LMFDB - Embedded newform 714.2.bl.a.199.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(31,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 27])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,0,0,0,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			199.7
Character	$\chi$	$=$	714.199
Dual form			714.2.bl.a.61.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.608761 + 0.793353i) q^{2} +(0.997859 - 0.0654031i) q^{3} +(-0.258819 - 0.965926i) q^{4} +(-3.70938 + 1.25917i) q^{5} +(-0.555570 + 0.831470i) q^{6} +(-1.85824 + 1.88333i) q^{7} +(0.923880 + 0.382683i) q^{8} +(0.991445 - 0.130526i) q^{9} +(1.25917 - 3.70938i) q^{10} +(0.0258861 + 0.0524919i) q^{11} +(-0.321439 - 0.946930i) q^{12} +(3.92397 - 3.92397i) q^{13} +(-0.362924 - 2.62074i) q^{14} +(-3.61909 + 1.49907i) q^{15} +(-0.866025 + 0.500000i) q^{16} +(-4.05095 + 0.767998i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-3.69010 - 2.83152i) q^{19} +(2.17632 + 3.25709i) q^{20} +(-1.73109 + 2.00084i) q^{21} +(-0.0574031 - 0.0114182i) q^{22} +(0.115231 - 1.75808i) q^{23} +(0.946930 + 0.321439i) q^{24} +(8.20724 - 6.29764i) q^{25} +(0.724334 + 5.50186i) q^{26} +(0.980785 - 0.195090i) q^{27} +(2.30011 + 1.30748i) q^{28} +(1.83587 - 9.22956i) q^{29} +(1.01386 - 3.78379i) q^{30} +(-0.241048 - 3.67768i) q^{31} +(0.130526 - 0.991445i) q^{32} +(0.0292639 + 0.0506865i) q^{33} +(1.85677 - 3.68136i) q^{34} +(4.52149 - 9.32583i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-1.88846 - 0.931284i) q^{37} +(4.49279 - 1.20384i) q^{38} +(3.65893 - 4.17221i) q^{39} +(-3.90888 - 0.256202i) q^{40} +(2.01165 + 10.1132i) q^{41} +(-0.533551 - 2.59139i) q^{42} +(1.12696 - 2.72072i) q^{43} +(0.0440035 - 0.0385900i) q^{44} +(-3.51329 + 1.73256i) q^{45} +(1.32463 + 1.16167i) q^{46} +(-11.4239 - 3.06102i) q^{47} +(-0.831470 + 0.555570i) q^{48} +(-0.0938864 - 6.99937i) q^{49} +10.3450i q^{50} +(-3.99205 + 1.03130i) q^{51} +(-4.80587 - 2.77467i) q^{52} +(-9.86701 - 1.29902i) q^{53} +(-0.442289 + 0.896873i) q^{54} +(-0.162118 - 0.162118i) q^{55} +(-2.43751 + 1.02886i) q^{56} +(-3.86739 - 2.58411i) q^{57} +(6.20469 + 7.07510i) q^{58} +(2.49823 + 3.25576i) q^{59} +(2.38468 + 3.10778i) q^{60} +(-3.28261 - 3.74310i) q^{61} +(3.06444 + 2.04760i) q^{62} +(-1.59652 + 2.10977i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-9.61458 + 19.4964i) q^{65} +(-0.0580270 - 0.00763940i) q^{66} +(8.49844 + 4.90657i) q^{67} +(1.79029 + 3.71414i) q^{68} -1.76185i q^{69} +(4.64617 + 9.26435i) q^{70} +(4.77482 - 3.19043i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-3.94352 - 3.45837i) q^{73} +(1.88846 - 0.931284i) q^{74} +(7.77779 - 6.82094i) q^{75} +(-1.77997 + 4.29722i) q^{76} +(-0.146962 - 0.0487903i) q^{77} +(1.08262 + 5.44271i) q^{78} +(-8.91497 - 0.584318i) q^{79} +(2.58284 - 2.94516i) q^{80} +(0.965926 - 0.258819i) q^{81} +(-9.24798 - 4.56060i) q^{82} +(-3.46655 - 8.36899i) q^{83} +(2.38070 + 1.15425i) q^{84} +(14.0595 - 7.94961i) q^{85} +(1.47245 + 2.55035i) q^{86} +(1.22830 - 9.32987i) q^{87} +(0.00382789 + 0.0584024i) q^{88} +(-0.198257 + 0.739906i) q^{89} +(0.764221 - 3.84200i) q^{90} +(0.0984633 + 14.6818i) q^{91} +(-1.72800 + 0.343720i) q^{92} +(-0.481064 - 3.65404i) q^{93} +(9.38289 - 7.19974i) q^{94} +(17.2533 + 5.85672i) q^{95} +(0.0654031 - 0.997859i) q^{96} +(4.91058 + 0.976775i) q^{97} +(5.61013 + 4.18646i) q^{98} +(0.0325162 + 0.0486640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) $ 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	−0.608761	+	0.793353i	−0.430459	+	0.560986i
$2$	−0.608761	+	0.793353i	−0.430459	+	0.560986i
$3$	0.997859	−	0.0654031i	0.576114	−	0.0377605i
$3$	0.997859	−	0.0654031i	0.576114	−	0.0377605i
$4$	−0.258819	−	0.965926i	−0.129410	−	0.482963i
$5$	−3.70938	+	1.25917i	−1.65889	+	0.563116i	−0.984519	−	0.175280i	$-0.943917\pi$
$5$	−3.70938	+	1.25917i	−1.65889	+	0.563116i	−0.674367	+	0.738396i	$0.735583\pi$
$6$	−0.555570	+	0.831470i	−0.226811	+	0.339446i
$7$	−1.85824	+	1.88333i	−0.702349	+	0.711833i
$7$	−1.85824	+	1.88333i	−0.702349	+	0.711833i
$8$	0.923880	+	0.382683i	0.326641	+	0.135299i
$9$	0.991445	−	0.130526i	0.330482	−	0.0435087i
$10$	1.25917	−	3.70938i	0.398183	−	1.17301i
$11$	0.0258861	+	0.0524919i	0.00780497	+	0.0158269i	0.900740	−	0.434358i	$-0.143025\pi$
$11$	0.0258861	+	0.0524919i	0.00780497	+	0.0158269i	−0.892935	+	0.450185i	$0.851358\pi$
$12$	−0.321439	−	0.946930i	−0.0927916	−	0.273355i
$13$	3.92397	−	3.92397i	1.08831	−	1.08831i	0.0926125	−	0.995702i	$-0.470478\pi$
$13$	3.92397	−	3.92397i	1.08831	−	1.08831i	0.995702	−	0.0926125i	$-0.0295218\pi$
$14$	−0.362924	−	2.62074i	−0.0969954	−	0.700423i
$15$	−3.61909	+	1.49907i	−0.934444	+	0.387059i
$16$	−0.866025	+	0.500000i	−0.216506	+	0.125000i
$17$	−4.05095	+	0.767998i	−0.982499	+	0.186267i
$17$	−4.05095	+	0.767998i	−0.982499	+	0.186267i
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−3.69010	−	2.83152i	−0.846568	−	0.649594i	0.0915921	−	0.995797i	$-0.470804\pi$
$19$	−3.69010	−	2.83152i	−0.846568	−	0.649594i	−0.938160	+	0.346202i	$0.887471\pi$
$20$	2.17632	+	3.25709i	0.486640	+	0.728308i
$21$	−1.73109	+	2.00084i	−0.377754	+	0.436618i
$22$	−0.0574031	−	0.0114182i	−0.0122384	−	0.00243437i
$23$	0.115231	−	1.75808i	0.0240272	−	0.366585i	−0.968867	−	0.247583i	$-0.920364\pi$
$23$	0.115231	−	1.75808i	0.0240272	−	0.366585i	0.992894	−	0.119002i	$-0.0379695\pi$
$24$	0.946930	+	0.321439i	0.193291	+	0.0656136i
$25$	8.20724	−	6.29764i	1.64145	−	1.25953i
$26$	0.724334	+	5.50186i	0.142054	+	1.07900i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	2.30011	+	1.30748i	0.434680	+	0.247090i
$29$	1.83587	−	9.22956i	0.340913	−	1.71389i	−0.306605	−	0.951837i	$-0.599193\pi$
$29$	1.83587	−	9.22956i	0.340913	−	1.71389i	0.647519	−	0.762050i	$-0.275807\pi$
$30$	1.01386	−	3.78379i	0.185105	−	0.690823i
$31$	−0.241048	−	3.67768i	−0.0432935	−	0.660531i	−0.963266	−	0.268549i	$-0.913456\pi$
$31$	−0.241048	−	3.67768i	−0.0432935	−	0.660531i	0.919973	−	0.391983i	$-0.128211\pi$
$32$	0.130526	−	0.991445i	0.0230740	−	0.175264i
$33$	0.0292639	+	0.0506865i	0.00509418	+	0.00882338i
$34$	1.85677	−	3.68136i	0.318433	−	0.631348i
$35$	4.52149	−	9.32583i	0.764272	−	1.57635i
$36$	−0.382683	−	0.923880i	−0.0637806	−	0.153980i
$37$	−1.88846	−	0.931284i	−0.310460	−	0.153102i	0.280383	−	0.959888i	$-0.409538\pi$
$37$	−1.88846	−	0.931284i	−0.310460	−	0.153102i	−0.590844	+	0.806786i	$0.701205\pi$
$38$	4.49279	−	1.20384i	0.728826	−	0.195288i
$39$	3.65893	−	4.17221i	0.585898	−	0.668089i
$40$	−3.90888	−	0.256202i	−0.618049	−	0.0405090i
$41$	2.01165	+	10.1132i	0.314166	+	1.57942i	0.738716	+	0.674017i	$0.235432\pi$
$41$	2.01165	+	10.1132i	0.314166	+	1.57942i	−0.424550	+	0.905405i	$0.639568\pi$
$42$	−0.533551	−	2.59139i	−0.0823287	−	0.399861i
$43$	1.12696	−	2.72072i	0.171860	−	0.414906i	−0.814357	−	0.580364i	$-0.802910\pi$
$43$	1.12696	−	2.72072i	0.171860	−	0.414906i	0.986217	+	0.165458i	$0.0529102\pi$
$44$	0.0440035	−	0.0385900i	0.00663377	−	0.00581766i
$45$	−3.51329	+	1.73256i	−0.523731	+	0.258275i
$46$	1.32463	+	1.16167i	0.195306	+	0.171279i
$47$	−11.4239	−	3.06102i	−1.66634	−	0.446495i	−0.702222	−	0.711958i	$-0.747809\pi$
$47$	−11.4239	−	3.06102i	−1.66634	−	0.446495i	−0.964121	+	0.265462i	$0.914475\pi$
$48$	−0.831470	+	0.555570i	−0.120012	+	0.0801897i
$49$	−0.0938864	−	6.99937i	−0.0134123	−	0.999910i
$50$			10.3450i			1.46300i
$51$	−3.99205	+	1.03130i	−0.558998	+	0.144411i
$52$	−4.80587	−	2.77467i	−0.666454	−	0.384777i
$53$	−9.86701	−	1.29902i	−1.35534	−	0.178434i	−0.582394	−	0.812907i	$-0.697884\pi$
$53$	−9.86701	−	1.29902i	−1.35534	−	0.178434i	−0.772945	+	0.634473i	$0.781217\pi$
$54$	−0.442289	+	0.896873i	−0.0601879	+	0.122049i
$55$	−0.162118	−	0.162118i	−0.0218599	−	0.0218599i
$56$	−2.43751	+	1.02886i	−0.325726	+	0.137487i
$57$	−3.86739	−	2.58411i	−0.512249	−	0.342274i
$58$	6.20469	+	7.07510i	0.814716	+	0.929006i
$59$	2.49823	+	3.25576i	0.325242	+	0.423864i	0.927143	−	0.374707i	$-0.122257\pi$
$59$	2.49823	+	3.25576i	0.325242	+	0.423864i	−0.601901	+	0.798570i	$0.705590\pi$
$60$	2.38468	+	3.10778i	0.307861	+	0.401213i
$61$	−3.28261	−	3.74310i	−0.420295	−	0.479254i	0.502483	−	0.864587i	$-0.332420\pi$
$61$	−3.28261	−	3.74310i	−0.420295	−	0.479254i	−0.922778	+	0.385333i	$0.874087\pi$
$62$	3.06444	+	2.04760i	0.389185	+	0.260045i
$63$	−1.59652	+	2.10977i	−0.201142	+	0.265806i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$	−9.61458	+	19.4964i	−1.19254	+	2.41824i
$66$	−0.0580270	−	0.00763940i	−0.00714263	−	0.000940345i
$67$	8.49844	+	4.90657i	1.03825	+	0.599434i	0.919337	−	0.393471i	$-0.128726\pi$
$67$	8.49844	+	4.90657i	1.03825	+	0.599434i	0.118912	+	0.992905i	$0.462059\pi$
$68$	1.79029	+	3.71414i	0.217105	+	0.450406i
$69$		−	1.76185i		−	0.212102i
$70$	4.64617	+	9.26435i	0.555323	+	1.10730i
$71$	4.77482	−	3.19043i	0.566666	−	0.378634i	−0.238986	−	0.971023i	$-0.576815\pi$
$71$	4.77482	−	3.19043i	0.566666	−	0.378634i	0.805652	+	0.592389i	$0.201815\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−3.94352	−	3.45837i	−0.461554	−	0.404772i	0.396740	−	0.917931i	$-0.370142\pi$
$73$	−3.94352	−	3.45837i	−0.461554	−	0.404772i	−0.858293	+	0.513159i	$0.828475\pi$
$74$	1.88846	−	0.931284i	0.219529	−	0.108260i
$75$	7.77779	−	6.82094i	0.898101	−	0.787614i
$76$	−1.77997	+	4.29722i	−0.204176	+	0.492925i
$77$	−0.146962	−	0.0487903i	−0.0167479	−	0.00556018i
$78$	1.08262	+	5.44271i	0.122583	+	0.616265i
$79$	−8.91497	−	0.584318i	−1.00301	−	0.0657409i	−0.444963	−	0.895549i	$-0.646783\pi$
$79$	−8.91497	−	0.584318i	−1.00301	−	0.0657409i	−0.558049	+	0.829808i	$0.688450\pi$
$80$	2.58284	−	2.94516i	0.288770	−	0.329279i
$81$	0.965926	−	0.258819i	0.107325	−	0.0287577i
$82$	−9.24798	−	4.56060i	−1.02127	−	0.503634i
$83$	−3.46655	−	8.36899i	−0.380503	−	0.918616i	−0.991868	−	0.127268i	$-0.959379\pi$
$83$	−3.46655	−	8.36899i	−0.380503	−	0.918616i	0.611365	−	0.791349i	$-0.290621\pi$
$84$	2.38070	+	1.15425i	0.259755	+	0.125939i
$85$	14.0595	−	7.94961i	1.52496	−	0.862256i
$86$	1.47245	+	2.55035i	0.158778	+	0.275011i
$87$	1.22830	−	9.32987i	0.131688	−	1.00027i
$88$	0.00382789	+	0.0584024i	0.000408055	+	0.00622572i
$89$	−0.198257	+	0.739906i	−0.0210152	+	0.0784299i	−0.975637	−	0.219391i	$-0.929593\pi$
$89$	−0.198257	+	0.739906i	−0.0210152	+	0.0784299i	0.954622	+	0.297821i	$0.0962597\pi$
$90$	0.764221	−	3.84200i	0.0805560	−	0.404982i
$91$	0.0984633	+	14.6818i	0.0103218	+	1.53907i
$92$	−1.72800	+	0.343720i	−0.180156	+	0.0358353i
$93$	−0.481064	−	3.65404i	−0.0498840	−	0.378907i
$94$	9.38289	−	7.19974i	0.967771	−	0.742597i
$95$	17.2533	+	5.85672i	1.77016	+	0.600887i
$96$	0.0654031	−	0.997859i	0.00667518	−	0.101844i
$97$	4.91058	+	0.976775i	0.498594	+	0.0991765i	0.437980	−	0.898985i	$-0.355694\pi$
$97$	4.91058	+	0.976775i	0.498594	+	0.0991765i	0.0606140	+	0.998161i	$0.480694\pi$
$98$	5.61013	+	4.18646i	0.566709	+	0.422896i
$99$	0.0325162	+	0.0486640i	0.00326801	+	0.00489092i
$100$	−8.20724	−	6.29764i	−0.820724	−	0.629764i
$101$	0.0339779	−	0.0588514i	0.00338093	−	0.00585593i	−0.864330	−	0.502925i	$-0.832257\pi$
$101$	0.0339779	−	0.0588514i	0.00338093	−	0.00585593i	0.867711	+	0.497069i	$0.165590\pi$
$102$	1.61202	−	3.79492i	0.159614	−	0.375753i
$103$	−5.70708	+	3.29499i	−0.562336	+	0.324665i	−0.754082	−	0.656780i	$-0.771918\pi$
$103$	−5.70708	+	3.29499i	−0.562336	+	0.324665i	0.191747	+	0.981444i	$0.438585\pi$
$104$	5.12692	−	2.12364i	0.502736	−	0.208240i
$105$	3.90187	−	9.60158i	0.380784	−	0.937019i
$106$	7.03724	−	7.03724i	0.683517	−	0.683517i
$107$	2.23746	+	6.59135i	0.216304	+	0.637210i	0.999873	+	0.0159065i	$0.00506340\pi$
$107$	2.23746	+	6.59135i	0.216304	+	0.637210i	−0.783570	+	0.621304i	$0.786603\pi$
$108$	−0.442289	−	0.896873i	−0.0425592	−	0.0863016i
$109$	−5.86059	+	17.2647i	−0.561342	+	1.65366i	0.180878	+	0.983506i	$0.442106\pi$
$109$	−5.86059	+	17.2647i	−0.561342	+	1.65366i	−0.742220	+	0.670156i	$0.766227\pi$
$110$	0.227307	−	0.0299256i	0.0216729	−	0.00285329i
$111$	−1.94532	−	0.805779i	−0.184642	−	0.0764812i
$112$	0.667617	−	2.56013i	0.0630839	−	0.241910i
$113$	−7.36634	+	11.0245i	−0.692967	+	1.03710i	0.303477	+	0.952839i	$0.401853\pi$
$113$	−7.36634	+	11.0245i	−0.692967	+	1.03710i	−0.996444	+	0.0842598i	$0.973147\pi$
$114$	4.40443	−	1.49510i	0.412513	−	0.140029i
$115$	1.78628	+	6.66648i	0.166571	+	0.621652i
$116$	−9.39023	+	0.615468i	−0.871861	+	0.0571448i
$117$	3.37822	−	4.40259i	0.312317	−	0.407019i
$118$	−4.10379			−0.377785
$119$	6.08124	−	9.05641i	0.557466	−	0.830200i
$120$	−3.91727			−0.357596
$121$	6.69429	−	8.72417i	0.608572	−	0.793106i
$122$	4.96792	−	0.325615i	0.449774	−	0.0294798i
$123$	2.66878	+	9.96001i	0.240635	+	0.898064i
$124$	−3.48998	+	1.18469i	−0.313410	+	0.106388i
$125$	−11.6324	+	17.4092i	−1.04044	+	1.55712i
$126$	−0.701894	−	2.55095i	−0.0625297	−	0.227257i
$127$	2.27184	+	0.941026i	0.201593	+	0.0835026i	0.481196	−	0.876613i	$-0.340203\pi$
$127$	2.27184	+	0.941026i	0.201593	+	0.0835026i	−0.279603	+	0.960116i	$0.590203\pi$
$128$	−0.991445	+	0.130526i	−0.0876322	+	0.0115370i
$129$	0.946604	−	2.78861i	0.0833438	−	0.245523i
$130$	−9.61458	−	19.4964i	−0.843255	−	1.70995i
$131$	1.07839	+	3.17683i	0.0942193	+	0.277561i	0.983815	−	0.179188i	$-0.0573470\pi$
$131$	1.07839	+	3.17683i	0.0942193	+	0.277561i	−0.889596	+	0.456749i	$0.849014\pi$
$132$	0.0413853	−	0.0413853i	0.00360213	−	0.00360213i
$133$	12.1898	−	1.68806i	1.05699	−	0.146373i
$134$	−9.06617	+	3.75533i	−0.783198	+	0.324411i
$135$	−3.39246	+	1.95864i	−0.291976	+	0.168572i
$136$	−4.03649	−	0.840693i	−0.346126	−	0.0720889i
$137$	8.82237	−	15.2808i	0.753746	−	1.30553i	−0.192250	−	0.981346i	$-0.561578\pi$
$137$	8.82237	−	15.2808i	0.753746	−	1.30553i	0.945996	−	0.324180i	$-0.105088\pi$
$138$	1.39777	+	1.07255i	0.118986	+	0.0913013i
$139$	−7.37612	−	11.0391i	−0.625634	−	0.936327i	−0.999959	−	0.00902987i	$-0.997126\pi$
$139$	−7.37612	−	11.0391i	−0.625634	−	0.936327i	0.374325	−	0.927297i	$-0.377874\pi$
$140$	−10.1783	−	1.95372i	−0.860224	−	0.165120i
$141$	−11.5996	−	2.30731i	−0.976864	−	0.194310i
$142$	−0.375585	+	5.73033i	−0.0315184	+	0.480878i
$143$	0.307553	+	0.104400i	0.0257189	+	0.00873039i
$144$	−0.793353	+	0.608761i	−0.0661128	+	0.0507301i
$145$	4.81159	+	36.5476i	0.399581	+	3.03512i
$146$	5.14437	−	1.02328i	0.425751	−	0.0846872i
$147$	−0.551466	−	6.97824i	−0.0454842	−	0.575556i
$148$	−0.410783	+	2.06514i	−0.0337661	+	0.169754i
$149$	4.11624	−	15.3620i	0.337216	−	1.25851i	−0.564232	−	0.825616i	$-0.690828\pi$
$149$	4.11624	−	15.3620i	0.337216	−	1.25851i	0.901447	−	0.432889i	$-0.142506\pi$
$150$	0.676596	+	10.3229i	0.0552438	+	0.842858i
$151$	−0.151868	+	1.15355i	−0.0123588	+	0.0938746i	−0.996513	−	0.0834425i	$-0.973408\pi$
$151$	−0.151868	+	1.15355i	−0.0123588	+	0.0938746i	0.984154	+	0.177317i	$0.0567418\pi$
$152$	−2.32564	−	4.02812i	−0.188634	−	0.326724i
$153$	−3.91605	+	1.29018i	−0.316594	+	0.104305i
$154$	0.128173	−	0.0868914i	0.0103285	−	0.00700191i
$155$	5.52495	+	13.3384i	0.443775	+	1.07137i
$156$	−4.97705	−	2.45441i	−0.398483	−	0.196510i
$157$	−7.49854	+	2.00923i	−0.598449	+	0.160354i	−0.545312	−	0.838233i	$-0.683589\pi$
$157$	−7.49854	+	2.00923i	−0.598449	+	0.160354i	−0.0531372	+	0.998587i	$0.516922\pi$
$158$	5.89066	−	6.71701i	0.468636	−	0.534376i
$159$	−9.93085	−	0.650902i	−0.787567	−	0.0516199i
$160$	0.764221	+	3.84200i	0.0604170	+	0.303737i
$161$	3.09692	+	3.48395i	0.244072	+	0.274574i
$162$	−0.382683	+	0.923880i	−0.0300665	+	0.0725868i
$163$	−6.11005	+	5.35837i	−0.478576	+	0.419700i	−0.864348	−	0.502894i	$-0.832268\pi$
$163$	−6.11005	+	5.35837i	−0.478576	+	0.419700i	0.385772	+	0.922594i	$0.373935\pi$
$164$	9.24798	−	4.56060i	0.722146	−	0.356123i
$165$	−0.172373	−	0.151167i	−0.0134193	−	0.0117684i
$166$	8.74987	+	2.34452i	0.679122	+	0.181970i
$167$	−16.9409	+	11.3195i	−1.31093	+	0.875933i	−0.997287	−	0.0736096i	$-0.976548\pi$
$167$	−16.9409	+	11.3195i	−1.31093	+	0.875933i	−0.313639	+	0.949542i	$0.601548\pi$
$168$	−2.36500	+	1.18607i	−0.182464	+	0.0915075i
$169$		−	17.7952i		−	1.36886i
$170$	−2.25202	+	15.9935i	−0.172722	+	1.22665i
$171$	−4.02812	−	2.32564i	−0.308038	−	0.177846i
$172$	−2.91970	−	0.384385i	−0.222625	−	0.0293091i
$173$	2.43402	−	4.93570i	0.185055	−	0.375254i	−0.784500	−	0.620129i	$-0.787080\pi$
$173$	2.43402	−	4.93570i	0.185055	−	0.375254i	0.969555	+	0.244875i	$0.0787468\pi$
$174$	6.65414	+	6.65414i	0.504449	+	0.504449i
$175$	−3.39048	+	27.1595i	−0.256296	+	2.05307i
$176$	−0.0486640	−	0.0325162i	−0.00366819	−	0.00245100i
$177$	2.70582	+	3.08540i	0.203382	+	0.231913i
$178$	−0.466316	−	0.607714i	−0.0349518	−	0.0455501i
$179$	−6.28836	−	8.19515i	−0.470014	−	0.612535i	0.496847	−	0.867838i	$-0.334491\pi$
$179$	−6.28836	−	8.19515i	−0.470014	−	0.612535i	−0.966861	+	0.255304i	$0.917825\pi$
$180$	2.58284	+	2.94516i	0.192513	+	0.219519i
$181$	−3.36119	−	2.24587i	−0.249835	−	0.166935i	0.424347	−	0.905500i	$-0.360504\pi$
$181$	−3.36119	−	2.24587i	−0.249835	−	0.166935i	−0.674182	+	0.738565i	$0.735504\pi$
$182$	−11.7078	−	8.85962i	−0.867842	−	0.656719i
$183$	−3.52039	−	3.52039i	−0.260235	−	0.260235i
$184$	0.779247	−	1.58016i	0.0574468	−	0.116491i
$185$	8.17765	+	1.07661i	0.601233	+	0.0791538i
$186$	3.19180	+	1.84279i	0.234034	+	0.135120i
$187$	−0.145177	−	0.192761i	−0.0106164	−	0.0140961i
$188$			11.8269i			0.862563i
$189$	−1.45511	+	2.20967i	−0.105844	+	0.160730i
$190$	−15.1496	+	10.1227i	−1.09907	+	0.734374i
$191$	9.64027	+	2.58310i	0.697546	+	0.186907i	0.590131	−	0.807308i	$-0.299076\pi$
$191$	9.64027	+	2.58310i	0.697546	+	0.186907i	0.107415	+	0.994214i	$0.465743\pi$
$192$	0.751840	+	0.659346i	0.0542594	+	0.0475842i
$193$	−11.6360	+	5.73824i	−0.837578	+	0.413048i	−0.809899	−	0.586569i	$-0.800478\pi$
$193$	−11.6360	+	5.73824i	−0.837578	+	0.413048i	−0.0276785	+	0.999617i	$0.508811\pi$
$194$	−3.76430	+	3.30120i	−0.270261	+	0.237013i
$195$	−8.31887	+	20.0835i	−0.595727	+	1.43821i
$196$	−6.73657	+	1.90226i	−0.481184	+	0.135876i
$197$	0.0140523	+	0.0706457i	0.00100119	+	0.00503330i	0.981283	−	0.192573i	$-0.0616832\pi$
$197$	0.0140523	+	0.0706457i	0.00100119	+	0.00503330i	−0.980281	+	0.197606i	$0.936683\pi$
$198$	−0.0584024	−	0.00382789i	−0.00415048	−	0.000272037i
$199$	−9.51806	+	10.8533i	−0.674718	+	0.769368i	−0.983332	−	0.181819i	$-0.941801\pi$
$199$	−9.51806	+	10.8533i	−0.674718	+	0.769368i	0.308614	+	0.951187i	$0.400135\pi$
$200$	9.99251	−	2.67748i	0.706577	−	0.189327i
$201$	8.80115	+	4.34025i	0.620785	+	0.306137i
$202$	0.0260055	+	0.0627829i	0.00182974	+	0.00441739i
$203$	13.9708	+	20.6083i	0.980561	+	1.44642i
$204$	2.02937	+	3.58910i	0.142085	+	0.251287i
$205$	−20.1962	−	34.9808i	−1.41056	−	2.44317i
$206$	0.860164	−	6.53359i	0.0599305	−	0.455217i
$207$	−0.115231	−	1.75808i	−0.00800908	−	0.122195i
$208$	−1.43627	+	5.36025i	−0.0995877	+	0.371666i
$209$	0.0531091	−	0.266998i	0.00367363	−	0.0184686i
$210$	5.24214	+	8.94064i	0.361742	+	0.616963i
$211$	8.58347	−	1.70736i	0.590911	−	0.117539i	0.109427	−	0.993995i	$-0.465098\pi$
$211$	8.58347	−	1.70736i	0.590911	−	0.117539i	0.481483	+	0.876455i	$0.340098\pi$
$212$	1.29902	+	9.86701i	0.0892169	+	0.677669i
$213$	4.55593	−	3.49589i	0.312167	−	0.239534i
$214$	−6.59135	−	2.23746i	−0.450576	−	0.152950i
$215$	−0.754486	+	11.5112i	−0.0514555	+	0.785059i
$216$	0.980785	+	0.195090i	0.0667340	+	0.0132742i
$217$	7.37423	+	6.38004i	0.500595	+	0.433106i
$218$	−10.1293	−	15.1596i	−0.686045	−	1.02674i
$219$	−4.16126	−	3.19305i	−0.281192	−	0.215766i
$220$	−0.114634	+	0.198553i	−0.00772865	+	0.0133864i
$221$	−12.8822	+	18.9094i	−0.866551	+	1.27199i
$222$	1.82351	−	1.05280i	0.122386	−	0.0706594i
$223$	−12.1533	+	5.03405i	−0.813843	+	0.337105i	−0.750486	−	0.660886i	$-0.770181\pi$
$223$	−12.1533	+	5.03405i	−0.813843	+	0.337105i	−0.0633565	+	0.997991i	$0.520181\pi$
$224$	1.62467	+	2.08817i	0.108553	+	0.139522i
$225$	7.31502	−	7.31502i	0.487668	−	0.487668i
$226$	−4.26199	−	12.5554i	−0.283503	−	0.835173i
$227$	8.67045	+	17.5819i	0.575478	+	1.16695i	0.968867	+	0.247582i	$0.0796360\pi$
$227$	8.67045	+	17.5819i	0.575478	+	1.16695i	−0.393389	+	0.919372i	$0.628697\pi$
$228$	−1.49510	+	4.40443i	−0.0990156	+	0.291691i
$229$	23.2462	−	3.06043i	1.53615	−	0.202239i	0.685543	−	0.728032i	$-0.259565\pi$
$229$	23.2462	−	3.06043i	1.53615	−	0.202239i	0.850612	+	0.525794i	$0.176232\pi$
$230$	−6.37629	−	2.64115i	−0.420440	−	0.174152i
$231$	−0.149839	−	0.0390741i	−0.00985867	−	0.00257089i
$232$	5.22813	−	7.82444i	0.343243	−	0.513700i
$233$	1.27258	−	0.431982i	0.0833693	−	0.0283001i	−0.279443	−	0.960162i	$-0.590150\pi$
$233$	1.27258	−	0.431982i	0.0833693	−	0.0283001i	0.362813	+	0.931862i	$0.381817\pi$
$234$	1.43627	+	5.36025i	0.0938922	+	0.350410i
$235$	46.2298	−	3.03006i	3.01570	−	0.197660i
$236$	2.49823	−	3.25576i	0.162621	−	0.211932i
$237$	−8.93409			−0.580332
$238$	3.48291	+	10.3378i	0.225763	+	0.670098i
$239$	−27.6716			−1.78993			−0.894964	−	0.446139i	$-0.852799\pi$
$239$	−27.6716			−1.78993			−0.894964	+	0.446139i	$0.852799\pi$
$240$	2.38468	−	3.10778i	0.153931	−	0.200606i
$241$	−6.97789	+	0.457355i	−0.449485	+	0.0294608i	−0.288465	−	0.957490i	$-0.593145\pi$
$241$	−6.97789	+	0.457355i	−0.449485	+	0.0294608i	−0.161020	+	0.986951i	$0.551478\pi$
$242$	2.84612	+	10.6219i	0.182956	+	0.682800i
$243$	0.946930	−	0.321439i	0.0607456	−	0.0206204i
$244$	−2.76595	+	4.13954i	−0.177072	+	0.265007i
$245$	9.16162	+	25.8451i	0.585315	+	1.65118i
$246$	−9.52645	−	3.94599i	−0.607385	−	0.251587i
$247$	−25.5907	+	3.36908i	−1.62830	+	0.214369i
$248$	1.18469	−	3.48998i	0.0752278	−	0.221614i
$249$	−4.00649	−	8.12435i	−0.253901	−	0.514860i
$250$	−6.73024	−	19.8267i	−0.425658	−	1.25395i
$251$	−9.59545	+	9.59545i	−0.605659	+	0.605659i	−0.941809	−	0.336149i	$-0.890875\pi$
$251$	−9.59545	+	9.59545i	−0.605659	+	0.605659i	0.336149	+	0.941809i	$0.390875\pi$
$252$	2.45109	+	0.996070i	0.154404	+	0.0627465i
$253$	0.0952678	−	0.0394612i	0.00598943	−	0.00248090i
$254$	−2.12957	+	1.22951i	−0.133621	+	0.0771463i
$255$	13.5094	−	8.85212i	0.845994	−	0.554341i
$256$	0.500000	−	0.866025i	0.0312500	−	0.0541266i
$257$	−14.9610	−	11.4799i	−0.933239	−	0.716099i	0.0257128	−	0.999669i	$-0.491814\pi$
$257$	−14.9610	−	11.4799i	−0.933239	−	0.716099i	−0.958951	+	0.283570i	$0.908481\pi$
$258$	1.63609	+	2.44859i	0.101859	+	0.152442i
$259$	5.26313	−	1.82604i	0.327035	−	0.113465i
$260$	21.3206	+	4.24092i	1.32225	+	0.263011i
$261$	0.615468	−	9.39023i	0.0380965	−	0.581241i
$262$	−3.17683	−	1.07839i	−0.196265	−	0.0666231i
$263$	14.7762	−	11.3382i	0.911142	−	0.699144i	−0.0428160	−	0.999083i	$-0.513633\pi$
$263$	14.7762	−	11.3382i	0.911142	−	0.699144i	0.953958	+	0.299939i	$0.0969663\pi$
$264$	0.00763940	+	0.0580270i	0.000470172	+	0.00357131i
$265$	38.2362	−	7.60565i	2.34883	−	0.467211i
$266$	−6.08145	+	10.6984i	−0.372877	+	0.655963i
$267$	−0.149441	+	0.751288i	−0.00914561	+	0.0459781i
$268$	2.53983	−	9.47877i	0.155145	−	0.579008i
$269$	−1.49125	−	22.7520i	−0.0909229	−	1.38722i	−0.762839	−	0.646589i	$-0.776195\pi$
$269$	−1.49125	−	22.7520i	−0.0909229	−	1.38722i	0.671916	−	0.740627i	$-0.265472\pi$
$270$	0.511306	−	3.88376i	0.0311171	−	0.236358i
$271$	−8.99513	−	15.5800i	−0.546415	−	0.946419i	−0.998516	−	0.0544524i	$-0.982659\pi$
$271$	−8.99513	−	15.5800i	−0.546415	−	0.946419i	0.452101	−	0.891967i	$-0.350675\pi$
$272$	3.12423	−	2.69058i	0.189434	−	0.163140i
$273$	1.05849	+	14.6440i	0.0640628	+	0.886293i
$274$	6.75235	+	16.3016i	0.407924	+	0.984816i
$275$	0.543029	+	0.267792i	0.0327459	+	0.0161485i
$276$	−1.70182	+	0.456001i	−0.102437	+	0.0274480i
$277$	0.364953	−	0.416149i	0.0219279	−	0.0250040i	−0.740772	−	0.671757i	$-0.765540\pi$
$277$	0.364953	−	0.416149i	0.0219279	−	0.0250040i	0.762700	+	0.646753i	$0.223873\pi$
$278$	13.2482	+	0.868335i	0.794576	+	0.0520793i
$279$	−0.719020	−	3.61476i	−0.0430466	−	0.216410i
$280$	7.74616	−	6.88564i	0.462921	−	0.411496i
$281$	11.1133	−	26.8300i	0.662967	−	1.60054i	−0.130165	−	0.991492i	$-0.541551\pi$
$281$	11.1133	−	26.8300i	0.662967	−	1.60054i	0.793131	−	0.609051i	$-0.208449\pi$
$282$	8.89191	−	7.79800i	0.529506	−	0.464364i
$283$	−16.9924	+	8.37974i	−1.01010	+	0.498124i	−0.870544	−	0.492091i	$-0.836233\pi$
$283$	−16.9924	+	8.37974i	−1.01010	+	0.498124i	−0.139551	+	0.990215i	$0.544566\pi$
$284$	−4.31753	−	3.78637i	−0.256198	−	0.224680i
$285$	17.5995	+	4.71576i	1.04250	+	0.279337i
$286$	−0.270053	+	0.180444i	−0.0159686	+	0.0106699i
$287$	−22.7847	−	15.0042i	−1.34494	−	0.885671i
$288$		−	1.00000i		−	0.0589256i
$289$	15.8204	−	6.22224i	0.930609	−	0.366014i
$290$	−31.9243	−	18.4315i	−1.87466	−	1.08233i
$291$	4.96395	+	0.653517i	0.290992	+	0.0383098i
$292$	−2.31987	+	4.70424i	−0.135760	+	0.275295i
$293$	−6.27497	−	6.27497i	−0.366588	−	0.366588i	0.499643	−	0.866231i	$-0.333464\pi$
$293$	−6.27497	−	6.27497i	−0.366588	−	0.366588i	−0.866231	+	0.499643i	$0.833464\pi$
$294$	5.87192	+	3.81058i	0.342458	+	0.222237i
$295$	−13.3664	−	8.93116i	−0.778224	−	0.519992i
$296$	−1.38832	−	1.58308i	−0.0806945	−	0.0920144i
$297$	0.0356294	+	0.0464331i	0.00206743	+	0.00269432i
$298$	9.68170	+	12.6174i	0.560846	+	0.730908i
$299$	−6.44649	−	7.35082i	−0.372810	−	0.425109i
$300$	−8.60156	−	5.74738i	−0.496611	−	0.331825i
$301$	3.02987	+	7.17820i	0.174639	+	0.413745i
$302$	−0.822722	−	0.822722i	−0.0473423	−	0.0473423i
$303$	0.0300561	−	0.0609477i	0.00172668	−	0.00350135i
$304$	4.61148	+	0.607113i	0.264487	+	0.0348203i
$305$	16.8896	+	9.75122i	0.967096	+	0.558353i
$306$	1.36037	−	3.89222i	0.0777671	−	0.222504i
$307$			22.4455i			1.28103i	0.767945	+	0.640516i	$0.221279\pi$
$307$			22.4455i			1.28103i	−0.767945	+	0.640516i	$0.778721\pi$
$308$	−0.00909118	+	0.154583i	−0.000518018	+	0.00880816i
$309$	−5.47936	+	3.66119i	−0.311710	+	0.208278i
$310$	−13.9454	−	3.73667i	−0.792048	−	0.212229i
$311$	−25.9593	−	22.7657i	−1.47202	−	1.29092i	−0.870604	−	0.491985i	$-0.836271\pi$
$311$	−25.9593	−	22.7657i	−1.47202	−	1.29092i	−0.601413	−	0.798939i	$-0.705395\pi$
$312$	4.97705	−	2.45441i	0.281770	−	0.138954i
$313$	6.12865	−	5.37468i	0.346412	−	0.303795i	−0.468405	−	0.883514i	$-0.655171\pi$
$313$	6.12865	−	5.37468i	0.346412	−	0.303795i	0.814816	+	0.579719i	$0.196838\pi$
$314$	2.97080	−	7.17214i	0.167652	−	0.404747i
$315$	3.26555	−	9.83622i	0.183993	−	0.554208i
$316$	1.74296	+	8.76243i	0.0980489	+	0.492925i
$317$	32.8199	+	2.15113i	1.84335	+	0.120819i	0.946739	−	0.322003i	$-0.104356\pi$
$317$	32.8199	+	2.15113i	1.84335	+	0.120819i	0.896609	+	0.442823i	$0.146023\pi$
$318$	6.56191	−	7.48243i	0.367974	−	0.419594i
$319$	0.532001	−	0.142549i	0.0297863	−	0.00798122i
$320$	−3.51329	−	1.73256i	−0.196399	−	0.0968533i
$321$	2.66377	+	6.43090i	0.148677	+	0.358938i
$322$	−4.64929	+	0.336059i	−0.259095	+	0.0187278i
$323$	17.1230	+	8.63633i	0.952750	+	0.480538i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	7.49324	−	56.9168i	0.415650	−	3.15718i
$326$	−0.531518	−	8.10940i	−0.0294381	−	0.449138i
$327$	−4.71887	+	17.6111i	−0.260954	+	0.973894i
$328$	−2.01165	+	10.1132i	−0.111075	+	0.558410i
$329$	26.9932	−	15.8269i	1.48818	−	0.872563i
$330$	0.224863	−	0.0447281i	0.0123783	−	0.00246220i
$331$	3.50595	+	26.6304i	0.192705	+	1.46374i	0.765181	+	0.643815i	$0.222650\pi$
$331$	3.50595	+	26.6304i	0.192705	+	1.46374i	−0.572476	+	0.819921i	$0.694017\pi$
$332$	−7.18662	+	5.51449i	−0.394417	+	0.302647i
$333$	−1.99386	−	0.676824i	−0.109263	−	0.0370897i
$334$	1.33257	−	20.3310i	0.0729147	−	1.11246i
$335$	−37.7021	−	7.49942i	−2.05989	−	0.409737i
$336$	0.498747	−	2.59832i	0.0272089	−	0.141750i
$337$	−10.0623	−	15.0593i	−0.548130	−	0.820335i	0.449195	−	0.893434i	$-0.351711\pi$
$337$	−10.0623	−	15.0593i	−0.548130	−	0.820335i	−0.997325	+	0.0730993i	$0.976711\pi$
$338$	14.1178	+	10.8330i	0.767909	+	0.589238i
$339$	−6.62953	+	11.4827i	−0.360067	+	0.623654i
$340$	−11.3176	−	11.5229i	−0.613783	−	0.624917i
$341$	0.186809	−	0.107854i	0.0101163	−	0.00584063i
$342$	4.29722	−	1.77997i	0.232367	−	0.0962495i
$343$	13.3566	+	12.8297i	0.721189	+	0.692738i
$344$	2.08235	−	2.08235i	0.112273	−	0.112273i
$345$	2.21846	+	6.53538i	0.119438	+	0.351853i
$346$	2.43402	+	4.93570i	0.130854	+	0.265345i
$347$	4.34727	−	12.8066i	0.233374	−	0.687497i	−0.765647	−	0.643261i	$-0.777581\pi$
$347$	4.34727	−	12.8066i	0.233374	−	0.687497i	0.999021	−	0.0442363i	$-0.0140854\pi$
$348$	−9.32987	+	1.22830i	−0.500134	+	0.0658438i
$349$	15.0309	+	6.22601i	0.804587	+	0.333271i	0.746792	−	0.665058i	$-0.231593\pi$
$349$	15.0309	+	6.22601i	0.804587	+	0.333271i	0.0577948	+	0.998328i	$0.481593\pi$
$350$	−19.4831	−	19.2235i	−1.04141	−	1.02754i
$351$	3.08305	−	4.61411i	0.164561	−	0.246283i
$352$	0.0554216	−	0.0188131i	0.00295398	−	0.00100274i
$353$	−6.11216	−	22.8109i	−0.325318	−	1.21410i	−0.913992	−	0.405732i	$-0.867017\pi$
$353$	−6.11216	−	22.8109i	−0.325318	−	1.21410i	0.588675	−	0.808370i	$-0.299650\pi$
$354$	−4.09501	+	0.268401i	−0.217647	+	0.0142653i
$355$	−13.6943	+	17.8468i	−0.726820	+	0.947210i
$356$	0.766007			0.0405983
$357$	5.47590	−	9.43475i	0.289815	−	0.499340i
$358$	10.3298			0.545945
$359$	−4.77302	+	6.22032i	−0.251910	+	0.328296i	−0.902141	−	0.431441i	$-0.858005\pi$
$359$	−4.77302	+	6.22032i	−0.251910	+	0.328296i	0.650231	+	0.759737i	$0.274672\pi$
$360$	−3.90888	+	0.256202i	−0.206016	+	0.0135030i
$361$	0.681819	+	2.54458i	0.0358852	+	0.133925i
$362$	3.82793	−	1.29941i	0.201192	−	0.0682954i
$363$	6.10937	−	9.14332i	0.320659	−	0.479900i
$364$	14.1561	−	3.89505i	0.741980	−	0.204156i
$365$	18.9827	+	7.86288i	0.993598	+	0.411562i
$366$	4.93599	−	0.649835i	0.258008	−	0.0339674i
$367$	2.85979	−	8.42466i	0.149280	−	0.439764i	−0.846408	−	0.532535i	$-0.821239\pi$
$367$	2.85979	−	8.42466i	0.149280	−	0.439764i	0.995687	+	0.0927717i	$0.0295727\pi$
$368$	0.779247	+	1.58016i	0.0406211	+	0.0823713i
$369$	3.31448	+	9.76414i	0.172545	+	0.508301i
$370$	−5.83237	+	5.83237i	−0.303210	+	0.303210i
$371$	20.7818	−	16.1690i	1.07894	−	0.839452i
$372$	−3.40503	+	1.41041i	−0.176542	+	0.0731262i
$373$	−9.47370	+	5.46965i	−0.490530	+	0.283208i	−0.724794	−	0.688965i	$-0.758065\pi$
$373$	−9.47370	+	5.46965i	−0.490530	+	0.283208i	0.234264	+	0.972173i	$0.424732\pi$
$374$	0.241306	+	0.00216904i	0.0124776	+	0.000112158i
$375$	−10.4689	+	18.1327i	−0.540612	+	0.936368i
$376$	−9.38289	−	7.19974i	−0.483885	−	0.371298i
$377$	−29.0126	−	43.4205i	−1.49423	−	2.23627i
$378$	−0.867231	−	2.49958i	−0.0446056	−	0.128565i
$379$	13.9672	+	2.77825i	0.717447	+	0.142709i	0.540296	−	0.841475i	$-0.318312\pi$
$379$	13.9672	+	2.77825i	0.717447	+	0.142709i	0.177150	+	0.984184i	$0.443312\pi$
$380$	1.19166	−	18.1813i	0.0611311	−	0.932680i
$381$	2.32852	+	0.790426i	0.119294	+	0.0404947i
$382$	−7.91794	+	6.07565i	−0.405117	+	0.310857i
$383$	−0.695785	−	5.28501i	−0.0355530	−	0.270052i	−0.999984	−	0.00571575i	$-0.998181\pi$
$383$	−0.695785	−	5.28501i	−0.0355530	−	0.270052i	0.964431	−	0.264336i	$-0.0851527\pi$
$384$	−0.980785	+	0.195090i	−0.0500505	+	0.00995566i
$385$	0.606575	−	0.00406798i	0.0309139	−	0.000207323i
$386$	2.53110	−	12.7247i	0.128829	−	0.647669i
$387$	0.762194	−	2.84455i	0.0387445	−	0.144596i
$388$	−0.327459	−	4.99606i	−0.0166242	−	0.253637i
$389$	−0.0706666	+	0.536766i	−0.00358294	+	0.0272151i	−0.993143	−	0.116906i	$-0.962702\pi$
$389$	−0.0706666	+	0.536766i	−0.00358294	+	0.0272151i	0.989560	+	0.144121i	$0.0460356\pi$
$390$	−10.8691	−	18.8259i	−0.550380	−	0.953286i
$391$	0.883407	+	7.21038i	0.0446758	+	0.364645i
$392$	2.59180	−	6.50250i	0.130906	−	0.328426i
$393$	1.28385	+	3.09950i	0.0647619	+	0.156349i
$394$	−0.0646015	−	0.0318579i	−0.00325458	−	0.00160498i
$395$	33.8048	−	9.05796i	1.70090	−	0.455755i
$396$	0.0385900	−	0.0440035i	0.00193922	−	0.00221126i
$397$	5.25745	+	0.344592i	0.263864	+	0.0172946i	0.196761	−	0.980451i	$-0.436958\pi$
$397$	5.25745	+	0.344592i	0.263864	+	0.0172946i	0.0671031	+	0.997746i	$0.478624\pi$
$398$	−2.81625	−	14.1582i	−0.141166	−	0.709689i
$399$	12.0533	−	2.48169i	0.603419	−	0.124240i
$400$	−3.95886	+	9.55754i	−0.197943	+	0.477877i
$401$	13.9306	−	12.2168i	0.695660	−	0.610077i	−0.236711	−	0.971580i	$-0.576070\pi$
$401$	13.9306	−	12.2168i	0.695660	−	0.610077i	0.932371	+	0.361503i	$0.117736\pi$
$402$	−8.80115	+	4.34025i	−0.438961	+	0.216472i
$403$	−15.3770	−	13.4853i	−0.765983	−	0.671749i
$404$	−0.0656402	−	0.0175882i	−0.00326572	−	0.000875048i
$405$	−3.25709	+	2.17632i	−0.161846	+	0.108142i
$406$	−24.8546	−	1.46173i	−1.23351	−	0.0725442i
$407$		−	0.123236i		−	0.00610858i
$408$	−4.08283	−	0.574894i	−0.202130	−	0.0284615i
$409$	7.44692	+	4.29948i	0.368227	+	0.212596i	0.672683	−	0.739930i	$-0.265142\pi$
$409$	7.44692	+	4.29948i	0.368227	+	0.212596i	−0.304457	+	0.952526i	$0.598475\pi$
$410$	40.0468	+	5.27226i	1.97777	+	0.260379i
$411$	7.80407	−	15.8251i	0.384946	−	0.780594i
$412$	4.65981	+	4.65981i	0.229573	+	0.229573i
$413$	−10.7740	−	1.34498i	−0.530153	−	0.0661821i
$414$	1.46493	+	0.978832i	0.0719972	+	0.0481070i
$415$	23.3967	+	26.6788i	1.14850	+	1.30961i
$416$	−3.37822	−	4.40259i	−0.165631	−	0.215855i
$417$	−8.08232	−	10.5331i	−0.395793	−	0.515807i
$418$	0.179493	+	0.204672i	0.00877927	+	0.0100108i
$419$	22.8827	+	15.2897i	1.11789	+	0.746953i	0.970254	−	0.242089i	$-0.0778325\pi$
$419$	22.8827	+	15.2897i	1.11789	+	0.746953i	0.147639	+	0.989041i	$0.452832\pi$
$420$	−10.2843	−	1.28385i	−0.501822	−	0.0626454i
$421$	−21.9966	−	21.9966i	−1.07205	−	1.07205i	−0.997195	−	0.0748526i	$-0.976151\pi$
$421$	−21.9966	−	21.9966i	−1.07205	−	1.07205i	−0.0748526	−	0.997195i	$-0.523849\pi$
$422$	−3.87075	+	7.84910i	−0.188425	+	0.382088i
$423$	−11.7257	−	1.54372i	−0.570122	−	0.0750580i
$424$	−8.61882	−	4.97608i	−0.418567	−	0.241660i
$425$	−28.4105	+	31.8146i	−1.37811	+	1.54323i
$426$			5.74262i			0.278231i
$427$	13.1494	+	0.773329i	0.636342	+	0.0374240i
$428$	5.78766	−	3.86719i	0.279757	−	0.186928i
$429$	0.313723	+	0.0840618i	0.0151467	+	0.00405854i
$430$	−8.67317	−	7.60617i	−0.418257	−	0.366802i
$431$	15.6539	−	7.71965i	0.754022	−	0.371842i	−0.0243027	−	0.999705i	$-0.507737\pi$
$431$	15.6539	−	7.71965i	0.754022	−	0.371842i	0.778324	+	0.627862i	$0.216070\pi$
$432$	−0.751840	+	0.659346i	−0.0361729	+	0.0317228i
$433$	−14.7168	+	35.5296i	−0.707246	+	1.70744i	−0.000475398		1.00000i	$0.500151\pi$
$433$	−14.7168	+	35.5296i	−0.707246	+	1.70744i	−0.706771	+	0.707443i	$0.749849\pi$
$434$	−9.55077	+	1.96644i	−0.458452	+	0.0943922i
$435$	7.19161	+	36.1547i	0.344811	+	1.73348i
$436$	18.1933	+	1.19245i	0.871300	+	0.0571080i
$437$	−5.40324	+	6.16122i	−0.258472	+	0.294731i
$438$	5.06643	−	1.35755i	0.242083	−	0.0648661i
$439$	30.3593	+	14.9715i	1.44897	+	0.714552i	0.985201	−	0.171405i	$-0.0548305\pi$
$439$	30.3593	+	14.9715i	1.44897	+	0.714552i	0.463768	+	0.885957i	$0.346497\pi$
$440$	−0.0877374	−	0.211817i	−0.00418272	−	0.0100980i
$441$	−1.00668	−	6.92724i	−0.0479373	−	0.329868i
$442$	−7.15966	−	21.7315i	−0.340550	−	1.03366i
$443$	5.39176	+	9.33880i	0.256170	+	0.443700i	0.965213	−	0.261466i	$-0.0842060\pi$
$443$	5.39176	+	9.33880i	0.256170	+	0.443700i	−0.709043	+	0.705166i	$0.750873\pi$
$444$	−0.274836	+	2.08759i	−0.0130432	+	0.0990726i
$445$	−0.196252	−	2.99423i	−0.00930325	−	0.141940i
$446$	3.40466	−	12.7064i	0.161215	−	0.601664i
$447$	3.10270	−	15.5983i	0.146753	−	0.737776i
$448$	−2.64569	+	0.0177433i	−0.124997	+	0.000838290i
$449$	−14.2714	+	2.83877i	−0.673511	+	0.133970i	−0.519986	−	0.854175i	$-0.674063\pi$
$449$	−14.2714	+	2.83877i	−0.673511	+	0.133970i	−0.153525	+	0.988145i	$0.549063\pi$
$450$	1.35029	+	10.2565i	0.0636535	+	0.483496i
$451$	−0.478789	+	0.367388i	−0.0225453	+	0.0172996i
$452$	12.5554	+	4.26199i	0.590557	+	0.200467i
$453$	−0.0760968	+	1.16101i	−0.00357534	+	0.0545492i
$454$	−19.2269	−	3.82447i	−0.902364	−	0.179491i
$455$	−18.8521	−	54.3366i	−0.883800	−	2.54734i
$456$	−2.58411	−	3.86739i	−0.121012	−	0.181107i
$457$	12.2337	+	9.38725i	0.572268	+	0.439117i	0.853923	−	0.520399i	$-0.174217\pi$
$457$	12.2337	+	9.38725i	0.572268	+	0.439117i	−0.281655	+	0.959516i	$0.590883\pi$
$458$	−11.7234	+	20.3055i	−0.547799	+	0.948816i
$459$	−3.82328	+	1.54354i	−0.178455	+	0.0720463i
$460$	5.97700	−	3.45082i	0.278679	−	0.160895i
$461$	21.0951	−	8.73786i	0.982495	−	0.406963i	0.167146	−	0.985932i	$-0.446545\pi$
$461$	21.0951	−	8.73786i	0.982495	−	0.406963i	0.815349	+	0.578970i	$0.196545\pi$
$462$	0.122216	−	0.0950883i	0.00568599	−	0.00442391i
$463$	−25.9336	+	25.9336i	−1.20524	+	1.20524i	−0.232685	+	0.972552i	$0.574751\pi$
$463$	−25.9336	+	25.9336i	−1.20524	+	1.20524i	−0.972552	+	0.232685i	$0.925249\pi$
$464$	3.02487	+	8.91097i	0.140426	+	0.413681i
$465$	6.38549	+	12.9485i	0.296120	+	0.600472i
$466$	−0.431982	+	1.27258i	−0.0200112	+	0.0589510i
$467$	−10.3313	+	1.36014i	−0.478075	+	0.0629398i	−0.365713	−	0.930728i	$-0.619175\pi$
$467$	−10.3313	+	1.36014i	−0.478075	+	0.0629398i	−0.112362	+	0.993667i	$0.535842\pi$
$468$	−5.12692	−	2.12364i	−0.236992	−	0.0981653i
$469$	−25.0329	+	6.88779i	−1.15591	+	0.318049i
$470$	−25.7390	+	38.5212i	−1.18725	+	1.77685i
$471$	−7.35108	+	2.49536i	−0.338720	+	0.114980i
$472$	1.06214	+	3.96396i	0.0488890	+	0.182456i
$473$	0.171989	−	0.0112727i	0.00790805	−	0.000518321i
$474$	5.43873	−	7.08789i	0.249809	−	0.325558i
$475$	−48.1175			−2.20778
$476$	−10.3218	−	3.53006i	−0.473097	−	0.161800i
$477$	−9.95216			−0.455678
$478$	16.8454	−	21.9534i	0.770491	−	1.00412i
$479$	−24.4576	+	1.60304i	−1.11750	+	0.0732446i	−0.612936	−	0.790132i	$-0.710012\pi$
$479$	−24.4576	+	1.60304i	−1.11750	+	0.0732446i	−0.504560	+	0.863377i	$0.668345\pi$
$480$	1.01386	+	3.78379i	0.0462764	+	0.172706i
$481$	−11.0646	+	3.75592i	−0.504502	+	0.171255i
$482$	3.88503	−	5.81435i	0.176958	−	0.264836i
$483$	3.31815	+	3.27394i	0.150981	+	0.148970i
$484$	−10.1595	−	4.20821i	−0.461796	−	0.191282i
$485$	−19.4451	+	2.56000i	−0.882958	+	0.116244i
$486$	−0.321439	+	0.946930i	−0.0145808	+	0.0429536i
$487$	12.6941	+	25.7412i	0.575226	+	1.16644i	0.968960	+	0.247219i	$0.0795167\pi$
$487$	12.6941	+	25.7412i	0.575226	+	1.16644i	−0.393733	+	0.919225i	$0.628817\pi$
$488$	−1.60031	−	4.71437i	−0.0724427	−	0.213409i
$489$	−5.74651	+	5.74651i	−0.259866	+	0.259866i
$490$	−26.0816	−	8.46510i	−1.17824	−	0.382414i
$491$	−2.45369	+	1.01635i	−0.110733	+	0.0458673i	−0.437362	−	0.899285i	$-0.644087\pi$
$491$	−2.45369	+	1.01635i	−0.110733	+	0.0458673i	0.326629	+	0.945153i	$0.394087\pi$
$492$	8.92990	−	5.15568i	0.402591	−	0.232436i
$493$	−0.348749	+	38.7984i	−0.0157068	+	1.74739i
$494$	12.9057	−	22.3534i	0.580657	−	1.00573i
$495$	−0.181891	−	0.139570i	−0.00817540	−	0.00627321i
$496$	2.04760	+	3.06444i	0.0919397	+	0.137598i
$497$	−2.86411	+	14.9212i	−0.128473	+	0.669305i
$498$	8.88448	+	1.76723i	0.398123	+	0.0791916i
$499$	−0.510713	+	7.79197i	−0.0228626	+	0.348816i	0.971068	+	0.238805i	$0.0767555\pi$
$499$	−0.510713	+	7.79197i	−0.0228626	+	0.348816i	−0.993930	+	0.110012i	$0.964911\pi$
$500$	19.8267	+	6.73024i	0.886675	+	0.300986i
$501$	−16.1643	+	12.4033i	−0.722167	+	0.554138i
$502$	−1.77124	−	13.4539i	−0.0790544	−	0.600478i
$503$	31.8666	−	6.33865i	1.42086	−	0.282627i	0.575928	−	0.817501i	$-0.304641\pi$
$503$	31.8666	−	6.33865i	1.42086	−	0.282627i	0.844932	+	0.534874i	$0.179641\pi$
$504$	−2.28236	+	1.33821i	−0.101665	+	0.0596087i
$505$	−0.0519333	+	0.261086i	−0.00231100	+	0.0116182i
$506$	−0.0266887	+	0.0996035i	−0.00118646	+	0.00442791i
$507$	−1.16386	−	17.7570i	−0.0516888	−	0.788618i
$508$	0.320966	−	2.43798i	0.0142406	−	0.108168i
$509$	−13.7039	−	23.7359i	−0.607415	−	1.05207i	−0.991665	−	0.128845i	$-0.958873\pi$
$509$	−13.7039	−	23.7359i	−0.607415	−	1.05207i	0.384250	−	0.923229i	$-0.374460\pi$
$510$	−1.20117	+	16.1066i	−0.0531886	+	0.713212i
$511$	13.8413	−	1.00047i	0.612302	−	0.0442582i
$512$	0.382683	+	0.923880i	0.0169124	+	0.0408301i
$513$	−4.17160	−	2.05721i	−0.184181	−	0.0908279i
$514$	18.2153	−	4.88078i	0.803443	−	0.215282i
$515$	17.0208	−	19.4085i	0.750027	−	0.855242i
$516$	−2.93859	−	0.192605i	−0.129364	−	0.00847896i
$517$	−0.135041	−	0.678899i	−0.00593911	−	0.0298579i
$518$	−1.75529	+	5.28714i	−0.0771230	+	0.232304i
$519$	2.10600	−	5.08433i	0.0924430	−	0.223177i
$520$	−16.3437	+	14.3330i	−0.716718	+	0.628545i
$521$	25.0016	−	12.3294i	1.09534	−	0.540163i	0.197421	−	0.980319i	$-0.436744\pi$
$521$	25.0016	−	12.3294i	1.09534	−	0.540163i	0.897921	+	0.440156i	$0.145077\pi$
$522$	7.07510	+	6.20469i	0.309669	+	0.271572i
$523$	34.7862	+	9.32093i	1.52109	+	0.407576i	0.920102	−	0.391680i	$-0.128106\pi$
$523$	34.7862	+	9.32093i	1.52109	+	0.407576i	0.600992	+	0.799255i	$0.294772\pi$
$524$	2.78948	−	1.86387i	0.121859	−	0.0814235i
$525$	−1.60690	+	27.3231i	−0.0701310	+	1.19248i
$526$			18.6251i			0.812091i
$527$	3.80092	+	14.7130i	0.165571	+	0.640907i
$528$	−0.0506865	−	0.0292639i	−0.00220585	−	0.00127355i
$529$	19.7257	+	2.59693i	0.857638	+	0.112910i
$530$	−17.2427	+	34.9648i	−0.748977	+	1.51878i
$531$	2.90182	+	2.90182i	0.125928	+	0.125928i
$532$	−4.78549	−	11.3375i	−0.207477	−	0.491544i
$533$	47.5777	+	31.7904i	2.06082	+	1.37700i
$534$	−0.505063	−	0.575915i	−0.0218562	−	0.0249223i
$535$	−16.5992	−	21.6325i	−0.717646	−	0.935255i
$536$	5.97387	+	7.78529i	0.258032	+	0.336274i
$537$	−6.81089	−	7.76633i	−0.293912	−	0.335142i
$538$	18.9582	+	12.6675i	0.817347	+	0.546134i
$539$	0.364980	−	0.186115i	0.0157208	−	0.00801654i
$540$	2.76993	+	2.76993i	0.119199	+	0.119199i
$541$	0.380234	−	0.771039i	0.0163475	−	0.0331495i	−0.888546	−	0.458788i	$-0.848284\pi$
$541$	0.380234	−	0.771039i	0.0163475	−	0.0331495i	0.904893	+	0.425638i	$0.139950\pi$
$542$	17.8364	+	2.34820i	0.766137	+	0.100864i
$543$	−3.50088	−	2.02123i	−0.150237	−	0.0867395i
$544$	0.232672	+	4.11654i	0.00997575	+	0.176495i
$545$		−	71.4209i		−	3.05934i
$546$	−12.2622	−	8.07492i	−0.524774	−	0.345575i
$547$	29.0682	−	19.4228i	1.24287	−	0.830457i	0.252321	−	0.967643i	$-0.418806\pi$
$547$	29.0682	−	19.4228i	1.24287	−	0.830457i	0.990545	+	0.137186i	$0.0438060\pi$
$548$	−17.0435	−	4.56679i	−0.728062	−	0.195084i
$549$	−3.74310	−	3.28261i	−0.159751	−	0.140098i
$550$	−0.543029	+	0.267792i	−0.0231548	+	0.0114187i
$551$	−32.9082	+	28.8597i	−1.40194	+	1.22947i
$552$	0.674231	−	1.62774i	0.0286972	−	0.0692811i
$553$	17.6666	−	15.7040i	0.751261	−	0.667804i
$554$	0.107984	+	0.542873i	0.00458780	+	0.0230644i
$555$	8.23055	+	0.539459i	0.349368	+	0.0228988i
$556$	−8.75391	+	9.98192i	−0.371248	+	0.423328i
$557$	−6.33575	+	1.69766i	−0.268454	+	0.0719321i	−0.390535	−	0.920588i	$-0.627710\pi$
$557$	−6.33575	+	1.69766i	−0.268454	+	0.0719321i	0.122081	+	0.992520i	$0.461043\pi$
$558$	3.30549	+	1.63009i	0.139933	+	0.0690071i
$559$	−6.25389	−	15.0982i	−0.264511	−	0.638586i
$560$	0.747187	+	10.3372i	0.0315744	+	0.436824i
$561$	−0.157473	−	0.182854i	−0.00664853	−	0.00772009i
$562$	14.5203	+	25.1499i	0.612501	+	1.06088i
$563$	0.638889	−	4.85284i	0.0269259	−	0.204523i	−0.972694	−	0.232091i	$-0.925443\pi$
$563$	0.638889	−	4.85284i	0.0269259	−	0.204523i	0.999620	+	0.0275686i	$0.00877647\pi$
$564$	0.773514	+	11.8015i	0.0325708	+	0.496935i
$565$	13.4429	−	50.1696i	0.565547	−	2.11065i
$566$	3.69624	−	18.5823i	0.155365	−	0.781071i
$567$	−1.30748	+	2.30011i	−0.0549090	+	0.0965955i
$568$	5.63228	−	1.12033i	0.236325	−	0.0470080i
$569$	−1.78671	−	13.5714i	−0.0749029	−	0.568944i	−0.987209	−	0.159434i	$-0.949033\pi$
$569$	−1.78671	−	13.5714i	−0.0749029	−	0.568944i	0.912306	−	0.409510i	$-0.134300\pi$
$570$	−14.4551	+	11.0918i	−0.605459	+	0.464585i
$571$	−10.5648	−	3.58627i	−0.442123	−	0.150081i	0.0914961	−	0.995805i	$-0.470835\pi$
$571$	−10.5648	−	3.58627i	−0.442123	−	0.150081i	−0.533619	+	0.845725i	$0.679168\pi$
$572$	0.0212423	−	0.324095i	0.000888184	−	0.0135511i
$573$	9.78858	+	1.94707i	0.408924	+	0.0813400i
$574$	25.7741	−	8.94233i	1.07579	−	0.373246i
$575$	−10.1260	−	15.1547i	−0.422284	−	0.631993i
$576$	0.793353	+	0.608761i	0.0330564	+	0.0253651i
$577$	−8.65505	+	14.9910i	−0.360314	+	0.624083i	−0.988012	−	0.154374i	$-0.950664\pi$
$577$	−8.65505	+	14.9910i	−0.360314	+	0.624083i	0.627698	+	0.778457i	$0.283997\pi$
$578$	−4.69439	+	16.3390i	−0.195261	+	0.679613i
$579$	−11.2358	+	6.48698i	−0.466943	+	0.269590i
$580$	34.0570	−	14.1069i	1.41414	−	0.585755i
$581$	22.2033	+	9.02293i	0.921147	+	0.374334i
$582$	−3.54033	+	3.54033i	−0.146751	+	0.146751i
$583$	−0.187231	−	0.551565i	−0.00775432	−	0.0228435i
$584$	−2.31987	−	4.70424i	−0.0959970	−	0.194663i
$585$	−6.98753	+	20.5846i	−0.288899	+	0.851069i
$586$	8.79823	−	1.15831i	0.363451	−	0.0478493i
$587$	−21.3504	−	8.84364i	−0.881227	−	0.365016i	−0.104255	−	0.994551i	$-0.533246\pi$
$587$	−21.3504	−	8.84364i	−0.881227	−	0.365016i	−0.776973	+	0.629534i	$0.783246\pi$
$588$	−6.59774	+	2.33878i	−0.272086	+	0.0964496i
$589$	−9.52392	+	14.2536i	−0.392426	+	0.587308i
$590$	15.2225	−	5.16735i	0.626702	−	0.212737i
$591$	0.0186427	+	0.0695754i	0.000766857	+	0.00286195i
$592$	2.10109	−	0.137713i	0.0863544	−	0.00565997i
$593$	−24.7737	+	32.2857i	−1.01733	+	1.32581i	−0.0728169	+	0.997345i	$0.523199\pi$
$593$	−24.7737	+	32.2857i	−1.01733	+	1.32581i	−0.944515	+	0.328468i	$0.893468\pi$
$594$	−0.0585277			−0.00240142
$595$	−11.1541	+	41.2510i	−0.457274	+	1.69112i
$596$	−15.9039			−0.651450
$597$	−8.78785	+	11.4525i	−0.359663	+	0.468722i
$598$	9.75617	−	0.639453i	0.398960	−	0.0261492i
$599$	−5.74235	−	21.4307i	−0.234626	−	0.875636i	−0.978317	−	0.207113i	$-0.933593\pi$
$599$	−5.74235	−	21.4307i	−0.234626	−	0.875636i	0.743691	−	0.668523i	$-0.233073\pi$
$600$	9.79600	−	3.32529i	0.399920	−	0.135755i
$601$	−7.81757	+	11.6998i	−0.318886	+	0.477246i	−0.955936	−	0.293577i	$-0.905154\pi$
$601$	−7.81757	+	11.6998i	−0.318886	+	0.477246i	0.637050	+	0.770822i	$0.280154\pi$
$602$	−7.53931	−	1.96606i	−0.307280	−	0.0801305i
$603$	9.06617	+	3.75533i	0.369203	+	0.152929i
$604$	1.15355	−	0.151868i	0.0469373	−	0.00617941i
$605$	−13.8465	+	40.7905i	−0.562940	+	1.65837i
$606$	0.0300561	+	0.0609477i	0.00122094	+	0.00247583i
$607$	−12.1676	−	35.8447i	−0.493869	−	1.45489i	−0.853152	−	0.521662i	$-0.825312\pi$
$607$	−12.1676	−	35.8447i	−0.493869	−	1.45489i	0.359284	−	0.933228i	$-0.383021\pi$
$608$	−3.28895	+	3.28895i	−0.133384	+	0.133384i
$609$	15.2888	+	19.6504i	0.619533	+	0.796276i
$610$	−18.0179	+	7.46326i	−0.729524	+	0.302179i
$611$	−56.8384	+	32.8156i	−2.29943	+	1.32758i
$612$	2.25977	+	3.44869i	0.0913457	+	0.139405i
$613$	17.8198	−	30.8648i	0.719735	−	1.24662i	−0.241370	−	0.970433i	$-0.577597\pi$
$613$	17.8198	−	30.8648i	0.719735	−	1.24662i	0.961105	−	0.276184i	$-0.0890700\pi$
$614$	−17.8072	−	13.6639i	−0.718640	−	0.551432i
$615$	−22.4408	−	33.5850i	−0.904901	−	1.35428i
$616$	−0.117104	−	0.101316i	−0.00471827	−	0.00408216i
$617$	−8.27744	−	1.64649i	−0.333237	−	0.0662850i	0.0256360	−	0.999671i	$-0.491839\pi$
$617$	−8.27744	−	1.64649i	−0.333237	−	0.0662850i	−0.358873	+	0.933386i	$0.616839\pi$
$618$	0.431005	−	6.57586i	0.0173376	−	0.264520i
$619$	−14.4682	−	4.91128i	−0.581524	−	0.197401i	0.0151488	−	0.999885i	$-0.495178\pi$
$619$	−14.4682	−	4.91128i	−0.581524	−	0.197401i	−0.596673	+	0.802484i	$0.703511\pi$
$620$	11.4539	−	8.78892i	0.460002	−	0.352972i
$621$	−0.229968	−	1.74678i	−0.00922829	−	0.0700958i
$622$	33.8642	−	6.73602i	1.35783	−	0.270090i
$623$	−1.02508	−	1.74831i	−0.0410690	−	0.0700445i
$624$	−1.08262	+	5.44271i	−0.0433396	+	0.217883i
$625$	7.84069	−	29.2619i	0.313628	−	1.17047i
$626$	0.533136	+	8.13408i	0.0213084	+	0.325103i
$627$	0.0355329	−	0.269899i	0.00141905	−	0.0107787i
$628$	3.88153	+	6.72301i	0.154890	+	0.268277i
$629$	8.36527	+	2.32225i	0.333545	+	0.0925943i
$630$	5.81566	+	8.57864i	0.231701	+	0.341781i
$631$	−6.76800	−	16.3394i	−0.269430	−	0.650461i	0.730027	−	0.683418i	$-0.239508\pi$
$631$	−6.76800	−	16.3394i	−0.269430	−	0.650461i	−0.999457	+	0.0329571i	$0.989508\pi$
$632$	−8.01275	−	3.95145i	−0.318730	−	0.157180i
$633$	8.45343	−	2.26509i	0.335994	−	0.0900292i
$634$	−21.6861	+	24.7282i	−0.861264	+	0.982084i
$635$	−9.61202	−	0.630005i	−0.381441	−	0.0250010i
$636$	1.94157	+	9.76093i	0.0769882	+	0.387046i
$637$	−27.8338	−	27.0969i	−1.10281	−	1.07362i
$638$	−0.210770	+	0.508843i	−0.00834445	+	0.0201453i
$639$	4.31753	−	3.78637i	0.170799	−	0.149787i
$640$	3.51329	−	1.73256i	0.138875	−	0.0684856i
$641$	−13.2240	−	11.5972i	−0.522318	−	0.458060i	0.357131	−	0.934054i	$-0.383755\pi$
$641$	−13.2240	−	11.5972i	−0.522318	−	0.458060i	−0.879449	+	0.475994i	$0.842088\pi$
$642$	−6.72358	−	1.80158i	−0.265359	−	0.0711026i
$643$	23.8119	−	15.9106i	0.939051	−	0.627454i	0.0110131	−	0.999939i	$-0.496494\pi$
$643$	23.8119	−	15.9106i	0.939051	−	0.627454i	0.928038	+	0.372485i	$0.121494\pi$
$644$	2.56370	−	3.89311i	0.101024	−	0.153410i
$645$			11.5359i			0.454227i
$646$	−17.2755	+	8.32713i	−0.679695	+	0.327627i
$647$	25.8777	+	14.9405i	1.01736	+	0.587372i	0.913338	−	0.407203i	$-0.133496\pi$
$647$	25.8777	+	14.9405i	1.01736	+	0.587372i	0.104021	+	0.994575i	$0.466829\pi$
$648$	0.991445	+	0.130526i	0.0389476	+	0.00512755i
$649$	−0.106231	+	0.215416i	−0.00416995	+	0.00845581i
$650$	40.5935	+	40.5935i	1.59221	+	1.59221i
$651$	7.77571	+	5.88409i	0.304754	+	0.230616i
$652$	6.75718	+	4.51501i	0.264632	+	0.176821i
$653$	13.4134	+	15.2950i	0.524905	+	0.598540i	0.952163	−	0.305590i	$-0.0988537\pi$
$653$	13.4134	+	15.2950i	0.524905	+	0.598540i	−0.427258	+	0.904130i	$0.640520\pi$
$654$	−11.0991	−	14.4647i	−0.434010	−	0.565613i
$655$	−8.00031	−	10.4262i	−0.312598	−	0.407386i
$656$	−6.79875	−	7.75249i	−0.265447	−	0.302684i
$657$	−4.36119	−	2.91405i	−0.170146	−	0.113688i
$658$	−3.87615	+	31.0499i	−0.151108	+	1.21045i
$659$	5.06298	+	5.06298i	0.197226	+	0.197226i	0.798810	−	0.601584i	$-0.205463\pi$
$659$	5.06298	+	5.06298i	0.197226	+	0.197226i	−0.601584	+	0.798810i	$0.705463\pi$
$660$	−0.101403	+	0.205625i	−0.00394711	+	0.00800394i
$661$	27.6801	+	3.64416i	1.07663	+	0.141741i	0.647926	−	0.761703i	$-0.275636\pi$
$661$	27.6801	+	3.64416i	1.07663	+	0.141741i	0.428706	+	0.903444i	$0.358970\pi$
$662$	−23.2616	−	13.4301i	−0.904087	−	0.521975i
$663$	−11.6179	+	19.7115i	−0.451202	+	0.765530i
$664$		−	9.05853i		−	0.351539i
$665$	−43.0910	+	21.6106i	−1.67100	+	0.838023i
$666$	1.75074	−	1.16981i	0.0678400	−	0.0453292i
$667$	−16.0147	−	4.29114i	−0.620094	−	0.166154i
$668$	15.3185	+	13.4339i	0.592689	+	0.519775i
$669$	−11.7980	+	5.81813i	−0.456137	+	0.224942i
$670$	28.9013	−	25.3458i	1.11655	−	0.979192i
$671$	0.111508	−	0.269205i	0.00430472	−	0.0103925i
$672$	1.75777	+	1.97744i	0.0678073	+	0.0762813i
$673$	−2.10363	−	10.5757i	−0.0810890	−	0.407662i	−0.999915	−	0.0130001i	$-0.995862\pi$
$673$	−2.10363	−	10.5757i	−0.0810890	−	0.407662i	0.918827	−	0.394662i	$-0.129138\pi$
$674$	18.0729	+	1.18456i	0.696144	+	0.0456277i
$675$	6.82094	−	7.77779i	0.262538	−	0.299367i
$676$	−17.1888	+	4.60572i	−0.661108	+	0.177143i
$677$	19.8649	+	9.79627i	0.763469	+	0.376501i	0.781961	−	0.623328i	$-0.214220\pi$
$677$	19.8649	+	9.79627i	0.763469	+	0.376501i	−0.0184915	+	0.999829i	$0.505886\pi$
$678$	−5.07402	−	12.2498i	−0.194867	−	0.470450i
$679$	−10.9646	+	7.43318i	−0.420784	+	0.285259i
$680$	16.0314	−	1.96415i	0.614778	−	0.0753218i
$681$	9.80180	+	16.9772i	0.375606	+	0.650568i
$682$	−0.0281556	+	0.213863i	−0.00107813	+	0.00818923i
$683$	2.98667	+	45.5677i	0.114282	+	1.74360i	0.542616	+	0.839981i	$0.317434\pi$
$683$	2.98667	+	45.5677i	0.114282	+	1.74360i	−0.428335	+	0.903620i	$0.640900\pi$
$684$	−1.20384	+	4.49279i	−0.0460299	+	0.171786i
$685$	−13.4845	+	67.7911i	−0.515216	+	2.59016i
$686$	−18.3095	+	2.78629i	−0.699059	+	0.106381i
$687$	22.9963	−	4.57425i	0.877364	−	0.174519i
$688$	0.384385	+	2.91970i	0.0146546	+	0.111312i
$689$	−43.8152	+	33.6206i	−1.66923	+	1.28084i
$690$	−6.53538	−	2.21846i	−0.248798	−	0.0844554i
$691$	2.26613	−	34.5744i	0.0862075	−	1.31527i	−0.707387	−	0.706826i	$-0.750126\pi$
$691$	2.26613	−	34.5744i	0.0862075	−	1.31527i	0.793595	−	0.608447i	$-0.208207\pi$
$692$	−5.39749	−	1.07363i	−0.205182	−	0.0408132i
$693$	−0.152074	−	0.0291905i	−0.00577680	−	0.00110885i
$694$	7.51374	+	11.2451i	0.285218	+	0.426859i
$695$	41.2609	+	31.6606i	1.56512	+	1.20096i
$696$	4.70519	−	8.14963i	0.178350	−	0.308911i
$697$	−15.9160	−	39.4232i	−0.602862	−	1.49326i
$698$	−14.0897	+	8.13468i	−0.533302	+	0.307902i
$699$	1.24160	−	0.514287i	0.0469616	−	0.0194521i
$700$	27.1116	−	3.75445i	1.02472	−	0.141905i
$701$	10.9482	−	10.9482i	0.413510	−	0.413510i	−0.469450	−	0.882959i	$-0.655548\pi$
$701$	10.9482	−	10.9482i	0.413510	−	0.413510i	0.882959	+	0.469450i	$0.155548\pi$
$702$	1.78378	+	5.25484i	0.0673243	+	0.198331i
$703$	4.33166	+	8.78373i	0.163372	+	0.331285i
$704$	−0.0188131	+	0.0554216i	−0.000709046	+	0.00208878i
$705$	45.9327	−	6.04715i	1.72993	−	0.227749i
$706$	21.8180	+	9.03729i	0.821129	+	0.340123i
$707$	0.0476977	+	0.173352i	0.00179386	+	0.00651956i
$708$	2.27995	−	3.41218i	0.0856856	−	0.128238i
$709$	−27.3878	+	9.29689i	−1.02857	+	0.349152i	−0.784186	−	0.620526i	$-0.786919\pi$
$709$	−27.3878	+	9.29689i	−1.02857	+	0.349152i	−0.244384	+	0.969679i	$0.578586\pi$
$710$	−5.82224	−	21.7289i	−0.218505	−	0.815471i
$711$	−8.91497	+	0.584318i	−0.334337	+	0.0219136i
$712$	−0.466316	+	0.607714i	−0.0174759	+	0.0227751i
$713$	−6.49343			−0.243181
$714$	4.15157	+	10.0878i	0.155369	+	0.377528i
$715$	−1.27229			−0.0475810
$716$	−6.28836	+	8.19515i	−0.235007	+	0.306267i
$717$	−27.6124	+	1.80981i	−1.03120	+	0.0675886i
$718$	−2.02928	−	7.57339i	−0.0757321	−	0.282636i
$719$	9.13620	−	3.10132i	0.340723	−	0.115660i	−0.145833	−	0.989309i	$-0.546586\pi$
$719$	9.13620	−	3.10132i	0.340723	−	0.115660i	0.486556	+	0.873649i	$0.338253\pi$
$720$	2.17632	−	3.25709i	0.0811066	−	0.121385i
$721$	4.39958	−	16.8712i	0.163849	−	0.628317i
$722$	−2.43382	−	1.00812i	−0.0905773	−	0.0375184i
$723$	−6.93304	+	0.912751i	−0.257842	+	0.0339456i
$724$	−1.29941	+	3.82793i	−0.0482921	+	0.142264i
$725$	−43.0570	−	87.3109i	−1.59910	−	3.24265i
$726$	3.53473	+	10.4130i	0.131186	+	0.386462i
$727$	−6.39504	+	6.39504i	−0.237179	+	0.237179i	−0.815681	−	0.578502i	$-0.803637\pi$
$727$	−6.39504	+	6.39504i	−0.237179	+	0.237179i	0.578502	+	0.815681i	$0.303637\pi$
$728$	−5.52753	+	13.6019i	−0.204864	+	0.504121i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	−17.7940	+	10.2733i	−0.658584	+	0.380234i
$731$	−2.47575	+	11.8870i	−0.0915689	+	0.439657i
$732$	−2.48929	+	4.31158i	−0.0920068	+	0.159360i
$733$	12.5746	+	9.64882i	0.464453	+	0.356387i	0.814324	−	0.580411i	$-0.197108\pi$
$733$	12.5746	+	9.64882i	0.464453	+	0.356387i	−0.349871	+	0.936798i	$0.613775\pi$
$734$	4.94280	+	7.39743i	0.182442	+	0.273044i
$735$	10.8324	+	25.1906i	0.399558	+	0.929168i
$736$	−1.72800	−	0.343720i	−0.0636948	−	0.0126697i
$737$	−0.0375637	+	0.573111i	−0.00138368	+	0.0211108i
$738$	−9.76414	−	3.31448i	−0.359423	−	0.122008i
$739$	11.7181	−	8.99163i	0.431058	−	0.330762i	−0.370338	−	0.928897i	$-0.620758\pi$
$739$	11.7181	−	8.99163i	0.431058	−	0.330762i	0.801395	+	0.598135i	$0.204091\pi$
$740$	−1.07661	−	8.17765i	−0.0395769	−	0.300616i
$741$	−25.3155	+	5.03557i	−0.929989	+	0.184986i
$742$	0.176584	+	26.3303i	0.00648259	+	0.966617i
$743$	−3.63488	+	18.2738i	−0.133351	+	0.670400i	0.855052	+	0.518543i	$0.173525\pi$
$743$	−3.63488	+	18.2738i	−0.133351	+	0.670400i	−0.988402	+	0.151857i	$0.951475\pi$
$744$	0.953897	−	3.55999i	0.0349715	−	0.130516i
$745$	4.07461	+	62.1666i	0.149282	+	2.27761i
$746$	1.42786	−	10.8457i	0.0522778	−	0.397089i
$747$	−4.52927	−	7.84492i	−0.165717	−	0.287031i
$748$	−0.148619	+	0.190121i	−0.00543404	+	0.00695150i
$749$	−16.5715	−	8.03443i	−0.605508	−	0.293572i
$750$	−8.01256	−	19.3440i	−0.292577	−	0.706344i
$751$	5.91647	+	2.91768i	0.215895	+	0.106468i	0.547021	−	0.837119i	$-0.315762\pi$
$751$	5.91647	+	2.91768i	0.215895	+	0.106468i	−0.331126	+	0.943587i	$0.607428\pi$
$752$	11.4239	−	3.06102i	0.416586	−	0.111624i
$753$	−8.94733	+	10.2025i	−0.326059	+	0.371799i
$754$	52.1096	+	3.41544i	1.89772	+	0.124383i
$755$	−0.889175	−	4.47018i	−0.0323604	−	0.162687i
$756$	2.51099	+	0.833628i	0.0913238	+	0.0303188i
$757$	4.08013	−	9.85031i	0.148295	−	0.358016i	−0.832224	−	0.554439i	$-0.812933\pi$
$757$	4.08013	−	9.85031i	0.148295	−	0.358016i	0.980519	+	0.196424i	$0.0629328\pi$
$758$	−10.7068	+	9.38963i	−0.388889	+	0.341047i
$759$	0.0924829	−	0.0456075i	0.00335692	−	0.00165545i
$760$	13.6987	+	12.0135i	0.496906	+	0.435775i
$761$	32.2036	+	8.62893i	1.16738	+	0.312798i	0.789910	−	0.613223i	$-0.210127\pi$
$761$	32.2036	+	8.62893i	1.16738	+	0.312798i	0.377470	+	0.926022i	$0.376794\pi$
$762$	−2.04460	+	1.36616i	−0.0740680	+	0.0494907i
$763$	−21.6249	−	43.1195i	−0.782872	−	1.56103i
$764$		−	9.98034i		−	0.361076i
$765$	12.9016	−	9.71673i	0.466457	−	0.351309i
$766$	4.61645	+	2.66531i	0.166799	+	0.0963015i
$767$	22.5785	+	2.97252i	0.815263	+	0.107331i
$768$	0.442289	−	0.896873i	0.0159597	−	0.0323631i
$769$	−17.0363	−	17.0363i	−0.614344	−	0.614344i	0.329731	−	0.944075i	$-0.393042\pi$
$769$	−17.0363	−	17.0363i	−0.614344	−	0.614344i	−0.944075	+	0.329731i	$0.893042\pi$
$770$	−0.366032	+	0.483704i	−0.0131909	+	0.0174315i
$771$	−15.6797	−	10.4769i	−0.564692	−	0.377315i
$772$	8.55433	+	9.75435i	0.307877	+	0.351067i
$773$	13.2571	+	17.2769i	0.476824	+	0.621409i	0.968393	−	0.249430i	$-0.0802432\pi$
$773$	13.2571	+	17.2769i	0.476824	+	0.621409i	−0.491569	+	0.870838i	$0.663577\pi$
$774$	1.79274	+	2.33634i	0.0644386	+	0.0839780i
$775$	−25.1391	−	28.6656i	−0.903022	−	1.02970i
$776$	4.16299	+	2.78162i	0.149443	+	0.0998544i
$777$	5.13243	−	2.16636i	0.184125	−	0.0777177i
$778$	−0.382826	−	0.382826i	−0.0137250	−	0.0137250i
$779$	21.2126	−	43.0149i	0.760020	−	1.54117i
$780$	21.5523	+	2.83741i	0.771695	+	0.101596i
$781$	0.291073	+	0.168051i	0.0104154	+	0.00601335i
$782$	−6.25817	−	3.68855i	−0.223792	−	0.131902i
$783$		−	9.41038i		−	0.336300i
$784$	3.58099	+	6.01469i	0.127893	+	0.214810i
$785$	25.2850	−	16.8949i	0.902461	−	0.603005i
$786$	−3.24056	−	0.868305i	−0.115587	−	0.0309714i
$787$	2.15973	+	1.89404i	0.0769862	+	0.0675151i	0.696974	−	0.717096i	$-0.254529\pi$
$787$	2.15973	+	1.89404i	0.0769862	+	0.0675151i	−0.619988	+	0.784611i	$0.712863\pi$
$788$	0.0646015	−	0.0318579i	0.00230133	−	0.00113489i
$789$	14.0031	−	12.2804i	0.498522	−	0.437192i
$790$	−13.3929	+	32.3333i	−0.476497	+	1.15037i
$791$	−7.07439	−	34.3595i	−0.251536	−	1.22168i
$792$	0.0114182	+	0.0574031i	0.000405728	+	0.00203973i
$793$	−27.5687	−	1.80695i	−0.978992	−	0.0641665i
$794$	−3.47392	+	3.96125i	−0.123285	+	0.140579i
$795$	37.6569	−	10.0901i	1.33555	−	0.357860i
$796$	12.9469	+	6.38471i	0.458891	+	0.226300i
$797$	14.9882	+	36.1846i	0.530908	+	1.28173i	0.930923	+	0.365217i	$0.119005\pi$
$797$	14.9882	+	36.1846i	0.530908	+	1.28173i	−0.400015	+	0.916509i	$0.630995\pi$
$798$	−5.36871	+	11.0733i	−0.190050	+	0.391990i
$799$	48.6284	+	3.62652i	1.72035	+	0.128297i
$800$	−5.17250	−	8.95904i	−0.182876	−	0.316750i
$801$	−0.0999840	+	0.759454i	−0.00353276	+	0.0268340i
$802$	1.21183	+	18.4890i	0.0427913	+	0.652868i
$803$	0.0794541	−	0.296527i	0.00280387	−	0.0104642i
$804$	1.91445	−	9.62459i	0.0675175	−	0.339433i
$805$	−15.8745	−	9.02376i	−0.559504	−	0.318046i
$806$	20.0595	−	3.99008i	0.706566	−	0.140545i
$807$	−2.97611	−	22.6058i	−0.104764	−	0.795761i
$808$	0.0539129	−	0.0413688i	0.00189665	−	0.00145535i
$809$	−9.50348	−	3.22600i	−0.334125	−	0.113420i	0.149335	−	0.988787i	$-0.452287\pi$
$809$	−9.50348	−	3.22600i	−0.334125	−	0.113420i	−0.483460	+	0.875367i	$0.660620\pi$
$810$	0.256202	−	3.90888i	0.00900201	−	0.137344i
$811$	−7.72911	−	1.53742i	−0.271406	−	0.0539859i	0.0575111	−	0.998345i	$-0.481684\pi$
$811$	−7.72911	−	1.53742i	−0.271406	−	0.0539859i	−0.328917	+	0.944359i	$0.606684\pi$
$812$	16.2902	−	18.8286i	0.571673	−	0.660755i
$813$	−9.99486	−	14.9584i	−0.350535	−	0.524613i
$814$	0.0977697	+	0.0750214i	0.00342683	+	0.00262950i
$815$	15.9174	−	27.5698i	0.557563	−	0.965728i
$816$	2.94156	−	2.88915i	0.102975	−	0.101141i
$817$	−11.8624	+	6.84875i	−0.415012	+	0.239607i
$818$	−7.94441	+	3.29068i	−0.277770	+	0.115056i
$819$	2.01399	+	14.5434i	0.0703743	+	0.508187i
$820$	−28.5617	+	28.5617i	−0.997419	+	0.997419i
$821$	0.612514	+	1.80441i	0.0213769	+	0.0629743i	0.957095	−	0.289775i	$-0.0935803\pi$
$821$	0.612514	+	1.80441i	0.0213769	+	0.0629743i	−0.935718	+	0.352749i	$0.885247\pi$
$822$	7.80407	+	15.8251i	0.272198	+	0.551963i
$823$	−17.5103	+	51.5836i	−0.610369	+	1.79809i	−0.00787194	+	0.999969i	$0.502506\pi$
$823$	−17.5103	+	51.5836i	−0.610369	+	1.79809i	−0.602497	+	0.798121i	$0.705828\pi$
$824$	−6.53359	+	0.860164i	−0.227609	+	0.0299652i
$825$	0.559381	+	0.231703i	0.0194751	+	0.00806687i
$826$	7.62583	−	7.72881i	0.265337	−	0.268920i
$827$	5.77584	−	8.64415i	0.200845	−	0.300587i	−0.717351	−	0.696712i	$-0.754646\pi$
$827$	5.77584	−	8.64415i	0.200845	−	0.300587i	0.918196	+	0.396126i	$0.129646\pi$
$828$	−1.66835	+	0.566329i	−0.0579792	+	0.0196813i
$829$	5.06840	+	18.9155i	0.176033	+	0.656963i	0.996373	+	0.0850881i	$0.0271172\pi$
$829$	5.06840	+	18.9155i	0.176033	+	0.656963i	−0.820341	+	0.571875i	$0.806216\pi$
$830$	−35.4087	+	2.32081i	−1.22906	+	0.0805566i
$831$	0.336954	−	0.439127i	0.0116888	−	0.0152332i
$832$	5.54934			0.192389
$833$	5.75583	+	28.2820i	0.199428	+	0.979913i
$834$	13.2767			0.459733
$835$	48.5871	−	63.3199i	1.68142	−	2.19128i
$836$	−0.271645	+	0.0178046i	−0.00939506	+	0.000615784i
$837$	−0.953897	−	3.55999i	−0.0329715	−	0.123051i
$838$	−26.0603	+	8.84627i	−0.900237	+	0.305589i
$839$	−7.00078	+	10.4774i	−0.241694	+	0.361720i	−0.932408	−	0.361408i	$-0.882296\pi$
$839$	−7.00078	+	10.4774i	−0.241694	+	0.361720i	0.690714	+	0.723128i	$0.257296\pi$
$840$	7.27923	−	7.37752i	0.251157	−	0.254549i
$841$	−55.0219	−	22.7908i	−1.89731	−	0.785890i
$842$	30.8417	−	4.06039i	1.06288	−	0.139930i
$843$	9.33479	−	27.4994i	0.321507	−	0.947129i
$844$	−3.87075	−	7.84910i	−0.133237	−	0.270177i
$845$	22.4070	+	66.0090i	0.770825	+	2.27078i
$846$	8.36286	−	8.36286i	0.287521	−	0.287521i
$847$	3.99092	+	28.8192i	0.137129	+	0.990239i
$848$	9.19459	−	3.80853i	0.315744	−	0.130785i
$849$	−16.4080	+	9.47316i	−0.563121	+	0.325118i
$850$	−7.94494	−	41.9071i	−0.272509	−	1.43740i
$851$	−1.85488	+	3.21274i	−0.0635844	+	0.110131i
$852$	−4.55593	−	3.49589i	−0.156084	−	0.119767i
$853$	−28.3510	−	42.4302i	−0.970718	−	1.45278i	−0.889954	−	0.456049i	$-0.849264\pi$
$853$	−28.3510	−	42.4302i	−0.970718	−	1.45278i	−0.0807638	−	0.996733i	$-0.525736\pi$
$854$	−8.61835	+	9.96132i	−0.294914	+	0.340869i
$855$	17.8702	+	3.55460i	0.611148	+	0.121565i
$856$	−0.455256	+	6.94586i	−0.0155603	+	0.237405i
$857$	−33.6783	−	11.4322i	−1.15043	−	0.390518i	−0.319877	−	0.947459i	$-0.603641\pi$
$857$	−33.6783	−	11.4322i	−1.15043	−	0.390518i	−0.830552	+	0.556941i	$0.811975\pi$
$858$	−0.257673	+	0.197720i	−0.00879682	+	0.00675004i
$859$	2.74096	+	20.8196i	0.0935202	+	0.710357i	0.972401	+	0.233315i	$0.0749574\pi$
$859$	2.74096	+	20.8196i	0.0935202	+	0.710357i	−0.878881	+	0.477041i	$0.841709\pi$
$860$	11.3143	−	2.25055i	0.385813	−	0.0767431i
$861$	−23.7172	−	13.4819i	−0.808281	−	0.459462i
$862$	−3.40508	+	17.1185i	−0.115978	+	0.583058i
$863$	−11.7120	+	43.7096i	−0.398679	+	1.48789i	0.416742	+	0.909025i	$0.363172\pi$
$863$	−11.7120	+	43.7096i	−0.398679	+	1.48789i	−0.815422	+	0.578867i	$0.803495\pi$
$864$	−0.0654031	−	0.997859i	−0.00222506	−	0.0339478i
$865$	−2.81384	+	21.3732i	−0.0956734	+	0.726712i
$866$	−19.2285	−	33.3047i	−0.653410	−	1.13174i
$867$	15.3795	−	7.24362i	0.522316	−	0.246006i
$868$	4.25406	−	8.77423i	0.144392	−	0.297817i
$869$	−0.200102	−	0.483089i	−0.00678800	−	0.0163877i
$870$	−33.0614	−	16.3041i	−1.12089	−	0.552760i
$871$	52.6009	−	14.0944i	1.78231	−	0.477570i
$872$	−12.0214	+	13.7078i	−0.407096	+	0.464204i
$873$	4.99606	+	0.327459i	0.169091	+	0.0110828i
$874$	−1.59874	−	8.03739i	−0.0540781	−	0.271869i
$875$	−11.1714	−	54.2582i	−0.377662	−	1.83426i
$876$	−2.00723	+	4.84589i	−0.0678182	+	0.163728i
$877$	9.65934	−	8.47101i	0.326173	−	0.286046i	−0.480561	−	0.876962i	$-0.659567\pi$
$877$	9.65934	−	8.47101i	0.326173	−	0.286046i	0.806733	+	0.590916i	$0.201233\pi$
$878$	−30.3593	+	14.9715i	−1.02458	+	0.505265i
$879$	−6.67194	−	5.85113i	−0.225039	−	0.197354i
$880$	0.221457	+	0.0593391i	0.00746530	+	0.00200032i
$881$	14.3925	−	9.61674i	0.484895	−	0.323996i	−0.288980	−	0.957335i	$-0.593316\pi$
$881$	14.3925	−	9.61674i	0.484895	−	0.323996i	0.773875	+	0.633339i	$0.218316\pi$
$882$	6.10858	+	3.41838i	0.205686	+	0.115103i
$883$			1.60446i			0.0539942i	0.999636	+	0.0269971i	$0.00859449\pi$
$883$			1.60446i			0.0539942i	−0.999636	+	0.0269971i	$0.991406\pi$
$884$	21.5993	+	7.54914i	0.726462	+	0.253905i
$885$	−13.9219	−	8.03783i	−0.467981	−	0.270189i
$886$	−10.6913	−	1.40753i	−0.359180	−	0.0472869i
$887$	15.3054	−	31.0364i	0.513907	−	1.04210i	−0.473038	−	0.881042i	$-0.656843\pi$
$887$	15.3054	−	31.0364i	0.513907	−	1.04210i	0.986945	−	0.161058i	$-0.0514905\pi$
$888$	−1.48889	−	1.48889i	−0.0499637	−	0.0499637i
$889$	−5.99389	+	2.52997i	−0.201028	+	0.0848526i
$890$	2.49495	+	1.66708i	0.0836311	+	0.0558805i
$891$	0.0385900	+	0.0440035i	0.00129281	+	0.00147417i
$892$	8.00801	+	10.4362i	0.268128	+	0.349431i
$893$	33.4880	+	43.6424i	1.12063	+	1.46044i
$894$	10.4862	+	11.9572i	0.350711	+	0.399909i
$895$	33.6450	+	22.4809i	1.12463	+	0.751452i
$896$	1.59652	−	2.10977i	0.0533359	−	0.0704825i
$897$	−6.91346	−	6.91346i	−0.230834	−	0.230834i
$898$	6.43576	−	13.0504i	0.214764	−	0.435498i
$899$	−34.3859	−	4.52699i	−1.14683	−	0.150984i
$900$	−8.95904	−	5.17250i	−0.298635	−	0.172417i
$901$	40.9684	−	2.31559i	1.36486	−	0.0771436i
$902$		−	0.603500i		−	0.0200944i
$903$	3.49285	+	6.96467i	0.116235	+	0.231770i
$904$	−11.0245	+	7.36634i	−0.366670	+	0.245001i
$905$	15.2959	+	4.09851i	0.508452	+	0.136239i
$906$	−0.874769	−	0.767152i	−0.0290622	−	0.0254869i
$907$	−42.3697	+	20.8944i	−1.40686	+	0.693789i	−0.977811	−	0.209490i	$-0.932820\pi$
$907$	−42.3697	+	20.8944i	−1.40686	+	0.693789i	−0.429054	+	0.903279i	$0.641153\pi$
$908$	14.7388	−	12.9256i	0.489123	−	0.428950i
$909$	0.0260055	−	0.0627829i	0.000862549	−	0.00208238i
$910$	54.5845	+	18.1216i	1.80946	+	0.600726i
$911$	4.56970	+	22.9734i	0.151401	+	0.761144i	0.979639	+	0.200767i	$0.0643436\pi$
$911$	4.56970	+	22.9734i	0.151401	+	0.761144i	−0.828238	+	0.560377i	$0.810656\pi$
$912$	4.64131	+	0.304208i	0.153689	+	0.0100733i
$913$	0.349569	−	0.398607i	0.0115690	−	0.0131920i
$914$	−14.8948	+	3.99105i	−0.492676	+	0.132012i
$915$	17.4912	+	8.62571i	0.578242	+	0.285157i
$916$	−8.97271	−	21.6620i	−0.296467	−	0.715734i
$917$	−7.98694	−	3.87235i	−0.263752	−	0.127876i
$918$	1.10289	−	3.97286i	0.0364009	−	0.131124i
$919$	−11.0978	−	19.2220i	−0.366083	−	0.634074i	0.622866	−	0.782328i	$-0.285968\pi$
$919$	−11.0978	−	19.2220i	−0.366083	−	0.634074i	−0.988949	+	0.148254i	$0.952635\pi$
$920$	−0.900846	+	6.84260i	−0.0297000	+	0.225594i
$921$	1.46800	+	22.3974i	0.0483724	+	0.738020i
$922$	−5.90965	+	22.0551i	−0.194624	+	0.726346i
$923$	6.21709	−	31.2554i	0.204638	−	1.02878i
$924$	0.00103847	+	0.154846i	3.41632e−5	+	0.00509407i
$925$	−21.3639	+	4.24955i	−0.702441	+	0.139724i
$926$	−4.78714	−	36.3619i	−0.157315	−	1.19493i
$927$	−5.22818	+	4.01172i	−0.171716	+	0.131762i
$928$	−8.91097	−	3.02487i	−0.292517	−	0.0992961i
$929$	0.918525	−	14.0140i	0.0301358	−	0.459784i	−0.955948	−	0.293536i	$-0.905168\pi$
$929$	0.918525	−	14.0140i	0.0301358	−	0.459784i	0.986084	−	0.166248i	$-0.0531653\pi$
$930$	−14.1600	−	2.81659i	−0.464324	−	0.0923598i
$931$	−19.4724	+	26.0942i	−0.638181	+	0.855204i
$932$	−0.746630	−	1.11741i	−0.0244567	−	0.0366020i
$933$	−27.3927	−	21.0191i	−0.896795	−	0.688135i
$934$	5.21022	−	9.02436i	0.170484	−	0.295286i
$935$	0.781236	+	0.532224i	0.0255491	+	0.0174056i
$936$	4.80587	−	2.77467i	0.157085	−	0.0906929i
$937$	52.1683	−	21.6088i	1.70426	−	0.705929i	0.704271	−	0.709932i	$-0.251274\pi$
$937$	52.1683	−	21.6088i	1.70426	−	0.705929i	0.999992	+	0.00400277i	$0.00127413\pi$
$938$	9.77458	−	24.0529i	0.319151	−	0.785356i
$939$	5.76400	−	5.76400i	0.188101	−	0.188101i
$940$	−14.8920	−	43.8704i	−0.485723	−	1.43089i
$941$	−9.18806	−	18.6315i	−0.299522	−	0.607371i	0.694132	−	0.719848i	$-0.255788\pi$
$941$	−9.18806	−	18.6315i	−0.299522	−	0.607371i	−0.993654	+	0.112477i	$0.964122\pi$
$942$	2.49536	−	7.35108i	0.0813031	−	0.239511i
$943$	18.0117	−	2.37128i	0.586540	−	0.0772195i
$944$	−3.79141	−	1.57045i	−0.123400	−	0.0511139i
$945$	2.61524	−	10.0287i	0.0850736	−	0.326235i
$946$	−0.0957568	+	0.143310i	−0.00311332	+	0.00465942i
$947$	−26.4290	+	8.97144i	−0.858828	+	0.291533i	−0.715902	−	0.698201i	$-0.753984\pi$
$947$	−26.4290	+	8.97144i	−0.858828	+	0.291533i	−0.142926	+	0.989733i	$0.545651\pi$
$948$	2.31231	+	8.62967i	0.0751005	+	0.280279i
$949$	−29.0448	+	1.90370i	−0.942835	+	0.0617967i
$950$	29.2920	−	38.1741i	0.950360	−	1.23853i
$951$	32.8903			1.06654
$952$	9.08407	−	6.03984i	0.294416	−	0.195752i
$953$	−0.0602407			−0.00195139			−0.000975694	−	1.00000i	$-0.500311\pi$
$953$	−0.0602407			−0.00195139			−0.000975694		1.00000i	$0.500311\pi$
$954$	6.05849	−	7.89558i	0.196151	−	0.255629i
$955$	−39.0120	+	2.55698i	−1.26240	+	0.0827420i
$956$	7.16194	+	26.7287i	0.231634	+	0.864468i
$957$	0.521539	−	0.177039i	0.0168590	−	0.00572284i
$958$	13.6171	−	20.3794i	0.439947	−	0.658428i
$959$	12.3847	+	45.0108i	0.399924	+	1.45348i
$960$	−3.61909	−	1.49907i	−0.116805	−	0.0483824i
$961$	17.2675	−	2.27332i	0.557018	−	0.0733328i
$962$	3.75592	−	11.0646i	0.121096	−	0.356737i
$963$	3.07867	+	6.24292i	0.0992086	+	0.201175i
$964$	2.24778	+	6.62175i	0.0723962	+	0.213272i
$965$	35.9370	−	35.9370i	1.15685	−	1.15685i
$966$	−4.61736	+	0.639417i	−0.148561	+	0.0205729i
$967$	4.32572	−	1.79177i	0.139106	−	0.0576195i	−0.312045	−	0.950067i	$-0.601014\pi$
$967$	4.32572	−	1.79177i	0.139106	−	0.0576195i	0.451150	+	0.892448i	$0.351014\pi$
$968$	9.52331	−	5.49829i	0.306091	−	0.176722i
$969$	17.6512	+	7.49794i	0.567038	+	0.240869i
$970$	9.80646	−	16.9853i	0.314867	−	0.545365i
$971$	17.3059	+	13.2793i	0.555373	+	0.426153i	0.847940	−	0.530092i	$-0.177843\pi$
$971$	17.3059	+	13.2793i	0.555373	+	0.426153i	−0.292567	+	0.956245i	$0.594509\pi$
$972$	−0.555570	−	0.831470i	−0.0178199	−	0.0266694i
$973$	34.4970	+	6.62169i	1.10592	+	0.212282i
$974$	−28.1495	−	5.59929i	−0.901970	−	0.179413i
$975$	3.75466	−	57.2850i	0.120245	−	1.83459i
$976$	4.71437	+	1.60031i	0.150903	+	0.0512247i
$977$	−10.4910	+	8.05001i	−0.335636	+	0.257543i	−0.762804	−	0.646630i	$-0.776178\pi$
$977$	−10.4910	+	8.05001i	−0.335636	+	0.257543i	0.427168	+	0.904172i	$0.359511\pi$
$978$	−1.06076	−	8.05727i	−0.0339194	−	0.257643i
$979$	−0.0439712	+	0.00874641i	−0.00140533	+	0.000279537i
$980$	22.5933	−	15.5387i	0.721715	−	0.496364i
$981$	−3.55695	+	17.8820i	−0.113565	+	0.570928i
$982$	0.687385	−	2.56536i	0.0219353	−	0.0818638i
$983$	2.70517	+	41.2729i	0.0862815	+	1.31640i	0.793137	+	0.609043i	$0.208446\pi$
$983$	2.70517	+	41.2729i	0.0862815	+	1.31640i	−0.706856	+	0.707358i	$0.749887\pi$
$984$	−1.34590	+	10.2231i	−0.0429058	+	0.325902i
$985$	−0.141080	−	0.244358i	−0.00449518	−	0.00778588i
$986$	−30.5686	−	23.8957i	−0.973501	−	0.760993i
$987$	25.9003	−	17.5584i	0.824416	−	0.558890i
$988$	9.87763	+	23.8467i	0.314249	+	0.758665i
$989$	−4.65339	−	2.29480i	−0.147969	−	0.0729703i
$990$	0.221457	−	0.0593391i	0.00703836	−	0.00188592i
$991$	−34.1673	+	38.9603i	−1.08536	+	1.23762i	−0.115667	+	0.993288i	$0.536901\pi$
$991$	−34.1673	+	38.9603i	−1.08536	+	1.23762i	−0.969693	+	0.244328i	$0.921433\pi$
$992$	−3.67768	−	0.241048i	−0.116767	−	0.00765328i
$993$	5.24015	+	26.3440i	0.166291	+	0.836003i
$994$	−10.0942	−	11.3557i	−0.320168	−	0.360180i
$995$	21.6401	−	52.2437i	0.686036	−	1.65624i
$996$	−6.81057	+	5.97271i	−0.215801	+	0.189252i
$997$	−36.1281	+	17.8164i	−1.14419	+	0.564251i	−0.912718	−	0.408591i	$-0.866020\pi$
$997$	−36.1281	+	17.8164i	−1.14419	+	0.564251i	−0.231471	+	0.972842i	$0.574354\pi$
$998$	−5.87088	−	5.14862i	−0.185839	−	0.162977i
$999$	−2.03386	−	0.544970i	−0.0643483	−	0.0172421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bl.a.199.7	yes	192
7.5	odd	6	inner	714.2.bl.a.607.7	yes	192
17.10	odd	16	inner	714.2.bl.a.367.7	yes	192
119.61	even	48	inner	714.2.bl.a.61.7	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bl.a.61.7	✓	192	119.61	even	48	inner
714.2.bl.a.199.7	yes	192	1.1	even	1	trivial
714.2.bl.a.367.7	yes	192	17.10	odd	16	inner
714.2.bl.a.607.7	yes	192	7.5	odd	6	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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.608761 + 0.793353i) q^{2} +(0.997859 - 0.0654031i) q^{3} +(-0.258819 - 0.965926i) q^{4} +(-3.70938 + 1.25917i) q^{5} +(-0.555570 + 0.831470i) q^{6} +(-1.85824 + 1.88333i) q^{7} +(0.923880 + 0.382683i) q^{8} +(0.991445 - 0.130526i) q^{9} +(1.25917 - 3.70938i) q^{10} +(0.0258861 + 0.0524919i) q^{11} +(-0.321439 - 0.946930i) q^{12} +(3.92397 - 3.92397i) q^{13} +(-0.362924 - 2.62074i) q^{14} +(-3.61909 + 1.49907i) q^{15} +(-0.866025 + 0.500000i) q^{16} +(-4.05095 + 0.767998i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-3.69010 - 2.83152i) q^{19} +(2.17632 + 3.25709i) q^{20} +(-1.73109 + 2.00084i) q^{21} +(-0.0574031 - 0.0114182i) q^{22} +(0.115231 - 1.75808i) q^{23} +(0.946930 + 0.321439i) q^{24} +(8.20724 - 6.29764i) q^{25} +(0.724334 + 5.50186i) q^{26} +(0.980785 - 0.195090i) q^{27} +(2.30011 + 1.30748i) q^{28} +(1.83587 - 9.22956i) q^{29} +(1.01386 - 3.78379i) q^{30} +(-0.241048 - 3.67768i) q^{31} +(0.130526 - 0.991445i) q^{32} +(0.0292639 + 0.0506865i) q^{33} +(1.85677 - 3.68136i) q^{34} +(4.52149 - 9.32583i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-1.88846 - 0.931284i) q^{37} +(4.49279 - 1.20384i) q^{38} +(3.65893 - 4.17221i) q^{39} +(-3.90888 - 0.256202i) q^{40} +(2.01165 + 10.1132i) q^{41} +(-0.533551 - 2.59139i) q^{42} +(1.12696 - 2.72072i) q^{43} +(0.0440035 - 0.0385900i) q^{44} +(-3.51329 + 1.73256i) q^{45} +(1.32463 + 1.16167i) q^{46} +(-11.4239 - 3.06102i) q^{47} +(-0.831470 + 0.555570i) q^{48} +(-0.0938864 - 6.99937i) q^{49} +10.3450i q^{50} +(-3.99205 + 1.03130i) q^{51} +(-4.80587 - 2.77467i) q^{52} +(-9.86701 - 1.29902i) q^{53} +(-0.442289 + 0.896873i) q^{54} +(-0.162118 - 0.162118i) q^{55} +(-2.43751 + 1.02886i) q^{56} +(-3.86739 - 2.58411i) q^{57} +(6.20469 + 7.07510i) q^{58} +(2.49823 + 3.25576i) q^{59} +(2.38468 + 3.10778i) q^{60} +(-3.28261 - 3.74310i) q^{61} +(3.06444 + 2.04760i) q^{62} +(-1.59652 + 2.10977i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-9.61458 + 19.4964i) q^{65} +(-0.0580270 - 0.00763940i) q^{66} +(8.49844 + 4.90657i) q^{67} +(1.79029 + 3.71414i) q^{68} -1.76185i q^{69} +(4.64617 + 9.26435i) q^{70} +(4.77482 - 3.19043i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-3.94352 - 3.45837i) q^{73} +(1.88846 - 0.931284i) q^{74} +(7.77779 - 6.82094i) q^{75} +(-1.77997 + 4.29722i) q^{76} +(-0.146962 - 0.0487903i) q^{77} +(1.08262 + 5.44271i) q^{78} +(-8.91497 - 0.584318i) q^{79} +(2.58284 - 2.94516i) q^{80} +(0.965926 - 0.258819i) q^{81} +(-9.24798 - 4.56060i) q^{82} +(-3.46655 - 8.36899i) q^{83} +(2.38070 + 1.15425i) q^{84} +(14.0595 - 7.94961i) q^{85} +(1.47245 + 2.55035i) q^{86} +(1.22830 - 9.32987i) q^{87} +(0.00382789 + 0.0584024i) q^{88} +(-0.198257 + 0.739906i) q^{89} +(0.764221 - 3.84200i) q^{90} +(0.0984633 + 14.6818i) q^{91} +(-1.72800 + 0.343720i) q^{92} +(-0.481064 - 3.65404i) q^{93} +(9.38289 - 7.19974i) q^{94} +(17.2533 + 5.85672i) q^{95} +(0.0654031 - 0.997859i) q^{96} +(4.91058 + 0.976775i) q^{97} +(5.61013 + 4.18646i) q^{98} +(0.0325162 + 0.0486640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) \) 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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