LMFDB - Embedded newform 798.2.cj.a.409.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] 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([0, 3, 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("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.5
Character	$\chi$	$=$	798.409
Dual form			798.2.cj.a.439.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 - 0.766044i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.30738 - 0.406854i) q^{5} +(0.642788 - 0.766044i) q^{6} +(-2.44133 - 1.01977i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-1.79483 - 1.50604i) q^{10} -5.80164 q^{11} -1.00000 q^{12} +(-1.42839 - 1.19856i) q^{13} +(0.788065 + 2.52566i) q^{14} +(0.801346 + 2.20168i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.13286 + 3.11250i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.16845 - 1.27437i) q^{19} +2.34298i q^{20} +(0.580345 - 2.58132i) q^{21} +(3.72922 + 4.44431i) q^{22} +(-0.670222 - 0.562383i) q^{23} +(0.642788 + 0.766044i) q^{24} +(0.460029 - 0.167437i) q^{25} +1.86463i q^{26} +(-0.500000 - 0.866025i) q^{27} +(1.42821 - 2.22716i) q^{28} +(-9.56515 - 1.68659i) q^{29} +(1.17149 - 2.02908i) q^{30} +(4.52843 + 7.84347i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-1.00744 - 5.71350i) q^{33} +(3.11250 - 1.13286i) q^{34} +(-6.04797 - 1.35974i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(5.05309 - 2.91740i) q^{37} +(1.70321 + 4.01237i) q^{38} +(0.932316 - 1.61482i) q^{39} +(1.79483 - 1.50604i) q^{40} +(9.24464 - 7.75717i) q^{41} +(-2.35044 + 1.21467i) q^{42} +(-2.22393 - 0.809445i) q^{43} +(1.00744 - 5.71350i) q^{44} +(-2.02908 + 1.17149i) q^{45} +0.874913i q^{46} +(0.179016 + 0.491843i) q^{47} +(0.173648 - 0.984808i) q^{48} +(4.92014 + 4.97918i) q^{49} +(-0.423965 - 0.244777i) q^{50} +(-3.26193 - 0.575166i) q^{51} +(1.42839 - 1.19856i) q^{52} +(-9.51187 - 1.67720i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-13.3866 + 2.36042i) q^{55} +(-2.62413 + 0.337517i) q^{56} +(0.531162 - 4.32642i) q^{57} +(4.85635 + 8.41145i) q^{58} +(-12.1975 - 4.43953i) q^{59} +(-2.30738 + 0.406854i) q^{60} +(3.01868 - 3.59752i) q^{61} +(3.09763 - 8.51067i) q^{62} +(2.64288 + 0.123287i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.78349 - 2.18440i) q^{65} +(-3.72922 + 4.44431i) q^{66} +(-1.87652 + 2.23635i) q^{67} +(-2.86849 - 1.65612i) q^{68} +(0.437456 - 0.757697i) q^{69} +(2.84594 + 5.50704i) q^{70} +(-4.04616 + 11.1167i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(-4.47491 + 0.789047i) q^{73} +(-5.48292 - 1.99562i) q^{74} +(0.244777 + 0.423965i) q^{75} +(1.97885 - 3.88383i) q^{76} +(14.1637 + 5.91633i) q^{77} +(-1.83630 + 0.323790i) q^{78} +(-1.90333 + 5.22936i) q^{79} +(-2.30738 - 0.406854i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-11.8847 - 2.09559i) q^{82} +(6.43322 + 3.71422i) q^{83} +(2.44133 + 1.01977i) q^{84} +(-1.34760 + 7.64263i) q^{85} +(0.809445 + 2.22393i) q^{86} -9.71271i q^{87} +(-5.02437 + 2.90082i) q^{88} +(0.595622 - 3.37794i) q^{89} +(2.20168 + 0.801346i) q^{90} +(2.26491 + 4.38271i) q^{91} +(0.670222 - 0.562383i) q^{92} +(-6.93796 + 5.82164i) q^{93} +(0.261704 - 0.453285i) q^{94} +(-10.1367 - 1.24450i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(1.81640 + 10.3013i) q^{97} +(0.651665 - 6.96960i) q^{98} +(5.45176 - 1.98428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	2.30738	−	0.406854i	1.03189	−	0.181951i	0.368037	−	0.929811i	$-0.380030\pi$
$5$	2.30738	−	0.406854i	1.03189	−	0.181951i	0.663856	+	0.747860i	$0.268919\pi$
$6$	0.642788	−	0.766044i	0.262417	−	0.312736i
$7$	−2.44133	−	1.01977i	−0.922734	−	0.385437i
$7$	−2.44133	−	1.01977i	−0.922734	−	0.385437i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−1.79483	−	1.50604i	−0.567574	−	0.476251i
$11$	−5.80164			−1.74926			−0.874630	−	0.484791i	$-0.838896\pi$
$11$	−5.80164			−1.74926			−0.874630	+	0.484791i	$0.838896\pi$
$12$	−1.00000			−0.288675
$13$	−1.42839	−	1.19856i	−0.396164	−	0.332421i	0.422845	−	0.906202i	$-0.361032\pi$
$13$	−1.42839	−	1.19856i	−0.396164	−	0.332421i	−0.819009	+	0.573781i	$0.805476\pi$
$14$	0.788065	+	2.52566i	0.210619	+	0.675011i
$15$	0.801346	+	2.20168i	0.206907	+	0.568471i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.13286	+	3.11250i	−0.274758	+	0.754891i	0.723177	+	0.690662i	$0.242681\pi$
$17$	−1.13286	+	3.11250i	−0.274758	+	0.754891i	−0.997935	+	0.0642288i	$0.979541\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−4.16845	−	1.27437i	−0.956308	−	0.292360i
$19$	−4.16845	−	1.27437i	−0.956308	−	0.292360i
$20$			2.34298i			0.523906i
$21$	0.580345	−	2.58132i	0.126642	−	0.563290i
$22$	3.72922	+	4.44431i	0.795073	+	0.947531i
$23$	−0.670222	−	0.562383i	−0.139751	−	0.117265i	0.570232	−	0.821483i	$-0.306853\pi$
$23$	−0.670222	−	0.562383i	−0.139751	−	0.117265i	−0.709983	+	0.704218i	$0.751298\pi$
$24$	0.642788	+	0.766044i	0.131208	+	0.156368i
$25$	0.460029	−	0.167437i	0.0920059	−	0.0334874i
$26$			1.86463i			0.365684i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	1.42821	−	2.22716i	0.269906	−	0.420893i
$29$	−9.56515	−	1.68659i	−1.77620	−	0.313193i	−0.813060	−	0.582180i	$-0.802200\pi$
$29$	−9.56515	−	1.68659i	−1.77620	−	0.313193i	−0.963144	+	0.268987i	$0.913311\pi$
$30$	1.17149	−	2.02908i	0.213884	−	0.370458i
$31$	4.52843	+	7.84347i	0.813330	+	1.40873i	0.910521	+	0.413463i	$0.135681\pi$
$31$	4.52843	+	7.84347i	0.813330	+	1.40873i	−0.0971906	+	0.995266i	$0.530986\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−1.00744	−	5.71350i	−0.175374	−	0.994593i
$34$	3.11250	−	1.13286i	0.533789	−	0.194283i
$35$	−6.04797	−	1.35974i	−1.02229	−	0.229837i
$36$	−0.173648	−	0.984808i	−0.0289414	−	0.164135i
$37$	5.05309	−	2.91740i	0.830723	−	0.479618i	−0.0233774	−	0.999727i	$-0.507442\pi$
$37$	5.05309	−	2.91740i	0.830723	−	0.479618i	0.854100	+	0.520109i	$0.174109\pi$
$38$	1.70321	+	4.01237i	0.276297	+	0.650892i
$39$	0.932316	−	1.61482i	0.149290	−	0.258578i
$40$	1.79483	−	1.50604i	0.283787	−	0.238126i
$41$	9.24464	−	7.75717i	1.44377	−	1.21147i	0.506797	−	0.862065i	$-0.330829\pi$
$41$	9.24464	−	7.75717i	1.44377	−	1.21147i	0.936973	−	0.349402i	$-0.113615\pi$
$42$	−2.35044	+	1.21467i	−0.362681	+	0.187427i
$43$	−2.22393	−	0.809445i	−0.339147	−	0.123439i	0.166832	−	0.985985i	$-0.446646\pi$
$43$	−2.22393	−	0.809445i	−0.339147	−	0.123439i	−0.505978	+	0.862546i	$0.668868\pi$
$44$	1.00744	−	5.71350i	0.151878	−	0.861343i
$45$	−2.02908	+	1.17149i	−0.302477	+	0.174635i
$46$			0.874913i			0.128999i
$47$	0.179016	+	0.491843i	0.0261122	+	0.0717426i	0.952064	−	0.305900i	$-0.0989572\pi$
$47$	0.179016	+	0.491843i	0.0261122	+	0.0717426i	−0.925952	+	0.377642i	$0.876735\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	4.92014	+	4.97918i	0.702877	+	0.711311i
$50$	−0.423965	−	0.244777i	−0.0599578	−	0.0346166i
$51$	−3.26193	−	0.575166i	−0.456761	−	0.0805394i
$52$	1.42839	−	1.19856i	0.198082	−	0.166211i
$53$	−9.51187	−	1.67720i	−1.30656	−	0.230381i	−0.523336	−	0.852126i	$-0.675313\pi$
$53$	−9.51187	−	1.67720i	−1.30656	−	0.230381i	−0.783219	+	0.621746i	$0.786424\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	−13.3866	+	2.36042i	−1.80505	+	0.318279i
$56$	−2.62413	+	0.337517i	−0.350665	+	0.0451026i
$57$	0.531162	−	4.32642i	0.0703541	−	0.573048i
$58$	4.85635	+	8.41145i	0.637670	+	1.10448i
$59$	−12.1975	−	4.43953i	−1.58798	−	0.577978i	−0.611061	−	0.791584i	$-0.709257\pi$
$59$	−12.1975	−	4.43953i	−1.58798	−	0.577978i	−0.976920	+	0.213606i	$0.931479\pi$
$60$	−2.30738	+	0.406854i	−0.297882	+	0.0525246i
$61$	3.01868	−	3.59752i	0.386502	−	0.460615i	−0.537353	−	0.843357i	$-0.680576\pi$
$61$	3.01868	−	3.59752i	0.386502	−	0.460615i	0.923855	+	0.382742i	$0.125020\pi$
$62$	3.09763	−	8.51067i	0.393399	−	1.08086i
$63$	2.64288	+	0.123287i	0.332971	+	0.0155327i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−3.78349	−	2.18440i	−0.469284	−	0.270941i
$66$	−3.72922	+	4.44431i	−0.459036	+	0.547057i
$67$	−1.87652	+	2.23635i	−0.229253	+	0.273214i	−0.868392	−	0.495878i	$-0.834846\pi$
$67$	−1.87652	+	2.23635i	−0.229253	+	0.273214i	0.639139	+	0.769091i	$0.279291\pi$
$68$	−2.86849	−	1.65612i	−0.347856	−	0.200835i
$69$	0.437456	−	0.757697i	0.0526636	−	0.0912160i
$70$	2.84594	+	5.50704i	0.340155	+	0.658217i
$71$	−4.04616	+	11.1167i	−0.480191	+	1.31931i	0.429140	+	0.903238i	$0.358817\pi$
$71$	−4.04616	+	11.1167i	−0.480191	+	1.31931i	−0.909330	+	0.416075i	$0.863405\pi$
$72$	−0.642788	+	0.766044i	−0.0757532	+	0.0902792i
$73$	−4.47491	+	0.789047i	−0.523748	+	0.0923510i	−0.429270	−	0.903176i	$-0.641229\pi$
$73$	−4.47491	+	0.789047i	−0.523748	+	0.0923510i	−0.0944779	+	0.995527i	$0.530118\pi$
$74$	−5.48292	−	1.99562i	−0.637377	−	0.231986i
$75$	0.244777	+	0.423965i	0.0282644	+	0.0489553i
$76$	1.97885	−	3.88383i	0.226990	−	0.445506i
$77$	14.1637	+	5.91633i	1.61410	+	0.674229i
$78$	−1.83630	+	0.323790i	−0.207920	+	0.0366620i
$79$	−1.90333	+	5.22936i	−0.214141	+	0.588349i	−0.999530	−	0.0306543i	$-0.990241\pi$
$79$	−1.90333	+	5.22936i	−0.214141	+	0.588349i	0.785389	+	0.619003i	$0.212463\pi$
$80$	−2.30738	−	0.406854i	−0.257973	−	0.0454877i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−11.8847	−	2.09559i	−1.31244	−	0.231419i
$83$	6.43322	+	3.71422i	0.706138	+	0.407689i	0.809629	−	0.586941i	$-0.199668\pi$
$83$	6.43322	+	3.71422i	0.706138	+	0.407689i	−0.103492	+	0.994630i	$0.533001\pi$
$84$	2.44133	+	1.01977i	0.266370	+	0.111266i
$85$	−1.34760	+	7.64263i	−0.146168	+	0.828960i
$86$	0.809445	+	2.22393i	0.0872847	+	0.239813i
$87$		−	9.71271i		−	1.04131i
$88$	−5.02437	+	2.90082i	−0.535599	+	0.309228i
$89$	0.595622	−	3.37794i	0.0631358	−	0.358061i	−0.936830	−	0.349785i	$-0.886255\pi$
$89$	0.595622	−	3.37794i	0.0631358	−	0.358061i	0.999966	−	0.00827573i	$-0.00263428\pi$
$90$	2.20168	+	0.801346i	0.232078	+	0.0844693i
$91$	2.26491	+	4.38271i	0.237427	+	0.459433i
$92$	0.670222	−	0.562383i	0.0698755	−	0.0586325i
$93$	−6.93796	+	5.82164i	−0.719433	+	0.603676i
$94$	0.261704	−	0.453285i	0.0269927	−	0.0467527i
$95$	−10.1367	−	1.24450i	−1.04000	−	0.127683i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	1.81640	+	10.3013i	0.184427	+	1.04594i	0.926689	+	0.375829i	$0.122642\pi$
$97$	1.81640	+	10.3013i	0.184427	+	1.04594i	−0.742262	+	0.670110i	$0.766247\pi$
$98$	0.651665	−	6.96960i	0.0658281	−	0.704036i
$99$	5.45176	−	1.98428i	0.547922	−	0.199427i
$100$	0.0850100	+	0.482116i	0.00850100	+	0.0482116i
$101$	−3.50364	−	9.62617i	−0.348625	−	0.957840i	−0.982804	−	0.184653i	$-0.940884\pi$
$101$	−3.50364	−	9.62617i	−0.348625	−	0.957840i	0.634179	−	0.773187i	$-0.281338\pi$
$102$	1.65612	+	2.86849i	0.163981	+	0.284023i
$103$	−2.19260	+	3.79770i	−0.216043	+	0.374198i	−0.953595	−	0.301093i	$-0.902649\pi$
$103$	−2.19260	+	3.79770i	−0.216043	+	0.374198i	0.737551	+	0.675291i	$0.235982\pi$
$104$	−1.83630	−	0.323790i	−0.180064	−	0.0317502i
$105$	0.288859	−	6.19221i	0.0281898	−	0.604298i
$106$	4.82930	+	8.36459i	0.469063	+	0.812441i
$107$		−	16.1118i		−	1.55759i	−0.627279	−	0.778794i	$-0.715832\pi$
$107$		−	16.1118i		−	1.55759i	0.627279	−	0.778794i	$-0.284168\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	5.89908	+	7.03025i	0.565029	+	0.673376i	0.970603	−	0.240687i	$-0.0773727\pi$
$109$	5.89908	+	7.03025i	0.565029	+	0.673376i	−0.405574	+	0.914062i	$0.632928\pi$
$110$	10.4129	+	8.73749i	0.992835	+	0.833087i
$111$	3.75054	+	4.46972i	0.355985	+	0.424247i
$112$	1.94531	+	1.79325i	0.183815	+	0.169446i
$113$			3.09086i			0.290764i	0.989376	+	0.145382i	$0.0464411\pi$
$113$			3.09086i			0.290764i	−0.989376	+	0.145382i	$0.953559\pi$
$114$	−3.65565	+	2.37407i	−0.342383	+	0.222352i
$115$	−1.77527	−	1.02495i	−0.165545	−	0.0955772i
$116$	3.32194	−	9.12696i	0.308435	−	0.847417i
$117$	1.75218	+	0.637741i	0.161989	+	0.0589592i
$118$	4.43953	+	12.1975i	0.408692	+	1.12287i
$119$	5.93970	−	6.44337i	0.544491	−	0.590662i
$120$	1.79483	+	1.50604i	0.163844	+	0.137482i
$121$	22.6590			2.05991
$122$	−4.69623			−0.425177
$123$	9.24464	+	7.75717i	0.833561	+	0.699441i
$124$	−8.51067	+	3.09763i	−0.764280	+	0.278175i
$125$	−9.15206	+	5.28394i	−0.818585	+	0.472610i
$126$	−1.60437	−	2.10381i	−0.142928	−	0.187422i
$127$	6.13569	−	7.31223i	0.544454	−	0.648856i	−0.421726	−	0.906723i	$-0.638575\pi$
$127$	6.13569	−	7.31223i	0.544454	−	0.648856i	0.966180	+	0.257868i	$0.0830199\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	0.410966	−	2.33070i	0.0361835	−	0.205207i
$130$	0.758633	+	4.30242i	0.0665365	+	0.377347i
$131$	−9.04151	−	10.7753i	−0.789961	−	0.941438i	0.209377	−	0.977835i	$-0.432856\pi$
$131$	−9.04151	−	10.7753i	−0.789961	−	0.941438i	−0.999337	+	0.0363967i	$0.988412\pi$
$132$	5.80164			0.504968
$133$	8.87699	+	7.36200i	0.769732	+	0.638367i
$134$	2.91935			0.252193
$135$	−1.50604	−	1.79483i	−0.129619	−	0.154474i
$136$	0.575166	+	3.26193i	0.0493201	+	0.279708i
$137$	1.79198	−	10.1628i	0.153099	−	0.868268i	−0.807404	−	0.589999i	$-0.799128\pi$
$137$	1.79198	−	10.1628i	0.153099	−	0.868268i	0.960503	−	0.278269i	$-0.0897607\pi$
$138$	−0.861621	+	0.151927i	−0.0733460	+	0.0129329i
$139$	7.71294	−	9.19193i	0.654203	−	0.779649i	−0.332338	−	0.943160i	$-0.607838\pi$
$139$	7.71294	−	9.19193i	0.654203	−	0.779649i	0.986541	+	0.163511i	$0.0522820\pi$
$140$	2.38930	−	5.71998i	0.201933	−	0.483426i
$141$	−0.453285	+	0.261704i	−0.0381734	+	0.0220394i
$142$	11.1167	−	4.04616i	0.932895	−	0.339546i
$143$	8.28701	+	6.95363i	0.692994	+	0.581491i
$144$	1.00000			0.0833333
$145$	−22.7567			−1.88984
$146$	3.48086	+	2.92079i	0.288078	+	0.241726i
$147$	−4.04916	+	5.71002i	−0.333969	+	0.470954i
$148$	1.99562	+	5.48292i	0.164039	+	0.450693i
$149$	15.3083	+	5.57177i	1.25411	+	0.456457i	0.881787	−	0.471648i	$-0.156341\pi$
$149$	15.3083	+	5.57177i	1.25411	+	0.456457i	0.372318	+	0.928105i	$0.378563\pi$
$150$	0.167437	−	0.460029i	0.0136712	−	0.0375612i
$151$	−5.48151	−	3.16475i	−0.446079	−	0.257544i	0.260094	−	0.965583i	$-0.416247\pi$
$151$	−5.48151	−	3.16475i	−0.446079	−	0.257544i	−0.706173	+	0.708039i	$0.749580\pi$
$152$	−4.24717	+	0.980592i	−0.344491	+	0.0795365i
$153$		−	3.31225i		−	0.267780i
$154$	−4.57207	−	14.6530i	−0.368428	−	1.18077i
$155$	13.6400	+	16.2555i	1.09559	+	1.30567i
$156$	1.42839	+	1.19856i	0.114363	+	0.0959618i
$157$	7.90694	+	9.42313i	0.631043	+	0.752048i	0.982927	−	0.183996i	$-0.0589034\pi$
$157$	7.90694	+	9.42313i	0.631043	+	0.752048i	−0.351884	+	0.936044i	$0.614459\pi$
$158$	5.22936	−	1.90333i	0.416025	−	0.151421i
$159$		−	9.65860i		−	0.765977i
$160$	1.17149	+	2.02908i	0.0926144	+	0.160413i
$161$	1.06273	+	2.05643i	0.0837548	+	0.162070i
$162$	−0.984808	−	0.173648i	−0.0773738	−	0.0136431i
$163$	−2.23061	+	3.86352i	−0.174715	+	0.302614i	−0.940062	−	0.341002i	$-0.889234\pi$
$163$	−2.23061	+	3.86352i	−0.174715	+	0.302614i	0.765348	+	0.643617i	$0.222567\pi$
$164$	6.03401	+	10.4512i	0.471177	+	0.816103i
$165$	−4.64912	−	12.7734i	−0.361934	−	0.994405i
$166$	−1.28994	−	7.31559i	−0.100118	−	0.567800i
$167$	−19.1138	+	6.95685i	−1.47907	+	0.538337i	−0.950547	−	0.310582i	$-0.899476\pi$
$167$	−19.1138	+	6.95685i	−1.47907	+	0.538337i	−0.528522	+	0.848919i	$0.677254\pi$
$168$	−0.788065	−	2.52566i	−0.0608006	−	0.194859i
$169$	−1.65368	−	9.37847i	−0.127206	−	0.721421i
$170$	6.72082	−	3.88027i	0.515463	−	0.297603i
$171$	4.35292	−	0.228182i	0.332876	−	0.0174495i
$172$	1.18333	−	2.04959i	0.0902280	−	0.156280i
$173$	−7.13482	+	5.98683i	−0.542451	+	0.455170i	−0.872375	−	0.488837i	$-0.837421\pi$
$173$	−7.13482	+	5.98683i	−0.542451	+	0.455170i	0.329924	+	0.944007i	$0.392977\pi$
$174$	−7.44037	+	6.24321i	−0.564053	+	0.473296i
$175$	−1.29383	−	0.0603556i	−0.0978043	−	0.00456245i
$176$	5.45176	+	1.98428i	0.410942	+	0.149571i
$177$	2.25401	−	12.7831i	0.169422	−	0.960838i
$178$	−2.97051	+	1.71502i	−0.222649	+	0.128547i
$179$			10.9969i			0.821945i	0.911648	+	0.410972i	$0.134811\pi$
$179$			10.9969i			0.821945i	−0.911648	+	0.410972i	$0.865189\pi$
$180$	−0.801346	−	2.20168i	−0.0597288	−	0.164104i
$181$	1.06791	−	6.05644i	0.0793774	−	0.450172i	−0.919051	−	0.394138i	$-0.871043\pi$
$181$	1.06791	−	6.05644i	0.0793774	−	0.450172i	0.998429	−	0.0560341i	$-0.0178456\pi$
$182$	1.90149	−	4.55217i	0.140948	−	0.337429i
$183$	4.06705	+	2.34811i	0.300645	+	0.173578i
$184$	−0.861621	−	0.151927i	−0.0635195	−	0.0112002i
$185$	10.4725	−	8.78744i	0.769951	−	0.646065i
$186$	8.91927	+	1.57271i	0.653992	+	0.115317i
$187$	6.57242	−	18.0576i	0.480623	−	1.32050i
$188$	−0.515456	+	0.0908888i	−0.0375935	+	0.00662875i
$189$	0.337517	+	2.62413i	0.0245507	+	0.190878i
$190$	5.56240	+	8.56511i	0.403539	+	0.621379i
$191$	−10.6424	−	18.4332i	−0.770057	−	1.33378i	−0.937531	−	0.347901i	$-0.886894\pi$
$191$	−10.6424	−	18.4332i	−0.770057	−	1.33378i	0.167474	−	0.985876i	$-0.446439\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	−4.92457	+	0.868335i	−0.354478	+	0.0625041i	−0.348052	−	0.937475i	$-0.613157\pi$
$193$	−4.92457	+	0.868335i	−0.354478	+	0.0625041i	−0.00642638	+	0.999979i	$0.502046\pi$
$194$	6.72370	−	8.01299i	0.482733	−	0.575299i
$195$	1.49422	−	4.10532i	0.107003	−	0.293988i
$196$	−5.75791	+	3.98077i	−0.411279	+	0.284341i
$197$	2.05725	−	3.56326i	0.146573	−	0.253872i	−0.783386	−	0.621536i	$-0.786509\pi$
$197$	2.05725	−	3.56326i	0.146573	−	0.253872i	0.929959	+	0.367664i	$0.119842\pi$
$198$	−5.02437	−	2.90082i	−0.357066	−	0.206152i
$199$	6.50983	−	7.75812i	0.461470	−	0.549958i	−0.484255	−	0.874927i	$-0.660909\pi$
$199$	6.50983	−	7.75812i	0.461470	−	0.549958i	0.945725	+	0.324969i	$0.105354\pi$
$200$	0.314679	−	0.375019i	0.0222511	−	0.0265179i
$201$	−2.52823	−	1.45967i	−0.178327	−	0.102957i
$202$	−5.12198	+	8.87153i	−0.360381	+	0.624198i
$203$	21.6317	+	13.8718i	1.51825	+	0.973607i
$204$	1.13286	−	3.11250i	0.0793158	−	0.217918i
$205$	18.1749	−	21.6600i	1.26939	−	1.51280i
$206$	4.31858	−	0.761482i	0.300890	−	0.0530550i
$207$	0.822149	+	0.299238i	0.0571433	+	0.0207985i
$208$	0.932316	+	1.61482i	0.0646445	+	0.111967i
$209$	24.1839	+	7.39342i	1.67283	+	0.511413i
$210$	−4.92918	+	3.75900i	−0.340146	+	0.259395i
$211$	20.6778	−	3.64605i	1.42352	−	0.251004i	0.591747	−	0.806124i	$-0.298439\pi$
$211$	20.6778	−	3.64605i	1.42352	−	0.251004i	0.831771	+	0.555120i	$0.187328\pi$
$212$	3.30344	−	9.07612i	0.226881	−	0.623350i
$213$	−11.6505	−	2.05429i	−0.798276	−	0.140758i
$214$	−12.3424	+	10.3565i	−0.843707	+	0.707954i
$215$	−5.46079	−	0.962885i	−0.372423	−	0.0656682i
$216$	−0.866025	−	0.500000i	−0.0589256	−	0.0340207i
$217$	−3.05684	−	23.7664i	−0.207512	−	1.61337i
$218$	1.59363	−	9.03791i	0.107934	−	0.612125i
$219$	−1.55412	−	4.26991i	−0.105018	−	0.288534i
$220$		−	13.5931i		−	0.916448i
$221$	5.34868	−	3.08806i	0.359791	−	0.207726i
$222$	1.01320	−	5.74616i	0.0680017	−	0.385657i
$223$	−10.8738	−	3.95773i	−0.728162	−	0.265029i	−0.0487753	−	0.998810i	$-0.515532\pi$
$223$	−10.8738	−	3.95773i	−0.728162	−	0.265029i	−0.679387	+	0.733781i	$0.737754\pi$
$224$	0.123287	−	2.64288i	0.00823747	−	0.176585i
$225$	−0.375019	+	0.314679i	−0.0250013	+	0.0209786i
$226$	2.36774	−	1.98677i	0.157500	−	0.132158i
$227$	−6.07468	+	10.5217i	−0.403191	+	0.698347i	−0.994109	−	0.108384i	$-0.965432\pi$
$227$	−6.07468	+	10.5217i	−0.403191	+	0.698347i	0.590918	+	0.806731i	$0.298766\pi$
$228$	4.16845	+	1.27437i	0.276062	+	0.0843970i
$229$	−5.41995	+	3.12921i	−0.358161	+	0.206784i	−0.668274	−	0.743916i	$-0.732966\pi$
$229$	−5.41995	+	3.12921i	−0.358161	+	0.206784i	0.310113	+	0.950700i	$0.399633\pi$
$230$	0.355962	+	2.01876i	0.0234714	+	0.133113i
$231$	−3.36695	+	14.9759i	−0.221529	+	0.985340i
$232$	−9.12696	+	3.32194i	−0.599214	+	0.218096i
$233$	3.34443	+	18.9672i	0.219101	+	1.24258i	0.873647	+	0.486561i	$0.161749\pi$
$233$	3.34443	+	18.9672i	0.219101	+	1.24258i	−0.654546	+	0.756023i	$0.727140\pi$
$234$	−0.637741	−	1.75218i	−0.0416905	−	0.114544i
$235$	0.613167	+	1.06204i	0.0399986	+	0.0692796i
$236$	6.49016	−	11.2413i	0.422473	−	0.731745i
$237$	−5.48042	−	0.966346i	−0.355992	−	0.0627709i
$238$	−8.75387	−	0.408358i	−0.567429	−	0.0264699i
$239$	0.116168	+	0.201209i	0.00751427	+	0.0130151i	0.869758	−	0.493478i	$-0.164275\pi$
$239$	0.116168	+	0.201209i	0.00751427	+	0.0130151i	−0.862244	+	0.506493i	$0.830941\pi$
$240$		−	2.34298i		−	0.151239i
$241$	12.9584	−	4.71647i	0.834723	−	0.303814i	0.110927	−	0.993829i	$-0.464618\pi$
$241$	12.9584	−	4.71647i	0.834723	−	0.303814i	0.723796	+	0.690014i	$0.242396\pi$
$242$	−14.5649	−	17.3578i	−0.936270	−	1.11580i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	3.01868	+	3.59752i	0.193251	+	0.230308i
$245$	13.3785	+	9.48710i	0.854718	+	0.606108i
$246$		−	12.0680i		−	0.769429i
$247$	4.42677	+	6.81644i	0.281669	+	0.433720i
$248$	7.84347	+	4.52843i	0.498061	+	0.287556i
$249$	−2.54068	+	6.98045i	−0.161009	+	0.442368i
$250$	9.93056	+	3.61443i	0.628064	+	0.228597i
$251$	−4.75074	−	13.0525i	−0.299864	−	0.823869i	−0.994522	−	0.104529i	$-0.966667\pi$
$251$	−4.75074	−	13.0525i	−0.299864	−	0.823869i	0.694658	−	0.719340i	$-0.255556\pi$
$252$	−0.580345	+	2.58132i	−0.0365583	+	0.162608i
$253$	3.88839	+	3.26274i	0.244461	+	0.205127i
$254$	−9.54544			−0.598934
$255$	−7.76053			−0.485983
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−23.7043	+	8.62767i	−1.47863	+	0.538179i	−0.950430	−	0.310938i	$-0.899357\pi$
$257$	−23.7043	+	8.62767i	−1.47863	+	0.538179i	−0.528205	+	0.849117i	$0.677135\pi$
$258$	−2.04959	+	1.18333i	−0.127602	+	0.0736709i
$259$	−15.3113	+	1.96934i	−0.951399	+	0.122369i
$260$	2.80821	−	3.34669i	0.174158	−	0.207553i
$261$	9.56515	−	1.68659i	0.592068	−	0.104398i
$262$	−2.44255	+	13.8524i	−0.150901	+	0.855804i
$263$	3.86408	+	21.9143i	0.238270	+	1.35129i	0.835618	+	0.549312i	$0.185110\pi$
$263$	3.86408	+	21.9143i	0.238270	+	1.35129i	−0.597348	+	0.801982i	$0.703779\pi$
$264$	−3.72922	−	4.44431i	−0.229518	−	0.273529i
$265$	−22.6299			−1.39014
$266$	−0.0663965	−	11.5324i	−0.00407103	−	0.707095i
$267$	3.43005			0.209916
$268$	−1.87652	−	2.23635i	−0.114627	−	0.136607i
$269$	1.63237	+	9.25764i	0.0995275	+	0.564448i	0.993266	+	0.115859i	$0.0369622\pi$
$269$	1.63237	+	9.25764i	0.0995275	+	0.564448i	−0.893738	+	0.448589i	$0.851927\pi$
$270$	−0.406854	+	2.30738i	−0.0247604	+	0.140423i
$271$	15.7549	−	2.77802i	0.957045	−	0.168753i	0.326752	−	0.945110i	$-0.394046\pi$
$271$	15.7549	−	2.77802i	0.957045	−	0.168753i	0.630293	+	0.776357i	$0.282935\pi$
$272$	2.12907	−	2.53733i	0.129094	−	0.153848i
$273$	−3.92283	+	2.99155i	−0.237420	+	0.181057i
$274$	−8.93703	+	5.15980i	−0.539906	+	0.311715i
$275$	−2.66893	+	0.971410i	−0.160942	+	0.0585782i
$276$	0.670222	+	0.562383i	0.0403426	+	0.0338515i
$277$	6.61648			0.397546			0.198773	−	0.980046i	$-0.436304\pi$
$277$	6.61648			0.397546			0.198773	+	0.980046i	$0.436304\pi$
$278$	−11.9992			−0.719665
$279$	−6.93796	−	5.82164i	−0.415365	−	0.348532i
$280$	−5.91757	+	1.84642i	−0.353642	+	0.110345i
$281$	4.38542	+	12.0489i	0.261612	+	0.718774i	0.999059	+	0.0433690i	$0.0138091\pi$
$281$	4.38542	+	12.0489i	0.261612	+	0.718774i	−0.737447	+	0.675405i	$0.763969\pi$
$282$	0.491843	+	0.179016i	0.0292888	+	0.0106602i
$283$	0.475063	−	1.30522i	0.0282396	−	0.0775876i	−0.924772	−	0.380522i	$-0.875744\pi$
$283$	0.475063	−	1.30522i	0.0282396	−	0.0775876i	0.953011	+	0.302935i	$0.0979664\pi$
$284$	−10.2452	−	5.91509i	−0.607943	−	0.350996i
$285$	−0.534625	−	10.1988i	−0.0316684	−	0.604125i
$286$		−	10.8179i		−	0.639677i
$287$	−30.4797	+	9.51039i	−1.79916	+	0.561380i
$288$	−0.642788	−	0.766044i	−0.0378766	−	0.0451396i
$289$	4.61848	+	3.87537i	0.271676	+	0.227963i
$290$	14.6277	+	17.4326i	0.858969	+	1.02368i
$291$	−9.82939	+	3.57760i	−0.576209	+	0.209723i
$292$		−	4.54394i		−	0.265914i
$293$	8.15121	+	14.1183i	0.476199	+	0.824800i	0.999628	−	0.0272687i	$-0.00868097\pi$
$293$	8.15121	+	14.1183i	0.476199	+	0.824800i	−0.523429	+	0.852069i	$0.675348\pi$
$294$	6.97688	−	0.568493i	0.406900	−	0.0331552i
$295$	−29.9506	−	5.28110i	−1.74379	−	0.307477i
$296$	2.91740	−	5.05309i	0.169571	−	0.293705i
$297$	2.90082	+	5.02437i	0.168323	+	0.291543i
$298$	−5.57177	−	15.3083i	−0.322764	−	0.886786i
$299$	0.283288	+	1.60661i	0.0163830	+	0.0929124i
$300$	−0.460029	+	0.167437i	−0.0265598	+	0.00966698i
$301$	4.60390	+	4.24402i	0.265364	+	0.244621i
$302$	1.09911	+	6.23335i	0.0632465	+	0.358689i
$303$	8.87153	−	5.12198i	0.509656	−	0.294250i
$304$	3.48120	+	2.62321i	0.199661	+	0.150451i
$305$	5.50158	−	9.52902i	0.315020	−	0.545630i
$306$	−2.53733	+	2.12907i	−0.145050	+	0.121711i
$307$	−13.1249	+	11.0131i	−0.749079	+	0.628552i	−0.935259	−	0.353964i	$-0.884834\pi$
$307$	−13.1249	+	11.0131i	−0.749079	+	0.628552i	0.186180	+	0.982516i	$0.440389\pi$
$308$	−8.28595	+	12.9212i	−0.472136	+	0.736251i
$309$	−4.12074	−	1.49983i	−0.234421	−	0.0853222i
$310$	3.68482	−	20.8977i	0.209284	−	1.18691i
$311$	15.1509	−	8.74737i	0.859128	−	0.496018i	−0.00459208	−	0.999989i	$-0.501462\pi$
$311$	15.1509	−	8.74737i	0.859128	−	0.496018i	0.863720	+	0.503972i	$0.168128\pi$
$312$		−	1.86463i		−	0.105564i
$313$	6.25396	+	17.1826i	0.353495	+	0.971218i	0.981238	+	0.192798i	$0.0617563\pi$
$313$	6.25396	+	17.1826i	0.353495	+	0.971218i	−0.627744	+	0.778420i	$0.716021\pi$
$314$	2.13605	−	12.1141i	0.120544	−	0.683641i
$315$	6.14829	−	0.790795i	0.346417	−	0.0445562i
$316$	−4.81940	−	2.78248i	−0.271113	−	0.156527i
$317$	7.91328	+	1.39532i	0.444454	+	0.0783693i	0.391396	−	0.920222i	$-0.371992\pi$
$317$	7.91328	+	1.39532i	0.444454	+	0.0783693i	0.0530578	+	0.998591i	$0.483103\pi$
$318$	−7.39892	+	6.20843i	−0.414911	+	0.348151i
$319$	55.4936	+	9.78501i	3.10704	+	0.547855i
$320$	0.801346	−	2.20168i	0.0447966	−	0.123078i
$321$	15.8670	−	2.79779i	0.885612	−	0.156157i
$322$	0.892209	−	2.13595i	0.0497209	−	0.119032i
$323$	8.68872	−	11.5306i	0.483453	−	0.641581i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−0.857785	−	0.312208i	−0.0475814	−	0.0173182i
$326$	4.39344	−	0.774681i	0.243330	−	0.0429056i
$327$	−5.89908	+	7.03025i	−0.326220	+	0.388774i
$328$	4.12751	−	11.3402i	0.227903	−	0.626159i
$329$	0.0645294	−	1.38330i	0.00355762	−	0.0762639i
$330$	−6.79656	+	11.7720i	−0.374138	+	0.648027i
$331$	1.36821	+	0.789935i	0.0752034	+	0.0434187i	0.537130	−	0.843499i	$-0.319508\pi$
$331$	1.36821	+	0.789935i	0.0752034	+	0.0434187i	−0.461927	+	0.886918i	$0.652842\pi$
$332$	−4.77491	+	5.69052i	−0.262057	+	0.312308i
$333$	−3.75054	+	4.46972i	−0.205528	+	0.244939i
$334$	17.6154	+	10.1702i	0.963870	+	0.556490i
$335$	−3.41998	+	5.92359i	−0.186854	+	0.323640i
$336$	−1.42821	+	2.22716i	−0.0779152	+	0.121501i
$337$	−12.0141	+	33.0086i	−0.654452	+	1.79809i	−0.0538428	+	0.998549i	$0.517147\pi$
$337$	−12.0141	+	33.0086i	−0.654452	+	1.79809i	−0.600609	+	0.799543i	$0.705075\pi$
$338$	−6.12136	+	7.29516i	−0.332958	+	0.396804i
$339$	−3.04391	+	0.536723i	−0.165322	+	0.0291508i
$340$	−7.29252	−	2.65426i	−0.395492	−	0.143947i
$341$	−26.2723	−	45.5050i	−1.42273	−	2.46423i
$342$	−2.97280	−	3.18786i	−0.160751	−	0.172380i
$343$	−6.93405	−	17.1732i	−0.374404	−	0.927266i
$344$	−2.33070	+	0.410966i	−0.125663	+	0.0221578i
$345$	0.701108	−	1.92628i	0.0377464	−	0.103707i
$346$	9.17235	+	1.61733i	0.493109	+	0.0869484i
$347$	26.1736	−	21.9622i	1.40507	−	1.17899i	0.446276	−	0.894895i	$-0.352750\pi$
$347$	26.1736	−	21.9622i	1.40507	−	1.17899i	0.958795	−	0.284099i	$-0.0916945\pi$
$348$	9.56515	+	1.68659i	0.512746	+	0.0904109i
$349$	−30.6289	−	17.6836i	−1.63953	−	0.946582i	−0.980996	−	0.194028i	$-0.937845\pi$
$349$	−30.6289	−	17.6836i	−1.63953	−	0.946582i	−0.658531	−	0.752553i	$-0.728822\pi$
$350$	0.785422	+	1.02993i	0.0419826	+	0.0550519i
$351$	−0.323790	+	1.83630i	−0.0172826	+	0.0980146i
$352$	−1.98428	−	5.45176i	−0.105762	−	0.290580i
$353$			8.25172i			0.439195i	0.975591	+	0.219597i	$0.0704744\pi$
$353$			8.25172i			0.439195i	−0.975591	+	0.219597i	$0.929526\pi$
$354$	−11.2413	+	6.49016i	−0.597468	+	0.344948i
$355$	−4.81316	+	27.2968i	−0.255456	+	1.44876i
$356$	3.22319	+	1.17315i	0.170829	+	0.0621766i
$357$	7.37689	+	4.73058i	0.390427	+	0.250369i
$358$	8.42409	−	7.06865i	0.445227	−	0.373590i
$359$	−18.1634	+	15.2409i	−0.958629	+	0.804385i	−0.980729	−	0.195371i	$-0.937409\pi$
$359$	−18.1634	+	15.2409i	−0.958629	+	0.804385i	0.0221007	+	0.999756i	$0.492965\pi$
$360$	−1.17149	+	2.02908i	−0.0617429	+	0.106942i
$361$	15.7520	+	10.6243i	0.829052	+	0.559172i
$362$	−5.32595	+	3.07494i	−0.279925	+	0.161615i
$363$	3.93470	+	22.3148i	0.206518	+	1.17122i
$364$	−4.70942	+	1.46945i	−0.246841	+	0.0770202i
$365$	−10.0043	+	3.64127i	−0.523649	+	0.190593i
$366$	−0.815492	−	4.62488i	−0.0426264	−	0.241747i
$367$	3.30390	+	9.07739i	0.172462	+	0.473836i	0.995567	−	0.0940533i	$-0.0299824\pi$
$367$	3.30390	+	9.07739i	0.172462	+	0.473836i	−0.823105	+	0.567889i	$0.807760\pi$
$368$	0.437456	+	0.757697i	0.0228040	+	0.0394977i
$369$	−6.03401	+	10.4512i	−0.314118	+	0.544068i
$370$	−13.4631	−	2.37391i	−0.699915	−	0.123414i
$371$	21.5112	+	13.7945i	1.11681	+	0.716174i
$372$	−4.52843	−	7.84347i	−0.234788	−	0.406665i
$373$		−	36.0122i		−	1.86464i	−0.361633	−	0.932320i	$-0.617781\pi$
$373$		−	36.0122i		−	1.86464i	0.361633	−	0.932320i	$-0.382219\pi$
$374$	−18.0576	+	6.57242i	−0.933736	+	0.339852i
$375$	−6.79291	−	8.09547i	−0.350784	−	0.418048i
$376$	0.400954	+	0.336440i	0.0206776	+	0.0173506i
$377$	11.6413	+	13.8735i	0.599556	+	0.714524i
$378$	1.79325	−	1.94531i	0.0922349	−	0.100056i
$379$			29.6395i			1.52248i	0.648470	+	0.761241i	$0.275409\pi$
$379$			29.6395i			1.52248i	−0.648470	+	0.761241i	$0.724591\pi$
$380$	2.98582	−	9.76660i	0.153169	−	0.501016i
$381$	8.26659	+	4.77272i	0.423510	+	0.244514i
$382$	−7.27983	+	20.0012i	−0.372468	+	1.02335i
$383$	−13.4545	−	4.89703i	−0.687492	−	0.250227i	−0.0254312	−	0.999677i	$-0.508096\pi$
$383$	−13.4545	−	4.89703i	−0.687492	−	0.250227i	−0.662061	+	0.749450i	$0.730318\pi$
$384$	−0.342020	−	0.939693i	−0.0174536	−	0.0479535i
$385$	35.0882	+	7.88870i	1.78826	+	0.402045i
$386$	3.83064	+	3.21428i	0.194974	+	0.163603i
$387$	2.36666			0.120304
$388$	−10.4602			−0.531037
$389$	6.86200	+	5.75790i	0.347917	+	0.291937i	0.799953	−	0.600062i	$-0.204858\pi$
$389$	6.86200	+	5.75790i	0.347917	+	0.291937i	−0.452036	+	0.892000i	$0.649302\pi$
$390$	−4.10532	+	1.49422i	−0.207881	+	0.0756625i
$391$	2.50968	−	1.44896i	0.126920	−	0.0732773i
$392$	6.75056	+	1.85202i	0.340955	+	0.0935413i
$393$	9.04151	−	10.7753i	0.456084	−	0.543540i
$394$	−4.05199	+	0.714475i	−0.204136	+	0.0359947i
$395$	−2.26413	+	12.8405i	−0.113921	+	0.646076i
$396$	1.00744	+	5.71350i	0.0506260	+	0.287114i
$397$	−15.4336	−	18.3931i	−0.774592	−	0.923122i	0.224084	−	0.974570i	$-0.428061\pi$
$397$	−15.4336	−	18.3931i	−0.774592	−	0.923122i	−0.998676	+	0.0514475i	$0.983617\pi$
$398$	−10.1275			−0.507646
$399$	−5.70868	+	10.0205i	−0.285792	+	0.501654i
$400$	−0.489553			−0.0244777
$401$	−20.3408	−	24.2412i	−1.01577	−	1.21055i	−0.977425	−	0.211282i	$-0.932236\pi$
$401$	−20.3408	−	24.2412i	−1.01577	−	1.21055i	−0.0383442	−	0.999265i	$-0.512208\pi$
$402$	0.506939	+	2.87499i	0.0252838	+	0.143392i
$403$	2.93252	−	16.6311i	0.146079	−	0.828456i
$404$	10.0883	−	1.77884i	0.501913	−	0.0885008i
$405$	1.50604	−	1.79483i	0.0748356	−	0.0891856i
$406$	−3.27820	−	25.4874i	−0.162694	−	1.26492i
$407$	−29.3162	+	16.9257i	−1.45315	+	0.838977i
$408$	−3.11250	+	1.13286i	−0.154092	+	0.0560847i
$409$	−21.1674	−	17.7615i	−1.04666	−	0.878252i	−0.0539210	−	0.998545i	$-0.517172\pi$
$409$	−21.1674	−	17.7615i	−1.04666	−	0.878252i	−0.992738	+	0.120294i	$0.961616\pi$
$410$	−28.2751			−1.39641
$411$	10.3196			0.509028
$412$	−3.35926	−	2.81875i	−0.165499	−	0.138870i
$413$	25.2508	+	23.2770i	1.24251	+	1.14539i
$414$	−0.299238	−	0.822149i	−0.0147067	−	0.0404064i
$415$	16.3551	+	5.95276i	0.802838	+	0.292209i
$416$	0.637741	−	1.75218i	0.0312678	−	0.0859077i
$417$	10.3916	+	5.99960i	0.508880	+	0.293802i
$418$	−9.88140	−	23.2783i	−0.483315	−	1.13858i
$419$		−	1.32934i		−	0.0649426i	−0.999473	−	0.0324713i	$-0.989662\pi$
$419$		−	1.32934i		−	0.0649426i	0.999473	−	0.0324713i	$-0.0103378\pi$
$420$	6.04797	+	1.35974i	0.295111	+	0.0663483i
$421$	−9.63134	−	11.4782i	−0.469403	−	0.559413i	0.478452	−	0.878113i	$-0.341198\pi$
$421$	−9.63134	−	11.4782i	−0.469403	−	0.559413i	−0.947855	+	0.318701i	$0.896753\pi$
$422$	−16.0845	−	13.4965i	−0.782979	−	0.656998i
$423$	−0.336440	−	0.400954i	−0.0163583	−	0.0194950i
$424$	−9.07612	+	3.30344i	−0.440775	+	0.160429i
$425$			1.62152i			0.0786554i
$426$	5.91509	+	10.2452i	0.286587	+	0.496383i
$427$	−11.0382	+	5.70436i	−0.534177	+	0.276054i
$428$	15.8670	+	2.79779i	0.766963	+	0.135236i
$429$	−5.40896	+	9.36859i	−0.261147	+	0.452320i
$430$	2.77252	+	4.80214i	0.133703	+	0.231580i
$431$	−7.65205	−	21.0238i	−0.368586	−	1.01268i	−0.975900	−	0.218220i	$-0.929975\pi$
$431$	−7.65205	−	21.0238i	−0.368586	−	1.01268i	0.607313	−	0.794463i	$-0.292247\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	−35.9741	+	13.0935i	−1.72880	+	0.629233i	−0.998544	−	0.0539371i	$-0.982823\pi$
$433$	−35.9741	+	13.0935i	−1.72880	+	0.629233i	−0.730259	+	0.683170i	$0.760601\pi$
$434$	−16.2412	+	17.6184i	−0.779604	+	0.845712i
$435$	−3.95165	−	22.4109i	−0.189467	−	1.07452i
$436$	−7.94781	+	4.58867i	−0.380631	+	0.219757i
$437$	2.07711	+	3.19838i	0.0993615	+	0.152999i
$438$	−2.27197	+	3.93517i	−0.108559	+	0.188030i
$439$	−12.8139	+	10.7521i	−0.611573	+	0.513171i	−0.895142	−	0.445781i	$-0.852926\pi$
$439$	−12.8139	+	10.7521i	−0.611573	+	0.513171i	0.283569	+	0.958952i	$0.408482\pi$
$440$	−10.4129	+	8.73749i	−0.496417	+	0.416544i
$441$	−6.32640	−	2.99611i	−0.301257	−	0.142672i
$442$	−5.80366	−	2.11236i	−0.276052	−	0.100475i
$443$	−3.57563	+	20.2784i	−0.169883	+	0.963456i	0.774002	+	0.633183i	$0.218252\pi$
$443$	−3.57563	+	20.2784i	−0.169883	+	0.963456i	−0.943885	+	0.330273i	$0.892859\pi$
$444$	−5.05309	+	2.91740i	−0.239809	+	0.138454i
$445$		−	8.03653i		−	0.380968i
$446$	3.95773	+	10.8738i	0.187404	+	0.514888i
$447$	−2.82886	+	16.0433i	−0.133801	+	0.758820i
$448$	−2.10381	+	1.60437i	−0.0993956	+	0.0757991i
$449$	−13.9395	−	8.04796i	−0.657845	−	0.379807i	0.133610	−	0.991034i	$-0.457343\pi$
$449$	−13.9395	−	8.04796i	−0.657845	−	0.379807i	−0.791455	+	0.611227i	$0.790676\pi$
$450$	0.482116	+	0.0850100i	0.0227272	+	0.00400741i
$451$	−53.6341	+	45.0043i	−2.52553	+	2.11917i
$452$	−3.04391	−	0.536723i	−0.143173	−	0.0252453i
$453$	2.16482	−	5.94779i	0.101712	−	0.279451i
$454$	11.9648	−	2.10972i	0.561535	−	0.0990138i
$455$	7.00914	+	9.19111i	0.328594	+	0.430886i
$456$	−1.70321	−	4.01237i	−0.0797600	−	0.187896i
$457$	−17.8063	−	30.8413i	−0.832941	−	1.44270i	−0.895696	−	0.444668i	$-0.853322\pi$
$457$	−17.8063	−	30.8413i	−0.832941	−	1.44270i	0.0627544	−	0.998029i	$-0.480012\pi$
$458$	5.88099	+	2.14051i	0.274801	+	0.100019i
$459$	3.26193	−	0.575166i	0.152254	−	0.0268465i
$460$	1.31765	−	1.57032i	0.0614358	−	0.0732164i
$461$	1.11075	−	3.05175i	0.0517327	−	0.142134i	−0.911135	−	0.412108i	$-0.864793\pi$
$461$	1.11075	−	3.05175i	0.0517327	−	0.142134i	0.962868	+	0.269973i	$0.0870149\pi$
$462$	13.6364	−	7.04707i	0.634424	−	0.327859i
$463$	−1.51502	+	2.62409i	−0.0704089	+	0.121952i	−0.899081	−	0.437783i	$-0.855764\pi$
$463$	−1.51502	+	2.62409i	−0.0704089	+	0.121952i	0.828672	+	0.559735i	$0.189097\pi$
$464$	8.41145	+	4.85635i	0.390492	+	0.225451i
$465$	−13.6400	+	16.2555i	−0.632539	+	0.753830i
$466$	12.3800	−	14.7539i	0.573491	−	0.683460i
$467$	−0.383934	−	0.221665i	−0.0177664	−	0.0102574i	0.491091	−	0.871109i	$-0.336598\pi$
$467$	−0.383934	−	0.221665i	−0.0177664	−	0.0102574i	−0.508857	+	0.860851i	$0.669932\pi$
$468$	−0.932316	+	1.61482i	−0.0430963	+	0.0746450i
$469$	6.86176	−	3.54604i	0.316846	−	0.163741i
$470$	0.419431	−	1.15238i	0.0193469	−	0.0531552i
$471$	−7.90694	+	9.42313i	−0.364333	+	0.434195i
$472$	−12.7831	+	2.25401i	−0.588391	+	0.103749i
$473$	12.9025	+	4.69611i	0.593256	+	0.215927i
$474$	2.78248	+	4.81940i	0.127804	+	0.221362i
$475$	−2.13099	+	0.111707i	−0.0977764	+	0.00512547i
$476$	5.31406	+	6.96834i	0.243569	+	0.319393i
$477$	9.51187	−	1.67720i	0.435518	−	0.0767936i
$478$	0.0794635	−	0.218324i	0.00363457	−	0.00998591i
$479$	−32.3799	−	5.70945i	−1.47948	−	0.260872i	−0.625107	−	0.780539i	$-0.714945\pi$
$479$	−32.3799	−	5.70945i	−1.47948	−	0.260872i	−0.854369	+	0.519667i	$0.826056\pi$
$480$	−1.79483	+	1.50604i	−0.0819222	+	0.0687409i
$481$	−10.7145	−	1.88925i	−0.488538	−	0.0861424i
$482$	−11.9425	−	6.89502i	−0.543967	−	0.314059i
$483$	−1.84065	+	1.40368i	−0.0837524	+	0.0638696i
$484$	−3.93470	+	22.3148i	−0.178850	+	1.01431i
$485$	8.38225	+	23.0301i	0.380619	+	1.04574i
$486$		−	1.00000i		−	0.0453609i
$487$	2.25070	−	1.29945i	0.101989	−	0.0588835i	−0.448138	−	0.893964i	$-0.647913\pi$
$487$	2.25070	−	1.29945i	0.101989	−	0.0588835i	0.550127	+	0.835081i	$0.314579\pi$
$488$	0.815492	−	4.62488i	0.0369156	−	0.209359i
$489$	−4.19217	−	1.52582i	−0.189576	−	0.0690002i
$490$	−1.33197	−	16.3467i	−0.0601722	−	0.738468i
$491$	13.3276	−	11.1832i	0.601468	−	0.504692i	−0.290449	−	0.956890i	$-0.593805\pi$
$491$	13.3276	−	11.1832i	0.601468	−	0.504692i	0.891917	+	0.452199i	$0.149360\pi$
$492$	−9.24464	+	7.75717i	−0.416781	+	0.349720i
$493$	16.0855	−	27.8608i	0.724452	−	1.25479i
$494$	2.37622	−	7.77263i	0.106911	−	0.349707i
$495$	11.7720	−	6.79656i	0.529112	−	0.305483i
$496$	−1.57271	−	8.91927i	−0.0706166	−	0.400487i
$497$	21.2145	−	23.0134i	0.951600	−	1.03229i
$498$	6.98045	−	2.54068i	0.312802	−	0.113850i
$499$	2.44652	+	13.8749i	0.109521	+	0.621127i	0.989318	+	0.145776i	$0.0465678\pi$
$499$	2.44652	+	13.8749i	0.109521	+	0.621127i	−0.879796	+	0.475351i	$0.842321\pi$
$500$	−3.61443	−	9.93056i	−0.161642	−	0.444108i
$501$	−10.1702	−	17.6154i	−0.454372	−	0.786996i
$502$	−6.94511	+	12.0293i	−0.309975	+	0.536893i
$503$	−24.8867	−	4.38819i	−1.10964	−	0.195660i	−0.411353	−	0.911476i	$-0.634944\pi$
$503$	−24.8867	−	4.38819i	−1.10964	−	0.195660i	−0.698289	+	0.715816i	$0.746055\pi$
$504$	2.35044	−	1.21467i	0.104697	−	0.0541057i
$505$	−12.0007	−	20.7858i	−0.534024	−	0.924956i
$506$		−	5.07593i		−	0.225653i
$507$	8.94883	−	3.25711i	0.397432	−	0.144653i
$508$	6.13569	+	7.31223i	0.272227	+	0.324428i
$509$	8.44952	+	7.08999i	0.374518	+	0.314258i	0.810546	−	0.585675i	$-0.199171\pi$
$509$	8.44952	+	7.08999i	0.374518	+	0.314258i	−0.436027	+	0.899933i	$0.643615\pi$
$510$	4.98837	+	5.94491i	0.220889	+	0.263245i
$511$	11.7294	+	2.63705i	0.518876	+	0.116656i
$512$		−	1.00000i		−	0.0441942i
$513$	0.980592	+	4.24717i	0.0432942	+	0.187517i
$514$	21.8460	+	12.6128i	0.963587	+	0.556327i
$515$	−3.51406	+	9.65481i	−0.154848	+	0.425442i
$516$	2.22393	+	0.809445i	0.0979032	+	0.0356338i
$517$	−1.03859	−	2.85349i	−0.0456770	−	0.125497i
$518$	11.3505	+	10.4633i	0.498713	+	0.459730i
$519$	−7.13482	−	5.98683i	−0.313184	−	0.262793i
$520$	−4.36879			−0.191584
$521$	22.1171			0.968967			0.484483	−	0.874800i	$-0.339008\pi$
$521$	22.1171			0.968967			0.484483	+	0.874800i	$0.339008\pi$
$522$	−7.44037	−	6.24321i	−0.325656	−	0.273258i
$523$	2.59152	−	0.943237i	0.113319	−	0.0412449i	−0.284738	−	0.958605i	$-0.591907\pi$
$523$	2.59152	−	0.943237i	0.113319	−	0.0412449i	0.398058	+	0.917360i	$0.369684\pi$
$524$	12.1816	−	7.03305i	0.532156	−	0.307240i
$525$	−0.165232	−	1.28465i	−0.00721133	−	0.0560669i
$526$	14.3035	−	17.0463i	0.623664	−	0.743254i
$527$	−29.5428	+	5.20920i	−1.28691	+	0.226916i
$528$	−1.00744	+	5.71350i	−0.0438434	+	0.248648i
$529$	−3.86099	−	21.8967i	−0.167869	−	0.952032i
$530$	14.5462	+	17.3355i	0.631848	+	0.753007i
$531$	12.9803			0.563298
$532$	−8.79163	+	7.46373i	−0.381166	+	0.323594i
$533$	−22.5024			−0.974688
$534$	−2.20479	−	2.62757i	−0.0954107	−	0.113706i
$535$	−6.55516	−	37.1762i	−0.283404	−	1.60727i
$536$	−0.506939	+	2.87499i	−0.0218964	+	0.124181i
$537$	−10.8298	+	1.90959i	−0.467341	+	0.0824048i
$538$	6.04250	−	7.20117i	0.260511	−	0.310464i
$539$	−28.5449	−	28.8874i	−1.22952	−	1.24427i
$540$	2.02908	−	1.17149i	0.0873177	−	0.0504129i
$541$	−5.81210	+	2.11543i	−0.249882	+	0.0909495i	−0.463924	−	0.885875i	$-0.653559\pi$
$541$	−5.81210	+	2.11543i	−0.249882	+	0.0909495i	0.214043	+	0.976824i	$0.431337\pi$
$542$	−12.2552	−	10.2833i	−0.526405	−	0.441706i
$543$	6.14987			0.263916
$544$	−3.31225			−0.142012
$545$	16.4717	+	13.8214i	0.705571	+	0.592045i
$546$	4.81321	+	1.08213i	0.205986	+	0.0463109i
$547$	3.89604	+	10.7043i	0.166582	+	0.457682i	0.994694	−	0.102883i	$-0.0328066\pi$
$547$	3.89604	+	10.7043i	0.166582	+	0.457682i	−0.828111	+	0.560564i	$0.810584\pi$
$548$	9.69725	+	3.52951i	0.414246	+	0.150773i
$549$	−1.60621	+	4.41301i	−0.0685512	+	0.188343i
$550$	2.45970	+	1.42011i	0.104882	+	0.0605535i
$551$	37.7225	+	19.2200i	1.60703	+	0.818799i
$552$		−	0.874913i		−	0.0372388i
$553$	9.97939	−	10.8256i	0.424367	−	0.460352i
$554$	−4.25299	−	5.06852i	−0.180692	−	0.215341i
$555$	10.4725	+	8.78744i	0.444531	+	0.373006i
$556$	7.71294	+	9.19193i	0.327102	+	0.389825i
$557$	−11.0985	+	4.03954i	−0.470260	+	0.171161i	−0.566270	−	0.824220i	$-0.691614\pi$
$557$	−11.0985	+	4.03954i	−0.470260	+	0.171161i	0.0960100	+	0.995380i	$0.469392\pi$
$558$			9.05686i			0.383408i
$559$	2.20647	+	3.82172i	0.0933239	+	0.161642i
$560$	5.21818	+	3.34626i	0.220508	+	0.141405i
$561$	18.9245	+	3.33691i	0.798995	+	0.140884i
$562$	6.41106	−	11.1043i	0.270434	−	0.468406i
$563$	−17.8036	−	30.8367i	−0.750332	−	1.29961i	−0.947662	−	0.319275i	$-0.896561\pi$
$563$	−17.8036	−	30.8367i	−0.750332	−	1.29961i	0.197330	−	0.980337i	$-0.436773\pi$
$564$	−0.179016	−	0.491843i	−0.00753793	−	0.0207103i
$565$	1.25753	+	7.13181i	0.0529047	+	0.300038i
$566$	−1.30522	+	0.475063i	−0.0548627	+	0.0199684i
$567$	−2.52566	+	0.788065i	−0.106068	+	0.0330956i
$568$	2.05429	+	11.6505i	0.0861960	+	0.488842i
$569$	3.91379	−	2.25963i	0.164075	−	0.0947285i	−0.415714	−	0.909495i	$-0.636468\pi$
$569$	3.91379	−	2.25963i	0.164075	−	0.0947285i	0.579789	+	0.814767i	$0.303135\pi$
$570$	−7.46909	+	6.96521i	−0.312846	+	0.291741i
$571$	−9.68350	+	16.7723i	−0.405242	+	0.701899i	−0.994350	−	0.106155i	$-0.966146\pi$
$571$	−9.68350	+	16.7723i	−0.405242	+	0.701899i	0.589108	+	0.808054i	$0.299479\pi$
$572$	−8.28701	+	6.95363i	−0.346497	+	0.290746i
$573$	16.3051	−	13.6816i	0.681155	−	0.571557i
$574$	26.8774	+	17.2356i	1.12184	+	0.719402i
$575$	−0.402486	−	0.146493i	−0.0167848	−	0.00610917i
$576$	−0.173648	+	0.984808i	−0.00723534	+	0.0410337i
$577$	18.8488	−	10.8823i	0.784685	−	0.453038i	−0.0534032	−	0.998573i	$-0.517007\pi$
$577$	18.8488	−	10.8823i	0.784685	−	0.453038i	0.838088	+	0.545535i	$0.183674\pi$
$578$		−	6.02900i		−	0.250773i
$579$	−1.71029	−	4.69897i	−0.0710770	−	0.195283i
$580$	3.95165	−	22.4109i	0.164084	−	0.930564i
$581$	−11.9179	−	15.6280i	−0.494439	−	0.648360i
$582$	9.05881	+	5.23011i	0.375500	+	0.216795i
$583$	55.1844	+	9.73050i	2.28551	+	0.402996i
$584$	−3.48086	+	2.92079i	−0.144039	+	0.120863i
$585$	4.30242	+	0.758633i	0.177883	+	0.0313656i
$586$	5.57575	−	15.3193i	0.230332	−	0.632833i
$587$	10.8793	−	1.91831i	0.449036	−	0.0791772i	0.0554428	−	0.998462i	$-0.482343\pi$
$587$	10.8793	−	1.91831i	0.449036	−	0.0791772i	0.393593	+	0.919285i	$0.371232\pi$
$588$	−4.92014	−	4.97918i	−0.202903	−	0.205338i
$589$	−8.88109	−	38.4660i	−0.365939	−	1.58496i
$590$	15.2063	+	26.3381i	0.626034	+	1.08432i
$591$	3.86636	+	1.40724i	0.159041	+	0.0578862i
$592$	−5.74616	+	1.01320i	−0.236166	+	0.0416424i
$593$	0.401554	−	0.478554i	0.0164899	−	0.0196519i	−0.757736	−	0.652561i	$-0.773695\pi$
$593$	0.401554	−	0.478554i	0.0164899	−	0.0196519i	0.774226	+	0.632909i	$0.218139\pi$
$594$	1.98428	−	5.45176i	0.0814159	−	0.223688i
$595$	11.0837	−	17.2839i	0.454386	−	0.708571i
$596$	−8.14538	+	14.1082i	−0.333648	+	0.577895i
$597$	8.77068	+	5.06375i	0.358960	+	0.207246i
$598$	1.04864	−	1.24972i	0.0428820	−	0.0511047i
$599$	13.5019	−	16.0910i	0.551674	−	0.657459i	−0.416089	−	0.909324i	$-0.636599\pi$
$599$	13.5019	−	16.0910i	0.551674	−	0.657459i	0.967762	+	0.251865i	$0.0810439\pi$
$600$	0.423965	+	0.244777i	0.0173083	+	0.00999296i
$601$	−0.777212	+	1.34617i	−0.0317032	+	0.0549115i	−0.881442	−	0.472293i	$-0.843426\pi$
$601$	−0.777212	+	1.34617i	−0.0317032	+	0.0549115i	0.849739	+	0.527204i	$0.176760\pi$
$602$	0.291779	−	6.25479i	0.0118920	−	0.254926i
$603$	0.998475	−	2.74329i	0.0406611	−	0.111715i
$604$	4.06853	−	4.84868i	0.165546	−	0.197290i
$605$	52.2831	−	9.21892i	2.12561	−	0.374803i
$606$	−9.62617	−	3.50364i	−0.391036	−	0.142326i
$607$	−10.9263	−	18.9248i	−0.443483	−	0.768135i	0.554462	−	0.832209i	$-0.312924\pi$
$607$	−10.9263	−	18.9248i	−0.443483	−	0.768135i	−0.997945	+	0.0640737i	$0.979591\pi$
$608$	−0.228182	−	4.35292i	−0.00925398	−	0.176534i
$609$	−9.90472	+	23.7119i	−0.401359	+	0.960854i
$610$	−10.8360	+	1.91068i	−0.438737	+	0.0773612i
$611$	0.333799	−	0.917105i	0.0135041	−	0.0371021i
$612$	3.26193	+	0.575166i	0.131856	+	0.0232497i
$613$	−19.6733	+	16.5079i	−0.794597	+	0.666746i	−0.946879	−	0.321591i	$-0.895782\pi$
$613$	−19.6733	+	16.5079i	−0.794597	+	0.666746i	0.152282	+	0.988337i	$0.451338\pi$
$614$	16.8731	+	2.97518i	0.680942	+	0.120068i
$615$	24.4870	+	14.1376i	0.987410	+	0.570082i
$616$	15.2243	−	1.95815i	0.613404	−	0.0788961i
$617$	6.70601	−	38.0317i	0.269974	−	1.53110i	−0.484514	−	0.874783i	$-0.661004\pi$
$617$	6.70601	−	38.0317i	0.269974	−	1.53110i	0.754488	−	0.656314i	$-0.227885\pi$
$618$	1.49983	+	4.12074i	0.0603319	+	0.165760i
$619$		−	23.2455i		−	0.934317i	−0.884174	−	0.467158i	$-0.845278\pi$
$619$		−	23.2455i		−	0.934317i	0.884174	−	0.467158i	$-0.154722\pi$
$620$	−18.3771	+	10.6100i	−0.738042	+	0.426109i
$621$	−0.151927	+	0.861621i	−0.00609662	+	0.0345757i
$622$	−16.4397	−	5.98355i	−0.659171	−	0.239919i
$623$	−4.89882	+	7.63925i	−0.196267	+	0.306060i
$624$	−1.42839	+	1.19856i	−0.0571814	+	0.0479809i
$625$	−20.8426	+	17.4890i	−0.833705	+	0.699561i
$626$	9.14267	−	15.8356i	0.365415	−	0.632917i
$627$	−3.08161	+	25.1003i	−0.123068	+	1.00241i
$628$	−10.6530	+	6.15051i	−0.425101	+	0.245432i
$629$	3.35598	+	19.0327i	0.133812	+	0.758884i
$630$	−4.55783	−	4.20155i	−0.181588	−	0.167394i
$631$	23.0184	−	8.37802i	0.916349	−	0.333524i	0.159564	−	0.987188i	$-0.448991\pi$
$631$	23.0184	−	8.37802i	0.916349	−	0.333524i	0.756785	+	0.653664i	$0.226769\pi$
$632$	0.966346	+	5.48042i	0.0384392	+	0.217999i
$633$	7.18132	+	19.7305i	0.285432	+	0.784217i
$634$	−4.01768	−	6.95882i	−0.159562	−	0.276370i
$635$	11.1824	−	19.3685i	0.443759	−	0.768614i
$636$	9.51187	+	1.67720i	0.377170	+	0.0665052i
$637$	−1.06003	−	13.0093i	−0.0419999	−	0.515447i
$638$	−28.1748	−	48.8002i	−1.11545	−	1.93202i
$639$		−	11.8302i		−	0.467995i
$640$	−2.20168	+	0.801346i	−0.0870291	+	0.0316760i
$641$	7.99028	+	9.52244i	0.315597	+	0.376114i	0.900401	−	0.435061i	$-0.143273\pi$
$641$	7.99028	+	9.52244i	0.315597	+	0.376114i	−0.584804	+	0.811175i	$0.698829\pi$
$642$	−12.3424	−	10.3565i	−0.487115	−	0.408738i
$643$	−17.0689	−	20.3419i	−0.673132	−	0.802207i	0.316075	−	0.948734i	$-0.397635\pi$
$643$	−17.0689	−	20.3419i	−0.673132	−	0.802207i	−0.989207	+	0.146527i	$0.953190\pi$
$644$	−2.20973	+	0.689488i	−0.0870756	+	0.0271696i
$645$		−	5.54503i		−	0.218336i
$646$	−14.4180	+	0.755794i	−0.567267	+	0.0297363i
$647$	20.5434	+	11.8607i	0.807643	+	0.466293i	0.846137	−	0.532966i	$-0.178923\pi$
$647$	20.5434	+	11.8607i	0.807643	+	0.466293i	−0.0384936	+	0.999259i	$0.512256\pi$
$648$	0.342020	−	0.939693i	0.0134358	−	0.0369146i
$649$	70.7656	+	25.7566i	2.77779	+	1.01103i
$650$	0.312208	+	0.857785i	0.0122458	+	0.0336451i
$651$	22.8745	−	7.13740i	0.896524	−	0.279737i
$652$	−3.41749	−	2.86761i	−0.133839	−	0.112304i
$653$	−45.5137			−1.78109			−0.890544	−	0.454898i	$-0.849676\pi$
$653$	−45.5137			−1.78109			−0.890544	+	0.454898i	$0.849676\pi$
$654$	9.17734			0.358862
$655$	−25.2462	−	21.1841i	−0.986451	−	0.827730i
$656$	−11.3402	+	4.12751i	−0.442762	+	0.161152i
$657$	3.93517	−	2.27197i	0.153526	−	0.0886380i
$658$	−1.10115	+	0.839737i	−0.0429273	+	0.0327364i
$659$	13.4754	−	16.0594i	0.524928	−	0.625585i	−0.436811	−	0.899554i	$-0.643892\pi$
$659$	13.4754	−	16.0594i	0.524928	−	0.625585i	0.961739	+	0.273969i	$0.0883364\pi$
$660$	13.3866	−	2.36042i	0.521073	−	0.0918793i
$661$	−5.43718	+	30.8358i	−0.211482	+	1.19937i	0.675426	+	0.737428i	$0.263960\pi$
$661$	−5.43718	+	30.8358i	−0.211482	+	1.19937i	−0.886908	+	0.461946i	$0.847151\pi$
$662$	−0.274341	−	1.55587i	−0.0106626	−	0.0604705i
$663$	3.96994	+	4.73119i	0.154180	+	0.183744i
$664$	7.42844			0.288280
$665$	23.4779	+	13.3753i	0.910433	+	0.518673i
$666$	5.83480			0.226094
$667$	5.46226	+	6.50967i	0.211500	+	0.252055i
$668$	−3.53208	−	20.0314i	−0.136660	−	0.775040i
$669$	2.00939	−	11.3958i	0.0776876	−	0.440588i
$670$	6.73605	−	1.18775i	0.260236	−	0.0458867i
$671$	−17.5133	+	20.8715i	−0.676093	+	0.805736i
$672$	2.62413	−	0.337517i	0.101228	−	0.0130200i
$673$	−37.4247	+	21.6072i	−1.44262	+	0.832895i	−0.998024	−	0.0628386i	$-0.979985\pi$
$673$	−37.4247	+	21.6072i	−1.44262	+	0.832895i	−0.444592	+	0.895733i	$0.646651\pi$
$674$	33.0086	−	12.0141i	1.27144	−	0.462767i
$675$	−0.375019	−	0.314679i	−0.0144345	−	0.0121120i
$676$	9.52315			0.366275
$677$	−39.8810			−1.53275			−0.766376	−	0.642392i	$-0.777942\pi$
$677$	−39.8810			−1.53275			−0.766376	+	0.642392i	$0.777942\pi$
$678$	2.36774	+	1.98677i	0.0909325	+	0.0763014i
$679$	6.07053	−	27.0011i	0.232966	−	1.03621i
$680$	2.65426	+	7.29252i	0.101786	+	0.279655i
$681$	−11.4167	−	4.15533i	−0.437488	−	0.159232i
$682$	−17.9713	+	49.3758i	−0.688158	+	1.89070i
$683$	3.68764	+	2.12906i	0.141104	+	0.0814662i	0.568890	−	0.822414i	$-0.307373\pi$
$683$	3.68764	+	2.12906i	0.141104	+	0.0814662i	−0.427786	+	0.903880i	$0.640706\pi$
$684$	−0.531162	+	4.32642i	−0.0203095	+	0.165425i
$685$		−	24.1786i		−	0.923817i
$686$	−8.69831	+	16.3505i	−0.332103	+	0.624266i
$687$	−4.02284	−	4.79423i	−0.153481	−	0.182911i
$688$	1.81297	+	1.52126i	0.0691187	+	0.0579975i
$689$	11.5764	+	13.7963i	0.441027	+	0.525595i
$690$	−1.92628	+	0.701108i	−0.0733322	+	0.0266907i
$691$			15.6917i			0.596942i	0.954419	+	0.298471i	$0.0964765\pi$
$691$			15.6917i			0.596942i	−0.954419	+	0.298471i	$0.903523\pi$
$692$	−4.65692	−	8.06603i	−0.177030	−	0.306624i
$693$	−15.3330	−	0.715268i	−0.582453	−	0.0271708i
$694$	−33.6481	−	5.93307i	−1.27726	−	0.225216i
$695$	14.0569	−	24.3474i	0.533210	−	0.923548i
$696$	−4.85635	−	8.41145i	−0.184080	−	0.318835i
$697$	13.6713	+	37.5617i	0.517839	+	1.42275i
$698$	6.14145	+	34.8299i	0.232457	+	1.31833i
$699$	−18.0983	+	6.58725i	−0.684541	+	0.249153i
$700$	0.284110	−	1.26369i	0.0107383	−	0.0477631i
$701$	−2.41850	−	13.7160i	−0.0913456	−	0.518047i	−0.995806	−	0.0914892i	$-0.970837\pi$
$701$	−2.41850	−	13.7160i	−0.0913456	−	0.518047i	0.904460	−	0.426557i	$-0.140274\pi$
$702$	1.61482	−	0.932316i	0.0609474	−	0.0351880i
$703$	−24.7814	+	5.72156i	−0.934648	+	0.215793i
$704$	−2.90082	+	5.02437i	−0.109329	+	0.189363i
$705$	−0.939426	+	0.788272i	−0.0353808	+	0.0296881i
$706$	6.32119	−	5.30411i	0.237901	−	0.199623i
$707$	−1.26295	+	27.0735i	−0.0474980	+	1.01820i
$708$	12.1975	+	4.43953i	0.458410	+	0.166848i
$709$	1.96843	−	11.1635i	0.0739259	−	0.419254i	−0.925275	−	0.379296i	$-0.876166\pi$
$709$	1.96843	−	11.1635i	0.0739259	−	0.419254i	0.999201	−	0.0399586i	$-0.0127226\pi$
$710$	24.0044	−	13.8589i	0.900868	−	0.520116i
$711$		−	5.56497i		−	0.208703i
$712$	−1.17315	−	3.22319i	−0.0439655	−	0.120794i
$713$	1.37598	−	7.80358i	0.0515309	−	0.292246i
$714$	−1.11794	−	8.69179i	−0.0418378	−	0.325282i
$715$	21.9504	+	12.6731i	0.820899	+	0.473946i
$716$	−10.8298	−	1.90959i	−0.404729	−	0.0713646i
$717$	−0.177979	+	0.149342i	−0.00664676	+	0.00557730i
$718$	23.3504	+	4.11731i	0.871431	+	0.153657i
$719$	2.57977	−	7.08787i	0.0962094	−	0.264333i	−0.882247	−	0.470787i	$-0.843970\pi$
$719$	2.57977	−	7.08787i	0.0962094	−	0.264333i	0.978456	+	0.206454i	$0.0661923\pi$
$720$	2.30738	−	0.406854i	0.0859911	−	0.0151626i
$721$	9.22562	−	7.03546i	0.343580	−	0.262014i
$722$	−1.98651	−	18.8959i	−0.0739303	−	0.703231i
$723$	6.89502	+	11.9425i	0.256428	+	0.444147i
$724$	5.77899	+	2.10338i	0.214774	+	0.0781715i
$725$	−4.68265	+	0.825677i	−0.173909	+	0.0306649i
$726$	14.5649	−	17.3578i	0.540556	−	0.644209i
$727$	5.39539	−	14.8237i	0.200104	−	0.549781i	−0.798534	−	0.601949i	$-0.794391\pi$
$727$	5.39539	−	14.8237i	0.200104	−	0.549781i	0.998638	+	0.0521679i	$0.0166131\pi$
$728$	4.15282	+	2.66308i	0.153914	+	0.0987004i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	9.22002	+	5.32318i	0.341248	+	0.197020i
$731$	5.03879	−	6.00500i	0.186366	−	0.222103i
$732$	−3.01868	+	3.59752i	−0.111574	+	0.132968i
$733$	−3.07606	−	1.77596i	−0.113617	−	0.0655967i	0.442115	−	0.896959i	$-0.354228\pi$
$733$	−3.07606	−	1.77596i	−0.113617	−	0.0655967i	−0.555732	+	0.831362i	$0.687562\pi$
$734$	4.82998	−	8.36577i	0.178278	−	0.308786i
$735$	−7.01982	+	14.8226i	−0.258930	+	0.546741i
$736$	0.299238	−	0.822149i	0.0110301	−	0.0303048i
$737$	10.8869	−	12.9745i	0.401024	−	0.477922i
$738$	11.8847	−	2.09559i	0.437481	−	0.0771397i
$739$	5.20484	+	1.89441i	0.191463	+	0.0696869i	0.435972	−	0.899960i	$-0.356405\pi$
$739$	5.20484	+	1.89441i	0.191463	+	0.0696869i	−0.244509	+	0.969647i	$0.578627\pi$
$740$	6.83541	+	11.8393i	0.251275	+	0.435221i
$741$	−5.94418	+	5.54318i	−0.218365	+	0.203634i
$742$	−3.25994	−	25.3455i	−0.119676	−	0.930461i
$743$	5.07243	−	0.894407i	0.186090	−	0.0328126i	−0.0798266	−	0.996809i	$-0.525437\pi$
$743$	5.07243	−	0.894407i	0.186090	−	0.0328126i	0.265916	+	0.963996i	$0.414326\pi$
$744$	−3.09763	+	8.51067i	−0.113565	+	0.312016i
$745$	37.5890	+	6.62796i	1.37716	+	0.242830i
$746$	−27.5869	+	23.1482i	−1.01003	+	0.847516i
$747$	−7.31559	−	1.28994i	−0.267663	−	0.0471963i
$748$	16.6420	+	9.60824i	0.608490	+	0.351312i
$749$	−16.4303	+	39.3342i	−0.600352	+	1.43724i
$750$	−1.83509	+	10.4073i	−0.0670082	+	0.380022i
$751$	7.18152	+	19.7311i	0.262057	+	0.719996i	0.999028	+	0.0440722i	$0.0140332\pi$
$751$	7.18152	+	19.7311i	0.262057	+	0.719996i	−0.736971	+	0.675924i	$0.763745\pi$
$752$		−	0.523408i		−	0.0190867i
$753$	12.0293	−	6.94511i	0.438371	−	0.253094i
$754$	3.14488	−	17.8355i	0.114530	−	0.649530i
$755$	−13.9355	−	5.07212i	−0.507167	−	0.184594i
$756$	−2.64288	−	0.123287i	−0.0961205	−	0.00448391i
$757$	−2.58360	+	2.16790i	−0.0939026	+	0.0787937i	−0.688530	−	0.725207i	$-0.741744\pi$
$757$	−2.58360	+	2.16790i	−0.0939026	+	0.0787937i	0.594628	+	0.804001i	$0.297299\pi$
$758$	22.7052	−	19.0519i	0.824690	−	0.691997i
$759$	−2.53796	+	4.39588i	−0.0921223	+	0.159560i
$760$	−9.40089	+	3.99058i	−0.341006	+	0.144754i
$761$	−13.6841	+	7.90053i	−0.496049	+	0.286394i	−0.727080	−	0.686552i	$-0.759123\pi$
$761$	−13.6841	+	7.90053i	−0.496049	+	0.286394i	0.231032	+	0.972946i	$0.425790\pi$
$762$	−1.65755	−	9.40042i	−0.0600466	−	0.340541i
$763$	−7.23234	−	23.1788i	−0.261828	−	0.839130i
$764$	20.0012	−	7.27983i	0.723617	−	0.263375i
$765$	−1.34760	−	7.64263i	−0.0487227	−	0.276320i
$766$	4.89703	+	13.4545i	0.176937	+	0.486131i
$767$	12.1018	+	20.9609i	0.436969	+	0.756852i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−6.45461	−	1.13812i	−0.232759	−	0.0410418i	0.0560517	−	0.998428i	$-0.482149\pi$
$769$	−6.45461	−	1.13812i	−0.232759	−	0.0410418i	−0.288811	+	0.957386i	$0.593260\pi$
$770$	−16.5111	−	31.9499i	−0.595020	−	1.15139i
$771$	−12.6128	−	21.8460i	−0.454239	−	0.786765i
$772$		−	5.00054i		−	0.179973i
$773$	−16.5337	+	6.01778i	−0.594676	+	0.216444i	−0.621785	−	0.783188i	$-0.713592\pi$
$773$	−16.5337	+	6.01778i	−0.594676	+	0.216444i	0.0271088	+	0.999632i	$0.491370\pi$
$774$	−1.52126	−	1.81297i	−0.0546805	−	0.0651657i
$775$	3.39650	+	2.85000i	0.122006	+	0.102375i
$776$	6.72370	+	8.01299i	0.241367	+	0.287650i
$777$	−4.59821	−	14.7367i	−0.164960	−	0.528677i
$778$		−	8.95771i		−	0.321149i
$779$	−48.4213	+	20.5543i	−1.73487	+	0.736436i
$780$	3.78349	+	2.18440i	0.135471	+	0.0782139i
$781$	23.4744	−	64.4953i	0.839979	−	2.30782i
$782$	−2.72316	−	0.991150i	−0.0973801	−	0.0354435i
$783$	3.32194	+	9.12696i	0.118716	+	0.326171i
$784$	−2.92044	−	6.36168i	−0.104301	−	0.227203i
$785$	22.0782	+	18.5258i	0.788005	+	0.661214i
$786$	−14.0661			−0.501721
$787$	30.4742			1.08629			0.543144	−	0.839640i	$-0.317234\pi$
$787$	30.4742			1.08629			0.543144	+	0.839640i	$0.317234\pi$
$788$	3.15189	+	2.64475i	0.112281	+	0.0942152i
$789$	−20.9104	+	7.61076i	−0.744429	+	0.270950i
$790$	11.2918	−	6.51930i	0.401743	−	0.231946i
$791$	3.15197	−	7.54581i	0.112071	−	0.268298i
$792$	3.72922	−	4.44431i	0.132512	−	0.157922i
$793$	−8.62370	+	1.52059i	−0.306237	+	0.0539978i
$794$	−4.16937	+	23.6457i	−0.147966	+	0.839154i
$795$	−3.92964	−	22.2861i	−0.139370	−	0.790407i
$796$	6.50983	+	7.75812i	0.230735	+	0.274979i
$797$	3.65414			0.129436			0.0647181	−	0.997904i	$-0.479385\pi$
$797$	3.65414			0.129436			0.0647181	+	0.997904i	$0.479385\pi$
$798$	11.3456	−	2.06796i	0.401631	−	0.0732051i
$799$	−1.73366			−0.0613324
$800$	0.314679	+	0.375019i	0.0111256	+	0.0132589i
$801$	0.595622	+	3.37794i	0.0210453	+	0.119354i
$802$	−5.49503	+	31.1639i	−0.194036	+	1.10043i
$803$	25.9618	−	4.57777i	0.916172	−	0.161546i
$804$	1.87652	−	2.23635i	0.0661797	−	0.0788699i
$805$	3.28879	+	4.31260i	0.115915	+	0.151999i
$806$	−14.6252	+	8.44385i	−0.515150	+	0.297422i
$807$	−8.83354	+	3.21515i	−0.310955	+	0.113178i
$808$	−7.84733	−	6.58469i	−0.276068	−	0.231649i
$809$	20.5871			0.723804			0.361902	−	0.932216i	$-0.382127\pi$
$809$	20.5871			0.723804			0.361902	+	0.932216i	$0.382127\pi$
$810$	−2.34298			−0.0823239
$811$	−4.67193	−	3.92022i	−0.164054	−	0.137657i	0.557065	−	0.830469i	$-0.311927\pi$
$811$	−4.67193	−	3.92022i	−0.164054	−	0.137657i	−0.721119	+	0.692811i	$0.756372\pi$
$812$	−17.4173	+	18.8943i	−0.611229	+	0.663059i
$813$	5.47164	+	15.0332i	0.191899	+	0.527237i
$814$	31.8099	+	11.5779i	1.11494	+	0.405804i
$815$	−3.57497	+	9.82216i	−0.125226	+	0.344055i
$816$	2.86849	+	1.65612i	0.100417	+	0.0579760i
$817$	8.23883	+	6.20824i	0.288240	+	0.217199i
$818$			27.6320i			0.966132i
$819$	−3.62729	−	3.34375i	−0.126748	−	0.116840i
$820$	18.1749	+	21.6600i	0.634695	+	0.756400i
$821$	12.3905	+	10.3969i	0.432432	+	0.362854i	0.832869	−	0.553471i	$-0.186697\pi$
$821$	12.3905	+	10.3969i	0.432432	+	0.362854i	−0.400436	+	0.916325i	$0.631141\pi$
$822$	−6.63331	−	7.90527i	−0.231363	−	0.275728i
$823$	−29.9489	+	10.9005i	−1.04395	+	0.379968i	−0.806377	−	0.591401i	$-0.798575\pi$
$823$	−29.9489	+	10.9005i	−1.04395	+	0.379968i	−0.237575	+	0.971369i	$0.576353\pi$
$824$			4.38520i			0.152766i
$825$	−1.42011	−	2.45970i	−0.0494417	−	0.0856356i
$826$	1.60031	−	34.3054i	0.0556818	−	1.19364i
$827$	2.02300	+	0.356709i	0.0703466	+	0.0124040i	0.208711	−	0.977977i	$-0.433073\pi$
$827$	2.02300	+	0.356709i	0.0703466	+	0.0124040i	−0.138364	+	0.990381i	$0.544184\pi$
$828$	−0.437456	+	0.757697i	−0.0152027	+	0.0263318i
$829$	−6.71673	−	11.6337i	−0.233282	−	0.404056i	0.725490	−	0.688232i	$-0.241613\pi$
$829$	−6.71673	−	11.6337i	−0.233282	−	0.404056i	−0.958772	+	0.284177i	$0.908280\pi$
$830$	−5.95276	−	16.3551i	−0.206623	−	0.567692i
$831$	1.14894	+	6.51596i	0.0398563	+	0.226036i
$832$	−1.75218	+	0.637741i	−0.0607459	+	0.0221097i
$833$	−21.0715	+	9.67323i	−0.730084	+	0.335158i
$834$	−2.08364	−	11.8169i	−0.0721506	−	0.409186i
$835$	−41.2724	+	23.8286i	−1.42829	+	0.824624i
$836$	−11.4806	+	22.5326i	−0.397064	+	0.779306i
$837$	4.52843	−	7.84347i	0.156525	−	0.271110i
$838$	−1.01834	+	0.854485i	−0.0351778	+	0.0295177i
$839$	−10.2709	+	8.61833i	−0.354592	+	0.297538i	−0.802631	−	0.596476i	$-0.796567\pi$
$839$	−10.2709	+	8.61833i	−0.354592	+	0.297538i	0.448039	+	0.894014i	$0.352123\pi$
$840$	−2.84594	−	5.50704i	−0.0981944	−	0.190011i
$841$	61.3964	+	22.3465i	2.11712	+	0.770568i
$842$	−2.60189	+	14.7561i	−0.0896672	+	0.508528i
$843$	−11.1043	+	6.41106i	−0.382452	+	0.220809i
$844$			20.9968i			0.722739i
$845$	−7.63134	−	20.9669i	−0.262526	−	0.721284i
$846$	−0.0908888	+	0.515456i	−0.00312482	+	0.0177217i
$847$	−55.3181	−	23.1070i	−1.90075	−	0.793966i
$848$	8.36459	+	4.82930i	0.287241	+	0.165839i
$849$	1.36789	+	0.241196i	0.0469458	+	0.00827782i
$850$	1.24216	−	1.04229i	0.0426057	−	0.0357504i
$851$	−5.02739	−	0.886464i	−0.172337	−	0.0303876i
$852$	4.04616	−	11.1167i	0.138619	−	0.380853i
$853$	12.8737	−	2.26998i	0.440787	−	0.0777227i	0.0511499	−	0.998691i	$-0.483711\pi$
$853$	12.8737	−	2.26998i	0.440787	−	0.0777227i	0.389638	+	0.920968i	$0.372600\pi$
$854$	11.4650	+	4.78907i	0.392325	+	0.163879i
$855$	9.95103	−	2.29751i	0.340318	−	0.0785731i
$856$	−8.05591	−	13.9532i	−0.275345	−	0.476912i
$857$	16.7110	+	6.08230i	0.570837	+	0.207768i	0.611280	−	0.791414i	$-0.290655\pi$
$857$	16.7110	+	6.08230i	0.570837	+	0.207768i	−0.0404436	+	0.999182i	$0.512877\pi$
$858$	10.6536	−	1.87851i	0.363707	−	0.0641314i
$859$	−1.66715	+	1.98683i	−0.0568825	+	0.0677899i	−0.793735	−	0.608263i	$-0.791867\pi$
$859$	−1.66715	+	1.98683i	−0.0568825	+	0.0677899i	0.736853	+	0.676053i	$0.236311\pi$
$860$	1.89651	−	5.21063i	0.0646706	−	0.177681i
$861$	−14.6586	−	28.3652i	−0.499565	−	0.966683i
$862$	−11.1866	+	19.3757i	−0.381015	+	0.659938i
$863$	−21.6864	−	12.5207i	−0.738214	−	0.426208i	0.0832058	−	0.996532i	$-0.473484\pi$
$863$	−21.6864	−	12.5207i	−0.738214	−	0.426208i	−0.821419	+	0.570324i	$0.806817\pi$
$864$	0.642788	−	0.766044i	0.0218681	−	0.0260614i
$865$	−14.0270	+	16.7167i	−0.476933	+	0.568386i
$866$	33.1539	+	19.1414i	1.12661	+	0.650451i
$867$	−3.01450	+	5.22127i	−0.102378	+	0.177324i
$868$	23.9362	+	1.11659i	0.812447	+	0.0378997i
$869$	11.0424	−	30.3389i	0.374589	−	1.02918i
$870$	−14.6277	+	17.4326i	−0.495926	+	0.591021i
$871$	5.36081	−	0.945255i	0.181644	−	0.0320287i
$872$	8.62388	+	3.13883i	0.292041	+	0.106294i
$873$	−5.23011	−	9.05881i	−0.177012	−	0.306594i
$874$	1.11496	−	3.64703i	0.0377141	−	0.123363i
$875$	27.7316	−	3.56684i	0.937498	−	0.120581i
$876$	4.47491	−	0.789047i	0.151193	−	0.0266594i
$877$	1.64469	−	4.51874i	0.0555371	−	0.152587i	−0.908822	−	0.417184i	$-0.863017\pi$
$877$	1.64469	−	4.51874i	0.0555371	−	0.152587i	0.964359	+	0.264598i	$0.0852391\pi$
$878$	16.4732	+	2.90467i	0.555944	+	0.0980279i
$879$	−12.4884	+	10.4790i	−0.421222	+	0.353448i
$880$	13.3866	+	2.36042i	0.451263	+	0.0795698i
$881$	−23.2650	−	13.4321i	−0.783818	−	0.452538i	0.0539637	−	0.998543i	$-0.482814\pi$
$881$	−23.2650	−	13.4321i	−0.783818	−	0.452538i	−0.837782	+	0.546005i	$0.816148\pi$
$882$	1.77138	+	6.77216i	0.0596454	+	0.228031i
$883$	−3.34044	+	18.9446i	−0.112415	+	0.637536i	0.875583	+	0.483068i	$0.160478\pi$
$883$	−3.34044	+	18.9446i	−0.112415	+	0.637536i	−0.987998	+	0.154468i	$0.950634\pi$
$884$	2.11236	+	5.80366i	0.0710463	+	0.195198i
$885$		−	30.4126i		−	1.02231i
$886$	17.8325	−	10.2956i	0.599096	−	0.345888i
$887$	1.52470	−	8.64699i	0.0511943	−	0.290337i	−0.948452	−	0.316920i	$-0.897351\pi$
$887$	1.52470	−	8.64699i	0.0511943	−	0.290337i	0.999647	+	0.0265825i	$0.00846246\pi$
$888$	5.48292	+	1.99562i	0.183995	+	0.0669686i
$889$	−22.4360	+	11.5945i	−0.752480	+	0.388869i
$890$	−6.15634	+	5.16578i	−0.206361	+	0.173158i
$891$	−4.44431	+	3.72922i	−0.148890	+	0.124934i
$892$	5.78581	−	10.0213i	0.193723	−	0.335539i
$893$	−0.119432	−	2.27835i	−0.00399664	−	0.0762422i
$894$	14.1082	−	8.14538i	0.471849	−	0.272422i
$895$	4.47412	+	25.3740i	0.149553	+	0.848160i
$896$	2.58132	+	0.580345i	0.0862358	+	0.0193880i
$897$	−1.53300	+	0.557968i	−0.0511855	+	0.0186300i
$898$	2.79503	+	15.8514i	0.0932713	+	0.528968i
$899$	−30.0864	−	82.6616i	−1.00344	−	2.75692i
$900$	−0.244777	−	0.423965i	−0.00815922	−	0.0141322i
$901$	15.9958	−	27.7056i	0.532899	−	0.923008i
$902$	68.9506	+	12.1579i	2.29581	+	0.404812i
$903$	−3.38008	+	5.27092i	−0.112482	+	0.175405i
$904$	1.54543	+	2.67677i	0.0514003	+	0.0890279i
$905$		−	14.4090i		−	0.478972i
$906$	−5.94779	+	2.16482i	−0.197602	+	0.0719213i
$907$	24.7582	+	29.5057i	0.822083	+	0.979720i	0.999991	−	0.00432716i	$-0.00137738\pi$
$907$	24.7582	+	29.5057i	0.822083	+	0.979720i	−0.177908	+	0.984047i	$0.556933\pi$
$908$	−9.30695	−	7.80946i	−0.308862	−	0.259166i
$909$	6.58469	+	7.84733i	0.218400	+	0.260279i
$910$	2.53541	−	11.2772i	0.0840479	−	0.373837i
$911$		−	13.8655i		−	0.459383i	−0.973263	−	0.229692i	$-0.926228\pi$
$911$		−	13.8655i		−	0.459383i	0.973263	−	0.229692i	$-0.0737718\pi$
$912$	−1.97885	+	3.88383i	−0.0655263	+	0.128607i
$913$	−37.3232	−	21.5486i	−1.23522	−	0.713154i
$914$	−12.1802	+	33.4648i	−0.402885	+	1.10692i
$915$	10.3396	+	3.76331i	0.341817	+	0.124411i
$916$	−2.14051	−	5.88099i	−0.0707243	−	0.194314i
$917$	11.0850	+	35.5262i	0.366059	+	1.17318i
$918$	−2.53733	−	2.12907i	−0.0837444	−	0.0702699i
$919$	35.8425			1.18234			0.591168	−	0.806548i	$-0.298667\pi$
$919$	35.8425			1.18234			0.591168	+	0.806548i	$0.298667\pi$
$920$	−2.04990			−0.0675833
$921$	−13.1249	−	11.0131i	−0.432481	−	0.362895i
$922$	−3.05175	+	1.11075i	−0.100504	+	0.0365805i
$923$	19.1036	−	11.0295i	0.628802	−	0.363039i
$924$	−14.1637	−	5.91633i	−0.465951	−	0.194633i
$925$	1.83609	−	2.18817i	0.0603702	−	0.0719464i
$926$	2.98400	−	0.526160i	0.0980605	−	0.0172907i
$927$	0.761482	−	4.31858i	0.0250104	−	0.141841i
$928$	−1.68659	−	9.56515i	−0.0553652	−	0.313991i
$929$	20.1308	+	23.9909i	0.660470	+	0.787117i	0.987453	−	0.157913i	$-0.0504766\pi$
$929$	20.1308	+	23.9909i	0.660470	+	0.787117i	−0.326983	+	0.945030i	$0.606032\pi$
$930$	21.2200			0.695833
$931$	−14.1641	−	27.0255i	−0.464209	−	0.885726i
$932$	−19.2598			−0.630876
$933$	11.2454	+	13.4017i	0.368158	+	0.438754i
$934$	0.0769833	+	0.436594i	0.00251897	+	0.0142858i
$935$	7.81831	−	44.3398i	0.255686	−	1.45007i
$936$	1.83630	−	0.323790i	0.0600215	−	0.0105834i
$937$	−3.06026	+	3.64707i	−0.0999742	+	0.119145i	−0.813712	−	0.581269i	$-0.802557\pi$
$937$	−3.06026	+	3.64707i	−0.0999742	+	0.119145i	0.713737	+	0.700413i	$0.247001\pi$
$938$	−7.12707	−	2.97706i	−0.232707	−	0.0972044i
$939$	−15.8356	+	9.14267i	−0.516774	+	0.298360i
$940$	−1.15238	+	0.419431i	−0.0375864	+	0.0136803i
$941$	−30.2486	−	25.3816i	−0.986075	−	0.827415i	−0.00108035	−	0.999999i	$-0.500344\pi$
$941$	−30.2486	−	25.3816i	−0.986075	−	0.827415i	−0.984995	+	0.172584i	$0.944788\pi$
$942$	12.3010			0.400789
$943$	−10.5585			−0.343831
$944$	9.94350	+	8.34359i	0.323633	+	0.271561i
$945$	1.84642	+	5.91757i	0.0600641	+	0.192498i
$946$	−4.69611	−	12.9025i	−0.152684	−	0.419495i
$947$	21.4311	+	7.80028i	0.696417	+	0.253475i	0.665880	−	0.746059i	$-0.268056\pi$
$947$	21.4311	+	7.80028i	0.696417	+	0.253475i	0.0305364	+	0.999534i	$0.490278\pi$
$948$	1.90333	−	5.22936i	0.0618173	−	0.169842i
$949$	7.33764	+	4.23639i	0.238190	+	0.137519i
$950$	1.45534	+	1.56063i	0.0472176	+	0.0506334i
$951$			8.03536i			0.260564i
$952$	1.92225	−	8.54997i	0.0623004	−	0.277106i
$953$	10.9469	+	13.0461i	0.354606	+	0.422603i	0.913629	−	0.406549i	$-0.133268\pi$
$953$	10.9469	+	13.0461i	0.354606	+	0.422603i	−0.559023	+	0.829152i	$0.688824\pi$
$954$	−7.39892	−	6.20843i	−0.239549	−	0.201005i
$955$	−32.0557	−	38.2025i	−1.03730	−	1.23620i
$956$	−0.218324	+	0.0794635i	−0.00706111	+	0.00257003i
$957$			56.3496i			1.82153i
$958$	16.4397	+	28.4744i	0.531143	+	0.919967i
$959$	−14.7385	+	22.9833i	−0.475932	+	0.742171i
$960$	2.30738	+	0.406854i	0.0744705	+	0.0131312i
$961$	−25.5134	+	44.1904i	−0.823012	+	1.42550i
$962$	5.43988	+	9.42215i	0.175389	+	0.303782i
$963$	5.51057	+	15.1402i	0.177576	+	0.487885i
$964$	2.39461	+	13.5805i	0.0771253	+	0.437399i
$965$	−11.0096	+	4.00716i	−0.354411	+	0.128995i
$966$	2.25843	+	0.507751i	0.0726637	+	0.0163366i
$967$	1.87602	+	10.6394i	0.0603287	+	0.342141i	1.00000		6.22967e-5i	$1.98297e-5\pi$
$967$	1.87602	+	10.6394i	0.0603287	+	0.342141i	−0.939671	+	0.342079i	$0.888869\pi$
$968$	19.6233	−	11.3295i	0.630717	−	0.364145i
$969$	12.8642	+	6.55445i	0.413258	+	0.210559i
$970$	12.2540	−	21.2246i	0.393453	−	0.681481i
$971$	19.6423	−	16.4818i	0.630351	−	0.528928i	−0.270687	−	0.962667i	$-0.587251\pi$
$971$	19.6423	−	16.4818i	0.630351	−	0.528928i	0.901038	+	0.433740i	$0.142806\pi$
$972$	−0.766044	+	0.642788i	−0.0245709	+	0.0206174i
$973$	−28.2034	+	14.5751i	−0.904161	+	0.467255i
$974$	−2.44216	−	0.888873i	−0.0782518	−	0.0284813i
$975$	0.158512	−	0.898968i	0.00507646	−	0.0287900i
$976$	−4.06705	+	2.34811i	−0.130183	+	0.0751613i
$977$			34.5530i			1.10545i	0.833365	+	0.552723i	$0.186411\pi$
$977$			34.5530i			1.10545i	−0.833365	+	0.552723i	$0.813589\pi$
$978$	1.52582	+	4.19217i	0.0487905	+	0.134051i
$979$	−3.45558	+	19.5976i	−0.110441	+	0.626342i
$980$	−11.6661	+	11.5278i	−0.372660	+	0.368242i
$981$	−7.94781	−	4.58867i	−0.253754	−	0.146505i
$982$	−17.1337	−	3.02113i	−0.546758	−	0.0964082i
$983$	−29.6732	+	24.8988i	−0.946429	+	0.794148i	−0.978692	−	0.205331i	$-0.934173\pi$
$983$	−29.6732	+	24.8988i	−0.946429	+	0.794148i	0.0322639	+	0.999479i	$0.489728\pi$
$984$	11.8847	+	2.09559i	0.378870	+	0.0668050i
$985$	3.29714	−	9.05881i	0.105056	−	0.288638i
$986$	−31.6822	+	5.58642i	−1.00897	+	0.177908i
$987$	1.37349	−	0.176659i	0.0437188	−	0.00562311i
$988$	−7.48158	+	3.17585i	−0.238021	+	0.101037i
$989$	1.03531	+	1.79321i	0.0329210	+	0.0570208i
$990$	−12.7734	−	4.64912i	−0.405964	−	0.147759i
$991$	−10.8295	+	1.90954i	−0.344011	+	0.0606585i	−0.342985	−	0.939341i	$-0.611438\pi$
$991$	−10.8295	+	1.90954i	−0.344011	+	0.0606585i	−0.00102670	+	0.999999i	$0.500327\pi$
$992$	−5.82164	+	6.93796i	−0.184837	+	0.220280i
$993$	−0.540347	+	1.48459i	−0.0171474	+	0.0471121i
$994$	−31.2657	−	1.45851i	−0.991688	−	0.0462611i
$995$	11.8643	−	20.5495i	0.376123	−	0.651463i
$996$	−6.43322	−	3.71422i	−0.203844	−	0.117690i
$997$	−15.7710	+	18.7951i	−0.499473	+	0.595248i	−0.955600	−	0.294666i	$-0.904792\pi$
$997$	−15.7710	+	18.7951i	−0.499473	+	0.595248i	0.456128	+	0.889914i	$0.349236\pi$
$998$	9.05621	−	10.7928i	0.286669	−	0.341639i
$999$	−5.05309	−	2.91740i	−0.159873	−	0.0923025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.a.409.5	yes	72
7.5	odd	6		798.2.ca.a.523.5	yes	72
19.2	odd	18		798.2.ca.a.325.5	✓	72
133.40	even	18	inner	798.2.cj.a.439.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.a.325.5	✓	72	19.2	odd	18
798.2.ca.a.523.5	yes	72	7.5	odd	6
798.2.cj.a.409.5	yes	72	1.1	even	1	trivial
798.2.cj.a.439.5	yes	72	133.40	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.30738 - 0.406854i) q^{5} +(0.642788 - 0.766044i) q^{6} +(-2.44133 - 1.01977i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-1.79483 - 1.50604i) q^{10} -5.80164 q^{11} -1.00000 q^{12} +(-1.42839 - 1.19856i) q^{13} +(0.788065 + 2.52566i) q^{14} +(0.801346 + 2.20168i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.13286 + 3.11250i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.16845 - 1.27437i) q^{19} +2.34298i q^{20} +(0.580345 - 2.58132i) q^{21} +(3.72922 + 4.44431i) q^{22} +(-0.670222 - 0.562383i) q^{23} +(0.642788 + 0.766044i) q^{24} +(0.460029 - 0.167437i) q^{25} +1.86463i q^{26} +(-0.500000 - 0.866025i) q^{27} +(1.42821 - 2.22716i) q^{28} +(-9.56515 - 1.68659i) q^{29} +(1.17149 - 2.02908i) q^{30} +(4.52843 + 7.84347i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-1.00744 - 5.71350i) q^{33} +(3.11250 - 1.13286i) q^{34} +(-6.04797 - 1.35974i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(5.05309 - 2.91740i) q^{37} +(1.70321 + 4.01237i) q^{38} +(0.932316 - 1.61482i) q^{39} +(1.79483 - 1.50604i) q^{40} +(9.24464 - 7.75717i) q^{41} +(-2.35044 + 1.21467i) q^{42} +(-2.22393 - 0.809445i) q^{43} +(1.00744 - 5.71350i) q^{44} +(-2.02908 + 1.17149i) q^{45} +0.874913i q^{46} +(0.179016 + 0.491843i) q^{47} +(0.173648 - 0.984808i) q^{48} +(4.92014 + 4.97918i) q^{49} +(-0.423965 - 0.244777i) q^{50} +(-3.26193 - 0.575166i) q^{51} +(1.42839 - 1.19856i) q^{52} +(-9.51187 - 1.67720i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-13.3866 + 2.36042i) q^{55} +(-2.62413 + 0.337517i) q^{56} +(0.531162 - 4.32642i) q^{57} +(4.85635 + 8.41145i) q^{58} +(-12.1975 - 4.43953i) q^{59} +(-2.30738 + 0.406854i) q^{60} +(3.01868 - 3.59752i) q^{61} +(3.09763 - 8.51067i) q^{62} +(2.64288 + 0.123287i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.78349 - 2.18440i) q^{65} +(-3.72922 + 4.44431i) q^{66} +(-1.87652 + 2.23635i) q^{67} +(-2.86849 - 1.65612i) q^{68} +(0.437456 - 0.757697i) q^{69} +(2.84594 + 5.50704i) q^{70} +(-4.04616 + 11.1167i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(-4.47491 + 0.789047i) q^{73} +(-5.48292 - 1.99562i) q^{74} +(0.244777 + 0.423965i) q^{75} +(1.97885 - 3.88383i) q^{76} +(14.1637 + 5.91633i) q^{77} +(-1.83630 + 0.323790i) q^{78} +(-1.90333 + 5.22936i) q^{79} +(-2.30738 - 0.406854i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-11.8847 - 2.09559i) q^{82} +(6.43322 + 3.71422i) q^{83} +(2.44133 + 1.01977i) q^{84} +(-1.34760 + 7.64263i) q^{85} +(0.809445 + 2.22393i) q^{86} -9.71271i q^{87} +(-5.02437 + 2.90082i) q^{88} +(0.595622 - 3.37794i) q^{89} +(2.20168 + 0.801346i) q^{90} +(2.26491 + 4.38271i) q^{91} +(0.670222 - 0.562383i) q^{92} +(-6.93796 + 5.82164i) q^{93} +(0.261704 - 0.453285i) q^{94} +(-10.1367 - 1.24450i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(1.81640 + 10.3013i) q^{97} +(0.651665 - 6.96960i) q^{98} +(5.45176 - 1.98428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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