0.0249665	+	0.0297539i
$987$	0.203476	+	0.197492i	0.00647671	+	0.00628625i
$988$	−13.1877	+	10.6683i	−0.419557	+	0.339402i
$989$	−4.13466	−	2.38715i	−0.131475	−	0.0759069i
$990$	−2.62940	+	15.9331i	−0.0835679	+	0.506386i
$991$	−32.1793	+	38.3498i	−1.02221	+	1.21822i	−0.0465541	+	0.998916i	$0.514824\pi$
$991$	−32.1793	+	38.3498i	−1.02221	+	1.21822i	−0.975656	+	0.219307i	$0.929620\pi$
$992$	−3.16454	+	8.69450i	−0.100474	+	0.276051i
$993$	35.3821	+	6.03874i	1.12282	+	0.191634i
$994$	2.74761	−	35.2296i	0.0871490	−	1.11741i
$995$	3.70903	−	2.14141i	0.117584	−	0.0678873i
$996$	−13.8034	+	8.07073i	−0.437376	+	0.255731i
$997$	−11.1658	−	4.06403i	−0.353625	−	0.128709i	0.159099	−	0.987263i	$-0.449141\pi$
$997$	−11.1658	−	4.06403i	−0.353625	−	0.128709i	−0.512724	+	0.858554i	$0.671363\pi$
$998$	20.2114	+	7.35634i	0.639780	+	0.232861i
$999$	−20.9487	+	12.5592i	−0.662786	+	0.397354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.b.611.20	yes	162
3.2	odd	2		798.2.bu.a.611.6	yes	162
7.4	even	3		798.2.cc.b.725.16	yes	162
19.13	odd	18		798.2.cc.a.317.12	yes	162
21.11	odd	6		798.2.cc.a.725.12	yes	162
57.32	even	18		798.2.cc.b.317.16	yes	162
133.32	odd	18		798.2.bu.a.431.6	✓	162
399.32	even	18	inner	798.2.bu.b.431.20	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.6	✓	162	133.32	odd	18
798.2.bu.a.611.6	yes	162	3.2	odd	2
798.2.bu.b.431.20	yes	162	399.32	even	18	inner
798.2.bu.b.611.20	yes	162	1.1	even	1	trivial
798.2.cc.a.317.12	yes	162	19.13	odd	18
798.2.cc.a.725.12	yes	162	21.11	odd	6
798.2.cc.b.317.16	yes	162	57.32	even	18
798.2.cc.b.725.16	yes	162	7.4	even	3

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.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.33292 + 1.10604i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.29205 + 1.53980i) q^{5} +(1.63082 + 0.583453i) q^{6} +(2.56194 + 0.660635i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.553349 + 2.94853i) q^{9} +(-0.687483 + 1.88884i) q^{10} -2.67795i q^{11} +(1.73202 - 0.00950808i) q^{12} +(-1.33096 + 3.65679i) q^{13} +(2.63339 - 0.255442i) q^{14} +(-3.42527 + 0.623375i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.293478 - 0.0517481i) q^{17} +(1.52843 + 2.58145i) q^{18} +(1.41705 + 4.12213i) q^{19} +2.01007i q^{20} +(2.68418 + 3.71419i) q^{21} +(-0.915914 - 2.51645i) q^{22} +(2.13849 - 5.87546i) q^{23} +(1.62432 - 0.601322i) q^{24} +(0.166639 + 0.945059i) q^{25} +3.89147i q^{26} +(-2.52362 + 4.54217i) q^{27} +(2.38721 - 1.14071i) q^{28} +(3.13515 - 2.63071i) q^{29} +(-3.00550 + 1.75729i) q^{30} +(-8.01290 - 4.62625i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.96192 - 3.56949i) q^{33} +(-0.293478 + 0.0517481i) q^{34} +(-4.32739 + 3.09131i) q^{35} +(2.31917 + 1.90302i) q^{36} +(4.07083 + 2.35029i) q^{37} +(2.74145 + 3.38887i) q^{38} +(-5.81862 + 3.40210i) q^{39} +(0.687483 + 1.88884i) q^{40} +(-1.17992 + 0.429457i) q^{41} +(3.79263 + 2.57215i) q^{42} +(0.132594 - 0.751977i) q^{43} +(-1.72135 - 2.05143i) q^{44} +(-5.25509 - 2.95758i) q^{45} -6.25254i q^{46} +(0.0609376 - 0.0107449i) q^{47} +(1.32070 - 1.12061i) q^{48} +(6.12712 + 3.38502i) q^{49} +(0.479819 + 0.831071i) q^{50} +(-0.333947 - 0.393574i) q^{51} +(1.33096 + 3.65679i) q^{52} +(-1.86260 + 1.56291i) q^{53} +(-0.817911 + 5.13138i) q^{54} +(4.12351 + 3.46003i) q^{55} +(1.85310 - 1.88839i) q^{56} +(-2.67042 + 7.06179i) q^{57} +(2.04633 - 3.54434i) q^{58} +(1.95384 - 11.0808i) q^{59} +(-2.22321 + 2.67926i) q^{60} +(12.7879 + 4.65441i) q^{61} +(-9.11193 - 1.60668i) q^{62} +(-0.530251 + 7.91952i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.91105 - 6.77414i) q^{65} +(1.56246 - 4.36727i) q^{66} +(0.168251 - 0.462267i) q^{67} +(-0.258080 + 0.149003i) q^{68} +(9.34894 - 5.46626i) q^{69} +(-3.00913 + 4.38494i) q^{70} +(2.31924 - 13.1531i) q^{71} +(2.83017 + 0.995048i) q^{72} +(-10.0116 - 8.40077i) q^{73} +(4.62917 + 0.816248i) q^{74} +(-0.823156 + 1.44400i) q^{75} +(3.73518 + 2.24687i) q^{76} +(1.76915 - 6.86077i) q^{77} +(-4.30412 + 5.18702i) q^{78} +(-8.33498 - 1.46968i) q^{79} +(1.29205 + 1.53980i) q^{80} +(-8.38761 + 3.26313i) q^{81} +(-0.961883 + 0.807115i) q^{82} +(-7.99484 + 4.61582i) q^{83} +(4.44363 + 1.11988i) q^{84} +(0.458868 - 0.385036i) q^{85} +(-0.132594 - 0.751977i) q^{86} +(7.08858 - 0.0389133i) q^{87} +(-2.31917 - 1.33898i) q^{88} +(-10.5089 + 8.81798i) q^{89} +(-5.94972 - 0.981871i) q^{90} +(-5.82565 + 8.48920i) q^{91} +(-2.13849 - 5.87546i) q^{92} +(-5.56373 - 15.0290i) q^{93} +(0.0535876 - 0.0309388i) q^{94} +(-8.17815 - 3.14400i) q^{95} +(0.857778 - 1.50473i) q^{96} +(12.3055 - 14.6652i) q^{97} +(6.91536 + 1.08528i) q^{98} +(7.89601 - 1.48184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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